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 http://www.archive.org/details/essentialsoflogiOOsell 
 
THE ESSENTIALS OF 
 LOGIC 
 
 R. W. SELLARS, Ph.D. 
 
 i » 
 
 A ssistantProfessor of Philosophy 
 University of Michigan 
 
 
 BOSTON NEW YORK CHICAGO 
 
 H&UGHTON MIFFLIN COMPANY 
 
 (gfce BitacrjffiDe $zc& Cambridge 
 
 

CONTENTS 
 
 I. Introductory 
 
 A Definition of Logic — The Value of Logic — The Kinds 
 of Logic — Introductory Logic — Relation of Logic to 
 Other Sciences — The Material of Logic — References. 
 
 II. The Nature and Setting of Thought . 
 
 What is Thought? — Discovery and Proof — The Psy- 
 chologist's View of Reasoning — Examples of Reasoning 
 
 — The Conditions and Occasions of Thought — The Set- 
 ting of Thought — Why we think — Processes Preliminary 
 to Reflective Thought — Fact and Theory — Knowledge a 
 Growth — References. 
 
 III. About Terms 
 
 The Unit of Thought — The Elements of the Proposition 
 
 — Words and Terms — Kinds of Terms — Other Kinds of 
 Terms — Connotation and Denotation — Synonyms for 
 Connotation and Denotation — The Inverse Variation of 
 Connotation and Denotation — Terms and Meaning — 
 References. 
 
 IV. The Use and Misuse of Language 
 
 The Necessity for Language — Language and Analysis 
 
 — The Logical Law of Language — Causes of Ambiguity 
 
 — Univocal Words — Equivocal Words — Words change 
 their Meanings — Vagueness — Abstract Terms particularly 
 subject to Vagueness — Logic and Language — References. 
 
 V. Classification and Division 
 
 Classification and Classes — The Need for Classification 
 
 — Types of Classification — Artificial Classification — Nat- 
 ural Classifications — Natural Classification in the Light 
 of Evolution — Character of Systematic Classification -— 
 Classification and Division — Technical Terms used in 
 Division — Rules of Division — Forms of Division — Di- 
 chotomous Division — Classificatory Division — Dangers 
 to be guarded against — References. 
 
COPYRIGHT, 1917, BY R. W SELLARS 
 
 ALL RIGHTS RESERVED 
 
 FEB -71917 ^ 
 
 CAMBRIDGE . MASSACHUSETTS 
 
 l<0 
 
CONTENTS 
 
 I. Introductory 1 
 
 A Definition of Logic — The Value of Logic — The Kinds 
 of Logic — Introductory Logic — Relation of Logic to 
 Other Sciences — The Material of Logic — References. 
 
 II. The Nature and Setting of Thought ... 10 
 
 What is Thought? — Discovery and Proof — The Psy- 
 chologist's View of Reasoning — Examples of Reasoning 
 
 — The Conditions and Occasions of Thought — The Set- 
 ting of Thought — Why we think — Processes Preliminary 
 to Reflective Thought — Fact and Theory — Knowledge a 
 Growth — References. 
 
 III. About Terms 27 
 
 The Unit of Thought — The Elements of the Proposition 
 
 — Words and Terms — Kinds of Terms — Other Kinds of 
 Terms — Connotation and Denotation — Synonyms for 
 Connotation and Denotation — The Inverse Variation of 
 Connotation and Denotation — Terms and Meaning — 
 References. 
 
 IV. The Use and Misuse of Language ... 40 
 
 The Necessity for Language — Language and Analysis 
 
 — The Logical Law of Language — Causes of Ambiguity 
 
 — Uni vocal Words — Equivocal Words — Words change 
 their Meanings — Vagueness — Abstract Terms particularly 
 subject to Vagueness — Logic and Language — References. 
 
 V. Classification and Division 50 
 
 Classification and Classes — The Need for Classification 
 
 — Types of Classification — Artificial Classification — Nat- 
 ural Classifications — Natural Classification in the Light 
 of Evolution — Character of Systematic Classification — 
 Classification and Division — Technical Terms used in 
 Division — Rules of Division — Forms of Division — Di- 
 chotomous Division — Classificatory Division — Dangers 
 to be guarded against — References. 
 
iv CONTENTS 
 
 VI. Principles of Definition 62 
 
 Why Definition is needed — The Purpose and Nature of 
 Definition — Logic stresses General Terms — Definition 
 and Classification — The Verification of Meaning — Rules 
 of Definition — Other Forms of Definition — The Pred- 
 icates — The Importance of Definition — References. 
 
 VII. Assertions and Propositions 76 
 
 An Important Distinction — Critical vs. Uncritical As- 
 sertion — What is an Assertion ? — Levels of Judgment — 
 Concepts and Judgment — Judgment defined — All Knowl- 
 edge Judgmental — The Part played by Language — The 
 Logical Treatment of Propositions — References. 
 
 VIII. The Logic of Propositions 89 
 
 A General Division of Propositions — The Quality and 
 Quantity of Propositions — Symbolic Classification of Prop- 
 ositions — Reduction of Propositions to Logical Form — The 
 Distribution of Terms — The Graphical Method — The Pur- 
 pose of Logical Analysis — References. 
 
 IX. The Implications of Propositions . . .98 
 
 Immediate Inference — The Oppositions of the Four 
 Kinds of Propositions — Conversion — Ob version — False 
 Ob version — Contraposition — Significance of Immediate 
 Inference — References. 
 
 X. The Syllogism as a Mechanism .... 107 
 
 The Nature of the Syllogism — An Analysis of the Syllo- 
 gism — The Elements of the Syllogism — The Rules of the 
 Syllogism — The Formal Syllogism and Actual Reasoning 
 — References. 
 
 XI. The Figures and Moods of the Syllogism . 118 
 
 The Figures of the Syllogism — The Moods of the Syllo- 
 gism — Reduction to the First Figure — Comparative 
 Value of the Figures — References. 
 
 XII. Abbreviated and Expanded Arguments — 
 
 Extra-Syllogistic Arguments . . . .126 
 
 Enthymeme — Prosyllogisms and Episyllogisms — Sori- 
 tes — Extra-Syllogistic Arguments — References. 
 
/ 3 J 
 
 CONTENTS v 
 
 XIII. Hypothetical and Disjunctive Syllogisms . 132 
 
 The Hypothetical Syllogism — The Rule of the Hypothet- 
 ical Syllogism — The Fallacies of the Hypothetical Syllo- 
 gism — Reduction to Categorical Form — The Disjunctive 
 Syllogism — The Dilemma — References. 
 
 XIV. Fallacies in Argumentation 141 
 
 What a Fallacy is — A Classification of Fallacies — 
 Classification of Deductive Fallacies — Fallacies of Equivo- 
 cation — Fallacies of Unwarranted Assumption — Conclu- 
 sion — References. 
 
 XV. The Nature of Induction 159 
 
 Induction and Deduction — A Glance at the History of 
 Logic — The Function of the Syllogism — Why the Syl- 
 logism is only a Part of Reasoning — Steps in Systematic 
 Investigation — Three Elements in Investigation — The 
 Problem of Generalization — The Implication of Generaliza- 
 tion — How Generalization differs from Expectation — The 
 Importance of Generalization — Testing Generalizations — 
 References. 
 
 XVI. The General Methods of Science . . . 173 
 
 How Science developed — The Need of Analysis — The 
 Value of Technique and Instruments — The Importance of 
 Measurement — Experimentation — The Use of Experi- 
 ment in Biology — Experimentation in Psychology — The 
 Statistical Method — The Method of Graphs —The Func- 
 tion of Hypotheses — References. 
 
 XVII. Observation and Fact 184 
 
 The Need of Observation — The Difficulty of securing 
 Data — Conditions of Accurate Observation — Errors in 
 Perception — Causes of Erroneous Perception — Summary 
 for Perception — Observation in Everyday Life and in 
 Science — Memory and Facts — Summary of Causes of 
 Mistaken Memory — Testimony — Facts differ in Differ- 
 ent Sciences — What are Relevant Facts? — References. 
 
 XVIII. The Origin and Use of Hypotheses . . 197 
 
 What is an Hypothesis? — Kinds of Hypotheses — Are 
 Hypotheses Necessary for Science? — The Origin of Hy- 
 
211 
 
 vi CONTENTS 
 
 potheses — A Glance at the Psychology of Conjecture — The 
 Value of Hypotheses — The Development of an Hypothesis 
 — The Proof of an Hypothesis — Fact, Theory, and Hypoth- 
 esis — Analogy as a Basis of Reasoning — False Analogy 
 
 — References. 
 
 XIX. The Discovery and Proof of Causal Rela- 
 
 tions 
 
 How Experience comes to us — What are Causal Connec- 
 tions?— Post Hoc ergo Propter Hoc— MilYs Methods— The 
 Method of Agreement — Examples of Induction by Agree- 
 ment — The Character of the Method — Difficulties con- 
 fronting the Method — The Method of Difference — Exam- 
 ples of the Method — Warnings — The Method of Concom- 
 itant Variations — Examples of the Method — Warning 
 
 — The Joint Method of Agreement and Difference — Ex- 
 amples — The Method of Residues — Examples — Re- 
 marks on Mill's Method? — References. 
 
 XX. Statistics . . . / 228 
 
 The Nature of Statistics — Stages in Statistical Investi- 
 gation — The Law of Statistical Regularity — Dangers in 
 the Use of Statistics — The Value of Statistics — Refer- 
 ences. 
 
 XXI. Probability 239 
 
 Abstract Laws vs. Concrete Events — Where Certainty is 
 Possible — The Meaning of Probability — Probability and 
 Chance — Three Kinds of Estimations — Empirical, or Non- 
 Quantitative, Probability — Probabilities based on Averages 
 — The Mathematical Treatment of Probability — Mistakes 
 in interpreting Probabilities — References. 
 
 XXII. Averages and Graphs 251 
 
 The Uses of Averages — The Arithmetical Average — 
 The ' Weighted ' Average —The Mode —The Median— The 
 Geometric Average — The Comparative Advantages of 
 these Averages — Graphs and Graphical Methods — 
 References. 
 
 XXIII. Testimony and Circumstantial Evidence . 264 
 
 Scientific Investigation vs. Judicial Proof — The Difficul- 
 ties confronting Judicial Proof — Distinction between Cir- 
 
CONTENTS vii 
 
 cumstantial and Testimonial Evidence — The Nature of Cir- 
 cumstantial Evidence — The Convergence of Evidence — 
 Direct or Testimonial Evidence — The Modern Critical At- 
 titude toward Testimony — Logical Standards and Tests 
 — The Movement of Judicial Proof — The Massing of 
 Mixed Evidence — References. 
 
 XXIV. Explanation and System-Formation . . 278 
 
 The Nature of Explanation — The Sentiment of Ration- 
 ality — The Role of Concepts — Proof and Explanation — 
 Systems are tentative — Levels of Explanation — General 
 Explanation and Specific Explanation — Typical Systems 
 of Knowledge — References. 
 
 XXV. Truth and its Tests 294 
 
 Back to the Definition of Logic — The Nature of Con- 
 sistent Thinking — The Laws of Thought — The Postu- 
 lates of Logic — The Question of Truth — The Criteria of 
 Truth — Degrees of Belief — What the Attainment of 
 True Ideas implies — The Meaning of Truth — ■ Truth and 
 the Will to Believe — The Logic of Doubt — References. 
 
 Questions and Exercises 311 
 
 Index 345 
 
THE ESSENTIALS OF LOGIC 
 
 CHAPTER I 
 
 INTRODUCTORY 
 
 A Definition of Logic. Logic may be defined as 
 the science of the principles and conditions of connect 
 thinking. To the beginner, a definition serves mainly 
 as a guide-post to direct his attention to the general 
 character of the subject which he is about to study. The 
 above definition should therefore be taken merely as an 
 indication of the field. The terms of which it is com- 
 posed will gather content and meaning as the various 
 topics are covered. Toward the end of the course, it is 
 to be hoped that the student will be able to come back 
 to the definition with a fuller grasp of its significance. 
 
 Logic is a science in the sense that it is organized 
 knowledge involving principles. The various sciences 
 have different fields for investigation, but all of them 
 agree in their purpose, which is the establishment of 
 satisfactory information bound together and illuminated 
 by laws. Thus, physics studies the most general charac- 
 teristics of the physical world and seeks to reduce to 
 order and interpret the facts it discovers ; botany ex- 
 amines the structures, functions, and histories of plants ; 
 and psychology gives its attention to the behavior of 
 creatures possessing consciousness. All these sciences 
 seek to replace the loose and hazy notions of popular 
 thought by exact and systematic knowledge. Now logic 
 
2 THE ESSENTIALS OF LOGIC 
 
 has the same purpose, but its field is peculiar. It can- 
 not be classed among the physical sciences which de- 
 pend upon perception and measurement, nor among the 
 biological sciences, nor, finally, among the social sciences. 
 In a very real sense modern logic presupposes all these 
 sciences and is somehow a science at second remove 
 from things. It is a science about the mental aspect of 
 the sciences. The mediaeval logicians pointed out that the 
 mind first ' intends,' or directs itself upon, the exter- 
 nal world, and that only afterwards does it direct itself 
 upon the mental processes and methods it has used. We 
 may say, then, that logic involves a thinking about 
 thinking. 
 
 Because man is naturally outward-looking and de- 
 sirous of practical results he is seldom clearly conscious 
 of his methods and of the mental processes involved in 
 thinking. It requires an effort for him to take this new 
 attitude and to think about thinking, about those mental 
 operations which make knowledge possible. But when 
 he does so, he finds that the mind does work in an 
 orderly fashion. It is the nature of this orderliness that 
 logic seeks to bring into clear consciousness. 
 
 The Value of Logic. So far as logic is a pure 
 science, its value is essentially of the same kind as that 
 of any other pure science. It satisfies an intellectual 
 curiosity, a desire to know. Before a teacher can appeal 
 strongly to such a value, the student must have expe- 
 rienced it; at some past time he must have forgotten 
 himself as an individual with private ambitions in the 
 enjoyment of seeing problems solved, of watching mean- 
 ing replace confusion ; he must have felt pleasure in 
 knowledge for its own sake. The logician who is loyal 
 
INTRODUCTORY 3 
 
 to his subject because he has faith in it asserts that logic 
 has a value as a pure science, that man likes to know 
 the working of his own mind just as he likes to know 
 the laws of celestial mechanics. Why not, indeed? Is 
 not the mind the supreme instrument which all must 
 employ? 
 
 But a pure science need not lack practical value. 
 Logic is not only a pure science, but also an art or an 
 applied science. An applied science is one which is able 
 to work out suggestions and rules based on a broad study 
 of the field involved. Looked at from this angle, logic 
 may be considered " a free study of some of the chief 
 risks of error in reasoning." 1 What logic can do for an 
 individual is to render him conscious of the best meth- 
 ods and the main difficulties in the various stages of 
 actual thinking so that he will be more exacting in his 
 mental operations. It should put him on his guard 
 against dangers. It calls his attention incessantly to the 
 value of clear and unambiguous ideas and to the proper 
 level of scrutiny to be maintained before a fact is ac- 
 cepted, an inference drawn, or a proposition admitted 
 as a premise in reasoning. The mind is an instrument, 
 and it should be polished instead of being left in a state 
 of nature. It is true that the exigencies of life force us 
 to be critical, but such criticism is too rough-and-ready 
 to be entirely satisfactory. Is there good reason to doubt 
 that care of the mind will pay at least as much as care 
 of the body? There are good mental habits just as there 
 are good physical habits; and neither comes without 
 effort and reflection. "Its [logic's] practical value in 
 general education is firstly this : that it demands very 
 
 1 Sidgwick, Elementary Logic, p. 8, Introduction. 
 
4 THE ESSENTIALS OF LOGIC 
 
 careful and exact thinking about its own subject-matter, 
 and thus tends to produce a habit of similar carefulness 
 in the study of any other subject. In this it only does 
 for the mind what a thorough training in any other 
 science might do. Secondly, it makes us realize better 
 what the general forms of speech that we habitually use 
 really mean, and familiarizes us with the task of examin- 
 ing our reasonings and looking to see whether they are 
 conclusive. In this it has an effect which the study of 
 some special science like botany is not equally calcu- 
 lated to produce. Thirdly, it brings into clearer con- 
 sciousness, as aforesaid, our ideal of what knowing is, 
 and so furnishes us with a sort of negative standard ; it 
 makes us more alive to shortcomings in our ordinary 
 opinions. But its chief value lies in its bearing upon 
 those ultimate problems, concerning the nature of real- 
 ity, and man's place and destiny in the world, from 
 which at first sight it might seem far remote." l 
 
 If logic can do even a part of this, it justifies itself 
 as a practical study. While logic does not create new 
 capacities in the mind of an individual, it helps to train 
 and sharpen the capacities already there. 
 
 The Kinds of Logic. Logic is one of the oldest of 
 the sciences and has had a varied history. The result 
 has been the growth of different branches emphasizing 
 different aspects of thinking and somewhat different in- 
 terpretations of the aim of logic. At times, these ' kinds 
 of logic' have seemed opposed to one another, but, of 
 late, they are seen to supplement one another and to 
 make logic a broader investigation than it would have 
 been without this branching. One kind of logic (exact 
 
 1 Joseph, An Introduction to Logic, p. 10. 
 
INTRODUCTORY 5 
 
 or symbolic) seeks to assimilate itself to mathematics 
 in its methods ; another (concrete) stresses its relation 
 to general philosophy, especially to theory of knowl- 
 edge ; another (empirical or inductive) lays its emphasis 
 upon the methods of the experimental and observational 
 sciences. Back of these historically and linking itself 
 with them in various ways — sometimes welcomed, some- 
 times an outcast — is what is called 'Formal Logic/ 
 We shall have a better idea of the limitations of Formal 
 Logic as we cover various topics such as the 6 syllogism,' 
 4 immediate inference,' and the 'logical form' of state- 
 ments. Certain doctrines and technicalities must be dis- 
 cussed and given as true and adequate a setting as pos- 
 sible. They have their value, though this value must 
 not be overestimated. 
 
 Introductory Logic. The Introductory Logic of 
 to-day in America seeks to organize together the essen- 
 tials of the various kinds of logic. It retains as much 
 of Formal Logic as seems valuable and combines it with 
 a concreter study of actual thinking with a view to de- 
 termine the principles and conditions of correct think- 
 ing. In this effort, it has been aided immensely by the 
 growth of psychology and philosophy, and the increasing 
 reflection, by scientists themselves, upon their methods. 
 Logic has acquired a new lease of life and is genuinely 
 growing. More is known about thinking than ever be- 
 fore, and this added knowledge has stimulated logic to 
 break away from formalities. Yet logic has a rich in- 
 heritance from the past which must not be belittled. 
 What is needed is a new perspective and a more vital 
 setting. We want to know the structure of our actual 
 thinking so as to guard against the risks of error. 
 
6 THE ESSENTIALS OF LOGIC 
 
 Relation of Logic to Other Sciences. The sciences 
 most closely related to logic are rhetoric and psychology. 
 The connection with psychology is obvious and we must 
 examine it in some detail. But first let us examine its 
 relation to grammar and rhetoric. 
 
 Thinking is intimately bound up with language; 
 language is, in fact, a necessary instrument to any sus- 
 tained thinking which involves general ideas. For gram- 
 mar, language is itself the subject-matter; for logic, it 
 is the instrument of thought. The function of words 
 is the fixation of meanings in our own mind and their 
 suggestion to others. In another chapter we shall discuss 
 the relation between thought and language. At present 
 we only wish to point out that the law of language 
 under its logical aspect is that of non-ambiguity . State- 
 ments must, so far as possible, be clear as regards their 
 significance. Accuracy and appropriateness in the use 
 of words go hand in hand with the discrimination of 
 ideas. 
 
 Rhetoric is more nearly akin to logic than is gram- 
 mar. While grammar treats of words largely apart 
 from their meanings, rhetoric concerns itself with the 
 expression of thought. Such expression is studied in 
 relation to the purpose in hand, which may be expo- 
 sition, description, argumentation or persuasion. It is 
 impossible to draw any hard-and-fast line between these 
 disciplines, for each is influenced by the results of the 
 other ; we may say, however, that to-day both rhetoric 
 and logic presuppose grammar as a preliminary and dif- 
 fer from each other in that which they stress. Logic is 
 more interested in the meaning which is expressed, 
 its implications, foundation, and validity, than in the 
 
INTRODUCTORY 7 
 
 mode or style in which it is expressed. Rhetoric, on 
 the other hand, culminates in the artistic use of lan- 
 guage. The fact that language is a necessary instrument 
 of thought brings these disciplines together ; but logic 
 has wider relations because thought is greater than its 
 instrument. Language is, after all, a tool. 
 
 The logician reflects upon the mental processes by 
 means of which knowledge is achieved and naturally 
 finds much assistance in psychology. So far as he in- 
 vestigates how the individual thinks and the conditions 
 of this thinking, he works hand in hand with the psy- 
 chologist. Both examine perception, conception, judg- 
 ment and reasoning and reach harmonious conclusions. 
 The main difference between them is that psychology 
 concerns itself more with the mental content, while 
 logic stresses the value of the product. Just because 
 the mind is a unity, it is impossible to find other than 
 a working distinction between them due to a division 
 of labor. They overlap, then, in the higher mental pro- 
 cesses, and logic passes on to a study of the structure 
 of knowledge and its validity, while psychology con- 
 cerns itself with the structure of consciousness, its rela- 
 tion to conduct, and its physiological conditions and 
 concomitants. The logician has the right to make use 
 of the knowledge psychology has achieved which bears 
 upon his own task. Their relation should be one of 
 mutual helpfulness. 
 
 The Material of Logic. All sciences are objective ; 
 that is, they consist of recognized facts and of princi- 
 ples which organize and interpret these facts. Now, 
 logic is, as we have already pointed out, a science about 
 the sciences. It is interested in the nature of proof and 
 
8 THE ESSENTIALS OF LOGIC 
 
 the laws of evidence ; it desires to see hoio knowledge 
 is built up and how the parts of knowledge depend 
 upon one another. This interest cannot be satisfied by- 
 introspection alone, but requires a close study of the 
 various sciences. In these it finds knowledge, and in 
 their history the record of the steps by which it was 
 obtained. We may say, then, that the material of logic 
 is to be found in generally accepted knowledge and 
 that this is approached with the purpose of discovering 
 the processes involved. Knowledge is the material of 
 logic much as the organism is the material of the 
 biologist and the inorganic world the material of the 
 physicist. 
 
 Inductive logic has always paid close attention to the 
 sciences which have so splendidly developed since the 
 Renaissance. It is an attempt to formulate the methods 
 which grew up unconsciously, or largely unconsciously, 
 in this new and wonderful extension of human knowl- 
 edge. The assumption controlling the series of inves- 
 tigations which have given us the inductive branch of 
 logic has been very well expressed by Whewell : " We 
 may best hope to understand the nature and conditions 
 of real knowledge by studying the nature and condi- 
 tions of the most certain knowledge which we pos- 
 sess ; and we are most likely to learn the best methods 
 of discovering truth by examining how truths, now uni- 
 versally recognized, have really been discovered." 1 
 
 BuF logic must concern itself with all sorts of think- 
 ing, with the conversations of daily life, with the argu- 
 ments to be found in the social sciences, in political 
 speeches, in essays, in editorials ; otherwise, it is apt to 
 
 1 Whewell, History of Scientific Ideas (3d ed.),vol. I, p. 4. 
 
INTRODUCTORY 9 
 
 become too formal and pedantic and to lose touch with 
 the flexibility and variety of actual thought. There is 
 another reason why the logician puts this emphasis on 
 less specialized thinking and refuses to let it be elbowed 
 away by the more technical levels of thought. We can 
 know what thinking is only by thinking ourselves and 
 then retracing our steps in memory to see exactly what 
 we have been doing. The material of logic can be found 
 ultimately only in consciousness. And, if the subject- 
 matter is to be realized and really reflected upon, it 
 must be reproduced and revivified in our own thought. 
 But it is not always easy to do this with past thinking 
 when this is technical and has an atmosphere of its 
 own. And, when all is said, familiar thinking illustrates 
 the essentials of the thinking process. Any one who 
 studies logic seriously must be willing to think for him- 
 self and to think about his thinking. 
 
 REFERENCES 
 
 Creighton, An Introductory Logic, chap. I. 
 Sigwart, Logic, vol. I, General Introduction. 
 Joseph, An Introduction to Logic, chap. I. 
 Sidgwick, Elementary Logic, Introduction. 
 Schiller, Formal Logic, chap. I. 
 
CHAPTER II 
 
 THE NATURE AND SETTING OF THOUGHT 
 
 What is Thought ? Thinking is the central opera- 
 tion for logic. It is the operation which underlies 
 knowledge and opinion and makes them possible. It 
 behooves us, therefore, to gain as clear an idea of its 
 nature and conditions as we can. If it is affected by 
 mental habits, we want to know what are the best hab- 
 its ; if it is controlled by feeling and emotion, we 
 want to know how to lessen such control. In short, 
 we wish to study the ways in which the human mind 
 assimilates and develops knowledge — especially that 
 knowledge which is called true. 
 
 It is not easy to define that mental process desig- 
 nated thinking. " No words are of tener on our lips 
 than thinking and thought. So profuse and varied, in- 
 deed, is our use of these words that it is not easy to 
 define just what we mean by them. Assistance may 
 be had by considering some typical ways in which the 
 terms are employed. In the first place, thought is used 
 broadly, not to say loosely. Everything that comes 
 to mind, that 'goes through our heads,' is called a 
 thought. To think of a thing is just to be conscious 
 of it in any way whatsoever. Second, the term is re- 
 stricted by excluding whatever is directly presented ; 
 we think (or think of) only such things as we do not 
 directly see, hear, smell, or taste. Then, third, the 
 meaning is further limited to beliefs that rest upon 
 
THE NATURE AND SETTING OF THOUGHT 11 
 
 some kind of evidence or testimony. Of this third type, 
 two kinds — or, rather, two degrees — must be dis- 
 criminated. In some cases, a belief is accepted with 
 slight or almost no attempt to state the grounds that 
 support it. In other cases, the ground or basis for a 
 belief is deliberately sought and its adequacy to sup- 
 port the belief examined. This process is called reflec- 
 tive thought." 1 Now, logic is chiefly interested in this 
 higher level of thinking where ideas are under control 
 and organized in relation to one another. In fact, many 
 logicians define logic as the science of proof or evidence. 
 
 Certain terms are used by logicians as practically 
 synonymous. Thus we shall have occasion to speak of 
 reflective thought, reasoning, and inference at various 
 times. These processes are much the same, though the 
 context will show slight differences of emphasis. Tak- 
 ing them as essentially the same, our present task is to 
 find out what is the nature of the mental operation 
 involved. What do we do when we reason or infer? 
 What we want now is a suggestion of the general char- 
 acter of the operation, leaving it to later chapters to 
 study the various steps in methodical reasoning. 
 
 Discovery and Proof. There are two parts to any 
 complete act of reasoning, discovery, and proof. We 
 reason when we are confronted by problems, by unfore- 
 seen situations to which our habits and usual ideas 
 are not immediately applicable. We are, as we say, at 
 a loss ; we don't know what to think or to do. But this 
 perplexity lasts for a time only. We make shift to size 
 up the situation, to compare it with what in the past 
 seems most like it, to analyze the various features, and 
 
 1 Dewey, How We Think, pp. 1-2. 
 
12 THE ESSENTIALS OF LOGIC 
 
 so on, until some idea suggests itself as a possible solu- 
 tion. Such is the stage of tentative discovery. But 
 another stage immediately sets in. The suggested solu- 
 tion must be tested or proved. In practical affairs, this 
 proving consists, in the main, of overt action. The 
 new idea is tried out to see whether it will work. The 
 proud possessor of a new auto finds himself compelled 
 to reason in this rough-and-ready way only too often. 
 This practical level of reasoning is sometimes called 
 4 trial-and-error.' The process is familiar to all. 
 
 In more theoretical reasoning, both the stage of dis- 
 covery and the stage of proof are reflective. The sci- 
 entist who makes a discovery has, as a rule, long 
 brooded over the problem. The idea of universal gravi- 
 tation did not come to Newton as a mere chance 
 thought ; his mind was ripe for it. Archimedes had 
 long been pondering over his particular problem before 
 he took his famous bath and discovered the principle of 
 specific gravity. But after the brilliant idea has sug- 
 gested itself, it must be proved in the light of the facts. 
 It must be shown to follow from certain premises or 
 data; it must be guaranteed by its reasons or grounds. 
 And this second task is often the more perplexing of 
 the two. By proof we mean the process of establishing 
 an idea on a firm intellectual foundation. Newton had 
 to work out the method of fluxions and make delicate 
 calculations on the basis of known measurements before 
 he could consider his hypothesis reasonably proved, 
 while Darwin had to make numerous experiments and 
 collect data of the most varied kinds before he was 
 willing to publish his theory. Proof must be considered 
 a very important part of reasoning. Scrupulousness in 
 
THE NATURE AND SETTING OF THOUGHT 13 
 
 regard to its standards is the sign of a trained mind. 
 It is not too much to say that logic is primarily the 
 science of proof. The question before the logician's 
 mind is, 'Is such and such a given conclusion war- 
 ranted ? ' Logic is retrospective and probative. 
 
 The Psychologist's View of Reasoning. In the 
 preceding chapter, we came to the conclusion that logic 
 and psychology overlap, that no hard-and-fast line can 
 be drawn between them. It may be of interest, there- 
 fore, to examine the psychologist's view of reasoning. 
 "To define reasoning fully it must be distinguished 
 from imagination and memory when observed from the 
 inside, and from instinct and habit when expressed in 
 action. Reasoning may be distinguished from memory 
 and imagination, not so much by the character of the 
 mental states or by the way that they are obtained, 
 as by the attitude that is taken toward them when they 
 arise. The idea that is attained by reasoning may be 
 exactly like an idea that on other occasions or by 
 another man is merely remembered. The laws that 
 govern the appearance of rational ideas are the laws of 
 association, controlled in the same way as in memory 
 and imagination. The important differences are : that 
 the results of reasoning are new and are accepted as 
 true ; the results of memory are true, but not new ; 
 and the results of imagination are new, but not true" 1 
 It is well to bear these contrasts in mind. Reasoning is 
 a mental process taking some time to occur and con- 
 trolled by the purpose of reaching accepted results. 
 The logician makes the further demand that these re- 
 sults be established by relation to their ground. 
 
 1 Pillsbury, Essentials of Psychology, p. 217. 
 
14 THE ESSENTIALS OF LOGIC 
 
 Examples of Reasoning. Let us take a case of 
 reasoning in regard to heavenly phenomena which was 
 made quite early in the history of civilization. Man 
 soon discovered that a shadow was caused by the inter- 
 vention of an opaque body between a source of light 
 and a distant surface. He did not know exactly what 
 took place, but he knew that the light was cut off from 
 the region back of the opaque body. Thus he arrived 
 at the universal proposition, * All shadows are caused 
 by the intervention of an opaque body.' But an eclipse 
 was soon recognized to be a case of shadow. Hence an 
 opaque body must have intervened between the earth 
 and the source of light. Here is a case of reasoning in 
 which the conclusion is reached by resemblance or anal- 
 ogy. An eclipse is a case of the intervention of an 
 opaque body because it is a case of shadow. This 
 reasoning contains the ground. Let us now examine a 
 case of bad reasoning. " According to some accounts, 
 the wise men of Spain argued with Columbus that he 
 could not reach India by sailing west, because if the 
 earth were round, as he asserted, he would at some 
 time reach a point where the ship would be going down- 
 hill and ultimately fall off, just as a minature vessel 
 would fall, if it should attempt to travel around an 
 artificial globe. If A is true (earth round), B must be 
 true (circumnavigation impossible). If there is a re- 
 semblance between earth and artificial globe in contour 
 of surface, there must be a further resemblance, so it 
 was held, in the relation of each to the objects upon 
 its surface. ... In making their comparison, the wise 
 men overlooked an important point of difference, viz., 
 that for an object on the artificial globe the point 
 
THE NATURE AND SETTING OF THOUGHT 15 
 
 towards which it gravitates is outside the globe, while 
 for objects on the earth this point is within the earth 
 itself." 1 
 
 Thinking may be more or less conscious and more or 
 less methodical. Logic seeks to induce individuals to 
 take thinking seriously, to make their thinking method- 
 ical and reflective. Especially does it stress evidence. 
 Reflective thought is careful, and evidence-loving. It 
 notes all the facts which can be thought to have bear- 
 ing upon the problem and tests any conclusion by its 
 consequences. 
 
 The Conditions and Occasions of Thought. Re- 
 flective thought or reasoning rests upon and grows out 
 of experience. It has its causes and conditions. Thought 
 does not arise just for no reason at all, but has its 
 definite conditions. These reasons for thinking can be 
 classified as social and personal. 
 
 The stimuli which lead individuals to think usually 
 come from the social environment. The pity is that 
 this environment is so moderately stimulating. The 
 more there is the spirit of intellectual and social adven- 
 ture, the more alive will men be. When the environ- 
 ment favors tradition and mere repetition and imitation, 
 comparatively little vital and creative thinking is done. 
 Life takes on the aspect of routine and habit, and 
 classification of a formal kind overshadows discovery. 
 Actions are repeated in the customary grooves, and no 
 attempt is made to better them. There are periods, as 
 during certain parts of the Middle Ages, when this 
 social attitude is largely dominant. At such times, be- 
 liefs are handed down by tradition and are not criti- 
 1 Bode, An Outline of Logic, pp. 2-3. 
 
16 THE ESSENTIALS OF LOGIC 
 
 cally examined. Such an atmosphere is not favorable 
 to thinking. The individual is not taught to analyze 
 and observe, to doubt and to form hypotheses. Thus, 
 there is a sociology of logic, or, rather, logic has its 
 social aspects which must not be lost sight of. Let me, 
 by means of an example, contrast the lethargy of thought 
 during the later Middle Ages with the eager spirit of 
 science at its best. 
 
 It is said that Francesco Sizzi, a Florentine astrono- 
 mer, argued against Galileo's discovery of a new planet 
 in the following way : — 
 
 " There are seven windows in the head : two nostrils, 
 two eyes, two ears, and a mouth ; so in the heavens 
 there are two favorable stars, two unpropitious, two 
 luminaries, and Mercury alone undecided and indiffer- 
 ent. From which and many other similar phenomena 
 of nature, such as the seven metals, etc., which it were 
 tedious to enumerate, we gather that the number of 
 planets is necessarily seven. 
 
 " Moreover, the satellites are invisible to the naked 
 eye, and therefore can have no influence on the earth, 
 and therefore would be useless, and therefore do not 
 exist. 
 
 " Besides, the Jews and other ancient nations as well 
 as modern Europeans have adopted the division of the 
 week into seven days and have named them from the 
 seven planets ; now, if w r e increase the number of the 
 planets this whole system falls to the ground." 1 
 
 The present is, on the whole, a period of skepticism 
 and inquiry. The individual is taught to think for him- 
 self, along certain lines at least, and not to accept ideas 
 
 1 Lodge, Pioneers of Science, p. 106. 
 
THE NATURE AND SETTING OF THOUGHT 17 
 
 unless he has pretty assured evidence for them. This 
 social atmosphere, encouraging to thought, is a very- 
 important condition of thinking. Logic has a perfect 
 right to champion such conditions. It is not called 
 upon to be a passive judge of consistency alone. 
 
 The personal conditions of thought are also impor- 
 tant. The prime condition is the recognition of a prob- 
 lem. Back of this recognition lies the attitude which 
 faces problems and even goes to meet them halfway. 
 This attitude is partly temperamental, partly the con- 
 sequence of training. On the practical side of life, so 
 long as our habitual ways of acting are sufficient to 
 meet the conditions which confront us, there is little 
 reflective thought because there is little need for it. 
 There is mental activity, of course, because we must 
 constantly recognize and classify things and situations ; 
 but this classificatory interpretation is usually so im- 
 mediate that the individual does not need to pause, or, 
 if he does pause, it is only for a moment. Difficulties 
 arise, however, frequently enough, and the course of 
 action is stayed. New adjustments must be worked 
 out, and these adjustments depend upon the proper 
 location of the difficulty and the discovery of its nature 
 and remedy. Thinking intervenes at such a time. It 
 is the sign and consequence of uncertainty, doubt, in- 
 ability to interpret. How successfully the individual 
 meets the problem depends upon his training, capacity, 
 and character. 
 
 The Setting of Thought. Thinking arises and 
 takes its course in the mind of an individual endowed 
 with a fund of past experiences. The problem which 
 occasions thinking involves a conflict within experi- 
 
18 THE ESSENTIALS OF LOGIC 
 
 ence and calls into play all that is in any way relevant. 
 Familiar ideas, prejudices, habits, memories, all enter 
 into the council-chamber and demand audience. Think- 
 ing is the individual's experience in process of internal 
 adjustment. 
 
 We may say, then, that thinking is purposive and 
 selective. It is an expression of the growth of the 
 mind. But the mind is distorted by old beliefs and 
 prejudices and is very frequently deflected from the 
 truth. It is like a river whose banks throw the current 
 from side to side and produce in it all sorts of treach- 
 erous eddies. The logician must do the work of an 
 engineer. He must point out the dangers which con- 
 front the mind which desires to think truly. 
 
 Why we think. Our study of the conditions and 
 setting of thought enables us to answer the question, 
 * Why do we think ? ' There is both a practical and a 
 theoretical urgency behind thought. Life demands that 
 problems be solved in order that we may act wisely. 
 When our habits push us in , different directions, we 
 must work out some suggestion which satisfies our mind 
 or we are distraught. Besides, we know from past ex- 
 perience how dangerous it is to trust to a chance idea. 
 We want to have a fair degree of assurance of the con- 
 sequences before we act. To think is to rehearse the 
 course of events beforehand and to meet every emer- 
 gency with its appropriate interpretation. 
 
 But psychologists inform us that it is the very nature 
 of the mind to work out harmonious ideas. The things 
 we see are the products of adjustments. However far 
 down we go in our. mental life, we find the endeavor 
 to harmonize various elements with one another. " The 
 
THE NATURE AND SETTING OF THOUGHT 19 
 
 sensations that are received are added to or changed to 
 make them correspond more exactly to what from our 
 different earlier experiences we know they must be. 
 One always corrects the shape of the table-top as it 
 appears in perspective. The angles are right angles as 
 we see them, although the image must have acute and 
 obtuse angles. One always makes an allowance for dis- 
 tance in the size of an object that is seen. The same 
 object is always given the same size no matter how far 
 away it may be, while the image on the retina dimin- 
 ishes constantly as the distance increases." 1 Thus, pro- 
 cesses of adjustment are characteristic of the mental 
 life at its different levels. This same tendency ex- 
 presses itself in thinking. Thinking arises naturally 
 and inevitably when the adjustment cannot be made 
 almost automatically. 
 
 We have stressed practical problems as an explana- 
 tion of thought ; but theoretical problems are, at the 
 present day, as fruitful in thought. These two types 
 of problems are intimately interwoven by the very na- 
 ture of life, for there are few ideas which do not have 
 a bearing upon conduct. Yet the interests involved 
 are fairly distinguishable. The growth of science has 
 assisted man to develop interests of an impersonal 
 kind, and about these interests and the investigations 
 connected with them arise theoretical problems. Facts 
 must be interpreted by theories and these theories 
 must be harmonized so far as possible. The trained 
 human mind is not satisfied with disorder and contra- 
 diction ; it seeks to bring harmony out of chaos and to 
 organize its ideas into a harmonious whole. Conflict in 
 
 1 Pillsbury, Essentials of Psychology, p. 157. 
 
20 THE ESSENTIALS OF LOGIC 
 
 any realm is to such a mind a stimulus to thought. The 
 process of thinking has back of it all the forces and 
 habits which demand order. To say that man is ra- 
 tional is to say that he seeks adjustment among his 
 ideas. 
 
 Processes preliminary to Reflective Thought. 
 The processes preliminary to reflective thought are, 
 roughly speaking, two : perception and conception. We 
 must have percepts and the ideas formed from them 
 before we can think. Together, they furnish the ma- 
 terial within which thinking goes on. It must not 
 be supposed that percepts and concepts (ideas) are 
 given apart from mental activity, but it is true to say 
 that the higher mental processes, such as judging, ana- 
 lyzing, drawing conclusions, and argumentation, occur 
 within a field of experience already fairly stable and 
 definite. We see the external world, recognize various 
 familiar objects in it, know what to expect of them, 
 and have a pretty generous fund of ideas when we are 
 engaged in the solution of any particular problem. 
 The individual's mind is constantly adding to its store 
 of information and its working system of distinctions, 
 classification, and expectations. It is correct, then, to 
 say that thinking represents the growing point of the 
 mind, and that it leaves a sediment, so to speak, of 
 ideas and habits and points of view. We must remem- 
 ber, however, that any part of this accepted knowledge 
 may be challenged by new problems and new experi- 
 ences ; hence we must think of the mind as a living 
 organism rather than as a building in which one story 
 is added to another. 
 
 The psychologist has much to tell us of sensations, of 
 
THE NATURE AND SETTING OF THOUGHT 21 
 
 their qualities and intensities and number. This infor- 
 mation does not have much bearing upon the subject- 
 matter of logic, interesting as it is in itself. We know 
 that the sense organs must be stimulated before we can 
 have these sensations with which, in the rough and un- 
 analyzed, we are all of us familiar. The next level after 
 sensation is perception. It is of advantage to the logi- 
 cian to realize that perception is a complex process and 
 that the percepts which we have as a result may be 
 partly false. Whenever there is possibility of error, the 
 logician cannot be indifferent. When we come to a 
 study of scientific method, we shall have considerable to 
 say about errors in observation. A few words about the 
 general character of percepts and perception may not 
 be amiss at this point. 
 
 Put technically, percepts are the mental objects 
 which result from the interpretation of sensory stimuli 
 by centrally aroused processes. They are the primary 
 mental objects of which we are aware when we use our 
 senses. There is a sensory basis in all percepts ; but 
 there is, furthermore, a large element of applied past 
 experience. A percept is really a mental product to the 
 making of which there has gone much trial, selection, 
 and adjustment. The cumulative result of these proc- 
 esses is given as an object, while the processes them- 
 selves seldom appear in consciousness. So far as more 
 is given in the percept than the senses warranty the 
 logician speaks of the inferential element in percep- 
 tion. It is because of this inferential element that per- 
 ceptions may be erroneous. We may see things which 
 are not present because we take a certain sensory cue 
 and add to it qualities which often have accompanied it 
 
22 
 
 THE ESSENTIALS OF LOGIC 
 
 in our experience. What we shall unconsciously add de- 
 pends largely upon the setting and upon the ideas which 
 are occupying our minds. The following examples may 
 make this possibility of error in perception more evident. 
 In the following figure taken from Jastrow, one can 
 actually see dim lines suggested by the heavy lines that 
 are drawn. These are supplied by memory. 1 
 
 EDITOR 
 
 This second figure may be seen as a rabbit's head or 
 as a duck's according to the thought which is upper- 
 most. 2 
 
 1 Jastrow, Fact and Fable in Psychology, Fig-. 2. 2 Ibid., Fig 1 . 19. 
 
THE NATURE AND SETTING OF THOUGHT 23 
 
 These illusions as they are called, serve to bring out 
 the amount of interpretation which is at work in every- 
 day life. Here is another example : " If a sportsman, 
 while shooting woodcock in cover, sees a bird about the 
 size and color of a woodcock get up and fly through the 
 foliage, not having time to see more than that it is a 
 bird of such a size and color, he immediately supplies 
 by inference the other qualities of a woodcock, and is 
 afterwards disgusted to find that he has shot a thrush. 
 I have done so myself, and could hardly believe that the 
 thrush was the bird I had fired at, so complete was my 
 mental supplement to my visual perception." x 
 
 Speaking of such illusions, William James says: 
 "Twenty times a day the lover, perambulating the 
 streets with his preoccupied fancy, will think he per- 
 ceives his idol's bonnet before him." 
 
 Conception arises upon perception as a foundation. 
 Concrete, perceived objects are dissected into elements, 
 and these elements, loosened from their particular con- 
 text, are capable of repeated recall. Concepts are men- 
 tal objects which are (1) not directly connected with 
 the stimulation of sense-organs, and (2) are under our 
 control so far as our having or not having them is con- 
 cerned. The mental processes which make concepts 
 possible are analysis and abstraction assisted by the 
 method of comparison. We note the likenesses and dif- 
 ferences between things. Certain qualities begin to stand 
 out and are selected by the attention. These quali- 
 
 1 Romanes, Mental Evolution in Animals : , p. 324. 
 
 2 The student will find James's discussions of illusions extremely in- 
 teresting*, especially pages 95 to 103 of the second volume of the Prin- 
 ciples of Psychology. MUnsterberg's On the Witness Stand, chap. I, is also 
 suggestive. 
 
24 THE ESSENTIALS OF LOGIC 
 
 ties and relations are then abstracted or considered by 
 themselves, while the other features of the thing are 
 disregarded. The result of this analysis is the isolation 
 of the quality or relation from its context and our 
 ability to recall it again and again at need. Such ab- 
 stracted, repeatable mental objects are called 6 con- 
 cepts.' Other terms, sometimes employed, are ' mean- 
 ings,' ' ideas,' 4 universals.' This last term stands for a 
 species of concept which is of special interest to the 
 logician, and frequently used in philosophy. A universal 
 is a concept which applies to an indefinite number of 
 individual things. Any class name is a good example 
 of a universal. We all have the idea of a horse, of an 
 auto, of a soldier, etc. Such ideas are universals. 
 
 The ability to form concepts is essential to reason- 
 ing and reflective thought in general. Conceptual ele- 
 ments, obtained by comparison and abstraction, are 
 organized together in all sorts of ways. Only by means 
 of concepts are we able to rise above the particular field 
 of concrete perception spread out before our senses. 
 Knowledge is primarily an affair of conception, of rules 
 and principles, facts and theories. But it must not be 
 forgotten that these elements work back into and con- 
 trol our interpretation *of the world we see about us. 
 There is a constant and responsible interplay of per- 
 ception and conception in our minds. Logic concerns 
 itself with this interplay so far as it can be made the 
 object of a critical reflection. 
 
 Fact and Theory. The distinction between percept 
 and concept is more characteristic of psychology than 
 of logic. For the latter, the more distinctive contrast is 
 between fact and theory. In any argument, we con- 
 
THE NATURE AND SETTING OF THOUGHT 25 
 
 stantly seek to separate what may be considered the 
 facts of the case from the theory which is added to it as 
 an interpretation. Argument and dispute arise where 
 fact and theory are not clearly separated ; and the first 
 step to the settlement of the argument is an agreement 
 as to what is fact and what is theory. Now, fact is that 
 which is admitted for the purpose of the argument ; it 
 is that which is, temporarily at least, considered indis- 
 putable. And it is interesting to note that fact in this 
 sense may be either concrete or abstract. The Law of 
 Gravitation is a fact because it is an assertion which I 
 do not question. A theory, on the other hand, is that 
 which is tentative and disputable. It needs support, 
 proof, corroboration. 
 
 The first step in reflective thought or argument is, 
 therefore, to distinguish fact from theory, the indisputa- 
 ble from the disputable. " In practice, assertions are 
 seldom or never wholly untrue, especially when they 
 correspond to a genuine belief. It is sometimes difficult, 
 but seldom impossible (if it be thought worth while), to 
 find a basis of agreement even with those whose view 
 seems most opposed to our own. Some part of the way 
 they go with us, and then the roads branch off. Why 
 did they leave our road, or why did we leave theirs ? 
 That question and its answer is the beginning of argu- 
 ment. The matter of argument is always matter of 
 opinion ; not fact but theory ; not fact but inference 
 from fact." 1 
 
 Knowledge a Growth. No problem or doubt which 
 gives rise to reflective thought challenges all the indi- 
 vidual's world. There is always fact as well as theory, 
 1 Sidgwick, The Process of Argument, p. 18. 
 
26 THE ESSENTIALS OF LOGIC 
 
 the accepted as well as the disputed. Knowledge is a 
 growth and, like every growth, has a structure of its 
 own. Logic has to pay considerable attention to the 
 structure of knowledge and its medium, language. If 
 argument is knowledge in the making, it would seem 
 impossible to understand it apart from pretty adequate 
 ideas of what knowledge as made consists in. All 
 through logic, then, we see process and product, growth 
 and achievement, dovetailed together. It is really im- 
 possible to understand one apart from the other. All 
 problems arise within the knowledge already attained 
 and reflect its structure. This fact explains why logic 
 has to take up so many topics which seem linguistic 
 or concern themselves with the divisions, classifica- 
 tions, and distinctions in knowledge rather than with 
 discovery, argument, and reasoning. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. I. 
 
 Bosanquet, The Essentials of Logic, Lecture II. 
 
 Dewey, How We Think, chap. I. 
 
 Pillsbury, Essentials of Psychology, chaps, vn and IX. 
 
 James, Principles of Psychology, vol. n, chap. xxn. 
 
CHAPTER III 
 
 ABOUT TERMS 
 
 The Unit of Thought. The logician considers the 
 judgment or the proposition as the unit of thought. 
 The conclusion of a vital act of thought may find ex- 
 pression in a proposition, but in nothing short of it. 
 Thus, in answer to a friend's question, I may say that a 
 certain man is reliable; but I cannot use the words 
 4 man ' and ' reliable ' in isolation and convey any as- 
 sured meaning. The unit of thought is a complex idea, 
 which is asserted or denied. Since thinking arises under 
 the stimulus of a problem, its result must be definite, 
 it must assert or deny something. This definite solution 
 of a problem is called a ' judgment ' and its verbal form 
 a ' proposition.' 
 
 The proposition can be analyzed into elements which 
 are called ' terms.' These terms exhibit the complexity 
 of the proposition, and are always present in a relation 
 characteristic of the concrete act of thought. 'Fire 
 burns,' 4 Justice is kingly,' are propositions in which 
 there is both unity and complexity, or, better yet, unity 
 in complexity. In trying to understand the judgment, 
 we must carefully distinguish between the mental proc- 
 ess of thinking which finds its goal in an accepted idea 
 and the accepted idea itself. It is this latter which finds 
 expression in the proposition and which is analyzed by 
 the logician. 
 
 The Elements of the Proposition. A proposition 
 is always analyzable into a subject and a predicate. The 
 
28 THE ESSENTIALS OF LOGIC 
 
 subject is that about which something is stated, while 
 the predicate is that which is stated about the subject. 
 These two elements are called the ' subject term ' and 
 the ' predicate term ' respectively. And this brings us 
 to the definition of a 'logical term.' It is any word or 
 group of words which can serve as the subject or the 
 predicate of a proposition. But these two terms do not 
 exhaust the proposition. There is, further, the word 
 which stands for the relation between these terms. This 
 is called the ' copula.' In the proposition, ' Abraham 
 Lincoln was a wise statesman,' the subject term con- 
 sists of two words and is a proper name, the predicate 
 term contains three words, while the copula is a form 
 of the verb * to be.' 
 
 Words and Terms. It should be noted that the 
 different parts of speech are not equally capable of 
 acting as terms or as the nucleus of terms. Nouns, pro- 
 nouns, verbs, and adjectives have the character or func- 
 tion which enables them to act as the essential part 
 of a term or even as a term. Such words are called 
 4 categorematic ' or asserting words. Other words are 
 not able to designate an object of thought, but are sub- 
 sidiary to such designation. They are called 4 syncate- 
 gorematic' Adverbs, conjunctions, and prepositions 
 are connective or qualifying words, and are therefore 
 classed as syncategorematic. 
 
 Since terms often consist of many words grouped to- 
 gether, categorematic words may be found combined 
 together by means of syncategorematic words. In the 
 proposition, * Justice is kingly though no lung be just,' 
 the words italicized are categorematic, while the others 
 are syncategorematic. This distinction is, perhaps, more 
 
ABOUT TERMS 29 
 
 grammatical than logical ; but it serves to stress the fact 
 that a logical term is other than a word. 
 
 Kinds of Terms. Terms fall into different classes 
 according to the point of view that is dominant. The 
 first division is into ' concrete ' and. ' abstract.' Concrete 
 terms, again, are divided into singular or individual, 
 general or class, and collective terms. Let us examine 
 these divisions, which are the most important, before 
 glancing at other kinds of terms. 
 
 An abstract term is the name of a quality or rela- 
 tion taken apart from its setting. In the study of con- 
 ception, the nature of abstraction was referred to. To 
 abstract is to draw off or take away. But an abstract 
 term is not simply a word which calls up an idea which 
 is conceptual in character, for all words do this, it is 
 a word which signifies an attribute or relation taken 
 apart from any individual object. It is the relation of 
 the idea to realities which are thing-like which is disre- 
 garded. Thus, ' sweetness ' is an abstract term because 
 it signifies a conceptual object obtained by abstract- 
 ing a quality of physical things and considering it by 
 itself. The objects signified by abstract terms cannot 
 possibly be perceived. 
 
 Some abstract terms are farther from sense-percep- 
 tion than are others. This is because the objects of which 
 they are characteristics involve more construction. Thus, 
 'equality,' ' animality,' 'constitutionality,' 'discipline,' 
 are abstract terms at second remove, so to speak. It is 
 to be noted that abstract terms are always nouns. 
 
 A few words need to be said concerning the dangers 
 involved in the use of abstract terms. Since they are 
 nouns, they are readily thought of as referring to indi- 
 
30 THE ESSENTIALS OF LOGIC 
 
 vidual things, more subtle than physical things, yet 
 somehow real after the same fashion. The result is a 
 fallacy which is usually called the ' fallacy of hyposta- 
 tization.' Other writers speak of it as the ' fallacy of 
 abstract terms.' It consists of treating abstractions as 
 veritable things. " Our everyday use of such terms as 
 4 conscience,' 6 memory,' and ' will ' shows further how 
 ingrained is this habit of treating abstractions as though 
 they were independent things. In reality these terms 
 are the names of attributes. It is not uncommon, how- 
 ever, to find that conscience, for example, is conceived, 
 in a vague fashion, as though it were some kind of thing, 
 inhabiting the inmost recesses of the soul and perform- 
 ing the functions of an oracle. Similarly, there is no 
 separate thing called memory or will, but only different 
 instances of remembering and willing." 1 
 
 In contrast to an abstract term, a concrete term is a 
 word or group of words which refers to a person or 
 a thing, or a group of persons or things. If there is 
 any doubt whether a given term is abstract or concrete, 
 the test to apply is, 4 What does it lead us to think of ? ' 
 If it lead us to think about definite individuals, it is 
 concrete ; if it lead us to think about attributes, it is 
 abstract. Thus, ; man,' 4 animal,' c a society,' ' Lake 
 Michigan,' ' a red apple ' are concrete terms ; fi hu- 
 manity,' ' animality,' ' society,' ' redness ' are abstract. 
 
 Concrete terms, we have said, are divisible into sin- 
 gular, general, and collective. These terms agree in their 
 function of calling to mind things ; they differ in the 
 number of things implied and in the way they are taken. 
 
 A singidar or individual term is one which applies 
 1 Bode, An Outline of Logic, p. 49. 
 
ABOUT TERMS 31 
 
 to only one thing. Such a term is selective and is used 
 to identify, or direct our thoughts to a thing or expe- 
 rience which is regarded as a distinct existence. Ex- 
 amples : i the large dictionary in this room,' ' the center 
 of the earth,' 6 the fifth page of this book.' 
 
 It should be noted that the point of view determines 
 in large measure what shall be regarded as a single 
 thing. A note of music may awaken an interest which 
 leads to a selective emphasis on it so that it stands out 
 from its setting, or it may be completely merged in the 
 whole composition. It is worth while to reflect upon this 
 relativity of what we shall consider a thing to our inter- 
 est We cut out things from continuous wholes much as 
 the housewife cuts out cookies from the pastry. We 
 divide up the world into larger or smaller parts in ac- 
 cordance with what attracts our attention. A mountain is 
 a thing, so is a boulder on its summit, so is a peculiarly 
 colored portion of the boulder, so is, perhaps, a molecule 
 in it, etc. A singular term helps the individual to carry 
 on this process of selective analysis, and enables him to 
 direct the thoughts of another person to the same goal. 
 
 There are two methods for the formation of singular 
 terms. The first method consists in the taking of a term 
 which applies equally well to many things and adding 
 new words until the application is obviously limited to 
 one thing alone. The definite article always indicates 
 the singular term. Very often the presence of the super- 
 lative form of an adjective or adverb helps to carry out 
 this process of narrowing the application of the term to 
 one thing. Examples : 4 the greatest politician in the 
 United States to-day,' ' the man who ran fastest in the 
 meet.' The second method is to adopt a term arbitrarily 
 
32 THE ESSENTIALS OF LOGIC 
 
 as a sign of a particular individual. Since language 
 is social, a social element enters here. This use of the 
 term must be consented to by the group. Personal 
 names are of this character. Individuals are christened 
 according to a socially recognized procedure. One is 
 called ' Bernard Shaw ' ; another, ' William Smith ' ; 
 another, ' If-Christ-had-not-died-you-would-have-been- 
 damned Barebones.' It is interesting to note that a 
 personal name is not always sufficient to select the one 
 person meant. In that case, some descriptive word or 
 words must be added. We all remember the ' Fiddler 
 Smiths ' and ' Little John Petersens ' of our boyhood. 
 
 A general term is one which applies to any number 
 of things. General terms are names of kinds or classes. 
 Grammar makes the distinction between common and 
 proper nouns which corresponds to a difference of nu- 
 merical application. Examples of general terms are, 
 4 dog,' ' member of Congress,' ' citizens of the United 
 States,' 'holidays.' 
 
 The objects covered by a general term are members 
 of a class. Such objects agree in certain characteris- 
 tics and are classed together because of this agreement. 
 These points of resemblance are called ' attributes ' of 
 the class. It should be noted that all objects have some- 
 thing in common, and that the number of possible classes 
 is infinite. In both practical life and science, kinds or 
 groups of objects having very much in common, are 
 worked out and established as a matter of general knowl- 
 edge. Such classes have accepted names. 4 Salts,' « halo- 
 gens,' * acids,' ' vertebrates,' ' mollusks,' ' constitutional 
 monarchies,' 4 fruits,' etc., are names of well-understood 
 classes. 
 
ABOUT TERMS 33 
 
 We shall have occasion to consider class names again 
 when we come to the distinction between ' denotation ' 
 and 'connotation.' We shall see that general terms have 
 two functions ; they denote the individuals to which they 
 apply and they connote the attributes which they imply. 
 
 Collective terms are a special class of concrete terms. 
 They arise from the ability the human mind has of 
 grouping objects together and considering them in their 
 collective aspect. A collective term is one which applies 
 to a group of objects in which the individual members 
 are lost sight of in the whole. Such terms may be 
 either singular or general. Examples of singular collec- 
 tives are, ' the American navy,' ' the crowd before the 
 courthouse,' * the woman's club. ' * Navy,' ' family,' 
 i tribe,' ' state,' 4 teacher's association,' are general col- 
 lectives. 
 
 When we are referring to some specific group, the 
 term is employed as a singular. ' The American navy 
 is fairly efficient.' ' This crowd of students is out for a 
 good time/ A general collective is used as a general 
 term on the ground that there are various groups with 
 the same characteristics. It is used distributively of the 
 particular groups covered and collectively of the mem- 
 bers of any one group. < Excited mobs are dangerous.' 
 4 Woman's clubs are becoming social centers.' This dis- 
 tinction will become clearer when we take up ' conno- 
 tation ' and 4 denotation.' It is necessary to go beyond 
 the mere form of the words to what is thought of in 
 order to distinguish between singular and general col- 
 lectives. 
 
 Ambiguity sometimes arises from the fact that the 
 English word * all ' is used both distributively and col- 
 
34 THE ESSENTIALS OF LOGIC 
 
 lectively. " That is, it may mean ' all taken together p 
 or ' each and every.' Thus, we can say : ' All the angles 
 of a triangle are less than two right angles,' and * All 
 the angles of a triangle are equal to two right angles.' 
 In the former sentence, the word * all ' is used distribu- 
 tively, in the latter collectively. In Latin two different 
 words are used : cuncti expresses the collective sense of 
 4 all,' and omnes its distributive signification." 1 
 
 Other Kinds of Terms. We have defined and ex- 
 amined abstract, concrete, singular, general, and collec- 
 tive terms. But terms are divided from other points of 
 view into ' absolute ' and ' relative,' and into ' positive,' 
 4 negative,' and 4 privative' terms. These distinctions 
 are significant enough to justify some consideration. 
 
 An absolute term is one which refers to an object 
 or quality considered by itself. The supposition is that 
 such an object of thought has meaning in its own right ; 
 it does not depend on its relation to something else for 
 an essential part of its meaning. Thus, 4 stone,' 4 build- 
 ing,' ' the State of Michigan ' are absolute terms. A 
 relative term is one which derives an essential part of 
 its meaning from its relation to something else. Ex- 
 amples of relative terms are, ' shepherd,' 4 patient,' 
 6 ruler,' ' citizen,' 4 pupil.' Relative terms usually go in 
 pairs which imply one another and are then called 4 cor- 
 relatives.' Thus, 4 teacher ' implies 4 pupils ' and 4 par- 
 ent ' implies 4 child ' ; and the reverse is also the case. 
 
 It is sometimes said that all things are relative in the 
 sense that they are interdependent. This is true, yet it 
 does not invalidate the logical distinction we have just 
 discussed. At the level of common sense, we usually 
 
 1 Creighton, An Introductory Logic, p. 51. 
 
ABOUT TERMS 35 
 
 ignore the relations which bind things to one another 
 because they do not come out in perception. Only when 
 relations stand out so clearly that they cannot be dis- 
 regarded, do they form an essential part of our thought. 
 Man is absolute, but a man as a teacher is relative. 
 This term stresses a relation into which a man may 
 enter. 
 
 But the term ' relative ' is sometimes used in another 
 sense. A word may involve a standard. 'Goodness,' 
 4 badness,' ' luxury,' ' poverty,' 6 beautiful,' and 6 slow- 
 ness ' are examples of relatives of this kind. The danger 
 lies in the fact that the standard is variable from per- 
 son to person, from class to class in society, and from 
 period to period in history. This variability, when not 
 recognized, is a fruitful source of confusion. " To rec- 
 ognize and point out this character of relativity may 
 on occasion serve to forestall much fruitless argument. 
 For example, the question may be asked, 'Are the 
 people of the present day more moral than those of the 
 past ? ' Before we undertake to express an opinion we 
 should ascertain what is meant by ' more moral.' To 
 judge the past by present-day standards is one thing : 
 to judge it by its own standards is quite another. Again, 
 the question may be raised whether or not students who 
 go into business are, as a rule, more capable than those 
 who adopt the profession of teaching. Discussions of a 
 question like this are prone to overlook the relativity of 
 a phrase like ' more capable.' Until we specify whether 
 we mean ' capable for business ' or ' capable for teach- 
 ing' or some other form of capableness, argument is 
 likely to be futile." x The teacher in social ethics is 
 
 1 Bode, An Outline of Logic, p. 46. 
 
36 THE ESSENTIALS OF LOGIC 
 
 bound to meet questions which turn around the estab- 
 lishment of &fair standard for such things as expendi- 
 ture. And this term ; fair ' is itself obviously a relative 
 term. 
 
 The distinction between positive and negative terms is 
 obvious enough. A positive term is one which implies 
 the presence of a quality or qualities. Thus, 4 efficient,' 
 4 selfish,' 4 happy,' and 4 heavy' are positive terms. A 
 negative term is one which implies the absence of 
 such qualities. 4 Inefficiency,' « disloyal,' 4 unselfish ' 
 are negative terms. In the English language, such pre- 
 fixes and suffixes as 4 un,' 4 in,' 4 dis,' * a,' and 4 less ' are 
 used to form negative from positive terms. It should be 
 noted that contrast-pairs formed in this way do not box 
 the compass. Take, for example, the terms 4 patient ' 
 and 4 impatient ' ; a man may not be exactly patient 
 while he is still far from impatient. The logician must 
 call attention to this fact, however trivial it may seem, 
 because words shift their meanings. When we come to 
 study the possible manipulations of a proposition, such 
 as obversion, we shall see why it is necessary to deter- 
 mine the exact opposite of a term. 4 Intemperate ' is not 
 the contradictory of 4 temperate.' A little reflection and 
 some care in the use of words are all that is needed. 
 Attention should be called to another point. Too much 
 stress should not be laid upon the mere form of words. 
 It is always best to penetrate to the meaning. Thus, 
 such terms as 4 invaluable ' and 4 unloosed ' are positive 
 in their meaning, while it seems nonsense to speak of 
 4 intemperance ' as negative. The absence of one quality 
 means the presence of a condition just as positive. The 
 negative form is an accident of language in such cases. 
 
ABOUT TERMS 37 
 
 For the sake of completeness, we referred to the class 
 of privative terms. A privative term is one which sig- 
 nifies the absence of a quality which is usually present. 
 Because of the importance of this lack to which they 
 refer, they are positive in form. Examples : ' maimed,' 
 4 deaf,' ' blind,' ' orphaned.' 
 
 Connotation and Denotation. General or class 
 terms have two functions : they apply to the members 
 of the class and they serve to recall the common attri- 
 butes of the class. Thus the term does double duty : it 
 enables us to bear individual things in mind while 
 thinking of them as belonging to a class, and it is a sign 
 of the essential attributes of the class. 
 
 This double function of class terms reflects the way 
 in which such terms develop. We notice that certain 
 things have points of similarity, and, if these common 
 qualities are important to us, we group these things to- 
 gether and think of them largely in terms of their com- 
 mon qualities. As a matter of fact, we never think of 
 the things without some thought of the qualities, nor of 
 the qualities without the implicit assumption that they 
 are possessed by things. We may say, then, that deno- 
 tation and connotation go together just as inevitably as 
 do qualities and things. They are the reflection into the 
 class term of this natural and constant distinction. It 
 is for this reason that general terms denote things and 
 connote qualities. 
 
