-~7 
 
 
LOGIC 
 
 INDUCTIVE AND DEDUCTIVE 
 
 AN INTRODUCTION TO SCIENTIFIC METHOD 
 
 BY 
 ADAM LEROY 
 
 ADJUNCT PROFESSOR OF PHILOSOPHY 
 IN COLUMBIA UNIVERSITY 
 
 NEW YORK 
 HENRY HOLT AND COMPANY 
 

 ,'*.* .COPYRIGHT, 1909, 
 
 BY 
 HENRY HOLT AND COMPANY 
 
UNIV 
 
 To 
 
 L. S. M. 
 
 574274 
 
PREFACE 
 
 THIS book is intended as a text-book and not at all 
 as a contribution to logical theory. It aims to present 
 {in outline of scientific method as briefly and as con- 
 cretely as possible. It is not designed to serve as an 
 introduction to general philosophy. Its chief claim to 
 novelty is in the arrangement of the subject matter. 
 The traditional arrangement in which the deductive 
 processes are presented first usually leaves with the 
 student the impression that method is chiefly deduction, 
 and that there is no very close connection between this 
 and the rest of subject. The arrangement, which is 
 here adopted, was selected on pedagogical grounds and 
 not in the interests of any epistemological theory. 
 
 The justification for dogmatic statements on dis- 
 puted points is also pedagogical. Argument on such 
 points in a text-book usually fails to interest the stu- 
 dent and often tends to make him think that the whole 
 subject is in an uncertain state and mostly a matter of 
 opinion. Some subjects are treated much more briefly 
 than they deserve, but I wished to keep them in due 
 proportion with the rest. 
 
 Fallacies are first discussed along with the processes 
 with which they are connected, but they are all brought 
 together in a later chapter. Many of the exercises are 
 new, but I have also drawn freely from other text- 
 books. The longer exercises at the end of the book 
 give the student an opportunity to bring to bear al- 
 
vi PREFACE 
 
 most the whole of scientific method, and for this reason 
 they seem to me to be very important. 
 
 My indebtedness to Jevons, Hyslop, Mill, and Bow- 
 ley will be obvious. I owe much to Aikins' Principles 
 of Logic; his broader treatment of many topics and 
 his chapters on Testimony, Averages, Statistics, etc., 
 were very suggestive. Sidgwick's The Use of Words 
 in Reasoning, Creighton's treatment of the Figures 
 of the Syllogism in his Introduction to Logic, Hibben's 
 use of the idea of system in his Logic and Cramer's 
 The Method of Darwin, were also suggestive. I have 
 tried to give credit in each case in which I am con- 
 scious of having borrowed. 
 
 I am much indebted to three of my former col- 
 leagues in Princeton University: to Professor W. T. 
 Marvin for going over the whole of the copy and giv- 
 ing me much useful advice, and to Professors W. H. 
 Sheldon and E. M. Rankin for assistance with the 
 proof; and to my colleagues, Professors Woodbridge 
 and Montague, for many valuable discussions of 
 logical problems. 
 
 A. L. J. 
 
 NEW YORK, April, 1909. 
 
CONTENTS 
 
 PART I 
 AN OUTLINE OF SCIENTIFIC METHOD 
 
 CHAPTER I 
 INTRODUCTORY 
 
 PAGE 
 
 Science and Common Sense Induction and Deduction in- 
 cluded in Scientific Method The Beginning of knowl- 
 edge Natural Sciences and others The Sources of 
 Knowledge, Direct and Indirect Organizing knowledge 
 Classification as a preliminary step Language as a 
 necessary instrument Further steps in organized knowl- 
 edge What is presupposed? 1 
 
 CHAPTER II 
 FIRST STAGES IN KNOWLEDGE 
 
 Facts and "the ways in which they are known Perception 
 and what it includes Indirect means to knowledge of 
 facts* ......... 13 
 
 CHAPTER III 
 CLASSIFICATION 
 
 Types of Classification Division Requirements of Classi- 
 fication . . . . . . . . o 32 
 
 CHAPTER IV 
 
 THE USE AND MISUSE OF WORDS 
 Discrimination, Conception, Abstraction Necessity for Lan- 
 guageTerms Kinds of Terms Definition Defects 
 
 of Definitions 45 
 
 vii 
 
viii CONTENTS 
 
 PAGS 
 CHAPTER V 
 
 PROPOSITIONS 
 
 Kinds of Propositions Propositions and Terms The Rela- 
 tion of Subject and Predicate The Distribution of 
 Terms in a proposition Euler's Method Ambiguous 
 Propositions 66 
 
 CHAPTER VI 
 INDUCTION 
 
 Generalization and what it includes Causal Connection 
 Testing Inductive inferences Complete Enumeration 
 How Generalizations are verified Observation and An- 
 alysis are pre-supposed Postponing inference till test 
 conditions are present The Inductive Methods. . . 79 
 
 CHAPTER VII 
 
 VERIFICATION AND DEDUCTION 
 Verification and Deduction Systematic Knowledge How 
 propositions are related to each other Relations of 
 Opposition among propositions which have not identical 
 terms Conversion Obversion Contraposition . . . 110 
 
 CHAPTER VIII 
 THE SYLLOGISM 
 
 The Principles of Syllogistic Reasoning The First Figure 
 and its Principles The Second Figure The Third 
 Figure The Fourth Figure 126 
 
 CHAPTER IX 
 TRADITIONAL TREATMENT OF THE 
 
 SYLLOGISM 
 
 Traditional treatment Moods Figures Note on the Re- 
 duction of the Moods and Figures 137 
 
 CHAPTER X 
 
 ABBREVIATED AND COMPLEX FORMS OF REASON' 
 ING HYPOTHETICAL AND DISJUNCTIVE 
 
 SYLLOGISMS 
 
 The Enthymeme Prosyllogism and Episyllogism The So- 
 rites Hypothetical Reasoning Disjunctive Reasoning 
 More Complex Forms Extra-syllogistic Reasoning . 15J 
 
CONTENTS ix 
 
 CHAPTER XI PAGE 
 
 I. PROOF AND DISPROOF II. FAILURE TO PROVE 
 Various Kinds of Proof Failures to Prove Fallacies . , 166 
 GENERAL EXERCISES *.. 171 
 
 PART II 
 SUPPLEMENTARY METHODS 
 
 CHAPTER I 
 STATISTICS 
 Statistics, their uses and limits Correlation The Processes 
 
 used in Statistical Investigations 189 
 
 CHAPTER II 
 AVERAGES 
 
 The Arithmetical Average The "Weighted" Average The 
 Mode The Median The Geometrical Average Meas- 
 uring Deviations from an average Measurement of phe- 
 nomena The Comparison of quantities which cannot be 
 measured 198 
 
 CHAPTER III 
 PROBABILITY 
 
 The Meaning of Probability Deducing the probability of a 
 phenomenon Dangers to be avoided in interpreting 
 probability 213 
 
 SUPPLEMENT TO PART II 
 
 The Graphic Method of Representing Data and Their Re- 
 lations 226 
 
 PART III 
 THE CONSTRUCTION OF SYSTEMS 
 
 CHAPTER I 
 
 EXPLANATION 
 
 What is Explanation? , , , 231 
 
x CONTENTS 
 
 PAGH 
 CHAPTER II 
 
 HYPOTHESIS 
 
 What is an Hypothesis? The Value of Hypotheses How 
 are Hypotheses suggested to us? Requisites of a good 
 hypothesis 246 
 
 CHAPTER III 
 
 TYPICAL SYSTEMS OF KNOWLEDGE 
 The Geometric System Others closely related to this Sys- 
 tems which are more concerned with concrete phenom- 
 ena Systems of Historical Facts 257 
 
 EXERCISES IN THE EXAMINATION OF COMPLEX REASONING 
 Professor James's Argument for his Theory of the Emotions 
 A. H. Fison on "The Evolution of Double Stars" 
 Huxley on " The Demonstrative Evidence of Evolution " 279 
 
PART I 
 AN OUTLINE OF SCIENTIFIC METHOD 
 
CHAPTER I 
 INTRODUCTORY 
 
 Science and Common Sense. The methods of sci- 1 
 ence are the methods of all correct thinking. In all 
 thinking we are concerned with getting and organiz- 
 ing knowledge, or with testing, applying, and devel- 
 oping the knowledge we have already acquired. We 
 are all aware that correct thinking differs from that 
 which is incorrect in its conformity to certain laws. 
 These laws are usually spoken of as the laws of 
 thought. They are not simply laws of thought, how- 
 ever ; they are laws of things as well ; they are the 
 laws of the world as we know it. They are adhered 
 to, consciously or unconsciously, in all correct think- 
 ing, whether casual or systematic. Science differs from 
 common sense " only as a veteran differs from a raw 
 recruit; and its methods differ from those of common 
 sense only so far as the guardsman's cut and thrust 
 differ from the manner in which the savage wields his 
 club. The primary power is the same in each case, 
 and perhaps the untutored savage has the more brawny 
 arm of the two. The real advantage lies in the point 
 and polish of the guardsman's weapon ; in the trained 
 eye, quick to spy out the weakness of the adversary; 
 in the ready hand, prompt to follow it upon the in- 
 stant. But, after all, the sword exercise is only the 
 hewing and poking of the clubman developed and 
 perfected. 
 
2 INTRODUCTORY 
 
 " So the vast results obtained by science are won 
 . . . by no mental processes other than those which 
 are practised in every one of the humblest and meanest 
 affairs of life. A detective policeman discovers a bur- 
 glar from the marks made by his shoe, by a mental 
 process identical with that by which Cuvier restored 
 the extinct animals of Montmartre from the fragments 
 of their bones. Nor does the process of induction and 
 deduction by which a lady, finding a stain of a peculiar 
 color upon her dress, concludes that somebody has up- 
 set the inkstand thereon, differ in any way, in kind, 
 from that by which Adams and Leverrier discovered a 
 new planet. The man of science, in fact, simply uses 
 with scrupulous exactness the methods which we all 
 habitually and at every moment use 'Carelessly ; and 
 the man of business must as much avail himself of the 
 scientific method must be as truly a man of science 
 as the veriest bookworm of us all." 1 ^ 
 
 It is of course true that the conclusions of science 
 are often in disagreement with those of common sense, 
 but the disagreement is due to the difference in the 
 thoroughness and completeness with which the facts 
 have been examined. In many cases the -common sense 
 of to-day is simply the science of yesterday, for com- 
 mon sense is usually very conservative, and often re- 
 gards the novelty of a conclusion as an argument 
 against it. 
 
 Induction and Deduction included in Scientific 
 Method. Scientific method being simply a more thor- 
 ough application of principles universally employed in 
 
 i Huxley, The Educational Value of the Natural History 
 Sciences. ' 
 
INDUCTION AND DEDUCTION 3 
 
 reasoning, a good means of getting a general view of 
 those principles will be to examine the procedure of 
 science. It includes both formal and inductive logic. 
 Formal or deductive logic is simply one part of scien- 
 tific method ; hence any exposition of scientific method 
 will include an examination of deduction. Sometimes 
 induction is identified with scientific method, but it is 
 often used in a narrower sense ; and, in any case, it 
 might seem to exclude deduction, which is an essen- 
 tial part of complete scientific method : therefore it 
 is less confusing to think of induction as simply a part 
 of scientific method. Inductive and deductive reason- 
 ing are constituent elements in a single system. For 
 purposes of study, it will be advisable to break up the 
 system into several parts. The first of these parts will 
 include the processes and principles involved in acquir- 
 ing a knowledge of facts ; the second, those employed 
 in the classification of facts ; the third, includes the 
 discovery and formulation of laws ; and the fourth, 
 the testing of these laws and their further organiza- 
 tion and application. Each of these processes will be 
 found to involve a number of subsidiary processes. As 
 they are parts of a system, they are, of course, mutu- 
 ally dependent; each leads up to or implies the 
 others. 
 
 The Beginning of Knowledge. Nowadays there is 
 almost universal agreement to the statement that all 
 knowledge begins in the perception of concrete facts. 
 It has sometimes been thought that the mind began 
 its -career with a capital stock of knowledge in the 
 form of " innate " ideas or principles. But no one 
 now maintains tlmt there is any knowledge before ex- 
 
4 INTRODUCTORY 
 
 perience begins. That, however, is no warrant for 
 the conclusion which John Locke drew. 2 He held that 
 the mind, at the beginning of its history, is like a sheet 
 of white paper or a waxen tablet or an empty cabinet, 
 and that experience, like some external force, writes 
 upon the tablet or fills the cabinet. To him the mind 
 seemed to be passive in the acquisition of knowledge, 
 able at most to combine and analyze its sensations and 
 ideas. Immanuel Kant, on the other hand, contended 3 
 that, even in those mental operations in which the mind 
 is seemingly least active, it is contributing essential 
 (elements; that it makes knowledge, as it were, out of 
 .the material which is furnished from without ; it cannot 
 roperate without material, hence there is no knowledge 
 [before sense-experience begins ; but this sense-experi- 
 ence itself is, in his view, a product of the mind's activ- 
 ity. We cannot pursue this question any further; our 
 concern is not with the philosophical problem of the 
 ultimate source of knowledge ; it is enough for our 
 purposes to know that knowledge begins in concrete 
 experience, in perception, in knowing sounds and 
 colors, odors, moving objects, pains, pleasures, emo- 
 tions, and so on. 
 
 Natural Sciences and Others. Things and events 
 and relations in the external world constitute the data 
 of what are sometimes known as the " natural " sci- 
 ences, such as biology, physics and chemistry. Mental 
 facts' and their relations make up the data of psychol- 
 ogy ; they are quite as concrete in their way as any 
 physical facts, and the methods employed by psychol- 
 
 2 In his Essay on the Human Understanding. 
 s In his Critique of the Pure Reason. 
 
THE SOURCES OF KNOWLEDGE 5 
 
 ogists are the same as those used in the physical 
 sciences. 
 
 Such sciences illustrate almost all the processes env 
 ployed in the acquisition of knowledge, whereas a sci- 
 ence like mathematics makes most use of a few of them, 
 which it applies and elaborates with great thorough- 
 ness. We shall attempt to follow, as closely as may be, 
 the stages in building up knowledge as they appear in 
 the natural sciences. As in knowledge generally, these 
 sciences begin with the perception of facts, external or 
 internal. Then sooner or later they proceed to classify 
 arid organize the knowledge thus gained. 
 
 The Sources of Knowledge, Direct and Indirect. 
 Perception of concrete facts comes first as a source 
 of knowledge, or rather as the primitive form of 
 knowledge. Its limitations are obvious ; it is often far 
 from clear ; it is frequently mistaken ; it embraces com- 
 paratively few facts at any one time, and it does not 
 extend beyond the present, or, at most, the immediate 
 past. If we had to depend upon it alone, we could 
 never get together a body of knowledge. It is possi- 
 ble dimly to picture a mind which could be aware only 
 of what was immediately present in time and space; 
 its knowledge would be rudimentary, and without 
 knowledge of something besides the present, the pres- 
 ent itself would be meaningless. In all but the lowest 
 types of consciousness there is a constant use of indi~ 
 red means to knowledge. Memory is the first of these. 4 
 Memory restores a larger or smaller part of the 
 
 4 It might perhaps be said that memory is direct knowledge of 
 the past, and this is true in a sense ; but the dependence of memory 
 jupon previous perception, the fact that we do not remember what' 
 we have not previously perceived, shows that it is also indirect. 
 
6 INTRODUCTORY 
 
 knowledge previously gained in perception, and thus 
 makes it possible to draw upon past as well as present 
 experience. 
 
 Another indirect means to knowledge is the testimony 
 of others ; by this means we can come into possession 
 of a knowledge of facts which have never come under 
 our own observation. Oral reports and written rec- 
 ords furnish incomparably more information than any 
 man's unaided observation could afford. 
 
 A further way of extending our knowledge is to be 
 found in inference. From knowledge which we already 
 possess we are able to arrive at conclusions which shall 
 be true of things which may never have been observed 
 by any one; we infer the cause of a distant sound, or 
 the character of the other side of the moon, or the 
 stature and habits of man's remote ancestors, or the 
 climate of the Northern Hemisphere in the Carbonifer- 
 ous Age, etc. As we shall see later, inference is in- 
 volved in greater or less degree in all the other means 
 to knowledge. 
 
 An inference may, of course, be wrong; if it is to 
 possess any degree of certainty, there must be a con- 
 siderable body of information about the facts in ques- 
 tion or about other facts closely related to them. The 
 same is true, to a great extent, of memory, and even 
 of perception, and to a very great extent in the case 
 of testimony. Errors may arise at any point, and 
 one of the most important problems in all thinking is 
 the detection and elimination of errors. 
 
 Organizing Knowledge. Classification as a Pre- 
 liminary Step. So far, attention has been fixed upon 
 the processes employed in acquiring knowledge of facts. 
 
LANGUAGE 7 
 
 In order to make this knowledge available, the data 
 thus acquired must be arranged or classified. The ob- 
 ject of science is to get organized knowledge, and 
 before knowledge can be organized it must be so ar- 
 ranged as to enable us to see what facts are similar 
 and what are different. Classification is the grouping 
 of phenomena according to their likenesses and differ- 
 ences ; those possessing a given characteristic are put 
 into a group or class ; those lacking it may be put into 
 one or more other classes. Classes may be grouped 
 together in a larger class or subdivided into smaller 
 ones. 
 
 Language as a Necessary Instrument. There is one 
 very important instrument for the acquisition of 
 knowledge which has not yet been mentioned ; and that 
 is language. Without some means of describing or 
 otherwise representing facts, only a very limited use 
 could be made of our perceptions: testimony would be 
 impossible without it; inference involves representing 
 to ourselves the consequences of certain principles or 
 facts or situations; imagination and memory are ways 
 of representing what is absent by means of pictures of 
 the facts themselves or by means of other symbols. A 
 great variety of symbols might be employed, but lan- 
 guage, spoken and written, supplies by far the most 
 important and complete set of symbols. The descrip- 
 tion and classification of facts would be practically 
 impossible without language. 
 
 Further Steps in Organized Knowledge. In some 
 sciences: we find little more than classified knowledge; 
 the so-called " classificatory sciences," such as botany 
 and zoology, have, until recently, consisted almost 
 
8 INTRODUCTORY 
 
 wholly of classified data. Science aims not simply at 
 classified knowledge, but at organized knowledge, at 
 knowledge organized into a coherent system. 5 It aims 
 at the discovery of the laws manifested by its data as 
 well as at the discovery of the data themselves and 
 their arrangement into groups. 
 
 What is a scientific law? A law in the -field of sci- 
 ence is a statement of the way in which things do 
 invariably behave. Unlike a moral law, a scientific 
 law has nothing to say about the way in which things 
 ought to behave, and, unlike a civil law, it does not 
 prescribe a mode of action whose violation involves a 
 penalty. The law of gravitation, for example, simply 
 states that bodies do attract each other in certain defi- 
 nite ways ; if bodies should fail to do this, the law of 
 gravitation would be no genuine law. A scientific law 
 states an invariable, unconditional -connection between 
 phenomena. 
 
 How are laws of this character discovered? They 
 are based originally upon observation of particular 
 instances of the behavior of phenomena. From ob- 
 served instances we draw an inference which covers all 
 other cases of the sort, past and future. This, that 
 and the other acid turns blue litmus paper red ; we 
 conclude that all acids will have a like effect. This 
 conclusion may, of course, be mistaken ; it is an infer- 
 ence, and must be tested or verified. 
 
 Verification is then the next step. It may be under- 
 taken in several ways: our conclusion may be com- 
 
 5 There are of course fields of science where classified knowledge 
 is the most that can be had, But the ideal of science goes beyond 
 this. 
 
PRESUPPOSITIONS d 
 
 pared with other things which we know about the facts 
 under investigation ; it may be shown to be a conse- 
 quence of some known law ; or it may be possible to 
 find some further fact which would be consistent with 
 our inference and with no alternative inference that 
 can be suggested. Speaking generally, verification in- 
 volves finding whether the inference in question fits in 
 with the system of things to which it belongs. If such 
 a test cannot be applied, if there is no such system of 
 which it can be shown to be a member, it remains 
 uncertain. 
 
 What is Presupposed? One important question re- 
 mains to be asked. Are there any laws or universal 
 propositions which do not require verification? Are 
 there any statements which are self-evident and not 
 open to question or to proof? Axioms, such as those 
 of mathematics, are sometimes said to be of this char- 
 acter. For example, take the statement that two 
 things equal to the same thing are equal to each other; 
 can this statement be doubted or can a proof for it 
 be conceived? Are there not propositions which are 
 so fundamental that they cannot be based upon any 
 which are more general, and so necessary to all thought 
 that they cannot be based upon perception, but are 
 presupposed in perception? This raises again the 
 question at issue between Locke and Kant; without 
 attempting to answer it, we may at least say that 
 no proposition which does not justify itself in experi- 
 ence can be accepted as true. Many propositions have 
 seemed to be self-evident only to be proved false by 
 later development in knowledge, and whatever else may 
 be urged in favor of any proposition, it must at any 
 
10 INTRODUCTORY 
 
 rate fit in with the rest of the things we know if it 
 is to be accepted as true. 
 
 Certain of these axioms or postulates are to be found 
 in every science. In logic they appear under the name 
 of the Laws of Thought. They are: 
 
 The Law of Identity, expressed by the formula: A 
 is A. 
 
 The Law of Contradiction, expressed by the formula : 
 A is not non-A. 
 
 The Law of Excluded Middle: Either A is B or A 
 is not B. 
 
 The Law of Sufficient Reason: Every thing which 
 exists has a sufficient reason or cause for being what 
 it is. 
 
 There is some disagreement regarding the meaning 
 of some of these laws. The Law of Identity, for ex- 
 ample, seems to be a mere tautology: to state that 
 A is A, or that a thing is what it is, does not seem to 
 give us any information. It is true, of course, that 
 in a world where the Law of Identity, in this sense, 
 did not hold, reason could do nothing. But the Law 
 of Identity is usually taken to mean also that there 
 must be an element of identity in every act of thought 
 and in every piece of reasoning. In the proposition 
 " Man is rational," it is obvious that man and rational 
 are not identical; still there is something common to 
 the two; without this core of identity no single judg- 
 ment would be possible. 
 
 The Law of Contradiction complements the Law of 
 Identity. A thing is not its opposite, and in so far 
 as there is opposition between two things it is neces- 
 sary to assert that one is not the other. 
 
THE LAWS OF THOUGHT 11 
 
 The Law of Excluded Middle asserts that of two 
 contradictory statements one or the other must be 
 true. The law does not hold if the two statements are 
 not contradictory, i.e., if there is any third possibility. 
 There is a middle ground between " A is brilliant " and 
 " A is stupid " : he may be an average person. But 
 " This figure is square " and " This figure is not 
 square " are contradictories. 
 
 All these laws are, of course, laws for thought, but 
 they are equally laws of things, and they are laws 
 for thought for that reason only. Certainly they 
 must hold for any world in which reason can operate. 
 
 The Law of Sufficient Reason asserts that the uni- 
 verse is a rational universe; that for everything that 
 exists there is a reason, and an adequate reason; that 
 things are capable of explanation, implying that the 
 world is a coherent system. In the words of Leibniz, 
 who gave the principle its rank, ". . . nothing 
 occurs for which one having sufficient knowledge might 
 not be able to give a sufficient reason why it is as it is 
 and not otherwise." 6 If the world were entirely 
 chaotic, knowledge, except that of the most primitive 
 sort, would be impossible ; there could be no general 
 knowledge, no knowledge of laws or principles, for laws 
 and principles would not exist. It is conceivable, how- 
 ever, that the world is only partly rational, that there 
 are things for which there is no sufficient reason ; if so, 
 rational knowledge would be limited to the fields within 
 which principles did hold. 
 
 Summarizing, we may say that every science aims 
 
 6 Principes de la Nature et de la Grace. Quoted in Dictionary 
 of Philosophy, Ed. J. Mark Baldwin, Art. "Sufficient Reason." 
 
12 INTRODUCTORY 
 
 at the discovery of the laws of the data with which 
 it deals, and at the organization of all its content into 
 a single systematic whole. A completely organized 
 system of knowledge would be one in which every part 
 would imply every other, and he who understood the 
 system perfectly could reconstruct the whole from any 
 part. Cuvier claimed that a naturalist could recon- 
 struct an animal from a single bone, and he himself, 
 as noted by Huxley in the passage quoted above, gave 
 evidence of the validity of his claim. Perfection of 
 organization is not to be found in any natural science; 
 the mathematical sciences show something approxi- 
 .mating completeness, but they do not deal directly with 
 concrete facts. 
 
CHAPTER II 
 FIRST STAGES IN KNOWLEDGE 
 
 I. Facts and the Ways in Which They are Known. 
 Knowledge begins with the perception of facts; and 
 these facts are of many kinds. What is a fact? 
 A fact is anything which exists ; it is that which 
 is real, apart from any opinion we may have about it 
 or any attitude which we may take toward it ; it is 
 that which is as opposed to that which is merely imag- 
 ined or conceived. When we ask for facts, we ask for 
 something which shall be independent of any belief 1 or 
 disbelief, approval or disapproval, on the part of any 
 person. 2 Some or all of these characteristics belong to 
 laws, but fact is distinguished from law in being con- 
 crete and particular, instead of abstract and general. 
 
 A. PERCEPTION AND WHAT IT INCLUDES. Facts 
 are known primarily through perception and memory ; 
 they are known directly only by means of perception, 
 
 1 Belief and disbelief, whether true or false, are themselves 
 facts; they are psychological facts. Belief in the Ptolemaic as- 
 tronomy was a fact; that is, the belief actually existed. A false 
 belief is one in which the thing believed is not a fact; it asserts 
 or assents to something which does not really exist. Belief or dis- 
 belief may bring about changes in facts; in other words, give rise 
 to new facts, as may any other existing thing. To say that a fact 
 is independent of our attitude means that its existence and char- 
 acter are what they are apart from our attitude and aside from 
 any possible effects which may be produced upon them by our 
 attitude. 
 
 2 This position is confessedly dogmatic. Further reflection 
 uiight show that nothing is independent, but for our present pur- 
 pose this position is justified. 
 
 13 
 
14 FIRST STAGES IN KNOWLEDGE 
 
 though there are various ways in which they may be 
 known indirectly. One of the most important of these 
 indirect means, and one which is an important element 
 in all the rest, is inference; a perceived fact may be 
 evidence to our minds of the existence of something 
 which we cannot perceive. 
 
 Much that is often included under perception must 
 be eliminated when we are trying to use the term with 
 scientific accuracy. For example, we say that we per- 
 ceive the inkstand upon the table, or a man on the 
 other side of the street, or that lightning has set fire 
 to a distant building, or that Mr. X is an able law- 
 yer, or that history repeats itself, and so on. Are any 
 of these pure perceptions? We may perceive certain 
 events, but to " perceive " that history is therein re- 
 peating itself involves, at the very least, these infer- 
 ences : that the words of historians represent what has 
 occurred in the past; that they are competent and 
 truthful and that we understand them; and that the 
 events we perceive are really like those which they have 
 described. In the example of the lawyer, we base our 
 belief on observation of certain acts of his which have 
 brought about desired results in spite of difficulties ; 
 and on the inferences that he understood the situation 
 and intended to bring about the results which actually 
 occurred. Again, though the flash and the distant 
 light were perceived, the conclusions that the flash was 
 lightning and that the light was that of a burning 
 building in the distance, and that the first of these was 
 the cause of the second, involve far more than percep- 
 tion. In such instances as these the presence of infer- 
 ence is evident and the importance of distinguishing 
 
PERCEPTION AND INFERENCE 15 
 
 what is perceived from what is inferred is obvious. 
 The perception might be correct, while the inference 
 was erroneous, or vice versa. By distinguishing the 
 two, the problems of discovering error and of correct- 
 ing it are much simplified. 
 
 But it is by no means easy to know where to draw 
 the line between perception and inference. We should 
 say ordinarily that we perceive the ink-well or the man 
 across the street, but even in these cases there is some- 
 thing which is very like inference. A perception con- 
 tains many different elements, and these get themselves 
 before the mind in a variety of ways ; comparatively 
 little in any perception can be said to come directly 
 from the object. In the perception of the ink-well or 
 the man all that we get directly is a spot of color 
 with certain variations of light, shade, and so on. But 
 we seem to see an object in three dimensions, of a cer- 
 tain size, at a given distance from us, and possessing 
 weight, resistance, a certain degree of hardness, a pe- 
 culiar internal structure and an indefinite number of 
 other qualities, which may be more or less definitely 
 present to the mind. If we had not, in the past, found 
 these qualities in combination with spots of color sim- 
 ilar to those now present, we should not be aware of 
 them now; but that does not mean that these qualities 
 are simply remembered, for they are present to the 
 mind as genuinely objective qualities, and we seem to 
 be as directly aware of them as we are of the color, 
 although reflection shows us that they could not be 
 given by sight alone. They all seem to present them- 
 selves together, while in remembering a number of 
 events, first one appears before the mind and then an- 
 
16 FIRST STAGES IN KNOWLEDGE 
 
 other; in perceiving an object, the qualities do not come 
 forward one after another, but all seem to be present 
 together in a single thing. A perception is a reaction 
 of the mind to an object, quality, or event of some kind. 
 !A mind which has had little experience in a given field 
 will react to an object in that field with a perception 
 of a comparatively simple sort; if one had seen and 
 handled oranges but had not tasted them, his percep- 
 tion would contain no suggestion of the flavor, as a 
 blind man's perception contains no suggestion of color 
 or other visual qualities. 
 
 Every time an object is perceived under new condi- 
 tions something is added which will modify future per- 
 ceptions in greater or less degree. The child builds up 
 his perceptions gradually ; from a first vague, indefi- 
 nite perception he advances to one that is more coher- 
 ent and complete. 
 
 The way in which any person will perceive an object 
 will depend largely upon his past experience: different 
 persons will consequently perceive the same object dif- 
 ferently; as no two persons have ever had precisely 
 the same experience, they will never see a given object 
 in precisely the same way. But in most instances the 
 differences will be slight, because there is so much that 
 is common in the experience of all, and in the percep- 
 tion of ordinary objects the differences are usually 
 small and comparatively unimportant. 
 
 " Fallacies " of Perception, and Their Causes. We 
 think of perception as a certain and infallible source 
 of knowledge ; but if in all perceptions there is a large 
 addition from past experience it is clear that many 
 of them are likely to be wrong. The present object may 
 
CAUSES OF MISTAKEN PERCEPTIONS 17 
 
 not be similar in all respects to like objects which we 
 have seen in the past. A spot of color of a certain 
 shape and apparent size may have stood invariably 
 for an orange ; in other words, it may have been found 
 along with other sensations indicating a solid spherical 
 object, of a certain flavor and odor, with a certain in- 
 ternal structure, and so on. If the spot of color again 
 appears we seem to be aware of the other qualities. 
 But there may be only a spot of color, as on the 
 painter's canvas. Again, when two persons are similar 
 in appearance, one may easily be mistaken for the 
 other. The visual appearance of A may seem to as- 
 sure the presence of the other qualities which, as a 
 matter of fact, belong to B. 
 
 The possibility of erroneous perceptions was com- 
 mented upon very early in the history of thought, and 
 because errors of this sort occur so frequently, some 
 thinkers concluded that the senses were altogether unre- 
 liable as sources of knowledge. Others urged that the 
 fault was not with the senses; they pointed out that 
 the trouble lay in adding to what the senses gave. 
 When we have a sensation of greenness, they said, 
 greenness is actually present to the mind ; if we go on 
 to say that there is present an apple, we are adding a 
 
 . number of qualities to those which are given by sensa- 
 tion, and the qualities we add may not really be there. 
 
 : If we should refrain from adding those other qualities 
 we should never be mistaken, but it is impossible en- 
 
 . tirely to separate the sensational element from the 
 others. The perception is a unit in spite of the com- 
 plexity of the qualities which make it up, and these 
 qualities are capable of modifying each other. The 
 
18 FIRST STAGES IN KNOWLEDGE 
 
 green of a picture or of a landscape does not look the 
 same if the scene is looked at upside down; of course 
 we should be correct in saying that we seem to see a 
 certain shade of green in the first case and a different 
 one in the second. We may be perfectly certain with 
 regard to what we seem to see ; but then we seem to see 
 an object as having three dimensions, when it may have 
 only two, as in a painting; what we usually want to 
 know is whether we see the thing as it is, whether other 
 people seem to see the same thing, whether we may 
 expect to seem to see it in the future, whether handling 
 the object would give confirmatory sensations, and so 
 on. The attempt to limit our statements to what is 
 unmistakably before the mind takes us a very little 
 way toward -certainty in knowledge. Perceptions in- 
 clude more than that. They should, of course, be made 
 as carefully as possible. But although errors are cer- 
 tain to occur, yet if we do not run this risk of error we 
 make little progress toward knowledge. 
 
 This first form then in which knowledge appears is 
 open to mistake ; there are mistaken perceptions. It 
 may be well to note the different types of error and 
 their chief causes. The types are usually said to be 
 two; and they have been called Mai-observation and 
 Non-observation. The names are self-explanatory. 
 Mai-observation is of two kinds : in the one, something 
 which does not belong to the object is added in the 
 perception ; in the other, the relations of the parts are 
 wrongly perceived, as when we read there for three. 
 Of course, both kinds of mal-observation may be pres- 
 ent together, and non-observation also. Otherwise 
 stated, there are really three kinds of error; omission, 
 
THREE KINDS OF ERROR 19 
 
 addition and wrong relation of the parts in a whole. 
 They may occur at any stage in knowledge, and they 
 are, in fact, the only kinds which can occur at any 
 stage. What are their causes in the field of percep- 
 tion? A passage from Bacon, quoted by Jevons, calls 
 attention to a number of the causes which give rise to 
 them: "Things escape the senses because the object 
 is not sufficient in quantity to strike the sense: as all 
 minute bodies; because the percussion of the object is 
 too great to be endured by the senses: as the form of 
 the sun when looking directly at it in mid-day ; be- 
 cause the time is not proportionate to actuate the 
 sense: as the motion of a bullet in the air, or the quick 
 circular motion of a fire-brand, which are too fast, or 
 the hour hand of a common clock, which is too slow; 
 from the distance of the object as to place: as the size 
 of celestial bodies, and the size and nature of all dis- 
 tant bodies; from prepossession by another object: as 
 one powerful smell renders other smells in the same 
 room imperceptible; from the interruption of interpos- 
 ing bodies : as the internal parts of animals ; and be- 
 cause the object is unfit to make an impression upon 
 the sense: as the air, or the invisible and untangible 
 spirit which is included in every living body." 
 
 The various kinds of causes may be classified as 
 follows : 
 
 1. In the first place, the external or physical con- 
 ditio-ns of the perception may be unfavorable ; in a red 
 or green light, the color of objects is wrongly seen; 
 in a fog, sounding objects seem nearer than they really 
 are; if the light is dim, details are overlooked; if we 
 look through an imperfect window-pane, objects ap- 
 
20 FIRST STAGES IN KNOWLEDGE 
 
 pear distorted. In all these cases there is something in 
 the medium through which the object is perceivec] 
 which leads to error. Similar difficulties arise when 
 instruments are employed to extend the range or in- 
 crease the accuracy of our perceptions. Any imper- 
 fection in the instrument is almost certain to be a fruit- 
 ful source of error. Other things might be cited in 
 this field, but these will suffice to illustrate the class. 
 
 2. Next in order we may mention the physiological 
 causes of mistaken perceptions. Imperfections in the 
 sense-organ, fatigue, illness, and the like are obvious 
 examples. There is one sort of perception which is 
 always inaccurate, that of the time at which an event 
 occurs ; a flash of lightning is seen a fraction of a 
 second after the light reaches our eyes ; a sound is not 
 heard in the instant at which it reaches our ears. The 
 reason is this : a thing cannot be perceived until the 
 nerve current which it sets up in our sense-organ has 
 passed along through the nerves to the brain ; this 
 takes time, and in some -cases, as in astronomy, the 
 errors which arise from this source may be very im- 
 portant. Again, we often tend to perceive an event 
 for a moment after it has ceased, since the nervous 
 system continues to reverberate, as it were, after the 
 original cause of its activity has ceased to act. Hence 
 the flash or sound seems to be present after it has 
 really passed. This is seen in our inability to distin- 
 guish the spokes of a rapidly revolving wheel or the 
 successive vibrations of a tone, or single views in mov- 
 ing pictures ; in all these the succeeding event begins 
 before we have ceased to perceive the one before it. 
 
 3. But if all physiological and physical conditions 
 
PSYCHOLOGICAL CAUSES OF ERROR 21 
 
 were favorable, if all organs and media and instru- 
 ments were perfect, there would still remain the psycho- 
 logical sources of error. These are often or even 
 always present along with the others. One of the psy- 
 chological causes has already been alluded to, namely, 
 (1) the tendency to see what we have previously seen 
 in similar circumstances. There is also (2) a tendency 
 to perceive what we expect or wish or hope or fear, or 
 what has been recently or habitually in the mind, or 
 that which has been vividly perceived or imagined. 
 What is known as the " proof-reader's " illusion illus- 
 trates one of these; in reading, the context often sug- 
 gests a certain word and we see that word and 
 overlook mistakes in spelling. In the following passage 
 (based on one in James's Psychology) few persons 
 reading at the ordinary rate, and with ordinary care, 
 would succeed in detecting all the mistakes in spelling : 
 Any one wateing in a dark plase and expectng or faer- 
 ing a certaon objectt will interpret an abrup seusation 
 to mean that object's presense. The boy playing " I 
 spy," the criminel skulhing from his persuers, the 
 superstitions personn hureying throuh the churchvard 
 at midnight, the man losst in the woods, the girl who 
 tremulusly has made an eveniug apointmnt with her 
 swain, all are subjec to ilusions of sight and sound 
 wkich make there hearts beat til they ate dispelld. 
 
 Another case illustrating some of these principles is 
 that of the prisoner who had already been convicted 
 of one crime and served his sentence, and who narrowly 
 escaped conviction a second time, although entirely 
 innocent in both cases. He bore a superficial resem- 
 blance to the real criminal; the witnesses were predis- 
 
22 FIRST STAGES IN KNOWLEDGE 
 
 posed to believe that he was the criminal, and they 
 positively identified him as the one whom they had seen 
 committing the crime. 
 
 The effectiveness of all these tendencies is enhanced 
 by (3) lack of attention or misplaced attention. The 
 inattentive reader overlooks misprints, and so does the 
 reader who is very intent upon the thought. Presti- 
 digitators, fraudulent spiritualistic mediums, and the 
 like, take advantage of these tendencies. They direct 
 attention to unimportant things in order that they 
 may do the important ones unobserved, and by leading 
 the spectator to expect certain events they can often 
 persuade him to believe that he actually witnesses them. 
 
 Mistakes as to the order of events are very easy in 
 some circumstances; if two events, one in the field of 
 sight and the other in that of sound, occur very nearly 
 at the same time, this often happens. (4) Lack of 
 training in observing events of a given kind may make 
 correct perception impossible; the use of the micro- 
 scope, finding and following a trail in the woods^ 
 seeing distant objects at sea or on the plains, distin- 
 guishing flavors, colors, etc., are examples. 
 
 (5) Abnormal psychological conditions, such aa, 
 nervous excitement, those produced by drugs, etc., 
 modify the keenness and accuracy of perceptions, 
 sometimes for the better and sometimes for the worse. 
 These various causes, physical, physiological and psy- 
 chological, are so closely bound up together that it is 
 often difficult to say which is chiefly operative in any 
 given case. 
 
 Careful and intelligent attention will prevent many 
 errors. A careful perception made with a purpose is 
 
OBSERVATION 23 
 
 called an observation. This term is sometimes used to 
 cover all perception whatsoever, but it will be used 
 here in the narrower sense. Still, the most carefully 
 made perception may prove to be mistaken. In some 
 of the sciences there are various special and technical 
 methods of eliminating error. 3 
 
 The discovery of error does not always lead to its 
 elimination nor enable us to make the requisite correc- 
 tion. In some cases it does ; we have already seen that 
 the perception of an event takes time; this time is 
 longer for some persons than for others, but for each 
 it is approximately constant under given conditions. 
 By means of a device which registers the exact time at 
 which a certain event occurs and the time at which the 
 observer indicates that he perceives it, it is possible to 
 determine his " personal error " and to make the 
 proper correction in cases in which the exact time of 
 the occurrence cannot be otherwise determined. But 
 in most cases it is riot possible to do this or even to 
 guess at the presence or the amount of error. Some- 
 times, as in the case of measurements, it may be pos- 
 sible to repeat the observation, and if the results 
 cannot be made to agree, we can sometimes get a result 
 approximately correct by taking an average. 
 
 Testing Perceptions. It can almost be said that 
 every observation should be held in suspicion until 
 tested. The test would consist in finding out whether 
 it agreed with other observations of the same fact or 
 of similar facts made by ourselves or others, whether it 
 was in agreement with the laws of the field in which it 
 was found, with the laws of Nature generally, and so 
 s See Jevons, Principles of Science, chap. xv. 
 
2.4 FIRST STAGES IN KNOWLEDGE 
 
 on. We always proceed upon the principle that ail 
 knowledge should hang together, should be consistent 
 and coherent ; that the world is a consistent and 
 coherent world ; and that correct perceptions will 
 agree with each other and with the rest of our expe- 
 rience. 
 
 When it is possible to repeat an observation, we have 
 at once a starting-point for testing it ; and when new 
 observations can be made under more exact conditions, 
 we are in a very favorable position for extending our 
 knowledge of the facts under observation. One of the 
 chief reasons why modern astronomy, for example, is 
 so far in advance of that of the Greeks is to be found 
 in the fact that modern instruments make the observa- 
 tions of astronomical phenomena so much more reli- 
 able. 
 
 Experiment. Sometimes it is possible to reproduce 
 at will the phenomenon under observation. This is the 
 case, to a great degree, in physics and chemistry: 
 sounds, chemical changes, and so on, can be repeated 
 indefinitely. Moreover, the circumstances in which the 
 phenomenon occurs may often be controlled and varied 
 more or less, and that is very often a matter of great 
 importance, as will appear later. To bring about an 
 event for the sake of observing it is to experiment. 
 An experiment may be performed for various reasons ; 
 it may be that we wish simply to get an additional ob- 
 servation as a basis for inference or a means of testing 
 the accuracy of one which we have made already; or 
 we may wish to see the result of changing certain of 
 the circumstances in which the phenomenon occurs ; or 
 of finding the consequences of any condi^on whatso" 
 
EXPERIMENT 25 
 
 ever. " Whenever we can, by our own agency, influence 
 the object we are investigating, we can remedy this 
 want [insufficient observation] by experiment. We 
 can institute at will a certain group of conditions C, 
 and so compel the causes which are really at work to 
 respond with an effect E, which would otherwise per- 
 haps have never come within the domain of our senses. 
 By varying at will the quantity and composition of 
 that C we can bring about in E a series of changes in 
 quantity and kind, which were still less likely to offer 
 themselves unsolicited to our observation. Again, we 
 can break up C into its component parts, and in each 
 experiment allow but one of these, or a definitely as- 
 signed group of several of them, to take effect, at the 
 same time cutting off the rest from action. The con- 
 stituent elements of the result E admit of being sepa- 
 rated in the same way, so that we learn which of them 
 depends upon which element of the compound C. Thus 
 experiment is the practical means by which we furnish 
 ourselves with observations in such number and involv- 
 ing such mutual differences and affinities as is requisite 
 in order to the elimination of what is unessential in 
 them. . . . Defined in this way, it is clear that ex- 
 periment only has an advantage over observation in so 
 far as it is capable of supplementing the usual defi- 
 ciencies of the latter ; its function is to furnish us with 
 suitable and fruitful observations instead of the un- 
 suitable and unfruitful ones which offer themselves. 
 . . . It is merely a way of preparing and setting be- 
 fore ourselves phenomena which it is of importance that 
 we should observe." 4 But its function is exceedingly 
 *Lotze, Logic, Bk. II, chap, vii, 260. 
 
26 FIRST STAGES IN KNOWLEDGE 
 
 important, and without it many sciences could make lit- 
 tle progress. 
 
 The peculiar advantage of being able to control and 
 vary the conditions of an event to be observed will be 
 evident at a later point. 
 
 B. INDIRECT MEANS TO KNOWLEDGE OF FACTS. 
 I. Memory and its Defects. So far in the present 
 chapter we have discussed only the direct means of 
 knowing facts. It appeared, however, that even in per- 
 ception there is much that is a revival of past experi- 
 ence, reinstated by the memory. Knowledge of the past, 
 reappearing in memory, bulks very large in the total of 
 our knowledge. True memory is simply the recall of 
 past experience accompanied by awareness of the fact 
 that it was our experience. If one experience or one 
 object of experience is similar to what is now before 
 our minds, or if it has been related to the latter in 
 any way, it tends to reappear. That tendency is often 
 overcome, otherwise practically everything would be 
 remembered. Not only do many things drop out of the 
 memory, but many are also changed in their character 
 or order, and some things may be added. Ordinary for- 
 getfulness corresponds to non-observation. It is prac- 
 tically always present in greater or less degree, and 
 it obviously tends to increase with the lapse of time. 
 Many things disappear altogether ; sometimes the main 
 outlines are remembered and details forgotten; some- 
 times only a few of the details remain. 
 
 Remembering wrongly corresponds to mal-observa- 
 tion: words which were correctly heard may be incor- 
 rectly remembered; an object which was seen as red 
 may be remembered as brown, and so on. Hardly ever 
 
DEFECTS OF MEMORY 27 
 
 do any two witnesses agree exactly in their memory of 
 events which could easily have been observed with little 
 danger of mistake. This is so generally recognized 
 that too close a correspondence between the stories of 
 two witnesses is regarded as an evidence of collusion 
 and dishonesty. 
 
 Besides the modification of details, the order of 
 events may be changed in memory or their relations may 
 be modified in other ways, and entirely new elements 
 may be introduced. Among the causes of mistaken 
 memory the following may be noted: 
 
 1. A tendency to remember what would usually have 
 happened in the circumstances. 
 
 2. A tendency to remember things or elements which 
 were particularly pleasant or unpleasant, desired or 
 feared, etc., at the expense of those which were more 
 neutral. Elements or events of this sort, which did not 
 occur but were suggested or expected, may be remem- 
 bered as if they had occurred. 
 
 3. A tendency to remember things in a way which 
 would make them more complete or logical, or more in 
 agreement with our own opinions or wishes, or more in 
 harmony with what we expected, or feared, etc. 
 
 4. Events which have often been described in one's 
 hearing may seem to be remembered. 
 
 The tests of memory, like those of perception, are 
 based upon the principle that genuine knowledge is 
 always consistent and coherent, that the world of facts 
 is throughout harmonious. 
 
 Where accurate records are available the memory, 
 as a source of knowledge of the past, becomes much 
 less important. Accurate records made at the time 
 
28 FIRST STAGES IN KNOWLEDGE 
 
 when the phenomena were perceived are an essential 
 part of all the concrete sciences. The methods of re- 
 cording are many, and they are too technical for pres- 
 ent discussion. 
 
 II. Testimony. Written records and oral reports 
 make up a large part of what is known as evidence. 
 Besides these, evidence includes historical remains of 
 every sort, products of man's activity, natural phe- 
 nomena of every kind, such as glacial scratches, geo- 
 logical deposits, etc., etc. The evidence may be of 
 something in the remote past, of something not ob- 
 served in the present, or of future events. The use of 
 evidence clearly involves making inferences; it also in- 
 volves perception. Some phenomenon is perceived, such 
 as an uttered sound or an inscription or a fossil, and 
 on the basis of this perception the observer draws con- 
 clusions concerning something which may never be per- 
 ceived. 
 
 Oral and written reports, or, in other words, testi- 
 mony, furnish a frequent ground of inference. Testi- 
 mony includes every statement of fact made by any 
 one. The opportunities for error in using it are so 
 numerous that it is surprising that correct information 
 can ever be reached by means of it. 
 
 1. In the first place, the person making the state- 
 ment was liable to error in many ways when he observed 
 the fact which his statement purports to represent. 
 
 2. In the second place, his memory is almost cer- 
 tainly inaccurate in one way or another. 
 
 3. Again, the words which he uses may not correctly 
 represent to us what he has in mind ; he may not use 
 words accurately, or he may use them in a sense unfa- 
 miliar to his hearer. 
 
DEFECTS OF TESTIMONY 29 
 
 4. In the fourth place, he may not be truthful; he 
 may never have witnessed what he pretends to report, 
 or he may intentionally misrepresent what he has wit- 
 nessed. 
 
 These difficulties are present in both oral and written 
 testimony ; in the latter there are additional difficulties. 
 What seems to be the witness of one person may be 
 a garbled account; or errors may have been intro- 
 duced by a copyist or an editor. In oral testimony 
 cross-examination gives a basis for testing statements 
 of the witness. In written testimony the substitute for 
 this is found in other statements by the same writers 
 and by contemporaries ; when these are not to be found, 
 little credence can be given to the testimony. 
 
 III. Inference. Inferences from facts of every sort 
 are also liable to error. In every -case the final test 
 is that of consistency and coherency. The application 
 of the tests. very often involves complicated reasoning 
 and a large body of special information ; it will be 
 discussed incidentally in later chapters; much of sci- 
 entific method is for the purpose of making such tests. 
 
 EXERCISES 
 
 1. How much is really observed in seeing a marksman 
 shoot a clay pigeon? In hearing an automobile pass, a 
 block away? In seeing a prestidigitator take an object 
 from a pocket in which it was not? 
 
 2. What are the causes of mal-observation and non-ob- 
 servation in the following cases? 
 
 (1) A straight stick partly immersed in water seems 
 
 to be bent. 
 
 (2) Two objects looked at through a stereoscope 
 
 seem to be one, and they seem to be solid in- 
 stead of flat. 
 
 (3) The sun seen through a fog sometimes appears 
 
 red. 
 
30 FIRST STAGES IN KNOWLEDGE 
 
 (4) Mirrors increase the apparent size of a room. 
 
 (5) Distant objects appear small. 
 
 (6) Patients often seem to feel pain in amputated 
 
 limbs. 
 
 (7) A table seems to throb if the fingers are pressed 
 
 against it. 
 
 (8) A rearrangement of the furniture in a room is 
 
 often unnoticed. 
 
 (9) We sometimes seem to feel the motion of a boat 
 
 after landing. 
 
 (10) There are marked differences in what the ordi- 
 
 nary good observer, the artist, and the botanist 
 see in a flower. 
 
 (11) Silas Marner mistook Effie's hair for the lost 
 
 gold. 
 
 (12) Looking at one's watch and not knowing the 
 
 time a moment later. 
 
 (13) Not seeing the people one meets. 
 
 (14) In Poe's Sphinx, a small animal on the window 
 
 pane is thought to be a large moth of a strange 
 species. 
 
 (15) Mistaking the order of numbers, as 546 for 564. 
 
 (16) Finding a likeness between an infant and its 
 
 parents. 
 
 (17) Macbeth seeing Birnam Wood coming to Dunsi- 
 
 nane. 
 
 (18) The pain of amputation when, instead of am- 
 
 putation, an icicle is drawn across a limb. 
 
 (19) Shooting a man for a deer when hunting in the 
 
 woods. 
 
 (20) The child's " seeing " things at night. 
 
 3. Give five examples of mistaken observation arising 
 from each kind of cause described in the text. 
 
 4. Suggest causes for errors of memory in the follow- 
 ing cases: 
 
 (1) Memory of "the good old days " as better than 
 
 the present. 
 
 (2) Remembering the childhood of men who later 
 
 became famous. 
 
EXERCISES 31 
 
 (3) In Ivanhoe, Wamba tells the travelers to go in 
 
 one direction*, but points in the other; one of 
 them remembers the verbal directions, the 
 other the direction pointed out. 
 
 (4) Forgetting cases which do not support one's 
 
 view. 
 
 (5) Forgetting certain items in lists of things to be 
 
 bought, etc. 
 
 (6) Dropping out characters or events in remember- 
 
 ing a story or play. 
 
 (7) Ascribing to one person words or deeds of an- 
 
 other. 
 
 (8) " Remembering " events which occurred before 
 
 one was born. 
 
 (9) " Remembering " the apt replies which one 
 
 might have made. 
 
 (10) Remembering as an actual experience what was 
 merely a fiction often related as an experi- 
 ence. 
 
 5. In how many different ways could you account for 
 the statement of a witness that he had seen a ghost? 
 
 6. Suppose three honest witnesses to have testified to 
 seeing a man catch a bullet in his teeth: What would 
 your conclusion be ? 
 
 7. How would you test the statement: General X was 
 killed in the battle of Gettysburg? 
 
CHAPTER III 
 CLASSIFICATION 
 
 OBJECTS of experience make their appearance in an 
 order which seems to be almost chaotic ; and in memory 
 they are often reproduced very much in the order in 
 which they originally occurred. But even in memory, 
 and still more in reflection, there is a tendency to 
 arrange things according to their likenesses and differ- 
 ences. This is the beginning of classification. Classi- 
 fication " is not identical with collection. It denotes 
 the systematic association of kindred facts, the collec- 
 tion, not of all, but of relevant and crucial facts." 
 
 A -classification is necessarily based on a similarity 
 of some sort: of quality or structure or origin, and so 
 on. Any given collection of things may be classified 
 in many different ways. Books, for example, may be 
 grouped according to subject, size, style of binding, 
 publisher, and so on ; minerals, according to composi- 
 tion, value or chemical properties ; the people of a city, 
 according to race, income, occupation or religion. Any 
 quality or relation whatever may serve as a basis of 
 classification. In the abstract, one may be as good as 
 another, and the one to be employed in a given instance 
 will be that which best serves the purpose we have in 
 hand. There are several different types of classification, 
 each serving a special purpose. 
 
 Types of Classification. 1. INDEX CLASSIFICATION. 
 
 1 Karl Pearson, The Grammar of Science, chap. III., n. 1. 
 
CLASSIFICATION 33 
 
 We may notice briefly the " Index Classification." 2 
 The purpose of this mode of grouping is to enable us 
 to get hold of a given fact quickly and easily. Cata- 
 logues are usually constructed with this end in view, 
 and they illustrate the principles involved. Certain 
 obvious characteristics are selected, and very often a 
 given item may appear under several different heads, 
 as in cross-references. Alphabetical catalogues are the 
 most familiar examples of the index classification. 
 
 2. DIAGNOSTIC CLASSIFICATION. A second type is 
 the " Diagnostic Classification " ; its purpose is the 
 identification of an object or the discovery of the group 
 to which it belongs. " Nature Study " books abound 
 in classifications of this sort. Here, too, certain obvi- 
 ous characteristics are made the basis of classification. 
 Flowers, for example, may be classified according to 
 color or time of appearance or habitat; or the main 
 divisions may be made upon one basis, as color, the first 
 subdivision on another, as time of appearance, etc. The 
 identification of ailments by the physician depends 
 upon a classification of symptoms made upon this plan. 
 
 3. " NATURAL " AND " ARTIFICIAL " CLASSIFICATIONS. 
 Both index and diagnostic classifications are useful, 
 but they do not, by themselves, lead directly to any 
 greater knowledge of the facts or of their essential re- 
 lations. They are based, for the greater part, upon 
 superficial and easily noticed characteristics, 3 and have 
 little relation to the essential properties of th& things 
 classified. It is often possible, however, so to group 
 
 2 See Jevons, Principles of Science, chap. xxx. 
 
 3 A diagnostic classification which is to be a sure means for the 
 identification of any and all cases should be based on essential 
 qualities. Those based on superficial and striking qualities serve 
 
34 CLASSIFICATION 
 
 phenomena as to display at once their most significant 
 characteristics. Compare, for example, the popular 
 classification of the whale as a fish with the scientific 
 classification of the same animal as a mammal. To call 
 a whale a fish is to imply that it lives in the water, but 
 tells little more ; to call it a mammal tells us that it has 
 warm blood, lungs instead of gills, a four-chambered 
 heart, certain peculiarities of the skeleton, and so on. 
 
 Grouping data in such a way as to make manifest 
 at once their essential characteristics is the aim of 
 classification in science. Since science aims at complete 
 and systematic knowledge, it will obviously select as 
 the basis of classification in any given case that quality 
 which does correlate the greatest amount of knowledge 
 about the facts under consideration. 
 
 Scientists usually make a distinction between " arti- 
 ficial " and " natural " classifications. " It would be 
 possible to classify all living things according to color, 
 as white, yellow, green organisms, etc. Such a classifi- 
 cation would, however, be artificial and destitute of sci- 
 entific value because based upon a purely artificial and 
 highly inconstant character. An interesting example 
 of an artificial classification formerly employed is the 
 system of Linnaeus, who classified flowering plants into 
 Monandria, Diandria, Triandria, Tetrandria, etc., ac- 
 cording to the number of stamens. This was sufficiently 
 convenient for a first rough arrangement, but was soon 
 found to lead to the most incongruous association of 
 plants agreeing in the number of stamens but differing 
 in almost all characters. From such cases it is plain 
 that plants and animals cannot be naturally classified 
 
 for ready identification of many cases, but not for all. See Bosar- 
 quet's Logic for a discussion of Diagnostic Classification as one 
 based upon deeper and more essential qualities. 
 
