H Warn M I ■ 1 1 B ! 0$9 H m Hi ■ H 18 i''H RHMMMRHNRnfitlfln BHulJmttfl awifff : ■ I SB ■ 1— — — HBBPWmWMOWI A il ■ 1 6 k -/■ *& "TV x ^ %V ,^ V ->, : A -r, > ^ '*. * «V a* V ^ •^ ^ % N a\ ,0o. ^ * N ^ V V *>_ "HA 4 <.° ^ ' .0 A, ^ A* #' % v W ^ ^ -M^J. o o x ->. ^*V ** <& // , "--' s A m* y i ^ ' - * S A\ . v i 8 , *U - > <£• ,*& o *>»■, .V - ^ V s o ^-. : ^%V ' \^ , *o ^> o ' „ ^ % / V* (L? A*' \* v-. * jh ^ -^ V V ? ; ** v ^ A CLASS ROOM LOGIC DEDUCTIVE AND INDUCTIVE WITH SPECIAL APPLICATION TO THE SCIENCE AND ART OF TEACHING BY GEORGE HASTINGS McNAIR, Ph. D. HEAD OF DEPARTMENT OF LOGIC AND MATHEMATICS, CITY TRAINING SCHOOL FOR TEACHERS. JAMAICA. NEW YORK CITY THE ETHLAS PRESS FIVE NORTH BROADWAY. NYACK. NEW YORK BC 101 .Ms COPTRIGHT, 1914, BY George Hastings McNaib DEC 15 1914 ©C1A391484 5fa MY WIFE. PREFACE. This treatise is an outgrowth of our class room work in logic. It has been published in the hope of removing some of the difficulties which handicap the average student. We trust that the language is simple and definite and that the illustrative exercises and diagrams may be help- ful in making clear some of the more abstruse topics. If a speedy review for examination is necessary, it is recommended that the briefer course as outlined on page 493 be followed and that the summaries closing each chapter be carefully read. Only the fundamentals of deductive and inductive logic have received attention. Moreover emphasis has been given to those phases which appear to commend them- selves because of their practical value. Further than this we trust that the book may fulfill in some small way the larger mission of inspiring better thinking and, in consequence, of leading to a more serviceable citizenship. Surely as civilization advances it is with the expecta- tion of giving greater significance to the assumption "that man is a rational animal." I am indebted to a number of writers on logic, notably to Mill, Lotze, Keynes, Hibben, Fowler, Aikins, Hyslop, Creighton and Jevons. I am likewise under obligation to Vlll PREFACE that large body of students who, by frankly revealing their difficulties, have given me a different point of view. For constructive criticism and definite encouragement I owe a personal debt of gratitude to Prof. Charles Gray Shaw of New York University, to Prof. Frank D. Blodgett of the Oneonta Normal School and to Prin. A. C. MacLachlan of the Jamaica Training School for Teachers. G. H. McN. City Training School for Teachers, Jamaica, N. Y. City. October 3, 1914. TABLE OF CONTENTS Page Chapter 1. — The Scope and Nature of Logic ... 1 The Mind, 1. Logic Related to Other Subjects, 2. Logic Defined, 3. The Value of Logic to the Student, 5. Outline, 7. Summary, 7. Review Questions, 8. Questions for Original Thought and Investigation, 9. Chapter 2. — Thought and Its Operation .... 10 The Knowing Mind Compared with the Thinking Mind, 10. Knowing by Intuition, 11. The Thinking Process, 12. Notions, Individual and General, 14. Knowledge and Idea as Related to the Notion, 15. The Logic of the Psychological Terms Involved in the Notion, 16. Thought in the Sensation and Percept, 18. Evolution and the Thinking Mind, 19. The Con- cept as a Thought Product, 21. The Judgment as a Thought Product, 22. Inference as a Thought Prod- uct, 24. Thinking and Apprehension, 24. Stages in Thinking, 25. Outline, 26. Summary, 27. Review Questions, 29. Questions for Original Thought and Investigation, 30. Chapter 3. — The Primary Laws of Thought ... 32 Two Fundamental Laws, 32. The Law of Identity, 32. The Law of Contradiction, 35. The Law of Ex- cluded Middle, 39. The Law of Sufficient Reason, 40. Unity of Primary Laws of Thought, 40. Outline, 41. Summary, 42. Illustrative Exercises, 43. Review Questions, 44. Questions for Original Thought and Investigation, 45. ix X CONTENTS Page Chapter 4. — Logical Terms 47 Logical Thought and Language Inseparable, 47. Meaning of Term, 47. Categorematic and Syncate- gorematic Words, 48. Singular Terms, 49. General Terms, 49. Collective and Distributive Terms, 50. Concrete and Abstract Terms, 51. Connotative and Non-connotative Terms, 52. Positive and Negative Terms, 53. Contradictory and Opposite Terms, 53. Privative and Nego-positive Terms, 55. Absolute and Relative Terms, 56. Outline, 57. Summary, 57. Illus- trative Exercises, 58. Review Questions, 59. Ques- tions for Original Thought and Investigation, 60. Chapter 5. — The Extension and Intension of Terms . 62 Two-fold Function of Connotative Terms, 62. Ex- tension and Intension Defined, 63. Extended Com- parison of Extension and Intension, 63. A List of Connotative Terms Used in Extension and Intension, 65. Other Forms of Expression for Extension and Intension, 66. Law of Variation in Extension and In- tension, 66. Important Facts in Law of Variation, 69. Law of Variation Diagrammatically Illustrated, 70. Outline, 72. Summary, 72. Illustrative Exercises, 73. Review Questions, 75. Questions for Original Thought and Investigation, 76. Chapter 6. — Definition 77 Importance, 77. The Predicables, 77. The Nature of a Definition, 82. Definition and Division Compared, 84. The Kinds of Definitions, 85. When the Three Kinds of Definitions are Serviceable, 87. The Rules of Logical Definition, 88. Terms Which Cannot be Defined Logically, 93. Definitions of Common Edu- cational Terms, 94. Outline, 97. Summary, 98. Illus- trative Exercises, 100. Review Questions, 102. Ques- tions for Original Thought and Investigation, 103. CONTENTS XI Page Chapter 7. — Logical Division and Classification . . 105 Nature of Logical Division, 105. Logical Division Distinguished from Enumeration, 106. Logical Divi- sion as Partition, 107. Four Rules of Logical Divi- sion, 108. Dichotomy, 110. Classification Compared with Division, 112. Kinds of Classification, 113. Two Rules of Classification, 114. Use of Division and Classification, 114. Outline, 115. Summary 116. Re- view Questions, 117. Questions for Original Thought and Investigation, 118. Chapter 8. — Logical Propositions 120 The Nature of Logical Propositions, 120. Kinds of Logical Propositions, 121. The Four Elements of a Categorical Proposition, 122. Logical and Grammatical Subject and Predicate Distinguished, 125. The Four Kinds of Categorical Propositions, 126. Propositions which do not Conform to Logical Type, 129. Propo- sitions not Necessarily Illogical, 138. The Relation between Subject and Predicate, 140. Outline, 150. Summary, 151. Illustrative Exercises, 154. Review Questions, 156. Questions for Original Thought and Investigation, 157. Chapter 9. — Immediate Inference — Opposition . . .159 The Nature of Inference, 159. Immediate and Medi- ate Inference, 159. The Forms of Immediate Infer- ence, 161. (1) Opposition, 161. Chapter 10. — Immediate Inference (Continued) . . 170 Immediate Inference by Obversion, 170. Immediate Inference by Conversion, 176. Immediate Inference by Contraversion, 181. Epitome of the Four Processes of Immediate Inference, 182. Inference by Inversion, 183. Outline, 183. Summary, 183. Illustrative Exer- cises, 185. Review Questions, 189. Problems for Original Thought and Investigation, 190. Xll CONTENTS Page Chapter 11. — Mediate Inference — The Syllogism . . 192 Inference and Reasoning, 192. The Syllogism, 192. The Rules of the Syllogism, 193. Rules of Syllogism Explained, 194. Aristotle's Dictum, 208. Canons of the Syllogism, 209. Mathematical Axioms, 210. Out- line, 210. Summary, 211. Illustrative Exercises, 213. Review Questions, 215. Questions for Original Thought and Investigation, 216. Chapter 12. — Figures and Moods of the Syllogism . 218 The Four Figures of the Syllogism, 218. The Moods of the Syllogism, 221. Testing the Validity of the Moods, 223. Special Canons of the Four Figures, 226. Special Canons Related, 233. Mnemonic Lines, 234. Relative Value of the Four Figures, 239. Out- line, 240. Summary, 241. Illustrative Exercises, 243. Review Questions, 245. Questions for Original Thought and Investigation, 245. Chapter 13. — Incomplete Syllogisms and Irregular Arguments . . . . . . 247 Enthymeme, 247. Epicheirema, 249. Polysyllogisms. Prosyllogism — Episyllogism, 250. Sorites, 251. Ir- regular Arguments, 258. Outline, 259. Summary, 260. Review Questions, 261. Questions for Original Thought and Investigation, 261. Chapter 14. — Categorical Arguments Tested According to Form 263 Arguments of Form and Matter, 263. Order of Pro- cedure in a Formal Testing of Arguments, 263. Il- lustrative Exercise in Testing Arguments which are Complete and whose Premises are Logical, 265. Illus- trative Exercise in Testing Completed Arguments, one or both of whose Premises are Illogical, 269. Incom- plete and Irregular Arguments, 277. Common Mis- takes of the Student, 281. Outline, 281. Summary, 282. Review Questions, 283. Questions for Original Thought and Investigation, 285. CONTENTS XI 11 Page Chapter 15. — Hypothetical and Disjunctive Arguments Including the Dilemma . . . 288 Three Kinds of Arguments, 288. Hypothetical Arguments, 288. Antecedent and Consequent, 289. Two Kinds of Hypothetical Arguments, 290. Rule and Two Fallacies of Hypothetical Argument, 291. Hypothetical Arguments Reduced to Categorical Form, 293. Illustrative Exercises Testing Hypothetical Argu- ments of All Kinds, 297. Disjunctive Arguments, 302. Two Kinds of Disjunctive Arguments, 302. First Dis- junctive Rule, 303. Second Disjunctive Rule, 306. Reduction of Disjunctive Argument, 307. The Di- lemma, 308. Four Forms of Dilemmatic Arguments, 309. The Rule of Dilemma, 311. Illustrative Exer- cises Testing Disjunctive and Dilemmatic Argument, 311. Ordinary Experiences Related to Disjunctive Proposition and Hypothetical Argument, 313. Out- line, 315. Summary, 316. Review Questions, 318. Questions for Original Thought and Investigation, 320. Chapter 16. — The Logical Fallacies of Deductive Reasoning 322 A Negative Aspect, 322. Paralogism and Sophism, 322. A Division of the Deductive Fallacies, 323. Gen- eral Divisions Explained, 325. Fallacies of Immediate Inference, 326. Fallacies in Language (Equivocation), 328. Fallacies in Thought (Assumption), 334. Out- line, 344. Summary, 345. Illustrative Exercises in Testing Arguments in Both Form and Meaning, 349. Review Questions, 350. Questions for Original Thought and Investigation, 353. Chapter 17. — Inductive Reasoning 355 Inductive and Deductive Reasoning Distinguished, 355. The "Inductive Hazard," 356. Complexity of the Problem of Induction, 358. Various Conceptions of XIV CONTENTS Page Induction, 359. Induction and Deduction Contiguous Processes, 360. Induction an Assumption, 361. Uni- versal Causation, 361. Uniformity of Nature, 362. Inductive Assumptions Justified, 364. Three Forms of Inductive Research, 365. Induction by Simple Enumeration, 367. Induction by Analogy, 368. Induc- tion by Analysis, 373. Perfect Induction, 375. Tra- duction, 377. Outline, 379. Summary, 380. Review Questions, 383. Questions for Original Thought and Investigation, 384. Chapter 18. — Mill's Five Special Methods of Obser- vation and Experiment .... 386 Aim of Five Methods, 386. Method of Agreement, 387. Method of Difference, 393. The Joint Method of Agreement and Difference, 397. The Method of Con- comitant Variations, 402. The Method of Residues, 406. General Purpose and Unity of Five Methods, 409. Outline, 411. Summary, 412. Review Ques- tions, 414. Questions for Original Thought and In- vestigation, 416. Chapter 19. — Auxiliary Elements in Induction. Obser- vation — Experiment — Hypothesis . 418 Foundation of Inductive Generalizations, 418. Ob- servation, 419. Experiment, 419. Rules for Logical Observation and Experiment, 420. Common Errors of Observation and Experiment, 423. The Hypothesis, 425. Induction and Hypothesis Distinguished, 426. Hypothesis and Theory Distinguished, 427. The Re- quirements of a Permissible Hypothesis, 427. Uses of Hypothesis, 429. Characteristics Needed by Scientific Investigators, 431. Outline, 432. Summary, 433. Re- view Questions, 435. Questions for Original Thought and Investigation, 435. CONTENTS XV Page Chapter 20. — Logic in the Class Room .... 437 Thought is King, 437. Special Functions of Induc- tion and Deduction, 438. Two Types of Minds, 438. Conservatism in School, 439. The Method of the Dis- coverer, 440. Real Inductive Method not in Vogue in Class Room Work, 444. As a Method of Instruction, Deduction Superior, 446. Conquest, not Knowledge, the Desideratum, 447. Motivation as Related to Spirit of Discovery, 449. Discoverer's Method Adapted to Class Room Work, 450. Question and Answer Method not Necessarily One of Discovery, 457. Outline, 458. Summary, 459. Review Questions, 461. Questions for Original Thought and Investigation, 462. Chapter 21. — Logic and Life 463 Logic Given a Place in a Secondary Course, 463. Man's Supremacy Due to Power of Thought, 463. Im- portance of Progressive Thinking, 465. Necessity of Right Thinking, 466. Indifferent and Careless Thought, 467. The Rationalization of the World of Chance, 468. The Rationalization of Business and Political Sophis- tries, 470. The Rationalization of the Spirit' of Prog- ress, 471. A Rationalization of the Attitude Toward Work, 474. The Logic of Success, 475. Outline, 477. Summary, 478. Review Questions, 479. Questions for Original Thought and Investigation, 480. General Exercises in Testing Categorical Arguments . 481 General Exercises in Testing Hypothetical, Disjunctive and dllemmatic arguments . . 484 Examination Questions for Training Schools and'Col- leges 486 Bibliography 492 Outline of Briefer Course 493 Index 495 CHAPTER 1. THE SCOPE AND NATURE OF LOGIC. 1. THE MIND. As to the true conception of matter the world is igno- rant. Yet when asked, "What does matter do ?" the reply is, "Matter moves, matter vibrates." Moreover, relative to the exact nature of mind, the world is likewise ignorant. But to the question, "What does mind do?" the response comes, "The Mind knows, the mind feels, the mind wills.'' The mind has ever manifested itself in these three ways. Because of this three-fold function it is easy to think of the mind as being separated into distinct compartments, each constituting an independent activity. This is erro- neous. The mind is a living unit having three sides but never acting one side at a time. When the mind knows it also feels in some way and wills to some extent. To illus- trate : Music is heard and one knows it to be Rubinstein's Melody in F. The execution being good one feels pleas- ure. That the pleasurable state may be augmented one wills a listening attitude. For analytical purposes the psychologists have a way of naming the state of mind from the predominating manifestation. 2. LOGIC RELATED TO OTHER SUBJECTS. What the mind is may in time be answered satis- factorily by philosophy; what the mind does is de- scribed by psychology ; what the mind knows is treated by logic. Again: the mind as a whole furnishes the subject 2 The Scope and Nature of Logic matter for psychology, whereas logic is concerned with the mind knowing, aesthetics with the mind feeling, and ethics with the mind willing. Ethics attempts to answer the question, "What is right?" aesthetics, "What is beau- tiful?" and logic, "What is true?" Though both psychology and logic treat of the knowing aspect of the mind, yet the fields are not identical. The former deals with the process of the knowing mind as a whole, while the latter is concerned mainly with the product of the knowing mind when it thinks. To be spe- cific: The mind knows when it becomes aware of any- thing, moreover, this condition of awareness appears in two ways : first, immediately or by intuition; second, after deliberation or by thinking. For example, one may know immediately or by intuition that the object in the hand is a lead pencil, but when requested to state the length of the pencil there is deliberation involving a comparison of the unknown length with a definite measure. It may now finally be asserted that the pencil is six inches long. When we know without hesitation the process involved is intuition, whereas when the knowledge comes after some sort of comparison the mental act is called thinking. It, therefore, becomes the business of psychology to deal with both intuition and thinking while logic devotes its atten- tion to thinking only, and even in this field the work of logic is more or less indirect. The specific scope of logic is the product of thinking or thought.* What are the ♦Note. Sometimes thinking and thought are used interchangeably. This is confusing. Properly, " thinking " is always a process of the knowing mind while " thought " is the product of this process, just as the flour of the gristmill is the product of the grinding process. Logic Related to Other Subjects 3 forms of thought? What are the laws of thought? Are the several thoughts true ? These are the questions which logic is supposed to answer. For the logician thought has two sources, his own mind and the mind of others. In the latter case thought becomes accessible through the medium of language. There is in consequence a close connection between logic, the science of thought, and grammar, the science of language. Because of this near relation logic is some- times called the "grammar of thought/' To study any science properly one must have thoughts and since logic is the science of all thought the subject may be regarded as the science of sciences. 3. LOGIC DEFINED. "Logic is the science of thought." This definition com- monly given is too brief to be helpful. Should not a defi- nition of any subject represent a working basis upon which one may build with some knowledge of what the structure is to be? The following, a little out of the ordi- nary, seems to supply this condition: Logic as a science makes known the laws and forms of thought and as an art suggests conditions which must be fulfilled to think rightly. In justification of the latter definition it may be argued that it covers the topics usually treated by logicians. It is said that a science teaches us to know while an art teaches us to do. As a science logic teaches us to know certain laws which underlie right thinking. For example, the law of identity which makes possible all affirmative judgments, such as "Some men are wise/' "All metals are 4 The Scope and Nature of Logic elements," etc. Likewise as a science logic acquaints us with certain universal forms to which thought shapes itself, such as definitions, classifications, inductions, de- ductions. Further, logic lays down definite rules which lead to right thinking. To wit: Because it is true of a part of a class it should not be assumed that it is true of the whole of that class: or, in short, do not distribute an undistributed term. A possible profit to the student may result from a study of certain authentic definitions herewith subjoined: (i) "Logic is the science of the laws of thought." Jevons. (2) "Logic is the science which investigates the process of thinking." Creighton. (3) "Logic as a science aims to ascertain what are the laws of thought; as an art it aims to apply these laws to the detection of fallacies or for the determination of correct reasoning." Hyslop. (4) "Logic is the art of thinking." Watts. (5) "Logic is the science and also the art of thinking." Whateley. (6) "Logic is the science of the formal and necessary laws of thought." Hamilton. (7) "Logic is the science of the regulative laws of the human understanding." Ueberweg. (8) "Logic treats of the nature and of the laws of thought." Hibben. (9) "Logic may be defined as the science of the conditions on which correct thoughts depend, and the art of attaining to correct and avoiding incorrect thoughts." Fowler. Logic Defined 5 (10) "Logic is the science of the operations of the understanding which are subservient to the estimation of evidence." Mill. (n) "Logic may be briefly described as a body of doctrines and rules having reference to truth." Bain. It would seem as if there were as many different defini- tions as there are books on the subject. This is due partly to the disposition of the older logicians to ignore the art of logic and partly to the difficulty of giving in a few words a satisfactory description of a broad subject. In the fundamentals of logical doctrine present-day authori- ties virtually agree. 4. THE VALUE OF LOGIC TO THE STUDENT. Logic is rapidly coming into favor as a major subject in institutions devoted to educational theory. Some of the reasons for this change of attitude are herewith subjoined: (i) Logic should stimulate the thought powers. This is the age of the survival of the thinker. The fact that the man who thinks best is the man who thinks much and carefully will be accepted by those who believe that prac- tice makes perfect. "One needs only to observe the aver- age commuter to conclude that a large percent, of our business men read too much and think too little." "Much readee and no thinkee" was the reply of a Chinaman when asked his opinion of the doings of the average American. "We as a people are newspaper mad, reading for enter- tainment, seldom for mental improvement." (2) Logic aims to secure correct thought. Are not 6 The Scope and Nature of Logic many of the sins and most of the failures in this world due to incorrect thinking? (3) Logic should train to clear thinking. It would be difficult to estimate the loss of energy to the brain worker because he has not the power to think clearly. Maxi- mum efficiency is impossible with a befogged brain. How discouraging it is to the student to attempt to get from the paragraph the thought of the author, who in trying to be profound succeeds in being profoundly abstruse. There is a probable need for broad, deep thoughts, but these when placed in a text book should be sharpened to a point. (4) Logic should aid one to estimate aright the state- ments and arguments of others. This is of especial value to the teacher who is constrained to teach largely from text books. Because it is found in a book is not proof positive that it is true. Why should we assume that the book is infallible when we know that the man behind the book is fallible? (5) Logic insists on definite, systematic procedure. To be logical is to be businesslike. A study of logic would, no doubt, benefit our churches and parliamentary orders as well as our schools. (6) Logic demands lucid, pointed, accurate expression. How we would increase our working efficiency could we but express our thoughts in an attractive and interesting manner. To listen to the speeches of some of our great and good men who are concerned in directing the "ship of state" is sufficient argument that the American schools need more logic. The Value of Logic to the Student 7 (7) Logic is especially adapted to a general mental training. Despite the swing of the pendulum of public opinion toward the bread-and-butter side of life, there are many of high repute who claim that for the sake of that mental acumen which distinguished the Greek from his contemporaries we cannot afford to sacrifice everything on the altar of commercialism. (8) Logic worships at the shrine of truth and adds to our store of knowledge. . What has aided the world more in its march onward than this deep-seated passion for truth and what has impeded it more than that vain and wanton indifference to truth which brought to the world its darkest age? 5. OUTLINE— The Scope and Nature of Logic. (1) The Mind. Three aspects. Unity of (2) Logic Related to Other Subjects. Mental philosophy, psychology, logic. Psychology, logic, aesthetics, ethics. Two ways of knowing. Special province of logic. Logic and language. A science of sciences. (3) Logic Defined. A general definition. A more satisfactory definition. A list of authentic definitions. (4) The Value of Logic to the Student. Eight reasons for its study. 6. SUMMARY. (1) The aspects of the mind are knowing, feeling and willing. 8 The Scope and Nature of Logic The mind is a living unit and never knows without feeling in some way and willing to some extent. (2) What the mind is must be answered by philosophy; what the mind does by psychology and what the mind knows by logic. Psychology treats of the mind as a whole, logic of the mind knowing, aesthetics of the mind feeling and ethics of the mind willing. Ethics answers the question, What is right ? Aesthetics, What is beautiful? Logic, What is true? The standpoint of logic is not identical with any particular por- tion of psychology. The mind knows in two ways : (a) by intuition, (b) by think- ing. Thinking is a process — thought a product. Logic deals in- directly with the former and directly with the latter. Generally speaking, logic is a systematic study of thought. For the logician thought has two sources : (a) his own mind and (b) spoken or written language. Because of the ambiguity of language logic has much to do with it as a faulty vehicle of thought. (3) Logic as a science makes known the laws and forms of thought and as an art suggests conditions which must be fulfilled to think rightly. Author. "Logic may be defined as the science of the conditions on which correct thoughts depend, and the art of attaining to correct and avoiding incorrect thoughts." Fowler. In the fundamentals of logical doctrine present day logicians virtually agree. (4) Logic should stimulate the thought powers; secure correct and clear thinking; aid in the estimation of arguments; inspire definite, systematic procedure; demand lucid, pointed, accurate expresssion and be especially adapted to general mental discipline. Logic adds to our store of knowledge and develops a passion for the truth. 7. REVIEW QUESTIONS. (1) Explain and illustrate the three ways in which the mind may manifest itself. (2) Illustrate the fact that the mind acts in unity. Review Questions (3) Show briefly how logic is related to mental philosophy, psychology, aesthetics, ethics and grammar. (4) Illustrate the two ways of knowing. (5) Distinguish between thinking and thought. (6) Give a general definition of logic. Why is this definition unsatisfactory? (7) What are the two sources of thought? (8) Why are logic and language so closely related? (9) Give that definition of logic which best satisfies you. (10) Summarize the benefits which you hope to derive from your study of logic. (11) Why should teachers be clear thinkers? (12) Why should teachers be especially on guard against incorrect statements of all kinds? (13) Show how logic might be of assistance to the business man. 8. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTI- GATION. (1) Prove that there is nothing real in the world save the mind itself. (2) "Logic is concerned primarily with how we ought to think and only in a secondary way with how we actually think." Explain this quotation. (3) Prove that there is no such thing as intuitive knowing. (4) Is there any difference between knowledge and thoughts? Illustrate. (5) Show by illustrations that the English language is ambig- uous. (6) Prove by concrete illustration that this is the age of the survival of the thinker. (7) Which is the more harmful: falsehood mixed with truth or unadulterated falsehood? Give reasons. (8) Give a concrete example of incorrect thinking. (9) Show that wrong thinking leads to wrong doing. (10) To be worth while must every subject have a practical value ? (11) "The 20th century virtue is a passion for truth." Prove the truth of this. CHAPTER 2. THOUGHT AND ITS OPERATION. 1. THE KNOWING MIND COMPARED WITH THE THINK- ING MIND. In the preceding chapter we were told that the mind may know in two ways (i) by intuition and (2) by think- ing. It is thus implied that the knowing mind includes the thinking mind plus intuition. Thinking always in- volves knowing, but knowing need not involve thinking, and when some logicians maintain that to know a thing one must think it, there is danger of being misled. They mean by this that in order to know anything in a perma- nent and highly serviceable way one must think it. All animals know, even such a stupid one as the oyster, and yet one would hardly give an oyster credit for thinking. Only the higher orders of animal life think. Some argue that the power is confined exclusively to the human fam- ily. This opinion is debatable. If the claimant means by thinking, reasoning then his ground is well taken. But if he is willing to give to thinking a broader content, then he has little defense for his stand. However, attach as broad I a meaning to thinking as the derivation of the word will I permit and even then it is a narrower term than knowing. Thinking plus intuition equals knowing, and in intuition there is probably no thinking. 10 Knowing by Intuition II 2. KNOWING BY INTUITION. It has been aff rmed that intuition is the process involved when the mind knows instantly* Illustrations : (i) As I raise my eyes a figure comes to view. My mind knows instantly that it is the figure three. (2) The ear catches immediately a tune which is being sung in the room below. Without deliberation the mind recog- nizes the tune as America. The mind may thus know by intuition through any one of the five senses. These are the wires of connection between the outer world and the mind within and transmission over these wires may be instantaneous or intuitive. This is not all. (3) My mind may center its attention on itself and may recognize there a mental picture or image of a pet dog. Since this activ- ity is without any apparent deliberation the process must: be intuitive. To define intuitive knowledge as that which comes to the mind through the senses only is incorrect, as it leaves out altogether the knowledge the mind may obtain of its own activity as in illustration "(3)." Knowledge is anything known. Intuitive knowledge is knowledge which comes to the mind immediately by direct observation. The field for intuitive knowledge may be the external world or the internal world though, of course, the former is the more common ground. It is here that the mind by intuition secures the most of its raw material which, through the process of thinking, is worked over into a connected, unified system of lasting value. •Intuitive knowing might be termed habitual knowing. 12 Thought and Its Operation The intuitions are the beginning and the basis of ail knowledge, and knowledge gained by intuition is the basis of all thinking. 3. THE THINKING PROCESS. It is claimed that think comes from the same root as thick. From this one would conclude that the process of thinking is virtually a process of thickening. Surely as one thinks he enriches or thickens his knowledge. As one thinks percepts into concepts and concepts into judgments he makes richer in meaning the various notions con- cerned. Thinking is largely a matter of pressing many into one: of linking together the disconnected fragments of the conscious field. Definition : Thinking is the deliberative process of affirming or denying connections. The same idea may be expressed in a variety of ways as the following indicate. ( i) "Thinking is the conscious adjustment of a means to an end in problematic situations." Miller. (2) "To think is to designate an object through a mark or attribute or what is the same thing, to determine a subject through a predicate." Bowen. (3) "Thought is the comprehension of a thing under a general notion or attribute." Wm. Hamilton. (4) "To think is to make clear through concepts the perceived objects." Dressier. In the foregoing definitions it is implied that thinking is a connecting or thickening process. In all forms of The Thinking Process 13 thinking from the simplest to the most complex the know- ing mind hunts for some basis of connection and having found it thinks the relationship into a unified whole. The thinking process is the digestive process of the mind. Much as the digestive organs assimilate the food stuff of the physical world, so the thinking organ assim- ilates the food stuff of the mental world. Illustrations of the Thinking Process : (1) The child is unable to explain the meaning of "hocus-pocus" as it occurs in the question, "What hocus- pocus is this ?" The child mind is unable to establish any connection between the word and its real meaning. In short, is unable to think into it a meaning; it therefore becomes necessary for the teacher to establish some basis of connection and this he does by suggesting nonsense as a synonym. (2) The teacher holds before the class an Egyptian house god and asks, "What is it?" After a moment of hesitation some child who has seen pictures of "his satanic majesty" avers that the object is a "little devil." Thus has a connection been established between the idol and pictures of satan. (3) John is unable to solve the following problem as he can discern no connection between the data given and the data required. Problem. 3/4 of my salary is $900, what is my salary? Data. Given : 3/4 of salary = $900. Required : 4/4 of salary = ? 14 Thought and Its Operation In order that John may think a solution the teacher must lead him to see some connection between 3/4 and 4/4. With this in mind the form of the data is changed to Given: 3-fourths = $900 Required: 4- fourths = ? or Given: 3 parts = $900 Required: 4 parts = ? John now notes that 4 parts is 4/3 times 3 parts and con- sequently writes 4/3 of $900, which is $1,200 as the an- swer. Or he may find the value of 1 part and then of 4 parts. 4. NOTIONS, INDIVIDUAL AND GENERAL. A notion is any product of the knowing mind — any- thing which the mind notes or becomes aware of. But the mind knows in two ways, by intuition and by thinking. In consequence the mind has two kinds of notions, those which are intuitive or individual notions and those which originally result from thinking or general notions. An individual notion is a notion of one thing. A gen- eral notion is a notion of a class of things. Note. Here it is necessary to distinguish between a thing and an object. An object is a thing which occupies space such as a pencil or a book. "Thing" is, therefore, a broader term than "object." "A thing is that which has individual existence." From the viewpoint of logic "thing" includes objects, qualities, relations, spiritual Notions, Individual and General 15 entities. Gravitation is a thing but not an object. A tree is both an object and a thing. Illustrations of Notions. My notion of the pencil with which I am writing is an individual notion, but my notion of pencil as a class name is general. My yellow dog, the honesty of Lincoln, Albert White, New York City, are individual notions, while dog, honesty, man, city, are general notions. A sure way to determine whether the notion is indi- vidual or general is to attempt to divide it into its kinds. Only general notions may be subdivided. 5. KNOWLEDGE AND IDEA AS RELATED TO THE NOTION. Knowledge is anything known, while anything of which the mind becomes aware is a notion. Notions are always bits of knowledge, but knowledge is not always a notion. Notions are mental products belonging to the mind which thinks them, while knowledge, though it must first be a mental product of someone's mind, may not necessarily be a product of yours or mine. Notions are always found in the mind, while knowledge may be found in books, but not necessarily in some individual mind. Knowledge stands for everything knoivn, the notion, for everything noted. The Egyptians may have possessed much knowl- edge of which we may never become aware. Much of their knozvledge may never become notions of the Ameri- can people. A notion is an existing state of consciousness. Said notion may be committed to paper, and then it may give way to another notion. It now ceases to be your no- 1 6 Thought and Its Operation tion, but remains on the printed page, as a bit of know! edge. "Idea," because of its ambiguity, really has no place in logic. The term is frequently restricted to a reproduced percept. To illustrate : When the pencil is before me the mental product is a percept, but when the pencil is with- drawn and I try to think of it, then have I an idea of "pencil." Probably idea is most commonly associated with meaning and belief. To illustrate: What is your idea as to the meaning of homogeny? or What are your ideas on the tariff? 6. THE LOGIC OF THE PSYCHOLOGICAL TERMS IN- VOLVED IN THE NOTION. Concerning the knowing mind the psychologist classifies its activities and their products as follows: Activity Product ( i ) Presentative (i) Sensation Sensation (2) Perception Percept (2) Representative (1) Imagination] (2) Memory ^ Image (3) Thinking (1) Conception Concept (2) Judging Judgment (3) Reasoning Inference The notion as any product of the knowing mind in- cludes the six products as indicated by the psychologist. The individual notion which is intuitive includes the sensation, percept and image ; the general notion which is The Logic of the Psychological Terms 17 Individual notion= intuitive products a thought product stands for the concept, judgment and inference. To put it mathematically — 'sensation^ percept image r - ° ^ J Ynotion [ concept General notion=*{ judgment j>=thought products [inference] As we shall have occasion frequently to refer to these psychological terms it may be well to define them. Logical Definition. Psychological Definition. A sensation is the first and simplest mental result of the stimulation of an incarrying nerve. A percept is a mental product which results from a consciousness of particu- lar material things present to the sense. An image is a mental product which results from particular material things not present to the sense. A concept is a re-pres- entation in our minds an- swering to a general name. A judgment is the result of asserting an agreement or disagreement between two ideas. A sensation is a vague, unlocalized mental product of the knowing mind. A percept is a consciously localized group of sensa- tions. An image is a reproduced percept. A concept is a mental product arising from think- ing many notions into one class. A judgment is the mental product arising from con- joining or disjoining no- tions. 1 8 Thought and Its Operation Psychological Definitions— Con. Logical Definitions— Con. An inference is a judg- An inference is a judg- I ment derived from per- ment derived from ante- f ceiving relations between cedent judgments, other judgments. It is seen that the sensations furnish the raw material. Ignoring the few exceptions we may then say that a per- cept is a made-over group of sensations; a concept a thought-made group of percepts; a judgment a thought- made group of concepts; an inference a judgment derived from other judgments. Developed thinking is first found in the concept, and as we study the thought products, "concept," "judgment" and "inference," the truth is forced upon us that thinking as a process aims to group the many into one. From many percepts is built the one concept, from two concepts is built the one judgment and from two judgments is built the one inference.* Speaking figuratively, thinking is a matter of picking up the fragments along the shore of consciousness and tying them into bundles. 7. Thought in the Sensation and Percept. So far in this discussion it has been assumed that there is no thinking involved in the sensation or the percept. There are good authorities, however, who insist on dignifying the sensation, even with a crude form of thinking. To illustrate: One may be reading an interesting novel. The mind is being entertained and ignores the activities of the objective world, yet we cannot say that the mind is dead to the world outside. There is a dim consciousness of certain noises without. These unlocalized sounds are sensations; but how is the mind able to recognize them as sounds or noises? To interpret the noises is Mediate Inference. The Logic of the Psychological Terms 19 it not necessary for the mind to affirm a connection between them and some past mental experience? Is it possible for the mind to know anything without establishing some kind of connection between the outside occurrence and an inner situation? If this is granted then in sensation there must be implicit thinking. As the percept is a localized group of sensations then there must be involved in perception a more complex form of think- ing, since in grouping sensations there is a recognition of connections. If there is thinking in the sensation which is the simplest and lowest form of the knowing-mind then thinking conditions all knowledge and really is the basic elemental cell of all knowing. On the other hand there are those who maintain that the sensation and percept are mere reflections of consciousness; the sensation being a reflected quality and the percept a reflected object. These mental situations come into being in- stantly — there is no time for thought and we all know that thought requires time. ("As quick as thought" is misleading, since light travels more rapidly by many times than the agencies of thought.) It will probably never be settled to the satisfaction of all just when thinking commences. The question is as difficult as some others which have never been solved. For example: Where does life commence? When does the plant merge into the ani- mal? Which was first the egg or the hen? Does the ob- jective world really exist or is it only a mental interpretation of vibrations? etc. Logically considered the question is immaterial. All will agree that developed thought is involved in the concept, judg- ment and inference, while, if it appears at all in the percept and sensation, it is more or less undeveloped and consequently lies quite without the province of the logical field. 8. EVOLUTION AND THE THINKING MIND. Speaking in general terms evolution is a development from a lower to a higher state. Thus have come the various species of the vegetable and animal world. The 20 Thought and Its Operation lower orders of life are simple in structure and func- tion. In the one-celled animate form a single organ performs all of the work needed to maintain life and perpetuate the species. If these simple life- forms are cut in two, life continues in the two parts as if nothing had happened. Aside from their simplicity there is little of interdependence of function and little of co-ordina- tion of organs in the lowest life-forms. In short there is no division of labor ; "each cell is a world unto itself." An analogous development is seen in the thinking mind. The little child thinks in lumps, and these lumps are only faultily linked together, but the adult thinks in terms of the grains of the lump, each grain having its place, which it must occupy for the sake of all the other grains as well as the entire lump. The child's thinking is vague, general and inaccurate, while the adult's think- ing should be definite, specialized and accurate. Think- ing in the lump means little discrimination and very faulty integration or unity, while thinking in terms of the grains means detailed discrimination and perfect integration. To illustrate : The child sees a dog trotting along the side walk which, according to the suggestion of his mother, he learns to call "bow-wow." Later he ob- serves a cat and at once says "bow-wow," because all that the child notes is that something with legs, ears and a tail is trotting along the side walk. Anything which fits these general marks is a "bow-wow." Similarly when a child first observes a robin perched on a gate post he fails to distinguish between the two — it is all bird from the top of the robin's head to the bottom of the gate post. The Logic of the Psychological Terms 21 Progress in thinking is measured by progress in dis- crimination. The skilled thinker divides the large unit into very small units, compares these with each other and then reunites them into a more perfect and unified whole. First there is an analysis and then a synthesis. Like a shuttle the power of thought works in and out; it goes in to separate, it comes out to unify. There is another aspect in the analogy between the life of the physical and mental worlds. Somewhere in the order of progress there is a connecting link between the mineral and vegetable kingdoms, likewise between the vegetable and animal kingdoms. The sensation is as much a state of feeling as an act of knowing and consequently is the connecting link between the feeling mind and the knowing mind. If the percept is the re- sult of thinking as well as intuition then it may stand for the dividing line between the knowing* mind and the thinking mind. 9. The Concept as a Thought Product. Conception is the process of thinking many notions into one class. The product of such a process is called a concept. (1) The concept may stand for a group of concrete general notions — as the concept man, which stands for the five general notions : Caucasian, Mongolian, Ethiopian, Malay and American Indian. (2) The concept may stand for a group of concrete individual notions. For example, the same concept man represents all of the individual men of the world. (3) The concept may stand for a group of abstract general notions. To wit: Virtue rep- resents such general notions as honesty, justice, industry, purity, etc. (These are general notions because they admit of a subdivision into kinds. Industry, for instance, may be di- * Intuitive Knowing. 22 Thought and Its Operation vided into two kinds: mental industry and physical industry.) j (4) The concept may stand for a group of abstract individual notions. To illustrate: Blueness stands for the various shades ! of blue, as sky blue, bird's egg blue, navy blue, etc. Thus does the concept stand for a group of all kinds of ; notions, individual and general, abstract and concrete. The Process of Conception Illustrated. I see for the first time in my life a pencil. In other words j I become conscious of a localized group of sensations — this i is a percept. I am told that the name of that which I see is I pencil. I note that this particular pencil has a thread of black j: lead encased in a cylindrical strip of wood which is brown in color. A second object is presented which I recognize as a ! pencil though the shape is prismatic rather than cylindrical and the color green rather than brown. But I call it a pencil ij because it has a thread of black lead encased in a strip of wood. The notion which I now have in mind stands for two pencils and is therefore represented by a class name. As I observe other pencils of various shapes, made of wood and paper with threads of different colored lead, my notion of pencil broadens till finally it stands for all pencils. This is the r. process of conception according to the definition, namely: "The j process of thinking many notions into one class." In this case I. the notions are individual. An examination of conception makes evident two distinct charac- ': teristics. First, I may be able to recignize each individual pencil be- ji cause of the two common qualities, a thread of lead and an encase- |i ment of some kind. This process of the knowing mind whereby it j. recognizes and affirms connections is called thinking as we have al- ready learned. Here is the thinking aspect of conception. Second, as | the instances of the observed objects are multiplied, my notion of r, pencil is broadened. It is a building process where many are cemented ' into one ; like the blocks of a cement wall. Here we find the charac- - teristic which enables us to call the process conception. This is the f mark which distinguishes conception from all the other thought ! processes. 10. The Judgment as a Thought Product. Judging is the process of conjoining and disjoining notions, j The Logic of the Psychological Terms 23 The product of judging is the judgment and all judgments are expressed by means of propositions. A proposition consists of one subject and one predicate connected by some form of the verb be or its equivalent. (1) A judgment may conjoin or disjoin two individual notions. To wit: Conjoined — This pencil belongs to Albert White. Disjoined — This pencil does not belong to Mary Smith. (2) A judgment may conjoin or disjoin two general notions. Conjoined — Some men are virtuous. Disjoined — Some men are not virtuous. (3) A judgment may conjoin or disjoin a general and an individual notion. Conjoined — Abraham Lincoln was virtuous. Disjoined — Edgar Allen Poe was not temperate. In order that the knowing mind may conjoin notions it must recognize some mark of similarity or connection. This is the thinking aspect of the judgment. It is likewise to a certain degree the judging aspect as the latter is simply a matter of affirming or denying connections between notions. But think- ing is a broader term than judging. There may be connections established between a name and a notion. For example in the case of the dog which the child sees trotting along the side- walk and which the mother refers to as a "bow-wow"; the term "bow-wow" is not a percept and has no meaning inde- pendent of its association with the dog, hence it is not a no- tion, yet some connection has been made in the child's mind between "bow-wow" and his notion of dog. This is a simple form of thinking, but not of judging, as the latter affirms or denies connections between notions only. The fact that judging and thinking so closely resemble each other has given just cause for some logicians to designate judging as the most fundamental element in all thinking. "The simplest form of thinking," says Creighton, "is judging." In order to think many notions into one class it is necessary to conjoin notions. To illustrate: The child who has a general notion of man sees for the first time a negro. If he recognizes the negro as a colored man he must conjoin his general notion of man with this individual notion. In short, a concept is built by means of a series of judgments. It may be said further 24 Thought and Its Operation that an inference is simply a made-over judgment. It is thus evident that judging appears in both the thought processes of conception and inference and, therefore, as a final conclusion it may be affirmed that judging, though perhaps not the sim- plest form of thinking, is the basic element of developed thought. 