 Synonyms for Connotation and Denotation. 
 Instead of 'denotation,' some logicians speak of the ' ex- 
 tension ' or * scope ' of the term. The corresponding 
 names for ' connotation ' are ' intension ' and 6 compre- 
 hension.' ' Denotation ' and ' connotation ' are prefer- 
 
38 THE ESSENTIALS OF LOGIC 
 
 able because they have the verb forms, ' denote and 
 ' connote,' and the adjective forms, 4 denotative ' and 
 ' connotative.' 
 
 The Inverse Variation of Connotation and De- 
 notation. The wider or higher the class, the fewer the 
 attributes which the members of the class have in com- 
 mon. As you pass from a species to a genus in biology, 
 the number of animals or plants covered by the term 
 increases while the common attributes decrease in num- 
 ber. This double fact is summarized by saying that de- 
 notation and connotation vary inversely. This variation 
 does not, however, follow any mathematical law. In- 
 crease the number of qualities possessed in common, 
 that is, widen the connotation, and the members of the 
 class possessing these qualities will be fewer in number. 
 The following series will illustrate this principle : 'man,' 
 4 Americans,' 4 Americans of European descent,' 'native- 
 born Americans,' ' native-born Americans who are citi- 
 zens of Michigan,' etc. 
 
 It should be noted that, in our actual thinking, the 
 connotation of a term is more apt to be explicit than 
 the denotation. We do not actually run over the various 
 members of the class, but, instead, have some individual 
 vaguely in mind as a specimen. 
 
 Terms and Meaning. All words have meaning. 
 This meaning varies from the most substantive and 
 definite to the most fugitive and fluctuating. The mean- 
 ing of a word is inseparable from the context in which 
 it is used. It is for this reason that both the logician 
 and the psychologist hold that the sentence or even the 
 paragraph is the lowest unit of thought. A word or a 
 group of words constitutes a term, and this term has a 
 
ABOUT TERMS 39 
 
 complex meaning. It is, however, best to distinguish be- 
 tween the meaning of a term and connotation. In the 
 first place, the distinction between denotation and conno- 
 tation comes out clearly only for class terms; in the second 
 place, the meaning of a class term includes both its de- 
 notation and its connotation. We mean the objects we 
 think of as well as the qualities they have in common. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. IV. 
 Creighton, An Introductory Logic, chap. iv. 
 Joseph, An Introduction to Logic, chap. II. 
 Schiller, Formal Logic, chap. u. 
 
CHAPTER IV 
 
 THE USE AND MISUSE OF LANGUAGE 
 
 The Necessity for Language. Logic deals with 
 thinking and with knowledge which is the resultant of 
 thinking. But thought is impossible without language. 
 It is for this reason that logic has to concern itself so 
 fully with language and its relation to thought. " Lan- 
 guage is not merely an accompaniment of ideational 
 activity ; it is an instrument essential to its develop- 
 ment. It is an appropriate means of fixing attention 
 upon ideally represented objects as distinguished from 
 percepts. It becomes the more necessary the more ab- 
 stract ideal representation is, — in other words, the less 
 it contains of the concrete details of actual sense-per- 
 ception. . . . Within the mind of the individual thinker 
 it serves to fix attention on the object of his own ideas ; 
 in communication with others, it serves to fix the atten- 
 tion of the hearer on the ideally represented objects 
 present to the mind of the speaker." * As we advance 
 in our study of logic, we shall realize, ever more clearly, 
 what an intimate part language plays. Systematic 
 knowledge is bound up with the use of a definite set 
 of symbols, though these symbols may be of various 
 kinds. Each special science works out its own technical 
 terms, while mathematics has advanced step by step 
 with its notation. 
 
 Language and Analysis. In a preceding chapter 2 
 
 1 Stout, Manual of Psychology, p. 462. 
 
 2 Chapter n, " The Nature and Setting of Thought." 
 
THE USE AND MISUSE OF LANGUAGE 41 
 
 we suggested that reasoning is based upon the percep- 
 tion of likeness and difference. Now, language assists 
 such discrimination by giving names to the common 
 factors and aiding in their recall and free manipulation 
 apart from perception. Gradually a world of ideas is 
 built up in which man may freely move. Words are 
 the means by which such ideas are fixated. It has been 
 proved by experiment that we both observe and remem- 
 ber features of our experience better if we possess 
 words to attach to them. 
 
 The Logical Law of Language. The logical law 
 of language is non-ambiguity. Actually, words are in- 
 definite and misty on their edges. We use them in a 
 rough-and-ready fashion. We feel their appropriateness 
 and develop habits in their use. The consequence is 
 that there is not enough delicacy in discrimination ; we 
 tend to class things together when we notice that they 
 have common features. Yet the differences may be of 
 more significance for the problem in hand than the 
 similarities. 
 
 The neglect of relevant distinctions, when these are 
 important for clear thinking or adequate statement, is 
 ambiguity. The ideal of the logician is to encourage 
 individuals in those mental habits of accuracy and dis- 
 crimination which are calculated to prevent ambiguity. 
 The logical law of language is non-ambiguity, an ideal 
 to which we should approach ever more nearly. 
 
 Causes of Ambiguity. There are many causes of 
 ambiguity, but the basic cause is mental. Ideas are 
 allowed to remain vague, and, as a consequence, they 
 overlap and get into one another's way. Just as things 
 are often classed roughly together because their differ- 
 
42 THE ESSENTIALS OF LOGIC 
 
 ences are not noted, so ideas are only too frequently 
 merged and confused. But clear and accurate thinking 
 depends as much upon the awareness of differences as 
 upon the awareness of similarities. Only he who is 
 willing to take the trouble to distinguish things and 
 ideas which are ordinarily grouped roughly together, 
 can escape the pitfall of ambiguity. 
 
 But ambiguity has a social significance. Incorrect 
 and inadequate thinking when expressed in language 
 appears as ambiguous statements and arguments. Such 
 statements are apt to deceive the unwary because they 
 also refuse to make an analysis of the ideas involved. 
 Hence ambiguities tend to propagate themselves and 
 father a series of fallacies. 
 
 Now, while unwillingness or inability to analyze the 
 various fields of experience, in order to build up clear- 
 cut ideas not easily confused, is the basic cause of ambi- 
 guity, there are other causes at work, the variation of 
 the meaning of words with the purpose or general con- 
 text, and the imperfections of language as an instru- 
 ment. It is difficult for language to keep pace with the 
 subtlety and flexibility of thought. It is so easy to sub- 
 stitute the average meaning for the particular meaning 
 which the situation demands. Again, a word may have, 
 and usually does have, more than one meaning of an 
 average sort ; and, to make matters worse, words are 
 constantly changing their meanings. We always have 
 more ideas than words with which to express them. It 
 may be said that this ability of a single word to do duty 
 for more than one idea is a perfection rather than an 
 imperfection, but it certainly brings its dangers. A 
 sharp eye for the context or purpose is the main safe- 
 
THE USE AND MISUSE OF LANGUAGE 43 
 
 guard. If this is not obvious to the reader or listener, 
 ambiguity is unavoidable. 
 
 Univocal Words. Words which have only one 
 meaning are called ' univocal.' The best examples of 
 univocal words are to be found in the technical terms 
 of the special sciences. In these, a term is adopted, or 
 made, as an accepted sign of a definite idea reached by 
 painstaking investigation. Consequently, the danger of 
 ambiguity is at a minimum. To secure such carefully 
 delimited ideas is one of the chief purposes of any sci- 
 ence ; it is a recognized condition of advance. The 
 technical terms of a special science when taken together 
 form its nomenclature. Thus, ' molecule,' i electron,' 
 ' vertebrate,' ' cell,' ' angle ' are technical terms. It 
 should, however, be noted that not all technical terms 
 are strictly univocal ; it is only when they are given in 
 the context of their special field that they have but one 
 meaning. But this context is easily recognized. 
 
 Equivocal Words. Words which have more than 
 one meaning are 'equivocal.' The vast majority of 
 words which do not apply to material things are equiv- 
 ocal, as can be seen by glancing over the columns of 
 any large dictionary. Thus, to take a simple word like 
 4 stop,' we find that it means (1) 'to close,' (2) 'to 
 confine,' (3) ' to arrest,' (4) ' to interrupt.' Besides 
 these popular uses, it has technical meanings in music, 
 rhetoric, optics, horticulture, and finance. It is no won- 
 der that a foreigner has difficulty in learning another 
 language, and I am sure that, if all the humorous 
 stories told in this connection are not true, at least 
 there is ground for most of them. The truth is that 
 there are not enough words to go around, and we are 
 
44 THE ESSENTIALS OF LOGIC 
 
 obliged to make one word do the duty of many. A per- 
 ception of the setting is essential if ambiguity is to be 
 avoided. The only practical advice the logician can 
 offer is to seek for the particular meaning and not trust 
 the average or general meaning of the term. 
 
 "Words change their Meanings. There are several 
 tendencies at work to change the meanings of words. 
 The three most important are generalization, specializa- 
 tion, and transfer of meaning by association and analogy. 
 
 At first, a word is the sign of a concrete thing or 
 class of things. It is later extended to all those things 
 which have a conspicuous attribute in common. As time 
 goes on, extensions to more abstract objects take place. 
 This change of application from a concrete particular 
 to analogous things and objects of thought is called 
 4 generalization.' " The word 6 law ' has undergone ex- 
 pansion under the pressure of physical research. Reg- 
 ularity, uniformity, constancy of occurrence is a much 
 wider idea than bare authoritative prescription enforc- 
 ing obedience under the threat of punishment — which 
 is the simple juridical conception." * How easily ambi- 
 guity arises when two meanings coexist can be seen 
 from the following quotation: "The existence of a 
 power is even implied in the phrase ' laws of nature,' 
 constantly used by science ; for wherever there is a law 
 there must be a lawgiver, and the lawgiver must be 
 presumed capable of suspending the operation of law." 2 
 Another instance of this ambiguity of the word law 
 has come to light in recent discussions bearing upon 
 the nature of 'international law.' The English word 
 
 1 Davidson, The Logic of Definition, p. 5. 
 
 2 Gold win Smith, Guesses at the Riddle of Existence, p. 143. 
 
THE USE AND MISUSE OF LANGUAGE 45 
 
 4 law ' translates what is expressed in continental tongues 
 by two words ; in German by recht and gesetz, in French 
 by droit and loi. Is there an international law ? If we 
 mean by 'law,' gesetz and loi, no ; if we mean recht and 
 droit, yes. It is obvious that we have too few words in 
 such a case. 
 
 Other simpler examples of this principle of general- 
 ization are « fluid,' 4 acid,' 4 curve,' and 4 oval.' We pass 
 from the particular to the more general and abstract. 
 
 Again, words may take on a more special meaning. 
 4 Priest,' 4 minister,' 4 captain,' 4 clerk ' are examples of 
 this tendency to select a special application of the more 
 general meaning and to ignore the other meanings. One 
 of the most interesting cases of this specialization which 
 has led to ambiguity is the word ' prove.' Originally it 
 meant 4 to test ' as in the saying, " The exception proves 
 the rule." Now it means * to test successfully.' I pre- 
 sume that many a one has wondered how the exception 
 could prove the rule. 
 
 There is, finally, the tendency to transfer a word to 
 analogous or associated objects. Thus, the word 4 church* 
 is used to designate the religious body, the building, and 
 some temporary group of worshipers. We speak of the 
 4 chair ' when w r e mean the presiding officer, or of the 
 4 bench ' when we mean the judiciary. It would be 
 right to list under this heading those epithets which are 
 based on felt analogies. Such epithets startle the mind 
 and force it to recognize similarities which would other- 
 wise have passed unnoticed. It is the poet, with his 
 keen sensing of likenesses and differences, who is most 
 apt to bring far-removed aspects of experience together 
 by an illuminating phrase. We feel the appropriateness 
 
46 THE ESSENTIALS OF LOGIC 
 
 of the expression while we hesitate to analyze it, so 
 subtle and elusive is the connection. 
 
 These classes of changes in the meanings of words 
 make us realize what a complex instrument language is. 
 It is necessary to know all the essential meanings of 
 commonly used words and to have some idea of how 
 new shades of significance are added. 
 
 Vagueness. Vagueness is often the cause of ambi- 
 guity, but it is not the same as ambiguity. Our ideas 
 of the meanings of the words we use may be hazy, but, 
 so long as the subject we are talking or thinking about 
 is simple, this lack of definiteness in our ideas may not 
 lead us astray. So long as the problem is general and 
 relatively practical, no great measure of analysis is 
 needed. We must remember that words are frequently 
 used just to indicate things and to suggest plans of ac- 
 tion and desirable attitudes. Thus, common nouns are 
 seldom used incorrectly even though the majority of 
 people would be hard put to it to give an exact defini- 
 tion. Yet, even here, there is doubt when those excep- 
 tional cases are met which fall on the dividing-line be- 
 tween two classes. Is this man a doctor or a quack? Is 
 this lawyer a genuine lawyer or a pettifogger? The 
 trouble is, of course, not so much one of language as of 
 classification. Classes shade into one another and their 
 edges are blurred. Accuracy and completeness of classi- 
 fication are the pre-conditions of clear ideas. 
 
 The reason for vagueness in the understanding and 
 application of words can partly be traced to the method 
 by means of which the individual's vocabulary is devel- 
 oped. Words are picked up in their special applications 
 and then extended to what are judged to be similar 
 
THE USE AND MISUSE OF LANGUAGE 47 
 
 cases. " The mode in which words are learned and ex- 
 tended may be studied most simply in the nursery. A 
 child, say, has learnt to say ' mambro ' when it sees its 
 nurse. The nurse works a hand-turned sewing machine, 
 and sings to it as she works. In the street the child 
 sees an organ-grinder singing as he turns his handle : 
 it calls ' mambro ' ; the nurse catches the meaning and 
 the child is overjoyed. The organ-grinder has a mon- 
 key: the child has an India-rubber monkey toy: it calls 
 this also ' mambro.' " 1 The individual's vocabulary is 
 built up under social control only of a rough-and-ready 
 sort. It is adequate for general purposes, but not where 
 accuracy is needed or where slight distinctions are very 
 important. Where the demands are more exacting, 
 vagueness is treacherous and leads to ambiguity. 
 
 Abstract Terms particularly subject to Vague- 
 ness. Where there is no chance to appeal to perception 
 as a test for the meaning of a term, vagueness is almost 
 certain to exist. We can pick up the word just as the 
 child does, but it is another thing to reproduce the idea. 
 That requires mental activity of a high degree. The 
 logician stresses the fact that concepts are primary and 
 words secondary. What is meant by such terms as 
 4 happiness,' ' liberty,' ' social justice ' ? I who have 
 spent years in analyzing their meanings feel that I have 
 a right to be skeptical of some glib use of the terms. 
 " When we come to words of which the logical concept 
 is a complex relation, an obscure or intangible attribute, 
 the defects of the popular conception and its tendencies 
 to change and confusion are of the greatest practical im- 
 portance. Take such words as ' Monarchy,' * tyranny/ 
 1 Minto, Logic, Inductive and Deductive, p. 83. 
 
48 THE ESSENTIALS OF LOGIC 
 
 'civil freedom,' 'freedom of contract,' 'landlord,' 'gen- 
 tleman,' 'prig,' 'culture,' 'education,' 'temperance/ 
 ' generosity.' Not merely should we find it difficult to 
 give an analytic definition of such words : we might 
 be unable to do so, and yet flatter ourselves that we 
 had a clear understanding of their meaning. But let 
 two men begin to discuss any proposition in which 
 any such word is involved and it will soon be found that 
 they take the word in different senses." 1 Such terms 
 are really technical and should be treated as such. The 
 difficulty is, however, practical as well as scientific. Peo- 
 ple are obliged to think about such subjects because 
 of their duties and needs as citizens, and because such 
 terms are frequent causes of dispute. What the logician 
 must warn against is dogmatism. The average man is 
 not easily persuaded that familiarity with a word does 
 not involve knowledge of what it means. Such dogma- 
 tism is one of the chief causes of error. 
 
 Logic and Language. Logic deals with thought, 
 but we can get at thought only through language. Now, 
 language is not a transparent medium ; it veils as well 
 as expresses the ideas and purposes which seek utter- 
 ance and the understanding of other minds. The logi- 
 cian must, therefore, be equal to the emergency of in- 
 terpretation if sufficient clues are given. " The practicing 
 logician, ever seeking behind the accidental parlance 
 the necessary sequence of idea, studies the idiomatic ex- 
 pression of thought, with which, however, and not with 
 the expression, his concern truly lies." 2 
 
 1 Minto, Logic, Inductive and Deductive, p. 86. 
 
 2 Macleane, Reason, Thought, and Language, p. 9. 
 
THE USE AND MISUSE OF LANGUAGE 49 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. in. 
 James, Principles of Psychology, vol. li, chap. xxii. 
 Jones, Logic, Inductive and Deductive, chap. iv. 
 Macleane, Reason, Thought, and Language, Introduction. 
 Minto, Logic, Inductive and Deductive, part 11, chap. I. 
 Stout, Manual of Psychology, bk. iv, chap. v. 
 
CHAPTER V 
 
 CLASSIFICATION AND DIVISION 
 
 Classification and Classes. In our study of terms 
 we distinguished class, or general, terms from the other 
 kinds of terms. It is our present purpose to study in 
 more detail the nature of classes and the character of 
 the processes by which they are obtained. We shall see 
 that the establishment of classes involves a large meas- 
 ure of mental activity. Certain classes suggest them- 
 selves quite naturally, while others are formed only after 
 a deal of effort has been expended in the discovery of 
 hidden relationships between things apparently different 
 in nature. At whatever level classes are formed, com- 
 parison, discrimination, analysis, and construction are 
 at work, though with different intensities. It must never 
 be forgotten that an object is not a member of a class 
 in its own right, but because a class has been conceived 
 by the human mind. Man and nature collaborate in 
 the construction of classes. When a class has been es- 
 tablished, however, its membership is potentially deter- 
 mined by that very fact. Having conceived of verte- 
 brates as a class, we cannot refuse membership to this 
 or that creature because of our dislike for its bad habits 
 or its ugly appearance. The Gila monster is as good 
 a vertebrate as the most docile pussy that ever slept in 
 her mistress's lap. 
 
 We may define classification as the process of group- 
 ing things together according to their possession of cer- 
 
CLASSIFICATION AND DIVISION 51 
 
 tain selected common attributes. The things possessing 
 these attributes are the members of the class, while the 
 class is the members taken together. Such classes may be 
 relatively permanent or quite temporary and occasional. 
 The following quotation will illustrate the wide range 
 of classes which the logician recognizes : " By a class 
 will here be meant any imagined group of individual 
 cases, whether real or unreal — a group in which every 
 individual is supposed to resemble all the others in some 
 respects, though differing in others. There are classes 
 of actions and events just as of everything else ; 'mir- 
 acle' is a class name, for instance; or 'coronation,' 
 *l>attle,' 4 eclipse ' ; in fact any name which is used so 
 as t0 admit of a plural — either simply, as ' miracles,' 
 4 kggroes,' 4 battles,' or in the more circuitous form of 
 4 pieces of gold,' 4 cases of deceit,' and so on." l There 
 are filmy classes as well as the more ponderous classes 
 of science. Both have their place for the mind of the 
 logician. 
 
 The Need for Classification. The world man is 
 confronted with is very complex. It consists of objects 
 and events of every conceivable kind. Moreover, this com- 
 plex of things, actions, and events does not come ready- 
 labeled. The world is not like a museum in which things 
 of a kind are put together for our convenience. Instead, 
 they are scattered about in space and time, and we 
 must be ready to identify them wherever they are found. 
 But identification involves mental activity. What is the 
 character of this mental activity and why is it aroused ? 
 
 The simplest form of identification is recognition. 
 Psychologists inform us that recognition is often imme- 
 1 Sidgwick, The Use of Words in Beasoning, p. 150. 
 
52 THE ESSENTIALS OP LOGIC 
 
 diate, that an object arouses associates, and these give 
 the sense of familiarity. " Part of the recognition of an 
 object that is not handled or that does not give rise 
 directly to movements is due to the fact that its uses 
 are appreciated, that, when it is recognized, one knows 
 at once what to do with it and how to use it." * Such 
 immediate recognition is an unconscious classification. 
 The character of the object is appreciated and the 
 proper habits and attitude are aroused. Thus there is a 
 practical aspect for identification. Similar things have 
 similar properties : fire burns ; this kind of tree bears 
 delicious fruit ; a silent baby is usually in mischief, 
 etc. If we had to deal separately with each thing, 
 we should not know what to do ; it would be impossible 
 to bring past experience to bear. We may say, then, that 
 classification, unconscious or conscious, is the only way 
 in which we can handle our complex world of individual 
 things. 
 
 Types of Classification. But a felt identification 
 is not sufficient for human needs. To handle things 
 properly and commodiously mankind has had to work 
 out methods and principles of grouping adapted to the 
 purpose in hand. There are two main types of classifi- 
 cation, the artificial and the natural, and these corre- 
 spond to the dominant purpose. In an artificial classifi- 
 cation, the purpose is to enable us to handle the facts 
 in a given realm as quickly and easily as possible ; that 
 is, the purpose is practical. In a natural classification, 
 the purpose is to allow things or facts to arrange them- 
 selves in accordance with their essential nature. Let 
 us look a little more closely at these two types. 
 
 1 Pillsbury, Essentials of Psychology, p. 209. 
 
CLASSIFICATION AND DIVISION 53 
 
 Artificial Classification. In artificial classifications 
 where the purpose is facility in handling, some obvious 
 and, as a rule, external attribute is selected as the basis. 
 A good example of this type is the method by which 
 books are catalogued in a library. The first letter of the 
 author's name determines the place of the book on the 
 shelves and in the catalogue. If this simple device is 
 insufficient, the subjects are likewise arranged alpha- 
 betically. This mode of artificial classification is usually 
 called 4 index classification.' 
 
 Another kind of artificial classification is the so-called 
 * diagnostic classification.' The purpose at work here is 
 the identification of an object. A doctor wishes to diag- 
 nose a disease so that he may know what procedure to 
 adopt in his treatment of it ; or a collector wishes to 
 label a butterfly which he has found. In both cases the 
 the search is made for characteristics which will indi- 
 cate the group to which the object belongs. Nature- 
 study books are full of devices for identification of plants 
 and animals according to pretty obvious traits. 
 
 Natural Classifications. Natural classifications are, 
 as we have said, based upon as thorough investigation 
 of the nature of the things classified as is attainable 
 at the time. The purpose is to find some arrangement 
 which corresponds to our knowledge and reflects a 
 kinship in the things themselves. Such an arrangement 
 is a difficult feat to achieve, and the growth of science 
 is traceable in the perfecting of systems of classi- 
 fication. It is practically always necessary to pene- 
 trate below the surface and to build on those underly- 
 ing attributes which reveal themselves only to the eye 
 of the trained observer. "Thus the classification of 
 
54 THE ESSENTIALS OF LOGIC 
 
 birds, for instance, is based largely upon fundamental 
 differences in anatomical structure. Birds, not as we 
 see them, but as they are when stripped of plumage and 
 in their nakedness, are the real objects of consideration 
 in such a system of classification. The result is that in 
 the same group there will appear side by side a number 
 of birds whose surface markings are exceedingly dispar- 
 ate, such as the blue jay and the crow, or the English 
 sparrow and the cardinal. It is always a broadening 
 experience, as regards our habits of thinking, when we 
 are able to discover some essential similarity at the 
 basis of a marked surface dissimilarity." 1 
 
 Natural classification is scientific classification and 
 reflects all the purposes and methods of science. The 
 ultimate aim is, of course, explanation, but there is also 
 the subordinate aim of convenience. This combination 
 of purposes is very well brought out by Jevons : " By 
 the classification of any series of objects is meant the 
 actual or ideal arrangement together of those things 
 which are like and the separation of those which are un- 
 like, the purpose of the arrangement being, primarily, 
 to disclose the correlations or laws of union of properties 
 and circumstances, and secondarily, to facilitate the oper- 
 ations of the mind in clearly conceiving and retaining 
 in memory the characters of the objects in question." 
 
 Natural Classification in the Light of Evolu- 
 tion. During the eighteenth and the first half of the nine- 
 teenth century, scientists believed in the existence of 
 natural kinds of species which were changeless in char- 
 acter and sharply distinct from one another. The task 
 of the anatomist was to dissect these species and deter- 
 
 1 Hibben, Logic, Deductive and Inductive, p. 58. 
 
CLASSIFICATION AND DIVISION 55 
 
 mine their essential or defining marks. The hope was 
 to enumerate and describe these fixed species once for 
 all, and ' then to erect a scheme of classification into 
 which they would all fit. But continued investiga- 
 tion convinced naturalists that there was something 
 scholastic and unreal in sharp distinctions ; that spe- 
 cies merged with one another on the edges. With 
 the gradual rise of the theory of evolution it came to 
 be recognized that there are genetic relationships run- 
 ning all through the organic realm and that species are, 
 so to speak, abstractions which over-simplify nature. 
 Species are not immutable, but, instead, shade over into 
 one another. Classification is a tool which must not be 
 read into the complex realm of things too naively. 
 
 Character of Systematic Classification. Partic- 
 ular classes are formed by grouping objects together 
 according to their likenesses and differences. But a 
 further task ensues, that of showing the relations be- 
 tween the classes thus formed. We are not satisfied to 
 leave particular classes in isolation, but demand a sys- 
 tem of classification in which classes are arranged in 
 accordance with conceived relations of coordination, 
 subordination, and superordination. Such systems 
 must express an internal unity which is manifested in 
 various ways in the subordinate classes. All the classes 
 must have certain attributes in common, and these com- 
 mon attributes must not contradict the more specific 
 attributes which differentiate the subordinate classes 
 from one another. To put the matter less technically : 
 classification works within some field of objects and 
 seeks to arrange them by selecting, first, those attri- 
 butes which they all possess, and, secondly, those groups 
 
56 
 
 THE ESSENTIALS OF LOGIC 
 
 of further and more specific attributes which divide the 
 whole field into related yet distinct classes. So far as 
 possible the differences which divide the whole into 
 parts must be seen in their relation to the fundamental 
 similarities. A particular class is a species (difference) 
 of (similarity) the genus. A good classification should 
 make it possible to see any fact in the light of the 
 whole. The following example brings out this presence 
 of an underlying agreement manifesting itself in differ- 
 ent ways: 1 — 
 
 Vegetable Kingdom 
 
 Rootless, leaf- 
 less, stemless 
 
 plants 
 (Thallophyta) 
 
 I 
 
 I 1 
 
 Moss-like 
 
 plants 
 (Bryophyta) 
 
 Fern-like 
 
 plants 
 (Pteridophyta) 
 
 3 
 
 
 & 
 
 ^ 
 
 02 /— s 
 
 B § 
 
 Pn 
 
 * 8. 
 
 CO i*» 
 co «g 
 
 351 
 
 
 Seed-bearing 
 
 plants 
 (Spermaphyta) 
 
 Wkj 3 
 
 CO o 
 
 eo c 
 
 1*8 
 
 S3 O 
 
 O^ 
 
 T3 
 
 0) 
 
 ■si 
 
 co *> 
 
 " &• 
 
 o 
 8 
 
 o 
 
 CD 
 
 0) 
 CO 
 
 a 
 
 a 
 
 
 The student should examine the type of classifica- 
 tion found in any good textbook in biology in order to 
 familiarize himself with the mechanism of the process. 
 
 Classification and Division. There is a very close 
 connection between classification and another logical 
 process called 'division.' The main difference in the 
 meaning of the two terms is this : that when we classify, 
 we think of ourselves as moving upward from the indi- 
 1 Quoted from Taylor, Elpmentqry Logic, p. 45. 
 
CLASSIFICATION AND DIVISION 57 
 
 vidual things to schemes of arrangement according to 
 likeness and difference ; that when we divide, we think 
 of ourselves as moving downward from the more gen- 
 eral and inclusive modes of grouping to more specific 
 sub-classes. Such a distinction is, however, rather arti- 
 ficial, for, in the solution of any real problem of ar- 
 rangement, our thought moves in both directions at 
 once. Yet, while recognizing to the full this double 
 movement of thought, it still remains true that logical 
 division is a method with a definitely conceived form 
 which can be used as a test of any classification. As a 
 method, it is inclined to be more doctrinaire and a 
 priori than classification. 
 
 Technical Terms used in Division. Division is a 
 process which may be carried through many stages. 
 The general class with which it starts is called the 
 4 summum genus/ that is, the highest genus. The sub- 
 class with which it stops is called the 6 infimae species,' 
 that is, the lowest species. Between these two extremes, 
 the terms 4 species ' and ' genus ' are used as purely 
 relative terms. In any series, the class above is the 
 genus of the class below which is its species. The class 
 directly above is the 'proximum genus' of the species 
 just below. Where more than one species have the 
 same proximum genus they are called ' coordinate spe- 
 cies.' The coordinate species of a genus are called its 
 'constituent species.' The principle used in dividing 
 is called the ' f undamentum divisionis,' or basis of di- 
 vision. It is that aspect of the summum genus which 
 enables us to separate its constituent species. The dif- 
 ferentia of a species is that characteristic which distin- 
 guishes it from its coordinate species. 
 
58 THE ESSENTIALS OF LOGIC 
 
 Rules of Division. To be valid, a logical division 
 must observe the following rules : — 
 
 1. A division must be complete. A complete division 
 is one which exhausts the constituent species of the 
 main class. 
 
 The necessity for this rule is at once apparent. The 
 neglect of any species may easily lead to confusion in 
 both theory and practice. 
 
 2. The constituent species into which the genus is 
 divided must not overlap. A division is imperfect if an 
 individual may belong to two species at the same time. 
 
 A few words in regard to these rules may be advisa- 
 ble. An incomplete division may be due to ignorance, 
 lack of persistence, or to the special difficulties of the 
 field. When the last is the case, it is sometimes met by 
 forming a miscellaneous class to include obscure data. 
 Such a miscellaneous class points to the tentative char- 
 acter of the classification which the division reflects. A 
 violation of the second rule leads to cross-division and 
 is the consequence of the employment of more than one 
 basis of division. The division of the citizens of a coun- 
 try into the rich, the poor, and the educated is an ex- 
 ample of cross-division. 
 
 Forms of Division. There are two forms of di- 
 vision, dichotomous and classificatory division. These 
 are readily distinguishable. In dichotomous, or bifur- 
 cate, division the genus is cut into two classes, those 
 which possess the character and those which do not. 
 The one is a positive group, the other is an indefinite, 
 negative group. Together, however, they are exhaus- 
 tive of the genus. This process can be further continued 
 on either of the two groups. The other form of division, 
 
CLASSIFICATION AND DIVISION 59 
 
 which I have called ' classificatory,' is the reverse aspect 
 of any system of classification. The species into which the 
 genus divides are positive and coordinate ; their num- 
 ber is determined by the nature of the field. We may 
 speak of such division as ' analytic ' and of the corre- 
 sponding classification as ' synthetic.' 
 
 Dichotomous Division. While dichotomous divi- 
 sion is simple and exhaustive, it easily becomes unwieldy 
 when carried far. Moreover, one side is negative and 
 indefinite. All that is known about it is that it lacks 
 the positive character the other side possesses. Under 
 certain circumstances, however, the lack of a quality 
 may be as interesting as its possession. Thus the di- 
 vision of the population into voters and non-voters, or 
 of the working-classes into skilled and unskilled, gives 
 us two groups which are really coordinate. Where we 
 are interested in some part of the field rather than in 
 the whole, tracing by dichotomy may be the easiest 
 way. The following example, usually called the ' Tree 
 of Porphyry,' makes the method clear : — 
 
 Substance 
 
 Corporeal Incorporeal 
 
 Animate Inanimate 
 
 A 
 
 Sensible Insensible 
 
 /\ k 
 
 Rational Irrational 
 /\ 
 
 — v 
 Mortal Immortal 
 
 This method of division mav be made instrumental 
 to the working-out of a definition of a term. Thus, ac- 
 cepting the adequacy of the above tree, we can define 
 man as 'a corporeal substance, animate, sensible, ra- 
 tional, and mortal.' Another example will serve to 
 
60 THE ESSENTIALS OF LOGIC 
 
 bring out this use sufficiently. " The term to be defined 
 is ' tuber ' ; the genus to which it is to be referred is 
 4 stem.' 
 
 Stem 
 
 creeping not creeping 
 
 underground not underground 
 
 much thickened not much thickened 
 
 possessing leaf-buds not possessing leaf-buds 
 
 in the form of ' eyes ' in the form of * eyes ' 
 
 " In this division, we reach, as our definition of a 
 tuber, 6 a stem creeping underground, much thickened, 
 and possessing leaf-buds in the form of eyes/ " * 
 
 Classificatory Division. This form of division is, 
 in its final expression, the same as a system of classifica- 
 tion. The species under any genus must be coordinate 
 and exhaustive. It should be remembered that the move- 
 ment in division is downward from the general to the 
 more particular, while in classification it is upward from 
 the particulars to the more general. Only one other 
 point needs, I think, to be mentioned. The funda- 
 mentum divisionis which is selected depends partly 
 upon the purpose, partly upon the character of the 
 subject-matter. 
 
 Dangers to be guarded against. Imperfect classi- 
 fication and division lead to the identification of things 
 and ideas which should be discriminated. This is, as we 
 have seen, the chief cause of ambiguity. It is, in fact, 
 impossible to treat definition and ambiguity apart from 
 the consideration of classification and division, for in 
 these processes we are studying the methods by which 
 
 1 Joseph, An Introduction to Logic, p. 113. 
 
CLASSIFICATION AND DIVISION 61 
 
 the mind orders and arranges its material. For the ma- 
 jority, an examination of the systems established in the 
 various sciences is of less value than the critical analy- 
 sis of less formal and better-known subjects. The chief 
 danger to be guarded against is the merging together 
 of things which should be distinguished. Natural law 
 should not be confused with moral law, nor this with 
 statute law. Education should not be identified with 
 erudition, nor cleverness with talent. 'Democracy' 
 should not be used as a blanket-term to cover repre- 
 sentative institutions and the absence of caste. The 
 proper use of terms is the result of the critical discrimi- 
 nation of different meanings, and these meanings them- 
 selves rest upon the keen perception and exhaustive 
 treatment of likenesses and differences. After classifica- 
 tion comes definition which is its fruition. 
 
 REFERENCES 
 
 Creighton, An Introductory Logic, chap. v. 
 Hibben, Logic, Deductive and Inductive, chap. VI. 
 Jones, Logic, Inductive and Deductive, chap. ill. 
 Joseph, An Introduction to Logic, chap. v. 
 Minto, Logic, Inductive and Deductive, part II, chap. I. 
 Schiller, Formal Logic, chap. vi. 
 
CHAPTER VI 
 
 PRINCIPLES OF DEFINITION 
 
 Why Definition is Needed. In a former chapter 
 we saw why language is a necessary instrument of 
 thought and what some of its imperfections are. " The 
 logical ideal of the relation between words and thoughts 
 is, of course, that every thought should have its own 
 name, and every name should have its own meaning." 1 
 This ideal is unrealizable because language is always 
 changing. New shades of meaning are constantly being 
 developed and old distinctions falling into disuse. But 
 ignorance and mental indolence are also at work to make 
 the use of words unclear. The correct employment of 
 words depends upon three things : a large vocabulary, 
 a fund of clear meanings, and the proper adjustment 
 of the two* Unless these three things are forthcom- 
 ing, there will be confusion in the individual's mind 
 and misunderstanding when he attempts to communi- 
 cate his ideas. Probably John Locke has pointed out 
 these dangers, which only definition can correct, as well 
 as any one : — 
 
 " For he that shall well consider the errors and ob- 
 scurity, the mistakes and confusion, that are spread in 
 the world by an ill use of words, will find some reason 
 to doubt whether language, as it has been employed, has 
 contributed more to the improvement or hindrance of 
 knowledge amongst mankind. How many are there, that, 
 1 Davidson, The Logic of Definition, p. 2. 
 
PRINCIPLES OF DEFINITION 63 
 
 when they would think on things, fix their thoughts 
 only on words, especially when they would apply their 
 minds to moral matters ; and who, then, can wonder if 
 the result of such contemplations and reasonings about 
 little more than sounds, whilst the ideas they annex to 
 them are very confused and very unsteady, or perhaps 
 none at all ; who can wonder, I say, that such thoughts 
 and reasonings end in nothing but obscurity and mis- 
 take, without any clear judgment or knowledge ? " * 
 
 We have said that definition can be of great assist- 
 ance in overcoming such confusion and misunderstand- 
 ing. But definition is a process which works with words 
 and ideas. The individual must be capable of handling 
 thousands of concepts and of distinguishing nice shades 
 of meaning ; he must also have a fairly large fund of 
 knowledge. On the verbal side, he must be able to dis- 
 criminate the uses of words. These are really two as- 
 pects of the same process, for I very much doubt whether 
 the Mrs. Malaprops are much more sensible in their use 
 of ideas than in their use of words. No one can make 
 nice discriminations between words who cannot do the 
 same for ideas. Both acts are achievements which do 
 not come without effort and the establishment of good 
 mental habits. And it is the belief of the logician that 
 the study of logic should assist in the formation of such 
 habits. It stresses the need and gives the general rules 
 and methods which should be followed. 
 
 The Purpose and Nature of Definition. Defini- 
 tion has a double aspect. On the one hand, terms are 
 defined in order to test correspondence in the use of 
 words. Two disputants wish to discover, for example, 
 1 Essay concerning Human Understanding, bk. in, chap. xi. 
 
64 THE ESSENTIALS OF LOGIC 
 
 whether they have the same understanding for a pivotal 
 word. If they do have, they can profitably proceed in 
 their discussion ; if they do not have the same idea, they 
 must go further back until they find some common 
 ground of agreement. On the other hand, definition 
 arises as the temporary completion of a field of investi- 
 gation. A definition is a summary in which ideas are 
 ordered in relation to one another. A definition is a 
 product just as the meanings concerned are products. 
 Looked at in this genetic way, definitions are seen to 
 be tentative. 
 
 There are two aspects to every definition because both 
 ideas and words are involved. Ideas must be achieved 
 and analyzed, and the meaning obtained must be at- 
 tached to a word as its meaning. According to the set- 
 ting, either of these aspects may be emphasized more 
 than the other. Logic has recognized this possibility in 
 the distinction between real and verbal definitions. 
 When the purpose is, predominantly, to indicate how 
 we intend to use a term, the result is a verbal definition. 
 Dictionary definitions are of assistance here because 
 they offer the average or common meaning. It must be 
 remembered that the peculiar purpose or point of view 
 of the individual enters in to qualify the average mean- 
 ing, which is in many ways an abstraction. Verbal defi- 
 nitions represent past achievements. When, on the other 
 hand, we are interested primarily in getting an ade- 
 quate idea, we are said to achieve real definitions. We 
 try to get behind words to the things and concepts for 
 which they stand. 
 
 To define is, then, to indicate the meaning of a word 
 by achieving an analyzed concept. Definition is an at- 
 
PRINCIPLES OF DEFINITION 65 
 
 tempt to attain to a definite meaning. On the mental 
 side, it is largely an outgrowth of classification and 
 division. 
 
 Logic stresses General Terms. Logic has been so 
 impressed by scientific method that it has connected 
 definition with classification and division. It is for this 
 reason that writers in logic usually define definition as 
 the process of determining the connotation of a term. 
 It will be remembered that general or class terms have 
 two aspects, the things to which they apply and the at- 
 tributes which they imply. To define such a term is to 
 state the attributes characteristic of the class and, indi- 
 rectly, to establish its denotation. 
 
 It is because vague terms become ambiguous that the 
 need for definition is felt. We wish to know exactly 
 what a term stands for. For example, is a ' communist ' 
 the same as a i communard' ? Now, in the case of proper 
 names the ambiguity can be overcome by pointing to 
 the person meant or by adding descriptive words to 
 make the reference definite. Much the same process is 
 necessary for abstract terms which are simple. If a man 
 asks me what 'redness' means, I can only reply by call- 
 ing his attention to some red object and indicating the 
 quality. I must assume his ability to abstract the qual- 
 ity and make it an object of thought. But the applica- 
 tion of class terms cannot be indicated in this simple 
 fashion. It is true that I can illustrate the use of such 
 a term by an example or specimen. " But any example 
 might illustrate a variety of things ; if two persons, each 
 of whom was entirely unacquainted with the language 
 of the other, should try to communicate by pointing to 
 objects to indicate the meaning of the words they were 
 
66 THE ESSENTIALS OF LOGIC 
 
 using, they would illustrate the uncertainly 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. x 
 
 Definition and Classification. It can readily be 
 seen that real definition, or the process of securing 
 clearer and more adequate ideas, is bound up with the 
 logic of classification. To obtain a clear idea of a class 
 we must see it as a part of a system. Thus the defini- 
 tion of a triangle, 4 as that section of a cone which is 
 formed by a plane passing through the vortex perpen- 
 dicularly to the base,' reveals the triangle as related to 
 a system of geometrical objects. The more scientific a 
 definition, the more it is the reflection of a classified 
 field. Definition is possible only when there is organized 
 knowledge. In a very true sense, the whole of logic 
 concerns itself with the method of obtaining well-defined 
 ideas. 
 
 The Verification of Meaning. The verification of 
 the meaning of a term is partly a social process, partly 
 a process of investigation of the things, actions, or 
 events indicated by the term. There is always a rough 
 approximation of the meaning with which to begin. 
 The problem is to narrow down and define the use. 
 Take, for example, such words as ' freedom,' ' liberty,' 
 'justice,' and 'equality.' These words are often on 
 people's lips, yet they are used vaguely. They refer to 
 the same social field, but stress different aspects of that 
 field. They are allied while at the same time distinct. 
 1 Jones, Logic, Inductive and Deductive, p. 58. 
 
PRINCIPLES OF DEFINITION 67 
 
 What must be done in order to verify their proper 
 meanings ? 
 
 There are two levels in the verification of meaning. 
 The first is to determine how the word is actually used ; 
 the second is to advance to a scientific concept which 
 fits into a thoroughly classified and analyzed depart- 
 ment of investigation. The first level gives us a clear 
 popular concept ; the second, if successful, gives us a 
 scientific concept. It goes without saying, however, that 
 the scientific concept is essentially a summary of the 
 total field under investigation. It is difficult, if not im- 
 possible, to get a clear vision of its contents and impli- 
 cations apkrt from an intimate acquaintance with the 
 field. Let the reader pick up a book on a subject with 
 which he is not familiar and attempt to understand the 
 technical terms while neglecting the facts and argument 
 with which they are connected, and he will understand 
 that the verification of scientific concepts is one with 
 scientific investigation itself. 
 
 But logic is also concerned with a more general play 
 of the mind which works for clear meanings whether 
 at the level of common sense or at that of science. It 
 can never be amiss to run over the denotation of a term 
 and to discuss with others their understanding of its 
 exact shade of meaning. The more complex the field, 
 the more valuable is this practice. This method of veri- 
 fication goes back to the Greeks, who made much use 
 of it when they realized how uncertainly terms are em- 
 ployed by the majority of men. Socrates crystallized 
 this procedure and it has consequently been called ' So- 
 cratic induction ' and c Socratic dialectic ' according as 
 stress is laid upon the running over of examples or 
 
68 THE ESSENTIALS OF LOGIC 
 
 upon the value of free discussion by means of question 
 and answer. Every one should read some one at least 
 of the earlier Socratic dialogues of Plato in which this 
 suggestive method is used as a tool for deepening and 
 defining the meanings of common terms. When this 
 method is skillfully applied, one can see, as it were, 
 meanings grow under one's eyes. Under such condi- 
 tions, the definition becomes a living thing into whose 
 secrets one is admitted. " The truth is — as most read- 
 ers of Plato know, only it is a truth difficult to retain 
 and apply — that what we gain by discussing a defini- 
 tion is often but slightly represented in the superior 
 fitness of the formula that we ultimately adopt ; it con- 
 sists chiefly in the greater clearness and fullness in 
 which the characteristics of the matter to which the 
 formula refers have been brought before the mind in 
 the process of seeking for it. . . . In comparing differ- 
 ent definitions our aim should be far less to decide 
 what we ought to adopt, than to apprehend and duly 
 consider the grounds on which each has commended it- 
 self to reflective minds. We shall generally find that 
 each writer has noted some relation, some resemblance 
 or difference, which others have overlooked ; and we 
 shall gain in completeness, and often in precision, of 
 view by following him in his observations, whether or 
 not we follow him in his conclusions." *■ This method is 
 especially advisable in the social sciences or in the 
 handling of those general topics which arise so fre- 
 quently for discussion. How few of us know exactly 
 what we mean by such terms as 'nature,' 'justice,' 
 
 1 Sidgwick, Political Economy, pp. 52-53 ; quoted from Minto, Logic, 
 Inductive and Deductive, p. 90. 
 
PRINCIPLES OF DEFINITION 69 
 
 4 law,' ; beauty,' etc. ! Familiarity with the word deceives 
 us into the belief that we understand the concept of 
 which it is the sign. 
 
 Rules of Definition. The following rules of defini- 
 tion should put the student on guard against bad defi- 
 nitions and should give him some assistance in his 
 attempts to formulate good definitions. All the techni- 
 cal terms needed have already been given in the chap- 
 ter on " Division and Classification." 
 
 1. A good definition is by proximate genus and 
 essential difference. We should try to find a larger 
 class with which to connect the thing defined and then 
 analyze and state the features of the thing defined 
 which distinguish it from the other members of this 
 larger class. By relating it to this larger class, we in a 
 measure explain it, for we connect it with something 
 more familiar. We are then in a position to pass down to 
 important differences. This rule of definition brings out 
 its intimate connection with classification and division. 
 
 When the difference offered is not essential or is 
 vaguely conceived, we have an imperfect definition. Many 
 imperfect definitions are suggestive because they reveal 
 the fact that the topic concerned has not yet been 
 clearly analyzed and classified. 
 
 2. A term shoidd not be defined by means of itself 
 or of words which are synonymous with it. We should 
 avoid tautology. Dictionaries transgress against this 
 obvious rule only too frequently. It is hardly enlight- 
 ening to be told that life is a ' vital force,' or that pleas- 
 ure is ' agreeable sensation,' or that altruistically is ' in 
 an altruistic manner.' 1 More serious cases of defining 
 
 1 For other examples see Davidson, The Logic of Definition, p. 62. 
 
70 THE ESSENTIALS OF LOGIC 
 
 a thing by itself are the following : ' Life is that which 
 distinguishes living from non-living things,' * A cause 
 is the invariable and unconditional antecedent of a 
 phenomenon.' Relative terms are often defined in terms 
 of each other. The consequence is that we go from one 
 to the other and then back again and are not greatly 
 advanced by the process. 
 
 3. A definition should be neither too broad nor too 
 narrow. It should not cover a larger field than usage 
 warrants nor a narrower field. Thus, to define a square 
 4 as a rectangle,' or a root as i that part of a plant which 
 grows underground,' would be cases of overbroad defi- 
 nitions ; while to define a dog 4 as a domesticated ani- 
 mal used to guard the home ' would obviously be too 
 narrow. This rule is really only a development of the 
 first rule, for, had the genus and essential difference 
 been worked out, the resultant definition would have 
 been neither too broad nor too narrow. 
 
 4. A definition should not be expressed in obscure 
 or figurative language. The purpose of a definition 
 should be kept clearly in mind. Where the field is 
 necessarily technical, the use of technical terms is in- 
 evitable, and these must not be considered obscure 
 however little they are understood by the layman. " The 
 scientific definition of life as the dynamic condition of 
 an organism would not be that of the plain man. The 
 plain man thinks he knows what ivy is, and is not 
 much wiser for being told that it is an epiphytic plant 
 of the genus hedera. But he, too, may learn something 
 from the definition of sickness as Nature's protest 
 against the misdirection of her forces, or from St. Aus- 
 tin's phrase, ' virtus est ordo amoris ' — the orderly and 
 
PRINCIPLES OF DEFINITION 71 
 
 progressive unfolding of love." 1 In this connection, Dr. 
 Johnson's famous definition of network, as " anything 
 reticulated or decussated at equal distances with inter- 
 stices between the intersections," is usually given as a 
 horrible example of misapplied learning. 
 
 5. A definition should be expressed in positive terms 
 whenever possible. A definition should tell what a 
 thing is, rather than what it is not. But ultimate con- 
 ceptions can often be suggested and indicated by neg- 
 ative terms. Thus, a geometer may define a point as 
 that which has neither length, breadth, nor thickness. 
 We must, however, stress the meaning of a definition 
 instead of its form. Where the concept defined is, itself, 
 essentially negative, there must be a negative element 
 in the definition. ' Liberty is absence of restraint.' 
 1 Uncertainty is the want of a fixed mental attitude.' 
 4 A bachelor is an unmarried man.' 'Injustice is the 
 not keeping of covenant.' These are all negative in 
 form, but as positive as their contents permit. 
 
 Other Forms of Definition. We have stressed 
 what may be called the ideal form of definition, that 
 through genus and differentia. In the Latin terminol- 
 ogy of logic it is called definition per proximum genus 
 et differentiam vel differentias. It is, as we have con- 
 stantly pointed out, the reflection of a system of clas- 
 sification. When such a basis cannot be appealed to, 
 resort must be had to other methods of making the 
 meaning of a term clear. The methods usually adopted 
 in such cases are as follows : — 
 
 1. Description. Individual things or events can be 
 described in such a way as to make the application of 
 1 Macleane, Reason, Thought, and Language, p. 175. 
 
72 THE ESSENTIALS OF LOGIC 
 
 the term clear. It is possible to select outstanding prop- 
 erties or traits which serve to distinguish one thing 
 from another. Accurate word-painting is an art which 
 can be used to reproduce in the mind of the hearer or 
 reader the essential characteristics of the scene or per- 
 son described. 
 
 2. Examples. If well-selected examples of the term 
 under discussion are given, it is possible to get a pop- 
 ular concept, at least, of the term. What does 4 good f 
 mean ? How natural it is to run over examples of good 
 men ! In doing so, we are trying to pass from the de- 
 notation to connotation, a part of the denotation being 
 less doubtful than the exact marks which make a man 
 good. It depends upon the purpose how far the use of 
 example is satisfactory. If this be practical, examples 
 may meet the need and thus serve as a sort of defini- 
 tion. 
 
 3. Genetic formula. It is frequently important to 
 know how a thing is made. Chemical formulae do not 
 tell us the essential properties of the thing unless they 
 reveal to us a scheme of classification connected with 
 such properties. They are, however, of distinct utility. 
 Recipes, diagrams, instructions are practical definitions 
 of a genetic kind. 
 
 The need lying back of definition is to understand 
 the application of a term. Whatever meets this need 
 is, in the broadest sense of that term, a definition. 
 Hence the logician must not be dogmatic and set up 
 only one type of definition. Purpose and setting must 
 be taken into account. " In defining we look to what 
 appears to be, for our immediate purpose, some striking 
 feature. We try to define everything by something 
 
PRINCIPLES OF DEFINITION 73 
 
 better known. A fox would not be defined in the same 
 way by a huntsman and by a naturalist. Death, which 
 to the physician is the cessation of all vital functions, 
 is to the singer of Hawthornden i the thaw of all those 
 vanities which the frost of life holdeth together.' "* 
 
 The Predicables. Logic is a very old science and 
 has accumulated traditions and technical names. It is 
 hardly justifiable to neglect these inherited distinctions, 
 yet they must not be allowed to occupy too much space. 
 Typical of this logical tradition are the 6 Five Predi- 
 cables.' A predicable is literally that which can be 
 predicated. Now, only that which is a general term can 
 be predicated of a subject. I can say that this object 
 is a cat, but I can't assert of any other object that it 
 is this particular object which I have just called a cat. 
 In other words, I can't predicate an individual thing of 
 another thing. What I can predicate is some attribute 
 of the thing. But attributes are of two kinds, defining 
 and not-defining. The result is that I discover the fol- 
 lowing division of attributes : — 
 
 Attributes 
 
 defining not-defining 
 
 r r 1 1 
 
 generic specific proprium accident 
 
 (differentia) 
 
 These are the Five Heads of Predicables. In relation 
 to the subject, the attributes found in the predicate may 
 be generic, specific, differential, a constant property, 
 and an accident. It is evident that these terms reflect 
 classification and division, and this fact brings out once 
 1 Macleane, Beason, Thought, and Language, p. 174. 
 
74 THE ESSENTIALS OF LOGIC 
 
 more the intimate relation between the ideal form of 
 definition and these processes. 
 
 The generic attributes give the connotation of the 
 genus, while the specific attributes are those which are 
 common to the species. It will be remembered that the 
 differentia is that attribute, or attributes, which distin- 
 guishes one species from its coordinate species. But 
 an object may possess, besides, some property not es- 
 sential enough to be used as a differentia yet always 
 present. When this property is deducible from the de- 
 fining attribute it is called a 'proprium.' Attributes 
 which sometimes belong to a class of objects and are 
 sometimes absent are called 4 accidents.' It is an acci- 
 dent that a university is located in one city rather than 
 in another; that is, it is no part of the nature of the 
 university to have this particular location. It is an ac- 
 cident of a thief to be in prison and of a politician to 
 be honest. It should be borne in mind, however, that 
 the term is here used in connection with classification 
 and division. In another sense of the word 6 accident,' 
 it may well be that nothing is an accident ; this means 
 that every feature of an individual thing has a cause. 
 
 The Importance of Definition. From its very be- 
 ginning, logic has stressed the importance of definition. 
 It is impossible to think clearly and to avoid ambigui- 
 ties without definite ideas and properly applied words. 
 The very familiarity of words may lead us to suppose 
 that we understand their use, and encourage us in the 
 mere manipulation of verbal counters to the neglect of 
 concepts. Verbal definition is important, but we must 
 never forget that it rests upon ordered knowledge. Or- 
 dered knowledge is, however, only another name for 
 
PRINCIPLES OF DEFINITION 75 
 
 real definition. When we once realize this fact, we im- 
 mediately become aware of the importance of definition, 
 both as a process and as a result, and of the value to 
 the individual of those mental habits of analyzing and 
 distinguishing which give structure and clearness of 
 outline to his accumulated knowledge. Definition is to 
 the mind what discipline is to an army. Without dis- 
 cipline, an army is like a mob ; it lacks both unity and 
 the means which make unity effective. Without defini- 
 tion, the mind lacks differentiation and distinctness in 
 its contents. 
 
 EEFERENCES 
 
 Creighton, An Introductory Logic, chap. V. 
 Davidson, The Logic of Definition, chap. in. 
 Hibben, Logic, Deductive and Inductive, chap. v. 
 Jones, Logic, Inductive and Deductive, chap. iv. 
 Macleane, Reason, Thought, and Language, chap. xi. 
 Schiller, Formal Logic, chap. vi. 
 
CHAPTER VII 
 
 ASSERTIONS AND PROPOSITIONS 
 
 An Important Distinction. As logic has grown 
 less formal and has been more influenced by psychology, 
 it has more and more recognized the necessity of draw- 
 ing a distinction between assertions and propositions. 
 An assertion is a living judgment which expresses the 
 conclusion reached by an individual as a result of his 
 thinking. ' True patriotism stands for ideals,' and, 6 1 
 must take more exercise,' are for me genuine assertions 
 which I understand. But when I glance at a list of ex- 
 ercises in a logic-text and come across the sentence, ' It 
 is hot,' I am not absolutely certain what ' it ' refers to. 
 I tend to assume that the weather is referred to, but 
 the writer may possibly have had a stove or a cup of 
 tea in mind. Such isolated sentences need interpreta- 
 tion. The reader must make a judgment out of them 
 by his own mental activity. And, as we all know, we 
 are sometimes mistaken even when the context is quite 
 complete. In contrast to personal, living assertions, 
 then, propositions are sentences, or verbal complexes, 
 which are supposed to symbolize such assertions ; they 
 are bodies into which some mind must breathe the 
 breath of life. Propositions can exist on paper, while 
 assertions can live only in the mind. 
 
 Under ideal conditions, the propositions put forward 
 in actual cases of argumentation may be correct substi- 
 tutes for assertions quite capable of conveying to other 
 
ASSERTIONS AND PROPOSITIONS 77 
 
 minds the exact shade of meaning intended, but such 
 is not always the case. Before this transference of 
 meaning from one mind to another is possible, there 
 must be painstaking effort on the part of the listeners 
 to comprehend those who are speaking. How often a 
 statement is misunderstood, or, as we are apt to say, 
 twisted and distorted ! The whole context, or universe 
 of discourse, must be appreciated before a statement is 
 given its correct setting. Such a context is present in 
 any actual judgment, but it cannot be attached directly 
 to the proposition. A sentence, spoken or written, can- 
 not contain very much. Take the famous line in Shake- 
 speare's Henry VI: " The Duke yet lives that Henry 
 shall depose" ; it is obvious that the ambiguity rests in 
 our inability to get to the real assertion, assuming that 
 there was one. 
 
 When conditions are very favorable, the distinction 
 between assertions and propositions can be allowed to 
 drop into the background. We suppose that we can 
 pass from one to the other with ease. But when propo- 
 sitions are given piecemeal and apart from their con- 
 text, it is often impossible to interpret them in any 
 final sense. Under such conditions we are forced to pay 
 attention to certain general aspects which should be 
 clear. We change propositions into assertions as com- 
 pletely as possible, and then proceed to analyze them. 
 But it is always well to bear in mind this important 
 distinction. 
 
 Critical vs. Uncritical Assertion. Some mental 
 processes are relatively unconscious, while others de- 
 mand attention for their very being. We often act and 
 speak habitually and imitatively. We do what we have 
 
78 THE ESSENTIALS OF LOGIC 
 
 been accustomed to do and to see others do, and we say- 
 things which come into our heads or which we have 
 heard other people say. The ideal of logic is to make 
 individuals critical, and this aim is furthered by the 
 knowledge it gains of mental processes and of scientific 
 methods. But when logic became very formal and gave 
 almost its entire attention to propositions taken sepa- 
 rately, it became too mechanical to help the individual 
 in his concrete thinking. What we shall try to do, then, 
 is to explain these older analyses of propositions and 
 give them a more vital setting. 
 
 Critical thinking seeks to determine the facts and 
 principles of the case, to test both, and then to see 
 whether the conclusion drawn is justified. It takes as 
 little for granted as possible. It brings all the facts 
 and principles into the open. This mental effort criti- 
 cally to interpret a case of reasoning which appears 
 doubtful, leads to the marshaling of all our resources, 
 to the bringing-out of all the facts and rules which 
 bear upon the problem, to the analysis of likenesses and 
 differences with other cases, to the more patient wait- 
 ing for suggestive ideas. The result is usually a more 
 adequate solution of the problem with a broader under- 
 standing of its meaning. Let me give an instance of 
 critical versus uncritical thinking. A student comes to 
 me and asks whether logic is a practical subject. I 
 know pretty well by past experience what he means by 
 the term ' practical.' But I ask him and he replies, ' Is 
 it of use in everyday life ? ' Obviously, by everyday 
 life he means business life. Will logic help him to suc- 
 ceed in his profession? It thus becomes a question of 
 the qualifications of a successful business man. I may 
 
ASSERTIONS AND PROPOSITIONS 79 
 
 deny that his ideal of. success is a wise and adequate 
 one, or I may try to show him that whatever makes 
 his thinking more accurate and critical has a tendency 
 to make him better qualified for business. The student 
 has made certain assumptions as shown by the very 
 words that he uses ; in fact, he has revealed an outlook 
 upon life. 
 
 What is an Assertion ? We may define an asser- 
 tion as a mental act and content arising out of and 
 concluding a process of interpretation. Such an asser- 
 tion is a judgment, a conclusion, a decision. Interpre- 
 tations, generalizations, theories, inferences, beliefs, 
 views, decisions are present from the early days of a 
 child's life, and represent the growing, synthetic side 
 of its mind. The growth of the mind, this putting two 
 and two together, this recognizing and analyzing and 
 comparing, is not a mechanical process. It is remark- 
 able how soon the child notices things and seeks to in- 
 terpret them. A little girl somewhat less than three 
 years old was looking at her teddy-bear and noted for 
 the first time the brown, hairless soles of its feet. The 
 color struck her attention and she said, " That 's blood." 
 Her brother, aged four, gave his judgment. " No, baby, 
 that's where the whiskers have come off." Baby re- 
 plied, " We must buy some at the store and put them 
 back on." 
 
 Of much of this continuous interpretation we are 
 not reflectively aware. It does not stand out so clearly 
 in consciousness that we remember it and can recall 
 the various steps. The individual's field of experience 
 seems to him always to have been much the same as it is 
 now. Out there is the realm of physical things open to 
 
80 THE ESSENTIALS OF LOGIC 
 
 inspection ; and these things fall into kinds which are 
 usually easily recognizable. In contrast to this common 
 world of physical things is the more personal domain 
 of the self with its feelings, valuations, and purposes ; 
 and there is, finally, the social realm of other minds. 
 In other words, the mind of each individual is full of 
 implicit assertions which cannot be accounted for apart 
 from pretty constant mental activity. Interpretation is 
 going on all the time and finds expression in judg- 
 ments. These judgments are assertions which deal with 
 these recognized realms. When I say, 4 That 's Smith,' 
 I mean that the person I see at a certain distance from 
 me goes by the name of Smith. When I say, ' Nitrates 
 are necessary for the soil in agriculture,' I take the 
 physical world for granted and make an assertion about 
 certain relations between it and plants. Thus we are 
 interested in, and pass judgments about, the world in 
 which we live. 
 
 Levels of Judgment. We have taken the term 
 « Judgment ' in a broad sense as standing for both the 
 process and the act of interpretation. Very often, the 
 mental steps just previous to the assertion do not rise 
 to the surface of consciousness, We feel certain that 
 the person over yonder is Jones, but we don't just know 
 why. He gives us the general impression of Jones. 
 Only when doubt is cast upon our interpretation of 
 our perception do we look more closely and analyze 
 this feature and that which are connected in our mind 
 with Jones. Perceptual judgments, or judgments bound 
 up very closely with what we are perceiving, are of this 
 almost intuitive character. 
 
 The more of a problem there is, the more reflective 
 
ASSERTIONS AND PROPOSITIONS 81 
 
 is judgment. The process of reaching a conclusion now 
 takes time, and we are aware of various suggestions and 
 steps. We try to find exactly what is given and where 
 the difficulty lies, and then ransack our experience to 
 find a satisfactory solution. Such a mental process is 
 called ' reasoning ' and may take a long time ; but when 
 a solution is found, it appears as a judgment. 
 
 It is customary for logicians to classify judgments 
 as 'dominantly perceptual' or as 4 dominantly con- 
 ceptual.' All judgments involve concepts, however, and 
 there is no sharp break between the judgments of per- 
 ception and the abstract judgments of history and of 
 science. A huge body of facts must be collected, an- 
 alyzed, compared, and organized before such abstract 
 judgments are possible. In the latter half of the book 
 we shall have much to say of these progressive steps 
 which raise us to such abstract judgments as ' The plan- 
 ets travel in elliptical paths, 5 and 4 Democracy is still in 
 process of development.' 
 
 Concepts and Judgment- Judgments always con- 
 tain concepts, or meanings. It was this fact that led 
 many of the older logicians to think of judgments as 
 formed from the union of two concepts. That is now 
 seen to be too mechanical an idea. The content of a 
 judgment is complex, but it is also unitary; it makes 
 up one assertion. 
 
 The relation between concepts and judgment is a 
 vital one and can be understood only when approached 
 in a genetic way. Concepts are the material of judg- 
 ment and are at the same time products of judgment. 
 To ask which is prior in any absolute way is like ask- 
 ing the old puzzle, Which came first, the hen or the 
 
82 THE ESSENTIALS OF LOGIC 
 
 egg ? Judgments grow out of conceptual material, but 
 this conceptual material is itself the deposit of other 
 judgments. Again, this conceptual material is modi- 
 fied by judging as a process and exists in an unique way 
 in any really new judgment. An example may make 
 this clearer. 
 
 Take a person who is visiting an aquarium for the 
 first time. Undoubtedly, he has some idea of many of 
 the kinds of fish which are on exhibit, but his ideas are 
 usually somewhat vague and unsettled. When he comes 
 before the tank in which is, for instance, the devil-fish 
 or ray, he makes the identification, and, in so doing, 
 modifies his concept. It is no longer the hazy concept 
 it once was. Again, take the student who comes to col- 
 lege. He has a general idea of what a college is for. 
 But, as he progresses from the freshman to the senior 
 year, he is compelled, by the very pressure of his com- 
 plex experience, to pass judgments in which this gen- 
 eral ideal is modified, deepened, and enlarged. Judg- 
 ment is, in fact, the individual's system of concepts in 
 process of adjustment and enlargement. Concepts drop 
 into the background so far as consciousness is con- 
 cerned and become potential or implicit when they are 
 not the living parts of a judgment. 
 
 Judgment defined. There are many definitions of 
 judgment, varying slightly in their form or their em- 
 phases from one another. Two aspects of every judg- 
 ment stand out clearly. There is, first, the complex 
 content which is held before the mind, and, second, the 
 attitude of belief or acceptance taken toward it. Let 
 us look a little more closely at these two aspects. 
 
 Every judgment involves a complex content. What 
 
ASSERTIONS AND PROPOSITIONS 83 
 
 the content is depends upon the location of the problem 
 which gives rise to it. It may be dominantly perceptual 
 with just a touch of conception at the point which 
 needed interpretation, as when I step outdoors of a 
 morning and exclaim, ' It 's a fine day after all ' ; or it 
 may be almost equally perceptual and conceptual, as 
 when I classify a plant which I run across in my stroll 
 through the woods ; or it may be entirely conceptual, as 
 in the statement of some law of nature. In every case, 
 however, the total content which I hold before my 
 mind is complex, the nature of the complexity varying 
 with the field involved and the nature of the problem 
 to which the judgment is an answer. Sometimes we 
 are interested in the qualities of things, sometimes in 
 classes and their relations to one another, sometimes in 
 comparisons, sometimes in personages and events. The 
 character of the content determines the type of judg- 
 ment with which we have to deal. 
 