NATURAL CLASSIFICATIONS 35 
 
 by likenesses or differences in a single character arti- 
 ficially selected. The entire organisms must be taken 
 into account, and the natural classification differs from 
 the artificial one in representing real relationship and 
 not merely superficial likeness. Modern biology teaches 
 that this relationship is of precisely the same nature 
 .as human relationship, i.e., that it is due to community 
 of descent from ancestral plants or animals. . . , 
 'The labor of determining the natural classification is 
 much lightened by the fact that certain structures are 
 often found as a matter of experience to be constantly 
 .associated or -correlated, so that the presence of one 
 indicates the presence of the others. In such cases a 
 single character may be taken as the basis of a classi- 
 fication which is natural, because agreement in one 
 character has been previously proved empirically to in- 
 dicate agreement in the others. For example, it has 
 been proved that the differences or resemblances of ani- 
 mals are correlated with corresponding differences or 
 resemblances in their teeth. Hence mammals, to a great 
 extent, can be classified according to the structure and 
 disposition of the teeth. And so in many groups it 
 is usually possible to discover empirically some one or 
 few characters on which, by reason of their constant 
 association with other characters, a natural classifica- 
 tion can be based." 4 
 
 Biology furnishes one of the best illustrations of a 
 field in which a natural classification can be made, al- 
 though even here in many cases there is no universal 
 agreement as to which is the natural classification. For 
 each of two characters or sets of characters might be 
 -correlated with a number of others, and it might be 
 4 Sedgwick and Wilson, Biology, p. 175. 
 
36 CLASSIFICATION 
 
 difficult to decide which of the two correlated the 
 greater number or the more important ones. Even if 
 there were such agreement, it would not necessarily be 
 permanent; new information might result in the selec- 
 tion of a new basis of relationship. The difference be- 
 tween natural and artificial classifications is, as Jevons 
 points out, one of degree only : " It will be found al- 
 most impossible to arrange objects according to any 
 circumstance without finding that some correlation of 
 other circumstances is thus made apparent." 
 
 The principle employed in classification for scientific 
 purposes is well stated in Huxley's definition, which was 
 modified somewhat by Jevons and stated in the follow- 
 ing form : " By the classification of any series of ob- 
 jects is meant the actual or ideal arrangement together 
 of those things which are like and the separation of 
 those which are unlike, the purpose of the arrangement 
 being, primarily, to disclose the correlations or laws of 
 union of properties and circumstances, and, secondarily, 
 to facilitate the operations of the mind in clearly con- 
 ceiving and retaining in memory the characters of the 
 objects in question." 
 
 A scientific classification is ordinarily designed to 
 serve the purposes here enumerated, but there may be 
 cases, especially in everyday life, where our primary 
 interest is not in getting a -complete knowledge of 
 things, but in getting together things which have a re- 
 lation to some common purpose or problem ; and in such 
 cases the grouping together of things which are, in 
 most respects, very dissimilar, may be justifiable. 
 Custom-house regulations, for example, proverbially 
 group together things which, apart from certain eco- 
 nomic considerations, may be totally unlike. The so- 
 
DIVISION - 37 
 
 called artificial classification may be entirely satisfac- 
 tory as an index or diagnostic classification, though in 
 a diagnostic classification, as we have seen, the use of 
 essential qualities would furnish a surer means for iden- 
 tifying doubtful cases than the use of obvious qualities. 
 
 Classification, of whatever sort, is not simply bring- 
 ing together data into a single group ; it involves the 
 further ordering of the data in sub-groups. 
 
 Division. Breaking up the group into sub-groups 
 is known in logic as " Division." The first thing to do 
 in making a logical division is to select some charac- 
 teristic which will serve to distinguish some members 
 of the group from the rest. It may belong to some 
 and not to others, or it may belong to all in different 
 degrees, etc. The technical name of a character used 
 for this purpose is fundamentum divisionis, or basis 
 of division. The simplest sort of division is that in 
 which the fundamentum divisionis is a character pres- 
 ent in some members of the class and lacking in the rest. 
 Material substances may be divided into those which 
 are mineral and those which are not; or, to cite an 
 ancient example, we may divide and subdivide sub- 
 stances as follows : 5 
 
 Substance 
 
 A " 
 
 Corporeal Incorporeal" 
 
 f \ 
 
 Animate Inanimate 
 
 A _ 
 
 t "S 
 
 Sensible Insensible 
 
 f \ 
 
 Rational Irrational, etc. 
 
 5 This is known as the Tree of Porphyry, so-named from the 
 Greek logician who was the earliest writer to give a distinct ac- 
 count of this type of division. 
 
38 
 
 CLASSIFICATION 
 
 Division of this kind is called dichotomous or bifur- 
 cate, from the fact that each group or sub-group is 
 always divided into two. 
 
 A more complex classification results from selecting 
 as the basis of division some character which is pos- 
 sessed by all the members of the class but with differ- 
 ences of degree or quality, etc. Books, for example, 
 if classified according to subject matter, would fall into 
 several groups, and each of these might again be sub- 
 divided into several more. 6 A dichotomous division 
 
 e As further examples of classification of this kind we may cite 
 the following from Hy slop's Logic, pages 96, 97. 
 
 Figures - 
 
 Plane., 
 
 Solid, 
 
 Rectilinear . 
 
 . Curvilinear. 
 
 Rectilinear. 
 
 Curvilinear. 
 
 Mechanical . 
 
 Science . 
 
 Physical, 
 
 Moral , 
 
 [ Trilateral 
 ] Quadrilateral 
 I Multilateral 
 
 Circular 
 Elliptical 
 Parabolic 
 Hyperbolic 
 
 Tetrahedrons 
 Pentahedrons 
 Cubes 
 Parallelepipeds, etc. 
 
 Spheres 
 Cones 
 Cylinders 
 Paraboloids 
 
 {Physics 
 Chemistry 
 
 I Organic { Biology 
 
 \ Physiology 
 
 f History 
 [ Polltlcal {Sociology 
 
 f Noetics 
 
 Psychological. -! Aesthetics 
 [ Ethics 
 
DICHOTOMOUS DIVISION 39 
 
 would, of course, be possible here ; we might have some- 
 thing like the following: 
 
 Books 
 
 On history Not on history 
 
 r \ 
 
 On chemistry Not on chemistry, etc. 
 
 But a dichotomous division would soon become un- 
 wieldly ; moreover, it does not present the classes in such 
 a way as to indicate which are coordinate. The ex- 
 ample just given might seem to make history coordi- 
 nate with all other subjects taken together, and 
 chemistry might seem to be subordinate to history. It 
 is desirable, usually, that the classification shall put 
 coordinate classes on the same plane, and this the 
 dichotomous division cannot do. 
 
 Moreover, this sort of division embodies very little 
 information ; it points out a class which has a certain 
 character and another which lacks it; the latter is de- 
 scribed in negative terms only. The other type of 
 classification presents a number of classes, each de- 
 scribed in terms of some positive quality. Still there 
 are many cases in which interest centers in those mem- 
 bers of a class which possess (or lack) some certain 
 character. For some purposes the division of popula- 
 tion into voters and non-voters, or into literate and 
 illiterate, may be quite as satisfactory as any other. 
 
 Sometimes our information regarding a class is so 
 imperfect that a dichotomous division is the only one 
 we can use, In a given shipload of immigrants we 
 might know that some were Italians ? and know nothing 
 
40 CLASSIFICATION 
 
 about the nationality of the rest except that they were 
 not Italians. Or it might be that those outside the 
 class positively characterized had so little in common 
 that no class or series of classes, coordinate with the 
 first, could include them all: the chemist's division of 
 elements into metals and non-metals illustrates this. 
 
 It has often been said that a dichotomous division is 
 the only one which insures against the omission of any 
 individual. Every member of a class must either pos- 
 sess a certain quality or be without it ; all that are ex- 
 cluded from the first class are necessarily included in 
 the second, while in the other sort of division it is easy 
 to overlook something. But if many classes are to be 
 included, the dichotomous division soon becomes almost 
 unmanageable, and if it is not carried out to the end 
 we will not discover every class, although all are for- 
 mally included. If it is carried out exhaustively, every- 
 thing will of course be identified ; but the same would 
 be true of any other type of classification. Jevons 
 holds that diagnostic classifications should usually be 
 dichotomous. 
 
 Requirements of Classification. In any scientific 
 classification (1) the sub-classes must include all that 
 is included in the main class; and (2) they must not 
 overlap, i. e., no individual should belong to two classes 
 at once. To classify people as large and small would 
 violate the first of these rules, while to classify them as 
 large, small, and blue-eyed, would violate both. Viola- 
 tion of the first rule results in incomplete division ; 
 violation of the second, in cross-division. 
 
 Incomplete division is a consequence of failure to 
 carry out a division to the end ; sometimes the principle 
 
FAULTY CLASSIFICATION 41 
 
 of division does not seem to permit this, or some of the 
 data included may be of so peculiar a character that 
 they do not seem to fall into any well-marked classes, 
 An escape from difficulties is sometimes found in a 
 miscellaneous class, which shall include all cases not 
 otherwise provided for. When this is employed, the 
 classification is certain to include all cases. The mis- 
 cellaneous class corresponds to the negative class in 
 dichotomous division. 
 
 Cross-division is a consequence of employing more 
 than one fundamentum divisionis. In the example 
 above, both size and eye-color were employed as bases 
 of division. 
 
 Every classification should be complete or exhaustive ; 
 it should provide a place for every item. But a sort of 
 cross-division may sometimes be very useful, as in index 
 or diagnostic classifications. Ordinary subject indexes, 
 classification of books under author and subject, or of 
 college courses under department and year, are cases 
 in point, as is also the classification of a disease under 
 ea-ch of its several symptoms. 
 
 A class which is divided into sub-classes is technically 
 called a genus; while each of the sub-classes is a species. 
 " Caucasian " is a species of the genus " man." If a 
 sub-class were to be divided it would be a genus in rela- 
 tion to its sub-classes : Slavs are a species of the genus 
 Caucasian. Any class, then, regarded as inclusive of 
 other classes is a genus, whereas if it is regarded as 
 subordinate to some higher class it is a species. A 
 class which is so wide that no other can contain it is 
 called a summum genus or highest genus ; it alone can 
 never be a species. A class which includes so little that 
 
42 CLASSIFICATION 
 
 it can not be subdivided is an infima species or lowest 
 species ; it can never become a genus. 
 
 An individual which is so unique that it can be in- 
 cluded in no class whatever is sui generis. 
 
 Under ordinary conditions there is little use for these 
 last three terms. It may be doubted whether there is 
 such a thing as an individual thing sui generis, and 
 whether there can be more than one summum genus, or 
 any infima species which is not a class of one member 
 only. In any given investigation they may be employed 
 in a relative sense. For anthropology, mammal might 
 be regarded as the summum genus; and an individual 
 whose peculiarities defy all attempts at classification on 
 usual lines might be spoken of as sui generis; a species 
 which could not usefully be divided might be regarded 
 as an infima species. But this use of the terms would 
 not be entirely accurate. 
 
 The use of genus and species as described above is 
 the traditional logical usage ; but in the biological sci- 
 ences they are used in a different sense. In those sci- 
 ences the terms are not relative ; a class is not a species 
 at one time and a genus at another. Homo is always a 
 genus ; formerly it was thought to have two species,, 
 man and the chimpanzee, but now man, homo sapiens, 
 is regarded as the only species in the genus. The Cau- 
 casian race is a variety under the species, homo sapiens. 
 Homo is included in the order, primates, etc. 
 
 EXERCISES 
 
 1. What is classification? 
 
 2. What is an Index-classification? What is its purpose 
 
EXERCISES 43 
 
 and on what sort of quality is it based? How would you 
 construct ait Index-classification of the rulers of Europe 
 during the Nineteenth Century? 
 
 3. What is a Diagnostic-classification? State its purpose 
 and its principles. How would you construct a classifica- 
 tion which would serve for the identification of birds? 
 
 4. What is the purpose of classification as used in scien- 
 tific work? What is the difference between an artificial 
 and a natural classification? 
 
 5. What is a Dichotomous Division, and what are its 
 strong and weak points? Make a dichotomous division of 
 educational institutions. What is a cross-division? How 
 is it caused, and when may it be useful ? Give examples of 
 a genus, a species, a summum genus, an infima species, a 
 thing sui generis. Contrast the biologist's use of " genus " 
 and " species " with the more general logical usage. 
 
 6. Criticise the following classifications and divisions: 
 a Men may be classified as white and colored. 
 
 b Trees, as fruit-trees, shade-trees and forest-trees. 
 
 c The fine arts, as sculpture, painting, drawing, 
 architecture, poetry and photography. (Fowler.) 
 
 d Books, as those on history, science, poetry, religion 
 and belles-lettres. 
 
 e Political parties, as conservative and radical. 
 
 / The states of New England, as Maine, New Hamp- 
 shire, Vermont, and Connecticut. 
 
 g Mind, into intellect, feeling and will. 
 
 h Body, into extension, weight, resistance, etc. (Mel- 
 lone.) 
 
 i Religious, into monotheistic and polytheistic. 
 
 j Americans, into white, black and foreign-born. 
 
 Ic Politicians, into honest and dishonest. 
 
 I Books, into dull and interesting. 
 
 m Games, into those which are athletic and those which 
 are intellectual. 
 
 n Pictures, into paintings, engravings, posters and pen 
 and ink sketches. 
 
 o Domestic animals, into those which are useful and 
 those which are pets. 
 
 p Motion, into molecular and molar. 
 
 ^ Bodies, into light, heavy, and dense. 
 
44 CLASSIFICATION 
 
 r Men, into those whose main pre-occupation is to get 
 through time and those whose aim it is to find 
 time for all that has to be got through. 
 Can you state circumstances in which any of the above 
 might be useful and satisfactory? 
 
 7. Divide and sub-divide: Propositions, Athletic sports, 
 College publications, Government, Poetry, Furniture, Races, 
 Schools. 
 
 8. Criticise the classing together of negroes, coal, and 
 black chalk on the ground that they are similar in being 
 black, solid, extended, divisible, heavy, etc. (MeHone.) 
 
CHAPTER IV 
 THE USE AND MISUSE OF WORDS 
 
 Discrimination, Conception, Abstraction. It will be 
 remembered that a thing is put into a given class by 
 virtue of its possession of some quality or relation, a 
 class being simply a group of things which have in 
 common one or more qualities or relations. Any given 
 thing might, therefore, be classified in several different 
 ways. Bucephalus, for example, might be classified as 
 a horse, or as a colored object, or as a consumer of 
 hay, or as a possession of Alexander the Great, and so 
 on. Indeed, most concrete objects might be classified 
 in hundreds of ways. For every characteristic which a 
 thing possesses there may be a class, and the way in 
 which we shall classify it in any given instance will 
 depend upon the purpose we have in view. For his 
 teacher the small boy is a pupil; for the cat, a source 
 of danger, and so on. And each mode of classification 
 is correct in its place. 
 
 But before an object can be classified in a given way 
 it is, of course, necessary to note what qualities it does 
 possess. Ordinarily we note very few of these. Most 
 of us see only the most obvious and striking qualities of 
 things, and we often see those very imperfectly. We 
 get a vague general impression and fail to analyse it 
 into its elements. The child, in his earliest experiences, 
 hardly discriminates the different qualities of a thing 
 at all, for his first experiences are very much confused. 
 
 45 
 
46 THE USE AND MISUSE OF WORDS 
 
 We know things only as we know their qualities and 
 relations, and the better we can distinguish and relate 
 these the better we know the object. Analysis of the 
 concrete datum is presupposed in classification and in 
 all the other higher manifestations of consciousness. 
 
 When we analyse a thing we pick out its various ele- 
 ments and think of them as more or less isolated from 
 the complex in which they were perceived. We can 
 think of greenness or roundness without thinking of 
 size or hardness or of any of the other qualities with 
 which greenness or hardness always occurs. We never 
 perceive greenness or hardness by themselves, but we 
 can think of them without taking into account the other 
 qualities. The mental act whereby we think of them in 
 that way cannot be perception ; nor can it be memory, 
 for memory, like perception, is of concrete complex 
 things, whereas these qualities are simple and abstract. 
 The mental act in which we bring before ourselves a 
 simple quality is conception; and the thought of the 
 quality is a concept. We have concepts of abstract 
 qualities, but we cannot have percepts of them. But 
 we may also have concepts of concrete things. Our 
 idea of some particular horse, say Bucephalus, is not 
 a memory, nor is it a perception ; it is a concept. 1 We 
 may also have concepts of things which we have per- 
 ceived; indeed, every perception involves conception as 
 well. We are immediately aware of certain qualities, 
 but, more than that, we have an idea of a complex whole 
 possessing more or less coherence, permanence, etc. 
 Whenever we think of a class of objects, qualities, or 
 
 i Both Concept and Conception are used for the idea of the 
 thing or quality. 
 
CONCEPTS 47 
 
 what not, we do so by means of conception. The 
 thought of anything is a concept. Some concepts are 
 universal, some are particular ; some are concrete, some 
 are abstract ; some are of real things, some of imaginary 
 things, and so on. Everything that is thought of is 
 thought of in a concept, or rather, the thought of any- 
 thing is a concept of that thing. 
 
 In conceiving anything two elements are present: 
 the symbol, and its meaning. In the concept " horse " 
 the symbol is the word " horse " ; the meaning is the 
 sum-total of qualities which that word implies or the 
 objects to which it may be applied. The symbol is not 
 necessarily a word: we might think of horses without 
 having in mind the word. The mental picture of a 
 horse might be the symbol. If we were trying to con- 
 vey the idea of a horse to a person who did not under- 
 stand English, we might use a drawing or imitate the 
 sound of galloping, and so on. In all these cases the 
 meaning would be the same, though the symbol would 
 not. The essential element in the concept is .the mean- 
 ing; so long as that remains the same we have the 
 same concept, no matter what the symbol. The same 
 thoughts may be present in two minds, one of which 
 thinks in English and the other in German, or one of 
 which thinks in words and the other in mental pictures. 
 The superiority of words as symbols will be discussed 
 presently. 
 
 It is customary to treat logic as if it dealt solely 
 with concepts, judgments and inferences; but in treat- 
 ing logic as a part of scientific method, as a part of 
 the science of getting knowledge, it will be well to con- 
 tinue to speak as if we were dealing directly with the 
 
48 THE USE AND MISUSE OF WORDS 
 
 facts and not with mental counters. In other words, 
 logic may be regarded as a science of things as well as 
 a science of thoughts. It deals, it is true, only with 
 the most general aspects of things ; not with their spe- 
 cial qualities, as do the special sciences, such as physics, 
 etc. It has to do with that which is common to 
 all fields of facts. In certain cases it may be more 
 convenient to speak of the concepts rather than of the 
 things conceived, as, for example, in -geometry, where 
 the things conceived are certain highly abstract rela- 
 tions and the like ; but even in such cases the other way 
 of speaking would be possible. 
 
 Necessity for Language. Mention has already been 
 made of the necessity for describing or in some way 
 representing the things we know. The means most uni- 
 versally employed and most completely developed is, of 
 course, language. A language, from the point of view 
 of logic and scientific method, is simply a highly com- 
 plex system of symbols for the representation of all 
 kinds of objects and experiences, of the conclusions 
 and constructions based upon experience, of laws, and 
 so on. Language, as already noted, is a -condition of 
 all progress beyond the merest rudiments of knowl- 
 edge. It might seem to be of no use in the field of 
 observation, but an observation made for some special 
 purpose or under experimental conditions implies a 
 previous statement or representation of the thing to be 
 observed. Memory includes a representation of past 
 experience by means either of a mental picture or of 
 some other sort of symbol, such as the name of the 
 thing. All spoken and written evidence, of course, im- 
 plies language; and inference involves the statement to 
 
LANGUAGE 49 
 
 ourselves of a conclusion from something observed or 
 thought of. Classification obviously requires the use 
 of symbols. 2 So important is language for the work 
 of thinking that logic has sometimes been defined as 
 a branch of the study of language. Whately said that 
 " Logic is entirely conversant about language." Some 
 have maintained that all growth in thought has fol- 
 lowed the development of language and would have 
 been impossible without it ; in other words, that lan- 
 guage always precedes thought ; that man is intelligent 
 because he has language and not vice versa. These 
 may be extreme views, but it is certain that systematic 
 knowledge cannot go far without a coherent system of 
 symbols, and that language is infinitely superior to all 
 other kinds of symbols. 3 Any examination of the 
 processes by which knowledge is attained must give 
 careful attention to the consideration of language. 
 
 If language were perfect, it would not be necessary 
 to discuss it at any length in this connection, but its 
 imperfections are such as to lead very often to mistaken 
 ideas and wrong conclusions. It will be necessary, 
 therefore, to examine language in order to discover 
 these imperfections and the means of avoiding them. 
 
 Terms. A word or group of words stands as the 
 representative of some thing, quality, relation, action, 
 
 2 Sometimes the mental picture of an individual may stand for 
 the class; the image of a tree may stand for the class tree, but 
 when we know the name of the class or kind, we usually represent 
 the class to ourselves by means of the name. Mental pictures are 
 liable to vagueness and to modification, and it has been shown that 
 scientists, for example, tend to represent things to themselves 
 almost exclusively by means of words, particularly as they advance 
 in years. 
 
 3 For a discussion of this question see Stout, Manual of Psy- 
 chology, chap. v. 
 
50 THE USE AND MISUSE OF WORDS 
 
 idea, and so on, or some group or combination of them. 
 Such a word or group of words is called a term. A 
 term might consist of any number of words and con- 
 tain various subordinate clauses, but if it stood as the 
 symbol of some single object of thought it would still 
 be one term. " Man " and " The torch in the hand of 
 the Statue of Liberty in New York Harbor " are 
 equally terms, for each stands for a single object of 
 thought. The inevitable difficulties with regard to the 
 use of terms arise from the fact that a word or a 
 group of words may stand for more than one thing; 
 it may have a variety of meanings and is therefore liable 
 to misinterpretation. Most words are used in more 
 senses than one, so the danger of confusion is always 
 present. There are several causes for this multiplica- 
 tion of meanings. One of the most important is (1) the 
 tendency to use a word in a sense wider than the one in 
 which it was formerly used, to use it more generally, to 
 generalize it. Lens meant originally only a double con- 
 vex piece of glass ; such words as curve, acid, metal, 
 salt, etc., illustrate this tendency. 
 
 There is also (2) a contrary tendency to limit the ap- 
 plication of words, to use a term in a narrower sense 
 than formerly, a tendency toward specialization. 
 Minister meant originally a servant; now it means, 
 among other things, the highest representative of a 
 state, one of the most exalted " servants " of a govern- 
 ment. " Deacon, bishop, clerk, queen, captain, general, 
 are all words which have undergone a like process of 
 specialization. In such words as telegraph, rail, signal, 
 station, and many other words arising from new inven- 
 tions, we mav trace the progress of change in a lif(v 
 
SPECIALIZATION OF TERMS 51 
 
 time." The use of Congressman to describe Repre- 
 sentatives only, and of Protection as a name for 
 an economic policy, are further illustrations of the 
 process. 
 
 These tendencies may affect a word and its deriva- 
 tives in different degrees and different directions. Com- 
 pare, for example, distinguish and distinguished; 
 dissolve, dissolute and dissolution; matter and material- 
 istic; respond and responsible; design, designer and de- 
 signing, etc. The popular and the technical uses of a 
 term are usually different, one being broader or nar- 
 rower than the other; phenomenon, sensation, idea, are 
 illustrations. Sometimes a special use of a word is only 
 local, as in dialects, or for a short space of time, as in 
 slang. 
 
 In addition to these tendencies to generalize and to 
 specialize the meaning of terms there is (3) another 
 by which there is a transfer, of meaning to associated 
 objects or to those which are analogous. The use of 
 the word church to designate a religious society, or of 
 chair to indicate a presiding officer, or of bench to 
 stand for the judiciary, are illustrations of the trans- 
 fer of meaning to associated objects, and such expres- 
 sions as a dull student, a hard examination, a brilliant 
 game, etc., illustrate the transfer to analogous objects. 
 
 There are (4) some other cases of less importance: 
 sometimes two words which were originally different and 
 of different derivations are alike in sound and spelling 
 and might possibly be mistaken for each other ; such 
 as, mean in the sense of middle and mean in the sense 
 of low; pound :n the sense of weight and pound meaning 
 a pen, pen as an inclosurc and pen as an instrument of 
 
52 THE USE AND MISUSE OF WORDS 
 
 writing, etc. Sometimes words are alike in sound but 
 different in spelling, as right, wright and rite, or rain 
 and reign; in other cases they are alike in spelling but 
 different in sound, as lead, the metal, and lead, some- 
 thing to be followed, etc. 4 These last three cases are 
 of little importance since the confusions resulting are 
 usually of only momentary duration. In the first three 
 cases, those of generalization, specialization and trans- 
 fer of meaning, the confusion results from the con- 
 tinued use of a word in the older sense after its meaning 
 has been extended to a new field. 
 
 If the various meanings are clearly distinguished and 
 widely separate, the context will usually make clear 
 which is intended ; but the meanings are most frequently 
 very similar or closely connected, otherwise the same 
 word would never have been used for both. The serious 
 consequences of these confusions are seen in the fact 
 that so many disputes and differences of opinion result 
 from a difference in the use of terms. 
 
 Kinds of Terms. 1. SINGULAR AND GENERAL. We 
 have discussed the causes of ambiguity in terms ; it will 
 be well to examine some of the different kinds of terms 
 in order to discover just what sorts of confusion are 
 likely to be found. There are some words, such as 
 proper names, which would not seem liable to ambi- 
 guity since they usually have little or no meaning; but 
 after all there may be uncertainty enough with regard 
 to the application of the name, as every case of mis- 
 taken identity shows. 
 
 Proper names are simply one variety of INDIVIDUAL 
 
 4 Most of the illustrations used in the two pages above have 
 been taken from Jevons, Lesson in Logic. 
 
SINGULAR AND GENERAL TERMS 53 
 
 or SINGULAR terms. " The first president of the United 
 States " is quite as definite in its application as any 
 proper name could be. A singular term is a term which 
 can be applied, in a given sense, to one single, indi- 
 vidual object only. On the other hand there are terms 
 which may be applied in the same sense to an indefinite 
 number of objects. Man, president, book, college, etc., 
 are GENERAL terms. A term which was originally sin- 
 gular may become general, as illustrated in the expres- 
 sions, " A Daniel come to judgment," " A Homer," " A 
 Hannibal," etc. On the other hand singular terms 
 may be so combined as to apply to only one individual ; 
 the first president, the wisest man in the world, the 
 longest river, the highest mountain, etc., are such 
 cases. 
 
 The chief difficulty in the case of singular terms is 
 the liability to error with regard to the individual to 
 whom the name applies. The form or the context usu- 
 ally shows clearly enough whether a term is singular 
 or general. 
 
 In the case of general terms there is much more diffi- 
 culty: in the first place the meaning may be vague; 
 the application of the term may not be definite; in the 
 case of such words as rich and poor, wise and ignorant, 
 and a great many others, there is no universal agree- 
 ment and there is seldom a definite notion as to tho 
 range of application in any particular case. Again, 
 where the term has a plurality of applications, each of 
 which may be sufficiently definite, the wrong one may be 
 employed or understood in any given case. The word 
 law, for example, means, in one field, a prescribed rule 
 of action, something imposed from without and having 
 
54 THE USE AND MISUSE OF WORDS 
 
 a binding force, as a civil law. In the natural sciences, 
 on the other hand, a law is simply a statement of the 
 way in which things do invariably behave. Obviously, 
 one who carries over into the consideration of natural 
 phenomena the conception of law employed in legal 
 practice, is liable to have a very mistaken view of 
 Nature. There is a multitude of terms in which such 
 differences are to be found. The Latin lex meant origi- 
 nally something fixed or set, so both these meanings 
 might be regarded as specializations in different direc- 
 tions of the original meanings. In other cases one 
 meaning is obviously more or less general than the 
 other. In the commandment, " Thou shalt not kill," 
 the word kill is obviously less general than is the state- 
 ment, " To kill is to deprive of life"; or again, the 
 words rest, sleep, etc., are not intended to cover all 
 possible cases in the statement, " Rest, food and sleep 
 are necessary to life." Any mistake as to the exact 
 sense in which a word is used will be certain to lead to 
 mistaken opinions. 
 
 2. CONCRETE AND ABSTRACT TERMS. This brings 
 us to the distinction between concrete and abstract 
 terms, or between terms used in an abstract sense and 
 the same terms as used in a concrete sense. 
 
 An abstract term, as the name implies, stands for 
 something which is the product of abstraction; it is 
 something separated from its context and considered by 
 itself. For example, qualities are known only as they 
 occur in an object, in a complex something which in- 
 cludes many other qualities. We have already seen that 
 these qualities are not recognized as separate things in 
 the child's earliest experience. 
 
ABSTRACT TERMS 55 
 
 If a quality always appeared in the same setting, it 
 would never be discriminated and hence could never be 
 abstracted. To quote Professor James's illustration, 
 if all wet things were cold and all cold things were 
 wet, we should never distinguish coldness from wet- 
 ness. But most qualities do occur in a variety of set- 
 tings and can therefore be discriminated and abstracted. 
 When a quality is abstracted it can be treated, for cer- 
 tain purposes, as a separate thing. In studying color, 
 we disregard the other properties of colored objects 
 and treat their -colors as something independent. 
 
 There are many degrees of abstraction : blue is ab- 
 stract as related to a blue object, but comparatively 
 concrete as related to color. An abstract term mav be 
 the name of a relation, as height, or an action, as 
 walking, or of any characteristic whatever, abstracted 
 from its setting and regarded as an independent thing. 
 The word which stands for this characteristic will be 
 an abstract term. A given term is often used in both 
 senses : in the sentence, " Government is necessary to 
 civilization," the term government is said to be used in 
 an abstract sense ; in the sentence, " This government is 
 a republic," it is concrete. To confuse the more general 
 with the less general meaning of a term or the abstract 
 with the concrete use of it, or to argue from a term 
 taken without qualification to the same term qualified 
 in some particular way, is to commit a fallacy, the 
 Fallacy of Accident. To conclude that it would be 
 meritorious to give a beggar a dollar because charity 
 is a virtue would be to commit this fallacy. To con- 
 clude that, because the only Filipinos you have seen are 
 small, a Filipino is a small person, would be to commit 
 
56 THE USE AND MISUSE OF WORDS 
 
 what is sometimes called the Converse Fallacy of Acci- 
 dent; in this, we argue from the concrete or the less 
 general or what is true in particular circumstances, to 
 the abstract or the more general or to what is true 
 apart from particular circumstances. 
 
 The ancient example, "What is bought in the mar- 
 ket is eaten ; raw meat is bought in the market ; there- 
 fore raw meat is eaten," illustrates the simple fallacy 
 of Accident. So also does the following: " The Greeks 
 produced masterpieces of art, and as the Spartans were 
 Greeks, they produced masterpieces of art." (Davis.) 
 " Greeks," in the major premise, is used in the generic 
 sense. In the minor, it has a more specific meaning. 
 
 To argue that strychnine should be freely sold be- 
 cause it is very useful (as a medicine) would be to com- 
 mit the converse fallacy. 
 
 3. COLLECTIVE AND DISTRIBUTIVE TERMS. Another 
 distinction which is of great importance in dealing with 
 terms is that between collective and distributive terms. 
 Army, for example, is a collective term; it stands for 
 a number of individuals taken together in a group; it 
 is a group term. A term like man, on the other hand, 
 has no such significance. It applies equally to any and 
 every individual in a class. In an expression like all 
 men, for example, there is danger of confusion ; it 
 might be taken to mean all taken together, as in " All 
 Jiving men number about 1,500,000,000 " ; or it might 
 be used distributively, as in " All men are mortal." 
 Synonyms of the terms collective and distributive are 
 jointly and severally. Obligations are sometimes laid 
 upon individuals which they are bound joiptly or sev- 
 erally to observe. 
 
COMPOSITION AND DIVISION 57 
 
 Confusion between the collective and the distributive 
 uses of a term leads to the Fallacies of Composition and 
 Division; arguing from the distributive to the collec- 
 tive use results in the fallacy of Composition. " Each 
 member of the committee is insufficiently informed, 
 therefore the committee as a whole is not sufficiently 
 informed," contains a fallacy of Composition. But to 
 argue that because a navy as a whole was weak, the 
 individual ships were therefore weak, would be to com- 
 mit a fallacy of Division. These fallacies should be 
 kept clearly distinct from the fallacy of Accident. Here 
 we are dealing with a group ; the question is, are we 
 dealing with it simply as a group, or are we thinking 
 of the individuals of which it is made up? In the other 
 case we were not concerned with a group at all. 
 
 4. OTHER KINDS OF TERMS. Various other distinc- 
 tions might be made among terms ; there is, for ex- 
 ample, a distinction between positive and negative 
 terms ; the former being those which imply the presence, 
 and the latter those which imply the absence, of a qual- 
 ity. White, just, warm, etc., illustrate the former; 
 blind, empty, unconscious, the latter. There is little 
 danger of confusion in this and in most of the other 
 cases which might be included, so we will pursue them 
 no further. 
 
 Definition. In any case in which misunderstanding 
 is likely to occur, the first thing to do is, obviously, to 
 make clear what it is that the term stands for. In the 
 case of a proper name the application of the term could 
 be shown by producing, or pointing out, or describing, 
 the individual thing for which it stands, and so of other 
 singular terms. But with general terms that is not 
 
58 THE USE AND MISUSE OF WORDS 
 
 possible ; a general term stands for all possible cases 
 of a given sort, past, present and to come, and any 
 example or series of examples could at most illustrate 
 the meaning of the term. Sometimes an example will 
 show clearly enough, for ordinary purposes, what is 
 meant. But any example might illustrate a variety of 
 things ; if two persons, each of whom was entirely un- 
 acquainted with the language of the other, should try 
 to communicate by pointing to objects to indicate the 
 meaning of the words they were using, they would illus- 
 trate the uncertainty of this method in its extreme form. 
 If one of them should point to a horse, he might mean 
 any one of a dozen different things: horse, or simply 
 animal, or useful animal, or large object, or gray, or 
 beautiful, or dangerous, and so on. In a minor degree 
 that sort of difficulty is always present when illustra- 
 tions are employed to indicate the meaning of terms, 
 and the method of illustrations is never entirely satis- 
 factory. 
 
 In Plato's Euthyphro Socrates asks Euthyphro, who 
 claims to have a precise knowledge of the subject, 
 " What is piety and what is impiety? " The reply is, 
 " Piety is doing as I am doing ; that is to say, prose- 
 cuting any one who is guilty of murder, sacrilege, or of 
 any other crime whether he be your father or mother 
 or some other person, that makes no difference ; and 
 not prosecuting them is impiety." But Socrates is not 
 satisfied with this. " Remember," he says, " that I did 
 not ask you to give me two or three examples of piety, 
 but to explain the general idea which makes all pious 
 things to be pious." In other words, what quality must 
 things possess in order to be called pious? When we 
 
THE MEANING OF TERMS 59 
 
 ask for a definition of a term we wish to know what 
 qualities a thing must have in order to make the term 
 applicable. 
 
 It should be noted that nearly all terms have two 
 aspects: they stand for objects and they imply the 
 qualities which those objects possess. The term man 
 stands_for any or all individual men, past, present and 
 to_come. It also implies all the qualities which a being 
 must possess in order to be included in the class. In 
 the case of a general term it is obvious that all the in- 
 dividuals for which it stands in technical language, 
 its total extension could never be presented. The only 
 way of indicating the full extent of its application is 
 to show what qualities it implies, to tell what its inten- 
 sion is. That might conceivably be done by enumerat- 
 ing all the qualities which were regarded as essential. 
 If things in a given group were so unique that they 
 could not be included in a larger class, enumeration of 
 their qualities would be the only way of showing what 
 they were. But in all ordinary circumstances, this proc- 
 ess can be abbreviated by stating (1) the class to which 
 the things belong and () the quality which distin- 
 guishes them from the other members of the class. 5 
 The class-name will obviously imply the presence of 
 
 5 " Definition " has been variously defined. " Given any set of 
 notions, a term jyt definable by means of these notions when, and 
 only when, it is the only term having to certain of these notions 
 a certain relation which itself is one of the said notions." (Rus- 
 sell, The Principles of Mathematics, Vol. I, chap, xi, sec. 108.) 
 A term is defined by being given a place in a set of notions, which 
 place can be occupied by it and by it alone. Instead of being 
 assigned to a class it is given its place in a complex system of 
 concepts. This last might be regarded as the more complete form 
 of definition, whereas the former, the traditional form, is less 
 complete, though adequate for ordinary purposes. 
 
60 THE USE AND MISUSE OF WORDS 
 
 the qualities which these things have in common with 
 the others in the class. 
 
 The class which includes a thing is its genus: " plane 
 figure " is the genus of " triangle." And the quality 
 which distinguishes it from the other members of the 
 class is its differentia or peculiar property; " three- 
 sided " is the differentia of " triangle." A property is 
 any essential quality: having an equal number of sides 
 and angles would be a property of " triangle." An 
 accident is a quality which may or may not be present 
 in any or all members of a group : having a right angle 
 is an accident of " triangle." 6 
 
 Defects of Definitions. There are several defects to 
 which definitions are liable. 
 
 1. They may be too broad, i. e., they may include 
 more than the term is intended to cover. To define a 
 square as a rectilinear figure would be a case in point. 
 In such definitions the differentia is not given or not 
 properly given. 
 
 #. Again, the definition may be too narrow, that is, 
 it may exclude part of what the term is intended to 
 cover. To define " American citizen " as one born in 
 the United States would exclude naturalized citizens. 
 In this case an accidental quality is taken as the dif- 
 ferentia. 
 
 3. Definitions are sometimes given in obscure or figur- 
 ative or ambiguous language. Dr. Johnson's defini- 
 tion of a network as " anything decussated or reticu- 
 lated with interstices between the intersections " is a 
 
 These four terms, genus, differentia, property and accident, 
 together with species, are what have been traditionally known in 
 logic as the five Heads of Predicables or the five ways in which 
 a predicate may be affirmed of a subject. 
 
DEFINITION 61 
 
 favorite illustration of the obscure definition, the defini- 
 tion of ignotum per ignotius. Spencer's definition of 
 evolution as " an integration of matter and a concom- 
 mitant dissipation of motion ; during which the matter 
 passes from an indefinite incoherent homogeneity to a 
 definite coherent heterogeneity; and during which the 
 retained motion undergoes a parallel transformation," 
 is sometimes charged with this fault. It should be re- 
 membered, however, that when a term is to be used with 
 scientific exactness it may be necessary to couch its 
 definition in very technical terms ; to one who had read 
 the discussions which lead up to it, Spencer's definition 
 would not seem obscure. Figurative and ambiguous 
 language should always be avoided when exactness is 
 the aim. Such language may give some suggestion of 
 the meaning of a term, but does not really define it. 
 
 4. Sometimes unessential attributes are employed 
 in defining a term : e. g., " Books are the things out of 
 which libraries are made." Such definitions are obvi- 
 ously faulty. They use an accident as the differentia 
 and do not give the meaning of the term. 
 
 5. Whenever it is possible, a definition should "be 
 stated in positive rather than negative terms ; to define 
 " an under-classman " as " a student who is not an up- 
 per-classman " is to tell what he is not instead of telling 
 what he is. 
 
 6. Another sort of bad definition is one in which the 
 definition contains the term to be defined or some syno- 
 nym or exact correlative of it. " Life is that which 
 distinguishes living from non-living things " would be 
 a flagrant case ; " A cause is that which produces an 
 effect " is little better. _A definition should state clearly 
 
62 THE USE AND MISUSE OF WORDS 
 
 the exact meaning of the term to be defined. There are 
 cases, however, where a complete definition is not neces- 
 sary. Where the hearer is in doubt which of two well- 
 known meanings is intended, or where the term is al- 
 ready familiar but is used with a slightly different 
 shade of meaning, in other words, where the genus is 
 already known, the briefest indication of the differentia 
 may suffice; sometimes the mention of any accidental 
 quality, or even the use of an illustration, may be 
 sufficient. 
 
 EXERCISES 
 
 1. Make a list of ten words which are sometimes misused 
 through the fact that they have undergone generalization; 
 a similar list of those which have undergone specialization; 
 a list of five in which there has been a transfer of mean- 
 ing to arralagous objects. 
 
 2. Bring ten examples of singular terms and ten of 
 general terms; five of general terms which were originally 
 singular or were derived from singular terms. 
 
 3. Give ten examples of collective terms and ten of dis- 
 tributive. Show how error might arise in this connection. 
 
 4. What is a definition? Compare definition and de- 
 scription. Define the following terms: Book, Party, Col- 
 lege, Republican, Honesty, Foot-ball, Dormitory, College- 
 spirit, Club, Money, Success, Trustee, Tariff, Saint, Geo- 
 metrical figure. 
 
 5. Criticise the following definitions: 
 
 (1) A phonograph is a mechanism xor recording and 
 
 reproducing sounds. 
 
 (2) A sea is a body of water, next in size to tho 
 
 oceans, entirely, or almost entirely, surrounded 
 by land. 
 
 (3) A library is a collection of books generally for 
 
 personal use and not meant for merchandise. 
 
 (4) A wagon is a conveyance mounted on wheels and 
 
 drawn by some animal, usually a horse. 
 
EXERCISES 63 
 
 (5) Oxygen is the most important gaseous element 
 
 known, without which combustion and animal 
 life would be impossible. 
 
 (6) A sensation is a modification of consciousness 
 
 produced by the excitation of a cortical cen- 
 ter through the agency of an afferent nerve- 
 current. 
 
 (7) " Life is a continuous adjustment of internal to 
 
 external relations." 
 
 (8) Logic is the Baedeker of the world of thought. 
 
 (9) A cause is that which produces an effect. 
 
 (10) A book is a combination of leaves and cover. 
 
 (11) A sun-dial is an affair for telling time by means 
 
 of the sun. 
 
 (12) Public opinion is the opinion of people gen- 
 
 erally. 
 
 (13) A student is one whose principal business is 
 
 study. 
 
 (14) A just judge is one who never shows partiality 
 
 in his decisions. 
 
 (15) Wood is the ligneous part of trees. 
 
 (16) Football is a game which is usually played in 
 
 America with a large ball in the shape of 
 an oblate spheroid, whereas in England a 
 spherical ball is used. 
 
 (17) A liar is a man who wilfully misplaces his onto- 
 
 logical predicates. 
 
 (18) A philosophical work is one which treats of some 
 
 metaphysical subject. 
 
 (19) A philosophical work is one which deals with 
 
 something abstract and difficult. 
 
 (20) A false weight is an abomination. 
 
 (21) The quality of a proposition is what tells us 
 
 whether it is affirmative or negative. 
 
 (22) Definition is telling what a word means. 
 
 (23) A religion is that which satisfies the highest 
 
 needs of man. 
 
 (24) Matter is the stuff out of which things are 
 
 made. 
 6. What fallacies are committed in the following cases? 
 
64- THE USE AND MISUSE OF WORDS 
 
 (1) The holder of some shares in a lottery is sure 
 
 to gain a prize, and as I am the holder of some 
 shares in a lottery I am sure to gain a prize. 
 (Hyslop.) 
 
 (2) A monopoly of the sugar-refining business is 
 
 beneficial to the sugar-refiners j and of the corn 
 trade to the corn growers; and of silk-manu- 
 facture to the silk weavers; and of labor to 
 the laborers. Now all these classes of men 
 make up the whole community. Therefore a 
 system of restrictions upon competition is 
 beneficial to the community. (Hyslop.) 
 
 (3) Who is most hungry eats most; who eats least 
 
 is most hungry; therefore who eats least eats 
 most. 
 
 (4) All the trees in the field make a dense shade; 
 
 therefore this elm tree, which is one of them, 
 makes a thick shade. 
 
 (5) Cities are governed by mayors; hence a mayoi 
 
 was the highest official in ancient Rome. 
 
 (6) The major received a D.S.O. for attacking the 
 
 enemy and appropriating their supplies ; there- 
 fore it is praiseworthy to steal. 
 
 (7) The Irish are quick-witted; hence that Irish 
 
 policeman must be quick-witted. 
 
 (8) This ship is one of the best in the world, for it 
 
 belongs to the British Navy, which is the best 
 in the world. 
 
 (9) Americans are liberal; hence this man may be 
 
 counted on to give liberally, since he is an 
 American. 
 
 (10) We can now see the results of giving the negro 
 
 all the rights and privileges of the white man. 
 Two months after he was placed in office, this 
 colored man absconded with all the funds un- 
 der his control. 
 
 (11) Every man has a right to teach his religious be- 
 
 liefs; therefore it is not out of place for a 
 college instructor to do so in the discharge of 
 his duties. 
 
EXERCISES 65 
 
 (12) Any student in college would stand higher in his 
 
 class if he received higher marks; hence if all 
 marks were raised 10% every man would 
 stand nearer the head of his class. 
 
 (13) Pine wood is good for lumber; matches are pine 
 
 wood; therefore matches are good for lumber. 
 (Hyslop.) 
 
 (14) To teach a child is to improve him; showing him 
 
 how to pick pockets is teaching him; hence 
 that improves him. 
 
 (15) Poisons cause death; nux vomica is a poison; 
 
 therefore it causes death. 
 
 (16) This reformer was working for selfish ends all 
 
 the time ; no more reformers for me. 
 
 (17) Since attending that socialist meeting I have 
 
 had no confidence in socialistic doctrines. 
 
 (18) He cannot be innocent, for he was a member of 
 
 the mob which committed the deed. 
 
 (19) Those two horses would make an excellent team, 
 
 for each is the best of its class. 
 
 (20) Five is an odd number; three and two are five; 
 
 and hence each is an odd number. 
 
CHAPTER V 
 PROPOSITIONS 
 
 DIFFICULTIES in the use of language are not all pro- 
 vided against by the correct definition of terms. Many 
 arise in the combination of words into sentences. A 
 term, as we have seen, is the representative in lan- 
 guage of some object of thought, real or imaginary, 
 concrete or abstract. But the mind never rests in the 
 contemplation of a single object; it always tends to 
 make an assertion or judgment about this object. 
 Most logicians are now of the opinion that, even in the 
 simplest perception, a judgment is either present or im- 
 plied. Introspection will show at once that when we 
 hold an object before the mind, there is an inevitable 
 tendency to think some assertion about it. The ex- 
 pression of this mental assertion or judgment in lan- 
 guage is a proposition. 
 
 Kinds of Propositions. Propositions are usually 
 distinguished according to quality and quantity. (1) 
 The qualities are two, affirmative and negative. The 
 difference between affirmative and negative propositions 
 is sufficiently familiar. It should be remembered, how- 
 ever, that the mere occurrence of not or some other 
 negative particle in a proposition does not necessarily 
 make the proposition negative. The proposition, 
 " Those who do not study are in danger of failing," 
 is not a negative proposition. It asserts positively 
 something about a certain class, namely, " those who 
 
 66 
 
QUALITY AND QUANTITY 67 
 
 do not study " ; these words constitute a negative term. 
 An affirmative statement can be made about a negative 
 subject as readily as about any other. In the proposi- 
 tion, " Those who do not study are unwise," the term 
 unwise is also negative, but the proposition is affirma- 
 tive. To decide whether any proposition is affirma- 
 tive or negative, determine whether something is 
 affirmed or denied of a subject. What the subject is, 
 and what the predicate is, makes no difference ; the only 
 question is, do we affirm something or do we deny some- 
 thing? (2) With regard to quantity, propositions 
 may be either universal or particular. A universal 
 proposition is one which expresses a judgment about 
 the whole of the class to which the subject applies. 
 " All the stars are suns " is a universal proposition ; so 
 is " No planets are self-luminous." (The latter propo- 
 sition is negative and denies something of all planets.) 
 " Some stars are double " is called a particular propo- 
 sition. It asserts something of some individuals of the 
 class " stars." By " particular proposition " is not 
 meant a statement about some particular individual. 
 The proposition " Jupiter is the largest of the 
 planets " is not a particular proposition. It is a sin- 
 gular proposition, but, since it expresses a judgment 
 about the whole of that for which the term " Jupiter " 
 stands, it may be treated as a universal proposition. 
 The so-called particular propositions are really indefi- 
 nite; if the " some " in any proposition meant certain 
 particular ones, as it does in certain cases, the propo- 
 sition would really be universal ; it would say something 
 about all those of whom the assertion was made: as 
 " some persons " (meaning A, B, C) " are certain to be 
 
68 
 
 PROPOSITIONS 
 
 late." As used ordinarily, some means certain unspeci- 
 fied individuals, it may or may not be all. The word 
 indefinite would certainly be more appropriate here, but 
 the word particular, with this special meaning, is the 
 one which has been used traditionally. 
 
 With this two-fold distinction of quality and quan- 
 tity we get four different kinds of propositions: uni- 
 versal affirmative, universal negative, particular affirm- 
 ative and particular negative. For the affirmative 
 propositions the letters A and I are used as symbols, 
 A standing for the universal affirmative and I for the 
 particular affirmative. E stands for the universal nega- 
 tive and O for the particular negative. (These letters 
 are from the Latin Affirmo and Nego.) 
 
 Propositions 
 
 Quality 
 
 Universal 
 
 Particular 
 
 f Affirmative 
 | Negative 
 
 f Universal 
 ( Particular 
 f Affirmative A 
 | Negative E 
 
 f Affirmative I 
 1 Negative O 
 
 Propositions and Terms. The Relation of Subject 
 to Predicate. The question of the relation of propo- 
 sitions and terms is one that naturally arises here. A 
 proposition obviously contains terms. Ordinarily it 
 is said that a proposition is made up of two terms and 
 a copula. One of these terms is the subject and the 
 other is the predicate. The copula is that which con- 
 
SUBJECT AND PREDICATE 69 
 
 nects subject and predicate; it is always some part of 
 the verb to be. Some propositions do not fall natu- 
 rally into this form : for example, " The earth moves." 
 This can, however, be expressed in this form : " The 
 earth is a body which moves." 
 
 This form, subject-copula-predicate, is called the 
 " logical form " of the proposition. It often seems 
 artificial, but for certain purposes it is convenient to 
 employ it, and the attempt to restate propositions in 
 this form is an excellent way of finding out just what 
 the proposition means. 
 
 The subject of a proposition stands for that about 
 which something is said. 1 
 
 The predicate is that which is asserted of the sub- 
 ject. The copula is that which connects the two terms 
 in a proposition; but the nature of that connection is 
 not always the same. In the propositions, " Aristotle 
 was the greatest pupil of Plato," " Aristotle was wise," 
 " Aristotle was traveling in Asia Minor," and " Aris- 
 totle was a philosopher," the copula has, in each case, a 
 different meaning. In the first, the relation is that of 
 
 1 A distinction may be made between the grammatical and 
 the logical subjects. The grammatical subject is the subject 
 of the proposition; it is, as we have seen, a term. The logical 
 subject has been variously defined. The definition of the logical 
 subject as the subject of the thought seem, on the whole, to be 
 the best. (See for discussion, Joseph, Introduction to Logic.) 
 The logical subject is that about which the judgment is made. 
 For example, in the proposition, " Acid turns blue litmus paper 
 red," the grammatical subject is, of course, the word " acid." 
 The grammatical predicate is that which stands for what is 
 asserted about the subject; in this case, the words "turns blue 
 litmus paper red." Changing the proposition into the form of 
 subject-copula-predicate, it would read " acid is that which 
 turns blue litmus paper red," and the complete predicate would 
 be the words following the copula. Now the form of the propo- 
 sition may not indicate the real logical subject. If the statement 
 just given were the answer to the question, "What can you say 
 
70 PROPOSITIONS 
 
 identity; in the second, that of subject and attribute; 
 in the third, that of agent and action; in the fourth, 
 that of inclusion of an individual in a class. .Logicians 
 have usually taken the last of these as the typical 
 relation ; the others can be transformed with more or 
 less success into it. The proposition, " Aristotle was 
 wise," can be put in the form, " Aristotle was a wise 
 man " ; and " Aristotle was traveling," etc., can be ex- 
 pressed in the form, " Aristotle was a man who was 
 traveling," etc. These forms are sometimes criticised 
 as not expressing the exact shade of meaning contained 
 in the other forms ; but the difference is usually not 
 serious, and the performance of certain logical opera- 
 tions is much facilitated by so expressing the judg- 
 ment as t'o indicate the inclusion of an individual, or a 
 class, in another class. 
 
 In the negative proposition the relation will, of 
 course, be that of exclusion. " Minors are not voters " 
 indicates the exclusion of the first class from the 
 second. 
 
 about acid, the grammatical and logical subjects would cor- 
 respond; but if the question were, "What is the effect of acid 
 on litmus paper?" the logical subject (i. e., the thing about 
 which the judgment is made) would be that which is expressed 
 by the grammatical predicate of the proposition. The form of 
 the sentence could be so changed as to make the grammatical 
 or verbal subject correspond to the logical subject; in a great 
 many cases they do not so correspond. Ordinarily the logical 
 subject can be determined only by the context, though sometimes 
 it can be indicated by emphasis on certain words. For example, 
 "Acid turns blue litmus paper red " would imply, as the subject, 
 what is expressed by the words, " the color to which blue litmus 
 is turned by acid." Unless otherwise specified the term subject 
 will be understood to mean grammatical subject; and 
 predicate will mean the term that is joined to the subject by 
 the copula. In the treatment of isolated propositions there is no 
 occasion for the distinction. It is sometimes said that reality 
 as a whole is the logical subject of every judgment. It might 
 better be called the ultimate or metaphysical subject. 
 
DISTRIBUTION 71 
 
 The Distribution of Terms in a Proposition, There 
 are degrees of inclusion and exclusion. In the illus- 
 tration just given the whole of the class minors is ex- 
 cluded from the whole of the class voters. In the 
 proposition, " Some men are not good citizens," only 
 some men or a part of the class men is excluded from 
 the class good citizens, but the whole of the class good 
 citizens is excluded from that part of the class men 
 which is included in the subject. In the proposition, 
 " Some men are healthy animals," a part of the class 
 men is included in the class healthy animals, and conse- 
 quently a part of the class healthy animals may be 
 included in the class men. Again, in the propo- 
 sition, " All men are bipeds," the whole of the class 
 men is included in the class bipeds, but so far 
 as this proposition informs us, only a part of the class 
 bipeds can be included in the class men. When- 
 ever, in a proposition, a term is used to indicate 
 the whole of the class for which it stands, it is said to 
 be distributed; when it covers only a part of the class, 
 it is undistributed. The subject of a universal proposi- 
 tion is always distributed, because, by definition, a uni- 
 versal proposition is one which asserts something about 
 the whole of its subject. It will be seen in the examples 
 given above that both the negative propositions dis- 
 tribute their predicates. That is always the case with 
 negative propositions. They always indicate the en- 
 tire exclusion of the predicate from the subject. The 
 proposition A, being universal and affirmative, will dis- 
 tribute its subject but not its predicate; /, being par- 
 ticular (indefinite) and affirmative, will distribute 
 neither; the particular negative, 0, will distribute the 
 
72 PROPOSITIONS 
 
 predicate, but not the subject, while the universal nega- 
 tive, E, will distribute both subject and predicate. 
 
 Euler's Method. Euler, a Swiss mathematician of 
 the Eighteenth Century, devised the following method 
 of representing the relation of subject and predicate 
 and the distribution of each. Let each term be repre- 
 sented by a circle ; then the E proposition will be rep- 
 resented as follows, S standing for the subject and P 
 
 for the predicate: ()(?) S and P are shown to be 
 
 entirely excluded from each other; each is distributed. 
 The A proposition would be represented in this way: 
 
 , --- x S is seen to be entirely included in P, while, so 
 ( P} ^ ar as we know, only a part of P falls within S ; 
 
 s x __ S S is distributed, P is not. In the I proposition 
 the circles would overlap. Each would be partially in- 
 \ eluded within the other: that is, neither would 
 
 1 S ( )P 
 
 \ y ./ be distributed. Whether cither extended fur- 
 
 ther would be left undetermined ; there are four possi- 
 bilities, in each of which at least some S is some P. In 
 the O proposition, part of S would be excluded 
 
 SOP 
 
 ^ ^-xfrom P; the rest would be left undetermined; 
 
 while all of P would be outside the specified part of S ; 
 S is not distributed, P is. 
 
 The distribution or non-distribution of terms in the 
 various propositions may be represented by the follow- 
 ing symbols : " - ' indicating an affirmative proposi- 
 tion, " x " a negative one, and a circle about a term 
 the fact that it is distributed. 2 
 
 A, -P; E, () x ; I, S-P; O, S x (5) 
 
 2 The last two of these symbols are adapted from Hyslop, 
 ments of Log\\,* 
 
AMBIGUOUS PROPOSITIONS 73 
 
 Ambiguous Propositions. There are several kinds 
 of ambiguous propositions. In the first place the ar- 
 rangement of the words and phrases may be such as 
 to admit of two interpretations. Familiar examples 
 are the prophecy in Shakespeare's Henry VI, " The 
 Duke yet lives that Henry shall depose," and the re- 
 sponse of the oracle, " Pyrrhus, I say, the Romans shall 
 subdue." The expression, " Twice two and three," is 
 ambiguous for the same reason, and so is the state- 
 ment, " He went away and returned yesterday." In 
 the two last, punctuation would, of course, remove the 
 ambiguity. Propositions, like " He jests at scars who 
 never felt a wound," will sometimes, mislead a careless 
 reader. Care in the construction of a proposition will 
 /obviate such difficulties ; where such sentences are 
 found, only the context can make clear what the mean- 
 ing is. Wrong conclusions in such cases are said to 
 result from committing the Fallacy of Amphiboly or 
 Amphibology. 
 