11. Inference as a Thought Product. Reasoning is the process of deriving a new judgment from a consideration of other judgments. The product of any reason- ing process may be called an inference, although, as will appear in a later chapter, inference is commonly used as indicating the process as well as the product. Often reasoning may assume a syllogistic form with the in- ference as its conclusion. A syllogism is an arrangement of three propositions using three different terms. The following are syllogisms : (1) All children should play. Mary is a child. Hence, Mary should play. (2) No teacher should judge hastily. You are a teacher. Hence, you should not judge hastily. In the second syllogism the inference, "you should not judge hastily," is derived from the other two judgments by merely eliminating the common term teacher and disjoining the re- maining two terms. The inference is consequently a new judg- ment. Therefore, reasoning is only a matter of judging carried to a more complex stage. To summarize — conception is largely a matter of conjoining a general notion with an individual notion, judging of conjoin- ing and disjoining all kinds of notions and inference of con- joining and disjoining judgments. All three processes go to form the larger process of thinking. The concept, the judg- ment and the inference are products arising from conjoining and disjoining notions. 12. THINKING AND APPREHENSION. Says Jevons: "Simple apprehension is the act of the mind by which we merely become aware of something, Thinking and Apprehension 25 or have an idea or impression of it brought into the mind;" while Hyslop states that "The process of knowledge which gives us percepts is apprehension." It is obvious that the idea of the latter is that appre- hension yields individual notions only, while Jevons, in citing the term iron as an illustration of his definition, would infer that the general notion is the product of apprehension. The term is strikingly ambiguous and will not be referred to often in this treatise. If the stu- dent desires a definition this will cover the concensus of opinion on the meaning of apprehension. Apprehension is that process of the knowing mind which yields the percept and concept. Some logicians give to the think- ing mind the three aspects of apprehension, judging and reasoning. 13. STAGES IN THINKING. In all thinking there are three steps or stages which may be termed discrimination, comparison, integration. In the case of the two pencils held in the hand, it is noted that one is longer than the other. Let us analyze the process which made possible this conclusion. Step one — Attention is given first to one pencil and then to the other. In each case the pencils are distinguished from the hand and the other surrounding objects. This is discrimination. Step two — The pencils are compared in length. Step three — The two notions are united in the judgment, "Pencil number one is longer than pencil number two." This is integration. Another illustration. The child is requested to solve 26 Thought and Its Operation this problem : If 8 tons of hay cost $165, what will 16 tons cost? Statement: Given: 8 tons cost $165 Required: 16 tons cost ? Discrimination. The child notes that 8 tons cost $165 and at this rate he is required to find the cost of 16 tons. Comparison. The child perceives that 16 tons is twice 8 tons. Integration. The child concludes that the cost of 16 tons will be twice the cost of 8 tons or $330. When we think, we first tear to pieces that we may become acquainted with every part. This may be called analysis. Then we put the related pieces together again. This may be called synthesis. Before, however, the parts are re-united a certain amount of comparison is necessary. The three stages of thought might thus be denominated: (1) analysis, (2) comparison, (3) synthesis. After the synthesis or integration it is necessary to name the result, consequently a fourth step is sometimes given, namely denomination. 14. OUTLINE. Thought and Its Operation. (1) The Knowing Mind Compared with the Thinking Mind. (2) Knowing by Intuition. (3) The Thinking Process. Denned. Other definitions. (4) Notions. Individual. General. Thing and object distinguished. Outline 27 (5) Knowledge and Idea as Related to the Notion. (6) The Logic of Psychological Terms Involved in the Notion. The sensation "1 The percept Llndividual notions. The image The concept "] The judgment LGeneral notions. The inference Terms defined. (7) Thought and the Sensation and Percept. (8) Evolution and the Thinking Mind. (9) The Concept as a Thought Product. (10) The Judgment as a Thought Product. The simplest form of thinking. (11) Inference as a Thought Product. (12) Thinking and Apprehension. (13) Stages in Thinking. Discrimination. Comparison. Integration. (Denomination.) 15. SUMMARY. (1) Knowing is a broader term than thinking as the former equals the latter plus intuition. (2) Intuitive knowledge is that which comes to the mind im- mediately by direct observation. Although intuitive knowledge comes to the mind without thought, yet such knowledge is essential to all thinking. Intuitive knowledge is the foundation upon which the thinking mind builds. (3) Thinking is the deliberative process of affirming and denying connections. Thinking is a "thickening process," the smaller units being pressed together to make a larger. Thinking is chiefly a matter of reducing plurality to unity. (4) A notion is any product of the knowing mind. An individual notion is the notion of one thing. A general notion is a notion of a class of things. 28 Thought and Its Operation A thing includes objects, qualities, relations or any existing entity. A thing is that which has individual existence. (5) A bit of knowledge must have been a notion of some one's mind, but may not necessarily be a notion of your mind. Knowl- edge may be found in books, but a notion is a mental product found only in the mind. Idea is ambiguous, though its meaning is usually restricted to an image, a meaning or a belief. (6) The products of the knowing mind are the sensation, the image, percept, concept, judgment, inference. The sensation, image and percept are individual notions, while the concept, judgment and inference are general notions. A sensation is a vague, unlocalized product of the knowing mind. A percept is a consciously localized group of sensations. An image is a reproduced percept. A concept is a mental product arising from thinking many notions into one class. A judgment is a mental product arising from conjoining and disjoining notions. An inference is a judgment derived from antecedent judgments. The developed thought processes are the concept, the. judgment and the inference. (7) Just where the simplest form of thinking appears in the various activities of the knowing mind is still an undecided ques- tion. It is agreed that thinking in its developed and more com- plex form is found in conception, judging and reasoning. (8) Thinking evolves from the simple to the more complex, just as life has evolved. The child thinks in vague, indefinite wholes, while the adult thinks in clear, definite parts. The child discriminates very imperfectly while the adult discriminates accurately. The sensation seems to be the connecting link between the feel- ing mind and the knowing mind, while the percept links together the knowing mind and the thinking mind. (9) Conception is the process of thinking many notions into one class. The product of such a process is a concept. The con- cept stands for groups of all kinds of objects. Conception has the two aspects of affirming connections and of building many into one. The first is the thinking side of the Outline 29 process and the second is the mark which distinguishes concep- tion from the other thought processes. (10) Judging is the process of conjoining or disjoining notions. Judgment is the product of judging. Judgments conjoin and disjoin all kinds of notions. Judging and thinking, though they closely resemble each other, are not synonomous terms. Thinking is a broader term in that connections may be established between a notion and a name for that notion. Judging is the most fundamental of all thinking, as the concept is built from a series of judgments and an inference is simply a made-over judgment. (11) Inference. Reasoning is the process of deriving a new judgment from a consideration of antecedent judgments. This derived judgment may be called an inference. Sometimes the term inference de- notes the process of reasoning as well as the product. Reasoning often takes the form of a syllogism. The concept, the judgment and the inference are products arising from conjoining and disjoining notions. (12) Some give to the thinking mind the three aspects, appre- hension, judging and reasoning. Apprehension is another word for the two processes, perception and conception. (13) The three important stages in thinking are discrimination, comparison, integration; or analysis, comparison and synthesis. 16. REVIEW QUESTIONS. (1) Show the difference between the knowing mind and the thinking mind. (2) Describe the process known as intuition. (3) What is intuitive knowledge? (4) Is the assumption that think comes from the same root as thick a feasible one? Explain. (5) Define thinking in at least two ways. (6) "Inability to think is due to inability to note connections." Show this by making use of some problem in arithmetic. (7) Distinguish between individual and general notions. (8) Which is the broader term, object or thing? Explain. 30 Thought and Its Operation (9) What kind of notions only admit of subdivisions? Illus- trate. (10) What is the difference between knowledge and notions? Explain. (11) Explain and illustrate the meaning of idea. (12) Classify the various activities of the knowing mind and define each. (13) Explain by definition and illustration the products of the knowing mind. (14) Relate the general notion to the psychological products of the knowing mind. (15) "The thinking mind is a unit." Explain fully. (16) Trace the analogy between the evolution of the physical world and the evolution of thought. (17) Show that the sensation and the percept may be regarded as connecting links between lower and higher states. (18) Define and illustrate conception. (19) Show that the concept stands for all kinds of notions. (20) Point out the thinking aspect of conception as distin- guished from the activity which gives the process its name. (21) Define the judgment. Illustrate two kinds. (22) Show that the concept is built by means of a series of judgments. (23) Show that judging is the fundamental element in the thought products. (24) Define and illustrate reasoning. (25) Describe the syllogism. (26) Explain the use of apprehension. (27) What are the stages in thinking? Illustrate fully. (28) Show that thinking is a matter of analysis and synthesis. 17. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Give your argument in favor of the statement, "Dogs think, but do not reason." (2) Show by illustration that thinking would be impossible without intuition. (3) "Thinking is the conscious adjustment of a means to an end in problematic situations." Illustrate this. Questions for Original Thought and Investigation 31 (4) The class is unable to solve the following problem: "I sell my house for $12,000, which is a gain of 25% on the cost. Find the cost." What is the trouble? State the problem so that some connection is apparent. (5) "Two-thirds of my salary is $2,400. What is my sal- ary?" A child solves this by dividing $2,400 by two and multiply- ing this result by three. Illustrate a plan for establishing right connections. (6) May a judgment express a general notion? Illustrate. (7) Is a thought a thing? Illustrate. (8) Show the illogic of dividing notions into individual, general and abstract. (9) Show that goodness is a general notion. (10) Is the concept an idea? Explain. (11) Prove that a mental image is always an individual notion. (12) "In sensation is there implicit thinking?" Argue both sides of the question. (13) Show that the concept, the judgment and the inference are products of the thinking mind. (14) Show by illustration where perception ceases and concep- tion begins. (15) Is there actually any difference between thinking and judging? Illustrate. (16) "Reasoning is controlled thought." Explain. (17) Of the three stages in thinking which one most concerns the teacher? Illustrate. CHAPTER 3. THE PRIMARY LAWS OF THOUGHT. 1. TWO FUNDAMENTAL LAWS. The elemental form of evolved thought is the judg- ment. The laws or axioms of thought may, therefore, be discovered by studying the judgment. Judging is the process of conjoining and disjoining notions. When these notions are conjoined the judg- ment is affirmative; when disjoined the judgment is negative. To illustrate: "Some men are wise," is an affirmative judgment, while "Some men are not wise," is a negative judgment. All judgments are either affirma- tive or negative and this suggests that there may be but two fundamental laws or axioms underlying judging or all forms of developed thinking. One law would condi- tion the affirmative judgment; the other the negative. Such is actually the case. The law which permits the affirmative judgment is called the law of identity, while the law which allows a negative judgment is known as the law of contradiction. There is a third law termed the law of excluded middle, which is in reality a com- bination of the other two. 2. THE LAW OF IDENTITY. In general the law of identity implies a certain perma- nency throughout the material world. That door is a door and always will be a door till the conditions change. If it were not for this law, that everything is 32 The Law of Identity 33 permanently identical with itself, it would be impossible to think at all. For example: Take away the notion of permanency from the door and thought becomes at once ridiculous. Suppose that while we are asserting that the object is a door, it changes to a tree, and while we insist that the object is now a tree, it changes to a cow, etc. We can readily see that it would hardly be worth while to think at all. The law of identity may be stated in three ways :• ( 1 ) Whatever is, is; (2) Everything remains identical with itself; (3) The same is the same. Absolute Identity — Complete and Incomplete. Applying the law of identity to the affirmative judg- ment expressed in the form of a proposition, we find two kinds of identity, absolute and relative. In the proposi- tions, "Socrates is Socrates," "dogs are dogs," "honesty is honesty," the subject is absolutely identical with the predi- cate — the same in form and meaning. If we were to illustrate the subject and predicate by two circles they would be of the same size and shape, the one coinciding with the other point to point. This kind of absolute identity which makes possible all truisms we may term, for want of a better name, complete absolute identity. This would imply that there is an incomplete absolute identity and such seems to be the case. Examining the definition, "A man is a rational animal," we observe that the notion man has the same content or meaning as the notion rational animal. In meaning, then, the two notions are absolutely identical. The one includes just as many objects or qualities as 34 The Primary Laws of Thought the other, and if we were to draw two circles repre- senting them, they would be of the same size. In form, in mode of expression, however, the notions differ and the circles, though coinciding, would need to differ in form, the boundary of one might be a solid line, the other a dotted. This we may call incomplete absolute identity. All logical definitions illustrate identities of this kind. Relative Identity. Relative identity is best understood by thinking of it as partial identity, just as we may think of absolute iden- tity as total identity. In relative identity the whole of one notion may be affirmed of a part of another notion; or a part of one notion may be affirmed of a part of another notion. To illustrate: (i) All men are mortal; (2) Some men are wise. These and their like are made possible because of the law of relative identity. In the first proposition all of the "men" class is identical with a part of the "mortar class. If we were to represent this rela- tion by circles, the "men" circle would be made smaller than the "mortal" circle and placed inside it, as in Fig. 1. Mortal [yen J Fig. 1. Fig. 2. Be it remembered that circles are surfaces, and in Fig. 1 the men circle is identical with that portion of the mortal circle which is immediately underneath it. The Law of Identity 35 The same relation may be indicated by a small pad being placed on top of a larger pad. Then the whole of the smaller pad could be thought of as being identical with that part of the larger pad which is immediately underneath. In the case of the second proposition a part of the "men" class is identical with a portion of the "wise" class. The two circles indicating this relation must inter- sect each other so that a portion of each may be common ground, as in Fig. 2 where the shaded part represents the identity. Thus we see that the law of identity underlies all affirmative propositions. Absolute identity making pos- sible the truism and definition, and relative identity con- ditioning all the universal and particular affirmative propositions which are neither truisms nor definitions. The three forms may be symbolized as follows : (1) A is A — Absolute complete (2) A is A — Absolute incomplete (3) A is B— Relative. The student will note that the "A's" of absolute in- complete differ in form. 3. LAW OF CONTRADICTION. The law of contradiction underlies all negative propo- sitions. It is the mission of this law to tear down or to be destructive in nature ; while the law of identity builds up or is constructive in nature. The law of contradiction may be stated in this way: It is impossible for the same thing to be and not to be at the same time and in the same place. Or better, it 36 The Primary Laws of Thought is impossible for the same thing to be itself and its con- tradictory at the same time. Bringing out a further aspect, no thing can have and not have the same attri- butes at the same time. The little word not bisects the universe. All the peo- ple in the world are either honest or not honest, virtuous or not virtuous. These are contradictory statements and j what is comprehended by the one cannot be comprehended by the other at the same time, any more than a man can shake his head and nod his head at the same time. If we assert the identity between two notions then we cannot in the same breath deny their identity. Illustrations : (1) A red flower cannot be a red flower and not a red flower at the same time. (2) No man can be guilty and not guilty at the same time. (3) A boy cannot be working and not working at the same time. If I assert that the flower is red, then I cannot affirr in the same breath that the flower is not red. Two Uses of Not. The word not when used with the copula of a given proposition makes that proposition negative;, as (1) "Some men are not wise." But when not is attached to the predicate by a hyphen, the predicate is made negative, not the proposition, as (2) "Some men are not-wise." Here the predicate not-wise is negative, but the proposi- tion in which it appears is affirmative. It is obvious that The Law of Contradiction 37 the proposition "Some men are not wise" illustrates the law of contradiction, since the some men referred to are contradicted of all which is wise. Whereas the proposition "Some men are not-wise" illustrates relative identity, since the subject "some men" is affirmed of a part of the predicate "not-wise." The student may be led to see these relations by drawing circles, the one to represent the subject, the other the predicate. (See page 141.) Further Illustrations : Some teachers are wise *] Some teachers are not-wise llllustrate the law of Some teachers are unwise j identity. Some teachers are not wise 1 ■ Some teachers are not not-wise llllustrate the law Some teachers are not unwise. j of contradiction. The student must understand that a term and its con- tradictory destroy each other. If we affirm something of the one, then we must deny it of the other, or we undermine the integrity of both. If it is affirmed of teachers A, B and C that they are wise, then it must be denied that they are not-wise. Illustrations : A, B and C are wise "1 These are mutually de- A, B and C are not-wise j structive. A, B and C are wise. 1 These are not mutually de- A, B and C are not not- I structive, but virtually wise. j mean the same thing. 38 The Primary Laws of Thought Symbolization of the Law of Contradiction. A is not not-A. A is not B. (As A is always A it or or would be absurd to say A is not not-B. that A is not A.) Contradictory and Opposite Terms. It is easy to use opposite terms in a contradictory sense. This leads to serious error. "Not-guilty" is the contradictory of "guilty," while "innocent" is the opposite of "guilty." We could hardly say that the water must either be cold or hot, as it might be warm. "Not-hot" is the only term which contradicts "hot." The law of contradiction has nothing to do with opposites. Further, it is dangerous to regard words with the nega- tive prefix as being contradictory of the affirmative form. For example: Valuable and invaluable are not contradictory. There is likewise some doubt as to the contradictory nature of such words as agreeable and dis- agreeable, though we are sure that agreeable and not- agreeable contradict each other. To use the "not" with a hyphen is safer than to depend upon some prefix which is supposed to mean "not." Illustrations of Contradictory and Opposite Terms. c pposite. A Contradictory. A bad good bad not-bad soft hard soft not-soft cold hot cold not-cold rough smooth rough not-rough The Law of Excluded Middle 39 Opposite — Continued Contradictory — Continued r good evil t good > not-good warm cool warm not- warm weak strong weak not-weak 4. THE LAW OF EXCLUDED MIDDLE. The law of excluded middle may be considered as a combination of identity and contradiction. Identity gives the proposition, "John Doe is honest." Contradiction, "John Doe is not honest." Combine the two using either and or and we have the excluded middle proposition, "Either John Doe is honest or he is not honest." Excluded middle explains itself. Of the two contra- dictory notions it must be either the one or the other. There is no "go-between" notion. The law may be stated in many ways, as will be seen by the following : ( 1 ) Everything must either be or not be. (2) Either a given judgment is true or its contra- dictory is true; there is no middle ground. (3) Of two contradictory judgments one must be true. (4) Every predicate may be affirmed or denied of every subject. Illustrations : (1) A man is either mortal or he is not mortal. (2) John Doe is either honest or not-honest. (3) Either you are going or you are not going. Symbolization of Excluded Middle. A is either A or not-A or A is either B or not-B. 40 The Primary Laws of Thought 5. THE LAW OF SUFFICIENT REASON. The law may be stated in this wise. Every phenome- non, event or relation must have a sufficient reason for being what it is. To illustrate : (i) If Venus is the even- ing star, there must be a sufficient reason. (2) If thfc ground is wet, there must be a cause. Many logicians argue that this law has no place in logic, its field being that of the physical sciences. The laws of identity, con- tradiction and excluded middle are, however, universally regarded as the Primary Laws of thought. 6. UNITY OF PRIMARY LAWS OF THOUGHT ILLUS- TRATED BY SYMBOLS. (1) Absolute Symbols Relative Symbols. Excluded middle. A is either A or not-A. A is either B or not-B. Contradiction. A is not not-A. Identity. A is A. A is not B or A is not not-B. A is not-B or A is B. (2) Propositions made to fit symbols. Excluded middle. A man is either a man A man is either honest or or a not-man. not-honest. Contradiction. A man is not a not-man. A man is not honest, or a man is not not-honest. Unity of Primary Laws of Thought 41 Identity. A man is a man. A man is not-honest, or a man is honest. The "excluded middle" propositions of the foregoing ex- press alternatives which are mutually contradictory. There is no middle ground. The "contradictory propo- sitions" contradict the identity of the subject with one alternative, while the "identity" propositions affirm the identity of the subject with the other alternative. This is made possible because of the principle, "Of two mutually contradictory terms, if one is true the other must be false." The foregoing scheme shows how closely "contradictory" and "identity" propositions are related to "excluded middle" propositions. Expressed mathematically: excluded middle = contradiction + identity. 7. OUTLINE. Primary Laws of Thought. (1) Two fundamental laws. Identity, contradiction. (2) Law of identity. Absolute — complete, incomplete. Relative. (3) Law of contradiction. Two uses of not. Contradictory and opposite terms. (4) Law of excluded middle. (5) Law of sufficient reason. (6) Unity of primary laws of thought. 42 The Primary Laws of Thought 8. SUMMARY. (1) The elemental forms of evolved thought are the affirm- ative and negative judgments. This suggests two fundamental laws of thought, the law of identity and the law of contradic- tion. The former conditions the affirmative judgment, the latter the negative. (2) The law of identity implies a permanency of being. "Everything remains identical with itself," is a statement of identity. Absolute identity may be divided into complete and incomplete identity. In complete absolute identity the subject is the same as the predicate in both form and meaning. Truisms illustrate this. In incomplete absolute identity the subject is identical with the predicate in meaning only. Illustrated by definitions. In relative identity the whole of the subject may be affirmed of a part of the predicate or a part of the subject may be affirmed of a part of the predicate. (3) "It is impossible for the same thing to be itself and its contradictory at the same time," is a statement of the law of contradiction. Identity is constructive while contradiction is destructive in nature. To make the proposition negative the word not must be used with the copula. "Not" attached to the predicate with a hyphen makes the predicate negative, but not the proposition. To use opposite terms in a contradictory sense leads to serious error. The safest way of making a positive term a contradictory negative term is to prefix "not" with a hyphen or use "non." (4) The law of excluded middle is virtually a combination of identity and contradiction. It may be stated as follows: "A thing must either be itself or its contradictory." (5) "Every condition must have a sufficient reason for its existence," is the law of sufficient reason. Its distinct province is physical science rather than logic. (6) The laws may be expressed mathematically: excluded middle = identity -j- contradiction. Summary Schematic Statement of Primary Laws. 43 Name Stated Symbolized Illustrated Absolute identity Whatever is, is A is A Work is work Relative identity The whole is identical All A is B Work is a blessing with a part or a part is Some A is B Some play is a blessing identical with a part Contradiction Nothing: can both be A is not not-A Work is not not-work and not be at the same or time A is not B John is not honest A is not not-B Albert is not not-honest Excluded middle Everything must either A is either A Fair play is either fair be or not be or not-A play or not-fair play A is either B This man is either edu- or not-B cated or not-educated 9. ILLUSTRATIVE EXERCISES. (la) Each of the following propositions is made possible because of the existence of which law of thought? In answering this question I summarize in my mind the mean- ing of each law of thought. Viz. : (1) In complete absolute identity the subject and predi- cate are the same in form and meaning. (2) In incomplete absolute identity the subject and predi- cate are the same in meaning, but not in form. (3) In relative identity either the whole or a part of the subject is identical with a part of the predicate. (4) The law of contradiction always denies the identity between subject and predicate. (5) Excluded middle conditions all alternative expres- sions. The Propositions. (1) "A thief is a thief." Complete absolute identity. (2) "Thinking is the process of affirming or denying connections." Incomplete absolute identity. 44 The Primary Laws of Thought (3) "All good men are wise." Relative identity. (4) "No triangle has interior angles whose sum is greater than two right angles." Contradiction. (5) "A stitch in time saves nine." Relative identity. (6) "Judging is the process of conjoining and disjoining notions." Incomplete absolute identity. (7) "You are either a voter in this district or you are not a voter in this district." Excluded middle. (8) "Some people do not know how to live." Contradiction. (9) "AH is well that ends well." Incomplete absolute identity. (10) "Some men teach school." Relative identity. (11) "None of the planets are as large as the sun." Con- tradictory. (12) "All the trees in this grove are maple." Relative identity, (lb) Indicate the law which conditions each of the following propositions : (1) "He who laughs last laughs best." (2) "Perfect is perfect." (3) "He is a wolf in sheep's clothing." (4) "Either your memory is poor or you are telling a deliberate falsehood." (5) "Some of our greatest teachers thought they were failures." (6) "No man of sense would ever try to get something for nothing." (7) "Failure is not to try." (8) "Success is the right man in the right place doing his best." (9) "Every man is insane on some topic." (10) "Some pupils are not industrious." (11) "You are either a genius or a successful fakir." (12) "Honesty is the best policy." 1C. REVIEW QUESTIONS. (1) How many kinds of judgments are there? Illustrate. (2) Name the fundamental laws of thought and explain how they are related to the kinds of judgments. Review Questions 45 (3) Show that it would be impossible to think at all were it not for the law of identity. (4) State the law of identity in three ways. (5) Explain the kinds of absolute identity. Illustrate by propositions and by circles. (6) Explain by word and by diagrammatical illustration relative identity. (7) Symbolize the three forms of identity. Fit words to these symbols. (8) State in three ways the law of contradiction. (9) Show by illustration that not bisects the world. (10) Explain the uses of not. (11) Prove that "John Doe is not-honest," illustrates identity and not contradiction. (12) Symbolize in three ways contradiction. Fit words to these symbols. (13) Illustrate contradictory and opposite terms. (14) Show that words with negative prefixes are not neces- sarily the contradictory of the corresponding affirmative forms. (15) State and explain the law of excluded middle. (16) Symbolize the law of excluded middle. (17) State the law of sufficient reason. Illustrate. (18) Illustrate the unity of the three primary laws of thought. 11. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Prove that the judgment is the elemental form of evolved thought. (2) What is meant by evolved thought? (3) Show that "Whatever is, is" is a statement of complete absolute identity only. (4) State incomplete absolute identity. (5) By means of one proposition state relative identity. (6) Show that incomplete absolute identity is a term mora or less illogical. (7) Show that these statements are exact expressions of relative identity : All men are some wise. Some men are some wise. 46 The Primary Laws of Thought. (8) Why is the law of contradiction so named? (9) Show that space may be bisected by drawing a circle upon the black board. (10) Show that there is a difference in meaning between "You are not honest" and "You are not-honest." (11) Is there any difference in meaning between disagreeable and not agreeable? (12) Which is the stronger term not-just or unjust? Why? (13) Give a list of words in which the contradictory forms are expressed by the ordinary prefixes. (14) Illustrate by circles the law of excluded middle. (15) Illustrate by a line-diagram the difference between con- tradictory and opposite terms. (16) Show that the province of the law of sufficient reason is physical science. CHAPTER 4. LOGICAL TERMS. 1. LOGICAL THOUGHT AND LANGUAGE INSEPARABLE. Any impression upon the mind tends to manifest itself in some form of expression. Impression which arouses thought tends to expression in the form of sym- bols. Thought and symbol go hand in hand. Expres- sion, taking the form of word-symbols, constitutes a word-language. It is commonly supposed that language is serviceable mainly in communicating one's thoughts to others, but language does service in another way which is quite as important. It tends to clarify and make definite all thought. Without a word-language thinking would lack continuity; would be vague, loose, illogical. The right use of a word-language, therefore, is a necessary adjunct to logical thought. The basic element of a word-language is the logical term. 2. MEANING OF LOGICAL TERM. A notion has been referred to as any product of the knowing mind. When we express these notions in words such expressions may be called logical terms. Definition. A logical term is a word or a group of words denoting a definite notion. Illustrations : Honesty, Chicago, tree, walking, the man who was ill, beautiful roses. This is a list of logical terms, because each word or group of words denotes a notion of some kind. It is 47 48 Logical Terms now evident that any subject or predicate with its modi- fiers constitutes a logical term. In the proposition, "The beautiful red house on the hill, owned by Mr. Jones, has burned," the term used as the subject consists of eleven words. The reader must not confuse logical terms with grammatical parts of speech. "Of" is a preposition but not a logical term, as no definite notion is indicated. 3. CATEGOREMATIC AND SYNCATEGOREMATIC WORDS. There are some words which, when used alone, denote definite notions, such as man, tree, dog, justice. On the other hand there are other words which, when used alone, do not stand for a definite notion, such as up, beautifully, a, and. Words like those in the first list are called categore- matic words, while those in the second list illustrate syncategorematic words. Definition. A categorematic word is one which forms a logical term unaided by other words. A syncategorematic word is one which must be used with other words to form a logical term. Any word or group of words which can be used as either subject or predicate of a proposition is a logical term. If the one word in question can be used as either subject or predicate of a proposition then it must be a categorematic word. If it is impossible to use the one word as either subject or predicate of a proposition then this is a sure indication that such a word is syn- Categorematic and Syncategorematic Terms 49 categorematic. For example, there is no sense in the expressions, "And is honest," "Of is not true" ; hence and and of are syncategorematic. We may conclude from this that nouns, descriptive adjectives and verbs may be categorematic words, while adverbs, prepositions and conjunctions are syncategore- matic words. 4. SINGULAR TERMS. A singular term is a term which denotes one object or one attribute. Proper nouns, when they stand for individuals, are singular terms, such as John Adams, Mississippi River, Socrates. Some proper names stand for a class of objects, as the Caesars, the Mephistopheles, the Napoleons. But when thus used they lose their character as proper names. Such names, therefore, are general terms, not singular. Common nouns may be made singular by some modify- ing word, as the first man, the pole star, the highest good, my pet dog, etc. Certain attributes which imply a oneness or a distinct individuality are singular, such as absolute justice, birds- egg blue, perfect happiness, etc. Some claim that terms like water, air, salt, etc., are singular, as they stand for one thing. This, however, cannot be if such terms admit the possibility of classi- fication as: hard water, soft water, mineral water. 5. GENERAL TERMS. A general term is one which denotes an indefinite number of objects or attributes. 50 Logical Terms Class-names are general terms, such as men, chair, tree, army, nation. Words like redness, sweetness, jus- tice, are probably general in that they denote a combi- nation of qualities or may be subdivided into kinds. The way the term is employed in the proposition should determine its singular or general nature. 6. COLLECTIVE AND DISTRIBUTIVE TERMS. A collective term is a general term which indicates an indefinite number of objects as one whole. Such words as class, crowd, army, forest, nation, are collective. A distributive term is a general term which indicates an indefinite number of objects as a whole, and also may be used to refer to each one of the group separately. Such as man, pupil, tree, book. It is easy to distinguish collective from distributive terms when we attempt to use them in the designation of individuals. Pointing to a body of troops, one may remark, "There is the regiment." But when pointing to one man in the regiment, he could hardly say, "There is the regiment." "Regiment" is therefore collective be- cause it may be used with reference to the whole body of troops but cannot be used in connection with any individual of that body. On the other hand in the sen- tence, "Man is mortal," "man" refers to the whole family of men. It also indicates any one of them. As, "This man, John Doe, is mortal." Thus "man" is distributive. The distributive term, therefore, can be used in a two- fold sense; namely, to denote the whole or to denote each. Concrete and Abstract Terms 51 It must be noted that, viewed from a different stand- point, some collective terms become distributive in na- ture. As for example in the proposition, "The army of the world is composed of able bodied men," army is used with reference to all armies. While it may be used to designate some particular army, as The American army. Collective terms have been classified as general terms. It must be borne in mind, however, that such may be made singular by some "modifying word. For example, people is a general term, but American people is a sing- ular term in that it refers to one people, being thus limited by the word American. 7. CONCRETE AND ABSTRACT TERMS. A concrete term is a term which denotes a thing; e. g., this man, that tree, John Doe, denote in each case a thing. Man and tree, denote many things. All are concrete. An abstract term is a term which denotes an attribute of a thing; e. g., whiteness, patience, squareness, are abstract terms. Such words as red, honest, just, are concrete; while redness, honesty, justice, are abstract. On first thought it might be inferred that "red" is the name of an attribute just as much as "redness." This is a mistaken thought, however, as when we use the word red we mean red something — an object which is red in color, not the color itself. For example, in saying the house is red, we refer to the thing that is red, not to the color redness. 52 Logical Terms Descriptive adjectives, because they describe things, are concrete. They do not alone name qualities of things, hence they are not abstract. 8. CONNOTATIVE AND NON-CONNOTATIVE TERMS. A connotative term is one which denotes a subject and I at the same time implies an attribute. (A subject is any- i thing which possesses attributes.) All concrete general terms are connotative because they denote subjects and at the same time stand for cer- tain attributes ; e. g., "man" denotes many subjects ; in fact, j it stands for all the men in the world; it also implies ' rationality, the power of speech, power of locomotion, etc. "Triangle" stands for all plane figures of three sides; it likewise stands for the qualities, three-sided, three-cor- nered, etc. Both "man" and "triangle" are connotative. I A non-connotative term is one which denotes a sub- ject only, or implies an attribute only. Such words as j Boston, Columbus, The Elizabeth White, denote a sub- j ject only. "Blueness," "justice," "width," imply an attri- ! bute only. All these terms are non-connotative. The \ words blue, just, wide, are connotative. "Blue," for ex- j ample, denotes all blue things, as the blue sky, the blue ; sea; at the same time "blue" implies that something pos- \ sesses the quality, blueness. Generally speaking, proper and abstract nouns are non-connotative; though such proper nouns as Mount I Washington, Mississippi River, are, no doubt, connota- i tive, as they denote an object and imply at least one attribute. In the case of Mount Washington an object Connotative and Non-Connotative Terms 53 is surely denoted, and the attribute mountainous is im- plied. Any proper noun which conveys definite infor- mation is connotative. It may be claimed that all proper nouns give information. For example, to many Boston indicates not only an object, but the qualities common to a city. In reply it may be said that "Boston" might indicate a boat, or a dog, or almost any individual object. 9. POSITIVE AND NEGATIVE TERMS. A positive term is one which signifies the possession of certain attributes; e. g., metal, man, teacher, happy, honest. A negative term is one which signifies the absence of certain attributes; e. g., inorganic, unhappy, non-metallic. Terms which have the prefix not, non, un, in, dis, etc., or the affix less, are usually considered negative. The fact that there are some exceptions to this must not be overlooked. For example, unloosed, invaluable, are positive terms. In theory every positive term has its corresponding negative; as pure, impure; organic, inorganic; metal, non-metal; good, not-good. In some instances the language does not supply the word with the negative prefix because no need of it has been felt. The only way to express the negative of such words as good, table, etc., is to prefix "not" or "non." 10. CONTRADICTORY AND OPPOSITE TERMS. (See page 38). Positive terms with their negatives have contradictory 54 Logical Terms meanings and therefore are referred to as contradictory terms. For example, honest and not-honest, metallic and non-metallic, perfect and imperfect, are contradictory terms. Such terms are mutually destructive. When we assert the truth of one we also imply the falsity of the other. If, for example, we assert that Abraham Lincoln was honest, we carry with this assertion the implication that Lincoln was not not-honest, or that any statement to the effect that he was not honest is false. Contradictory terms, when used in a sentence, illus- trate the law of excluded middle, as in the statements: "John's recitation is either perfect or imperfect." "This teacher is either just or not-just." There is no middle ground in such propositions. When contradictory terms are used in classification the whole is divided into but two classes ; e. g. : honest not-honest agreeable not-agreeable metallic non-metallic perfect imperfect pure impure organic inorganic All the men in the world are either honest or not- honest. All the substances in existence are either or- ganic or inorganic, etc. It will also be seen from this list that the contradictory of the positive form is not always indicated by using the prefix. Honest and dishonest, or agreeable and dis- agreeable, are not contradictory terms. In the case of agreeable and disagreeable, there seems to be the middle Contradictory and Opposite Terms 55 ground of absolute indifference. For example: the music of the orchestra is agreeable while the humming of the enthusiast back of me is decidedly disagreeable; but as to the noise upon the street, it is neither agreeable nor disagreeable as long practice has made me indifferent to it. When there is any doubt as to the terms being con- tradictory, the safest plan is to prefix "not" or "non" to the positive form. Terms which oppose each other but do not contradict are said to be opposite or contrary terms. The follow- ing list illustrate opposite terms : hot cold cool warm less greater wise foolish bitter sweet soft hard tall short agreeable disagreeable All these terms admit of a medium. In the case of hot or cold, for example, a substance need not necessarily be either. It may be warm or cool. Terms seem to be contradictory when it is a matter of quality, but opposite when it is a question of quantity or degree. 11. PRIVATIVE AND NEGO-POSITIVE TERMS. A privative term is one which is positive in form but negative in meaning. Such words as blind, deaf, dumb, 56 Logical Terms dead, maimed, orphaned, are privative terms, in that there is no negative prefix or suffix and yet they denote the absence of certain qualities. "Blind," for example, is positive in form, but denotes absence of sight. A nego-positive term is one which is negative in form but positive in meaning. Such terms as invaluable, un- loosed, immoral, indwell, are nego-positive because, though they have negative prefixes, yet they possess a certain positive meaning. "Invaluable," for instance, does not mean not-valuable, but very valuable. 12. ABSOLUTE AND RELATIVE TERMS. An absolute term is one whose meaning becomes in- telligible without reference to other terms. Automobile, water, tree, house, book, are absolute terms. Any of them may be made clear to a child or a foreigner with- out special reference to other terms. For example, the child will recognize from certain common marks the automobile every time he sees it. The marks of tree, house, flower, are apparent to every one. A relative term is one which derives its meaning from its relation to some other term. Parent, teacher, shep- herd, monarch, eldest, cause, commander, are relative terms. For example, in explaining the meaning of "parent" to a foreigner, reference must be made to "child." The pairs of terms thus associated are spoken of as correlatives. Parent and child, teacher and pupil, shepherd and flock, monarch and subject, eldest and youngest, cause and effect, commander and army, are correlative terms. Either one of each pair is the corre- Absolute and Relative Terms 57 late to the other, and every relative term needs its correlate to make its meaning clear. To say that a rela- tive term denotes an object which cannot be thought of without reference to some other object, is confusing, as it is quite impossible to think of any object without call- ing to mind some other object or notion. Fire calls to mind water; tree suggests shade, etc. 13. OUTLINE. Logical Terms. (1) Meaning of term. (2) Categorematic and syncategorematic words. (3) Kinds of terms. Singular terms. General terms. (a) Collective terms. (b) Distributive terms. Concrete and abstract terms. Connotative and non-connotative terms. Positive and negative terms. Contradictory and opposite terms. Privative and nego-positive terms. Absolute and relative terms. 14. SUMMARY. A logical term is a word or group of words denoting a definite notion. A singular term is a term which denotes one object or one attribute. A general term is a term which denotes an indefinite number of objects or attributes. General terms are collective or distributive. A collective term is a general term which indicates an indefi- nite number of objects considered as one whole. A distributive term is a general term which indicates an in- 58 Logical Terms definite number of objects as a whole and also may be used to refer to each one of the group separately. A concrete term is a term, which denotes a thing. An abstract term is a term which denotes the attribute of a thing. A connotative term is one which denotes a subject and at the same time implies an attribute. A non-connotative term is one which denotes a subject only or implies an attribute only. A positive term is one which signifies the possession of certain attributes. A negative term is one which signifies the absence of certain attributes. In theory every positive term has its negative. As related to each other positive and negative terms are said to be con- tradictory. If one denotes a true notion then the other denotes a false notion. Some terms oppose each other but do not flatly contradict. As related to each other such terms are said to be opposite. A privative term is one which is positive in form but negative in meaning. A nego-positive term is one which is negative in form but positive in meaning. An absolute term is one whose meaning becomes intelligible without reference to other terms. A relative term is one which derives its meaning from its relation to some other term. 15. ILLUSTRATIVE EXERCISES. (la) The words in italics are categoremaftic. (1) "Honesty is the best policy. (2) "A wise teacher never scolds." (3) "The woodcock has a long bill and eyes high up on the head." Note — If there is any doubt as to such words as never, on, etc., being syncategorematic, attempt to use them as subject or predicate of a proposition; e. g., John is never. Illustrative Exercises 59 (lb) Underscore the categorematic words in the following: (1) "Socrates was the greatest teacher of pagan times." (2) "Play is nature's way of teaching a child how to work." (3) "A man may be what he chooses if he is willing to pay the price." (2a) In the following, words enclosed in parentheses are logical terms : (1) ("All men) are (mortal.") (2) ("The law of identity) is (one of the primary laws of thought.") (3) ("Judging) is (the process of conjoining and dis- joining notions.") (2b) Indicate the logical terms in the sentences under lb. (3a) The logical characteristics of the term teacher are (1) general term, (2) distributive term, (3) concrete term, (4) connotative term, (5) positive term, (6) relative term. (3b) The logical characteristics of other terms are as follows : (1) Goodness — general, abstract, non-connotative, posi- tive, abstract. (2) Soft — general, concrete, non-connotative, positive, "hard" is its opposite, "not-soft" is its contradictory, absolute. (3) Disagreeable — general, concrete, non-connotative, "agreeable" is its opposite, "not-disagreeable" is its contradictory, nego-positive, absolute. (4) Aristotle — singular, concrete, non-connotative, positive, absolute. (5) Class — general, collective, concrete, connotative, posi- tive, relative. (3c) Give the logical characteristics of the following terms: justice, Abraham Lincoln, tree, library, America, president, prin- ciple, sympathy, dumb, nation. 