 Again, every judgment involves a mental attitude 
 which is that of belief or assertion. As a rule, the 
 psychologist prefers the term ' belief,' while the logician 
 speaks of 4 assertion.' The content is believed or asserted 
 to hold of the realm which is under discussion. When 
 we use the term • belief,' we keep a more personal 
 reference. ' It is my belief, or my judgment, that Napo- 
 leon was a worn-out man by the time of the Russian 
 campaign.' Here a complex idea concerning itself with 
 European history of somewhat over a century ago is 
 accepted as true. I feel constrained by the pressure of 
 the facts to think of Napoleon in this way. This mental 
 constraint which arises out of the facts, says the logi- 
 cian, leads me to make the assertion, 'Napoleon was a 
 
84 THE ESSENTIALS OF LOGIC 
 
 worn-out man,' etc. Napoleon and the Europe of his 
 day are objects before my mind's eye, and I determine 
 to think of one feature, which has been open to ques- 
 tion, in this way rather than in that. The rest of my 
 knowledge furnishes the setting for this once moot 
 point which I now take to be settled. 
 
 A judgment is, then, a complex mental content which 
 is asserted or toward which we take the attitude of 
 belief. Such an assertion must be either true or false. 
 It is this concern with truth or falsity which is distinc- 
 tive of a judgment. In language, this characteristic 
 finds expression in the indicative mood in contrast to 
 commands, wishes, and questions. The reason for this 
 difference rests ultimately in the fact that knowledge 
 is claimed or assumed in the one form, while not in 
 the others. When I ask a question, I request some one 
 else to make an assertion, but do not myself make one. 
 When I issue a command, I am concerned with an 
 action which I am trying to bring about. In neither 
 case am I expressing a belief. 
 
 All Knowledge Judgmental. We have stressed 
 the fact that live judgments spring from problems. But 
 such problems must always be local or concern points of 
 doubt within a larger field about which there is, for the 
 time being, no question. This larger field which fur- 
 nishes the setting of the new judgment is itself, how- 
 ever, the product of the continuously accumulating 
 judgments of the mind and the content of the new 
 judgment is knit to it like new cells in a growing or- 
 ganism to the old. It is strictly true to say that all our 
 knowledge has been, at one time or other, a part of the 
 content of a judgment and that it is more or less im- 
 
ASSERTIONS AND PROPOSITIONS 85 
 
 plied as a foundation for the new judgment. For this 
 reason it must be ready to defend itself and to pass 
 from a potential, or passive condition, to the center of 
 the mental stage. Each of us possesses a system of con- 
 cepts which has been the growth of years of guided 
 and unguided mental effort. This system controls our 
 thinking and is in turn controlled by it. Only a small 
 part of it can appear overtly in the field of attention at 
 any one time, but we have good reason to believe that 
 all of it is there in a more or less effective way. 
 
 It is this implication of a larger setting for any new 
 judgment, a setting which is usually more implicit than 
 explicit, that the philosophical logician always stresses. 
 And it is well to remember that logic is, after all, a 
 philosophical discipline. I make no apology, therefore, 
 for the introduction of the following quotation from 
 Bosanquet : " We may then sum up so far : our knowl- 
 edge, or our world in knowledge, exists for us as a 
 judgment, that is, as an affirmation in which our present 
 perception is amplified by an ideal interpretation which 
 is identified with it. This interpretation or enlargement 
 claims necessity or universality, and is therefore objec- 
 tive as our world, i.e., is what we are obliged to think, 
 and what we are all obliged to think. The whole system 
 in process of construction, viz., our present perception 
 as extended by interpretation, is what we mean by 
 reality, only with a reservation in favour of forms of 
 experience which are not intellectual at all. Every judg- 
 ment then affirms something to be real, and therefore 
 affirms reality to be defined, in part, by that something. 
 Knowledge exists in the form of affirmations about 
 reality. And our world as existing for us in the medium 
 
86 THE ESSENTIALS OF LOGIC 
 
 of knowledge consists, for us, of a standing affirmation 
 about reality," l 
 
 It is for theory of knowledge to decide tlie character 
 of knowledge and its relation to reality, while it is the 
 function of metaphysics to determine the nature of 
 reality. Logic takes both knowledge and reality for 
 granted, and investigates the empirical question of how 
 knowledge is actually built up and sustained by human 
 minds. The conclusion which is forced upon us is that 
 all knowledge is judgmental and is that which we are 
 constrained to think by the pressure of our experience. 
 
 The Part played by Language. The actual oper- 
 ation of judging is often hard to recover. The modern 
 logician, working hand in hand with the psychologist, 
 is more and more convinced that this operation is not 
 truly reflected in the verbal form which is called the 
 proposition. So far as consciousness goes, the mental 
 operation is usually simpler than the verbal form. 
 Language is more analytic and detailed than the think- 
 ing of any one moment. There are two reasons for 
 this. Language is used for communication and re- 
 flects all the distinctions painstakingly made in the 
 past. The other reason lies deeper, language is a 
 mechanism and, while instrumental to thought, is not 
 identical with it. This disunion came out clearly in 
 several of the preceding chapters, especially in the 
 chapters entitled " Ambiguity and Language " and 
 "Principles of Definition." It would be impossible 
 for any mechanism to equal the fluidity and organic 
 unity of thought. We must not take the skeleton for 
 the living animal. Consciousness is a qualitative com- 
 1 The Essentials of Logic, p. 32. 
 
ASSERTIONS AND PROPOSITIONS 87 
 
 plex in which purpose, context, perception, and the 
 whole apperceptive background of accumulated ex- 
 perience somehow coexist in a forward movement of 
 interpretation. Language, on the other hand, is spread 
 out in space and time, and necessarily adapts itself to 
 this process of extension. The purpose of language is 
 not to reflect the actual genesis of a thought, but to 
 express the result in a comprehensible way. An argu- 
 ment should be capable of explicit formulation in such 
 a way as to give the conclusion in relation to its 
 grounds. So far as logic is a science of proof, it deals 
 with the overt and not with the hidden ; and the overt 
 must find expression in language. 
 
 The Logical Treatment of Propositions. Mod- 
 ern logic tries to be as concrete and flexible as possible. 
 It insists upon a study of the context to determine the 
 point of view of the person who enunciated a given 
 proposition. But within such a setting, or, as it is 
 called, universe of discourse, a proposition or group of 
 propositions is a bit of supposed knowledge which has 
 to stand by itself as does a work of art which has once 
 left the atelier of the master for the gallery. The 
 proposition, as treated by the logician, is an instrument 
 of analysis much as a sensation is for the modern psy- 
 chologist. The student must be warned that the tradi- 
 tional analysis of the proposition to which we now pass 
 is dominated by the mechanism of the syllogism and 
 the idea of class relations which finds expression therein. 
 For this reason, the ' logical form ' of propositions is 
 often a procrustean bed for propositions which do not 
 naturally express class relations. The art side of logic 
 will come to the fore in the next few chapters. 
 
88 THE ESSENTIALS OF LOGIC 
 
 REFERENCES 
 
 Bosanquet, The Essentials of Logic, Lecture rv. 
 Dewey, How We Think, part n, chap. Vin. 
 James, Principles of Psychology, vol. n, chap. xxi. 
 Minto, Logic, Inductive and Deductive, part I, chap. II. 
 Schiller, Formal Logic, chap. Vin. 
 
CHAPTER VIII 
 
 THE LOGIC OF PROPOSITIONS 
 
 A General Division of Propositions. Proposi- 
 tions are divided into ' categorical,' 4 hypothetical,' and 
 4 disjunctive.' A proposition is said to be categori- 
 cal when it makes a direct assertion. In it a predicate 
 is denied or affirmed of a subject. 6 The Romans were 
 a strong race,' and ' Dead men don't bite,' are examples. 
 A hypothetical proposition combines a condition with 
 a consequent. If the condition is fulfilled, the conse- 
 quent is held to be true. ' If the great war continues, 
 the nations will be near bankruptcy,' and ' If there is 
 an early frost, the peach crop will be spoiled,' are cases 
 in point. A disjunctive proposition asserts that one of 
 two or more alternatives is true. ' Man is either mortal 
 or immortal,' and ; This rock is either marble or 
 quartz,' are disjunctive in character. 
 
 The categorical type of proposition with its direct 
 assertion is the simplest of the three forms and is 
 always examined in logic before the others. It is the 
 basis of the categorical syllogism. We shall take up 
 the other types for discussion afterwards. 
 
 The Quality and Quantity of Propositions. Cate- 
 gorical propositions are classified according to quantity 
 and quality. As regards quantity, they are either sin- 
 gular, or particular, or universal. The quantity of a 
 proposition is an aspect of the subject term. If the 
 subject denotes only one individual, the proposition is 
 
90 THE ESSENTIALS OF LOGIC 
 
 said to be singular] if it denotes all the members of a 
 class, universal ; if only some members of the class are 
 denoted, particular. ' Abraham Lincoln was a sagacious 
 statesman ' is a singular proposition because the subject 
 term denotes only one individual. ' Some vines bear 
 edible fruit ' is a particular proposition because the 
 subject term covers only a part of the class. The word 
 'some,' or an equivalent, is the sign of a particular 
 proposition. 'All citizens are entitled to a vote' is a 
 universal proposition. Its sign is 6 all ' or « no ' Q none '), 
 or an equivalent. 
 
 The quantity of a proposition is not always definitely 
 indicated by the appropriate logical sign. When this 
 is the case, the proposition is called 4 indefinite ' or 
 4 preindesignate.' The first task of the logician is to 
 determine the quantity of such an assertion, for a 
 really indefinite proposition is ambiguous and can have 
 no place in an argument until its ambiguity is removed. 
 Since the mechanism of the syllogism stresses quantity, 
 it is absolutely necessary to classify an assertion before 
 it can be used as a premise. The following examples 
 will show how frequently propositions are left with 
 their quantity implicit and even uncertain : — 
 
 * Uneasy lies the head that wears a crown/ 
 ' Every single day has its blessing.' 
 
 * All flesh is not the same flesh.' 
 
 ' The race is not always to the swift.' 
 'Haste makes waste.' 
 
 * A man 'c a man for all that.' 
 
 It is necessary to penetrate beneath the verbal form 
 to the meaning and decide the denotation of the sub- 
 ject term. 
 
THE LOGIC OF PROPOSITIONS 91 
 
 Quality, when applied to propositions, is a term 
 which refers to their character as affirmative or 
 negative. An affirmative proposition asserts a predi- 
 cate of a subject, while a negative denies it. The 
 distinction is too familiar and ultimate to require elu- 
 cidation. There are, however, certain dangers in inter- 
 pretation which must be guarded against. The mere 
 presence of a negative word in a proposition does not 
 necessarily make it negative in quality. Such a word 
 may be a part of either the subject or the predicate 
 term. Only when the negative element involves the 
 assertion of a relation of exclusion between the com- 
 ponent terms is the quality negative. Take the prop- 
 osition, 6 Those who do not use their opportunities are 
 unwise.' This is affirmative in quality because a posi- 
 tive relation between the two terms is asserted. Whether 
 the subject or the predicate is positive or negative does 
 not affect the quality of the proposition. 
 
 Symbolic Classification of Propositions. For 
 the sake of easy handling, logic has classified all cate- 
 gorical propositions into four kinds according to their 
 quantity and quality. This treatment has the syllogism 
 for its end in view. While it is artificial and one-sided, 
 it is convenient and often leads to a better understand- 
 ing of the import of the propositions. These four kinds 
 are, ' universal affirmative,' ' universal negative,' ' par- 
 ticular affirmative,' and ' particular negative.' To sym- 
 bolize these the vowels A, E, I, and O are used. A 
 and /stand for the universal and particular affirma- 
 tive respectively, and are taken from the Latin affirmo ; 
 E and O stand for the universal and particular nega- 
 tive, and are taken from nego. It should be noted 
 
92 THE ESSENTIALS OF LOGIC 
 
 that the singular proposition is considered a universal. 
 It can be treated as such in the syllogism. Taking S 
 and P for the subject term and predicate term re- 
 spectively, we have the following classification : — 
 
 < Affirmative : All S is P. A 
 
 Universal < XT , . XT . n ™ 
 
 ( Negative : is o S is P. E 
 
 . r Affirmative : Some Sis P. I 
 
 \ Negative : Some S is not P. 
 
 Reduction of Propositions to Logical Form. 
 
 The reduction of the varied statements of ordinary life 
 to a form corresponding to this symbolism is a practi- 
 cal exercise which has some value. How much it is 
 very hard to tell. " The indirect use is to familiarize us 
 with what the forms of common speech imply, and thus 
 strengthen the intellect for interpreting the condensed 
 and elliptical expression in which common speech 
 abounds." 2 Such an interpretation is often difficult. 
 For instance, it is not always easy to decide whether a 
 sentence is particular or universal, affirmative or nega- 
 tive. Take such sentences as the following and decide 
 into which of the four kinds they fall : — 
 
 ' A flower is a beautiful object.' 
 
 * Few were saved.' 
 
 * Women are jealous.' 
 
 ' Only ignorant persons bold sucb opinions.' 
 
 The reduction of statements to logical form meets 
 with three classes of difficulties. The statement may be 
 ambiguous because of the grammatical order of its parts 
 or because of the character of certain of its terms ; or 
 it may contain a reference to time. Let us look at these 
 three classes in some detail. 
 
 1 Minto, Logic, Inductive and Deductive, p. 69. 
 
THE LOGIC OF PROPOSITIONS 93 
 
 The order of subject and predicate may be inverted. 
 * Wide is man's mind ' is an example of such inversion. 
 The problem is so simple that there is no need to dwell 
 on it. Again, a clause may be separated from the word 
 it modifies ; for example, 6 He jests at scars who never 
 felt a wound.' In such cases the only rule is to pene- 
 trate to the exact meaning. Lastly, some compound 
 sentences really contain more than one proposition. 
 
 In the second class come partitive, exclusive, and 
 exceptive propositions. A partitive proposition is one 
 which makes a statement about one part of a class and 
 implies another statement about the rest. There is, then, 
 a sort of double meaning. Such words as ' all . . . not,' 
 4 some,' * a few,' etc., involve this ambiguity and double 
 significance. ' All these children are not of school age ' 
 means that some are not, and, probably, that some are. 
 Accent plays some part here. l Few are chosen ' means 
 that most are not chosen. 
 
 An exclusive proposition is one which is introduced 
 by such words as 4 only,' ' none but,' c alone,' and the 
 like. 'None but ticket-holders are admitted' is a typi- 
 cal exclusive proposition. This means that all those who 
 are not ticket-holders are not admitted. Thus the ref- 
 erence is to those who do not belong to the privileged 
 class. As so interpreted, it is an E proposition. But it 
 may also be treated as an A proposition by interchanging 
 subject and predicate : 4 All who are admitted are ticket- 
 holders.' The old predicate lies within the subject-class. 
 An exceptive proposition is one which makes a state- 
 ment of all the members except certain designated ones. 
 Such sentences are introduced by such expressions as 
 * all but,' ; all except,' etc. ' All but the very poor enjoy 
 
94 THE ESSENTIALS OF LOGIC 
 
 liberty ' is an example. Two statements are usually in- 
 volved : ' All who are not very poor enjoy liberty,' and 
 4 All who are very poor do not enjoy liberty.' The first 
 of these is more certainly implied than the second. It 
 is therefore best to restate the proposition dropping out 
 the exceptive particle. 
 
 The third class of difficulties is technical in character. 
 The logical form, * 8 is i 3 ,' is the statement of a rela- 
 tion between classes and does not express either time or 
 modality. The customary way is to throw this verbal 
 element into the predicate. Thus, 4 The soldiers had 
 retreated ' becomes ' The soldiers are in the class of 
 those who had retreated,' and 4 It may rain ' becomes 
 i Earning is an event which may occur.' When we are 
 trying to bring out class relationships, we must not be 
 affrighted by the clumsiness of the result. 
 
 The Distribution of Terms. The logical form 
 stresses the denotation of the subject and predicate 
 terms. If, in a proposition, an assertion is made about 
 the entire denotation of a class, the term indicating that 
 class is said to be ' distributed ' ; if it is made of only a 
 part of the class, the term is ' undistributed. 9 The dis- 
 tribution of the terms in the four kinds of categorical 
 propositions has been worked out and is, besides, pretty 
 obvious. The universal affirmative distributes only the 
 subject term. Thus in the sentence, 4 All mammals are 
 vertebrates,' the assertion is made of every mammal, 
 but there is no corresponding reference to the whole 
 class of vertebrates. We have the right to say only that 
 some vertebrates are mammals. The particular affirm- 
 ative distributes neither the subject nor the predicate 
 term. i Some men are loyal' is an /proposition, and 
 
THE LOGIC OF PROPOSITIONS 95 
 
 there is in this no reference to the entire denotation of 
 either class. Turning to negative propositions, we find 
 that an E 'proposition distributes both terms. Both 
 terms are entirely excluded from one another, and this 
 means that there is some knowledge about all the mem- 
 bers of both classes, just enough to validate this exclu- 
 sion. ' No man is perfect ' informs us that not a single 
 man is perfect, and that not a single perfect being is a 
 man. Lastly, an O proposition distributes the predi- 
 cate and does not distribute the subject. i Some men 
 are not honest ' tells us something only about some men, 
 but we must know something about all individuals who 
 are honest in order to know that some men are totally 
 excluded. Examining the distribution of the terms in 
 the four kinds of propositions, we find the following 
 rule : negative propositions distribute their predicates, 
 while affirmative propositions distribute only the sub- 
 ject and this only when the proposition is universal. 
 
 The Graphical Method. The relation between the 
 subject and the predicate, as regards their denotation 
 and the distribution of each term, can be graphically 
 represented for the four kinds of propositions by Euler's 
 method. If each term be represented by a circle, the 
 result is as follows : For A, — 
 #, the subject class, is seen to fall en- 
 tirely within P, the pred- 
 icate class, for the vast 
 majority of cases. (Fig. 
 1.) Only in the case of 
 definitions, in which the two classes co- 
 Flg ' 2, incide, do we find the relation that of 
 
 Fig. 2. The shading shows the distribution. 
 
96 
 
 THE ESSENTIALS OF LOGIC 
 
 For^, 
 
 Fig. 3. 
 
 S falls entirely outside P. Both terms are distributed, 
 For L — 
 
 Fig. 4. 
 
 S and P overlap. Neither term is distributed. 
 For O,— 
 
 ■vFig.5. 
 
 some S is known to be excluded by P. The predicate 
 term is distributed. 
 
 Euler's method is applicable to the syllogism also. 
 Hence it is well to become familiar with this graphical 
 treatment of the denotative aspect of propositions. 
 
 The Purpose of Logical Analysis. This manipu- 
 lation of sentences will undoubtedly strike the reader 
 as artificial. When we say, 6 All men are mortal,' we 
 
THE LOGIC OF PROPOSITIONS 97 
 
 do not mean that men are in the class of mortal beings. 
 We think of the predicate in its connotation rather than 
 in its denotation. But there is a purpose back of this 
 stress upon denotation and class relationships, that of 
 syllogistic analysis and testing. The ; logical form ' is the 
 syllogistic form. When the modern logician is not in- 
 tent upon proof, he tries to understand the exact shade 
 of meaning and the exact character of the relation pres- 
 ent in a proposition. He seeks to classify propositions 
 into natural types corresponding to levels of knowledge 
 and reflection. But as a syllogizer, he is a specialist in- 
 tent upon his method and bending everything to it. He 
 then selects one aspect of propositions and moulds them 
 in such a way as to bring out this aspect most clearly. 
 4 All S is JP' means that 'All S is contained in JFV 
 It is the denotation of related classes that he has in 
 mind. For a few chapters we shall be dominated by this 
 purpose, and the student should bear this fact in mind 
 if he cannot always see the importance of certain rather 
 formal processes. The means secure their value from the 
 end and are as valuable as the end. But it can further 
 be said that the thorough study of the denotative aspect 
 of categorical propositions cannot help but increase our 
 understanding of their reach and meaning. 
 
 REFERENCES 
 
 Creighton, An Introductory Logic, chap. VI. 
 
 Jones, Logic, Inductive and Deductive, chap. V. 
 
 Keynes, Formal Logic, part n, chap. i. 
 
 Minto, Logic, Inductive and Deductive, part I, chap. II. 
 
 Taylor, Elementary Logic, chap. vn. 
 
CHAPTEK IX 
 
 THE IMPLICATIONS OF PROPOSITIONS 
 
 Immediate Inference. Since the proposition is for 
 the logician the unit of knowledge, he wishes to ex- 
 haust its meaning. He studies a proposition with the 
 express purpose of finding out all that it implies. Now, 
 it has been found that we can pass from one proposi- 
 tion to others containing the same two terms or their 
 contradictories. Thus, ' All men are rational ' enables 
 us to say also that c No men are irrational ' and ' No 
 irrational beings are men.' Such a passage from one 
 proposition to others is called 'immediate inference.' 
 The logician has usually been less concerned with the 
 mental processes involved than with the validity and 
 formal mechanism of the step. 
 
 Let us recall the distinction between a judgment and 
 a proposition. A proposition is the verbal expression 
 of a judgment. It is usually more stereotyped than the 
 living judgment and practically always stresses some 
 one aspect of the situation to the exclusion of others. 
 Once a proposition is formulated, however, we can go 
 back over it and analyze it, turn it about and see it 
 from different angles. Thus, when I make the asser- 
 tion, ' This book is on the desk,' I can afterwards note 
 that ' The desk must be under the book.' Such a 
 spatial relation has a double direction. Only one di- 
 rection is brought out in the original proposition, but 
 I realize that the other, also, exists. In like manner, as 
 
THE IMPLICATIONS OF PROPOSITIONS 99 
 
 we shall see, the logical form to which the logician re- 
 duces categorical propositions stresses a relation be- 
 tween terms and the denotation of these terms. The 
 consequence is that other propositions can be seen to 
 follow from any one formulation. 
 
 But because other propositions can be asserted on 
 the basis of a given proposition, it does not follow that 
 these other propositions present themselves without any 
 mental effort on the part of the thinker. Immediate 
 inference is not immediate in the sense that it is intui- 
 tive. The nature of the relations must be clearly grasped 
 before such implications can be quickly drawn. It is 
 for this reason that logical analysis is of value. Only 
 one who has mastered this analysis can answer such 
 questions as those given at the end of the chapter. 
 Why, then, does the logician speak of the development 
 of the implications of propositions as ' immediate infer- 
 ence ' ? Because he has in mind, as a contrast, the draw- 
 ing of a conclusion from the putting together of two 
 other propositions called ' premises.' In other words, 
 the historical contrast is with the syllogism and its dif- 
 ferent mechanism. 
 
 There axe/our headings under which different kinds 
 of immediate inference are brought: 'Opposition/ 
 * Conversion,' ' Ob version,' and 'Contraposition.' We 
 shall now examine these in order and as briefly as is 
 consonant with completeness and clearness. 
 
 The Oppositions of the Four Kinds of Propo- 
 sitions. Propositions are said to be opposed when they 
 have the same terms as subject and predicate, but dif- 
 fer in quantity, or in quality, or in both. Within the 
 setting given by the logic of propositions, we are able 
 
100 
 
 THE ESSENTIALS OF LOGIC 
 
 to note certain relations of inclusion and exclusion 
 which such statements bear to one another. The study 
 of these relations will give us a better idea of the reach 
 of each kind of proposition. It will likewise teach us 
 how to establish each kind and what its denial implies. 
 If the symbols of the four kinds of propositions be 
 placed at the four corners of a square with the uni- 
 versal at the top and the corresponding particulars at 
 the bottom, we shall obtain the so-called ' Square of 
 
 Opposition.' The 
 
 Contraries .El sides and diago- 
 
 nals of this square 
 represent relations 
 between A, E, I, 
 and O. Close in- 
 spection has re- 
 vealed four kinds 
 of relation among 
 them : — 
 
 A and E are 
 called 'contraries/ 
 They differ in qual- 
 ity while the same 
 If we examine them 
 that both may be 
 
 Fig. 6. 
 
 in quantity, both being universal. 
 
 in relation to each other, we find 
 
 false while only one can be true. Thus, 'All swans 
 
 are white' and 'No swans are white' are contraries. 
 
 They cannot both be true, yet they may both be false. 
 
 As a matter of fact, we know that some swans are 
 
 white while others are black. 
 
 A and 0, E and /, are called ' contradictories.' They 
 differ in both quantity and quality. Thus the members 
 
THE IMPLICATIONS OF PROPOSITIONS 101 
 
 of these couples are exact opposites. One must be true 
 and the other false. 4 All politicians are honest ' and 
 4 Some politicians are not honest ' are contradictories. 
 They cannot both be true nor both false. It follows 
 that the assertion of I involves the denial of E, and 
 the denial of A the assertion of 0. 
 
 I and O are called ' subcontraries.' They agree in 
 quantity and differ in quality. Both may be true, but 
 both cannot be false. ' Some men are brave ' and 4 Some 
 men are not brave ' are subcontraries. Our experience 
 tells us that both these propositions are true. When, 
 however, we are able to state a universal, the one sub- 
 contrary is true, while the other, which is the contra- 
 dictory of the universal, is false. 
 
 A and i", E and 0, are called 6 subalterns.' They 
 agree in quality, but differ in quantity. Subalterns are 
 both true when the universal is true. When the con- 
 trary universal is true, both subalterns are false. 6 All 
 men are rational' and 'Some men are rational' are 
 subalterns. 
 
 It is a good exercise, to test the recognition of these 
 interrelations, to start with the truth of any one kind 
 of proposition and determine what follows for the other 
 three. Granted E, I must be false as its contradictory, 
 O must be true as its subaltern, and A must be false 
 as its contrary. If we deny E, we automatically affirm 
 I. It should be noted that common speech talks of 
 contradiction whether we affirm the contrary or the 
 contradictory of a given proposition. It is, however, 
 convenient to have the two terms for these oppositions. 
 Both are opposed to the given proposition, but the con- 
 trary is harder to establish than the contradictory. 
 
102 THE ESSENTIALS OF LOGIC 
 
 Conversion. Conversion is the process of inter- 
 changing subject and predicate while the quality of 
 the proposition remains the same. 4 No man is perfect ' 
 becomes 'No perfect being is a man.' The original 
 proposition is called the 4 convertend ' and the new one 
 the ' converse.' 
 
 We must not forget that in conversion we are deal- 
 ing with propositions which have been reduced to logical 
 form and that the relation stressed is that of the deno- 
 tation of the class terms. This relation is mutual. The 
 situation is analogous to the arithmetical relation of 
 equality between two quantities. If A = B, then B « 
 A. If S is contained in JP, P is to some extent con- 
 tained in S. 
 
 The rule of conversion is that no term may be dis- 
 tributed in the converse which was not distributed in 
 the convertend, The reason for this rule is obvious. A 
 violation of it would involve making an assertion not 
 justified by the denotation given in the original propo- 
 sition. We should be going beyond our data. 
 
 There are two kinds of conversion : (a) simple con- 
 version ; (6) conversion by limitation, or per accidens. 
 Simple conversion is the mere exchange of subject term 
 and predicate term. E and I can be converted simply. 
 Thus, ' No men are unaffected by self-interest ' becomes 
 4 No individuals unaffected by self-interest are men.' 
 Both terms are distributed in the converse, but they 
 were already distributed in the convertend. Hence the 
 rule is not violated. ' Some men are honest ' becomes 
 ' Some honest beings are men.' Both terms are undis- 
 tributed in the first as in the second proposition. A 
 must be converted by limitation. Thus, i All voters are 
 
THE IMPLICATIONS OF PROPOSITIONS 103 
 
 citizens ' becomes ' Some citizens are voters.' In con- 
 verting a universal affirmative, we are forced to pass 
 from A to an L It will be remembered that the predi- 
 cate of an affirmative proposition is undistributed. 
 
 We have pointed out how E, A, and / can be con- 
 verted. There remains O. But O cannot be converted 
 because the result of an attempt would violate the rule. 
 The undistributed subject term would become the predi- 
 cate of a negative proposition and hence automatically 
 claim distribution. The only way to interchange sub- 
 ject and predicate in the case of an O proposition is to 
 obvert first and then convert. This double process is 
 called ' contraposition.' Before we pass to it, we must 
 examine obversion. 
 
 Obversion. Ohversion is the process of changing 
 the quality of a proposition while retaining its mean- 
 ing. We may wish to state an affirmative proposition 
 in its corresponding negative form, or vice versa. When 
 this is the case, we must obvert. Which form is first 
 used depends upon the purpose and psychological setting. 
 But it is often convenient to restate the proposition so 
 as to bring out another emphasis. The mechanism of 
 the syllogism, also, makes it preferable at times to 
 change the quality. v --^ 
 
 The method of obversion is to take the contradictory, 
 or negative, of the predicate and then change the quality 
 of the proposition. Its principle is that the denial of 
 the contradictory of a predicate is the same as the affir- 
 mation of the predicate, and the affirmation of the contra- 
 dictory the same as the denial of the original predicate. 
 No mistake must be made in taking the exact opposite, 
 or contradictory, of the predicate. The contradictory of 
 
104 THE ESSENTIALS OF LOGIC 
 
 a negative predicate gives, of course, a positive term. 
 Let us take, first, the symbolic logical form, ' All /Sis P,' 
 and obvert in order to show the mechanism of the proc- 
 ess. P becomes not-_P, the quality is changed, and the 
 proposition becomes ; No S is not-P.' The proposition 
 i None of the crew were saved' becomes ' All of the crew 
 were individuals who were not saved,' which, rendered 
 into good English, is, 4 All of the crew perished.' 
 
 The following examples may make this discussion of 
 principle and method clearer : — 
 
 A, 'All the people were rescued,' becomes, E, 'None of the 
 people were lost.' 
 
 E, 'No practical men are poets,' becomes, A, 'All practical men 
 are not-poets.' 
 
 /, ' Some vegetables are edible,' becomes, 0, ' Some vegetables 
 are not inedible.' 
 
 0, ' Some houses are not beautiful,' becomes, /, ' Some houses 
 are ugly.' 
 
 The student must be on his guard against two things : 
 misinterpretation of the original proposition, the obver- 
 tend, and the wrong treatment of the 
 predicate. 
 
 The principle of obversion can be 
 represented graphically by means of a 
 circle divided into two compartments. 
 Fig. 7. (See fig. 7). 
 
 " Then any given thing will fall into one or 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 jTis not P."* 
 
 1 Jones, Logic, Inductive and Deductive, p. 122. 
 
THE IMPLICATIONS OF PROPOSITIONS 105 
 
 False Ob version. In valid ob version, the contradic- 
 tory of the predicate is affirmed or denied, as the case 
 may be, of the original subject. We have just noted the 
 theory of such a change of quality. 
 The universe is divided into P and 
 not-P, and to affirm one is the same 
 as to deny the other. This is the so- 
 called 'law of counter-indication.' 
 But this law does not hold of the 
 subject in its relation to the predi- 
 
 Fie* 8 
 
 cate because the predicate is the 
 
 larger term. If all S is P, it does not follow that 
 
 no not-# is JP, as can be seen from the use of Euler's 
 
 circles. 
 
 An example of false obversion may make this situa- 
 tion clearer. Take the proposition, ' All who are con- 
 nected with this affair are honest.' Valid obversion 
 would give, ' None who are connected with this affair 
 are dishonest,' while false obversion would give, ' None 
 who are not connected with this affair are honest.' It 
 is obvious that the last proposition is not the equivalent 
 of the other two. 
 
 Contraposition. Contraposition is a process which 
 combines obversion and conversion. Thus the quality 
 of the proposition is changed and its terms are inter- 
 changed. 4 No voters are aliens ' becomes by obversion, 
 4 All voters are not-aliens (citizens),' and this, by con- 
 version, becomes, 6 Some not-aliens (citizens) are voters.' 
 No new principle is raised by contraposition. The prac- 
 tical difficulty is to keep the first step clearly in mind 
 while passing to the second. Inspection shows that the 
 contrapositive has for its subject the contradictory of 
 
106 THE ESSENTIALS OF LOGIC 
 
 the original predicate, while the quality is changed. 
 This manipulation has value especially for the propo- 
 sition. It will be remembered that an O statement 
 cannot be converted because of the lack of distribution 
 of the subject. By obversion becomes 7, and this can 
 be converted simply. For example, ' Some men are not 
 inventors ' becomes, successively, ' Some men are indi- 
 viduals who are not inventors ' and 6 Some individuals 
 who are not inventors are men.' 
 
 Significance of Immediate Inference. The stu- 
 dent can now better judge for himself the significance 
 of immediate inference. Does he understand more com- 
 pletely the meaning of propositions when he can work 
 out their implications ? The processes are not hard to 
 master and do repay attention. He who has mastered 
 them does not have to guess whether one proposition is 
 or is not equivalent to another. On the technical side, 
 these processes are analogous to mental arithmetic, and, 
 since they are always combined with the problem of 
 reduction to logical form, give valuable discipline. The 
 thinker must be in a position to handle propositions 
 skillfully and correctly if he wishes to analyze and test 
 his conclusions and those of others. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. v. 
 Creighton, An Introductory Logic, chap. VII. 
 Jones, Logic, Inductive and Deductive, chap. VII. 
 Keynes, Formal Logic, chaps, ii, in, and iv. 
 
CHAPTER X 
 
 THE SYLLOGISM AS A MECHANISM 
 
 The Nature of the Syllogism. The syllogism was 
 the discovery of Aristotle, that is, he was the first to 
 work out its theory and its rules. His own definition 
 should therefore serve very well to introduce us to a 
 brief study of its nature. In the Prior Analytics, he 
 offers the following broad one : " Discourse in which 
 certain things being posited, something else than what 
 is posited necessarily follows on their being true." To 
 syllogize is to reason things together and draw a neces- 
 sary conclusion. But when we examine the Aristotelian 
 syllogism more closely and see it in its context, we real- 
 ize that this definition is too broad. There is necessary 
 reasoning which is not syllogistic. What, then, is the 
 differentia? This is to be found in the character of the 
 things posited. A syllogism is a discourse, or argu- 
 ment, in which three propositions are so related that 
 one of them (the conclusion^) follows from the other 
 two. The germ of the invention was the analysis of 
 propositions into terms. The syllogism was conceived 
 by Aristotle as a reasoning together of terms. His 
 prime discovery was that whenever two propositions 
 necessarily contain or imply a conclusion they have a 
 common term, that is, only three terms between them. 1 
 In the last few chapters we have studied propositions 
 separately, analyzing them, working out their implica- 
 
 1 Minto, Logic, Inductive and Deductive, p. 170. 
 
108 THE ESSENTIALS OF LOGIC 
 
 tions, reducing them to logical form. Now we must 
 consider their interdependence. 
 
 A single proposition taken by itself is an assertion 
 which does not give its ground. When it is advanced 
 by a person other than ourselves, we are almost sure 
 to demand why this conclusion is reached rather than 
 another. In other words, we want the assertion con- 
 nected with some generally accepted principle as its 
 consequence before we are inclined to give it assent. 
 This backward movement to more basic propositions is 
 characteristic of the syllogism, and gives us a clue to 
 its purpose : it is an instrument of testing rather than 
 an instrument of discovery. I would not say that it 
 never leads to new conclusions, but it is primarily a 
 method of determining the consistency of propositions 
 already thrown out for acceptance. There has been 
 much misunderstanding on this point both now and in 
 the past. John Locke was protesting against the idea, 
 commonly enough held in his day, that men should do 
 their creative thinking in terms of the syllogism, when 
 he made the oft-quoted gibe, " God has not been so 
 sparing to men, to make them barely two-legged crea- 
 tures, and left it to Aristotle to make them rational." 
 Even to-day there are not wanting psychologists who 
 are at great pains to demonstrate that the syllogism is 
 not an adequate description of how reasoning actually 
 takes place in human minds. But any argument should 
 be capable of being thrown into the syllogistic form or 
 something analogous to it for purposes of testing its 
 validity and assumptions. If the conclusion follows nec- 
 essarily from other propositions, the argument is valid 
 or self -consistent. The conclusion need not, however, be 
 
THE SYLLOGISM AS A MECHANISM 109 
 
 true. Only if the other propositions, from which it is a 
 valid deduction, are true, is it true. 
 
 Thus, the syllogism is an instrument which plays a 
 part within a larger whole, that of experience and re- 
 flection. When we come to study the logic of science, 
 we shall better understand whence the propositions 
 come which appear in the syllogism. The main point to 
 realize now is that the syllogism cannot prove their 
 truth and does not try to ; what it does try to prove, and 
 can prove, is the consistency or inconsistency of their 
 interrelations. 
 
 An Analysis of the Syllogism. Having got a clear 
 idea of the nature ' and work of the syllogism, we can 
 now describe it. It is a very simple bit of mechanism 
 resting on the analysis of propositions into their logical 
 form as assertions or denials of relation between the 
 denotation of classes. This relation to which attention 
 is directed is that of inclusion and exclusion. It will be 
 recalled that an A proposition is symbolized thus : ' All 
 S is contained in P.' Now, Aristotle saw that two 
 terms could be combined in a proposition as a result of 
 their relation to a third term. The following typical 
 syllogism will illustrate this simple underlying idea : — 
 
 All men are mortal; 
 Socrates is a man; 
 Therefore Socrates is mortal. 
 
 The three terms are, ' Socrates,' < mortal,' and 'man.' 
 It is evident that ' Socrates ' and ' mortal,' the two 
 terms brought together in the conclusion, are estab- 
 lished in their relation by means of a third term to 
 which both are related. What is the character of this 
 relation which holds between these terms and makes 
 
110 THE ESSENTIALS OF LOGIC 
 
 them into a system ? It is the relation of inclusion or 
 exclusion, as the case may be, between their denota- 
 tions. Applying Euler's circles to the above syllogism, 
 we have — 
 
 Pig. 9. 
 
 Aristotle's idea comes out clearly enough in the so- 
 called < Dictum de omni et nullo ' (statement concern- 
 ing all and none) which is called the ' Axiom of the 
 Syllogism.' " Whatever is predicated of All or None of 
 a term is predicated of whatever is contained in that 
 term." On the denotative side, this axiom is suffi- 
 ciently expressed as follows : " A part of a part is a part 
 of the whole." Thus, 4 all men ' is a part of i mortals ' 
 and ' Socrates ' is a part of ' all men.' This is as much 
 of an axiom as the corresponding one of geometry. 
 
 The Elements of the Syllogism. We noted that 
 Aristotle thought of the syllogism as a means of estab- 
 lishing a relation, negative or positive, between two 
 terms by reason of their relation to a common third 
 term. This common third term necessarily appears in 
 each of the premises, but does not appear in the con- 
 clusion. The elements of the syllogism are, therefore, 
 three terms and three propositions. The term common 
 to the first two propositions is called the 4 middle term,' 
 and these propositions are the ' premises.' The conclud- 
 
THE SYLLOGISM AS A MECHANISM 111 
 
 ing proposition is the ' conclusion.' The other two terms, 
 which appear in the conclusion, are the 4 extremes.' 
 The subject of the conclusion, is called the 'minor 
 term,' while its predicate is the 4 major term.' These 
 are the extremes mediated by the middle term. The 
 premise which contains the major term is the major 
 premise and is usually stated first ; while the premise 
 which contains the minor term is the minor premise. 
 
 The conclusion is the moot point, the problem or the- 
 sis in dispute. It is from it, therefore, that our thought 
 starts. This fact shows that we are concerned in the 
 syllogism with the mechanism of proof rather than with 
 a movement of discovery. The question before our 
 minds is, What premises will justify the conclusion? 
 We are seeking the grounds of the conclusion. At this 
 point we must note a certain difference in language 
 form according as our thought moves downward to the 
 conclusion from the premises or backward to the prem- 
 ises from the conclusion. In the first case, we use such 
 terms as ' therefore,' 6 hence,' etc. ; in the second case, 
 such terms as ' because ' and ' since.' 
 
 The major premise is, characteristically, the state- 
 ment of some broad general principle, some generaliza- 
 tion from experience which can be applied to particular 
 instances. It serves both to interpret and support the 
 conclusion. The minor premise, on the other hand, 
 points to the specific application which is in question. 
 It is, characteristically, more factual than the major 
 premise. 
 
 The Rules of the Syllogism. Having once com- 
 prehended the mechanism of the syllogism and related 
 it to the logical treatment of propositions as relations 
 
112 THE ESSENTIALS OF LOGIC 
 
 of exclusion and inclusion between classes, it is easy to 
 formulate and to prove certain rules which no valid 
 syllogism can violate. They are as follows : — 
 
 1. In every syllogism there should be three, and not 
 more than three, terms, and these terms must be used 
 throughout in the same sense. 
 
 2. The middle term must be distributed at least 
 once in the premises. 
 
 3. No term ought to be distributed in the conclusion 
 that was not distributed in the premises. 
 
 4. No conclusion can be drawn from two negative 
 premises. 
 
 5. If one premise is negative, the conclusion must 
 be negative. 
 
 6. No conclusion can be drawn from two particular 
 propositions. 
 
 7. If one premise is particular, the conclusion must 
 be particular. 
 
 The first rule follows from the mechanism of the 
 syllogism. It is founded, as we saw, on the recognition 
 of a relation between the major and minor terms be- 
 cause of their relation to a middle, or standard, term. 
 The violation of this rule gives rise to the 6 Fallacy of 
 Four Terms.' If the four terms were clearly distin- 
 guishable, no one would try to syllogize them together. 
 Thus, it would obviously be absurd to seek to draw a 
 conclusion from such disparate propositions as, 'All 
 men are mortal,' and ' Politics are improving in the 
 United States.' But it sometimes happens that a term 
 is ambiguous, there seem to be three when there are 
 actually four terms. 
 
 The second rule brings out the condition without 
 
THE SYLLOGISM AS A MECHANISM 113 
 
 which the middle term cannot perform its assigned 
 function. Were both the major and the minor terms 
 related to only a part of the middle term, we could 
 
 Fig. 10. 
 
 have no assurance that they were related to the same 
 part. In other words, the information given would not 
 tell us about the relative position of the terms to ap- 
 pear in the conclusion. This indefiniteness reveals itself 
 in the relations of the circles representing the three 
 terms. If in accordance with tradition, we let S, P, 
 and M stand for minor, major, and middle term respec- 
 tively, an undistributed middle shows itself in the exist- 
 ence of different possibilities. (Fig. 10.) 
 
 This is illustrated more concretely in the following 
 
 argument : — 
 
 All voters are citizens; 
 These men are citizens; 
 Therefore these men are voters. 
 
 Diagrammatically, this syllogism is unsettled. We 
 are not able to determine a fixed relative position for 
 the two classes, these men and voters. (Fig. 11.) 
 
 A breach of this second rule involves the fallacy 
 known as « Undistributed Middle.' 
 
114 
 
 THE ESSENTIALS OF LOGIC 
 
 The basis for the third rule is the very nature of the 
 conclusion as a logical sequence from the premises. We 
 have no right to say more about a term in the conclu- 
 sion than was said in its premise. This principle has 
 already appeared in ' Immediate Inference ' in conver- 
 sion. A violation of the third rule in connection 
 with the major term is called c Illicit Process of the 
 Major,' or, more briefly, ' illicit major ' ; its violation 
 in connection with the minor term, ' Illicit Process of 
 the Minor,' or i illicit minor.' One example may serve 
 
 for both. 
 
 All good citizens are voters; 
 This person is not a good citizen; 
 Therefore this person is not a voter. 
 
 The conclusion is a singular proposition and nega- 
 tive. It will be remembered that the predicate of a 
 
 negative proposition is distrib- 
 uted. But this term is not dis* 
 tributed in the major premise. 
 Hence this is a case of illicit 
 major. This fallacy may be il- 
 lustrated by circles. 
 
 The fourth rule is understood 
 as soon as we realize that two 
 negative premises mean that 
 there is no term by means of which we can locate the 
 major and minor with reference to each other. Func- 
 tionally, there is no middle, or mediating, term. We 
 know that 8 and P both fall outside of Jf, but that 
 fact gives us no clue in regard to their interrelation. 
 This lack of mediation appears in the following argu- 
 ment : — 
 
 rig. 11. 
 
THE SYLLOGISM AS A MECHANISM 115 
 
 No bird is a bat; 
 This is not a bird; 
 Therefore this is a bat. 
 
 The use of circles may make the situation clearer. 
 
 I Birds I (creature) I Bats J 
 
 Fig. 12. 
 
 What the rule points to is our inability to draw a 
 conclusion from the information given in the premises. 
 This may be a bat, but there are other possibilities. 
 In applying this rule, we must be on our guard against 
 propositions which are only apparently negative. Care 
 in the analysis of sentences must precede the use of 
 these formal rules. 
 
 The fifth rule is seen to hold as soon as we note that 
 the two terms related in the conclusion do not have the 
 same relation to the middle term. If one premise is 
 negative, one of the extremes must be excluded in 
 whole or in part from the middle term. But the other 
 premise must be affirmative by rule four, and therefore 
 asserts a partial or total inclusion in the middle term. 
 This alliance with a term which excludes the other ex- 
 treme involves it also as a party to the exclusion. 
 
 The sixth rule can be demonstrated by means of the 
 preceding rules. Both premises cannot be particular 
 and contain the necessary distribution. In the first 
 place, only one of the two particulars can be negative 
 (rule 4). There are left three possibilities, /_/", / 0, 
 and 01 II fails because it does not distribute the 
 
116 THE ESSENTIALS OF LOGIC 
 
 middle term. / and I fail for another reason ; 
 they involve a negative conclusion (rule 5). But a 
 negative conclusion means that the major term must 
 be distributed in the major premise. But neither I 
 nor / can distribute more than one term. Hence 
 an argument having two particular premises is invalid 
 because it commits either the fallacy of undistributed 
 middle or that of illicit major. 
 
 The seventh and last rule can be demonstrated in 
 much ,the same way as the sixth. If one premise be 
 particular, there are three general possibilities, a com- 
 bination of A and I, of A and 0, and of E and L If 
 A and / have a universal conclusion, the minor term, 
 the subject of the conclusion, must be distributed in the 
 minor premise to avoid an illicit minor. But the pre- 
 mises together distribute only one term, and this must 
 be the middle (rule 2). Bearing in mind the distri- 
 bution of the terms in the four kinds of propositions, 
 the student can easily prove why A O and E I cannot 
 have universal conclusions. 
 
 The Formal Syllogism and Actual Reasoning. 
 In the present chapter, we have treated the syllogism 
 as a mechanism for testing the consistency of an argu- 
 ment. While such knowledge as we have gained is 
 useful, there are vital objections to this purely formal 
 view. In the first place, if the major premise is known 
 to be true, the instance subsumed must already be 
 known. We cannot know that all men are mortal 
 without feeling that Socrates is mortal. There is no 
 real advance in thought from the major through the 
 minor to the conclusion. To this criticism of the syl- 
 logism, it is usually replied that the major premise is 
 
THE SYLLOGISM AS A MECHANISM 117 
 
 really the statement of a rule which we take to be with- 
 out exceptions^ and the minor is the statement of an 
 instance. If so, there is always a hazard in the syllo- 
 gism, a point which we shall understand better when 
 we come to the actual movement of scientific thinking. 
 Another objection to the syllogism concerns the middle 
 term. In an actual argument, how can you be certain 
 that you have an unambiguous middle term ? Take the 
 following example : — 
 
 All men love good stories; 
 Smith is a man; 
 Therefore Smith loves this good story. 
 
 " Smith is in general a 4 man,' and, therefore, loves 
 good stories, but he is not a i man ' for the purpose of 
 this particular conclusion ; and so the sense of * man ' 
 in the two premises is not the same, and this vitiates 
 the argument." 1 This example brings out the fact that 
 it is not always easy to apply a rule or, conversely, to 
 know when an instance comes under a rule. Differ- 
 ences may be very important. 
 
 In actual reasoning, induction and deduction march 
 together. Our knowledge of general principles develops 
 as we apply them. There is an interpretation of rules 
 by new facts and, at the same time, a reading of facts 
 in terms of rules. 
 
 REFERENCES 
 
 Creighton, An Introductory Logic, chap. vni. 
 Jones, Logic, Inductive and Deductive, chap. virr. 
 Minto, Logic, Inductive and Deductive, part IV, chap. I. 
 Schiller, Formal Logic, chap. xvi. 
 
 1 Schiller, Formal Logic, p. 200. 
 
CHAPTER XI 
 
 THE FIGURES AND MOODS OF THE SYLLOGISM 
 
 The Figures of the Syllogism. The ' figure ' of a 
 syllogism is determined by the position of the middle 
 term. Since the middle term may be subject or predi- 
 cate in each of the two premises, four arrangements or 
 figures are possible. Using the conventional symbols, 
 we may state these four figures as follows : — 
 
 1. M is P 2. P is M 3. M is P 4. P is M 
 
 SisM SisM MisS MisS 
 
 S is P SisP S is P S is P 
 
 Inspecting these arrangements of the three terms in 
 the two premises, we find that the middle term is the 
 subject of the major premise and the predicate of the 
 minor in the first figure. This figure was considered by 
 Aristotle the most satisfactory and was therefore called 
 the perfect figure. The middle term is contained in the 
 major, and the minor in the middle term. 
 
 In the second figure, the middle term is the predicate 
 of both premises. 
 
 In the third figure, it is the subject of both predi- 
 cates. 
 
 In the fourth figure, it is the predicate of the major 
 premise and the subject of the minor premise. 
 
 The Moods of the Syllogism. The ' mood ' of a 
 syllogism depends upon the quality and quantity of the 
 propositions composing it. It will be remembered that 
 there are four kinds of propositions symbolized by the 
 
FIGURES AND MOODS OF THE SYLLOGISM 119 
 
 letters J., E, I, and 0. If we leave out all question o£ 
 validity, these letters may be combined in threes to 
 make the possible moods of the syllogism. The sixty- 
 four possible moods thus obtained are as follows : — 
 
 AAA ArE-A: A-^A- Ar-O-A- EAA E-E-A- EI A E-G^A 
 
 AAE AEE A IE AOE EAE EEE E I E EOE 
 
 AA I AE-*- A I I ArO-t &A4- -frE-t E-t-4- -E-O-i- 
 
 AAO AEO A I AOO EAO EEO EIO EOO - 
 
 ^rAr 3-E"Ar H-A- *-OtA- OAA OEA OIA O O A - 
 
 ^AdE- I-EE- 4-H3- I OE OAE OEE IE OOE 
 
 I A I *-E-I- HHE- i-e-t -O^-I- OE I O I I 00 I - 
 
 *-ArO- (I E.O) -Hfc-G- *-frO- OAO OEO 010 00 - 
 
 Fig. 13. 
 
 Many of these mathematically possible moods are soon 
 seen to be invalid. Thus, by applying rules 4 and 5, 
 that no conclusion can be drawn from two negative or 
 two particular premises, we can decide on the invalidity 
 of those moods through which a line is drawn. I E O 
 must also be discarded because it sins against rule 3 ; 
 it is clearly a case of illicit major. We are left with 
 eleven moods, some of which are valid in certain of the 
 four figures and invalid in others. The reason for this 
 variation in validity according to figure is the relation 
 between distribution and the position of the terms. We 
 must now ask ourselves what moods are valid in the 
 first, second, third, and fourth figures respectively. 
 
 There are two ways of determining the valid moods 
 of each figure : by inspection and by the establishment 
 of special rules for each figure. We shall use both 
 methods for the first figure and then only state the 
 
wo 
 
 THE ESSENTIALS OF LOGIC 
 
 special rules for the other figures, leaving it to the 
 student to demonstrate them. 
 
 Taking the eleven moods which were left us after the 
 first general elimination and arranging the terms in 
 accordance with the first figure, we have the following 
 results : — 
 
 A. All 2His P 
 A. All 51s M 
 A. All S is P 
 
 A. All M is P 
 A. All 5 is M 
 I. Some £ is P 
 
 A. A113fisP 
 I. Some S is Mi 
 L Some 5 is P 
 
 . E. No M is P 
 
 lot P A. All S is M 
 
 t P - JE7. No 5 is P 
 
 JSJ. NoikTisP 
 I. Some S> is M 
 0. Some 5 is not P 
 
 JE7. NoilfisP 
 
 ^.. All S is M 
 
 P : 0. Some £ is not P 
 Fig. 14. 
 
 Applying to these possible moods of the first figure 
 the general rules of the syllogism, we soon discover that 
 A EE, AE O, A 0, I A I, and O A O are in- 
 valid because of an undistributed middle or an illicit 
 major. Crossing these out, we have AAA, A A I, 
 All, EAE,EA O, and EIO left as valid. Of 
 these A A /and E A are the same as A A A and 
 E A E in the premises and have weakened conclusions ; 
 they have therefore no essential independent value. 
 
FIGURES AND MOODS OF THE SYLLOGISM 121 
 
 This analysis of the possible moods of the first figure 
 should illustrate the use made of distribution in the 
 syllogism. An inspection of the valid moods leads to the 
 discovery of the two following special rules for the first 
 figure : — 
 
 1. The minor premise must be affirmative. 
 
 2. The major premise must be universal. 
 
 These two rules can also be demonstrated by means 
 of the general rules of the syllogism. To prove that the 
 minor premise must be affirmative, we use the indirect 
 method of approach. Suppose it to be negative ; then 
 the conclusion must be negative (rule 5). But if the 
 conclusion is negative, the major term must be dis- 
 tributed (rule 3). To distribute P, the major premise 
 must be negative since only the predicates of negative 
 propositions are distributed. But by hypothesis, the 
 minor premise is already negative. Hence we should 
 have two negative premises, which is impossible. It fol- 
 lows that the minor premise must be affirmative. 
 
 Having established this rule, we can easily show that 
 the major premise must be universal. An affirmative 
 minor does not distribute the middle term in the first 
 figure. Hence it must be distributed in the major prem- 
 ise (rule 2). But only a universal will do this. Thus 
 the second special rule follows. 
 
 A similar method is applicable to the three other 
 figures. For the sake of completeness, the special rules 
 for these figures will be given. There is no need to bur- 
 den the memory with them, however, as in actual prac- 
 tice the general rules will be found sufficient as tests of 
 validity. 
 
 The rules for the second figure are : — 
 
122 THE ESSENTIALS OF LOGIC 
 
 1. The conclusion must be negative, and one premise 
 must, also, be negative. 
 
 2. The major premise must be universal. 
 
 For the third figure they are : — 
 
 1. The conclusion must be particular. 
 
 2. The minor premise must be affirmative. 
 
 For the fourth they are as follows : — 
 
 1. If either premise be negative, the major premise 
 must be universal. 
 
 2. If the major premise be affirmative, the minor 
 
 must be universal. 
 
 3. If the minor premise be affirmative, the conclu- 
 sion must be particular. 
 
 Reduction to the First Figure. We noted that 
 Aristotle regarded the first as the perfect figure. He 
 did so because the Axiom of the Syllogism has in it 
 its simplest application. On the propositional side, the 
 minor premise is subsumed under the major, which is a 
 universal. The process of changing the other figures to 
 the valid moods of the first is called * reduction.' Dur- 
 ing the Middle Ages, when the syllogism held such a 
 revered place, elaborate rules for this reduction were 
 worked out and embodied in mnemonic lines. This pro- 
 cess and these lines have had such a place in history 
 that it would seem unwise not to mention them. There 
 is an inimitable flavor of the past about them. Reduc- 
 tion is, moreover, a process which casts light upon the 
 mechanism of the syllogism and connects it with con- 
 version. 
 
 The following verses in scholastic Latin served the 
 
FIGURES AND MOODS OF THE SYLLOGISM 123 
 
 double function of recalling the valid moods of each 
 figure and of giving rules for reduction : — 
 
 Barbara, Celarent, Dam, Yerioqxie prioris ; 
 Cesare, Camestres, Yestino, Baroko, secundaB ; 
 Tertia, Darapti, Disamis, Datisis, Yelapton, 
 Bokardo, Yerison, habet; quarta insuper addit 
 Bramantip, Camenes, Dimaris, Yesapo, Yresison. 
 
 Unless one has a very facile memory, there is not 
 sufficient value in the stanza to justify memorizing. It 
 is interesting to see its construction and to realize how 
 it was used. The vowels in the names give the moods. 
 Thus, ' Barbara ' is the AAA mood of the first figure. 
 The words in genuine Latin indicate the figures. Sup- 
 pose we select ' Disamis ' in the third line. Since it is 
 in the third figure we must write it in logical symbols 
 as follows : — 
 
 /. Some If is P. 
 
 4- All M is £. 
 
 /. Therefore some S is P. 
 
 The first letter of each mood of the ' imperfect ' fig- 
 ures indicates the corresponding valid mood of the first 
 figure to which it can be reduced. Thus, * Cesare ' and 
 4 Camestres' of the second figure are reducible to 
 4 Celarent ' of the first. The letters s, m, and p also have 
 their meaning for the process of reduction. Placed after 
 a vowel, s indicates that the proposition represented by 
 the vowel must be converted simply ; m (muta) indicates 
 that the premises must be interchanged; while p shows 
 that the proposition after which it is placed must be con- 
 verted by limitation, or per accidens. An example of 
 reduction will make this clearer. Take 4 Disamis ' again. 
 The initial letter indicates that i Darii ' is the corre- 
 
124 THE ESSENTIALS OF LOGIC 
 
 sponding mood of the first figure. I A I oi the third 
 figure becomes A I Ioi the first by conversion of the 
 major premise, interchange of the premises, and, finally, 
 conversion of the conclusion to correspond to the trans- 
 formation of the major term into a minor. 
 
 Comparative Value of the Figures. While the 
 tradition in logic has favored the view that the first 
 figure is somehow better than the others, a closer anal- 
 ysis has shown that they are independently valid and 
 do not need reduction. They are independent types. 
 In other words, the Axiom of the Syllogism holds 
 primarily of the first figure and does not apply directly 
 to the others. Different classes of arguments naturally 
 fall into different forms. Thus, arguments involving the 
 subsumption of an instance under a general principle 
 take the first figure ; while those drawing negative con- 
 clusions from the absence of distinctive signs take the 
 second. The following example of a second-figure syl- 
 logism will bring out this difference : — 
 
 All fever-stricken patients are thirsty. 
 This patient is not thirsty. 
 He is not fever-stricken. 1 
 
 A close inspection of this argument reveals the realiza- 
 tion that if thirstiness is taken as a sign of fever, its 
 absence is necessarily a sign of the lack of fever. It is 
 for this reason that Minto speaks of the second as the 
 * Figure of Negative Diagnosis/ The third and fourth 
 figures are of little value. It should be remembered 
 that the third can give only a particular conclusion. 
 For this reason it has sometimes been called the 
 
 1 Minto, Logic* 
 
FIGURES AND MOODS OF THE SYLLOGISM 125 
 
 'Inductive Figure.' The fourth is more of a tour de 
 force and is not always admitted. Arguments do not 
 naturally fall into it. 
 
 REFERENCES 
 
 Creighton, An Introductory Logic, chap. ix. 
 Hibben, Logic, Deductive and Inductive, part I, chap. XVI. 
 Jones, Logic, Inductive and Deductive, chap. IX. 
 Minto, Logic, Inductive and Deductive, bk. i, part IV, chaps. II 
 and in. 
 
CHAPTER XII 
 
 ABBREVIATED AND EXPANDED ARGUMENTS — EXTRA- 
 SYLLOGISTIC ARGUMENTS 
 
 Enthymeme. It is seldom that all the parts of an 
 argument are stated fully and explicitly. Some premise 
 is taken for granted or is considered too obvious to 
 justify formal statement. The thinker himself has not 
 taken the time to analyze and formulate the grounds 
 for his conclusion or he feels that his listeners wish 
 only the salient points and can supply the remainder. 
 In the first case, what he says reflects what has been up- 
 permost in his mind ; in the second case, he wishes to 
 state only the necessary in order not to be wooden and 
 pedantic. All this is natural and there is nothing in it 
 which the logician has the right to condemn. Neverthe- 
 less, such condensation has its dangers against which 
 the logician must issue his warning. Oftentimes sup- 
 pressed premises are debatable and pass just because 
 attention has not been called to them. They slink by, 
 as it were, because they wear caps of darkness which 
 hide their faces from scrutiny. 
 
 The logician does not wish to be the enemy of wit, 
 but he can never forget that he is the guardian of rea- 
 son. Brevity is the soul of wit and of the epigram, yet 
 such syncopation must be capable of valid enlarge- 
 ment. It is of the character of such enlargement that 
 the syllogism informs us. When a premise or the con- 
 clusion of an argument is not stated, the argument 
 has the form of an enthymeme. The reasoning is not 
 
ABBREVIATED ARGUMENTS 127 
 
 fully expressed. An enthymeme is, in brief, an ellip- 
 tical argument. A few examples will make this clear: — 
 
 4 Death cannot be an evil, being ^universal.' * 
 
 4 He is in love. He brushes his hat.' 2 
 
 4 She is a woman, therefore may be won.' 3 
 
 Carlyle says of Sansculottism : 4 It too came from 
 God ; for has it not been ? ' 
 
 It will be seen from these examples that literature is 
 full of enthymemes. They add to the charm of a writer 
 if not used too lavishly. On the other hand, they do 
 not have so assured a place in arguments of a more di- 
 dactic character as in science and philosophy. Not to 
 leave things obscure is a merit in these fields. 
 
 Enthymemes are of the first, second, or third order 
 according as the major premise, the minor premise, or 
 the conclusion is wanting. The absence of the conclu- 
 sion is a rhetorical device to make it more emphatic. 
 
 It is usually quite easy to supply the missing part 
 of the argument. The two propositions which are given 
 contain the three terms. Hence all that is needed is 
 the perception of what proposition is absent and its 
 construction. Thus the quotation from Goethe given 
 above becomes — 
 
 Whatever is universal is not an evil; 
 Death is universal ; 
 Death is not an evil. 
 
 Frosyllogisms and Episyllogisms. Either prem- 
 ise of a syllogism may be justified by making it the 
 conclusion of another syllogism. When this is done, the 
 result is a complex argument in which one syllogism 
 prepares the way for a second. The grounds of one of 
 
 1 Goethe. 2 Much Ado About Nothing. 3 Titus Andronicus. 
 
Prosyllogism 
 
 Episyllogism 
 
 128 THE ESSENTIALS OF LOGIC 
 
 the premises of the final conclusion are offered. The first 
 syllogism in such a complex is called the ' prosyllogism/ 
 and the last the 'episyllogism.' Any connected argu- 
 ment of length involves the existence of interrelated 
 syllogisms. The following is a good example : — 
 
 'Everything which is able to restrain trade is a 
 
 source of danger ; 
 Every monopoly is able to restrain trade ; 
 Hence, every monopoly is a source of danger. 
 " A company which has a complete control of a 
 
 certain commodity is a monopoly ; 
 This trust has complete control of a certain 
 
 commodity ; 
 Hence, this trust is a monopoly. 
 
 Final Conclusion. This trust is a source of danger. 1 
 
 It will be noted that the conclusions of the first two 
 syllogisms are the premises of the final conclusion. 
 
 Sorites. When many syllogisms are combined, as 
 above, the combination is called a ' polysyllogism.' When 
 all the intermediate conclusions are suppressed, a poly- 
 syllogism becomes a ' sorites.' A sorites is a chain or, 
 literally, a piling-up of premises leading to a conclusion. 
 The argument gathers weight as it proceeds. 
 
 Two types of sorites have been distinguished, the 
 'Progressive' or 'Aristotelian,' and the 'Regressive' 
 or 'Goclenian.' The Aristotelian sorites moves from 
 the least inclusive term to the most inclusive, from the 
 subject of the conclusion to the predicate. 
 
 A is B. All Frenchmen are Europeans ; 
 B is C, All Europeans are men ; 
 C is D. All men are animals ; 
 D is E. All animals are mortal ; 
 A is E. All Frenchmen are mortal. 
 
 1 Jones, Logic, Inductive and Deductive. 
 
EXTRA-SYLLOGISTIC ARGUMENTS 129 
 
 The Goclenian sorites moves in the opposite direc- 
 tion. 
 
 D is E. All animals are mortal ; 
 
 C is Z). All men are animals ; 
 
 B is C. All Europeans are men ; 
 
 A is B. All Frenchmen are Europeans ; 
 
 A is E. All Frenchmen are mortal. 
 
 A sorites can be expanded into a polysyllogism of 
 which each unit is a syllogism of the first figure. In- 
 spection will show the student that the order of each 
 pair of premises must be changed to accomplish this ex- 
 pansion. 
 
 The following example of the use of the sorites in 
 poetry is worth quoting to show how a logical form may 
 be clothed upon and become a thing of beauty : — 
 
 The longer life the more offence, 
 The more offence the greater paine, 
 The greater paine the lesse defence, 
 The less defence the lesser gaine ; 
 The loss of gaine long yll doth trye, 
 Wherefore come death and let mee dye. 
 
 Come gentle Death, the ebbe of care, 
 The ebbe of care the flood of life, 
 The flood of life the joyf ull fare, 
 The joyf ull fare the end of strife, 
 The end of strife that thing wish I ; 
 Wherefore come death and let mee dye. 1 
 
 Extra-Syllogistic Arguments. Not all forms of 
 reasoning are syllogistic in type. For example, 'A^B, 
 B = (7 .-. A = C.' We all recognize the cogency of this 
 reasoning, yet we have no tendency to reduce it to syl- 
 logistic form. Instead, it is perceived to be an instance 
 of an axiom which appeals to us as undeniable, namely, 
 
 1 Sir Thomas Wyatt, 1503-44. 
 
130 THE ESSENTIALS OF LOGIC 
 
 things which are equal to the same thing are equal to 
 each other. The argument is in accord with the axiom, 
 yet the axiom does not appear as a major premise in it. 
 Deny the axiom, and you would be forced to reject the 
 instance ; but it is possible to accept the instance and 
 seal its cogency without formulating the axiom. 1 
 
 At one time there was a tendency to interpret such an 
 argument as really syllogistic, as an enthymeme with an 
 unformulated major premise, and to complete it thus : — 
 
 Things equal to the same thing are equal to each other ; 
 A and C are things equal to the same thing ; 
 A and C are equal to each other. 
 