 Certain other cases of ambiguity might be brought 
 under this heading. One of these is found in the use 
 of " all ... not." In the statement, "All these 
 men are not swift-footed," it might be thought that the 
 meaning was, " None of these men is swift-footed " ; 
 that is, that the subject, these men, was distributed, and 
 that_ the proposition was an E proposition. It is 
 usually interpreted as meaning " some are not swift- 
 footed," not " all are." It is an E proposition in form, 
 but an O proposition in meaning. Again, it might 
 seem to imply that " some are swift- footed " ; but this 
 last implication is not to be trusted, for we could make 
 the original statement if we knew that some of these 
 
74 PROPOSITIONS 
 
 were not swift without knowing anything about the 
 rest. The word some, as already noted, is indefinite ; in 
 an affirmative proposition, such as " Some are going," 
 it seems to imply the corresponding negative, " Some 
 are not going," and vice versa ; but these implications 
 count for nothing if not confirmed in some other way. 
 In interpreting a proposition the only safe rule is to in- 
 clude in its meaning only what it must mean, not what 
 it may mean. 
 
 In still other cases it is not so much the arrangement 
 as it is the character of the terms that occasions diffi- 
 culty. Propositions which are introduced by the word 
 few are ambiguous. " Few are completely masters of 
 themselves " really means that most are not masters of 
 themselves, or that not many are. It is an O proposi- 
 tion in meaning, though like an I proposition in form. 
 It may also seem to suggest the corresponding I propo- 
 sition, " Some are masters," etc. The importance of 
 making clear the negative force of such a proposition 
 may be illustrated thus : suppose we have also the state- 
 ment, " All who are masters of themselves are mature 
 individuals " ; it might seem that we could conclude 
 that few are mature individuals. If the proposition 
 " Few," etc., be put in the negative form given above 
 there will be no temptation to draw the erroneous con- 
 clusion. Thus in, " Most men are not masters, etc. ; 
 those who are, are mature," etc. ; the conclusion, " Most 
 men are not mature," does not even seem to follow. 
 Professor Hyslop, in his Elements of Logic, calls propo- 
 sitions of this sort partitive propositions, because they 
 " express a part of a whole of which the implied propo- 
 sition is a complementary part." 
 
PARTITIVE AND EXCLUSIVE 75 
 
 Another sort, similar in certain respects to these, is 
 found in the exclusive propositions; they are such as 
 have their application determined by such expressions 
 as only, alone, none but, and the like. " None but 
 native-born citizens are eligible to the presidency," 
 " Only students will be admitted," etc., are exclusive 
 propositions. These statements do not mean that all 
 native-born citizens are eligible nor that all students 
 will be admitted. They are not universal propositions ; 
 they do not distribute their subjects. They are equiva- 
 lent to the propositions, " Those who are not native- 
 born are not eligible," " Those who are not students 
 will not be admitted," which are the complementary 
 opposites of the original propositions, and are in this 
 case E propositions. As the original propositions stand 
 they really limit the application of their predicates, 
 i. e. 9 they include the whole of the predicate in the sub- 
 ject. Thus they distribute the predicate, in spite of 
 the fact that they are affirmative propositions. They 
 are, therefore, exceptions to the rule for affirmative 
 propositions (p. 71). Another way of restating ex- 
 clusive propositions is to convert them, making the 
 converse a universal proposition. Thus : " All persons 
 eligible to the presidency are native-born citizens " ; 
 " All who are to be admitted are college students." 
 
 One other sort of proposition of this general class 
 may' be mentioned, the exceptive proposition: it is in- 
 troduced by such words as " All except," " all but," 
 etc. For example : " All but the best will be excluded." 
 In addition to the positive statement, a corresponding 
 negative is suggested, namely, " The best will not be " ; 
 though this last is not certainly true. It is well to re- 
 
76 PROPOSITIONS 
 
 state such propositions, eliminating the exceptive par- 
 ticle. Thus : " All those who are not the best," etc. 
 
 Figurative statements are peculiarly liable to mis- 
 interpretation ; Hyperbole and metaphor, symbolical 
 and allegorical statements, may all be mistaken for 
 literal statements, or if recognized as figurative, they 
 may be wrongly interpreted on account of the inherent 
 vagueness of most figurative expressions. Fallacies 
 arising from this cause are known as Fallacies of Figure 
 of Speech. 3 
 
 Another source of ambiguity and misinterpretation 
 in propositions is to be found in misplaced emphasis. 
 Wrong emphasis gives rise to what is known as the 
 Fallacy of Accent. To quote from Jevons : " It is cu- 
 rious to observe how many and various may be the 
 meanings attributable to the same sentence according 
 as emphasis is thrown on one word or another. Thus 
 the sentence, ' The study of Logic is not supposed to 
 communicate the knowledge of many useful facts,' 
 may be made to imply that the study of Logic does 
 communicate such a knowledge although it is not sup- 
 posed to do so ; or that it communicates a knowledge 
 of a few useful facts ; or that it communicates a knowl- 
 edge of many useless facts. . . . Jeremy Bentham 
 was so much afraid of being misled by this fal- 
 lacy of accent that he employed a person to read to 
 him, as I have heard, who had a peculiarly monotonous 
 manner of reading." To introduce italics into a quo- 
 tation, with no mention of the fact that they did not 
 
 3 It has been said that some of Locke's erroneous conclusions, 
 in his Essay on the Human Understanding, resulted from his own 
 use of " the sheet of white paper " as a figure representing the 
 mind before experience has begun. 
 
THE FALLACY OF ACCENT 77 
 
 occur in the original, is usually to misrepresent the 
 meaning of the original. De Morgan and others have 
 pointed out that taking words or passages out of their 
 context may have the same consequences. Isolated 
 texts from sacred writings are often misused in this 
 way ; e. g., " Eat, drink and be merry, for to-morrow 
 ye die," "Take no thought for the morrow," etc. 
 
 Quoting an argument which an author has presented 
 only in order to refute it, without mention of his pur- 
 pose, is another case of the same sort. 
 
 EXERCISES 
 
 1. In each of the following propositions give (a) the 
 complete subject and (b) the complete predicate; (c) re- 
 state each in its logical form; (d) give its quantity and 
 quality and the letter which symbolizes it. And state 
 whether (e) the subject and (f) the predicate are dis- 
 tributed. , 
 
 (1) He laughs best who laughs last. 
 
 (2) Few are able to endure such hardships. 
 
 (3) Not all who are called are chosen. 
 
 (4) Nothing of worth is without honor. 
 
 (5) Only genius could have accomplished it. 
 
 (6) He little knows you, who can speak of you in 
 
 such terms. 
 
 (7) Every bit of success makes further success 
 
 easier. 
 
 (8) Like cures like. 
 
 (9) There is nothing either good or bad but thinking 
 
 makes it so. 
 
 (10) It is the first step that costs. 
 
 (11) Everything has its limit. 
 
 (12) We demand non-partisan judges. 
 
 (13) His lack of enterprise cost him his position. 
 
 (14) The plowman homeward plods his weary way. 
 
 (15) Contentment is better than riches. 
 
 (16) Every deed returns upon the doer. 
 
 (17) All's fair in war, 
 
78 PROPOSITIONS 
 
 (18) Many a morning on the moorland have we heard 
 
 the copses ring. 
 
 (19) Perfection is beyond the reach of man. 
 
 (20) My mind to me a kingdom is. 
 
 (21) No admission except to ticket holders. 
 
 (22) Every one has the defects of his qualities. 
 
 (23) Socrates taught that no man would knowingly 
 
 do wrong. 
 
 (24) And silence,, like a poultice, comes to heal the 
 
 wounds of sound. 
 
 (25) All the world admires heroism. 
 
 (26) It rains. 
 
CHAPTER VI 
 INDUCTION 
 
 Generalization and What it Involves In the 
 two last chapters we have been studying the use of lan- 
 guage, the most important instrument of thought. We 
 now return to the consideration of the further proc- 
 esses mentioned in our preliminary survey of scientific 
 method. (Chap. I.) Observation and classification 
 have been discussed already ; it remains to examine the 
 way in which laws * can be discovered after considerable 
 body of facts has been observed and classified. We 
 have seen that a law is a statement of the way in which 
 facts of a certain kind behave, how they are related to 
 other facts, what are the universal relations in which 
 they stand. Our first question is : How are these laws 
 suggested? What is the source of these general state- 
 ments of relationship? And our second question is: 
 How is a supposed law to be established or verified? 
 
 In answer to the first question, it may be said that a 
 general statement is usually arrived at by generalizing 
 some observed relationship. If we have observed one 
 or more instances in which a cold winter has been fol- 
 lowed by a hot summer, we may generalize the connec- 
 tion and assert that a cold winter is always followed by 
 a hot summer, that there is an invariable and inevitable 
 
 i The previous chapter has dealt, in part, with. universal propo- 
 sitions; the present one is a discussion of the way in which such 
 propositions are established. 
 
 79 
 
80 INDUCTION 
 
 connection between them. And similarly in any other 
 case : A has been followed by B and we conclude that 
 every A is followed by B 9 that every A has its B. A 
 single instance may be enough to suggest a generaliza- 
 tion. A generalization is a universal assertion, not a 
 mjore^attitude of expectation. The lower animals ex- 
 hibit a tendency to expect a given thing when another, 
 which has occurred along with this, reappears ; when 
 an animal hears a certain call he may expect food, be- 
 cause in the past the two have been connected; when 
 he sees a blow descending he may expect pain, and so 
 on. But to expect a thing on the recurrence of another 
 formerly connected with it, is not the same as to infer a 
 universal connection. When I perceive A, I may re- 
 member and expect B, without ever having thought of 
 a universal relation between the two, without asserting 
 that B always follows A. There is no proof that an 
 animal can generalize, that he can think to himself: 
 " A call of a certain sort is followed by food," " A 
 blow causes pain," and so on. He hears the call and 
 expects food, but he does not generalize the connection. 
 To do the latter would be difficult if not impossible, 
 without language. Tlais^power to generalize, to iise_ 
 general and abstract ideas, is usually regarded as one 
 of the most important differences between human and 
 animal intelligence. "" 
 
 Without generalization, our knowledge would be con- 
 fined to individual facts or to groups of these. We 
 have seen that knowledge is not completed by the mere 
 accumulation of observations and the classification of 
 what has been observed. The aim of science is usually 
 said to be the discovery of laws. Now a law, as already 
 
LAWS 81 
 
 remarked, is the statement of the way in which phe- 
 nomena behave, or the way in which they are inevitably 
 related to other phenomena. 
 
 This tendency to generalize is, then, a pre-condition 
 of all but the most primitive kind of knowledge. But, 
 of course, our generalization may not turn out to be a 
 law. A law states a universal connection which ac- 
 tually holds true, whereas our hasty generalization may 
 be entirely unsound. A generalization arrived at in 
 the way described above is an inductive inference. An 
 inductive inference is a judgment about a whole class 
 of facts based upon the observation of individual cases. 
 It is a universal conclusion based upon one or more 
 particular instances. Obviously, an inductive inference 
 must be tested or verified; but before proceeding to the 
 discussion of verification it will be well to mention cer- 
 tain other terms which are frequently employed in this 
 connection. 
 
 Causal Connection. The terms, cause, causal con- 
 nection^ causal law, occur constantly in this part of 
 scientific method. What is a cause? The term implies 
 a connection of some sort between phenomena; but of 
 what sort? In ordinary usage it probably means most 
 frequently something which produces or brings about 
 something else. It has been objected that we can never 
 observe one thing producing another; that we can at 
 most observe that one thing is followed by another, and 
 perhaps find reason for believing that it will always 
 have such a connection; and that to say that A pro- 
 duces B, is to raise a metaphysical question with which 
 science and everyday thinking are not concerned. But 
 if we give up this way of conceiving cause, what can we 
 
82 INDUCTION 
 
 put in its place ? Is it sufficient to say that cause means 
 simply invariable succession? No, for the succession of 
 day and night is an invariable succession. The notion 
 of cause implies that the relation of cause and effect 
 not only is invariable, but also that it must be so ; that 
 there is an unconditional or necessary -connection be- 
 tween the two; that if the first does not happen, the 
 second cannot. In the field of physical phenomena, it 
 is held also that the amount of energy in the cause is 
 exactly equal to the amount of energy in the sum-total 
 of its effects; in other words, that no energy is either 
 lost or created. This is known as the Law of the Con- 
 servation of Energy. Whether it applies where mental 
 phenomena are concerned has been questioned. How- 
 ever this may be, cause always means unconditional 
 connection. 2 Two things stand in a relation of causal 
 connection when they are so related that one is the un- 
 conditional accompaniment of the other ; the cause usu- 
 ally occurs or begins before the effect, but there are 
 cases in which both seem to begin together. Heat is 
 a cause of expansion, but a body does not first become 
 hot and then expand; the two phenomena occur simul- 
 taneously. A causal law is a statement, in general 
 terms, of a causal connection. Thus : " Heat causes ex- 
 pansion." 
 
 The sort of generalization which is most frequently 
 of interest and importance is one which asserts a -con- 
 nection of this sort, although this is not the only sort 
 which may be investigated. For instance, the universal 
 
 2 Of course, the fact that a connection is unconditional cannot 
 be observed. The reasons for asserting that it is unconditional 
 will appetrrpresently. 
 
CO-EXISTENCE AND CAUSATION 83 
 
 concurrence of two properties in a given substance may 
 be a matter of importance, but their connection would 
 not be called a causal connection. The specific gravity 
 and the atomic weight of carbon would be a case in 
 point. The co-existence of gravity and inertia is an- 
 other example mentioned by Bain ; the sciences furnish 
 innumerable instances of a like sort. Bain remarks that 
 " there are very few general laws of pure co-existence ; 
 causation is singular in providing a comprehensive uni- 
 formity that may be appealed to deductively for all 
 cases. The uniformities of co-existence (independent 
 of causation) can be proved only piecemeal; each stands 
 on its own evidence of observation in detail; no one 
 assists us to prove another." The causal law is the one 
 to which we shall give most attention. 
 
 Testing Inductive Inferences. We return to the 
 question, " How can we prove an inductive inference to 
 be true? How can we show that it is a law? " There 
 are several things which would show that it was not 
 true; if we found that there were facts which were in- 
 consistent with it, or if it were found to be inconsistent 
 with itself, or if it proved to be in disagreement with 
 any established law, it could be rejected at once. But 
 suppose that none of these things were found ; should 
 the inference be accepted as true? Not necessarily; it 
 might be that our observation or our reflection on the 
 case had been insufficient to show us exceptions or in- 
 consistencies if such did exist. If we have inferred a 
 universal connection we are very likely to overlook 
 exceptions or to forget those which we have observed. 
 A good many people still believe that Friday is an un- 
 lucky day and that the number 13 brings misfortune. 
 
84 INDUCTION 
 
 But even if no exceptions have occurred and if the in- 
 ference is not inconsistent with known laws, how can 
 we be assured that exceptions may not occur in the 
 future, or that further reflection might not discover 
 fatal inconsistencies? A large number of favorable 
 cases is not alone sufficient to give this assurance. The 
 example of the succession of day and night illustrates 
 that. Millions of cases do not prove inevitable con- 
 nection. On the other hand, a single experiment made 
 .by some scientist in his laboratory may be sufficient to 
 establish some very important law. " Why," asks Mill, 
 " is a single instance in some cases sufficient for a com- 
 plete induction, while in others myriads of concurring 
 instances, without a single exception known or pre- 
 sumed, go such a very little way towards establishing 
 an universal proposition? Whoever can answer this 
 question knows more of the philosophy of logic than the 
 wisest of the ancients, and has solved the problem of 
 Induction." Mill himself aided very materially in the 
 formulation of the conditions under which we do regard 
 our inductive inference as established, and the inductive 
 methods presently to be discussed are usually called 
 " Mill's methods." Whether or not he has solved the 
 whole problem of induction is another question and one 
 with which we shall not at present concern ourselves. 
 
 Complete Enumeration. There are -cases in which 
 the establishment of universal conclusion might seem 
 to be comparatively easy. It is sometimes possible that 
 all the cases of a given sort may have been observed. 
 For example, observation has shown that Mercury re- 
 volves about the sun ; that Venus does also ; and like- 
 wise of the Earth, Mars, Jupiter and each of the other 
 
COMPLETE ENUMERATION 85 
 
 planets. We can say then with perfect safety, that all 
 the planets 3 revolve about the sun. The universal 
 statement is warranted because each of the instances 
 which it covers has been observed. We are saying no 
 more in the conclusion than we had already said in the 
 several statements on which the conclusion is based. 
 The universal is, in fact, simply a summary way of 
 expressing what had already been said. It is merely a 
 " telescoping " of the other statements, as it were. This 
 act of basing a general statement on a complete enum- 
 eration of the particular cases which it covers has been 
 called Perfect Induction. It was so called because the 
 conclusion is one which possesses complete certainty, 
 whereas most inductive inferences are more or less un- 
 certain. It might seem then that this was the solution 
 of the problem raised above ; you are sure of your uni- 
 versal if you have seen all the particulars which it 
 covers. But how can we be sure that we have counted 
 all the particulars? The field of observation may be 
 so small and so easily explored that every existing case 
 may be observed. But even if all existing cases have 
 been observed, how can we be sure that others may not 
 arise, and that they may not differ from those we have 
 observed? We may have such knowledge about a class 
 of objects as will enable us to say that if any other 
 members of the class should come into existence they 
 would be like those already known. We may know 
 that the sum of the angles of every plane triangle 
 which may ever exist will be equal to two right angles, 
 not because we have counted cases, but because we know 
 that this necessarily follows from the properties essen- 
 s Leaving the asteroids out of consideration. 
 
86 INDUCTION 
 
 tial to all triangles. However numerous the class 
 which has been completely observed, the knowledge 
 that each of the observed members stands in certain 
 relations does not by itself assure us that other con- 
 ceivable members of the class would be like them in this 
 respect. Complete enumeration is useful as an abbre- 
 viated way of stating certain kinds of information, but 
 it throws no light on the methods of discovering uncon- 
 ditional connections. 4 
 
 The judgments which result from the complete enum- 
 eration of cases have been called, by some writers, 
 Enumerative Judgments and by others, Collective Judg- 
 ments. 
 
 How Generalizations can be Verified It appears 
 then that enumeration of all the existing members of 
 a class does not enable us to establish laws. Anything 
 short of that might seem to leave us still farther from 
 that goal. And it is of course true, as appeared on 
 page 84, that an incomplete enumeration of instances 
 furnishes no verification. Then if verification is pos- 
 sible at all it can not rest on mere enumeration, or 
 counting of cases. Suppose that the observation of one 
 
 4 It may be well to note one case in which a statement in 
 the universal form must be distinguished from a law. As an 
 example, we may take, " Every three-sided figure is a triangle.'* 
 This is not an inductive inference; it is not based upon the ob- 
 servation of individual instances at all. It is true in all cases, 
 but it is true because we have previously said, "If any figure 
 has three sides we will call it a triangle." In other words, it is 
 true by definition. It is like an inductive generalization in apply- 
 ing to all possible cases, past, present and to come, real and 
 imaginary, etc., but it is not based upon the observation of in- 
 dividual facts. Other judgments and operations, which must be 
 distinguished from those which are present in induction properly 
 so called, will be discussed in a later chapter; and still others 
 may be found by referring to Mill's Logic, Book III, chapter ii. 
 
VERIFICATION 87 
 
 or more instances in which B has followed A has sug- 
 gested to us the inference that A and B are causally 
 related. Let us ask ourselves what consequences would 
 follow upon the truth of this inference. In the first 
 place we could conclude that if B were present in any 
 case A must have been present also ; and, again, if A 
 were absent in any case, its supposed effect B must have 
 been absent also ; or if either A or B varied in amount 
 or degree the other should show a corresponding varia- 
 tion. All these things should be true of phenomena 
 which are causally related. Phenomena which failed 
 to satisfy such conditions could not be unconditionally 
 connected. Suppose we had inferred that absence of 
 oxygen would cause death. If that is true, an animal 
 immersed in nitrogen should die. If experiment showed 
 that an animal could live under such conditions, our 
 inference would, of course, be disproved ; but suppose 
 the animal did die, would the inference be proved? Not 
 necessarily. Perhaps the nitrogen acted as a poison 
 or perhaps the death of the animal was due to rough 
 handling, etc. Our inductive inference would be com- 
 pletely verified only if we could show that death could 
 not have been due to anything except the absence of 
 oxygen. If we could be sure that all the circumstances 
 which were present before the experiment remained pre- 
 cisely the same with the one exception that oxygen was 
 present in the first case and absent in the second, then 
 we should have shown a necessary connection between 
 the absence of oxygen and the occurrence of death. 
 Nothing else could have been the cause because all were 
 present when death did not occur. If a second circum- 
 stance were present when the phenomenon occurred and 
 
88 INDUCTION 
 
 absent when it did not occur, it would dispute with the 
 first the right to be called the cause and no final con- 
 clusion would be possible. When all other possibilities 
 can be excluded, the one which remains is the -cause. 
 When no other inference is consistent with the facts, 
 the one which is consistent must be accepted as true. 
 
 We can say, then, that an inductive inference is com- 
 pletely verified when we have found facts which are con- 
 sistent with its truth and inconsistent with any possible 
 rival inference; or more briefly, when it fits the facts 
 and no alternative inference does. We establish one in- 
 ference by eliminating all others. We reason that the 
 phenomenon under investigation has some cause; this 
 other phenomenon, A, may be the cause; it fulfills the 
 requirements and no other does ; therefore, this one is 
 and must be the cause in question. There are several 
 ways of selecting or grouping instances so as to show 
 that some one factor alone satisfies the requirements. 
 These are known as the INDUCTIVE METHODS. 
 
 Observation, and Analysis are Presupposed. One 
 thing should not be forgotten. It is that the application 
 of such principles as these presupposes very careful ob- 
 servation ; if we are to be certain that no other circum- 
 stance is present when a given phenomenon is present 
 or absent when it is absent, we must have observed all 
 the other circumstances. In ordinary observation we 
 note only a few of the circumstances ; if we are un- 
 trained observers it may be impossible for us to ob- 
 serve more than a few. It is quite impossible for a child 
 to observe in a flower all that a trained botanist can 
 observe there. Accurate observation presupposes anal- 
 ysis, i. e. t breaking up the total complex phenome- 
 
TEST CONDITIONS 89 
 
 non into its element. The beginner in any science is 
 unable to handle the facts properly because he is un- 
 able to analyse them; he sees only their most obvious 
 characteristics. 
 
 Postponing Inference till Test Conditions are Pres- 
 ent Before we begin the more detailed examination of 
 the methods of verifying an inductive inference, there 
 is one more statement to be made, namely this : instead 
 of making a generalization and then searching for 
 means of verifying it, we may refrain from drawing 
 any inference until we have before us a group of facts 
 which will make it possible to draw a correct inference. 
 In other words, we may make our inference under test 
 conditions. Suppose, for example, that we are trying 
 to discover the cause of eclipses. Before making any 
 theories on the subject we might observe a number of 
 cases. If we found that whenever an eclipse occurred 
 there was an opaque body between us and the source 
 of light and that at other times everything was the 
 same except that there was no body in that position, we 
 should infer at once that the presence of the opaque 
 body in that position wa*s the cause of the eclipse. And 
 so in any other case we might form no theory until we 
 had facts which would make it possible to form a cor- 
 rect one. 
 
 " If a chemist discovers a new element, he will pro- 
 ceed to try a variety of experiments in order to de- 
 termine the proportions in which it will combine with 
 other elements as well as to discover the various prop- 
 erties of such combinations. Supposing such experi- 
 ments to have been properly conducted, the inductions 
 at which he arrives will be perfectly valid, though he 
 
90 INDUCTION 
 
 may have formed no previous theories as to the results 
 of his researches. Occasionally, too, an induction will 
 not be the result of any definite course of investigation, 
 but will be obtruded on our notice." 5 But such cases are 
 rare, and ordinarily we have some theory before we have 
 the facts which will verify it. 
 
 It is often better to draw an inference early in the 
 investigation ; the reasons for this will be discussed in 
 a later chapter. 6 In the meantime it should be remem- 
 bered that the Inductive Methods which are now to be 
 discussed may be used either to test an inference al- 
 ready made or to furnish a basis for drawing a correct 
 inference if none has previously been drawn. 
 
 The Inductive Methods. I. AGREEMENT. Sup- 
 pose we find that A was followed by B in a number of 
 instances, but that the attendant circumstances varied 
 greatly. Suppose, for example, that three or four in- 
 dividuals, of different races, different habits of life, 
 and otherwise as different as possible, were all bitten 
 by a certain kind of mosquito and that each developed 
 yellow fever: would not such a set of cases give some 
 warrant to the inference that \he bite of the mosquito 
 was causally connected with the development of the 
 fever? The fact that these individuals were different 
 in all other respects would seem to exclude the possi- 
 bility that anything else could have been the cause. 
 
 Or suppose again that we find dew deposited on two 
 or more objects which differ in position, chemical com- 
 position, character of surface, and, in short, all respects 
 except that both are cooler than the surrounding atmo- 
 
 B Fowler, Inductive Logic, p. 11. 
 Part III, chapter ii, Hypothesis. 
 
THE METHOD OF AGREEMENT 91 
 
 sphere ; we should have good grounds for believing that 
 this last characteristic was causally related to the dep- 
 osition of dew. 
 
 Or, once more, if a number of persons who recovered 
 from a given disease were similar only in having used 
 a certain drug, the inference would be that the drug 
 was causally related to the cure. 
 
 In each of these examples we have a set of instances 
 in which a given phenomenon is present, an attack of 
 fever, deposition of dew, recovery from illness ; nothing 
 else is present in all cases except one other phenomenon, 
 being bitten by the mosquito, being cooler than the 
 surrounding air, having used a certain drug. Our infer- 
 ence is that the phenomena which are constantly pres- 
 ent together are causally related. If A is causally, i. e. 9 
 unconditionally, related to something else, that thing 
 must be present when A is present. As only one other 
 phenomenon is present in all cases, that alone among 
 all those at any time present can be causally related 
 to the first. This method of isolating the phenomena 
 which are so related is known as the Method of Agree- 
 ment. Mill's statement of the Canon of Agreement is 
 as follows : " If two or more instances of the phenom- 
 enon under investigation" [fever, deposition of dew, 
 etc.], " have only one circumstance in common " [being 
 bitten by a mosquito, being cooler than the surrounding 
 air, etc. ] , " the circumstances in which alone all the in- 
 stances agree is the cause (or effect) of the given phe- 
 nomenon." His statement of the axiom of this method 
 is : " Whatever circumstance can be excluded without 
 prejudice to the phenomenon, or can be absent notwith- 
 standing its presence, is not connected with it in the way 
 
92 INDUCTION 
 
 of causation." The only circumstance which is com- 
 mon to a number of instances in which a given phe- 
 nomenon is present, is causally related to it, because all 
 the rest are excluded by the fact that they are separable 
 from it. 
 
 In this method, as in the others to be discussed, 
 the point of first importance is that we are selecting 
 instances of the occurrence of a phenomenon, and 
 selecting them in such a way as to identify the cir- 
 cumstance or circumstances causally related to the 
 phenomenon. We might re-word the main points as 
 follows: select instances in which the phenomenon under 
 investigation is present, but which are as different as 
 possible in all other respects ; if there is one circum- 
 stance and one only which is always present when the 
 phenomenon under investigation is present, that cir- 
 cumstance is causally related to the phenomenon. 
 
 Difficulties in Using this Method. An ideal case 
 might be represented symbolically in this way: let the 
 phenomenon under investigation be represented by x; 
 and let the accompanying circumstances, in the severaJ. 
 instances we have selected be represented by abcde* 
 afghi, ajklm, respectively ; or the phenomenon and its 
 accompanying circumstances by : 
 
 abcdex 
 a-fgliix 
 ajklmx. 
 
 The only circumstances common to all the instances is 
 a. Therefore a is causally related to x. No actual 
 
DIFFICULTIES 93 
 
 case would be quite so simple ; any phenomenon has 
 among its accompanying circumstances everything that 
 is happening in the universe at the time of its occur- 
 rence. Most of these circumstances can, of -course, be 
 eliminated as irrelevant ; still it is easily possible to 
 overlook something that is relevant. 
 
 1. Circumstances which might seem to have no con- 
 nection with the phenomenon may be causally related 
 to it. For example, it might be supposed that the 
 number of sun-spots had no relation to financial con- 
 ditions ; yet it has been shown that the periods when 
 sun-spots are most numerous have the same frequency 
 as the periods when panics occur ; and it has been sug- 
 gested that sun-spots influence climatic conditions, that 
 these in turn, by influencing crops, and so on, do affect 
 financial conditions. Whether there is any truth in this 
 or not, it will remind us that it is not easy to determine 
 just what circumstances are relevant. 
 
 2. Another difficulty arises from the fact that analy- 
 sis is never complete; not all the elements are singled 
 out, and some of those which have been overlooked may 
 be all-important. For example : it had been noticed that 
 persons who had been much out of doors at night were 
 more likely than others to be attacked by malaria; it 
 was inferred that " night-air " was a cause of malaria, 
 and consequently people tried to exclude it from their 
 houses. Later it was shown that the attacks of mos- 
 quitoes were the causes. Mosquitoes are more active at 
 night, but instead of noting this, the more obvious fact 
 that " night-air " is damp, and so on, was selected as 
 the important one. When it was found that the bite 
 
94 INDUCTION 
 
 of the mosquito was the circumstance always present, 
 while the time of the attack made no difference, the 
 older theory was overthrown. 
 
 In symbolizing an actual case we should need some- 
 thing to represent the circumstances which were dis- 
 regarded or overlooked. We might use the symbol 
 X; the accompanying circumstances would then be rep- 
 resented by abode. .X 9 afghi. .X, etc. This would in- 
 dicate that there is a margin of uncertainty in such 
 cases. 
 
 3. There is one other difficulty in the application of 
 the method of Agreement. It may be illustrated in this 
 way : suppose a man should drink coffee with his lunch- 
 eon on one day and afterwards smoke a strong cigar; 
 suppose on the following day, with a different bill of 
 fare, he should drink tea and smoke a cigar; on both 
 days he has a headache in the afternoon. The applica- 
 tion of the method of Agreement would lead him to be- 
 lieve that the cigar was the -cause of the headache,, 
 whereas the cause may have been the coffee in one in- 
 stance and the tea in the other. This illustrates what 
 is known as the Plurality of Causes. A given phenome- 
 non may have one cause in one instance and another 
 cause in a second instance. It is sometimes said that if 
 our analysis were complete we should find that a given 
 phenomenon always had the same cause ; that in the in- 
 stances just mentioned, the cause of the headache wag 
 something common to tea and coffee ; or that the head- 
 ache caused by coffee differs from that caused by tea 
 and that two things which are different never can pro- 
 duce the same effect. Perhaps that is true, but the fact 
 still remains that, in practice, effects which are so simi- 
 
THE METHOD OF DIFFERENCE 95 
 
 lar as to be indistinguishable may be produced by causes 
 that, for ordinary observation, are very different. This 
 makes a very serious limitation to the application of 
 the method of Agreement. The method is still valuable 
 as suggesting causal relations, though imperfect as a 
 means of proof. May it not be possible to select in- 
 stances on some other principle in such a way as to 
 obviate some of these difficulties? 
 
 II. THE METHOD OF DIFFERENCE. Take another 
 concrete case : suppose two individuals as similar as 
 possible in all respects, race, family, occupation, man- 
 ner of living, state of health and so on; one of these 
 is bitten by mosquitos of a certain sort and the other 
 protects himself against their attacks ; the first con- 
 tracts the fever, the second escapes it. We should 
 regard such a group of facts as warranting the conclu- 
 sion that the bite of the mosquito and the contraction 
 of yellow fever were causally related. 
 
 Or, if two objects of similar chemical construction, 
 character of surface, location, etc., differed only in that 
 one was for some reason cooler than the surrounding 
 air, while the other was not, and if dew were deposited 
 on the first and not on the second, we should conclude 
 that the cooler temperature of the one was causally 
 related to the deposition of dew upon it. , 
 
 Cases like these illustrate the Method of Difference." 
 Mill's statment of the Canon of this method is : 
 
 " If an instance in which the phenomenon under in- 
 vestigation occurs, and an instance in which it does not 
 occur, have every circumstance in common save one, 
 that one occurring only in the former; the circum- 
 stance in which alone the two instances differ is the 
 
96 INDUCTION 
 
 effect or the cause, or an indispensable part of the 
 cause, of the phenomenon." Its axioms, in the words 
 of the same writer, are : " Whatever antecedent cannot be 
 excluded without preventing the phenomenon, is the 
 cause, or a condition of the phenomenon; whatever con- 
 sequent can be excluded with no other difference in the 
 antecedents than the exclusion of a particular one, is 
 the effect of that one." 
 
 Relation of this to the First Method. We quote 
 from Mill again regarding the relation of this method 
 to the other: 
 
 " Instead of comparing different instances of a phe- 
 nomenon to discover in what they agree, this method 
 compares an instance of its occurrence with an instance 
 of its non-occurrence, to discover in what they differ. 
 . . . Both are methods of elimination. ... The 
 Method of Agreement stands on the ground that what- 
 ever can be eliminated is not connected with the phe- 
 nomenon by any law. The Method of Difference has 
 for its foundation, that whatever cannot be eliminated 
 is connected with the phenomenon by a law." 
 
 Incomplete analysis of the circumstances attending 
 the phenomenon may vitiate the inference in both 
 methods: in the method of Agreement as already 
 stated; in the method of Difference, by leading us to 
 overlook points of difference in cases supposed to be 
 alike except in the particulars specified in the Canon 
 of this method. 
 
 Difficulties in Using the Method of Difference. 1. 
 One danger in employing the method of Difference 
 results from the possibility of the Composition of 
 Causes. It often happens that a given phenomenon 
 
DIFFICULTIES 97 
 
 is the effect of the joint action of several causes. Heat, 
 light, moisture, etc., are all causally related to the life 
 of plants. If two plants were similarly situated as 
 regards all but moisture, it would be incorrect to con- 
 clude that moisture was the sole cause of the life of 
 the one because its absence was followed by the death 
 of the other. Application of the method of Difference 
 does show that the antecedent is causally related to the 
 consequent, but not that it is the sole or adequate cause. 
 
 If we could supplement the method of Difference by 
 the method of Agreement, if we could find a set of in- 
 stances in which the supposed cause was alone common 
 to the cases in which the phenomenon was present, then 
 we could conclude that this supposed cause was ade- 
 quate to produce the phenomenon. 
 
 . Another source of difficulty closely connected with 
 the one just discussed is to be found in the existence of 
 Counteracting Causes. Even if a cause is adequate to 
 the production of an effect under ordinary conditions, 
 it may fail to produce it owing to the presence of some 
 opposed tendency. The poison can be counteracted by 
 an antidote ; the tendency of the moon to fall to the 
 earth is in part overcome by centrifugal force, and so 
 on. The presence of a counteracting cause might lead 
 us to overlook the real cause of the phenomenon. The 
 cause is present without the effect; that is, without the 
 usual effect. In such a case its effect is to be found in 
 its modification of the counteracting cause. The ten- 
 dency of the moon to fall does modify the effect which 
 would otherwise be produced by its tendency to fly off at 
 a tangent. We may symbolize one sort of case in which 
 error might arise, as follows : Let m be the phenomenon 
 
98 INDUCTION 
 
 whose cause we are seeking and suppose that we have 
 
 abed X 
 abcr X m 
 
 We should probably conclude that r was the cause of 
 m, whereas it might well be that a was the real cause, but 
 that it was counteracted in the first instance by d. It 
 is no doubt true that in an ideal application of the 
 methods there would be little difficulty ; if we could get 
 cases which differed in only one circumstance it would 
 at any rate be easy to see that the absence of the effect 
 m was connected with the presence of the circumstance 
 d; we should still have to search for the cause of m's 
 presence. But in actual cases the matter is not so sim- 
 ple; we cannot find ideal cases and the instances we 
 select for the application of the method of Difference 
 may differ in more than one respect, as in the case just 
 discussed. 
 
 III. THE JOINT METHOD. Nature presents very 
 few instances in which the method of Difference can be 
 directly applied, and even experiment fails to present 
 ideal conditions. It seldom happens that the conditions 
 stated in the Canon of Difference are realized. The 
 same is true to a great extent with regard to the method 
 of Agreement. Usually two or more cases in which a 
 given phenomenon occurs are similar in more than one 
 circumstance. In such cases it is sometimes possible to 
 use a combination of the two methods. The following 
 instance illustrates the use of The Joint Method of 
 Agreement and Difference: a large number of cases of 
 typhoid fever occurred at about the same time in a 
 college community. It happened that all those who de- 
 
THE JOINT METHOD 99 
 
 veloped the disease ate at a certain few fraternity and 
 boarding-house tables. The water supply was first in- 
 vestigated. It was found that all these places used 
 water from the same source. But it was also true that 
 the other houses were supplied from the same source, 
 so this possible cause was eliminated. The fresh vege- 
 tables were supplied from various sources; some of the 
 places in which the disease was developed used one 
 ; source, others a different one ; moreover, the places in 
 which the disease was not developed were supplied from 
 the same variety of sources. The other food supplies 
 fcame from various places and the method of Agreement 
 ncould not be applied so far as they were concerned, with 
 cone exception ; it appeared that the milk supply was the 
 same for all the places in which the fever was developed, 
 whereas none of the places which escaped used milk 
 from that source. The inference was that the milk 
 contained the cause of the disease. Further, it was 
 found that when milk from this source was no longer 
 used, no new cases of the disease appeared. There were 
 two sets of cases: in one the disease was developed, in 
 the other it was not. Those in which it appeared were 
 alike in several respects ; the ages, habits and previous 
 general health were similar in all ; the water supply was 
 the same and also the milk supply ; it might be any one 
 of these; the method of Agreement could not be suc- 
 cessfully applied. The other set of cases, those in which 
 the disease did not appear, were like the first in many 
 respects, but there was no one of these which differed 
 from any one of the others, in one respect only. There 
 was one and one only circumstance in which all the 
 members of the first group differed from all the mem~ 
 
100 INDUCTION 
 
 bers of the second, namely in the milk supply. All of 
 one group agreed in having a given milk supply and 
 developing typhoid fever; all of the other group 
 agreed in using milk from another source and escaping 
 the disease. Comparing group with group the method 
 of Difference could be used. There was only one cir- 
 cumstance in which all the instances in which fever was 
 developed differed from all of those in which it was not 
 developed. Within each set of instances there is a 
 partial application of the method of Agreement. One 
 set agreed in having the disease and also in having an- 
 other common circumstance ; but more than one circum- 
 stance was common, so the application could not be 
 complete; similarly the other set of instances agreed 
 in the absence of the fever and in the absence of this 
 circumstance; but they also agreed in lacking va- 
 rious other circumstances. However, they agreed 
 in lacking only one which was present in all those 
 of the other set, and that is the important 
 point. 
 
 The two sets of instances might be symbolized thus ; 
 p representing the phenomenon under investigation: 
 
 abcdr X p bcJcr 
 
 abefr X p eflr 
 
 aefgr X p fgmr 
 
 afghrX p ghnr 
 
 Both a and r are common to all the instances in which p 
 is present, but r is excluded by the fact that it is pres- 
 ent in those in which p is absent. 
 
 Mill's statement of the Canon of the Joint Method 
 reads : " If two or more instances in which the phe- 
 
THE JOINT METHOD,. . 101 
 
 nomenon occurs have only one circumstance iji com- 
 mon, while two or more instances in .wMrii it du?s; r;o]fc, 
 occur have nothing in common save the absence of that 
 circumstance, the -circumstance in which alone the two 
 sets of instances differ is the effect or the cause, or an 
 indispensable part of the cause, of the phenomenon." 
 This statement does not quite cover a case like that 
 described above. The instances in which the phenome- 
 non occurs may have more than one circumstance in 
 common, provided that there is only one which is at the 
 same time common to these and absent from those in 
 which the phenomenon does not occur. We might re- 
 state it thus : " If two or more instances in which a 
 phenomenon occurs have in common one circumstance 
 which is at the same time the only circumstance present 
 in these instances and absent from two or more instances 
 in which the phenomenon does not occur, that circum- 
 stance is causally related to the phenomenon." This 
 form of statement avoids the difficulty just mentioned 
 and also another. It is practically impossible to find 
 a set of instances which have nothing in common save 
 the absence of one circumstance. In the example just 
 given, the instances in which typhoid fever did not oc- 
 cur agreed in not being Esquimaux nor octogenarians 
 nor coal-miners, and so on indefinitely. On the other 
 hand it would have been easily possible to find a group 
 of instances in which there would have been fewer cir- 
 cumstances absent from all. One might select a num- 
 ber of individuals from different races, of different ages, 
 occupations, and so on. Fewer circumstances would be 
 absent from all of these than from a homogeneous group 
 of college students. But such instances might be en- 
 
102 INDUCTION 
 
 tirely insignificant fW the purpose of discovering the 
 C'l-usr. of tlte "disease.' --Of course, if the group of nega- 
 tive instances included examples from all varieties of 
 those who lacked the phenomenon in question, and we 
 could discover the only circumstance lacking in these, 
 and present in the cases where the phenomenon was 
 present, a conclusion could be drawn; but, in the first 
 place, it would be impossible to get such a group, for 
 it would be infinite in extent ; and, secondly, if the group 
 i could be had, the discovery of the only circumstance 
 "lacking from all of them would be an endless task. Most 
 i of such instances might at once be eliminated as irrele- 
 vant, though Mill's canon does not provide for that. 
 .It is important that the instances in which the phe- 
 -nomenon is absent should be similar to those in which 
 :'it is present, for if there are many points of difference 
 Jit will be difficult or impossible to select those which are 
 causally related to the phenomenon. 
 
 IV. CONCOMITANT VARIATIONS. There are still 
 otlier methods of discovering causal relations. Suppose 
 a case in which such instances as are demanded for the 
 application of any of the foregoing methods cannot be 
 obtained; it may be possible to find instances in which 
 the phenomenon occurs in varying degrees or in dif- 
 ferent quantities, while some other phenomenon varies 
 concomitantly. " The effects of heat are known only 
 through proportionate variation. We can not deprive 
 a body of all its heat ; the nature of the agency forbids 
 us. But by making changes in the amount, we ascer- 
 tain concomitant changes in the accompanying cir- 
 cumstances, and can so establish cause and effect. It is 
 thus that we arrive at the law of the expansion of bodies 
 by heat. In the same way we prove the equivalence of 
 
CONCOMITANT VARIATIONS 103 
 
 heat and mechanical force as a branch of the great 
 law of Conservation of Persistence of Force." 
 
 " The proof of the First Law of Motion, as given 
 by Newton, assumed the form of Concomitant Varia- 
 tions. On the earth, there is no instance of motion 
 persisting indefinitely. In proportion, however, as the 
 known obstructions to motion friction and the resist- 
 ance of the air are abated, the motion of a body is 
 prolonged. A wheel spinning in an exhausted receiver 
 upon a smooth axle runs a very long time. In Borda's 
 experiment with the pendulum, the swing was prolonged 
 to more than thirty' hours, by diminishing the friction 
 and exhausting the air. Now, comparing the whole 
 series of cases, from speedy exhaustion of movement to 
 prolonged continuance, we find that there is a strict 
 concomitance between the degree of obstruction and the 
 arrest ; we hence infer that if the obstruction were en- 
 tirely absent, motion would be perpetual. The statis- 
 tics of crime reveal causes by the method of Variations. 
 When we find crimes diminishing according as labor is 
 abundant, according as habits of sobriety have in- 
 creased, according to the multiplication of the means of 
 detection, or according to the system of punishments, 
 we may presume a causal connection, in circumstances 
 not admitting of the method of Difference." 7 
 
 We may symbolize a Set of instances to which this 
 method is applicable in this way: 
 
 a bed X p 
 !(2fl) bee X (2p) 
 (4a) bef X (3p), etc. 
 
 The Canon of the Method of Concomitant Variations 
 7 Bain, Logic, pp. 62-63. 
 
104 INDUCTION 
 
 is : " Whatever phenomenon varies in any manner 
 whenever another phenomenon varies in some particular 
 manner, is either a cause or an effect of that phenome- 
 non, or is connected with it through some fact of cau- 
 sation." 
 
 V. THE METHOD OF RESIDUES. This method is 
 usually included with the others and completes the list. 
 Its canon is : " Subduct from any phenomenon such 
 part as is known by previous inductions to be the effect 
 of certain antecedents, and the residue of the phenom- 
 enon is the effect of the remaining antecedents." Its 
 principle, like that of the other methods, is that of ex- 
 clusion. If we have a complex phenomenon or a group 
 of phenomena represented by the letters xyzlm, and a 
 group of antecedent circumstances represented by 
 abcdf, and if we know that a causes x and b causes /, c 
 causes z and d causes Z, the conclusion will be that the 
 remaining m is the effect of /. This method would be 
 equally applicable in an instance in which the causes 
 were present with the effects instead of being ante- 
 cedent to them only. Thus, if we had a phenomenon 
 m in a group of circumstances, dbcdjxyzlm, and knew 
 as before that a and #, b and y, c and z, and d and I 
 were causally related, the connection of / and m would 
 be evident. We must, of course, be careful to include 
 all the relevant circumstances in the group. 
 
 If a phenomenon has occurred and all the known ante- 
 cedents of this phenomenon are known not to contain 
 its cause, the cause must be sought for in some phe- 
 nomenon not yet discovered. There were certain per- 
 turbations in the movement of the planet Uranus, not 
 accounted for bjr the attractive force of any known 
 
THE METHOD OF RESIDUES 105 
 
 heavenly body; they must, then, be due to some body 
 not yet discovered ; this line of reasoning led to the dis- 
 covery of the planet Neptune. 
 
 Again, the weight of atmospheric nitrogen was 
 found to be greater than that of nitrogen produced 
 chemically ; further examination revealed the presence 
 in the atmosphere of another element, argon. 
 
 Obviously the method of Residues can be applied 
 only when we have fairly complete knowledge of the 
 field of facts in which the phenomenon is found. We 
 must know the causal relations of all the circumstances 
 involved in the case except the phenomenon under inves- 
 tigation. 
 
 The following example, though not formally in- 
 cluded under Mill's canon, employs the principle of 
 Residues : If only four men were capable of doing a cer- 
 tain act and if we learned that one of these was tempo- 
 rarily unable to do it, through illness, and that the two 
 others were a thousand miles away when the act was 
 performed, the fourth must have committed the act. 
 
 If, in any way, we can assure ourselves that of all the 
 possible causes of a phenomenon all but one are ex- 
 cluded, that one must be the cause. The several methods 
 are ways of doing this. 
 
 EXERCISES 
 
 Examine the following arguments and criticise the rea- 
 soning as fully as possible; state the method used: 
 
 1. The newly discovered painting must be a Rubens; 
 for the conception, the drawing, the tone and the tints are 
 precisely those seen in the authentic works of that master. 
 (Hyslop.) 
 
106 
 
 INDUCTION 
 
 2. In nine counties, in which the population is from 100 
 to 150 per square mile, the births to 100 marriages are 396; 
 in sixteen counties, with a population of 150 to 200 per 
 square mile, the births are 390 to 100 marriages. There- 
 fore the number of births per marriage is inversely related 
 to the density of population and contradicts Malthus's 
 theory of the law of population. (Hyslop.) 
 
 3. The great famine in Ireland began in 1845 and in- 
 creased until it reached a climax in 1848. During this 
 time agrarian crime increased very rapidly until, in 1848, 
 it was more than three times as great as in 1845. After 
 this it decreased with the return of better crops until, in 
 1851, it was only 50 per cent, more than in 1845. It is 
 evident from this that a close relation of cause and effect 
 exists between famine and agrarian crime. (Hyslop.) 
 
 4. The influence of heat in changing the level of the 
 ground upon which the temple of Jupiter Serapis stands 
 might be inferred from several circumstances. In the first 
 place, there are numerous hot springs in the vicinity, and 
 when we reflect on the dates of the principal oscillations of 
 level this conclusion is made much more probable. Thus, 
 before the Christian era, when Vesuvius was regarded as a 
 spent volcano, the ground on which the temple stood was 
 several feet above water. But after the eruption of Vesu- 
 vius in 79 B. c., the temple was sinking. Subsequently 
 Vesuvius became dormant and the foundations of the tem- 
 ple began to rise. Again Vesuvius became active, and has 
 remained so ever since. During this time the temple has 
 been subsiding again, so far as we know its history. 
 (Hyslop.) 
 
 5. Take a bottle of charged water, slightly warmer than 
 a given temperature registered by the thermopile, and mark 
 the deflection it causes. Then cut the string which holds it 
 and the cork will be driven out by the elastic force of the 
 carbonic acid gas. The gas performs its work, and in so 
 doing it consumes heat and the deflection of the thermopile 
 shows that the bottle is cooler than before, heat having 
 been lost in the process. (Hyslop.) 
 
 6. As an evidence of the extreme antiquity of highly 
 civilized man, we have the following facts : On one of the 
 remote islands of the Pacific Easter Island two thousand 
 
EXERCISES 107 
 
 miles from South America, two thousand miles from the' 
 Marquesas, and more than one thousand miles from the; 
 Gambier Islands, are found hundreds of gigantic stone' 
 images, now mostly in ruins. They are often forty feet- 
 high, while many seem to have been larger, the crowns of 
 their heads, cut out of red stone, being sometimes ten feet 
 in diameter, while even the head and neck of one is said 
 to have been twenty feet high. The island containing 
 these remarkable works has an area of about thirty square 
 miles, and as the smallest image is about eight feet high, 
 weighing four tons, and as the largest must weigh over a 
 hundred tons or much more, their existence implies a large 
 population, abundance of food, and an established govern- 
 ment which so small an island could not supply. (Hyslop.) 
 
 7. We observe very frequently that very poor handwrit- 
 ing characterizes the manuscripts of able men, while the 
 best handwriting is as frequent with those who do little 
 mental work when compared with those whose penmanship 
 is poor. We may, therefore, infer that poor penmanship 
 is caused by the influence of severe mental occupation. 
 (Hyslop.) 
 
 8. In the following instances crystallization takes place: 
 the freezing of water; cooling and solidifying of molten 
 metals and minerals; deposition of salts from solutions; 
 volatilization of solutions; deposition of solids from the 
 gaseous state, as iodine; pressure; slow internal change, as 
 in rocks; the transformation of metals from the tough to 
 the brittle condition, by hammering; vibration, and re- 
 peated heatings and coolings. We may then conclude that 
 the cause of crystallization is the increased scope and oper- 
 ation of the molecular or solid-forming cohesion. (Bain.) 
 
 9- When the barometer was carried to the top of the Puy 
 de Dome it was found that the mercury stood lower than 
 before. It was inferred that the pressure of the air was 
 the cause of the rise of mercury in the tube. 
 
 10. The chemical action between two substances is much 
 greater when they are in a liquid than when they are in a 
 gaseous state. We may conclude that there is an inverse 
 relation between cohesion and chemical activity. 
 
 11. Goldscheider proved that muscular sensations play 
 no considerable part in pur consciousness of the movement 
 
108 INDUCTION* 
 
 of our limbs, by having his arm suspended in a frame and 
 moved by an attendant. Under these circumstances, where 
 no work devolved on the muscles, he found that he could 
 distinguish as small an angular movement of the arm as 
 when he moved and supported it himself. 
 
 He also proved that the chief source of movement-con- 
 sciousness is pressure-sensations from the inner surface of 
 the joints, by having his arm held so that the joint sur- 
 faces are pressed more closely together, and finding that 
 a smaller movement was now perceptible. (Creighton.) 
 
 12. " That the Tempest belongs to the latest period of 
 Shakespeare's literary activity is shown, inter alia, by the 
 absence of rhyme, the large number of ' run on ' (un- 
 stopped) lines, the high proportion of weak and light end- 
 ings, and the comparative rarity of puns in the low scenes." 
 (Mellone.) 
 
 13. That the feeling of effort is largely, if not entirely, 
 of peripheral origin, appears from such experiments as the 
 following: Hold the finger as if to pull the trigger of a 
 pistol. Think vigorously of bending the finger, but do not 
 bend it. An unmistakable feeling of effort results. Re- 
 peat the experiment, and notice that the breath is involun- 
 tarily held, and that there are tensions in the other mus- 
 cles. Repeat the experiment again, taking care to keep 
 the breathing regular and the other muscles passive. Little 
 or no feeling of effort will now accompany the imaginary 
 bending of the finger. (Ferrier, quoted by Hibben.) 
 
 14. Sir Charles Lyell, by studying the fact that the rivtr 
 Ganges yearly conveys to the ocean as much earth as would 
 form sixty of the great pyramids of Egypt, was enabled 
 to infer that the ordinary slow causes now in operation 
 upon the earth would account for the immense geological 
 changes that have occurred, without having recourse to the 
 less reasonable theory of sudden catastrophes. (Hibben.) 
 
 15. Count Rumford in 1798 proved that the common 
 notion that heat was a substance was false, by boring a 
 large piece of brass, under great pressure of the bore, 
 whilst the brass was in a gallon of water; and at the end 
 of two and one-half hours the water actually boiled. (Hib- 
 ben.) 
 
 16. How would you set out to discover the causal rela- 
 
EXERCISES 109 
 
 tions of the following phenomena? Suggest instances and 
 indicate the method to be used: 
 
 (1) Heat and expansion. 
 
 (2) Heat and friction. 
 
 (3) Mosquitos and malaria. 
 
 (4) The tubercle bacillus and consumption. 
 
 (5) Golden-rod and hay fever. 
 
 (6) A rainy spring and mosquitos. 
 
 (7) The presence of oxygen and the burning of a 
 
 candle flame. 
 
 (8) Cocaine and the absence of pain. 
 
 (9) Moisture and vegetation. 
 
 (10) The gulf-stream and climate. 
 
 (11) The cause of the tides. 
 
 (12) The cause of the trade winds. 
 
 (13) The course of a glancing bullet. 
 
 17. Cite ten cases of the composition of causes. 
 
 18. Cite ten of the plurality of causes. 
 
 19. Cite ten cases of counteracting causes. 
 
 20. Bring in five cases illustrating each of the methods. 
 
CHAPTER VII 
 VERIFICATION AND DEDUCTION 
 
 Verification and Deduction. All these methods 
 are means by which a sound inference may be drawn or 
 an inference already drawn may be verified. They all 
 involve finding certain facts which inevitably follow 
 from the inference in question, and they are not con- 
 clusive if these facts can be shown to be consistent with 
 any rival hypothesis. 
 
 There is another way of testing the truth of any in- 
 ference ; if we can show that the inference follows from 
 something already known we shall establish the truth 
 of the inference itself. Instead of searching for the 
 consequences of the inferences and trying to determine 
 their truth, we find a law of which our inference is it- 
 self a necessary consequence. Conversely if an infer- 
 ence is inconsistent with a known law it is necessarily 
 false. In applying this it is necessary to remember 
 that many supposed laws have proved to be false and 
 that when an inference disagrees with a supposed law, 
 it may be that the latter or both must be rejected. 
 The fact that an inference is consistent with known 
 laws does not prove its truth, but only its possible 
 truth, for two rival hypotheses may be consistent with 
 all the known facts and laws to which they are related. 
 For proof, the connection must be closer than mere con- 
 sistency. The inference must not only agree with the 
 law, it must follow from it; in other words, the truth 
 of the law must insure the truth of the inference, 
 
 HP 
 
SYSTEMATIC KNOWLEDGE 111 
 
 An inference from a law or general principle to some 
 consequence of the principle is a deductive inference. 
 When we reason in this way we reason deductively, we 
 deduce a conclusion, we employ deduction. 
 
 Systematic Knowledge. -When we show that an in- 
 ductive inference is a reliable statement of the relation 
 of certain phenomena to each other, or when we show 
 that any inference whatever is a consequence of some 
 general principle, we establish the fact that the infer- 
 ence with which we are dealing belongs to a system of 
 facts or truths. 1 In a system all the parts and elements 
 are so related that the truth of one part implies the 
 truth of the rest ; we cannot hold to one part and reject 
 the rest without inconsistency and contradiction. A sys- 
 tem may consist of comparatively few members and be 
 comparatively simple, as in an isolated syllogism, or it 
 may be very broad in its scope and its internal relations 
 may be exceedingly complex. For example, a philo- 
 sophical system attempts to state the laws which hold 
 for all reality. 
 
 We shall begin our examination of systems with the 
 syllogism. When we argue, to use the most ancient of 
 illustrations, that " Socrates is mortal because all men 
 are mortal and Socrates is a man," we are basing the 
 truth of our conclusion upon a universal proposition, 
 " All men are mortal," and the further proposition, 
 " Socrates belongs to the class men." 
 
 Criticism of the Syllogism. It might be urged, as 
 an objection to the syllogism, that "it gives us no new 
 
 l Professor Hibben in his Logic, Deductive and Inductive, 
 makes much use of this conception in discussing the nature of 
 deduction and induction. 
 
VERIFICATION AND DEDUCTION 
 
 information ; if the conclusion is really contained in 
 the major premise, 2 as it must be if the reasoning is to 
 be valid, why go to the trouble of making a syllogism? 
 We knew beforehand that all members of the class 
 designated by the subject were included in that desig- 
 nated by the predicate, or possessed the quality, rela- 
 tion, or whatever it may be, for which the predicate 
 stands; if we did not know that Socrates was mortal, 
 how could we say that all men are mortal? Therefore, 
 it is a matter of course that the subject of the conclu- 
 sion, which is included in the subject of the major 
 premise, will have that predicate. This objection would 
 lead to the condemnation of such a science as geom- 
 etry, for all its conclusions are contained in its postu- 
 lates and axioms. Still we do get information by 
 means of such processes. 
 