16. REVIEW QUESTIONS. (1) What is the connection between logical thinking and language ? 60 Logical Terms (2) Why is man a categorematic word? (3) Why is beautifully syncategorematic? (4) Distinguish between singular and general terms. (5) Show how a collective term may be used in a distributive sense. (6) Why are the words tree and book distributive? (7) Distinguish between concrete and abstract terms. (8) Define and illustrate a non-connotative term. (9) Why are concrete general terms connotative? (10) Distinguish between positive and privative terms. (11) Why is not the word immoral negative? (12) Give the opposite of "hot." What is the contradictory of "hot"? (13) Distinguish by definition and illustration between rela- tive and absolute terms. (14) What is the correlate of the word effect? 17. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Is it possible to think independent of language? (2) May words be spoken or written without thought? Il- lustrate. (3) Are categorematic words always logical terms? (4) Must all the words of a logical term be categorematic? (5) Are pronouns and auxiliary verbs categorematic? (6) Indicate the logical connection between the terms of a proposition and the termini of a railroad. (7) Show that attribute is a broader term than quality. (8) Is the word Washington general or singular? Give reasons. (9) Make the word dog a singular term. (10) Give an illustration where the word class would not be collective. (11) "All the members of the baseball team are star players." How has the term star players been used, collectively or dis- tributive^ ? (12) Why may the term New York City be connotative to a New Yorker and non-connotative to a Patagonian? Questions for Original Thought 61 (13) So far as your present knowledge of the martyred president Abraham Lincoln is concerned, is the term, Abraham Lincoln connotative or non-connotative ? (14) Are non-connotative terms always singular? Illustrate. (15) Are singular terms always non-connotative? (16) What is the differenece in meaning between immoral and unmoral, disagreeable and not-agreeable? (17) Why is immoral a nego-positive term while unmoral is negative? (18) What is the contradictory of the opposite of wise? (19) Show that there is some ground for believing all terms to be relative. (20) Is army a relative term? If "army" were used so as to be distributive in nature would it then be general or collective? (21) Why should the pronoun be ignored by the logician? (22) Show the difference between thing and subject. (23) Argue to the effect that no term can be non-contotative. CHAPTER 5. THE EXTENSION AND INTENSION OF TERMS. 1. TWO-FOLD FUNCTION OF CONNOTATIVE TERMS. (See page 52). It has been indicated that a connotative term is one which possesses the double function of signifying a subject as well as an attribute. It may be observed here that an attribute of a notion is any mark, property or characteristic of that notion. Attribute, then, repre- sents quality, relation or quantity. By a subject is meant anything which possesses attributes. Most sub- jects stand for objects and most attributes are qualities; consequently, for the sake of simplicity, we may use subject and object interchangeably; likewise, attribute and quality. A connotative term, therefore, denotes an object at the same time it implies a quality. To illustrate: The symbol man stands for the various individual men of the world, such as Lincoln, Washington, Alfred the Great, etc., or for certain qualities like rationality, power of speech and power of locomotion. The connotative term teacher may be used to denote Socrates, Pestalozzi, Thomas Arnold, or connote such qualities as ability to instruct, sympathy, and scholarship. The term planet stands for such objects as Venus, Earth, and Mars, and for such qualities as rotation upon axis, revolution about sun, and opaque or semi-opaque bodies. In each of the 62 Two-fold Function of Connotative Terms 63 three illustrations the term is employed in the two- fold sense of denoting objects and of implying qualities. 2. EXTENSION AND INTENSION DEFINED. This double function of connotative terms furnishes an important topic for the student of logic — the Exten- sion and Intension of Terms. In short, some authorities claim that to master the extension and intension of terms is virtually to master the entire subject of logic. Though this position may be an exaggerated one, yet it tends to emphasize the importance of the topic. A term is used in extension when it is employed with reference to the objects for which the term stands. When the term triangle is used to refer to the objects isosceles triangle, scalene triangle, right triangle, it is employed in extension. A term is used in intension when it is employed with reference to the attributes for which the term stands. The term triangle is employed in intension when we use it to refer to the qualities, three sided and three angled. 3. EXTENDED COMPARISON OF EXTENSION AND IN- TENSION. A connotative term seems to be two dimensional — it has extent or length and intent or depth. "Extension consists of the things to which the term applies," while "intension consists of the properties which the term implies." Extension is quantitative, while intension is qualita- tive. An extensional use means to point out or num- 64 The Extension and Intension of Terms ber objects, while an intensional use means to describe by naming qualities. To name is to use a term in ex- tension — to describe is to use a term in intension. To divide a term into its kinds we must regard it in an extensional sense ; e. g., the term man may be divided into Caucasian, Mongolian, Malay, Ethiopian, American Indian. To define a term we must regard it in an intensional sense; e. g., man is a rational animal. Etymologically considered extension means to stretch out, intension, to stretch within. To use a term exten- sionally one must look out. To use a term intensionally one must look in. In attempting to use a term in extension we may ask ourselves the question, "What are the kinds?" or "To what objects may the term be applied?" While if we would use a term in intension the question should be, "What does it mean?" or "What are the qualities?" Let us, for example, use the term metal in the two senses, first in extension, second in intension. Question: To what objects may the term metal be applied? An- swer: Metal may be applied to the objects silver, gold and iron. Thus has metal been employed in extension. Question: What are the qualities of metal ? Answer: The qualities are element, metallic lustre, good conductor of heat and electricity. Thus has metal been used in intension. Note. Since an attribute is anything which belongs to a subject, then the parts of a subject must be classed as attributes. Hence, a term is used intensionally when reference is made to its parts. List of Connotative Terms 65 4. A LIST OF CONNOTATIVE TERMS USED IN EXTEN- SION AND INTENSION. The Term. Extensional Use. Intensional Use. [roots, branches, trunk, tree. maple, oak, beech. «j or (woody-fiber, sap, bark. house. stone, brick, cement, foundation, frame-work, roof. dog. shepherd, fox terrier, carnivorous, quadruped, bull. propensity to bark. book. textbook, dictionary, cover, leaves, binding, encyclopaedia. quadrilateral, trapezium, trapezoid, four sides, four angles, parallelogram. limited plane. logic. theoretical logic, ap- science of thinking, art of plied logic, educa- right thinking, treats of tional logic. laws of thought. star. Sirius, Arcturus, heavenly body, gives light Vega. and heat, twinkles. force. gravitation, molecular, [produces motion atomic. -{changes motion (^destroys motion. term. general, singular, word or group of words, non-connotative. definite idea. government. monarchy, aristocracy, body of people, estab- democracy. lished form of law, banded together for mu- tual protection. bird. crow, robin, pigeon, biped, feathered, winged. 66 The Extension and Intension of Terms 5 OTHER FORMS OF EXPRESSION FOR EXTENSION AND INTENSION. Extension. Intension. comprehension content extent intent breadth depth denotation connotation application implication Formerly the words extension and intension were ap- plied to concepts while denotation and connotation were applied to terms representing the concepts, but now the words are interchangeable. Denotation, the noun, and denote, the verb, signify, etymologically, a marking off. To denote is to mark off or indicate the objects or classes of objects for which the term stands. Connotation, the noun, and connote, the verb, signify to mark along with. To connote is to mark along with the object, its attributes. The terms which should be remembered are extension f intension or [» and *J or denotation J I connotation 6. LAW OF VARIATION IN EXTENSION AND INTEN- SION. It has been noted that the intension of a term has reference to its qualities while extension considers its application to various objects. It may be wise to ex- periment with the extension and the intension of certain terms as types with a view of ascertaining how the two ideas are related to each other. For the sake of defi- niteness let us make use of the following scheme : The Law of Variation in Extension and Intension 67 Intensional (1) four sides (2) parallel sides (3) equal sides (4) right angles (1) four sides (2) parallel sides L (3) equal sides I. common qualities of common qualities of (1) four sides 1 common (2) parallel sides \ qualities of (1) four sides ( 1 ) heavenly body common quality of II. ) common j quality of (1) heavenly body ) common (2) self-luminous ( qualities of Extensional } (1) squares (1) squares (2) rhombs (1) squares (2) rhombs (3) rectangles (4) rhomboids (1) squares (2) rhombs (3) rectangles (4) rhomboids (5) trapezoids (6) trapeziums (1) nebulae (2) fixed stars (3) sun (4) comets (5) meteors (6) moon (1) nebulae (2) fixed stars (3) sun (4) comets 68 The Extension and Intension of Terms common qualities J (i) (2) (3) nebulae fixed stars sun common *" qualities of common qualities of | (i) (2) nebulae fixed stars (i) nebulae (i) heavenly body (2) self-luminous (3) fixed (1) heavenly body (2) self-luminous (3) fixed (4) twinkle (1) heavenly body (2) self-luminous (3) fixed (4) twinkle (5) foggy In considering the first illustration we observe that as the number of qualities is decreased, the number of ob- jects increases. While in the second example as the qualities are increased, the number of objects decreases. It would appear from this that the intension and exten- sion of a term are inversely related to each other. As the one increases the other decreases and vice versa. It is customary to state this relation in the form of a law known as the law of variation. "As the intension of a term is increased its extension is decreased and vice versa/' or the extension and intension of a term vary in an inverse ratio to each other. To further illustrate: this book refers to a large number of objects; add to the qualities of book those of text book and the application is much reduced. In other words as we increase the intension, the extension is diminished. Increase the intension further by adding the quality English text book and the extension becomes still less. Two Important Facts in the Law of Variation 6g 6a. TWO IMPORTANT FACTS IN THE LAW OF VARIA- TION. In studying the law of variation two facts are espe- cially evident, (i) The law applies only to a series of terms representing notions of the same family. The ex- tension and intension of "text book," for example, could not be compared with the extension and intension of "house" as they belong to a different class of words, the genus of text book being book, while the genus of house is building. To illustrate the law of variation, determine upon any class name, then think of its proximate genus (the next higher-up class to which it belongs). Continue this till the series is sufficiently complete to illustrate the law. Or proceed in the opposite direction. That is, after se- lecting the class name think of the next lower term in the class and thus continue till series is complete. Il- lustration: The class name man is determined upon; the proximate genus of man is biped, the proximate genus of biped is animal, and so on. Or thinking downward: a proximate species of man is white man, of white man, European, etc. Thus the series: animal biped man white man European (2) As a second fact: the increase and decrease is not a mathematical one. That is, by doubling the ex- yo The Extension and Intension of Terms tension the intension is not halved. Or if the intension is decreased by one quality the extension is not neces- sarily increased by one object. Thus "man" stands for one billion seven hundred million beings or objects. De- crease the intension of "man" by the one quality of ra- tionality and the extension would include all bipeds — many billion objects. 6b. THE LAW OF VARIATION DIAGRAM MATICALLY ILLUSTRATED. In a general way lines may be used to represent the variation in extension and intension. For example: we may let a line an inch long represent the extension of man, one two inches long represent the extension of biped, three inches long represent the extension of animal, etc. While on the other hand, if a line an inch long represents the intension of man, a line one-half inch long may be used to represent the intension of biped, one a quarter of an inch long to represent the intension of animal, etc. The following illustrates this scheme in connection with another series of words: Extension Intension barn building structure object ' In the foregoing scheme building refers to a greater number of objects than bam, hence the line under exten- sion representing building should be longer than the line for barn. Likewise structure, referring to a greater num- ber of objects than building, is represented by a longer Law of Variation Diagrammatic ally Illustrated Ji line. Thus when the series is viewed from top to bottom a gradual increase in extension is noted. Giving atten- tion to the intensional use of the series we note that building has fewer qualities than barn, structure fewer than building and object fewer than structure. There- fore, from top to bottom, the intension of the terms gradually decreases. The variation may be made still more apparent if triangles are used, one triangle being placed upon the other, vertex to base, like the following: EyzleriiSi "Biped" is written near the base or in the broadest part of the extension triangle because it denotes the greatest number of objects, and is, therefore, broadest in exten- sion. "Man" occupies a narrower part of the extension triangle because it refers to fewer objects or is narrower in extension than "biped." "Arnold" occupies the nar- rowest part of the extension triangle because it is the nar- rowest in extension. On the other hand "Arnold" occu- pies the broadest part of the intension triangle because in- tensionally it possesses more qualities than the others, *]2 The Extension and Intension of Terms while "biped," having the least depth in intension or pos- sessing the fewest qualities, occupies the narrowest por- tion of the intension triangle. 7. OUTLINE. The Extension and Intension of Terms. 1. Two-fold Function of Connotative Terms. 2. Extension and Intension Defined. 3. Extended Comparison of Extension and Intension. 4. A List of Connotative Terms used in Extension and Intension. 5. Other Forms of Expression for Extension and Intension. 6. Law of Variation in Extension and Intension. 6a. Two Important Facts in the Law of Variation. 6b. The Law of Variation Diagrammatically Illustrated. 8. SUMMARY. 1. Connotative terms are used in a two-fold sense : first, to denote objects;, second, to imply qualities. 2. A term is used in extension when it is employed with reference to the objects for which the term stands. A term is used in intension when . it is employed with reference to the qualities for which the term stands. 3. The answer to either of the following questions will lead one to use any term in extension: First, what are the kinds? or second, to what objects may the term be applied? The answer to either of the following questions will lead to the use of any term in intension : First, what does it mean ? or second, what are the qualities? 4. To illustrate extension and intension it is best to use the class-names in every day speech. 5. The word denotation is commonly used for extension and connotation for intension. 6. "As the intension of a term is increased its extension is decreased and vice versa," is a statement of the Law of Vari- ation in the extension and intension of terms. 6a. The law of variation applies only to a series of terms representing notions of the same class or family, the words Summary 73 being arranged in a species-genus order. The increase and de- crease of the extension and intension of a series is not propor- tional. 6b. The law of variation is best explained by using two triangles, one super-imposed upon the other vertex to base and base to vertex. 9. ILLUSTRATIVE EXERCISES. la. Employ the following terms in extension — European, flower, term, truth. ("Russian [lily European-] Englishman nower-j rose [Scotchman (pansy [singular Truth has no extension. Since term-J distributive it refers to a quality only, it [collective is non-connotative. lb. Employ the following in extension — grain, rock, soil, precious stone. 2a. Use intensionally bird, quadruped, letter, John. [two feet ("four feet bird-! ability to fly quadruped-/ back bone [^feathers . I hairy covering ("heading John has no intension. Since letter-jbody it refers to an object only, it [complimentary close is non-connotative. 2b. Use the following in intension — word, table, purity, gov- ernment. 3a. The use of a term in extension follows when attempting to answer two questions: First, what are the kinds? Second, to what objects may the term be applied? Make application of this with reference to the term man. 1. What are the kinds of men? Caucasian, Malay, Mongo- lian, Ethiopian, Redman. 2. To what objects does the term man refer? George Wash- ington, Chas. Hughes, John Smith. 74 The Extension and Intension of Terms In both 1 and 2 the word man is used to denote objects, hence it is employed in extension. 3b. Use the term vegetable in extension by answering the two questions in 3a. 4a. Decrease one by one the qualities of some common object with a view of noting how when the intension is decreased the extension is increased. Intension binding leaves cover printed matter designed for instruction instruction in arithmetic binding leaves cover printed matter designed for instruction binding leaves cover printed matter binding leaves Extension school arithmetic school arithmetic school grammar school speller, etc. "school arithmetic school grammar school speller, etc. encyclopaedia novel 'school arithmetic school grammar school speller, etc. encyclopaedia novel note book 4b. With a view of noting how when the intension is de- creased the extension is increased, decrease one by one the common qualities of peach tree. 5a. In the following series what word could be substituted for "mammal" and why? Being, organized being, animal, vertebrate, mammal. Answer: Fish, reptile, or bird; because there are at Illustrative Exercises 75 least seven classes of animals which belong to the vertebrate fam- ily, any one of which could be used to complete the series. 5b. Form a series of which "Baldwin apple" has the narrow- est extension. What terms may be substituted for "Baldwin apple ?" 6a. In a series of which "pupil" is a member show that the increase and decrease is not proportional. The series: logic pupil, pupil, youth, human being, being. In decreasing the inten- sion of "logic pupil"- by dropping the one quality, logic, the ex- tension is made larger by many more than one, as "pupil" repre- sents many more objects than "logic pupil." Therefore, the in- crease is not in proportion to the decrease. 6b. In a series in which "ruler" appears, show that the in- crease and decrease is not proportional. 7. From the following list select the proper words of the series; arrange them; draw and name the triangles: Caesar, brute, man, Roman, American, biped, sensuous being, animal, individual. 10. REVIEW QUESTIONS. 1. What is a connotative term? Illustrate. 2. Which is the broader term, quality or attribute? Why? 3. When is a term used in extension? 4. Use the term triangle in intension. 5. As an aid to using a term in extension or intension what questions may one ask himself? 6. By asking these questions use the term clock in both ex- tension and intension. 7. By experimenting with the qualities of a rectangle show that as the intension is decreased the extension is increased. 8. Write a list of five connotative terms. Prove that they are connotative by illustrating their extension and intension. 9. The term metal < connotes ( su ch qualities as element, metal- lic lustre, conductor of heat and electricity. In the foregoing which of the two words following the brace should be used? Give reasons. 10. State the law of variation in two ways. y6 The Extension and Intension of Terms 11. As one studies the law of variation what two facts are especially evident? Explain fully. 12. For the purpose of illustrating the law of variation form a series of which desk is a member. Draw and name the tri- angles. 11. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. 1. Which is the broader term, subject or object? Prove it. 2. If a term like Caesar is given extension does it become a general term? Why? 3. Using "man" as a member of each, arrange at least three different series. 4. Why may it be said that a connotative term is two dimen- sional ? 5. Is there a word which has a broader extension than "being"? Why? 6. Prove that youth has less intension than human being. 7. Devise a series of words in which the variation is propor- tional. 8. Advance arguments supporting the hypothesis that the term John has neither extension nor intension. 9. Suggest arguments to prove that "George Washington" has both extension and intension. CHAPTER 6. DEFINITION 1. IMPORTANCE. To be clear, cogent,' concise and consistent is to be logical. Reference has been made to a striking tendency on the part of writers and speakers to use words loosely. It is a noticeable fact that scholars generally aim to be profound rather than clear, philosophical rather than' pointed. In the use of text books more or less pedagogical these are the common complaints : "I don't understand what he means" or "You have to read so much to get so little." This condition gives to the topic of definition a prominence which cannot be overlooked by those who are seeking the truth; because the definition is the clear- est, briefest and altogether the most satisfactory way of describing an idea. Likewise the habit of defining any doubtful term reduces to a minimum the possibility of misunderstanding. The subject must appeal strongly to the instructor, as he, above all others, should make his work stand for clearness, pointedness and continuity. 2. THE PREDICABLE8. A predicable is a term which can be affirmed or predi- cated of any subject. In the proposition, "A man is a rational animal," the term "rational animal" is a pred- 77 yS Definition icable, because it can be affirmed of the subject man. To gain a clear knowledge of the definition it is quite necessary to understand the five predicables which we shall consider in the following order : 1. Genus. 2. Species. 3. Differentia (difference). 4. Property. 5. Accident. (1) Genus and (2) Species. Genus and species are relative terms and can best be denned together. A genus is a term which stands for two or more sub- ordinate classes. A species is a term which represents one of the sub- ordinate classes. The genus may be subdivided into species ; the species together form the genus. . To illustrate: The term man stands for five sub- ordinate classes or species, as white, black, brown, yellow and red. "Man" is, therefore, a genus, while "white man" and "black man," etc., are species. The term "polygon" is a genus with reference to "trigon," "tetragon," "penta- gon," etc., while "trigon" is a species of "polygon." Any given genus may be a species of some higher class. That is, "man," which is a genus with reference to the kinds of men, is a species of the higher class "biped," while "biped" is a species of "animal," "animal" a species of "organized being," "organized being" of "material being," "material being" of "being." But here The Predicables 79 we stop, as there is no higher grade to which "being" can be referred. This highest genus takes the name of summum genus. Similarly any given species may be a genus of some lower class. "White man," for example, which is a spe- cies of "man," is a genus of "American," Englishman," "German," Frenchman," etc. "American" is a genus of "New Yorker," "Californian," etc., while "New Yorker" is s a genus of "Smith of Jamaica." This last term is an in- dividual and cannot be subdivided. It represents the lowest possible species and is referred to in logic as infima species. It is obvious that the highest genus cannot become a species, neither can the lowest species become a genus. Proximate Genus. The proximate genus is the next class above. To illus- trate: "Animal" is a genus of "man," but "biped" is the proximate genus of "man." "Quadrilateral" is the genus of "square," but "rectangle" is the proximate genus. The next class above "trigon" is polygon not figure. Hence "polygon" is the proximate genus of "trigon." Genus and Species of Natural History. In natural history the following terms are used to de- note the various grades of kinship in any scheme of classification: (1) kingdom, (2) class, (3) order, (4) family, (5) genus, (6) species, (7) variety, (8) the in- dividual thing. Here "genus" and "species" are absolute not relative and occupy a fixed place in the scheme, while from a logical viewpoint any of the grades indi- cated between the lowest and highest would be the species 80 Definition of the next higher grade or a genus of the next lower; e. g., order is a species of "class," while it is the genus of "family." Genus, a Double Meaning. We recall that any class name or genus has a double use, extensional and intensional. When considered from the standpoint of its extension, a genus represents a group of objects or is mathematical in its application, but when used in an intensional sense it represents a group of qualities or is logical in its application. Considered extensionally the genus refers to a larger number of objects than the species. But when viewed intensionally the species refers to more qualities than the genus. This was made clear when discussing the law of variation in the extension and intension of terms. (3) Differentia. The differentia of a term is that attribute which dis- tinguishes a given species from all the other species of the genus. It has been observed that the species refers to more qualities than the genus. In fact, it represents all the attributes of the genus plus those which distinguish the particular species from the other species of the genus. These additional qualities are the differentiae of the particular species. To Illustrate: The attribute which distinguishes man from the other bipeds of the world is his rationality. That which dis- tinguishes the rectangle from the other parallelograms The Predicables 81 is its four right angles. The attributes rationality and right angles are differentiae. (4) Property. A property of a term is any attribute which helps to make the term what it is. Thus "consciousness" is a property of man, "binding" a property of book, "angles" a property of triangle. Deprive the terms of these attri- butes and their true nature is altered. A differentia is a property according to the foregoing definition. However, Jevons defines "property" as "Any quality which is common to the whole of a class, but is not necessary to mark out the class from other classes." This viewpoint excludes "differentia" from the notion of prop- erty. The difference in opinion is of slight importance. (5) Accident. An accident of a term is any attribute zvhich does' not help to make the term what it is. It may indif- ferently belong or not belong to the term. Deprive a term of an accident and the nature of the term remains unchanged. Thus, a teacher's position, a man's watch, the fact that the angle is one of 80 ° are all accidents. It is obvious that a property is a constant attribute while an accident is variable. This gives to the former a universal validity while the latter is more or less shifting and uncertain. All triangles must have three angles (property) while the value of each angle in degrees (accident) admits of unlimited variation. Some logicians divide accidents into separable and inseparable. A man's hat would be a separable accident while his birthplace would be an inseparable accident. 82 Definition Five Predicables Illustrated. In the following brief descriptions the five predicables are designated: (species) (genus) (differentia) (1) This rectangle is a parallelogram with four right angles (accident) its longer sides being ten inches. (species) (differentia) (prox. genus) (2) This man is a rational biped with the (property) (accident) power of locomotion and a ruddy complexion. (species) (genus) (differentia) (property) (3) A trigon is a polygon of three sides and three angles, (accident) the sum of the angles being equal to two right angles. 3. THE NATURE OF A DEFINITION. It will be remembered that an individual notion is a notion of a single thing or attribute, while a general notion is a notion of a class of things or a group of at- tributes. A term which represents an individual notion is known as a singular term, while a term which stands for a general notion is referred to as a general term. One may explain the meaning of a singular term which stands for one thing by enumerating its various attri-, butes. For example, such attributes as a piercing bark, a yellow color, intelligent, companionable, a strong liking for sweetmeats, explain the meaning of the singular term "Fido." Likewise we may explain the meaning of a gen- eral term by enumerating its attributes. To illustrate: The Nature of a Definition 83 power of speech, rationality, ability to laugh, etc., explain the meaning of the general term man. The explanation of the singular term fits only Fido. There is probably no other dog in the world just like Fido. But the explana- tion of the general term man may be applied to all men. A brief enumeration of attributes which may be ap- plied to a class of things often takes the form of a defi- nition. The word definition comes from the word definire, meaning to limit or fix the bounds of. A definition, then, consists of the enumeration of -such attributes as distinguish a term from all other terms. In this sense it would seem that the singular term Fido, as well as the general term man, admits of definition, but it is usual for logicians to confine definition to the general term. Singular terms may be described; general terms, defined. A Definition of> Definition. A definition of a term is a statement of its meaning by enumerating its characteristic attributes. That the enumeration must be in terms of its dis- tinguishing or characteristic attributes is implied in the derivation of the term definition. The attributes must establish limits or bounds, just as a line fence limits a land owner's possessions. To indicate that man is a crea- ture possessing the power of locomotion, sense of sight and ability to eat, is surely not a definition, as the marks are not characteristic of men only. These attributes set no boundary between man and horse, consequently the statement is a faulty description of man, not a definition. 84 Definition But when the enumeration includes such attributes as power of speech, rationality and ability to laugh, then does the description become a definition. To put it differently : A definition is a description of a term by means of its dis- tinguishing attributes. This statement may be considered a definition of man, though somewhat faulty : "A man is a creature who is rational and who possesses the power of speech and ability to laugh." 4. DEFINITION AND DIVISION COMPARED. We have learned that general terms when connotative may be used extensionally or intensionally. A definition indicates the intensional nature of a term, while a statement which points out the extensional na- ture of a term is known as logical division. More briefly : A definition is an intensional statement of the nature of the term, while logical division is an extensional state- ment of the nature of the term. To illustrate: The following statements are defini- tions : (i) A dog is a domesticated quadruped of the genus canis and given to barking. (2) A quadrilateral is a rectilinear figure of four sides. (3) Soil is a substance composed of pulverized rock and decayed vegetable matter in which plants will grow. The following represent Logical Division : (1) Dogs are divided into hounds, terriers, bull, etc. Definition and Division Compared 85 (2) The kinds of quadrilaterals are trapeziums, trapezoids and parallelograms. (3) The various soils are loam, sand, clay, muck, etc. 5. THE KINDS OF DEFINITIONS. Generally speaking there are three kinds of definitions, namely, (1) Etymological, (2) Descriptive, (3) Logical. 1 (1) An etymological definition is one based upon the derivation of the term. This kind of a definition, which gives merely the mean- ing of the symbol, is sometimes called a nominal or verbal definition; while a real definition is regarded as one which gives the meaning of the notion for which the sym- bol stands. The modern logician is inclined to ignore this classification on the argument that to make a distinction between a symbol and the notion it symbolizes is simply to misunderstand the relation which exists between them. If the definition does not agree with the thing then it cannot correctly explain the term which represents the thing. Define correctly the term and one has defined correctly the notion signified by the term. The attributes of a term may be separated into three classes: differentia, property and accident. It would ap- pear possible, therefore, to define a term by enumerating the accidents only or by enumerating the properties, or, finally, by stating the differentiae. But if the enumera- tion is confined to accidents the chances are that the state- ment will be a description, not a definition, as accidents are seldom sufficiently characteristic to determine the * Hyslop's Elements of Logic (1901), page 100. 86 Definition boundaries of a term. This leaves open two distinct ways of defining a term: First, by naming the properties or properties and accidents only; second, by stating the dif- ferentiae only. The former kind is the so-called descrip- tive definition, while the latter is the logical. (2) A descriptive definition of a term is a description of its nature by means of its properties and accidents. (3) A logical definition of a term is a description of its nature by means of its digerentice. The Three Kinds of Definitions Illustrated and Compared. Etymological Definition of Trigon. A trigon is a figure of three corners. Descriptive : A trigon is a figure which has three sides and three angles, the sum of the latter being equal to two right angles. Logical : A trigon is a polygon of three angles. It is seen that an etymological definition is simply a root-word analysis. In' the case of trigon, the prefix comes from the Greek, meaning three, while the root-word comes from the Greek meaning corner. The descriptive definition of trigon names the proper- ties, "three sides and three angles" (differentiae) and the accident, "the sum of the angles of which equals two right angles." The logical definition of trigon simply states the proxi- mate genus, "polygon," and the differentia, "three angles." When Definitions Are Serviceable 87 6. WHEN THE THREE KINDS OF DEFINITIONS ARE SERVICEABLE. The etymological definition is helpful in furnishing a cue for remembering the descriptive and logical defini- tions. It also leads to precision of expression — the right word in the right place. Here is where the knowledge of a foreign language, particularly Latin, is helpful. The descriptive definition is best adapted to the child- mind. Children think in the large ; are not given to hair- splitting discriminations, and, therefore, many character- istic marks must be mentioned in order to insure a mastery of the content. With children the logical defini- tion is often too brief to be clear. For example, it is easy to see which of the following definitions would be better adapted to the child-mind. Logical: A square is an equilateral rectangle. Descriptive: A square is a figure of four equal sides and four right angles. The logical definition may be introduced to the student of the secondary school. Few exercises are better adapted to the development of powers of discrimination and precision than practice in defining logically the common terms of every-day life. For example: "A book is a pack of paper-sheets bound together." "A chair is a piece of furniture with back and seat, designed for the seating of one person." "A lead pencil is a cylindrical writing implement with lead through the center." "A door is an obstacle designed to swing in and out to open and close an entrance." "An eraser is an implement made to rub out written or printed char- acters." 88 Definition These definitions, coming from training school stu- dents, are not above criticism, yet they illustrate the point in hand. 7. THE RULES OF LOGICAL DEFINITION. Five rules summarize the requirements to which a logical definition must conform. First Rule. A logical definition should state the essential attributes of the species defined. This means that a logical definition should contain the species, the proximate genus and the differentia. As the terms species, genus and differentia have been explained, it will be sufficient to briefly illustrate this rule. Logical According to the First Rule. species genus differentia (1) A bird is a biped with feathers. species genus differentia (2) A mascot is a person supposed to bring good luck, species genus differentia (3) Religion is a system of faith and worship, species genus differentia (4) A moonbeam is a ray of light from the moon. Illogical According to the First Rule. (i) A man is a rational animal. ("Biped" is the proximate genus, not "animal.") The Rules of Logical Definition 89 (2) A connotative term always denotes both an ob- ject and an attribute. (No genus.) (3) A trigon is a polygon. (No differentia.) (4) It is a term which denotes an indefinite number of objects or attributes. (No species.) The Foregoing Illogical Definitions Made Logical. (1) A man is a rational biped. (2) A connotative term is a term which denotes both an object and an attribute. (3) A trigon is a polygon of three angles. (4) A general term is a term which denotes an indefi- nite number of objects or attributes. Second Rule. A logical definition should be exactly equivalent to the species defined. This means that the species must equal the genus plus the differentia or the subject and predicate of the definition must be co-extensive — of the same bigness. The subject must refer to the same number of objects as the predicate. A man upon the witness stand makes the declaration that he will testify to the truth, the whole truth and nothing but the truth. A logical definition must contain the species, the whole species and nothing but the species. If the definition does not include all the species, it is too narrow; while on the other hand, if it includes other species of the genus it is too broad. go Definition An excellent test of this second requirement is to inter- change subject and predicate. If the interchanged prop- osition means the same as the original then the conditions have been met. To illustrate: Original — A trigon is a polygon of three angles. Interchanged — A polygon of three angles is a trigon. The very best way of making the definition conform to this rule is to put to oneself these three questions: i. Does it include all of the species? 2. Does it exclude all other species of the genus? 3. Has it any unnecessary marks ? To exemplify: Let us ask the three questions rela- tive to the following logical definitions : (1) A parallelogram is a quadrilateral whose oppo- site sides are parallel. (2) A bird is a biped with feathers. Questions: ( 1 ) Does the definition include all the parallelograms ? Yes. Does it exclude all other quadrilaterals? Yes. Are there any unnecessary marks ? No. (2) Does it include all birds? Yes. Does it exclude all other bipeds ? Yes. Any unnecessary marks? No. Illogical According to the Second Rule. (1) A man is a vertebrate animal. (Too broad. Does not exclude other species of the genus, such as horses, dogs, etc.) (2) A barn is a building where horses are kept. (Too narrow. Does not include all of the species, such as cow barn.) The Rules of Logical Definition 91 (3) An equilateral triangle is a triangle all of whose sides and angles are equal. (Equal angles is an unnecessary mark.) The Foregoing Definitions Made Logical. (1) A man is a rational biped. (Proximate genus.) (2) A barn is a building where horses and cattle are kept and hay and grain are stored. (3) An equilateral triangle is a triangle all of whose sides are equal. Third Rule. A definition must not repeat the name to be defined nor contain any synonym of it. A violation of this rule is known as "a circle in de- fining" ( cir cuius in definiendo ) . There are some exceptions to this rule, as in the case of compound words and a species which takes its name from its proximate genus. To say that a hobby- horse is a horse, or that an equilateral triangle is a tri- angle, is not only allowable but necessary, that the proxi- mate genus may be used. The follozving definitions are illogical according to the third rule: ( 1 ) A teacher is one who teaches. (2) Life is the sum of the vital functions. (3) A sensation is that which comes to the mind through the senses. Fourth Rule. A definition must not be expressed in obscure, figurative or ambiguous language. 92 Definition A violation of this rule is referred to in logic as "defin- ing the unknown by the still more unknown" (ignotum per ignotius). It is known that the purpose of definition is to make clear some obscure term, consequently unless every word used is understood the chief aim of the definition has been defeated. From this it must not be inferred that all definitions should be free from technical terms. Such a restriction would make the defining of many terms unsatisfactory and in a few cases practically impossible. To the student of evolution the following definition by Spencer is intel- ligible, while to the uninitiated it would appear obscure : "Evolution is a continuous change from an indefinite, incoherent homogeneity to a definite coherent heterogene- ity through successive differentiations and integrations. " This rule insists upon simple language when it is pos- sible to use such in giving an accurate and comprehensive meaning to the term defined. Illogical Definitions According to the Fourth Rule. (i) "A net is something which is reticulated and decussated, with interstices between the intersections." Dr. Johnson. (2) "Thought is only a cognition of the necessary relations of our concepts." (3) "The soul is the entelechy, or first form of an organized body which has potential life." Aristotle. Fifth Rule. When possible the definition must be affirmative rather than negative. The Rules of Logical Definition 93 The fact that there are a considerable number of terms which admit of a negative definition only, takes from the force of this rule. Such terms as deafness, inexpressible, infidel and the like can best be defined negatively. It likewise happens that when words are used in pairs it is expedient to define one affirmatively and the other negatively. Recall, for example, the definitions of rela- tive and absolute terms : "A relative term is one which needs another term to make its meaning clear." "An absolute term is one which does not need another term to make its meaning clear." Illogical Definitions According to the Fifth Rule. (1) A gentleman is a man who is not rude. (2) An element is a substance which is not a com- pound. (3) An univocal term is a term which does not have more than one meaning. 8. TERMS WHICH CANNOT BE DEFINED LOGICALLY. A logical definition insists upon a proximate genus and differentia. But as there is no genus higher than the highest genus (summum genus) then surely such cannot be defined logically. The words being and thing illus- trate terms of this class. Moreover, it is impossible to give a satisfactory definition of an individual (infima species) as no attributes can be mentioned which will dis- tinguish definitely and permanently the individual from others of the class. We may perceive the attributes but not those that are possessed solely by the individual. To say that Abraham Lincoln was a man who was simple 94 Definition and honest is not a definition, as other men have had the same characteristics. Again there are a few terms such as life, death, time and space which cannot be defined satisfactorily. These terms seem to be in a class by themselves or of their own genus (sui generis). Since a definition of a term is a brief explanation of it by means of its attributes, it follows that collective terms and terms standing for a single attribute are in- capable of definition. Such terms as group, pain, attri- bute, belong to this class. We may say, then, that there are some terms too high, some too low and some too peculiar to come within the province of logical definition. In short, "summum genus," "infima species" and "sui generis" are incapable of defi- nition. 9. DEFINITIONS OF COMMON EDUCATIONAL TERMS. (i) Development is the process whereby the latent possibilities of an individual are unfolded or the invisible conditions of a situation are made apparent. Development means expansion according to principle, while unfolding may or may not involve a principle. (2) Education is the process employed in developing systematically, symmetrically and progressively all of the capabilities of a single life ; or (3) Education is the process of modifying experience in order to make the life as valuable as it ought to be. (4) Teaching is the art of occasioning those activities which result in knowledge, power and skill. Definitions of Common Educational Terms 95 It is the duty of the true teacher to inspire the child to activity along right lines. Through his own activity the child shapes his inner world which is sometimes termed character. Knowledge is anything known, power is ability to act. skill is a readiness of action. (5) Instruction is the art of occasioning those activi- ties which result in knowledge. Instruction develops the understanding; teaching de- velops character. (6) Training is the occasioning of those activities which, by means of directed exercise, result in power and skill. Training and education are not interchangeable. Train- ing implies an outside authority, while education, which involves inner development, may proceed without super- vision. (7) Knowledge is anything acquired by the act of knowing. (8) Learning is the act of acquiring knowledge or skill. (9) Instruction, training, teaching, learning and edu- cation all involve activity. Instruction arouses activity which results in knowledge ; training directs activity which produces power and skill ; teaching includes both instruction and training. Learning is an activity which results in knowledge and skill, while education is a developing process which involves all the others. (10) A science is knowledge classified for the pur- pose of discovering general truths. g6 Definition ( 1 1 ) An art is a skillful application of knowledge and power to practice. "A science teaches us to know, an art to do." (12) A fact is a single, individual, particular thing made or done. A truth is general knowledge which exactly conforms to the facts. A truth may be a definition, rule, law, or principle. (13) A fact as opposed to hypothesis is an occurrence which is true beyond doubt. An hypothesis is a supposition advanced to explain an occurrence or a group of occurrences. A theory is a general hypothesis which has been partly verified. (14) Theory as opposed to practice means general knowledge, while practice involves the putting into opera- tion one's theories. (15) A fact as opposed to phenomenon is something accomplished. A phenomenon is something shown. (16) A method-whole is any subdivision of the mat- ter for instruction which leads to a generalization. (17) Method is an orderly procedure according to a recognized system of rules and principles. As the term is commonly used it includes not only the arrangement of the subject matter for instruction but the mode of presenting the same to the mind. (18) Induction is the process of proceeding from the less general to the more general. Deduction is the process of proceeding from the more general to the less general. Definitions of Common Educational Terms 97 (19) The terms induction and deduction may have reference to forms of reasoning or to methods of teach- ing. The inductive method is the method of deriving a gen- eral truth from individual instances. The deductive method is the method of applying a general truth to individual instances. The inductive method is objective, while the deductive method is subjective. Induction is the method of dis- covery; deduction is the method of instruction. (20) Analysis is the process of separating a whole into its related parts. Synthesis is the process of uniting the related parts to form the whole. (21) The analytic method is the method of proceed- ing from the whole to the related parts. The synthetic method is the method of proceeding from the related parts to the completed whole. (22) Analysis and synthesis deal with single things, while induction and deduction are concerned with classes of things. (23) The complete method consists of three elements : (1) induction, (2) deduction, (3) verification or proof. When the emphasis is placed on the inductive phase, the complete method is sometimes termed the develop- ment method. 