 But inspection shows that our minor premise is not 
 an exact reproduction of the original argument, which 
 was that A and C are both equal to B. Even with this 
 correction, we are not over our difficulties, for ' A and 
 <7,' the apparent minor term, is not a term at all but 
 two objects. 
 
 The truth is, that the syllogism is limited to the re- 
 lations between classes in the way of inclusion and ex- 
 clusion. So far as there is an axiom involved, such as 
 the dictum de omni et nullo, this axiom is no more a 
 major premise than the axiom, that things equal to the 
 same thing are equal to each other, is an implied ma- 
 jor premise for the mathematical argument referred to 
 above. Deny either axiom, and, of course, the particu- 
 lar arguments fall to the ground. An examination of 
 other types of arguments may make the situation clearer 
 and enable us to realize that in the syllogism we are 
 dealing with a comparatively simple sort of relation be- 
 tween classes. The point is, that in extra-syllogistic 
 
 ^See Joseph, An Introduction to Logic, p. 273. 
 
EXTRA-SYLLOGISTIC ARGUMENTS 131 
 
 reasoning we have to do with different systems of re- 
 lation, some of which are definite and some of which 
 are indefinite. Only when the system is well enough 
 known to justify a conclusion can we move freely 
 within it. 
 
 Quantitative Relations 
 
 A is greater than B) 
 
 B is greater than C V Conclusion valid 
 
 A is greater than C) 
 
 Relations of Direction 
 
 A is north of B\ 
 
 B is north of C f Conclusion valid 
 
 A is north of C) 
 
 In these cases, we move within a unitary system and 
 can travel, as it were, back and forth in it. Each sys- 
 tem has an axiom, but the axiom is founded on some- 
 thing of the nature of immediate perception. In the 
 following instance the absence of such a unitary field 
 of relations between things is immediately recognized : — 
 
 A is the employer of B\ 
 
 B is the employer of C Y Conclusion invalid 
 
 A is the employer of C) 
 
 The study of extra-syllogistic reasoning is valuable 
 because it brings into relief the character of the syllo- 
 gism. It enables us to see that the subject-matter 
 is fundamentally important. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. VI. 
 Creighton, An Introductory Logic, chap. x. 
 Bradley, The Principles of Logic, pp. 348-60. 
 Joseph, An Introduction to Logic, chaps, xvi and xvii. 
 
CHAPTER XIII 
 
 HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 
 
 In a very real sense all propositions are categorical, 
 for they all make assertions. But it has been customary 
 for logic to distinguish propositions in which a predicate 
 is directly asserted of a subject from two other forms 
 of assertion, the hypothetical and the disjunctive. It will 
 be remembered that these propositional forms were 
 briefly defined in a previous chapter. They are of 
 interest to us now because they appear as the major 
 premises of two other kinds of syllogisms called, respec- 
 tively, the ' hypothetical ' and the 4 disjunctive.' 
 
 The Hypothetical Syllogism. A hypothetical 
 proposition combines a condition with a consequent. 
 4 If this, then this,' is the general form. Thus, * If it 
 rains this afternoon, I shall not go out for a walk,' and 
 * If business is good, I shall buy an auto,' are examples 
 of this form of assertion in which an antecedent is re- 
 lated to an inevitable consequent. A little reflection 
 shows how extensive is this expression of a relation be- 
 tween two events. It is not too much to say that modern 
 science is chiefly concerned with the discovery of rela- 
 tions. In practical life, again, we wish to know what to 
 do in order to secure certain desirable results. If we can 
 once find a rule, we have only to apply it. 
 
 In a hypothetical syllogism, the major premise is 
 hypothetical, while the minor is categorical. The cate- 
 gorical minor either affirms the antecedent or denies 
 
HYPOTHETICAL SYLLOGISMS 133 
 
 the consequent of the major premise. When it affirms 
 the antecedent, the syllogism is said to be ' constructive,' 
 or in the modus ponens; when it denies the consequent, 
 the syllogism is ; destructive,' or in the modus tollens. 
 An example of each type may make this distinction 
 clearer : — 
 
 If the winter is really over, we shall have some warm weather ; 
 
 The winter is really over ; 
 
 Therefore we shall have some warm weather. 
 
 This argument is constructive because we affirm the 
 antecedent and thereby have the right to affirm the 
 consequent in the conclusion. In the following, how- 
 ever, we deny the consequent : — 
 
 If human life were considered precious, war would be judged 
 a crime ; 
 War is not judged a crime ; 
 Therefore human life is not considered precious. 
 
 It should be noted that the distinction between affirm- 
 ative and negative has no meaning for hypothetical 
 propositions. We are either able to affirm a connection 
 between an antecedent and a consequent or we are not 
 able so to do. In the latter case we are not able to pass 
 any judgment of this character. The most we can do is 
 to state a probability. In a later chapter we shall study 
 the nature of probability ; but it would complicate things 
 too greatly to introduce it here. 
 
 Another point needs attention. Either the anteced- 
 ent or the consequent or both may be negative. In such 
 a case the categorical minor may be negative in form and 
 yet affirm the antecedent, or affirmative in form and 
 yet deny the consequent. The way to avoid error is to 
 get both parts of the major premise clearly before the 
 
134 THE ESSENTIALS OF LOGIC 
 
 mind, and then to see them in their relation to the minor. 
 In the following syllogism the minor is negative in form, 
 yet it affirms the antecedent : — 
 
 If there is not a strike at the works, the union has been dis- 
 rupted ; 
 
 There is not a strike at the works ; 
 Therefore the union has been disrupted. 
 
 The Rule of the Hypothetical Syllogism. The 
 
 rule of the hypothetical syllogism is sometimes spoken 
 of as the ' Law of Reason and Consequent.' It is for- 
 mulated thus: The truth of the consequent follows from 
 the truth of the antecedent, and the falsehood of the an- 
 tecedent from the falsehood of the consequent. This law 
 expresses the nature of the necessary relation affirmed 
 to exist between them. 
 
 The Fallacies of the Hypothetical Syllogism. 
 To attempt to draw a conclusion by denying the anteced- 
 ent or by affirming the consequent gives rise to error. 
 The reason for this is apparent so soon as we realize that 
 one event may have more than one antecedent. If we 
 have information that tells us that B occurs only when 
 A occurs, we are able to build up four valid hypotheti- 
 cal syllogisms : — 
 
 If A, then B ; A is; therefore B is. 
 
 If A , then B ; A is not ; therefore B is not. 
 
 If A, then B ; B is ; therefore A is. 
 
 If A, then B ; B is not ; therefore A is not. 
 
 In such a case, we are able to move in both direc- 
 tions because B's existence is bound up only with A's. 
 But ordinarily this is not the case. Hence B may exist 
 even when A does not. An example may make this 
 clearer : — 
 
HYPOTHETICAL SYLLOGISMS 135 
 
 If the harbor is frozen, the ships cannot come in ; 
 The harbor is not frozen ; 
 
 Can we draw a conclusion in this case ? No ; because 
 there may be other reasons why the ships cannot come 
 in. The harbor may be mined, or there may be a storm. 
 
 Reduction to Categorical Form. It has been 
 customary to reduce hypothetical syllogisms to the cate- 
 gorical form and to find analogies therein for these two 
 fallacies. But to reduce the simple to the complex is 
 wasted effort, and there is little doubt that much of our 
 thinking falls naturally into the hypothetical form. It 
 would seem more reasonable to reduce categorical syllo- 
 gisms to this simpler form. For the sake of completeness, 
 I shall perform both reductions. 
 
 If war is not declared, our country will escape disaster; 
 
 But war will not be declared; 
 
 Therefore our country will escape disaster. 
 
 Eeduced to categorical form, this becomes: — 
 
 All cases of war not being declared are cases of our country 
 escaping disaster; 
 
 This is a case of war not being declared; 
 
 Therefore this is a case of our country escaping disaster. 
 
 It will be noted that a relation of events is changed 
 into an inclusion of classes. As a matter of fact, the 
 major premise of a categorical syllogism usually states 
 a principle, and the minor premise an instance. Its 
 meaning is often more clearly expressed as a hypo- 
 thetical. 
 
 All men are mortal; 
 Socrates is a man; 
 Therefore Socrates is mortal. 
 
 really means : — 
 
136 THE ESSENTIALS OF LOGIC 
 
 If man, then mortal; 
 Socrates is a man ; 
 Therefore Socrates is mortal. 
 
 8 All men are mortal ' is not an enumerative proposi- 
 tion, but the statement of a relation between man's 
 nature and his mortality. If it were enumerative, we 
 should already know that Socrates was mortal. The 
 logician must be the first to recognize that language 
 forms are often accidental. 
 
 The Disjunctive Syllogism. In a disjunctive syl- 
 logism, the major premise is disjunctive, while the 
 minor is categorical. Thus, the major premise expresses 
 alternative possibilities among which the minor makes 
 a selection. ' The inventor of the calculus was either 
 Leibnitz or Newton,' and 6 That bird was either a sand 
 martin or a swallow,' are typical disjunctives. The 
 minor premise either asserts or denies one of the alter- 
 natives. The conclusion either denies or asserts the 
 other. For example : — 
 
 This man is either very clever or a cheat; 
 He is not very clever; 
 Therefore he is a cheat. 
 
 The source of danger is in the major premise. The 
 alternatives there offered must be exclusive of each 
 other. Unless this is the case, the affirmation of one of 
 them does not enable us to make an assured statement. 
 Hence, we may say that the ideal form of disjunction 
 is that between contradictories. ' Sempronius is either 
 honest or dishonest,' 'This man acquired his wealth 
 worthily or by fraud,' 4 He was either married or un- 
 married ' are examples of clear-cut exclusion. On the 
 other hand, a man may be both a knave and a fool. If 
 
DISJUNCTIVE SYLLOGISMS 137 
 
 so, the assertion that he is a fool does not enable us to 
 proclaim that he is not a knave. Again, it is only too 
 common to assume that a man must be moved either 
 by self-interest or by altruism, whereas motives are 
 nearly always mixed. Great care must be taken in for- 
 mulating the major premise of a disjunctive syllogism. 
 
 The Dilemma, A dilemma is technically defined 
 as an argument in which the major premise is a com- 
 plex hypothetical proposition and the minor is disjunc- 
 tive. Practically, it means the presentation of two or 
 more alternatives, all of which are unpleasant. 
 
 A dilemma may be constructive or destructive, sim- 
 ple or complex. If the antecedents of the hypothetical 
 major are affirmed in the minor premise, the dilemma 
 is said to be ' constructive ' ; if the consequents are 
 denied, it is * destructive.' Thus the rule at work is the 
 Law of Eeason and Consequent. The new element is 
 the disjunctive minor. A dilemma is simple when the 
 consequents are the same for both antecedents; com- 
 plex, when the consequents of the hypothetical major 
 are not the same for both antecedents. 
 
 The following is an example of a simple constructive 
 dilemma : — 
 
 If A is B, C is D; and if E is F, C is D; 
 But either A is B or E is F; 
 Therefore C is D. 
 
 If a man acts in accordance with his own judgment, he will be 
 criticized ; and if he is guided by the opinions and rules of others, 
 he will be criticized; 
 
 But he must either act in accordance with his own judgment, 
 or be guided by the opinions of others ; 
 
 Therefore, in any case, he will be criticized. 1 
 
 1 Creighton, An Introductory Logic* 
 
138 THE ESSENTIALS OF LOGIC 
 
 The structure of the complex constructive dilemma 
 is exemplified in this argument : — 
 
 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 inconsistency; 
 
 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. 
 
 It should be noted that the conclusion of this argu- 
 ment is disjunctive. The following is an oft-quoted 
 complex destructive dilemma : — 
 
 If this man were wise he would not speak irreverently of the 
 Scripture in jest; and if he were good he would not do it in ear- 
 nest; 
 
 But he does it either in jest or in earnest; 
 
 Therefore he is either not wise or not good. 
 
 There are three ways of meeting a dilemma, all of 
 which have picturesque names. One may try to escape 
 between the horns of a dilemma, these being the alter- 
 natives on which you are to be impaled. To escape is 
 to show that there is some other alternative. One may 
 try to rebut a dilemma by constructing another with a 
 contradictory conclusion. Or, finally, one may try to 
 take a dilemma by the horns by accepting an alterna- 
 tive and proving that the consequence asserted does not 
 follow. 
 
 Since it is difficult to get an exhaustive disjunction 
 for the minor premise, it is usually easiest to escape 
 between the horns. The rebuttal of a dilemma is an in- 
 teresting process, and many examples have come down 
 to us from antiquity, chief of which is the story of Pro- 
 tagoras and Euathlus. This story, called Litigiosus, is 
 as follows : — 
 
DISJUNCTIVE SYLLOGISMS 139 
 
 Protagoras had agreed with Euathlus to teach him 
 rhetoric for a fee, of which half was to be paid at the 
 conclusion of the instruction, and the remainder when 
 Euathlus won his first suit in court. Observing that 
 the latter delayed to practice, Protagoras thought he 
 was endeavoring to evade payment, and therefore him- 
 self brought a suit for the recovery of the second half 
 of his fee. He then argued with the jury that Euathlus 
 ought to pay him, in the following way : — 
 
 If Euathlus loses this case, he ought to pay by the judgment 
 of the court; and if he wins it, he ought to pay by his own agree- 
 ment; 
 
 But he must either lose it or win it; 
 
 Therefore he ought to pay. 
 
 Euathlus rebutted this dilemma by a counter-dilem- 
 ma: — 
 
 If I win this case, I ought not to pay by the judgment of the 
 court; and if I lose it, I ought not to pay by my own agreement; 
 But I must either win or lose it; 
 Therefore I ought not to pay. 
 
 An examination of these two dilemmas shows that 
 each antecedent has two consequents, one only of which 
 is used in each dilemma. There are, in other words, 
 two standards and each disputant uses them only when 
 convenient. This conflict of standards must first be set- 
 tled before the problem can be cleared. Has Protagoras 
 ground for action ? He could sue him only for refusing 
 to plead. But is there evidence that Euathlus had 
 agreed to become a pleader ? 
 
 The dilemma is a controversial instrument. When 
 validly constructed, it is very effective. But it is an 
 instrument which may be turned against the user and 
 
140 THE ESSENTIALS OF LOGIC 
 
 then becomes a trap in which the hunter is himself 
 taken. Before resorting to the dilemma, one should be 
 certain that the situation is itself dilemmatic. 
 
 REFERENCES 
 
 Creighton, An Introductory Logic, chap. XI. 
 Bode, An Outline of Logic, chap. vil. 
 Joseph, An Introduction to Logic, chap. xvi. 
 Welton, Manual of Logic, vol. I, bk. iv, chap. v. 
 
CHAPTER XIV 
 
 FALLACIES IN ARGUMENTATION 
 
 What a Fallacy is. A fallacy is, broadly speak- 
 ing, an error in reasoning. This error may occur at 
 any step. We may misinterpret our perceptions, or 
 classify things wrongly, or work out bad definitions, or 
 confuse ideas, or draw invalid conclusions from prem- 
 ises. The risk of misjudgment is constantly present. 
 The task confronting the human mind is twofold, that 
 of attaining knowledge and that of handling it properly 
 after it has been attained ; and neither part of this task is 
 easy. Mistakes are constantly being made. But since 
 human beings must think, because of the very require- 
 ments of their life, the best they can do is to examine 
 every stage and aspect of thinking in order to reduce 
 mistakes to a minimum. It was this need which gave 
 rise to logic. We may say, then, that thinking is an 
 adventure and that fallacies are misadventures. 
 
 A Classification of Fallacies. The traditional 
 classification of fallacies is into 'deductive' and 'induc- 
 tive ' fallacies. We shall interpret this classification as 
 corresponding to the twofold task referred to above. 
 Man must correctly handle the knowledge he already 
 has, both in his private thinking and in his arguments 
 with other people ; and he must be able to make inves- 
 tigations into new fields. Where errors creep into one's 
 own thinking or into argumentation, although no es- 
 sentially new data or principles are involved, we have 
 
1 42 THE ESSENTIALS OF LOGIC 
 
 to do with 'deductive' fallacies or fallacies in argu- 
 mentation; where, on the other hand, errors arise in 
 attempts to extend the boundaries of knowledge, they 
 are better called 'inductive' fallacies. In the present 
 chapter, we are concerned primarily with the former. 
 
 Classification of Deductive Fallacies. It is dif- 
 ficult to get a single positive principle of classification 
 for fallacies. The usual division is into ' formal ' and 
 4 material.' Formal fallacies are those which involve 
 some breach of the logical rules of the syllogism. Since 
 obversion and conversion are closely connected with the 
 syllogism, false conversion and false obversion may be 
 placed here. Material fallacies result from a misappre- 
 hension of the content or from false assumption. 
 
 Formal fallacies have been treated in detail in con- 
 nection with the chapters devoted to the syllogism. I 
 shall run over the list and suggest that the student 
 seek to clear up his memory in regard to them. They 
 are as follows : (1) False conversion ; (2) False ob- 
 version ; (3) Four Terms; (4) Undistributed Mid- 
 dle; (5) Illicit Major ; (6) Illicit Minor ; (7) Two 
 Negative Premises ; (8) Two Particular Premises ; 
 
 (9) Affirmative Conclusion with Negative Premise; 
 
 (10) Denying the Antecedent; (11) Affirming the 
 Consequent ; (12) Incomplete Disjunction. Of these, 
 special stress should be put on the Undistributed Mid- 
 dle and the fallacy of Four Terms. All verbal fallacies 
 appear syllogistically as Four Terms. Whenever the 
 middle term is vague or indefinite, there is danger of 
 an ambiguous middle. While M is jP, yet S may bo 
 M with a difference. 
 
 Material fallacies fall into two main divisions, those 
 
FALLACIES IN ARGUMENTATION 143 
 
 connected with definition and those involving unwar- 
 ranted assumption. If terms are not clearly defined, 
 some form of ambiguity is almost sure to appear. On 
 the other hand, the logic of argumentation demands 
 that the conclusion be not assumed but deduced from 
 accepted premises. The following classification will 
 serve as a guide : — 
 
 Material Fallacies 
 
 Fallacies of Equivocation Fallacies of Unwarranted 
 
 Assumption 
 
 1. Ambiguous and Shifting 1. Begging the Question. 
 Terms. 2. Complex Question. 
 
 2. Amphiboly. 3. Irrational Evidence. 
 
 3. Composition. (a) Argumentum ad hominem. 
 
 4. Division. (b) Argumentum ad populum. 
 
 5. Accident. (c) Argumentum ad ignoran- 
 
 6. Accent. tiam. 
 
 7. Figure of Speech. (c?) Argumentum ad vericun- 
 
 diam. 
 
 4. Irrelevant Conclusion. 
 
 5. Non sequitur. 
 
 Fallacies of Equivocation. 1. Words may be in- 
 definite and yet not ambiguous. When, however, there 
 is the slightest danger of misunderstanding, words 
 should be defined or else clearly qualified by the con- 
 text. In literature, the suggestiveness of a word may 
 depend upon its capacity to awaken many lines of asso- 
 ciation. But precision rather than suggestiveness is fun- 
 damental for reasoning. Especially is this the case in 
 long arguments in which the meaning of a term may 
 $hift from stage to stage if care be not taken. For in- 
 stanee, an argument may start with legal right and 
 conclude with moral right. The following fallacious 
 
144 THE ESSENTIALS OF LOGIC 
 
 syllogism may serve as an example of a subtle form of 
 equivocation called c Ambiguous Middle ' : — 
 
 All able men are consistent with themselves; 
 
 He who changes his opinions is not consistent with himself; 
 
 He who changes his opinions is not an able man. 
 
 A moment's reflection shows that the reference to 
 time is different in the two premises. 
 
 2. When the ambiguity lies in the very structure of 
 the sentence, the resultant fallacy is called * Amphib- 
 oly.' The sentence permits of a double interpretation. 
 Such cases as occur to-day are accidental and have 
 little significance except as a warning against careless 
 writing. The following want-advertisements are good 
 examples : — 
 
 Wanted: a groom to look after two horses of a pious turn of 
 mind. 1 
 
 A second-hand morris-chair is wanted by a bachelor with richly 
 carved claw-feet. 
 
 The classical cases of Amphiboly are the decrees of 
 the oracle at Delphi. The response of the oracle to 
 Pyrrhus is an excellent instance: "Pyrrhus the Ro- 
 mans can, I say, subdue." 
 
 3. The fallacy of Composition arises when an attri- 
 bute is predicated of a whole, which holds only of a 
 part. The object to which the property is fallaciously 
 assigned is usually an aggregate. Thus, to argue that 
 a country is prosperous because many business men 
 are making money, is essentially to commit the fallacy 
 of Composition. Very similar to this is the following 
 argument : — 
 
 1 Gibson, The Problem of Logic. 
 
FALLACIES IN ARGUMENTATION 145 
 
 The manufacturers of woolens are benefited by the duty on 
 woolen goods; the manufacturers of cotton by the duty on cotton; 
 the farmer by the duties on wool and grain; and so on for all the 
 other producing classes; therefore, if all the products of the 
 country were protected by an import duty, all the producing 
 classes would be benefited thereby. 
 
 It will be noted that the mind easily tends to pass 
 from individual cases and classes to larger wholes with- 
 out thought of the new influences and relations which 
 are at work in such a whole. 
 
 4. The fallacy of Division is the converse of Com- 
 position. It consists in the assignment to the part of 
 attributes which are true only of the whole. We can 
 bring this fallacy into touch with the distinction be- 
 tween the collective and the distributive use of terms 
 by saying that it arises from a disregard of these two 
 uses. In the major premise, the term may be used col- 
 lectively, while it is employed distributively in the 
 minor. The following example illustrates this hasty 
 movement from the whole to the parts : — 
 
 He cannot be innocent, for he was a member of the mob which 
 committed the deed. 
 
 We are especially liable to fall into this error in 
 discussions upon social and political topics. Because 
 people act rather foolishly or selfishly as units in a 
 group, it does not follow that their conduct will be of 
 the same character when they are acting as individuals. 
 As one writer has forcefully put it, individual morality 
 has outstripped crowd morality by many centuries. 
 " Perhaps the commonest form of the fallacy is that 
 which it takes in such arguments as, 4 It must be 
 wrong for you to act in this manner, because if every 
 
146 THE ESSENTIALS OF LOGIC 
 
 one did so, the consequences would be disastrous/ We 
 start by urging that if A and B and C . . . (conjunc- 
 tive) acted in some specified manner — the welfare of 
 the world would be fatally affected, and we go on to 
 argue that no less fatal consequences must follow 
 when A or B or C (disjunctive) act in the manner 
 specified." * 
 
 5. The fallacy of Accident consists in the applica- 
 tion of an abstract principle without allowance for 
 qualifying conditions. Because water boils at 212° 
 Fahrenheit and such water will boil an egg in five 
 minutes, it does not follow that boiling water on the 
 top of a mountain will cook an egg in that number of 
 minutes. Because charity is a virtue, we must not con- 
 clude that it is necessarily virtuous to give a beggar a 
 dollar. It may do him more harm than good. Such ab- 
 stract principles are not true universals and the mis- 
 take lies in so taking them. In argument, it is so easy 
 to make general pronouncements and shove to one side 
 those qualifications which a keener desire for truth 
 would take account of. u There is no fallacy more in- 
 sidious than that of treating a statement which for 
 many purposes is true as if it were true always and with- 
 out qualification." 2 
 
 The converse fallacy of Accident consists in the pas- 
 sage from what is true under certain circumstances to 
 an abstract principle based upon these instances. In- 
 ductively, it takes the form of a hasty generalization. 
 An individual who argued that a college education was 
 
 1 Gibson, The Problem of Logic, p. 284. Cf. Welton, Manual of 
 Logic, vol. ii, p. 247. 
 
 2 Joseph, An Introduction to Logic, p. 549. 
 
FALLACIES IN ARGUMENTATION 147 
 
 valueless because Edison and Ford did not have one 
 would be committing this fallacy. The type of argu- 
 ment is, I think, easily recognized. 
 
 Both the direct and the converse fallacies of Acci- 
 dent are important because they bear witness to a 
 deep-seated tendency to think abstractly and dogmati- 
 cally. Only the careful thinker does justice to both 
 principles and facts. Lotze, a German philosopher of 
 the last century, wrote the following very sane com- 
 ment : " Two general modes of fallacious thought are 
 developed by the habitual commission of these fallacies, 
 and illustrate them on a grand scale. The first is doc- 
 trinairism, the second narrow-mindedness. The doctri- 
 naire is an idealist who refuses to see that though 
 ideas may be right in the abstract, yet the nature of 
 the circumstances under which and of the objects to 
 which they are to be applied, must limit not only 
 their practicality, but even their binding force. The 
 narrow-minded, on the other hand, can recognize and 
 esteem no truth and no ideal, even the most univer- 
 sally valid, except in that special form to which they 
 have become accustomed within a limited circle of 
 thought and personal observation. Life is a school 
 which corrects these habits of mind. The parochially 
 minded man sees things persist, in spite of himself, in 
 taking shapes which he considers unprecedented, but 
 he finds the world somehow survives it, and learns at 
 last that a system of life may be excellent and precious, 
 but that it is rash from that to argue that it is the only 
 proper mode of orderly existence. And the enthusiast 
 for ideals, when he sees the curtailment which every at- 
 tempt at realization inflicts on them, learns the lesson 
 
148 THE ESSENTIALS OF LOGIC 
 
 which the disjunctive theorem might have taught 
 him." 1 
 
 6. The fallacy of Accent is due to a misleading 
 emphasis. When words are taken from their context, 
 they often seem to have a meaning which an investiga- 
 tion shows was not the intent of the author. This error 
 is near enough to misinterpretation caused by mis- 
 placed emphasis to be classified with it. Another in- 
 stance is the use of italics in a quotation where no 
 words were originally italicized. Jevons points out a 
 laughable case of the use of italics lending itself to 
 misunderstanding. In the First Book of Kings, xiii, 27, 
 the translators added a word to complete the sentence 
 and put it in italics to indicate this fact. The result was 
 as follows : " And he spake to his sons, saying, Saddle 
 me an ass. And they saddled Aim." " It is curious," 
 continues Jevons, " to observe how many and various 
 may be the meanings attributable to the same sentence 
 according as emphasis is thrown on one word or an- 
 other. Thus the sentence, ' The study of logic is not 
 supposed to communicate the knowledge of many use- 
 ful facts,' may be made to imply that the study of 
 logic does communicate such a knowledge, although it 
 is not supposed to do so ; or that it communicates a 
 knowledge of many useless facts." 2 
 
 7. The fallacy of Figure of Speech is due to the 
 ambiguous character of some verbal inflection. It is not 
 of much importance in a language like English in which 
 inflection is at a minimum. The best case, and the one 
 usually quoted by logicians, is found in Mill's book, 
 Utilitarianism. He is trying to prove that pleasure is 
 
 1 Logic, vol. ii, p. 5 (Eng. trans.). 2 Lessons in Logic, p. 175. 
 
FALLACIES IN ARGUMENTATION 149 
 
 the chief good. " The only proof," he writes, " capable 
 of being given that an object is visible is that people 
 actually see it. The only proof that a sound is audible is 
 that people hear it : and so of the other sources of our 
 experience. In like manner, I apprehend, the sole evi- 
 dence it is possible to produce that anything is desirable, 
 is that people actually desire it." But ' visible ' and ' au- 
 dible ' mean what can be seen and heard, while ' desira- 
 ble ' means what is worth desire or ought to be desired. 
 Mill did not notice the change in meaning because he 
 was paying too strict attention to the form of the words. 
 A similar mistake is sometimes made when the original 
 or etymological meaning of a word is stressed and the 
 more usual meaning of the present disregarded. Thus, 
 to argue that representatives must passively represent 
 their constituents is to commit this fallacy. 
 
 Fallacies of Unwarranted Assumption. These 
 fallacies consist in the entrance into the argument of 
 an unwarranted element of assumption. Either the 
 point at issue is assumed (Begging the Question, and 
 Complex Question), or the evidence adduced is irrele- 
 vant (Irrational Evidence), or the conclusion is beside 
 the point (Irrelevant Conclusion, and JVbn Sequitur). 
 In all these cases, the conclusion is not demonstrated 
 and the fallacy consists in the assumption that it is. 
 
 1. Begging the Question, or Petitio Principii, is 
 the assumption of the point to be proved. In an argu- 
 ment, it consists in the taking for granted what an op- 
 ponent would not admit if its significance were under- 
 stood ; it is the " surreptitious assumption of a truth 
 you are pretending to prove." 
 
 There are two distinguishable types of question- 
 
150 THE ESSENTIALS OF LOGIC 
 
 begging. In the one, the conclusion we wish to prove 
 is directly assumed under another name ; in the other, 
 some larger general principle which includes the point 
 in dispute is taken for granted. 
 
 The first type appears either as a question-begging 
 epithet or as reasoning in a circle. To call a prisoner 
 before the bar a worthless good-for-nothing whom every 
 one has suspected for a long time is not to prove that 
 he has committed the crime of which he is accused, but 
 to prejudice the jury against him. Epithets are insidi- 
 ous attempts to lead the minds of the listeners in the 
 desired direction independently of genuine evidence. 
 Nowhere is this procedure more frequently resorted to 
 than in politics. Mud-slinging is the bane of political 
 life, and, unfortunately, it has its bad ethical effect. 
 Those who drop into the practice must lose some meas- 
 ure of their intellectual integrity. Logic has its morali- 
 ties. Reasoning in a circle consists in the use of a prem- 
 ise which is only the desired conclusion stated in other 
 words. It is difficult to offer a good example in brief 
 compass of this species of Begging the Question, since 
 it is more apt to occur in a long argument. Often argu- 
 ments do not make any advance, but twist and turn and 
 repeat the same things in different words. Absence of 
 a clear-cut argument is nearly always a sign of an ele- 
 ment of circular thinking. The individual tries desper- 
 ately to make an advance, but really turns around the 
 same fixed ideas with much noise of asseveration. It is 
 a form of logical hemming and hawing. When there 
 is a sophistic element, an intent to deceive and to se- 
 cure victory at all hazards, reasoning in a circle becomes 
 argument in a circle. A frequently used device in Eng- 
 
FALLACIES IN ARGUMENTATION 151 
 
 lish is to state the proposition to be proved in words 
 of Saxon origin and then to give as reason for it the 
 same proposition in words of classical origin. The fol- 
 lowing example from Whately is much quoted in this 
 connection : " To allow every man an unbounded free- 
 dom of speech must always be, on the whole, advanta- 
 geous to the State, for it is highly conducive to the 
 interests of the community that each individual should 
 enjoy a liberty perfectly unlimited of expressing his 
 sentiments." 
 
 The second general type of question-begging consists, 
 as we have said, in the assumption of a larger principle 
 than the one in dispute from which this latter may be 
 deduced. It has much in common with the fallacy of 
 Accident. Thus, if a piece of legislation concerning a 
 particular remediable wrong were under discussion, it 
 would be question-begging to make appeal to some 
 abstract principle, like ' All legislation which interferes 
 with the right of free contract is bad.' At one time — 
 in the past, I am thankful to say — certain abstract 
 principles of political economy were used in this way 
 as maxims against remedial legislation ; and we all know 
 how both the conservative and the demagogue make 
 use of slogans. 
 
 In regard to this fallacy, it is well to bear in mind 
 what De Morgan called its opponent fallacy : " It is 
 the habit of many to treat an advanced proposition as 
 a begging of the question the moment they see that, if 
 established, it would establish the question." Such an 
 attitude is not playing fair. 
 
 2. When a question is so stated ^s to involve a ques- 
 tionable assumption, it is called a ' Complex Question.' 
 
158 THE ESSENTIALS OF LOGIC 
 
 Any direct answer to such a question implies the ad- 
 mission of the point assumed. Complex Question may- 
 be a trick as in the following examples : 4 Have you left 
 off beating your wife?' 'Has the practice of heavy 
 drinking ceased in your part of the country ? ' Or it 
 may be due to the fact that the interrogator has not 
 analyzed all that his question involves. A teacher in 
 philosophy may be asked how he explains telepathy. 
 
 3. " The characteristic appeal which Science, in its 
 processes of reasoning, makes to the mind is the argu- 
 mentum ad judicium, or appeal to reason. When the 
 appeal is not to the impartial reason, but to the feelings, 
 passions, prejudices of men, it is, from the logical point 
 of view, radically irrelevant, and involves the fallacy of 
 Irrational Evidence." 1 
 
 This fallacy is akin to the first type of Begging the 
 Question ; the difference lies in the openness of the ap- 
 peal to the non-logical. Locke's treatment of the vari- 
 ous forms of this fallacy is classic. " Of all the argu- 
 ments," he writes, " that men ordinarily make use of, 
 the argument ad judicium alone brings true instruction 
 with it, and advances us in the way to knowledge. . . . 
 For (1) it argues not another man's opinion to be right, 
 because I, out of respect, or any other consideration but 
 that of conviction, will not contradict him. (2) It proves 
 not another man to be in the right way, nor that I ought 
 to take the same with him, because I know not abetter. 
 (3) Nor does it follow that another man is in the right 
 way because he has shown me that I am in the wrong." 2 
 Putting these conclusions into touch with the experience 
 
 1 Gibson, The Problem of Logic, p. 287. 
 
 2 Locke, Essay concerning Human Understanding, bk. iv, chap. xvn. 
 
FALLACIES IN ARGUMENTATION 153 
 
 that any appeal to feeling must be regarded with sus- 
 picion, logicians have distinguished the following varie- 
 ties of Irrational Evidence : — 
 
 (a) Argumentum ad hominem. In this fallacy the 
 argument is directed against the character of the man 
 who is the opponent instead of adhering to its proper 
 task of proving the point at issue. Too often, calumny 
 and gossip are resorted to in order to make out a case 
 and win the decision. Here, again, logic touches upon 
 ethics. If the ideal held is that the end justifies the 
 means, such arguments come under rhetoric and the 
 only point of attack is their effectiveness. They are 
 more non-logical than illogical. As a matter of fact, 
 they are usually employed by individuals who are fully 
 aware of what they are doing. They are the tricks of 
 the sophist. A story is told of O'Connell that on one 
 occasion, when he had to defend a man who was clearly 
 in the wrong, the counsel for the prosecution was a cer- 
 tain Mr. Kiefe, who had come in for some money in 
 rather a questionable way, and had taken the name of 
 O'Kiefe. O'Connell commenced his defense by address- 
 ing his opponent : — 
 
 "Mr. Kiefe O'Kiefe, 
 I see by your brief o'brief 
 That you are a thief o'thief," — 
 
 which so disconcerted Mr. O'Kiefe and so tickled the 
 jury that a verdict was returned for the defendant. At 
 least there was wit in this case of argumentum ad homi- 
 nem. Any argument in which there is appeal to motives 
 and facts which do not bear upon the objective truth 
 of the position at issue can be classed under this title, 
 (6) Argumentum ad populum is an appeal to the 
 
154 THE ESSENTIALS OF LOGIC 
 
 feelings, passions, and prejudices of the group ad- 
 dressed instead of to the intellect. Almost all political 
 speeches and, I fear, nearly all writings which have 
 become popular in times of excitement, have contained 
 an ingredient of emotional incitement. The logician 
 must follow the psychologist in the study of crowd 
 psychology. He will then better know the power of 
 suggestion. The individual thinks most clearly and in- 
 dependently when he is alone. Let him be on his guard 
 against suggestions of an emotional sort which do not 
 leave a deposit of definable ideas. The thinker needs the 
 will to analyze and the power to put passion and preju- 
 dice far away from him. Let him remember that we call 
 6 enthusiasm ' in ourselves and those who think like us 
 what we call ' fanaticism ' in our opponents. The ideal 
 of objectivity is not a bad thing to set before one. 
 
 The best instance in literature of argumentum ad 
 populum, according to one writer, 1 is Anthony's 
 speech to the Roman mob in Shakespeare's Julius 
 Ccesar. Let the student pick up his high-school copy 
 and re-read the passage. 
 
 A species of argumentum ad populum sometimes re- 
 ferred to is argumentum ad misericordiam, an appeal 
 to pity or sympathy for a cause or person when the 
 facts do not warrant it. We Americans are soft-hearted 
 and sometimes foolishly sentimental. 
 
 (c) Argumentum ad ignorantiam consists in the 
 attempt to throw the burden of disproof upon the other 
 party to an argument. To maintain that telepathy is 
 true just because it cannot be positively disproved is 
 an example of such a policy. Mystics are constantly 
 
 1 Taylor, Elementary Logic, p. 180. 
 
FALLACIES IN ARGUMENTATION 155 
 
 resorting to this fallacy. As Creighton points out, the 
 reasoning seems to be as follows : — 
 
 It is not impossible that this is so; 
 What is not impossible is possible; 
 Therefore it is possible that this is so; 
 
 Mere abstract possibility is not enough ; there must be 
 some evidence of a factual character. 
 
 (d) Argumentum ad vericundiam is an appeal to a 
 man's modesty in the face of the reverence people feel 
 for authority and tradition. It is fallacious because it 
 involves the refusal to examine a case on its real merits 
 and the willingness to give more weight to the ipse 
 dixit of accepted authorities than to reason and fact. 
 This fallacy is rooted in the conservative and conform- 
 ist instincts of society. Locke felt the weight of the 
 scholasticism of his day and his quaintly phrased pro- 
 test is well worth quoting : " When men are established 
 in any kind of dignity, it is thought a breach of mod- 
 esty for others to derogate any way from it, and ques- 
 tion the authority of men who are in possession of it. 
 This is apt to be censured, as carrying with it too much 
 pride, when a man does not readily yield to the deter- 
 mination of approved authors, which is wont to be re- 
 ceived with respect and submission by others." We 
 must give weight to the views of men with established 
 reputations, but there is no obligation to be too docile. 
 
 Another form of the same fallacy is the tendency to 
 transfer reputation from one field to another. To quote 
 a famous inventor on a point of theology, an energetic 
 business man on problems of broad statesmanship, or 
 an explorer on questions of social ethics is to commit 
 this fallacy. A man may be competent in one field and 
 
156 THE ESSENTIALS OF LOGIC 
 
 have no special competence in another. The logician 
 must try to hold before the mind the meaning and con- 
 ditions of competence. To tell what constitutes proof 
 is also to tell what is not proof. 
 
 4. Irrelevant Conclusion consists in proving some- 
 thing different from the actual point at issue. It is an 
 evasion or ignoring of the proposition to be proved. 
 " Instead of proving that • this prisoner has committed 
 an atrocious fraud,' you prove that the fraud he is 
 accused of is atrocious : instead of proving (as in the 
 well-known tale of Cyrus and the two coats) that the 
 taller boy had a right to force the other boy to exchange 
 coats with him, you prove that the exchange would have 
 been advantageous to both : instead of proving that the 
 poor ought to be relieved in this way rather than in 
 that, you prove that the poor ought to be relieved." x 
 
 This fallacy is most easily committed in a long argu- 
 ment in which the original question passes from the 
 mind in the heat of the debate. One point leads to an- 
 other, and, if some one of the contestants is not clear- 
 headed, the concluding thesis is apt to be decidedly differ- 
 ent from the beginning one. " The person who commits 
 the fallacy of irrelevancy is, of course, quite unaware 
 of his error, unless his purpose be to mislead. He does 
 not see that the proposition which he proves is related 
 to the point at issue only through a questionable assump- 
 tion. But in criticizing an irrelevant argument it is not 
 necessary to point out the nature of the assumption 
 which underlies the argument. Merely to show that 
 what is proved is not what ought to be proved or what 
 is supposed to be proved, answers the purpose of criti- 
 
 1 Whately, Elements of Logic, 
 
FALLACIES IN ARGUMENTATION 157 
 
 cism. 4 True, but irrelevant,' is often the most concise 
 and effectual criticism. 'Thus, when in a discussion 
 one party vindicates, on the ground of general expedi- 
 ency, a particular instance of resistance to government 
 in a case of intolerable oppression, the opponent may 
 gravely maintain that we ought not to do evil that good 
 may come — a proposition which, of course, had never 
 been denied, the point in dispute being whether resist- 
 ance in this particular case were doing evil or not. Or 
 again, by way of disproving the assertion of the right 
 of private judgment in religion, one may hear a grave 
 argument to prove that it is impossible every one can 
 be right in his judgment.' The first of these arguments 
 assumes, as a second premise, that ' this is a case of 
 doing evil that good may come ' ; while the second takes 
 for granted that 'if every one cannot be right in his 
 judgment, then private judgment should not be per- 
 mitted.' These assumptions, however, are highly ques- 
 tionable, and until they are proved the arguments are 
 beside the point." * 
 
 All who have argued much with people are aware of 
 how difficult it is to keep their attention fixed on the 
 point which first arose for discussion. This tendency to 
 wander off the track is the psychological cause of such 
 irrelevancies as do not have a sophistic origin. 
 
 5. Nan sequitur is the name usually now given to a 
 conclusion which does not follow from the premises. 
 The premises may be quite true, but they do not lead 
 to the proposition which is attached beneath them. In 
 the case of this fallacy, as in practically all of those 
 which come under the caption, ' Unwarranted Assump- 
 1 Bode, An Outline of Logic, pp. 103-04. 
 
158 THE ESSENTIALS OF LOGIC 
 
 tion/ the argument in which it occurs is nearly always 
 long-winded. If we are not very much interested in the 
 assumption, or if we are not inclined to be analytic, a 
 boldly advanced conclusion may be accepted at its face 
 value. The following illustration of De Morgan's is a 
 fair sample: — 
 
 Episcopacy is of Scripture origin. 
 
 The Church of England is the only Episcopal Church in Eng- 
 land. 
 
 Therefore, the church established is the church that should be 
 supported. 
 
 I am willing to hazard the opinion, that such an argu- 
 ment, extended over many pages by means of historical 
 details, would convince those who were already favor- 
 ably inclined. 
 
 Conclusion. The chief advantage in a summary dis- 
 cussion of the fallacies lies in the training of the atten- 
 tion it involves. It is a well-known principle of psy- 
 chology that we can see best what we are looking for. 
 Now, when we feel that an argument is fallacious, it is 
 of great assistance to have in mind certain general 
 types of fallacy which are possibly relevant. Once the 
 classification is made, a standard interpretation and de- 
 scription of the fault is within our grasp. 
 
 REFERENCES 
 
 Bode, A n Outline of Logic, chap. vni. 
 Creighton, An Introductory Logic, chap. xn. 
 Sidgwick, Fallacies. 
 Whately, Elements of Logic, bk. ni. 
 
CHAPTER XV 
 
 THE NATURE OF INDUCTION 
 
 Induction and Deduction. Very often in the his- 
 tory of a science, inappropriate terms fasten themselves 
 on the terminology and are with difficulty removed. 
 Logic presents us with such a case which is of the nature 
 of a false contrast. Until very recently, it has been cus- 
 tomary to divide logic into two distinct parts called, re- 
 spectively, 'deductive' and 'inductive' logic. But it is 
 being evermore clearly realized that this division is not 
 satisfactory. What has been called ' inductive logic ' is 
 really the logic of scientific method or the logic of all con- 
 tinuous and systematic investigation in a comparatively 
 new field where principles are still to be discovered. 
 And the logic of systematic investigation deals with 
 the whole of concrete reasoning ; it concerns itself with 
 the discovery of facts, their classification, correlation, 
 and explanation. 
 
 If logic is the science of correct reasoning, it must 
 examine the principles and methods used in such sys- 
 tematic investigation. It must study the nature of syste- 
 matic inference from facts and the construction of sys- 
 tems of knowledge as well as the more formal principles 
 of classification, definition, and syllogistic argumenta- 
 tion. Logicians have realized this necessity and have 
 given increasing attention to the larger field thus opened. 
 As a consequence, every recent text devotes much of its 
 space to scientific method and to the dangers which con- 
 front the various stages of concrete inference. 
 
160 THE ESSENTIALS OF LOGIC 
 
 Now, when we examine concrete reasoning which 
 does not take its facts and principles for granted, we 
 discover that it includes both induction and deduction. 
 These are really supplementary and inseparable phases 
 of any complete act of reasoning. The mind passes back 
 and forth between fact and theory, evidence and infer- 
 ence, and, in so doing, both elements are modified. In 
 other words, principles and hypotheses are always ten- 
 tative and experimental, while facts need selection and 
 interpretation. 
 
 The term ' induction ' is often used roughly for the 
 passage from facts and less general propositions to laws 
 and more general propositions ; while ' deduction ' refers 
 to the process of analyzing ideas and using them in the 
 interpretation of facts. As we proceed, we shall realize 
 ever more clearly that the solution of any problem in- 
 volves the continuance of this double movement in the 
 course of which facts are gathered, selected, and inter- 
 preted, and principles are suggested and developed. In- 
 duction is, then, only a phase of concrete reasoning or 
 investigation ; it is not a process which can exist apart. 
 But because we have neglected this phase, relatively, up 
 to now and have laid stress upon language, definition, 
 and the syllogism, we must emphasize it in the follow- 
 ing chapters. 
 
 A Glance at the History of Logic. What we 
 have wished to point out is that the terms, i deductive ' 
 and 6 inductive,' were applied to the older and newer 
 phases of logic as the result of an historical accident 
 and that they are misnomers. The older logic tended 
 to be static and to stress consistency and implication, 
 while the newer developments were filled with the spirit 
 
THE NATURE OF INDUCTION 161 
 
 of science and stressed its methods and mode of inves- 
 tigation ; the older logic was one of consistency and 
 order, the newer was one which concerned itself with 
 the laws of systematic and progressive inference. Now, 
 the syllogism, which shows how a conclusion follows in- 
 evitably from the subsumption of an instance under a 
 rule, was the dominant element in the older logic and 
 this was therefore called 4 deductive ' ; the movement 
 from fact to law was the conspicuous feature of the 
 newer developments and the resultant logical doctrines 
 were classified together as * inductive.' Thus these terms 
 stood for an historical contrast. 
 
 But this historical contrast has lost its sharpness with 
 the lapse of time. There is no longer need to thunder 
 against the scholastics as did Locke and Francis Bacon. 
 Logic is, after all, one science and not two. The old 
 factions have disappeared, and thinkers on logic see 
 clearly that consistency and growth are not opposed to 
 each other. The older logic has consented to be modi- 
 fied by the spirit of the new. Logic has become less 
 formal all along the line, and lays more stress upon the 
 material of thought and the importance of purpose. 
 
 Since we have not taken much space for the history 
 of our subject, a brief reference to the purposes domi- 
 nating logic at different epochs may be advisable. " Per- 
 haps the simplest way of disentangling the leading 
 features of the departments of Logic is to take them in 
 relation to historical circumstances. These features are 
 writ large, as it were, in history. If we recognize that 
 all bodies of doctrine have their origin in practical 
 needs, we may conceive different ages as controlled 
 each by a distinctive spirit, which issues its mandate 
 
1G2 THE ESSENTIALS OF LOGIC 
 
 to the men of the age, assigning to them their distinc- 
 tive work. The mandate issued to the age of Plato and 
 Aristotle was, Bring your beliefs into harmony one 
 with another. The Aristotelian logic was framed in re- 
 sponse to this order: its main aim was to devise instru- 
 ments for making clear the coherence, the concatena- 
 tion, the mutual implication of current beliefs. The 
 mandate of the Mediaeval Spirit was, Bring your be- 
 liefs into harmony with dogma. The mediaeval logic 
 was contracted from Aristotle's under this impulse. 
 Then, as science developed, a new spirit was roused the 
 mandate of which was, Bring your beliefs into har- 
 mony with facts. It was under this impulse that a body 
 of methodical doctrine vaguely called Induction gradu- 
 ally originated." * 
 
 Now, the first and last mandates, at least, are perma- 
 nent ones which will always correspond to a need of 
 human life. Must we not always try to bring our beliefs 
 into harmony with one another and with fact ? In exposi- 
 tion there is a good pedagogical reason for treating the 
 logic of consistency first ; it is such a systematic body 
 of doctrine pivoting around the syllogism. But in the 
 logician's thought it must be brought into touch with 
 concrete reasoning in order to gain in vitality. The 
 student, also, must be prepared to make this synthesis. 
 
 The Function of the Syllogism. The chief aim of 
 logic for many centuries was, then, to determine the 
 conditions of correct conclusion from accepted premises. 
 Because of this limited aim the syllogism was the pivot 
 around which logical analysis turned. This simplifica- 
 tion of logic had its advantages, but likewise its disad- 
 1 Minto, Logic, Inductive and Deductive, pp. 243-44. 
 
THE NATURE OF INDUCTION 163 
 
 vantages. Because the syllogism was not seen in its 
 larger setting as only a part of actual reasoning, it was 
 formalized and mechanized. The chief difficulties of 
 creative thinking were ignored. While the keener 
 minds were aware that it gave only a logic of consist- 
 ency and order, the majority deluded themselves into 
 assuming that it was an instrument of truth and of 
 genuine inference. This misinterpretation was, how- 
 ever, due largely to the time-spirit of dogmatism which 
 prevailed for so long a period. With the advent of sci- 
 ence, logic went into the melting-pot and is only gradu- 
 ally re-forming in the mould of a wider outlook and a 
 truer perspective. The syllogism still remains intact, 
 but a juster view of its function is held. It is now seen 
 that its function and even its character depend upon 
 the purpose which is uppermost. 
 
 When the purpose is the limited one of testing the 
 consistency of a given argument, the syllogism is a 
 valuable instrument. It offers a technique by which the 
 argument can be analyzed and its parts seen in their 
 mutual relations. We can decide whether all the ele- 
 ments of a complete argument are present, whether the 
 terms are really only three in number, whether the mid- 
 dle term has the same meaning in the two premises, 
 whether the conclusion follows, etc. In short, the syllo- 
 gism and its theory presents the would-be analyst with 
 satisfactory methods for his task. He knows what to 
 demand and where the dangers lie. Relatively to this 
 purpose, the syllogism can no more be outgrown than 
 human thought itself. 
 
 But this purpose is, after all, a narrow one. We are 
 more frequently interested to-day in the increase of 
 
164 THE ESSENTIALS OF LOGIC 
 
 knowledge and in its factual verification. We want to 
 see how knowledge grows through investigation and the 
 formation of hypotheses. We are more inclined to go 
 back of the premises of an argument and to consider 
 principles for which evidence is not advanced as dogmas. 
 Moreover, probability plays a larger part to-day than 
 ever before, and it will be remembered that the syllo- 
 gism is suited only to certainty. Hence argument is 
 not so easy a matter as it once was. Not only must an 
 argument be self -consistent ; it must also be consistent 
 with the facts. But purposes can coexist ; the narrower 
 ideal of formal consistency has its validity just as has 
 the wider purpose. The wider purpose must be able to 
 include the narrower. 
 
 When the syllogism is a part of inductive-deductive 
 reasoning, the premises are essentally tentative : they 
 lead to a certain conclusion ; but if this conclusion 
 does not agree with the facts, the premises must be 
 modified. The syllogism is a phase of a larger process. 
 We shall understand this aspect of the case better 
 when we come to consider the part played by hypothe- 
 ses in modern science. It is important to us at present 
 chiefly as showing how the older doctrines are being 
 modified by a larger setting. 
 
 Why the Syllogism is only a Fart of Reasoning. 
 In the formal doctrine of the syllogism, the most diffi- 
 cult problems of actual thinking are disregarded. If 
 your opponent is kind enough to grant you certain 
 premises, he is undoubtedly obliged to admit the truth 
 of the implied conclusion. But whence do these prem- 
 ises come? And is your opponent obliged to admit 
 their truth? If he does not, the argument is at a 
 
THE NATURE OF INDUCTION 165 
 
 standstill until premises are agreed upon. Otherwise, 
 the syllogism involves a begging of the question. It is 
 obvious that the syllogism is a part of a larger whole 
 unless appeal to intuition is permitted. 
 
 Let us verify this conclusion by an examination of 
 the three kinds of syllogism. The categorical syllogism 
 deals with classes, but it does not tell us how classes 
 are formed and tested. Yet such formation and testing 
 constitute one of the most difficult tasks of science. If 
 we bear in mind the fact that real argument arises 
 only as the result of doubt and perplexity, we can ap- 
 preciate the importance of the processes largely pre- 
 liminary to the syllogism. All syllogisms require at 
 least one universal proposition, but universal proposi- 
 tions do not grow on every bush. 
 
 The hypothetical syllogism is in essentially the same 
 situation. The major premise states a universal or nec- 
 essary connection between an antecedent and a conse- 
 quent. But such principles must first be achieved, and 
 they represent the maturity of a science rather than 
 its beginning. Otherwise, they are essentially experi- 
 mental. So long as the major is tentative, the conclu- 
 sion is a challenge to fact ; but then the syllogism be- 
 comes a part of a progressive movement of knowledge. 
 
 The disjunctive syllogism is obviously in the same 
 situation. The alternatives must be complete and mutu- 
 ally exclusive. But the attainment of such alternatives 
 in any new field is not an easy matter. Of course, it 
 is an easy matter to work up such alternatives as 
 honest and dishonest, truthful and untruthful. These 
 are simple contradictories and are not apt to lead to 
 confusion. But to prove that certain theories alone 
 
166 THE ESSENTIALS OF LOGIC 
 
 hold the field is an achievement lying back of the 
 disjunctive syllogism. 
 
 Steps in Systematic Investigation. There are 
 at least four stages in any systematic investigation. 
 These have been stated variously, and certain writers 
 have felt themselves compelled to break up one or 
 more of the stages into parts. I must warn the student 
 against supposing that these stages are temporally dis- 
 tinct so that one stage can be completed before the 
 next begins. The mind of the true investigator keeps 
 them as contemporaneous as possible, and passes up 
 and down his chain of reasoning from fact to theory 
 and from theory to fact. In a sense, the active thinker 
 observes while he theorizes and theorizes while he 
 observes. 
 
 The first stage in systematic investigation is obser- 
 vation ; the second is the formation of hypotheses ; the 
 third is the development of these hypotheses ; and the 
 fourth is their progressive testing and verification by 
 renewed observation. These steps are fairly separable 
 for logical analysis though they do not exist in such 
 isolation in actual investigation. Each stage is con- 
 fronted by characteristic dangers and involves logical 
 and psychological principles of importance. Only by 
 means of this massive and systematic advance with its 
 constant hazards is new knowledge obtained. 
 
 Three Elements in Investigation. There are 
 three elements or distinguishable mental processes in all 
 investigation. We may call the first the inductive ele- 
 ment par excellence. In both observation, the begin- 
 ning of investigation, and verification, its end, the 
 stress is laid upon facts. The essential principle of 
 
THE NATURE OF INDUCTION 167 
 
 this element in the attainment of knowledge is fidelity 
 to relevant fact. Science has always stressed fact as 
 the beginning and only firm foundation of knowledge. 
 
 The second element is the formation of hypotheses. 
 The creative investigator must be capable of making 
 fruitful conjectures as to the relations which hold be- 
 tween facts or lie back of them. He must have what 
 one psychologist speaks of as a creative imagination. 
 Francis Darwin in his biography of his father remarks 
 as follows : " He often said that no one could be a 
 good observer unless he was an active theorizer. This 
 brings me back to what I said about his instinct for 
 arresting exceptions ; it was as though he were charged 
 with theorizing power ready to flow into any channel 
 on the slightest disturbance, so that no fact, however 
 small, could avoid releasing a stream of theory, and 
 thus the fact became magnified into importance." We 
 shall have much to say of this constructive, conjectural 
 element as we proceed. 
 
 The third element is the deductive reasoning out of 
 the implications of hypotheses and theories to see what 
 they imply in the light of knowledge already possessed. 
 Some writers in logic speak of this element as < de- 
 ductive inference ' ; others speak of it as ' reasoning.' 
 In any case, the significance of the hypothesis is devel- 
 oped as completely as possible and its implications 
 noted. These implications lead back to the sphere of 
 fact again and so we return to the inductive element. 
 
 The Problem of Generalization. As has been well 
 said, syllogism never generalizes. How, then, do we 
 secure universal or semi-universal propositions to serve 
 as premises ? The difficulty arises from the fact that 
 
168 THE ESSENTIALS OF LOGIC 
 
 experience gives us only particular events and things. 
 We note that this medicine seems to have a beneficial 
 effect, and that this piece of metal has certain proper- 
 ties ; but how do we go beyond the instance to a rule ? 
 We must, first of all, be careful to set the problem 
 correctly. Modern psychology informs us that every 
 instance is interpreted in the light of past experience 
 at the time it enters consciousness. Things and events 
 are noted as members of a familiar class or as members 
 of a potential class. Observation and generalization, 
 perception and interpretation, sensation and association 
 go hand in hand. We interpret as we perceive and gen^ 
 eralize as we observe. The mind is, moreover, selective 
 and stresses what is regarded as important or even essen- 
 tial. If this medicine cures an ill, then curing this kind 
 of ill is an essential property of this kind of medicine. 
 We expect classes and other instances. Why ? Because 
 it is the very nature of the mind to note similarities 
 and differences and so to classify. " It is for the sake 
 of generalization that we observe at all, and the very 
 act of observing intelligently is nothing else than the 
 act of generalizing from what we observe." We do not 
 so much pass from particular instance to particular in- 
 stance as from a beginning class to a growing class. 
 
 A little reflection must convince us that the mental 
 process leading to generalization does not depend upon 
 the application of any consciously held principle — even 
 though its logical validity may imply some such princi- 
 ple. As writers since the days of David Hume have 
 pointed out, the child unconsciously generalizes things 
 and events and builds up practical rules to act upon. 
 Wild plums are very sweet when they are ripe ; fish 
 
THE NATURE OF INDUCTION 169 
 
 bite best on cloudy days ; the river will be swollen after 
 a rain ; a circus always has a band, etc. Such classifica- 
 tions are gradually built up because the process of gen- 
 eralization continually repeats itself in our minds ; and 
 our lives are guided at every moment by the maxims 
 and rules thus obtained. What science does is to ex- 
 tend experience and to control it by completer analysis 
 and experiment. It does reflectively and methodically 
 what common sense has been doing all along. 
 
 This tendency to put two and two together, to regard 
 one thing as an indication of another, is evidently a part 
 of our mental constitution. This linkage of terms com- 
 bined with the recognition of likenesses and differences 
 accounts for a large share of what we call reasoning. 
 Professor Dewey goes so far as to assert that the estab- 
 lishment of one thing as a sign of another is the cen- 
 tral factor of thinking. " Reflection thus implies that 
 something is believed in (or disbelieved in), not on its 
 own direct account, but through something else which 
 stands as witness, evidence, proof, voucher, warrant ; 
 that is, as ground of belief At one time, rain is actu- 
 ally felt or directly experienced ; at another time, we 
 infer that it has rained from the looks of the grass and 
 trees, or that it is going to rain because of the condi- 
 tion of the air or the state of the barometer. At one 
 time, we see a man (or suppose we do) without any 
 intermediary fact ; at another time, we are not quite sure 
 what we see, and hunt for accompanying facts that will 
 serve as signs, indications, tokens of what is to be be- 
 lieved." 1 
 
 The Implication of Generalization. Logic does 
 
 1 Dewey, How We Think, p. 8. 
 
170 THE ESSENTIALS OF LOGIC 
 
 not impugn the act of generalization, but tries to under- 
 stand what takes place and what principle is implied. 
 It is evident that an event acquires meaning as a sign 
 of another event so that an internal relation between 
 them is developed in the mind. It is also apparent that 
 any one event is regarded as typical of a class. We 
 pass quickly from this event to an event of this class 
 as soon as our minds are preparing to generalize. Sup- 
 pose a savage goes out on a hunt for game, and, as he 
 steps into the forest, a rabbit crosses his path. It hap- 
 pens that he has no luck that day. If he is supersti- 
 tious, he is liable to connect this lack of success with the 
 appearance of the rabbit. But he has no reason to sup- 
 pose that there is anything peculiar about this particular 
 rabbit ; hence it sinks back into the class. It is the rab- 
 bit as a recognizable class of animals that presages bad 
 luck. Unless there is strong reason to the contrary, the 
 individual instance tends to be merged in the idea of 
 the class. Psychologically, the class is as primitive as 
 the individual. 
 
 But if the logician does not impugn the tendency to 
 generalize, he is aware, nevertheless, that a principle is 
 involved which must be valid if the generalization is 
 valid. This principle or postulate is usually called the 
 « Principle of the Uniformity of Nature.' We assume, 
 consciously or unconsciously, that there are universal 
 connections or relations in nature. This assumption, 
 when formulated explicitly, is suggested by the way the 
 mind works and the degree to which nature seems to 
 recognize the tendency to relate terms as invariable 
 signs of one another. But logicians have come to the 
 conclusion that the principle cannot be proved by expe- 
 
THE NATURE OF INDUCTION 171 
 
 rience, but can only be relatively confirmed by it. For 
 this reason, it is frequently called a ' postulate.' 
 
 How Generalization differs from Expectation. 
 Animals develop expectations in much the same way 
 that human beings do. A doctor's horse expects to turn 
 in at a certain farmhouse because it has done so on 
 previous trips. A dog anticipates a walk when his mas- 
 ter takes down his hat from the wall. The formation 
 of associations of this character is natural to the mind 
 at fairly low levels as well as at the human level. Is 
 generalization more than this ? Though based on it in 
 part, it certainly goes beyond mere expectation. Other 
 mental processes than those of association enter in. The 
 animal glides from the one event to the other without 
 holding them both before the mind as distinct objects of 
 attention. But man does hold both terms of the rela- 
 tion before his mind at one and the same time, and 
 makes them and their internal connection a single com- 
 plex object of thought. This the animal cannot do. We 
 may say, then, that generalization is a higher develop- 
 ment than expectation and depends upon the capacity 
 to conceive two events as classes and to relate them in- 
 ternally as somehow bound together. A generalization 
 is a more or less explicit assertion that two terms are 
 related. 
 
 The Importance of Generalization. It may not 
 be amiss to call attention once more to the importance 
 of generalization. Were we literally confined to par- 
 ticulars, we should be unable to reason. The very na- 
 ture of reasoning is the passage from what is given to 
 what is not directly given. As we say, we infer that 
 so-and-so will happen because something else has oc- 
 
172 THE ESSENTIALS OF LOGIC 
 
 curred. This something else is taken as a sign of the 
 event inferred. Thus we apply rules to our present ex- 
 perience in order to interpret it and to pass in concep- 
 tion beyond it. But such rules can come only from 
 generalization. 
 
 Testing Generalizations. While we cannot prove 
 the Principle of the Uniformity of Nature, we can test 
 specific inductive inferences to see whether they really 
 come under the principle. If they stand all the empiri- 
 cal tests we can apply, we call them laws of nature. 
 Science has for centuries been engaged in the discovery 
 of laws of this character, laws which the hasty observa- 
 tions and inadequate methods of common sense cannot 
 discover. The generalizations of common sense are rules 
 and maxims which hold in the main rather than laws 
 which are universal or do not admit of exceptions. Why 
 common sense is not able to formulate many universal 
 propositions will become clearer to us as we proceed. 
 Its maxims are not founded on analytic methods which 
 exclude the irrelevant. The strength of science rests 
 on the development of such methods and the technique 
 which accompanies them. It is to the consideration of 
 this technique and these methods in their general as- 
 pects that we now turn our attention. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. ix. 
 
 Creighton, An Introductory Logic, chap. xm. 
 
 Dewey, How We Think, chaps. I and vn. 
 
 Minto, Logic, Inductive and Deductive,bk. II, Introduction. 
 
 Sidgwick, The Process of Argument, chaps, iv and vin. 
 
CHAPTER XVI 
 
 THE GENERAL METHODS OF SCIENCE 
 
 How Science developed. Science grew to its pres- 
 ent stature by the efforts of men who attempted to 
 solve problems which attracted their attention. There 
 was much groping before suitable methods and a fairly 
 satisfactory technique were worked out. The simplest 
 aspects of nature were attacked before it was even pos- 
 sible to approach the more complex fields. The growth 
 of science was the result of the painstaking care and 
 genius of such men as Galileo, Kepler, Newton, Lavoi- 
 sier, Liebig, and others too numerous to mention. 
 Their sagacity, fertility of suggestion, experimental in- 
 genuity, and thoroughness led to the gradual accumu- 
 lation of facts and the appearance of just notions about 
 the constitution and mode of working of the inorganic 
 realm. Bit by bit, problems were properly defined, in- 
 vestigated, theorized over, experimented upon and ex- 
 plained. The technique of measurement was evolved, 
 mathematics applied, and instruments invented. Thus, 
 step by step, facts were discovered and fundamental 
 principles like the c laws of Kepler * and the theory of 
 gravitation of Newton were enunciated. All this was 
 a growth of the most subtle kind which substituted a 
 world of laws and conceptual elements for the familiar 
 mass of changing things. The early scientists were 
 confronted by a world of happenings and of unana- 
 lyzed things, and it was with the greatest difficulty 
 
174 THE ESSENTIALS OF LOGIC 
 
 that they learned how to handle it and make it tell its 
 secrets. Let the student try to remove from his thought 
 of the world such ideas as mass, inertia, gravitation, the 
 laws of motion, the chemical elements, energy, etc., and 
 he will better understand how much he owes to the 
 constructive genius of these men. 
 
 Since our purpose is to understand, and do justice 
 to, all the factors in systematic inference, we must not 
 neglect the ways in which these typical fathers of sci- 
 ence made their contributions. Probably there is no 
 better example for study than Galileo. "In 1581, 
 while watching a lamp set swinging in the cathedral of 
 Pisa, he observed that, whatever the range of its oscil- 
 lations, they were invariably executed in equal times. 
 The experimental verification of this fact led him to 
 the important discovery of the isochronism of the pen- 
 dulum." Here we note the alert attention ready to 
 notice and meditate upon features of the surrounding 
 world which would escape the vast majority, and the 
 experimental facility which enables the analyst to sep- 
 arate out special factors and control their occurrence. 
 During two years which he spent as a lecturer on math- 
 ematics at the University of Pisa, " he carried on that 
 remarkable series of experiments by which he estab- 
 lished the first principles of dynamics and earned the 
 undying hostility of bigoted Aristotelians. From the 
 leaning tower of Pisa he afforded to all the professors 
 and students ocular demonstration of the falsehood of 
 the Peripatetic doctrine that heavy bodies fall with 
 velocities proportional to their weights." l Galileo was 
 a keen observer, a suggestive interpreter, and a clever 
 
 1 Encyclopcedia Britannica, art. " Galileo." 
 
THE GENERAL METHODS OF SCIENCE 175 
 
 inventor. He saw problems and had the ingenuity to 
 meet them. 
 