 We may know it to be a general law that all iron 
 compounds have certain properties without knowing 
 the chemical composition of a compound we have in our 
 hands ; as soon as we discover that it is a compound of 
 iron, we can draw our conclusion. Of course, if our 
 major premise were not a law, our conclusion would 
 not be trustworthy. If the general statement about 
 iron compounds were an unverified inductive inference, 
 then we could not state it with certainty so long as 
 we were not sure that the present compound, if it proves 
 to be iron, would possess the given properties. If all 
 inductive inferences were simply enumerative or collec- 
 tive judgments (page 86), if "perfect induction" 
 were the ideal form of induction, then there would be 
 ground for the objection we have mentioned. But if 
 
 2 The universal proposition on which the reasoning is based, in 
 this case, "All men are mortal." is called the major premise. 
 
VALUE OF THE SYLLOGISM 113 
 
 we may know that whenever a given phenomenon oc- 
 curs, a certain circumstance must inevitably be pres- 
 ent, or that any two properties are invariably con- 
 nected, we have information which will apply to many 
 cases of whose character we may yet be in ignorance. 
 The syllogism is the typical form of reasoning. The 
 quotation which follows is from Professor James's Psy- 
 chology; it states the claim that reasoning is precisely 
 that form of mental activity which does enable us to 
 deal with new situations, with novel data. 
 
 " A thing inferred by reasoning need neither have 
 been an habitual associate of the datum from which we 
 infer it, nor need it be similar to it. It may be a thing 
 entirely unknown to our previous experience, something 
 which no simple association of concretes could ever have 
 evoked. The great difference, in fact, between that 
 simple kind of rational thinking which consists in the 
 concrete objects of past experience merely suggesting 
 each other and reasoning distinctly so-called is this: 
 that whilst empirical thinking is only reproductive, 
 reasoning is productive. An empirical, or * rule-of- 
 thumb,' thinker can deduce nothing from data with 
 whose behaviour and associates in the concrete he is un- 
 familiar. But put a reasoner amongst a set of con- 
 crete objects, which he has neither seen nor heard of 
 before, and with a little time, if he is a good reasoner, 
 he will make such inferences from them as will quite 
 atone for all his ignorance. Reasoning helps us out 
 of unprecedented situations situations for which all 
 our common associative wisdom, all the * education * 
 which we share in common with the beasts, leaves us 
 without resource." Psychology, Briefer Course, page 
 
114 VERIFICATION AND DEDUCTION 
 
 As soon as we see that the present case belongs to a 
 certain class or is of a certain type, the laws which are 
 known to apply to that class or type may immediately 
 be applied to it. 
 
 How Propositions are Related to each other 
 The syllogism as illustrated above shows that a univer- 
 sal judgment may be made the basis for certain other 
 statements. There are several kinds of syllogisms, but 
 before discussing these it will be well to examine propo- 
 sitions generally with a view to discovering what rela- 
 tions different kinds of statements bear to each other 
 and whether there may not be other ways than that 
 illustrated in the syllogism, in which one statement may 
 be made the basis for another. We have already dis- 
 cussed four kinds of propositions ; those which are 
 universal and affirmative, universal and negative, par- 
 ticular and affirmative, and particular and negative. It 
 will be remembered that the symbols for these were A, 
 E, I, and O respectively. Their relations to each other 
 are best shown by means of what is known as the 
 " Square of Opposition," a diagram which has remained 
 practically unchanged since the time of Aristotle. 
 (All x is y) (No x is y) 
 
 A Contraries E 
 
 1 
 * 
 
 I Subcontraries O 
 
 (Some x is y) (Some x is not y) 
 
RELATIONS OF OPPOSITION 115 
 
 Let us take as an illustration of the A proposition, " All 
 men are rational." Its contrary will be " No men are 
 rational." What exactly are the relations between 
 these two propositions? If A be true, it is obvious that 
 E will be false, and if E be true A will be false. But 
 if A be false, what about E? It may be true or false, 
 for the falsity of A leaves those two possibilities ; in 
 other words, the truth or falsity of E is undetermined. 
 Similarly of A, if E be false. If either be false, there is 
 a middle ground; thus, it may be that some men are 
 rational and some are not. Two propositions are con- 
 trary when only one can be true and both can be false. 
 
 "All men are rational" (A), and " Some men are 
 not rational" (O), are contradictory propositions. If 
 A be true, O will be false, and if A be false, O will be 
 true ; likewise if O be true, A will be false, and if 
 O be false A will be true. There is no middle ground ; 
 there is no third possibility. Only one can be true, and 
 only one can be false, or in other words, both cannot 
 be true and both cannot be false. Two propositions are 
 contradictory when they are exact opposites; one must 
 be true and the other must be -false. 
 
 Of sub-contrary propositions, both may be true, but 
 only one can be false. The propositions, " Some men 
 are rational " and " Some men are not rational," are 
 in the relation of sub-contraries. If either be false the 
 other must be true, and if one be true the other may be 
 true also ; both may be true, and one must be. The 
 propositions I and O are consistent, whereas contraries 
 and contradictories are inconsistent. 
 
 4 Two propositions which are to stand in a relation of op- 
 position to each other must have identical terms. This is true 
 in the traditional treatment, but exceptions will be noted later. 
 
116 VERIFICATION AND DEDUCTION 
 
 In the case of subalterns, both propositions are of 
 the same quality, but they differ in quantity. " All 
 men are rational " and " Some men are rational " are 
 subalterns. // the universal be true the particular will 
 of course be true also; but if the universal be false the 
 other is left indeterminate; it may be true or it may be 
 false. On the other hand, if the particular proposition 
 be false, the universal will necessarily be false too; if 
 it is false that " Some men are rational," it cannot be 
 true that " All men are " ; but if the particular be true 
 it is by no means certain that the other will be. Thus, 
 if we know that some men are rational, that does not 
 give us a right either to affirm or to deny that all men 
 are rational ; in other words, the truth of the universal 
 is left indeterminate. 
 
 To summarize: contrary propositions are such that 
 only one can be true, and both may be false. 
 
 Contradictory propositions are so related that one 
 must be true and the other must be false. 
 
 Sub-contraries may both be true, but only one can 
 be false. 
 
 Subalterns may both be true or both false. The 
 truth of the universal assures the truth of the par- 
 ticular, but the falsity of the universal does not in- 
 volve the falsity of the particular; the falsity of the 
 particular involves the falsity of the universal, but the 
 truth of the particular does not assure the truth of the 
 universal. 
 
 Relations of Opposition among Propositions which 
 have not Identical Terms. These relations are most 
 easily detected between propositions which have the 
 same subject and the same predicate, but it is possible 
 
RELATIONS OF OPPOSITION 117 
 
 to find them in propositions which do not answer to this 
 description. The propositions, " All men are rational " 
 and " All men are idiots," are contraries. Both cannot 
 be true, but both may be false. 
 
 Or again, " Socrates was the wisest of the Greeks " 
 and " Aristotle was the wisest of the Greeks," are con- 
 trary propositions. Only one of them could be true, 
 while both might be false. 
 
 This will be found to be the case with a great many 
 inconsistent propositions. In fact all inconsistent 
 propositions which are not contradictories are con- 
 traries. Many pairs of such inconsistent propositions 
 would not fit into the square of opposition, for both 
 might be affirmative or both might be negative. A and 
 E propositions which have identical terms are contra- 
 ries : we need not consider the meaning of the proposition 
 to discover that, for it is evident from their form. In 
 other cases we must take into account the meaning as 
 well. " A is B " and " A is not B " are contraries so 
 long as the meaning of the terms A and B remains the 
 same, no matter what that meaning is ; but the relation 
 between " A is X " and " A is Y " can be determined 
 only after we know the meaning of X and Y. If we 
 learn that X and Y are opposites we can, of course, re- 
 state our second proposition, "A is Y," in the form 
 " A is not X," the contrary of " A is X." If X and 
 Y prove to be the same or similar in meaning the two 
 original propositions are of course consistent. 
 
 Subject and predicate may both be different; e. g., 
 " Oxygen is heavier than nitrogen " and " Nitrogen is 
 heavier than oxygen." Only one cannot be true ; both 
 might be false. If two propositions, alike in quality, 
 
118 VERIFICATION AND DEDUCTION 
 
 have the same subject but have predicates which are 
 complete opposites, as X and not-X, the propositions 
 will be contradictories. Such pairs of terms as " ra- 
 tional and non-rational," " square and not-square," are 
 examples. 
 
 Cases sometimes occur in which propositions having 
 the same predicates but different subjects will be con- 
 tradictory in meaning: thus, " Man alone is rational "; 
 " Some being besides man is rational." 
 
 Similarly, propositions with unlike terms may stand 
 in the relation of sub-contraries. For example : " Some 
 men are rational " and " Some men are irrational," and 
 66 Simple substances make up a large part of the 
 earth's crust " and " Compound substances make up 
 a large part, etc.," are pairs of sub-contraries. 
 
 And likewise in the case of subalterns : for example, 
 " All men are vertebrates " and " All men are mam- 
 mals " ; " No mental states can be weighed," " No emo- 
 tions can be weighed." The relation of subaltern may 
 hold between two propositions even if one of them is not 
 universal. Thus, " Most books are worthless " and 
 " Some books are worthless." Of course, " The recent 
 novels are worthless," is not necessarily a subalterna.te 
 of either of these propositions. 
 
 Singular propositions require special notice. " Soc- 
 rates was the noblest of men " and " Socrates was not 
 the noblest of men " are apparently contrary propo- 
 sitions, but as a matter of fact they are contradictories. 
 Singular propositions which have the same terms are 
 never contraries except in form. On the other hand, 
 " Socrates was an Athenian " and " Socrates was a 
 Spartan " are contraries. 
 
 Conversion. A proposition is the verbal expression 
 
CONVERSION 119 
 
 of a judgment, and a judgment is an act of thought 
 wherein we assert that certain relations hold among cer- 
 tain objects of thought, as, A is B, A Is not B, some A 
 is Y, and so on. Now it is often possible to formulate 
 other propositions which are equivalent to these or 
 which are obviously true if the original proposition be 
 true. The proposition, " No conic sections are rectan- 
 gular figures," is equivalent to " No rectangular figures 
 are conic sections." The only difference between the 
 two is in the order of the terms. The original subject 
 and predicate have been interchanged. This process 
 is known as Conversion. The proposition just con- 
 verted was an E proposition and all E propositions can 
 be converted. 
 
 Again, the proposition, " Some metals are elements " 
 can be converted into " Some elements are metals." 
 Both are I propositions. From the proposition, " Some 
 quadrupeds are horses," we can get only " Some horses 
 are quadrupeds," We happen to know that the same 
 could be said of all horses, but we do not get that 
 knowledge from the original proposition. The original 
 statement is affirmative and affirmative propositions, as 
 we have seen, do not give information about the whole 
 of the predicate. But the statement, "All horses are 
 quadrupeds," being universal, affirms something about 
 the whole class horses. 
 
 The first general rule of conversion is that no term 
 may be distributed in the converse "which was not dis- 
 tributed in the original proposition. A proposition, 
 then, such as " All A propositions are universal," can 
 have as its converse only an I proposition, " Some uni- 
 versal propositions are A propositions." 
 
 Each of the propositions dealt with above has had as 
 
120 VERIFICATION AND DEDUCTION 
 
 its converse another proposition having the same 
 quality. In all cases the converse of a proposition must 
 have the same quality as the original proposition. This 
 is a second rule of conversion. From this and the for- 
 mer rule it follows that the proposition can have no 
 converse. Its subject is undistributed and its quality 
 negative ; but in the converse, the original subject, hav- 
 ing become the predicate of a negative proposition, 
 would be distributed, a violation of the first rule. 
 
 Proposition Converse 
 
 The converse of A is I: All S is P; Some P is S. 
 
 The converse of I is I: Some S is P; Some P is S. 
 
 The converse of E is E: No S is P; No P is S. 
 O has no converse. 
 
 The use of Euler's circles 5 will help to make these re- 
 
 A (Pi's) All S is P or (at least) some P is S. 
 
 E (S) No S is P or no P is S. 
 
 I ( <~p) (At least) some S is P or some P is S. 
 
 (?)) Some S is not P but all P may be S, 
 or no P may be S, or some may be and some may 
 not be. 
 
 lations clear. We see that propositions E and I are 
 converted into E and I ; in technical language they are 
 converted " simply." A can be converted only into I ; 
 
 5 The forms here used are taken from Hyslop's Elements of 
 Logic. 
 
OBVERSION 
 
 that is, it is converted into a proposition which is less 
 general than itself, into a particular proposition. Such 
 conversion is known as conversion by limitation or per 
 accidens. 
 
 Obversion. Again, we may find for all ordinary 
 propositions an equivalent of the opposite quality : " All 
 men are wise " is equivalent to " No men are unwise " \ 
 " Some men are just " can be expressed as " Some men 
 are not unjust " ; " No animals are moral " as " All ani- 
 mals are unmoral " ; " Some men are not honest " as 
 " Some men are dishonest." It will be noticed that in 
 every case the subject is unchanged. (In " All men are 
 wise," and " No men are wise,'"' .the subject is in both 
 cases " All men " ; the " No " belongs to the statement 
 as a whole, not to the subject. The negative of " All 
 men " would be "All who are not men.") This process 
 is called Obversion. The quality of the proposition if 
 changed and the predicate of the obverse is the com- 
 plete opposite of the predicate of the original proposi- 
 tion. 
 
 Proposition Obverse 
 
 The obverse of A is EJ All S is P; No S is not-P. 
 
 The obverse of I is O: Some S is P; Some S is not not-P. 
 
 The obverse of E is A: No S is P; All S is not-P. 
 
 The obverse of O is I: Some S is not P; Some S is not-P. 
 
 If the predicate in the original proposition be nega- 
 tive, as non-conductor, it will be replaced in the obverse 
 by the corresponding positive term, conductor. " Some 
 S is not-P " will have as its obverse " Some S is not 
 P." Difficulty is likely to arise with regard to the 
 predicate and its opposite. For example, the proposi- 
 tion, " No animals are moral," is not equivalent to " All 
 
VERIFICATION AND DEDUCTION 
 
 animals are immoral." They may be neither moral nor 
 immoral. The predicate in the new proposition must 
 be completely opposite or contradictory to the original 
 predicate. Sometimes it can not be expressed simply. 
 For example, take the proposition, " The president is 
 the nation's highest executive officer." In the obverse 
 the whole of the predicate must be made negative, not 
 simply " highest " or " executive " or " officer." It 
 might read, " The president is not any one who is not 
 the nation's highest executive officer." 
 
 The following symbols may be employed to indicate 
 the relations considered in obversion. Suppose we have 
 a proposition with the predicate P or not-P. Every- 
 thing in the universe either has or has not the predicate 
 P, that is, everything has one or the other of the 
 predicates P and not-P. We may represent this fact by 
 a circle divided into two compartments, thus : 
 
 Then any given thing will fall into one or the other of 
 those compartments. If our proposition asserts that 
 it falls into one, that is tantamount to asserting that it 
 falls outside the other ; the latter assertion would be 
 the obverse of the former. S is P, implies that S is not 
 not-P ; T is not-P, implies that T is not P. 
 
 Contraposition. These changes in the form of prop- 
 ositions may both be present together and repeatedly. 
 Let us take the proposition, " No men are immortal." 
 
CONTRAPOSITION 
 
 The obverse would be, " All men are mortal " ; the con- 
 verse of this, " Some mortals are men " ; the obverse of 
 this again, " Some mortals are not not-men " (not 
 anything else than men) ; and this, being an O propo- 
 sition, has no converse. We might, of course, have 
 begun with conversion. 
 
 What is known as Contraposition is equivalent 
 to obversion plus conversion. 6 The contrapositive of 
 " No men are immortal " is " Some mortals are men " ; 
 the contrapositive of " All men are mortal " would be 
 " No immortals are men." In the contrapositive the 
 subject is the opposite of the original predicate, the 
 predicate is the original subject, and the quality of the 
 proposition is the opposite of that of the original prop- 
 osition. An application of the rules for conversion will 
 show that the I proposition has no contrapositive. The 
 contrapositives of the various propositions are as fol- 
 lows: 
 
 Proposition Contrapositive 
 
 A, contrapositive E: All S is P; No not-P is S. 
 I, no contrapositive. 
 
 E, contrapositve I: No S is P; Some not-P is S. 
 
 O, contrapositive I: Some S is not P; Some not-P is S. 
 
 In Conversion, Obversion, and Contraposition we 
 have found certain variations in the forms in which a 
 given thought content can be expressed. Such varia- 
 tions in the form of expression help to make clearer 
 just what the content of the judgment really is. In 
 these processes the changes in the form of expression 
 are due to a change in the order of subject and predi- 
 
 6 Some logicians add a second obversion. See Hibben, Logic. 
 
VERIFICATION AND DEDUCTION 
 
 cate or a change in the quality of predicate and copula s 
 or both. 
 
 EXERCISES 
 
 1. Give contrary, contradictory, and subaltern of each of 
 the propositions in Exercises " 5," pages 62-65 ; where it is 
 not possible to give all, state the reason why. 
 
 2. Classify the subjoined propositions into the four fol- 
 lowing groups: 
 
 1. Those which can be inferred from (1). 
 
 2. Those from which (1) can be inferred. 
 
 3. Those which do not contradict (1) but cannot be 
 
 inferred from it. 
 
 4. Those which contradict (1). 
 
 (1) All just acts are expedient acts.- 
 
 (2) No expedient acts are unjust. 
 
 (3) No just acts are inexpedient. 
 (4-) All inexpedient acts are unjust. 
 
 (5) Some unjust acts are inexpedient. 
 
 (6) No expedient acts are just. 
 
 (7) Some inexpedient acts are unjust. 
 
 (8) All expedient acts are just. 
 
 (9) No inexpedient acts are unjust. 
 
 (10) All unjust acts are inexpedient. 
 
 (11) Some inexpedient acts are just acts. 
 
 (12) Some expedient acts are just. 
 
 (13) Some just acts are expedient. 
 
 (14) Some unjust acts are expedient. (Jevons.) 
 
 3. Give the converse, the obverse, and the contrapositive 
 of each of the following propositions : 
 
 (1) All who were present were unprepared. 
 
 (2) No wise man would undertake such a task. 
 
 (3) Not to make the attempt is to confess yourself 
 
 a coward. 
 
 (4) Charity begins at home. 
 
 (5) No statesman could have stooped to such a deed. 
 
 (6) Only a fanatic believes in panaceas. 
 
 (7) Discontent is frequently a symptom o ineffi- 
 
 ciency. 
 
EXERCISES 125 
 
 (8) A revolution is a surgical operation which self- 
 
 appointed healers of social diseases are very 
 ready to recommend as a preliminary to every 
 cure. 
 
 (9) Uneasy rests the head which wears a crown. 
 
 (10) All organic substances contain carbon. 
 
 (11) Better late than never. 
 
 (12) Not many of the metals are lighter than water. 
 4. State the relation of each of the following proposi- 
 tions to the succeeding one: 
 
 (1) All the metals are elements. 
 
 (2) No metals are non-elements. 
 
 (3) No non-elements are metals. 
 
 (4) All non-elements are not-metals. 
 
 (5) All metals are elements. 
 
 (6) Some elements are metals. 
 
 (7) Some metals are elements. 
 
 (8) No metals are elements. (Hyslop.) 
 
CHAPTER VIII* 
 THE SYLLOGISM 
 
 The Principles of Syllogistic Reasoning. Let us re- 
 turn to the examination of the syllogism. Every com- 
 plete syllogism contains three propositions and only 
 three. They are a major premise, a minor premise and 
 a conclusion. In the syllogism, " All men are mortal ; 
 Socrates is a man; therefore Socrates is mortal," the 
 first proposition is the major premise, the second is the 
 minor premise, and the third is, of course, the conclu- 
 sion. The major premise is the broad foundation on 
 which the reasoning rests. It is a universal proposi- 
 tion in syllogisms of this form. It may be either affirm- 
 ative or negative. Thus we may have, " No men are 
 immortal ; Socrates is a man ; therefore Socrates is not 
 immortal." The major premise asserts that the whole 
 of a certain class is included in another class or excluded 
 from it, or it assigns a certain predicate to the whole 
 of a certain subject. 1 The minor premise asserts that 
 certain things are included in the first class; and the 
 conclusion applies to these things the assertion which 
 was made about the first class. 
 
 *This chapter may be omitted. The traditional treatment is 
 given in chap. ix. 
 
 iWe have seen that all propositions may be regarded as stat- 
 ing a relation between classes, and that this way of regarding 
 them is most useful and convenient. But other types of rela- 
 tions between subject and predicate exist and should not be 
 forgotten. 
 
 126 
 
THE FIRST FIGURE 
 
 Behind this reasoning lies the principle called the 
 Dictum de Omni et Nullo; i. e., " Whatever state- 
 ment may be made with regard to a class taken gen- 
 erally may be made of each and every member of that 
 class" or " Whatever is true of each of the members 
 of a class will be true of everything found to be a 
 member of that class." 
 
 The application of this principle in the two syllo- 
 gisms employed for illustration is perhaps obvious, but 
 it may be well to represent the relation of the various 
 terms graphically. For this purpose Euler's diagrams 
 are valuable. 
 
 The class men is first included in the class mortal; 
 the individual Socrates is then included in the class 
 men and must in consequence be included in the class 
 mortal. In the second case men is excluded from im- 
 mortal and hence Socrates, who is included in men, will 
 necessarily be excluded from immortal. 
 
 It will readily be seen that (1) the minor premise in 
 a syllogism of this sort cannot be negative. A nega- 
 tive minor premise would assert that something did not 
 belong to the class indicated by the subject of the major 
 premise, and would give no ground for a further con- 
 clusion. The fact that something is true of a whole 
 class of objects does not tell us whether it will or will 
 
128 THE SYLLOGISM 
 
 not be true of some things not included in that class. 
 Thus the premises, " All men are rational beings ; 
 monkeys are not men," do not warrant the conclusion 
 that monkeys are not rational. 2 Other conclusions are 
 
 possible and we could not prove this one without using 
 information not contained in our premises. If we tried 
 to prove it by those premises alone, our reasoning 
 would be invalid. An invalid syllogism is one in which 
 the conclusion is not proved or made necessary by the 
 premises. The conclusion may be true, but the func- 
 tion of the syllogism is to furnish a conclusion which 
 must be true if the premises are true. Reasoning which 
 does not prove the conclusion is fallacious, or in other 
 words, it contains a fallacy. 
 
 We have seen that the minor premise in a syllogism of 
 this form cannot be negative. It will be obvious that 
 () if the major premise be affirmative the conclusion 
 must be affirmative and that if the premise be negative 
 the conclusion must be negative. If we affirm something 
 of a whole class we cannot deny it of a part of the 
 
 2 These diagrams may be employed in illustrating the later 
 rules also. 
 
THE SECOND FIGURE 
 
 class, and if we deny it of the whole class we cannot 
 assert it of a part. It is true also that (3) the major 
 premise cannot be particular. If we have the premises, 
 " Some animals can be domesticated ; the wolf is an 
 animal," we are obviously not justified in concluding 
 that the wolf can be domesticated. 
 
 And again (4) if the minor premise be particular, the 
 conclusion cannot be universal; it must be particular 
 too. From the premises, " All works of art are valu- 
 able; some of the objects in this collection are works 
 of art," we cannot conclude that all the objects in this 
 collection are valuable. In no case can our conclusion 
 contain more than was contained in the premises. 
 
 Syllogistic Proof. In examining syllogistic reason- 
 ing the first question is not " Is the conclusion true? " 
 but " Does the conclusion follow necessarily from the 
 premises? " If the syllogism of this form correctly 
 applies the Dictum de Omni et Nullo the reasoning is 
 valid. A syllogism of this form is said to be in the 
 First Figure, and this is the only form of syllogism 
 which can be used to prove a universal affirmative prop- 
 osition. 
 
 A Second Type of Syllogism. There are sev- 
 eral other varieties of syllogisms, each having certain 
 special principles of its own. The one next to be dis- 
 cussed is used to prove that two facts or groups of 
 facts are not the same ; it proves negative conclusions 
 and only those. Its Principle is this: if one of two 
 things is included in a class from which the other is 
 excluded, 3 these things are excluded from each other. 
 To illustrate : " Every college-bred man has read that 
 
 s Or if one has a predicate which the other lacks. 
 
130 THE SYLLOGISM 
 
 book; this man has not read the book; therefore, this 
 man is not college-bred." The fact that two subjects 
 are included in the same class or that they possess the 
 same predicate does not, on the other hand, prove that 
 they are the same or that they are related in any other 
 way. They might be even identical, it is true, but in 
 the conclusion of a syllogism we are entitled to include 
 only what must be. 
 
 Special rules. In this sort of syllogism (1) no con- 
 clusion can be drawn -from two affirmative premises. 
 Either of the premises may be negative and one of 
 them must be. In the illustration given above, the 
 minor premise was negative. We might have " No col- 
 lege man would do this deed; this man has done it; 
 therefore, he is not a college man." 
 
 On the other hand (2), both premises can not be 
 negative; only one may be negative. If two things 
 both lack the same predicate that fact alone does not 
 warrant any further statement. " No Indians are Cau- 
 casians " and " No Chinamen are Caucasians " does not 
 furnish any basis for a statement concerning the rela- 
 tion between Indians and Chinamen. 
 
 (3) The major premise in a syllogism of this sort 
 must be universal. If our major premise were " Some 
 college men are informed upon this subject," it would 
 be possible that some were not, and the fact that a 
 given man was ignorant of it would not prove that he 
 was not a college man. 
 
 (4) The minor premise may be either universal or 
 particular; if it is particular, the conclusion must be 
 particular; if it is universal, the conclusion may be uni- 
 versal. It is obvious that if we make a statement about 
 only a part of the class for which the subject of the 
 
MAJOR AND MINOR PREMISES 131 
 
 minor premise stands, we cannot make a statement 
 about the whole of it in the conclusion. In every syllo- 
 gism, the information contained in the conclusion must 
 be furnished in the premises. 
 
 Major and Minor Premises. It is not always easy 
 to know immediately which is the major premise in a 
 syllogism of this form. There is, however, a rule which 
 can be applied to all syllogisms. The major premise 
 is the one which contains the major term. The major 
 term is the predicate of the conclusion. In an affirm- 
 ative conclusion the subject may be regarded as con- 
 tained in the predicate. In the proposition, " All 
 triangles are geometrical figures," the class triangle 
 is included in the class geometrical figures. The latter 
 term is the major because it stands for the wider class. 
 In negative propositions, the predicate is not neces- 
 sarily wider ; in the proposition, " No conic sections are 
 triangles," the predicate is not wider than the subject. 
 Still, for the sake of uniformity, the predicate of the 
 conclusion is always called the major term. The syllo- 
 gism first discussed is a syllogism in the First Figure 
 and the other is in the Second Figure. 
 
 The Third Figure. In the next type of syllogism, 
 the subject is the same in both premises, but the predi- 
 cates are different, or in other words, the subject is 
 related by inclusion or exclusion to one -class in the 
 major premise and to another in the minor premise. 
 The Principles of the Figure might be stated as follows : 
 1. // a class (or individual) is included in 
 each of two other*classes those classes include 
 
 I -T T- 
 
 each other, at least in part. All X is Y and I 
 all X is Z ; therefore, some Z is Y. 
 
 2. // a class (or individual) is excluded from a 
 
132 THE SYLLOGISM 
 
 second class and included in a third, then a 
 flr ^ at l eas t> f the third is excluded from the 
 
 second. No X is Y and all X is Z ; therefore, 
 some Z is not Y. 4 
 
 In some cases a conclusion is possible if only a part 
 of the subject is described in one of the premises. 
 Some of the special rules which follow state the condi- 
 tions in which this is true. (1) One of the premises 
 must be universal. For example, " No precious metals 
 are soluble in sulphuric acid; some precious metals are 
 soluble in nitric acid; therefore, some things soluble in 
 nitric acid are not soluble in sulphuric acid." If the 
 first makes an assertion about only a part of the class 
 and the second likewise, we can not be certain that the 
 two parts are the same and thus we learn nothing about 
 the relation of their predicates. Thus, " Some triangles 
 are scalene " and " Some triangles are right-angled " 
 are premises which warrant no conclusion regarding the 
 relation of scalene to right-angled figures. (2) The 
 major premise in this Figure may be either affirmative 
 or negative. The conclusion will have the same quality 
 as the major premise. If " No A is B," and " Some (or 
 all) A is C," then " Some C is not B " ; or if " All A is 
 B," and " Some A is C," then " Some C is B." (3) The 
 minor premise can not be negative. If " All deer are 
 herbivorous," and '"' No deer are hollow-horned ani- 
 mals," we cannot conclude that " No hollow-horned 
 animals are herbivorous." (4) The conclusion of a syl- 
 logism in the Third Figure is, in all cases, particular. 
 From " All men are mammals " and*" All men are bi- 
 
 4 The student should test each of the special rules by the use 
 of such diagrams. 
 
THE FOURTH FIGURE 133 
 
 peds " we can not conclude that " All bipeds are mam- 
 mals." The fact that some or all of a certain class are 
 included in another class or possess a given predicate 
 (the minor premise asserts this) does give us infor- 
 mation about a part of that predicate, but not about 
 the whole (it does not distribute the predicate) ; as 
 that predicate becomes the subject of the conclusion, 
 the conclusion must be a particular proposition. 
 
 The Fourth Figure. "The three figures already dis- 
 cussed were described by Aristotle. The fourth is the 
 invention of later logicians and is usually regarded as 
 much less important than any of the others. In it the 
 minor premise states something about the predicate of 
 the major premise, and the conclusion in turn states 
 something about the conclusion of the minor premise. 
 Thus, " All great poems are the products of genius ; 
 all the products of genius are inimitable ; therefore, some 
 inimitable things are great poems." (If the conclu- 
 sion were, " Great poems are inimitable," we should have 
 a syllogism of the First Figure, and " All the products 
 of genius, etc.," would be the major premise). The 
 Principles of this Figure are: 1. // a class is included 
 in a second class and this in turn is included in a third, 
 then the third will be partly coextensive with the first. 
 
 All X is Y 
 All Y is Z 
 
 Some Z is X 
 
 . If a class is excluded from a second and the lat- 
 ter is included in a third, then a part, at least, of the 
 third will be excluded from the -first. 
 
134 THE SYLLOGISM 
 
 No Y is X 
 All X is Z 
 
 Some Z is not Y 
 
 3. If a class is included in a second and the latter is 
 excluded from a third, then the third will be excluded 
 from the first. 
 
 All X is Y 
 No Y is Z 
 
 No Z is X 
 
 In the illustration we have used it is obvious that we 
 can not conclude that " All inimitable things are great 
 poems." Our minor premise has not given us any in- 
 formation about the whole of the class, " inimitable 
 things," so we can not have a universal conclusion in 
 this instance. If our syllogism were, " All great poems 
 are the products of genius; some products of genius 
 are inimitable," it would be impossible to draw a con- 
 clusion. Poems might not happen to belong to the 
 things included in the minor premise. The result would 
 be similar if the minor premise were " Some products 
 of genius are not inimitable." If the minor premise 
 were, " No products of genius are inimitable," we could 
 of course conclude that no inimitable things were poems. 
 We can formulate this rule: (1) // the major premise 
 be affirmative the minor premise must be universal. In 
 all these instances, the major premise was the same and 
 it was universal. Suppose we had " Some great poems 
 
THE FOURTH FIGURE 135 
 
 were the products of genius." It will be seen that the 
 minor premise, " All works of genius, etc.," will give a 
 valid conclusion, but that none of the others will. 
 () // the major premise be affirmative and particular, 
 the minor premise must be universal and affirmative. 
 With the minor premise " No products of genius are 
 inimitable," no conclusion can be drawn; since only 
 some great poems have been included in works of 
 genius, it may well be that some inimitable things may 
 be found among those not so included. (3) The major 
 premise may be negative. " No great statesmen are 
 selfish politicians ; some (or all) selfish politicians amass 
 great fortunes ; therefore, some persons who amass 
 great fortunes are not great statesmen." Some such 
 persons might be great statesmen, so far as our pre- 
 mises are concerned; hence we have no right to con- 
 clude that no persons who amassed great fortunes were 
 great statesmen. 
 
 EXERCISES 
 
 State the Figure and point out the errors in reasoning in 
 the following syllogisms: 
 
 (1) All wisdom is desirable, but a knowledge of 
 
 slang is not wisdom, and is, therefore, not 
 desirable. 
 
 (2) Logic and mathematics furnish good mental 
 
 training, and consequently the latter may be 
 regarded as a branch of the former. 
 
 (3) Some athletes are susceptible to pneumonia, and 
 
 as all these men are athletes some of them 
 must be susceptible to pneumonia. 
 
 (4) Some industrious people are also bright, for there 
 
 are both bright and industrious students in 
 that group. 
 
136 THE SYLLOGISM 
 
 (5) Some statues are very lifelike, and no lifelike 
 
 things are contrary to the laws of nature; 
 hence, nothing contrary to -';he laws of nature 
 is a statue. 
 
 (6) Some gymnastic exercises are good for increasing 
 
 strength, but swimming is not, and hence is 
 not a gymnastic exercise. 
 
 (7) All Democrats voted against the bill, and as 
 
 most of our Congressmen are Democrats, they 
 must all have voted against the bill. 
 
 (8) All M is P; 
 No M is S; 
 
 /.No S is P. 
 
 (9) Europeans cannot endure that climate; neither 
 
 can Americans; hence, Americans may be re- 
 garded as a species of European. 
 
 (10) All ballads are interesting, and some interest- 
 
 ing things are very old; hence, some very old 
 things are ballads. 
 
 (11) All text-books are to be had at this store, but 
 
 some novels are not to be had here, which 
 proves that novels are not text-books. 
 For further examples see page 150 and page 177f. 
 
CHAPTER IX 
 
 TRADITIONAL TREATMENT OF THE SYLLO- 
 GISM 
 
 THE traditional treatment of the syllogism is sim- 
 ple though very formal. The syllogism is regarded as 
 a form of reasoning in which each of two terms is 
 compared with a third and as a result the two terms 
 are found to be related to each other. Each of the 
 two is compared with the third in a premise. The re- 
 sult of the comparison is stated in the conclusion. 
 
 is P) 
 
 > Premises. 
 
 () is M) 
 ' () is P Conclusion. 
 
 P and S are found to stand in certain relations to M. 
 In this case and in many others we are justified in as- 
 serting a relation between S and P : S and P are found 
 to be related through M as a medium. For this rea- 
 son M is called the Middle Term and the syllogism is 
 said to embody Mediate Reasoning. 
 
 The validity of the reasoning is tested by the appli- 
 cation of a number of rules. These rules have to do 
 with the relation and distribution of the several terms 
 in the syllogism. They are as follows: 
 
 1. Every syllogism contains three propositions and 
 only three. 
 
 2. Every syllogism has three terms and only three. 
 (If any term is ambiguous this rule is violated.) 
 
 137 
 
138 TREATMENT OF THE SYLLOGISM 
 
 3. The middle term must be distributed at least 
 once. 
 
 4. No term may be distributed in the conclusion which 
 was not distributed in one of the premises. 
 
 5. From two negative premises nothing can be in- 
 ferred. 
 
 6. If one premise be negative, the conclusion must 
 be negative ; if both premises be affirmative, the con- 
 clusion must be affirmative. 
 
 7. From two particular premises no conclusion can 
 be drawn. 
 
 8. If one premise be particular, the conclusion must 
 be particular. 
 
 Let us examine these rules in the order given. 
 
 1. With more than three propositions, we should have 
 more than a syllogism, though our reasoning might be 
 valid. 
 
 2. The violation of rule two gives rise to the Fallacy 
 of Four Terms. Unless two of the terms are confused 
 this fallacy is not likely to arise. No one would try 
 to draw a conclusion from the propositions, " Socrates 
 was a philosopher," and " The earth revolves about the 
 sun." But one might be tempted to draw a conclusion 
 from the premises, " Steel is made from iron ; iron is 
 dug from the ground." Still, it would be wrong to con- 
 clude that steel is dug from the ground. The terms 
 here are, " steel," " (something) made from iron," 
 "iron," and " (something) dug from the ground." 
 
 3. The violation of rule three gives rise to the Fal- 
 lacy of Undistributed Middle. Thus, the premises, 
 " Some men are brave ; and some men are strong," do 
 not prove anything ; nor do these : " All brave men 
 
THE UNDISTRIBUTED MIDDLE 139 
 
 should be respected; and, all just men should be re- 
 spected." 
 
 Let us represent the middle term by M, the minor 
 term (subject of the conclusion) by S, and the major 
 term (predicate of conclusion) by P. We are not jus- 
 tified by the premises in making any statement about 
 the relation of S and P, for they may be wholly or 
 partially identical or they may be mutually exclusive. 
 But if the middle term were distributed we might be 
 able to draw a conclusion. If all M is P and all S is M, 
 we may conclude that all S is P. 
 
 Or if no M is P and all S is M, then no S is P. 
 
 An invalid syllogism is one in which it is not possible 
 to determine fully the relation of the circles to each 
 other, since there are conflicting possibilities. In the 
 case of Undistributed Middle cited above, all, some, or 
 none of S may be included in P. 
 
140 TREATMENT OF THE SYLLOGISM 
 
 In valid syllogisms there may sometimes be a margin 
 of indefiniteness (owing to the indefinite character of 
 the "particular" propositions), but a certain amount 
 of definite information regarding the relation of S and 
 P is always given and the relation of the circles sym- 
 bolizing major and minor terms is not left wholly in 
 doubt. 
 
 The reason for the rule requiring the distribution of 
 the middle term may be stated in this way: If each of 
 two things is related to a part of a third, we can not 
 conclude that they are related to each other, for they 
 may not be related to the same part; but if one (or 
 both) is related to the whole of the third, then it may 
 be possible to assert a relation between the two. Thus : 
 
 All M is P No M is P All P is M 
 
 All S is M All S is M All S is M 
 All S is P No S is P No conclusion. 
 
 and so on 
 
 Some M is P 
 All S is M 
 No conclusion. 
 
 4. The reason for rule four is obvious: if we know 
 something about only part of a class in the premise, 
 
ILLICIT MAJOR AND MINOR 
 
 we can not say something about all of it in the con- 
 clusion. The violation of this rule gives rise to two 
 fallacies : the Illicit Process of the Major Term and the 
 Illicit Process, of the Minor Term. In the syllogism, 
 " All men (M) are vertebrates (P) ; all men (M) are 
 rational (S) ; therefore, all rational beings (S) are 
 vertebrates (P)," we have an illustration of the Illicit 
 Process of the Minor Term, or Illicit Minor, as it is 
 usually called. In the syllogism, " All Chinamen (M) 
 are Mongolians (P) ; no Japanese (S) are Chinamen 
 (M) ; therefore no Japanese (S) are Mongolians (P)," 
 the Illicit Process of the Major Term occurs. Using 
 the circles, we have for the first ; 
 
 and for the second: 
 
 The dotted lines indicate possible boundaries of S. 
 
 The premises do not justify us in including all of S 
 within the circle P in the first, nor of excluding all P 
 from the circle S in the second. S may be outside of 
 M, but still be wholly or partially within P. 
 
 5. With two negative premises, both major and 
 
TREATMENT OF THE SYLLOGISM 
 
 minor terms are excluded from the middle term, but 
 that does not tell us whether they are or are not ex- 
 cluded from each other. 
 
 6. With one negative premise, either major or minor 
 term is excluded from the middle term, while the other 
 is not; therefore, if any relation can be asserted be- 
 tween major and minor terms, it must be one of ex- 
 clusion. 
 
 7-8. The reasons for the two last rules can be more 
 easily understood after we have considered the Moods 
 and Figures of the syllogism. It will then be seen 
 that the violation of these rules means a violation of 
 rule three or rule four or both. 
 
 The Figure of a syllogism is determined by the posi- 
 tions of the middle term. 1 
 
 The Four Figures are as follows: 
 
 1. M is P 2. P is M 3. M is P 4. P is M 
 S is M S is M M is S M is S 
 
 .'.S is P /.S is P /.S is P /.S is P 
 
 In the First Figure, the Middle Term is the subject 
 of the Major Premise and the predicate of the Minor 
 Premise. 
 
 In the Second Figure it is the predicate of each. 
 
 In the Third Figure it is the subject of each. 
 
 In the Fourth Figure it is the predicate of the Major 
 Premise and the subject of the Minor Premise. 
 
 The position of the Middle Term in the Third Figure 
 
 1 We have already seen that the Figures differ in other ways, 
 but the traditional mode of distinguishing them is the one 
 just mentioned. 
 
THE MOODS OF THE SYLLOGISM 
 
 is the opposite of that which it occupies in the Second ; 
 and in the Fourth it is the opposite of that in the First. 
 The Mood of a syllogism is determined by the quan- 
 tity and quality of the several propositions which it 
 contains. Propositions, as we have seen, are of four 
 kinds with respect to quantity and quality, and are 
 represented by the four letters, A, E, I, and O. The 
 letters AAA would symbolize a syllogism in which each 
 proposition was a universal affirmative. There are 
 sixty- four possible moods : 
 
 AAA AT? A ATA AHA "F A A T?T? A T?T A TO A 
 
 Xi.XXjfjL Xl.,l_fXX 3TX -L-TX 'Xi.x-/ZTC ^EjiTCTTC i_!7A-7i"3T J-VX'XTT "iJ7\^/XX 
 
 -AAE- AEE AIB AGE EAE EEE -EIE EGE- 
 AAI AM- AH -AGt -EAI- -EEJ- -EH- -EGI- 
 AAG AEG -AJO- AGO EAO EEG EIO EGG 
 
 .IAA -IEA- KA -IGA- -GAA GEA GIA GGA 
 
 T A T> TT^T^ TTT? TQT^ f\ A T? Q'PT? r>TT? QQT? 
 ~Xi"3r 7 "tL J^J^* "A A "J JT* "A V-/A-J" "\_/"TA^ >V "Vi/ J ^"i-? v^XX-/ vZ/VAE7 
 
 TAT TT?T TTT TOT. O AT QT?T QTT HOT. 
 
 JLXxJ. "J. JJvx" JLJLi ' ivyi" 1 "\_/Xi.A" "V^ J-V"3T "Vy i Jtr \y Vx jr 
 
 ^AG- (IEO)-G- iGG- GAG GEG GIG GGG 
 
 Many of these are at once seen to be invalid : thus, ap- 
 plying the rules for negative and particular premises, 
 we can eliminate those moods through which a line is 
 drawn. The mood IEO does not violate any of those 
 rules, but examination will show that it will give a fal- 
 lacy of Illicit Major in each of the Figures. The con- 
 clusion is negative and hence distributes its predicate, 
 the major term. The major premise is an I proposi- 
 tion and hence distributes neither of its terms ; there- 
 
144 TREATMENT OF THE SYLLOGISM 
 
 fore, the major term can not be distributed in the 
 premise, and hence this mood may be eliminated 
 also. 
 
 There remain only eleven moods which may be valid, 
 but many of those are invalid in some of the figures. 
 We will examine each of these moods in each of the 
 figures. 2 
 
 In the First Figure we should have the following re- 
 sults : 
 
 A. 
 A. 
 A. 
 
 - P 
 
 A. @-P 
 
 I. S - P 
 
 E. 
 
 E. x E. x(P) 
 A. (S)- M A. (S)-M 
 E. x O. S x 
 
 It is evident that the following are invalid in the First 
 Figure: AEE, AEO, AOO, IAI, and OAO. IAI and 
 OAO are invalid because of an Undistributed Middle, 
 the others because of Illicit Majors. 
 
 The valid moods are AAA, AAI, AH, EAE, EAO, 
 and EIO. AAI and EAO are necessarily valid since 
 AAA and EAE are valid. I and O are called weakened 
 conclusions because they are less general than they 
 
 2 To facilitate dealing with them we shall employ the symbols 
 used in the exposition of Conversion and Obversion. 
 
THE SECOND FIGURE 
 
 145 
 
 might be. A comparison of these moods will show that 
 two general statements may be made regarding reason- 
 ing in this figure : 
 
 1. The Major premise must be universal. 
 
 %. The minor premise must be affirmative, 
 
 Examination of the illustrations given in the pre- 
 vious discussion of this Figure (page 127) will show 
 that every syllogism which violated either of these two 
 rules failed to give a valid conclusion. 
 
 In the Second Figure the results are different : 
 
 A. - M 
 O. S x 
 O. Sx(P) 
 
 A. - M 
 
 E. x 
 
 E. x 
 
 E. x 
 A. - M 
 E. (S)x(P) 
 
 A.- M 
 E. x 
 O. Sx 
 
 E. x 
 A. - M 
 O. Sx 
 
 Here the moods, AAA, AAI, AH, IAI, and OAO are 
 
 invalid, the last because of Illicit Major, the others be- 
 cause of Undistributed Middle. 
 
 The valid moods are AEE, AEO, AGO, EAE, EAO, 
 and EIO. O is a weakened conclusion in AEO and 
 EAO. Here we find that in the Second Figure; 
 
146 TREATMENT OF THE SYLLOGISM 
 
 1. The major premise must be universal. 2. One prem- 
 ise must be negative and the conclusion likewise must 
 be negative. 
 
 These rules, like those of the First Figure, might 
 have been formulated on the basis of the typical cases 
 presented in the earlier discussion. (See p. 130.) 
 
 Again in the Third Figure : 
 
 A. @-P 
 I. M-S 
 I. S - P 
 
 E. x(g 
 I. M -S 
 O. Sx 
 
 E. x(P) 
 A. -S 
 O. Sx(P) 
 
 I. M -P 
 A. -S 
 I. S - P 
 
 O. Mx(P) 
 A. @-S 
 O. Sx(|) 
 
 In this case the invalid moods are AAA, AEE, AEO, 
 AOO, EAE. Of these, AAA and EAE are cases of 
 Illicit Minor; and the rest, of Illicit Majors. The 
 valid moods here are AAI, AH, EAO, EIO, IAI, and 
 OAO. In the Third Figure: 
 
 1. The conclusion must be particular. 
 
 2. The minor premise must be affirmative. 
 
 In this case, as in the others, the rules might have 
 been discovered, without consideration of the moods, by 
 a direct examination of cases. 
 
THE FOURTH FIGURE 
 
 In the Fourth Figure we have: 
 
 A. (P)-M 
 A. @-S 
 I. S - P 
 
 A. (P)-M 
 E. x(S) 
 
 o. sx 
 
 E. x(g 
 A - S. 
 O. SxfP) 
 
 Here the invalid moods are AAA, AH, AGO, EAE, and 
 OAO. AAA and EAE give Illicit Minor, AH and AGO 
 give Undistributed Middle, and OAO gives Illicit Ma- 
 jor. The valid moods are AAI, AEE, AEO, EIO, IAL 
 We get these rules for the Fourth Figure : 
 
 1. If the major premise be affirmative, the minor 
 premise must be universal. 
 
 2. If the major premise be also particular, the minor 
 premise must be affirmative. 
 
 3. // the minor premise be affirmative, the conclusion 
 must be particular. 
 
 4. // either premise be negative, the major must be 
 universal. 
 
 5. The conclusion may not be a universal affirmative 
 proposition. 
 
148 TREATMENT OF THE SYLLOGISM 
 
 Comparison of all the valid moods shows that the 
 mood AAA is valid in the First Figure only. As this 
 is the only mood in which A appears as a valid con- 
 clusion, it will be evident that a universal affirmative 
 conclusion can be proved in the First Figure only. 
 
 REDUCTION OF THE MOODS AND FIGURES. 
 
 The Medieval schoolmen invented a set of menemonic verses 
 to serve as an aid to the memory in recalling the valid modes in 
 the several Figures. The verses consisted of barbarous Latin 
 terms. The words contain also letters for guidance in reduction 
 of the other Figures into the First. These verses, with their 
 interpretation, are as follows: 
 
 Barbara, Celarent, Dam, Fenoque prioris; 
 Cesare, Camestres Festino, Baroko secundae; 
 Tertia, Darapti, Disarms, Datisi, Felapton, 
 Bokardo, Fm'son, habet, quarta insuper addit 
 Bramanttp, Camenes; Dimaris, Fesapo, Fresison. 
 
 The moods are indicated by the italicised letters. All the 
 valid moods are included except those in which there are so- 
 called weakened conclusions, i. e., cases in which a particular 
 conclusion is drawn, though a universal would be valid, such as 
 AAI or EAO in the First Figure. The first line indicates the 
 moods of the First Figure, the second line, of the Second, the 
 third and the first half of the fourth indicate those of the 
 Third Figure, and the last line, those of the Fourth Figure. 
 
 The First Figure was regarded as the Perfect Figure, and the 
 others were transformed into it by making certain changes in 
 their various members. This process was called the Reduction 
 of the Imperfect Figures. These words contain letters which 
 stand for the changes which must be made. The capital letters 
 in the last four lines indicate the mood of the First Figure to 
 which the mood, indicated by the word in which they are found, 
 may be reduced. Thus Cesare may be reduced to Celarent. 
 p indicates that the preceding proposition is to be converted 
 per accidens or by limitation; s indicates that the preceding 
 proposition is to be converted simply, and m indicates that the 
 premises are to be transposed. 
 
 CAMESTRES CELARENT 
 
 AH A is C C is not B 
 
 (All stars are suns) (No suns are planets) 
 
 No B is C All A is C 
 
 (No planets are suns) (All stars are suns) 
 
 Therefore, B is not A Therefore, no A is B. 
 
 (No planets are stars) (No stars are planets) 
 
REDUCTION OF THE FIGURES 149 
 
 The minor premise in Camestres is first converted, then the 
 two premises are transposed, and finally the conclusion is con- 
 verted. To reduce Cesare to Celarent we need only convert 
 the major premise. 
 
 As a second example we may take the reduction of Bramantip 
 to Barbara. 
 
 BRAMANTIP BARBARA 
 
 All C is B All B is A 
 
 All B is A All C is B 
 
 Some A is C All C is A 
 
 In this case, the premises are transposed, and the conclusion 
 is converted. This would give AAI. But the conclusion A would 
 be valid from these premises. The p in this case may be taken 
 as indicating that, instead of a conclusion less in quantity than 
 the original proposition, we may have one which is greater in 
 quantity, namely, universal. 
 
 There is one more significant letter in these words, the letter 
 k. It indicates that the reduction must be made by indirect 
 means. Take, for example, Bokardo which reduces to Bar- 
 bara. 
 
 BOKARDO BARBARA 
 
 Some A is not C All B is C 
 
 All A is B All A is B 
 
 Therefore, some B is not C Therefore, all A is C 
 
 In this case the major premise of Bokardo is the contradictory 
 of the conclusion of Barbara; and the conclusion of Bokardo 
 is the contradictory of the major premise of Barbara. Suppose 
 the conclusion of Bokardo to be false ; then its contradictory, " All 
 B is C," will be true; taking this as the major premise of a new 
 syllogism and the proposition, " all A is B," as the minor pre- 
 mise, the conclusion will be the contradictory of the major premise 
 of Bokardo and the new syllogism will be in the mood Barbara. 
 Bokardo may be also be reduced to Darii. First obvert, then con- 
 vert, the major premise; transposing the two premises, we then 
 have Darii. All this mechanism is entirely unscientific and its 
 interest is purely historical. 
 
 EXERCISES ON THE SYLLOGISM 
 
 1. What kinds of propositions are incapable of proof in 
 the Second, Third and Fourth Figures respectively? Give 
 the reasons for your reply. 
 
 2. If either premise of a syllogism is O, what must the 
 other be? 
 
 3. With I as the major premise, what must the minor 
 premise be? 
 
150 TREATMENT OF THE SYLLOGISM 
 
 4. Show that an E proposition is highly efficient as a 
 major premise. (J.) s 
 
 5. Show that O is seldom admissible as a minor premise. 
 
 (j.) 
 
 6. Prove that there must always be in the premises one 
 more distributed term than in the conclusion. (J.) 
 
 7. Prove from the general rules of the syllogism, that 
 when the major term is the predicate in its premise, the 
 minor premise must be affirmative. (J.) 
 
 8. Point out which of the following pairs of premises 
 will give a syllogistic conclusion, and name the obstacle 
 which exists in other cases. 
 
 (1) No A is B; some B is not C. 
 
 (2) No A is B; some not C is B. 
 
 (3) All B is not A; some not A is B. 
 
 (4) Some not A is B; no C is B. 
 
 (5) All not B is C; some not A is B. 
 
 (6) All A is B; all not C is B. 
 
 (7) All not B is not C; all not A is not B. 
 
 (8) All A is not B; no B is C. 
 
 (9) All C is not B ; no A is not B. 
 
 3 (J) refers to Jevons, Studies in Deductive Logic, where 
 a great many more questions of this character may be found 
 The following exercise is from the same source. 
 
CHAPTER X 
 
 ABBREVIATED AND COMPLEX FORMS OF 
 
 REASONING - - HYPOTHETICAL AND 
 
 DISJUNCTIVE SYLLOGISMS 
 
 The Enthymeme. Usually our reasoning does not 
 fall into the form of a perfect syllogism. In the first 
 place it very often happens that one or another of the 
 propositions is omitted. For example, " This object 
 can be magnetized, for it is made of iron," omits the 
 major premise, " All things made of iron can be mag- 
 netized." Again, in " Every member of the jury voted 
 for acquittal, therefore X voted for acquittal," the 
 minor premise, " X was a member of the jury," is 
 omitted. In " All metals are elements ; this is a metal," 
 the conclusion is omitted. 
 
 Syllogisms from which one proposition is missing are 
 called Enthymemes. The missing premise can usually 
 be found without difficulty. The two propositions which 
 are given contain the three terms of the syllogism ; one 
 of these will be common to the two propositions, and the 
 missing proposition will contain the other two terms. 
 Thus with the proposition, " S is M ; hence, S is P," 
 the missing premise is clearly " M is P," or " P is M." 
 With " M is P ; therefore, S is P," the missing premise 
 will contain S and M. 
 
 The danger of false reasoning is greater here than 
 in the complete syllogism, since the proposition which 
 is not expressed may be false or inadequate, and if the 
 
 151 
 
152 HYPOTHETICAL SYLLOGISMS 
 
 proposition is not definitely stated its inadequacy is 
 easily overlooked. 
 
 The Enthymeme is an incomplete form of syllogistic 
 reasoning ; it is less than a syllogism. There are several 
 complex forms in which we find more than a syllogism. 
 
 PROSYLLOGISM AND EPISYLLOGISM. Two complete 
 syllogisms may be united by having a proposition in 
 common. Thus : 
 
 r All the Romance languages are derived from 
 
 Prosyllogism J v Latl , n; . 
 
 rrench is a Romance language; 
 
 ^-Therefore, French is derived from Latin, 
 f This man speaks French; 
 
 Episyllogism J Therefore, this man speaks a language de- 
 { rived from Latin. 
 
 In this example the conclusion of the first syllogism 
 is the major premise of the second. This is known as 
 Prosyllogism and Episyllogism, the conclusion of the 
 Prosyllogism being the major premise of the Episyllo- 
 gism. One syllogism might, of course, establish the 
 minor premise of the other: 
 
 f French is a Romance language; 
 J This man speaks French. 
 1 ] Therefore, this man speaks a Romance larr- 
 [ guage. 
 f All the Romance languages are derived from 
 
 Episyllogism J rr Latin ; i . 
 
 I Hence, this man speaks a language derived 
 
 [ from Latin, 
 
 Again, it might have each of its premises established 
 by another syllogism: 
 
PROSYLLOGISM AND EPISYLLOGISM 153 
 
 Everything which is able to restrain trade 
 
 is a source of danger; 
 Prosyllogism ^ Every monopoly is able to restrain trade; 
 
 Hence, every monopoly is a source of 
 
 danger. 
 
 A company which has complete control of 
 
 a certain commodity is a monopoly; 
 
 Prosyllogism^ This trust has complete control of a cer- 
 tain commodity; 
 Hence, this trust is a monopoly. 
 Conclusion: Therefore, this trust is a 
 source of danger. 
 
 An enthymeme might take the place of the complete 
 syllogism in the case of either or both of the prosyllo- 
 gisms. Further, the premises of the prosyllogisms 
 might themselves be supported by other syllogisms. 
 
 A great many syllogisms may be combined into one 
 reasoning process, and most reasoning processes con- 
 tain several syllogisms, complete or abbreviated. 1 
 
 i Geometrical reasoning illustrates abbreviated reasoning very 
 clearly. For example take the proof of the proposition that " All 
 straight angles are equal." 
 
 A S B 
 
 D I F 
 
 "Let the angles ACB and DEF be any two straight angles. 
 To prove that the angle ACB equals the angle DEF. 
 
 " Place the angle ACB on the angle DEF, so that the vertex C 
 shall fall on the vertex E, and the side CB on the side EF. Then 
 CA will fall on ED. Therefore the angle ACB equals the angle 
 DEF." (Wentworth, Plane Geometry, page 14.) 
 
 This is the proof in an abbreviated form. It might be more 
 fully expressed as follows: (See page 154.) 
 
154 HYPOTHETICAL SYLLOGISMS 
 
 We might have a chain of syllogisms in which the 
 conclusion of each was the minor premise of the one 
 following. 
 
 All ungulates are mammals. 
 All mammals are warm-blooded. 
 All ungulates are warm-blooded. 
 
 All warm-blooded animals have lungs. 
 All ungulates are warm-blooded animals. 
 All ungulates have lungs. 
 
 All animals that have lungs require air. 
 All ungulates have lungs. 
 All ungulates require air. 
 
 " What is true of the angles ACB and DEF will be true of all 
 straight angles. 
 