10. OUTLINE. Definition. (1) Importance. 98 Definition (2) The Predicables. Genus — species — summum genus — infima species. Proximate Genus. Genus and Species of Natural History. Genus, Double meaning of Differentia. Property. Accident. Separable, Inseparable. (3) Nature of Definition. (4) Definition and Division Compared. (5) The Kinds of Definitions. (1) Etymological. (2) Descriptive. (3) Logical. Three Kinds Illustrated and Compared. (6) When the Three Kinds are Serviceable. (7) The Rules of Logical Definition. (1) Essentials. (2) Same size. (3) Do not repeat. (4) Unambiguous. (5) Language affirmative. (8) Terms Which Cannot be Defined Logically. Summum genus. Infima species. Sui generis. Collective terms. A single attribute. 11. SUMMARY. (1) To be logical one must acquire the habit of accurate definition. This topic ought to appeal strongly to the school teacher, who should above all others make his work stand for clearness, pointedness and continuity. (2) A predicable is a term which can be affirmed or predi- cated of any subject. Summary 99 The five predicables are Genus, Species, Differentia, Property and Accident (1) A Genus is a term which stands for two or more sub- ordinate classes. (2) A Species is a term which represents one of the sub- ordinate classes. The proximate genus of a species is the next class above the species, while the summum genus is the highest pos- sible class in any graded series of terms. The lowest class is the infima species of that series. The lowest class may be individual. In natural history genus and species are not relative terms, but absolute, having a fixed place in the series of gradations. The term genus possesses a double meaning: it may be used to represent objects (extensionally) or qualities (intensionally). (3) The differentia is that attribute which distinguishes a given species from all the other species of the genus. (4) A property of a term is any attribute which helps to make that term what it is. Differentia is a property according to definition. Some logicians would not include the differentia in the content of the term property. (5) An accident of a term is any attribute which does not help to make it what it is. Some authorities divide accidents into separable and inseparable. (3) A definition of a term is a statement of its meaning by enumerating its characteristic attributes. (4) Definitions explain a term intensionally, while logical division explains a term extensionally. (5) There are three kinds of definitions: (1) etymological, (2) descriptive, (3) logical. An etymological definition is based upon the derivation of the term; a descriptive definition states the characteristic properties and accidents of a term, while a logical definition is simply a statement of the differentia of a term. ioo Definition (6) The etymological definition leads to precision of expres- sion, the descriptive definition is best adapted to the child-mind, while the logical definition belongs to the realm of secondary education. (7) Five rules summarize the requirements to which a logical definition must conform. In a word or two these five rules are: Every logical definition must (1) state the genus and differentia, (2) be equivalent to the species defined, (3) not repeat the name to be defined, (4) not be expressed in obscure language, (5) commonly be affirmative. (8) Some terms are too high (summum genus), some too low (infima species), some too peculiar (sui generis) to come within the province of logical definition. 12. ILLUSTRATIVE EXERCISES. la. The italicized words in the following propositions are predicables because they are affirmed of the subject: (1) "This man weighs one hundred fifty pounds." (2) "A bird is a feathered biped." (3) "The earnest teacher is an indefatigable worker." (4) "Walking is the most beneficial outdoor exercise." lb. Underscore the predicables in the following : (1) "All men are rational." (2) "Teachers must be just." (3) "Every form of unhappiness springs from a wrong con- dition of the mind." (4) "Calmness of mind is one of the beautiful jewels of wisdom." 2a. To clarify our ideas it is an excellent plan to select a group of words belonging to the same genus with a view of de- fining them as simply and expeditiously as possible. As an illus- tration building may be selected as a genus. The word kind will suggest to us the species, such as dwelling, church, theatre, school, barn, bird-house, granary and smoke-house. Next it is necessary to discover the basis of distinction. This seems to be the use to which the building is put. Now we are ready for the definitions : Illustrative Exercises 101 Species Genus Differentia A dwelling is a building where people live. " church U <( where people worship. " theatre (( it where people act. " school a a where children are taught. " barn a <« where domestic animals, hay and grain are kept. " bird-house " n a designed for birds. " granary (t (C where grain is stored. " smoke-house " a a where meat is smoked. 2b. By selecting man as the genus, define the terms Caucasian, Mongolian, Ethiopian, Malay and American Indian. Treat the term chair in the same manner. 3a. One may easily distinguish a property from an accident by asking himself the question, "Would subtracting the attribute from the term alter its identity"? For example in the following, I find that the words italicized are properties because subtracting each from the term changes its identity : Term • Attributes man age, rationality, possessions, book binding, leaves, size, color, contents, radium emits intense light and heat, costs a million dol- lars a pound, snail . air-breathing mollusk, moves slowly, slush soft mud and snow, six inches deep. 3b. Indicate the common attributes of the following terms, underscoring the properties : Tree, teacher, garden, house, river. 4. The rules summarize well the essentials of the subject mat- ter of the logical definition. Therefore, it is highly important for the student to have these rules at the "tip of the tongue." With this in view a device of this nature may be helpful. Make each letter of the word rules stand for the initial letter of a sug- gestive word in each of the five rules. For example: r (repeat), u (unambiguous), 1 (language affirmative), e (essential), s (same size). With a little study "r and repeat," "u and unambiguous," "1 and language affirmative," "e and essential," "s and same size" may be firmly linked together in the memory. Repeat suggests the third rule, do not repeat the name, etc.; unambiguous, the fourth rule, 102 Definition not ambiguous language, etc.; language affirmative, the fifth rule; essentials, the first rule; same size, the second rule, subject and predicate must be of same size. The fact that the rules are not recalled in order of treatment is inconsequential. It is the writer's experience that fifteen minutes of concen- trated study upon this device or one similar to it will indelibly stamp upon the mind these troublesome rules. The student may be able to devise a more helpful keyword. 13. REVIEW QUESTIONS. (1) Why should the subject of definition appeal strongly to the school teacher? (2) Define a predicable. (3) Name in order the five predicables. (4) Define and illustrate the terms genus and species. (5) Explain the terms summum genus, infima species, sui generis. (6) Illustrate proximate genus. (7) Explain the terms genus and species as used in natural history. (8) Exemplify the double meaning of the genus man. (9) Define and illustrate differentia. (10) In what sense is the species a richer term than the genus? (11) Distinguish between property and accident. (12) Illustrate separable and inseparable accidents. (13) Give descriptive definitions of the following, indicating the five predicables : logic, general term, non-connotative term, obversion. (14) Define definition; illustrate. (15) Distinguish between definition and division. (16) Name, define and illustrate the three kinds of definitions. (17) Distinguish between real and verbal definitions. (18) Define in three ways the following: king, government, city, metal. (19) State the rules of logical definition. (20) What words may be used as cues to aid in recalling the rules for logical definition? (21) Under what circumstances will the wise teacher make use of each of three kinds of definitions? Review Questions 103 (22) Relative to the second rule for logical definition what are the three questions that one should ask himself? (23) Explain the exceptions to the third rule. (24) In connection with the fourth rule what may be said as to the use of technical terms? (25) What facts take from the force of the fifth rule? (26) What classes of words do not admit of logical definition? Illustrate. (27) Define education, teaching, instruction, training. (28) Distinguish by illustration between induction and syn- thesis ; deduction and analysis. 14. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Why should the scholar be tempted to speak and write illogically ? (2) Name the parts of speech that may be classed as pred- icables. (3) Explain the ten categories as given by Aristotle. (4) Show that genus and species are relative terms. (5) Why should the definition be needed most in the abstract sciences, such as theology, ethics, political economy, juris-pru- dence and psychology? (6) Define sin, life, wrong, personality, habit, character. (7) From the viewpoint of natural history find the species in the series of terms of which polygon is a member. (8) What is the plural of differentia? (9) Why should logic insist upon the proximate genus ? (10) (a) Man is a rational animal. (b) Man is a rational biped (proximate genus). In the case of the immature mind the first definition would be clearer. Why ? (11) "A property of a term is any mark or characteristic which belongs to that term." Is this definition logical? Give reasons. (12) What is the difference between the logical and the popular conception of property? (13) Is there any difference between the logical and popular conception of accidents? (14) "The term confer entia might be used to stand for the 104 Definition essence of the genus, as the term differentia represents the es- sence of the species." 1 Explain this. (15) John Stuart Mill affirms that there is no such thing as a real definition. Discuss this. (16) In your opinion, of the five rules of logical definition what one is violated most by the average teacher? Give reasons. (17) Distinguish between symbol and content. (18) Why are descriptive definitions best for young children? What educational principle is involved? (19) From the standpoint of the five rules for logical defini- tion criticise the following: (1) A man is a reasonable vertebrate. (2) A gentleman is a man with no visible means of support. (3) A man is an organized entity whose cognitive powers function rationally. (4) A metal is an element with a metallic luster. (5) A triangle is a figure of three sides. (6) A teacher is one who imparts knowledge. (7) Education is the process of drawing out all that is beautiful in the body and noble in the soul. (8) A democrat is a man who believes in free trade. (9) A government is a commonwealth controlled by di- rect vote of the people. (20) Write the foregoing definitions in logical form. (21) Since man is the only animal given to laughter, why is not the following a logical definition : "Man is a laughing animal." (22) "A logical definition should contain the species, the genus and the appropriate differentia." Is there any reason for using the term appropriate? (23) In connection with genus and species explain subaltern. (24) Is laughter a property of human being or an accident? (25) Show how a pedagogue may be an instructor but not a teacher. (26) Illustrate the complete method. (27) Show that induction may consist of a series of analyses; also a series of syntheses. l Hyslop. CHAPTER 7. LOGICAL DIVISION AND CLASSIFICATION. 1. NATURE OF LOGICAL DIVISION. The term genus is used for any class name which stands for two or more subordinate classes while the term species is made to stand for any one of the sub- ordinate classes. The proximate genus of any species is the next class above. For example the proximate genus of man is biped, not animal. Logical division is the process of separating a proximate genus into its co-ordinate species. Illustrations : Genus (i) Heavenly bodies (2) Vertebrates Species Fixed stars Planets Satellites Comets Meteors Nebulae Leptocardians Fishes Amphibians Reptiles Birds Mammals 105 io6 Logical Division and Classification (3) Man (4) Government Caucasian Mongolian Malay Ethiopian American Indian Monarchy Aristocracy Democracy 2. LOGICAL DIVISION DISTINGUISHED FROM ENUMERA- TION. When the genus is separated at once into individual objects the process is not logical division, but simple enumeration. Logical division implies a separating into smaller class terms, each term being a genus of still smaller subdivisions. This process may be continued till the last division gives individuals as species. Enumera- tion takes place when the first subdivision results in a list of individuals. To illustrate: Teacher Logical Division. Science teacher Mathematics teacher J English teacher I Modern language teacher Enumeration. Teacher John J. Brown H. G. White Mary Jones Alice Smith .ogical Division as Partition 10: 3. LOGICAL DIVISION AS PARTITION. Partition is the process of separating an individual thing into its parts. The partition is quantitative or mathematical when the separation is in terms of space or time, but when other- wise the partition becomes qualitative or logical. Or to put it in another way, the partition is mathematical when the separation gives parts and logical when the separation gives ingredients. To illustrate: ( i ) Tree- (2) House- 1 quantitative or (mathematical) qualitative or (logical) quantitative or (mathematical) branches leaves roots trunk Voody fibre capillary attraction sap chlorophyll [roof 1 frame-work [foundation wood iron stone plaster qualitative or (logical) An easy way to determine that the separation involves logical division proper and not partition is to affirm the connection between a class and a sub-class. To wit: A man is a biped ; a square is a rectangle ; a Caucasian is a 108 Logical Division and Classification man, etc. If such an affirmation cannot be made then the separation involved is not properly logical division but probably partition. For example it cannot be said that a roof is a house, or that sap is a tree. It is seen, then, that a logical division of any genus may be sum- marized in the form of a series of judgments of which a species is the subject and the genus is the predicate. For example, by a logical division quadrilaterals may be di- vided into trapeziums, trapezoids and parallelograms; this process may then be summarized in a series of three judgments: (i) A trapezium is a quadrilateral; (2) A trapezoid is a quadrilateral; (3) A parallelogram is a quadrilateral. 4. RULES OF LOGICAL DIVISION. When the logical division of a genus is under consider- ation there are four rules which should be observed. First Rule. There must be but one principle of divi- sion (fundamentum divisionis). To divide mankind into white man, Australian, yellow man, African and red man is a violation of this rule as the two principles of color and geographical location are involved. A division in which more than one principle is used is sometimes referred to as cross division because the various species cross each other. For example in the foregoing there are many white men who are Australians. This rule applies only to one division. Where there is a series of divisions a new principle may be employed in each division. For example, in dividing triangles into scalene, isosceles and equilateral, the equality of sides is Rules of Logical Division 109 the principle involved, but, in subdividing isosceles tri- angles into right angled and oblique angled, the principle employed concerns the nature of the angle. Second Rule. The co-ordinate species must be mu- tually exclusive. There must be no overlapping. The il- lustration given in the first rule is likewise a violation of this rule. Another example in which this second rule is not obeyed may be found in most geometries where tri- angles are divided into scalene, isosceles and equilateral. Here the second and third classes are not mutually ex- clusive since all equilateral triangles are isosceles accord- ing to the usual definition, "An isosceles triangle is a triangle having two equal sides." All equilateral triangles have two equal sides. Third Rule. The division must be exhaustive. That is, the species taken together must equal the whole genus. The sum of the species must be co-extensive with the genus. Dividing man into Caucasian, Ethiopian and Mongolian would be a violation of this rule, as there are at least two other species of man, Malay and American Indian. A distinction should be made between an exhaustive division and a complete division as the latter is not a logical requirement. To divide government into mon- archy, aristocracy and democracy is exhaustive but in- complete. Exhaustive because there is no other kind of government, all the species are included ; but incomplete in that monarchy may be divided into absolute and limited; democracy into pure and representative. Fourth Rule. The division must proceed from the no Logical Division and Classification proximate genus to the immediate species. There should be no sudden jumps from a high genus to a low species. The division must be gradual and continuous; step by- step. To divide government into limited monarchy, abso- lute monarchy, pure democracy and representative de- mocracy would be a violation of this rule, as government is the proximate genus of monarchy, not of limited mon- archy, therefore one step has been omitted. Such an omis- sion involves a step from grandfather to grandchild, so to speak, the generation of father having been left out. A violation of this rule is most insidious when some of the species of a subdivision are immediate while others are not. To wit : dividing government into monarchy, aristocracy, pure democracy and republic, or dividing quadrilaterals into trapeziums, trapezoids, rectangles, squares, rhomboids and rhombs. 5. DICHOTOMY. Dichotomy comes from the Greek, meaning to cut in two. Dichotomy is a continual division of a genus into two species which are contradictory in nature. Contradictory terms are such as admit of no middle ground. They divide the whole universe of thought into two classes. For example, honest and not-honest, pure and impure, perfect and imperfect, are contradictory terms. Dichotomy thus affords an easy opportunity for an ex- haustive division as in the use of contradictories nothing in the universe need be omitted. An historical illustration of dichotomy is the "Tree of Dichotomy in Porphyry" named after Porphyrius, a Neo-Platonic philosopher of the third century. Tree of Porphyry. Substance. Corporeal Incorporeal Body Animate Inanimate Living Being Sensible Insensible Animal Rational Irrational Man Socrates Plato Other Men H2 Logical Division and Classification This kind of division is not altogether satisfactory as the negative side is too indefinite. On the other hand, if both subdivisions are made positive then there is danger of making the opposing terms contrary rather than con- tradictory. This, of course, would be a serious logical fallacy, as contrary terms admit of middle ground while contradictory terms give no choice, it is either the one or the other. The use of dichotomy becomes evident in situations where new and unexpected discoveries may be made. Without disturbing the classification the new species may be appended to the negative side of the division. The following illustrates : Vertebrates i ' 1 Leptocardians Not-leptocardians Fish Not-Fish I ' — l Amphibians Not-amphibians 1 ' 1 . Reptiles Not-reptiles i Birds Not-birds •'-— 1 Mammals Not-mammals I The New Species 6. CLASSIFICATION— COMPARED WITH DIVISION. Classification is the process of grouping notions ac- cording to their resemblances or connections. So far as results are concerned there is no difference Classification — Compared with Division 113 between logical division and classification. Both processes may give us the same orderly scheme of heads and sub- heads. The difference lies in the process itself. Division is deductive in nature as it proceeds from the more gen- eral genus to the less general species. While classifica- tion is inductive as it groups the less general species under the more general genus. Division differentiates unity into multiplicity, while classification reduces multiplicity to unity. It follows that the one is the inverse of the other. The difference in the mode of procedure may be illustrated by using the common classification or division of triangles. For example : Without any knowledge of the kinds of triangles the student discovers by examining the various shapes of many triangles that there is a group in which none of the sides are equal. For the lack of a better name he terms these non-equilateral (scalene). Further observation dis- closes another group in which two of the sides are equal. These he names bi-equilateral (isosceles). Finally a third group is designated as tri-equilateral (equilateral). This process is classification. Division would consist in separating the genus triangle into the three kinds — scalene, isosceles, equilateral. 7. KINDS OF CLASSIFICATION— ARTIFICIAL AND NATURAL. An artificial classification is one in which the grouping is made on the basis of some arbitrary connection. Cata- loguing alphabetically the books in a library illustrates this kind of classification. Likewise the arrangement of H4 Logical Division and Classification the names in a directory or a telephone book. The con- necting mark being the initial letter of the title or name. The reason why Mills and Meyers are put in the same group is that both names happen to commence with the letter M. Artificial classifications are resorted to for some special purpose, designed by man, not by nature. Consequently artificial classifications are sometimes called special or working classifications. A natural classification is one in which the grouping is made on the basis of some inherent mark of resemblance. Classifications in animal and plant life are the best il- lustrations of this kind. Such classifications are sug- gested by nature and not by man, and may, therefore, be called general or scientific. The main aim of natural classification is to derive general truths and arrange knowledge so that it may be easily remembered. 8. TWO RULES OF CLASSIFICATION. The rules of logical division are applicable in the mak- ing of a logical classification. In addition to these an artificial classification should be made to conform to the one rule: The classification must be appropriate to the purpose in hand. Likewise a natural classification should be made to conform to the rule: Every classification should afford opportunity for the greatest possible num- ber of general assertions. 9. USE OF DIVISION AND CLASSIFICATION IN THE SCHOOL ROOM. It has been stated that classification and division aim Use of Classification and Division 115 at the same result. Classification reduces multiplicity to unity while division differentiates unity into multiplicity. In short, division is deductive while classification is inductive in mode of procedure. Therefore, classification should be used in those situations which call for induc- tion and division in cases where deduction is the better method. Speaking generally, classification should be used with small children when the essential thing is to present the concrete facts with a view of leading the children to dis- cover for themselves the truths contained therein. With older pupils division may be used, if the purpose is to set in order facts which are already known. 10. TOPICAL OUTLINE. Logical Division and Classification. (1) Nature of Logical Division. Genus — species. Illustrations. (2) Logical Division Distinguished from Enumeration. Illustrations. (3) Logical Division and Partition. Quantitative — qualitative. How summarized. (4) Four Rules of Logical Division. (1) One principle — cross division. (2) Mutually exclusive. (3) Exhaustive — complete. (4) Immediate species. (5) Dichotomy. Contradictory terms. Tree of Porphyry. Use illustrated. n6 Logical Division and Classification (6) Classification Compared with Division. (7) Kinds. Artificial— Natural. (8) Two Rules of Classification. (1) Appropriate, (2) Afford many Assertions. (9) Use of Division and Classification. 11. SUMMARY. (1) Logical division is the process of separating a proximate genus into its co-ordinate species. (2) The first subdivision in a logical division gives class terms, while the first subdivision in an enumeration gives indi- vidual objects. (3) Partition is the process of separating an individual thing into its parts. These parts may be either quantitative or qualitative. A logical division of any genus may be summarized in a series of judgments of which a species is the subject and the genus is the predicate. (4) The four rules of logical division are: the division must (1) be based on one principle, (2) have species mutually ex- clusive, (3) be exhaustive and (4) proceed from proximate genus to immediate species. A violation of the first rule gives a cross division. Exhaustive division is easily confused with a complete or finished division. (5) Dichotomy is a continual division of a genus into two species which are contradictory in nature. An historical illustration of dichotomy is the Tree of Porphyry. Dichotomy is of service in the field of new and unexpected discoveries. (6) Classification is the process of grouping notions accord- ing to their resemblances or connections. Classification is inductive in nature, division deductive. Classi- fication unifies, division differentiates. (7) An artificial classification is made on the basis of some arbitrary connection; a natural classification, on some inherent mark of resemblance. (8) The rules of logical division are applicable in any classi- fication. In addition to these a classification should (1) be ap- Summary 117 propriate and (2) afford opportunity for the greatest possible number of assertions. (9) Classification should be the mode of procedure in the lower grades, division in the higher grades. 12. REVIEW QUESTIONS. (1) Define and illustrate logical division. (2) What is the meaning of proximate genus ? (3) How does logical division differ from enumeration? Illustrate. (4) Distinguish between logical division, and physical division or partition. (5) Illustrate a quantitative partition; a qualitative partition. (6) Illustrate how a logical division may be summarized in the form of a series of judgments. (7) State and explain the rules of logical division. (8) State the rules violated in the following divisions, explaining in full 'Primary Secondary r In fancy Collegiate Childhood (1) Education Technical (2) Life Youth Scientific Old age Professional Caucasian Cement Frame Ethiopian Stone (3) Man - Malay Mongolian (4) Buildings Dwellings Barns American Churches (9) Show the difference between contradictory and opposite terms. (10) Define dichotomy. (11) Illustrate the Tree of Porphyry and indicate its use to scientists. (12) Illustrate the difference between classification and division. (13) Why should classification be the mode of procedure when dealing with immature minds ? n8 Logical Division and Classification (14) Illustrate the difference between an artificial and a natural classification. (15) State and explain the two rules of classification. (16) Show which of the following divisions are logical and which are not : (1) The manifestations of the mind into knowing, think- ing and feeling. (2) Books into mathematical and non-mathematical. (3) Students into those who are industrious, athletic and shiftless. (4) Flowers into roses, carnations and lilies. (5) Planets into those which are larger than the earth and those which are smaller. 13. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Analyze by mathematical partition the terms world, plant, book. (2) Analyze by logical partition the terms granite, water, air. (3) What rule is violated if the logical division is applied to the genus rather than the proximate genus ? (4) Divide logically the following terms : school, religion, book, vegetable, life. (5) "Each new subdivision may adopt a new principle of divi- sion." Illustrate this. (6) Explain and illustrate the meaning of the terms super- ordinate, sub-ordinate and co-ordinate. (7) Define and illustrate metaphysical division and verbal division. (8) Give a definition of an isosceles triangle which will make logical the division of triangles into scalene, isosceles and equi- lateral. (9) "The evolution of all truth develops progressively through three stages." "The first is the thesis ; the second is the antithesis ; the third is the synthesis." Explain this in terms of trichotomy. (10) Illustrate the difference between a complete division and an exhaustive division. Questions for Original Thought 119 (11) Show in what ways, if any, the following divisions violate the rules of logical division. Human Learning (by Bacon) Memory (History) Imagination (Poetry) Reason (Philosophy) or (the Sciences) Sciences (by Comte) 1 Mathematics 2 Astronomy 3 Physics 4 Chemistry 5 Biology 6 Sociology 7 Morals CHAPTER 8. LOGICAL PROPOSITIONS 1. THE NATURE OF LOGICAL PROPOSITIONS. Judging has been defined as the process of conjoining or disjoining notions. This may be put in another way: "Judging is the process of asserting or denying the agree- ment between two notions." The product of the act of judging is a judgment and when judgments are put in word- form such expressions are called logical propositions. Definition: A logical proposition is a judgment ex- pressed in words. Just as percept and concept notions are expressed by means of logical terms so judgment notions may be expressed by logical propositions. To illustrate : The terms the squirrel and cracking a nut express two notions, and when an agreement between them is asserted and the product is expressed in word form, then such an expression becomes the logical propo- sition, "The squirrel is cracking a nut." The following being expressed judgments are logical propositions : (i) All men are mortal. (2) Some men are wise. (3) No men are immortal. (4) Some men are not wise. (5) No sane person is a lover of vice. (6) Some good orators are not good statesmen. (7) Every man is fallible. 120 The Nature of Logical Propositions 121 (8) If it rains, I shall not go. (9) He is either sane or insane. 2. KINDS OF LOGICAL PROPOSITIONS. There are three kinds of logical propositions; namely, categorical, hypothetical and disjunctive. A categorical proposition is one in which the assertion is made unconditionally. An hypothetical proposition is one in which the assertion depends upon a condition. A disjunctive proposition is one which asserts an alternative. The Three Kinds Illustrated : ( 1 ) "Every dog has his day." Categorical. (2) "If you do your best, success will reward you." Hypothetical. (3) "He is either stupid or indolent." Dis- junctive. (4) "All vices are reprehensible." Categorical. (5) "Either you are very talented or very indus- trious." Disjunctive. (6) "If capital punishment does not aid society, it should be abolished." Hypothetical. (7) "You may go provided your teacher is will- ing." Hypothetical. (8) "No intelligent man can ignore the practice of temperance." Categorical. By studying the illustrations it will be observed that the categorical propositions are direct, bold, assertive state- ments, whereas the hypothetical are limited by conditions which make them less forceful. In the second proposi- tion, for example, "success will reward you," is limited 122 Logical Propositions by the condition, "If you do your best." The disjunctive may be regarded as categorical in form, but hypothetical in meaning, because in such a proposition as, "He is either, stupid or indolent," a direct assertion is made which sug- gests the categorical, and yet it may be implied that, if he is stupid then he is not indolent; this is indicative of the hypothetical. Some logicians classify propositions as categorical and conditional, the conditional being subdivided into hypo- thetical and disjunctive. The first classification seems preferable, however, as it conforms to the three modes of reasoning. The common word-signs of the categorical proposition are all, every, each, any, no and some, while those of the hypothetical are if, even if, unless, although, though, pro- vided that, when, or any word or group of words denoting a condition. The disjunctive symbols are either — or. 3. THE FOUR ELEMENTS OF A CATEGORICAL PROPO- SITION. Every categorical proposition should have four ele- ments; namely, the quantity sign, the logical subject, the copula and the logical predicate. In the foregoing cate- gorical propositions the quantity signs are respectively, every, all and no. In any case the quantity sign is always attached to the subject and indicates its breadth or extension. For example, in the two propositions, "All men are mortal" and "Some men are wise," the quantity sign all makes the term man much broader than does the quantity sign some. The Four Elements of a Categorical Proposition 123 The logical subject of a categorical proposition is the term of which something is affirmed or denied, whereas the logical predicate of a categorical proposition is the term which is affirmed or denied of the subject. In the two propositions, "All men are mortal" and "No men are immortal," the term about which something is affirmed or denied is men, while the terms which are affirmed and denied of the subject are respectively mortal and im- mortal. "Men" is, therefore, the logical subject of each proposition, while "mortal" is the logical predicate of the first and "immortal" the logical predicate of the second. The copula is the connecting word between the logical subject and predicate and denotes whether or not the latter is affirmed or denied of the former. The copula is always some form of "to be" or its equivalent. When the predicate is denied of the subject, "nof } may be used with the copula and considered a part of it. To illustrate : in the logical proposition, "Some men are not wise," "are not" may be regarded as the copula. The four elements are indicated in the following cate- gorical propositions : ntitysig 'n Logical subject Copula Logical predicate All fixed stars are self-luminous No wise man is going to steal Some quadrupeds are domestic animals Some glittering things are not gold Some boys are not discreet A few men are multi-millionaires Every citizen is duty-bound to vote 124 Logical Propositions The student must ever keep in mind the fact that to be absolutely logical all categorical propositions must be expressed in terms of the four elements. However, life is too short and man is too busy to speak always in terms of the four elements. Moreover, to be logical may often compel an awkwardness of expression and a lack of euphony which could hardly be tolerated. For these rea- sons the utterances in ordinary conversation are fre- quently illogical so far as the four elements are con- cerned, though not necessarily illogical in meaning. When it is desired to test the validity of any series of statements leading up to some generalization, it may become neces- sary to express the statement in terms of the four ele- ments. The student should gain some facility in this, otherwise he may be readily led into fallacious reasoning. The following statements taken at random from news- papers are given in the original and then expressed in terms of the four elements : The Original In Terms of the Four Elements (1) You came too late. (1) The person is one who came too late. (2) I saw the swell turnout (2) The man was one who saw coming along. the swell turnout coming along. (3) All of the men walked. (3) All of the men were those who walked. (4) The robbers cut a hole in (4) All the robbers were the this floor. ones who cut a hole in this floor. (5) Some of these flew away. (5) Some birds were those which flew away. The Four Elements of a Categorical Proposition 125 (6) The rain interfered with (6) The rain was that which the attendance. interfered with the at- tendance. (7) Our habits make or un- (7) All our habits are forces make us. which make or unmake us. (8) We all had a fine time. (8) All the party were those who had a fine time. In argumentative discourse it is often sufficient to "think the proposition" in terms of the four elements without taking the time to actually express it. 4. LOGICAL AND GRAMMATICAL SUBJECT AND PREDI- CATE DISTINGUISHED. The grammatical subject is one word while the logical subject is the grammatical subject with all its modifiers except the quantity sign. For example: in the proposi- tion, "All white men are Caucasians," men is the gram- matical subject, while white men is the logical subject. All being the quantity sign simply indicates the extension of men and is not a part of the logical subject. The grammatical predicate is the verb-form together with any predicate noun or adjective, while the logical predicate is the predicate word or words and all its modi- fiers. The grammatical predicate includes the copula, but the logical predicate never includes the copula. The grammatical predicate does not include the object, while the logical predicate always includes what is equivalent to the object and all its modifiers. To illustrate: in the proposition, "Some men are wise," are wise is the gram- matical predicate, while wise is the logical predicate. And in the proposition, "He burned the red house on the 126 Logical Propositions hill," burned is the grammatical predicate, while the one who burned the red house on the hill is the logical predi- cate. 5. THE FOUR KINDS OF CATEGORICAL PROPOSITIONS. Categorical propositions are divided according to their quantity into Universal and Particular and according to their quality into Affirmative and Negative. A universal proposition is one in which the predicate refers to the whole of the logical subject. Illustrations : (i) All men are mortal. (2) All civilized men cook their food. (3) No dogs are immortal. (4) Every man was once a boy. Considering the first proposition, "mortal'' the logical predicate, refers to the whole of the logical subject "men." Similarly "cook their food" refers to the whole of the term "civilized men" ; "immortal" to the whole of the term "dogs," and "once a boy" to the whole of the term "man." In considering the definition of a universal proposition it is necessary to keep in mind the distinction between a logical and a grammatical subject, as in the second propo- sition the logical predicate, "cook their food," refers to only a part of the grammatical subject, men, and, there- fore, the proposition might fallaciously be termed a par- ticular proposition rather than a universal. A particular proposition is one in which the predicate refers to only a part of the logical subject. The Four Kinds of Categorical Propositions 127 Illustrations : ( 1 ) Some men are wise. (2) Some animals are not quadrupeds. (3) Most elements are metals. (4) Many children are mischievous. In the foregoing propositions some, most and many are quantity signs and, therefore, must not be considered as a part of the logical subjects. Considering the logical subjects and predicates in order, the term wise refers to only a part of the men in the world, quadrupeds to only a part of the animals, metals to only a part of the ele- ments and mischievous to only a part of the children. An affirmative proposition is one which expresses an agreement between subject and predicate. A negative proposition is one which expresses a dis- agreement between subject and predicate. Affirmative propositions conjoin terms, negative propo- sitions disjoin terms. In the first the agreement is af- firmed; in the second the agreement is denied. Illustrations : None of the captives escaped. Negative. Some teachers are just. Affirmative. All trees grow towards heaven. Affirmative. Some people are not companionable. Negative. No person is above criticism. Negative. Dividing both universal and particular propositions as to quality, gives four kinds ; namely, universal affirmative, universal negative, particular affirmative and particular negative. No topic in logic demands greater familiarity than 128 Logical Propositions these four types, as every proposition must be reduced to one of the four before it can be used as a basis of reasoning. For the sake of brevity the symbols A, E, I and O are used to designate respectively the universal affirmative, the universal negative, the particular affirmative and the particular negative. A and I, symbolizing the affirmative propositions, are the first and second vowels in Affirmo, while E and O, symbolizing the negatives, are the vowels in Nego. The common sign of the universal affirmative, or the A proposition is all; of the universal negative, or E proposition no; of the particular affirmative, or I propo- sition some; of the particular negative, or O proposi- tion some with not as a part of the copula. The accom- panying classification summarizes these facts, S and P being used to symbolize the terms "subject" and "predicate." Illustrations f Affirmative- A All S is P Universal «j „ L . , I Negative-E No S is P Categorical i »» » Propositions f Affirmative-I Some S is P Particular -j [Negative-O Some S is not P Henceforth the symbols A, E, I, O will be used to desig- nate the four kinds of categorical propositions. The propositions have other quantity signs aside from the ones used above. These may be summarized : A — all, every, each, any, whole. E — no, none, ail-not. <; I — some, certain, most, a few, many, the greatest part, any number. [O — some - - not, few. Quantity signs of Propositions Which do not Conform 129 6. PROPOSITIONS WHICH DO NOT CONFORM TO THE LOGICAL TYPE. It has been observed that all expressed judgments must be reduced to one of the four logical types A, E, I or O, before they can be used argumentatively. Logic insists upon definiteness and clearness — there must be no am- biguity, no opportunity for a wrong interpretation. From this viewpoint the four types fulfill every requirement. Their meaning cannot be misunderstood. To any one with normal intelligence their significance may be made perfectly clear. Any argument when once put in terms of the four types may be spelled out with mathematical pre- cision. In consequence it is of prime importance that the four types not only be well understood, but that a certain facility be gained in reducing ordinary conversa- tion to some one of these types. ( 1 ) Indefinite and Elliptical Propositions. It is known that every logical proposition must be ex- pressed in terms of the four elements — quantity sign, logical subject, copula and logical predicate, consequently the four types A, E, I and O which epitomize every form of logical proposition, are expressed in terms of these four elements. But in common conversation often the quantity sign, as well as the copula, is omitted. See section 3. Propositions without the quantity sign are called indefi- nite, while those with the suppressed copula may be termed elliptical propositions. Both may be made logical as the attending illustrations will indicate : 130 Logical Propositions Illogical Indefinite Men are fighting animals. Lilies are not roses. Good is the object of moral approbation. Perfect happiness is impos- sible. Elliptical Fashion rules the world. Trees grow. Children play. Some men cheat. Logical All men are fighting ani- mals. (A) No lilies are roses. (E) All good is the object of moral approbation. (A) In all cases perfect happi- ness is impossible. (A) All fashions are ruling the world. (A) All trees are plants zuhich grow. (A) All children are playful. , (A) Some men are persons who cheat. (I) Here it is noted that the logical form of some proposi- tions is not always the most forceful. Often the logical form gives an awkward construction and should be re- sorted to only for purposes of logical argument. The reduction of either kind to the logical form must be determined by the meaning of the proposition. As a usual thing the indefinite is universal (either an A or an E) in meaning, while the problem of the elliptical is to give it in terms of the copula, expressed with as little awkwardness as possible. General truths, because attended with no quantity sign, might be classed as indefinite propositions, though theii Propositions Which do not Conform 131 universality is so apparent that they may be unhesitatingly classed as universals. Illustrations : "Things equal to the same thing are equal to each other." "Trees grow in direct opposition to gravity." "Honesty is the best policy." "A stitch in time saves nine." Because the indefinite proposition is so frequently of a general nature, it is sometimes classed as general rather than indefinite. Sir William Hamilton would class the indefinite as an indesignate proposition. (2) Grammatical Sentences. The grammarian divides sentences into five kinds; namely, declarative, interrogative, imperative, optative, exclamatory. But logic recognizes only the declarative, as it has already been seen that the four logical types are declarative in nature. A logical proposition, then, is al- ways a sentence, but all sentences are not logical proposi- tions. The four kinds of sentences which are not logical propositions may be usually reduced to one of the four types as the attending illustrations will indicate : Illogical Logical Interrogative. Do men have the The question is asked, Do men power of rea- have the power of reason?* son? (A) Imperative. "Thou shalt not All men are commanded not to steal." steal, or you are one who should not steal. (E) Men do have the power of reason. 132 Logical Propositions Optative. "I would I had a I am one who desires a million million." dollars. (A) Exclamatory. "Oh, how you You are one who frightened frightened me!" me. (A) (3) Individual Propositions. An individual proposition is one which has a singular subject; e. g., Abraham Lincoln was an honest man. Peter the Great was Russia's greatest ruler. The maple tree in my yard is dying of old age. These propositions, having a singular term as subject, are individual or singu- lar in nature. As the predicate refers to the whole of the logical subject, individual propositions are classed as universal. (4) Plurative Propositions. Plurative propositions are those introduced by "most," "few," "a few," or equivalent quantity signs. For exam- ple, "Most birds are useful to man" ; "Few men know how to live" ; "A few of the prisoners escaped," are plurative propositions. "Most" means more than half, while "few" and "a few" mean less than half. In either case the prop- osition is particular. Stated logically, the illustrative propositions would take the form of "Some birds are use- ful to man"; "Some men do not know how to live"; "Some of the prisoners escaped." The reader will observe the difference in significance between few and a few. The former is negative in char- acter and when introducing a proposition makes it a par- ticular negative (O). The latter always introduces a particular affirmative (I). Propositions Which do not Conform 133 (5) Partitive Propositions. Partitive propositions are particulars which imply a complementary opposite. These arise through the am- biguous use of ail-not, some and few. Ail-not may some- times be interpreted as not all and sometimes as no. To illustrate: The proposition, "All men are not mortal," is distinctly a universal negative or an E, while the propo- sition, "All that glitters is not gold," is a particular nega- tive or an O. The logical form of the first is, "No men are mortal," and of the second, "Some glittering things are not gold." When used in the "not-all" sense, the prop- osition is partitive because if the O-meaning is intended the I is implied. For example, "All that glitters is not gold," is partitive because the statement implies that some glittering things are gold (I) as well as the complement, "Some glittering things are not gold" (O). A knowledge of both the affirmative and negative aspects is taken for granted in the statement of either the one or the other. "Ail-not," then, is negative in any case, but universal when it means no and particular when it means not all. Any proposition is partitive in nature when the quantity sign is not all, or ail-not interpreted as the equivalent of not all. It may be observed here that all has two distinct uses. First, it may be used in a collective sense; second, in a distributive sense. For example: All is used in the collective sense in such propositions as, "All the members of the football team weighed exactly one ton," or "All the angles of the triangle are equal to two right angles." Using all in the distributive sense would make 134 Logical Propositions true these : "All the members of the football team weigh more than 140 pounds" ; "All the angles of a triangle are less than two right angles." All is used collectively when reference is made to an aggregate, but distributively when reference is made to each. The quantity sign some is likewise ambiguous, as it may mean (1) some only — some, but not all, or (2) some at least — some, it may be all or not all. When "some" is used as the quantity sign of any particular proposition which has been accepted as logical, the second meaning, "some at least," is always implied. This interpretation of "some" will be explained more in detail in a succeeding section. When some is used in the sense of some only, the parti- tive nature of the proposition is apparent, as both I and O are implied. For example, with reference to the human family, to say that "some only are wise" necessitates an investigation, which leads to the discovery that some are wise, while others are not wise. If the proposition be an I, then its complementary O is implied, or if it be an O, the I is implied. Few given as a sign of a plurative proposition also serves as a sign of the partitive. The plurative aspect is prominent when it is said that "Few men can be million- aires" and emphasis is placed upon the meaning that "Most men cannot be millionaires." But when emphasis is given to "few," as meaning few only rather than the most are not, then the I and the O are both implied; e. g., Some men become millionaires, but the most do not. To put it in a word, "ail-not," "some" and "few" intro- Propositions Which do not Conform 135 duce partitive propositions when the meaning implies both an I and an O. When treating such in logic the meaning whiclr seems to be given the greater prominence must be accepted. Surely in the statement, "All that glitters is not gold," the O-interpretation is the one intended; namely, "Some things which glitter are not gold." Illustrations : (1) "All men are not honest." (2) "Few men live to be a hundred." (3) "Some men are consistent." The first proposition with the emphasis placed upon all suggesting that some men are not honest, is the in- tended proposition while some men are honest is the im- plied. In reducing it to the logical form the intended proposition is the one which should be used. With the emphasis upon few and some, the second and third propositions may be interpreted as follows: (2) Intended proposition, Some men do not live to be a hundred. Implied proposition, Some men do live to be a hundred. (3) Intended proposition, Some men are consistent. Implied proposition, Some men are not con- sistent. (6) Exceptive Propositions. These are introduced by such signs as all except, all but, all save. To wit: (1) "All except James and John may be excused"; (2) "All but a few of the culprits have been arrested"; (3) "All birds save the English sparrow are serviceable to man" are exceptive propositions. Exceptive propositions are universal when the excep- tions are mentioned. Universal propositions necessitate a 136 Logical Propositions subject more or less definite, as the predicate of such must refer to the whole of a definite subject. It follows that in exceptive statements definiteness is secured when the exceptions are mentioned, therefore it becomes clear how all such propositions must be universal. Of the illustra- tions, the first and third propositions are universal. Any exceptive proposition is particular when the exceptions are referred to in general terms or when the subject is followed by et cetera. The second illustrative proposi- tion is particular. (7) Exclusive Propositions. Of all propositions which vary from the logical form the exclusive is the most misleading. Exclusives are ac- companied by such words as "only," "alone," "none but," and "except." Their peculiarity rests in the fact that ref- erence is made to the whole of the predicate, but only to a part of the subject. For example, in the exclusive propo- sition, "Only elements are metals," metals is referred to as a whole while elements is considered only in part. The true meaning is "Some elements are all metals," or to put it in logical form, "All metals are elements." The easiest way to deal with an exclusive is to interchange subject and predicate {convert simply) and call the proposition an A. Process Illustrated : Exclusive Proposition Reduced to Logical Form 1. None but high school gradu- All who enter Training School ates may enter Training must be high school grad- School. uates. 