 The Need of Analysis. The progress of science evi- 
 dently depends upon all the processes by means of 
 which facts are gathered, analyzed, and interpreted. 
 Such collection of data involves selection, and this se- 
 lection is facilitated by processes of comparison and 
 analysis. The purpose is to eliminate the irrelevant and 
 accidental and to center attention on the important 
 and essential. Whatever aids in this task is of primary 
 importance for systematic inference. Only after surface 
 appearances are passed and irrelevant but confusing 
 circumstances eliminated can the problem be defined 
 and its probable answer suggested. Analysis by com- 
 parison and experimentation is the pre-condition of 
 explanatory conceptions. 
 
 But we must never forget that the determination of 
 what is important and relevant is no easy matter and 
 is, indeed, the outgrowth of that prior knowledge for 
 which the scientist has served an apprenticeship. Every 
 problem requires a more or less special method and 
 technique, and these reflect the ideas which are in the 
 mind of the investigator. If he have the wrong notion, 
 he may lose much time and labor to no account until 
 some fact, or facts, makes him realize that he has been 
 guided by a false conception. Logic can give no royal 
 road to discovery. It can only abet the teacher of sci- 
 ence in making the student conscious of the best meth- 
 ods, mental habits and ideals and warning him against 
 the dangers of haste and dogmatism. 
 
 The Value of Technique and Instruments. The 
 scientific man is on his guard against hasty conclusions. 
 
176 THE ESSENTIALS OF LOGIC 
 
 He knows how easy it is to be led into errors of fact 
 or theory by his interests and prejudices. It is this 
 awareness of the difficulties confronting valid induction 
 that leads him to collect so many facts and to use in- 
 struments wherever possible. " The technique of scien- 
 tific inquiry thus consists in the various processes that 
 tend to exclude over-hasty ' reading in ' of meanings ; 
 devices that aim to give a purely ' objective ' unbiased 
 rendering of the data to be interpreted. Flushed cheeks 
 usually mean heightened temperature ; paleness means 
 lowered temperature. The clinical thermometer records 
 automatically the actual temperature and hence checks 
 up the habitual associations that might lead to error in 
 a given case. All the instrumentalities of observation 
 — the various meters and -graphs and -scopes — fill a 
 part of their scientific role in helping to eliminate 
 meanings supplied because of habit, prejudice, the 
 strong momentary preoccupation of excitement and an- 
 ticipation, and by the vogue of existing theories. Pho- 
 tographs, phonographs, kymographs, actinographs, seis- 
 mographs, phethysmographs, and the like, moreover, 
 give records that are permanent, so that they can be 
 employed by different persons and by the same person 
 in different states of mind, i.e., under the influence of 
 varying expectations and dominant beliefs." 1 
 
 The attention of the scientist is more sustained and 
 his observations are more systematic and unprejudiced 
 than those of the untrained man. He possesses a men- 
 tal technique of habits as well as the technique of instru- 
 ments. But with modern methods of education, no one 
 should be without some tincture of these methods and 
 1 Dewey, How We Think, pp. 87-88. 
 
THE GENERAL METHODS OF SCIENCE 177 
 
 attitudes. Logic seeks to inculcate those mental quali- 
 ties which make for good thinking, such as caution, care- 
 fulness, thoroughness, orderliness, exactness, eritical- 
 ness. In this sense, education is primarily the formation 
 of logical dispositions, of " careful, alert, and thorough 
 habits of thinking." 
 
 The Importance of Measurement. Definite knowl- 
 edge has developed step by step with the power to meas- 
 ure phenomena. In the physical sciences at least, laws 
 are equations between the measurable elements of phe- 
 nomena. Hence the invention of new and more exact in- 
 struments of measurement has usually led to marked 
 advances in the analysis of nature. " It would be a mat- 
 ter of great interest to trace out the dependence of this 
 vast progress upon the introduction of new instruments. 
 The astrolabe of Ptolemy, the telescope of Galileo, the 
 pendulum of Galileo and Huygens, the micrometer of 
 Horrocks, and the telescopic sights and micrometer of 
 Gascoyne and Picard, Roemer's transit instrument, 
 Newton's and Hadley's quadrant, Dollond's achromatic 
 lenses, Harrison's chronometer and Ramsden's dividing 
 engine — such were some of the principal additions to 
 astronomical apparatus. The result is, that we now take 
 note of quantities, 300,000 or 400,000 times as small as 
 in the time of the Chaldeans." * 
 
 Experimentation. The devising of experiments is 
 one of the important elements in a scientific investiga- 
 tion. An experiment works towards an analysis of nature 
 and a control of the field under study which will make 
 the important facts stand out clearly. The modern stu- 
 dent desires to control the order of occurrence of his 
 1 Jevons, The Principles of Science , vol. i, p. 315. 
 
178 THE ESSENTIALS OF LOGIC 
 
 phenomena and to vary the factors which are present. 
 Under such conditions, he is able to eliminate features 
 and notice the effect, and to introduce new features and 
 see what happens. Within certain limits, he can do 
 with nature as he wishes and make it answer his ques- 
 tions. Thus experimentation is a method of controlled 
 analysis, synthesis, and variation which enables man to 
 make combinations that could never be observed free in 
 nature. 
 
 There are essentially three advantages in experiment. 
 We can vary the combinations and circumstances of 
 things at will; we can produce factors at will which we 
 might have to wait years for otherwise or even never 
 obtain ; lastly we can overcome the rigidity of things as 
 they ordinarily present themselves. The following ac- 
 count of experimentation brings out very well its place 
 in investigation : " All inductive methods rest upon the 
 regulation of the conditions of observation and memory ; 
 experiment is simply the most adequate regulation pos- 
 sible of these conditions. We try to make the observa- 
 tion such that every factor entering into it, together 
 with the mode and the amount of its operation, may be 
 open to recognition. Such making of observations con- 
 stitutes experiment." 1 Ingenuity in experimentation is 
 certainly one of the prime qualifications of an investi- 
 gator in the physical sciences. Such men as Faraday, 
 Liebig, Pasteur, Darwin, and Davy were noted for 
 their fertility in ideas and methods. 
 
 The first stage of a science is dominantly observational 
 in its mode of gathering and testing facts. Many sciences, 
 like geology, find it difficult to pass beyond this stage 
 
 1 Dewey, How We Think, p. 91. 
 
THE GENERAL METHODS OP SCIENCE 179 
 
 because of the nature of the material with which they 
 have to deal. But the ideal, at least, in all the sciences 
 is the testing of hypotheses by carefully planned ob- 
 servations. We are all so familiar with the use of ex- 
 periment in physics and chemistry that we scarcely give 
 it enough thought, but the application of experimental 
 methods to biology arid psychology is newer and not so 
 familiar. Yet, in these fields, also, nature is being com- 
 pelled to react to conditions which would be unlikely to 
 occur apart from human purpose. It is evident, then, 
 that experimentation is a method of investigation and 
 that it is the servant of ideas which are seeking to find 
 themselves verified. 
 
 The Use of Experiment in Biology. Experimental 
 biology dates back only a few decades and is only now 
 being developed to the extent it deserves. It has been 
 found that growing organisms can be interfered with at 
 various stages in a grossly mechanical way without pre- 
 venting the production of normal forms. " A particu- 
 larly striking case is that of Clavellina, an ascidian, 
 that is to say, an animal organism of considerable com- 
 plexity. 4 You first isolate the branchial apparatus from 
 the other part of the body (which other part contains 
 heart, stomach, and most of the intestine), and then 
 you cut in two in whatever direction you please. Pro- 
 vided they survive and do not die, as indeed many of 
 them do, the pieces obtained by this operation will each 
 lose its organization (becoming a mere sphere of cells 
 devoid of specialized structure) • • . and then will each 
 acquire another one, and this new organization is also 
 that of a complete little Clavellina. ' " * 
 
 1 McDougall, Body and Mind, p. 240. 
 
180 THE ESSENTIALS OF LOGIC 
 
 Experimentation in Psychology. James's pic- 
 turesque description of the rise of experiment in psy- 
 chology is well worth quoting in this connection : 
 " Within a few years what one may call a microscopic 
 psychology has arisen in Germany, carried on by exper- 
 imental methods, asking of course every moment for 
 introspective data, but eliminating their uncertainty by 
 operating on a large scale and taking statistical means. 
 This method taxes patience to the utmost, and could 
 hardly have arisen in a country whose natives could be 
 bored. Such Germans as Weber, Fechner, Vierordt, 
 and Wundt obviously cannot ; and their success has 
 brought into the field an array of younger experimental 
 psychologists, bent on studying the elements of the 
 mental life, dissecting them out from the gross results 
 in which they are embedded, and as far as possible re- 
 ducing them to quantitative scales. The simple and 
 open method of attack having done what it can, the 
 method of patience, starving out, and harassing to death 
 is tried. . . . There is little of the grand style about 
 these new prism, pendulum, and chronograph-philoso- 
 phers. They mean business, not chivalry." 1 The an- 
 alytic character of experimentation comes out clearly in 
 this quotation. The experimenter tries to dissect and 
 abstract, and he is helped in his effort by instruments 
 and methods of control. 
 
 The Statistical Method. In complex fields science 
 has gradually been forced to methods of tabulation in 
 which results are set down in their appropriate places 
 and averaged. The observation of specific things has 
 given way to the gathering and arrangement of data. 
 
 1 Principles of Psychology , vol. I, p. 192. 
 
THE GENERAL METHODS OF SCIENCE 181 
 
 Only after these data are collected and tabulated is 
 there any attempt made to interpret them and to draw 
 the proper inferences. Combined with statistical meth- 
 ods is the use of averages of various sorts, such as the 
 arithmetical, the ' weighted,' the geometrical, the mode, 
 and the median. 
 
 Statistical methods are particularly employed in 
 fields where experimental analysis cannot be obtained. 
 Thus there is much use of statistics in the social sci- 
 ences and in such a field as meteorology. After the 
 4 primary statistical quantities ' are gathered, they must 
 be arranged in tables in such a manner as to bring out 
 important correlations. As we shall see when we take 
 up the method in more detail, there are many possibili- 
 ties of fallacy in both the gathering and the manipula- 
 tion of statistics. 
 
 The Method of Graphs. When relations between 
 variables are complex and cannot be easily intuited, 
 resort is increasingly had to the use of graphs. In a 
 graph, a curve is plotted to bring out in a spatial way 
 the relation involved. In this way, the correlation be- 
 comes visible to the eye and is grasped without dif- 
 ficulty. The interesting thing is, that such projection 
 of variable quantities often leads to the discovery of re- 
 lations which the investigator would not otherwise have 
 noticed. 
 
 Graphs are used in statistical investigation as a means 
 of bringing out the import of the data in a vivid way. 
 We are all familiar with this use of diagrams to illus- 
 trate the comparative populations of the various coun- 
 tries, or the relative sizes of their armies and navies, or 
 the wheat production in different years. Investigations 
 
182 THE ESSENTIALS OF LOGIC 
 
 in criminology are usually condensed by the aid of 
 graphs. In brief, the graphical method is one both of 
 investigation and of exposition. 
 
 The Function of Hypotheses. In our treatment 
 of scientific method, we have thus far called attention 
 to the more external processes and technique which sci- 
 ence has developed. But we must never forget that these 
 processes require an informing spirit to guide them. 
 There must always be a purpose at work and some 
 fairly specific problem in sight before this machinery 
 begins to move. To become familiar with the technique 
 and instrumentation of science does not make a creative 
 scientist ; nor is it enough to stare passively at test- 
 tubes and microscopes. Facts are not objects to be col- 
 lected like pebbles. They are not things which stand 
 out in the environment with an external unity and 
 identity of their own, but are dependent for their exist- 
 ence, in one sense, and certainly for their perception, 
 upon the mind of the investigator. Facts do not pass 
 into the mind ready-made, nor do they offer themselves. 
 The scientist must be on the watch for them and must 
 aid them to express themselves. His mind must be 
 sensitive to them. Without mental activity, it would be 
 impossible to gather facts. Why is this ? It is founded 
 on the very nature of voluntary attention. We attend 
 to what we are interested in ; other things pass unr 
 noticed. 
 
 The facts connected with any investigation must be 
 relevant facts. And this word gives us our clue. To be 
 relevant is to be related to a purpose and a set of ideas. 
 We must have some standard of selection, some way of 
 telling what is important and what is unimportant. 
 
THE GENERAL METHODS OF SCIENCE 183 
 
 There is a hazard in this, but the investigator must 
 always take his chance. The warning that science gives 
 by its history is general, and the individual scientist 
 must make his own judgments and collect his own in- 
 stances. 
 
 While the mind must be active in observation, it 
 must be still more active, and certainly more creative, 
 in experimentation. Some theory or hypothesis is always 
 at the basis of an experiment. The experimenter has 
 some idea of what he expects to find. The experiment 
 is, in fact, usually devised consciously to test a concep- 
 tion which has gained favor. If oxygen is the essential 
 factor in combustion, then its removal should prevent it. 
 The resultant experiment is the crucial instance for the 
 theory. If we are forced to deny a consequent, we are 
 forced to deny the antecedent likewise, and to reject 
 the idea which was gaining ground. It was in such a 
 way as this that the phlogiston theory, which held sway 
 before oxygen was discovered, was disposed of. 
 
 In a later chapter we shall have more to say of the 
 origin and function of hypotheses. What we wish to 
 stress just now is the activity of the mind in every 
 stage of investigation. To leave out the mind is like 
 removing Hamlet from the play. 
 
 REFERENCES 
 
 Dewey, How We Think, chap. vn. 
 
 James, Principles of Psychology, vol. I, p. 192/. 
 
 Jevons, Principles of Science, vol. I, chap. xv. 
 
 Merz, History of European Thought, vols. I and II, passim. 
 
 Welton, Manual of Logic, vol. II, chap. VI. 
 
CHAPTER XVII 
 
 OBSERVATION AND FACT 
 
 The Need of Observation. Since the principle 
 which should control all investigation is fidelity to rele- 
 vant fact, we must emphasize the part played by obser- 
 vation. Mere speculation uncontrolled by fact is almost 
 certain to lose touch with reality. It may lead to the 
 construction of beautiful systems but these systems for 
 all their splendor and subtlety are sure to lack value 
 as means of interpreting the world in which we actu- 
 ally live. True systems of knowledge must be given a 
 factual foundation. Fact is both the stimulus to, and 
 the test of, knowledge. But fact can be obtained only 
 by observation, direct or indirect. The investigator 
 must either gather his data himself or else trust to the 
 testimony of others. The precept which the logician 
 feels called upon to enforce is that the observational 
 side of investigations should be thorough and unbiased. 
 Only in this way can data approach that objectivity 
 which is the ideal of logical thought. 
 
 The Difficulty of securing Data. The sources of 
 knowledge, so far as facts are concerned, are direct and 
 indirect. The only direct way is by means of personal 
 observation, and this involves perception. Even mem- 
 ory must be regarded as an indirect source since mem- 
 ory is the more or less correct revival of what has once 
 been experienced. Another motive for classifying mem- 
 ory among the indirect sources of knowledge is the 
 
OBSERVATION AND FACT 185 
 
 greater danger of mistake. Slight, if not gross, errors 
 in memory are so frequent that careful thinkers feel 
 compelled to take the greatest precautions and to insti- 
 tute some method of record which will serve as a sub- 
 stitute for the details which are so easily forgotten or 
 changed. 
 
 Conditions of Accurate Observation. The psy- 
 chologist informs us that we notice only the things 
 which interest us. Many stimuli come to our senses 
 which never pass into consciousness because they do 
 not awaken even a passing attention. This control of 
 observation by interest is strikingly exemplified by the 
 different accounts of events given by eye-witnesses. 
 The records of the law courts are full of such conflict- 
 ing testimonies on the part of eye-witnesses, and the 
 experimental psychologist has been making experi- 
 ments to study the degree of accuracy to be expected. 
 The following example may make clearer the difficulty 
 in securing trustworthy data when the series of events 
 to be observed is complex : " A few years ago a painful 
 scene occurred in Berlin, in the University Seminary 
 of Professor von Liszt, the famous criminologist. The 
 Professor had spoken about a book. One of the older 
 students suddenly shouts, 'I wanted to throw light 
 on the matter from the standpoint of Christian mor- 
 ality ! ' Another student throws in, ' I cannot stand 
 that ! ' The first starts up, exclaiming, ' You have in- 
 sulted me ! ' The second clenches his fist and cries, ' If 
 you say another word — ' The first draws a revolver, 
 The second rushes madly upon him. The Professor 
 steps between them and, as he grasps the man's arm, 
 the revolver goes off. General uproar. In that moment 
 
186 THE ESSENTIALS OF LOGIC 
 
 Professor Liszt secures order and asks a part of the 
 students to write an exact account of all that has hap- 
 pened. The whole had been a comedy, carefully planned 
 and rehearsed by the three actors for the purpose of 
 studying the exactitude of observation and recollection. 
 Those who did not write the report at once were, part 
 of them, asked to write it the next day or a week later ; 
 and others had to depose their observations under cross- 
 examination. The whole objective performance was cut 
 up into fourteen little parts which referred partly to 
 actions, partly to words. As mistakes there were counted 
 the omissions, the wrong additions, and the alterations. 
 The smallest number of mistakes gave twenty-six per 
 cent of erroneous statements ; the largest was eighty per 
 cent. The reports with reference to the second half of 
 the performance, which was more strongly emotional, 
 gave an average of fifteen per cent more mistakes than 
 those of the first half. Words were put into the mouths 
 of men who had been silent spectators during the whole 
 short episode ; actions were attributed to the chief par- 
 ticipants of which not the slightest trace existed ; and 
 essential parts of the tragi-comedy were completely 
 eliminated from the memory of a number of witnesses." l 
 In such cases there is hardly such a thing as pure per- 
 ception. Suggestion, imagination, and inference shoot 
 through what is called i perception.' It is obvious 
 that it is not very easy to find fact even when we wish 
 to be faithful to it. But forewarned is at least fore- 
 armed. 
 
 In physical science the facts to observe are seldom 
 as complex as in social matters. Yet the warning is not 
 
 1 Miinsterberg, On the Witness Stand, pp. 49-50. 
 
OBSERVATION AND FACT 187 
 
 out of place in the physical field. The chief advantage 
 which the scientist has is that he can repeat his facts 
 until he is satisfied that he has them correctly. 
 
 Haphazard observation occurs when there is no very 
 definite purpose back of the series of perceptions. 
 Things and events are then noted at random according 
 to the interests and associations which happen to come 
 uppermost. When such haphazard observations are ex- 
 amined, they are nearly always found to be too inac- 
 curate or fragmentary to be of much value. We see, 
 then, that one of the prime conditions of good obser- 
 vation is definiteness of purpose. The investigator must 
 be on the outlook for facts of a known character or he 
 will miss them. We are all aware that we are more apt 
 to find a lost article if we know what to look for. The 
 scientist who is carrying on an investigation has a 
 fairly definite problem in mind which narrows the field 
 of attention. This is one of the reasons why experi- 
 mentation is so satisfactory. 
 
 Another condition of good observation is the posses- 
 sion of good mental habits. He who is on his guard 
 against the influences constantly at work to distort ob- 
 servation is more apt to observe correctly. He will try 
 to keep his mind open, to thrust prejudices and pre- 
 conceptions aside, to allow facts repugnant to him, for 
 one reason or another, as much weight as favorable facts ; 
 in short, he will try to keep his mind as receptive to all 
 relevant facts as he is able. This neutrality of mind is 
 harder to attain to than is generally supposed. It is an 
 achievement of training and education. 
 
 Errors in Perception. Errors in perception are 
 usually classified under two headings, ; mal-observation ' 
 
188 THE ESSENTIALS OF LOGIC 
 
 and ' non-observation/ Mal-observation is, again, of two 
 kinds : addition to what is present and wrong arrange- 
 ment of the parts. Non-observation is essentially omis- 
 sion. Let us consider these types of perceptual error 
 in some detail. 
 
 We constantly add elements to interpret or enlarge 
 what we actually perceive. This is not surprising when 
 we remember that sensation is only a small part of per- 
 ception. Association and suggestion are fundamental 
 factors in perception, and we see what we wish to see 
 or expect to see so long as the sense-factors and the 
 general situation do not forbid us. When common sense 
 says that seeing is believing, it is not aware of the part 
 played by past experience and by desire in what we 
 ordinarily take to be given. And this ignorance that 
 perception is a product accounts for the dogmatism of 
 common sense and for its perplexity when confronted 
 by varying stories of the same events. In his book en- 
 titled On the Witness Stand, Professor Miinsterberg 
 illustrates the influence of mental factors in perception 
 by the following instances : " In some Bowery wrangle, 
 one witness was quite certain a rowdy had taken a beer- 
 mug and kept it in his fist while he beat with it the 
 skull of his comrade ; while others saw that the two 
 were separated by a long table, and that the assailant 
 used the mug as a missile, throwing it a distance of six 
 or eight feet. In another trial, one witness noticed at 
 the seashore in moonlight a woman with a child, while 
 another witness was not less sure that it was a man 
 with a dog. And only recently passengers in a train 
 which passed a courtyard were sure, and swore, that 
 they had taken in at a glance the distinct picture of a 
 
OBSERVATION AND FACT 189 
 
 man whipping a child ; one swore that he had a clean- 
 shaven face, a hat, and was standing, while another 
 swore that he had a full beard, no hat, and was sitting 
 on a bench. The other day two most reliable expert 
 shorthand writers felt sure that they heard the utterances 
 which they wrote down, and yet the records differed 
 widely in important points." 
 
 Non-observation is the overlooking of facts which 
 ought to be observed. "It is exceeding rare to find 
 persons who can with perfect fairness estimate and reg- 
 ister facts for and against their own peculiar views and 
 theories. Among uncultivated observers the tendency 
 to remark favorable and forget unfavorable events is 
 so great that no reliance can be placed upon their sup- 
 posed observations. Thence arises the enduring fallacy 
 that the changes of the weather coincide in some way 
 or other with the changes of the moon, although exact 
 and impartial registers give no countenance to the fact. 
 The whole race of prophets and quacks live upon the 
 overwhelming effect of one success, compared with 
 hundreds of failures which are unmentioned and for- 
 gotten. As Bacon says, ' Men mark when they hit, and 
 never mark when they miss.' We should do well to 
 bear in mind the ancient story, quoted by Bacon, of one 
 who in pagan times was shown a temple with a picture 
 of all the persons who had been saved from shipwreck, 
 after paying their vows. When asked whether he did 
 not now acknowledge the power of the gods, ' Aye,' 
 he answered, ' but where are they painted that were 
 drowned after their vows ? * " x 
 
 Causes of Erroneous Perception. A helpful 
 
 1 Jevons, The Principles of Science, vol. n, p. 5. 
 
190 THE ESSENTIALS OF LOGIC 
 
 classification of the causes of erroneous perception is 
 into physical, physiological, and psychological. 
 
 Physical conditions are very important for correct 
 observation. When the atmosphere is unclear, the sci- 
 entist does not ; make observations,' for he knows that his 
 data will be faulty. But since we are as much concerned 
 with everyday reasoning as with science, w r e must note 
 some of the difficulties due to external conditions. Ob- 
 jects change their colors according to the source of illu- 
 mination. In a fog, objects look immense because our 
 ordinary standards are removed. The dweller in the plain 
 is unable for a long time to estimate distances in a 
 mountainous region correctly. On the more technical 
 side, we may mention the fact that instruments affect 
 perception in various ways. Unless these sources of 
 change are recognized and met, the data obtained may 
 be misleading. 
 
 Physiological conditions are likewise important. 
 Taste and color are affected by the condition of the 
 body. Again, the registration of flashes of light in their 
 time-relations cannot be made by perception because of 
 a certain inertia in the nervous system. A glare of 
 light is necessarily seen some fraction of a second aftSHP 
 the eye has been stimulated. In delicate scientific work, 
 the part played by the organism in perception is taken 
 account of and automatic registrations are employed 
 wherever possible. 
 
 Psychological factors are of more importance, but, 
 since we have made some mention of them already, we 
 will not dwell upon the topic. Misplaced attention leads 
 to faulty observation. This cause is important in the 
 activity of the prestidigitator, the false medium, the 
 
OBSERVATION AND FACT 191 
 
 pickpocket ; they direct the attention of their subjects 
 away from what is actually of most importance to 
 them. Another instance of the significance of the psy- 
 chological element is the value of training in the use 
 of instruments such as the microscope. Again, the mind 
 is affected by bad health. There is not the same possi- 
 bility of controlled and tireless attention under abnor- 
 mal conditions, however induced. An individual must 
 be physically and mentally fit to be in a good condition 
 for observation. 
 
 Summary for Perception. Seeing is not the sim- 
 ple and direct operation so often assumed. It has its 
 conditions, physical, physiological, and psychological. 
 Of these, the psychological are of the greatest impor- 
 tance for everyday life. Association and past experi- 
 ence in general play into perception, and its direction 
 and content are determined by interest, desire, and 
 other obscurer factors. Consequently, perception, even, 
 cannot be taken at its face value when much is at 
 stake ; it must be tested and, if possible, repeated. We 
 see much less than we suppose, and that is why obser- 
 vation is fullest when we have a definite purpose. 
 
 Observation in Everyday Life and in Science. 
 Because the scientist has become aware of these dangers, 
 he has made observation a more careful and intelligent 
 operation than it is in everyday life. The scientist 
 makes an observation. He knows what he is about 
 and guards against dangers so far as possible. One ad- 
 vantage he usually has is that his observations can be 
 repeated. An individual who is called before a court 
 as a witness is only too painfully conscious that he did 
 not know just what to observe ; his attention was too 
 
192 THE ESSENTIALS OF LOGIC 
 
 diffused and unguided to give definite results. He has, 
 moreover, no records and must trust to memory with 
 its attendant errors. 
 
 Memory and Facts. Memory is selective much 
 as perception is. We are likely to remember only 
 those events which w r e have expressly attended to ; 
 and a further elimination comes from the fact that 
 we are much more apt to remember favorable than un- 
 favorable things. This tendency to forget what is 
 unpleasant was recognized by Darwin. "I had also," 
 he writes, " during many years, followed a golden rule 
 — namely, whenever a published fact, a new observa- 
 tion or thought came across me, which was opposed to 
 my general results, to make a memorandum of it with- 
 out fail and at once ; for I had found by experience 
 that such facts and thoughts were far more apt to 
 escape from the memory than favorable ones. Owing 
 to this habit, very few objections were raised against 
 my views which I had not at least noticed and at- 
 tempted to answer." 1 
 
 Habits of mind or customary points of view furnish 
 the centers for this unconscious selection. Events which 
 cannot be made to fit into the scheme of values and 
 ideas which is gradually established in the personality 
 drop into the background and finally cease to appear 
 in consciousness. Not only is there omission, there is 
 also distortion and coloring of what is remembered. 
 A person who writes his autobiography is apt to dis- 
 tort the facts of his life. That is why such narra- 
 tives must always be checked where possible by ex- 
 ternal evidence. We must not say that Wagner and 
 
 1 Autobiography, p. 87. 
 
OBSERVATION AND FACT 193 
 
 Disraeli lied, they simply deceived themselves. Who, 
 moreover, can be perfectly frank, even to himself, 
 about himself? Inhibitions of various sorts and our 
 dramatic sense are at work upon the materials of our 
 past life to make them more presentable. 
 
 Summary of Causes of Mistaken Memory. The 
 following summary of the causes of mistaken memory 
 may be helpful : — 
 
 We tend to remember what has usually happened 
 and to forget the exceptional unless it is very striking. 
 
 We tend to remember events which are pleasant 
 and fit in with the general trend of our lives and the 
 drift of our ideas. 
 
 We tend to remember the heights and depths and 
 to allow the more colorless events to lapse. 
 
 We tend to dramatize and develop events by an un- 
 conscious process of construction and inference. 
 
 The logician is aware that memory is not an intui- 
 tion but a product, and that it must be tested by its 
 inner consistency and by means of external evidence. 
 The shorter the time which has elapsed, the more 
 truthful it is found to be. 
 
 Testimony. Testimony is a still more indirect source 
 of knowledge than memory. When we ourselves have 
 not been the witnesses of an occurrence, we are com- 
 pelled to have recourse to the statements of eye-wit- 
 nesses. But a double danger of error is now present. 
 We must be certain that those who claim to be were 
 actually witnesses at first hand. Even so, they were sub- 
 ject to all the causes of mal-observation which we have 
 already stressed, and, added to this, is the liability to 
 change which their testimony is subject to in its passage 
 
194 THE ESSENTIALS OF LOGIC 
 
 to our minds. Mal-observation, fallacious memory, in- 
 accurate expression, misinterpretation, this is the series 
 of distorting tendencies which makes ' fact ' always 
 more or less hypothetical. The consequence is that 
 such tentative facts must be carefully examined before 
 they are accepted. Methodical tests must be worked 
 out and carefully applied ; it is not too much to say 
 that facts are critical judgments rather than something 
 passively given. 
 
 Facts differ in Different Sciences. The data to 
 which the investigator must adhere in his achievement 
 of systematic knowledge vary from science to science. 
 It is very important to bear this in mind, for, other- 
 wise, it is impossible to understand differences in the 
 methodology and technique of these various sciences. 
 Inductive logic cannot be formal to the same extent 
 that the logic of consistency is able to be. The geo- 
 metrician secures his data by means of axioms and 
 postulates which seem to him self -consistent, and which 
 he relates to a spatial system lending itself to construc- 
 tion and manipulation. His methods reflect this founda- 
 tion and are dominantly inspectional and deductive. 
 The physical sciences obtain their data by active ob- 
 servation aided by experimentation. These observations 
 lend themselves to repetition. The historical and social 
 sciences have more difficulty in securing their data ; in 
 fact, data are more the end-terms of their investiga- 
 tions than the beginning. In their cases, we must dis- 
 tinguish between the crude material with which they 
 start and the conclusions upon which they base their 
 final interpretations. Between these stages lies a per- 
 fected technique of criticism and analysis. Thus the 
 
OBSERVATION AND FACT 195 
 
 character of investigation is modified by the nature of 
 the problem, the aim of the investigator, and the kind 
 of knowledge achieved. In spite of this variation, there 
 is, however, the constant presence of the three elements 
 to which we referred in the chapter introductory to 
 this part of logic. There must be observation and col- 
 lection of data, conjecture, systematic reasoning about 
 the conjecture, and, finally, a return to observation. 
 Only as the result of such systematic inference can 
 knowledge be achieved. 
 
 What are Relevant Facts? We speak of the 
 facts of a case and of relevant facts ; how do we know 
 what facts are relevant and what facts do actually be- 
 long to the case ? They do not come labeled nor is the 
 degree of their importance visibly stamped upon them. 
 A prime condition of the acquisition of essential facts 
 is guidance by some idea. We must know what we 
 want, must have insight, judgment, discernment. Such 
 discernment is, in part, the effect of familiarity with 
 the field. The expert knows what to look for ; he is 
 able to narrow down the search to data of a certain 
 character. There is in this sense of location what the 
 psychologist calls an apperceptive or deductive element. 
 Past experience is funded. We see and judge with the 
 mind. Strictly speaking, there is no such thing as 
 purely passive observation. There is usually a decid- 
 edly purposive factor at work. Guesses and conjectures 
 arise to guide the direction in which to look for evi- 
 dence. Especially is this the case when resort is had 
 to experimentation. We may say, then, that all obser- 
 vation involves the selection of what is thought to be 
 essential. The mind picks from the crowd of facts press- 
 
196 THE ESSENTIALS OF LOGIC 
 
 ing upon attention those which are judged to be rele- 
 vant. In other words, observation is in the service of a 
 continuous process of interpretation and judgment. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. xiii. 
 Gibson, The Problem of Logic, chap. xiii. 
 Jevons, Lessons in Logic, chap. xxvn. 
 Jones, Logic, Inductive and Deductive, chap. II. 
 Sidgwick, The Process of Argument, chap. vin. 
 
CHAPTER XVIII 
 
 THE ORIGIN AND USE OF HYPOTHESES 
 
 What is an Hypothesis? An hypothesis is any 
 conception by which the mind goes beyond the known 
 facts and seeks to establish relations between data of 
 testimony and perception, so long as that conception 
 is one among alternative possibilities and is not con- 
 sidered a fact. This definition, adapted from Bosan- 
 quet's larger Logic, brings out the essential position of 
 an hypothesis as between accepted fact and accepted 
 theory. It is a conjecture, a guess, a provisional expla- 
 nation. Just because an hypothesis is conjectural, it is 
 primarily a mental contribution whose aim is the solu- 
 tion of some problem. It is an interpretation or en- 
 largement of what is given. 
 
 As a tentative solution of a problem, an hypothesis 
 is an idea held before the mind in answer to a purpose, 
 that of explanation. But this purpose cannot be ful- 
 filled until many further steps are taken. The implica- 
 tions of the conjecture must be reasoned out and the 
 attempt made to bring them into touch with a com- 
 pleter survey of the facts. Hence, a genuine hypothesis 
 arises in fact and keeps in touch with fact throughout 
 its history. Because of this continuous responsibility 
 to, and control by, fact, the conjectural stage in inves- 
 tigation does not sin against the inductive principle of 
 Fidelity to Fact. All that must be guarded against is 
 that dreamy sort of speculation which soars into the 
 
198 THE ESSENTIALS OF LOGIC 
 
 heavens and never seeks to return. " The truly scien- 
 tific thinker has none of the spirit which says, ' If the 
 facts do not agree with the theory, so much the worse 
 for the facts.' " 1 
 
 Kinds of Hypotheses. The nature of a particular 
 hypothesis depends upon the character of the problem 
 for which it is a tentative answer. Sometimes we are 
 on the lookout for a fact, as when we are in search for 
 a particular cause of an occurrence like a fire or a 
 crime ; sometimes we wish to establish a law of nature, 
 such as a law of physical chemistry ; sometimes we de- 
 sire to conceive the structure of an empirical substance 
 like rubber or protoplasm ; sometimes we are pressing 
 forward to some immense generalization like the prin- 
 ciple of the conservation of energy or the theory of 
 evolution. In each case, the mind must suggest ideas 
 and then seek to establish them. The nature of the 
 problem determines the character of the explanatory 
 conjecture. 
 
 Are Hypotheses necessary for Science? At 
 various times in its history, science has been skeptical 
 of the necessity and even of the value of hypotheses. 
 During such periods, the ideal is to let facts speak for 
 themselves. It is supposed that, if facts enough are 
 collected and tabulated, the principle which is sought 
 will somehow stand out from them and force itself on 
 the attention. " The natural goal of science based on 
 this radically empirical method is to become a Science 
 of Statistics so compiled and arranged as to force upon 
 the methodical collector of observations the laws which 
 the facts require to explain them. In this way, labori- 
 1 Welton, Manual of Logic, vol. n, p. 86. 
 
THE ORIGIN AND USE OF HYPOTHESES 199 
 
 ous method takes the place of the scientific imagination 
 and the happy idea." 1 This way of approach is often 
 called the ' Baconian method ' after Francis Bacon, one 
 of the founders of modern logic. It represents a pro- 
 test against an overspeculative tendency not fed on 
 facts. It is, however, itself obviously another extreme. 
 The relative importance of theory and fact varies from 
 time to time and from subject to subject. It is now 
 pretty generally held that the situation controls the 
 amount of conjecture, but that a free play of the mind 
 must always be present. It is psychologically impos- 
 sible for principles to arise from facts without the col- 
 laboration of the mind. Neither observation nor concep- 
 tion is a passive event. Science is not a mere collection 
 of facts. 
 
 A brilliant group of men who were at once scientists 
 of recognized rank and thinkers championed the cause 
 of hypotheses during the latter part of the nineteenth 
 century, and their vindication of the controlled use of 
 hypotheses has won general acceptance. These men 
 worked in both the physical and the biological sciences. 
 The following quotation from Huxley is typical : " It 
 is a favorite popular delusion that the scientific inquirer 
 is under a sort of moral obligation to abstain from going 
 beyond that generalization of observed facts which is 
 absurdly called ' Baconian ' induction. But any one who 
 is practically acquainted with scientific work is aware 
 that those who refuse to go beyond fact rarely get as far 
 as fact ; and any one who has studied the history of science 
 knows that almost every great step therein has been 
 made by 4 anticipation of nature,' that is, by the inven- 
 1 Gibson, The Problem of Logic, p. 313. 
 
200 THE ESSENTIALS OF LOGIC 
 
 tion of hypotheses which, though verifiable, often had 
 little foundation to start with, and not infrequently, in 
 spite of a long career of usefulness, turned out to be 
 wholly erroneous in the long run." 2 
 
 The Origin of Hypotheses. There are at least two 
 conditions leading to the formation of hypotheses, the 
 possession of facts bearing upon a problem and mental 
 spontaneity. There is a constant interaction between 
 these two factors the one creative and the other con- 
 trolling and suggestive. As a rule, an hypothesis is not 
 a sudden intuition, but a mental growth which matures 
 in the fertile soil of accurate and extensive knowledge. 
 When the history of any progressive investigation is 
 written, analysis shows that there is a continuous trans- 
 verse movement between data and conjecture. Conjecture 
 guides observation and experimentation while the results 
 of such further observation modify conjectures and se- 
 lect among them. We must always remember that the 
 steps of induction which the logician separates out for 
 study do not exist separately as mutually exclusive stages. 
 
 There is pretty general agreement that fruitful hy- 
 potheses are creations of constructive imagination. In 
 its higher levels, such constructive imagination is a rare 
 gift. A great scientist must combine many capacities ; 
 he must be a tireless observer and classifier ; he must 
 be able to organize his material and include it in one 
 comprehensive survey ; but he must also be able to seize 
 that idea which will illuminate it and give it life and 
 meaning. Tyndall was aware of the importance of this 
 more personal factor of imaginative interpretation when 
 he wrote : " With accurate experiment and observation 
 1 Methods and Results, p. 62. 
 
THE ORIGIN AND USE OF HYPOTHESES 201 
 
 to work upon, Imagination becomes the architect of 
 physical theory. Newton's passage from a falling apple 
 to a falling moon was an act of the prepared imagina- 
 tion, without which the ' laws of Kepler ' could never 
 have been traced to their foundations. Out of the facts 
 of chemistry the constructive imagination of Dalton 
 formed the atomic theory. Davy was richly endowed 
 with the imaginative faculty, while with Faraday its 
 exercise was incessant, preceding, accompanying, and 
 guiding all his experiments. His strength and fertility 
 as a discoverer is to be referred in great part to the 
 stimulus of his imagination. Scientific men fight shy of 
 the word because of its ultra-scientific connotations ; but 
 the fact is, that, without the exercise of this power, our 
 knowledge of nature would be a mere tabulation of co- 
 existences and sequences." l 
 
 A G-lance at the Psychology of Conjecture. The 
 form of scientific imagination varies with the nature of 
 the science. " No one will question that mathematicians 
 have a way of thinking all their own ; but even this is too 
 general. The arithmetician, the algebraist, and more 
 generally the analyst, in whom invention obtains in the 
 most abstract form of discontinuous functions — sym- 
 bols and their relations — cannot imagine like the 
 geometrician." 2 The case seems to be that the nature 
 of the materials is a factor of first importance ; it is deter- 
 mining, and indicates to the mind the direction in which 
 it is turned. Furthermore, some individuals are better 
 able, by the very constitution of their minds, to work 
 in a certain kind of material than in other kinds. Again, 
 
 1 Fragments of Science, pp. 111-12. 
 
 2 Ribot, Essay on the Creative Imagination, p. 237. 
 
202 THE ESSENTIALS OF LOGIC 
 
 there are distinct differences in type when we come to 
 consider the way in which the illuminating idea arrives. 
 Roughly speaking, there are two types of creative minds, 
 the intuitive and the reflective. 
 
 With the intuitive mind, the preparation is largely 
 unconscious. The illuminating idea, when it does come, 
 seems to burst upon the individual like a stroke of in- 
 spiration. There is a cry of 'Eureka' and the new view 
 is born. Musicians and poets are more likely to have this 
 type of creative imagination than are scientists; yet 
 " Hauy drops a bit of crystallized calcium spar, and, 
 looking at one of the broken prisms, cries out, * All is 
 found ! ' and immediately verifies his quick intuition in 
 regard to the nature of crystallization." * 
 
 The reflective mind, on the other hand, realizes that 
 there is a problem to solve and approaches its solution 
 systematically. Such an individual gathers his material 
 and broods over it. An interpretative idea gradually 
 forms itself and is developed little by little. Perhaps it 
 is soon rejected, and another grows up to supply its 
 place. Kepler is a good example of the reflective mind. 
 He devoted a large part of his life to trying new and 
 strange hypotheses about the planetary movements until 
 the day he discovered the elliptical orbit of Mars. 
 
 According to Ribot, the differences between these 
 two types of minds are largely reducible to temperament 
 and disposition. He works out the contrast as follows : — 
 
 Intuitive type Reflective type 
 
 Ready-witted minds, excelling in Logically developing minds, 
 conception, making the whole excelling in elaboration, 
 almost out of one piece. 
 
 1 Ribot, Essay on the Creative Imagination, p. 247. 
 
THE ORIGIN AND USE OF HYPOTHESES 203 
 
 Intuitive type Reflective type 
 
 Work primarily unconscious. Patience the preponderating 
 
 role. 
 Work primarily conscious. 
 Actions quick. Actions slow. 
 
 When we contrast these two types of mind, it be- 
 comes evident that logic has more to learn from, and 
 more to convey to, the reflective type. But we must not 
 forget that in any complex field of investigation to-day, 
 the contrast is quite relative. There must always be 
 patience and conscious effort. 
 
 Running all through logic is an almost moral ele- 
 ment. The history of investigation proves that certain 
 attitudes are favorable to invention and discovery while 
 others are distinctly unfavorable. Creative imagination 
 does not exist in a mind that is conventional and domi- 
 nated by habit and routine. " Alertness, flexibility, cu- 
 riosity, are the essentials ; dogmatism, rigidity, prejudice, 
 caprice, arising from routine, passion, and flippancy 
 are fatal." l 
 
 The Value of Hypotheses. We have already said 
 enough to indicate wherein the value of an hypothesis 
 lies. It sharpens and guides the mental eye. The fol- 
 lowing anecdote from the life of Darwin brings out this 
 feature very well : " Darwin tells of a geological trip 
 through Wales which he took while a student at Cam- 
 bridge, in company with Sedgwick, the professor of 
 geology. It must be remembered that this was before 
 Agassiz had come forward with his theory of a glacial 
 period in the world's history. Darwin writes : ' We 
 spent many hours in Cwm Idwal, examining all the 
 1 Dewey, How We Think, pp. 105-06. 
 
204 THE ESSENTIALS OF LOGIC 
 
 rocks with supreme care, as Sedgwick was anxious to 
 find fossils in them ; but neither of us saw a trace of 
 the wonderful glacial phenomena all around us ; we did 
 not notice the plainly scored rocks, the perched bould- 
 ers, the lateral and terminal moraines. Yet the phe- 
 nomena are so conspicuous that, as I declared in a paper 
 published many years afterward in the Philosophical 
 Magazine, a house burnt down by fire did not tell its 
 story more plainly than did this valley. If it had been 
 filled by a glacier, the phenomena would have been less 
 distinct than they are now.' ,?1 As James put it, " The 
 only things which we commonly see are those which we 
 pre-perceive." 
 
 But an hypothesis is of value also because it begins 
 a systematic analysis and synthesis of the facts. It is 
 the beginning of an explanatory view which seeks to 
 penetrate below appearances to the causes at work and 
 their structure. When verified, hypotheses become the- 
 ories and so enter as substantial elements in our knowl- 
 edge of the world. 
 
 It is now generally admitted that an hypothesis 
 which afterwards turns out to be false may have justi- 
 fied itself in a measure by its serviceableness. It is a 
 nice question whether this relative serviceableness can 
 be connected with an element of truth in its constitu- 
 tion or whether it is due to the guidance which it exer- 
 cises. Any conjecture exerts a steadying control on 
 attention and encourages the collection of facts, some 
 of which may lead to its own dethronement. We must 
 not forget, however, that an accepted hypothesis may 
 prevent the consideration of truer ones and may in 
 1 Life and Letters of Charles Darwin, quoted from Creighton. 
 
THE ORIGIN AND USE OF HYPOTHESES 205 
 
 this way retard progress. Certainly it is better to deal 
 with true hypotheses than wiih erroneous ones. The 
 Ptolemaic Hypothesis and the^Newtonian Corpuscular 
 Theory of Light are famous examples of long accepted 
 hypotheses which were finally rejected. 
 
 The danger in the use of hypotheses is due to the 
 tendency to dogmatism. All scientists are liable to 
 "the partiality of intellectual parentage." One way to 
 counteract this latent dogmatism which blinds the men- 
 tal vision is to become conversant with the history of 
 the various sciences. When we see theory succeed the- 
 ory and even those which have stood the acid test of 
 years of investigation modified in more or less essential 
 points, we are less apt to retain our primitive assertive- 
 ness. Another way to prevent dogmatism is to keep 
 before the mind at one and the same time a number of 
 rival hypotheses. This is called the ' Method of Multiple 
 Working Hypotheses.' 
 
 The Development of an Hypothesis. An hy- 
 pothesis is barren which cannot be so developed as to 
 imply verifiable consequences. The development of an 
 hypothesis is sometimes called ' reasoning,' sometimes 
 1 deduction.' What we do is to work out its conse- 
 quences in the light of our knowledge of the system in- 
 volved. Ideas which at first glance seemed plausible 
 frequently turn out to be quite impossible. This maul- 
 ing-over of ideas to get their bearings is essential. Let 
 me first take a very simple case to illustrate the 
 method. I see footprints on the beds in the garden 
 which I have just planted. The idea comes to me that 
 my young son has been disobeying my injunctions. But 
 if these are his footprints, they will be only so large. I 
 
206 THE ESSENTIALS OF LOGIC 
 
 look more closely and discover that they are larger. 
 Thus my hypothesis has been developed and tested. 
 This same process is apparent in all cases of reasoning. 
 Detective stories are full of rather artificial examples 
 of developed guesses which are valid or invalid as the 
 case may be. 
 
 Science is replete with hypotheses which have lent 
 themselves to development. Thus, Torricelli's theory 
 that the air has weight implied that heavier liquids 
 would not be raised so high in a vacuum as lighter 
 liquids. This implication was tested and found to hold. 
 Another implication was that the mercury would not 
 stand so high on a mountain as on a plain. This also was 
 verified. The implications of an idea can often be worked 
 out only by one who is cognizant with the whole system 
 of relations and facts within which the idea must fit. 
 Thus, Foucault showed that it takes longer for light to 
 travel in a dense medium than in a rare medium. But 
 the Corpuscular Theory of Newton had the reverse of 
 this for its implication, and was therefore disproved. 
 The general form of reasoning about an idea is hypo- 
 thetical : if this is so, then this other is so ; but if this 
 other is so, then this fact follows. The chain may be 
 short or long, but it must eventually end in a datum 
 theoretically open to observation. 
 
 The Proof of an Hypothesis. A distinction must 
 be made between verifying an hypothesis and proving 
 it. An hypothesis is verified so far as its logical conse- 
 quences in the system of knowledge of which it claims 
 to be part are harmonious with the facts. 4 If A is By 
 we may decide, ' then C is DS We observe with or 
 without experimentation and discover that C is D. 
 
THE ORIGIN AND USE OF HYPOTHESES 207 
 
 This agreement reinforces our inclination for the posi- 
 tion that A is B. So long as there is no other claimant, 
 we tend to regard the conjecture as true. It cannot, 
 however, he said to be proved in any final sense until 
 it can be shown that no other hypothesis can account 
 for the facts. The logical situation involves the princi- 
 ple of the hypothetical syllogism. It will be remem- 
 bered that it is impossible to affirm the consequent and 
 draw a certainly valid conclusion. Because C is D, it 
 does not follow that A is B. But it is impossible to 
 eliminate all other possible theories because we can 
 never be certain of working within a complete disjunc- 
 tion. What, then, determines our confidence in a suc- 
 cessful hypothesis ? Ultimately a consilience of results. 
 When a very large field is covered and coordinated by 
 a conjecture and no other plausible idea is in sight or 
 seems likely to be advanced, we give our assent and 
 regard the hypothesis as proved. 
 
 Fact, Theory, and Hypothesis. Facts are of two 
 kinds, facts of observation and facts of belief. While 
 it must not be forgotten that even facts of observation 
 are really statements which are open to reasonable 
 doubt, the judgments and tests involved are usually 
 simpler than for the second kind of facts. This second 
 class of facts are complex statements which have 
 reached the stage of practical certainty. They are far- 
 ther away from perception than the first and involve 
 conceptual construction of an advanced degree. It is a 
 fact of observation that a stick seems bent in the water, 
 but a fact of assent that the earth revolves around the 
 sun. Both classes have this in common that we give 
 their members whole-hearted belief. 
 
208 THE ESSENTIALS OF LOGIC 
 
 When an idea is first suggested and entertained by 
 the mind, it is called an * hypothesis.' When its conse- 
 quences are deduced and verified, it is apt to be digni- 
 fied by the name of i theory.' When it has gained un- 
 questioned acceptance, it is likely to be spoken of as a 
 4 fact ' or a ' principle.' Not so long ago, evolution was 
 referred to as an hypothesis ; then it became a theory ; 
 now it has attained the standing of a fact or a princi- 
 ple. We must remember that there is no court of adju- 
 dication, so that what is a principle to one may be an 
 hypothesis to another. 
 
 Analogy as a Basis of Reasoning. The remark 
 is often made that such-and-such a conclusion was 
 reached by analogy. We admittedly reason by analogy 
 from one field to another. Examining such reasoning, 
 logicians point out that it consists of the passage from 
 one thing or group of things to another because of a 
 recognized resemblance between them. " Two things 
 resemble each other in one or more respects ; a certain 
 proposition is true of one, therefore it is true of the 
 other." * Now such a passage is usually tentative and 
 is therefore of the nature of ah hypothesis ; this fact is 
 our justification for treating the topic in this chapter. 
 
 The symbolic form of analogy is as follows : A re- 
 sembles B in certain respects ; A exhibits the charac- 
 ter V) therefore B will exhibit the character "Falso. In 
 other words, we tend to hold that if two things agree in 
 certain respects they are apt to agree in others. All 
 classification is really based on analogy in this broad 
 sense; but in classification the similarities noted are 
 many and fundamental and we are dealing with what 
 1 Mill, System of Logic, bk. in, chap, xx, par. 2. 
 
THE ORIGIN AND USE OF HYPOTHESES 209 
 
 we have reason to believe are things of the same kind. 
 There is, however, no decided break between what is 
 clearly classification and what would be admitted by all 
 to be mere analogy. " Where analogy is very close, and 
 well tested, and familiar, as between cancer and cancer, 
 or man and man, class-names have generally been in- 
 vented. It is newly seen likeness, doubtful likeness, or 
 likeness where the examples are rare, that we have to 
 recognize as well as we can without the aid of class- 
 names. And it is to these kinds of likeness especially 
 that, as a rule, we give the name ' analogy.' " 1 It is 
 not too much to say that all the reasoning in a new 
 field bases itself upon analogies with more familiar do- 
 mains. Thus the wave character of the propagation of 
 light was inferred from the known fact that sound 
 which also was reflected traveled in waves. 
 
 False Analogy. Analogies are very apt to be mis- 
 leading. After all, things may be similar in this respect 
 or that while differing in almost everything else. The 
 points of similarity are often superficial and not corre- 
 lated with the properties which are important for the 
 problem in hand. Because a whale lives in the water 
 and is shaped very much like a fish, it does not follow 
 — as was at one time supposed — that it has the deeper 
 structure of a fish. Because a municipality is a gov- 
 ernment, it does not follow that it must have the same 
 type of organization as the Federal Government. An 
 argument from analogy has a high degree of probabil- 
 ity only when the points of resemblance are rooted deep 
 in the nature of the two things and there is reason to 
 believe that in the familiar field there is a connection 
 
 1 Sidgwick, The Process of Argument, p. 40. 
 
210 THE ESSENTIALS OF LOGIC 
 
 between the points of resemblance and the property 
 which we wish to infer in the new field. A good in- 
 stance of what must be regarded as a false analogy is 
 Carlyle's argument against the representative form of 
 government. " According to Carlyle, this kind of gov- 
 ernment is bound to fail, since, as he puts it, a ship 
 could never be taken around Cape Horn if the captain 
 were obliged to consult the crew every time before 
 changing his course. A generalization is implied, some- 
 thing like, 4 The sharing of power involves a lack .of 
 efficiency.' Granted that this holds true on ships, is it 
 also true in government ? The argument asserts that 
 the two cases are alike, but it offers no proof that the 
 difference in circumstances is immaterial. The appar- 
 ent difference, however, is so great that caution is ad- 
 visable. It may be that the lack of efficiency is due to 
 the sharing of power under certain conditions peculiar 
 to the management of ships." 1 
 
 It is obvious that analogy must be controlled by anal- 
 ysis. False analogies always rest upon the disregard of 
 differences. Thus analogy is a fruitful source of sug- 
 gestions but these must be tested by a further survey 
 of the facts and an estimation of their meaning. Re- 
 semblance may, as the saying goes, be only skin deep. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. XX. 
 Joseph, An Introduction to Logic, chap. xxiv. 
 Ribot, Essay on the Creative Imagination, chap. IV. 
 Sidgwick, The Process of Argument, chap. IV. 
 Welton, Manual of Logic, vol. n, chaps, in and IV. 
 
 1 Bode, An Outline of Logic, p, 163. 
 
CHAPTER XIX 
 
 THE DISCOVERY AND PROOF OF CAUSAL RELATIONS 
 
 How Experience comes to us. The individual's 
 experience comes to him in an accidental, haphazard 
 way, and it is only as the result of unconscious or 
 semiconscious sorting and generalization that he re- 
 duces it to some show of order. Things are recognized 
 and classified into kinds, and these kinds are supposed 
 to have certain properties which can be predicted 
 and counted on. Iron is malleable ; coal burns ; swans 
 are white; apple trees yield apples after their kind, 
 etc. By means of these classifications and generaliza- 
 tions, we are able to handle things and adapt ourselves 
 to our environment. 
 
 But there is another feature of our experience which 
 is equally important. We soon learn to note that 
 events in which we are interested are controlled bv 
 conditions. If we want B to happen, we must see that 
 A is added. If we want the garden to produce an 
 abundant crop, we must add fertilizer in the proper 
 proportions. If the manufacturer wishes to have steel 
 of a certain degree of hardness, he must add manga- 
 nese. When any factor is known to be an invariable 
 antecedent of some event or situation, and it is also 
 known that this event does not occur in the absence of 
 this factor, it is called a cause. Such a cause is a 
 means to an end, and is of practical significance. If 
 we wish to achieve any result, we must see that all the 
 conditions are present. 
 
212 THE ESSENTIALS OF LOGIC 
 
 What are Causal Connections ? It is usually 
 said that science deals with the causes of things. What 
 is meant by this expression ? And what is a cause ? A 
 little reflection warns us that, because we are studying 
 the actual methods of science, we have to do with a 
 purely empirical problem. What the scientist is search- 
 ing for is the condition of changes. Something hap- 
 pens, and he wants to know why* He is on the outlook 
 for the factor which has led to the change in which he 
 is interested. As soon as I add sulphuric acid to the 
 test-tube which I hold in my hand, I begin to get a 
 reaction, and I soon see a deposit at the bottom of the 
 tube. Cause has, in short, to do with change in vari- 
 ous parts of nature. We desire to know what disturbs 
 the previous equilibrium and thus leads to novelty. A 
 cause is, then, a factor which, so far as we can deter- 
 mine, is the occasion of the event which is selected as 
 the effect. 
 
 When we come to reflect upon the relation between 
 a cause and its effect, we note at once its temporal 
 character. The entrance of the causal factor is the an- 
 tecedent of the effect. But we are not willing to con- 
 sider the entering factor a cause unless its absence 
 involves the absence of the effect. It must be an indis- 
 pensable antecedent. And it is not always easy to 
 decide what factor is indispensable. We must know 
 enough about the field to make a good guess or guesses, 
 and we must then experiment to find out whether a 
 fuller knowledge agrees with the guess. 
 ^Post Hoc ergo Propter Hoc. Even the older logi- 
 cians were perfectly aware of the danger of false gen- 
 eralization. Because one event precedes another, we 
 
CAUSAL RELATIONS 213 
 
 must not jump to the conclusion that they are caus- 
 ally related. If we take the antecedent of an event in 
 a purely temporal way, it includes the whole range of 
 occurrences which can be dated before the event which 
 we are interested in. A causal relation involves more 
 than this temporal antecedence; it implies conviction 
 that certain specific events located in some definite 
 part of space are most intimately connected with the 
 effect. He who is on the outlook for causal relations 
 is seeking special strands of connection. He wants to 
 find constantly repeated, invariable, dependable connec- 
 tions. His ideal is to analyze nature into uniformities 
 which can be made the basis of prediction and control. 
 
 Early man had much the same tendency to treat 
 temporal relations as causal that we have to-day, but 
 he was far more credulous and hasty in his generaliza- 
 tions. What we call superstition and magic consisted 
 largely of uncritical beliefs of this character. Chance 
 association by contiguity or likeness was the founda- 
 tion of accepted laws. The mind was ruled by ideas 
 and made its selections accordingly with practically no 
 thought of verification. It seemed very likely that the 
 eating of a lion's heart would supply courage to the 
 warrior ; and had not B been unlucky when a rabbit 
 crossed his path ? The selection among events was per- 
 sonal and controlled by chance ideas and associations. 
 To the critic the reply would have been, Why not? 
 And there was a dearth of critics. It took time and 
 hard experience to produce them. 
 
 The tendency to regard events as causally related 
 just because one has been observed to follow the other 
 has been christened ' Post Hoc ergo Propter Hoc? 
 
214 THE ESSENTIALS OF LOGIC 
 
 i.e., * After, therefore, Because of.' " The history of the 
 progress of human knowledge shows, with increasing 
 clearness, that better solutions are given in proportion 
 as we recognize our own liability to be misled by first 
 appearances. It is the testing and verification of 
 theories, not the easy belief that they need no testing, 
 that helps forward our knowledge of the ways of 
 Nature." 1 
 
 Mill's Methods. The human mind has gradually 
 hit upon methods for discovering and testing causal 
 relations. These were first sensed in the concrete by 
 scientists in the pursuit of particular problems and 
 were formulated some time after when reflection upon 
 the general methods employed had arisen. The meth- 
 ods for determining causal relations were partially 
 formulated by Herschel in his Discourse on the Study 
 of Natural Philosophy, and were given their nearly 
 final form by John Stuart Mill. For this reason, they 
 are usually spoken of as 4 Mill's Methods.' How can 
 causal generalizations be discovered and verified ? This 
 is the problem around which they turn. 
 
 Mill formulated five methods, but the principles in- 
 volved are essentially two. " The simplest and most 
 obvious modes of singling out from among the circum- 
 stances which precede or follow a phenomenon (any 
 event), those with which it is really connected by an 
 invariable law, are two in number. One is by com- 
 paring together different instances in which the phe- 
 nomenon occurs. The other is by comparing instances 
 in which the phenomenon does occur, with instances in 
 other respects similar in which it does not. These two 
 
 1 Sidgwick, The Process of Argument, pp. 132-33. 
 
CAUSAL RELATIONS 215 
 
 methods may be respectively denominated the i Method 
 of Agreement ' and ' Method of Difference.' " These 
 two principles would seem to follow from the very nature 
 of the causal relation. If a cause is the indispensable 
 antecedent of a phenomenon, can we not conclude (1) 
 that the antecedent in the absence of which the phe- 
 nomenon occurs is not the cause, and (2) that the ante- 
 cedent in whose presence the phenomenon fails to occur 
 is not the cause ? It would seem possible, therefore, to 
 eliminate factors which are absent when a particular 
 effect occurs and to test those which remain by seeing 
 whether their absence involves the absence of the effect. 
 In this way, resort can be made to experimentation. 
 
 The Method of Agreement. " If two or more 
 instances of the phenomenon under investigation have 
 only one circumstance in common^ the circumstance in 
 which alone all the instances agree is the cause (or 
 effect) of the given phenomenon" Such is Mill's state- 
 ment of the Canon of Agreement. It is possible to 
 represent this canon schematically. Let X be the 
 effect whose cause we wish to find, and let the accompa- 
 nying circumstances be represented by abcde, afklm, and 
 aghno in three cases of the appearance of the effect. 
 Putting down these groups in the above order, we have : — 
 
 ahcdeX 
 qfklmX 
 aghnoX. 
 
 Comparing these groups, we see that a is the sole factor 
 which always accompanies X, and hence we feel the 
 right to conclude that a is the cause of X. 
 
 Such a schematic arrangement, while it illustrates the 
 
216 THE ESSENTIALS OF LOGIC 
 
 canon, is apt to be misleading because of its simplicity 
 and artificiality. Much of the work of investigation 
 must be done before any such neat little scheme can be 
 constructed. But, after all, we are seeking just now to 
 get the principle clearly in mind and we can note the 
 setting and difficulties of the method afterwards. 
 
 Examples of Induction by Agreement. One of 
 the classic examples in science of the application of this 
 method is the discovery by Sir David Brewster that the 
 material of mother-of-pearl has nothing to do with the 
 brilliant display of color supposed to be characteristic 
 of it. By accident, he took an impression of a piece of 
 mother-of-pearl in beeswax and found, much to his sur- 
 prise, that the colors were reproduced upon its surface. 
 His interest being attracted, he carried on the experi- 
 ment with other materials such as gum-arabic, balsam, 
 etc. In each case, the colors appeared. The inference 
 was obvious. The only feature these objects had in com- 
 mon was the form secured by impression from the 
 mother-of-pearl. 
 
 "When Sir Isaac Newton was investigating the prop- 
 erty of physical objects called ' mass,' he had to deter- 
 mine that the material of which the body was made did 
 not affect this property. In the same way, Galileo proved 
 that bodies fall to the ground at a rate irrespective of 
 their weight by the simple expedient of dropping bodies 
 of different weights from the leaning tower of Pisa. 
 
 Let us suppose that an epidemic of typhoid fever 
 has appeared in a city. In order to prevent its further 
 spread, the health authorities will wish to locate the 
 source of the disease. Past experience will suggest cer- 
 tain possible sources, such as the milk supply, the water 
 
CAUSAL RELATIONS 217 
 
 supply, the food, etc. Examining the milk supply, the 
 authorities may find that the various patients secure 
 their milk from different dairies. This fact makes the 
 milk an improbable source. Turning to the food supply, 
 they may find that no one article of food is obtained 
 at the same store. The water supply, on the other hand, 
 is common. This agreement will suggest to them very 
 strongly that the infection was spread by contaminated 
 water. ' If, furthermore, they find no other common 
 articles of consumption, they will undoubtedly conclude 
 that the water supply was at fault. 
 
 The Character of the Method. The Method of 
 Agreement is more one of observation than of experi- 
 mentation. As a rule, a large number of instances is 
 necessary in order to make certain the inclusion of the 
 cause among the factors noted. In practice, the method 
 is preliminary and does not do much more than elimi- 
 nate theoretically possible factors and narrow down the 
 field for experimentation. It is an empirical way of 
 approach to a problem and stresses observation. It does 
 not get us far beneath the surface of things. " Thus 
 varying the circumstances so as to bring out a common 
 antecedent, though it does not end in exact proof, may 
 indicate causal connection though it does not prove what 
 the nature of the connection is. Roger Bacon's obser- 
 vations indicated that the production of rainbow colors 
 was connected with the passage of light through a 
 transparent globe or prism. It was reserved for Newton 
 to prove by other methods that white light was composed 
 of rays, and that those rays were differently refracted 
 in passing through the transparent medium." 1 
 1 Minto, Logic, Inductive and Deductive, p. 325. 
 
218 THE ESSENTIALS OF LOGIC 
 
 Difficulties confronting the Method. There are 
 two important difficulties confronting this method. 
 First comes the inability to determine in any dogmatic 
 way what factors are present ; and, added to this, the 
 possibility that the effect may be produced by different 
 factors on different occasions. Let us examine these 
 difficulties somewhat closely. 
 
 It is so easy to ignore factors because they do not 
 seem to have any connection with the effect. Hasty 
 elimination of factors as the result of prejudice can 
 easily lead to false results. Again, analysis is often too 
 incomplete to enable the observer to recognize the con- 
 stant factor. A very good instance of this oversight of 
 the really important factor was the theory, held before 
 the part played by micro-organisms in the propagation 
 of disease was understood, that night air was the cause 
 of malaria. It was noticed that people who caught ma- 
 laria were generally exposed to the night air, but the 
 fact that they were bitten by mosquitoes was not thought 
 important and was therefore disregarded. 
 
 The fact that about the same effect can be produced 
 by several causes is expressed by the phrase, ' plurality 
 of causes.' Death, for instance, can be caused in many 
 ways, and so can headaches and sickness generally. 
 The common factor — when I take only a few cases — 
 may not be the effective antecedent. My headache may 
 be caused one night by smoking a cigar and, another 
 night, by drinking too much coffee. We must conclude 
 that the method of agreement is preliminary and that 
 it is final in very simple cases only. The scientist re- 
 gards it as a stepping-stone to experimentation; it 
 leads to guesses which can be tested. 
 
CAUSAL RELATIONS 219 
 
 The Method of Difference. " If an instance in 
 which the phenomenon under investigation occurs, and 
 an instance in which it does not occur, have every cir- 
 cumstance in common save one, that one occurring only 
 in the former ; the circumstance in which alone the two 
 instances differ is the effect or the cause, or an indis- 
 pensable part of the cause, of the phenomenon." A more 
 succinct statement of the canon, bringing out its experi- 
 mental character, is as follows : " When the addition of 
 an agent is followed by the appearance, or its subtrac- 
 tion by the disappearance, of a certain event, other 
 circumstances remaining the same, that agent is the 
 cause of the event." l It should be noted that only one 
 factor should be changed. Great technical skill is often 
 needed to fulfill this essential condition. The investi- 
 gator must have control of his material. 
 