 Two angles which can be so placed upon each other that 
 their vertices coincide and their sides coincide are 
 equal, each with the other. 
 
 ( Any figure may be moved from one place to another 
 ) without altering its shape. (Axiom of superposi- 
 j tion.) Therefore, the figure ACB may be placed 
 upon the figure DEF without altering its shape. 
 Straight angles are such as have their sides ex- 
 tending in opposite directions so as to be in 
 the same straight line. Th'e angles ACB and 
 DEF have their sides so extending. Hence 
 the lines AB and EF are straight lines. 
 
 Two straight lines which have two 
 points in common coincide and 
 and form but one line. 
 When the figure ACB is super- 
 posed on the figure DEF so that 
 the vertex C shall fall on the ver- 
 tex E, and the side CB on the 
 side EF, the straight line AB 
 falls on the straight line DF and 
 they coincide; the line CA falls 
 on the line ED, and coincides 
 with it, CB coincides with EF, 
 [And C coincides with E]. 
 
 |^ Therefore the angle ACB and the angle DEF are equal. 
 Therefore all straight angles are equal. 
 Geometrical reasoning is not all syllogistic in the narrowest 
 sense of the word. See chapter xvii. 
 
THE SORITES 155 
 
 THE SORITES. Now, instead of putting the conclu- 
 sion in words and repeating it in the succeeding propo- 
 sition, we may omit everything except the new premises 
 until we are ready to draw the final conclusion. Thus : 
 
 All ungulates are mammals. A is B 
 
 All mammals are warm-blooded. B is C 
 
 All warm-blooded animals have lungs. C is D 
 All animals that have lungs require air. D is E 
 Hence, All ungulates require air. A is E. 
 
 This is known as the Sorites; a Sorites may have any 
 number of members. There are two forms. That given 
 above, is an example of the Progressive or Aristotelian 
 Sorites. The premise containing the subject of the 
 conclusion (the Final Minor) comes first in order; that 
 containing its predicate (The Prime Major) comes 
 last; the intermediate propositions serve to connect the 
 two. In the Regressive or Goclenian Sorites, the Prime 
 Major comes first and the Final Minor last among the 
 premises. If expanded into a chain of prosyllogisms 
 and episyllogisms, the conclusion of each syllogism 
 would be the major premise of the one following. For 
 example : 
 
 A European is a Caucasian. B is A 
 A Frenchman is a European. C is B 
 A Parisian is a Frenchman. D is C 
 
 This author is a Parisian. E is D 
 
 Hence, This author is a Caucasian. E is A 
 
 In both forms of the sorites the reasoning is in the 
 first figure of the syllogism. With the exception of 
 the terms which are contained in the conclusion, every 
 term in the sorites is a middle term. The greatest 
 source of danger in this form of reasoning is to be 
 found in ambiguous terms. 
 
156 HYPOTHETICAL SYLLOGISMS 
 
 Only the Final Minor premise may be particular; 
 only the Prime Major may be negative. 
 
 Hypothetical Reasoning. The forms of reasoning 
 with which we have been dealing in the last three chap- 
 ters have employed only declarative sentences, or Cate- 
 gorical Propositions, as they are called in Logic. A 
 categorical proposition is an unconditional statement. 
 " A is B " or " A is not B " are typical forms. But 
 there are other kinds of propositions ; one of these is 
 the Hypothetical Proposition. A hypothetical prop- 
 osition is one containing a categorical proposition and 
 the statement of a condition on which the truth of the 
 categorical depends. The conditional member of the 
 proposition is .called the Antecedent; the categorical 
 member is called the Consequent. A hypothetical propo- 
 sition may be made the major premise of a syllogism. 
 
 Such a syllogism would be a HYPOTHETICAL SYLLO- 
 GISM. The Hypothetical syllogism has four forms. 
 
 1. If A is B, C is D. If the substance is carbon, it will 
 
 burn. 
 
 A is B It is carbon. 
 
 .*. C is D .'.It will burn. 
 
 2. If A is B, C is D. If the substance is carbon, it will 
 
 burn. 
 
 A is not B It is not carbon. 
 
 .*. C is not D .'.It will not burn. 
 
 3. If A is B, C is D. If the substance is carbon, it will 
 
 burn. 
 
 C is D It will burn. 
 
 .'.A is B .'.It is carbon. 
 
 4. If A is B, C is D. If the substance is carbon, it will 
 
 burn. 
 
 C is not D It will irot burn. 
 
 .'.A is not B .".It is not carbon. 
 
THE HYPOTHETICAL SYLLOGISM 157 
 
 The first of these affirms the antecedent, the second 
 denies it; the third affirms the consequent, and the 
 fourth denies it. The second and third are obviously 
 invalid. The fact that the substance is not carbon 
 gives us no further information about qualities ; and the 
 fact that it will burn does not insure its being carbon. 
 These instances are typical and illustrate the general 
 rule that Denying the antecedent or affirming the conse- 
 quent in a hypothetical syllogism are invalid forms of 
 reasoning. 2 
 
 We may have a hypothetical syllogism in which the 
 minor premise is also a hypothetical proposition. 
 
 If A is B, C is D. If he is nominated, he will be 
 
 elected. 
 
 If C is D, E is F. If he is elected, this measure 
 
 will not pass. 
 
 .'.If A is B, E is F. .'.If he is nominated, this meas- 
 ure will not pass. 
 
 Disjunctive Reasoning. There is a third kind of 
 so-called syllogism with still another sort of proposi- 
 tion as its major premise. This is the Disjunctive 
 Syllogism and its major premise is a Disjunctive Prop- 
 osition. A disjunctive proposition is one which states 
 an alternative. " A is either B or C " ; " It will either 
 rain or snow." The minor premise either affirms or 
 
 2 There are cases, however, in which these forms give true 
 conclusions. If the antecedent is the only one on which the con- 
 sequent would follow then all the forms of the hypothetical syllo- 
 gism would give valid conclusions. For example, if we had the 
 major premise, " If A is B, and in no other case, C will be D," 
 then to deny that A is B would necessitate the conclusion that C 
 is not D. We may take, as a concrete case, " If a triangle is 
 equilateral, and in no other circumstances, it will be equiangular. 
 This triangle is not equiangular; hence it is not equilateral"; or, 
 " This triangle is equilateral, therefore it is equiangular," and 
 so on. 
 
158 HYPOTHETICAL SYLLOGISMS 
 
 denies one of the alternatives. The conclusion either 
 denies or affirms the other. 
 
 A is either B or C It will either rain or snow. 
 
 A is B It will rain. 
 
 /.A is not C .'.It will not snow. 
 
 A is either B or C It will either rain or snow. 
 
 A is C It will snow. 
 
 /.A is not B .".It will not rain. 
 
 A is either B or C It will either rain or snow. 
 
 A is rrot B It will not rain. 
 
 .'.A is C /.It will snow. 
 
 A is either B or C It will either rain or snow. 
 
 A is not C It will not snow. 
 
 ,*.A is B /.It will rain. 
 
 All these forms are valid. The only source of danger 
 is in the major premise. If the alternatives are not 
 true alternatives, the conclusion can not be trusted. If 
 A can be anything else than B or C, or if it can be both 
 at the same time, the denial or affirmation of one alter- 
 native cannot assure us of the truth or falsity of the 
 others. 
 
 There are more -complex forms of disjunctive reason- 
 ing ; we might, for example, have the proposition, " A 
 is B or C or D, etc." In this case the affirmation of one 
 would mean the denial of the other two ; but the de- 
 nial of one would give as the conclusion a disjunctive 
 proposition containing the two others as alternatives. 
 Thus " A is not B ; A is either C or D, etc." Similarly 
 the assertion " A is B or C " would give the conclusion 
 " A is not D, etc.," and so on. 
 
THE DILEMMA 159 
 
 There are certain imperfect forms of this syllogism 
 which are sometimes useful. Sometimes we know that 
 A is B or C or, it may be, both. In such a case, if we 
 know that A is not B, then it must be C, but if we know 
 that it is B, we do not know that it is not also C. With 
 such a major premise, the minor premises which are 
 affirmative do not give valid -conclusions. It would be 
 simpler in such cases to state the three possibilities as 
 mutually exclusive, " A is B or C, or both B and C," and 
 proceed as in the perfect forms of the hypothetical 
 syllogism. 
 
 More Complex Forms. THE DILEMMA. There are 
 more complex forms of reasoning in which hypothetical 
 and disjunctive propositions are combined. Thus we 
 may have: 
 
 If A is B, C is D or E (or C is D or E is F). 
 A is B. .'. C is D or E (or C is D or E is F). 
 
 More concretely : 
 
 If he fails, he will leave college or drop back a class. 
 But he is sure to fail. 
 .". He will leave college or drop back a class. 
 
 If the antecedent were denied there could be no valid 
 conclusion ; in this and all other respects this syllogism 
 is like a simple hypothetical syllogism except in having 
 a disjunctive consequent, instead of a categorical one. 
 We get more complicated forms when the major pre- 
 mise consists of two hypothetical propositions, in which 
 either the antecedents or the consequents are found to 
 
160 HYPOTHETICAL SYLLOGISMS 
 
 be alternative: the minor premise is a disjunctive 
 proposition, and the resulting syllogism is a Di- 
 lemma. 
 
 If A is B, C is D; aiid if E is F, C is D. 
 But either A is B or E is F. 
 .'. C is D. 
 
 If a college education gives a student useful information, 
 it is valuable to him. 
 
 If it gives him mental training it is valuable to him. 
 
 But it either gives him useful information or mental 
 training. 
 
 .'.It is valuable to him. 
 
 This is a Simple Constructive Dilemma: simple be- 
 cause the consequents of the hypothetical propositions 
 in the major premise are the same in both cases; con- 
 structive because it establishes an affirmative conclu- 
 sion. 
 
 If the consequents were denied we should not have a 
 dilemma, but two simple hypothetical syllogisms. There 
 would be no disjunctive premise. 
 
 The second form of the dilemma is the Complex Con- 
 structive Dilemma. In this, the consequents of the 
 hypothetical propositions in the major premise are not 
 the same. 
 
 If A is B, C is D ; and if E is F, G is H. 
 But either A is B or E is F. 
 .'. Either C is D, or G is H. 
 
 " If a statesman who sees his former opinions to be 
 wrong does not alter his course he is guilty of deceit; and 
 if he does alter his course he is open to a charge of incon- 
 sistency; but either he does not alter his course or he does; 
 therefore, he is either guilty of deceit, or he is open to a 
 charge of inconsistency." (Jevons, Lessons in Logic, p. 
 168.) 
 
THE DILEMMA 161 
 
 Unlike the simple dilemma, this has a disjunctive 
 conclusion. 
 
 The Complex Destructive Dilemma has a negative 
 minor premise and a negative -conclusion, 
 
 If A is B, C is D; and if E is F, G is H. 
 But either C is not D or G is not H. 
 .". Either A is not B or E is not F. 
 
 "If this man were wise, he would not speak irreverently 
 of the Scripture in jest; and if he were good he would not 
 do so in earnest; but he does it either in jest or in earnest; 
 therefore, he is either not wise, or not good. (Whately, 
 Elements of Logic.) 
 
 If the minor premise were " Neither C is D nor G is 
 H " we should not have a dilemma. The minor premise 
 would not be disjunctive and we should have two simple 
 hypothetical syllogisms. 
 
 Asserting that one or the other of the antecedents 
 was false, or that one or the other of the consequents 
 was true would be fallacious, as in the case of the simple 
 hypothetical syllogism. 
 
 In practice it is very difficult to find true major 
 premises for a dilemma. Moreover, " a dilemma can 
 often be retorted by producing as cogent a dilemma to 
 a contrary effect. Thus an Athenian mother, accord- 
 ing to Aristotle, addressed her son in the following 
 words : " Do not enter into public business ; for if you 
 say what is just, men will hate you; and if you say 
 what is unjust, the gods will hate you." To which 
 Aristotle suggests the following retort : " I ought to 
 enter into public affairs ; for if I say what is just, the 
 gods will love me; and if I say what is unjust, men 
 will love me." (Jevons.) 
 
162 HYPOTHETICAL SYLLOGISMS 
 
 The conclusion of a dilemma, as of any other form 
 of reasoning, may serve as a premise for further rea- 
 soning. 
 
 Extra-syllogistic Reasoning. Certain other forms 
 of reasoning call for some discussion here. They are 
 not syllogistic, but they are closely related to syllo- 
 gistic reasoning. For example, " A is taller than B ; 
 B is taller than C ; therefore A is taller than C." This 
 is not a syllogism. There are five terms in the reason- 
 ing; A, B, C, taller than B, and taller than C. There 
 is a similar difficulty in this : " M is east of N ; N is 
 east of O, therefore M is east of O." It would, of 
 course, be possible to construct a syllogism which would 
 cover the ground in each of these -cases. Thus, " What- 
 ever is taller than another thing is taller than every- 
 thing which is shorter than that thing; A, B, and C 
 present a case, etc." And similarly in the other example. 
 Some such principles as these are implied, but the rea- 
 soning as stated is not in the form of a simple syllo- 
 gism. We have here a system of relations which is more 
 complicated than that found in the ordinary syllogism. 
 In the latter we need have only our premises and the 
 ordinary laws of reasoning, to assure our conclusion ; 
 in reasoning of the sort illustrated in these examples 
 we must have, besides our premises, a supply of in- 
 formation about the general system of things to which 
 the data in question belong. When such reasoning is 
 thrown into the syllogistic form the major premise 
 states the main principles of the system, as in the ex- 
 ample above. Sometimes our information about the sys- 
 tem would be sufficient to warrant a conclusion and 
 sometimes it would not; sometimes the fact that two 
 
EXTRA-SYLLOGISTIC REASONING 163 
 
 things are related to a third gives us information re- 
 garding their relations to each other and sometimes it 
 does not. From the statements that " A is the employer 
 or friend or enemy of B " and that " B is the em- 
 ployer or friend or enemy of C," we could not draw 
 any conclusion with regard to A's direct relations to 
 C. Things equal to the same thing are equal to each 
 other, but it is not necessarily true that things unequal 
 to the same thing will be unequal to each other. In 
 the latter case there are two possibilities ; the system 
 is not clearly enough defined to make certain any con- 
 clusion at all. This was true in some of the illustra- 
 tions given above. To decide in any given case we must 
 first determine whether the set of relations involved is 
 completely enough known to justify a conclusion; in 
 other words, Is more than one conclusion possible? 
 Sometimes the system may be very complex, but its parts 
 may be so related to each other and so -completely 
 known as to make a conclusion possible. A conclusion 
 may simply state the relation of the terms in a reverse 
 order. " A is east of B, therefore B is west of A." The' 
 conclusion may represent a pathway through a system 
 from one particular part to another ; while the premise 
 may be merely the same pathway followed from the 
 other end. If A is the son-in-law of the half-sister of 
 B's grandfather, then B is the grandson of the half- 
 brother of A's mother-in-law. The system might have 
 any degree of complication whatever, but if the several 
 relations could be read from either end the pathway 
 could jpe followed in either direction. Reasoning of 
 this sort might be regarded as a broader form of con- 
 sion. 3 
 See Aikins, Principles of Logic, chap. xi. 
 
164 HYPOTHETICAL SYLLOGISMS 
 
 EXERCISES. 
 
 1. Supply the missing proposition's in the following: 
 
 (1) He is a politician and therefore not to be 
 
 trusted. 
 
 (2) They were all brave men and this man was one 
 
 of them. 
 
 (3) Whales have warm blood but fish do not. 
 
 (4) Only members will be admitted; that excludes 
 
 you. 
 
 2. Determine which of the following give valid conclu- 
 sions and which do not; point out the fallacies involved: 
 
 (1) If he goes, I shall remain; but he will not go. 
 
 (2) If he goes, I shall remain; and I shall remain. 
 
 main. 
 
 (3) I shall remain if he goes; and he will go. 
 
 (4) If it rains to-morrow, the game will be post- 
 
 poned; the game will be postponed. 
 
 (5) If all the sides of this triangle are equal its 
 
 angles are equal too; now its angles are not 
 equal. 
 
 (6) If he fails it will be because he has not worked 
 
 hard ; and he has not worked hard. 
 
 3. Criticise the following, stating the form of reasoning 
 in each case: 
 
 (1) A great man must either have extraordinary 
 
 natural ability or exceptional capacity for 
 work; this man had extraordinary natural 
 ability, hence we may assume that his capacity 
 or work was rrot unusual. 
 
 (2) If the government enacts such a law it must 
 
 either adopt socialism or go into bankruptcy; 
 but it will not enact such a law; so there is iro 
 danger of either socialism or bankruptcy. 
 (Hyslop.) 
 
 (3) If capital punishment involves cruelty to its 
 
 victims it ought to be abolished in favor of 
 some other permlty; if it does no good for so- 
 ciety it should also be abolished. But either 
 it involves cruelty to its victims or it does no 
 
EXERCISES 165 
 
 good to society, and hence it ought to be abol- 
 ished. (Hyslop.) 
 
 (4) If he sinks he will be drowned, and if he swims 
 
 he will be captured by the enemy; but he must 
 either sink or swim; therefore, he will either 
 be drowned or captured by the enemy. 
 
 (5) If he tells the truth he will be forgiven, and 
 
 if he does not he will escape detection; but 
 either he will be forgiven or he will escape 
 detection; hence he will either tell the truth 
 or he will not. 
 
 (6) If he did that intentionally he is not wise, and 
 
 if he did it unintentionally he is not lucky; 
 but he is neither wise nor lucky; therefore, he 
 did it neither intentionally nor unintention- 
 ally. 
 4. In a sorites why must all the premises except the 
 
 prime major be affirmative and all except the final minor 
 
 be universal? 
 
CHAPTER XI 
 
 I. PROOF AND DISPROOF. II. FAILURE TO 
 PROVE 
 
 I. Various Kinds of Proof. The conclusion of a 
 valid syllogism is proved; and so also is the conclusion 
 of each of the other forms of reasoning which we have 
 examined. A proposition is proved when it is shown 
 to be the necessary consequence of any combination of 
 admitted propositions. All the cases which we have so 
 .far examined are instances of direct proof. In direct 
 proof we show that, granted certain things, the con- 
 clusion necessarily follows. A conclusion is proved only 
 when it is shown that the conclusion must be true. 
 
 There are several other kinds of proof ; in this chap- 
 ter we shall consider the other kinds, and also the va- 
 rious forms of failure to prove, or fallacy. 
 
 INDIRECT PROOF. The first to be considered is 
 indirect proof ; we prove a proposition indirectly by dis- 
 proving its contradictory, i. e., by showing that its con- 
 tradictory cannot be true. 
 
 To disprove a proposition it is necessary to find some 
 ^admitted fact or truth which is inconsistent with it. 
 Tor instance, if we can show that the contrary or con- 
 tradictory of a proposition is true, the proposition 
 must be false. More concretely, if we have an A propo- 
 sition, the contradictory would be an O proposition ; if 
 we can show that O is true, A is necessarily false, and 
 to show the truth of O we need find only one real ex' 
 
 166 
 
INDIRECT PROOF 167 
 
 ception to A. Showing the truth of E would also dis- 
 prove A; but E is a universal proposition, and it is 
 obviously much more difficult, in ordinary circum- 
 stances, to prove a universal than it is to prove a par- 
 ticular. Similarly the truth of I or of A would mean 
 the falsity of E, etc. 
 
 In indirect proof, we disprove the contradictory, not 
 the contrary, for the" falsity of the contrary does not 
 prove the truth of the proposition, since both contraries 
 may be false ; but if the contradictory is false, the prop- 
 osition must be true, for one of two contradictories 
 must be true. Suppose then that we wish to prove 
 an A proposition : if we can show, in any way, that the 
 corresponding O proposition would be false or absurd 
 contrary to fact or reason our thesis is proved. 
 
 The contradictory is usually disproved by show- 
 ing that some of its necessary consequences are ab- 
 surd. 
 
 Indirect proof is frequently employed in geometry 
 and it is there that the best examples of it are to be 
 found. It is also a frequent resource in political de- 
 bate, but in that field the facts are so complicated and 
 the matter of establishing any proposition so liable to 
 error chat the grounds of any conclusion established 
 in this way must be very carefully examined. 
 
 We shall consider briefly two other special forms of 
 proof, which are perhaps reducible to direct proof, but 
 they are apparently very different from what we find 
 in the syllogism and they will therefore be considered 
 separately. The first is found in geometrical reasoning. 
 
 PROOF IN GEOMETRY. In geometrical proof we seem 
 
168 PROOF AND DISPROOF 
 
 to be founding a universal conclusion upon a single 
 case ; how is it possible for us to have perfect confidence 
 in a conclusion which seems at first sight to be an in- 
 duction from one isolated figure? If the individual 
 peculiarities of the figure had anything to do with sup- 
 porting the conclusion the latter would of course be 
 of very slight value ; we should have no assurance that 
 the next example might not be inconsistent with the 
 conclusion. The certainty of the conclusion rests upon 
 the fact that the figure used in the demonstration is, in 
 all essential respects, like every other figure to which 
 the proof is supposed to apply. The figure employed 
 is purely symbolical ; it stands for certain universal re- 
 lations. If the truth of the conclusion follows from 
 the characteristics which the present figure has in com- 
 mon with all others of the class, then it will be true for 
 all such figures, and the peculiar characteristics will 
 have nothing to do with the case. The major premise 
 underlying demonstration by means of figures is this: 
 " The present figure is an adequate representative of 
 all figures to which the present proof applies." 
 
 The second special form of proof which we shall 
 examine is found in what is known as mathematical in- 
 duction. 
 
 PROOF BY MATHEMATICAL INDUCTION. The follow- 
 ing illustration is a typical example of reasoning of the 
 sort just mentioned. " If we take the first two consecu- 
 tive odd numbers, 1 and 3, and add them together the 
 sum is 4, or exactly twice two; if we take three such 
 numbers, 1 + 3 + 5, the sum is 9, or exactly three times 
 three; if we take four, namely 1 + 3 + 5 + 7, the sum is 
 
MATHEMATICAL INDUCTION 169 
 
 16, or exactly four times jour; or generally, if we take 
 any number of the series, l + 3 + 5' + 7 + ...., the sum 
 is equal to the number of terms multiplied by itself. 
 Any one who knows a little algebra can prove that this 
 remarkable law is universally true, as follows : Let n be 
 the number of terms, and assume for the moment that 
 this law is true up to n terms, thus: 
 
 1+3+5+7+ ____ +(2n-I)=n 2 
 
 Now add 2ft + 1 to each side of the equation. It fol- 
 lows that: 
 
 1+3+5+T+ ____ 
 
 But the last quantity, 7& 2 + 2n + l, is just equal to 
 (n + 1) 2 ; so that if the law is true for n terms it is true 
 also for n + 1 terms. We are enabled to argue from 
 each single case of the law to the next case ; but we 
 have already shown that it is true of the first few cases, 
 therefore it must be true of all." L If what is true of 
 any case is true of the one following it, it will be true of 
 all cases whatsoever. It sometimes happens that some- 
 thing is true of a great many successive cases without 
 being really general. To quote again from Jevons: 
 " It was at one time believed that if any integral num- 
 ber were multiplied by itself, added to itself, and then 
 added to 41, the result would be a prime number, that 
 is, a number which could not be divided by any other 
 integral number except unity ; in symbols, x 2 + x + 41 
 = prime number. This was believed solely on the 
 ground of trial and experience, and it certainly holds 
 l Jevons, Lessons in Logic, pp. 220-221. 
 
170 PROOF AND DISPROOF 
 
 for a great many values of x . . . . No reason, how- 
 ever, could be given why it should always be true. . . . 
 it fails when x = 40."' " We can perceive no simi- 
 larity between all prime numbers which assures that be- 
 cause one is represented by a certain formula, also 
 another is ; but we do find such similarity between the 
 sums of odd numbers." 
 
 Here, as elsewhere, if one or a few cases are adequate 
 representatives of a whole class of cases, what is true 
 of the present case or cases will be true of all, and a 
 universal conclusion can be drawn from a single -case. 
 The great difficulty in ordinary inductions is to be sure 
 that the given case is an adequate representative. Or- 
 dinarily the facts are very complex and the inspection 
 of a single case is not sufficient to show us the charac- 
 teristics which an adequate representative of the class 
 should possess. In other words, we do not know what 
 circumstances are relevant. In selecting cases for the 
 application of the several inductive methods, the selec- 
 tion is for the purpose of enabling us to determine what 
 circumstances are relevant. 
 
 II. Failure to Prove: Fallacies. Let us examine 
 the various ways in which proof may be vitiated, the 
 various fallacies to which reasoning is liable. Some 
 of these have been discussed already, but they will be 
 mentioned again here and the other fallacies not pre- 
 viously noted will be examined. 
 
 FALLACIES OF LANGUAGE. In the first place we may 
 mistake the meaning of the premises owing to the fact 
 that we have not understood the language in which they 
 are expressed. The Fallacies of Amphiboly, Accent, 
 Figure of Speech (see chapter v), are cases in point. 
 
FALLACIES 171 
 
 Again, to mistake the general for the specific use o 
 a term,, or the concrete for the abstract, or to use a, 
 term in one sense in one part of the reasoning and ini 
 another sense in another part, would render the con- 
 clusion unsound; the Fallacy of Accident must he- 
 guarded against. (See page 55.) 
 
 Once more, we may mistake the collective for the dis-- 
 tributive use of a term or vice versa, or we may use a. 
 term in one of these senses in one part of the reasoning; 
 and in the other sense .in another part ; this would in- 
 volve us in a Fallacy of Composition or of Division., 
 (See page 57.) 
 
 FALLACIES OF ASSUMPTION. Again, if we use as a. 
 premise in our reasoning a proposition which is not 
 established, such as an insufficiently verified inductive 
 inference, our conclusion is not proved. It may be true, 
 or it may not be, but a conclusion is not proved so long 
 as there is a possibility that it may be false. When we 
 use a proposition of this sort to support a conclusion 
 we are said to commit the Fallacy of Begging the Ques- 
 tion, or, to use the scholastic term, Petitio Principii. It 
 is frequent in cases in which one has a thesis to prove 
 and he sees that a certain proposition will enable him to; 
 prove it (it may be either premise in a syllogism or 
 both). He therefore assumes the truth of this proposi- 
 tion on insufficient grounds, sometimes on very slight 
 grounds. 
 
 To decline to admit a premise because we see that it 
 necessitates an unwelcome conclusion is to commit this 
 fallacy. 
 
 A false categorical proposition, an incorrect hypo- 
 thetical proposition, or a disjunctive proposition in 
 
172 PROOF AND DISPROOF 
 
 which the disjunction is not complete, would also, if 
 used as premises, be illustrations of this fallacy. It is 
 not even necessary to use a complete proposition to 
 commit this- fallacy ; the use of a name or an epithet 
 may lead to fallacious conclusions ; the name or epithet 
 does, to be sure, imply a proposition. To argue that 
 this criminal should be punished, because all criminals 
 are a menace to society, begs the question if it has not 
 been shown that this man is a criminal. The epithet is 
 sometimes more dangerous than the implied proposition 
 would be, for we are less likely to notice that something 
 has been assumed when the Droposition is only sug- 
 gested. 
 
 One form of the Petitio Principii is Arguing in a 
 Circle, or Circulus in Probando. In this, the premise is 
 simply the desired conclusion stated in other words. To 
 say that man is a conscious being because he has mental 
 states, is to argue in a circle, since to be a conscious 
 being is to have mental states. When the argument 
 is short there is little to be feared from this fallacy ; 
 the identity in meaning of the two statements is easily 
 discovered if they come close together ; but in a long 
 argument the first may be only vaguely remembered by 
 the time the second is made, and if the reasoning has 
 not hitherto been questioned the fallacy may escape 
 detection. A language like English, which is very rich 
 in synonyms, offers very many occasions for this fal- 
 lacy. 
 
 Another closely related fallacy is that known as the 
 Fallacy of Many Questions or sometimes Double Ques- 
 tion. One of the traditional illustrations is, " Have 
 you left off beating your wife? " Whichever answer is 
 
FALLACIES 173 
 
 given, Yes or No, seems to admit the truth of the im- 
 plication. In this fallacy, the question assumes the 
 truth of something which is not proved or admitted, and 
 which may be false. It demands a direct answer, and 
 no direct answer can be given without an apparent ad- 
 mission of the thing assumed. 
 
 FORMAL, FALLACIES. There are several fallacies 
 which result from the violation of the principles of 
 syllogistic reasoning. These are usually called the 
 Formal Fallacies, because they are said to result from 
 violating the formal laws of the syllogism, the laws re- 
 lating to the number of terms and the distribution of 
 terms in the syllogism. We might include also, Fal- 
 lacies of Illicit Conversion and Obversion. Creighton 
 includes them in Fallacies of Interpretation. 2 Using 
 four terms instead of three gives the Fallacy of Four 
 Terms. Distributing the major term in the conclusion 
 when it has not been distributed in the premise gives 
 the Fallacy of Illicit Distribution of the Major Term, 
 and distributing the minor term in the -conclusion when 
 it was not distributed in the premise gives the cor- 
 responding Fallacy of the Minor Term. Failing to 
 distribute the middle term gives the Fallacy of Undis- 
 tributed Middle. There are also the Fallacies of Two 
 Negative Premises, and Two Particular Premises. 
 
 This is the way in which violations of the laws of 
 syllogistic reasoning have usually been classified. As 
 we have already seen, these violations can also be dealt 
 with as failures to comply with the principles of the 
 Four Figures. The latter method is less formal and 
 more in accordance with our ordinary habits of thought. 
 2 See his Logic, chapter xii. 
 
174 PROOF AND DISPROOF 
 
 The Fallacies of Hypothetical Reasoning, Denying 
 the Antecedent and Affirming the Consequent, belong 
 in the class just discussed. 
 
 THE CONCLUSION MAY NOT FOLLOW FROM THE 
 PREMISES. There is a form of false reasoning known 
 as the Non Sequitur. In this the premises may be clear 
 and true and there may be no fallacies of distribution 
 or of negative premises, but the conclusion does not 
 follow from the premises. It may be true enough and 
 provable on other grounds but it does not belong to the 
 propositions on which it has been based. It was origi- 
 nally called the Fallacy of False Consequent and had to 
 do with hypothetical reasoning, but the term Non 
 Sequitur is now applied to categorical reasoning in 
 which the conclusion does not follow from the premises. 
 De Morgan's illustration (quoted by Hyslop) is as fol- 
 lows: 
 
 Episcopacy is of Scripture origin. 
 
 The Church of England is the only Episcopal Church 
 in England. 
 
 Therefore, the church established is the church that 
 should be supported. 
 
 This fallacy, like the rest, is more likely to pass un- 
 noticed in a long argument than in a short one. 
 
 A similar fallacy, sometimes treated as a form of the 
 last, is that of False Cause, or Non Causa pro Causa, 
 or Post Hoc ergo Propter Hoc. This consists in argu- 
 ing that because one thing has followed another, it is 
 therefore the effect of that other, as if one should argue 
 that because a panic followed the adoption of a certain 
 measure, it was therefore caused by that measure. 
 
 MISSING THE POINT. One more fallacy is to be 
 
FALLACIES 
 
 noted ; that in which the argument is not to the point. 
 The reasoning may with entire correctness prove some- 
 thing but it is not the thing which was to be proved. 
 An opponent is sometimes charged with shifting the 
 ground of debate ; that means usually that he is no 
 longer trying to prove the thesis with which he started 
 but something else more or less closely related to it. 
 This is known as the Fallacy of Ignoratio Elenchi. 
 Several forms have been distinguished. One of these is 
 the Ad Hominem argument; in this, instead of being 
 to the point, the argument is directed against the char- 
 acter or consistency, etc., of the opponent or some 
 other person. When an advocate proves the prisoner's 
 good character and assumes that he has proved his in- 
 nocence of the crime with which he is charged, he is 
 guilty of this fallacy. When a debater attacks his op- 
 ponent instead of proving his thesis he commits this 
 fallacy. It is a method of silencing an opponent but 
 not of proving a case. Appeals to authority, to pre- 
 judice, to emotion, are all forms of the fallacy of 
 Ignoratio Elenchi, as is also the argument in which the 
 victory depends upon the fact that the opponent has 
 not the information necessary to enable him to meet 
 the argument. 
 
 When w r e assume that a proposition is false because 
 the arguments in its support have been discredited, we 
 commit this fallacy. The proposition is only not 
 proved, instead of being disproved. A good cause may 
 suffer from bad arguments because of the widespread 
 tendency to commit this fallacy. 
 
 In most arguments many of the propositions involved 
 are unexpressed. In such cases it is often difficult to 
 know what fallacy to charge against reasoning which 
 
176 PROOF AND DISPROOF 
 
 is obviously unsound. Suppose we have the argument, 
 " A classical course is useless because it trains for no 
 profession;" what fallacies might be charged? In the 
 first place we might say that the fallacy was a Non 
 Sequitur; the conclusion does not follow from the 
 grounds which have been stated. It might be replied 
 that there was a further premise understood, namely, 
 " Every college course which does not train for a pro- 
 fession is useless." The fallacy of Non Sequitur would 
 be disposed of, but it would now be possible to charge 
 the fallacy of Begging the Question, in the premise 
 which has been supplied. Or it might be that the pre- 
 mise understood was " Most courses of study which do 
 not train for a profession are useless." That might 
 possibly be true, but even admitting it, the reasoning is 
 not valid, because it violates the principles of syllogistic 
 reasoning. 
 
 In cases of doubt the only way of being certain that 
 we have been fair to an absent opponent or have met 
 all replies to our criticisms, is to follow some such pro- 
 cedure as that just illustrated and show that if one 
 criticism can be met another cannot, or that, if the con- 
 clusion is to be established, such and such propositions 
 must be shown to be true. 
 
 These fallacies are usually discussed in connection 
 with the syllogism, but they may occur in the more com- 
 plicated forms of reasoning as well. As we have 
 already seen, the syllogism is the typical form of de- 
 ductive reasoning, but there is much reasoning that is 
 extra-syllogistic: although this might perhaps be put 
 into syllogistic form such an operation is unnecessary 
 if the premises and the steps in the argument are clear. 
 
FALLACIES 177 
 
 In more complicated trains of reasoning which involve 
 induction as well as deduction we must make sure not 
 only of the reasoning processes, and of the clear state- 
 ment of the premises, but also of the soundness of the 
 premises, and of the grounds on which they are based. 
 
 EXERCISES 
 
 In the following exercises,, supply missing premises, state 
 the Figure in which the argument falls, and criticise fully 
 the reasoning, noting the fallacies of every sort: 
 
 1. Personal deformity is an affliction of nature; dis- 
 grace is not an affliction of nature; personal deformity is 
 not a disgrace. 
 
 2. All paper is useful, and all that is useful is a source 
 of comfort to man ; therefore, all paper is a source of com- 
 fort to man. 
 
 3. If Caesar were a tyrant, he deserved to die; but he 
 was not a tyrant, and therefore did not deserve to die. 
 
 4. Every one desires his own good; justice and temper- 
 ance are everyone's good; hence, every one desires justice 
 and temperance. 
 
 5. Some of the inhabitants of the earth are more civi- 
 lized than others; no savages are more civilized than other 
 races; therefore, no savages are inhabitants of the earth. 
 
 6. He must be a Mohammedan, for all Mohammedans 
 hold these opinions. 
 
 7. He must be a Christian, for only Christians hold these 
 opinions. 
 
 8. All valid syllogisms have three terms; this syllogism 
 has three terms, and is therefore valid. 
 
 9. None but despots possess absolute power; the Czar 
 of Russia is a despot; therefore, he possesses absolute 
 power. 
 
 10. The right should be enforced by law; the exercise of 
 the suffrage is a right, and should therefore be enforced 
 by law. 
 
 11. Nothing is better than wisdom; dry bread is better 
 than nothing; therefore, dry bread is better than wisdom. 
 
 12. Every rule has exceptions; this is a rule and there- 
 
178 PROOF AND DISPROOF 
 
 fore has exceptions; therefore, there are some rules that 
 have no exceptions. 
 
 13. For those who are bent on cultivating their minds 
 by diligent study, the incitement of academical honors is 
 unnecessary; and it is ineffectual for the idle and such as 
 are indifferent to mental improvement; therefore, the in- 
 citement of academical honors is either unnecessary or 
 ineffectual. 
 
 14. Suicide is not always to be condemned, for it is but 
 voluntary death, and this has been gladly embraced by 
 many of the greatest heroes of antiquity. 
 
 15. Theft is a crime; theft was encouraged by the laws 
 of Sparta; therefore, the laws of Sparta encouraged crime. 
 
 16. Nothing but the express train carries the mail, and 
 as the last train was an express, it must have carried the 
 mail. 
 
 17- Protective laws should be abolished, for they are in- 
 jurious if they produce scarcity and useless if they do not. 
 
 18. Whosoever intentionally kills another should suffer 
 death ; a soldier, therefore who kills his enemy should suf- 
 fer death. 
 
 1Q. The people of the country are suffering from famine; 
 and as A, B, and C are people of the country, they are 
 therefore suffering from famine. 3 
 
 20. Each of the books in the library is large; hence the 
 library is large. 
 
 21. Hunger is a sign of health; therefore, famine which 
 causes hunger is a good thing. 
 
 22. Arsenic will kill a man ; hence, this medicine will kill 
 you as it contains arsenic. 
 
 23. The coat, hat and dress were each in* good taste; 
 therefore, the costume as a whole was in good taste. 
 
 24. You can always trust to the majority to do what is 
 right in the long run; this man is a member of the ma- 
 jority, and therefore he can be trusted to do what is right 
 in the long run. 
 
 25. Eating opium degrades and brutalizes a man; hence 
 
 3 Most of the examples from 1 to 19 were borrowed from Hys- 
 lop's Elements of Logic. A good many of them belong to the 
 common stock. 
 
EXERCISES 179 
 
 DeQuincy and Coleridge were low and degraded crea- 
 tures. 
 
 26. It is wrong to take life of fellow creatures; hence 
 it is wrong to kill a mad dog. 
 
 27. Human life will at some time disappear from the 
 earth, for every man must die. 
 
 28. America is a Christian country; hence, every Ameri- 
 can is a Christian. 
 
 29- The members of the college are students, teachers, 
 and administrative officers. The members of the football 
 team are members of the college, and hence are students, 
 teachers, and administrative officers. 
 
 30. If it is admitted that men who are proficient in 
 engraving are of great service to a community, it must be 
 true that the greater the degree of excellence possessed by 
 the counterfeiter, the better for the government. 
 
 31. You must allow that this measure will do untold 
 good to the country that the whole community will prosper 
 and that our nation will take its place with the foremost. 
 You say you grant all this and still you maintain that it will 
 ruin your particular section. Is not your section a part of 
 the nation, and will it not be benefited as well as the rest 
 of the country? 
 
 32. The population of the United States increased 20% 
 between 1890 and 1900; hence, the population of Vermont 
 must have increased at that rate during the same period. 
 
 33. Slavery was harmful to the development of the 
 whole country, and hence to the South. 
 
 34. Policemen must arrest all persons who block the 
 highways or interfere with traffic. The policeman at this 
 crowded corner does this, and should therefore be arrested. 
 
 35. Kant held that all the proofs for the existence of 
 God were fallacious. He was therefore an atheist. 
 
 36. At the time of the Galveston flood men worked six- 
 teen hours a day; hence, to talk of an eight-hour day as a 
 necessity for the working classes is absurd. 
 
 37. The evidence of the creator is the thing created. 
 
 38. Before you stands the vile wretch who has been 
 accused of murder. 
 
 39. Why has man one more rib than woman? 
 
180 PROOF AND DISPROOF 
 
 40. The candidate is very fond of children., and so no 
 doubt she would be a good kindergarten teacher. 
 
 41. This man's arguments are worthless, for he is no" 
 toriously dishonest. 
 
 42. In answer to the argument that women, as intelli- 
 gent human beings, are entitled to all the privileges of 
 citizenship, I ask you: Are not women like our sainted 
 mothers, who never held a ballot in their hands, good enough 
 for us? 
 
 43. " Woman as well as man should have a part in the 
 world's political affairs; for government is nothing but 
 national housekeeping." 
 
 44. " More coffee is consumed in the United States than 
 anywhere else, and America has become the strongest 
 nation." 
 
 45. My opponent presents a formidable array of sta- 
 tistics to prove that the country is financially unfit for war; 
 to which I am proud to reply that the old flag has never yet 
 touched the ground. 
 
 46. Agassiz did not accept the theory of Evolution; 
 hence I, who know very little of biology, am not justified 
 in accepting it. 
 
 47. This man was a good football player, and hence will 
 be a good man to write up the present football situation. 
 
 48. A vacuum is impossible, for if there is nothing be- 
 tween two bodies they must be in contact. 
 
 49. The government should be in the hands of the Demo- 
 cratic party, for the country could not help prospering un- 
 der the supervision of the followers of Jefferson. 
 
 50. It is indeed an opinion strangely prevailing amongst 
 men, that houses, mountains, rivers, and in a word all sen- 
 sible objects, have an existence, natural or real, distinct 
 from their being perceived by the understanding. But 
 with how great an assurance and acquiescence soever this 
 principle be entertained in the world, yet whoever shall find 
 it in his heart to call it in question may, if I mistake not, 
 perceive it to involve a manifest contradiction. For, what 
 are the fore-mentioned objects but the things we perceire 
 by sense? and what do we perceive besides our own ideas 
 or sensations ? and is it not plainly repugnant that any one 
 of these^ or any combination of them, should exist unper- 
 
EXERCISES 181 
 
 ceived? Berkeley, Principles of Human Knowledge, 
 Sec. 4. 
 
 51. If there were external bodies it is impossible we 
 should ever come to know it; and if there were not we 
 might have the very same reasons to think there were that 
 we have now. Suppose what no one can deny possible 
 an intelligence without the help of external bodies, to be 
 affected with the same train of sensation or ideas that you 
 are, imprinted in the same order arrd with like vividness 
 in his mind. I ask whether that intelligence hath not all 
 the reason to believe in the existence of corporeal sub- 
 stances, represented by his ideas and exciting them in his 
 mind, that you can possibly have for believing the same 
 thing? Berkeley, Principles of Human Knowledge, 
 Sec. 20. 
 
 52. In the business of gravitation or mutual attraction, 
 because it appears in many instances, some are straightway 
 for pronouncing it universal; and that it attract and be 
 attracted by every other body is an essential quality inher- 
 ent in all bodies whatsoever. Whereas, it is evident that 
 the fixed stars have no such tendency towards each other; 
 and so far is that gravitation from being essential to bodies 
 that in some instances a quite contrary principle seems to 
 show itself; as in the perpendicular growth of plants in 
 the elasticity of the air. Berkeley, Principles of Human 
 Knowledge, Sec. 106. 
 
 53. " The family, the state, religion and morality are 
 all in danger in this country on account of divorces, accord- 
 ing to the speakers at an Episcopal meeting in New York 
 on Sunday. But are things in so bad a way? " In Eng- 
 land, " so ' horrible ' were the revelations of angry discon- 
 tent with the married state made by hundreds of the cor- 
 respondents of a London paper, that it was compelled 
 recently to bring a discussion of the marriage question to 
 an abrupt end." 
 
 54. In arguing against the Darwinian Hypothesis, 
 Agassiz is said to have urged the following: " If species 
 do not exist, how can they vary ? " 
 
 55. Vegetarianism is a healthy diet, for all vegetarians 
 find it so. 
 
 56. No educated, much less a scientific person, who is 
 
182 PROOF AND DISPROOF 
 
 convinced of the immutable order of things, can now- 
 adays believe in miracles. Buchner, Force and Matter. 
 
 57. Either the laws of nature govern, or the eternal 
 reason governs; if both govern together they must be in 
 continual conflict; the government of the latter would 
 render that of the former unnecessary, whilst the action of 
 unalterable laws admits of no personal interference, and 
 can on that account scarcely be called governing. A main 
 point in the proof that the laws of nature are those of 
 reason is, that by thought we are able to deduce other laws 
 of nature from those known to us, so that we find them in 
 experience, and if this does not happen, we naturally con- 
 clude that we have formed erroneous conclusions. Buch- 
 ner, Force and Matter. 
 
 58. In all parts of knowledge, rightly so termed, things 
 most general are most strong; thus it must be, inasmuch 
 as the certainty of our persuasion touching particulars de- 
 pendeth altogether upon the credit of those generalities 
 out of which they grow. Hooker, Ecclesiastical Polity, 
 i, 12. 
 
 59. A spirit independent of nature cannot exist; for 
 never has an unprejudiced mind, cultivated by science, per- 
 ceived its manifestations. . . . How is it possible that 
 the unalterable order in which things move should ever be 
 disturbed without producing an irremediable gap in the 
 world, without delivering us and everything up to an arbi- 
 trary power, without reducing all science and every earthly 
 endeavor to a vain and childish effort? Buchner, Force 
 and Matter. 
 
 60. Order and progress are two incompatible elements. 
 Progress is accompanied by disorder, by anarchy. For 
 what is progress if not precisely the overturning of a given 
 social order so as to institute a new one? Draghicesco, 
 Le probleme de la conscience. 
 
 61. Sunshine is necessary for plants; for vegetable or- 
 ganisms can not increase in size, sending roots into the soil 
 and stems into the air, without the light and heat of the 
 great solar luminary. 
 
 62. Nothing is so bad that it cannot be worse. 
 
 63. " The canals are not so maintained. They are fall- 
 ing into decay and disuse. The old boats are rotting and 
 
EXERCISES 183 
 
 few new boats are built. The business of the canals falls 
 off, and the city of New York, which thirty years ago had 
 75 per cent, of the foreign trade of the country, now lias 
 less than 50 per cent." 
 
 64. " Philosophy bakes no bread." Then why waste 
 time upon it? 
 
 65. Men have a right to vote. Then where is the justice 
 of depriving criminals of this right ? 
 
 66. Two and three are even and odd; two and three are 
 five; hence five is even and odd. 
 
 67. To inflict capital punishment is to violate one of the 
 commandments in the Decalogue. 
 
 68. " The French drink more wine than any other nation 
 and in literature and art they occupy a foremost place." 
 
 69. "... it deals with the question exactly when the 
 monstrous tariff is to be tenderly revised by its friends. 
 The answer is ' Never/ The thing cannot be done in pros- 
 perous times, because it would disturb business. In a 
 period of depression, it is out of the question, as we then 
 have troubles enough without opening Pandora's box. When 
 affairs are just betwixt and between, neither very good nor 
 very bad, no sagacious Republican would think of meddling 
 with the tariff. Therefore, we say the exact position of the 
 Republicans is, that an unj ust tariff is crying out for urgent 
 revision, that they are the only ones who can do the work, 
 and that they will do it just one day after never." 
 
 70. " The justice complains bitterly that the court has 
 been obliged to resort to subterfuges in order to employ 
 competent process-servers, the eligible lists providing only 
 worn-out soldiers who lack the essentials of youth, deter- 
 mination, agility and vigor. He is therefore in favor of 
 going back to the discredited system of ' pass examina- 
 tions ' or of re-enacting the starchless civil service law." 
 
 71. In the domain of physics, to the exploration of 
 which Lord Kelvin has devoted an honored lifetime, he 
 would be a bold man who would cross swords with him. 
 But for dogmatic utterance on biological questions there is 
 no reason to suppose that he is better equipped than any 
 person of average intelligence ... in the latter (organic 
 nature) scientific thought is * compelled to accept the idea 
 of creative power.' That transcends the possibilities of 
 
184 PROOF AND DISPROOF 
 
 scientific investigation . . . Lord Kelvin, in effect, wipes 
 out by a stroke of the pen the whole position won* for us 
 by Darwin. And in so doing, it can hardly be denied that 
 his present position is inconsistent with the principle laid 
 down in: his British Association address at Edinburgh in 
 1871. Extracts from letters written to the London Times 
 apropos of Lord Kelvin's assertion regarding the limits of 
 science. (Reprinted in Science.) 
 
 72. The fact is so improbable that extremely good 
 evidence is needed to make us believe it; and this evidence 
 is not good, for how can you trust people who believe in 
 such absurdities? 
 
 73. The axioms of mathematics and the fundamental 
 moral principles are inborn ; for they are accepted by every- 
 body. Moreover no reasonable being can deny them when 
 he understands what they mean. 
 
 74. I may doubt everything except that I think. I 
 think, therefore I exist. 
 
 75. A parliamentary government is sure to fail in the 
 long run ; a battle may be won by a poor general but never 
 by a debating society. 
 
 76. Can anything be more ludicrous than first to build 
 all our certainty of the assistance of the Holy Ghost upon 
 the certainty of tradition and then afterwards to make the 
 certainty of tradition to rely upon the assistance of the 
 Holy Ghost. Tillotson, Rules of Faith. 
 
 77. If men are not likely to be influenced in the per- 
 formance of a known duty by taking an oath to perform 
 it, the oaths commonly administered are superfluous; if 
 they are likely to be so influenced, every one should be 
 made to take an oath to behave rightly throughout his life; 
 but one or the other of these must be the case; therefore 
 either the oaths commonly administered are superfluous 
 or every man should be made to take an oath to behave 
 rightly throughout his life. 4 . 
 
 78. Few treatises of science convey important truths, 
 without any intermixture of error, irr a perspicuous and in- 
 teresting form; and therefore, though a treatise would 
 deserve much attention which should possess such excellence, 
 
 * The exercises from 77 to 90 are from WhatelyV Clements of 
 Logic, 
 
EXERCISES iss 
 
 it is plain that few treatises of science do deserve much 
 attention. 
 
 79- No one who lives with another on terms of con- 
 fidence is justified, on any pretense, in killing him; Brutus 
 lived on terms of confidence with Caesar; therefore, he was 
 not justified, on the pretense he pleaded, in killing him. 
 
 80. He that destroys a man who usurps despotic power 
 in a free country deserves well of his countrymen; Brutus 
 destroyed Caesar, who usurped despotic power in Rome; 
 therefore, he deserved well of the Romans. 
 
 81. Nothing which is of less frequent occurrence than 
 the falsity of testimony can be fairly established by testi- 
 mony; any extraordinary and unusual fact is a thing of 
 less frequent occurrence than the falsity of testimony (that 
 being very common) ; therefore, no extraordinary and un- 
 usual fact can be fairly established by testimony. 
 
 82. Testimony is a kind of evidence which is very likely 
 to be false; the evidence on which most men believe that 
 there are pyramids in Egypt is testimony; therefore, the 
 evidence on which most men believe that there are pyramids 
 in Egypt is very likely to be false. 
 
 83. He who cannot possibly act otherwise than he does, 
 has neither merit nor demerit in his action; a liberal and 
 benevolent man cannot possibly act otherwise than he does 
 in relieving the poor; therefore, such a man has neither 
 merit nor demerit in his action. 
 
 84. The religion of the ancient Greeks and Romans was 
 extravagant fables and groundless superstitions, credited 
 by the vulgar and weak, and maintained by the more en- 
 lightened, from selfish or political views ; the same was 
 clearly the case with the religion of the Egyptians; the 
 same may be said of the Brahminical worship o India, and 
 the religion of Fo, professed by the Chinese; the same, of 
 the mythological systems of the Peruvians, of the stern and 
 bloody rites of the Mexicans, and those of the Britons and 
 Saxons ; hence we may conclude that all systems of religion, 
 however varied in circumstances, agree in being super- 
 stitions kept up among the vulgar, from interested or 
 political views of the more enlightened classes. 
 
 85. What happens every day is not improbable; some 
 things against which the chances are many thousands to 
 
186 PROOF AND DISPROOF 
 
 one, happen every day; therefore, some things against 
 which the chances are many thousands to one are not im- 
 probable. 
 
 86. The principles of justice are variable; the appoint- 
 ments of nature are invariable; therefore, the principles of 
 justice are not appointments of nature. 
 
 87. Of two evils, the less is to be preferred; occasional 
 turbulence, therefore, being a less evil than rigid despotism, 
 is to be preferred to it. 
 
 88. No evil should be allowed that good may come of it; 
 all punishment is arr evil; therefore, no punishment should 
 be allowed that good may come of it. 
 
 89. Repentance is a good thing; wicked men abound in 
 repentance; therefore, wicked men abound in what is good. 
 
 90. If the exhibition of criminals, publicly executed, 
 tends to heighten in others the dread of undergoing the 
 same fate, it may be expected that those soldiers who have 
 seen the most service, should have the most dread of death 
 in battle; but the reverse of this is the case; therefore, the 
 former is not to be believed. 
 
 91. Why does a ball, when dropped from the masthead 
 of a ship in full sail, fall not exactly at the foot of the 
 mast but nearer the stern of the vessel? Davis, Logic. 
 
 92. " The impious, whoever he may be, ought not to go 
 unpunished. For do not men regard Zeus as the best and 
 most righteous of the gods? And even they admit that he 
 bourrd his father because he wickedly devoured his sons." 
 Plato, Euthyphro. 
 
 93. The soul is unchangeable; the unchangeable is 
 simple; the simple is indissoluble; the indissoluble is in- 
 destructible; therefore, the soul is immortal. See Plato, 
 Phaedo. 
 
PART II 
 SUPPLEMENTARY METHODS 
 
CHAPTER I. 
 STATISTICS 
 
 The value of any cnnrlufiinn drpmrh Inrgply 
 the soundness of the premises from which it is drawn; 
 a great many of these premises, as we have seen, are 
 inductions from particular facts. When these inductive 
 inferences have been tested by one or another of the 
 " Inductive Methods " they can be regarded as trust- 
 worthy ; but the successful application of the methods 
 presupposes a fairly complete analysis of the phe- 
 nomena under investigation, for it is by this analysis 
 that we determine the circumstances in which the 
 phenomenon occurs. If we cannot determine the cir- 
 cumstances it is obvious that we cannot apply the 
 Methods. It might seem to follow from this that if 
 the circumstances in which a phenomenon occurs are so 
 complex as to defy analysis, or if the phenomenon itself 
 cannot be separated into its elements, it would be im- 
 possible to make any reliable generalizations regarding 
 the relations of the phenomenon in question. Or if we 
 were quite unable to surmise which of a multitude of 
 circumstances was significant, or to isolate any of them 
 by means of the Methods, we could not decide which was 
 causally related to the phenomenon and which was not. 
 There are many fields in which analysis is possible in 
 only a slight degree ; social phenomena and phenomena 
 of the weather are cases in point. A moment's reflec- 
 
 189 
 
190 STATISTICS 
 
 tion will show the difficulty of applying the Method of 
 Agreement, for instance, in the study of the weather, 
 or of the death rate. The phenomena are so exceed- 
 ingly complex that anything approaching a complete 
 statement of their elements is quite out of the question. 
 The fallibility of most popular generalizations in these 
 fields is evidence of the difficulty of dealing with such 
 facts. Must we be content then simply to guess at the 
 relations of such phenomena, with the slight assistance 
 which is to be gained from so precarious a method as 
 that of Simple Enumeration? In instances of this sort 
 another method, a method which is closely related to 
 the method of Simple Enumeration, becomes important : 
 it is the Method of Statistics. In statistics we have an 
 exact enumeration of cases. If a small number of cases 
 does not enable us to detect the causal relations of a 
 phenomenon, it sometimes happens that a large number, 
 accurately counted, and taken from a field widely ex- 
 tended in time and space, will lead to a solution of the 
 problem. 
 
 But how can the counting of cases aid in the discov- 
 ery of a causal relation? It does so by showing the 
 relative frequency of the phenomenon, its frequency as 
 compared with some particular circumstance or circum- 
 stances. If we noted only the phenomenon itself, knowl- 
 edge of its frequency would be of little use. But if, in 
 a large number of cases, taken from a wide field, we 
 can find some other phenomenon correlated with the one 
 we are investigating, then we have ground for a con- 
 clusion. We proceed upon the principle that if the con- 
 currence of two phenomena is merely a coincidence, the 
 
THE MEANING OF CORRELATION 191 
 
 frequency of one should make no difference in the oc- 
 currence of the other, and conversely that if there is a 
 correlation, there must be some causal relation. If the 
 frequency of two phenomena is the same, or if varia- 
 tions in the frequency of one correspond to variations 
 in the frequency of the other, or if any change in the 
 quantity or quality of one corresponds to changes in 
 the frequency of the other, we are usually justified in 
 inferring that something more than a coincidence is 
 present. 
 
 Correlation may be either positive or negative; in 
 positive correlation the presence of a phenomenon A 
 would mean the presence of the phenomenon B in a 
 certain proportion of cases or in a -certain amount, and 
 so on ; in negative correlation the presence of A would 
 of course mean the absence of B in a certain propor- 
 tion of cases, and so on. The relation between illiteracy 
 and crime would be an instance of the former and the 
 relation between vaccination and smallpox would illus- 
 trate the latter. The total absence of correlation might 
 perhaps be represented by the relation between the 
 weather and the day of the month. Correlation can bq 
 measured mathematically ; that is to say, it is possible 
 to determine just what degree of correlation there is 
 between two phenomena. The number which expresses 
 this is called the coefficient of correlation. Complete 
 positive correlation would be expressed by + 100, com- 
 plete negative correlation by - 100, and absence of 
 correlation by ; A coefficient of + 63 between two 
 phenomena would mean that one was present in 63 per 
 cent, of the cases in which the other was present, or that 
 
192 STATISTICS 
 
 the amount, or amount of increase, and so on, of one, 
 was 63 per cent, of that of the other. 1 
 
 Sometimes 2 a correlation would not prove a direct 
 causal relation ; the fact that the mortality among men 
 is higher than that among women and bears a certain 
 numerical relation to it, or the fact that about 106 
 boys are born for every 100 girls, are examples of this. 
 But there is nothing peculiar to statistics in this. The 
 same thing appeared in connection with the method of 
 Agreement; here, as there, the concurrence of two phe- 
 nomena may mean that both are connected with some 
 one underlying set of complex or undiscovered con- 
 ditions. And even frequent concurrence may be acci- 
 dental, though a thoroughgoing investigation would 
 eliminate one which was entirely accidental. 
 