2. Only first-class passengers All parlor cars are for first- are allowed in parlor cars. class passengers. Propositions Which do not Conform 137 3. Residents alone are licensed All who are licensed to teach to teach. are residents. 4. No admittance except on All who have business may be business. admitted. 5. Only bad men are not-wise. All who are not-wise are bad men. 6. Only some men are wise. All who are wise are men. It is claimed by good authority that the real nature of the exclusive is best expressed by negating the subject and calling the proposition an E; e. g., exclusive: "Only ele- ments are metals"; logical form: "No not-elements are metals" (E). In a succeeding chapter it is explained how an E admits of first simple conversion and then obversion. The following illustrate these two processes: Original E: "No not-elements are metals." Simple conversion: "No metals are not-elements." Obversion: "All metals are elements." From this it may be seen that the statement, "The easiest way to deal with an exclusive is to interchange subject and predicate and call the proposition an A," is substantially correct. (8) Inverted Propositions. The poet often employs the inverted proposition, illus- trated by the following: "Blessed are the merciful;" "Great is this man of war." An interchanging of subject and predicate makes these poetical constructions logical; e. g., "All the merciful are blessed;" "This man of war is great." Note. — The student should not be misled by the rela- tive clause. Often it may be interpreted as a part of the Logical Propositions i£> ex. predicate rather than the subject. To wit: "No man friend who betrays a confidence"; clearly the logical subject is no man who betrays a confidence. 7. PROPOSITIONS WHICH ARE NOT NECESSARILY ILLOGICAL. (i) Analytic and Synthetic Propositions. An analytic proposition is one in which the predicate gives information already implied in the subject. Thus, "Fire burns" "Water is zvet" "A triangle has three angles" are analytic propositions because the predicates do not give added information to one who has any con- ception of the subjects. Because the attribute mentioned by the predicate is an essential one, analytic propositions are sometimes termed essential propositions . Other names for the same kind of proposition are verbal and explicative. A synthetic proposition is one in which the predicate gives information not necessarily implied in the subject. "Fire protects men from the wild animal." "A cubic foot of water weighs 62^/2 lbs." "The sum of the interior angles of a triangle is equal to two right angles." These are synthetic because a common conception of the mean- ing of the subject would not need to include the informa- tion given by the predicate. Other names for synthetic propositions are accidental, real and ampliative. The distinction between analytic and synthetic propo- sitions is not so clear as would on first thought appear. "Fire burns" might give added information to the child or savage who knows only of the light emitted by fire* Proportions Which are not Necessarily Illogical 139 To them, then, the proposition would be synthetic. The distinction must be based upon the assumption that the same words mean about the same thing to people in general. This analytic-synthetic division of propositions finds a significance in the domain of philosophy. To the logician the distinction is of slight importance save in the so- called verbal disputes, viz. : disputes which turn on the meaning of words. (2) Modal and Pure Propositions. A modal proposition states the mode or manner in which the predicate belongs to the subject. The signs of modal propositions are the adverbs of time, place, degree, manner. Illustrations: "James is walking rapidly." "Honesty is always the best policy." "Aristotle was probably the greatest thinker of ancient times. " A pure proposition simply states that the predicate belongs, or does not belong, to the subject. Illustrations : "James is walking." "Honesty is the best policy." "Aristotle was the greatest thinker of ancient times." Some logicians refer to modal propositions as being such as indicate degrees of belief. Such words as "prob- ably," "certainly," etc., would indicate their modality. As logic has to do with the pure proposition and not the modal, the difference of opinion is of little import. (3) Truistic Propositions. A truistic proposition is one in which the predicate re- peats the words and the meaning of the subject. Illus- trations: "A man is a man," "A beast is a beast," "A traitor is a traitor," "What I have done I have done." 140 Logical Propositions The truistic proposition is of little importance except in cases where the subject is used extensionally while the predicate is used intensionally. In the illustration, "A man is a man," the subject merely stands for a member of the man family, while the predicate may indicate cer- tain manly qualities. Against such ambiguities the logician must be on guard. 8. THE RELATION BETWEEN SUBJECT AND PREDI- CATE. In Chapter 5 the extension and intension of terms was explained. The student recalls, for instance, that the term "man" may be used to denote objects, as "white man," "black man," "red man," etc. In this sense the term "man" is used extensionally. But when made to stand for the attributes "rationality," "power of speech," etc., the term "man" is used intensionally. In, considering the relation between subject and predi- cate it is customary to employ the terms in an extensional sense only, since such a restriction serves the purpose of syllogistic reasoning and conversion. Let us, then, give attention to the extension of the subject and predicate of the categorical propositions A, E, I, O. ( 1 ) The Universal Affirmative or A Proposition. All S is P symbolizes the A proposition. This may be interpreted as meaning that all of the subject belongs to a part of the predicate, or that all of the subject belongs to all of the predicate. The first interpretation is the usual one and may be illustrated by the following propositions : The Relation Between Subject and Predicate 141 1. "All men are mortal." 2. "All trees grow/' 3. "All metals are elements." It is obvious that the subjects of these propositions in- clude every specimen of the particular class mentioned. For example: The subject all men includes every speci- men of the human family; all trees includes every object of that class ; all metals covers everything which the scien- tist classes as such. In the three propositions, then, refer- ence is made to the whole subject but to only a part of the predicate, as other beings beside men, such as the horse, are mortal ; and other plants aside from trees, such as the sun flower, grow ; other substances, namely oxygen, are elements. For the sake of making the logical meaning of the four propositions clearer, recourse may be made to Euler's diagrams, so named because the Swiss mathematician and logician, Leonhard Euler, first used them. The first illustration of the A proposition, "All men are mortal," may be represented by two circles, a larger circle standing for the predicate, mortal, and a smaller circle entirely inside the larger representing the subject, men. Thus: Fig. 1. 142 Logical Propositions It is evident that all of the smaller circle belongs to the larger. This diagram will then fit any proposition where it may be said that all of the subject belongs to a part of the predicate, or which may be symbolized as "All S is some P." (All the subject is some of the predicate.) The student knows that circles are plane surfaces and when such a statement as "All men are mortal" is given, reference is made to only that part of the "mortal" circle which is directly underneath the "men" circle. Nothing has been said relative to the remaining part of the "mortal" circle. "A" propositions which may be interpreted as meaning "All S is all P" are called co-extensive A's because the subject and predicate are exactly equal in extension. Such propositions are best illustrated by definitions ; e. g. : i. "A man is a rational biped." 2. "A trigon is a polygon of three sides." 3. "Teaching is the art of occasioning those activities which result in knowledge, power and skill." To represent the meaning of the co-extensive A by the Euler diagram, two circles of the same size may be drawn, one coinciding at every point with the other. If the first circle is drawn heavily in black and the second dotted in red, it will make clear to the eye that there are two circles. (2) The Universal Negative or E Proposition. "No S is P" best symbolizes the E proposition, though sometimes the universal negative is written "All S is not P." This latter form, as has been explained, is ambigu- ous and therefore illogical. "No S is P" surely means that no part of the subject The Relation Between Subject and Predicate 143 belongs to any part of the predicate and no part of the predicate belongs to any part of the subject. The subject and predicate are mutually exclusive. The following illustrate the E proposition : 1. "No man is immortal." 2. "No true teacher works for money." 3. "No thorough student can remain unwise." The E proposition may be represented by two circles, the one entirely without the other as in Fig. 2 : ( Man ] Fig. 2. (3) The Particular Affirmative or I Proposition. This may be symbolized as ce Some S is P," and consid- ered as meaning that a part of the subject belongs to a part of the predicate. It has already been noted that "some" is ambiguous and that its logical signification is "some at least." (It may be all or it may not be all.) For example, the only logical interpretation which can be placed on "Some men are wise" is, that the investigation has resulted in finding only a part of the man family wise. Whether or not all are wise is unknown as the entire field has not received attention. In no case can it be assumed that all the others are not wise. 144 Logical Propositions The I proposition illustrated: i. "Some men are wise." 2. "Some animals are vertebrates." 3. "Some teachers are inspiring." The meaning of the I proposition may be represented by two circles intersecting each other : Fig. 3. The significant feature of the diagram is the shaded part which represents a part of the "men" circle as be- longing to a part of the "wise" circle. The unshaded part of each circle is the unknown field. (4) The Particular Negative or O Proposition. The common symbolization of the O is "Some S is not P." Put in statement form: Some of the subject is ex- cluded from the whole of the predicate. Here, as in the I, the same logical import must be given to some; e. g., in the proposition, "Some men are not wise," our knowl- edge is comfined to the group who are not wise. Whether or not the others are wise or not-wise is unknown. Illustrations of the O proposition : 1. "Some men are not wise." 2. "Some laws are not just." 3. "Some novels are not helpful." The Relation Between Subject and Predicate 145 The significance of the O proposition may be shown by two intersecting circles as in Fig. 4 : Fig. 4. A similar diagram represents the I proposition, the only difference being in the part shaded. In the O proposition the investigated field is all of the "men" circle outside of the "wise" circle, while in the I proposition the known field is that part of the "men" circle inside the "wise" circle. In comparing the four diagrams the student will note that the affirmative propositions are inclusive, while the negative propositions are exclusive. (5) The Distribution of Subject and Predicate. A term is said to be distributed when it is referred to as a definite whole. In the proposition, "All men are mortal," the subject all men is considered as a whole. "All men" stands for every specimen of the human race; not a single one has been left out. Again, the whole is definite ; any one, if he were given the time and opportunity, could ascertain by actual count just how many "all men" represented. It should be observed that if the word definite is not incorporated in the definition of a distributed term, there 146 Logical Propositions is afforded an opportunity for error. The attending illus- trations will make this clear : 1. "All the students except John and James are dis- missed." 2. "All the students except John, James, etc., are dismissed." The subject of the first proposition is distributed, while the subject of the second is undistributed. Reasons: The first subject, "All the students except John and James," is referred to as a whole and that whole is definite, there- fore, it is distributed; the second subject, "All the stu- dents except John, James, etc.," is referred to as a whole, but as the whole is not definite, the term is not distri- buted. Because all is the quantity sign of the second sub- ject the casual observer might easily be misled in desig- nating it as a distributed term. Here it may be well to explain that when reference is made to subject or predicate the logical subject or predi- cate is meant. Unless this is constantly kept in mind error results; e. g., in the proposition, "All white men are Caucasians," the logical subject is "white men," not "men." If the subject were "men," it would be undis- tributed, as the whole of the man family is not considered, but the actual subject, being "white men," is distributed because the predicate refers to all white men. Recurring to the illustration, "All men are mortal," we have concluded that the subject "all men" is distributed. The predicate, "mortal," however, is undistributed, as reference is made to it only in part; i. e., there are other beings aside from men that are mortal, such as "trees," The Relation Between Subject and Predicate 147 "horses," "dogs," etc. In all A propositions of the type of u all men are mortal" the subject is distributed while the predicate is undistributed. This relation is clearly shown by the diagrammatical illustration, Fig. I. Here all of the "men" circle is identical with only a part of the "mortal" circle. In other words, the whole of the "men" circle is considered, while reference is made to only a part of the "mortal" circle. In the case of the co-extensive A both subject and predicate are distributed. Relative to the co-extensive "All men are rational animals," it could likewise be said that "all rational animals are men," or that "all men are all of the rational animals." Reference is thus made to all of the definite predicate as well as to all of the definite subject. In the E propositions, such as "No men are immortal," the whole of the subject is excluded from the whole of the predicate. This makes evident the fact that both terms are distributed. See Fig. 2. The I proposition, such as "Some men are wise," con- cerns itself with only a part of the subject and only a part of the predicate, consequently neither subject nor predicate is distributed. This relation is verified by the representation, Fig. 3. In the O proposition the subject is undistributed, while the predicate is distributed. For example, in the propo- sition, "Some men are not wise," "some men" would indicate that only a part of the logical subject is under consideration. But the predicate is distributed because "some men" is denied of the whole of the predicate, 148 Logical Propositions "wise." This may become clear by studying Fig. 4. Here all of the shaded part which stands for the subject, "some men," is excluded from the whole of the "wise" circle. But all of the shaded part is only a part of the entire "men" circle, consequently the subject which the shaded part represents (some men) is undistributed. The predicate, "wise," however, is distributed, as the subject is excluded from every part of it. It is well to remember that not, when used with the copula, distributes the predicate which follows it. If the student is to succeed in testing the value of argu- ments, he must ever have "at the tip of his tongue" his knowledge of the distribution of the terms of the four logical propositions. With this in view the following schemes are offered: I. Subject Predicate A distributed undistributed E distributed distributed I undistributed undistributed O undistributed distributed A distributed II. undistributed O undistributed distributed E distributed distributed I undistributed undistributed A All S is P III. E I No S is P 1 — 1 1 — 1 Some S is P | O Some S is not P The Relation Between Subject and Predicate 149 Referring to scheme II it may be observed that A and O contradict each other; i. e., where A is distributed O is undistributed and vice versa. A similar relation exists between E and I. In scheme III the bracket ^__ under the symbol indicates the term which is distributed. IV. As a fourth scheme a "key word" might be adopted. Any of these three might be used: (1) saepeo, or (2) asebinop, or (3) uaesneop. The significance of "saepeo" is this : "s" stands for subject distributed, "p" for predi- cate distributed, "a," "e" "0" for the logical propositions where any distribution occurs. Putting the letters together gives this: subject distributed of propositions A and E, predicate distributed of propositions E and O. Similarly, "asebinop" stands for this : "as," a distributes its subject; "eb," e distributes froth; "in" i distributes neither; "op" distributes the predicate. In the coined word "uaesneop" appear six letters which compose "saepeo," and the letters have the same signifi- cance. The two additional letters, u and n, stand for uni- versal and negative. The interpretation of the entire word, therefore, is this: "uaes" the wniversals a and e distribute their subjects; neop, the negatives e and dis- tribute their predicates. It seems to me that the last word is the most helpful as it emphasizes the two facts which are the most used; namely, (1) Only the universals distribute their subjects; (2) Only the negatives distribute their predicates. If the student will visualize "uaesneop" so thoroughly as never to forget it, he will not experience difficulty in 150 Logical Propositions determining the distribution of the terms of the four logical propositions. 9. OUTLINE. Logical Propositions. (1) The nature of logical propositions. (2) Kinds of logical propositions. Categorical Hypothetical Disjunctive (3) The four elements of a categorical proposition. (4) Logical and grammatical subject and predicate distin- guished. (5) The four kinds of categorical propositions. Universal affirmative A Universal negative E Particular affirmative I Particular negative O (6) Propositions which do not conform to the logical type. Indefinite and elliptical. Grammatical sentences Individual Plurative Partitive Exceptive Exclusive Inverted (7) Propositions not necessarily illogical. Analytic and synthetic. Modal and pure. Truistic (8)) The relation between subject and predicate of the four logical propositions. Euler's diagrams. Distribution of subject and predicate. Uaesneop Asebinop Saepeo Summary 151 10. SUMMARY. (1) A logical proposition is a judgment expressed in words. (2) The three kinds of logical propositions are categorical, hypothetical, disjunctive. A categorical proposition is one in which the assertion is made unconditionally. A hypothetical proposition is one in which the assertion depends upon a condition. A disjunctive proposition is one which asserts an alterna- tive. The most common word-signs of the categorical proposition are "all," "no," "some" and "some-not," of the hypothetical, "if" and of the disjunctive, "either — or." (3) Every logical categorical proposition has the four ele- ments: quantity sign, subject, copula and predicate. The quantity sign indicates the extension of the proposition; the logical subject is that of which something is affirmed or denied; the logical predicate is the term which is affirmed or denied of the subject; the copula is always some form of "to be" and is used to connect subject and predicate. "Not" is some- times used with the copula. The statements of ordinary conversation are usually not ex- pressed in terms of the four elements, but must be, before they can be used in testing arguments. (4) One word usually constitutes the grammatical subject while a word with all its modifiers goes to make up the logical subject. The verb with any predicate word is the grammatical predicate. The logical predicate is all which follows the copula — it may include the predicate-word and all its modifiers as well as the modified object. (5) Categorical propositions are divided into four kinds; uni- versal affirmative (A), universal negative (E), particular affirma- tive (I), particular negative (O). For the sake of brevity these four are respectively denoted by the vowels A, E, I, O. An A proposition is one in which the predicate affirms something of all of the logical subject. An E proposition is one in which the predicate denies something of all of the logical subject. 152 Logical Propositions An I proposition is one in which the predicate affirms something of a part of the logical subject. An O proposition is one in which the predicate denies something of a part of the logical subject. Every proposition must be reduced to one of the four types before it can be used as a basis of argumentation. It is incumbent on the student to recognize these four types with precision and accuracy. (6) There are a few proposition types which are recognized as being illogical in form. These may be denned as follows : (1) An indefinite proposition is one without the quantity sign. It usually may be classed as universal. (2) An elliptical proposition is one in which the copula is suppressed. (3) An individual proposition is one which has a singular subject. It is universal in content. (4) Plurative propositions are those introduced by "most," "a few," or some equivalent quantity sign. These are particular in meaning. (5) Partitive propositions are particulars which imply a complementary opposite. These arise through the ambiguous use of "ail-not," "some" and "few." "Ail-not" sometimes means "no," while at other times it may mean "not-all." If the quantity sign means the latter, then it introduces a partitive proposition. "Some" may mean "some only" or "some at least" The latter is the logical meaning. The former interpretation makes the proposition partitive. When "few" means "few only," it is partitive in nature. (6) Exceptive propositions are those introduced by such signs as "all except," "all but," "all save," etc. They are universal only when the exceptions are mentioned. (7) Exclusive propositions are those introduced by such words as "only," "alone," "none but" and "except." In an exclusive the predicate and not the subject is distributed. Consequently the easiest way to make an exclusive logical is to interchange subject and predicate and call it an A. Summary 153 (8) An inverted proposition is one where the predicate precedes the subject. Interchanging them gives the logical form. Of the grammatical sentences only the declarative is logical. The relative clause, though out of place, must be used with the word it modifies. (7) There are other propositions, though not illogical, to which the logician usually gives some attention. These may be defined as f ollows : (1) An analytical proposition is one in which the predi- cate gives information already implied in the sub- ject. (2) A synthetic proposition is one in which the predicate gives information not implied in the subject. (3) A modal proposition is one which states the manner in which the predicate belongs to the subject. The adverbs of time, place, degree and manner are the signs of the modal proposition. (4) A pure proposition simply states that the predicate belongs or does not belong to the subject. (5) A truistic or tautologous proposition is one in which the predicate repeats the words and meaning of the subject. (8) In considering the relation which may exist between sub- ject and predicate, the two terms are employed in extension only, as this use best serves the interests of inference. The extensional relation between subject and predicate of the four logical propositions may be stated as follows : Ordinary A — All of the subject belongs to a part of the predicate. Co-extensive A — All of the subject belongs to all of the predicate. E — None of the subject belongs to any part of the predi- cate. I — Some of the subject belongs to some of the predicate. O — Some of the subject is excluded from the whole of the predicate. 154 Logical Propositions In general it may be said that the affirmative propositions are inclusive while the negatives are prelusive. A term is said to be distributed when it is referred to as a definite whole. "A" distributes the logical subject only, "E" both logical sub- ject and logical predicate, "I" neither logical subject nor logical predicate, "O" the logical predicate only. The co-extensive "A" distributes both subject and predicate. It is essential that the student know by heart the distribution of the terms of the logical propositions. Some keyword like uaesneop may be used as an aid to the memory. This means the wniversals A and E distribute their subjects, while the nega- tives E and O distribute their predicates. 11. ILLUSTRATIVE EXERCISES. (la) Examine the following list of propositions with a view to classifying them as "A's," "E's," "I's" or "O's." E 1. "None of the inmates voted." A 2. "Benj. Franklin was the best educated American." / 3. "Some doctors deem it right to lie to their patients." A 4. "All earnest teachers need to observe the teaching of others." / 5. "Some politicians are honest." A 6. "Fools rush in where angels fear to tread." O 7. "Some proverbs are not true to life." E 8. "No man should infringe upon the rights of others." I recall that an affirmative proposition in which the predicate refers to the whole of the subject is an A, while one where the predicate refers to only a part of the subject is an I. Further, a negative proposition where the predicate refers to the whole of the subject is an E, while one in which the predicate refers to only a part of the subject is an O. With these facts in mind, I classify the propositions as indicated. (lb) In a similar manner classify as to quantity and quality the following: (1) "All worthy workers grow to look like their work." Illustrative Exercises 155 (2) "Every dog has his day." (3) "Some of the presidents were not popular." (4) "No unskilled laborer can afford to own an auto- mobile." (5) "Some of the 'election prophets' were sadly mis- taken." (2a) Classify the following propositions and make the illogical, logical : (1) "Only first-class passengers may ride in parlor cars." (2) "Haste makes waste." (3) "Few men know how to act under stress." (4) "All which seems to ring true is not true." (5) "Members alone are admitted." (6) "None but men of integrity need apply." (7) "Horses trot." (8) "Blessed are they which are persecuted for righteous- ness sake." The first proposition is an exclusive and may be made logical by converting and calling it an A, viz. : "All who ride in parlor cars are first-class passengers." (A) The second is indefinite and elliptical and is made logical by prefixing the universal quantity sign and expressing in terms of the four elements. The logical form is, "All who make haste are those who are wasteful." (A) The third is plurative in nature and means, "Most men do not know how to act under stress." It would be classed as an O. The fourth is partitive in nature because of the ambiguous use of "all — not." It means, "Some who seem to ring true are not true." (O) The fifth is an exclusive. By converting and changing to an A the proposition takes the logical form, "All who are admitted are members." The sixth is likewise an exclusive, the logical form being,' "All who apply must be men of integrity." The seventh is an elliptical proposition. Logical form : "All horses are trotting animals." The eighth is an inverted or poetical proposition. It is made logical by interchanging subject and predicate. Logical form: "Those who are persecuted for righteousness sake are blessed." 156 Logical Propositions (2b) Classify the attending propositions and change to the logical form, if necessary: (1) "Only truthful men are honest." (2) "The stokers alone were saved." (3) "All who run do not think." (4) "Honesty is the best policy." (5) "They laugh that win." (6) "The good alone are happy." (7) "Knowledge is power." (8) "Only the actions of the just smell sweet and blossom in the dust." 12. REVIEW QUESTIONS. (1) Define and illustrate logical propositions. (2) Define and exemplify the three kinds of logical prop- ositions. (3) What are the usual quantity signs of the four kinds of propositions? (4) Name and define the four elements of a logical proposi- tion. (5) Select from the printed page five propositions which are not expressed in terms of the four elements, and so express them. (6) Distinguish between logical and grammatical subject; likewise between logical and grammatical predicate. (7) Define and illustrate the four kinds of categorical prop- ositions. (8) What makes an understanding of the four logical prop- ositions so important? (9) Give the unusual quantity signs of the logical propositions. (10) What should guide one in making an indefinite proposi- tion logical? (11) How are general truths usually classified? (12) Change birds fly to the logical form. (13) How many and what kinds of grammatical sentences are logical? (14) How would the logician deal with interrogative sen- tences ? Review Questions 157 (15) Give illustrations of individual propositions. How are they usually classified? (16) Explain the logical mode of dealing with the plurative proposition. (17) Exemplify the ambiguity of "ail-not," "some" and "few." (18) Why are propositions introduced by "ail-not," "some" and "few" called partitive? (19) Use "all" in both a partitive and collective sense. Which signification has logic adopted? (20) When are exceptive propositions universal and when par- ticular ? (21) What is an exclusive proposition? (22) Explain by circles the exclusive. (23) Tell in full how to change an exclusive to logical form. (24) Tell how the logician would deal with such poetical ex- pressions as "Blessed are the pure in heart," "Tell me not in mournful numbers," "Strenuous is the man of state." (25) What distinction does the logician make between analytic and synthetic propositions? (26) Illustrate the difference between the so-called modal and pure propositions. (27) Explain and illustrate the truistic proposition. (28) Show by circles the relation existing between the subject and predicate of all the logical propositions. (29) State in good English the relation between the subject and predicate of all the logical propositions. (30) Relative to the distribution of terms apply the words "uaesneop" and "asebinop." Which one is the more serviceable? (31) Distinguish between the grammatical and logical subject. (32) Explain by circles the distribution of the terms of the four logical propositions. (33) The statement, "A part of the subject is excluded from the whole of the predicate," describes which proposition? Ex- plain how it indicates that the predicate is distributed. 13. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Show that a judgment may be an individual notion as well as a general notion. 158 Logical Propositions (2) Many logicians classify logical propositions in this wise: ("Categorical Propositions , T _ , . , {Conditional f Hypothetical *■ (Disjunctive Give arguments for and against such a classification. (3) "All men are bipeds" is a judgment of extension, while "Man is wise" is a judgment of intension. Explain. (4) "To be logical is to be pedantic." Discuss this. (5) Why is the proposition, "He runs," illogical? Make it logical. (6) Point out the reasons for calling, "White men are Cau- casians," a particular proposition. (7) What makes it necessary to change the propositions of ordinary conversation to those of the four logical types? (8) Some would call the individual proposition particular. Argue the question. (9) Make a list of five propositions in common speech and show how their partitive implication may mislead. (10) Explain by circles some only and some at least. (11) Explain how "et cetera" may change a universal to a particular proposition. . (12) "The real nature of an exclusive is best shown by ne- gating the subject and calling the proposition an E." Give argu- ments for and against this statement. (13) Show that with the immature mind all propositions must be synthetical. (14) Explain how a proposition may be truistic in form but not in meaning. (15) Show by the Euler diagram how easy it is for the care- less student to think that an "O" does not distribute its predicate. (16) Explain by the use of two pads (a small yellow one and a large white one) the distribution of terms. (17) When the logician makes reference to the subject of a proposition, show that he should exercise care in designating it as the logical subject. CHAPTER 9. IMMEDIATE INFERENCE OPPOSITION. 1. THE NATURE OF INFERENCE. Inference is the thought process of deriving a judgment from one or two antecedent judgments. The process is simply a matter of expressing explicitly in a final judgment, a truth that was implied in one or two previous judgments. To exemplify: From the ante- cedent truth, that "All teachers should be fair minded," one may derive a consequent truth that "This teacher, Albert White, should be fair minded." Or from the state- ment, "All men are mortal," one may derive the judg- ment, "No men are immortal." Because the ground is wet we conclude that it has rained. If all dogs are quad- rupeds then surely some dogs are quadrupeds. Finally from the two propositions, "All training school students are high school graduates," and "Mary Jones is a train- ing school student," we are led to conclude that "Mary Jones is a high school graduate." 2. IMMEDIATE AND MEDIATE INFERENCE. It has been noted that a truth may be derived from d consideration of one or two antecedent judgments. To illustrate further: From the judgment, "All men are fallible," we may derive the conclusion that "No men are infallible"; or, from the two judgments, "All men are fallible," and "Socrates was a man," we may readily infer 159 i6o Immediate Inference that "Socrates was fallible." These two modes of infer- ence take the names of immediate inference and mediate inference. Let us express these two kinds in equation form: I. Ordinary Form. Equation Form, Using Initial Letters. Antecedent judgment: All men are fallible. Conclusion: No men are infalli- ble. II. First antecedent judgment: All men are fallible. Second antecedent judgment : Socrates was a man. Conclusion : Socrates was falli- ble. Giving attention to the antecedent judgments of the second argument it is noted that the terms "f and "S" are referred to the common term "m" In logic this common term is known as the middle term. As there is but one antecedent judgment in the first argument there can be no common or middle term. The first argument is an illustration of immediate inference; the second of mediate inference. This suggests the definitions: Immediate inference is inference without the use of a middle term. Mediate inference is inference by means of a middle term. All m are f No m are i All m are f S was m .'. S was f The Forms of Immediate Inference 161 3. THE FORMS OF IMMEDIATE INFERENCE. Many logicians recognize four forms of immediate in- ference. These four forms are (i) opposition, (2) ob- version, (3) conversion, (4) controversion* (1) IMMEDIATE INFERENCE BY OPPOSI- TION. We have learned that to be logical all categorical asser- tions must be reduced to some one of the four proposi- tions, A, E, I, O. If these four logical propositions be given the same subject and predicate, certain definite rela- tions will become evident; therefore, Opposition is said to exist between propositions which are given the same subject and predicate, but differ in quality, or in quantity, or in both. The following illustrative outline will make this clear: 1. 2. Original Proposition. Opposite in Quantity. I. All men are mortal. (A) Some men are mortal. (I) II. No men are immortal. (E) Some men are not immortal. (O) III. Some men are wise. (1) All men are wise. (A) IV. Some men are mortal. (I) All men are mortal. (A) V. Some men are not wise. (O) No men are wise. (E) VI. Some men are not immor- No men are immortal. (E) tal. (O) 3. 4. Opposite in Quality. Opposite in Both. No men are mortal. (E) Some men are not mortal. (O) All men are immortal. (A) Some men are immortal. (I) Some men are not wise. (O) No men are wise. (E) Some men are not mortal. (O) No men are mortal. (E) Some men are wise. (I) All men are wise. (A) Some men are immortal. (I) All men are immortal. (A) * Sometimes called contraposition. 1 62 Immediate Inference Granting the truth of the propositions in the first col- umn, it follows that those in the second column differ in quantity. That is, in "Some men are mortal," a smaller number of men is referred to than in "All men are mor- tal." A similar variation in quantity obtains with the other propositions in the second column. Moreover, the propositions in the third column are the negative of the corresponding ones in the first; while the fourth column propositions differ from the first in both quantity and quality. Thus opposition exists to a greater or less de- gree between all. We may now ask ourselves the question, "When the propositions are related to each other in oppo- sition which ones are true and which ones are false ?" Giv- ing attention to the propositions in row "I," we note that if the universal affirmative, "All men are mortal," is true, then the particular affirmative, "Some men are mortal," is likewise true; because of the principle, "What is true of the whole of the class is true of a part of that class." But the universal negative, "No men are mortal," and the particular negative, "Some men are not mortal," are both false. Briefly stated: If A is true, then I is true, but, both E and O are false. Regarding row "II" we may conclude that if E is true, then O is likewise true, but both A and I are false. As to rows "III" and "IV," granting the truth of the I propositions, "Some men are wise" and "Some men are mortal," we are able to assert that of the two A proposi- tions, "All men are wise," and "All men are mortal," the first is false while the second is true. A is, therefore, in- determinate, or doubtful. Of the O propositions, "Some The Forms of Immediate Inference 163 men are not wise," is true while, "Some men are not mor- tal," is false. Therefore, O is doubtful. Both of the E propositions are false. Hence, the conclusion relative to rows "III" and "IV" is : If I is true, A and O are doubt- ful, while E is false. Concerning rows "V" and "VI" it will be seen without further explanation that if O is true, then E and I are doubtful and A is false. The Scheme of Opposition. The conditions of opposition are easily comprehended and remembered when recourse is made to the following scheme : A E I O If A be true If E be true If I be true If O be true To use the above scheme, read horizontally from left to right. For example : If A be true, then all in the row opposite obtains; that is, A is true, E is false, I is true, and O is false. (We take it for granted that the student will see that the first column belongs to A, the second to E, the third to I, and the fourth to O.) If E be true, then A is false, E is true, I is false, O is true, etc. The whole of opposition is comprehended in two facts which are based upon one principle. This is the principle : Whatever may be said of the entire class may be said of true false true Jafee"" false Ixtie fafee" true doubt fajse^ true doubt false^ doubt doubt ^true 164 Immediate Inference a part of that class. To put it in another way : Whatever is affirmed of all may be affirmed of some, or, Whatever is denied of all may be denied of some. To illustrate: Accepted truth: All planets rotate. (A) Accepted inference: Some planets rotate. (I) or Accepted truth: No planet is a sun. (E) Accepted inference : Some planets are not suns. (O) These are the two facts : First, a particular affirmative may be derived from a universal affirmative. Second, a particular negative may be derived from a universal negative. Or, more briefly: An I may be derived from an A, and an O from an E. Square of Opposition. Aristotle represented the relations of the four logical propositions by what is termed the square of opposition. A Contraries E The Forms of Immediate Inference 165 Viewed from the standpoint of the square, the relations may be summed up as follows : 1. Contrary Propositions. Why so named. As related to each other, A and E are said to be con- trary because they seem to express contrariety to the greatest degree. Relation stated. If one is true, the other must be false, but both may be false. Illustrations. (1) If one is true, the other must be false; e. g., if A is true, as "All metals are elements," then E is false, as "No metals are elements." Or, if E is true, as "No birds are quadrupeds," then A is false, as "All birds are quadrupeds." (2) Both may be false. If A is false, as "All men are wise/' then E may be false, as "No men are wise." 2. Subcontrary Propositions. Why so named. Propositions I and O are said to be related to each other in a subcontrary manner because they are contrary as to each other and "under" their universals A and E. Relation stated. If one is false, the other must be true, or, both may be true. Illustrations. (1) If one is false, the other must be true. If I is false, as "Some metals are compounds," then, O is true, as "Some metals (at least) are not compounds." 1 66 Immediate Inference Or, if O is false, as "Some metals are not elements," then I is true, as "Some metals are elements." (2) Both may be true. If I is true, as "Some men are wise," then O also may be true, as "Some men are not wise." 3. Subalterns. Why so named. Etymologically considered subaltern means under the one, thus proposition I is under A, and O is under E. Relation stated. First Relation. Subalterns are related to each other as are the uni- versal and particulars ; hence, (1) If the universal is true, the particular under it is also true ; while if the particular is true, the corresponding universal may, or, may not, be true. Illustrations. (a) If the universal is true, the particular under it is true. If A is true, as "All metals are elements," then I is true, as "Some metals are elements." Or, if E is true, as "No metals are compounds," then, O is also true, as "Some metals (at least) are not compounds." (b) If the particular is true, the corresponding uni- versal may, or, may not, be true. If I is true, as "Some men are wise," or, "Some men are mortal," then A may be false, as "All men are wise," or, A may be true, as "All men are mortal." Or, if O is true, as "Some men are not wise," or, "Some men are not The Forms of Immediate Inference 167 immortal," then E may be false, as "No men are wise" ; or, true, as "No men are immortal." Second Relation. (2) If the universal is false, the particular under it may or may not be true, but, if the particular is false, the universal above it must be false. Illustrations. (a) If the universal is false, the particular under it may or may not be true. If A is false, as "All metals are compounds," or "All men are wise," then I may be false, as "Some metals are compounds," or, I may be true, as "Some men are wise." Or, if E is false, as "No men are mortal," or, "No men are wise," then O may be false, as "Some men are not mortal," or, O may be true, as "Some men are not wise." (b) If the particular is false, the universal above it must be false. If I is false, as "Some men are trees," then A is false, as "All men are trees." Or, if O is false, as "Some men are not bipeds," then E is also false, as "No men are bipeds." 4. Contradictory Propositions. Why so named. The propositions A and O, likewise E and I, are called contradictory propositions because they oppose each other in both quantity and quality. They are mutually opposed to each other or absolutely contradictory. Relation stated. If one is true the other must be false. 