 Examples of the Method. Suppose we have been 
 led to ask ourselves why it is that a feather does not 
 fall to the ground as fast as does a stone. The idea 
 may come to us that the presence of the air is the 
 cause. If we can remove this and keep the other fac- 
 tors the same, we will be able to test our conjecture. 
 The two instances will be as follows : — 
 
 Antecedent conditions Effect 
 
 1st instance : stone and feather dropped in stone falls first 
 
 the air 
 2d instance: stone and feather dropped in both fall together 
 
 a vacuum 
 
 This method is used primarily in physics and chem- 
 istry, for the material of these sciences lends itself to 
 a literal analysis and synthesis under experimental con- 
 
 1 Mellone, An Introductory Text-Book of Logic, p. 274. 
 
220 THE ESSENTIALS OF LOGIC 
 
 ditions. It is less e^sy to apply it to organisms and to 
 social conditions. 
 
 Warnings. When the method can be applied under 
 experimental conditions so that only one factor varies, 
 the only danger lies in the interpretation of the result. 
 The factor may not be the only cause which is able to 
 produce the effect. A plant may die when water is 
 withheld, but it will also die when heat is removed. A 
 positive effect often demands the cooperative presence 
 of many conditions, and then the removal of any one 
 of these will prevent the occurrence of the effect. An- 
 other difficulty lies in the possible presence of counter- 
 acting causes. A man who is very healthy may be able 
 to resist infection, and so may a man who has had the 
 disease and is now immune. So long as there is incom- 
 plete analysis of the situation, interpretation of the 
 result of an experiment has its dangers. Only as fur- 
 ther knowledge is gained, does the only possible inter- 
 pretation begin to stand out. 
 
 When experimental conditions cannot be obtained, 
 there is great danger that the two instances may 
 differ in more than one point. " As an exemplifi- 
 cation of this, we may cite an inference that was sup- 
 posed to be warranted by the experience of one of our 
 larger cities, which had voted to increase materially 
 the price of liquor licenses. The police records, for the 
 period immediately subsequent to the time when the 
 new law went into effect, showed a distinct decrease in 
 the amount of crime. By the method of difference we 
 should naturally attribute this fact to the high license. 
 But it was found that after the election the officials 
 who issued the licenses had been much more careful 
 
CAUSAL RELATIONS 221 
 
 than' before to issue licenses only to applicants of good 
 moral character. This fact alone might account for the 
 decrease in crime, leaving the higher license without 
 effect upon the result." 1 
 
 The Method of Concomitant Variations. 
 " Whatever phenomenon varies in any manner, ichen- 
 ever another phenomenon varies in some particular 
 manner, is either a cause or an effect of that phenom- 
 enon, or is connected with it through some fact of 
 causation" The development of quantitative methods 
 in modern science has made it possible to measure the 
 variations of the important antecedents of an effect 
 and to note corresponding variations in the effect 
 itself. This mode of procedure is especially valuable 
 when the conjectured cause cannot be removed com- 
 pletely but only decreased and increased. The method 
 can be used either as a substitute for the Method of 
 Difference or as a reinforcement of it when the interest 
 of the experimenter travels to the study of the quanti- 
 tative aspects of the causal relation. 
 
 Examples of the Method. The history of science 
 is replete with instances of the application of the 
 Method of Concomitant Variation. By the experiment 
 of Count Kumford, heat was shown to be the effect of 
 motion. " In this famous experiment, which disproved 
 the material theory of heat, a blunt steel borer 3J 
 inches wide was turned by horse power 32 times a 
 minute inside a brass cylinder weighing 113 pounds. 
 In two and a half hours the water surrounding the 
 cylinder and weighing 18| pounds was heated from 
 60° F. to the boiling point. Only 4145 grains of 
 1 Bode, An Outline of Logic, p. 139. 
 
222 THE ESSENTIALS OF LOGIC 
 
 the metal were abraded. Rumford correctly concluded 
 that this large amount of heat, which appeared to be 
 inexhaustible, could not have been derived from the 
 abraded metal, which at the same time had not lost 
 any of its capacity for heat." x The First Law of 
 Motion, Boyle's Law, the theory of the thermometer, 
 the connection of air with the propagation of sound 
 are all dependent, in whole or in part, upon the use of 
 this method. 
 
 Warning. This method stresses the ratio between 
 the change in the causal factor and the change in the 
 effect. It has been found, however, that there is such 
 a thing as discontinuous variation. Metals do not 
 continue to expand at the same rate as the temperature 
 increases, nor do they contract at the same rate as the 
 temperature is lowered. Another point should be 
 noted. It often happens that both of the quantities 
 measured are co-effects of a third factor. Hence, where 
 possible, the Method of Concomitant Variations should 
 be supplemented by the Method of Difference. 
 
 The Joint Method of Agreement and Differ- 
 ence. " If two or more instances in which the phe- 
 nomenon occurs have only one circumstance in com- 
 mon, while two or more instances in which it does not 
 occur have nothing in common save the absence of that 
 circumstance, the circumstance in which alone the two 
 sets of instances differ is the effect, or the cause, or an 
 indispensable part of the cause, of the phenomenon" 
 The Joint Method is a combination of the Method of 
 Agreement and the Method of Difference, and is espe- 
 cially applicable when experimental conditions are not 
 
 1 Carhart, University Physics, pt. n, p. 4. 
 
CAUSAL RELATIONS 223 
 
 obtainable. It is a method of group comparisons. The 
 investigator collects cases in which the desired effect 
 is present and compares the instances to see in what 
 they agree ; he then collects other cases in which the 
 effect is absent and compares these instances to see in 
 what they agree. Finally, he examines the two groups 
 to see wherein they differ. In this way, he approaches 
 as nearly to the Method of Difference as can be done 
 without experimentation. Without some control of the 
 factors, the conclusion can be regarded only as tenta- 
 tive. 
 
 Examples. " 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 hap- 
 pened that all those who developed the disease ate at a 
 certain few fraternity and boarding-house tables. The 
 water supply was first investigated. 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 elimi- 
 nated. The fresh vegetables were supplied from vari- 
 ous 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 de- 
 veloped were supplied from the same variety of sources. 
 The other food supplies came from various places and 
 the Method of Agreement could not be applied so far 
 as they were concerned, with one 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 
 
224 THE ESSENTIALS OF LOGIC 
 
 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 dis- 
 ease appeared." l Another good example is to be found 
 in the work of Darwin upon the cross-fertilization of 
 flowers. In this investigation, Darwin placed a net 
 about one hundred flower heads to protect them from 
 bees. At the same time he exposed another hundred 
 flowers to the bees. Here we have the two groups be- 
 tween which comparison is to be made. He obtained 
 the following results : The protected flowers failed to 
 yield a single seed, while the others produced 68 grains' 
 weight of seed, which he estimated as numbering 2720 
 seeds. 
 
 These examples show that the Joint Method is really 
 the complete application of the two principles of Agree- 
 ment and Difference, and that any exhaustive investi- 
 gation is bound to take this form. Another point stands 
 out clearly. In any actual study the mind is always 
 making conjectures and testing them by these methods. 
 The scientist is not a merely passive tabulator. He 
 knows that the cause must be present when the effect is, 
 and that it must be absent when the effect is absent. 
 Hence, he is on the constant lookout for factors which 
 may fulfill these conditions. 
 
 The Method of Residues. " Subduct from any 
 phenomenon such part as is known by previous indue- 
 tions to be the effect of certain antecedents, and the res- 
 idue of the phenomenon is the effect of the remaining 
 antecedents." This method can be employed only when 
 there is nearly complete information in regard to the 
 1 Jones, Logic, Inductive and Deductive, pp. 98-99. 
 
CAUSAL RELATIONS 225 
 
 field under investigation. By means of this knowledge, 
 we are able to eliminate causal couples until we are left 
 with the few factors remaining for which causal rela- 
 tions have not been determined. In this way, past 
 knowledge enables the investigator to narrow the field. 
 After this is accomplished, he can observe more closely 
 and often experiment. Like the Method of Agreement, 
 the Method of Residues is usually a preliminary pro- 
 cess which needs supplementation. 
 
 Examples. The Method of Residues comes out 
 most clearly where quantitative methods are being em- 
 ployed. For astronomy, the classic example is the dis- 
 covery of the planet Neptune. Certain perturbations in 
 the movement of Uranus could not be accounted for 
 by known gravitational forces. The natural inference 
 was that some unknown planet was at work producing 
 this added increment, the residual effect. Adams in 
 England and Leverrier in France made this hypothesis 
 independently of each other and calculated the prob- 
 able place of the new planet. Following the directions 
 of the latter, Professor Galle, of Berlin, found the new 
 planet in almost exactly the place indicated. Another 
 instance of discovery due to residual effects is that of 
 the rarer elements in the atmosphere such as argon and 
 helium. "In chemical analysis this method is con- 
 stantly employed to determine the proportional weight 
 of substances which combine together. Thus the com- 
 position of water is ascertained by taking a known 
 weight of oxide of copper, passing hydrogen over it in 
 a heated tube, and condensing the water produced in 
 a tube containing sulphuric acid. If we subtract the 
 original weight of the condensing tube from its final 
 
226 THE ESSENTIALS OF LOGIC 
 
 weight we learn how much water is produced; the 
 quantity of oxygen in it is found by subtracting the 
 final weight of the oxide of copper from its original 
 weight. If we then subtract the weight of the oxygen 
 from that of the water we learn the weight of the hy- 
 drogen, which we have combined with the oxygen." 1 
 
 This method is primarily one of quantitative analy- 
 sis. It concerns itself with residual phenomena, with 
 exceptions. Speaking of his father, Francis Darwin 
 says : " There was one quality of mind which seemed to 
 be of special and extreme advantage in leading him to 
 make discoveries. It was the power of never letting 
 exceptions pass unnoticed." Such a habit of mind is 
 assuredly worth cultivation. 
 
 Remarks on Mill's Methods. There is pretty 
 general agreement now among logicians that Mill's 
 Methods can be employed only within a larger induc- 
 tive setting. They are not rules which can be applied 
 mechanically to new and complex fields. The mind 
 must be active in conjecture, interpretation and analy- 
 sis. In the first part of his Logic, Mill is far more Bacon- 
 ian than he is in the latter part. The following quota- 
 tion gives all the correction that is needed and reveals 
 how the Methods are taken up into the concrete process 
 of investigation : " The process of tracing regularity in 
 any complicated, and at first sight confused set of ap- 
 pearances, is necessarily tentative : we begin by making 
 any supposition, even a false one, to see what conse- 
 quences will follow from it; and by observing how 
 these differ from the real phenomena, we learn what 
 corrections to make in our assumption." Increasing 
 
 1 Jevons, Lessons in Logic, p. 254. 
 
CAUSAL RELATIONS 227 
 
 analysis, working hypotheses, gradual elimination of 
 irrelevant factors, and final decision as to the essential 
 connections are the steps in induction. 
 
 REFERENCES 
 
 Creighton, An Introductory Logic, chaps, xvi and xvn. 
 
 Gibson, The Problems of Logic, chap. xiii. 
 
 Jones, Logic, Inductive and Deductive, chap. vi. 
 
 Mill, Logic, bk. in, chaps, vin and ix. 
 
 Minto, Logic, Inductive and Deductive, bk. n, chaps, in, iv, and v. 
 
CHAPTER XX 
 
 STATISTICS 
 
 In many fields of investigation it is impossible to 
 apply the traditional methods. The problem is of such 
 a character and covers such a wide territory that indi- 
 vidual observation cannot furnish the factual material. 
 Furthermore, experimental methods cannot be applied. 
 What is needed is a very broad survey of the facts and 
 a clear tabulation of the results obtained. Out of this 
 necessity has arisen statistical science. "It would be a 
 man of exceptional mnemonic power who could, after 
 listening to the reading of two lists of one hundred 
 items each stating the names and wealth of the respec- 
 tive inhabitants of two villages, give any intelligent 
 opinion as to the comparative riches of the two communi- 
 ties. If this is true for such small groups as this, it evi- 
 dently would be utterly impossible to make comparisons 
 of the wealth of great nations without some manner of 
 reducing the mass of separate facts to a simple whole. 
 The same would, of course, be true in the case of any 
 other phenomena involving large numbers. What could 
 one understand of the amount of lumber contained in a 
 forest from a description of the separate trees ? How 
 could one compare the climates of different localities by 
 a study of their daily weather records ? It is for the 
 purpose of simplifying these unwieldy masses of facts 
 that statistical science is useful. It reduces them to 
 numerical totals or averages which may be abstractly 
 
STATISTICS 229 
 
 handled like any other mere numbers. It draws pictures 
 and diagrams to illustrate general tendencies and, thus, 
 in many ways adapts these groups of ideas to the capac- 
 ity of our intellects." 1 
 
 If the student will recall the discussion of " Classi- 
 fication," he will remember that it was regarded as a 
 process which enables us to handle the complex world 
 of individual things in which we live. Could we not 
 treat things as kinds and know what to expect from 
 them, we should be unable to adapt ourselves to our 
 environment by using our past experience. Now, statis- 
 tics is a way of dealing with particulars which can be 
 counted and which are so numerous that we need to 
 achieve some bird's-eye view of them before we can 
 begin to interpret them. It is a way of collecting and 
 organizing data which are important in masses rather 
 than individually. " The proper function of statistics," 
 writes Bowley, "is to enlarge individual experience." 
 Originally the workers in statistics concerned them- 
 selves almost entirely with facts respecting the condition 
 of the people in a state, but now data in biology and 
 astronomy are also investigated by statistical methods. 
 
 We have frequently pointed out that science always 
 involves analysis. Mental work must be done upon the 
 facts before they yield a meaning and can be applied 
 to the solution of a problem. This element stands out 
 very clearly in the following definition of statistics : 
 " The science of statistics is the method of judging col- 
 lective natural or social phenomena from the results 
 obtained by the analysis of an enumeration or collec- 
 tion of estimates." 2 
 
 1 King, Elements of Statistical Method, p. 24. 2 Ibid., p. 23. 
 
230 THE ESSENTIALS OF LOGIC 
 
 The stages in a statistical investigation are roughly 
 as follows : (1) The setting of the problem ; (2) the 
 collection of the material ; (3) its tabulation ; (4) the 
 summary; (5) a critical examination of the results. 
 Let us look at these stages somewhat closely. 
 
 " Special importance, it seems, must be attached to 
 the question of what are the objects of any particular 
 statistical record. It is not enough to observe the facts 
 at random. Most of the records of statistics, although 
 not all of them, are deliberately arranged to be kept by 
 a community for the purpose of the information of the 
 whole community. . . . The object, then, of any par- 
 ticular statistical record is the first thing about it to be 
 studied, and both the Government in making the rec- 
 ords and the students who come to use them afterwards 
 should have the most distinct ideas upon this point." l 
 This point is stressed by all statisticians. " The first 
 thing upon which the statistical investigator, when be- 
 ginning his work, must decide is the exact nature of 
 the problem which he desires to solve. Even a slight 
 change in its scope or form may require an entirely or 
 partially different method of procedure. If, for illustra- 
 tion, a person wishes to begin a study of comparative 
 wages in order to demonstrate some general theory or 
 proposition, he must first decide as to whether the re- 
 quirements of his problem demand a knowledge of 
 money wages or real wages. Next, he must be sure as to 
 whether he needs to know the wages paid for a definite 
 amount of effort, for making a certain product, or for 
 working a certain length of time, or whether the in- 
 quiry relates to the income of the working man him- 
 
 1 Sir Robert Giffen, Statistics, pp. 4-5. 
 
STATISTICS 231 
 
 self per year or to the total income of the man and 
 his family for the same period. Each of these problems 
 is a distinct one and would require entirely different 
 modes of determination." 1 
 
 Definition of the problem also involves definition of 
 the unit. What shall we mean by 'unemployment' ? by 
 4 person ' ? by * a farm ' ? by 4 sickness ' ? Just as classi- 
 fication and its principles are important for statistical 
 investigation, so is definition. Thus a recent work on 
 Unemployment gives a chapter to the "Meaning and 
 Measurement of Unemployment " and devotes much of 
 its space to the working-out of a definition. " Are we, 
 for example, to include among the unemployed those 
 who are idle because they do not want to work ? Are 
 we to include sick persons, or workmen out on strike, 
 or the various classes of individual who are, for one 
 reason or another, 'unemployable'?" Just as an idea 
 must not be allowed to change its meaning in the course 
 of an argument, so the unit must not be altered in the 
 course of an investigation. The prerequisites of clear 
 thinking are essentially the same for argument of a 
 deductive character and for investigation. 
 
 Before the collection of the material is begun, the 
 problem must be studied in all its details. " Problems, 
 factors, units, questions, schedules, enumerators, tabu- 
 lation, methods of work, time, expense, etc., are among 
 the items that must be carefully gone over in minute 
 detail." The methods of collection must be determined 
 by experience with due regard to the characteristics of 
 the particular problem. The field must be defined and 
 must be as wide as possible. If questions are used, these 
 
 1 King, Elements of Statistical Method, p. 39. 
 
232 THE ESSENTIALS OF LOGIC 
 
 must be comparatively few in number, must be simple 
 enough to be readily understood, and must not arouse 
 prejudices. As in all the other divisions of science, per- 
 sonal judgment cannot be eliminated. Investigation is 
 not a mechanical process. 
 
 " 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 
 instrument of investigation any more than a kiln of 
 bricks is a monument of architecture. They need to be 
 arranged, classified, tabulated, and brought into con- 
 nection 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." * The 
 figures must be grouped in tables under appropriate 
 headings in such a way as to bring out the desired per- 
 centages and correlations. " The power to analyze a 
 table, interpret the results correctly, and state the con- 
 clusions lucidly and succinctly is one of the character- 
 istics indispensable in a good statistician." 
 
 The Law of Statistical Regularity. It has been 
 discovered that a moderately large number of items 
 taken at random from a very large group, are almost 
 sure, on the average, to have the characteristics of the 
 larger group. " Thus, if two persons, blindfolded, were 
 to pick here and there three hundred walnuts each from 
 a bin containing a million nuts, the average weight of 
 the nuts picked out by each person would be almost 
 identical even though the nuts varied considerably in 
 size." Corresponding to this law is its corollary, the 
 
 1 Mayo-Smith, Statistics and Sociology, p. 18. 
 
STATISTICS 233 
 
 law of inertia of large numbers. Logicians have been 
 accustomed to speak of this law as the constancy of 
 averages. " If we take a succession of periods, and di- 
 vide the total number of any kind of event by the num- 
 ber of periods, we get what is called the average for 
 that period: and it observed that such averages are 
 maintained from period to period. Over a series of 
 years there is a fixed proportion between good harvests 
 and bad, between wet days and dry : every year nearly 
 the same number of suicides takes place, the same num- 
 ber of crimes, of accidents to life and limb, even of sui- 
 cides, crimes, or injuries by particular means: every 
 year in a town nearly the same number of children 
 stray from their parents and are restored by the police : 
 every year nearly the same number of persons post 
 letters without putting an address on them." 2 
 
 Dangers in the Use of Statistics. Great care 
 must be taken in the use of statistics. It has been said 
 that " you can prove anything by statistics." And this 
 skepticism reflects the constant misuse of figures. Every 
 stage in the development of tables is liable to its pecul- 
 iar errors which resemble those which face all inves- 
 tigation. Prejudice, inaccuracy, faulty observation, 
 mistakes in copying, wrong interpretation, all exist as 
 possible sources of falsehood. Another cause of error is 
 the lack of recognition given to the difference between 
 quantity and quality. " In sociological science the im- 
 portance of differences of quality is enormous, and the 
 effect of these differences on the conclusions to be 
 drawn from figures is sometimes neglected, or insuffi- 
 ciently recognized, even by men of unquestionable 
 1 Minto, Logic, Inductive and Deductive, p. 351. 
 
234 THE ESSENTIALS OF LOGIC 
 
 ability and good faith. The majority of politicians, so- 
 cial ' reformers ' and amateur handlers of statistics gen- 
 erally are in the habit of drawing the conclusions that 
 seem good to them from such figures as they may ob- 
 tain, merely by treating as homogeneous quantities 
 which are heterogeneous, and as comparable quantities 
 which are not comparable. Even to the conscientious 
 and intelligent inquirer the difficulty of avoiding mis- 
 takes in using statistics prepared by other persons is 
 very great. There are usually 'pitfalls' even in the 
 simplest statistical statement, the position and nature 
 of which are known only to the persons who have actu- 
 ally handled what may be called the ' raw material ' of 
 the statistics in question; and in regard to complex 
 statistical statements the ' outsider ' cannot be too care- 
 ful to ascertain from those who compiled them as far 
 as possible what are the points requiring elucidation." 1 
 So frequent a use is made of statistics now that the 
 logician feels it a part of his duty to stress these 
 warnings. The following example may serve to indicate 
 how easily fallacy may creep in : " An example of such 
 a fallacy, due to the use of erroneous factors, was fur- 
 nished by a newspaper in a discussion of the American 
 navy during the Spanish- American War. It was stated 
 that the death-rate in the navy during the war period 
 was only nine per thousand, while in the city of New 
 York for the same period the death-rate was sixteen 
 per thousand. The conclusion was drawn that it was 
 safer to be a sailor in our navy in war-time than to live 
 in New York City. A little reflection, however, will 
 convince one that such a conclusion is not warranted 
 
 1 Encyclopaedia Britannica, art. " Statistics." 
 
STATISTICS 235 
 
 by the figures given. In obtaining this ratio, the total 
 number of deaths was taken as the numerator in each 
 case and the denominators were respectively the total 
 number of persons living in New York City and the 
 total number of sailors in the navy. But, as a matter 
 of fact, these numbers were wholly incomparable. It is 
 a well-known fact that the death-rate is very high 
 among young children and among old people. But the 
 personnel of the navy is composed almost wholly of 
 young men in the prime of strength and vigor. Not 
 only this, but each must pass a strict examination to 
 show that he is healthy and robust. Thus, the weak 
 and diseased are eliminated. Evidently, the facts would 
 require that the death-rate in the navy be compared 
 with the death-rate of a similar picked body of men in 
 New York City before any legitimate conclusions could 
 be drawn regarding the comparative chances of death 
 in the two places." * 
 
 The Value of Statistics. There are three main 
 ends subserved by statistics : Its employment contrib- 
 utes to a descriptive survey of a field which cannot be 
 otherwise grasped. Figures are then merely a method 
 of expressing facts, as the amount of wheat produced, 
 the quantity of exports, the amount of the national 
 wealth. Such information is often of the greatest sig- 
 nificance. We may wish to compare one country with 
 another, or the same country at different times. Very 
 frequently the data obtained can be used to test a theory 
 which has been worked out more or less deductively. 
 Wherever there is induction, there must be appeal to 
 relevant fact ; and in many fields, statistics is the only 
 
 1 King", Elements of Statistics, p. 40. 
 
236 THE ESSENTIALS OF LOGIC 
 
 means of securing such facts. In the second place, the 
 discovery of averages which are fairly constant enables 
 man to predict the general run of cases in the future. 
 As we shall see in the next chapter, the theory and 
 practice of life insurance are founded upon the exist- 
 ence of such averages which are being continually de- 
 veloped and rendered more accurate. In the third 
 place, tables of statistics often reveal correlations which 
 would not otherwise have been discovered because of 
 the complexity of the material and our inability to ana- 
 lyze it into distinct strands of causal uniformities. 
 When data are properly arranged, the field is condensed 
 and simplified and it is possible to note relations which 
 would have remained hidden. The use of graphs is 
 often an aid because they make a direct appeal to the 
 eye. An example of a correlation which suggests the 
 presence of causal relations is the fluctuation of the num- 
 ber of births in a country correspondent with the food 
 prices of the previous year. Let us consider this third 
 function of statistics a little more fully. 
 
 The principle underlying the deduction of causal re- 
 lations from correlations is the assumption that if the 
 events are unconnected, their frequencies should not 
 fluctuate together nor coincide beyond a certain amount. 
 Bain formulated the following rule : " Consider the 
 positive frequency of the phenomena themselves, and 
 how great frequency of coincidence must follow from 
 that, supposing there is neither connection nor repug- 
 nance. If there be greater frequency, there is connec- 
 tion ; if less, repugnance." Repugnance is usually spoken 
 of in statistics as negative correlation. An example 
 would be the relation between vaccination and small- 
 
STATISTICS 237 
 
 pox. In delicate cases, it is very difficult to estimate 
 the degree of coincidence between non-causal events. 
 How often, for instance, must dreams and their apparent 
 fulfillment coincide to pass beyond mere coincidence ? 
 
 Variation in averages is a fruitful source for the dis- 
 covery of causal relations. If we assume that the con- 
 stancy of the averages is due to the maintenance of the 
 relative proportions of the same factors in the field 
 under investigation, then any change in the average 
 must be due to an alteration in this proportion or to 
 the entrance of a new factor. A study of the geo- 
 graphical distribution of suicide is a good instance of 
 the suggestive character of comparative statistics. We 
 immediately ask ourselves why one country leads, what 
 can be the peculiar conditions which cause more people 
 to commit suicide there. It will be noted that such 
 comparison involves a near approach to the method of 
 differences. But experiment is impossible. When an 
 average begins to change, the investigator seeks the pres- 
 ence of some new cause or the increase of some cause 
 already operative. " The number of homicides in the 
 United States in 1894 far exceeded the annual num- 
 ber observed for the years preceding. This discrepancy 
 is easily accounted for by the fact that the natural 
 number was swollen by the deaths caused by the strik- 
 ers and rioters in the month of July of that year. So 
 also a marked departure from the annual death-rate of 
 such a city as New York is at once an urgent sugges- 
 tion to the Board of Health to start investigations that 
 will unearth the hidden cause that one is constrained 
 to believe must be present. Such causes as defective 
 drains, prevalence of epidemics, etc., are again and 
 
238 THE ESSENTIALS OF LOGIC 
 
 again found to accompany an increase of the average 
 death-rate." * The principle involved is essentially that 
 of concomitant variation. 
 
 REFERENCES 
 
 King, Elements of Statistical Method, chaps, I, n, and in. 
 
 Bowley, Elements of Statistics, passim. 
 
 G iff en, Statistics, chap. i. 
 
 Creighton, An Introductory Logic, chap. xv. 
 
 Elderton, Primer of Statistics. 
 
 Hibben, Logic, Deductive and Inductive, chap. xv. 
 
 Mayo-Smith, Statistics and Sociology, chaps. I, n, and ill. 
 
 1 Hibben, Logic, Deductive and Inductive, p. 344. 
 
CHAPTER XXI 
 
 PROBABILITY 
 
 Abstract Laws versus Concrete Events. While 
 the physical sciences are chiefly interested in the dis- 
 covery of universally valid causal laws and in the 
 construction of illuminating general principles and 
 theories, problems of another sort come to the front in 
 practical life, the applied sciences, and those fields of 
 research in which experimental control is impossible. 
 Where experiment is possible, factors can be eliminated 
 as irrelevant or confusing, and the remaining elements 
 can then be analyzed into couples uniformly connected. 
 But where such experimental control and simplification 
 is out of the question, causes counteract one another in 
 the most complex ways or else combine to produce 
 effects which are not deducible from any one of them. 
 In other words, such causal uniformities as we discover 
 by experiment are blurred when they enter this whirli- 
 gig of a world, and it is with the greatest uncertainty 
 that we predict the course of events. 
 
 In science, the investigator usually passes from effect 
 to cause; in everyday life, the problem is to pass from 
 the play of events to the probable result. What it is 
 now desired to ascertain is what will probably happen 
 in the tangled skein of events which cannot be com- 
 pletely analyzed beforehand. Will the country be 
 prosperous a year from now or plunged in a panic? 
 Will this bank be solvent or will it fail? Will the 
 
240 THE ESSENTIALS OF LOGIC 
 
 crops be good this year? Such questions make us 
 realize the complexity of things and our inability to 
 deduce events from the few uniformities we have as 
 yet discovered. Most laws have their exceptions be- 
 cause the essential factors are masked by the interplay 
 of their fellows. 
 
 "Where Certainty is possible. Certainty as to the 
 future is possible only when all the factors whose opera- 
 tions will produce it are known. Moisture causes 
 plants to grow when it is combined in the proper pro- 
 portion with heat and sunshine and good soil. It is 
 evident that quantities are important if we are to pre- 
 dict. Thus, we must have knowledge of the essential 
 conditions, qualitative and quantitative, of an event 
 and have assurance of their presence before we have 
 the logical right to predict an event with certainty. In 
 a carefully conducted experiment in chemistry where 
 quantities and qualities are both under control, expec- 
 tation is based on exact knowledge, and all that we need 
 to assume is the general principle of the Uniformity of 
 Nature. Again, prediction is possible in astronomy 
 where the forces at work are relatively few in number 
 and measurable. In this realm of giant masses and gravi- 
 tational forces acting according to well-known laws, it 
 is possible to foretell the relative positions of bodies 
 and so arrange in tables, centuries ahead or behind the 
 present, those eclipses and juxtapositions which are of 
 human interest. But when the antecedents cannot be 
 analyzed in this fashion and are known to be more 
 fluctuating in their permutations and combinations, 
 prediction loses certainty and drops to probability. 
 
 The Meaning of Probability. Probability at- 
 
PROBABILITY 241 
 
 taclies to particular facts and to generalizations. We 
 use the term when we feel that the balance of evidence 
 is in favor of a principle or an individual fact even 
 though it has not been raised above reasonable doubt. 
 So far as principles are concerned, their probability re- 
 flects the degree to which they are supported by the 
 collected evidence. It may be that all the evidence 
 thus far attained is favorable but that we do not re- 
 gard it as extensive enough ; or it may be that the evi- 
 dence is conflicting. When we are concerned with the 
 probability of the occurrence of an event, on the other 
 hand, we are attempting to make an estimate of our 
 admittedly insufficient knowledge to determine whether 
 it is in favor of, or against, this particular occurrence. 
 We temper the degree of our expectation in accordance 
 with such relevant knowledge as we can gather. In 
 contrast with certainty, we may say that probability is 
 the degree of expectation which is judged to be war- 
 ranted by the facts. We say that an event is probable, 
 or quite probable, or very probable, or extremely 
 probable. 
 
 Probability and Chance. Probability must not 
 be confused with objective chance. The principle of the 
 Uniformity of Nature is essentially the denial of any- 
 thing like real chance in the world. But nature is so 
 complex that we are not able to note and analyze all 
 the conditions of the majority of events. Causal fac- 
 tors reinforce and counteract one another in unforeseen 
 ways, and the actual result can be learned only from 
 experience. That I turned up an ace of spades the last 
 time I cut for the deal was, so far as my knowledge 
 went, a case of chance. In short, chance is a term ex- 
 
242 THE ESSENTIALS OF LOGIC 
 
 pressive of my ignorance of what is taking place. 
 "There is no doubt in lightning,' ' writes Jevons, " as 
 to the point it shall strike ; in the greatest storm there 
 is nothing capricious; not a grain of sand lies upon 
 the beach but infinite knowledge would account for its 
 lying there ; and the course of every falling leaf is 
 guided by the same principles of mechanics as rule 
 the motions of the heavenly bodies." 1 
 
 Three Kinds of Estimations. Eoughly speaking, 
 we may distinguish three kinds of probability-estima- 
 tions. The first is empirical and largely qualitative; 
 the second deals with averages and is closely connected 
 with the development of statistics ; the third is of a de- 
 ductive, mathematical type. What logic is interested 
 in is the nature of the induction and the dangers 
 run. 
 
 1/ Empirical, or Non-Quantitative, Probability. 
 As regards most events, we do not keep any exact record 
 of how things have happened in the past, but trust 
 to a general impression, to a sort of cumulative esti- 
 mation expressive of past experience. This judgment 
 is then related to the particular circumstances of the 
 case in hand and a feeling of probability arises in con- 
 sciousness. Suppose that you hear that a person whose 
 name is not given has met with an accident in the city 
 of Washington. The idea may come to you that it may 
 be your brother who lives there ; but the idea is sure 
 to be dismissed unless other information points in the 
 same direction. Suppose that the accident happens in 
 a government building where he works, and that the 
 description of the individual tallies somewhat with his 
 
 1 Principles of Science, vol. I, p. 225. 
 
PROBABILITY 243 
 
 appearance, your passing idea begins to be entertained 
 more seriously and you await some letter or telegram. 
 If it does not come within a day or so, you dismiss the 
 suggestion. You know that there are many govern- 
 ment employees and that rough descriptions apply to 
 large numbers of individuals equally well. 
 
 Probabilities based on Averages. A frequently 
 employed method of calculating probabilities is the 
 study of averages for classes. Sometimes such a study 
 is non-statistical, but it readily passes into the stage of 
 statistics. An individual may calculate that he has many 
 more years to live because he is healthy and fairly 
 young and is working in a profession where the risks 
 are small. " This type of reasoning is duplicated in 
 many other instances. When we mail a letter, we 
 count pretty confidently upon its safe arrival. From 
 time to time, letters get lost, through carelessness, in 
 railroad wrecks, or as a result of other causes, but the 
 number of those is so small a proportion of the total 
 number that we treat it as practically a negligible 
 quantity. For the same reason we leave out of account 
 the possibility that at some time we shall be struck by 
 lightning, or, when we make a journey, that our train 
 will be wrecked, or that our home will be destroyed by 
 an earthquake, or that a stranger o£ whom we make 
 inquiries as to directions will be insolent or show an- 
 noyance." 1 
 
 The best familiar example of the calculation of prob- 
 abilities for a class is to be found in the field of life in- 
 surance. Tables are worked out for the various trades 
 and professions and for individuals of different ages. 
 
 1 Bode, An Outline of Logic, p. 150. 
 
244 THE ESSENTIALS OF LOGIC 
 
 Any applicant is classified and his probable length of 
 life estimated by reference to the group in which he is 
 classified. A danger of fallacy lurks in this method 
 when its meaning is misunderstood. It must be borne 
 in mind that such probability only applies to the class 
 and not directly to the individual. We are not able to 
 predict which individuals will die, but only that about 
 so many out of every thousand of a certain age will die. 
 It is upon the constancy of these averages that the com- 
 pany calculates the necessary premium. 
 
 Estimates of probability are made more accurate by 
 deepening the classifications made. The greater the 
 number of essential characteristics that are included, 
 the smaller and more homogeneous the class.t-Thus, 
 teachers and ministers are known to have a far longer 
 average of life than miners and textile workers. Statis- 
 tics have shown that the average length of life of the 
 rich is greater than that of the poor. It has been esti- 
 mated that in England the average duration of life 
 among the wealthy classes is from fifty-five to fifty-six 
 years, while in the working classes it falls to twenty- 
 eight years, or even lower. 
 
 A word of warning may, perhaps, be advisable at 
 this point. Probability of this objective sort is based 
 on the use of statistics. Now the growth of statistics 
 has shown a constancy in the number of crimes com- 
 mitted in a certain country in the course of a year, in 
 the number of suicides, in the number of fires, etc. 
 In the preceding chapter, we spoke of this regularity as 
 the 4 law of inertia of large numbers.' The meaning of 
 this law has been much misunderstood, many fearing 
 that it implied a kind of mechanical necessity at work 
 
PROBABILITY U5 
 
 in society corresponding to the 'reign of law ' in nature. 
 It is well to bear in mind that such expressions are 
 metaphorical and that we must penetrate behind them 
 to the exact facts of the case. Laws are human formu- 
 lations and do not reign in the physical world by divine 
 right or otherwise. In the same way, statistical constan- 
 cies are only formulations of data and do not imply any 
 fate lying back of, and controlling, society. The follow- 
 ing passage from Quetelet, the famous Belgian statis- 
 tician, is worth quoting in this connection : " Amongst 
 the facts disclosed in my book, the one which has given 
 rise to most alarm is the constancy of crime from year 
 to year. By a comparison of numbers, I believed I had 
 data for inferring, as a natural consequence, that in a 
 given country, under the same conditions and influ- 
 ences, we might expect a repetition of the same facts, 
 a reproduction of the same crimes and the same con- 
 demnations. But how was this received ? A crowd of 
 timid people raised the cry of fatalism ! Now, what do 
 the facts teach us ? This, simply, — that in any given 
 state, subject to the influence of the same causes, the 
 effects will not differ appreciably ; they will oscillate 
 more or less about some mean. Now, mark what I have 
 said: subject to the influence of the same causes; so 
 that, therefore, if those causes change, the effects will 
 be likewise modified. But, since the laws and principles 
 of religion and morality are the source of the influences 
 in question, I cherish not only the hope, but — what 
 you perhaps do not — the deepest conviction even, that 
 society can be reformed and ameliorated." The clear- 
 sighted student will realize that we are here skirting 
 some of the most interesting problems of philosophy. 
 
246 THE ESSENTIALS OF LOGIC 
 
 What it is important and easy to realize is that con- 
 stancy in averages does not involve fatalism. 
 ^^The Mathematical Treatment of Probability. 
 We can divide the mathematical treatment of probabil- 
 ity into two parts, the conditions for the application of 
 a calculus of probability and the rules for estimating 
 probability. 
 
 The first condition for the application of a calculus 
 of probability to events is the possession of knowledge 
 sufficient to assure us that some one or other of a defi- 
 nite number of ways of happening are possible, but not 
 sufficient to inform us in which particular way the event 
 will occur. There must be this peculiar mixture of 
 knowledge and ignorance. " For example, if a penny is 
 tossed it will fall with either head or tail uppermost. 
 Now, which will be uppermost in any particular throw 
 will be exactly determined by such conditions as the 
 position of the coin at starting, how it is grasped in the 
 fingers, the force and direction of the twist, etc. But 
 what special form these conditions will take we are to- 
 tally ignorant." 1 The second condition is that the same 
 general set of conditions and antecedents must be pres- 
 ent and operative during the whole course of the events 
 for which a calculation is being made. For instance, to 
 substitute another coin with a curve on one of its sur- 
 faces for the original one would make a calculation im- 
 possible. Both of these conditions are secured in games 
 of chance. Since it is not the function of the logician 
 to enter into the mathematics of probability in detail 
 but only into the logical theory at its foundation, we 
 shall consider only the simplest cases. 
 
 1 Welton, Manual of Logic, vol. 11, p. 167. 
 
PROBABILITY 247 
 
 The probability of a single event is expressed by a 
 fraction whose numerator is the number of favorable 
 alternatives, and denominator the total number of al- 
 ternatives. Since a coin has only two sides, the proba- 
 bility of getting heads in any one trial is J. We say 
 that the chances for heads and tails are equal and that 
 the probability of each is i. In the case of dice, the 
 number of sides is greater and, accordingly, the prob- 
 ability for any one side is less. The denominator is 6 
 while the numerator is 1 for any one side. This is ex- 
 pressed in mathematical form by saying that the prob- 
 ability for each side is J. The method of reasoning in the 
 case of playing cards is essentially the same. The total 
 number of possibilities is 52 and the chance for any one 
 card is •£%. The chance of getting an ace would be -^ . 
 
 There are two rules with compound events according 
 as such events are (1) independent or (2) dependent 
 on one another. 
 
 The probability of obtaining any combination of in- 
 dependent events is the product of the probabilities of 
 the several events. Let us take the throwing of dice as 
 an example. " If one die is thrown the probability 
 that it will fall with the side bearing six pips upper- 
 most is ^, as the die has six sides, and the probability 
 of being uppermost is equal for them all. If a second 
 die is thrown the probability that in that throw six will 
 be uppermost is also 1 ; consequently the probability 
 that six will be thrown in each of two throws is i X ^ = -§§ . 
 In this case, it is obviously immaterial whether two dice 
 are thrown simultaneously or whether the same die is 
 thrown successively." 1 Obviously the number of pos- 
 1 Welton, Manual of Logic, p. 174. 
 
248 THE ESSENTIALS OF LOGIC 
 
 sibilities is 36 and only one of these is the combination 
 desired. 
 
 If two events are mutually exclusive, the probability 
 of getting one or the other is the sum of their inde- 
 pendent probabilities. Thus, in throwing dice, the 
 probability of getting a six or a five is | -f- J, or J. The 
 principle is the same as for simple events. 
 
 We come now to compound events in which the 
 occurrence of the first affects the probability of the 
 occurrence of the others. In such cases the probability 
 of the compound event is the product of the probability 
 of the first with the probability of the second as af- 
 fected by the first. "For example, what is the proba- 
 bility of drawing two white balls in succession, without 
 replacing the first drawn, from an urn containing two 
 white balls and one black one? If a black is drawn 
 first, the estimate is rendered impossible. The proba- 
 bility of drawing a white first is |. If it is drawn, the 
 constitution of the urn for the second draw is modified 
 by the first draw. There are now only two balls, one 
 white and one black, in the urn ; and the probability of 
 drawing the white is 1." Therefore, the probability of 
 drawing two whites is § X J = -J. 
 
 Mistakes in interpreting Probabilities. Mis- 
 takes are often made in the interpretation of probabili- 
 ties. Probabilities based on averages, as in life insur- 
 ance, do not give us any information in regard to any 
 particular individual. " Statistics, from the very nature 
 of the subject, cannot and never will be able to take 
 into account individual cases." 1 When we come to de- 
 ductive, or mathematical, probability, other warnings 
 1 King-, Elements of Statistics, p. 35. 
 
PROBABILITY 249 
 
 must be issued, especially for the non-mathematician. 
 He must bear the above rules in mind and remember, 
 for instance, that the throws " in which we get a six 
 with either of two dice are not so common as the throws 
 in which we get either a six or an ace with one die. 
 We turn up as many sixes with the two dice as we turn 
 up sixes and aces with one ; but since the two sixes are 
 on different dice and are therefore not incompatible, 
 they come together in one throw out of thirty-six, and 
 we do not turn them up in so many separate throws." l 
 Another point is of interest. The past run of throws 
 can offer no basis for an inference as to the character 
 of the next throw. " To expect that, because a coin has 
 come up heads several times in succession, it is there- 
 fore more likely to come up tails the next time, is 
 wholly to misunderstand the meaning of probability. 
 Indeed, a preponderance 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 one 
 half." 2 We see, then, that the calculus of probability 
 is only a guide which we take when we cannot secure 
 definite information about particular cases. Moreover, 
 it is only when certain conditions are fulfilled that the 
 probability in favor of a certain occurrence can be esti- 
 mated with any large degree of mathematical accuracy. 
 
 1 Aikins, The Principles of Logic, p. 340. 
 
 2 Jones, Logic Inductive and Deductive, p. 223. 
 
250 THE ESSENTIALS OF LOGIC 
 
 REFERENCES 
 
 Aikins, The Principles of Logic, chap. xxxn. 
 Bode, An Outline of Logic, chap. xi. 
 Coffey, The Science of Logic, vol. n, p. v, chap. II. 
 Jones, Logic, Inductive and Deductive, pt. n, chap. in. 
 Welton, Manual of Logic, bk. v, chap. vi. 
 
CHAPTER XXII 
 
 AVERAGES AND GRAPHS 
 
 The Uses of Averages. In the two preceding chap- 
 ters we have had frequent occasion to speak of aver- 
 ages. Statistics does not concern itself with the individual 
 case, but with the average for a group or collection. 
 Thus, we are presented with the average income per 
 capita, the average number of rooms in the houses oc- 
 cupied by working people, the typical expenditure of a 
 family for food, etc. Insurance, industrial, and health 
 statistics all take this form. It behooves us, therefore, 
 to have some knowledge of the methods used in obtain- 
 ing such averages and the ways in which they are best 
 presented to the mind. 
 
 The following uses summarize very well the view of 
 the modern investigator : — 
 
 "Averages are used: 1. To give a concise picture 
 of a large group. We could not grasp the idea well 
 if given the height of every tree in a forest, but the 
 average height is something definite and comprehen- 
 sible. 
 
 " 2. To compare different groups by means of these 
 simple pictures. Thus, two forests can only be com- 
 pared by means of totals or averages of some sort. 
 
 " 3. To obtain a picture of a complete group by the 
 use of sample data only. An average obtained from a 
 few hundred samples is so close to the exact average of 
 the whole that the difference is negligible. 
 
252 THE ESSENTIALS OF LOGIC 
 
 " 4. To give a mathematical concept to the relation* 
 ship between different groups. We may say that the 
 trees in one forest are taller than in another, but in 
 order to find any definite ratio of heights, it is neces- 
 sary to resort to averages." l 
 
 The logic of such a situation is clear. In statistics, 
 we stress the quantitative or measurable side of things ; 
 and we take them, not as individuals, but as groups. 
 The only way to institute a comparison is to reduce 
 them to some common unit. What this common unit 
 will be depends largely upon the purpose. We shall 
 briefly describe the common averages used and point 
 out their special value. 
 
 The Arithmetical Average. The arithmetical 
 average is the sum of the particular items divided by 
 their number. By means of such an average, we are 
 able to handle all the items as a single typical unit 
 which we are able to compare with other like units. 
 Thus, two football teams may be compared in regard 
 to their weight by this means. Suppose the weights of 
 the members of one team were 162, 180, 190, 155, 
 170, 176, 182, 167, 205, 169, 158 pounds; then 
 the average weight would be 174 pounds. The same 
 method would be used to determine the average for the 
 other team, and so a comparison could be instituted. 
 
 It is obvious that such information as the above has 
 its limitations. It makes a deal of difference where the 
 weight in a team is distributed, and a general average 
 for the whole group does not bring this out. Hence 
 smaller groups are taken, such as the backfield or the 
 line, and further comparisons instituted. The advan- 
 
 1 King 1 , Elements of Statistics, p. 121. 
 
AVERAGES AND GRAPHS 253 
 
 tages and disadvantages of the arithmetical average 
 will be discussed later. 
 
 The ' "Weighted ' Average. "By a 'weighted' 
 average, we mean one whose constituent items have 
 been multiplied by certain weights before being added, 
 the sum thus obtained being divided by the sum of the 
 weights instead of by the number of items." There are 
 two types of weighted averages : one in which groups 
 with varying numbers of members are already averaged 
 and we desire to secure the arithmetical average for the 
 groups taken together ; and the other in which the 
 weights stand for estimates of relative importance. 
 
 An example will make the first type clear. If, for 
 example, a department store had seven departments 
 and the average wage for each department was known, 
 to obtain the weighted average it would be necessary 
 to multiply the average wage for each department by 
 the number of workers in it, add the results together, 
 and divide by the total number of workers. 
 
 The second type appears in the use of 4 index-num- 
 bers ' which represent the estimated importance of the 
 various groups. The following discussion by Bowley 
 brings out very well the nature of the problem and the 
 way in which it is met : — 
 
 The classical and most useful application of weights 
 is the formation of an index-number for the change of 
 prices by fitting suitable weights to the changes meas- 
 ured in the prices of various commodities. It is re- 
 quired to find the change in the value of gold when 
 measured by the prices of other commodities. Suppose 
 that we are given that prices of certain commodities 
 between two years were in the following ratios : — 
 
254 THE ESSENTIALS OF LOGIC 
 
 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 when ex- 
 pressed in commodities. But it is at once clear that we 
 cannot allow the commodities given to have equal influ- 
 ences 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 follow- 
 ing table : — 
 
 *_* •SkSt* 1 JSft »■*- 
 
 Wheat 77 7 539 
 
 Silver 60 1 60 
 
 Meat 90 3 270 
 
 Sugar 40 2 80 
 
 Cotton J*5 j* 340 
 
 352 17 1289 
 
 1289 
 Weighted average is ... * == 75.8 
 
 352 
 
 Unweighted average is. . = 70.4 * 
 
 5 
 
 Weights are expressions of expert judgment and are 
 to a certain extent relative. The logician must recog- 
 nize that a possibility of error lies in their assignment. 
 
 1 Bowley, Elements of Statistics, pp. 111-12, quoted from Jones. 
 
AVERAGES AND GRAPHS 255 
 
 Fortunately, it can be demonstrated that an error in 
 weights is less serious in its effects than a mistake in 
 the size of the original items. 
 
 The Mode. Another average which is very useful 
 is the mode. It is variously defined as the most fre- 
 quent size of item, the positions of greatest density, and 
 the quantity which occurs with the greatest frequency. 
 It is what we usually have in mind when we speak of 
 4 the average man,' 4 the average income,' ' the average 
 sized apple,' etc. We may say that the mode represents 
 the type. 
 
 The mode is not always easily determinable. When 
 the case is simple, the mode can be determined by an 
 examination of a frequency table. The following exam- 
 ple should make the method clear : — 
 
 Frequency Table showing Heights of Cornstalks 
 
 ight in ft. (size of item) 
 
 No. of stalks (frequency) 
 
 m 
 
 f 
 
 3-4 
 
 3 
 
 4-5 
 
 7 
 
 5-6 
 
 22 
 
 6-7 
 
 60 
 
 7-8 
 
 85 
 
 8-9 
 
 32 
 
 9-10 
 
 8 
 
 n==217 
 
 It will be noticed that size 7-8 is found 85 times, 
 which is the greatest frequency, and is therefore the 
 mode. There may be two or more frequencies with 
 about equal claims to be the most usual occurrence. 
 Such is the case in the variations of animal forms where 
 one type shades continuously over into another. The 
 
25G THE ESSENTIALS OF LOGIC 
 
 finer the grades, the easier it is to determine the domi- 
 nant mode. 
 
 The value of the mode comes out in the following 
 examples : " The mode rather than the average in chest- 
 measurements is the number most suitable for the 
 ready-made clothier. For providing 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." 
 
 The Median. The median is the middle quantity in 
 a series. " If a number of similar objects are placed 
 side by side in order of their size, they are said to be 
 arrayed. If any group of objects is thus arrayed, the 
 middle one is known as the median item." 
 
 The median is of particular value when the data 
 dealt with are not susceptible of measurement in defi- 
 nite units. Psychological phenomena come in this class 
 of material. " It is impossible to measure in specific 
 units the mental characteristics of a child but it is per- 
 fectly possible to array a group of children according 
 to their respective mentality." 1 For this reason, the 
 median was used by Francis Galton in his investiga- 
 tions in inheritance and is being used in fields where 
 quality can be graded in a series. 
 
 The Geometric Average. The geometric average 
 is obtained by multiplication of the n items of a series, 
 and the extraction of the nth root of the produce. This 
 average soon reaches a complexity which makes it im- 
 possible of easy application for those not familiar with 
 
 1 King, Elements of Statistics, p. 131. 
 
AVERAGES AND GRAPHS 257 
 
 mathematics. Beyond the square and cube root, it in- 
 volves the use of logarithms. It is very little used at 
 the present. 
 
 The Comparative Advantages of these Aver- 
 ages. The mode is of advantage where we are not con- 
 cerned with extreme variations which are few in num- 
 ber, but with the type. Its disadvantage is that it is 
 not always easy to determine. The median is easily lo- 
 cated and can be determined for all data which can be 
 arrayed in a series. Its chief advantage is that it is ap- 
 plicable to relatively qualitative fields. The arithmetical 
 average is readily calculated and gives weight to all the 
 items; its chief disadvantage is that it requires the 
 presence of all the items and even emphasizes the ex- 
 tremes. The weighted average is a correction of the 
 arithmetical when the series is made up of groups ; its 
 chief importance, however, lies in its adaptation to the 
 use of index-numbers. The average used in any con- 
 crete investigation is determined by the character of 
 the problem and the nature of the material. Often more 
 than one average is calculated. 
 
 Graphs and Graphical Methods. Diagrams are 
 often employed to summarize tables in a picturesque 
 and striking way. Various devices have been worked 
 out to render the meaning of masses of figures clear 
 and unambiguous. The following simple diagrams are 
 often used in the exposition of statistical data : — 
 
 1, Cartograms. Phenomena with a geographical 
 location can be brought clearly before the eye by means 
 of maps with devices to show variations. Colored print- 
 ing is sometimes used, but, since this is expensive, va- 
 rious modes of barring are employed. The rainfall maps 
 
258 THE ESSENTIALS OF LOGIC 
 
 printed in the newspapers are good examples of this 
 class. Another method is the use of dots to indicate the 
 relative amount of the product under investigation, 
 each dot standing for a given quantity. Such things as 
 wheat and corn production can be represented in this 
 way so that the results appeal directly to the eye. 
 
 2. Pictograms. Pictures of comparative sizes, bar 
 diagrams, block pictograms, and circles divided into 
 segments are some of the devices used to bring data 
 before the eye. The importance of such pictorial meth- 
 ods for exposition can hardly be overestimated. "After 
 a person has collected data and studied a proposition 
 with great care so that his own mind is made up as to 
 the best solution for the problem, he is apt to feel that 
 his work is about completed. Usually, however, when 
 his own mind is made up, his task is only half done. 
 The larger and more difficult part of the work is to 
 convince the minds of others that the proposed solution 
 is the best one — that all the recommendations are 
 really necessary." 1 One of the advantages of the 
 graphic method is that the facts can be so presented 
 that the reader can make deductions of his own. 
 
 Experience has shown that some forms of charts are 
 far superior to others and that faulty arrangements are 
 easily adopted when criticism has not been directed 
 against them. The bar method has many advantages 
 in that it permits an exact estimation of the component 
 parts and the use of colors to distinguish them. A 
 development of the bar method by subdivision bars is 
 shown in Fig. 15. 2 The sector method is widely used in 
 
 1 Brinton, Graphic Methods for Presenting Facts, p. 1. 
 
 2 Figures 15, 16, and 17, on pages 259, 260, 261, are taken from Brin- 
 ton's Graphic Methods for Presenting Facts, by permission of the pub- 
 lishers, The Engineering Magazine* 
 
£ *> 
 
 H *»3 
 
 fi 
 
 M 
 
 U°bl 
 
 II 
 
 -I 
 M 
 
 el 
 
 li 
 
 fi 
 
260 
 
 THE ESSENTIALS OF LOGIC 
 
 popular magazines ; its disadvantage lies in its lack of 
 flexibility and the difficulty of arranging and lettering 
 the sectors of the circle. Fig. 16, taken from The 
 Survey, is a good example of pictorial presentation. 
 
 In almost every chapter we have been compelled to 
 stress the importance of analysis for thinking. What 
 is called ' scientific management ' is beginning to point 
 out its importance for social and industrial fields. The 
 way in which the graphic method is being employed 
 for this purpose is shown in Fig. 17, taken from System. 
 
 Fig. 16. DISPOSITION OP A FAMILY INCOME OF FROM 
 $900 TO $1000 
 
 This cut shows an attempt to put figures in popular form. The eye is likely 
 to judge by the size of the pictures rather than by the angles of the sectors. 
 
g | 
 
 g s 
 
 M 2 
 
 2 s 
 
 s 1 
 
 Q ° 
 
 125 
 
 < 
 3 
 
 
 -a 
 
 1 
 
 A 
 
 5 J 
 
 a .a 
 
 e 5 
 
262 THE ESSENTIALS OF LOGIC 
 
 "Authority reaches down through the several branches 
 of an organization like descent of blood, and, if prop- 
 erly planned, it will be as irregular for a factor in an 
 organization to be in doubt as to the person in authority 
 over him as for the child to deny the parentage of his 
 father. • . . It should be graphically shown what posi- 
 tions are only temporarily filled, so that when new men 
 are engaged they will fit into the scheme with functions 
 planned, "* In such classification, we are dealing with 
 parts of a system rather than with genera and species 
 as in natural science. 
 
 3. Frequency Graphs. Frequency tables are reduced 
 to graphs in various ways. The foundation is the em- 
 ployment of coordinates cutting each other at right 
 angles at a point called the ' origin.' One set of data 
 is measured along the axis of abscissae, while the other 
 set is measured along the ordinate. A line drawn through 
 points determined in this way is called a ' graph' and 
 shows the essential points of the table. " For example, 
 if the world's production of wheat over a number of 
 years be plotted, a poor yield is represented by a de- 
 pression, a rich one by a peak, a uniform one over 
 several years by a horizontal line, and so on." It has 
 been found that graphs dealing with different cases of 
 the same phenomenon can be plotted on the same co- 
 ordinates and so compared. Often considerable ingenu- 
 ity is demanded before the graphs assume a form which 
 lends itself to comparison. 
 
 1 Brinton, Graphic Methods for Presenting Facts, p. 16. 
 
AVERAGES AND GRAPHS 263 
 
 REFERENCES 
 
 Bowley, Elements of Statistics. 
 
 Brinton, Graphic Methods for Presenting Facts. 
 
 Davenport, Statistical Methods with Special Reference to Biological 
 Variation* 
 
 Elderton, Primer of Statistics. 
 
 Jones, Logic, Inductive and Deductive, pt. II, chap, n, and Sup- 
 plement. 
 
 King, Elements of Statistics. 
 
CHAPTER XXIII 
 
 TESTIMONY AND CIRCUMSTANTIAL EVIDENCE 
 
 Scientific Investigation vs. Judicial Proof. Thus 
 far we have largely concerned ourselves with the meth- 
 ods and logical processes of those investigations whose 
 object is the discovery of laws and principles. Such 
 investigations are essentially impersonal and theoretical. 
 They can be carried on in the laboratory and the study, 
 and there is usually less controversy in regard to the 
 facts than in regard to the hypotheses to be erected 
 upon them. Many seekers in the same field, having 
 much the same training, accumulate facts by means of 
 critical observation, and these facts are to furnish the 
 foundation of the science. These accepted facts grad- 
 ually converge in the direction of some satisfactory 
 hypothesis, and so a law of nature or of society is tenta- 
 tively established. We see, then, that science is coop- 
 erative and largely impersonal, its data can be increased 
 by recognized methods until they are sufficient, and it 
 is not limited in the amount of time at its disposal. 
 Nature is besieged rather than taken by storm. How 
 long Newton worked before he published his results is 
 well known, but it is not so well known that Darwin 
 worked upon the development of his theory in regard 
 to the origin of species for more than twenty years. 
 
 But there is Another great field of systematic reason- 
 ing which deserves the attention of the logician. If the 
 methods and temper of the scientist have of late influ- 
 
CIRCUMSTANTIAL EVIDENCE 265 
 
 enced the popular mind in the direction of greater care 
 and exactitude, a similar influence has long been exerted 
 by the methods and principles of legal reasoning. Sci- 
 entific temper is paralleled in great measure by judicial 
 temper. And we must remember that the situation in 
 which legal reasoning is carried on is quite different 
 from that in which scientific investigation takes place, 
 and is much less favorable to good reasoning. The air 
 is full of contention and of the personal element, the 
 time in which to reach a decision is limited, and the 
 necessary facts are often hard to find and verify. Judi- 
 cial proof is less creative than scientific investigation, 
 but it is in many ways more difficult. 
 
 The Difficulties confronting Judicial Proof. The 
 difficulties confronting judicial proof are very similar 
 to those which arise in practical life when the problem 
 is controversial in character. The juror is not in a posi- 
 tion to observe the facts, but must reach his decision 
 through the testimony of others and through inference 
 from what is called 'circumstantial evidence.' The sci- 
 entific investigator can repeat his facts at wish, but this 
 the juror, no more than the historian, can do. " The 
 same combination of circumstances which go to make 
 up a case of crime cannot, where they are at all numer- 
 ous, be expected to occur again. And even if it could or 
 did occur, it would answer no purpose ; for it is the 
 identical transaction which took place, and as it took 
 place, which is to be the sole subject of inquiry." 1 The 
 juror's observation is of an indirect, dependent, and 
 therefore inferior kind. Again, the original observer of 
 the facts was seldom aware of their importance. " Many 
 
 1 Burrill, A Treatise on Circumstantial Evidence, p. 94. 
 
266 THE ESSENTIALS OF LOGIC 
 
 of the facts . . . not only present themselves to the 
 senses, incidentally, unexpectedly, and transiently, but 
 are, outwardly, and as they present themselves, of the 
 most ordinary and familiar kind, having nothing on 
 their face to attract or arrest attention in any consider- 
 able degree ; and not to be distinguished from the great 
 mass of facts and events which are constantly passing 
 before the eyes of men, in their daily intercourse with 
 each other. Hence, where they are perceived merely by 
 the organs of sense, without any act on the part of the 
 observer, to give them connection with himself, they 
 are usually perceived in a general and superficial man- 
 ner." Thus, there is a large amount of possible error 
 in this incomplete and indirect observation upon which, 
 as a foundation, the juror must build his construction 
 of the case. The court must be certain of the identity 
 of the witness and of his general competency, that he 
 was actually an observer of what he testifies to, that 
 his testimony is not biased, etc. Finally, the juror must 
 be able to mass all this evidence, much of which is con- 
 flicting, together and draw a conclusion which seems to 
 him to explain the facts of the case. He is compelled to 
 pass judgment after judgment and then to estimate 
 the comparative value of these integral yet subordinate 
 conclusions in a total view of the problem. Neither the 
 steps nor the final synthesis is easy of accomplishment 
 in complex cases. 
 
 Distinction between Circumstantial and Testi- 
 monial Evidence. All evidence involves an inference 
 from some fact to the proposition to be proved. To be 
 evidence, a fact must have a recognizable bearing upon 
 the issue or probandum. In such a bearing lies its rel- 
 
CIRCUMSTANTIAL EVIDENCE 267 
 
 evance. Evidence divides itself into two classes, called 
 respectively ' direct ' or i testimonial evidence ' and 6 cir- 
 cumstantial evidence.' The distinction between these 
 two types is as follows : Direct or testimonial evidence 
 consists of information derived from assertions made 
 by those who have actual knowledge of the fact ; cir- 
 cumstantial evidence consists of facts from which in- 
 ferences to the principal fact can be drawn. Thus, 
 testimonial evidence is made up of the assertions of 
 witnesses who are presumed to have first-hand knowledge 
 of the fact at issue, while circumstantial evidence con- 
 sists of * circumstances ' from which the fact at issue 
 can be inferred according to known laws. It must be 
 remembered, however, that these * circumstances ' must 
 themselves be proved by testimony. 
 
 The Nature of Circumstantial Evidence. It is 
 obvious that circumstantial evidence gains its chief im- 
 portance as supplementary to direct evidence. A com- 
 mon direction for these two kinds of evidence is almost 
 bound to carry conviction. Thus, there may be only one 
 witness who testifies to having seen a crime committed, 
 while many may have seen the accused near the place 
 and showing signs of agitation or marks which fit in 
 with the inference suggested by the prosecution. Thus, 
 testimonial and circumstantial evidence are usually in- 
 tertwined. But cases occur in which there is no direct 
 evidence, i.e., in which no one has witnessed the com- 
 mission of the crime. At such times, reliance must be 
 placed wholly upon inference from circumstances. For 
 instance : " A house has been robbed. All the property 
 stolen from it is found directly after the robbery in the 
 possession of A. Besides this, at the time when the 
 
268 THE ESSENTIALS OF LOGIC 
 
 robbery is discovered, a hat, usually worn by A, is found 
 in the house. It is almost certain as a general proposi- 
 tion, that any man of whom these facts are true, must 
 be the robber. And assuming it to be conclusively 
 established that both these facts are true of A, we may 
 conclude with an approach to absolute certainty that A 
 is guilty of the robbery." When we come to examine 
 all such cases of circumstantial evidence, we find that 
 the principle of explanation is the same as that used in 
 science. Given certain facts, we must form an hypothe- 
 sis to explain them. In a case like the above, the 
 hypothesis that A is the robber is the one that naturally 
 occurs. We are certain, at least, that if he is not the 
 robber, he must know who the robber is. From the 
 standpoint of logic, the proof of the hypothesis consists 
 in the elimination of all alternative possibilities. The 
 student will recall that Mill's Methods depended largely 
 upon the scientist's ability to exclude possible causes 
 and so narrow down the field. 
 
 The Convergence of Evidence. It is seldom that 
 a single circumstance is given such value as to be re- 
 garded as conclusive. One instance occurred which 
 should serve to put us on our guard against the easy 
 assumption that there is no other possible hypothesis 
 but the one which most naturally occurs to us. " A man 
 was convicted and executed for stealing a horse, on the 
 strength of the presumption of the animal's being found 
 in his possession on the same day on which it was stolen ; 
 but it afterwards appeared that the real thief, being 
 closely pursued by the officers of the law, had met the 
 unfortunate man, to whom he was a total stranger, and 
 requested him to walk his horse for him for a while. 
 
CIRCUMSTANTIAL EVIDENCE 269 
 
 He had then escaped." In practically all cases, then, 
 the prosecution builds up a framework of evidence 
 which converges on the hypothesis that the accused is the 
 guilty man. The two facts to be connected are the 
 crime and the individual charged with its commission. 
 The evidentiary facts are shown to converge upon such 
 a suggested connection. The figure most frequently em- 
 ployed is that of a chain, but the analogy has a weak- 
 ness so far as it implies that the disproof of a single 
 link will break the chain. As a matter of fact, the con- 
 nection is more like a cable woven of strands than a 
 single chain. When each single inference from a circum- 
 stance to the issue is probable, the combination of these 
 separate probabilities may lead to a moral certainty 
 through the impossibility of finding an hypothesis, other 
 than the one championed, which will cover them all. 
 The defense then tries to break down the framework 
 of evidence by trying to disprove certain of the alleged 
 facts, by attempting to show that the interpretation of 
 other facts is false, and, in short, by seeking to bring 
 forward another hypothesis as an explanation. And so 
 the struggle between the two sides continues, with the 
 jury as the deciding body. 
 