 And even if the cause of a phenomenon is not dis- 
 covered in this way, it may be that its frequency 
 is a matter of interest or of practical importance ; for 
 its frequency may itself be a factor in determining our 
 conduct ; the number of passengers stopping at a given 
 railway station or the comparative number of boys and 
 girls in a city may be worth knowing, even if not 
 understood. The census reports contain a multitude of 
 facts of this kind ; eventually the causal relations of 
 many of them may be discovered. 
 
 A statistical record like any other enables us to cor- 
 
 1 For further discussion, see Thorndike, Mental and Social 
 Measurements; Bowley, Elements of Statistics; Pearson, The 
 Chances of Death. 
 
 2 It will be noted that the principles here employed are related 
 to those used in the Methods of Agreement and of Concomitant 
 Variations, but here analysis may be very incomplete; frequency 
 instead of quantity is considered, and principles of the method 
 of Difference may be employed in conjunction with the others. 
 
STATISTICS 193 
 
 rect mistakes of memory, and so on ; as, for example, in 
 matters such as the increase or decrease of crimes, or 
 the decreasing or increasing coldness of winters. 
 
 Usually the cause discovered by means of statistics 
 is only a part of the cause of the phenomenon ; the phe- 
 nomenon is the result of a number of circumstances 
 working together (Composition of Causes), and not al- 
 ways of the same circumstances (Plurality of Causes). 
 
 We may know already that a certain circumstance 
 is causally related to a certain phenomenon but that it 
 is sometimes present without the latter (through the 
 agency of a Counteracting Cause or the absence of 
 necessary supplementing circumstances). In such a 
 case statistics enable us to discover how frequently, in 
 what proportion of instances, the phenomenon will be 
 present along with that circumstance. 
 
 It must be remembered that the statistical method 
 means more than the mere collection of cases. " With 
 the collection of statistical data, only the first step has 
 been taken. The statistics in that condition are only 
 raw material showing nothing. They are not an in- 
 strument of investigation any more than a kiln of bricks 
 is a monument of architecture. They need to be ar- 
 ranged, classified, tabulated, and brought into connec- 
 tion with other statistics by the statistician. Then only 
 do they become an instrument of investigation, just as 
 a tool is nothing more than a mass of wood or metal* 
 except in the hands of a skilled workman." 3 
 
 The processes used in statistical investigations differ 
 widely, but the following are generally given in discus- 
 sions of the subject: (1) The Collection of Material, 
 3 Mayo-Smith, Statistics .and Sociology, p. 18, 
 
194 STATISTICS 
 
 (2) its Tabulation, (3) the Summary, and (4) a Criti- 
 cal Examination of its results. " In collection and 
 tabulation common sense is the chief requisite, and ex- 
 perience the chief teacher ; no more than a knowledge 
 of the simplest arithmetic is necessary for the actual 
 processes; but since ... all parts of an investi- 
 gation are interdependent, it is expedient to understand 
 the whole before attempting to carry out a part. For 
 summarizing, it is well to have acquaintance with the 
 various algebraic averages, and with enough geometry 
 for the interpretation of simple curves, though all the 
 operations can be performed without the use of alge- 
 braic symbols." 4 
 
 The collection of statistics is carried out by various 
 methods, some of them very technical ; we can note only 
 a few general principles here. In the first place the 
 data should be collected over a wide field. Just as in 
 the non-statistical application of the inductive methods, 
 it is necessary to collect data over a field wide enough 
 to insure us against mistaking a coincidence for a cause 
 or over-emphasizing the importance of one out of a 
 number of cooperating causes, or regarding as the sole 
 cause one which is only one of a number of different 
 causes capable of bringing about the phenomenon. 
 
 One danger to be guarded against arises from the 
 failure of different observers to use terms in exactly 
 the same sense. If poverty means in some cases in- 
 ability to obtain luxuries and in others, positive want, 
 we can make little use of statistics of poverty. 
 
 Again, in many statistical investigations, the data 
 are obtained by means of questions addressed to a great 
 *Bowley, Elements of Statistics, p. 17. 
 
TABULATION 195 
 
 many individuals ; these questions should be so worded 
 as to minimize as far as possible the tendencies to care- 
 less or biased observation, faulty memory, preju- 
 dice, dishonesty, and imperfect description of the 
 facts. 
 
 Tabulation involves classification, and the scheme of 
 tabulation should be determined by the purposes of the 
 investigation the problems which it is intended to 
 solve. " In general, the scheme of investigation re- 
 quires knowledge of certain groups ; and the totals re- 
 sulting from tabulation should show the number of 
 items in these, so that after tabulation, instead of the 
 chaotic mass of infinitely varying items, we have a 
 definite general outline of the whole group in question." 
 
 The totals and averages must be so presented as to 
 give a true impression to an inquirer. The subject of 
 averages will be discussed more fully in a later chapter. 
 
 In the summary, the aim is to present the results in 
 the clearest, most comprehensive, and most suggestive 
 way. The use of averages, and representation by charts 
 and diagrams, are important here. In correlating the 
 results great care is needed to avoid wrong interpreta- 
 tions. An increase in the number of arrests might be 
 causally related to increasing severity in the enforce- 
 ment of law and not to an increase in crime. 
 
 A critical examination of the results is possible only 
 when the sources of the data, the methods of their tab- 
 ulation, and the mode of summarizing and drawing 
 conclusions, are fully described. 
 
 There are, of course, many cases in which the use of 
 statistics would be unnecessary : " In order to prove 
 the relation between savagery and fetichism it is not 
 
196 STATISTICS 
 
 necessary for us to have statistics either of economic 
 condition or of religious confession. The fact stands 
 out of itself simply by the -consensus of observation of 
 travelers and historians.*" 5 
 
 Where the law of the data is already known the fre- 
 quency of their occurrence is of no further interest to 
 science. The number of times an acid has combined 
 with a base to form a salt is of no importance to the 
 chemist. If we know the laws and the circumstances, 
 the frequency of the event and the times of its occur- 
 rence can easily be determined. " There was some 
 interest in counting how many eclipses of the moon and 
 sun took place every year, so long as they occurred 
 unexpectedly and inexplicably ; since the rule has been 
 found according to which they occur and can be calcu- 
 lated for centuries past and to come, that interest has 
 vanished. But we still count how many thunderstorms 
 and hailstorms occur at a given place or within a given 
 district, how many persons die, and how many bushels 
 of fruit a given area produces, because we are not in a 
 position to calculate these events from their con- 
 ditions." 6 
 
 In other cases the method of statistics may be in- 
 applicable. " It is difficult to express the relation be- 
 tween economic condition or religious feeling and 
 aesthetic development in a civilized state, because music, 
 painting, and sculpture cannot in any way be measured 
 statistically. This is a question of quality and not in 
 any sense of quantity." 
 
 B Mayo-Smith, Statistics and Sociology, p. 9. 
 
 6 Sigwart, Logic, Part III, chap, iv, 3. 
 
 7 Mayo-Smith, loc. cit. See, however, page 210 on the ways of 
 applying exact methods in investigating such phenomena. 
 
DIFFICULTIES IN USE OF STATISTICS 197 
 
 The use of statistics is often severely criticised and 
 there is much popular distrust of the results attained 
 by their employment. There are, of course, many dif- 
 ficulties to be met, and many conclusions based upon 
 statistics may be false. They are liable to most of the 
 errors which occur in connection with the handling of 
 individual facts. The original observations may have 
 been faulty ; in so far as memory was employed, further 
 errors may have entered; ignorance, prejudice or inac- 
 curate statements may have vitiated whatever testimony 
 was employed ; the records may have been faulty or mis- 
 takes may have been made in copying; the facts ob- 
 served may not have been representative ; in comparing 
 different groups and in noting correlations we may 
 mistake a mere coincidence for causal relation. If all 
 the precautions which are employed in a scientific ex- 
 amination of individual facts are made use of here, 
 statistics may furnish a perfectly valid basis for infer- 
 ence. One practical difficulty is the unfamiliarity of 
 the average reader with the use of statistics and his 
 consequent inability to criticise them, and another is 
 the frequent failure on the part of the investigator to 
 furnish data for criticism. 8 
 
 s Interesting illustrations of the use of statistics are easy to 
 find. The field of vital statistics is a good one for this purpose. 
 One very interesting study is Dr. Allyn A. Young's A Discussion 
 of Age 'Statistics, Bulletin 13 of the Bureau of the Census. 
 
CHAPTER II 
 
 AVERAGES 
 
 The Arithmetical Average. In statisti-cal investiga- 
 
 tions and in all others in which quantitative data are 
 
 employed, the use of averages is often very important. 
 
 An average is a single quantity which represents two or 
 
 more other quantities. There are several kinds of aver- 
 
 ages ; that with which we are most familiar is the Arith- 
 
 metical Average. It is obtained by adding together 
 
 the various quantities to be averaged and dividing their 
 
 sum by the number of quantities. The weights of the 
 
 members of a college football team were respectively, 
 
 ^ 175, 195, 187, 183, 230, 187, 169, 147, 159, 178 and 
 
 \ V \ 185. The average was 181 4-11. The average is less 
 
 ^ ^ cumbersome than the whole series of quantities or their 
 
 | } sum. The greater the number or size of the quantities 
 
 W" the more important does the average become. 
 
 The average tells us nothing about the individual 
 
 ^<- 
 \ 'Le 
 
 \ Leases. In this example the average is not the same as 
 single one of the quantities averaged. To take an- 
 
 other case : the death rate of a city gives no informa- 
 jdptnTregarding the death rate of any given ward, nor 
 the number of deaths in any given thousand of the 
 population. An average simply serves as a means for 
 representing the whole series of quantities and for com- 
 paring it with other series. It gives no information 
 regarding the homogeneity of the group : 180 is the 
 average of 179 and 181 and also of 359 and 1. 
 
 There are many cases in which the simple form of the 
 
 198 
 
THE WEIGHTED AVERAGE 199 
 
 arithmetical average or mean is inadequate ; sometimes 
 a modified form of it can be used. 
 
 The "Weighted"Average. Suppose we know that 
 of six groups of men the average weights are respect- 
 ively 180, 148, 172, 164, 156 and 152 pounds. The 
 average is 162. Can we say that this average satis- 
 factorily represents the whole series of groups? That 
 will depend upon the circumstances. If the groups 
 were of approximately the same size it might be suffi- 
 cient, but if in the first group there were 10; in the 
 second, 200 ; in the third, 50 ; in the fourth, 20 ; in the 
 fifth, 100; and in the sixth, 150, our average will be a 
 very imperfect representative of the groups. If, on 
 the other hand, we multiply each of the averages in the 
 series by the number of individuals in the group which 
 it represents and divide the sum of these products by 
 the total number of individuals, we get the average 
 154 6-53, which is much more accurate than that first 
 given. 
 
 180x10+148x900+172x50+164x20+156x100+152x150 = , 
 10 + 200 + 50 + 20 + 100 + 150 
 
 This is an illustration of what is known as a weighted 
 average; it is a special form of arithmetical average. 
 Where the groups represented by a series of averages 
 vary greatly in size we have conditions which call for 
 " weighting the averages." " The classical and most 
 useful application of weights is the formation of an 
 index-number for the change of prices by fitting suit- 
 able weights to the changes measured in the prices of 
 various commodities. It is required to find the change 
 in the value of gold when measured by the prices of 
 other commodities. Suppose that we are given that 
 
200 AVERAGES 
 
 prices of certain commodities between two years were 
 in the following ratios : 
 
 Wheat Silver Meat Sugar Cotton 
 
 First year 100 100 100 100 100 
 
 Second year 77 60 90 40 85 
 
 The simplest way to estimate for the general fall 
 in price is to take the simple average of the numbers 
 in the second year, viz., 70.4, and say that the general 
 prices in the second year were 70.4 : 100 1 when ex- 
 pressed in commodities. But it is at once clear that 
 we can not allow the commodities given to have equal 
 influences on the result ; wheat is of greater importance 
 than sugar and meat than silver; and again we have 
 taken arbitrarily three items to represent food and one 
 for clothing; we need some means of deciding relative 
 importance. Suppose we decide that wheat, cotton, 
 meat and sugar are respectively 7, 4, 3, times and twice 
 as important as silver, we should get the following 
 table : 
 
 Commodity Relative prices Weight Product 
 
 in second year Assigned 
 
 Wheat 77 7 539 
 
 Silver 60 1 60 
 
 Meat 90 3 270 
 
 Sugar 40 2 80 
 
 Cotton 85 4 340 
 
 352 17 1289 
 
 1289 
 Weighted average is ==75.3 
 
 17 
 352 
 
 Unweighted average is =70.4 2 
 
 5 
 
 1 That is, prices of commodities have fallen in this rate or the 
 value of gold has increased correspondingly. 
 
 2 Bowley, Elements of Statistics, pp. 111-llC. 
 
THE MODE 01 
 
 It is not always easy to tell what weights should be 
 assigned, but considerable variation is possible without 
 much modification of the result. 
 
 The Mode. Another sort of average which is often 
 of great importance is what is known as the Mode. It 
 is that quantity which occurs with the greatest fre- 
 quency. It is what we frequently have in mind when 
 we speak of the average man, the average student, etc. 
 If in a class of students, 10 receive the grade A; 20, 
 the grade B; 50, the grade C; 100, the grade D; and 
 25, the grade F, the mode is D. The mode very often 
 represents the type more accurately than does the aver- 
 age. It gives us no information about any one indi- 
 vidual, but it does indicate the sort of individual which 
 occurs more frequently than any other sort. There 
 might well be two or more modes in a given series of 
 quantities. If a class were made up of very bright and 
 very dull students, the numbers receiving the various 
 grades might be A, 25; B, 50; C, 20; D, 100; and F, 
 25. The two modes are at B and D. 
 
 The mode is not always easy to determine. In these 
 examples the grade B, for instance, means a range be- 
 tween the grade which is just high enough to escape 
 C and that which is the smallest fraction short of A. 
 It might well be that of the 50 who were in C, 35 were 
 in the lower half of the group, while of those that were 
 in D 80 were in the upper half of the group, so that the 
 mode was really in a group which might be indicated by 
 the expression D +, C . The degree of accuracy re- 
 quired in the results would determine the degree of 
 exactness with which we should state the mode. 
 
 The mode is often most useful. " The mode rather 
 than the average in chest-measurements is the number 
 
202 AVERAGES 
 
 most suitable for the ready-made clothier. For pro- 
 viding a post-office or a store, the mode in postal-orders 
 or prices of tea needs to be known rather than any other 
 average. Even the favorite coin in a collection may 
 show the spirit of the congregation better than the 
 arithmetic average of their contributions." 3 
 
 If the series under consideration is very irregular it 
 may be quite impossible to apply the mode. 
 
 The mode has this advantage over the arithmetical 
 average : it is uninfluenced by extreme cases. In the 
 illustration on page 198, the average weight of the 
 players would be considerably changed if a player 
 weighing 180 pounds were substituted for the one 
 weighing 230 ; let us see what would happen in the case 
 of the mode. More of the quantities fall between 180 
 and 189 than within any other equal range. This 
 range, 180-189, then, will be the mode. The substitu- 
 tion of the lighter player does not modify the mode. 
 Where the number of quantities is so small as in this 
 illustration, the individual quantities are often men* 
 tioned, but where that is not the case, the mode is often 
 useful either as a supplement to the arithmetical aver- 
 age or as a subsitute for it. 
 
 The Median. Another kind of average useful in 
 many cases is the Median. The Median is the middle 
 quantity in a series. The weights of the players, in 
 the order of their magnitude, were 147, 159, 169, 175, 
 178, 183, 185, 187, 187, 195, 230. The median is 183. 
 There are just as many items above it as there are 
 below. The median, like the mode, is unaffected by ex- 
 treme cases. " The existence of any number of million- 
 aires has no more effect on the median income than of 
 sBowley, Elements of Statistics, p. 123c 
 
THE MEDIAN 203 
 
 an equal number of other persons whose incomes are 
 above the median." 4 The median is very easy to find, 
 since it is only necessary to arrange the items in the 
 order of their magnitude and find which occupies the 
 middle position. If there is an even number of items 
 the median lies between the two middle ones. Even if 
 our information regarding the items is incomplete it is 
 often possible to find the median with a fair degree of 
 accuracy. " It may be that in the ' wage census ' 
 100,000 persons whose wages were far below the aver- 
 age did not come into the returns at all, and it is ver.y 
 difficult to estimate their effect on the arithmetical aver- 
 age, for want of information as to their earnings ; but 
 to find the median exactly we need only know their num- 
 ber, not their earnings ; and if we can assign a maximum 
 for their number, we still can place the median within 
 narrow limits." 
 
 One great advantage in the use of the median is to 
 be found in the fact that it can be employed in dealing 
 with quantities for which no accurate measurements 
 can be obtained. This is especially important in deal- 
 ing with psychological phenomena. We may be able 
 to say that A has a better memory than B without being 
 able to measure either, or to state the exact amount 
 in which A is superior to B. The members of a class of 
 any size might be arranged in the order of their excel- 
 lence in any quality whatever and the median found as 
 in the case of numbers. Francis Galton, in his Natural 
 
 4 "The magnitudes one-quarter and three-quarters up the series 
 are called the quartels; those one, two, .... nine-tenths of the 
 
 way up are the deciles; those one, two, ninety-nine hun- 
 
 dredths up are the percentiles." Bowley, Elements of Statistics, 
 p. 124. 
 
204 AVERAGES 
 
 Inheritance and in other works, developed and applied 
 this type of average with great effectiveness. 
 
 The median may be a very imperfect representative 
 of the type. If, in a group of 100 men, the weights of 
 50 were between 190 and 210 pounds, while the others 
 ranged between 130 and 150 pounds, the median would 
 be 170. " The median is then chiefly useful when we 
 are dealing with a series of objects of which the main 
 part lie fairly close together ; a few extremes do not 
 affect it." 5 
 
 The Geometrical Average. Another kind of average 
 useful in certain cases is the Geometrical average. It 
 is related to the arithmetical average somewhat as com- 
 pound is to simple interest. The population of Great 
 Britain and Ireland increased from 12 millions in 1789 
 to 38 millions in 1890. Obviously it would be unsafe 
 to say that the average increase was the total increase, 
 26 millions, divided by the number of years. We should 
 expect the annual increase to be greater as the popula- 
 tion became larger, and, other things being equal, the 
 two would vary together. When we have only two 
 quantities to deal with, the geometrical average is easily 
 found. In such a case it is the mean proportional. The 
 geometrical average of 4 and 16 is 8. The geometrical 
 average of 5 and 9 is the square root of 45, or '3 
 into the square root of 5. If we were dealing with 
 three quantities the geometrical average would be the 
 cube root of their product ; if with five, it would be the 
 fifth root of their product; the general formula for n 
 quantities is the nth root of a^ a 2 . ... a n . With large 
 or numerous quantities logarithms should be used. The 
 name logarithmic mean is sometimes employed for this 
 B Bowley, Elements of Statistics, p. 126. 
 
THE GEOMETRICAL AVERAGE 205 
 
 kind of average. The geometrical or logarithmic mean 
 is a quantity which can be substituted for each of the 
 quantities when they are multiplied together and give 
 the same product, whereas the arithmetical mean is one 
 which can be substituted for each of them when they 
 are added together. " Which mean we should choose is 
 simply a question of which we believe will best represent 
 the facts. If the growth of cities depended altogether 
 upon the birth of children within their boundaries, we 
 should naturally choose the geometrical mean, for the 
 larger the city (other things being equal) the more 
 children will be born in it. If, on the other hand, the 
 population of a city, like that of a prison or hospital, 
 were made up altogether of certain kinds of people 
 who were sent there from without, there would (?) be 
 no reason why a large city should gain more inhabi- 
 tants than a small one ; and the more appropriate aver- 
 age would be the arithmetical. With most cities the 
 natural rate of growth is only partly geometrical and 
 partly arithmetical; so that neither a series of means 
 of the one sort nor a series of the other would give a 
 wholly satisfactory representation of the mean growth 
 from year to year between one census and another. If 
 in any case or set of -cases we have reason to believe 
 that the true mean lies somewhere between the arith- 
 metical and the geometrical, and if we wish to represent 
 the facts as accurately as they can be represented bj 
 any mean, we must take a mean that does lie between 
 the two." 6 
 
 Measuring Deviations from an Average. It is often 
 important when using averages to know something 
 about the closeness with which the several quantities 
 Aikins, The Principles of Logic, p. 315. 
 
206 AVERAGES 
 
 approximate the average. Suppose for example, that 
 we had a number of different measurements of a given 
 quantity, say the distance between two points: if there 
 was little variation among the measurements we should 
 usually regard their average as a fairly accurate repre- 
 sentation of the real quantity ; but if the variation were 
 very great we might have little or no confidence in the 
 average. We shall need some way of indicating the 
 amount of divergence within the group, or, in other 
 words, the closeness with which the several quantities 
 were grouped about the average. 
 
 1. One simple way of doing this is to take the aver- 
 age of the deviations from the mean or average. Eight 
 is the average of 5, 6, 11, and 10, and also of 1, 2, 15, 
 and 14. The deviations in the first series are 3, 2, 3, 
 and 2. The average of these deviations is 1 % or 2/4. 
 The deviations in the second series are 7, 6, 7 and 6; 
 the average deviation is 6%. 
 
 (The deviations are technically known as " errors," 
 and their average as the Average Error.) 
 
 The smaller the average error the more closely are 
 the quantities grouped about the average ; and the more 
 closely they are grouped about the average the more 
 homogeneous is the group. 
 
 2. Another kind of average frequently employed in 
 this connection is the Median or Probable Error (P. 
 E.). Arrange the errors in the order of their magni- 
 tude ; the Median of these will be the so-called Probable 
 Error, or the quantity within which half of the errors 
 fall. Thus, if we have the quantities, 1, 3, 6, 8, 9, 12, 
 13, 15, 16, 17, the average will be 10. The errors will 
 be 9, 7, 4, 2, 1, 2, 3, 5, 6, 7. Arranging these in the 
 order of their magnitude we have 1, 2, 2, 3, 4, 5, 6, 7, 7, 
 
PROBABLE ERROR 207 
 
 9. The median will fall between 4 and 5, i. e., 4%. In 
 other words, 4% is the quantity below which half the 
 errors fall and above which we will find the other half. 
 Assuming that our data are representative of the class 
 of facts for which they stand, any new number standing 
 for things in the same class is as likely to be within 
 4J of the average as it is to be beyond it. Exactly half 
 of the quantities already determined lie within that 
 range (in the example, between the numbers 5% and 
 14%), and those already determined are, according to 
 our supposition, selected from a wide enough field to be 
 regarded as representative of the whole. An average 
 of 10 with a probable error of 4.5 means a series of 
 quantities in which there is a wide range of variation. 
 An average of 100 and a P. E. of .1 would indicate 
 a very homogeneous group. In the case of measure- 
 ments it would mean that there was a close agreement 
 among the different measurements and that the average 
 was therefore a fairly accurate approximation to the 
 true measurement (providing, of course, that constant 
 errors had been eliminated). 
 
 " An approximation to the probable error for a 
 given series of observations is obtained by arranging all 
 the observations in order of magnitude ; marking the 
 magnitude, say a, above which 25 per cent, of the ob- 
 servations lie, and the magnitude, say &, below which 
 25 per cent. lie. Half the difference between a and b 
 is the probable error. A useful way of illustrating this 
 is to say that if one observation is chosen at random 
 out of a group, it is as likely as not that it will not 
 lie further from the average than the probable 
 error." 7 
 
 7 Bowley, Elements of Statistics, p. 282. 
 
208 AVERAGES 
 
 Measurement of Phenomena. In the more advanced 
 stages of most sciences the exact measurement of phe- 
 nomena becomes more and more important. To deter- 
 mine the relations of a phenomenon it is not only 
 necessary to know when it happens and what its accom- 
 paniments are, but also how much of it is correlated 
 with given amounts of other phenomena. This is evi- 
 dent in the employment of the methods of Concomitant 
 Variations, for this method deals with cases in which 
 the quantity of the phenomenon varies. In the method 
 of Residues also, quantitative measurements are of great 
 importance; indeed, they are usually necessary. We 
 observe how much of a given phenomenon is due to one 
 cause, how much to a second, and so on ; the remainder 
 is due to something else not previously known to be a 
 cause, etc. 
 
 The physical sciences are very largely quantitative, 
 and more recently biology has come to employ the 
 methods of exact measurements in many of its investi- 
 gations. 8 Measurement usually means the employment 
 of instruments. Measurements of magnitudes by the 
 unassisted eye are exceedingly .inexact, and measure- 
 ments of degree of quality are even more so. White 
 marble painted in a picture representing an architec- 
 tural view by moonlight seems to be of about the same 
 degree of brightness as the actual moonlit marble would 
 be, but Helmholz has calculated that it is from ten to 
 twenty thousand times as bright. 9 
 
 To make measurements it is necessary to fix units in 
 
 s The name of Karl Pearson is most closely associated with 
 " Biometry." 
 
 e James, Psychology, Briefer Course, p. 155. 
 
MEASUREMENT 209 
 
 terms of which the magnitudes are to be expressed. 
 These are usually determined arbitrarily. Units, stand- 
 ards, and instruments of measurement vary with the 
 phenomena to be measured and can not be discussed 
 further here. 10 
 
 Many errors may occur in making measurements, and 
 although it is often possible to eliminate some of them, 
 in the vast majority of instances the measurement is 
 almost certainly inexact. Repeated measurements are 
 very seldom in exact agreement. If phenomena were 
 broken up into units of uniform magnitude there would 
 be less difficulty, but most phenomena are continuous. 
 Time is not broken up into minutes, and with the most 
 exact instruments it is impossible to say when a minute 
 has passed. It can be determined within millionths of 
 a second but not with absolute exactness. For most 
 practical purposes rough measurements are sufficient ; 
 thus, for the train dispatcher it may be enough to deter- 
 mine the time to a second, but for astronomical calcu- 
 lations the smallest possible error may be of serious 
 importance. Most measurements are only approxi- 
 mately true ; the problem is to make the approximation 
 as close as possible. 
 
 There are various conditions to be observed and 
 various methods which can be used in attempting 
 to get exact measurements, but they are too technical 
 to be included here. 11 Constant errors, such as the 
 personal error, 12 can often be determined and allowance 
 can be made for them. But after all such allowances 
 
 10 See Jevons, Principles of Science, chap. xiv. 
 
 11 See Jevons, Principles of Science, chap. xiii. 
 
 12 See page 23. 
 
210 AVERAGES 
 
 have been made and after all the means for avoiding 
 and minimizing error have been employed, there yet 
 remains a margin of uncertainty. In such cases it is 
 possible to obtain a close approximation to the true 
 measurement by taking a number of measurements and 
 striking an average. After constant errors have been 
 eliminated any given measurement is as likely to be too 
 great as it is to be too small ; hence, in a large number 
 of measurements there will probably be as many of 
 those which exceed the true magnitude as there are of 
 those which fall short of it. If the number of measure- 
 ments is small this is more doubtful, but if a great many 
 measurements have been made, we can rely upon the 
 average with safety. The average of all these measure- 
 ments is the closest approximation which we can get. 
 Different kinds of average are used ac-cording to cir- 
 cumstances. The closeness with which the several meas- 
 urements are grouped about the average will be 
 indicated here, as in all cases of the use of 
 average, by the size of the error. If the error is 
 small, the measurement is reliable, if large, more doubt- 
 ful. 
 
 The Comparison of Quantities which Cannot be 
 Measured. In the study of many phenomena the prob- 
 lem of quantitative comparison is made very difficult by 
 our inability to find an exact quantitative equivalent 
 for the phenomena. " Many mental phenomena elude 
 altogether direct measurement in terms of amount. How 
 many thefts equal in wickedness a murder? If the 
 piety of John Wesley is 100, how much is the piety of 
 St. Augustine? How much more ability as a dramatist 
 had Shakespeare than Middleton? What per cent, must 
 
COMPARISON OF QUANTITIES 
 
 be added to the political ability of the Jewish race to 
 make it equal to the Irish race? . . . Nevertheless, 
 such phenomena can be measured and subjected to quan- 
 titative treatment." 13 
 
 The method to be employed in such cases, as Pro- 
 fessor Thorndike goes on to show, is to arrange the 
 individuals (or other unmeasurable data) according to. 
 their rank. We may not be able to say how much 
 more eminent A is than B, but if we can say that A is 
 in the first rank, whereas B is in the tenth, we have a 
 true basis of comparison. We cannot measure directly 
 the intelligence of students in a class, but we may be 
 able to say that one is in the first group, whereas an- 
 other is in the fourth. Thus, with any number, it would 
 be possible to give each his proper place in the group. 
 This method can be applied to any trait whatever. The 
 great difficulty is in making sure that the ranking is 
 correct. Single observations and individual judgments 
 are subject to the same errors here as in all other cases 
 of observation. 
 
 EXERCISES. 
 
 1. What sort of average should be employed in deter- 
 mining the standard size of an article to be manufactured 
 in large quantities say window shades ? 
 
 2. What sort of average should be employed in getting 
 a number to represent the value of articles in a large and 
 varied invoice of merchandise? 
 
 3. If a college had 400 students in 1880 and 1000 stu- 
 dents in 1905, how many did it have in the year which falls 
 
 is Thorndike, An Introduction to the Theory of Mental and 
 Social Measurements, p. 18. This book is an exposition of the 
 methods of measuring individuals, groups, variability of perform- 
 ances, etc., including an exposition of the necessary modes of 
 presenting the facts, making calculations, and so oa 
 
AVERAGES 
 
 half way between, provided that the rate of increase was 
 constant ? 
 
 4. What averages might be employed and which would 
 be preferable in comparing the stature of soldiers in the 
 French army with those in the American army? In com- 
 paring the standing of successive classes in college? In 
 comparing the salaries of members of the faculty in two 
 universities? In comparing the rate of growth of a large 
 university and a small college? 
 
 5. How would you indicate the degree of closeness with 
 which a series of quantities approached their average? 
 
 6. What is the difference between " Average Error " and 
 "Probable Error?" 
 
CHAPTER III 
 PROBABILITY 
 
 THE conclusions at which we arrive by the assistance 
 of statistical methods and the employment of averages 
 often fall far short of the certainty attaching to scien- 
 tific laws. The conditions required for establishing a 
 scientific law are not fully present, and consequently 
 many of such conclusions, if not all of them, lack com- 
 plete verification. It does not follow, however, that 
 these are valueless. As a matter of fact, most of the 
 generalizations which we use in everyday life are in- 
 completely verified; they are extremely valuable as in- 
 struments of knowledge and practice; indeed, in the 
 absence of scientific laws, they are indispensable. So 
 long as their provisional character is remembered, there 
 is no serious danger in using them. 
 
 A generalization of this character is said to be prob- 
 able or to possess some degree of probability. Proba- 
 bility belongs also to particular propositions. What do 
 we mean by probability, by saying that a statement is 
 probably true, that an event will probably happen? 
 As we use the term ordinarily, it means that we believe 
 we -have a right to accept a statement or expect an 
 event, without feeling perfectly certain of it. This 
 attitude, when it has any justification, is based upon the 
 belief that the grounds for accepting the statement are 
 stronger than those for rejecting it. It may be that 
 we know of no positive reasons against it, but do not 
 regard the reasons in its favor as conclusive ; or it may 
 
 213 
 
PROBABILITY 
 
 be that there are positive reasons against it, but that 
 those in its favor are stronger or more numerous. These 
 reasons or grounds may be of various kinds. There may 
 be many things pointing toward the occurrence of 
 such an event ; as, for example, in the statement that 
 life will probably at some time cease upon the earth. 
 Or conditions at the present time may be similar to 
 those in which the event has happened before ; the out- 
 come of an examination of instances according to the 
 principles of the method of Agreement gives a result 
 which is usually only probable. In all these cases it 
 is impossible not to feel that a great deal of vagueness 
 attaches to our statement that anything is probable. 
 We are not able to say how probable it is. There is 
 such a thing, however, as mathematical or quantitative 
 probability. It is based upon the comparative number 
 of times an event or connection of events has occurred. 
 If a given circumstance A has been observed 1000 times, 
 and if, in 700 cases of its occurrence, a phenomenon B 
 has also been present, we have definite grounds for in- 
 ferring that A will probably be accompanied by B 
 again. Every time A and B have occurred together 
 in the past is an argument in favor of their occurring 
 together in the future, and every time A has occurred 
 without B is an argument against this connection; if 
 the cases of the latter sort are many in comparison with 
 those of the former, we say that the connection in the 
 future is improbable. In the case just mentioned we 
 should express the degree of probability by the frac- 
 tion %o- Now in dealing with the matter in this quan- 
 titative way, the term " probability " has a meaning 
 which is somewhat different from that in which we 
 
THE MEANING OF PROBABILITY 
 
 ordinarily use it. It would mean, in the present case, 
 that in the future we should have a right to expect B 
 along with A in seven cases out of ten. It means noth- 
 ing with regard to the next case; we have no more 
 reason for expecting one outcome than the other; our 
 information has value only for the long run ; we have 
 no right to expect that in the next ten cases B will be 
 present seven or any other particular number of times ; 
 but in the long run we may expect this proportion to 
 hold and the longer the run the closer is the approxi- 
 mation which we may expect. 
 
 Compare this with one of the former illustrations, 
 " Life will probably cease upon the earth." That does 
 not mean that in a large number of cases of the sort 
 before us life would cease in most of them ; we are here 
 dealing with the particular case and all our arguments 
 apply to it. In quantitative probability we know noth- 
 ing of the circumstances of the particular case ; it is 
 simply one of a certain group, and certain members 
 of this group behave in one way, whereas others behave 
 in a different way, and we cannot determine the circum- 
 stances of their behavior in either case. The fraction 
 expressing the degree of probability tells us that, in 
 the past, the phenomenon has appeared in connection 
 with a certain circumstance in such and such a pro- 
 portion of cases and that we may, unless there are 
 reasons to the contrary, expect this proportion to hold 
 in the future. (We proceed here as elsewhere, upon 
 the assumption that the future will be like the past and 
 that any set of phenomena will behave in the future as 
 it has in the past, in the absence of any new and dis- 
 turbing factor.) 
 
216 PROBABILITY 
 
 Probability, in this connection, does not necessarily 
 mean favorable odds. The event may have occurred in 
 only one-tenth of the cases ; its probability will then be 
 %o If it has occurred in one-half the number of cases, 
 the probability will be %, etc. 
 
 The calculations of insurance companies are based 
 upon data showing the number of deaths per year for 
 individuals of various ages, and so on. The great value 
 of vital statistics and of statistics of many other sorts 
 is to enable us to determine the probability of events 
 which we cannot bring entirely under laws. 
 
 Deducing the Probability of a Phenomenon. There 
 are certain circumstances in which the probability of a 
 phenomenon may be determined deductively. For ex- 
 ample, we can say at once that in tossing a coin the 
 probability of getting heads is % ; we know that there 
 are two possibilities and only two ; if the coin is prop- 
 erly made we know of no reason why one side should, 
 in any particular case or in the long run, fall any 
 oftener than the other. 1 
 
 We say that their chances are equal and that the 
 probability of each is %. In the case of a die the proba- 
 bility that any specified side will come uppermost is %. 
 There are six possibilities, all equal. In the long run 
 we expect each side to turn up as frequently as any 
 other, viz., in one-sixth of the cases. The chances of 
 any one are as 1:5; one for, and five against. If we 
 have a bag containing twenty balls, three of which are 
 white and the rest black, the probability of drawing a 
 white ball is %o. In this instance there are twenty pos- 
 
 i It is essential in such calculations that there be no known 
 factor favoring a given result more than any other, 
 
DEDUCING PROBABILITY 
 
 sibilities, three of which would give the desired result ; 
 drawing a white ball may be brought about by realizing 
 any one of three possibilities; or, out of twenty possi- 
 bilities, three are favorable. In instances of this sort 
 we have a definitely known number of possibilities, with 
 no reason to believe that there is anything tending to 
 bring about one rather than another. The probability 
 of any specified one among them will be expressed by 
 a fraction having 1 as its numerator and the number 
 of possibilities as its denominator. In the case last 
 cited the probability of drawing any particular ball is 
 Ho- If among these possibilities any number of them 
 favor the realization of any particular phenomenon, the 
 probability of that phenomenon will be expressed by 
 a fraction having as its denominator the total num- 
 ber of possibilities and as its numerator the number of 
 possibilities favorable to the occurrence of the phe- 
 nomenon in question. If all the possibilities were fa- 
 vorable (e. g., if all twenty balls were white), the frac- 
 tion would be 2 %o or 1, which is the symbol for cer- 
 tainty, or the upper limit of probability ; if none were 
 favorable, it would be %o of 0, the lower limit, or im- 
 possibility. 
 
 Suppose we toss the coin twice (or toss two coins), 
 what is the probability of getting heads both times? 
 There are four possibilities, as follows : 
 
 H H 
 
 H T 
 
 T H 
 
 T T 
 
218 PROBABILITY 
 
 We might get heads in both, or heads in the first 
 and tails in the second, or tails in the first and heads in 
 the second, or tails in both. In only one of these does 
 heads come in both throws ; the probability is therefore 
 %. It is the same for two tails. For one heads and 
 one tails it is %. For heads in the first throw and tails 
 in the second it is again %, and so on. 
 
 If we should toss it three times, the probability of 
 getting heads each time would be %. There are eight 
 possibilities : 
 
 H H H T H H 
 
 H H T T H T 
 
 H T T T T H 
 
 H T H T T T 
 
 We can get the probability -for any number of throws 
 by multiplying together the probabilities for each of the 
 several throws; for two throws, % x%, or /4 ; for three, 
 
 y 2 x y 2 x y 2 , O r y s ; for five, y 2 x y 2 x % x % x y>, or y 32 , 
 
 and so on. The results would be the same if we should 
 throw several coins at once instead of throwing one 
 several times. Suppose we are drawing balls from two 
 bags ; one of them contains three white and seventeen 
 black balls ; the other contains two white and eight 
 black balls. What is the probability of drawing a 
 white ball from each? The probability, in one case, is 
 %o, and in the other %o ; the probability of getting a 
 white from each is therefore %oo or %oo. Each in one 
 bag might be drawn with any one in the other ; hence 
 there are 200 possibilities, only six of which are favor- 
 able ; each of the two whites in one bag might be drawn 
 with each of the three in the other. 
 
DETERMINING PROBABILITIES 
 
 The probability of getting any combination of in- 
 dependent events is thus obtained by taking the product 
 of the probabilities of the several events. 
 
 If two events are mutually exclusive the probability 
 of getting one or the other would be the sum of their 
 independent probabilities. In tossing a coin, the prob- 
 ability of getting heads is % and that of getting tails 
 is the same ; the probability of getting one or the other 
 is the sum of the two or 1 = certainty. In throwing a 
 die, the probability of getting a five is %, the proba- 
 bility of getting a six is the same, the probability of 
 getting one or the other is %. 
 
 In tossing a coin twice, " It might be argued that 
 since the probability of throwing heads at the first 
 trial is % and at the second trial also %, the 
 probability of throwing it in the first two throws 
 is 1, or certainty. The true result is %, or the proba- 
 bility of heads at the first throw, added to the exclusive 
 probability that if it does not come at the first, it 
 will come at the second." 2 The probability that it will 
 come in the first is %. The probability that it will not 
 come in the first is also % ; the probability that it will 
 come in the second is also %. The. product of the two 
 last gives the probability that if it does not come in the 
 first, it will in the second. This product, added to the 
 first %, gives the probability that it will come in at 
 least one of the two throws. There are, of course, four 
 possibilities in two throws, and three of them give at 
 least one heads. 
 
 If we represent the probability that an event will 
 happen by p, then the probability that it will not hap- 
 
 2 Jevons, Principles of Science, chap, x, 3. 
 
220 PROBABILITY 
 
 pen is 1 p. The probability in throwing a die that 
 five will not come up is 1 - % or %. 
 
 Let us suppose a case in which six coins are tossed 
 (or in which one coin is tossed six times) ; what are the 
 probabilities of 6, 5, 4, 3, 2, 1 and heads respectively? 
 There will be 64 possibilities, as follows : 
 
 6 
 
 HHHHHH TTTTTT 
 
 5 1 
 
 HHHHHT HTTTTT 
 
 HHHHTH THTTTT 
 
 HHHTHH TTHTTT 
 
 HHTHHH TTTHTT 
 
 HTHHHH TTTTHT 
 
 THHHHH TTTTTH 
 
 4 2 
 
 HHHHTT HHTTTT 
 
 HHHTTH THHTTT 
 
 HHTTHH TTHHTT 
 
 HTTHHH TTTHHT 
 
 TTHHHH TTTTHH 
 
 HHHTHT HTHTTT 
 
 HHTHTH THTHTT 
 
 HTHTHH TTHTHT 
 
 THTHHH TTTHTH 
 
 HHTHHT HTTHTT 
 
 HTHHTH THTTHT 
 
 THHTHH TTHTTH 
 
 HTHHHT HTTTHT 
 
 THHHTH THTTTH 
 
 THHHHT HTTTTH 
 
PROBABILITY 221 
 
 3 3 
 
 HHHTTT HHTHTT 
 
 HHTTTH HTHTTH 
 
 HTTTHH THTTHH 
 
 TTTHHH HTHHTT 
 
 HHTTHT THHTTH 
 
 HTTHTH THHTHT 
 
 TTHTHH THTHHT 
 
 HTTHHT THTHTH 
 
 TTHHTH HTHTHT 
 
 T T H H H T T H H H T T 
 
 One combination gives six heads, six give five, etc. 
 The probabilities for 6, 5, 4, 3, 2, 1, and heads are 
 respectively % 4 , %4, 15 /64, 2 %4, 15 /64, %4, y 64 . In ten 
 throws the number of possibilities would be 1024; the 
 numbers favoring 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and 
 heads would be respectively, 1, 10, 45, 120, 210, 252, 
 210, 120, 45, 10, 1. Examination will show that these 
 series of numbers (1, 6, 15, 20, etc., and 1, 10, 45, 120, 
 etc.) are the coefficients of the terms of a binominal 
 raised to the power indicated by the number of throws 
 (6, 10, etc.). In these cases the phenomena are not mu- 
 tually exclusive. The fact that heads comes (or does 
 not come) in any throw makes no difference to the other 
 throws. 
 
 There are important scientific applications of the 
 facts just brought out. 1 " Suppose, for the sake of 
 argument, that all persons were naturally of the equal 
 stature of five feet, but enjoyed during youth seven 
 independent chances of growing one inch in addition* 
 ijevons, Principles of Science, chap, ix, 5. 
 
PROBABILITY 
 
 Of these seven chances, one, two, three, or more, mny 
 happen favorably to any individual; . . . out of every 
 128 people: 
 
 1 person would have the stature of ,5 feet inches. 
 7 persons " " " " 5 " 1 " 
 
 O1 it U U U U K 
 
 35 " " " " " 5 " 3 " 
 
 35 " " " " " 5 " 4 " 
 
 4)1 it U U U K (.1 K 
 
 iy U 4< U U U ")"() " 
 
 | u a <c u a 5 u 7 " 
 
 The probability of a stature of 5 feet 1 inch would be 
 %28, the whole number of possibilities being the de- 
 nominator. 
 
 There are sometimes cases in which an event has hap- 
 pened in all the instances in which a given circumstance 
 or set of circumstances has been present B has always 
 followed A. What is the probability of its happening 
 the next time the circumstance or circumstances recur? 
 Let the number of times it has happened be represented 
 by m. Then the probability of its happening the next 
 time is expressed by the fraction ^^. This may 
 be determined by a series of mathematical operations or 
 more simply as follows : " In this fraction the de- 
 nominator represents the sum of conceivable cases, since 
 after m real cases have occurred there are always two 
 additional cases, which we can think of as occurring, 
 viz., the repetition or non-repetition of E (the event) ; 
 the numerator as usual denotes the number of favorable 
 chances. The example usually adduced is that as the 
 
DANGERS TO BE AVOIDED 225 
 
 alteration of day with night has now been historically 
 attested for 5,000 years, the probability of the same 
 alternation recurring to-day = 1,826,214 : 1,826,215 ; 
 that is, one may bet 1,826,214 to 1 on its occurring 
 again." 3 
 
 Dangers to be Avoided in Interpreting Proba- 
 bilities. Care is needed in the employment and inter- 
 pretation of probabilities. When we say that the prob- 
 ability of heads is %, we do not mean that in two throws 
 we shall get heads once, nor do we mean that in any 
 definite number of throws the number of heads and tails 
 will be equal. Indeed, a run of heads of any finite length 
 is possible. The probability of a run of ten is Vw24. 
 But the longer the series the more closely should we 
 expect the proportion of heads to approximate that in- 
 dicated by the statement of its probability. If heads 
 have come up four times already the probability of their 
 coming up the next time is still % ; the same is true if 
 they have come up ten or any other number of times. 
 The past throws have nothing to do with the present 
 or future. To expect that, because a coin has come up 
 heads several times in succession, it is therefore more 
 likely to come up tails the next time, 4 is wholly to mis- 
 understand the meaning of probability. Indeed, a pre- 
 ponderance of heads in the past throws would suggest 
 that the -coin was not true, that there was a hidden 
 cause favoring heads, and that as a matter of fact the 
 probability of heads was greater than %. In no case 
 does the knowledge of the probability of an event give 
 any definite information regarding the next or any other 
 
 3 Lotze, Logic, Book IT, chap. 9. 
 
 4 This is sometimes called the " gambler's fallacy." 
 
PROBABILITY 
 
 specified case. It simply tells us that in the long run 
 we have a right to expect a certain proportion of oc- 
 currences, and the longer the run, the closer the ap- 
 proximation. So far as " luck," pure and simple (fav- 
 orable or unfavorable accident), is -concerned, we might 
 expect that, in the long run, and taking an infinite num- 
 ber of individuals, " good luck " and " bad luck " would 
 be equal, though particular individuals might be always 
 lucky or unlucky, or their good or bad luck might begin 
 or end at any point whatever. Bad luck in the past 
 would be no evidence of bad luck in the future. Of 
 course, a great deal that we ordinarily call luck or 
 chance is really the result of ability, foresight, and sa 
 on, or of their opposites. 
 
 EXERCISES. 
 
 1. What does each of the following propositions mean; 1 
 
 (1) He is probably an official of some sort. 
 
 (2) There is a strong probability in favor of his 
 
 being elected. 
 
 (3) The probability of ten more years of life for a 
 
 man of his age is %. 
 
 2. " The probability that a new-born child will live to 
 the age of 25 years is % ; and if it lives to that age, the 
 probability of its being well-educated is %; and if it is 
 well-educated, the probability of its beirrg a distinguished 
 person is % * Calculate the probability of the new-born 
 child's being a distinguished pe'rson." Ray, Logic. 
 
 S. Thirty per cent, of the men in college are Freshmen, 
 and twenty per cent, of the Freshmen come from the West. 
 What is the probability that the next student who passes 
 will be a Freshman from the West? A Freshman and not 
 from the West? Not a Freshman? 
 
 4. What is the probability that a die will fall with the 
 same side up five times in succession ? 
 
EXERCISES 225 
 
 5. What is the probability that a given side of a die 
 will come up at least once in two throws ? In three throws ? 
 
 6. In tossing a coin four times, what is the probability 
 of getting heads three times? 
 
 7. Suppose that an event had happened in one thousand 
 cases in which a given phenomenon had been present and 
 had never failed to happen when the latter was present; 
 what would be the probability of its happening when next 
 the phenomenon was present? 
 
SUPPLEMENT TO PART II 
 
 THE GRAPHIC METHOD OF REPRESENTING 
 DATA AND THEIR RELATIONS 
 
 WHEN large groups of figures are to be presented 
 it is often useful to employ diagrams which will enable 
 the eye to grasp at once the series as a whole. There 
 
 G. Britain.. 1,633,000 
 
 U. S 611,500 
 
 France 609,000 
 
 Germany ....529,000 
 
 Japan 374,000 
 
 Russia 207,500 
 
 Austria 113,000 
 
 are many varieties, 
 ular discussions of 
 parative populations, 
 wealth, navies, and so on, 
 often represent the 
 ious figures by lines 
 surfaces which are 
 juxtaposed as to show at 
 once to the ere the 
 Hons of the several quan- 
 tities. Thus, the 
 nage of .the eight great- 
 est navies of the world in 
 1907 was approximately Fig. 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 1 
 op- 
 
 3m- 
 
 >ns, 
 
 
 
 
 
 on, 
 
 
 
 
 
 or 
 
 
 
 
 
 at 
 
 
 
 
 
 
 
 G.B. 
 
 
 
 sla- 
 
 
 
 
 
 
 U.S. 
 
 
 an- 
 
 
 
 
 
 F. 
 
 
 
 
 
 
 
 G. 
 
 
 
 
 
 
 
 J. 
 
 
 
 
 
 at- 
 
 
 R. 
 
 
 
 
 
 
 l in 
 
 A. 
 
 
 
 
 
 
 
THE GRAPHIC METHOD 
 
 227 
 
 as above. Or we might employ rectangles with equal 
 bases, or points on a curve. 
 
 The relation between two series of numbers or quan- 
 tities may be represented graphically. Let us take a 
 case in which successive quantities are related to suc- 
 cessive years. The population of the United States 
 at each census, from 1820 to 1900, was approximately: 
 1820, 9 millions; 1830, 12 millions; 1840, 17 millions; 
 1850, 23 millions; I860, 31 millions; 1870, 38 millions; 
 1880, 50 millions; 1890, 62 millions; 1900, 76 millions, 
 These facts could be represented thus : 
 
 Millions of population 
 
 * * N3 Co -C*. t/i ON -vjO( 
 
 ooo ooo oc 
 
 
 
 
 
 
 
 
 
 (76) 
 
 
 
 
 
 
 
 
 (62) 
 
 
 
 
 
 
 
 
 (50) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (31) 
 
 
 
 
 
 
 
 
 
 (23) 
 
 
 
 
 
 
 
 (9) 
 
 (12) 
 
 (17) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Years 1820 '30 
 
 '40 '50 '60 
 
 FIG. 3. 
 
 '70 '60 '90 1900 
 
 70 
 
 50 
 
 v> 30 
 O 
 3 20 
 
 Years 1820 '30 '40 '50 '60 '70 '80 
 
 PIG. 4. 
 
 '90 1900 
 
228 DATA AND THEIR RELATIONS 
 
 In the first figure the successive quantities are repre- 
 sented by rectangles with equal bases, the years being 
 indicated on the base line and the population on the 
 
 FIG. 5. 
 
 vertical. Or we can indicate the quantities by a series 
 of points located according to their size and date and 
 join these points by a curve, as in figure 4. 
 
AN ILLUSTRATION 229 
 
 Figure 5 is borrowed from Bowley's Elements of 
 Statistics, and represents the following data: 
 
 SHILLINGS 
 
 rom 15 to 
 
 16 
 
 200 
 
 66 
 
 16 
 
 to 
 
 17 
 
 400 
 
 66 
 
 17 
 
 to 
 
 18 
 
 100 
 
 
 
 18 
 
 to 
 
 19 
 
 100 
 
 66 
 
 19 
 
 to 
 
 20 
 
 200 
 
 66 
 
 20 
 
 to 
 
 21 
 
 200 
 
 66 
 
 21 
 
 to 
 
 22 
 
 300 
 
 66 
 
 22 
 
 to 
 
 23 
 
 300 
 
 
 
 23 
 
 to 
 
 24 
 
 500 
 
 66 
 
 24 
 
 to 
 
 25 
 
 900 
 
 66 
 
 25 
 
 to 
 
 26 
 
 1200 
 
 66 
 
 26 
 
 to 
 
 27 
 
 800 
 
 66 
 
 27 
 
 to 
 
 28 
 
 700 
 
 66 
 
 28 
 
 to 
 
 29 
 
 500 
 
 66 
 
 29 
 
 to 
 
 30 
 
 300 
 
 66 
 
 30 
 
 to 
 
 31 
 
 300 
 
 66 
 
 31 
 
 to 
 
 32 
 
 400 
 
 66 
 
 32 
 
 to 
 
 33 
 
 400 
 
 66 
 
 33 
 
 to 
 
 34 
 
 500 
 
 66 
 
 34 
 
 to 
 
 35 
 
 500 
 
 66 
 
 35 
 
 to 
 
 36 
 
 600 
 
 66 
 
 36 
 
 to 
 
 37 
 
 400 
 
 66 
 
 37 
 
 to 
 
 38 
 
 100 
 
 66 
 
 38 
 
 to 
 
 39 
 
 80 
 
 66 
 
 39 
 
 to 
 
 40 
 
 20 
 
 Median, 26/9 (26 shillings, 9d) ; Quartiles, 24/2, .32. 
 Deciles, 20, 23/6, 24/9, 25/8, 26/9, 28/2, '31, 33/4, 
 35/4. 
 
230 DATA AND THEIR RELATIONS 
 
 Mode, 25/3; secondary positions (modes), 16/6, 36. 
 
 Curves may also be employed to show the relations 
 
 between two or more sets of variable quantities. Thus: 
 
 Marriage rate per 1000 
 
 Imports and Exports per head 
 
 Price of Wheat per quarter 
 
 20 
 
 $15 
 10 
 
 m 
 
 i i \ 
 
 \ 1 
 
 00 
 
 1860 
 
 n \\ 
 < 
 
 
 
 
 o tfl 
 
 60 
 
 ,1870 
 
 1880 
 FIG. 6. 
 
 1890 
 
 There are many opportunities for error in such a 
 case as this. For example if the scale for the marriage 
 rate were twice as great, the fluctuations in the curve 
 'would appear to be greater in comparison with those 
 
THE PROBABILITY CURVE 231 
 
 in the other curves. (See Bowley, loc. cit.) Great 
 caution is necessary in the comparison of curves. 
 
 
 
 n 
 
 \ 
 
 
 
 
 
 / 
 
 \ 
 
 
 
 
 / 
 
 / 
 
 \ 
 
 \ 
 
 
 A ^ 
 
 7 
 
 
 
 
 
 s 
 
 FIG. 7. 
 
 The Probability Curve. The curve represented by 
 Fig. 7 is of great value in scientific investigations. It 
 is sometimes known as the Probability Curve, or the 
 Normal Curve of Error. Suppose a large number of 
 measurements of a given quantity, or variations from 
 a given standard; if no causes of constant error 
 are present, errors of excess are equally probable with 
 errors of the opposite sort as we have already seen 
 (page 210) ; moreover large errors are less probable 
 than small errors and very large errors are very improb- 
 able. Let the line Mm represent the correct measure^ 
 ment ; let the part of the curve to the right of this line 
 represent the positive errors (errors in excess), and the 
 part to the left, those which are negative ; the size of an 
 
DATA AND THEIR RELATIONS 
 
 error would be indicated by its distance from M along 
 the base line. MF would indicate a small positive 
 error ; MS, a large negative one ; height above the base 
 line indicates the comparative number of the errors; 
 thus the line Ff means a large number of small errors ; 
 the line Ss, a small number of large ones. The curve 
 may represent not only errors, but any series of quan- 
 tities grouped about a type, when the causes of variation 
 are very numerous and are independent of each other. 
 In an earlier example it appeared that in tossing a coin 
 the various possible series of runs of heads or tails 
 could be stated in a series of figures which were related 
 to each other as are the coefficients in the expansion 
 of a binomial to the power indicated by the number of 
 throws. 
 
 This formula can be used in any case in which a 
 number of independent variable factors is concerned. 
 If the number is very large the chances of the various 
 possible -combinations can be represented by the curve 
 we are discussing, as for example, in the case of the 
 stature of adult males. Many factors enter into the 
 determination of stature, such as heredity, health in 
 childhood, kind and quality of food, occupation, and 
 so on ; the statures of men in any given community are 
 ranged on either side of the mode in such a way as to 
 be represented with substantial accuracy by the proba- 
 bility curve (or the Curve of Frequency or of Distri- 
 bution, or the Normal Curve of Error, as it is vari- 
 ously called). 
 
 Let us suppose, however, that some -constant factor 
 is introduced tending to alter stature in a given direc- 
 tion; what effect will this have on the curve? It will 
 
IRREGULAR CURVES 
 
 233 
 
 obviously change its form, for a greater number of 
 cases will appear on one side of the former mode and a 
 smaller number on the other; instead of being sym- 
 metrical it will be skewed to one side or the other, thus : 
 
 FIG. 8. 
 
 The presence of a skew always indicates the opera- 
 tion of some constant factor. If in tossing coins we 
 found such a skew toward the side representing a large 
 number of heads we should have evidence of the pres- 
 ence of some constant factor favoring heads. 
 
 Sometimes the representation of a series of quan- 
 tities would produce a curve of still more irregular 
 shape, such as this: 
 
 FIG. 9. 
 
 Such a curve would show that the group was not 
 homogeneous ; that there was really a combination of 
 two groups ; or that certain factors were operative in 
 one part of the series and not in another. Professor 
 
DATA AND THEIR RELATIONS 
 
 Thorndike 1 gives the following curve as representative 
 of the frequency of death at different ages, the age 
 
 FIG. 10. 
 
 increasing as we go from left to right. Certain factors 
 are operative in early infancy that play no part later. 
 
 i In his Theory of Mental and Social Measurements, p. 51. See 
 this book for discussion of measurement. 
 