1 68 Immediate Inference Illustrations. (i) A and O compared. If A is true, as "All metals are elements," then, O is false, as "Some metals are not elements." Or, if O is true, as "Some metals are not compounds," then A is false, as "All metals are compounds." (2) E and I compared. If E is true, as "No birds are quadrupeds," then I is false, as "Some birds are quadrupeds." Or, if I is true, as "Some birds are bipeds," then E is false, as "No birds are bipeds." The chief value of the square of opposition springs from the contradictory propositions. The square shows conclusively that any universal affirmative assertion (an A) may best be contradicted by proving a particular nega- tive (an O). For example: To satisfactorily refute the statement that, in this section, all birds migrate to the south in winter, it would be sufficient to prove that the English sparrow and starling do not migrate to the south. The square likewise makes evident that any universal negative (an E) may be conclusively denied by establish- ing the truth of a particular affirmative (an I). To illus- trate : The easiest way to prove the falsity of "No trusts are honest" is to present facts showing that at least trusts A and B are honest. The Individual Proposition. An individual proposition is one with an individual sub- ject such as "Aristotle was wise." In logic, the indi- vidual proposition is classed as a universal. This seems to be a bit irregular, as with the individual proposition The Forms of Immediate Inference 169 there is no particular, while, the strictly logical universal always implies a particular. Because of this variation from the true logical form the relations, as indicated by the square of opposition, do not apply to the individual proposition. For example: According to the square A and E are contrary, but, when individual, A and E con- tradict each other, as "Aristotle was wise" (A) — "Aris- totle was not wise" (E). CHAPTER 10. IMMEDIATE INFERENCE (CONTINUED) OBVERSION, CON- VERSION, CONTRAVERSION AND INVERSION. (2) IMMEDIATE INFERENCE BY OBVER- SION. Obversion is the process of changmg a proposition from the affirmative form to its equivalent negative or from the negative form to its equivalent affirmative. Some authorities refer to this process as "Inference by Privitive Conception/' but Obversion seems to be a better term. Obversion is based upon the principle that two nega- tives are equivalent to one affirmative. With this double negative principle in mind let us experiment with the four logical propositions, A, E, I, O. The A Proposition. Example: "All thoughtful men are wise." Insert the double negative and the proposition reads: "All thought- ful men are not not-wise." Changed to the logical form this becomes: "No thoughtful men are not-wise." Sim- plified and we have, finally : "No thoughtful men are un- wise." Thus by the process of obversion we have passed from the original proposition, "All thoughtful men are wise," to "No thoughtful men are unwise." In the first proposition the subject "thoughtful men" is denied of the predicate "unwise." Assuming that "unwise" is the con- tradictory of "wise," then : "What is affirmed of a predi- 170 Immediate Inference by Obversion 171 cate may be denied of its contradictory." Recourse to cir- cles will make this clearer. In the previous chapter it has been suggested that not bisects the world. For example : What can not be included in the wise class may be placed under the not-wise or unzvise class. Likewise a circle bisects space — there is the space inside the circle and the space outside the circle. Let the space inside the circle represent all wise beings, then the space outside the circle would represent all not-wise or unwise beings ; e. g., unwise ( Wise J unwise wise unwise unwise Fig. 5. Now representing thoughtful men by a smaller circle and placing it inside the larger we have, unwise unwise #*«i««y#«*/— unwise 172 Immediate Inference Referring to Fig. 6 we note that all of the smaller cir- cle belongs to the larger or that none of the smaller circle belongs to the space outside of the larger. Hence the two propositions: "All thoughtful men are wise" (A), and "No thoughtful men are unwise" (E) have virtually the same meaning though the same subject is related to different predicates. The use of the positive or negative form depends upon circumstances. Often the negative puts the thought in a more forceful way. In passing from, "All thoughtful men are wise," to "No thoughtful men are unwise," it was necessary to pre- fix not to the predicate wise and substitute for not its equivalent tin. If the original predicate were unwise or not-wise, then the reverse order of dropping the un or not could be followed. This process of prefixing the not to an affirmative predicate or of dropping the not from a negative predicate is referred to as negating the predi- cate. Before substituting in, im, un, etc., for not, one must make sure that the substitution really gives the con- tradictory; there are some logicians who claim that un- wise, for instance, is not the contradictory of wise. In comparing the first proposition with the second it is observed that the first is an A, while the second is an E, also that the predicate of the first was negated to form the predicate of the second. Thus the rule: Negate the predicate and change A to E. To sum up: The obversion of an A proposition. Immediate Inference by Obversion 173 1. Principle: Two negatives are equivalent to one affirmative. 2. Rule: Negate the predicate and change the A to an E by using the sign no instead of all. 3. Process illustrated. The Original Proposition (A) The Obverse (E) All men are mortal. No men are immortal. All maples are trees. No maples are not-trees. All teachers should be sympa- No teacher should be un- thetic. sympathetic. All pain is unpleasant. No pain is pleasant. All men are imperfect. No men are perfect. All birds are feathered ani* No birds are non- mals. feathered animals. All men are not-trees. No men are trees. All scalene triangles are non- No scalene triangles are equilateral. equilateral. The E Proposition. It is obvious that the process of obverting an E is sim- ply the reverse of obverting an A. Consequently, the same principle obtains ; whereas the process may be illus- trated by reading the foregoing illustrations reversely. The rule for obverting E is : Negate the predicate and change the E to an A by changing the sign no to all. The I Proposition. Let us note the result when the double negative prin- ciple is applied to the I proposition. Original : "Some men are wise." Adding two negatives: "Some men are not not-wise." 174 Immediate Inference The foregoing simplified: "Some men are not unwise." In comparing the first proposition with the last it is ob- served that the first is an I while the last is an O; it is also observed that the predicate of the first was negated in order to form the predicate of the last. Thus the rule : "Negate the predicate and change the I to an O." The use of circles may make this clearer: unwise unwise Mori Hi Ia/j.*;* I unwise The significant part of Fig. 7 is that which is inked. Here we have represented the part of the "men" circle which is common to the "wise" circle. Thus the inked part represents "Some men are wise." If the inked part is entirely inside of the "wise" circle, no part of it can belong to the "unwise" space without. Thus the obverse, "Some men are not unwise." Summary. The obversion of an I proposition. 1. Principle: Same as with A. 2. Rule: Negate the predicate and change the I to an O. Immediate Inference by Obversion 175 3. Process illustrated. The Original Proposition (I) The Obverse (0) Some water is pure. Some water is not impure. Some curves are perfect. Some curves are not imper- fect. Some friends are loyal. Some friends are not dis- loyal. Some men are true. Some men are not not-true. Some precious stones are Some precious stones are imperfect. not perfect. Some plants are not-trees. Some plants are not trees. Some boys are not-honest. Some boys are not honest. It must be borne in mind that when "nof ' is used without the hyphen it makes the proposition negative, because when "unhyphened" "not" must be thought of in connec- tion with the copula and not in connection with the predi- cate ; while "nof attached to the predicate with a hyphen simply makes the predicate negative without affecting the quality of the proposition ; e. g., "Some plants are not trees" is a negative proposition, while "Some plants are not-trees ,, is an affirmative proposition with a negative predicate. It may not be clearly seen how it is possible, by follow- ing the rule given, to pass from such a proposition as "Some plants are not-trees," to "Some plants are not trees/' Let us illustrate the steps : 1. The original: "Some plants are not-trees." 2. Negating predicate : "Some plants are trees." 3. Changing to an O : "Some plants are not trees." 176 Immediate Inference Dropping the not from "1" and then adding it again to "2" is simply putting into operation the double negative idea, so that there is no violation of the principle. The Proposition. O bears the same relation to I that E bears to A. The principle involved is the same. The process is illustrated by reading reversely the scheme of illustrations under I. The rule is as follows : To obvert an O negate the predi- cate and cliange the O to an I by eliminating the not. Summary of Obverting the Four Logical Propositions. 1. Principle: Two negatives are equivalent to one affirmative. 2. Rules: f (1) A to E J ( 2 Negate the predicate J (2) E to A and change 1 (3) I to O ^ (4) O to I (3) IMMEDIATE INFERENCE BY CONVER- SION. Conversion is the process of inferring from a given proposition another which has, as its subject, the predicate of the given proposition, and, as its predicate, the subject of the given proposition. It is simply a matter of trans- posing subject and predicate. The original proposition is called the convertend while the derived proposition is named the converse. The process of conversion is limited by two rules. First rule. No term must be distributed in the converse which is not distributed in the convertend. Second rule. The quality of the converse must be the same as that of Immediate Inference by Conversion 177 the convertend. More briefly: (1) Do not distribute an undistributed term. (2) Do not change the quality. We recall that a term is distributed when it is referred to as a definite whole. An undistributed term is referred to only in part. The principle underlying rule "1" there- fore, is the one which forms the basis of inference by opposition ; namely, "Whatever may be said of the entire class may be said of a part of that class." The converse of this is not true, that is, "What is said of part of a class cannot be said of the whole of that class.'' When we dis- tribute an undistributed term we are saying of the whole class what was said only of a part of that class. This is fallacious. On the other hand, we may say of a part what was said of the whole, or "undistribute" a distributed term. , We recall that the conclusion of the whole matter of inference by opposition was, that only an I could be in- ferred from an A and only an O from an E, or to put it in another way: Only an affirmative from an affirmative and only a negative from a negative. This establishes the truth of the second rule in conversion: "Do not change the quality." Let us apply the two rules to the four logical proposi- tions. Converting an A proposition. Take as a type, "All horses are quadrupeds." Here the subject " horses" is distributed, but the predicate "quad- rupeds" is undistributed. In transposing subject and predicate we cannot distribute the term "quadrupeds," according to the rule which says, "Do not distribute an 178 Immediate Inference undistributed term." Hence in interchanging subject and predicate we cannot say, "All quadrupeds are horses," but must limit the assertion to, "Some quadrupeds are horses." Logicians call this process Conversion by Limita- tion. Conversion by Limitation Exemplified Further. Convertend Converse. All metals are elements. Some elements are metals. All bees buzz. Some buzzing insects are bees. All men are fallible. Some fallible beings are men. All good teachers are sym- Some sympathetic persons pathetic. are good teachers. The conclusions from the foregoing are these: First, the usual mode of converting an A is to interchange sub- ject and predicate, limiting the latter by the word "some" or a word of similar significance. Second, this mode is called conversion by limitation. Third, the converse of an A is an I. The Co-extensive A. In the conversion of A propositions there is the one ex- ception of "co-extensive A's," such as truisms and defini- tions. It will be remembered that with these both subject and predicate are distributed; hence, they may be inter- changed without limiting the predicate by "some." To illustrate: The converse of the truism, "A man is a man," is "A man is a man," while the converse of the definition, "A man is a rational animal," is "A rational animal is a man." This mode of interchanging subject and predicate Immediate Inference by Conversion 179 without limiting the latter is called Simple Conversion. The ordinary A proposition is thus converted by limita- tion, while the co-extensive A is converted simply. Converting an E proposition. As both terms of the E proposition are distributed it is not possible to violate the rule of distribution. It is to be remembered that no fallacy is committed by "undis- tributing" a term which is already distributed. Illustrations. Convertend. Converse. No men are immortal. No immortals are men. Simply. No birds are quadrupeds. No quadrupeds are birds. Simply. No metals are compounds. No compounds are metals. Simply. No men are immortal. S#me immortals (at least) are not men. Limitation. No birds are quadrupeds. Same quadrupeds are not birds. Limitation. No metals are compounds. Some compounds are not metals. Limitation. Three facts are evident relative to the converting of an E. First: An E proposition may be converted either simply or by limitation. Second: E may be converted into either E or O. Third: If the converse is an O then is the inference a weakened one, being particular when it could just as well be universal. Converting an I proposition. With an I proposition neither term is distributed. 180 Immediate Inference Thus care must be used lest an undistributed term in the convertend be distributed in the converse. Illustrations: Convertend. Converse. Some men are wise. Some wise beings are men. Some teachers scold. Some who scold are teachers. Some high school graduates Some who enter college are enter college. high school graduates. Some Americans live simply. Some who live simply are Americans. From the foregoing we conclude first, that I is con- verted simply; second, that I is converted into I. The Proposition. With an O proposition the subject is undistributed while the predicate is distributed. This condition presents a peculiar difficulty. Consider, for example, the O proposi- tion, "Some men are not wise." Convert this into, "Some wise beings are not men," and the undistributed subject of the convertend, which is "men," becomes the distributed predicate of the converse. Thus the proposition cannot be converted without violating the rule for distribution. A Summary of How the Four Logical Propositions May be Converted. i. A. The ordinary A proposition may be con- verted by limitation only. The co- extensive A may be converted simply. 2. E. The E proposition is converted simply. The E may also be converted by limita- tion, but the inference thus obtained is weakened. 3. /. The I proposition may be converted simply only. 4. O. The O proposition cannot be converted. Immediate Inference by Contr aversion 181 (4) INFERENCE BY CONTRAVERSION. (Contraposition). This mode of inference is usually referred to as in- ference by contraposition, but contraversion, indicating more definitely the nature of the process, is a better term. Contraversion involves two steps: First, obversion; sec- ond, conversion. The same principles and rules evident in these two processes obtain in inference by contraver- sion. The following scheme, therefore, ought to be sufficient to make the matter clear: Inference by Contraversion. 1. The Given Proposition. 2. Obverted. A. All men are mortal. No men are immortal. All trees are plants. No trees are not-plants. E. No men are infallible. All men are fallible. No men are trees. All men are not-trees. I. Some men are wise. Some men are not not-wise. O. Some water is not pure. Some water is impure. Some houses are not white. Some houses are not-white. 3. Converted; giving the contraverse of the original proposition. No immortals are men. No not-plants are trees. Some fallible beings are men. Some not-trees are men. An O cannot be converted, consequently the contraversion of an I is impossible. Some impure liquids are water. Some not-white buildings are houses. It is indicated in the foregoing scheme that "I" cannot be contraverted. This is due to the fact that the obverse 182 Immediate Inference of an I is an O, and it will be remembered that "O" cannot be converted. All the other propositions admit of contraversion. 4. EPITOME OF THE FOUR PROCESSES OF IMMEDIATE INFERENCE IN CONNECTION WITH THE FOUR LOGICAL PROPOSITIONS. Proposition symbolized Name of Process Inference symbolized Principle involved A All S is P* Opposition Obversion Some S is P (i) No S is not-P (E) Conversion by Some P is S (i) Limitation Contraversion No not-P is S (E) What is said of all may be said of some. Two negatives are equivalent to one affirmative. An undistributed term cannot be distributed. Same principles which obtain in obvertingf A and convert- in? E. E No Sis P Opposition Some S is not P (0) What is said of all may be said of some. Obversion All S is not-P (A) Two negatives are equivalent to one affirmative. Simple Conversion No P is S (E) Distribution not affected. Contraversion Some not-P is S (l) An undistributed term cannot be distributed. I Some S is P Opposition Doubtful None. Obversion Some S is not not-P (o) Two negatives are equivalent to one affirmative. Conversion Some P is S (i) Distribution not affected. Contraversion Impossible None. O Some S is not P Opposition Doubtful None. Obversion Some S is not-P (i) Two negatives are equivalent to one affirmative. Conversion Impossible None. Contraversion Some not-P is S (i) Same as in obversion of O and conversion of I. *S" represents any subject and "P" any predicate. Inference by Inversion 183 Inference By Inversion. Some logicians treat of a form of immediate inference known as inversion though it is of small importance and of little practical value. The process can be applied only to propositions A and E. In the one case the contradictory subject is limited by "some" and then denied of the predicate, whereas, in the other case, the contradictory subject is merely affirmed of the predicate. Illustrations. The Given Proposition. The Inverse. I. All S is P. (A) Some not-S is not P. (O) All planets rotate. Some not-planets do not rotate. II. No S is P. (E) Some not-S is P. (I) No men are immortal. Some not-men are immortal. From the foregoing we are able to conclude that the inverse of "A" is found by negating the subject and changing to an "O" ; while the inverse of "E" is found by negating the subject and changing to an "I." 5. OUTLINE. Immediate Inference — Opposition — Obversion, Conversion, contraversion and inversion. 1. The Nature of Inference. 2. Immediate and Mediate Inference. 3. The Forms of Immediate Inference. (1) Opposition. (a) Scheme of Opposition. (b) Square of Opposition. (2) Obversion. (3) Conversion. (a) Simply. (b) By Limitation. (4) Contraversion. Inversion. 6. SUMMARY. 1. Inference is the thought process of deriving a judgment from one or two antecedent judgments. 184 Immediate Inference 2. Immediate inference is inference without the use of a middle term. Mediate inference is inference by means of a middle term. 3. The four common forms of immediate inference are (1) opposition, (2) obversion, (3) conversion, (4) contraversion. (1) The name opposition stands for certain definite relations which exist between the logical propositions v/hen they are given the same subject and predicate. The one principle underlying opposition is : Whatever is said of the entire class may be said of a part of that class. The two statements which sum up oppo- sition are first, an I may be derived from an A; and second, an O may be derived from an E. The crucial fact made obvious by the square of opposition is that A and O are mutually contradictory; likewise E and I. (2) Obversion is the process of passing from an affirmative to its equivalent negative or from a negative to its equivalent affirmative. "Two negatives are equivalent to one affirmative," is the basic principle of obversion. The proposition A may be obverted by negating the predicate and changing to an E. "E" is obverted by negating the predicate and changing to an A. "I" is obverted by negating the predicate and changing to an O. "O" is obverted by negating the predicate and changing to an I. (3) Conversion is the process of inferring from a given propo- sition another which has as its subject the predicate of the given proposition and as its predicate the subject of the given proposition. Conversion is limited by the two rules, (1) do not distribute an undistributed term; (2) do not change the quality. To convert an A interchange subject and predicate, limiting the latter by some, or a word of like significance. This is called conversion by limitation. The co-extensive A may be converted without limiting the predicate. This is called simple conversion. An E proposition may be converted either simply or by limita- tion. When converted by limitation the inference is a weakened one. An I proposition is converted simply only. Summary 185 The O proposition does not admit of conversion. (4) Immediate inference by contraversion is a process involv- ing first obversion and then conversion. "A," "E" and "O" may be controverted ; "I" cannot be con- travened. 7. ILLUSTRATIVE EXERCISES. (la) From the antecedent judgment, "All weeds are plants," I am able to derive by immediate inference these judgments: (1) "All weeds are not not-plants," or "No weeds are not plants." (2) "No not-plants are weeds." (3) "Some plants are weeds." (4) "Some weeds are plants." (lb) "All vertebrates have a backbone." From the foregoing judgment derive immediately five different conclusions. (2a) "All good citizens try to vote," ^'Albert White is a good citizen/' Hence, "Albert White will try to vote." I know that the above is an example of mediate inference be- cause the two antecedent judgments make use of the middle term, "good citizen" (2b) Why is the following illustrative of mediate inference? "All wise men are close observers," "All wise men are thoughtful," Hence, "Some thoughtful men are close observers." (3a) Derive immediate inferences by opposition from the fol- lowing : (1) "Good men are wise." (2) "No teacher can afford to be unjust." (3) "All birds fly." (4) "None of the inner planets are as large as the earth." I first determine that "1" and "3" are A propositions, while "2" and "4" are E's. Then I recall that by opposition an I may be derived from an A and an O from an E. Hence, the inferences are: (1) "Some good men are wise." (2) "Some teachers cannot afford to be unjust." (3) "Some birds fly." (4) "Some of the inner planets are not so large as the earth." 1 86 Immediate Inference '3b) Derive by opposition inferences from the following: (1) "No true woman will neglect her home for society." (2) "All patriotic men love the flag." (3) "Fools rush in where angels fear to tread." (4a) Obvert the following: (1) "All earnest teachers are diligent students." (2) "No self-respecting man can afford to be careless in his personal appearance." (3) "Some of the great teachers of the past did not practice what they preached." (4) "Some weeds are beautiful." I determine first the logical character of each proposition, finding the first to be an A, the second an E, the third an O and the fourth an I. Then I recall that in obversion the predicate must always be negated and an A must be changed to an E or an E to an A ; also an I must be changed to an O or an O to an I. Hence, the obverse of each proposition is : (1) "No earnest teacher is a not-diligent student." (2) "All self-respecting men can afford to be not-careless (careful) in their personal appearance." (3) "Some of the great teachers of the past did not- practice (failed to practice) what they preached." (4) "Some weeds are not not-beautiful." (4b) Infer by obversion from the following: (1) "All roses are beautiful." (2) "None of the members of the stock exchange are dishonest." (3) "Some pupils are not industrious." (4) "Some teachers are tactful." (5a) Convert the following: (1) "All that glitters is not gold." (2) "All good men are wise." (3) "Some books are to be chewed and digested." (4) "No man is perfectly happy." It is first necessary to determine the logical character of each proposition. Carelessness might lead one to call the first propo- sition an A because it is introduced by the quantity sign "all." But on second thought we note that the meaning is to the effect that some glittering things are not gold; this is an O. It is clear Illustrative Exercises 187 that the second is an A, the third an I and the fourth an E. It is now expedient to recall the rules regarding conversion. These are, (1) do not distribute an undistributed term; (2) do not change the quality. We may now attempt to interchange the subject and predicate of each proposition, with the following results : (1) Conversion impossible. (2) "Some wise men are good men." (3) "Some things to be chewed and digested are books." (4) "No perfectly happy being is a man." When attempting to convert proposition (1), I find that the subject which is undistributed becomes distributed, hence the rule pertaining to distribution is violated. This conclusion is verified by recalling the fact that an O proposition cannot be con- verted. The second proposition, being an A, is converted by limita- tion; while the third and fourth are converted simply, as is the natural procedure with all Fs and E's. (5b) Convert these propositions : (1) "Blessed are the meek." (All the meek are blessed.) (2) "None but material bodies gravitate." (All gravita- ting bodies are material.) (3) "Gold is not a compound substance." (4) "Usually cruel men are cowards." Note.. — The first proposition is poetical while the second is an exclusive. (6a) Contravert the following propositions : (1) "All virtue is praiseworthy." (2) "Some teachers are not tactful." (3) "A man who lies is not to be trusted." Contraversion consists in obverting first, and then converting; consequently, the contraverse of the three propositions is as follows : (1) "No unpraiseworthy deed is virtue." (2) "Some not-tactful persons are teachers." (3) "Some untrustworthy men are those who lie." (6b) Write the contraverse of the following: (1) "All honest men pay their debts." (2) "All men are rational." 1 88 Immediate Inference (3) "Nearly all the troops have left the town." (4) "Some teachers are not patient." (7a) The attending scheme indicates the logical process and rule involved in passing from one proposition to another: A. "All men are imperfect." E. -a c rt CD W as c _o o .2 '-S "to U CD Ih CD bfl V Ch C > CD rt »Q •C! O CD o CO CO £ CD C o U co n5 CD .2 CD > -d c Ih CD Ih rt > c c o Ih O U cu > o co o CO CD CD CD 23 * ; Some not-men are perfect beings. Illustrative Exercises 189 (7b) Treat in a manner similar to the above the proposition, "All horses are quadrupeds." 8. REVIEW QUESTIONS. (1) What is inference? (2) What is the meaning of antecedent? (3) Define (1) judging, (2) a judgment. (4) All roses are beautiful, This flower is a rose, This flower is beautiful. Write this example of mediate inference in equation form. Name the middle term. (5) Define immediate inference. Illustrate. (6) Define mediate inference. Illustrate. (7) Name the five forms of immediate inference. (8) What principle is involved in inference by opposition? (9) Draw the scheme of opposition. (10) Make use of this scheme in deriving inferences from the following propositions : (a) "Good men are wise." (b) "No king is infallible." (c) "Cattle are ruminants." (d) "All who cheat the railroads are not honest." (11) What are contradictory propositions? Illustrate. (12) What would be the simplest way of disproving the state- ment that "No great religious teacher has been consistent?" (13) Why are A and E said to be contrary propositions? (14) Define obversion. (15) By what other name is obversion known? (16) State the basic principle of obversion. (17) Illustrate the process known as negating the predicate. (18) State the rule for obverting an A proposition. (19) Obvert the following: (1) "All the boys in my room are industrious." (2) "Honesty is the best policy." (3) "Only the industrious are truly successful." 190 Immediate Inference (20) First state the rule and then obvert the following: (1) "Some plants are biennial." (2) "Planets are not suns." (3) "Blessed are the merciful." (4) "These samples are not perfect." (21) Define conversion. (22) State and illustrate the rules which condition the process of conversion. (23) Convert, if possible, the following: (1) "Some men practice sophistry." (2) "Few men know how to live." (3) "Some of the inhabitants are not civilized." (4) "All the world is a stage." (5) "None of my pupils failed." (6) "Experience is a hard taskmaster." (24) Wiry may co-extensive propositions be converted simply? (25) Describe the process of inference by contraversion. 9. PROBLEMS FOR ORIGINAL THOUGHT AND INVESTI- GATION. (1) What ground is there for the belief that immediate in- ference, so called, is merely a matter of the interpretation of propositions ? (2) Is there any difference between reasoning and inference? (3) When the conclusion is reached that two rooms are of the same width, because each is five yards wide, what is the middle term? (4) Put in equation form: All teachers instruct, John Jones is a teacher, John Jones instructs. Show that the equations are not absolutely true. (5) Indicate the true relation between the subjects and predi- cates of the foregoing by using the algebraic signs > and < (6) Why cannot an A be derived from an I? (7) Why cannot an O be derived from an A? (8) The basic principle of obversion is "Two negatives are equivalent to one affirmative." Show by means of circles that Problems for Original Thought and Investigation 191 this is not absolutely true ; take as an illustrative proposition, "No men are not mortal." (9) Show that agreeable and disagreeable are not contra- dictory terms. (10) Why should the logician class individual propositions as universal ? (11) Show by circles that there is a difference in signification between, "Some men are not wise" and Some men are not-wise." (12) Show by circles that the O proposition cannot be con- verted. (13) "The I proposition cannot be contraverted." Make this clear. (14) Is there any difference in meaning between, "All illogical work is unscholarly" and "No illogical work is scholarly?" Explain by circles. (15) State the logical process involved in passing from each proposition to its succeeding one: (1) "All men are imperfect." (2) "No men are perfect." (3) "No perfect beings are men." (4) "Some not-men are perfect beings." (5) "Some perfect beings are not-men." ' (6) "Some perfect beings are not men." (16) It is sometimes said that in sub-contraries there is really no opposition. Do you agree? Give arguments. CHAPTER 11. MEDIATE INFERENCE. THE SYLLOGISM. 1. INFERENCE AND REASONING. Inference has been denned as both a product and a process. When used to indicate a process the term in- ference becomes synonomous with reasoning. If logicians could agree to confine inference to the product and reasoning to the process, it would remove an am- biguity which is more or less misleading. But since this has not become the custom, we shall use inference as indicating the process as well as the product. Definitions — Middle Term Explained. Inference is the thought process of deriving a judg- ment from one or two antecedent judgments. Mediate inference is inference by means of a middle term. Reasoning of this nature involves three terms, two of which are compared with a third or middle term, and then related to each other to form a new judgment. The middle term is the common unit, or the standard^ by which the other terms are measured. To illustrate: If John and James are each six feet tall, then plainly, they are of the same height. The standard, or middle term, is "six feet tall." 2. THE SYLLOGISM. Just as the judgment is expressed by means of the proposition, so mediate inference is best expressed by 192 The Syllogism 193 means of the syllogism.* The following are syllogisms: (1) James is six feet tall, John is six feet tall, Hence James is as tall as John. (2) All true teachers are just, You are a true teacher, Hence you are just. (3) All men are mortal, You are a man, Hence you are mortal. 3. THE RULES OF THE SYLLOGISM. All syllogistic reasoning is conditioned by the follow- ing eight rules: (1) A syllogism must have three, and only three, different terms. (2) A syllogism must have three, and only three, propositions. (3) The middle term must be distributed at least once. (4) No term must be distributed in the conclu- sion which is not also distributed in a premise. (5) No conclusion can be drawn from two negative premises. (6) If one premise be negative, the conclusion must be negative; and conversely, to prove a negative conclusion, one of the premises must be negative. * From the Greek meaning to reason with. 194 Mediate Inference — The Syllogism (7) No conclusion can be drawn from two particular premises. (8) If one premise be particular, the conclusion must be particular. These rules are exceedingly important, as their observance is necessary in all mediate reasoning. The student needs, not only to understand the meaning of these rules, but he needs to commit them to memory so thoroughly that they may be recalled without hesita- tion or mistake. To aid the memory, the eight rules may be divided into these four groups : I. Rules one and two relate to the composition of the syllogism. II. Rules three and four pertain to the distribution of terms. III. Rules five and six have reference to negative premises. IV. Rules seven and eight concern particular premises. 4. RULES OF THE SYLLOGISM EXPLAINED. (1) A syllogism must have three and only three terms. It is common to represent the various syllogistic forms by symbols, the same symbols always standing for the same terms. In this treatment we shall let cap- ital G stand for the major term, as "major" means greater; capital S. for the minor term, as " minor " means smaller, and capital M for the middle term. G, S and M, the initial letters of greater (major), smaller (minor) and middle, will be the constant symbols for Rules of the Syllogism Explained 195 these terms; just as A, E, I and O are used as the constant symbols for the four logical propositions. Illustration . Syllogism written in full: All men are mortal, Socrates is a man, (Therefore) Socrates is mortal. Syllogism symbolized: All M is G S is M .'. S is G The major term is always the predicate and the minor term the subject of the conclusion. The conclusion of the foregoing syllogism is, " Socrates is mortal." Since G stands for the predicate of every conclusion, then it stands for " mortal" the predicate of the above con- clusion. For a similar reason, S stands for the sub- ject, namely, " Socrates'' ; while M represents the middle term, " man." Since every syllogism must have three propositions, and since it takes two terms to form a proposition, then it follows that every syllogism must contain six terms. But, as no syllogism can have more than three different terms, we conclude that each term of the syllogism must be used twice. In the foregoing example, G thus appears, not only in the last proposition, or conclusion, but in the first proposition also. Similarly, both S and M occur twice. Every logical syllogism, then, contains 196 Mediate Inference — The Syllogism first, a major term, which is always the predicate of the conclusion and appears once in the premises; second, a minor term, which is always the subject of the conclu- sion and appears once in the premises; and third, a middle term to which the other two terms are referred. There are two ways of locating the middle term; first, it is the term which is used in both the premises; second, it is the term which never appears in the con- clusion. Likewise, there are two ways of locating the major and minor terms; first, the major term is always the predicate and the minor term the subject of the con- clusion; second, the major term is usually the broader and the minor term the narrower of the two. If the major and minor terms seem to be of about the same extension or breadth, then the term in the first proposition, which is not the middle term, is the major. In the attending syllogisms the three terms are designated : (middle) (major) (1) All true teachers are sympathetic, (minor) (middle) 1 1 You are a true teacher, (minor) (major) .'. You are sympathetic. (major) (middle) (2) No shell fish are vertebrates, (minor) (middle) Rules of the Syllogism Explained 197 All trout are vertebrates, (minor) (major) .*. No trout are shell fish. The necessity of having but three different terms in any syllogism may be understood by supposing that there are four different terms; then it would follow that there could be no standard or common link. In the axiom, " Things equal to the same thing are equal to each other," the same thing is the common standard or link. Two things which equal two different things are not equal to each other. The impossibility of reasoning from four terms may be shown by circles. All men are mortal. All trees grow. Fig. 8. These circles show that no connection can be estab- lished between either group. Using four terms in any syllogism is known as the fallacy of four terms. (2) A syllogism must have three and only three propositions. The proposition containing the major term is called the major premise, while the one contain- ing the minor term is called the minor premise. In a strictly logical syllogism the major premise is written 198 Mediate Inference — The Syllogism first, the minor premise second and the conclusion third. In common parlance, however, the minor premise or even the conclusion may appear first. The conclusion of a syllogism is always preceded by therefore, or its equivalent, which may be written or understood. The premises always answer the question, Why is the conclusion true? The premises are often preceded by such words as for and because. The attending irregular syllogisms are arranged logically and the premises and conclusions indicated: (ia) Illogical. "You must take an examination because all who enter the school are examined and you, as I understand it, are planning to enter." (2a.) "Some of these books are not well bound, for they are going to pieces as no well bound book would do." (ib) Logical. All who enter this school are examined, Major premise. You are planning to enter this school, Minor premise. You must be examined. Conclusion. (2b) No well bound book goes to pieces, Major premise. Some of these books are going to pieces, Minor premise. Some of these books are not well bound. Conclusion. Rules of the Syllogism Explained 199 The fact that all syllogisms must have three and only three premises follows from rule "1." One premise must compare the middle term with the "major"; another premise must compare the middle term with the " minor " ; while the conclusion links together the " major " and the " minor." (3) The middle term must be distributed at least once. The rule is usually given in this way, " The mid- dle term must be distributed once at least, and must not be ambiguous." In this treatment the last part of the rule has been omitted because it must be apparent to the student that a middle term used in two senses is virtually equivalent to two different terms; such an "ambiguous middle" would, in consequence, give a syllogism of four terms. Rules 3 and 4 are of greater importance than the others because they are more frequently violated. If the middle term is not distributed at least once, the fallacy is referred to as "undistributed middle" If the distributed major term of the conclusion is not dis- tributed in the major premise, then the fallacy is called, "illicit process of the major term" ; and finally, if the distributed minor term of the conclusion is not distrib- uted in the minor premise the fallacy is denominated an illicit process of the minor term." These two illicit processes may be abbreviated to illicit major and illicit minor. Recall that any term is distributed when it is referred to as a definite whole. Unless the whole of the middle term is considered it fails to become a common standard 200 Mediate Inference — The Syllogism of comparison. This becomes clear when recourse is made to the circles. Illustration. Syllogism in which the middle term is not distributed: All men are mortal, All trees are mortal, .'. All trees are men. All the propositions are A's and consequently the predi- cates of each are undistributed, as A distributes the subject only. Therefore the middle term, "mortal," is not distributed in either of the premises and thus the fallacy. Fallacy shown by circles : Fig. 9. These circles indicate the correct meaning of the two premises. By them it is seen that all of the " men " circle belongs to the " mortal " circle and all of the "tree" circle belongs to the "mortal" circle, but in this case there is no connection between the "men" and "tree' cir- cles. Thus, to say that "All trees are men," is fallacious. We have no right to either affirm or deny the connection between men and trees. If "mortal" were distributed we would have this right as the following will make clear : Rules of the Syllogism Explained 201 All men are mortal, No stones are mortal, .'. No stones are men. JloirtaiX f 5tones\ w Fig. 10. Here the middle term mortal is distributed in the second premise as in it the subject "stones" is excluded from the entire mortal territory. This conclusion is verified by the formal statement that " E " distributes both subject and predicate. Since all of the " men " circle belongs to the " mortal " circle and none of the "stones" circle belongs to the "mortal" circle then none of the " stones " circle can belong to the " men " circle. (4) No term must be distributed in the conclusion which is not also distributed in its premise. It has been affirmed that a term is distributed when it is referred to as a definite whole. To put it in another way, a term is distributed when it is employed in its fullest sense. It is obvious that we should not employ a term in its fullest sense in the conclusion when it has been used only in a partial sense in its premise. What is said of the part cannot necessarily be said of the whole. For example: Because some men are honest it does not follow that all men are honest. Of course the converse of this is true, namely, if it could be proved that all men are honest then surely it would 202 Mediate Inference — The Syllogism follow that some of the men are honest. To put it briefly : What is true of all is true of some but what is true of some is not necessarily true of all. To distribute a term in the conclusion when it is not distributed in the premise where it occurs is equivalent to saying, " what is true of some is true of all." This error which violates rule " 4 " leads to the two fallacies of illicit process of the major and minor terms. The following illustrate the two fallacies. Syllogism illustrating illicit major: All trees grow, No men are trees, .'. No men grow. The first premise is an A and consequently its subject is distributed. The second premise and conclusion being E's have both subject and predicate distributed. Thus grow, as used in the conclusion, is distributed, but, as used in the major premise, it is not distributed. Fallacy shown by circles : Fig. 11. Here all of the " tree " circle belongs to the " grow " circle and none of the " men " circle belongs to the " tree " circle, hence the diagram correctly represents Rules of the Syllogism Explained 203 the meaning of the two premises and shows the fallacy of concluding that no men grow. The "men" circle, being entirely within the " grow " circle, indicates that all men grow. Syllogism illustrating illicit minor : All true teachers are just, All true teachers are sympathetic, .'. All the sympathetic are just. Each proposition being an A distributes its subject. But the subject of the conclusion which is "the sympathetic" is not distributed in the minor premise, as an A propo- sition distributes its subject only. Hence the fallacy of illicit minor. Fallacy shown by circles : Fig. 12. The diagram correctly represents the two premises since all of the " true teacher " circle belongs to both the " just " and " sympathetic " circles. But all of the "sympathetic" circle does not belong to the "just" circle. Hence the fallacy. (5) No conclusion can be drawn from two negative premises. When two terms are both denied of a third term, it is quite impossible to draw any conclusion relative to 204 Mediate Inference — The Syllogism the two terms, as the absolute exclusion of the third term eliminates any possibility of a common link or standard. The circles will make this apparent : No men are immortal, No trees are immortal, Wen\ [//nmortal] Fig, 13. " No trees are men " is the conclusion represented by Fig- 13. Other possible conclusions are, "All trees are men," "All men are trees" and "Some men are trees." It is thus seen that no definite conclusion can be drawn. It may now be said that when the major and minor terms are used in two negative premises the con- nection between them is indeterminate. This violation of rule "5" may be termed the fallacy of two negatives. (6) // one premise be nagtive the conclusion must be negative; and conversely, to prove a negative con- clusion one of the premises must be negative. Referring to the first part of this rule, it may be said of two terms that if one is affirmed and the other denied of a third term, then the two terms must be denied of Rules of the Syllogism Explained 205 each other. The attending syllogism and its " circled " representation will throw light upon this : No men are immortal, All Americans are men, .'. No Americans are immortal. Fig. 14. Since none of the " men " circle belongs to the " immortal " circle and all of the "American " circle is inside the " men " circle, it is evident that none of the "American " circle can belong to any part of the " immortal " circle. Thus it is manifest that an affirma- tive conclusion like, "All Americans are immortal," is invalid. The converse of rule 6, " To prove a negative con- clusion, one of the premises must be negative," may be explained by the general principle in logic that when two terms are known to disagree, one must agree with a third term while the other must disagree. If both agreed with a third, then the conclusion would of necessity be affirmative. If both disagreed no conclu- sion could be drawn. A violation of rule 6 may be called the fallacy of negative conclusion. (7) No conclusion can be drawn from two particular premises. Proof : 206 Mediate Inference — The Syllogism (i) All the possible combinations of the two particular premises I and O are, (i) IO, (2) OI, (3) II, (4) 00. "IO" considered. (2) Since O is a negative premise the conclusion would have to be negative according to rule 6, (If one premise is negative, the conclusion must be negative.) (3) If the conclusion is negative, then its predi- cate, which is the major term, must be dis- tributed. (All negative propositions distribute their predicates.) (4) If the major term is distributed in the con- clusion, it must be distributed in the major premise, rule 4 (No term must be distributed in the conclusion, which is not also distributed in one of the premises.) (5) Hence two terms must be distributed in the premises, the major term according to (4) and the middle term according to rule 3. (6) But I distributes neither term and O dis- tributes its predicate only; I and O together, then, distribute but one term. (7) To draw a negative conclusion the premises must distribute two terms, the middle and the major, according to the foregoing. (8) Hence a conclusion from I and O is untenable. The same may be said of " OI." "II" considered. Rules of the Syllogism Explained 207 (1) The I proposition distributes neither subject nor predicate, hence the premises " II " would distribute no term. (2) But the middle term must be distributed at least once according to rule 3. (3) Therefore no conclusion can be drawn from " II." A valid conclusion from " 00 " is impossible according to rule 5. (8) If one premise be particular the conclusion must be particular. Proof: The possible combinations conditioned by rule 8 are AI, AO, EI, EO, IO, II, 00. "AI" considered. (1) Proposition A distributes its subject, prop- osition I neither ; hence "AI " together distribute but one term. (2) According to rule 3 this one term must be the middle term. (3) The minor term must, therefore, be undis- tributed in the minor premise, and in con- sequence undistributed in the conclusion. (4) But this undistributed minor term is the sub- ject of the conclusion; hence said conclusion must be particular, as only particulars have an undistributed subject. "AO" and "EI" considered. Proof: (1) "AO" distribute two terms; so do "EL" (2) Both "AO " and " EI " must have negative conclusions according to rule 6. 208 Mediate Inference — The Syllogism (3) A negative conclusion distributes its predicate which is the major term. (4) The major term and the middle term must be distributed in the premises. Rules 4 and 3. (5) Thus the third term, which is the minor, cannot be distributed in the minor premise and, consequently, the minor cannot be distributed in the conclusion. (6) This necessitates a particular conclusion. Premises EO and OO, being negative, cannot yield a conclusion according to rule 5 ; similarly, neither can the particulars IO and II because of rule 7. 5. THE DICTUM OF ARISTOTLE. Aristotle gives an axiom on which all syllogistic in- ference is based. Indeed from this fundamental prin- ciple the significant rules of the syllogism could be de- rived. The dictum is stated in this wise : " Whatever is predicated, whether affirmatively or negatively, of a term distributed may be predicated in the manner of everything contained under it." The following state- ments represent various ways of explaining this dictum : (1) Whatever is said of a term used in its fullest sense may likewise be said of that term when used only in a partial sense. (2) What is true of the whole is true of the part. (3) "What pertains to the higher class pertains also to the lower." Since this dictum is the basic principle The Dictum of Aristotle 209 underlying the important rules of the syllogism, it is unnecessary to dwell longer upon it; because an explanation of the rules is, virtually, an explanation of the dictum. 6. CANONS OF THE SYLLOGISM. The dictum of Aristotle is ostensibly a self-evident truth, and some logicians have put this truth in the form of three axiomatic statements which are known as the canons of the syllogism. These are as follows: (1) "Two terms agreeing with one and the same third term agree with each other." (2) " Two terms of wmich one agrees and the other does not agree with one and the same third term, do not agree with each other." (3) " Two terms both disagreeing with one and the same third term may or may not agree with each other." Making use of the symbols as explained on a previous page of this chapter, it will be seen that the first canon conforms to this syllogistic type: All M is G All S is M .". All S is G The two terms are S and G, while M is the third term. The attending symbolizations illustrate, respectively, the second and third canons: No M is G All S is M No S is G 210 Mediate Inference — The Syllogism No M is G No S is M Conclusion indeterminate. 