 Direct or Testimonial Evidence. When we are 
 dealing with past events, as in a case of crime and in 
 history, we are compelled to rest our beliefs upon some 
 sort of testimony. Testimony, if true, enables us to reap 
 the results of the perceptions of others, to see indirectly 
 with their eyes. Hence, testimony has an unique value. 
 But it has also its dangers against which the whole 
 procedure of historical investigation and the theory of 
 judicial proof are directed. It is a far cry from the naive 
 
270 THE ESSENTIALS OF LOGIC 
 
 credulity of the child to the methodical skepticism of the 
 trained historian and the legal expert ; yet experience 
 of error has forced this change. " Our first natural 
 attitude toward testimony is one of trust ; not because 
 we have reasoned that it is trustworthy, but merely be- 
 cause we cannot help it. If it had not always been 
 natural to accept the statements of those about us as 
 substantially true, we should probably not be alive now 
 to discuss the matter ; for the telling of the truth on the 
 one hand and confidence in the story told on the other 
 are very important means for the preservation of the 
 race." 1 But experience soon qualifies this tendency. 
 We discover that we must hear as much evidence as we 
 can, and then compare, sift, and weigh it. Such collection, 
 sifting, and comparing is at first rough and ready. It is 
 soon developed into a careful technique with accepted 
 principles and maxims. The two best examples of such 
 technique are, of course, historical method and legal 
 method. We shall, in the main, concern ourselves with 
 the principles of legal method, but shall now and then 
 call attention to historical method and its manner of 
 dealing with the documents of the past. 
 
 The Modern Critical Attitude toward Testi- 
 mony. " Any assertion, taken as the basis of an in- 
 ference to the existence of the matter asserted, is testi- 
 mony, whether made in court or not. Assertions made 
 on the witness stand are merely the commonest class of 
 testimonial evidence." 2 Such assertions are, then, the 
 raw material of proof. They must be tested until a 
 residuum is left as morally certain fact. 
 
 1 Aikins, The Principles of Logic, p. 364. 
 
 2 Wigmore, Principles of Judicial Proof p. 312. 
 
CIRCUMSTANTIAL EVIDENCE 271 
 
 When a witness's assertion is examined from the 
 logical standpoint, it is seen to involve at least three 
 elements, perception, memory, and narration. In the 
 chapter dealing with " Observation and Fact," we be- 
 came aware of the ever-present danger of error in 
 both observation and memory. What was said then 
 could be reinforced by case after case in the annals of 
 law. 1 
 
 " A thousand mistakes of every description would be 
 avoided if people did not base their conclusions upon prem- 
 ises furnished by others, take as established fact what is 
 only possibility, or as a constantly recurring incident 
 what has only been observed once. ... I am assuming 
 that the witness is really desirous of speaking the truth 
 and is merely a bad observer." 2 Much testimony can be 
 proved to be mistaken by fairly simple tests. " Suppose 
 a witness affirms that he was beaten by Hiov ten min- 
 utes. Let a watch be placed before him and ask him to 
 take good note of how long ten minutes lasts and then say 
 whether it was really ten minutes. After a quarter of 
 a minute he will exclaim, ' It certainly did not last 
 longer than that.' " 
 
 Cross-examination is often of great assistance in 
 determining the validity of assertions. New statements 
 may be made by the witness which will disagree 
 with his other statements, or further developments 
 may be indicated. " 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 
 
 1 See Wigmore, Principles of Judicial Proof pp. 296-726. 
 
 2 Hans Gross, Criminal Investigation, p. 22. 
 
272 THE ESSENTIALS OF LOGIC 
 
 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 moon- 
 light. 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 
 incompetence, as shown in this example." 1 
 
 Logic has little concern with the practical difficulties 
 due to the temperament of the witness. There are 
 dull and stupid witnesses, timid and self-conscious, 
 hostile, dogged, etc. Logic must, however, stress 
 the part played by suggestion, and the difficulty 
 many people have of expressing themselves adequately. 
 The exhaustive study of testimony in the modern 
 schools of scientific law calls logic, ethics, anthropology 
 experimental psychology, and psychiatry to its aid. 
 Race, age, sex, mental disease, moral character, feeling, 
 interest, and experience, all affect the character of the 
 testimony given. 
 
 After the identity of the witness has been estab- 
 lished, the first problem is : Was the witness in a posi- 
 tion to perceive the facts ? The court wishes to know 
 the witness's opportunities. Next comes the question 
 whether he has any strong bias or motive for falsifying. 
 Very often the testimony of interested parties is re- 
 jected; it is at least somewhat discounted. When the 
 testimony given is against the advantage of the witness, 
 it is, however, regarded as having peculiar weight. 
 Such testimony usually occurs under cross-examina- 
 tion. 
 
 1 Quoted from Jones, Logic, Inductive and Deductive, p. 272. 
 
CIRCUMSTANTIAL EVIDENCE 273 
 
 Logical Standards and Tests. There are certain 
 logical tests which are directly applicable to the story- 
 told by a witness. It must be self consistent ; it must be 
 consistent with other known facts of the case; and 
 must be consistent with the larger run of human ex- 
 perience. Let us look at these three logical tests some- 
 what closely. 
 
 To be acceptable, the testimony of a witness must 
 be coherent and self-consistent. When two of his asser- 
 tions are shown to conflict, not only are we unable to 
 decide which is the true one, but we are also rightly in- 
 clined to be suspicious of the rest of his story. 
 
 Again, if the story told conflicts with facts which 
 are otherwise known beyond reasonable doubt, doubt is 
 thereby cast upon it. This is especially the case where 
 the facts are important and conspicuous. The agree- 
 ment or disagreement of the particular testimony with 
 that advanced by other witnesses enters here as con- 
 tradiction or convergent confirmation. 
 
 Lastly, the statements made must not conflict with 
 the laws of nature or with the tested possibilities of 
 the case. When a man testifies that he saw clearly 
 what occurred in a darkened room when he was look- 
 ing in from outside, we have good reason to reject his 
 testimony. Of course, assertions must not be too lightly 
 and hastily rejected. 
 
 These three tests imply both internal and external 
 evidence. A very good example from history of their 
 application is the determination of the false authorship 
 of the Donation of Constantine. This famous docu- 
 ment was the supposed grant by the Emperor Constan- 
 tine to Pope Silvester and his successors, not only of 
 
£74 THE ESSENTIALS OF LOGIC 
 
 spiritual supremacy over the other great patriarchates 
 and over all matters of faith and worship, but also of 
 temporal dominion over Eome and Italy and the prov- 
 inces, places, and civitates of the western regions. A 
 close study of the document, including the style, lan- 
 guage, and references, has convinced scholars, both 
 Catholic and Protestant, that the document is a forgery 
 dating from the eighth century. This painstaking ap- 
 plication of internal and external evidence has been 
 applied to the Old and New Testament, and is usually 
 called the 4 Higher Criticism.' It is very seldom that 
 the alleged author turns out to be the real author. 
 
 The Movement of Judicial Proof. Having exam- 
 ined the nature of both circumstantial and testimonial 
 evidence, it may be well to glance at a summary state- 
 ment of the actual movement of evidence and argument. 
 We shall refer to the asserter of the fact as the * Pro- 
 ponent' and the opposer as the ; Opponent.' In the 
 
 following outline, the sign ^> signifies ' tends to 
 
 prove ' ; the sign o — >> signifies ' tends to dis- 
 prove ' ; the sign <^ signifies ' explains away ' ; letter 
 T stands for a testimonial evidential fact; letter C 
 stands for a circumstantial evidential fact. 
 
 Circumstantial Evidence Process 
 
 Prohandum : X stabbed Y with a knife at a certain time and 
 place. 
 Proponent's Evidential Fact — C= Bloody knife was found on 
 
 X > Prohandum. 
 
 Proponent's Evidential Fact ex- 
 plained by Opponent — C = X drew it from the wound 
 
 after the fray on coming 
 to Y *s assistance < Pro- 
 ponent's Evidential Fact. 
 
 \ 
 
CIRCUMSTANTIAL EVIDENCE 275 
 
 or,— 
 Proponent's Evidential Fact de- 
 nied by Opponent — C = Bloody knife was not found 
 
 on X — o — > Propo- 
 nent's Evidential Fact, 
 and this the opponent may do, either — 
 
 (1) by adducing new evidential 
 
 facts — T=M's assertion that on 
 
 searching X no knife 
 was found. 
 C = No trace of blood from the 
 knife appeared on X's 
 garments. 
 
 (2) or by questioning the inference from the T or C on which 
 Proponent's Evidential Fact itself rested as a probandum. 
 
 Finally, — 
 Eival New Facts adduced by 
 
 Opponent — C=.X had no quarrel or other 
 
 motive to stab Y — o — > 
 Probandum. 
 and T= N a bystander asserts that 
 X did not stab Y — o — > 
 Probandum. 1 
 
 The Massing of Mixed Evidence. In any com- 
 plex case, a huge mass of more or less conflicting evi- 
 dence is presented to the juror's mind, and he must 
 arrange it in such a way as to weigh it correctly. 
 " Many data, perhaps multifarious, are thrust upon us 
 as tending to produce belief or disbelief. Each of them 
 (by hypothesis) has some probative bearing. Conse- 
 quently, we should not permit ourselves to reach a con- 
 clusion without considering all of them and the relative 
 value of each." What the mind ordinarily does under 
 such cases is to pass back and forth from significant 
 
 1 Adapted from Wigmore, Principles of Judicial Proof p. 26. 
 
276 THE ESSENTIALS OF LOGIC 
 
 fact to significant fact allowing itself to balance one 
 fact against another. The result is a drift in a certain 
 direction. In this way, a series of subordinate judg- 
 ments is passed, and these prepare the field for more 
 comprehensive judgments of a final sort. The mind 
 then goes back over the material in the light of its ten- 
 tative decision to see whether all the facts fall into line. 
 If they do, the decision is accepted as final. The fun- 
 damental mental necessity is the ability to coordinate 
 the data and weigh them in their relation to one an- 
 other. Along with this must go openness of mind and 
 willingness to go back and forth over the facts with 
 all the reasonable hypotheses in mind to see how ade- 
 quately they fit. 
 
 In such complex reasoning the strands of argument 
 are so many and so interwoven that fallacies of one 
 kind or another are almost sure to creep in unless the 
 utmost vigilance is exercised. Neglect of other possi- 
 bilities, false disjunction, false analogy, argumentum 
 ad populum are fairly common features of forensic 
 contests. In summing up, however, the fallacy which 
 should be most zealously guarded against is the fallacy 
 of the ' neglected aspect/ It is so easy to assume that 
 all the relevant factors have been taken into account 
 and have been given their due weight ; yet nothing is 
 more common than to over-simplify a problem and to 
 neglect important causes and facts. How many of us 
 have committed this fallacy of neglected aspect in con- 
 nection with the European War or in connection with 
 social problems like poverty and drunkenness ! 
 
 The following newspaper argument against prohibi- 
 tion illustrates this tendency very well : " You destroy 
 
CIRCUMSTANTIAL EVIDENCE 277 
 
 the jobs of people upon whom about 5000 of the popu- 
 lation depend; you take the jobs away from about 
 2000 room-rent or house-rent payers or home-owners ; 
 you deprive the city itself of about 1300,000 of direct 
 revenue, in the way of excise taxes and property taxes ; 
 you depreciate the rental value of about 15,000,000 
 worth of property in the town." Granted that the as- 
 sertions are correct, " if the facts which they bring for- 
 ward were the only ones to be considered, the inference 
 as to prohibition would be inevitable. If, however, the 
 liquor traffic is as pernicious in its influence as its op- 
 ponents claim it to be, the benefits which result from it 
 are far outweighed by the evil it produces. This aspect 
 of the case is neglected however, and so the argument 
 remains inconclusive." * 
 
 REFERENCES 
 
 Aikins, The Principles of Logic, chap. xxxv. 
 
 Bode, An Outline of Logic, chap. xn. 
 
 Hibben, Logic, Deductive and Inductive, chap. xiv. 
 
 Jones, Logic, Inductive and Deductive, pt. m, chap. in. 
 
 Wigmore, Principles of Judicial Proof, Introductory, and passim, 
 
 1 Bode, An Outline of Logic, p. 196. 
 
CHAPTER XXIV 
 
 EXPLANATION AND SYSTEM-FORMATION 
 
 The Nature of Explanation. To explain any- 
 thing is to show that it follows from something else 
 already known, A fact is explained when it is inter- 
 preted by means of a law or a principle. The specific 
 is explained by the general ; and the less general by 
 the more general. In explanation, we move downward 
 from rules to cases, from principles to their exemplifi- 
 cations. We see the temporary and the changing in 
 the light of the more permanent and relatively un- 
 changing. 
 
 That all explanation is in its essence deduction 1 has 
 been generally recognized by logicians. We try to re- 
 late the given to those generalizations which we have 
 slowly worked out as both rules of action and rules of 
 interpretation. We are not comfortable with mere 
 facts which are unordered and unrelated. They challenge 
 us as chaotic and meaningless until we can somehow 
 put them together as parts of a permanent whole which 
 can be conceived. Thus, in the domain of the physical 
 sciences, a fact is felt to be explained when it is re- 
 lated to the terms of a general principle. 
 
 The Sentiment of Rationality. A given fact by 
 itself seems like a shot out of a pistol. It is, — our 
 senses are, perhaps, witnesses to its occurrence, — but 
 it stands in isolation. So far as this is the case, our 
 
 1 Sigwart, Logic, vol. II, p. 417. 
 
EXPLANATION AND SYSTEM-FORMATION 279 
 
 minds cannot really grasp it and give it meaning for the 
 simple reason that past experience cannot be brought to 
 bear upon it. It remains, then, a brute sensational event 
 to which our concepts cannot attach themselves. But 
 because our minds try to find some point of attachment, 
 some way of striking up a friendship with the event, 
 they feel baffled and uncomfortable. Thus, the senti- 
 ment of rationality, the desire to explain and interpret, 
 is an expression of the very mode of working of human 
 consciousness. When any event or thing is given, our 
 minds seek to find relations between it and other facts 
 already familiar and more or less interpreted. In this 
 way it is assimilated and given a local habitation and a 
 name. " All knowledge, all science, thus aims to grasp 
 the meaning of objects and events, and this process 
 always consists in taking them out of their apparent 
 brute isolation as events, and finding them to be parts 
 of some larger whole, suggested by them, which, in 
 turn, accounts for, explains, interprets them; i.e., 
 renders them significant. Suppose that a stone with 
 peculiar markings has been found. What do these 
 scratches mean ? So far as the object forces the rais- 
 ing of this question, it is not understood ; while so far 
 as the color and form that we see mean to us a stone, 
 the object is understood. It is such peculiar combina- 
 tions of the understood and the non-understood that 
 provoke thought. If at the end of the inquiry, the 
 markings are decided to mean glacial scratches, obscure 
 and perplexing traits have been translated into mean- 
 ings already understood : namely, the moving and 
 grinding power of large bodies of ice and the friction 
 thus induced of one rock upon another. Something 
 
280 THE ESSENTIALS OF LOGIC 
 
 already understood in one situation has been transferred 
 and applied to what is strange and perplexing in an- 
 other, and thereby the latter has become plain and 
 familiar, i.e., understood. This summary illustration 
 discloses that our power to think effectively depends 
 upon possession of a capital fund of meanings which 
 may be applied when desired" l 
 
 The Role of Concepts. Concepts play a tremen- 
 dously important part in both reasoning and explana- 
 tion. Let us try- to bring out the deductive side of 
 explanation referred to above by stressing the role of 
 concepts in experience. Because concepts are accepted 
 organizations of experience, anything related to them is 
 naturalized, so to speak, and becomes, thenceforth, a 
 citizen of the mind. Relation to the concepts gives it 
 its credentials. Thus the foundation of all explanation 
 is the capacity of the mind to generalize and to secure 
 by means of analysis, abstraction and synthetic imagin- 
 ation those general ideas and principles which illumin- 
 ate and organize experience. Our study of induction 
 has been essentially a tracing of the steps and activities 
 involved in the attainment of such concepts. We have 
 seen how facts are observed and selected at the instance 
 of some problem, how comparisons and analyses are 
 made, how guesses at the causes or principles at work 
 are made by fertile minds, how these guesses are tested 
 and modified and re-tested, how systems of conceptual 
 knowledge slowly arise and are used to give meaning 
 to new facts as well as to the old from which they 
 sprung. Now it is to this property of such conceptual 
 systems to give meaning to new facts that we are call- 
 
 1 Dewey, How We Think, pp. 117-18. 
 
EXPLANATION AND SYSTEM-FORMATION 281 
 
 ing attention. It is in this property that explanation 
 consists. 
 
 It is significant that this explanatory property of 
 concepts can be connected with the syllogism. It will 
 be remembered that the typical syllogism has a univer- 
 sal proposition for its major premise. The minor pre- 
 mise then states a concrete case which can be subsumed 
 under the universal principle, while the conclusion con- 
 sists of the actual identification of the concrete case 
 with the principle. 
 
 All cases of M are cases of P;' 
 S is a case of M; 
 Therefore S is a case of P. 
 
 Both M and JP are abstract characters or universals; 
 they are concepts which have gradually been achieved 
 by the human mind as the result of that sentiment of 
 rationality to which we have referred above. " This is, 
 in fact, a world in which general laws obtain, in which 
 universal propositions are true, and in which reasoning 
 is therefore possible." We reason down from such 
 general concepts to facts and thereby explain them. 
 
 Concepts are " instruments (1) of identification ; 
 (2) of supplementation ; and (3) of placing in a sys- 
 tem. Suppose a little speck of light hitherto unseen is 
 detected in the heavens. Unless there is a store of 
 meanings to fall back upon as tools of inquiry and 
 reasoning, that speck of light will remain just what it 
 is to the senses — a mere speck of light. For all that 
 it leads to, it might as well be a mere irritation of the 
 optic nerve. Given the stock of meanings acquired in 
 prior experience, this speck of light is mentally attacked 
 by means of appropriate concepts. Does it indicate 
 
282 THE ESSENTIALS OF LOGIC 
 
 asteroid, or comet, or a new-forming sun, or a nebula 
 resulting from some cosmic collision or disintegration ? 
 Each of these conceptions has its own specific and dif- 
 ferentiating characters, which are then sought for by 
 minute and persistent inquiry. As a result, then, the 
 speck is identified, we will say, as a comet. Through a 
 standard meaning, it gets identity and stability of 
 character. Supplementation then takes place. All the 
 known qualities of comets are read into this particular 
 thing, even though they have not been as yet observed. 
 All that astronomers of the past have learned about 
 the paths and structure of comets becomes available 
 capital with which to interpret the speck of light. 
 Finally, this comet-meaning is itself not isolated ; it is 
 a related portion of the whole system of astronomic 
 knowledge. Suns, planets, satellites, nebulas, comets, 
 meteors, star-dust — all these conceptions have a cer- 
 tain mutuality of reference and interaction, and when 
 the speck of light is identified as meaning a comet, it 
 is at once adopted as a full member in this vast king- 
 dom of beliefs." 1 A fact which is identified, supple- 
 mented in this broad way, and put into a system is 
 explained ; it has been removed from its isolation, 
 given relations to other things, and interpreted by 
 general principles. 
 
 Proof and Explanation. A proposition is proved 
 when it is shown to follow from accepted premises, 
 while a fact or specific rule is explained when it is 
 shown to be the natural consequence of principles. It 
 is evident that proof and explanation are essentially the 
 same ; in both the deductive element dominates. Thus 
 1 Dewey, How We Think, pp. 126-27. 
 
EXPLANATION AND SYSTEM-FORMATION 283 
 
 far we have looked at the problem mainly from the 
 angle of explanation ; let us now examine it from the 
 side of proof. Why does the application of the major 
 premise to a case constitute proof ? " The answer is 
 that it serves to connect the conclusion with the system 
 of concepts or general principles that have previously 
 been accepted. When one sees that the new suggestion 
 comes under the old principles, the belief that has been 
 developed for the system of knowledge extends to the 
 particular instance. The laws and principles that have 
 been established and accepted are connected with the 
 conclusion that is in doubt, and the doubt disappears. 
 Each doubt that is solved increases the belief in the 
 principle, since it assures its connection with a new 
 fact. It should be added that the process of reference 
 to the system of knowledge, not merely justifies the old, 
 but also increases the number of applications of the 
 old. It extends its application, and when the conclu- 
 sion itself is confirmed in practice, the general principle 
 receives new warrant." 1 This quotation brings out ad- 
 mirably the fact that knowledge consists of the growth 
 of systems of knowledge which must take up new facts 
 into themselves. Such systems possess mental author- 
 ity, and proof is the expression of this authority. 
 Combined with such authority there must exist the 
 mental perception of the inner coherence of system and 
 fact. The system must be capable of assimilating the 
 fact ; it is here that the deductive element enters. 
 
 Systems are tentative. Systems are no longer re- 
 garded as having either their final form or content. 
 There is less dogmatism in all fields to-day than formerly. 
 
 1 Pillsbury, Essentials of Psychology, pp. 234-35. 
 
284 THE ESSENTIALS OF LOGIC 
 
 The trial-and-error feature of knowledge is more clearly 
 recognized. We may allow ourselves to speak of sys- 
 tems of knowledge as growths, but we must not be mis- 
 led by the organic analogy. There are differences as 
 well as similarities between the growth of systems of 
 ideas and the growth of organisms. The difference I 
 would stress lies in this, that the innate or determined 
 factor is less obviously in control in systems of knowl- 
 edge than in the growth of a particular organism. To 
 put this point concretely, systems of knowledge do not 
 have an heredity. If we desire an analogy, it is far 
 better to compare the development of knowledge in a 
 particular field with the adaptation of a human being 
 to his environment. Habits are necessarily tentative and 
 revocable just as ideas are. Man has found that he 
 must relinquish habits and customs and institutions, 
 much as he is forced at times to give up ideas once 
 fondly cherished. In both domains, however, we have 
 good reason to believe that it is not a case of mere 
 supplanting, but that there is a genuine advance, a 
 real progress. I cannot do better in this connection 
 than to quote what Bertrand Russell writes in regard 
 to the attitude and contributions of Henri Poincare to 
 modern science : " Another reason which makes a phi- 
 losophy of science specially useful at the present time 
 is the revolutionary progress, the sweeping-away of 
 what had seemed fixed landmarks, which has so far 
 characterized this century, especially in physics. The 
 conception of the 4 working hypothesis,' provisional, 
 approximate, and merely useful, has more and more 
 pushed aside the comfortable eighteenth-century con- 
 ception of ' laws of nature.' Even the Newtonian dy- 
 
EXPLANATION AND SYSTEM-FOEMATION 285 
 
 namics, which for over two hundred years had seemed 
 to embody a definite conquest, must now be regarded 
 as doubtful, and as probably only a first rough sketch 
 of the ways of matter. And thus, in virtue of the very 
 rapidity of our progress, a new theory of knowledge has 
 to be sought, more tentative and more modest than that 
 of more confident but less successful generations." x 
 
 Levels of Explanation. We may distinguish dif- 
 ferent levels in explanations. The first stage is classifi- 
 cation. The dominant purpose at this level is to gather 
 objects, compare them, and, finally, classify them. When 
 systems of classification are worked out, specimens can 
 be ordered in relation to one another and new cases 
 can be identified and put in their proper place. No 
 matter how external and superficial such systems of 
 classification are, they represent the beginning of sci- 
 entific explanation ; things are removed from their iso- 
 lation. As the system of classification is penetrated by 
 perception of more essential characteristics, this stage 
 passes to the next, which may be called * the empirical/ 
 
 At the empirical level, subordinate laws and princi- 
 ples are discovered. For example, many strands of cau- 
 sal uniformity and laws of action and reaction become 
 known. In medicine, it is discovered that certain drugs 
 have definite effects upon the organism, and that the 
 individual reacts in certain ways to various toxins. In 
 chemistry, laws and principles are often known while 
 there is doubt of their real significance. One of the 
 best historical instances of the empirical stage is the 
 situation in astronomy after Kepler and before New- 
 ton. Kepler discovered that the planetary orbits are 
 1 Russell, Preface to Poincar^'s Science and Method, pp. 6-7. 
 
286 THE ESSENTIALS OF LOGIC 
 
 elliptical instead of circular as had been supposed. 
 Kepler generalized the known facts in terms of his 
 three laws : (1) that the planets move in ellipses round 
 the sun, with the sun in one of the foci ; (2) that they 
 describe equal areas in equal times ; (3) that the cubes 
 of their mean distances vary as the squares of their 
 periodic times. Although many suggestions were made 
 and analysis of motion was carried further by various 
 physicists, it remained to Newton to carry astronomy 
 over to the third level, that of explanation proper. 
 
 Newton did two things : " He conceived that the 
 force which deflected the planets into their orbits was 
 the same as that which made bodies fall to the earth ; 
 or, to put it differently, he identified celestial attraction 
 with terrestrial gravity, and conceived the earth as es- 
 sentially falling out of a straight path towards the sun, 
 and the moon towards the earth ; and he invented a 
 mathematical calculus by which he could work out 
 what were the theoretical consequences of the princi- 
 ples he assumed" 1 Examining these two things which 
 Newton accomplished, we see that they were, first, an 
 extension of the idea of gravity to all cases of physical 
 bodies, an act of universalization, and second, the en- 
 trance of a distinctly deductive element. The more de- 
 duction increases, the more has the level of explanation 
 been achieved. 
 
 The ideal often held by the physical sciences is well 
 expressed by Helmholtz. In his little book on the Con- 
 servation of Force, he writes : " So that at last the task 
 of Physics resolves itself into this, to refer phenomena 
 to inalterable attractive and repulsive forces whose in- 
 
 1 Joseph, An Introduction to Logic, p. 479. 
 
EXPLANATION AND SYSTEM-FORMATION 287 
 
 tensity varies with distance. The solution of this task 
 would at the same time be the condition of Nature s 
 complete intelligibility ." For Helmholtz, in other words, 
 partial explanations in science must be subsumed under 
 completer, more deductive ones until the ideal he sets 
 forth is reached. This is not the place to discuss this 
 ideal from the philosophical side. It may be of interest 
 to the student, however, to point out that it is a clear 
 statement of the mechanical view of the world. 
 
 General Explanation and Specific Explanation. 
 Sometimes the scientist is primarily interested in dis- 
 covering general laws and then carrying these laws 
 themselves back to still more general principles ; at 
 other times, he wishes to explain particular facts. The 
 more concrete the science, the more is there an interest 
 in the particular for its own sake. Thus, history is 
 mainly concerned with events or customs which have 
 been brought about by the interaction of many forces 
 and agencies. Such events cannot be deduced from ele- 
 mentary and universal principles. There is not repeti- 
 tion enough, and the factors concerned are too complex 
 and mutable. Where deduction can afford genuine 
 prediction, there must be relative simplicity. It is pos- 
 sible to predict the transit of Venus, the effect of Ice- 
 land spar upon a beam of light, and the product of the 
 union of hydrogen and oxygen ; but it is impossible to 
 predict what will happen after the present great war. 
 The historian must grope his way to generalizations 
 which are only tendencies ; his chief interest must be 
 directed to the understanding of events which have al- 
 ready happened by tracing their known antecedents. 
 But when the physical scientist seeks to understand just 
 
288 THE ESSENTIALS OF LOGIC 
 
 why some specific event happened, he, also, must search 
 out all the relevant circumstances. The main difference 
 is that time is a less important factor for him than it is for 
 the historian. In fact, as we pass from the abstract sci- 
 ences through the biological to the human sciences, time 
 increases in importance. Institutions and events are 
 best interpreted when we know how they arose. Our 
 conclusion is, that sciences differ in their emphases. 
 Some, the more abstract, aim to furnish general prin- 
 ciples only and leave the specific and the unique to the 
 concreter sciences ; while the more concrete sciences de- 
 vote much of their attention to particular events which 
 are judged to be important. 
 
 Typical Systems of Knowledge. Many logicians 
 have attempted to classify the sciences according to 
 some one principle. Such classifications must, however, 
 be recognized to be relative to the principle adopted. 
 Suppose that we use the relative proportion of general 
 law and specific fact as the standard of division. We 
 shall then commence with mathematics, pass to me- 
 chanics, thence to chemistry ; from chemistry we shall 
 go to biology and psychology, and, finally, to the 
 human sciences which all involve the methods of his- 
 tory. Corresponding to such a passage from the more 
 abstract to the more concrete is a change in the nature 
 of the material studied. We begin with the abstract 
 properties of physical things and end with highly or- 
 ganized and changing wholes. Let us glance briefly at 
 the two extremes to see what the respective systems are 
 like and how they are developed. 
 
 Mathematics is a typical deductive science. It does 
 not involve an appeal to particular facts which must be 
 
EXPLANATION AND SYSTEM-FORMATION 289 
 
 generalized. Geometry, for example, does not begin with 
 concrete things as do the physical sciences, but with 
 certain concepts, given in definitions, axioms, and pos- 
 tulates, and with the nature of abstract space. " It is 
 because space relations are unaffected by locality that 
 what I have seen to be a property of this circle must 
 be a property of any circle." * What mathematics rests 
 on, then, is an apprehension of the relations between 
 the elements of space and quantity. In a very real sense, 
 there are no particular instances which have relevant 
 qualities of their own. Thus, the data of mathematics 
 are few in number and essentially changeless, ichich is 
 another way of saying that they are conceptual rather 
 than perceptual. The generalization-aspect of the sci- 
 ence is taken care of at the very start. It follows that 
 the test of the truth of any conclusion cannot be of a 
 perceptual character; rather is it of the nature of a 
 recognized agreement with the principles and theorems 
 already developed. A geometrical system is primarily a 
 realm of internal consistency. " Thus the space-intui- 
 tion which is so essential an aid to the study of logic 
 is logically irrelevant : it does not enter into the prem- 
 ises when they are properly stated, nor into any step 
 of the reasoning," 2 The true method of studying geom- 
 etry is to conceive "interesting simple figures, such 
 as the triangle, the parallelogram, and the circle, and 
 to investigate the correlations between their various 
 parts. The geometer has in his mind not a detached 
 proposition, but a figure with its various parts mutually 
 
 1 Joseph, An Introduction to Logic, p. 506. Mr. Joseph's chapter on 
 44 Mathematical Reasoning " is well worth study. 
 
 2 Whitehead, Introduction to Mathematics, p. 242. 
 
290 THE ESSENTIALS OF LOGIC 
 
 inter-dependent." 1 Such figures are seen in the light 
 of the primary set of axioms and postulates. We may 
 say, then, that mathematics deals with abstract entities 
 which are conceived. 
 
 The historical sciences, on the other hand, are founded 
 on concrete data. These data may be classified into two 
 groups, material facts and testimony. The first duty 
 of the historian is to gather all the data available. As 
 a rule, such data consist of documents, which are records 
 in various forms of the thoughts and actions of men of 
 former times. 2 No one who has not given some thought 
 to the matter can appreciate the effort required to 
 bring about even a partially satisfactory fund of mate- 
 rial, especially where the very distant past is concerned. 
 The next step is the estimation of the relative value 
 of the various items. It is to this problem that much 
 of the historian's ingenuity is directed. Both internal 
 and external evidence must be adduced, analyses made, 
 and exact scholarship brought to bear. As material is 
 evaluated, a certain body of more or less certain fact is 
 established and worked up into an interpretative narra- 
 tive of the development of a people. Such a narrative 
 is being constantly purified by the elimination of data, 
 too credulously accepted, and deepened by the addition 
 of new data and new points of view. 
 
 The logician's interest in history concerns the meth- 
 ods used to secure the material, the presence of selec- 
 tion, analysis and interpretation, the part played by 
 guiding-ideas, and the importance of constructive im- 
 agination. Modern scientific method in history is a 
 
 1 Whitehead, Introduction to Mathematics, p. 238. 
 
 2 See Langlois and Seignobos, Introduction to the Study of History. 
 
EXPLANATION AND SYSTEM-FORMATION 291 
 
 monument to the ideal of truth in a complex field in 
 which difficulties exist at every step. The historian has 
 been forced by his problems into self-consciousness so 
 that there are several excellent discussions of historical 
 method easily obtainable. Let us look at some of the 
 conclusions which bear upon the elements of induction. 
 
 First of all, there have been spirited controversies in 
 regard to the purpose of history. There have been po- 
 litical historians, moral historians, sociological histori- 
 ans ; and, corresponding to these, there have been his- 
 torical schools. Upon only one point have all agreed, 
 viz., that truth must be the ideal. Within minor diver- 
 gencies, a large guiding-idea is now held in common. 
 Development is the keynote. " We have noted that the 
 scope of history has broadened by taking more and 
 more factors into account. Wars and statecraft are now 
 regarded as a less important part of national life. This 
 has come about not merely through curiosity to find 
 out how people lived in time past, but in the search 
 after the explanation of national development . . . 
 The thread upon which the story of any nation hangs 
 is development from the past into the present." 1 His- 
 tory seeks to explain, just as any other developed sci- 
 ence does, but it explains by development. The com- 
 position of causes back of an event or institution is 
 always more or less unique. 
 
 The search for documents is a science in itself and 
 involves the collaboration of many subordinate sci- 
 ences, such as palaeography, epigraphy, and philology. 
 But this technique is controlled by the plans and ideas 
 of investigators. Given the material, the next step 
 
 1 Vincent, Historical Research, p. 10. 
 
292 THE ESSENTIALS OF LOGIC 
 
 is the determination of facts. "The document is the 
 starting-point, the fact the goal. Between this start- 
 ing-point and this goal he has to pass through a com- 
 plicated series of inferences, closely interwoven with 
 each other, in which there are innumerable chances of 
 error; while the least error, whether committed at the 
 beginning, middle, or end of the work, may vitiate all 
 his conclusions." * The facts of history, in other words, 
 are judgments, not observations. 
 
 There are many sources of error of a distinctly men- 
 tal character. Sometimes there is reason to doubt the 
 good faith of the author. Sympathy often plays its se- 
 lective and distorting part ; again, vanity and deference 
 to public opinion may be at work. The result of expe- 
 rience has been the rise of a defensive canon, called 
 4 methodical distrust.' This canon will bring home to 
 the student the discussion of some of the causes of error 
 in observation given in Chapter XVII. With a char- 
 acteristic statement of it we shall close the present dis- 
 cussion of scientific systems, for it generalizes that atti- 
 tude of reflection and criticism which it is the task of 
 logic on its practical side to enforce. " We must not 
 postpone doubt till it is forced upon us by conflicting 
 statements in documents ; we must begin by doubting." 2 
 We must try to secure " that methodically analytical, 
 distrustful, not too respectful turn of mind which is 
 often mystically called ' the critical sense ' but which is 
 nothing else than an unconscious habit of criticism." 3 
 
 1 Lang-lois and Seignobos, Introduction to the Study of History, p. 64. 
 
 2 Ibid., p. 157. 8 Ibid., p. 190. 
 
EXPLANATION AND SYSTEM-FORMATION 293 
 
 REFERENCES 
 
 Dewey, How We Think, chap. ix. 
 
 Jones, Logic, Inductive and Deductive, pt. in, chaps. I and in. 
 
 Joseph, An Introduction to Logic, chap, xxiii. 
 
 Pillsbury, Essentials of Psychology, chap. ix. 
 
 Poincare', Science and Method, passim. 
 
 Whitehead, Introduction to Mathematics, chap. XVI. 
 
 Langlois and Seignobos, Introduction to the Study of History. 
 
CHAPTER XXV 
 
 TRUTH AND ITS TESTS 
 
 Back to the Definition of Logic. Logic was de- 
 fined as ■ the science of the principles and conditions of 
 correct thinking.' This definition was offered as a guide- 
 post to direct attention to the general character of the 
 subject. Now that we have covered the various topics, 
 we must come back to the definition, analyze the terms, 
 and permit ourselves to suggest and briefly discuss some 
 of the larger and more philosophical problems which 
 have all along hovered in the background. What stu- 
 dent has not asked himself Pilate's question. If logic 
 deals with the conditions and principles of correct think- 
 ing, it must contain some standard of correctness. While 
 it is not the business of logic to decide what ideas are 
 true, — i.e., what the empirical content of truth is, — 
 it does seem to be a part of its task to give analytic 
 knowledge of the meaning of truth and of the princi- 
 ples and methods actually used in testing assertions 
 which lay claim to this apotheosis. 
 
 In order to think correctly, we must think both con- 
 sistently and truly. Let us look at these two pre- 
 requisites for a moment. It is impossible to think truly 
 without thinking consistently, but it is possible to think 
 consistently without thinking truly. But very few men 
 want to think only consistently. The one is a means to 
 the other, valued largely because of this relation. 
 
 The Nature of Consistent Thinking. To think 
 
TRUTH AND ITS TESTS 29,5 
 
 consistently means to avoid self-contradiction. The 
 conclusions we draw must be related to the premises we 
 accept in accordance with logical necessity. Consistent 
 thinking must not sin against the Laws of Thought and 
 must contain a recognized harmony among its parts. 
 When such thinking is also in agreement with the facts, 
 we are apt to speak of it as true and its product as truth 
 or valid knowledge. 
 
 We have come to see that clear and well-organized 
 ideas are essential conditions of consistent thinking. 
 Definition and analysis help to make the ideas we use 
 clear and unambiguous, w r hile classification, in which 
 concepts are ordered in relations of coordination, sub- 
 ordination, and superordination, is another prime con- 
 dition of good thinking. Only knowledge which is dis- 
 tinct and well organized can be handled without serious 
 danger of error. 
 
 Thought discovers internal relations between proposi- 
 tions of such a character that one follows from others. 
 The sign of such a logical relation is words like ' there- 
 fore ' and ' hence.' M is P and S is M; therefore S is 
 jP. If we grant the premises, it is impossible to deny 
 the conclusion without self-contradiction. If the damp- 
 ness of the sidewalk is the sign of either rain or dew, 
 this case of dampness signifies that it rained last night 
 or that there was a fall of dew. The mind feels itself 
 forced to draw the conclusion, once it has admitted a 
 general rule and recognized a specific instance as com- 
 ing under the rule. Such logical necessity is, in a sense, 
 the inverse of the act of generalization. Were we un- 
 able to generalize, we should be unable to infer, and the 
 word, therefore, would have no meaning for us. This 
 
296 THE ESSENTIALS OF LOGIC 
 
 fact reveals the intimate relation of induction and de- 
 duction. 
 
 The Laws of Thought. We have postponed the 
 treatment of the traditional Laws or Axioms of Thought, 
 because they are apt to appear trivial and meaningless 
 when taken up at the beginning without a logical context. 
 These primary axioms of thought are three in number 
 and state the recognized conditions of consistent think- 
 ing. So far as I can see, they arise from and express 
 the very nature of conceptual thinking. For that rea- 
 son, however, they are as self-evident as the axioms of 
 Euclidian geometry. After formulating them, I shall 
 try to relate them to the act of thinking. 
 
 The Laws of Thought are : — 
 
 (1) The Law of Identity. A is A. 
 
 (2) The Law of Contradiction. A is not not- J.. 
 
 (3) The Law of Excluded Middle. Everything is 
 either A or not- A. 
 
 It is obvious that these axioms need some interpreta- 
 tion in order to give meaning to the symbolic form in 
 which they are stated. We shall start with the Law of 
 Identity, develop its meaning, and then show that the 
 other laws are simply further explications of it in the 
 light of the negative. 
 
 The Law of Identity carries us back to the nature of 
 concepts. A concept is a mental object which we can 
 hold before the attention, think about, and distinguish 
 from other objects. But before this can be done, these 
 mental objects must have a certain degree of stability 
 and distinctness of content. Hazy, vague, uncertain 
 thoughts are condemned by logic because they are not 
 full-fledged ideas. We all know when we have such im- 
 
TRUTH AND ITS TESTS 297 
 
 mature concepts before our minds — at least, we do 
 when we are reflective and have learned to distinguish 
 between concepts and words. Since one of the princi- 
 ples of logic is non-ambiguity, one of its ideals must be 
 clear and distinct concepts. Now, such clear and dis- 
 tinct concepts are recognizable and distinguishable from 
 others. It is this fact that the Law of Identity points 
 out. No thought and no judgment is possible where 
 concepts cannot be held before the mind, retained, re- 
 produced, and recognized as the same. This sense of 
 sameness is, as James phrased it, " the very keel and 
 backbone of thinking.'' 
 
 The Law of Contradiction is the negative side of the 
 Law of Identity. If we are able to present clear ideas 
 to the mind, we must also be able to distinguish them 
 from one another. To apprehend A is also to know that 
 it is not not-^L 
 
 There is another form of the Law of Contradiction 
 which concerns itself with judgment rather than with 
 the character of concepts. This other form is usually 
 called the Aristotelian and is as follows : " It is impos- 
 sible that the same predicate can both belong, and not be- 
 long, to the same subject, at the same time, and in the 
 same sense." This formulation brings out sharply the na- 
 ture and meaning of contradiction by calling attention 
 to the fact that the human mind cannot accept the judg- 
 ments 4 A is BJ and ' A is not B ' at the same time. 
 
 The Law of Excluded Middle is a further definition 
 of the relation between a term and its contradictory. 
 It asserts that of two contradictory assertions one is 
 necessarily true. There can be no third possibility. In 
 formal logic, this principle appears in the fact that 
 
298 THE ESSENTIALS OF LOGIC 
 
 there are only two qualities^ the affirmative and the 
 negative. 
 
 The Postulates of Logic. Besides these axioms, 
 certain postulates are sometimes advanced as essential 
 to logic. The following is a partial list : (1) Every as- 
 sertion is either true or false. (2) Some propositions 
 may be recognized as true. (3) The mind is able to 
 apprehend objects. (4) There are universal connections 
 in nature, and some at least of these can be discovered. 
 
 (5) The world is essentially the same for all observers. 
 
 (6) Individuals who communicate can mean essentially 
 the same by their terms. The investigation of these 
 postulates is usually assigned to epistemology and 
 metaphysics. 
 
 The Question of Truth. Consistency with other 
 propositions is not by itself a sufficient criterion of 
 truth. An assertion may follow with due logical neces- 
 sity from temporarily accepted premises, but such an 
 internal relation cannot guarantee the system as a whole. 
 While the accepted premises justify the conclusion, 
 they themselves must be justified. But does not this 
 situation lead us into a difficulty ? Can we have any- 
 thing more than consistency? Suppose that we use the 
 term 6 valid ' for a conclusion which follows from ac- 
 cepted premises with logical necessity. The question 
 which confronts us is this, Can we attain anything but 
 valid assertions ? But, if this be the case, our ultimate 
 premises must either be given with their credentials by 
 some sort of extra-logical intuition, or must be accepted 
 on authority, or, finally, be postulated. Is there any 
 way to avoid this unwelcome series of disjunctions ? 
 
 I hope that the student has seen that this way of 
 
TRUTH AND ITS TESTS 299 
 
 approach to the question of truth has stressed the de- 
 ductive side of logic to the exclusion of induction. 
 Were thinking only deductive, we should be compelled 
 to face the unwelcome alternatives outlined above. It 
 has been the prime fallacy of many of the philosophical 
 systems of the past to seek some one principle from 
 which to deduce reality as experienced. In my opinion, 
 such an attempt is illogical because it exalts deduction 
 over induction and does not see that knowledge is a 
 growth in which both aspects, or phases, of thinking are 
 at work. 
 
 'Validity' is, then, essentially a deductive term 
 while 4 truth ' corresponds more to that intimate inter- 
 play of induction and deduction which has been pre- 
 sented in our study of science. It will be remembered 
 that there are three elements, or distinguishable mental 
 processes in all systematic investigation, namely, the 
 inductive element par excellence, whose principle is ob- 
 servation with its fidelity to fact ; the generalizing and 
 hypothesis-forming element ; and, lastly, deductive rea- 
 soning out of implications. These elements are inter- 
 twined according to the exigencies of the case. It is 
 out of the inductive-deductive interaction of fact and 
 theory that truth, as distinct from mere validity, arises. 
 
 The Criteria of Truth. It has been customary to 
 speak of truth and to contrast it with error. This col- 
 lective way of speaking about truth as a body of doc- 
 trine has too often led people to think of truth in a 
 mystical fashion. Even critical thinkers have com- 
 mitted the ' fallacy of abstract terms,' 1 and thought of 
 truth as an abstract entity. In order to avoid this dan- 
 
 1 See chapter in. 
 
300 THE ESSENTIALS OF LOGIC 
 
 ger, it is best to distinguish between true ideas and 
 false ideas. And, by ideas, we shall mean assertions, 
 propositions, judgments, theories, in fact all mental 
 objects in regard to which we make the truth-claim. 
 Our present purpose is to discover the actual, empirical 
 tests which are used in investigation to decide between 
 ideas which tentatively claim truth and yet conflict. 
 What are the criteria of true ideas ? And what is the 
 logical setting of these criteria f 
 
 Reviewing our study of systematic investigation, we 
 note that investigation is begun only when some prob- 
 lem arises. Every such problem must have a concrete 
 and specific character. In truth, the scientist is well 
 aware that his first task is to define his problem, for any 
 lack of clearness in the statement of the problem is cer- 
 tain to thwart his efforts. To work on an ill-defined 
 problem is like hunting for something of which one 
 has no clear picture. The next step is the separation of 
 what is certain from what is uncertain. He wants to 
 know what he can depend on, what is beyond question 
 for the purpose in hand. The logician calls the certain- 
 ties of the field relevant to the specific problem the 
 4 data,' and contrasts the conjectures and hypotheses, 
 which arise in the fertile mind of the scientist, with 
 these data as 'theory.' It must be remembered that 
 such theories develop in the mind of the expert who 
 has detailed familiarity with what has been discovered 
 and achieved in this particular field and in those ad- 
 joining. An hypothesis is not external to the knowledge 
 of the field but is a genuine branch of it. The tree of 
 human knowledge is vigorous and puts forth many 
 shoots, some of which must be lopped off. The process 
 
TRUTH AND ITS TESTS 301 
 
 of selecting among competing explanations by marking 
 their capacity to cover and organize the facts and so 
 solve the specific problem is called verification. Veri- 
 fication involves responsibility to fact, freedom from 
 self-contradiction, and a flexible harmony with other 
 accepted theories which have passed through the same 
 test. In any particular case, such testing is a complex 
 process in which the mind works back and forth be- 
 tween data and theory, adding new data and modifying 
 the theory. The criteria of truth are not external but 
 internal. It is absurd to look for some touchstone which 
 can be applied in a mechanical fashion to propositions 
 claiming truth. 
 
 Degrees of Belief. Assertions are not made with 
 the same degree of assurance, nor, to state the same fact 
 in more psychological language, is there only one degree 
 of belief. The traditional logic was accustomed to rec- 
 ognize this fact in its theory of modals. i The earth re- 
 volves around the sun ' is an assertoric judgment. A 
 dictum is asserted flatly. ' It may rain this afternoon f 
 is a problematic judgment. In science, the stage of 
 conjecture represents the problematic mode. ' Gravita- 
 tion may be explained in terms of electricity,' 6 Mass 
 may turn out to be a dynamic effect of something more 
 ultimate,' are examples. An apodeictic judgment, on the 
 other hand, expresses a sense of logical necessity. The 
 grounds for the judgment are given or intimated. 
 4 There must be a presidential election this year ' is apo- 
 deictic. The ground intimated is, of course, the federal 
 law on the subject. 
 
 Modality reflects the fact that ideas have different 
 settings. Beliefs are held with more or less faith. The 
 
302 THE ESSENTIALS OF LOGIC 
 
 upper limit of belief is dogmatic certainty, while the 
 other extreme is a low degree of probability. The logi- 
 cian encourages individuals to give up dogmatic cer- 
 tainty and to make practical certainty the highest de- 
 gree of belief. There is a continuous shading of belief 
 from mere probability, in which the evidence is weak, 
 to practical certainty in which there is no longer any 
 factually motivated doubt. Rational belief is belief 
 founded on grounds, and such grounds must ultimately 
 come back to critically tested fact. 
 
 What the Attainment of True Ideas implies. 
 There are at least four things implied in the attain- 
 ment of true ideas : (1) the ability to obtain facts (ob- 
 servations, testimony, evidence) ; (2) the right to 
 make use of past experience which is not challenged by 
 reasonable doubt ; (3) the Principle of Universal Con- 
 nections, the Uniformity of Nature, the Law of Uni- 
 versal Causation ; (4) the mental capacity for analysis, 
 conjecture, construction, and deductive reasoning. 
 
 These four things are largely self-explanatory when 
 taken in the light of what has already been said about 
 them in the preceding chapters. Unless we could obtain 
 facts, which are assertions about which there is no 
 motivated doubt, it would be impossible to generalize, 
 to form hypotheses, or to verify by the convergence of 
 evidence. Unless past knowledge were applicable, it 
 would be impossible to have guidance in an attack on 
 new problems or to determine what was relevant and 
 what irrelevant ; again, it would be impossible to build 
 up systems of knowledge such as are found in the vari- 
 ous sciences as well as in practical life. Knowledge is, 
 as we have so often pointed out, a growth. While the 
 
TRUTH AND ITS TESTS 303 
 
 old may be modified by the new facts and theories, it 
 yet remains as something substantial within which to 
 work. That universal connections exist and can be dis- 
 covered is a postulate which underlies all scientific in- 
 vestigation. It cannot be proved in any demonstrative 
 way, but is suggested and in a way verified by expe- 
 rience. Finally, logic assumes that the mental capaci- 
 ties which human beings possess, working upon the ma- 
 terial given by observation and testimony, are able to 
 achieve ideas which give genuine knowledge. To doubt 
 this ability to attain knowledge is for logic an ultimate 
 scepticism which it refuses to acknowledge. Both our 
 practical and our intellectual instincts revolt against the 
 suggestion that what we take to be knowledge is not 
 knowledge. 
 
 The Meaning of Truth. Having given the empiri- 
 cal criteria of ; truth ' and their logical setting, let us 
 be bold enough to discuss the meaning of this term. 
 What do we mean by ' true ' ideas ? How do such 
 ideas differ from ' false ' ideas ? Controversial battles 
 have been waged in philosophy over the meaning of 
 these terms. Into the details of such controversies, it 
 is not here the place to enter. We must be brief and 
 clear, and trust that the position adopted will commend 
 itself to the reason of those who have carefully studied 
 the preceding pages. 
 
 Let us admit the hazard that what we take to be 
 true may not be true. The problem still remains that 
 we mean something by this term. An idea is true which 
 meets the empirical criteria and which tve therefore 
 take to be a case of knowledge. An idea is true which 
 has stood the test of motivated doubt, has come out 
 
304 THE ESSENTIALS OF LOGIC 
 
 victorious, and, due to that fact, is accepted by the 
 mind as fulfilling its claim to be an idea of, or about, 
 something. It is the very nature of an idea to claim to 
 give knowledge. When this claim is granted by the 
 mind, the idea is accredited or accepted as genuine 
 knowledge ; and the term true is used to express this 
 attitude of approval. Thus, it is a contrast term with 
 4 false ' as its counterpart. Just as actions are quali- 
 fied as right or wrong, so ideas — i.e., judgments, pro- 
 positions, assertions — are qualified as true or false. 
 This latter qualification gets its meaning, however, from 
 the claim to be cases of knowledge which it is the very 
 nature of such judgments to assert. 
 
 There can be little doubt that the methods by which 
 ideas are tested enter into the meaning of truth to a 
 greater or lesser extent. What is called 4 pragmatism' 
 is a stimulating but, I believe, one-sided emphasis on this 
 aspect of the meaning of truth. " True ideas" writes 
 James, " are those that we can assimilate, validate, 
 corroborate and verify. False ideas are those that we 
 cannot. That is the practical difference it makes to us 
 to have true ideas ; that, therefore, is the meaning of 
 truth, for it is all that truth is known-as." l It will be 
 noticed that the meaning of being an actual case of 
 knowledge, which is a part of the content and setting of 
 every assertion, is omitted. This aspect is, in our opin- 
 ion, fundamental. The logician who understands his 
 science does not deny the empirical character of the 
 criteria of trueness, but he does assert that the claim 
 of an idea to be knowledge is also essential. " Knowl- 
 edge is an achievement and possession of minds as these 
 
 1 James, Pragmatism, p. 201. 
 
TRUTH AND ITS TESTS 305 
 
 have evolved under the stimulus of their environment. 
 As a meaning, knowledge precedes truth, which is a 
 reflective deepening of the sense of knowledge in the 
 light of an awakened doubt. The criteria of truth are, 
 therefore, the same as those of knowledge. Thus truth 
 is accepted and tested knowledge. To say that an idea 
 is true is to say that it is actually a case of knowledge 
 as it claims to be. Truth is knowledge triumphant in- 
 stead of knowledge militant ; yet it is knowledge, as 
 can be seen when we combine the two terms and speak 
 of true knowledge." x 
 
 Truth and the Will to believe. Of recent years 
 there have been several stimulating essays on the rela- 
 tion of will and our passional nature in general to be- 
 lief. By consensus of opinion, the two most striking of 
 these are James's The Will to Believe and Clifford's 
 The Ethics of Belief These two writers hold positions 
 which are different both in their tenor and in their con- 
 clusions. It will repay us to examine their discussions 
 of the foundations of belief for this will introduce us 
 to the larger setting of logic. 
 
 Let us begin with The Will to Believe. As a psy- 
 chologist, James rightly first considers the actual psy- 
 chology of human opinion. " When we look at certain 
 facts, it seems as if our passional and volitional nature 
 lay at the root of all our convictions. When we look 
 at others, it seems as if they could do nothing when the 
 intellect had once said its say." 2 Taking up the latter 
 facts first, he writes : " Does it not seem preposterous 
 
 1 Sellars, Critical Realism, p. 282. 
 
 2 James, The Will to Believe; page references are to Representative 
 Essays in Modern Thought, 
 
306 THE ESSENTIALS OF LOGIC 
 
 on the very face of it to talk of our opinions being 
 modifiable at will? Can we, by just willing it, believe 
 that Abraham Lincoln's existence is a myth, and that 
 the portraits of him in Mc duress Magazine are all of 
 some one else? . . . We can say any of these things, 
 but we are absolutely impotent to believe them ; and 
 of just such things is the whole fabric of the truths 
 that we do believe in made up, — matters of fact, im- 
 mediate or remote, as Hume said, and relations between 
 ideas, which are either there or not there for us if we 
 see them so, and which if not there cannot be put there 
 by any action of our own" (p. 76). I feel that it is 
 best to quote this side of James's teaching quite fully, 
 since justice has not been done to it. James permits 
 the 'will to believe' only in certain fields and under 
 certain circumstances. " The talk of believing by our 
 volition seems, then, from one point of view, simply 
 silly. From another point of view it is worse than silly ; 
 it is vile. When one turns to the magnificent edifice of 
 the physical sciences, and sees how it was reared ; what 
 thousands of disinterested moral lives of men lie buried 
 in its mere foundations ; what patience and postpone- 
 ment, what choking down of preference, what submis- 
 sion to the icy laws of outer fact are wrought into its 
 very stones and mortar ; how absolutely impersonal it 
 stands in its vast augustness, — then how besotted 
 and contemptible seems every little sentimentalist who 
 comes blowing his voluntary smoke wreaths, and pre- 
 tending to decide things from out of his private dream " 
 (p. 78). 
 
 But, as James points out, there is an interaction be- 
 tween our knowledge, our values, our aspirations, and 
 
TRUTH AND ITS TESTS 307 
 
 our prejudices. The mind is an organic whole, and it 
 is impossible to find an intellect separate from the 
 movement of experience. Facts and theories are not 
 independent, for their discovery, selection, relative im- 
 portance and control, of the outlook of the individual ; 
 and this outlook is a synthesis of ideas and feelings. 
 That this is the case we have tried to bring out in the 
 study of induction. But the logician urges the individ- 
 ual to allow the outlook to be more a function of in- 
 vestigation, to make the factual side the control-side. 
 The logician sets an ideal which he admits is seldom 
 approached. This control of outlook by ' fact ' is the 
 aim which lies back of the inductive principle of fidelity 
 to fact and the internal criteria of truth, the conver- 
 gence of relevant evidence. Thus logic stresses the 
 avoidance of error, on the one hand, and the positive 
 methods of attaining new truth on the other. Its aim 
 is to make the individual critically reflective toward 
 assertions and beliefs. 
 
 Let us now turn to the thesis which James defends : 
 " Our passional nature not only lawfully may, but 
 must, decide an option between propositions, whenever 
 it is a genuine option that cannot by its nature be de- 
 cided cm intellectual grounds ; for to say, under such 
 circumstances, 4 Do not decide, but leave the question 
 open,' is itself a passional decision, — just like decid- 
 ing yes or no — and is attended with the same risk of 
 losing the truth" What strikes the logician in this 
 thesis is the assumption that there are problems " which 
 by their very nature cannot be decided on intellectual 
 grounds " (p. 81). It is this assumption that the logician 
 cannot admit if by intellectual grounds are meant factual 
 
308 THE ESSENTIALS OF LOGIC 
 
 grounds. Such problems could not be formulated and 
 defined. 
 
 But James at least suggests that other problems than 
 non-rational ones are also to be treated by our passional 
 nature. And here there is an ambiguity in his treat- 
 ment. As against Clifford, he insists that we do not 
 need to shut our eyes to a possibility of belief just be- 
 cause the problem has not been settled and there is also 
 a possibility of error. With this I agree. There are 
 degrees of belief ; and, when evidence can be advanced 
 both for and against a position, neither affirmation nor 
 negation should be dogmatic. I can understand why 
 such a temperament as James's rebelled against the stoi- 
 cism of Clough, Huxley, and Clifford which sang: — 
 
 It fortifies my soul to know- 
 That, though I perish, Truth is so. 
 
 When there is probability only, probability is by its 
 very nature both for and against. The probability of 
 throwing a six-spot is one sixth and the chances against 
 are five sixths. James has the right to stress the prob- 
 ability for, while Clifford has an equal right to stress 
 the negative side, the motivated doubt. 
 
 But there runs through James the suggestion of an- 
 other test of truth than that worked out by science and 
 logic. It is not prominent, but it is present enough to 
 have led many to interpret his position in accordance 
 with it. This second standard consists in an appeal to 
 personal feelings and satisfactions as a foundation 
 for truth. Such feelings are facts, but they are not 
 the only facts, nor are they the least changing and com- 
 mon of facts. To make them the dominant criteria is, 
 therefore, to forsake an objective and thorough inves- 
 
TRUTH AND ITS TESTS 309 
 
 tigation in favor of what experience has proved to be 
 personal and incomplete. 
 
 The Logic of Doubt. In contrast to the essay by 
 James, Clifford's treatment savors almost of a justifica- 
 tion of doubt. And, from the logician's standpoint, 
 much can be said in favor of such an attitude. Belief, 
 as a rule, takes care of itself, while doubt and open- 
 mindedness are trained habits not easily acquired. Clif- 
 ford stresses what may be called the i ethical aspect ' 
 of logic ; and in his attitude there is much that reminds 
 us of the Puritan and the Stoic. James was a brilliant, 
 tender-minded, broad-minded mystic; Clifford was a 
 rigorous, tough-minded, intellectual idealist. 
 
 " A shipowner was about to send to sea an emigrant 
 ship. He knew that she was old, and not overwell 
 built at the first ; that she had seen many seas and 
 climes, and often had needed repairs. Doubts had been 
 suggested to him that possibly she was not seaworthy. 
 These doubts preyed upon his mind, and made him un- 
 happy ; he thought that perhaps he ought to have her 
 thoroughly overhauled and refitted, even though this 
 should put him to great expense. Before the ship 
 sailed, however, he had succeeded in overcoming these 
 melancholy reflections. . . . He would dismiss from 
 his mind all ungenerous suspicions about the honesty 
 of builders and contractors. In such ways he acquired 
 a sincere and comfortable conviction that his vessel 
 was thoroughly safe and seaworthy . . . ; and he got 
 his insurance money when she went down in midocean 
 and told no tales. 
 
 " What shall we say of him ? Surely this, that he 
 was verily guilty of the death of those men. It is ad- 
 
310 THE ESSENTIALS OF LOGIC 
 
 mitted that he did sincerely believe in the soundness of 
 his ship; but the sincerity of his conviction can in no 
 wise help him, because he had no right to believe on 
 such evidence as teas before him. He had acquired his 
 belief not by honestly earning it in patient investiga- 
 tion, but by stifling his doubts." 1 
 
 Clifford's conclusion is : " It is wrong always, every- 
 where, and for any one, to believe anything upon insuf- 
 ficient evidence" (p. 54). " 'But,' says one, *I am a 
 busy man ; I have no time for the long course of study 
 which would be necessary to make me in any degree a 
 competent judge of certain questions, or even able to 
 understand the nature of the arguments.' Then he 
 should have no time to believe" (p. 54). It must have 
 been this last pronouncement which made James call 
 him " that delicious enfant terrible" Let us soften it 
 somewhat by saying that he should have no time for 
 dogmatic belief, for that belief which shuts out evi- 
 dence when it comes and passes harshly and uncom- 
 promisingly into action. 
 
 REFERENCES 
 
 Bode, An Outline of Logic, chap. XV. 
 
 James, The Will to Believe and other Essays in Popular Philos- 
 ophy. 
 
 James, Pragmatism, chap. VT. 
 
 Clifford, The Ethics of Belief . 
 
 Gibson, The Problem of Logic, chaps. I and in. 
 
 Sellars, Critical Realism, chap. X. 
 
 1 Clifford, The Ethics of Belief, Bepresentative Essays, pp. 46-47. 
 
QUESTIONS AND EXERCISES 
 
 CHAPTER I 
 
 1. Analyze the definition of logic given, and compare it 
 with definitions to be found in other texts. 
 
 2. Distinguish between a theoretical and an applied sci- 
 ence. Give examples of both. 
 
 3. What is meant by 'utilitarian' when the term is used in 
 its narrower sense? 
 
 4. Point out and explain why logic has a practical value in 
 education. 
 
 5. Name the various kinds of logic. Why have these 
 developed? 
 
 6. With what other sciences is logic related? 
 
 7. How does the purpose of logic differ from that of rhetoric? 
 
 8. To what extent do logic and psychology have the same 
 subject-matter ? 
 
 9. Where does logic find its material? Why is introspec- 
 tion alone not sufficient? 
 
 10. Recall an actual case of reasoning and try to analyze it. 
 
 CHAPTER II 
 
 1. State some of the mental processes to which the term 
 'thinking' is applied. Give examples to bring out dif- 
 ferent levels of thinking. 
 
 2. Distinguish between 'imagination,' 'memory,' and 'rea- 
 soning.' Make two illustrations of each. 
 
 3. What are some of the social conditions of thought? Name 
 some of the great periods in history distinguished by 
 mental boldness and energy. 
 
 4. Can you name any great men who owed much to some 
 stimulus which awakened their mental curiosity? 
 
 5. "Thinking arises out of the need for adjustment." 
 Explain. 
 
 6. What processes are preliminary to reasoning? Distin- 
 guish between 'perception' and 'conception.' 
 
SU QUESTIONS AND EXERCISES 
 
 7. Collect five statements which you would call * facts.' 
 Can you find any element of inference or theory in them? 
 
 8. Take any field in which you are especially interested, 
 and show that your insight has increased with further 
 study. 
 
 9. Give at least four cases where your perception of a thing 
 or of an event has been changed by further knowledge. 
 
 10. Do you think that the public schools in America stimu- 
 late genuine thinking as much as is desirable? Be pre- 
 pared to support your opinion. 
 
 CHAPTER III 
 
 1. Distinguish between a 'logical term' and a 'word/ 
 
 2. In the following list, point out which terms are concrete 
 and which are abstract: — 
 
 virtue education solitude life 
 
 American democracy asparagus time will 
 
 detachment consciousness auto cavalry 
 
 iron man paper fate 
 
 3. Make a list of five examples of collective terms. 
 
 4. Distinguish between general and singular terms. Make 
 a list of five of each kind. 
 
 5. Do you think that the distinction between singular and 
 general can be applied to abstract terms? 
 
 6. Explain the fallacy of hypostatization. Give three 
 examples which show at least an approach to this 
 fallacy. 
 
 7. What are relative terms? Give five examples. 
 
 8. Explain the danger in discussions about 'poverty,' 
 'educational progress,' 'the growth of democracy.' 
 
 9. Distinguish between positive and negative terms. Give 
 three examples of each. Is the form always an index to 
 the meaning? 
 
 10. Explain the distinction between 'denotation' and 'con- 
 notation.' 
 
 11. Make a series of at least six terms arranged in order of 
 increasing denotation. Arrange the same terms in order 
 of increasing connotation. 
 
 12. Show that terms which do not have any connotation 
 still have meaning. 
 
QUESTIONS AND EXERCISES 313 
 
 CHAPTER IV 
 
 1. Why is language such an important condition of think- 
 ing? 
 
 2. State the logical law of language. 
 
 3. What are some of the causes of ambiguity? 
 
 4. Give ten examples of univocal words. Are technical 
 terms always univocal? 
 
 5. In the following exercises select those terms of which 
 the meaning is most uncertain. State and justify the 
 meaning which you think belongs to the term in its 
 present context: — 
 
 (1) We should live according to Nature. 
 
 (2) All men have natural rights. 
 
 (3) America is a democratic country. 
 
 (4) International law must be binding on all peoples. 
 
 6. Make a list of five words which have decidedly changed 
 their meaning during the last hundred years. 
 
 7. Distinguish between vagueness and ambiguity. Show 
 why abstract terms are peculiarly liable to vagueness. 
 
 8. Try to formulate the divergent notions of * force,' ' mat- 
 ter,' and ' motion ' that are expressed or implied in the 
 following extracts from Buechner's Force and Matter: — 
 
 "No force without matter — no matter without 
 force. One is no more possible, and no more imagin- 
 able by itself than the other. . . . Force and matter 
 are fundamentally the same thing, contemplated 
 from different standpoints. In the material world 
 we know of no example of a particle of matter not 
 endowed with force or working by it. We must further 
 admit on closer investigation, that matter as such 
 could make no impression on our sense-organs or 
 minds; it can only do this by means of the forces 
 united with or at work within it. A piece of lead held 
 in the hand presses on it because of the attractive 
 force of the earth and so produces the idea of weight. 
 . . . Nothing can prove to us the real existence of a 
 force, except the properties, changes and movements, 
 which we become conscious of in matter, and these 
 we call different 'forces' according to the resemblances 
 or differences in such manifestations; any knowledge 
 
314 QUESTIONS AND EXERCISES 
 
 of them by other ways is impossible. . . . Force may 
 be defined as a condition of activity or a motion of 
 matter or of the minutest particles of matter or a 
 capacity thereof; yet more precisely, as an expression 
 for the reason of a possible or actual movement. . . . 
 