PART III 
 THE CONSTRUCTION OF SYSTEMS 
 
CHAPTER I 
 EXPLANATION 
 
 What is Explanation ?-Prob ability, classification and 
 the discovery of laws all have to do with facts. 
 Probability tells us the frequency with which a fact 
 may be expected to occur; classification puts the fact 
 into a group of like facts, and the better the classifica- 
 tion from a scientific point of view, the more does the 
 placing of the particular fact tell us with regard to 
 its relations of resemblance and difference with other 
 facts. A law states the conditions under which a fact 
 occurs. In which of these cases can we be said to 
 explain a fact? 
 
 The statement of the frequency with which an event 
 occurs does not explain the event. We may say that 
 the order of nature is such that, unless some change in 
 the conditions is introduced, we may expect an event to 
 occur with the same frequency in the future as it has 
 manifested in the past; but that is obviously very far 
 from an adequate explanation. 
 
 Do we explain an event when we classify it? When 
 we ask why a given body fell to the ground, do we ex- 
 plain the phenomenon by saying that it was a heavy 
 body? Not entirely, and if we did not already know 
 some law holding for heavy bodies, our statement would 
 throw no light on the subject. It is quite true that a 
 statement of this sort may be a preliminary to ex- 
 planation. 
 
 237 
 
238 EXPLANATION 
 
 A law tells us how phenomena of a given sort be- 
 have ; it states the conditions of their occurrence, and 
 if we can not say what sort of thing a given fact is we 
 can not state its conditions. In bringing a fact under 
 a law we first approach an explanation of it. Explana- 
 tion has been defined as (in positive science) " the 
 reduction of a phenomenon to the terms of a general 
 principle, whatever that principle may be." 
 
 Have we reached a final and -complete explanation 
 of a fact when we have brought it under a general prin- 
 ciple ? In many cases this seems to be sufficient ; if 
 we are familiar with the law and if we can see its bear- 
 ing upon the fact in question, we are ordinarily content 
 with this sort of explanation. An eclipse of the moon 
 is sufficiently explained for ordinary purposes if we 
 are told that it is caused by the presence of an opaque 
 object between it and the source of its light. Or the 
 revolution of the moon about the earth may be ex- 
 plained by saying that it is the resultant of the opera- 
 tion of centripetal and centrifugal forces. 
 
 But there are two further questions that may be 
 asked. First, what are the circumstances in which the 
 law operates in the present case? and second, how is the 
 law itself to be accounted for? Let us consider the 
 second question: How is a law to be explained? The 
 answer is : By showing that the law is itself a case of 
 a more general law. The attraction of the earth for 
 bodies on its surface is explained by showing that it 
 is a case under the law of gravitation. " It has often 
 been found that scientific men were in possession of 
 
 i Dictionary of Philosophy, etc. Ed. Professor J. Mark Bald- 
 win. 
 
SYSTEMATIZING DATA 239 
 
 several well-known laws without perceiving the bond 
 which connected them together. Men, for instance, had 
 long known that all heavy bodies tended to fall towards 
 the earth, and before the time of Newton it was known 
 to Hooke, Huyghens and others, that some force prob- 
 ably connected the earth with the sun and moon. It 
 was Newton, however, who clearly brought these and 
 many other facts under one general law, so that each 
 fact or less general law throws light upon every 
 other." 2 
 
 How far can this be carried? Do we not at last 
 arrive at laws which are elementary and not to be ex-* 
 plained by reference to anything simpler or more fun- 
 damental? Are we then to regard these elementary 
 laws as inexplicable? No, for reference to simpler and 
 more 'fundamental laws is merely one method of bring- 
 ing the data into a system. If the elementary law can 
 be shown to be a part of a system, made up, for example 
 of other elementary laws, we have all the explanation 
 which can be demanded. The parts are explained by 
 being given their proper place in the whole. If the 
 whole were in turn a part of a larger whole it could be 
 explained in the same way. But suppose the whole 
 were ultimate : could it be explained ? Could the uni- 
 verse, not simply the physical universe, but the whole 
 of reality of whatever kind, could it be explained? 
 The only kind of explanation which could be given 
 would be a statement of the relation between this whole 
 and its parts, and it is hard to see what other kind 
 could be asked for. One might ask for the purpose of 
 it all, but in the broad way in which we are conceiving 
 .2 Jevons, Lessons in Logic, p. 268. 
 
240 EXPLANATION 
 
 of it, whatever purpose existed would be included in the 
 whole itself. 3 
 
 The explanation of a law (or fact) involves not 
 merely showing that it is a case under a general rule, 
 but also in discovering its relations to other laws and 
 facts aside from the general rule under which it is 
 brought. Along with other laws and facts it consti- 
 tutes an interrelated whole, and explanation might 
 better be defined as giving the thing to be explained 
 its place in an organized system. We may wish to 
 know not only the general law or laws under which the 
 special case falls, but also the other special cases which 
 are related to it; or in other words, we may wish to 
 know the general law and also the circumstances of its 
 application in the present case. 
 
 We can distinguish between explanation in general 
 terms and specific explanation. The first consists in 
 assigning the general law; the second in showing, in 
 addition to this, how the general law applies. The 
 explanation of the moon's eclipse as given above is of 
 the first sort ; if we should supplement it by stating 
 that the intervening body is the earth and show how 
 the earth and moon are situated with reference to the 
 sun, we should have a nearer approach to a specific 
 explanation. If we should go further and give an ac- 
 count of the way in which they happened to be in these 
 positions at this particular time we should have a still 
 more complete and specific explanation. The explana- 
 tion of a fact, to be absolutely complete and specific, 
 would have to contain a statement of all the laws of 
 
 a See Hobhouse, The Theory of Knowledge, chapter on *' Ex- 
 planation." 
 
COMPLETE EXPLANATION 
 
 the system to which the fact belonged and also a de- 
 scription of all the facts contained in the system. Or 
 otherwise expressed, a complete specific explanation 
 would present all the facts which were related to the 
 one to be explained, together with the laws under which 
 each and every one of these relations fell, in a single 
 unified whole. If an explanation is complete we can 
 start with the laws and circumstances involved and 
 show that the phenomenon to be explained would neces- 
 sarily follow from them. Such an explanation might 
 be possible in some parts of the field of astronomy ; if 
 not an absolutely complete explanation, it could be suf- 
 ficiently complete for all ordinary purposes. Complete 
 grasp of a system would enable us to reconstruct the 
 past or predict the future of the system. The astrono- 
 mer's knowledge of the solar system is so thorough that, 
 starting from the present position of any member of 
 the solar system and knowing the relation in which it 
 stands to each of the others, he is able to calculate the 
 present position of any of the others and also to recon- 
 struct their relative positions in the past or to predict 
 their positions in the future ; he can state the number 
 and dates of eclipses which took place a thousand years 
 ago and he can calculate the relations of any member of 
 the system to any other at any given time. The only 
 limits to such calculations are those which result from 
 an imperfect knowledge of the solar system itself and 
 ignorance of many possible disturbances from without. 
 If a system were entirely isolated and if its laws were 
 completely known, then a description of the system at 
 any given time would make possible a description of it 
 at any other time. Needless to say there is no system 
 
EXPLANATION 
 
 of facts in nature which is entirely independent of the 
 rest. Every system of facts is related to every other 
 system, either directly or indirectly. To get a com- 
 plete explanation of any single fact it would be neces- 
 sary to know the whole system of nature. To a knowl- 
 edge of all the laws of nature and all their relations 
 to each other, it would be necessary to add a complete 
 description of the relations of the parts of the system 
 to each other. Then we could have an explanation of 
 the fact which would show its relations to the whole 
 and to every part of the whole. Obviously, an ex- 
 planation of this sort can not be given for any fact. 
 If it could be given for one it could be given for all. 
 In this sense, Tennyson's lines are literally true: 
 
 " Flower in the crannied wall, 
 
 If I could understand 
 What you are, root and all, and all in all, 
 I should know what God and man is." 
 
 Sometimes we are satisfied with an explanation in 
 general terms, in terms of some familiar law. Some- 
 times we call for an explanation of the law and are 
 satisfied if it can be referred to some more general law 
 or to some familiar system. 4 
 
 4 Each of the " explanatory " sciences deals with some limited 
 group of facts and attempts to discover the system of laws which 
 holds within that field. Every one of the positive sciences takes 
 for granted certain general principles, valid for all knowledge, and 
 tries to discover a system of laws which shall be valid for its own 
 field. A demand for the explanation of a physical fact, which is 
 not satisfied with a statement of its relation to other physical 
 facts in terms of physical laws, is not a problem for the science 
 of physics. Ultimate explanations are for an ultimate science; 
 philosophy is sometimes defined as this ultimate science. The 
 laws which underly all the other sciences would be the province 
 
THE AIM OF MOST SCIENCES 
 
 The aim of most of the sciences is not to explain par- 
 ticular facts but to furnish the general laws, which may 
 be employed in explanation of facts in a given field. A 
 Science like mechanics, for example, " lays down prop^ 
 ositions which are true in the same way of all fluids, all 
 gases, etc., and represents them as general consequences 
 of general presuppositions." " It does not descend 
 into the whole manifold of the given, inasmuch as it 
 deals only with events which take place in a similar 
 manner in bodies differing in many other respects. 
 That this or that phenomenon falls under these laws is 
 a matter for subsumption in dealing with the particu- 
 lar ; it is not necessary to the completeness of the ar- 
 rangement as a whole. The mechanical theory of gases 
 disregards their chemical differences in so far as they 
 do not affect its special province by giving rise to dif- 
 ferences of specific gravity ; it is no part of its task to 
 enumerate how many sorts of gases there are: it is 
 enough to say that if a body is a gas it conforms to 
 certain laws of compressibility, of expansion by heat, 
 or of capacity for heat, etc." 
 
 Corresponding statements might be made about any 
 one of the sciences which aim at the discovery of laws 
 (as distinguished from the classificatory sciences, which 
 aim only at the complete classification of facts). 
 
 of such a universal science. It would be related to the particular 
 sciences as they are related to the concrete data which they in- 
 vestigate. It would not be complete till each of them was com- 
 plete, nor could any of them be final until it had reached its 
 goal; just as, in any one of them, no fact is completely known 
 unless the general body of laws is known, and the body of laws 
 can not be completely known until every fact can be accounted 
 for. Progress consists in alternate advancements toward com- 
 pleteness along both lines, from both directions. 
 5 See Sigwart, Loyic, Part III, chap. vi. 
 
EXPLANATION 
 
 Specific Explanation. But in practical life and in 
 the historical sciences we are concerned with the con- 
 crete individual fact; hence propositions which deal 
 with general properties and the like are of no use to 
 us unless we can see how they apply in the particular 
 case; and usually we cannot see that unless we have 
 independent knowledge of the attendant circumstances. 
 The knowledge of the single fact and of the general 
 law under which it falls does not ordinarily enable us 
 to reconstruct the system; our knowledge of both fact 
 and laws is too incomplete to enable us to get a specific 
 explanation ; and a general explanation is not sufficient 
 as a guide for action. 
 
 Suppose that the fact under investigation were a 
 criminal act of some sort; the object of the prosecut- 
 ing attorney is to fix the responsibility for the act. In 
 order to do this it is necessary for him to reconstruct 
 the circumstances surrounding the doing of the act. 
 In other words, he must build up the system of con- 
 crete facts to which the act belongs. A Sherlock 
 Holmes might be able, by superior powers of observa- 
 tion, unusual knowledge of the laws of criminal be- 
 havior, and so on, and by extraordinary skill in bringing 
 each fact observed under the proper law, to reconstruct 
 the whole system of facts without reliance upon the 
 testimony of others ; but ordinary mortals would usu- 
 ally find it necessary to collect evidence from all pos- 
 sible sources, and then, out of the scattered bits, to 
 restore some semblance of the original whole. One 
 fact, sufficiently described, and a thorough grasp of the 
 principles of the system, might be enough ; lacking that, 
 
THE APPLICATION OF SCIENCE 
 
 as 'many fragments as possible must be collected, and 
 even then no certain result might be reached. 
 
 Knowledge of the laws alone does not ordinarily 
 suffice, and even if that knowledge were complete it 
 might be possible to go astray in applying it. The 
 greatest scientist might fail in the attempt to give a 
 specific explanation of a concrete fact if he should over- 
 look the circumstances surrounding the fact. Specific 
 explanation is a matter for the application of science, 
 and theory alone is proverbially insufficient as a guide 
 for practice, no matter how correct the theory may be 
 in the abstract. The " theorist " may have an incorrect 
 theory or he may fail to note the special circumstances 
 in applying one which is correct. 
 
 Closely related to the processes of explanation are 
 those of prediction. They are complementary. In 
 explaining, we give the laws and circumstances which 
 account for a fact or a supposed fact ; in prediction 
 we set out from a set of laws and circumstances and 
 attempt to show that a certain fact will occur in the 
 future or will be found on further investigation to 
 exist. Successful prediction is, as we have seen in 
 studying the inductive methods, a test of the validity 
 of the laws we are employing. If we do not know the 
 laws and circumstances we can not predict successfully, 
 except occasionally and by accident. Prediction may 
 be said to represent the practical application of 
 science. 
 
CHAPTER II 
 HYPOTHESIS 
 
 What is an Hypothesis? Before we go on to the 
 discussion of certain typical systems, it is necessary to 
 give some attention to another matter involved in most 
 explanations, namely, the use of hypotheses. The 
 term hypothesis is used in several different senses, but 
 for our purposes an hypothesis is a provisional explan- 
 ation. Fictions made for the purpose of argument, 
 illustration, or simplification may also be regarded as 
 hypotheses, but we shall use the term in the narrower 
 sense. 1 
 
 Hypotheses, or provisional explanations, may assert 
 the existence of a fact, as when we assume that a de- 
 fective flue was the cause of a fire ; or of a law, as 
 when we infer a causal connection between vaccination 
 and freedom from smallpox ; or of a complex system 
 of laws and facts, as when we infer the existence of a 
 matriarchal system in the early history of certain 
 peoples. Inductive inferences, which were discussed in 
 chapter vi., would fall under the head of hypotheses. 
 
 The Value of Hypotheses. There has been much 
 disagreement regarding the value of hypotheses and 
 their use in science. A good many scientists have de- 
 clared that hypotheses are not only unnecessary but 
 
 i For an interesting discussion of the subject, see Muir- 
 head, Philosophy and Life, Art. " Hypothesis." 
 
 246 
 
OPPOSITION TO USE OF HYPOTHESES 
 
 are positively harmful, and Newton's " Hypotheses 
 non fingo " is often quoted in defense of their position. 
 To apply this literally would mean that a science would 
 remain merely a body of carefully observed and classi- 
 fied facts, unless laws should somehow or other spring 
 ready made from them without having been previously 
 put forward as possible laws and then tested by further 
 observation and experiment. Now, it might sometimes 
 be possible to collect our facts over a very wide range 
 and classify them and their relations in such a way 
 as to show at once the law of their connections ; the 
 inductive methods indicate the sort of grouping 
 that would be necessary ; but even with their assistance 
 it would rarely happen that a fully verified law would 
 appear without previous unsuccessful attempts at its 
 discovery. Previous to the Nineteenth Century the 
 progress of science was seriously retarded by what 
 Romanes has called the Bugbear of Speculation. In the 
 introduction to his Darwin and after Darwin he 
 gives the following statement of the situation in the 
 natural sciences : " Fully awakened to the dangers of 
 web-spinning from the ever fertile resources of their 
 own inner consciousness, naturalists became more and 
 more convinced that their science ought to consist in 
 a mere observation of facts, or tabulation of phe- 
 nomena without attempt at theorization upon their 
 philosophical import. If the facts and phenomena pre- 
 sented any such import, that was an affair of the man 
 of letters to deal with ; but as men of science, it w r as 
 their duty to avoid the seductive temptations of the 
 world, the flesh and the devil, in the form of specula- 
 tion, deduction, and generalization . . . this was the 
 
248 HYPOTHESIS 
 
 orthodox and general view." It was current in the 
 time of Linnseus and even to the time of Cuvier. " The 
 Origin of Species made an epoch . . . Darwin dis- 
 played the true principle which ought to govern bio- 
 logical research ... he never loses sight of the dis- 
 tinction between fact and theory . . . but his idea of 
 the scientific use of facts is plainly that of furnishing 
 legitimate material for the construction of theories 
 . . . the spirit of speculation is the same as the spirit 
 of science, namely, to know the causes of things . . . 
 If it be causes or principles as distinguished from facts 
 or phenomena, that constitute the final aim of scientific 
 research, obviously the advancement of such research 
 can be attained only by the framing of hypotheses. 
 And to frame such hypotheses is to speculate." Dar- 
 win said of himself that he made an hypothesis on every 
 subject. " He was as productive of hypotheses as 
 nature is of living things, and like her, he subjected 
 them all to the principle of natural selection." 2 
 
 Hypotheses are necessary for science. " All science 
 starts with hypotheses, in other words, with assump- 
 tions that are unproved, while they may be and often 
 are erroneous; but which are better than nothing to 
 the seeker after order in the maze of phenomena." 3 
 
 An erroneous hypothesis may be quite as effective 
 in the field of practical activity as a true one could be. 
 " The theory that some god would destroy the tribe if it 
 did not wash at a particular time was a very crude ex- 
 planation of an observed fact ; but it nevertheless has 
 its merits. It caused the tribe to wash occasionally - 
 
 2 Cramer, The Method of Darwin, p. 40. 
 
 3 Huxley, Hume, p. 65. 
 
MISTAKEN HYPOTHESES 249 
 
 a thing it would never have done. It furnished a 
 theory which tended to prevent disease. It recognized 
 the truth which bacteriological science has only just 
 grown up to in the present generation : that the pen- 
 alty for violation of law was visited not so much on 
 the individual as on the community. 4 
 
 The Ptolemaic System was an erroneous hypothesis, 
 but without it, or some other theory, astronomical 
 knowledge would have progressed much more slowly 
 than it did. " The superiority of the Greeks to their 
 Oriental neighbors in science has often been accounted 
 for by their fertility in theory. The Oriental peoples 
 were, at the time of which we write (Cosmological 
 Period), considerably richer than the Greeks in accu- 
 mulated facts, though these facts had certainly not 
 been observed for any scientific purpose, and their pos- 
 session never suggested a revision of the primitive view 
 of the world." 5 
 
 The danger in using hypotheses lies in the fact that 
 we are so likely to forget that they are only hypotheses. 
 We find some explanation which seems to fit the facts 
 or which supports some other belief of ours, and we 
 forget that our hypothesis has not been verified. We 
 tend to have too great a fondness for hypotheses which 
 we have ourselves made ; we are liable to " the partiality 
 of intellectual parentage." Darwin's example may 
 again be cited as the right one. " I have steadily en-' 
 deavored to keep my mind free so as to give up any 
 hypothesis, however much beloved (and I cannot resist 
 
 4 President Hadley, in an article in the Atlantic Monthly, Feb*> 
 ruary, 1903, p. 153. 
 
 5 Burnet, Early Greek Philosophy, 1st Ed., p. 22. 
 
250 HYPOTHESIS 
 
 forming one on every subject), as soon as the facts 
 are shown to be opposed to it. Indeed, I have had no 
 choice but to act in this manner, for, with the exception 
 of the Coral Reefs, I cannot remember a single first- 
 formed hypothesis which had not after a short time 
 to be given up or greatly modified." 6 
 
 It has been said that an hypothesis is a question. 7 
 When we form an hypothesis our attitude should be 
 described by the inquiry : " Is this the true explanation 
 of the facts? " If that attitude could be preserved the 
 danger from hypotheses would be very small. We often 
 hear of " working hypotheses." They are simply 
 hypotheses which are confessedly unverified but valu- 
 able as a basis on which to work toward an explanation. 
 There may be many degrees of verification, from the 
 most complete to the most imperfect ; strictly speak- 
 ing, one might say that until an hypothesis has been 
 proved true and shown to be a law (and therefore no 
 longer a mere hypothesis) it remains a working hypo- 
 thesis ; but in ordinary usage this term is used to de- 
 scribe hypotheses which are useful but in no sense 
 established. 
 
 One way of holding the mind open to the fact that a 
 given hypothesis is not to be trusted too far would 
 be to keep before us a number of different rival hypo- 
 theses. 8 
 
 6 Life and Letters, Vol. I, p. 83, quoted in Cramer's Method of 
 Darwin. 
 
 i Langlois and Seignobos, Introduction to the Study of History. 
 
 8 This method, which has been called the " Method of Multiple 
 Working Hypotheses," has been recommended as promoting thor- 
 oughness, suggesting lines of inquiry, as a means of sharpening 
 discrimination, increasing fertility in reasoning processes, etc. 
 See Chamberlain, The Method of Multiple Working Hypotheses t 
 Science. Feb. 7. 1890. 
 
THE DERIVATION OF HYPOTHESES 251 
 
 How are Hypotheses Suggested to Us? We have 
 already seen that the groupings of facts or sequences 
 such as we use in applying the method of Agreement 
 and the rest lead to the formation of inductive hypo- 
 theses. Indeed (1) any sequence may do this. If we 
 notice that A is followed by B, we tend naturally, in 
 the absence of evidence to the contrary, to believe that 
 the second will always follow the first. The statement 
 that these two are universally and necessarily -connected 
 in this way is an hypothesis unless or until further ex- 
 amination shows that the statement is either true or 
 false. 
 
 () ANALOGY. A second 9 source of hypothesis is 
 found in Analogy. The term analogy has been used in 
 a good many different senses. 10 In its broadest sense 
 it means any kind of resemblance. An inference from 
 analogy is inference from the resemblance of two cases 
 in certain observed points to their resemblance in a fur- 
 ther particular which has been observed in only one of 
 them. For example, we may observe, in examining the 
 skulls of certain extinct animals, that they all have 
 sharp canine teeth and rudimentary molars ; in this 
 respect they resemble modern carnivorous animals; 
 hence we infer that these extinct animals were carnivo- 
 rous. Or we know that a boy who is ill has eaten unripe 
 fruit ; we infer that another boy who shows similar 
 symptoms has been guilty of a similar indiscretion. 
 Inference from analogy is usually to some particular 
 
 9 A third source of hypotheses is found by Sigwart in the Con- 
 version of propositions. For example, isosceles triangles have 
 the angles at the base equal. Is the converse true? See Sig- 
 wart, Logic, ii, p. 83. 
 
 10 See Minto, Logic, p. 367. 
 
252 HYPOTHESIS 
 
 fact or situation, though it may be further extended 
 to a general principle. 
 
 Analogy alone is notoriously an unsafe guide; but 
 if certain general rules are kept in mind it may often 
 be employed to advantage. 
 
 1. If two sets of facts resembled each other in only 
 one particular or in very few, an inference as to their 
 resemblance in another particular would be very haz- 
 ardous. The fact that two men were born in the same 
 city gives no ground for the conclusion that one will 
 have the same profession as the other. 
 
 2. If two sets of facts resembled each other in every 
 particular except such as were irrelevant, the inference 
 would be safe. Reasoning by analogy in geometry 
 illustrates this. Again, if two animals were alike except 
 in color, the fact that one was carnivorous would be 
 good ground for believing that the other was too. 
 
 3. In so far as two things or two sets of facts dif- 
 fered in relevant particulars the inference would be of 
 doubtful value. If one of two twins had been educated 
 in one way and the other in a different way, it would 
 not be safe to infer that one would be interested in the 
 things in which the other was interested. 
 
 4. If one of two similar things possessed a char- 
 acteristic inconsistent with a characteristic possessed 
 by the other, it would of course be impossible to infer 
 that the first thing possessed the latter characteristic. 
 If A is a singer we cannot infer that his twin brother 
 B is, if the latter is deaf and dumb. 
 
 5. If the points of resemblance outnumbered the 
 points of difference, we should have more reasons for 
 than against the inference, provided, of course, that 
 
ANALOGY 253 
 
 the various points were equally important in determin- 
 ing the character of the things in question. As a mat- 
 ter of fact they never are of equal importance, so 
 that the relative importance of the various character- 
 istics should be taken into account; a difference in 
 health would count more against equal strength in two 
 men than similarity of stature, weight and age would 
 count in its favor. 
 
 6. In counting resemblances and differences, only 
 those which are independent should be counted; the 
 fact that a planet possesses atmosphere and that it 
 refracts light passing near its surface are not inde- 
 pendent; to count these as two points of likeness when 
 trying to find ground for the conclusion that one 
 planet resembled another in any particular respect 
 would be incorrect. 
 
 In practice it is not easy to say just what char- 
 acteristics are relevant or to be sure whether two points 
 are independent. 11 
 
 Analogy may be employed in connection with other 
 grounds of inference ; for example, if a given situation 
 possesses factors which are partly like and partly un- 
 like those in another situation we might sometimes infer 
 the presence in the second of some further character- 
 istic possessed by the first, but in less degree. One 
 man might exhibit some of the symptoms exhibited by 
 another who was known to have taken a certain "drug; 
 we might infer that the first had taken a smaller quan- 
 tity of the same drug, and so on. 
 
 Requisites of a Good Hypothesis. Having made 
 our hypothesis on whatever ground, we should ask our- 
 11 See Hothouse, Theory of Knowledge, page 289, seq. 
 
254 HYPOTHESIS 
 
 selves whether it is worthy of serious consideration. 
 To put the question in its usual form, What are the 
 requisites of a good hypothesis? 
 
 1. In the first place it must serve the purpose for 
 which it is made; it must offer an explanation for 
 data which have not previously been explained cor- 
 rectly. Sometimes certain other explanations may 
 have been offered and found insufficient ; sometimes the 
 data may have been entirely unexplained. An hypothe- 
 sis which does not connect at least two facts hitherto 
 not properly connected is worthless. 
 
 2. A good hypothesis must, of course, be consistent 
 with itself and with all the data concerned. It is some- 
 times said that an hypothesis must not contradict known 
 laws; if there are laws which are completely verified, 
 the hypothesis must be in agreement with them. 
 
 That does not mean that an hypothesis must not 
 disagree with any principles which have been hitherto 
 accepted. Such reasoning would have ruled out the 
 Copernican Hypothesis, and it did, as a matter of fact, 
 lead many to reject that theory. Strictly speaking, 
 any hypothesis which offers a consistent account of the 
 data and their relations has a claim to consideration. 
 In practical life we are often warranted in neglecting 
 new theories which contravene accepted principles, at 
 least until they have been shown to approach in value 
 and soundness those already current ; but the specialist 
 in any field is .not justified in rejecting a theory simply 
 on the ground that it disagrees with those he has held 
 in the past. It is his duty to test all of them. 
 
 3. An hypothesis, to be worthy of consideration, 
 must be capable of verification. If data for its verifi- 
 
REQUISITES OF HYPOTHESES 255 
 
 cation are not already at hand they must at least be 
 conceivable and their discovery must be within the 
 bounds of possibility. Herodotus, in discussing the 
 various theories of the rise of the Nile, says of the one 
 which connected it with the mythical stream of Ocean: 
 " The person who speaks about the Ocean, since he has 
 transported the question to the dominion of the in- 
 scrutable, does not admit of refutation." 12 
 
 4. Other things being equal, choose the simplest 
 hypothesis. 
 
 Making hypotheses involves mental activities which 
 go beyond perception and memory. They are often 
 discussed under the heading of " Imagination." But 
 imagination in this sense is not simply imagination in 
 the limited sense of making mental pictures. It involves 
 constructive activities often of a highly complicated 
 sort. As " creative " imagination it differs from that 
 of the poet in that it does not have to do necessarily 
 nor primarily with concrete experiences. 13 
 
 EXERCISES. 
 
 State the ground of the hypothesis in each of the follow- 
 ing examples and estimate the value of the hypothesis: 
 
 1. Geologists, watching at what rate changes are occur- 
 ring in the earth's surface at the present time, e. g., mak- 
 ing of valleys, glacier movements, etc., determine the 
 length of time it must have taken to produce the corre- 
 sponding changes during the so-called geological periods. 
 
 2. In looking at the pictures in an art gallery, our atten- 
 tion is specially attracted by one picture whose character- 
 istics impress themselves in our mind. Years afterward, 
 in another country, we again see those characteristics in 
 another picture and we feel certain that both pictures are 
 the work of the same artist. 
 
 12 Gomperz, Greek Thinkers, Bk. IIL chap, p 6 
 
 13 Minto, Logic, pp. 335, 33G. 
 
256 HYPOTHESIS 
 
 3. Cutting tools have edges and places for handles. 
 These flints have edges and places for handles; they are 
 therefore, cutting tools. 
 
 4. Some Northwest Coast Indians after seeing and hear- 
 ing a phonograph for the first time, were asked what they 
 thought it was. Their answer was that it was a very power- 
 ful echo which the white man controlled by means of a 
 " strong medicine " or magic. 
 
 5. The theory that many philologists hold, that many of 
 the languages of the world may be traced back to a common 
 stock, known as the Aryan, is based on analogy. In 
 Persian, Greek, Sanscrit, etc., several very simple words, 
 usually verbs, such as to give and to be, are found to have 
 almost identically the same root, from which resemblances 
 the common descent is argued. 
 
 6. Certain mountains, which have large deposits of ba- 
 salt, contain gold. When large deposits of basalt are found 
 ire other mountains, we may suppose that they also contain 
 gold. If gold is not found, tin is. There seems to be a 
 relation between deposits of basalt and deposits of gold. 
 
 7. Noting that certain substances expand when they 
 crystallize, and noting also that certain other substances 
 expand when heated, I might infer that heat causes the lat- 
 ter substance to crystallize and hence to expand. 
 
 8. Since ether has been offered as the medium of trans- 
 mission of light-waves, and since some forms of electricity 
 are forms of wave-motion, we might say that ether is the 
 medium of transmission of electricity. 
 
 9. The U. S. is a republic and its citizens are prosperous 
 and contented; we may therefore infer that if Cuba were a 
 republic, her citizens would be prosperous and happy too. 
 
 10. Hydrochloric acid turns blue litmus paper red; sul- 
 phuric acid has similar properties, and we may infer that 
 it, too, will turn blue litmus paper red. 
 
 11. Bones resembling those of an elephant were found 
 in a given 4 locality. We conclude that, at some time or 
 other, elephants lived in this locality. 
 
 12. Cotton is grown in the U. S. in a moist, warm 
 climate and a sandy soil; we may infer that Egypt, which 
 has these characteristics, will also grow cotton. 
 
CHAPTER III 
 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 AN examination of the methods employed in estab- 
 lishing certain typical varieties of systems of knowledge 
 may help to make clearer the complexity of knowledge 
 and the relations of the processes involved in getting 
 it. Every system, as we have seen, contains laws. 
 Some of them are systems of laws and general concepts ; 
 others include also concrete facts. Let us take as an ex- 
 ample of the first, the sort of system which is to be 
 found in mathematics or mechanics ; and as examples 
 of the second, the system of related facts which the 
 historian or the criminal lawyer aims to establish. The 
 other sciences lie between. 
 
 We cannot, in our present discussion, begin at the 
 very beginning. We must grant to the historian and 
 the lawyer the generally accepted laws of human be- 
 havior, the accepted principles of science, in short, the 
 working materials of his science. To the mathema- 
 tician, we must grant his concepts and axioms and 
 postulates, and to both the general principles of scien- 
 tific method. We wish merely to see how each employs 
 these principles, what his method is. All these concepts 
 and principles have been brought to light in the course 
 of human experience. The mathematician employs 
 chiefly the processes of analysis and deductive reason* 
 ing. Observation, testimony and, in general, the means 
 
258 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 for knowing the concrete are, for the most part, left 
 aside in his work. 
 
 The Geometric System. Let us take an example of 
 scientific method as it appears in the science of geome- 
 try. Other fields of mathematics differ from this in 
 important respects, but for the purposes of illustra- 
 tion geometry will be sufficiently representative. What 
 is the starting point in geometry and what sort of sys- 
 tem does it attempt to build? 1 Geometry starts, not 
 with perceived objects as the natural sciences do, but 
 with a set of concepts and propositions. Among its 
 concepts are those of point, line, magnitude, equality, 
 and so on. Some of these are definable in terms of the 
 others, as " a point is that which has no magnitude." 
 There remain, however, certain concepts which are inde- 
 finable, viz., those by means of which all the others are 
 defined. Of these concepts there are two kinds : con- 
 cepts of elements, and concepts of relations. Besides 
 these concepts geometry has among its data certain 
 propositions which express the relations which hold 
 among its elements. These propositions are known as 
 axioms and postulates. 2 
 
 1 See Oswald Veblen, Popular Science Monthly, Vol. LXVIII, 
 Art. "The Foundations of Geometry"; and Transactions of the 
 American Mathematical Society, Vol. 5, No. 3, Art. "A System 
 of Axioms for Geometry." 
 
 2 No clear line of distinction was drawn by Euclid between 
 axioms and postulates. Both were regarded as unproved and un- 
 provable propositions which must be admitted as true by every 
 one who understood them, as a priori truths. At the present day 
 their a priori character is very widely questioned, but they are 
 unprovable in that they can not be deduced from any simpler 
 propositions. One way of distinguishing them was to define the 
 axioms as common notions and the postulates as geometrical pre- 
 mises which must be taken for granted. But the line was not 
 clearly drawn and propositions which sometimes appeared as pos* 
 tulates were at other times put among the axioms. 
 
MATHEMATICAL SYSTEMS 259 
 
 As an axiom we may cite the first in the list: 
 " Things which are equal to the same thing are equal 
 to one another " ; and as a postulate : " A straight line 
 may be drawn from any one point to any other point." 
 " All right angles are equal to one another " has some- 
 times been classed as an axiom and sometimes as a pos- 
 tulate. Euclidian geometry may be defined as " a 
 system of propositions codifying in a definite way our 
 spatial judgments." Every one of its propositions 
 can be deduced from its axioms and postulates, except- 
 ing, of course, the axioms and postulates themselves. 
 To prove any proposition we have simply to combine 
 certain concepts and propositions into a coherent 
 whole. 
 
 Let us examine Proposition XV, Book I. " Where 
 two straight lines (AB, CD) intersect each other, the 
 vertically opposite angles made by them, are equal." 
 
 The demonstration is as follows : " For the angk 
 CFA + the angle AFD = two right angles (prop. 13), 
 and also the angle AFD + the angle DFB = two right 
 angles ; therefore the angle CFA -f the angle AFD = 
 the angle AFD + the angle DFB (axiom 1) ; and the 
 common angle AFD being taken away from both, there 
 remains the angle CFA = the angle DFB (axiom 3) ; 
 but these are vertically opposite angles. In like man- 
 ner it may be proved that the vertically opposite angles 
 
260 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 AFD and BFC are equal." What are the concepts 
 and propositions employed in the proof of this theorem? 
 We have concepts of number (two, e. g\), straight 
 lines, point, circle, intersection, angles, right angles, 
 vertically opposite angles, equality, addition, subtrac- 
 tion, remainder, etc. 
 
 We employ, among the propositions, Proposition 
 XIII (When a straight line standing upon another 
 straight line makes angles with it they are either two 
 right angles or together equal to two right angles) ; 
 this proposition was proved from certain others all 
 resting ultimately upon the axioms and postulates. We 
 employ Postulate 3 (A circle may be described from 
 any center, with any interval from that center) ; Postu- 
 late 1 (A straight line may be drawn from any one 
 point to any other point) ; Definition 12 (A circle is a 
 plane figure bounded by one line called the circumfer- 
 ence or periphery ; to which all straight lines drawn 
 from a certain point within the figure, are equal) ; also 
 Axiom 1 (Things which are equal to the same thing 
 are equal to each other). 
 
 Geometrical demonstrations are made with reference 
 to figures, and it might seem as if we were really dealing 
 with a concrete particular case instead of with general 
 concepts alone ; but the concrete case is simply an 
 illustration and the whole demonstration is absolutely 
 general. Accurate measurements of the figure would 
 undoubtedly show inequalities between the vertically 
 opposite angles for the reason that the lines are not 
 absolutely straight; the figure symbolizes the intersec- 
 tion of any two absolutely straight lines and the dem- 
 onstration is true of all such lines and only of such. 
 
PURE SCIENCES 
 
 Similar statements apply to all the figures used in dem- 
 onstrating geometrical propositions. Euclidian geom- 
 etry as a whole is simply a complex system built up in 
 the manner illustrated by the example above. 
 
 The data of the geometrician are comparatively few 
 and simple. His general principles are already deter- 
 mined ; his tests of truth are agreement with his prin- 
 ciples, and not absolute agreement with concrete fa-cts ; 
 however, he believes that if it were possible to observe 
 and measure the facts accurately, and if facts could 
 be found to agree with his definitions of straight line, 
 circle, etc., for example, his conclusions would be found 
 in correspondence with them. 3 
 
 The system which we have just examined aims at the 
 organization of a set of judgments having a general 
 application and not with any specific data. The science 
 of geometry is not interested in this or that geometrical 
 figure ; it gives us information regarding figures of 
 certain kinds, leaving the question of its application 
 to particular cases to the applied sciences. All of the 
 so-called "pure sciences" are like geometry in this re- 
 spect. They deal with general principles, not with 
 particular cases. Sometimes the arts and sciences are 
 distinguished along this line, the arts being defined as 
 the application in practice of the principles embodied 
 in the sciences. The science of geometry is a system 
 founded upon a certain few general principles which 
 are described as axiomatic. 
 
 Most of the sciences include, besides axiomatic prin- 
 
 s Recently, other systems of geometry have been built up. The 
 methods employed are the same as those of Euclidian geometry, 
 but they assume different postulates. The only requirement- is 
 that the system built upon them shall be a coherent whole. 
 
262 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 ciples, others which are the outcome of the application 
 of the methods of science to the study of empirical 
 data. The science of Mechanics is an example of this. 
 As we have seen, it " lays down propositions which are 
 true in the same way of all fluids, all gases, etc." 
 These laws were discovered as a result of a multitude 
 of observations of the behavior of particular bodies of 
 fluid, gas, etc. ; the observations were recorded, 
 classified and made the basis of inductive inferences, 
 which were tested as completely as possible. Hence 
 all the processes included in the scientific method of es- 
 tablishing laws are employed, but strong emphasis is 
 placed upon the establishment of further conclusions 
 on the basis of these laws, in other words, the deductive 
 part of scientific method is emphasized. 
 
 Somewhat similar statements may be made regarding 
 the science of Chemistry, though chemistry is perhaps 
 less independent of particular facts and less able to 
 proceed deductively on the basis of generalizations al- 
 ready established ; and certain departments of chem- 
 istry are concerned rather with the classification of 
 facts than with attempts to found a deductive science. 
 Observation, analysis, classification and induction are 
 all employed. Still, even in chemistry there is much 
 that is deductive, and the interest of the chemist in 
 particular facts tends to become only indirect. 
 
 Biology and Psychology may also be mentioned at 
 this point. Both are interested in concrete phenomena 
 mainly for the sake of the general conclusions which 
 may be based upon them. Both employ the whole of 
 scientific method, including the use of statistics, aver- 
 ages and probability. Both are farther than chemis' 
 
PSYCHOLOGY AND BIOLOGY 263 
 
 try from the point at which a science begins to be 
 primarily deductive. The employment of statistics 
 and of methods of exact measurement has become of 
 very great importance in these two sciences within the 
 past few years. Reference to the recent literature of 
 both subjects makes this very evident. As examples in 
 psychology we might cite studies of animal behavior 
 and studies in child psychology ; 4 in biology, the in- 
 vestigations connected with Mendel's Law, the study 
 of Variation, and so on. 5 
 
 The pages from the works of Professor James (pages 
 280-284), illustrate psychological analysis, which docs 
 not employ statistics ; and the essay from Huxley's 
 works (pages 287-300) illustrates the same thing in 
 the field of biology. Neither passage can be regarded 
 as representative of the studies which are most fre- 
 quent at the present time. Both are exceptionally 
 broad in scope and deductive in character, but both 
 do illustrate the desire of scientists in both fields to 
 arrive at general conclusions and to establish coherent 
 systems. 
 
 Systems Which are More Concerned with Concrete 
 Data. We wish now to consider systems which have 
 to do with concrete data in a different way ; systems 
 which give to specific instances their exact place in a 
 system of concrete facts ; systems which not only pre- 
 sent a body of general laws, but also apply them to the 
 explanation of specific cases ; systems which state com- 
 pletely the causes of given phenomena or enable us to 
 
 4 See Yerkes, The Dancing Mouse; Washburn, The Animal 
 Mind; Thorndike, Educational Psychology; and articles in jour- 
 nals. 
 
 o See Punnett, Mendelivm; and articles in journals. 
 
264 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 establish the existence of given events or situations 
 not at present open to observation. 
 
 History, in so far as it is concerned with the recon- 
 struction of the past, is a case in point ; so also is the 
 criminal lawyer's attempt to discover the individual 
 guilty of a crime ; again Geology, when it aims at the 
 discovery of past changes and conditions of the earth 
 falls in the same class. In geology the primary data 
 are almost entirely the present character of the earth's 
 surface and the changes which are constantly going 
 on. It includes, of course, many of the data and con- 
 clusions of physics, chemistry, and biology. On the 
 basis of these data it is able to arrive at well-founded 
 conclusions concerning changes which never could have 
 been observed. It assumes, as does all science, that 
 unless there is evidence to the contrary, the past and 
 the unobserved are like the present and the observed. 
 
 " Many of the changes which have indisputably taken 
 place are such as no man has ever observed, because 
 they are brought about so slowly or so deep down 
 within the crust that no direct observation is pos- 
 sible, and we can only infer the mode of procedure by 
 examining the result. No human eye has ever witnessed 
 the birth of a mountain range, or has seen the beds 
 of solid rock folded and crumpled like so many sheets 
 of paper, or observed the processes by which rock is 
 changed in all its essential characteristics ; ' metamor- 
 phosed ' as it is technically called." 6 Conclusions of 
 this character imply the existence of a well organized 
 body of knowledge concerning the relations of facts 
 in the given field. 
 
 o Scott, Introduction to Qeology, p. 30, 
 
ASTRONOMY 265 
 
 The data of the science were obtained by observation ; 
 the facts observed were classified and correlated ; laws 
 were gradually discovered and verified ; systems were 
 constructed and rejected until eventually a set of gen- 
 eral principles emerged upon which geologists could 
 agree; but the working out of the details and the ex- 
 position of the system of concrete facts involved 
 in other words the history of the earth has progressed 
 only a little way. In geometry observation is only 
 incidental ; in any concrete science it is a constant neces- 
 sity. In a historical science the particular fact occu- 
 pies the center of the field; in other sciences the pri- 
 mary interest is in generalizations. 
 
 The discovery of the planet Neptune implied the 
 construction of a similar system -in Astronomy. The 
 planets move in elliptical orbits; these orbits, how- 
 ever, are not perfect ellipses ; there are variations (per- 
 turbations) due to the influence of other planets. The 
 amount of variation due to any planet can be calcu- 
 lated. In the case of the planet Uranus, after all the 
 perturbations due to the known planets had been taken 
 into ac-count, there remained a residue unaccounted for. 
 Adams and Leverrier calculated that this residue could 
 be accounted for by the hypothesis of another planet 
 in a given direction and at a given distance from 
 Uranus ; and this planet was soon after discovered with 
 the aid of the telescope and was named Neptune. The 
 discovery of Neptune presupposed a knowledge of the 
 general laws of the solar system and a comprehensive 
 description of the relation in which its known mem- 
 bers stood to each other. It was the result of the ap- 
 plication of the general laws to a concrete situation. 
 
266 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 Systems of Historical Facts. Both astronomy and 
 geology find a large part of the concrete data with 
 which they deal open to observation; geology to some 
 extent and astronomy to a great extent depend upon 
 the testimony of past observers. In the courts and in 
 the investigations of the historian, testimony is of the 
 first importance. We may then classify the data in 
 these investigations as follows : 
 
 1. Material facts. 
 
 . Testimony. 
 
 Examples of material facts would be the articles 
 found on the scene of the crime, etc., etc. ; and in 
 historical inquiries, the ruins of buildings, roads, and 
 other public works, tombs, ancient implements, works 
 of art, etc., etc. The testimony may be either oral 
 or written. Usually the historian must rely princi- 
 pally upon written testimony. It is of many kinds, 
 from the pictographs of primitive man to historical 
 accounts like those of Thucydides and Tacitus. The 
 problems of the historian are to collect the data, weigh 
 the value of each of the items, and construct an account 
 which will best organize the data into a coherent whole. 
 
 A. His first duty will be to collect all the data pos- 
 sible. The methods employed by the lawyer are suffi- 
 ciently familiar in their general outlines. Details of 
 his methods are beyond the scope of our discussion. 
 We shall consider the procedure of the historian a 
 little more closely. He must search for documents. 
 " Documents are traces which have been left by the 
 thoughts and actions of men of former times" 7 whether 
 
 1 Langlois and Seignobos, Introduction to the Study of History. 
 This is a most valuable introduction to the method of history and 
 should be read by every student of scientific method. 
 
HISTORY 267 
 
 material facts, such as works of art and the like, or 
 written records. Some historians have described events 
 so recent that it was possible to obtain the testimony 
 of eye-witnesses. They were thus able to obtain a 
 quantity of testimony not available for the later writer 
 and to cross-examine their witnesses. Usually the dis- 
 covery of documents has meant a search in all sorts of 
 places for the testimony of contemporaries ; the ex- 
 peditions and excavations carried on by the archaeolo- 
 gists have as their object the discovery of such records. 
 Archives, state papers, early histories, memoirs, in- 
 scriptions, etc., furnish the chief sources. The problem 
 grows easier with the growth of collections and li- 
 braries. But new documents are constantly being 
 found, and no one can say when the data have all been 
 discovered. 
 
 B. After the collection of the data comes the esti- 
 mation of the value of its various items. Estimating 
 the value of testimony is a special problem and we 
 shall treat of it first. 8 The problem is to discover 
 what facts the documents establish. The questions to 
 be raised are such as these: Who did such and such an 
 act? Who wrote such and such a poem? Who founded 
 Rome? The answer involves the establishment of a 
 system of facts and inferences justifying some one 
 
 conclusion to the exclusion of all others. The establish- 
 
 
 
 ment of such a system means the discovery of facts, 
 their classification, the construction of hypotheses, and 
 
 s Estimating the value of testimony is so important a matter 
 in inquiries of the sort we are now considering that the questions 
 involved will be discussed somewhat more fully than in the intro- 
 ductory chapter. All the machinery of scientific method may be 
 needed to enable the historian to decide whether or not a record 
 is trustworthy. 
 
268 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 the 'verification of these, and the organization of facts 
 and generalizations into a system. We know facts by 
 observation, by memory aided by inference, by infer- 
 ence from the testimony of others, by inference from 
 remains of former human activities, and from all sorts 
 of natural events, and natural processes ; we group the 
 data with reference to their bearing on various parts 
 of the problem ; we use the inferences based upon past 
 experience and formulate new ones ; we test our con- 
 structions by all known means. 
 
 Sometimes observations of natural phenomena may 
 make up most of the data. Observations made by others 
 may sometimes be easily verified. Experiments may 
 be repeated ; the problem of getting correct descrip- 
 tions of the facts may frequently be comparatively 
 easy. But the sort of case which illustrates the estab- 
 lishment of a system of concrete facts in all its com- 
 plexity is that in which human testimony, as well as all 
 other kinds of data is employed to determine the 
 existence and character of some fact. Let us examine 
 in outline the processes involved in guarding against 
 error in the use of testimony. A number of pre- 
 liminary questions must be raised: 
 
 (1) The first of them is this : What is the testimony? 
 What does the witness say? What is the content of 
 the document. The testimony ^ the starting point. 
 We must know what the words mean, what they pur- 
 port to tell, what facts they are intended to represent. 
 (a) In the case of the witness on the stand this ques- 
 tion, though all-important, is usually comparatively 
 easy of solution. In case of doubt he can be called 
 upon for further statements, which will make plain his 
 meaning. When he speaks in a foreign language there 
 
HISTORY 269 
 
 Is more difficulty, but in any ordinary description of 
 facts, the difficulty is not great, (b) In the case of 
 historical documents the difficulty may be insurmount- 
 able. For centuries hieroglyphics could not be inter- 
 preted at all ; and translations from ancient documents 
 are always attended with danger. The difficulty of find- 
 ing in one language exact equivalents of the words of 
 another needs no emphasis. In such a case the most 
 thoroughgoing comparison of the two languages may 
 be necessary in order to determine the meaning of a 
 document. Whole sciences, such as epigraphy or palae- 
 ography, are devoted to the interpretation of ancient 
 writings. 
 
 (2) If the meaning of the statements contained in 
 the testimony has been made clear, the next question 
 is, of course: Are the statements true? And in order 
 to answer this we may ask next: () Who made the, 
 statements, and is he qualified by knowledge, honesty 
 and accuracy sufficient to enable us to rely upon what 
 he says? In the law courts, the identity of the witness 
 is the first thing to be determined and made a matter 
 of record. When the witness is before us the question 
 of his identity is usually very easy to answer, though 
 there are, of course, numerous cases in which error and 
 deception might occur. And in the case of the pris- 
 oner, the determination of identity is often an ex- 
 tremely difficult matter, involving testimony and many 
 other kinds of evidence. 
 
 In the case of written documents the determination 
 
 of authorship is one of the most difficult problems which 
 
 the historian has to solve. 9 The name upon the title 
 
 page of a book is, by itself, not conclusive as evidence 
 
 See Langlois and Seignobos, Book II, chap. iii. 
 
270 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 of authorship. In modern books the indications of 
 authorship are usually fully given and are ordinarily 
 reliable; fraud is possible, but is usually easily de- 
 tected, though forgeries in the name of dead authors 
 may be successful. But in the case of early books, and 
 above all in the case of manuscripts, the difficulties are 
 very great ; in the first place there may be no formal 
 indications of authorship; or the work is perhaps 
 ascribed to such and such a person. Was he the author? 
 We should ask first: Did such a person ever exist? 
 To answer this, only the testimony of contempo- 
 raries would be conclusive. In many cases it is not 
 necessary to pause over this question, for there may be 
 no doubt about the existence of the author ; but in case 
 there should be, the testimony to his having existed 
 must be tested like any other such evidence. Con- 
 sistency of testimony and corroboration of one piece 
 of testimony by another are necessary here as else- 
 where. One of the best known examples of this problem 
 is that of the existence of Homer. Absence of testi- 
 mony in this and other cases is usually a presumption 
 against the truth of what is alleged. 
 
 Granted that there was such a person as the author, 
 
 did he write the document before us? What evidence 
 
 is there of the genuineness of the document? The 
 
 evidence is of two kinds, internal and external. In 
 
 examining internal evidence, the question is : Is 
 
 the document such as the alleged author could or 
 
 would have written? Is the handwriting of a sort that 
 
 was employed during the lifetime and in the country, 
 
 *tc., of the supposed author? If the document is in 
 
 Handwriting of the Eleventh or the Thirteenth Century, 
 
INTERNAL AND EXTERNAL EVIDENCE 271 
 
 it was not written by an author of the Twelfth Century. 
 And with regard to the style and forms of expression 
 the same question may be raised. In legal documents 
 this is a valuable test, for legal phraseology is very 
 definite. Modern words or phrases in a supposed an- 
 cient writing are, of course, conclusive against any 
 argument for its genuineness. 
 
 Mention of facts and allusions to events of every 
 sort are most valuable in this connection ; and lastly, 
 the opinions expressed or implied .in the document are 
 of great assistance in determining its genuineness, for 
 some opinions could not possibly have been held at the 
 time the document purports to have been written. Ex^ 
 ternal evidence is to be found in references to the 
 document, quotations, etc., by contemporaries or by 
 those of later periods. 
 
 Another complication is often present to add to the 
 difficulty of determining authorship ; the document may 
 be the work of two or more individuals, or changes may 
 have been introduced by those who have edited the 
 texts, or there may have been mistakes in copying. 
 In all these cases one should not necessarily reject the 
 work as a whole; it may give some information and we 
 may be able to detect the changes from the original, 
 and it may be of great importance to determine just 
 what was done by the original author or just what was 
 written by each of several collaborators. The methods 
 to be employed are of course those described above. 
 It is simply a question of several authors instead of 
 one. 
 
 (b) Having assured ourselves of the identity of the 
 witness or witnesses, the next question is: Was he in a 
 
TYPICAL SYSTEMS OF KNOWLEDGE 
 
 position to know the facts to which he is testifying? 
 Does he assert that he witnessed them himself? 10 And 
 was it humanly possible for any one to have observed 
 the facts in question? And if this question can be an- 
 swered in the affirmative, we have next to ask whether 
 there is any reason why the witness himself could not 
 have observed them. Was he (i) competent to observe 
 and remember the facts? Was there any defect in his 
 powers of observation, or is there any evidence against 
 his having been at a place where the observation could 
 have been made? Here again, when we have the wit- 
 ness before us, the difficulty of solving the problem is 
 much easier than when we have to rely upon written 
 testimony, or other evidence of an indirect sort. 
 
 Cross-examination is a method of getting at once an 
 addition to the testimony on the points already raised 
 and of furnishing immediately statements which will 
 corroborate or disagree with statements already made, 
 or with known facts. In Lincoln's first murder trial, 
 the chief witness had testified to seeing the murder 
 committed by the prisoner. In the cross-examination 
 he added a number of details : that the shooting was at 
 ten o'clock at night, in beech timber, in August, that 
 he was twenty feet or more away, that he could see the 
 pistol and how it hung; that the nearest lights were 
 half a mile away, and that he saw it all by moonlight. 
 Lincoln showed that the moon did not rise till one 
 o'clock in the morning. Cross-examination may bring 
 out inconsistencies due to dishonesty as well as incom- 
 petence, as shown in this example. Where cross-ex- 
 
 10 As Bain asserts (Logic, Appendix I), "The supreme canon 
 of historical evidence is testimony of a contemporary " of one 
 who may have observed the fact. 
 
TESTIMONY 273 
 
 amination is impossible, as in written testimony, it may 
 be impossible to convict a dishonest witness. 
 
 (ii) If the witness has withstood all the preceding 
 tests we have next to ask whether there is anything in 
 his record which would lead us to doubt his honesty or 
 whether he is likely to have any reason for falsifying in 
 the present case. The two questions are distinct; a 
 general good reputation would be a presumption in 
 favor of his honesty in the present case, but it would 
 not make it certain that he was proof against all temp- 
 tation. In the courts, cross-examination of the wit- 
 ness himself and the testimony of other witnesses fur- 
 nish the data for answering the question ; in written 
 testimony, other statements of his own and the state- 
 ments of his contemporaries must be taken into ac- 
 count; what is implied is often more important than 
 what is stated outright. 
 
 There are two cases in which the testimony of a wit- 
 ness may be regarded as particularly free from wilful 
 falsification. The first is that in which the witness be- 
 lieves the evidence is to his discredit or disadvantage. 
 One exception must be made : the witness, for the 
 sake of satisfying a grudge or shielding someone else, 
 might be willing to sacrifice his own reputation and 
 advantage. In any case, such testimony would need 
 further corroboration, but it would, with the excep- 
 tion above mentioned, be excellent evidence of the good 
 faith of the witness. 
 
 The second case is that in which evidence is given 
 undesignedly. The witness makes statements of whose 
 import he is unaware or he is surprised into statements 
 which bring out facts which he has been attempting to 
 
274 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 conceal. An incident related in Voltaire's " Zadig " 
 will illustrate this: 
 
 Zadig's master, Setoc, had lent money in the presence 
 of two witnesses who had died before the debt was paid. 
 The debtor denied having received any money. The money 
 had been counted out upon a stone near Mount Horeb. 
 Zadig undertook to conduct the case. He summoned the 
 debtor before a tribunal and demanded that the five hun- 
 dred ounces of silver be returned to his master. " Have you 
 witnesses? " asked the judge. " No/' replied Zadig, " they 
 are dead; but there is a large stone on which the money 
 was counted out; if it please Your Highness to order that 
 the stone be sought out, I hope that it will bear witness; 
 the debtor and I will remain here until the stone arrives; 
 I will have it hunted up at the expense of my master." 
 " Very well," replied the judge, and he turned his atten- 
 tion to something else. At the end of the sitting he said 
 to Zadig, "Well, your stone has not yet arrived?" The 
 debtor laughed and said: " If your Highness should re- 
 main here till to-morrow the stone would not have arrived; 
 it is more than six miles away and it would require fifteen 
 men to move it." " Well," cried Zadig, " I told you that 
 the stone would bear witness; since this man knows where 
 it is, he admits that it was upon it that the money was 
 counted out." Voltaire, Zadig, Chap. x. 
 
 Testimony which is false is of course evidence of 
 something, of the opinion of the witness, or of his 
 character, or of the existence of certain ideas, etc., at 
 the time in which he lived. 
 
 But all these questions are more or less preliminary. 
 A witness of good reputation and a good observer, 
 with no motive to falsify, may, of course, be mistaken 
 in the case under examination. And a witness who is 
 not usually reliable or who is a bad observer or one with 
 every reason to falsify, may be telling the truth. In the 
 
TESTIMONY 275 
 
 first case the presumption would of course be in favor 
 of the testimony and in the second against it, but in 
 neither case could we regard the reliability of the testi- 
 mony as settled. There are three conditions to the ac- 
 ceptance of every piece of testimony. (1) It must bq 
 self-consistent and internally coherent; (2) it must be 
 consistent and coherent with other known facts re- 
 lating to the same case; (3) it must be consistent with 
 ordinary experience. 
 