7. THREE MATHEMATICAL AXIOMS. Analogous to the three canons treated in "6," there are certain mathematical axioms which are here stated : (i) "Things equal to the same thing are equal to each other." (2) "One thing equal to and the other thing not equal to the same third thing are not equal to each other." (3) "Things not equal to the same thing may or may not equal each other." Illustrations of the three axioms : (1) If x equals 5, and y equals 5, then x equals y. (2) If x equals 5, and y does not equal 5, then x does not equal y. (3) If x does not equal 5, and y does not equal 5, then x may or may not equal y. 8. OUTLINE. Mediate Inference. (1) Inference and reasoning. Definitions. Middle term explained. (2) The analogy between the judgment and the syllogism. (3) Rules of the syllogism given. Eight in number. (4) Rules of the syllogism explained : Rule 1. Syllogistic symbols. Major, minor, and middle terms; how found. Fallacy of four terms. Outline 211 Rule 2. Major and minor premises and conclusion, how determined. Logical arrangement. Reason for three propositions. Rule 3. Reason for omitting "ambiguous middle" from rule. Undistributed and distributed middle explained. Rule 4. Illicit major and minor explained and illustrated. Rule 5. Fallacy of two negatives. Rule 6. Fallacy of negative conclusion. Rule 7. Fallacy of two particulars. Rule 8. Fallacy of particular conclusion. (5) Aristotle's dictum. (6) Canons of the syllogism. (7) Mathematical axioms. 9. SUMMARY. (1) Inference is a term used to denote a process as well as a product. As a process reasoning and inference are in reality synonomous terms. Inference is a thought process of deriving a judgment from one or two antecedent judgments. Mediate inference is inference by means of a middle term. Mediate inference makes use of three terms, two of which are compared with a third term as a standard. This third term is called the middle term. (2) The syllogism is the common mode of expression for mediate inference. (3) Valid syllogistic reasoning is conditioned by eight rules. The first and second relate to the composition of the syllogism; the third and fourth to the distribution of terms; the fifth and sixth to negative premises; the seventh and eighth to particular premises. (4) All syllogisms must have three terms: the major, the minor, and the middle. The middle term occurs twice in the premises but never appears in the conclusion. The minor term is always the subject, and the major term the predicate of the conclusion. The major term is usually broader than the minor. No conclusion can be drawn from four terms. To attempt this gives rise to the fallacy of four terms. 212 Mediate Inference — The Syllogism All syllogisms must have three propositions, the major and the minor premises, and the conclusion. The major premise first and the minor second is the more logical arrangement, although the common conversational form is to use the minor premise first. Ambiguous middle amounts to the fallacy of four terms. Unless the middle term is distributed at least once in the syllogism, it fails to become a common standard. Distributing a term in the conclusion, without its being dis- tributed in its premise, is equivalent to asserting that, "What is true of a part is true of the whole." This error results in the fallacies of illicit major and minor. A conclusion from two negatives is impossible, because of the total exclusion of the middle term. Of two terms, if one is affirmed and the other denied of a third term, then they must be denied of each other; and, conversely, if two terms are to be denied of each other, one must be affirmed and the other denied of a given third term. This fundamental principle necessitates deriving a negative conclusion from two premises when one is negative. It, likewise, compels the converse of this. A valid conclusion from two particulars is untenable because of the two negative fallacies, or some fallacy relative to the distribution of terms. One particular premise forces a particular conclusion because of the fallacies of two negatives, two particulars, and illicit minor. (5) Aristotle's dictum simplified means, "What is true of the whole is true of the part." (6) The canons of the syllogism, three in number, are: (1) "Two terms agreeing with one and the same third term agree with each other." (2) "Two terms of which one agrees and the other does not agree with one and the same third term do not agree with each other." (3) "Two terms both disagreeing with one and the same third term may or may not agree with each other." (7) The foregoing canons may be stated as mathematical axioms. Illustrative Exercises 213 10. ILLUSTRATIVE EXERCISES. (la) Make use of the proper symbols and indicate the three terms of each of the attending syllogisms : (1) All fixed stars twinkle, Vega is a fixed star, .*. Vega twinkles. (2) All men are rational beings, No tree is a rational being, .*. No trees are men. (3) All good citizens are law abiding, All good citizens vote, .*. Some who vote are law abiding. I recall that the three terms are the middle, the major and the minor, and that the "middle" does not occur in the conclusion, whereas the "major" is always the predicate and the "minor" the subject of the conclusion. The symbols M, G and S being the initial letters of middle, greater and smaller, I make use of these in designating the three terms, as the following will illustrate : M G (1) All fixed stars twinkle, S M Vega is a fixed star, S G .". Vega twinkles. "Twinkles" being the predicate of the conclusion is designated as being the major term by putting the letter G above it. Then "G" is placed above the term "twinkle" in the first premise. "S" is placed above the subject of the conclusion to indicate that it is the minor term. "S" is also placed above "Vega," the minor term, as found in the second premise. The remaining term, "fixed stars," must be the middle term, therefore I place "M" above it. The fact that "fixed star" does not occur in the conclusion verifies this. 214 Mediate Inference — The Syllogism Using only the symbols, the syllogism takes this form: All M is G S is M S is G Using the symbols to represent the other syllogisms, we have (2) All G is M (3) All M is G No S is M All M is S .*. No S is G .*. Some S is G (lb) Indicate by symbols the three terms of the following syllogisms : (1) No trees are men, All rational beings are men, .*. No rational being is a tree. (2) All men have the power of speech, You are a man, .*. You have the power of speech. (3) Some men are wise, All men are rational, .'. Some rational beings are wise. (2a) Illustrate by syllogism the fallacy of undistributed middle. An easy way is to use the middle term as the predicate of two A premises. This yields the fallacy because an A propo- sition does not distribute the predicate. The illustration: distributed terms underscored. All true teachers are students, All scholars are students, All scholars are true teachers. (2b) Give two illustrations of undistributed middle. (3a) Give syllogistic illustrations of the fallacies of illicit major and minor. Illustrative Exercises 215 Illicit Major. Use the middle term as the subject of an A proposition, and then as the predicate of an E proposition. This would necessitate a negative conclusion in which the major term is distributed. But the major term is not distributed in the major premise, hence the fallacy. Illustration in which the distributed terms are underscored: All men are mortal, No trees are men, No trees are mortal. Illicit Minor. To illustrate this fallacy one may use the middle term as the subject of two A premises. This would give an A conclusion in which the subject is distributed. But this same term is not dis- tributed in its premise because here it is used as the predicate of an A. Illustration: All earnest students study, All earnest students desire to succeed, ,*. All who desire to succeed study. 11. REVIEW QUESTIONS. (1) Distinguish between inference and reasoning. (2) Define inference. Mediate inference. (3) Illustrate the difference between mediate and immediate inference. (4) Explain by illustration the use of the middle term. (5) Exemplify the syllogism. (6) State the rules of the syllogism. (7) From the attending syllogisms select the three terms : (1) All patriotic citizens vote, ^ You are a patriotic citizen, You should vote. (2) No honest man would misrepresent, (but) John Smith did misrepresent, ■' t* Or , __,, M .*. John Smith is not honest. r- «> 4> 5 j 7> I0 > I2 j x 3 an d 15; whereas the rule for par- ticulars throws out 9 and 14. This leaves the following as the probable valid moods in one or more of the figures : 1, 3, 6, 8, 11, 16. But to be certain of this the investiga- tion must be continued. The mood A has stood the test A A of the rules for negative and particular conclusions ; now let us test this mood from the standpoint of the distribu- tion of terms, using it in all four figures : First Second Third Fourth A M — G G — M M — G G — M A S — M S — M M — S M — S A S — G As an A proposition distributes its subject only, we underscore the subject of each proposition in all the figures. (This underscoring is a simple way to indicate distribution.) We now find that the mood is valid in the first figure, because the middle term is distributed at least once; 224 Figures and Moods of the Syllogism namely, in the major premise, and there is no term dis- tributed in the conclusion which is not already distributed in the premise where it occurs. On the other hand, the A mood A is invalid in the second, because of "undistributed A middle/' and invalid in the third and fourth, because S is distributed in the conclusion but not distributed in the premise where it occurs (illicit minor). Let us try All in the four figures : A M — G G — M M — G G — M IS— M S — M M — S M — S IS— G S — G S — G S — G We underscore the subject of the A proposition in each of the four figures. As I distributes neither subject nor predicate, no other term should be underscored. It is A now evident that I is not valid in figures two and four, I because in both figures the middle term is undistributed (undistributed middle). In a like manner all the other moods might be tested. Logicians, who have done this, have found 24 to be valid. Five of these have weakened conclusions; i. e., a particular conclusion when it could just as well be uni- A versal. E illustrates this as the conclusion could be E. O Testing the Validity of the Moods 225 This syllogism exemplifies the weakened conclusion : A All trees grow, E No sticks are trees, O .'. Some sticks do not grow. This conclusion is true, since "some" means "some at least." Yet the conclusion is weak, because there is nothing to interfere with the broader and stronger con- clusion that, "No sticks grow." There are, therefore, only 19 valid and serviceable moods. These are as follows : (1) (2) (3) (4) (5) (6) A E A E — -1 First figure A A I I — -I A E I O — -J E A A E -\ Second figure A E O I — E E O O — -J A I A E O E l Third figure A A I A A 1 I I I O O oj A A I E E -1 Fourth figure A E A A I -!■ I E I O O -J 14 19 Of these nineteen moods it is not much of a tax to A remember that A is valid only in the first figure ; whereas A 226 Figures and Moods of the Syllogism E A A is valid in the first and second figures ; I in the first E I E and third; while I is valid in all. This knowledge, O however, should be used only as one would employ the answers in arithmetic. Testing the validity of a mood in the four figures is an exceedingly valuable thought- exercise, which a knowledge of the final result might easily vitiate. It is, no doubt, best to test the value of any mood without such knowledge, and then compare the result by referring to the foregoing list of valid moods. It is not always wise to work with the answer in mind, yet it is most satisfying to know of a certainty that one's reasoning has led to a truth which others have verified. 4. SPECIAL CANONS OF THE FOUR FIGURES. As a deductive exercise in clear, logical thought, the indirect proof involved in establishing certain principles underlying the four figures, is of immense value. On no account should this section be omitted. The mere fact that it appears to be a difficult section is proof positive that the student is in need of just such exercises. Canons of the first figure. ( i ) The minor premise must be affirmative. (2) The major premise must be universal. Problem: The minor premise must be affirmative. Special Canons of the Four Figures 22J Data: Given the form of the first figure, which is, M — G S — M S — G Proof: (1) If the minor premise is not affirmative then it must be negative ; because affirmative and negative propositions, being contradictory in nature, admit of no middle ground. (2) If the minor premise is negative, the conclusion must be negative ; for the reason that a negative premise necessitates a negative conclusion. (3) If the conclusion is negative then its predicate, G, must be distributed; since all negatives distribute their predicates. (4) If the predicate of the conclusion, which is the major term, is distributed, then it must be distributed in the premise where it occurs, which is the major premise; for any term which is distributed in the conclusion must be distributed in the premise where it occurs. (5) If the major term, which is the predicate of the major premise, is distributed, then the major premise must be negative; because only negatives distribute their predicates. (6) The result of this argument, then, gives two nega- tive premises, and we know from rule 3 that a conclusion from two negatives is untenable. (7) Since the minor premise cannot be negative, it must be affirmative. Problem: To prove that the major premise must be universal. 228 Figures and Moods of the Syllogism Data: Given the form of the first figure: M — G S — M S — G Proof: (i) The predicate of the minor premise, M, which is the middle term, is undistributed; because no affirmative proposition distributes its predicate. (2) The middle term must be distributed in the major premise; since in any syllogism the middle term must be distributed at least once. (3) As the middle term, M, used as the subject of the major premise, must be distributed, then the major premise must be universal; because only universals distribute their subjects. Epitome. In the first figure, the minor premise must be affirma- tive, since making it negative necessitates making the major premise negative also; the major premise must be universal in order to distribute the middle term at least once. Special canons of the second figure. ( 1 ) One premise must be negative. (2) The major premise must be universal. Problem: To prove that one premise must be negative. Data: Given the form of the second figure: G — M S — M S — G Special Canons of the Four Figures 229 Proof: (1) The middle term, M, is the predicate of both premises. (2) The middle term must be distributed at least once, according to rule 3. (3) Hence one premise must be negative; since only negatives distribute their predicates. Problem: To prove that the major premise must be universal. Data: Given the form of the second figure: G — M S — M S — G Proof: (1) As one premise must be negative, it fol- lows that the conclusion must be negative according to rule 6. (2) If the conclusion is negative, then its predicate, G, the major term, must be distributed ; since all negatives distribute their predicates. (3) When distributed in the conclusion, the major term, G, must also be distributed in the major premise, where it is used as the subject. See rule 4. (4) Hence the major premise must be universal; for only universals distribute their subjects. Epitome. In the second figure one premise must be negative in order to distribute the middle term at least once; and the major premise must be universal that the major term, which is distributed in the conclusion, may be distributed in the premise where it occurs. 230 Figures and Moods of the Syllogism Canons of the third figure. (1) The minor premise must be affirmative. (2) The conclusion must be particular. Problem: To prove that the minor premise must be affirmative. Data: Given the form of the third figure, which is, M — G M— S S — G Proof: ( 1 ) Suppose the minor premise were negative, then the conclusion would have to be negative, and this would distribute the predicate G. (2) A distributed predicate would necessitate its being distributed in the major premise. (3) But G, being the conclusion of the major premise, could be distributed only by a negative proposition. (4) This would result in two negatives; therefore no conclusion could be drawn, if the minor premise were negative. Problem: To prove that the conclusion must be particular. Data: Given the form of the third figure: M — G M— S S — G Proof: (1) The minor term, which is the predicate of the affirmative minor premise, is undistributed ; because no affirmative distributes its predicate. (2) If undistributed in the premise, then the minor Special Canons of the Four Figures 231 term must remain undistributed in the conclusion, where it is used as the subject. (3) The conclusion must, then, be particular; since all universals distribute their subjects. Epitome. In the third figure, unless the minor premise be af- firmative, there can be no conclusion; since a negative minor would necessitate a negative major. An affirma- tive minor compels a particular conclusion, in order that the minor term, in the conclusion, may remain undis- tributed. Canons of the fourth figure. (1) If the major premise is affirmative, the minor premise must be universal. (2) If the minor premise is affirmative, the conclusion must be particular. (3) If either premise is negative, the major must be universal. Problem: To prove that if the major is affirmative, the minor must be universal. Data: Given the form of the fourth figure: G — M M— S S — G Proof: (1) If the major premise is affirmative, then its predicate which is the middle term, M, is undis- tributed ; for no affirmative distributes its predicate. (2) The middle term must then be distributed in the "minor" according to rule 3. 232 Figures and Moods of the Syllogism (3) Then the "minor" must be universal; since only universals distribute their subjects. Problem: To prove that if the minor is affirmative, the conclusion must be particular. Data: Given the form of the fourth figure: G — M M— S S — G Proof: (1) If the minor premise be affirmative, then S, its predicate, must be undistributed ; because no affirma- tive distributes its predicate. (2) Since S is undistributed in the minor premise, it must remain undistributed in the conclusion where it is used as the subject. Problem: To prove that if either premise is negative, the major must be universal. Data: Given the form of the fourth figure: G — M M— S S — G Proof: (1) If one of the premises is negative, then the conclusion must be negative according to rule 6. (2) If the conclusion is negative, then the predicate, G, must be distributed. (3) If G is distributed in the conclusion, it must be distributed in the major premise. (4) The major premise must be universal ; as G is used as its subject, and only universals distribute their subjects. Epitome. Special Canons of the Four Figures 233 In the fourth figure, if the "major" is affirmative, the "niMor" must be universal in order to distribute the mid- dle term. If the minor is affirmative, the conclusion must be particular; otherzvise the fallacy of illicit minor would result. If either premise is negative, the major must be universal to avoid the fallacy of illicit major. 5. SPECIAL CANONS RELATED. After a particular mood has been tested in the regular way, it has been intimated that the student may refer to the tabulated list of valid moods to ascertain, with a cer- tainty, the validity of his reasoning. This is equivalent to referring to the answers in arithmetic; for if the student is unable to find the mood in the figure in which he has proved it valid, then he knows that he has made some mis- take in his reasoning. A second check, though not abso- lute, is to recall the special canons of section four. If, A for example, our reasoning has led us to believe that E E is valid in the first figure, we may recall that the minor premise of the first figure must be affirmative and there- fore AEE cannot be valid. A few suggestions relative to memorizing the special canons may not be out of place. The two canons of the first figure must be committed, and then it may be re- membered that the second figure is the negative figure of logic. Other figures may yield a negative conclusion, but the second must yield a negative conclusion. Since a negative conclusion necessitates a negative premise, it follows that the second figure must always appear with 234 Figures and Moods of the Syllogism one premise negative. The other canon which pertains to the major premise is the same as the "major premise" canon of the first figure. The third figure is the particular figure of logic. Other figures may yield particular conclusions, but the third must do so. This helps us to remember the canon that the conclusion of the third figure must be particular. The other canon which relates to the minor premise is the same as the "minor premise" canon of the first figure. The canons of the fourth figure are in reality a summary of the canons of the other three figures. 6. MNEMONIC LINES. As a device for remembering the 19 valid moods, the logicians of an earlier day originated a combination of coined words which, though rather unscientific, may be easily committed to memory. Since, however, it is of much more value to test the moods by means of the gen- eral rules of the syllogism than it is to try to remember these moods, the mnemonic lines are of slight value. They are treated here merely as an item of historical interest. ( 1 ) Barbara, Celarent, Darii, Ferioque prioris ; (2) Cesare, Camestres, Festino, Baroko, secundae; (3) Tertia, Darapti, Disamis, Datisi, Felapton. Bokardo, Ferison, habet; Quarta insuper addit (4) Bramantip , Camenes, Dimaris, Fesapo, Fresison. The only letters in these lines which mean nothing are 1, n, r, t and small b and d; all the others have a sig- nification. For example, the vowels of the italicized Mnemonic Lines 235 words signify the various valid moods, as e. g., the first line indicates the moods AAA, EAE, All, EIO. The Latin words, printed in ordinary type, are intended to make evident that the moods indicated by the artificial italicized words of the first line, belong to the first figure ; that the moods of the next four words, belong to the second figure ; while the third figure includes the next six, and the fourth figure the last five. It is now seen that Festino, for example, stands for that mood of the second figure which has an E for its major premise, an I for its minor premise, and an O for its conclusion. The first figure was called by Aristotle the perfect figure, whereas the second and third were the imperfect figures. The fourth figure was given no place in the works of Aristotle; its discovery is credited to Galen, a celebrated teacher of medicine of the second century. According to Aristotle, the first figure is the most service- able and the most convincing and, therefore, as a final test of their validity, the moods of the other figures should be changed to the first. This process in logic is termed Reduction. In this reduction of the imperfect figures to the perfect, the capital letters of the artificial words, together with s, p, m, and k, have a definite meaning. The capital letters indicate that certain moods of the imperfect figures can be reduced to the correspond- ing moods of the first figure; e. g., Festino (eio) of the second figure, Felapton (eao) of the third figure, and Fesapo (eao) of the fourth figure may all be reduced to Ferio (eio) of the first figure. This is known because F 236 Figures and Moods of the Syllogism is the initial letter of each word, j signifies that the prop- osition denoted by the preceding vowel is to be converted simply. To illustrate: s in Fesapo means that the major E premise E of the mood A of the fourth figure must be O converted simply in order to change the mood to Ferio of the first figure, p indicates that the proposition repre- sented by the vowel which precedes p must be converted by limitation (per accidens). m (mutare) makes evi- dent that the premises are to be interchanged, the major of the old becoming the minor of the new, and the minor of the old becoming the major of the new. k denotes that the mood, such as Baroko, must be reduced by a special process known as indirect reduction. These directions may now be followed as illustrative of the process of reduction. A (1) Given: A syllogism in Darapti A I M G A All true teachers are just, M S A All true teachers are sympathetic, S G I .'. Some sympathetic persons are just. A The symbols indicate that the mood is A or is in I Darapti and that this mood is used in the third figure. Mnemonic Lines 237 A Problem: To reduce A of the third figure to some I mood of the first figure. Process: D, being the initial letter of Darapti, sug- gests that its mood must be reduced to one indicated by a word of the first figure whose initial letter is D. This A mood is in Darii, or is I. I The p in Darapti indicates that the proposition repre- sented by the preceding vowel must be converted by limitation. This proposition is the minor premise; con- verting it by limitation gives : "Some sympathetic persons are true teachers." As there are no other significant let- ters the reduction is complete and we have this : M G A All true teachers are just, S M I Some sympathetic persons are true teachers, S G I .'. Some sympathetic persons are just. A The symbolization indicates that the mood is I of the first I figure, or is in Darii. A (2) Given: A syllogism in Camestres E E 238 Figures and Moods of the Syllogism G M A All true teachers are just, S M E No one who shows partiality is just, S G E .'. No one who shows partiality is a true teacher. The symbols show that the mood is AEE of the second figure or in Camestres. Judging from the initial letter C, the mood in Camestres must be reduced to the mood in E Celarent A. E The letter m between a and e indicates that the major and minor premises of the given syllogism must be interchanged. The letters following both e's suggest that the minor premise and the conclusion of the syllogism must be converted simply. This is the resulting syllogism: M G E No just person shows partiality, S M A All true teachers are just persons, S G E .'. No true teacher shows partiality. E Here, then, is the A of the first figure or the mood in E Celarent. According to the ancient theory, reduction is necessary as a matter of final and absolute proof that the conclusion Mnemonic Lines 239. follows from the given premises. But, as this claim has been satisfactorily refuted by modern logicians, we need not give more space to the process. The meaning of k, as related to "indirect reduction/ 3 is explained in most of the earlier works on logic. See Hyslop, page 193. 7. RELATIVE VALUE OF THE FOUR FIGURES. The first figure. The first figure is known as the perfect figure ; because it is the only one which proves all of the four logical propositions. Recalling the moods of the first figure makes this evident : A E A E A A I I A E I O It is likewise the more natural figure ; because it is the only one which uses both the subject and predicate of the conclusion in the same relative places as they appear in the premises. Symbolizing the figure makes this apparent : M — G S — M S — G The first figure, being the only figure which proves a "universal affirmation" (A), is used most by the scientist; as the object of science is to establish universal affirmative truths. The second figure. As the second figure conditions negative conclusions only, it is called the figure of disproof, or the exclusive 240 Figures and Moods of the Syllogism figure. It is easy to see how negative conclusions may be used to narrow the inquiry down to one definite theory. For example, suppose it is desired to ascertain which boy of the five broke the window; by a series of deductions the teacher may be able to prove that the culprit is not A, not B, not C and not D ; hence the guilty one must be E. This figure is virtually the one used in diagnosing most diseases. The third figure. The third figure admits of particular conclusions only, and in consequence is of little value to the scientist. Since, however, the easiest way to contradict a universal affirma- tive (A) or a universal negative (E), is to prove the truth, respectively, of a particular negative (O) and a particular affirmavite (I), it follows that the third figure serves a purpose. The fourth figure. This figure is so nearly like the first that it is of little value; in fact, it may be changed to the first by simply interchanging the major and minor premises. Some authorities refuse to recognize the fourth figure. 8. OUTLINE. Figures and Moods of the Syllogism. (1) The four figures of the syllogism. Definition — symbolization Illustrations — device for remembering. (2) The moods of the syllogism. Twenty-four valid. (3) Testing the validity of the moods. Application of the general rules of the syllogism. Weakened conclusion — five. Summary 241 Nineteen useful moods. A thought exercise. (4) Special canons of the four figures. Proof of the two canons of the first figure. " " " " " " " second figure. " " " " " " u third figure. " " " three " " " fourth figure. (5) Special canons related. Used as checks. (6) Mnemonic lines. Their use explained. Reduction. (7) Relative value of the four figures. 9. SUMMARY. (1) By a syllogistic figure is meant some particular arrange- ment of the three terms in the two premises. This arrangement yields four figures which are designated by the position of the middle term. To be logical, any syllogism must conform to one of the four figures. The first figure is suggested by the position of the terms of the "Socrates is mortal" syllogism. The second is derived by converting the major premise of the first; while the third figure results from converting the minor premise of the first, and the fourth by converting both major and minor of the first. (2) By a mood of a syllogism is meant some particular ar- rangement of the propositions which compose it. There are 64 moods but only 24 are valid. (3) The validity of the various moods may be tested by applying to them the rules of the syllogism. No mood is valid if it violates any one of the eight rules. A "weakened conclusion" is a particular conclusion which could just as well be universal. Of the 24 valid moods five have weakened conclusions. This leaves but 19 useful moods. Testing the validity of the various moods in the four figures is a most valuable thought exercise. (4) The deductive exercise involved in establishing certain 242 Figures and Moods of the Syllogism special canons of the four figures is of immense value and should not be omitted. In the first figure it may be proved (1) that the minor premise must be affirmative; since making it negative necessitates making the major premise negative,, and no conclusion can be drawn from two negatives; (2) that the major premise must be universal in order to distribute the middle term at least once. In the second figure it may be proved (1) that one premise must be negative in order to distribute the middle term; (2) that the major premise must be universal in order to distribute its subject, which is distributed in the negative conclusion where it appears as the predicate. In the third figure it may be proved (1) that the miner premise must be affirmative in order to prevent the "two negative" fallacy; (2) that an affirmative minor necessitates a particular conclusion, because the minor term in the conclusion must remain undistributed. In the fourth figure it may be proved (1) that if the major is affirmative, the minor must be universal in order to distribute the middle term; (2) that if the minor is affirmative, the con- clusion must be particular in order to avoid committing the fallacy of illicit minor; (3). that if either premise is negative, the major must be universal to avoid the fallacy of illicit major. (5) A knowledge of the special canons is helpful in that it may be used to check fallacious reasoning. (6) Certain mnemonic lines were used by the Schoolmen as an aid in recalling the nineteen valid moods, and also as a suggestive device to aid in the process known as Reduction. The process of reduction is merely a matter of changing to the first figure the moods of the other figures. This process is no longer thought to be necessary. (7) The first figure, called the perfect figure, is the one used most by scientists, as it is the only figure which proves a uni- versal affirmative truth. The second figure is the negative, or figure of disproof, and is used mainly for the purpose of elimi- nating all the conditions of the inquiry save one. The third figure serves a purpose in affording an easy way to contradict a universal assertion; this is the figure of particulars. The fourth figure, because it so closely resembles the first, is of little value. Illustrative Exercises 243 10. ILLUSTRATIVE EXERCISES. Question la. By making use of the rules for negatives and particulars, test the validity of the following moods : A A 1 I A A A I Answer: The first mood has the negative O as its major premise, and the affirmative A as its conclusion; the mood is thus invalid; because a negative premise necessitates a negative conclusion according to rule 6. The second mood contains the particular proposition I as its minor premise, and thus should have a particular conclusion according to rule 8. But the conclusion A is universal and, therefore, the mood is invalid. The premises of the third mood are universal and the con- clusion particular. The mood, however, is valid, because rule 8 does not work both ways, as does rule 6. When a universal can just as well be drawn, then the particular becomes a weakened conclusion. (lb) Using the rules for negatives and particulars, test the A E E validity of the following : A O A . E O O (2a) Paying no regard to "figure," derive as many conclusions as possible from the following sets of premises: E A I E Answer: j . The major piemise of this mood, being negative, necessitates a negative conclusion, according to rule 6, and the minor premise, being particular, compels a particular conclusion, according to rule 8. Since the conclusion must be negative and particular, then O is the only one which can be drawn. The E completed mood is I. O P . This mood must have a negative conclusion, because the minor premise is negative; this would necessitate either E or O; 244 Figures and Moods of the Syllogism but O as a conclusion would be, in this case, a weakened one; since E distributing both terms would necessarily distribute the minor; which fact would permit the minor to be distributed in the conclusion. Thus the conclusion could just as well be A universal as particular. The completed mood is E. E (2b) From the following sets of premises derive as many conclusions as possible paying no attention to figure : E A O AAA. (3a) Making use of all the general rules of the syllogism, A test the validity of the following mood in all the figures : A. I 12 3 4 Answer : A M — G G — M M — G G — M A S — M S— M M— S M— S I S — G S — G S — G S — G An underscored symbol indicates a distributed term. Since A distributes its subject, the subjects of both premises are under- scored in all the figures. No term is underscored in the con- clusions; since I distributes neither term. In the first figure the middle term is distributed in the major premise, and no term is distributed in the conclusion. Since both premises are affirmative, the rules for negatives are not applicable; and as a particular may be drawn from two universals, if there is no violation of the rules for distribution, this mood seems to be valid in the first figure. It is, however, a weakened conclusion; since an A could just as well be drawn. The mood is invalid in the second figure because of undistributed middle, but valid in (both the third and fourth ; since in both cases the middle term is distributed at least once. (3b) Determine the 'validity of the attending moods in all I A E the figures giving reasons : A O A I O O Review Questions 245 11. REVIEW QUESTIONS. (1) Define a logical figure and illustrate by means of some ordinary syllogistic argument. (2) Symbolize the four figures and give suggestions for remembering them. (3) Write syllogisms which illustrate each of the four figures. (4) Define mood as it is used in logic. Illustrate. (5) How many moods are valid? (6) Explain by illustration a "weakened conclusion." A E (7) Test the validity of E in the third figure; of I in the third. E O (8) Independent of all helps, prove the truth of the canons of the first figure. (9) In a similar way prove the canons of the second, third and fourth figures. (10) So far as testing arguments is concerned, what use may be made of the special canons of the syllogism? (11) Offer a few suggestions for remembering the special canons. (12) Why did Aristotle attach so much importance to reduc- tion in logic? (13) Justify calling the first figure the "perfect figure," and the others the "imperfect figures." (14) Treat of the relative value of the four figures. (15) Show by illustration that the second figure is the ex- clusive figure. E O I (16) Test the following moods in all the figures: I A A A O I AEEAAEAAA E I A E I E O A I. O O O O E I I I I 12. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Give an illustration of a syllogism in the fourth figure which might just as well be written in the first figure. 246 Figures and Moods of the Syllogism (2) May a syllogism, which is invalid in the fourth figure, be made valid by writing it in the form of the first figure? Prove it. (3) Show why it is impossible to apply all the rules of the (4) Show the difference between a direct and an indirect to the figures. (4) Show the difference between a direct and an indirect proof. A (5) Show that A is valid in the first figure when the major O premise (A) is co-extensive. (6) The third figure is known as the figure of particular conclusions. Why should not the second canon of that figure be, "One premise must be particular" rather than "The conclusion must be particular?" (7) Show that there is some ground for thinking that, as a final test, moods in the other figures should be reduced to the first. (8) Illustrate the fact that the second figure is the figure of disproof; whereas the third is the figure of contradictions. (9) "To be logical a syllogism must conform to one of the four figures, but this does not mean, necessarily, that all argu- ments must conform to some figure." Explain this. CHAPTER 13. INCOMPLETE SYLLOGISMS AND IRREGULAR ARGUMENTS. 1. ENTHYMEME. An enthymeme is a syllogism in which one of the three propositions is omitted. Suppressing the major premise gives an enthymeme of the first order; whereas if the minor premise be sup- pressed, the enthymeme becomes one of the second order; while omitting the conclusions gives an enthymeme of the third order. Illustrations: Complete syllogism. All true teachers are just, You are a true teacher, (Hence) You are just. Enthymeme of first order; major premise omitted. You are a true teacher, (Hence) You are just. Enthymeme of second order; minor premise omitted. All true teachers are just, (Hence) You are just. Enthymeme of the third order; conclusion omitted. All true teachers are just, (And) You are a true teacher, 247 248 Incomplete Syllogisms To argue in terms of the complete syllogism is the unusual, not the usual method. We have a way of ab- breviating our remarks; expressing only the necessary and leaving the obvious to be taken for granted. Thus the enthymeme becomes the natural form of expression. But the mere fact that a part of the argument is omitted, makes it more essential for the student to think clearly and with careful continuity, that no error may intrude itself. Probably the most common enthymemes are those of the first order. This may be explained by the fact that the major premise is usually the most universal of the three propositions, and, in consequence, the one which would be the most generally understood. The following represent enthymemes of this order, gleaned from the ordinary conversation of ordinary people : ( 1 ) "Your beets won't grow, because you are plant- ing them in the wrong time of the moon." (2) "You, being a member of the Sunday School, should be ashamed of such language." (3) "Being the son of your father, you ought to have some pride in this matter." (4) "We are going to have an open winter, because I have observed that the hornets' nests are near the ground." (5) "You had better put in lots of coal, for I have noticed that the squirrels have gathered in more nuts than usual." Judging from these enthymemes, it would seem to be more natural to assert the conclusion and follow this by Enthymeme 249 a reason in the form of a minor premise, leaving the major to the intelligence of the auditor. The enthymeme of the second order occurs only in- frequently, since it seems to be an unnatural mode of expression, though sometimes it appears to lend emphasis to the conclusion; e. g., "All untrustworthy boys come to a bad end, and I predict that you will come to a bad end." Enthymemes of the third order are commonly used for the sake of emphasis, as the following make evident : (1) "No business man wants an indolent boy, and you are indolent." (2) "All successful teachers are interested in their work, and you plan to be a successful teacher." (3) "Humility is a sign of greatness, and Lincoln possessed this quality." 2. EP1CHEIREMA. An epicheirema is a syllogism in which one or both of the premises is an enthymeme. To put it in another way : An epicheirema is a syllogism in which one or both of the premises is supported by a reason. When one premise is an enthymeme the syllogism is termed a single epicheirema ; whereas when both premises are enthymemes it becomes a double epicheirema. Single epicheirema. All men are mortal, because all men die, Socrates was a man, .". Socrates was mortal. Double epicheirema. All men are mortal, because all men die, 250 Incomplete Syllogisms Socrates was a man, because he was a rational animal, .'. Socrates was mortal. It is obvious that supporting each premise with a reason lends strength to the argument. This justifies the use of the epicheirema. 3. POLYSYLLOGISM. A poly syllogism is a series of syllogisms in which the conclusion of a preceding syllogism becomes a premise of a succeeding one. The syllogism in the series whose conclusion becomes a premise of the succeeding syllogism is termed a pro- syllogism; while the syllogism which uses as one of its premises the conclusion of the preceding syllogism is called an episyllogism. Illustrations. fA quadruped is an animal/ A dog is a quadruped, >Prosyllogism Polysyllogism\ . ' . A dog is an animal. 1 Fido is a dog, \-Episyllogism . Fido is an animal. All who libel an associate are^ unprofessional, This teacher has libelled her Pro- associate, J syllogism Poly- .'. This teacher is unprofes- syllogism \ sional. All who are unprofessional YEpi- should be disciplined, \ syllogism This teacher should be dis- ciplined. Sorites 251 4. SORITES. A sorites is a series of syllogisms in which all of the conclusions are omitted except the last one. Just as the epicheirema is a combination of enthymemes of the first and second orders, so the sorites is a combina- tion of enthymemes of the third order. If each conclu- sion were written, the sorites would take the form of prosyllogisms and episyllogisms. Two forms of the sorites are recognized by logicians. These are the pro- gressive or Aristotelian, and the regressive or Goclenian. Illustrations. Progressive Symbolised. Put in Word Form. All A is B Thomas Arnold was a teacher, All B is C A teacher is a man, All C is D A man is a biped, All D is E A biped is an animal, Hence all A is E Hence Thomas Arnold was an animal. Regressive All A is B A biped is an animal, All C is A A man is a biped, All D is C A teacher is a man, All E is D Thomas Arnold was a teacher, Hence all E is B Hence Thomas Arnold was an animal. When regarded from the viewpoint of extension, the progressive sorites proceeds from the smaller to the larger while the regressive is the converse of this. The point may be illustrated by circles : 252 Incomplete Syllogisms Circle I stands for Thomas Arnold. " 2 " " teacher. " 3 " man. " 4 " " biped. " 5 " " animal. Fig. 15. The progressive sorites proceeds from the smaller circle to the larger, thus : All of circle I belongs to 2 2 •t 3 3 tc tt 4 4 tt a 5 i a tt 5 Hence, " " The regressive sorites proceeds from the larger to the smaller ; i. e. : All of circle 4 belongs to 5 3 4 2 a tt 3 1 a a 2 1 tt it 5 Hence, " " Other differences become apparent when the omitted conclusions are expressed. Progressive Symbolized Word Form All A is B T. Arnold was a teacher, {A) All B is C A teacher is a man, {A) .'. All A is C .'. T. Arnold was a man. (A) All C is D A man is a biped, (A) Sorites 253 .\ All A is D .'. T. Arnold was a biped. (A) All D is E A biped is an animal, (A) .'. All A is E .*. T. Arnold was an animal. (A) In the three completed syllogisms it becomes evident that the progressive sorites uses the minor as its first premise and in consequence takes the form of the fourth figure, though the reasoning is according to the first figure^ The progressive sorites must conform to the following rules: (1) The first premise may be universal or particular, all the others must be universal. (2) The last premise may be affirmative or negative; all the others must be affirmative. A violation of the first rule would result in undis- tributed middle; whereas a violation of the second rule would give illicit major. These rules may be illustrated by giving attention to the symbols of the foregoing completed syllogisms. The first completed syllogism of the sorites is: All A is B All B is C .*. All A is C Securing a logical arrangement by interchanging the major and minor premises gives : ( M ) ( G) ( First premise universal ) is C (M) is B (G) is C (A) All B (S) (A) All A (S) (A) .-. All A 254 Incomplete Syllogisms Applying the rules we find this syllogism valid, or we may A recall that A is valid in the first figure. A Let us now make the first premise of the sorites par- ticular and test. Some A is B All B is C .'. Some A is C Arranged logically: (M) (G) (A) All B is C (S) (M) (I) Some A is B (S) (G) (I) • '. Some A is C Proof: Since one premise is particular the conclusion must be particular. (Rule 7) As there are no negatives in the argument, only one conclusion is possible; namely, a par- ticular affirmative (I). Thus, instead of the conclusion, "All A is C," which is an (A), it must be, "Some A is C," or an (I). Underscoring the distributed term, it is seen that the middle term is distributed in the major premise and that no term is distributed in the conclusion. Thus the mood is valid. This is "checked" when we recall that All is always valid in the first figure. We have now shown that the first premise of a progressive sorites may be universal or particular. Let us further Sorites 255 proceed to prove that all the other premises must be universal. Data: Given the first completed syllogism of the sorites: All A is B All B is C .'. All A is C Proof: Let any other premise, such as the second, be particular; this gives the following: All A is B Some B is C .*. Some A is C Arranged logically: Mood, figure, and distribution indi- cated. (M) (G) ( I ) Some B is C (S) (M) (A) All A is B (S) (G) (I) .'. Some A is C We note at once that the middle term is undistributed, I hence the mood A is invalid in the first figure ; reference I to the valid moods in figure one "checks" this conclusion. Since no premise, other than the first, can be particular, then all save the first must be universal. The truth of the first rule has been demonstrated, and now we may follow a similar plan to prove the truth of the second rule. 256 Incomplete Syllogisms Problem: To prove that the last premise may be nega- tive.* Data : Given the last completed syllogism : All A is D All D is E All A is E Let us make the last premise negative (E) and test the result. (As all but the first must be universal we cannot use an O.) All A is D No D is E .'. No A is E Arranged logically and symbolised: (M) (G) (E) No D is E (i) (M) (A) All A is D (S) (G) (E) . '. No A is E Proof: Negative premise ; negative conclusion. No par- ticulars. Middle term distributed in major premise. No term distributed in conclusion which is not distributed in premise where it occurs. Syllogism valid. We must now prove that all the other premises must be affirmative. Problem: To prove that no other premise can be nega- tive, or that all others must be affirmative. Data: Given last syllogism of sorites with the first premise negative. (Any other may be taken.) *The student should prove that the last premise may be affirmative. Sorites 257 No A is D All D is E • No A is E logically and symbolized: (M) (G) (A) All D is E (S) (M) (E) No A is D (S) (G) (E) No A is E Proof: "G" is distributed in the conclusion but not in the major premise. Fallacy of illicit major. Hence no other premise can be negative. We may now consider the completed syllogisms of the regressive sorites. All A is B All C is A .*. All C is B All D is C .*. All D is B All E is D .'. All E is B By examining the foregoing it becomes apparent that the regressive sorites, both in form and in the reasoning, adapts itself to the first figure. The rules of the regressive sorites are just the reverse of the progressive. These are : ( 1 ) The first premise may be negative ; all the others must be affirmative. 258 Incomplete Syllogisms (2) The last premise may be particular; all the others must be universal. It would be a valuable exercise for the student to test these rules according to the plan pursued in treating the progressive sorites. 5. IRREGULAR ARGUMENTS. It has been intimated that a syllogistic argument, in order to be logical, should be made to conform to the rules of the syllogism. It must not be inferred from this, however, that all deductive reasoning is included by the logical forms here treated. There seem to be arguments which yield valid conclusions, and yet which are not logical in the strict sense of the word. The following illustrate some of these forms : (1) Quantitative Arguments. John is taller than James, Albert is taller than John, .'