 "Motion must be regarded as an eternal and insepa- 
 rable property or as a necessary condition of matter. 
 Matter without motion exists no more than matter 
 without force; motion without matter exists as little 
 as force without matter. Nor can motion be deduced 
 from any force, for it is the very essence of force it- 
 self, and can therefore have no origin, but must be in 
 all places. . . . The most solid body owes its condi- 
 tion only to the mutual attractive force of its minutest 
 particles, which continually oscillate or swing round 
 the so-called center of gravity, and without which it 
 would at once fall to pieces. That these particles are 
 never able to attain a condition of relative rest is 
 proved by the universally present force of heat, which 
 is known to be nothing more than a mode of motion 
 and which, since all bodies without exception contain 
 heat, keep these smallest particles or molecules in a 
 state of continual movement. . . . Motion must there- 
 fore be regarded as the primal condition or in some 
 measure as the soul of matter." l 
 
 CHAPTER V 
 
 1. What is classification? Out of what need does it arise? 
 
 2. Distinguish between 'artificial' and 'natural* classi- 
 fications. 
 
 3. How has the theory of evolution affected scientific 
 classification? 
 
 4. What is a 'dichotomous' division? Under what condi- 
 tions might it be advantageous? 
 
 5. Criticize the following divisions : — 
 
 (1) Religions, into Christian, Mohammedan, and 
 non-Christian. 
 
 (2) Pictures, into paintings, engravings, posters, and 
 pen-and-ink sketches. 
 
 1 Quoted from Bode. An Outline of Logic. 
 
QUESTIONS AND EXERCISES 315 
 
 (3) Schools, into technical, vocational, and public. 
 
 (4) Furniture, into Colonial, Sheraton, Adams, office, 
 and home. 
 
 (5) Political parties, into Republican, Radical, and 
 Conservative. 
 
 6. Divide and subdivide the following : — 
 
 Governments, Sciences, Sports, Schools. 
 
 7. State and explain the technical terms used in division. 
 
 8. What part does purpose play in both classification and 
 division? 
 
 CHAPTER VI 
 
 1. Why is definition needed? 
 
 2. Show the relation between ' definition' and 'classifica- 
 tion.' 
 
 3. Define the following terms by proximate genus and es- 
 sential difference : — 
 
 Democracy, Education, Tariff, Politics, American, 
 Honor, Wealth, Neutrality. 
 
 4. Examine the following definitions to see whether they 
 conform to the logical rules of definition: — 
 
 (1) The body is the emblem or visible garment of the 
 soul. 
 
 (2) Life is a continuous adjustment of internal to ex- 
 ternal relations. 
 
 (3) A phonograph is a mechanism for recording and 
 reproducing sounds. 
 
 (4) Life is the opposite of death. 
 
 (5) Psychology is the science of the processes whereby 
 an individual becomes aware of a world of objects 
 and adjusts his actions accordingly. 1 
 
 (6) Psychology is the science of the phenomena of 
 consciousness. 2 
 
 (7) Education is the eternal process of superior ad- 
 justment of the physically and mentally developed, 
 free, conscious human being to God, as mani- 
 fested in the intellectual, emotional, and volitional 
 environment of man. 3 
 
 (8) Education is conscious or voluntary evolution. 4 
 
 1 Stout. 2 Baldwin. 3 Home. * Davidson. 
 
316 QUESTIONS AND EXERCISES 
 
 (9) Religion consists in the feeling of absolute de- 
 pendence. 1 
 
 (10) Religion is a desire manifested by prayer, sacri- 
 fice, and faith. 2 
 
 (11) Religion is a faculty of the mind by which, inde- 
 pendently of the senses and of reason, man is able 
 to perceive the Infinite. 3 
 
 5. Show that a definition is always relative to the purpose 
 entertained. 
 
 6. What are the predicables? Distinguish between a 'dif- 
 ferentia' and an 'accident.' 
 
 7. Write out a list of at least five words or phrases which 
 you regard as catch-words which need definition. 
 
 8. Look up the platforms of the various political parties for 
 words which seem to you to need definition. 
 
 CHAPTER VII 
 
 1. Distinguish between 'assertions' and 'propositions.' 
 What was the error of the more formal logic of the past? 
 
 2. Show that judgment is a process of interpretation end- 
 ing in an assertion. 
 
 3. Bring out by at least three examples the genetic side of 
 judgment. 
 
 4. Show that the world as we experience it is a product of 
 past mental activity. 
 
 5. In what sense are there levels of judgment? Give cases 
 to prove the increasing complexity of judgment as we 
 pass from concrete things to principles. 
 
 6. What two aspects are there to every judgment? 
 
 7. Distinguish between the actual operation of judging and 
 its verbal expression. What is the purpose which con- 
 trols language? 
 
 8. What is meant by the 'universe of discourse'? Indicate 
 the reason for its importance in the proper interpretation 
 of propositions. 
 
 1 Schleiermacher. 2 Feuerbach. 8 Max Mtiller. 
 
QUESTIONS AND EXERCISES 317 
 
 CHAPTER VIII 
 
 1. Distinguish between 'categorical/ 'hypothetical,' and 
 'disjunctive' propositions. 
 
 2. What is meant by the 'quantity' of propositions? By 
 their 'quality'? 
 
 3. Throw the following propositions into logical form, 
 give the letter that symbolizes the quantity and quality, 
 and state the distribution of the terms: — 
 
 (1) Not all who are called are chosen. 
 
 (2) Few were saved. 
 
 (3) None of the planets except the earth is inhabited. 
 
 (4) He can't be wrong whose life is in the right. 
 
 (5) More haste less speed. 
 
 (6) All politicians are not dishonest. 
 
 (7) Only noble deeds deserve praise. 
 
 (8) Mercy but murders, pardoning those that kill. 
 
 (9) No one is always happy. 
 
 (10) Only some citizens have the right to vote. 
 
 4. Explain why negative propositions always distribute the 
 predicate. 
 
 5. Apply the graphical method to the four kinds of cate- 
 gorical propositions. 
 
 6. What is the purpose underlying the logical manipulation 
 of propositions. 
 
 CHAPTER IX 
 
 1. What is immediate inference? 
 
 2. Be prepared to write down and explain the Square of 
 Opposition. 
 
 3. What propositions are true, false, or doubtful', — 
 
 (1) when A is false; (3) when I is false; 
 
 (2) when E is false; (4) when is false? 
 
 4. What is the simplest proposition which must be estab- 
 lished in order to disprove the following statements: — 
 
 (1) All men desire wealth. 
 
 (2) No man is perfectly happy. 
 
 (3) Some knowledge is not of any value. 
 
 (4) Pain alone is evil. 
 
 (5) All is not lost. 1 
 
 1 Creighton. 
 
318 QUESTIONS AND EXERCISES 
 
 5. Give the converse, the obverse, and the contrapositive 
 of each of the following propositions : — 
 
 (1) Only a fanatic believes in panaceas. 
 
 (2) Uneasy lies the head that wears a crown. 
 
 (3) No men are always happy. 
 
 (4) Most of the nations were unprepared. 
 
 (5) None but the industrious deserve to succeed. 
 
 (6) All men are mortal. 
 
 (7) Discontent is frequently a symptom of inefficiency. 
 
 (8) Children are noisy on rainy days. 
 
 6. By what process do we pass from each of the following 
 propositions to the next? 
 
 (1) No knowledge is useless. 
 
 (2) No useless thing is knowledge. 
 
 (3) All knowledge is not useless. 
 
 (4) All knowledge is useful. 
 
 (5) What is not useful is not knowledge. 
 
 (6) What is useless is not knowledge. 
 
 (7) No knowledge is useless. 1 
 
 7. Test the following arguments by obversion and con- 
 version: — 
 
 (1) When we hear that all the righteous people are 
 happy, it is hard to avoid exclaiming, What! are 
 all the unhappy persons we see to be thought un- 
 righteous? 
 
 (2) If a man who has been accustomed to enjoy lib- 
 erty cannot be happy in the condition of a slave, 
 does it follow that a man who has not been accus- 
 tomed to liberty can be happy as a slave? 
 
 CHAPTER X 
 
 1. How did Aristotle define the syllogism? What was the 
 germ of his invention? 
 
 2. What is the Dictum de omni et nullo ? 
 
 3. Be prepared to demonstrate each of the rules of the 
 syllogism. 
 
 4. What criticism would you be inclined to pass upon the 
 syllogism when treated very formally? 
 
 5. Select and name the various propositions and terms of 
 
 1 Jevons. 
 
QUESTIONS AND EXERCISES 319 
 
 the syllogism in the following informally stated argu- 
 ments. Then reconstruct them so as to make formally 
 correct syllogisms : — 
 
 (1) All leeches must be true worms; for all annelids 
 are worms, and leeches are annelids. 
 
 (2) Caterpillars have true legs; worms do not; and so 
 caterpillars are not worms. 
 
 (3) Amphibians are not reptiles, since they breathe 
 by gills in the larval stage, and reptiles do not. 1 
 
 6. If either premise of a syllogism is 0, what must the other 
 be? 
 
 7. Prove that there must be in the premises one more dis- 
 tributed term than in the conclusion. 
 
 8. Prove that if one, but only one, premise is negative, and 
 both premises are universal, they will between them dis- 
 tribute three terms. 
 
 9. Put the following argument into syllogistic form: — 
 
 How can any one maintain that pain is always an evil, 
 who admits that remorse involves pain, and yet may 
 sometimes be a real good? 
 
 CHAPTER XI 
 
 1. Arrange the following arguments in logical order. Name 
 the figure of the syllogism, and if the argument is in- 
 valid, state the formal fallacy involved: — 
 
 (1) All M is P; no M is S; therefore no S is P. 
 
 (2) No P is M; some S is M; therefore some S is 
 not P. 
 
 (3) Some useful metals are becoming rarer; iron is a 
 useful metal, and is therefore becoming rarer. 
 
 (4) None but whites are civilized; the ancient Ger- 
 mans were white; therefore they were civilized. 
 
 (5) Since the virtuous alone are happy, he must be 
 virtuous if he is happy, and he must be happy if 
 he is virtuous. 
 
 (6) It is not true that a man cannot do a great work 
 without a strong physique; for the philosopher 
 Kant did a great work and his physique was any- 
 thing but strong. 
 
 i Taylor. 
 
320 QUESTIONS AND EXERCISES 
 
 (7) Only animals are sentient beings; fishes are ani- 
 mals; therefore fishes are sentient beings. 
 
 (8) Good men write good books; this is a good book; 
 therefore its writer was a good man. 
 
 (9) Every book is liable to error; every book is a hu- 
 man production; therefore all human productions 
 are liable to error. 
 
 2. Write out the sixty-four moods of the syllogism and 
 strike out the fifty-three invalid ones. 
 
 3. Prepare to prove the special canons of each of the four 
 figures. 
 
 4. Make a syllogism in E I 0, any figure, and exhibit the 
 conversions necessary to accommodate it to each of the 
 other figures. 1 
 
 5. Why is the first figure usually considered the standard 
 figure? 
 
 6. Supply premises for the following conclusions: — 
 
 (1) Some politicians are not dishonest. 
 
 (2) The moon tends to fall to the earth. 
 
 (3) Banks sometimes fail. 
 
 (4) Some logicians are not good reasoners. 
 
 CHAPTER XII 
 
 1. Complete the following arguments, determine their 
 mood and figure, and decide whether they are valid: — 
 
 (1) Blessed are the meek, for they shall inherit the 
 earth. 
 
 (2) Only the good are fit to die, therefore capital pun- 
 ishment is wrong. 
 
 (3) Let us meet her. Why? They say she's mad. 
 
 (4) Because thou art virtuous, shall there be no more 
 cakes and ale? 
 
 (5) None but material bodies gravitate; therefore air 
 is a material body. 
 
 2. Construct an enthymeme of each of the three orders. 
 
 3. Construct a complex argument containing a prosyl- 
 logism and an episyllogism. 
 
 4. Show why all the premises except the first must be uni- 
 versal in an Aristotelian Sorites. 
 
 i Taylor. 
 
QUESTIONS AND EXERCISES 321 
 
 5. Prove by graphical methods that in the Goclenian So- 
 rites the first premise alone can be negative, and the 
 last alone particular. 
 
 6. What is an extra-syllogistic argument? Contrast it with 
 syllogistic inference. 
 
 7. Why are fallacies more apt to exist in condensed argu- 
 ments than in expansed ones? 
 
 CHAPTER XIII 
 
 1. Determine which of the following give valid conclusions 
 and which do not; in case of invalidity, name the fallacy: 
 
 (1) If the door were locked, the horse would not be 
 stolen; but the horse is not stolen, therefore the 
 door must have been locked. 
 
 (2) If all men were capable of perfection, some would 
 have attained it; but none having done so, none 
 are capable of it. 
 
 (3) If every ghost story is to be believed, we must 
 accept the general standpoint of the spiritualists; 
 but we cannot accept their general standpoint; 
 therefore we cannot believe ghost stories. 1 
 
 (4) 'If he has not studied, he will fail in the examina- 
 tion.' With this proposition as a major premise, 
 what can be inferred if we take as minor premise : — 
 
 (1) He has not studied. 
 
 (2) He will fail. 
 
 (3) He will not fail. 
 
 (4) He has studied. 
 
 (5) If it becomes colder to-night, there will be a frost; 
 but it will not become colder to-night; therefore 
 there will be no frost. 
 
 2. Does the categorical or the hypothetical syllogism seem to 
 you the simpler? Which of the two stresses denotation? 
 
 3. Where is the source of danger in the disjunctive syllo- 
 gism? 
 
 4. Work out a dilemma on some subject of debate. 
 
 5. Examine the following arguments : — 
 
 (1) It is either raining or not raining; it is not raining; 
 therefore it is raining. 
 
 1 Aikins. 
 
322 QUESTIONS AND EXERCISES 
 
 (2) No honest man can advocate a change in the 
 creed of his church; for he must either believe it 
 or not believe it; and if he believes it, he cannot 
 honestly help to change it, while if he does not 
 believe it he cannot honestly belong to the church 
 at all. 
 
 (3) In order to move, a body must move either in the 
 place where it is or in the place where it is not. 
 But it cannot move in the place where it is, since 
 that place is already occupied. Neither can it 
 move in the place where it is not. Motion is there- 
 fore impossible. 
 
 (4) If transportation is not felt as a severe punishment, 
 it is in itself ill-suited to the prevention of crime; 
 if it is so felt, much of its severity is wasted, from 
 its taking place at too great a distance to affect 
 the feeling, or even come to the knowledge, of most 
 of those whom it is designed to deter; but one or 
 the other of these must be the case; therefore trans- 
 portation is not calculated to answer the purpose 
 of preventing crime. 
 
 CHAPTER XIV 
 
 1. Distinguish between a 'sophism' and a 'fallacy.' 
 
 2. Review the formal fallacies. 
 
 3. Be able to classify material fallacies under two appro- 
 priate headings. 
 
 4. Look up advertisements to see whether you can find 
 some examples of amphiboly. 
 
 5. Give an example of the fallacy of accident. Also of the 
 converse fallacy of accident. 
 
 6. Explain the difference between 'begging the question' 
 
 and 'irrelevant conclusion.' 
 
 7. Give an example each of Argumentum ad hominem, Ar- 
 gumentum ad populum, Argumentum ad ignorantiam, 
 and Argumentum ad vericundiam. 
 
 8. Note and classify the fallacies in the following argu- 
 ments : — 
 
 (1) A monopoly of the sugar-refining business is bene- 
 ficial to the sugar-refiners; and of the corn trade to 
 
QUESTIONS AND EXERCISES 323 
 
 the corn-growers; and of silk manufacture to the 
 silk-weavers; and of labor to the laborers. Now, 
 all these classes of men make up the whole com- 
 munity. Therefore a system of restrictions upon 
 competition is beneficial to the community. 1 
 
 (2) Any student in college would stand higher in his 
 class if he received higher marks; hence, if all 
 marks were raised ten per cent every man would 
 stand nearer the head of his class. 
 
 (3) Since attending that mass meeting of students, I 
 have had no confidence in decisions reached in 
 that way. 
 
 (4) Wine is a stimulant; therefore, in every case where 
 a stimulant is harmful, wine is harmful. 
 
 (5) We know that God exists, because the Bible tells 
 us so; and we know that whatever the Bible affirms 
 is true, because it is of divine origin. 
 
 (6) A miracle is incredible because it contradicts the 
 laws of nature. 
 
 (7) We charge him (King Charles the Second) with 
 having broken his coronation oath, and we are 
 told that he kept his marriage vows; we accuse 
 him of having given up his people to the merciless 
 infliction of the most hot-headed and hard-hearted 
 of prelates, and the defense is that he took his little 
 son on his knee and kissed him; we censure him for 
 having violated the articles of the Petition of 
 Rights, after having for a good and valuable con- 
 sideration promised to observe them, and we are 
 informed that he was accustomed to hear prayers 
 at six o'clock in the morning. 
 
 What fallacy does Macaulay refer to in this 
 passage? 2 
 
 (8) If it is fated that you die, you will die whether 
 you call in a doctor or not, and if it is fated that 
 you will recover, you will recover whether you call 
 in a doctor or not. But it must be fated either that 
 you die or that you recover. Therefore, you will 
 either die or recover, whether you call in a doctor 
 or not. 
 
 1 Hyslop. l Russell. 
 
324 QUESTIONS AND EXERCISES 
 
 (9) Every incident in the narration is probable; hence, 
 the narrative is probable. 
 (10) The growing size of London bodes evil to England 
 because London is the heart of England, and a 
 swollen heart is a sign of disease. 
 9. "The President of the United States can veto bills, but 
 he can only veto a bill as a whole. It is therefore not 
 uncommon for Congress to tack on to a bill which the 
 President feels bound to pass a clause containing a 
 measure to which it is known that he objects." Show 
 that this is a practical application of a fallacy. 
 
 10. "One of the most remarkable examples of fallacy is 
 furnished by the political theory of Hobbes and Rous- 
 seau, known as the theory of the 'social compact.' We 
 are supposed bound by the promise entered into by our 
 ancestors before society was called into existence; but 
 there is no such thing as an obligatory promise until so- 
 ciety has been formed." What important assumption is 
 made in this criticism of the compact-theory? 
 
 11. "How is it that we hear so much of French immorality, 
 and nothing, or next to nothing, of Italian? How is it 
 that, in France, we have heard so much of English bar- 
 barity and cruelty, whilst the accounts of Turkish 
 cruelty were received with the smile of incredulity or 
 the shrug of indifference?" * What tendency to fallacy 
 does this quotation illustrate? Give other instances. 
 
 12. "Achilles and a tortoise run a race together. Achilles 
 runs ten times quicker than the tortoise, and accepts, in 
 consequence, a handicap of a hundred yards. Under these 
 conditions, argued Zeno, Achilles will never overtake the 
 tortoise; for when the tortoise has gone ten yards, Achilles 
 will still be ten yards behind him. When these ten 
 yards are caught up, the tortoise will still be ahead by 
 one yard. When this yard is caught up, one-tenth of a 
 yard will still separate them, and so on indefinitely. 
 Achilles, then, though he will be continually drawing 
 nearer to the tortoise, will never actually overtake him." 
 How would you criticize this argument? 
 
 1 Hammerton, French and English. 
 
QUESTIONS AND EXERCISES 325 
 
 FURTHER EXAMPLES OF DEDUCTIVE 
 ARGUMENTS 
 
 CHAPTERS X TO XIV 
 
 1. The right should be enforced by law; the exercise of the 
 suffrage is a right, and should therefore be enforced by 
 law. 
 
 2. Every rule has exceptions; this is a rule, and therefore 
 has exceptions; therefore there are some rules that have 
 no exceptions. 
 
 3. Is a stone a body? Yes. Then is not an animal a body? 
 Yes. Are you an animal? I think so. Ergo, you are a 
 stone, being a body. 
 
 4. His imbecility of character might have been inferred 
 from his proneness to favorites; for all weak princes 
 have this failing. 
 
 5. At the time of the Galveston flood men worked sixteen 
 hours a day; hence, to talk of an eight-hour day as a 
 necessity for the working classes is absurd. 1 
 
 6. Haste makes waste, and waste makes want; therefore 
 a man never loses by delay. 
 
 7. A college education does not pay for most self-made 
 Americans have succeeded without it. 
 
 8. All material bodies impress the senses; mind does not 
 impress the senses. What is the inference? 2 
 
 9. Art is not fostered by money ; for a true artist would prac- 
 tice his art for its own sake, and a bad artist should not 
 be encouraged. 
 
 10. Wealth is in proportion to value, value to efforts, efforts 
 to obstacles; therefore wealth is in proportion to ob- 
 stacles. 
 
 11. For those who are bent on cultivating their minds by 
 diligent study, the incitement of academic honors is 
 unnecessary; and it is ineffectual for the idle and such 
 as are indifferent to mental improvement; therefore the 
 incitement of academic honors should be abolished. 
 
 12. It is impossible to be a good shot without having a 
 
 1 Jones. 2 Tavlor. 
 
326 QUESTIONS AND EXERCISES 
 
 steady hand; John has a steady hand; he is capable, 
 therefore, of becoming a good shot. 
 IS. The theory of evolution is not true, for it was not ac- 
 cepted by Agassiz or by Gladstone; moreover, you cannot 
 accept this doctrine, for it is disclaimed by the au- 
 thorities of your church. 1 
 
 14. The end of a thing is its perfection; death is the end of 
 life; therefore death is the perfection of life. 
 
 15. Improbable events happen almost every day; but what 
 happens almost every day is a very probable event; 
 therefore improbable events are very probable events. 
 
 16. No evil should be allowed that good may come of it; all 
 punishment is an evil; therefore no punishment should 
 be allowed that good many come of it. 
 
 17. 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 to the stern of the vessel? 
 
 18. Written examinations are not absolutely fair tests of a 
 student's scholarship — much less of his industry and 
 intelligence. It is therefore wrong to base his grade 
 upon them. 
 
 19. A vacuum is impossible, for if there is nothing between 
 two bodies they must be in contact. 
 
 20. "They tell us that we are weak, unable to cope with so 
 formidable an adversary; but when shall we be stronger? " 
 
 21. Nothing is better than wisdom; dry bread is better than 
 nothing; therefore dry bread is better than wisdom. 
 
 22. Whoever believes this is a heretic; so that you are no 
 heretic, for you do not believe this. 
 
 23. If a man is educated, he does not want to work with his 
 hands; consequently, if education is universal, industry 
 will cease. 
 
 24. M The railroads have usually acted upon the apparent pol- 
 icy that it is none of the public's business whether they 
 are overcapitalized or not. It remained for the counsel 
 for the N. and N. Railroad, a road notorious for its 
 stock-watering operations, publicly to declare — in form 
 of a question, it is true, but none the less bluntly — the 
 railroad position. If the N. and N. 'charges reasonable 
 rates,' demands its counsel, 'what is it to the public 
 
 1 Creighton. 
 
QUESTIONS AND EXERCISES 327 
 
 whether its capitalization be high or low?'" What 
 assumption is involved in this question? 1 
 
 25. Berkeley's Theory of the Non-Existence of Matter is 
 palpably absurd, for it is impossible even to place one's 
 foot on the ground without experiencing the resistance 
 of matter. 
 
 26. I have no hesitation in saying that the proposition, how- 
 ever good in theory, is in practice utterly absurd. 
 
 27. Epimenides the Cretan says that "all Cretans are liars," 
 but Epimenides is himself a Cretan; therefore he is him- 
 self a liar. But if he be a liar, what he says is untrue, and 
 consequently the Cretans are veracious; but Epimenides 
 is a Cretan, and therefore what he says is true; hence the 
 Cretans are liars, Epimenides is himself a liar, and what 
 he says is untrue. Thus we may go on alternately 
 proving that Epimenides and the Cretans are truth- 
 ful and untruthful. 
 
 28. There exist many differences of opinion and much un- 
 certainty with regard to many questions connected with 
 geology; consequently geology is not a science, and any 
 arguments which assume the truth of geological theories 
 must invariably be regarded with considerable sus- 
 picion. 
 
 29. Personal deformity is an affliction of nature; disgrace is not 
 an affliction of nature; personal deformity is not a disgrace. 
 
 SO. 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 pyra- 
 mids in Egypt is very likely to be false. 
 
 31. Why should any but professional moralists trouble them- 
 selves with the solution of moral difficulties? For, as 
 we resort to a physician in case of any physical disease, 
 so, in the case of any moral doubt or any moral disor- 
 ganization, it seems natural that we should rely on 
 the judgment of some man especially skilled in the 
 treatment of such subjects. 
 
 32. "A asserts with incorrigible optimism that 'without too 
 much you cannot have enough of anything. Lots of 
 inferior books, lots of bad statues, lots of dull speeches, 
 
 i Bode. 
 
328 QUESTIONS AND EXERCISES 
 
 of tenth-rate men and women, as a condition of the few- 
 precious specimens in either kind being realized/ As 
 the condition, yes; but as the cause, no. We can never 
 have the precious things in literature merely by adding 
 to the multitude of cheap things/' x 
 
 33. "An abundant stream divides two limits of one prop- 
 erty . . . and over this stream stood a bridge; and at 
 the head of it a gallows, over which were appointed four 
 judges to decide according to the law established by the 
 lord of the stream, the bridge, and the territory. The 
 law ran in this wise: 'If any one shall pass over this 
 bridge from one side to the other, he must first swear as 
 to whence he comes and on what business he is bound, 
 and if he swear truly, he must be allowed to go; but if 
 he swear falsely, he shall on that account die by hanging 
 on the gallows which is there; and that without remis- 
 sion whatever.' This law and its stern conditions being 
 known, many went over; and as soon as it was perceived 
 that they swore truly, the judges allowed them to pass 
 freely. It happened, however, that on swearing one 
 man, he took the oath and declared that he was going 
 to die on that gallows, and that he had no other business. 
 The judges consulted the terms of the oath, and said: 
 'If we allow that man to go free, he has sworn falsely, and 
 according to the law he ought to die; and if we hang him, 
 the oath that he was going to hang on that gallows was 
 true, and according to the same law he ought to be free.' " 2 
 
 34. We must either gratify our vicious propensities, or re- 
 sist them; the former course will involve us in sin and 
 misery; the latter requires self-denial; therefore we must 
 either fall into sin and misery or practice self-denial. 
 
 35. "America has still a long vista of years stretching before 
 her in which she will enjoy conditions far more auspi- 
 cious than any European country can count upon. And 
 that America marks the highest level, not only of ma- 
 terial well-being, but of intelligence and happiness, 
 which the race has yet attained, will be the judgment of 
 those who look, not at the favored few for whose bene- 
 fit the world seems hitherto to have framed its institu- 
 tions, but at the whole body of the people." 3 
 
 1 Creighton. 2 From Don Quixote. 3 James Bryce. 
 
QUESTIONS AND EXERCISES 329 
 
 36. This is a party measure and therefore we must vote for it. 
 
 37. "Philosophy bakes no bread." Then why waste time 
 upon it? 
 
 38. I oppose this bill because it involves an infringement of 
 the rights of the liberty-loving citizens of this State. 
 
 CHAPTER XV 
 
 1. Why are 'induction' and "deduction* somewhat mis- 
 leading terms? 
 
 2. Show how the perspective of logic has shifted from age 
 to age. 
 
 3. Distinguish between the 'logic of consistency' and the 
 'logic of investigation.' 
 
 4. Look up an instance of systematic investigation, such 
 as can be found in Darwin, Newton, Faraday, etc., and 
 analyze the various logical steps taken. 
 
 5. What are the three elements which can be distinguished 
 in investigation? 
 
 6. What is involved in generalization? Exemplify the pas- 
 sage from the particular to the general. 
 
 7. What is meant by an 'internal relation'? How does the 
 relation between a sign and that which it signifies differ 
 from association? 
 
 8. Do animals generalize? 
 
 9. Discuss the statement, assigned to Wundt, that "ani- 
 mals never reason and man seldom." 
 
 10. Is the tendency to test generalizations as characteristic 
 of man as the tendency to generalize itself? 
 
 CHAPTER XVI 
 
 1. What do you understand by science? What are some of 
 its guiding ideals? 
 
 2. Look up the history of some science with which you are 
 fairly familiar, and ask yourself what its growth consists 
 in. 
 
 3. Why is analysis so basic for science? 
 
 4. Point out the significance of technique and instru- 
 ments. Are they, in your opinion, sometimes overesti- 
 mated at the expense of mental factors? 
 
330 QUESTIONS AND EXERCISES 
 
 5. What is the nature of experimentation? Indicate the 
 advantages of experimentation as against passive ob- 
 servation. 
 
 6. Find and analyze at least two important experiments in 
 each of the following sciences : physics, chemistry, biology, 
 and psychology. 
 
 7. What other methods have grown up in modern investi- 
 gation? 
 
 8. What reaction has science had upon common-sense 
 thinking? 
 
 9. Become acquainted with the mental life of at least one 
 great scientist. 
 
 CHAPTER XVII 
 
 1. What principle should guide induction? 
 
 2. What is meant by 'mere speculation,' and why is it con- 
 demned? 
 
 3. State some of the mental and physical conditions of ac- 
 curate observation. 
 
 4. Show that perception is a process involving associated 
 ideas as well as sensations. 
 
 5. 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) The sun seen through a fog sometimes appears 
 red. 
 
 (3) Patients often seem to feel pain in amputated 
 limbs. 
 
 (4) A rearrangement of the furniture in a room is often 
 unnoticed. 
 
 (5) There are marked differences in what the ordinary 
 good observer, the artist, and the botanist see in 
 a flower. 
 
 (6) Silas Marner mistook Erne's hair for the lost gold. 
 
 (7) Looking at one's watch and not knowing the time 
 a moment later. 
 
 (8) Shooting a man for a deer when hunting in the 
 woods. 1 
 
 » Jones. 
 
QUESTIONS AND EXERCISES 331 
 
 6. Seek for cases of erroneous perception in your own ex- 
 perience, and try to explain them. 
 
 7. Is memory a direct intuition of the past? 
 
 8. How do the sciences try to eliminate errors due to 
 memory? Why cannot this be done in the courts of law? 
 
 9. Present at least five instances of erroneous memory. 
 10. How is the relevancy of facts determined? 
 
 CHAPTER XVIII 
 
 1. What is an hypothesis? And what are its conditions? 
 
 2. Show by examples that hypotheses always arise in answer 
 to problems. 
 
 3. Criticize the Baconian view of science. 
 
 4. What do men like Ernst Mach and Wilhelm Ostwald 
 mean by hypotheses when they are inclined to urge 
 scientists to avoid them so far as possible? 
 
 5. Take any two instances of hypotheses which have be- 
 come accepted theories and show that only the expert 
 could have thought of them. 
 
 6. Distinguish between the 'intuitive' and the 'reflective* 
 type of mind. Are these types easily recognizable in 
 practice? 
 
 7. Name three famous men who represent, on the whole, 
 the intuitive type, and three who are quite clearly of the 
 reflective type. 
 
 8. What is the relation between observation and the pos- 
 session of an hypothesis? 
 
 9. Explain the nature of the development of an hypothesis. 
 Why does such development require systematic knowl- 
 edge? 
 
 10. Is a barren hypothesis the same as an un verifiable one? 
 
 11. Distinguish between 'proof and 'verification/ 
 
 12. Why is analogy such an important source of hypotheses? 
 
 13. What is meant by 'false analogy'? Give at least five 
 examples. 
 
 14. Take any two important theories generally accepted 
 to-day and study their history. Exactly what was the 
 problem which they were developed to explain? 
 
 15. What danger is there in arguing from the assumption 
 that society is an organism? 
 
332 QUESTIONS AND EXERCISES 
 
 CHAPTER XIX 
 
 Analyze the following examples of inductive argumenta- 
 tion, and state the method implied. Do the facts seem to you 
 to be sufficient to found a rule upon? 
 
 1. It maybe a coincidence merely; but, if so, it is remark- 
 ably strange that while the chloroform has not changed, 
 while the constitutions of the patients have not changed, 
 where the use of the inhaler is the rule, there are fre- 
 quent deaths from chloroform; whilst in Scotland and 
 Ireland, where the use of the inhaler is the exception, 
 deaths are proportionally rare. 1 
 
 2. Sir Charles Lyell, by studying the fact that the river 
 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 catas- 
 trophes. 
 
 3. 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 works, 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. 
 
 4. Any one who examines the records will soon find out for 
 himself that those students who 'scatter' most in their 
 choice of studies are those who accomplish least in any 
 of them; and when he sees this he ought to realize the 
 harm that can be done by a system of absolutely free 
 electives. 2 
 
 5. It was a general belief at St. Kilda that the arrival of a 
 ship gave all the inhabitants colds. Dr. John Campbell 
 took pains to ascertain the fact and to explain it as the 
 effect of effluvia arising from human bodies; it was dis- 
 
 1 Creighton. a Aikins. 
 
QUESTIONS AND EXERCISES 333 
 
 covered, however, that the situation of St. Kilda renders 
 a northeast wind indispensably necessary before a ship 
 can make a landing. * 
 
 6. The great famine in Ireland began in 1845 and increased 
 until it reached a climax in 1848. During this time agra- 
 rian 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 fifty per cent more than in 1845. It is evi- 
 dent from this that a close relation of cause and effect 
 exists between famine and agrarian crime. 
 
 7. Wages in the United States are higher than in England, 
 because the former country is a republic and has a pro- 
 tective tariff. 
 
 8. In Sir Humphry Davy's experiments upon the de- 
 composition of water by galvanism, it was found that, 
 besides the two components of water, oxygen and hydro- 
 gen, an acid and an alkali were developed at the two 
 opposite poles of the machine. The insight of Davy 
 conjectured that there might be some hidden cause of 
 this portion of the effect: the glass containing the water 
 might suffer partial decomposition, or some foreign 
 matter might be mingled with the water, and the acid and 
 alkali be disengaged from it, so that the water would 
 have no share in their production. . . . By the substitu- 
 tion of gold vessels for glass, without any change in the 
 effect, he at once determined that the glass was not the 
 cause. Employing distilled water, he found a marked 
 diminution of the quantity of acid and alkali evolved; 
 yet there was enough to show that the cause, whatever 
 it was, was still in operation. . . . He now conceived 
 that the perspiration from the hands touching the in- 
 struments might affect the case, as it would contain com- 
 mon salt, and an acid and an alkali would result from its 
 decomposition under the agency of electricity. By care- 
 fully avoiding such contact, he reduced the quantity of 
 the products still further until no more than slight traces 
 of them were perceptible. What remained of the effect 
 might be traceable to impurities of the atmosphere, de- 
 
 i Hibben. 
 
334 QUESTIONS AND EXERCISES 
 
 composed by contact with the electrical apparatus. An 
 experiment determined this: the machine was put under 
 an exhausted receiver, and, when thus secured from 
 atmospheric influence, it no longer evolved the acid and 
 the alkali. 1 
 9. In a simple fracture of the ribs if the lung be punctured 
 by a fragment, the blood effused into the pleural cavity, 
 although freely mixed with air, undergoes no decompo- 
 sition. That is not the case if air enter directly through 
 a wound in the chest. This difference in result must be 
 causally connected with special circumstances — viz., 
 passage of air through tissues in the lungs. 2 
 
 10. "The two females were then seated upon two chairs 
 placed near together, their heels resting on cushions, their 
 lower limbs extended, with the toes elevated and the 
 feet separated from each other. The object in this ex- 
 periment was to secure a position in which the ligaments 
 of the knee-joints should be made tense and no oppor- 
 tunity offered to make pressure with the foot. We were 
 pretty well satisfied that the displacement of the bones 
 requisite for the sounds could not be effected unless a 
 fulcrum were obtained by resting one foot upon the 
 other or on some resisting body. The company, seated 
 in a semicircle, quietly waited for the * manifestations' 
 for more than half an hour. . . . On resuming the usual 
 position on the sofa, the feet resting on the floor, knock- 
 ings very soon began to be heard. . . . The conclusion 
 seemed clear that the Rochester knockings emanate 
 from the knee joint." 3 
 
 11. Give two examples for each of the methods, preferably 
 from ordinary experience rather than from science. 
 
 12. Show that Mill's Methods imply a large fund of relevant 
 knowledge. 
 
 13. Analyze the causal relation in such a way as to bring 
 out methods of testing supposed uniformities. 
 
 14. In what way is the Method of Difference an advance 
 upon the Method of Agreement? 
 
 1 Gore, The Art of Scientific Discovery. 2 Russell. 
 
 8 Description of the exposure of a spiritualistic seance, quoted by Podmore, and 
 adapted by Taylor. 
 
QUESTIONS AND EXEKCISES 335 
 
 15, By what methods should the following problems be 
 investigated? 
 
 (1) An individual becoming sick after a meal. 
 
 (2) The possibility of a connection between rag-weed 
 and hay fever. 
 
 (3) The effect of a new tariff upon the prosperity of a 
 country. 
 
 (4) Education and the decrease of superstition. 
 
 (5) The relation between mosquitos and malaria. 
 
 (6) Bad eyes and criminality. 
 
 (7) A crime and the arrest of a suspected person. 
 
 (8) The rapidity of growth of trees and the kind of 
 soil. 
 
 (9) Poverty and tuberculosis. 
 
 (10) The effect of radium upon cancer. 
 
 CHAPTER XX 
 
 1. When are statistics resorted to? How do they enable us 
 to grasp a field which would otherwise be unmanage- 
 able? 
 
 2. Why is definition of the problem and of the terms used 
 so important? 
 
 3. Name the stages of any thorough statistical investiga- 
 tion. What are the special dangers confronting each of 
 these stages? 
 
 4. State the law of statistical regularity, and try to explain 
 its foundation. 
 
 5. In what sciences are statistics of greatest significance? 
 Why? 
 
 6. Look up cases of erroneously interpreted statistics and 
 show wherein the error lies. 
 
 7. "In Sweden the population and the smallpox mortality 
 have both been known year by year since 1774. Before 
 vaccination the mortality from smallpox for thirty years 
 averaged 2045 per million. With permissive vaccination 
 from 1802 to 1816 it was reduced to 480; during seventy- 
 seven years of compulsory vaccination the mortality 
 averaged 155 per million; and for ten years ending 1894 
 it has been down to 2 per million. . . . 
 
336 QUESTIONS AND EXERCISES 
 
 "If we compare the rate of smallpox mortality in the 
 different countries, we see an enormous difference be- 
 tween the well vaccinated and the badly vaccinated 
 populations. Here is a table, given by Dr. Edwardes, of 
 the mortality rates per million in the five years 1889 to 
 1893: — 
 
 Smallpox 
 
 mortality 
 
 per million 
 
 Germany 2.3 
 
 England and Wales 13.6 
 
 Chief French towns 147. 6 
 
 Italy. 180.8 
 
 Belgium 253 
 
 Austria 313 
 
 Spain 638 
 
 Russia, three years only, including Asi- 
 atic Russia 836 
 
 "In Germany, vaccination and revaccination are both 
 compulsory. In the other countries revaccination was, 
 at that time at least, nowhere enforced." * 
 
 8. "More men than women die every year. This is due to 
 the greater mortality attending the life of the male." 2 
 What does this mean? How can it be possible? "In 
 Germany 109 men die each year for every 100 women." 
 What can we conclude from this? Why is it better to 
 know that in Germany 28.6 out of every thousand males 
 die each year and 25.3 out of every thousand females? 
 Since everybody must die sooner or later how is it possible 
 that there should be in any country (or in the whole 
 world) a permanently greater death-rate for one sex 
 than for the other? 
 
 9. Show the importance of the qualitative side of social 
 phenomena. Why are quantitative data apt to be mis- 
 leading in certain fields? 
 
 i Edinburgh Review, vol. 189, pp. 350-52. 
 2 Mayo-Smith, Statistics and Sociology. 
 
QUESTIONS AND EXERCISES 
 
 10. Interpret the following statistics: — 
 
 A table giving the percentage of accidents occurring 
 according to the time of the day 
 
 337 
 
 Time 
 
 Germany 
 
 Italy 
 
 12- 3 a.m. 
 
 1.93 
 
 1.09 
 
 3- 6 a.m. 
 
 2.55 
 
 2.47 
 
 6-9 A.M. 
 
 13.87 
 
 15.40 
 
 9-12 A.M. 
 
 28.42 
 
 29.20 
 
 12-3 p.m. 
 
 13.81 
 
 14.55 
 
 3-6 p.m. 
 
 26.62 
 
 26.48 
 
 6-9 p.m. 
 
 9.25 
 
 7.83 
 
 9-12 p.m. 
 
 3.85 
 
 2.54 
 
 11. Study carefully some one chapter of Mayo-Smith's Statis- 
 tics and Sociology with especial attention to the reflective 
 analysis which he gives at the end of the chapter. 
 
 12. What statistical investigations would seem to you very 
 important for a modern, democratic society? 
 
 13. In the United States census of 1890, the question of 
 color — whether black, mulatto, quadroon, or octoroon 
 — was asked. Why was such a question faulty from the 
 standpoint of statistics? 
 
 14. Point out the sociological bearing of the following statis- 
 tics from the United States Life Tables: Of 100,000 
 negro females, 18,507 die before the age of one year, 
 while of 100,000 white females, 10, 460 die before reaching 
 the same age. 
 
 15. It is undeniable that tenancy is increasing in the United 
 States. From the Twelfth Census, we have the follow- 
 ing comparison : — 
 
 
 Total 
 number 
 of farms 
 
 Number operated by 
 
 
 Owners 
 
 Cask 
 tenants 
 
 Share 
 tenants 
 
 1880 
 
 4,008,907 
 5,739,657 
 
 2,984,306 
 3,713,371 
 
 322,357 
 752,920 
 
 702,244 
 
 1900 
 
 1,273,366 
 
 
 
338 QUESTIONS AND EXERCISES 
 
 The Marxian Socialist maintains that this increase 
 proves concentration in farming. Does any other ex- 
 planation suggest itself to you? 
 
 CHAPTER XXI 
 
 1. Under what conditions can science predict with accu- 
 racy the occurrence of particular events? Give concrete 
 examples. 
 
 2. Are effects always found when their causes are present? Be 
 prepared to defend your answer by means of instances. 
 
 3. What does each of the following propositions mean? 
 
 (1) The child will probably catch the measles. 
 
 (2) The earth will probably grow colder in the distant 
 future. 
 
 (3) The probability in favor of a long life for a man 
 of his profession is very great. 
 
 4. Distinguish between • probability ' and ' objective chance/ 
 How can you harmonize the existence of probability 
 with the Principle of the Uniformity of Nature? 
 
 5. Is there any difference between saying that a certain 
 horse is the most likely to win the race and saying that 
 it is likely to win? l 
 
 6. How should life-insurance statistics be interpreted? Can 
 they be made to apply to any one individual? If so, in 
 what sense? 
 
 7. What reply can be made to the following? "You say 
 that the prisoner is probably guilty. I grant it. But this 
 only means that the prisoners in most cases of this sort 
 are guilty. It does not mean that this particular prisoner 
 has even a touch of guilt. Your very use of the word 
 'probable' is a confession that for all you know he may 
 be absolutely innocent. How then can you ask the jury 
 to condemn him to an awful fate? " 2 
 
 8. Discuss the following statement: "Nine times out of 
 ten we can act only on probability." 
 
 9. What is the probability that a die will fall with the same 
 side up four times in succession? 
 
 10. What is the probability that you will draw either an 
 ace or a five of hearts from a full deck of cards? 
 
 1 Aikins. 2 Aikins. 
 
QUESTIONS AND EXERCISES 339 
 
 11. "The regularities of the mass have no compelling force 
 over the individual." x Against what fallacy is this state- 
 ment directed? 
 
 CHAPTER XXII 
 
 1. Give some common examples of the use of an arithmetical 
 average. Explain such an expression as the * average 
 rate of interest.' 
 
 2. Show that percentage of increase in the population of a 
 town or city is a case of arithmetical average. 
 
 3. What average would be of most use for the following? 
 
 (1) The standard size of a manufactured article. 
 
 (2) A stock of hats for a clothing store. 
 
 (3) The physical estimation of a varsity crew. 
 
 (4) The salary of teachers. 
 
 4. Find, or work out, a set of statistics and discover the 
 mode and the median. 
 
 5. Examine critically the phrase, * the average man.' What 
 danger of misinterpretation lurks behind the phrase? 
 
 6. Why are graphical methods being used so freely at the 
 present time? 
 
 7. Find at least five devices for graphical representation in 
 common use and compare their effectiveness. 2 
 
 8. Look up cases of graphical representation in the popular 
 magazines and make a report upon at least four which 
 particularly attracted your attention. 
 
 9. "An average must not be a mere numerical average, for 
 that amounts to nothing. It must be a typical average, 
 expressive of about what the real condition of things is." 
 Explain this statement in the light of the preceding 
 chapters. 
 
 CHAPTER XXIII 
 
 1. Contrast * scientific investigation' and * judicial proof 
 as regards their methods and social surroundings. 
 
 2. Estimate the following arguments : — 
 
 (1) If you believe in the survival of the fittest, you 
 must believe that this old manuscript was one of 
 
 1 Mayo-Smith. * See Brinton on this question. 
 
340 QUESTIONS AND EXERCISES 
 
 the best of its time, for it is the only one that 
 has survived. 
 
 (2) This book is authentic; then why should we not 
 believe what it says? 
 
 (3) This text of Cicero dates from the twelfth century 
 and that dates only from the fourteenth; then 
 why is n't this a better one to go by than that? 
 
 (4) This text has great value for the historian, for it 
 was restored at infinite pains, and there is now 
 every reason to believe that it is substantially 
 correct. 
 
 (5) "Come and have your fortune told by Blank's 
 system of palmistry. No man of science has ever 
 disputed the claims of this system." l 
 
 3. Take any striking criminal case before the courts and 
 work out the circumstantial evidence for and against the 
 issue in the way suggested in the text. 
 
 4. What is, in your opinion, the comparative probative 
 value of circumstantial and testimonial evidence? 
 
 5. Connect the possibility of a plurality of causes with the 
 methods used in explaining events. 
 
 6. What seems to you to be a reasonable doubt? 
 
 7. Examine the following case. Do you think that there 
 was a reasonable doubt of Bradford's guilt? 
 
 "Jonathan Bradford, in 1736, kept an inn, in Ox- 
 fordshire, on the London road to Oxford. He bore a 
 very exceptional character. Mr. Hayes, a gentleman 
 of fortune, being on his way to Oxford, on a visit to 
 a relation, put up at Bradford's. He there joined com- 
 pany with two gentlemen, with whom he supped, and, 
 in conversation, unguardedly mentioned that he had 
 then about him a sum of money. In due time they 
 retired to their respective chambers; the gentlemen 
 to a two-bedded room, leaving, as is customary with 
 many, a candle burning in the chimney corner. Some 
 hours after they were in bed, one of the gentlemen, 
 being awake, thought he heard a groan in an adjoining 
 chamber; and this being repeated, he softly awaked 
 his friend. They listened together, and the groans 
 increasing, as of one dying and in pain, thev both 
 
 1 Aikins. 
 
QUESTIONS AND EXERCISES 341 
 
 instantly arose and proceeded silently to the door of 
 the next chamber, whence they had heard the groans, 
 and, the door being ajar, saw a light in the room. They 
 entered, and perceived a person weltering in his blood 
 in the bed, and a man standing over him with a dark 
 lantern in one hand and a knife in the other! The man 
 seemed as petrified as themselves, but his terror car- 
 ried with it all the terror of guilt. The gentlemen soon 
 discovered that the murdered person was the stranger 
 with whom they had that night supped, and that the 
 man standing over him was their host. They seized 
 Bradford directly, disarmed him of his knife, and 
 charged him with being the murderer. He assumed, 
 by this time, the air of innocence, positively denied 
 the crime, and asserted that he came there with the 
 same humane intentions as themselves; for that, hear- 
 ing a noise, which was succeeded by a groaning, he 
 got out of bed, struck a light, armed himself with a 
 knife for his defense, and was but that minute entered 
 the room before them. These assertions were of little 
 avail; he was kept in close custody till the morning, 
 and then taken before a neighboring justice of the 
 peace. Bradford still denied the murder, but, never- 
 theless, with such apparent indications of guilt, that 
 the justice hesitated not to make use of this most ex- 
 traordinary expression, on writing out his mittimus, 
 'Mr. Bradford, either you or myself committed this 
 murder.' " 
 
 8. How does the mind work in passing judgment upon a 
 
 very complex case? Study your own method of reach- 
 ing a conclusion in some particular problem of a high 
 degree of complexity. 
 
 9. Analyze one of Conan Doyle's Sherlock Holmes stories 
 
 to see just how the circumstantial evidence is used 
 both to lead and to mislead. 
 10. What is the fallacy of 'neglected factor'? Give at least 
 two examples which have come within your experi- 
 
 1 If the teacher can secure the book, he will find many interesting examples for all 
 the difficulties confronting evidence in Wigmore's Principles of Judicial Proof. These 
 examples are too long to quote in the present text. 
 
342 QUESTIONS AND EXERCISES 
 
 11. Look up the investigation of some historical myth like 
 
 that of William Tell. What is its interest to the lo- 
 gician? 
 
 12. Newton was of the opinion that oral tradition could be 
 
 trusted for eighty years after the event. Others have 
 named forty years. Why are such estimations rather 
 absurd? 
 
 13. It is asserted by many recent historians of the American 
 
 Revolution that our school histories contain a deal 
 of myth along with a fair percentage of fact. What 
 causes might lead to legend and myth about the 
 founders of the American Republic? 
 
 CHAPTER XXIV 
 
 1. What is the nature of explanation? 
 
 2. Take any two problems which have arisen lately in your 
 experience and try to grasp the exact character of the 
 explanation given them. 
 
 3. What is meant by the 'sentiment of rationality'? Show 
 that it depends upon the constitution of our minds. 
 
 4. Is explanation possible apart from concepts? 
 
 5. Apply Dewey's analysis of the role of concepts to at 
 least two cases of interpretation, stressing identification, 
 supplementation, and placing in a system. 
 
 6. What difference of setting have the two terms, 'proof 
 and 'explanation'? What have they in common? 
 
 7. How are induction and deduction united in the process 
 of explanation? Illustrate by examples either from prac- 
 tical life or from science. 
 
 8. Are all systems equally tentative? Can you think of any 
 system which seems to you to be in final shape? 
 
 9. How would you distinguish between 'general' and 'spe- 
 cific' explanation? 
 
 10. What principle would you adopt as a means of arranging 
 the sciences in an orderly fashion? Do you think that 
 such an ordering of them gives a penetrative classifica- 
 tion? 
 
 11. Why is mathematics usually spoken of as 'deductive'? 
 Does this seem to you the best term that could be 
 used? 
 
QUESTIONS AND EXERCISES 343 
 
 12. Examine historical investigation in the light of your 
 present knowledge of logic. Show especially that all facts 
 are judgments. 
 
 CHAPTER XXV 
 
 1. Distinguish clearly between 'consistent thinking' and 
 * true thinking.' 
 
 2. What is meant by 'logical necessity'? 
 
 3. State and explain the 'Laws of Thought.' 
 
 4. What principles are implied in all investigation which 
 seeks to determine truth? 
 
 5. How would you formulate your conception of the inter- 
 nal criteria of truth? 
 
 6. Explain the conception of degrees of belief. Relate your 
 views to the modality of judgments. 
 
 7. Does language express adequately the different degrees 
 of belief we actually hold? 
 
 8. Show that the meaning of knowledge is intimately bound 
 up with the meaning of truth. 
 
 9. Read Tennyson's In Memoriam, xxxiv. Does it seem 
 to you to imply an appeal to a standard of truth other 
 than the logical? 
 
 10. Be prepared to defend James's position or Clifford's ac- 
 cording as the one or the other strikes you as the sounder. 
 
INDEX 
 
 (Kindly arranged by Mr. Douglas Clapperton) 
 
 Absolute term, 29, 34. 
 
 Abstract sciences, 288. 
 
 Accident, fallacy of, 148. 
 
 Agreement and difference, joint 
 method of, 215, 217. 
 
 Agreement, method of, 215, 217. 
 
 Aikins, quoted, 249, 270. 
 
 Ambiguity, 41; causes of, 41. 
 
 Ambiguous terms, fallacy of, 143. 
 
 Amphiboly, 144. 
 
 Analogy, as basis of reasoning, 
 208; false, 209. 
 
 Analytic division, 59. 
 
 Apodeictic judgment, 301. 
 
 Argumentum ad Hominem, 153; 
 ad ignorantiam, 154; ad popu- 
 lum, 153; ad verecundiam, 155. 
 
 Aristotle's definition of syllog- 
 ism, 107. 
 
 Arithmetical average, 252, 257. 
 
 Assertions, 76, 79. 
 
 Assertoric judgment, 301. 
 
 Average, geometric, 256, 257; 
 median, 256, 257; uses of, 251 ; 
 weighted, 253, 257. 
 
 Bain, quoted, 236. 
 
 Belief, degrees of, 301. 
 
 Bode, quoted, 15, 30, 35, 157, 
 
 210, 221, 243, 277. 
 Bosanquet, quoted, 85, 197. 
 Bowley, quoted, 229, 253. 
 Brinton, quoted, 258, 262. 
 Burrill, quoted, 265. 
 
 Carhart, quoted, 222. 
 Cartograms, 257. 
 
 Categorematic words, 28. 
 
 Cause, definition of, 211. 
 
 Certainty, possibility of, in fore- 
 casting events, 240. 
 
 Change in meaning of words, 
 44. 
 
 Circumstantial evidence, 265; 
 nature of, 267; circumstantial 
 and testimonial evidence, 266. 
 
 Classes, 51; coordination of, 55; 
 subordination of, 55; super- 
 ordination of, 55. 
 
 Classification, artificial, 52, 53; 
 definition of, 50; diagnostic, 
 53; index, 53; natural, 52, 53. 
 
 Classificatory division, 60. 
 
 Clifford, quoted, 309, 310. 
 
 Collective terms, 33. 
 
 Complex question, 151. 
 
 Composition, fallacy of, 144. 
 
 Concepts, 20, 96; use of, in 
 explanation, 280. 
 
 Concomitant variations, method 
 of, 221. 
 
 Concrete logic, 5. 
 
 Concrete sciences, 290, 291. 
 
 Concrete term, 30. 
 
 Conditions and occasions of 
 thought, 15; personal condi- 
 tions, 17. 
 
 Connotation, 37, 38. 
 
 Consistent thinking, nature of, 
 294; relation to truth, 294. 
 
 Constancy of averages, 233, 245. 
 
 Constituent species, 57. 
 
 Contradiction, law of, 207. 
 
 Contradictories, 100. 
 
346 
 
 INDEX 
 
 Contraries, 100. 
 
 Conversion, 102; by contraposi- 
 tion, 105; by limitation, 102; 
 simple, 102. 
 
 Coordinate species, 57. 
 
 Copula, 28. 
 
 Correlatives, 34. 
 
 Creighton, quoted, 34, 137. 
 
 Darwin, quoted, 192; from 
 Creighton, 204. 
 
 Davidson, quoted, 44, 62, 69. 
 
 Definition, nature of, 64; pur- 
 pose of, 63, 64; definition and 
 classification, 66. 
 
 Definition of logic, 1. 
 
 Denotation, 37, 38. 
 
 Dewey, quoted, 11, 169, 176, 
 178, 203, 279, 282. 
 
 Dichotomous division, 58, 59. 
 
 Dictum, 301. 
 
 Difference, method of, 219. 
 
 Differentia, 57. 
 
 Dilemma, 137. 
 
 Direct evidence, 269. 
 
 Discovery and proof, 11. 
 
 Disjunctive syllogism, 136. 
 
 Distribution of terms, 94. 
 
 Division, 56. 
 
 Division, fallacy of, 145. 
 
 Doubt, logic of, 309. 
 
 Empirical logic, 5. 
 Enthymeme, 126. 
 Episyllogisms, 127. 
 Equivocal words, 43. 
 Erroneous perception, cause of, 
 
 189. 
 Events, prediction of, 239. 
 Evidence, convergence of, 268; 
 
 fallacies in weighing evidence, 
 
 275. 
 Exceptive proposition, 93. 
 Excluded middle, law of; 297. 
 Exclusive propositions; 93. 
 
 Experimentation, 177; in biol- 
 ogy, 179; in psychology, 180. 
 
 Explanation, general, 287; levels 
 of, 285; nature of, 278; and 
 proof, 282; specific, 287. 
 
 Extension, 37. 
 
 Extra-syllogistic reasoning; 129. 
 
 Fact, theory and, 24, 25. 
 Facts, 194; relevant, 195. 
 Fallacies, 141; classification of, 
 
 142; deductive, 142. 
 Fallacy, of four terms, 112; 
 
 of unwarranted assumption, 
 
 149. 
 Figure of speech, fallacy of, 
 
 148. 
 Figures of the syllogism, 118. 
 Frequency graphs, 262. 
 Fundamentum divisionis, 57. 
 
 General term, 32. 
 
 Genus, 56. 
 
 Geometric average, 256, 257. 
 
 Gibson, quoted, 144, 146, 149, 
 152. 
 
 Giffen, quoted, 230. 
 
 Graphs, cartogram, 257; fre- 
 quency, 262; and graphical 
 methods, 257; pictogram, 258. 
 
 Gross, quoted, 271. 
 
 Helmholtz, quoted, 286. 
 
 Hibben, quoted, 54, 237. 
 
 Historical science, 290, 291. 
 
 History of logic, 160. 
 
 Huxley, quoted, 199. 
 
 Hypotheses, definition of, 197; 
 development of, 205 ; function 
 of, 182; kinds of, 198; origin 
 of, 200; proof of, 206; value 
 of, 203; hypothesis, theory 
 and fact, 207. 
 
 Hypothetical syllogism, 132; 
 rule of, 134. 
 
INDEX 
 
 347 
 
 Identity, law of, 296. 
 Immediate inference, 98. 
 Indefinite propositions, 90. 
 Induction and deduction, 159. 
 Inductive logic, 5. 
 Inertia of large numbers, law of, 
 
 233. 
 Inferential element in precepts, 
 
 21. 
 Infimse species, 57. 
 Intention, 37. 
 Introductory logic, 5. 
 Intuitive mind, 202. 
 Irrational evidence, fallacy of, 
 
 152. 
 Irrelevant conclusion, 156. 
 
 James, quoted, 23, 180, 204, 
 
 297, 304, 305, 306, 307. 
 Jevons, quoted, 54, 148, 177, 
 
 189, 226, 242. 
 Jones, quoted, 66 , 104, 128, 223, 
 
 249, 272. 
 Joseph, quoted, 3, 4, 60, 130, 
 
 146, 286, 289. 
 Judgment, 27; and concepts, 81; 
 
 definition of, 84; levels of, 80; 
 
 relation of, to knowledge, 84. 
 Judicial proof, 264; difficulties 
 
 confronting, 265. 
 
 Kinds of logic, 4. 
 King, quoted, 228, 229, 230, 
 234, 248, 252, 256. 
 
 Langlois and Seignobos, quoted, 
 290, 292. 
 
 Language, 48; law of, in logic, 6; 
 purpose of, 87. 
 
 Law of contradiction, 297; of 
 excluded middle, 297; of iden- 
 tity, 296; of language, 6. 
 
 Laws of thought, 296. 
 
 Legal reasoning, 264. 
 
 Locke, quoted, 63, 108, 152, 155. 
 
 Lodge, quoted, 16. 
 
 Logic, definition of, 1; as ap- 
 plied science, 3; kinds of, 4; 
 value of, 2; concrete, 5; em- 
 pirical, or inductive, 5; intro- 
 ductory, 5; material of, 7; 
 relation of, to other sciences, 
 6; symbolic, 5; of systematic 
 investigation, 159. 
 
 Lotze, quoted, 147. 
 
 McDougall, quoted, 179. 
 
 Macleane, quoted, 48, 71, 73. 
 
 Major term, 11. 
 
 Material of logic, 7. 
 
 Mayo-Smith, quoted, 232. 
 
 Meaning of terms, 38. 
 
 Measurement, importance of, 
 177. 
 
 Median, 256, 257. 
 
 Mellone, quoted, 219. 
 
 Memory, errors of, 192. 
 
 Middle term, 110. 
 
 Mill, quoted, 208, 226. 
 
 Mill's methods of testing con- 
 nections, 214; method of 
 agreement, 215; of difference, 
 219. 
 
 Minor term, 111. 
 
 Minto, quoted, 47, 48, 92, 107, 
 124, 162, 217, 233. 
 
 Mode, 255, 257. 
 
 Modus ponens, 133; tollens, 133. 
 
 Moods, of syllogisms, 118. 
 
 Multiple working hypotheses, 
 method of, 205. 
 
 Miinsterberg, quoted, 186, 188. 
 
 Negative correlation, 236. 
 Negative term, 56. 
 Non-sequitur, 157. 
 
 Observation, conditions of, 185. 
 
 Ob version, 103. 
 
 Opposition of propositions, 99. 
 
348 
 
 INDEX 
 
 Partitive propositions, 93. 
 
 Percept, definition of, 20, 21; 
 inferential element in, 21. 
 
 Perception, errors in, 187. 
 
 Petitio principii, 149. 
 
 Pictograms, 258. 
 
 Pillsbury, quoted, 13, 19, 52, 283. 
 
 Positive term, 36. 
 
 Post hoc, ergo propter hoc, 212. 
 
 Postulates of logic, 298. 
 
 Predicables, 73. 
 
 Preindesignate propositions, 90. 
 
 Privitive term, 37. 
 
 Probabilities, mistakes in inter- 
 pretation of, 248. 
 
 Probability, meaning of, 240; 
 empirical, 242; based on aver- 
 ages, 243; and chance, 241; 
 contrasted with certainty, 
 241; estimating kinds of, 242; 
 probability in regard to 
 events, 241; in regard to 
 principles, 241. 
 
 Problem of generalization, 167. 
 
 Problematic judgment, 301. 
 
 Processes preliminary to reflec- 
 tive thought, 20. 
 
 Proof, and explanation, 282; and 
 discovery, 11. 
 
 Propositions, 27, 76, 98, cate- 
 gorical, 89; disjunctive, 89; 
 hypothetical, 89; quality of, 
 89; quantity of, 89. 
 
 Prosyllogisms, 127. 
 
 Proximum genus, 57. 
 
 Psychologist's view of reason- 
 ing, 13. 
 
 Quality of propositions, 89, 90. 
 Quantity of propositions, 89, 90. 
 Quetelet, quoted, 245. 
 
 Real definition, 64. 
 Reasoning, examples of, 14; 
 psychologist's view of, 13. 
 
 Reflective mind, 202. 
 
 Reflective thought, processes 
 preliminary to, 20. 
 
 Relation of logic to other sci- 
 ences, 6. 
 
 Relative term, 34. 
 
 Residues, method of, 224. 
 
 Ribot, quoted, 201, 202. 
 
 Romanes, quoted, 23. 
 
 Rules, of definition, 69-71; of 
 division, 58; for mathematical 
 probability, 246; of syllogism, 
 112. 
 
 Russell, quoted, 284 
 
 Schiller, quoted, 117. 
 
 Science, development of, 173; 
 method of graphs in, 181; 
 statistical method in, 180. 
 
 Scientific investigation, 264. 
 
 Sellars, quoted, 305. 
 
 Setting of thought, 17. 
 
 Sidgwick, quoted, 3, 25, 51, 68, 
 209, 214. 
 
 Sigwart, quoted, 278. 
 
 Singular term, 30, 31. 
 
 Smith, quoted, 44. 
 
 Sociology of logic, 16. 
 
 Socratic dialectic, 67. 
 
 Sorites, 128; Aristotelian, 128; 
 Goclenian, 129. 
 
 Species, 56. 
 
 Square of opposition, 100. 
 
 Statistical investigation, stages 
 in, 230. 
 
 Statistical regularity, law of, 
 232. 
 
 Statistics, definition of, 229; in 
 causal relations, 236; dangers 
 in use of, 233; inertia of large 
 numbers, 233; value of, 235. 
 
 Steps in systematic investiga- 
 tion, 166. 
 
 Stout, quoted, 40. 
 
 Subalterns, 100. 
 
INDEX 
 
 349 
 
 Subcontraries, 100. 
 
 Summum genus, 57. 
 
 Syllogism, axiom of, 110; de- 
 fined, 107; disjunctive, 136; 
 elements of, 110; figures of, 
 118; function of, 162; hypo- 
 thetical, 132; moods of, 118; 
 
 r nature of, 107; rules of, 112. 
 
 Symbolic classification of propo- 
 sitions, 91. 
 
 Symbolic logic, 5. 
 
 Syncategorematic words, 28. 
 
 Synthetic classification, 59. 
 
 Systems of knowledge, typical, 
 288. 
 
 Systems, tentative nature of, 283. 
 
 Taylor, quoted, 56, 154. 
 Technique and instruments, 
 
 value of, 175. 
 Terms, 27, 28. 
 
 Testimonial evidence, 266, 269. 
 Testimony, definition of, 270; 
 
 critical attitude toward, 270; 
 
 errors in, 193; logical tests of, 
 
 273. 
 Theory and fact, 24, 25. 
 Thinking, definition of, 18; 
 
 purpose of, 18. 
 
 Thought, conditions and occa- 
 sions of, 15; laws of, 296; 
 setting of, 17; what is, 10. 
 
 True idea, definition of, 303. 
 
 Truth, 298; criteria of, 299; 
 definitions of, 304; meaning 
 of, 303; pragmatic definition 
 of, 304; truth and validity, 
 299; and will to believe, 305. 
 
 Tyndall, quoted, 200. 
 
 Uniformity of nature, principle 
 
 of, 170. 
 Uni vocal words, 43. 
 
 Vagueness, 46; of abstract 
 
 terms, 47. 
 Value of logic, 2. 
 Verbal definition, 64. 
 Verification, 300. 
 Vincent, quoted, 291. 
 
 Weighted average, 253, 257. 
 Welton, quoted, 198, 246, 247. 
 Whately, quoted, 156. 
 Whewell, quoted, 8. 
 Whitehead, quoted, 289. 
 Wigmore, quoted, 270, 271, 
 274. 
 
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