 1. If a witness, in one part of his testimony, makes 
 a statement inconsistent with what he has stated pre- 
 viously, his testimony is discredited. One of his state- 
 ments may be true or both may be false; it may be 
 possible to show that one of them is consistent with the 
 rest of his testimony, while the other is not, but the 
 disagreement of these statements would tend to throw 
 doubt upon the others, and without external corrobora- 
 tion his whole story would be open to question. More- 
 over, his statements, to have the greatest force, must 
 not only be consistent, they must be coherent ; they must 
 describe a connected series of events. If a lawyer can 
 by cross-examination show that the witness has made 
 inconsistent statements, the force of his testimony is 
 often entirely destroyed ; and it is usually very much 
 weakened, at the very least. 
 
 But even the most coherent body of testimony would, 
 by itself, be insufficient to prove the existence of the 
 facts alleged. Otherwise we should be obliged to ac- 
 cept as true many acknowledged fictions. Indeed, too 
 great coherence, too good a story, rouses the suspicion 
 that it has been manufactured or at least modified, since 
 most men are too inaccurate both in observing and in 
 
276 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 remembering to describe any complex set of events 
 without minor inconsistencies. 
 
 By itself, then, internal evidence is not conclusive; 
 without the support of other testimony or of facts 
 otherwise known any piece of testimony must be held 
 as doubtful. A possible exception might be noted: 
 if the testimony were of such a character that its falsity 
 would be more difficult to understand and explain than 
 its truth, we should have some ground for accepting 
 it even in the absence of other corroboration ; but such 
 cases would obviously be rare. 
 
 Negative Evidence. The absence of testimony to 
 the existence of a fact which could hardly have failed 
 of mention by contemporaries is a strong presumption 
 against its existence. If an alleged work, or doctrine, 
 or what not, is referred to by no contemporary and is 
 first mentioned by some later writer, it is probably 
 false. The tradition regarding individuals, cities, and 
 so on, often becomes more extensive and circumstantial 
 as the objects of the tradition get farther away. 11 
 
 2. In oral testimony, one of the most frequent sources 
 of corroboration is to be found in the testimony of 
 other witnesses. But too close an agreement, instead of 
 being evidence of the truth of the testimony, raises a 
 suspicion that the witnesses are in collusion and that 
 the whole story may be false. The inevitable inaccu- 
 racies of observation and 'of memory render it prac- 
 tically impossible that two witnesses should tell stories 
 that should agree in all particulars ; some differences 
 are to be expected, and sometimes there are differences 
 regarding some of the most important points. In writ- 
 
 11 For illustrations, see Hay ward, Essays, "The Pearls and 
 Mock Pearls of History." 
 
TESTIMONY 277 
 
 ten testimony, if there are several documents very 
 closely similar, the presumption is that, instead of being 
 independent pieces of testimony, they are all derived 
 from the same source. This presumption is particu- 
 larly strong if the errors happen to be the same in 
 all ; if, for example, the same words are misspelled or the 
 same misstatements of fact are made in all, this is 
 good evidence that one of the documents was the source 
 of the rest or that all were derived from some common 
 source. Of course disagreement does not prove the 
 truth of any one of the bodies of testimony, but it is 
 good evidence of their independent origin. Where the 
 truth lies must be discovered by further comparison 
 and construction. 
 
 3. The thir.d test mentioned above was agreement 
 with ordinary experience. What is known as the Argu- 
 ment to Antecedent Probability would be included here. 
 We ask : Is the alleged event one that would have been 
 probable in the circumstances? Is it consistent with 
 the known laws of nature and their familiar modes of 
 operation? This test might, in practice, be applied 
 first ; if, for example, testimony contained statements 
 violating all ordinary experience or well-tested laws of 
 nature, we might decline to go to the trouble of ap- 
 plying the other tests. But this test is not necessarily 
 final, for statements which disagree with our past ex- 
 perience are very frequently found to be true and it has 
 more than once happened that a supposed law of na- 
 ture has been stated too broadly and has needed quali- 
 fication. A too ready rejection of unusual statements 
 is no more justified by a sound method than is a too 
 ready credulity. But if the application of other tests 
 leaves the truth of the testimony inconclusive, a viola- 
 
278 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 tion of ordinary experience would warrant the rejection 
 of the testimony. If alleged facts were in contradic- 
 tion to supposed laws of Nature, their existence could 
 be established only by evidence which was stronger than 
 the whole body of evidence in favor of the supposed law. 
 Proof of the violation of all the laws of Nature would 
 be impossible; for all proof requires the use of some 
 law. We are often over-hasty in concluding that a 
 statement is inconsistent with another or with some of 
 the consequences of the latter, and we tend too readily 
 to condemn anything which is apparently inconsistent 
 with established principles. Rejection of the Coper- 
 nican Hypothesis on the ground of its inconsistency 
 with the principles of religion was a case of this sort. 
 
 There are two or three topics which call for a little 
 further discussion at this point. One of these is what 
 is known as hearsay evidence; in this the witness re- 
 ports not what he himself observed, but what he has 
 heard some one else describe. Its value is very much 
 less than is that of testimony to the fact itself. To the 
 errors of the original observer, the errors of observa- 
 tion, of memory, of description, and possible bad faith 
 on the part of the original observer, we have added 
 those of a second person, who is liable to the same errors 
 and defects with regard to the words of the first. 
 
 Tradition is simply hearsay evidence with a multi- 
 plication of the number of intermediates between the 
 last hearer and the original observer, if indeed, there 
 were any observations at the beginning. It is evident 
 that tradition is exceedingly poor evidence of the ex- 
 istence of any fact. 
 
COMPLETE SYSTEMS 279 
 
 Circumstantial evidence is merely indirect evidence ; 
 there may be no witnesses who have observed the facts 
 themselves, but certain other facts may be incapable of 
 explanation on any theory other than the one which 
 asserts the existence of these facts. 
 
 We have been discussing the problems of discovering 
 and evaluating historical facts ; the principles involved 
 in building up a system when the data are derived from 
 both testimony and observation are, of course, the same 
 as those involved in constructing a system from data 
 obtained in any other way. We wish to get a complete, 
 coherent whole. The framework of general statements 
 or laws, and the particular structure which we build, 
 must provide a place for the facts which are the ma- 
 terials to be built into a system. If there are facts 
 which do not fit, if there are parts of the framework 
 which interfere with each other, if the laws of such 
 structures are violated, the construction can not be 
 accepted. A place for every fact, and a complete struc- 
 ture when all the facts are in place, are the require- 
 ments of a scientific structure, or, in other words, of 
 any structure of knowledge which is to satisfy the de- 
 mands of a reasonable being. 
 
 The details of historical construction are beyond the 
 scope of this outline and an illustration which should 
 show them with any degree of fullness would occupy 
 too much space. Huxley's argument, quoted on pages 
 287-300), illustrates a few of the points. The student 
 is referred to Langlois and Seignobos's Introduction to 
 the Study of History for further discussion and illus- 
 tration. 
 
280 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 EXERCISES 
 
 In the following examples, outline the argument and 
 state the general principles employed, and the way in 
 which these principles were or might have been estab- 
 lished; examine each step in the reasoning and determine 
 whether or not it is valid; where inductive inference is 
 used describe its foundation, and criticise, if possible; 
 where the argument is incomplete state 'what would be 
 necessary in order to complete it: 
 
 I. Professor James's argument for his theory of the 
 emotions, as given in his Psychology, Briefer 
 Course, pp. 375 to 380. 
 
 " The feeling, in the coarser emotions, results from the 
 bodily expression. Our natural way of thinking about the 
 coarser emotions is that the mental perception of some 
 fact excites the mental affection called the emotion, and 
 that the latter state of mind gives rise to the bodily ex- 
 pression. My theory, on the contrary, is that the bodily 
 changes follow directly the perception of the exciting fact, 
 and that our feeling of the same changes as they occur IS 
 the emotion. Common sense says, we lose our fortune, are 
 sorry and weep; we meet a bear, are frightened and run; 
 we are insulted by a rival, are angry and strike. The 
 hypothesis here to be defended says that this order of 
 sequence is incorrect, that the one mental state is not imme- 
 diately induced by the other, that the bodily manifestations 
 must first be interposed between, and that the more rational 
 statement is that we feel sorry because we cry, angry be- 
 cause we strike, afraid because we tremble, and not that 
 we cry, strike, or tremble because we are sorry, angry, or 
 fearful, as the case may be. Without the bodily states 
 following on the perception, the latter would be purely 
 cognitive in form, pale, colorless, destitute of emotional 
 warmth. We might then see the bear and judge it best to 
 run, receive the insult and deem it right to strike, but we 
 should not feel afraid or angry. 
 
 " Stated in this crude way, the hypothesis ir pretty sure 
 
JAMES' THEORY OF EMOTION 281 
 
 to meet with immediate disbelief. And yet neither many 
 nor far-fetched considerations are required to mitigate itg 
 paradoxical character, and possibly to produce conviction 
 of its truth. 
 
 " 1. To begin with, particular perceptions certainly do 
 produce widespread bodily effects by a sort of immediate 
 physical influence, antecedent to the arousal of an emotion 
 or emotional idea. In listening to poetry, drama, or heroic 
 narrative, we are often surprised at the cutaneous shiver 
 which like a sudden wave flows over us, and at the heart- 
 swelling and lachrymal effusion that unexpectedly catch 
 us at intervals. In hearing music the same is even more 
 strikingly true. If we abruptly see a dark moving form 
 in the woods, our heart stops beating, and we catch our 
 breath instantly and before any articulate idea of danger 
 can arise. If our friend goes near to the edge of a preci- 
 pice, we get the well-known feeling of ' all-overishness/ 
 and we shrink back, although we positively know him to be 
 safe, and have no distinct imagination of his fall. The 
 writer well remembers his astonishment, when a boy of 
 seven or eight, at fainting when a horse was bled. The 
 blood was in a bucket, with a stick in it, and, if memory 
 does not deceive him, he stirred it round and saw it drip 
 from the stick with no feeling save that of childish curios- 
 ity. Suddenly the world grew black before his eyes, his 
 ears began to buzz, and he knew no more. He had never 
 heard of the sight of blood producing faintness or sickness, 
 and he had so little repugnance to it, and so little appre- 
 hension of any other sort of danger from it, that even at 
 that tender age, as he well remembers, he could not help 
 wondering how the mere physical presence of a pailful of 
 crimson fluid could occasion in him such formidable bodily 
 effects. 
 
 " 2. The best proof that the immediate cause of emotion 
 is a physical effect on the nerves is furnished by those 
 pathological cases in which the emotion is objectless. One 
 of the chief merits, in fact, of the view which I propose, 
 seems to be that we can so easily formulate by its means 
 pathological cases and normal cases under a common 
 scheme. In every asylum we find examples of absolutely 
 unmotived fear, anger, melancholy, or conceit; and others 
 
TYPICAL SYSTEMS OF KNOWLEDGE 
 
 of an equally unmotived apathy which persists in spite of 
 the best outward reasons why it should give way. In the 
 former cases we must suppose the nervous machinery to be 
 so ' labile ' in some one emotional direction that almost any 
 stimulus (however inappropriate) causes it to upset in that 
 way, and to engender the particular complex of feelings of 
 which the psychic body of the emotion corresponds. Thus, 
 to take one special instance, if inability to draw a deep 
 breath, fluttering of the heart, and that peculiar gastric 
 change felt as ' precordial anxiety/ with an irresistible 
 tendency to take a somewhat crouching attitude and to sit 
 still, with perhaps other visceral processes not now known, 
 all spontaneously occur together in a certain person, his 
 feeling of the combination is the emotion of dread, and he 
 is the victim of what is known as morbid fear. A friend 
 who has occasional attacks of this most distressing of all 
 maladies tells me that in his case the whole drama seems 
 to center about the region of the heart and respiratory 
 apparatus, that his main effort during the attacks is to get 
 control of his inspirations and to slow his heart, and that 
 the moment he attains to breathing deeply and holding him- 
 self erect, the dread, ipso facto, seems to depart. 
 
 " The emotion here is nothing but the feeling of a bodily 
 state, and it has a purely bodily cause. 
 
 " 3. The next thing to be noticed is this, that every one 
 of the bodily changes, whatsoever it be, is FELT, acutely 
 or obscurely, the moment it occurs. If the reader has never 
 paid attention to this matter he will be both interested and 
 astonished to learn how many different bodily feelings he 
 can detect in himself as characteristic of his various emo- 
 tional moods. It would be perhaps too much to expect of 
 him to arrest the tide of any strong gust of passion for the 
 sake of any such curious analysis as this ; but he can observe 
 more tranquil states, and that may be assumed to be true 
 of the greatest which is shown to be true of the less. Our 
 whole cubic capacity is sensibly alive; and each morsel of 
 it contributes its pulsations of feeling, dim or sharp, 
 pleasant, painful, or dubious, to that sense of personality 
 that every one of us unfailingly carries with him. It is 
 surprising what little items give accent to these complexes 
 of sensibility. When worried by any slight trouble, one 
 
JAMES' THEORY OF EMOTION 283 
 
 may find that the focus of one's bodily consciousness is the 
 contraction, often quite inconsiderable, of the eyes and: 
 brows. When momentarily embarrassed, it is something in 
 the pharynx that compels either a swallowing, a clearing 
 of the throat, or a slight cough; and so on for as many 
 more instances as might be named. The various permuta- 
 tions of which these organic changes are susceptible make 
 it abstractly possible that no shade of emotion should be 
 without a bodily reverberation as unique, when taken in its 
 totality, as is the mental mood itself. The immense num- 
 ber of parts modified is what makes it so difficult for us to 
 reproduce in cold blood the total and integral expression of 
 any one emotion. We may catch the trick with the vol- 
 untary muscles, but fail with the skin, glands, heart, and 
 other viscera. Just as an artificially imitated sneeze lacks 
 something of the reality, so the attempt to imitate grief 
 or enthusiasm in the absence of its normal instigating cause 
 is apt to be rather ' hollow.' 
 
 " 4. I now proceed to the vital point of my whole theory, 
 which is this: If we fancy some strong emotion, and then 
 try to abstract from our consciousness of it all the feelings 
 of its bodily symptoms, we find we have nothing left behind, 
 no ' mind stuff ' out of which the emotion can be con- 
 stituted, and that a cold and neutral state of intellectual 
 perception is all that remains. It is true that, although 
 most people, when asked, say that their introspection verifies 
 tfiis statement, some persist in saying that theirs does not. 
 Many of them cannot be made to understand the question. 
 When you beg them to imagine away every feeling of laugh- 
 ter and of the tendency to laugh from their conscious- 
 ness of the ludicrousness of the object, and then to tell 
 you what the feeling of its ludicrousness is like, whether 
 it be anything more than the perception that the object 
 belongs to the class ' funny,' they persist in replying that 
 the thing is a physical impossibility, and they always must 
 laugh if they see a funny object. Of course the task pro- 
 posed is not the impossible one of seeing a ludicrous object 
 and annihilating one's tendency to laugh. It is the purely 
 speculative one of subtracting certain elements of feeling 
 from an emotional state supposed to exist in its fullness, 
 and saying what the residual elements are. I cannot help 
 
284 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 thinking that all who rightly apprehend this problem will 
 agree with the proposition above laid down. What kind of 
 an emotion of fear would be left if the feeling neither of 
 quickened heart-beats nor of shallow breathing, neither 
 of trembling lips nor of weakened limbs, neither of goose- 
 flesh nor of visceral stirrings, were present, it is quite im- 
 possible for me to think. Can one fancy the state of rage 
 and picture no ebullition in the chest, no flushing of the 
 face, no dilatation of the nostrils, no clenching of the teeth, 
 no impulse to vigorous action, but in their stead limp mus- 
 cles, calm breathing, and a placid face? The present 
 writer, for one, certainly cannot. The rage is as com- 
 pletely evaporated as the sensation of its so-called mani- 
 festations, and the only thing that can possibly be sup- 
 posed to take its place is some cold-blooded and dispas- 
 sionate judicial sentence, confined entirely to the intellec- 
 tual realm, to the effect that a certain person or persons 
 merit chastisement for their sins. In like manner of grief: 
 what would it be without its tears, its sobs, its suffocation 
 of the heart, its pang in the breast bone? A feelingless 
 cognition that certain circumstances are deplorable and 
 nothing more. Every passion in turn tells the same story. 
 A disembodied human emotion is a sheer nonentity. I do 
 not say that it is a contradiction in the nature of things, 
 or that pure spirits are necessarily condemned to cold, 
 intellectual lives ; but I say that for us emotion disassociated 
 from all bodily feeling is inconceivable. The more closely 
 I scrutinize my states, the more persuaded I become that 
 whatever ' coarse ' affections and passions I have are in 
 very truth constituted by, and made up of, those bodily 
 changes which we ordinarily call their expression or con- 
 sequence; and the more it seems to me that, if I were to 
 become corporeally anaesthetic, I should be excluded from 
 the life of the affections, harsh and tender alike, and drag 
 out an existence of merely cognitive or intellectual form." 
 
 II. Extract from a lecture by A. H. Fison on " The 
 Evolution of Double Stars " in Lectures on the 
 Method of Science, Edited by T. B. Strong: 
 
 The leading points of Darwin's 12 investigations of the 
 12 Professor George Darwin. 
 
DOUBLE STARS 285 
 
 past history of the moon: " From the fact that the intensity 
 of the moon's attraction is greater upon the parts of the 
 Earth that are nearer to it than upon the parts that are 
 more remote there arises a tendency for the earth to be- 
 come stretched along the diameter that is at that particular 
 instant directed towards the Moon. If the Earth were 
 fluid, it would yield to this tendency, but, as it is in the 
 main solid, it is unable to do so. The waters upon its 
 surface are, however, free, and they consequently flow, con- 
 tinually tending to accumulate in two high tides, one im- 
 mediately under the Moon, and the other at the part of the 
 Earth's surface that is most remote from it. If the period 
 of the Earth's rotation was the same as that of the Moon's 
 revolution round it, the Moon would continually face the 
 same regions of the Earth, and in the course of time, pos- 
 sibly a few months or years, the water would reach a 
 position of equilibrium, forming permanent high tides at 
 the opposite ends of the diameter that would then be per- 
 manently directed to the Moon. 
 
 " This simple condition is, however, profoundly modified 
 by the Earth's rotation. As the Earth turns under the 
 Moon in a period of slightly less than twenty-five hours, 
 the regions presented to the Moon those at which the 
 water tends to accumulate are continually changing, and 
 before any portion of water could move appreciably to- 
 wards them, the forces acting upon it would change it and 
 it would be urged in some other direction. The problem 
 thus becomes extremely complicated. The general result, 
 however, is, that in its continual endeavor to move towards 
 the ends of the terrestrial diameter that is at each given 
 instant pointing to the Moon, the water on the Earth's 
 surface is thrown into the continual motion that we recog- 
 nize as tidal ebb and flow. 
 
 "If the movement of the water were urrresisted by fric- 
 tion, tidal ebb and flow would possess no cosmical signifi- 
 cance, but friction is experienced in the motion of the tidal 
 wave over the surface of shores and estuaries, and in in- 
 ternal motions of the water itself. The destruction of 
 motion by friction develops heat, and the Earth is conse- 
 quently warmed by its tides; moreover, since heat is a 
 form of energy, some other form of energy, equivalent in 
 
TYPICAL SYSTEMS OF KNOWLEDGE 
 
 amount, must disappear in producing it. From considera- 
 tions of a not very difficult nature, it can be shown that this 
 energy is that of the Earth's rotation, so that we are pre- 
 sented with the remarkable fact that the speed of the 
 Earth's rotation is being reduced in consequence of the 
 tides. The period of the Earth's rotation determines the 
 day, and consequently the day must be increasing in length. 
 No doubt the rate of increase is now very slight, but there 
 can be little doubt that this has not always been the case. 
 The Earth was at one time a mass of molten rock, in which 
 bodily tides must have been formed, while friction must 
 have been far greater in the case of such a viscous mass 
 than in water. Further, as we shall see, the Moon must 
 have been nearer the Earth than it is now, and its tide- 
 producing power consequently more intense. Under these 
 conditions we can well imagine that the loss of rotation 
 proceeded at a comparatively rapid pace, and that the day 
 was formerly far shorter than it is at the present time. 
 
 " The slackening of the Earth's rotation is not, however, 
 the only result of tidal friction. A reaction upon the Moon 
 is inevitable, and it appears that, as a necessary conse- 
 quence, the Moon must recede from the Earth, its orbital 
 speed decreasing at the same time. Its period of revolu- 
 tion round the Earth, which we may define as the month, 
 is therefore increasing, so that in consequence of the tides, 
 the day and the month are both becoming longer. It fol- 
 lows, however, from simple considerations, that this cannot 
 continue indefinitely. The day is increasing, and so also 
 is the month, but there must come a time when the day must 
 increase more rapidly than the month (already past), and 
 it must ultimately overtake it. The length of each will 
 then be fifty-five of our present days. The Earth, then 
 rotating in the same period as that of the Moon's revolution 
 round it, will continually present the same regions to the 
 Moon, as the Moon already presents the same face to it. 
 At the ends of the terrestrial diameter that will then be 
 constantly pointing towards the Moon, permanent high 
 tides will accumulate; ebb and flow, and with it tidal fric- 
 tion will cease, and a state of stable equilibrium will be 
 reached. It is impossible to determine the epoch of this 
 stage, but under the most favorable conditions it must be 
 
DOUBLE STARS 287 
 
 measured by hundreds of millions of years from the present 
 time. ... In the past the Earth must have rotated 
 more rapidly, the Moon must have been nearer, and it must 
 have revolved in a shorter period than at present. From 
 the application of mathematics to the problem, Darwin has 
 shown that there must have been a time when the Moon 
 was quite close to the surface of the Earth, and, when in 
 this condition, the further suggestive fact appears that its 
 period of revolution, the month, coincided, as it will again 
 coincide in the last stage, with that of the Earth's rotation, 
 the day. Both must then have been between three and 
 five hours in length. In this first, as in the last condition, 
 we see Earth and Moon rotating as a whole about their 
 common center of mass, each continually presenting the 
 same face to each other. While, however, in the first con- 
 dition they are nearly in contact and represent a passing 
 phase, in the last they are far apart, and their condition 
 is permanent. It is possible to show that the first stage 
 could not have occurred less than 50,000,000 years ago." 
 
 III. Huxley's lecture on " The Demonstrative Evidence 
 of Evolution " (with a few omissions) : 
 
 " The occurrence of historical facts is said to be demon- 
 strated, when the evidence that they happened is of such 
 a character as to render the assumption that they did not 
 happen in the highest degree improbable; and the question 
 I now have to deal with is, whether evidence in favor of 
 the evolution of animals of this degree of cogency is, or is 
 not, obtainable from the record of the succession of living 
 forms which is presented to us by fossil remains. 
 
 " Those who have attended to the progress of palaeon- 
 tology are aware that evidence of the character which I 
 have defined has been produced in considerable and con- 
 tinually increasing quantity during the last few years. In- 
 deed, the amount and the satisfactory nature of that 
 evidence are somewhat surprising, when we consider the 
 conditions under which alone we can* hope to obtain it. 
 
 " It is obviously useless to seek for such evidence, except 
 in localities in which the physical conditions have been 
 
288 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 such as to permit of the deposit of an unbroken, or but 
 rarely interrupted,, series of strata through a long period 
 of time; in which the group of animals to be investigated 
 has existed in such abundance as to furnish the requisite 
 supply of remains; and in which, finally, the materials 
 composing the strata are such as to insure the preservation 
 of these remains in a tolerably perfect and undisturbed 
 state. 
 
 " It so happens that the case which, at present, most 
 nearly fulfills all these conditions is that of the series of 
 extinct animals which culminates in the Horses; by which 
 term I mean to denote not merely the domestic animals 
 with which we are so well acquainted, but their allies, the 
 ass, zebra, quagga, and the like. In short, I use ' horses ' 
 as the equivalent of the technical term Equidce, which is 
 applied to the whole group of existing equine animals. 
 
 " The horse is in many ways a remarkable animal; not 
 least so in the fact that it presents us with air example of 
 one of the most perfect pieces of machinery in the living 
 world. In truth, among the works of human ingenuity it 
 cannot be said that there is any locomotive so perfectly 
 adapted to its purposes, doing so much work with so small 
 a quantity of fuel, as this machine of nature's manufacture 
 the horse. . ^ . . Look at the perfect balance of his 
 form, and the rhythm and force of its action. The loco- 
 motive machinery is, as you are aware, resident in its 
 slender fore and hind limbs; they are flexible and elastic 
 levers, capable of being moved by very powerful muscles; 
 and, in order to supply the engines which work these levers 
 with the force which they expend, the horse is provided with 
 a very perfect apparatus for grinding its food and extract- 
 ing therefrom the requisite fuel. 
 
 " Without attempting to take you very far into the 
 region of osteological detail, I must nevertheless trouble 
 you with some statements respecting the anatomical struc- 
 ture of the horse; and, more especially, will it be needful 
 to obtain a general conception of the structure of its fore 
 and hind limbs, and of its teeth. But I shall only touch 
 upon those points which are absolutely essential to our 
 inquiry. 
 
 " Let us turn in the first place to the fore-limb. In 
 
HUXLEY ON EVOLUTION 289 
 
 most quadrupeds, as in ourselves, the fore-arm contains 
 distinct bones, called the radius and the ulna. The cor- 
 responding region in the horse seems at first to possess but 
 one bone. Careful observation, however, enables us to 
 distinguish in this bone a part which clearly answers to the 
 upper eird of the ulna. This is closely united with the chief 
 mass of the bone which represents the radius, and runs 
 out into a slender shaft which may be traced for some dis- 
 tance downwards upon the back of the radius, and then in 
 most cases thins out and vanishes. It takes still more 
 trouble to make sure of what is nevertheless the fact, that 
 a small part of the lower end of the bone of a horse's fore- 
 arm, which is only distinct in a very young foal, is really 
 the lower extremity of the ulna. 
 
 " What is commonly called the knee of a horse is its 
 wrist. The ' cannon bone ' answers to the middle bone 
 of the five metacarpal bones, which support the palm of 
 the hand in ourselves. The ' pastern/ ' coronary/ and 
 ' coffin' bones of veterinarians answer to the joints of our 
 middle fingers, while the hoof is simply a greatly enlarged 
 and thickened nail. But if what lies below the horse's 
 ' knee ' thus corresponds to the. middle finger in ourselves, 
 what has become of the four other fingers or digits? We 
 find in the places of the second and fourth digits only two 
 slender, splint-like bones, about two-thirds as long as the 
 cannon bone, which gradually taper to the lower ends and 
 bear no finger joints, or as they are termed, phalanges. 
 Sometimes, small bony or gristly nodules are to be found 
 at the bases of these two metacarpal splints, and it is prob- 
 able that these represent rudiments of the first and fifth 
 toes. Thus the part of the horse's skeleton which cor- 
 responds with that of the human hand contains one over- 
 grown middle digit, and at least two imperfect lateral 
 digits; and these answer, respectively, to the third, the 
 second, and the fourth fingers in man. 
 
 " Corresponding modifications are found in the hind 
 limb. In ourselves, and in most quadrupeds, the leg con- 
 tains two distinct bones a large bone, the tibia, and a 
 smaller and more slender bone, the fibular. But, in the 
 horse, the fibular seems, at first, to be reduced to its upper 
 end ; a short, slender bone, united with the tibia and ending 
 
290 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 in a point below, occupying its place. Examination of the 
 lower end of a young foal's shin-bone, however, shows a 
 distinct portion of osseous matter which is the lower end of 
 the fibula; so that the apparently single lower end of the 
 shin-bone is really made up of the coalesced ends of the 
 tibia and fibula, just as the apparently single lower end 
 of the fore-arm bone is composed of the coalesced radius 
 and ulna. 
 
 " The heel of the horse is the part commonly known as 
 the hock. The hinder cannon bone answers to the middle 
 metatarsal bone of the human foot; the pastern, coronary, 
 and coffin bones, to the middle toe bones; the hind hoof to 
 the nail; as in the fore-foot. And, as in the fore- foot, 
 there are merely two splints to represent the second and 
 the fourth toes. Sometimes a rudiment of the fifth toe 
 appears to be traceable. 
 
 " The teeth of the horse are not less peculiar than its 
 limbs. The living engine, like all others, must be well stoked 
 if it is to do its work; and the horse, if it is to make 
 good its wear and tear, and to exert the enormous amount 
 of force required for its propulsion, must be well and 
 rapidly fed. To this end> good cutting instruments and 
 powerful and lasting crushers are needful. Accordingly, 
 the twelve cutting teeth of a horse are close-set and con- 
 centrated in the fore part of its mouth, like so many adzes 
 or chisels. The grinders or molars are large, and have 
 an extremely complicated structure, being composed of a 
 number of different substances of unequal hardness. The 
 consequence of this is that they wear away at different 
 rates; and, hence, the surface of each grinder is always as 
 uneven as that of a good mill-stone. 
 
 " I have said that the structure of the grinding teeth is 
 very complicated, the harder and the softer parts being, 
 as it were, interlaced with one another. The result of this 
 is that, as the tooth wears, the crown presents a peculiar 
 pattern, the nature of which is not very easily deciphered at 
 first, but which it is important that we should understand 
 clearly. Each grinding tooth of the upper jaw has an 
 outer wall so shaped that, on the worn crown, it exhibits 
 the form of two crescents, one in front and one behind, 
 with their concave sides turned outwards. From the inner 
 
HUXLEY ON EVOLUTION 291 
 
 sides of the front crescent, a crescentic front ridge passes 
 inwards and backwards, and its inner face enlarges into a 
 strong logitudinal fold or pillar. From the front part of 
 the hinder crescent, a back-ridge takes a like- direction, and 
 also has its pillar. 
 
 " The deep interspaces or valleys between these ridges 
 and the outer wall are filled by bony substance, which is 
 called cement, and coats the whole tooth. 
 
 " The pattern of the worn face of each grinding tooth of 
 the lower jaw is quite different. It appears to be formed 
 of two crescent-shaped ridges, the convexities of which are 
 turned outwards. The free extremity of each crescent has 
 a pillar, and there is a large double pillar where the two 
 crescents meet. The whole structure is, as it were, em- 
 bedded in cement, which fills up the valleys, as in the 
 upper grinders. 
 
 "If the grinding faces of an upper and of a lower 
 molar are applied together, it will be seen that the opposed 
 ridges are nowhere parallel, but that they frequently cross ; 
 and that thus, in the act of mastication, a hard surface 
 in the one is constantly applied to a soft surface in the 
 other and vice versa. They thus constitute a grinding ap- 
 paratus of great efficiency, and one which is repaired as fast 
 as it wears, owing to the long continued growth of the 
 teeth. 
 
 " Some other peculiarities of the dentition of the horse 
 must be noticed, as they bear upon what I shall have to 
 say by-and-by. Thus, the crowns of the cutting teeth 
 have a peculiar deep pit, which gives rise to the well-known 
 ' mark ' of the horse. There is a large space between the 
 outer incisors and the front grinder. In this space the 
 adult male horse presents, near the incisors, one on each 
 side, above and below, a canine or ' tush,' which is com- 
 monly absent in mares. In a young horse, moreover, there 
 is not infrequently to be seen, in front of the first grinder, 
 a very small tooth, which soon falls out. If this small tooth 
 be counted as one, it will be found that there are seven 
 teeth behind the canine on each side, namely, the small 
 tooth in question, and six great grinders, among which, by 
 an unusual peculiarity, the foremost tooth is rather larger 
 than those which follow it. 
 
292 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 " I have now enumerated those characteristic structures 
 of the horse which are of most importance for the pur- 
 pose we have in view. 
 
 " To any one who is acquainted with the morphology of 
 vertebrated animals, they show that the horse deviates 
 widely from the general structure of mammals; and that 
 the horse type is, in many respects, an extreme modifica- 
 tion of the general mammalian plan. The least modified 
 mammals, in fact, have the radius and ulna, the tibia and 
 fibula, distinct and separate. They have five distinct and 
 complete digits on each foot, and no one of these digits 
 is very much larger than the rest. Moreover, in the least 
 modified mammals, the total number of the teeth is very 
 generally forty-four, while in horses the usual number is 
 forty, and in the absence of the canines it may be reduced 
 to thirty-six; the incisor teeth are devoid of the fold seen 
 in those of the horse; the grinders regularly diminish in 
 size from the middle of the series to its front end; while 
 their crowns are short, early attain their full length, and 
 exhibit simple ridges or tubercles, in place of the complex 
 foldings of the horse's grinders. 
 
 " Hence, the general principles of the hypothesis of evo- 
 lution lead to the conclusion that the horse must have been 
 derived from some quadruped which possessed five com- 
 plete digits on each foot; which had the bones of the fore- 
 arm and of the leg complete and separate; and which 
 possessed forty-four teeth, among which the crowns of the 
 incisors and grinders had a simple structure, while the lat- 
 ter gradually increased in size from before backwards, at 
 any rate in the anterior part of the series, and had short 
 crowns. 
 
 " And if the horse has been thus evolved, and the remains 
 of the different stages of its evolution have been preserved, 
 they ought to present us with a series of forms in which the 
 number of the digits becomes reduced; the bones of the 
 fore-arm and leg gradually take on the equine condition*; 
 and the form and arrangement of the teeth successively 
 approximate to those which obtain in existing horses. 
 
 " Let us turn to the facts and see how far they fulfil 
 these requirements of the doctrine of evolution. 
 
 " In Europe abundant remains of horses are found in 
 
HUXLEY ON EVOLUTION 293 
 
 the Quaternary and later Tertiary strata as far as the 
 Pliocene formation. But these horses, which are so com- 
 mon in the cave deposits and in the gravels of Europe, 
 are in all essential respects like existing horses. And that 
 is true of all the horses of the latter part of the Pliocene 
 epoch. But in deposits which belong to the earlier Plio- 
 cene and later Miocene epochs, and which occur in Britain, 
 in France, in Germany, in Greece, in India, we find ani- 
 mals which are extremely like horses which, in fact, are 
 so similar to horses, that you may follow descriptions given 
 in works upon the anatomy of the horse upon the skeletons 
 of these animals but which differ in some important par- 
 ticulars. For example, the structure of their fore and hind 
 limbs is somewhat different. The bones which, in the 
 horse, are represented by two splints, imperfect below, are 
 as long as the metacarpal and metatarsal bones; and at- 
 tached to the extremity of each is a digit with three joints 
 of the same general character as those of the middle digit, 
 only very much smaller. These small digits are so disposed 
 that they could have had but very little functional impor- 
 tance, and they must have been rather of the nature of 
 the dew-claws, such as are to be found in many animals. 
 The Hipparion, as the extinct European three-toed horse 
 is called, in fact, presents a foot similar to that of the 
 American Protophippus (Fig. 12), except that, in the Hip- 
 parion, the smaller digits are situated further back, and 
 are of smaller proportional size, than in the Protohippus. 
 
 " The ulna is slightly more distinct than in the horse ; 
 and the whole length of it, as a very slender shaft, inti- 
 mately united with the radius, is completely traceable. The 
 fibula appears to be in the same condition as in the horse. 
 The teeth of the Hipparion are essentially similar to those 
 of the horse, but the pattern of the grinders is in some 
 respects a little more complex, and there is a depression 
 on the face of the skull in front of the orbit which is not 
 seen in existing horses. 
 
 " In the earlier Miocene and perhaps the later Eocene 
 deposits of some parts of Europe, another extinct animal 
 has been discovered, which Cuvier, who first described 
 some fragments of it, considered to be a Palceotherium. 
 But as further discoveries threw no light upon its struc- 
 
294 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 ture, it was recognized as a distinct genus, under the name 
 of Anchitherium. 
 
 " In its general characters, the skeleton of Anchitherium 
 is very similar to that of the horse. In fact, Lartet and 
 De Blainville called it Palceotherium equinum or hippoides; 
 and De Christol, in 1847, said that it differed from Hip- 
 parion in little more than the characters of its teeth, and 
 gave it the name of Hipparitherium. Each foot possesses 
 three complete toes; while the lateral toes are much larger 
 in proportion to the middle toe than in Hipparwn, and 
 doubtless rested on the ground in ordinary locomotion. 
 
 " The ulna is complete and quite distinct from the 
 radius, though firmly united with the latter. The fibula 
 seems also to have been complete. Its lower end, though 
 intimately united with that of the tibia, is clearly marked 
 off from the latter bone. 
 
 " There are forty-four teeth. The incisors have no 
 Strong pit. The canines seem to be well developed in both 
 : sexes. The first of the seven grinders, which, as I have 
 ; said, is frequently absent, and, when it does exist, is small 
 in the horse, is a good-sized and permanent tooth, while 
 tthe grinder which follows it is but little larger than the 
 ihinder one. The crowns of the grinders are short, and 
 though the fundamental pattern of the horse-tooth is dis- 
 cernible, the front and back ridges are less curved, the 
 accessory pillars are wanting, and the valleys, much shal- 
 lower, are not filled up with cement. 
 
 " Seven years ago, when I happened to be looking criti- 
 cally into the bearing of palaeorrtological facts upon the 
 (doctrine of evolution, it appeared to me that the Anchithe- 
 Tium, the Hipparion, and the modern horse constitute a 
 series in which the modifications of structure coincide with 
 the order of chronological occurrence, in the manner in 
 which they must coincide if the modern horses really are 
 the result of a gradual metamorphosis, in the course of the 
 Tertiary epoch, of a less specialized ancestral form. And 
 I found by correspondence with the late eminent French 
 anatomist and paleontologist, M. Lartet, that he had arrived 
 at the same conclusion from the same data. 
 
 " That the Anchitherium type had become metamor- 
 phosed into the Hipparion type, and the latter into the 
 Equine type, in the course of that period of time which 
 
HUXLEY ON EVOLUTION 295 
 
 is represented by the latter half of the Tertiary deposits, 
 seemed to me to be the only explanation of the facts for 
 which there was even a shadow of probability. 
 
 " And, hence, I have ever since held that these facts 
 afford evidence of the occurrence of evolution, which, in 
 the sense already defined, may be termed demonstrative. 
 
 " All who have occupied themselves with the structure 
 of Anchitherium, from Cuvier onwards, have acknowledged 
 its many points of likeness to a well-known genus of ex- 
 tinct Eocene mammals, P alee other mm. Indeed, as we have 
 seen, Cuvier regarded his remains of Anchitherium as those 
 of a species of Palceotherium. Hence, in attempting to 
 trace the pedigree of the horse beyond the Miocene epoch 
 and the Anchitheroid form, I naturally sought among the 
 various species of Palseotheroid animals for its nearest 
 ally, and I was led to conclude that the Palceotherium minus 
 (Plagiolophus) represented the next step more nearly than 
 any other form then known. 
 
 " I think that this opinion was fully justifiable; but the 
 progress of investigation has thrown an unexpected light 
 on the question, and has brought us much nearer than could 
 have been anticipated to a knowledge of the true series of 
 the progenitors of the horse. 
 
 " You are all aware that when your country was first 
 discovered by Europeans, there were no traces of the ex- 
 istence of the horse in any part of the American continent. 
 The accounts of the conquest of Mexico dwell upon the 
 astonishment of the natives of that country when they first 
 became acquainted with that astounding phenomenon a 
 man seated upon a horse. Nevertheless, the investigations 
 of American geologists have proved that the remains of 
 horses occur in the most superficial deposits of both North 
 and South America, just as they do in Europe. Therefore, 
 for some reason or other, no feasible suggestion on that 
 subject, so far as I know, has been made, the horse must 
 have died out in this continent at some period preceding 
 the discovery of America. Of late years there has been 
 discovered in your Western Territories that marvellous ac- 
 cumulation of deposits, admirably adapted for the preser- 
 vation of organic remains, to which I referred the other 
 evening, and which furnishes us with a consecutive series 
 of records of the fauna of the older half of the Tertiary 
 
296 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 epoch, for which we have no parallel in Europe. They 
 have yielded fossils in an excellent state of conservation 
 and in unexampled number and variety. The researches 
 
 Fore Hind Pore 
 Foot. Foot. Arm. 
 
 Lower 
 . Upper Molar. Molar. 
 
 MIOHIPPUS. 
 
 (Anchilherium) 
 
 MESOHIPPUS 
 
 EOCENE. 
 
 OROHIPPUS. 
 
 FIG. 12. 
 
 of Leidy and others have shown that forms allied to the 
 Hipparion and the Anchitherium are tP be found among 
 
HUXLEY ON EVOLUTION 297 
 
 these remains. And it is only recently that the admirably 
 conceived and most thoroughly and patiently worked-out 
 investigations of Professor Marsh have given us a just idea 
 of the vast fossil wealth and of the scientific importance 
 of these deposits. I have had the advantage of glancing 
 over the collections in Yale Museum, and I can truly say 
 that, so far as my knowledge extends, there is no collection 
 from any one region and series of strata comparable for 
 extent, or for the care with which the remains have been 
 got together, or for their scientific importance, to the series 
 of fossils which he has deposited there. This vast collec- 
 tion has yielded evidence bearing upon the pedigree of the 
 horse of the most, striking character. It tends to show 
 that we must look to America, rather than to Europe, for 
 the original seat of the equine series; and that the archaic 
 forms and successive modifications of the horse's ancestry 
 are far better preserved here than in Europe. 
 
 " Professor Marsh's kindness has enabled me to put be- 
 fore you a diagram, every figure in which is an actual repre- 
 sentation of some specimen which is to be seen at Yale 
 at this present time (Fig. 12). 
 
 " The succession of forms which he has brought together 
 carries us from the top to the bottom of the Tertiaries. 
 Firstly, there is the true horse. Next we have the American 
 Pliocene form of the horse (Pliohippus) ; in the conforma- 
 tion of its limbs it presents some very slight deviations 
 from the ordinary horse, and the crowns of the grinding 
 teeth are shorter. Then comes the Protohippus, which 
 represents the European Hipparion, having one large digit 
 and two small ones on each foot, and the general charac- 
 ter of the fore-arm and leg to which I have referred. But 
 it is more valuable than the European Hipparion for the 
 reason that it is devoid of some of the peculiarities of that 
 form peculiarities which tend to show that the European 
 Hipparion is rather a member of a collateral branch than 1 
 a form in the direct line of succession. Next, in the back- 
 ward order in time, is the Miohippus, which corresponds 
 pretty nearly with the Anchitherium of Europe. It pre- 
 sents three complete toes one large median and two smal- 
 ler lateral ones ; and there is a rudiment of that digit which 
 answers to the little finger of the human hand. 
 
 " The European record of the pedigree of the horse 
 
298 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 stops here; in the American Tertiaries, on the contrary, 
 the series of ancestral equine forms is continued into the 
 Eocene formations. An older Miocene form, termed Meso- 
 hippus, has three toes in front, with a large splint-like 
 rudiment representing the little finger, and three toes be- 
 hind. The radius and the ulna, the tibia and the fibula, 
 are distinct, and the short-crowned molar teeth are Anchi- 
 theroid in pattern. 
 
 " But the most important discovery of all is the Oro- 
 hippus, which comes from the Eocene formation, and is the 
 oldest member of the equine series, as yet known. Here 
 we find four complete toes on the front limb, three toes 
 on the hind limb, a well-developed ulna, a well-developed 
 fibula, and short-crowned grinders of simple pattern. 
 
 " Thus, thanks to these important researches, it has be- 
 come evident that, so far as our present knowledge ex- 
 tends, the history of the horse-type is exactly that which 
 could have been predicted from a knowledge of the prin- 
 ciples of evolution. And the knowledge we now possess 
 justifies us completely in the anticipation that when the 
 still lower Eocene deposits, and those which belong to the 
 Cretaceous epoch, have yielded up their remains of ances- 
 tral equine animals, we shall find, first, a form with four 
 complete toes and a rudiment of the innermost first digit 
 in front, with probably, a rudiment of the fifth digit in 
 the hind foot ; 13 while, in still older forms, the series of 
 digits will be more and more complete, until we come to the 
 five-toed animals, in which, if the doctrine of evolution is 
 well-founded, the whole series must have taken* its origin. 
 
 " This is what I mean by the demonstrative evidence 
 of evolution. An inductive hypothesis is said to be demon- 
 strated when the facts are shown to be in entire accordance 
 with it. If that is not scientific proof, there are no merely 
 inductive conclusions which can be said to be proved. And 
 the doctrine of evolution, at the present time, rests upon 
 exactly as secure a foundation as the Copernican theory 
 of the motions of the heavenly bodies did at the time of its 
 promulgation. Its logical basis is precisely of the same 
 character the coincidence of the observed facts with theo- 
 retical requirements. 
 
 is Remains of animals corresponding very closely to this de- 
 scription were afterwards discovered. 
 
HUXLEY ON EVOLUTION 299> 
 
 " Tl:e only way of escape, if it be a way of escape, from* 
 the conclusions which I have just indicated, is the suppo- 
 sition that all these different equine forms have been 
 created separately at separate epochs of time; and, I re- 
 peat, that of such an hypothesis as this there neither is, 
 nor can be, any scientific evidence; and assuredly, so far 
 as I know, there is none which is supported, or pretends 
 to be supported, by evidence or authority of any other 
 kind. I can but think that the time will come when such 
 suggestions as these, such obvious attempts to escape the 
 force of demonstration, will be put upon the same footing 
 as the supposition made by some writers, who are, I be- 
 lieve, not completely extinct at present, that fossils are 
 mere simulacra, are no indications of the former existence 
 of the animals to which they seem to belong ; but that they 
 are either sports of Nature, or special creations. . . . 
 
 " In fact, the whole evidence is in favor of evolution, and 
 there is none against it. And I say this, although perfectly 
 well aware of the seeming difficulties which have been 
 built up upon what appears to the uninformed to be a 
 solid foundation. I meet constantly with the argument 
 that the doctrine of evolution cannot be well founded, be- 
 cause it requires the lapse of a very vast period of time; 
 while the duration of life upon the earth, thus implied, is 
 inconsistent with the conclusions arrived at by the as- 
 tronomer and the physicist. I may venture to say that I 
 am familiar with those conclusions, inasmuch as some years 
 ago, when President of the Geological Society of London, 
 I took the liberty of criticising them, and of showing in 
 what respects, as it appeared to me, they lacked complete 
 and thorough demonstration. But, putting that point aside, 
 suppose that, as the astronomers, or some of them, and 
 some physical philosophers, tell us, it is impossible that life 
 could have endured upon the earth for as long a period 
 as is required by the doctrine of evolution supposing that 
 to be proved I desire to be informed what is the founda- 
 tion for the statement that evolution does require so great 
 a time. The biologist knows nothing whatever of the 
 amount of time which may be required for the process of 
 evolution. It is a matter of fact that the equine forms, 
 which I have described to you, occur in the order stated in 
 the Tertiary formations, But I have not the slightest 
 
300 TYPICAL SYSTEMS OF KNOWLEDGE 
 
 means of guessing whether it took a million of years, or 
 ten millions, or a hundred millions, or a thousand millions 
 of years, to give rise to that series of change. 
 
 " A biologist has no means of arriving at any conclusion 
 as to the amount of time which may be needed for a certain 
 quantity of organic change. He takes his time from the 
 geologist. The geologist, considering the rate at which de- 
 posits are formed and the rate at which denudation goes 
 on upon the surface of the earth, arrives at more or less 
 justifiable conclusions as to the time required for the de- 
 posit of a certain thickness of rocks ; and if he tells me 
 that the Tertiary formations required 500,000,000 years 
 for their deposit, I suppose he has good ground for what 
 he says, and I take that as a measure of the duration of 
 the evolution of the horse from the Orohippus up to its 
 present condition. And, if he is right, undoubtedly evolu- 
 tion is a very slow process, and requires a great deal of 
 time. But suppose, now, that an astronomer or a physicist 
 for instance, my friend, Sir William Thomson tells me 
 that my geological authority is quite wrong; and that he 
 has weighty evidence to show that life could not possibly 
 have existed upon the surface of the earth 500,000,000 
 years ago, because the earth would have then been too hot 
 to allow of life, my reply is : ' That is not my affair ; set- 
 tle that with the geologist, and when you have come to an 
 agreement among yourselves, I will adopt your conclu- 
 sion/ We take our time from the geologists and physicists ; 
 and it is monstrous that, having taken our time from the 
 physical philosopher's clock, the physical philosopher should 
 turn round upon us, and say we are too fast or too slow. 
 What we desire to know is, is it a fact that evolution* took 
 place ? As to the amount of time which evolution may have 
 occupied, we are in the hands of the physicists and as- 
 tronomers, whose business it is to deal with those questions." 
 
INDEX 
 
 Abstractions, 45 
 
 Abstract terms, 54 
 
 Aikins, 163, 205 
 
 Amphibology, 73 
 
 Analogy, 251; rules of, 252 
 
 Analysis, 46, 88 
 
 Antecedent probability, 277 
 
 Astronomy, 265 
 
 Average deviation, 206 
 
 A ve_rage v . deviation from, 205 
 
 Average error, 206 
 
 Averages, 195, 198; arithmet- 
 ical, 198; geometrical, 204; 
 the median, 202; the mode, 
 201 ; " weighted " averages, 
 199 
 
 Bain, 104, 271 
 
 Baldwin, 11, 238 
 
 Biology, 35, 42, 208, 262 
 
 Bosanuqet, 34 
 
 Bowley, 192, 194, 200, 202, 203, 
 
 204, 207, 229, 230. 
 Burnet, 249 
 
 Causal law, 81, 82 
 Cause, 81 
 Chamberlain, 250 
 Chemistry, 262 
 Circumstantial evidence, 279 
 Collective judgments, 86 
 Collective terms, 56 
 .Collusion, 276 
 Composition of causes, 97, 193 
 
 Classification, 6, 32, 49, 79, 195; 
 artificial, 33; diagnostic, 33; 
 index, 32; natural, 33; req- 
 uisites of, 40, 49 
 
 Common sense, 1 
 
 Comparison of quantities, 210 
 
 Composition, fallacy of, 57 
 
 Concept, conception, 45 
 
 Concrete terms, 54 
 
 Contradictory propositions, 114 
 
 Contraposition, 122 
 
 Contrary propositions, 114 
 
 Conversion, 119 
 
 Correlation, 191 
 
 Counteracting causes, 97, 193 
 
 Cramer, 248, 250 
 
 Cross-division, 41 
 
 Curves, 226 
 
 Cuvier, 12 
 
 Darwin, 248, 249 
 
 Deduction, 110; a part of 
 
 scientific method, 2 
 Definition, 57; defects of, 60 
 DeMorgan, 77 
 Deviations from an average, 
 
 205 
 
 Dilemma, The, 159 
 Discrimination, 45 
 Disjunctive reasoning, 157 
 Distributive terms, 56 
 Distribution of terms, 71 
 Division, 37; dichotomous, 38; 
 
 incomplete, 40; rules of, 40; 
 
 fallacy of, 56 
 
 801 
 
302 
 
 INDEX 
 
 Documents, 266 
 
 Elimination in the inductive 
 methods, 96 
 
 Enthymeme, 151 
 
 Enumeration, complete, 84; in- 
 complete or simple, 83, 190 
 
 Error, 206; curve of, 231 
 
 Errors, three kinds, 18; causes 
 of, 19 
 
 Euclid, 258 
 
 Euler's Method, 72, 120 
 
 Evidence, 48 ; circumstantial, 
 279; external, 270; hearsay, 
 278; indirect, 278; internal, 
 270 
 
 Exceptive propositions, 76 
 
 Exclusive propositions, 75 
 
 Experiment, 24 
 
 Explanation, 237; general, 240; 
 specific, 240, 244 
 
 External evidence, 270 
 
 Extra-syllogistic reasoning, 162 
 
 Fallacies, formal, 138, 173; of 
 accent, 76; of amphibology, 
 73; of assumption, 171; of 
 converse accident, 55; of 
 composition, 57; of division, 
 57; of figure of speech, 76; 
 of four terms, 138; of hypo- 
 thetical reasoning, 157; of 
 illicit major, 141; of illicit 
 minor, 141 ; of missing the 
 point, 171 ; of non-sequitur, 
 174; of perception, 16; of 
 petitio principii, 172; of post 
 hoc ergo propter hoc, 174; of 
 undistributed middle, 138 
 
 Figures of the syllogism, 126, 
 142; principles of, 126; rules 
 for, 126 
 
 Fison, 284 
 
 Fowler, 90 
 
 Fundamentun division, 34, 41 
 
 Facts, 13 
 
 Galton, 203 
 Generalization, 79 
 General terms, 52 
 Genus, 41 
 Geology, 264 
 Geometry, 258 
 Gomperz, 255 
 Graphic method, 266 
 
 Hadley, 249 
 
 Hayward, 276 
 
 Hearsay evidence, 278 
 
 Helmholz, 208 
 
 Hibben, 111, 123 
 
 History, 264 
 
 Hobhouse, 240, 253 
 
 Huxley, 1, 12, 36, 248, 278 
 
 Hypotheses, 246; value of, 
 246; value of erroneous, 249; 
 how suggested, 251; requi- 
 sites of, 253 
 
 Hypothetical reasoning, 157; 
 rules of, 157 
 
 Hyslop, 38, 73, 75, 120 
 
 Induction, 2, 79; perfect, 85; 
 mathematical, 168 
 
 Inductive inference, SI 
 
 Indjiclise-jaethods^ 8 ; agree- 
 ment, 90; difference, 95; the 
 joint method, 98; concomi- 
 tant variations, 102; residues, 
 104 
 
 Inference, 6, 14, 15, 29 
 
 Infima species, 42 
 
 Internal evidence, 270 
 
INDEX 
 
 303 
 
 James, 21, 113, 208, 263, 280; 
 
 theory of the emotions, 280 
 Jevons, 33, 36, 76, 150, 209, 219, 
 
 221, 239 
 Joseph, 69 
 
 Kant, 4, 9 
 
 Knowledge, the beginning of, 
 
 3; the sources of, 5; organ- 
 
 izing, 6 
 
 Langlois and Seignobos, 250, 
 
 266, 269, 279 
 Language, 7, 48 
 
 Xaw, 79, 237; how discovered. 
 ^~8, 189 ~ 
 
 Laws of thought, 1, 10 
 Linnaeus, 34 
 Locke, 4, 9, 76 
 Lotze, 223 
 
 Material facts, 266 
 Mayo-Smith, 196 
 Meaning, 47 
 Measurement, 208 
 Mechanics, 262 
 
 Median error, 206 , 
 MemoryTsT 26, 48 ^ 
 Mendel's Law, 263 
 Methods, inductive, 88 
 Mill, 84, 86, 91, 95, 96, 101, 102, 
 
 105 
 
 Minto, 251, 255 
 Mode, the, 201 
 
 Moods of the syllogism, 140 
 Muirhead, 245 
 
 Natural classifications, 33 
 Natural science, 4, 12 
 Negative evidence, 276 
 Newton, 247 
 
 Observation, 18, 48, 79, 88; 
 
 mistakes of, 18 
 Obversion, 121 
 
 Opposition of propositions, 114 
 Order, 42 
 
 Pearson, 32, 192, 208 
 
 Perception, 5 3 13 ; " fallacies " 
 of, 16; how tested, 23 
 
 Predicables, 60 
 
 Predicate, 68 
 
 Plurality of causes, 94, 193 
 
 Porphyry, 37 
 
 Premises, 126 
 
 Presuppositions of knowledge, 
 9 
 
 Proof, 166; direct, 166; indi- 
 rect, 166; in geometry, 168 
 
 Probability, 213 ; curve of, 231 ; 
 deduction of, 216; dangers in 
 interpreting, 223 
 
 Probable error, 206 
 
 Propositions, 66; (juantity and 
 quality of, 66; and terms, 
 68; ambiguous, 73; exceptive, 
 76; exclusive 75 
 
 Pro-syllogism and epi-syllo- 
 gism, 152 
 
 Psychology, 262 
 
 Punnett, 253 
 
 Reduction of the moods and 
 
 figures, 158 
 Romanes, 247 
 Russell, 59 
 
 Scientific law, 8 
 
 Science and common sense, 1 
 
 Science, 259 
 
 Scott, 264 
 
 Sedjjwick and Wilson, 35 
 
304 
 
 INDEX 
 
 Seignobos, Langlois and, 250, 
 266, 269, 279 
 
 Self-evident propositions, 79 
 
 Sigwart, 196, 243, 251 
 
 Singular terms, 52 
 
 Sorites, 155 
 
 Species, 41 
 
 Spencer, 61 
 _Statistics, 189 ; collection of, 
 
 ^1931 T31"; tabulation, 194; 
 summary, 194; critical exam- 
 ination of, 194; often un- 
 necessary, 195; often inappli- 
 cable, 196 
 
 Subalterns, 114 
 
 Subcontraries, 114 
 
 Subject, 68; grammatical, 68; 
 logical, 68; metaphysical or 
 ultimate, 69 
 
 Sui generis, 42 
 
 Summun genus, 41 
 
 Syllogism, 111; criticism of, 
 111; principles of, 126; rules 
 of, 137 
 
 Symbols, 47 
 
 Systematic knowledge, 111 
 
 Terms, 49; distribution of, 71; 
 generalization of, 50; spe- 
 cialization of, 50; transfer of 
 meaning of, 51; kinds of, 52; 
 and propositions, 68 
 
 Testimony, 6, 28, 266; sources 
 of error in, 28 
 
 Testing inductive inference, 83, 
 89 
 
 Testing perceptions, 23 
 
 Thorndike, 192, 211, 234, 263 
 
 Tradition, 278 
 
 Variety, 42 
 Veblen, 258 
 
 Verification, 8, 81, 86, 110 
 Voltaire, 274 
 
 Washburn, 253 
 Witness, The, 269 
 Wilson, Sedgwick and, 35 
 
 Yerkes, 263 
 Young, 197 
 
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