. Albert is taller than James. Here, apparently, is a fallacy of four terms : these four terms are (1) John, (2) taller than James, (3) Albert, (4) taller than John. Yet we know that the argument is valid. There is not a particle of doubt in the mind rela- tive to the truth of the conclusion that "Albert is taller than James." We are consequently forced to the infer- ence that such quantitative arguments lie outside the field of syllogistic reasoning. The argument involves this new principle, "Whatever is greater than a second thing which is greater than a third thing is itself greater than a third thing." Irregular Arguments 259 There are many other arguments similar to this which are not syllogistic in nature. To wit: A equals B, B equals C, C equals D ; A equals D. A is a brother of B, B is a brother of C, C is a brother of D ; A is a brother of D. A is west of B, B is west of C, C is west of D; A is west of D. (2) Plurative Arguments. These are arguments in which the propositions are introduced by more or most; e. g. : Most (more than half) of the team are seniors, Most (at least half) of the team are under twenty, .'. Some students under twenty are seniors. I Here we have an I which is evidently valid. No term I distributed and yet the conclusion is unquestionably true. This is due to the fact that the propositions are so worded as to force an overlapping of the major and minor terms. The student may illustrate this relation by circles. 6. OUTLINE. Incomplete Syllogisms and Irregular Arguments. (1) Enthymeme. First, second and third orders. Natural form. (2) Epicheirema. Single, double. (3) Polysyllogism. Prosyllogism, episyllogism. (4) Sorites. Progressive, regressive. Two rules of each. (5) Irregular Arguments. Quantitative, plurative. 260 Incomplete Syllogisms 7. SUMMARY. (1) An enthymeme is a syllogism in which one of the three propositions is omitted. Suppressing the major premise gives an enthymeme of the first order; omitting the minor gives one of the second order; while omitting the conclusion gives one of the third order. The enthymeme is really the natural form of expression. En- thymemes of the first order are the most common while those of the third order are the most emphatic. (2) An epicheirema is a syllogism in which one or more of the premises is an enthymeme. An epicheirema is said to \>e single when but one premise is an enthymeme, and double when both premises are enthymemes. (3) A polysyllogism is a series of syllogisms in which the conclusion of the preceding syllogism becomes a premise of the succeeding one. The one of the series whose conclusion becomes a premise is termed a prosyllogism ; while the one which uses the conclusion as a premise is called an episyllogism. (4) A sorites is a series of syllogisms in which all the conclu- sions are omitted except the last one. The two kinds of sorites are the progressive and regressive. The progressive uses the "minor" as its first premise and adopts the form of the fourth figure, whereas the regressive uses the "maj or" as its first premise and adopts the form of the first figure, The two rules of the progressive sorites are, (1) "The first premise may be particular, all the others must be universal"; (2) "The last premise may be negative, all the others must be affirmative." The two rules of the regressive are, (1) "The first premise may be negative, all the others must be affirmative"; (2) "The last premise may be particular, all the others must be universal". (5) Irregular arguments are such as yield valid conclusions and yet do not conform to the syllogistic rules. The quantitative argument expresses quantity and contains four terms. This argument is based on the principle, "What ever is greater than a second thing which is greater than a third thing is itself greater than a third thing." Plurative arguments are introduced by "more" or "most" and Summary 26 r give in consequence a valid conclusion from two particulars. This is due to the overlapping of the major and minor terms. 8. REVIEW QUESTIONS. (1) Define and illustrate an enthymeme. (2) Illustrate the enthymemes of the three orders and point out their distinct uses. (3) Why should the enthymeme demand closer thought than the ordinary syllogism ? (4) Define and illustrate the epicheirema. (5) Of what use is the epicheirema ? Illustrate. (6) Define and illustrate a prosyllogism and an episyllogism. (7) Why are polysyllogisms so called ? (8) Define and illustrate the sorites. (9) Relate the sorites and the epicheirema to the enthymeme. (10) Illustrate the two forms of sorites. (11) Explain the two forms of sorites by means of a diagram. (12) Prove the truth of the two rules of the progressive sorites. (13) Illustrate two kinds of irregular arguments and show that they are valid. (14) Complete the five enthymemes of page 248 and indicate their mood and figure. 9. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Why should enthymemes of the second order be less common than those of the first? (2) You desire to make it evident to a child that a small beginning often leads to a momentous ending; do so in terms of the enthymeme of the first order. (3) Show that prosyllogism and episyllogism are relative terms. (4) When the common premise of the "pro" and "epi" syllogism is omitted what abbreviated form results? (5) From the viewpoint of your definition criticise this : "A sorites is a series of prosyllogisms and episyllogisms in which all of the conclusions are suppressed except the last." (6) Prove the truth of the two rules of the regressive sorites. 262 Incomplete Syllogisms (7) Show that the prosyllogism and the episyllogism may be progressive or regressive. (8) "Reasoning from cause to effect" — is such progressive or regressive ? Explain. (9) Which is inductive in nature, the progressive form of rea- soning or the regressive? Explain. (10) Test the validity of the enthymemes on pages 248 and 249. (11) "A sorites is at least as immediately convincing as the chain of syllogisms into which it can be decomposed." Discuss this. CHAPTER 14. CATEGORICAL ARGUMENTS TESTED ACCORDING TO FORM. 1. ARGUMENTS OF FORM AND MATTER. The matter relative to the syllogism treated in chapters ii, 12 and 13 is given primarily to enable the reader to test the validity of categorical arguments. Such argu- ments must be viewed from the two standpoints of form and matter, since it is one of the chief purposes of logic to enable the student to detect fallacious reasoning, no matter how subtly it may be concealed. Therefore, that one may gain marked facility in this kind of work, it becomes necessary to proceed with thoroughness and confidence. The meaning of arguments and the various material fallacies may be treated later; but we are now equipped with sufficient knowledge and experience to test the validity of arguments from the viewpoint of form. 2. ORDER OF PROCEDURE IN THE FORMAL TESTING OF ARGUMENTS. In testing categorical arguments three things are essen- tial; first, to follow a definite plan; second, to give rea- sons; third, to give the author the benefit of the doubt. In view of these essentials, we suggest this outline which may be helpful to the inexperienced : (1) Arrange logically and complete the syllogism. (2) Determine the figure and mood by using symbols. (3) Apply the rules for negatives and particulars. 264 Categorical Arguments Tested (4) Indicate the distribution by underscoring the terms distributed. (5) Apply the rules for distribution. (6) Name fallacies, if any, giving reasons. We recall that to be strictly logical any categorical argument must take this form: first, major premise; second, minor premise; third, conclusion. Often in com- mon conversation either the minor premise or conclusion is given first. Illustrations of this: (1) "He cannot be a gentleman (conclusion) ; for no gentleman would do such a thing (major premise), and there is no doubt but that he did it" (minor premise). (2) "He has the making of a good teacher (conclusion) ; because he not only knows, but he knows how to impart what he knows (minor premise), and this is a sure sign of a good teacher" (major premise). When the argument appears in this illogical form, the first duty of the student is to arrange it logically. To do this he must be able to recognize readily the premises and the conclusion. To this end these facts may be of assistance: (1) A premise always answers the question "Why", and is often introduced by such words as "/or," "because'/ "since;' and the like. (2) The conclusion is usually introduced by "there- fore;' "hence;' "it follows," etc. (3) When there are no word-signs those mentioned in the foregoing may be inserted with a view of determining which is the conclusion, and which are the premises. Order of Procedure in Testing of Arguments 265 Suggestions relative to completing abbreviated argu- ments: (1) If the conclusion is to be supplied, select the term used twice in the premises; this, the middle term, must not appear in the conclusion. The other two terms may now be connected (copulated) to form the conclusion, the narrower term (minor) being used as the subject, unless it occurs in what clearly seems to be the major premise. (2) If either premise is to be supplied, unite the middle term with the subject of the conclusion for the minor premise, and with the predicate of the conclusion for the major premise. (3) In supplying any missing proposition, care should be taken to make the argument valid, if this can be done in conformity with good Eng- lish, good sense, and the rules of logic. As regards the determination of the figure it is well to locate the middle term first, placing above it the symbol M. Then "G" (greater) may be placed above the major term and "S" (smaller) above the minor. 3. ILLUSTRATIVE EXERCISES IN TESTING ARGUMENTS WHICH ARE ALREADY COMPLETE, REGULAR, AND LOGICALLY ARRANGED. M G (1) A All dogs are quadrupeds, S M A All greyhounds are dogs, S G All greyhounds are quadrupeds. 266 Categorical Arguments Tested \ A This argument is in the first figure, the mood being -J A. l A All the propositions are affirmative and universal, conse- quently the rules pertaining to negatives and particulars are inapplicable. "A" distributes the subject only, hence all the subjects are underscored. The middle term "dog" is distributed in the major premise, and the minor term "greyhound" which is distributed in the conclusion, is likewise distributed in the minor premise. The argument is, therefore, valid in form. This may be verified by referring to a list of valid moods in the first figure. G M (2) E No prejudiced person is open to conviction, S M All fair minded persons are open to con- viction, S G No fair minded person is prejudiced. The argument is in the second figure; mood IE There is one negative premise and the conclusion is nega- tive; no particulars. "E" distributes both terms, "A" the subject only. The middle term is distributed in the major premise. Both major and minor terms are distributed in the conclusion, but they are likewise distributed in the premises where they are used. The argument is, there- Illustrative Exercises in Testing Arguments 267 fore, valid. Reference to the valid moods of the second figure confirms this conclusion. M G (3) A All good citizens vote, M S A All good citizens obey the law, S G A .*. All who obey the law vote. fA The mood is -l A used in the third figure. All the prop- ositions are A's, hence the negative and particular rules are inapplicable. "A" distributes its subject. The middle term is distributed in both premises. "All who obey the law" is distributed in the conclusion but not in the premise where it is used. Therefore the argument is fA invalid. The fallacy being illicit minor. ■ in the third figure's list of valid moods. M G (4) A All good citizens vote, A is not found A S M E No criminal is a good citizen, S G E .*. No criminal votes. . (A The mood of this argument is -{E used in the first 268 Categorical Arguments Tested figure. One premise negative; conclusion negative; no particulars. "A" distributes the subject only; "E" both subject and predicate. The middle term, "good citizens," is distributed in both premises. The major term, "votes," is distributed in the conclusion but not in the premise where it is used. The argument is invalid, the fallacy (A E is not found in the first figure's E being illicit major. list of valid moods. G M (5) A All true teachers are sympathetic, S M A All lovers of children are sympathetic, S G A .*. All lovers of children are true teachers. The mood of this argument is (A A used in the second A figure. There are no negatives and no particulars. "A" distributes its subject only. The middle term, "sympa- thetic," is distributed in neither premise, hence the argu- ment is invalid. Fallacy of undistributed middle. Re- ' A ferring to the list of valid moods, we do not find -| A in the second figure. M G (6) A All thoughtful men are humane, Illustrative Exercises in Testing Arguments 269 S M A All good citizens are thoughtful men, S G I .'. Some good citizens are humane. r A The mood is J A in the first figure. No negatives ; no I particulars. "A" distributes its subject only; "I" dis- tributes neither term. Middle term, distributed in the major premise; no term distributed in the conclusion. The argument is, therefore, valid. The conclusion is weakened as it could just as well be an A. The mood A A in the first figure is valid, but of little value because I of the weakened conclusion. 4. ILLUSTRATIVE EXERCISE IN TESTING COMPLETED ARGUMENTS, ONE OR BOTH PREMISES BEING IL- LOGICAL. Arguments containing exclusive propositions. ( 1 ) Only first class passengers may ride in the parlor car, All these are first class passengers, .'. They may ride in the parlor car. Propositions introduced by such words as only, none but, alone and their equivalents are exclusive proposi- tions. Since these distribute their predicates, but do not distribute their subjects, the most convenient way of deal- ing with them is to interchange subject and predicate and 270 Categorical Arguments Tested then regard them as "A" propositions. As the first prop- osition of the argument is an exclusive, we must deal with it accordingly. Interchanging subject and predicate and introducing it with all places the argument in this form: G M A (All) The parlor car is reserved for first class passengers, S M A All these are first class passengers, ~~S~ G A .'. All these may ride in the parlor car. XA The mood of this argument is^j A in the second figure . l A No negatives; no particulars. "A" distributes its sub- ject only; the middle term is thus undistributed. The argument is invalid, the fallacy being that of undistributed middle. (2) "No one but a thief would take these books with- out asking for them, and it has been proved that you took the books; that is the reason I have called you a thief." It is clear that "no one but" is equivalent to "only." Thus the first proposition of the argument is an ex- clusive, and may be made logical by interchanging subject and predicate and calling it an "A." As a result of this the argument takes the following form: M G A (All) These books were taken by a thief, Exercise in Testing Completed Arguments 271 S M You took these books, S G A .'. You are a thief. We have now had sufficient experience to recognize the validity of mood AAA in the first figure. (3) "None but the brave deserve the fair, And you are not fair." Making the exclusive logical and completing gives : M G A (All) The fair deserve the brave, S M You are not fair, S G . You do not deserve the brave. The mood of this argument is t 2 , t 3 Antecedents Phenomenon s d h w t x e d h w 1 2 s b h w 1 3 s d a w 1 4 V standing for route through the woods, is seen to be the invariable antecedent. (4) Concrete example illustrating the second state- ment. The Problem: To determine the effect of direct primaries. 390 Methods of Observation and Experiment First trial. Antecedent Direct primary Second trial. Direct primary « Third trial. Direct primary Consequents i. Greater expense to candidate, 2. Greater interest shown, 3. Better men nominated, 4. "Bumper" crops. 1. Greater expense to candidate, 2. Greater interest shown, 3. Better men nominated, 4. Crops below average. 1. No greater expense, 2. Greater interest shown, 3. Better men nominated, 4. Crops average. Fourth trial. Direct primary 1. No greater expense, 2. No greater interest, 3. Better men nominated, 4. Crops average. It is seen that the invariable consequent is, "Better men nominated." We may, therefore, conclude that this is a probable effect of "Direct primaries." (5) Distinguishing features of method of agreement. The essential characteristics of the method of agree- ment are three: First, The phenomenon always occurs. Second, There is at least one invariable antecedent. Third, The other antecedents vary. i Method of Agreement 391 Giving attention to the attending symbolized illustrations it may be noted that "P," the phenomenon, always hap- pens ; while in the case of the first symbolization, "D" is the invariable antecedent and "A, B, C, E, G, L, M, F, I" are the variable antecedents. "K" is the invariable ante- cedent of the second and "H, I, L, T, M, W, X, Y, Z, S" are the variable antecedents. Antecedents Consequents 1. A B C D E V x A B C D G P 2 L B C D M P 3 A F G D M P 4 L B C D I P 5 2. H I K L T P t KLMT W P 2 M T L K W P 3 X H K Y Z P 4 T W L K S P 5 (6) A Matter of Observation and Experiment. On studying the problem relative to the tardiness of John, it appears that in obtaining the various antecedents the work would be largely a matter of observation. Carrying the father's dinner, the route through the woods, etc., are facts which observation would make evident. However, when it becomes necessary to vary these ante- cedents with a view to finding the invariable one, the procedure is experimental as well as a matter of casual observation. Moreover, in connection with the direct primary problem the question would be largely a matter 39 2 Methods of Observation and Experiment of experiment; though observation would obtain as a subsidiary condition. We may conclude from this that the method of agreement involves both observation and experiment; and since the student will discover that the other methods impose similar demands, we are justified in designating these five special methods of induction as those of observation as well as of experiment. (7) Advantages and Disadvantages of the Method of Agreement. The concrete cases given to illustrate the method of agreement present a simple combination of antecedents and consequents. In life, however, such simplicity does not usually obtain and in consequence the method of agreement gives rise to a few serious difficulties. These may be summarized as (a) Plurality of causes; (b) Im- material antecedents ; (c) Complexity of phenomena; (d) Uncertainty of conclusion. (a) Plurality of causes is mentioned by Mill as con- stituting the "characteristic imperfection" of the method of agreement. As the term signifies, plurality of causes represents a condition where a given phenomenon has more than one cause, or where different causes produce the same effect. For example, "A poor crop" may be due to drought, neglect, pests, etc. ; heat may be caused by friction, electricity, combustion. Unfavorable home con- ditions; ill health; dislike for teacher — any one of these might be followed by irregular attendance. (b) Immaterial antecedents are those which precede a given phenomenon and yet, under the most favorable situations, have no causal connection with said phe- Method of Agreement 393 nomenon. For example, the various antecedents of the heavy rain may have been a south wind, forgetting to take an umbrella, missing the car and having to walk, etc. Clearly these antecedents, with the exception of the first, are immaterial. (c) The law of agreement demands that all the mate- rial antecedents receive consideration, but often the situa- tion is too complex to make this possible; a fair illustra- tion of such would be an attempt to ascertain all of the antecedents of "the high cost of living." (d) The law of agreement never precludes the possi- bility of error ; as it is quite impossible to carry the analy- sis to the point of absolute certainty. Of all the methods, "agreement" is the least reliable. Despite the foregoing objections, however, the method is of positive value because of its suggestiveness ; opening the door to plausible hypotheses it gives the investigators a working basis. 3. METHOD OF DIFFERENCE. (1) Principle stated. Says Mill, "If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circum- stance in which alone the two instances differ is the effect or the cause of an indispensable part of the cause, of the phenomenon." To put this in simple terms: Whatever is invariably 394 Methods of Observation and Experiment present zvhcn the phenomenon occurs and invariably ab- sent when the phenomenon does not occur, other circum- stances remaining the same, is probably the cause or the effect of the phenomenon. (2) Method symbolized. Using the same symbols as were used in "Agreement." Antecedents Consequents A B C D P — BCD — or P A B C D _ -BCD In the first instance A is probably the cause of the phenomenon, since it is present when the phenomenon occurs and absent when it does not occur. For a similar reason, A is the effect in the second case. (3) Concrete illustrations. (A) A wise teacher in ascertaining the cause of John's tardiness would have suggested at once a change of route. Using as symbols the initial letters of the key- words of the antecedents in the case, the following results : s d h w r t sdh— — (B) First trial. Problem: Unprepared home work. Antecedents Consequents 1. Length of lesson, ") 2. Definiteness of lesson, | Work not properly 3. Amount of interest shown, [ prepared. 4. Physical condition the same. Method of Difference 395 ; Second trial. 1. Length of lesson the same, 2. Lesson made more definite, T . . V ^Work properly prepared. 3. Interest the same, 4. Physical condition the same. The foregoing symbolized: L D I C W L — I C — It is seen that indefiniteness of lesson assignment is the cause of the unprepared home work. (4) Advantages and disadvantages of the Method of Difference. The main difficulty attending the use of the method of difference is the complexity of phenomenon. The very nature of the method insists as an essential requirement that only one material antecedent shall be varied at a time. In life the variations are more or less confused, and it is often not only impossible to observe cases of a single variation, but frequently error comes through overlooking antecedents which are material to the case under investigation. For these reasons the Method of Difference is more a method of experiment than it is a method of observation. By controlling the circumstances it becomes possible to vary but one antecedent at a time, and also to bring into prominence all of the material antecedents. Bacon claims that all "crucial instances" are merely applications of the Method of Difference. By crucial in- stance he means any fact which will enable us to deter- mine at once which supposition is the correct one. For 396 Method of Observation and Experiment example, the physician may not know whether it is ma- laria or typhoid fever till he takes a blood test ; such a test typifies "crucial instances." The various tests in chem- istry are likewise cases of crucial instances, and, in conse- quence, this science makes use of "Difference" more than any other method. (5) Characteristic features of Method of Difference. There are three distinguishing marks of the Method of Difference: these are, (1) The phenomenon does not always happen; (2) One antecedent is variable; (3) The other antecedents are more or less invariable. The following symbolizations will make these three characteristics evident : Antecedents Consequents (1) ABC P A — C — (2) — B C — X B C P (3) L M T K P L M — K — Agreement and Difference Compared. (a) The methods of Agreement and Difference are complementary as may be discerned by comparing their characteristic features: In Agreement the phenomenon ahvays occurs; in Difference the phenomenon does not always occur : In Agreement there is one invariable ante- cedent; whereas in Difference there is one variable ante- cedent : In Agreement the other antecedents are more or less variable; but in Difference the other antecedents are more or less invariable. Method of Difference 397 (b) According to Mill the Method of Agreement in- sists that what can be eliminated is not connected; whereas the Method of Difference implies that what cannot be eliminated is connected. (c) The Method of Agreement is more a method of 4 observation, since it is chiefly concerned with the dis- covery of causes. The Method of Difference is dis- tinctly a method of experiment, because its usual aim is to discover effects. (d) The Method of Agreement is so called because the object is to compare several instances to determine in what respect they agree; but in the case of Difference instances are compared to determine in what respects they differ. (e) The conclusions of the Method of Difference in- volve greater certainty than those of Agreement and, therefore, the former method should be adopted when there is a choice. 4. THE JOINT METHOD OF AGREEMENT AND DIFFER- ENCE. (1) Principle stated. The uncertainty of the conclusions of Agreement and the impossibility at times of employing directly the Method of Difference, give rise to the use of the com- bination of Agreement and Difference known as the Joint Method. As stated by Mill, the principle condi- tioning the Joint Method is this: "If two or more in- stances in which the phenomenon occurs have only one circumstance in common, while two or more instances 398 Methods of Observation and Experiment 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." More briefly the notion may be stated in this wise: Among many instances, if one cir- cumstance is invariably present when the phenomenon occurs, and invariably absent when the phenomenon does not occur this circumstance is probably the cause or the effect of the phenomenon. This principle differs from the one underlying the Method of Difference in that the instances considered are more varied and more numerous. The principle of Difference requires but two sets of instances, while the Joint Method demands at least three; two when the phenomenon occurs and one when it does not occur. A study of the symbolizations and illustrations will clarify this distinction. (2) Joint Method symbolized. If we use circumstances and phenomenon in place of antecedents and consequent, then one symbolization may be made to stand for ascertaining either the invariable antecedent, or the invariable consequent. Circumstances Phenomenon 1. A B C D P x 2. A D E F ■ P 2 3. A L M N P 3 4. A O P Q P 4 5- O P Q - The Joint Method of Agreement and Difference 399 6. L M N — 7. D E F — 8. B C D — It is obvious that the first, second, third and fourth groups of instances illustrate the principle of Agreement; whereas the first and eighth, the second and seventh, the third and sixth, and the fourth and fifth illustrate in each case, the principle of Difference. (3) Concrete Examples illustrating Joint Method. The problem: Too much whispering. Antecedents Consequent 1. Insufficient work, Lack of interest, iMuch whispering. Seated near a friend. J 2. More work, Lack of interest, Seated near a friend. 3. More work, More interest, [►Much whispering. Seated near a friend.) 4. More work, More interest, }>Not much whispering. Not seated near friend. J 5. More work, Lack of interest, J>Not much whispering. Not seated near friend. J 6. Insufficient work, Lack of interest, |-Not much whispering. Not seated near friend.] Much whispering. 400 Methods of Observation and Experiment ►Poor recitation. From this it may be concluded that the undue amount of whispering is caused by seating particular friends near each other. The problem: Poor recitations. Antecedents Consequent i. Long lesson, Faulty assignment of lesson, J-Poor recitation. Fear of teacher. 2. Lesson made shorter, Faulty assignment, Fear of teacher. 3. Lesson made shorter, A more careful assignment, [-Poor recitation. Fear of teacher. 4. Lesson made shorter, A more careful assignment, J-Good recitation. Removal of fear of teacher. J 5. Lesson made shorter, Faulty assignment, No fear of teacher. 6. Lesson long, Faulty assignment, No fear of teacher. Fear of teacher is the cause of the poor recitation. (4) Distinguishing features. Being a combination of Agreement and Difference the Joint Method possesses the characteristics of each, though more or less modified. The distinguishing marks may be summarized as follows : Good recitation. Good recitation. The Joint Method of Agreement and Difference 401 (1) Of the first group of instances : (1) The phenomenon must always occur, (2) One antecedent must be invariable, (3) The other antecedents must be more or less variable. (2) Of the second group of instances : (1) The phenomenon must never occur, (2) One antecedent must be variable, (3) The other antecedents must be more or less invariable. Briefly, the one principle concerned is this: There must be an invariable conjunction between the phenome- non involved and the antecedent suspected of being the cause. (5) Advantages and Disadvantages of the Joint Method. Since the Joint Method permits a consideration of the negative aspect of the question as well as the affirmative, the opportunities for testing the many instances con- cerned are doubled. In consequence, the conclusions of the Joint Method are more positive than those of the other methods. It follows that this same opportunity to multiply the instances would tend to lessen the other ob- jections raised against the Method of Agreement; viz., plurality of causes, immaterial antecedents, complexity of phenomenon. The student must regard the given illustrative sym- bolizations and concrete examples as being of the sim- plest form; in life such are the exceptions rather than the rule. When investigating questions, like the cause of 402 Methods of Observation and Experiment the high cost of living, the effect of high tariff, the reason for the typhoid epidemic, etc., there is often a confusion of circumstances which makes the Joint Method unsatis- factory, even though it furnishes a larger opportunity for the multiplication of instances. The strongest case which the Joint Method is able to present is when the negative instances repeat the positive in every detail, with the one exception of the variable antecedent. To wit: Strong Argument: Circumstances Phenomenon A B C P x ALM P 2 — LM — — BC — Weak Argument: A B C F x ALM : P 2 — R S — — TK — Despite the disadvantages, the conditions of the Joint Method are more or less ideal; since the positive branch of the argument suggests the hypothesis, while the nega- tive branch proves the accuracy or inaccuracy of such. 5. METHOD OF CONCOMITANT VARIATIONS. (i) Principle stated. Mill's statement is this : "Whatever phenomenon varies in any manner whenever another phenomenon varies in a Method of Concomitant Variations 403 particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation." To put it differently : // when one phenomenon varies alone, another also varies alone, the one is either the cause or the effect of the other. (2) Concomitant Variations symbolized. Circumstances Phenomenon A P A + a P + p ( A+ a)-a ■ (P + p)-p It is evident from this that little "a" is the cause or the effect of little "p." To put it in concrete form : Let A = X number of calories of heat, And P = 68° F., the original temperature of room, " a = candle burning in room for Yi hour, " p = 2 F. Then Antecedents Consequent X no. of cal. of heat in room = 68° F. temp, of room x u u « « « + burning candle _ 68° + 2 = 70 x (« u « « « ^.burning candle)— burning candle — (68°+2°)— 2°=68° As large "A" is increased and decreased by little "a" so large "P" appears to be increased and decreased by little "p." This strongly suggests a causal connection between little "a" and little "p." (3) Other concrete illustrations. 404 Methods of Observation and Experiment Problem: To ascertain nature of sound. Antecedent Consequent Bell rung when within a glass jar filled with air, Loud sound. Some of the air pumped out of the jar, Sound not sg loud. More air pumped into jar again, Sound louder again. The conclusion must be that air has something to do with the production of sound. Problem: To find best feed for egg production. ioo lbs. beef scraps, ioo lbs. wheat, ioo lbs. oats, ioo lbs. corn, 50 lbs. beef scraps, 100 lbs. wheat, 100 lbs. oats, 100 lbs. corn, 90 lbs. beef scraps, 100 lbs. wheat, 100 lbs. oats, 100 lbs. corn, Since the variation in the amount of beef scraps is accompanied by a like variation in the number of eggs produced, it may be assumed that beef scraps are essen- tial to large egg production. (4) Distinguishing features. The phenomenon always occurs but in varying degrees ; 30 doz. eggs. >2J doz. eggs. ►28 doz. eggs. Method of Concomitant Variations 405 One antecedent varies in degree ; The other antecedents are invariable. (5) Advantages and disadvantages. Concomitant Variations is applicable in cases when it is impossible to use Difference. Recourse is made to the latter when the phenomenon can be made to appear or disappear at will, but there are times when it is impossible to cause the phenomenon to disappear altogether. For example, in the case of the varying degrees of heat in the room it would be scientifically impossible to take all of the heat out of the room ; or in experimenting with gravitation, to do away with its in- fluence entirely, is beyond the power of man. It is thus evident that Concomitant Variations may be used in cases where the conditions forbid doing away entirely with the prenomenon. The special function of Concomitant Variations seems to be to establish the exact quantitative relation between the varying cause and the varying effect. To illustrate: As a general law it is known that bodies attract each other in varying degrees according to their distances apart and according to their relative sizes; by Concomi- tant Variations this law has been given definite quantita- tive value and reads like this : "Bodies attract each other directly as the product of their masses, and inversely as the square of the distance between them." This illus- tration suggests that the variation between antecedent and consequent may be direct or inverse. The error most common in this method is the assump- tion that the quantitative relation between two varying 406 Methods of Observation and Experiment phenomena will always be according to a constant ratio. For example, when being reduced from a high tempera- ture to 39 1-5 F., water steadily contracts; but at 39 1-5 F. it commences to expand until it becomes ice. Thus the ratio of contraction of water is constant only within certain limits. In any event the established ratio of variation can with absolute safety be applied only to the instances investigated. Another disadvantage inci- dent to this method, is the situation of two elements varying together constantly, and yet having no causal connection whatever. 6. THE METHOD OF RESIDUES. (1) Principle stated. As stated by Mill the principle of residue is this: "Subtract from any phenomenon such part as is known by previous inductions to be the effect of certain ante- cedents, and the residue of the phenomenon is the effect of the remaining antecedents." In simpler form the notion is this: Subtract from any phenomenon those parts of it zvhich are known to be the effect of certain antecedents, and what is left of the phenomenon is the effect of the remaining antecedents. (2) Principle symbolized. Antecedent Consequent A x B y C z The total cause of the phenomenon xyz is ABC. The Method of Residues 407 But it is known that the cause of x is the antecedent A ; whereas the cause of y is the antecedent B ; hence it is concluded that the cause of z is the antecedent C. (3) Concrete illustrations. Problem: To find the weight of coal. Antecedents Consequents Weight of driver, Weight of wagon, Weight of coal. = 4200 lbs. Weight of driver, ) __^ 200 ibs.|_ , Weight of wagon. \ ~^200O lbs.(" Hence we may conclude that the weight of coal is 4200 lbs. — 2200 lbs., or 2000 lbs. Perhaps the most noted instance in history of the application of this method, was the one which resulted in the discovery of Neptune. In calculating the orbit of Uranus, it was found that the combined attractions of the sun and the known planets did not account for the path which Uranus took. There was some unknown influence at work. Assuming that this unaccountable attraction was due to the presence of another planet beyond the orbit of Uranus, an Englishman by the name of Adams, and later the Frenchman Leverrier, were able to indicate by the principle of Residues, the spot where this planet should be. By directing the tele- scope toward this point, Neptune was discovered. (4) Distinguishing features: The phenomenon always occurs, The antecedents are usually invariable, 408 Methods of Observation and Experiment Some of the antecedents are known to be the cause of a part of the phenomenon. (5) Advantages and disadvantages. The Method of Residues gives three distinct results: First, it tells what is left over after all the other parts of the phenomenon have been explained. Second, it tells how much is left over, and third, it calls attention to the unexplained parts of the phenomenon. For ex- ample, in the first concrete illustration, by subtracting the known quantities from the total quantity, what is left over is found to be coal; not only so but we are able to calculate the exact amount of coal. This illus- trates the first and second results of the Method of Residues. (Like concomitant variations it is seen that residues is serviceable in given definite quantitative values.) The discovery of Neptune illustrates well the third result of this method; i. e., after accounting for every other force, it was found that there was yet a force at work which had never been explained. It is this third feature of unexplained residues which has placed "Science in its present advanced state." "Most of the phenomena which nature presents are compli- cated; and when the effects of all known causes are estimated with exactness, and subducted, the residual facts are constantly appearing in the form of phenome- na altogether new, and leading to the most important conclusions." So says John Herschel. Almost all of the discoveries in astronomy have come about in this way. If a heavenly body does not behave as it should according to the established theory, then either the The Method of Residues 409 theory is wrong or there is some residual phenomenon which needs to be explained. Its suggestiveness is, therefore, the most important function of this method, though this very feature is the one which makes evi- dent its greatest disadvantage. The unexplained resid- ual phenomenon may be very complex and, therefore, a careless observer is apt to overlook a lurking element which in reality is the true cause. 7. THE GENERAL PURPOSE AND UNITY OF THE FIVE METHODS. Thinking has been defined as the deliberative process of affirming and denying connections. It is obvious that these five methods are a matter of affirming and denying connections between antecedents and consequents. As soon as the looked for connections are established, the antecedents and consequents are known to be related to each other as causes and effects. In this attempt to find and prove connections the Method of Agreement is chiefly valuable in suggesting workable hypotheses, and the method of difference in verifying, through experi- ment, the correctness or incorrectness of these hypo- theses. In substance the principle conditioning both methods is this : "If a single antecedent is invariably present when the phenomenon is present and invariably absent zvhen the phenomenon is absent then this antecedent is the cause of the phenomenon." To put it still more briefly: Between two phenomena there is a causal connection, if the conjunction between the two is invariable. It is 4io Methods of Observation and Experiment the business of Agreement to single out the one ante- cedent and of Difference to show, by presenting the nega- tive as well as the affirmative side of the case, that the conjunction of the one antecedent and the particular phenomenon is invariable. The Joint Method is merely a combination of Agreement and Difference carried into more varied and complex situations. The methods of Concomitant Variations and Residues are merely modi- fications of Difference; the former being used when the chief feature is the fluctuation of the phenomenon, and the latter when it is desired to find what is left over. Agreement suggests the hypothesis, "difference'' proves it; the joint method is "difference" more or less compli- cated, concomitant variations is "difference" applied to fluctuating phenomena, residues is "difference" used to find what and how much is left over. Agreement is the method of observation and belongs to the physician and nature student. Difference and the Joint Method are experimental devices which are used by the physicist and chemist. Concomitant Variations is the method of unstable phenomena and naturally attaches itself to the economist and statistician. Residues is the method of "lurking exceptions" and is favored by the astronomer and mathematician. Residues, being the method of "what is left over,'' is the most common in daily affairs.* All the five methods are forms of inductive thinking which lead to the establishment of causal connections by * All cases of finding the net proceeds are examples of the law of residue. Purpose and Unity of the Five Methods 411 means of the principle of the invariable conjunction of phenomena. 8. OUTLINE. The Five Special Methods of Observation and Experiment. (1) Aim of Five Methods. Fundamental fact of causation. Aim of analysis. ' agreement difference Methods of \ joint concomitant variations residues (2) Method of Agreement. Principle stated Method symbolized Method illustrated Distinguishing features of method A matter of observation and experiment Advantages and disadvantages (3) Method of Difference. Principle stated Method symbolized Method illustrated Advantages and disadvantages Characteristic features Agreement and Difference compared (4) The Joint Method of Agreement and Difference Principle stated Method symbolized Concrete illustrations Distinguishing features Advantages and disadvantages (5) Method of Concomitant Variations Principle stated Method symbolized Concrete illustrations 412 Methods of Observation and Experiment Distinguishing features Advantages and disadvantages (6) The Method of Residues Principle stated Method symbolized Concrete illustrations Distinguishing features Advantages and disadvantages (7) General Purpose and Unity of Five Methods One fundamental principle 9. SUMMARY. (1) The fundamental fact of causation underlies the three forms of induction, but is most conspicuous in the method of analysis and may be ascertained by recourse to one of the experimental methods. (2) The principle of the method of agreement may be summed up in the two statements : The sole invariable ante- cedent of a phenomenon is probably its cause and the sole in- variable consequent of a phenomenon is probably its effect. These two statements may be symbolized and illustrated. The essential characteristics of the method of agreement are the phenomenon always occurs ; there is at least one invariable antecedent; the other antecedents vary. The method of agreement together with the other four methods may justly be termed methods of experiment as well as methods of observation. The difficulties of the method of agreement are in the main plurality of causes, immaterial antecedents, complexity of phenomenon and uncertainty of conclusion. These difficulties may be summarized as involving a phenomenon which may have several causes ; may be preceded by conditions of no causal con- sequence; may be so involved as to prevent exhaustive examina- tion; and may give unreliable conclusions. Agreement is valuable chiefly in furnishing to the investigator plausible hypotheses. (3) The principle of difference is this : "Whatever is in- variably present when the phenomenon occurs and invariably Summary 413 absent when the phenomenon does not occur, other circumstances remaining the same, is probably the cause or the effect of the phenomenon." Like agreement, difference admits of symbolization and illus- tration by concrete examples. The chief difficulties attending difference are: in nature vary- ing one antecedent at a time is infrequent, and it is easy to overlook antecedents which are closely related to the case under investigation. Difference is the most common method of the experimental sciences. The characteristic features of difference are, the phe- nomenon does not always occur, one antecedent is variable, while the others are invariable. The methods of agreement and difference are complementary processes. Agreement attempts to eliminate all the antecedents but one, while difference aims to eliminate one only. Agreement is a method of observation, while difference is a method of ex- periment. The conclusion of the method of difference gives greater certainty than that of the method of agreement. (4) The joint method may be stated in this way: Among n any instances if one circumstance is invariably present when the phenomenon occurs and invariably absent when the phenom- enon does not occur, this circumstance is probably the cause or the effect of the phenomenon. The instances of the joint method are more numerous and more varied than those of either agreement or difference. The joint method has the distinguishing characteristics of both agreement and difference. Because it furnishes greater opportunities for multiplying and varying the instances involved, the joint method presents fewer objections than either of the two separate methods. The positive branch of the joint method suggests the hypothe- sis, while the negative branch proves it. This makes the method somewhat ideal. (5) The principle of concomitant variations may be stated as follows : If when one phenomenon varies alone, and another also varies alone, the one is either the cause or the effect of the other. This is the method of fluctuation, and is used when it is 414 Methods of Observation and Experiment impossible to make the phenomenon disappear altogether, as in the case of difference. The chief function of concomitant variations is to establish exact quantitative relations between cause and effect. (6) The principle of residues is this: Subtract from any phenomenon those parts of it which are known to be the effect of certain antecedents, and what is left of the phenomenon is the effect of the remaining antecedent. The most valuable feature of residues is its suggestiveness ; an attempt to explain the "residual phenomenon" has led to many important scientific discoveries. (7) The five methods are concerned with the establishment of causal connections between phenomena. Agreement suggests the connection while difference proves it. The other methods are modified applications of difference, necessitated by some peculiar form which the phenomenon may take. A statement of the one principle involved is: "If the conjunction between two phenomena is invariable then there is a causal connection." All of the methods are forms of inductive thinking. 10. REVIEW QUESTIONS. (1) Explain "the fundamental fact of causation." (2) Show that the fact of causation is most conspicuous in induction by analysis. (3) Name the five special inductive methods of observation and experiment. (4) State, symbolize, and illustrate the method of agreement. (5) Give examples of antecedents which do not function as causes. (6) Show that the "special methods" are a matter of both observation and experiment. (7) Give the distinguishing features of the method of agreement; illustrate by reference to the symbols. (8) Exemplify the plurality of causes ; immaterial antecedents ; complexity of phenomenon. (9) Show that the conclusions of agreement are largely hypothetical. Review Questions 415 (10) State, symbolize, and illustrate the method of difference. (11) Show by illustration that, in the method of difference, only one antecedent should be varied at a time. (12) Show that difference is naturally a method of experi- ment. (13) Explain Bacon's use of the term "crucial instances." (14) Name and explain the characteristic features of the method of difference. (15) Show that agreement and difference are complementary. (16) Explain and illustrate the joint method. (17) What inference may be drawn from the following instances : Antecedents Consequents ALMT pqrg BLME zqrx BCME rzxy AM T H p q g o (18) "Mr. Darwin, in his experiment on cross and self fer- tilization in the vegetable kingdom, placed a net about one hundred flower heads, thus protecting them from the bees. He at the same time placed one hundred other flower heads of the same variety of plant where they would be exposed to the bees. He obtained the following result: The protected flowers failed to yield a single seed. The others yielded about 2,720 seeds. Thus cross-fertilization was proved." (Hibben). What method did Darwin employ? Symbolize the experiment. (19) Summarize the distinguishing marks of the joint method. (20) Show that the joint method is more ideal than either agreement or difference. (21) State and give concrete illustrations of the law ot con- comitant variations. (22) What is the chief function of concomitant variations? Illustrate. (23) Give instances where it would be impossible to use difference, but easy to use concomitant variations. (24) Explain this : "The quantitative variation between ante- cedent and consequent may be either direct or inverse." 416 Methods of Observation and Experiment (25.) State and explain by illustration the method of residues. (26) What are the advantages and disadvantages of the principle of residues? (27) State the principle which virtually sums up the five methods. (28) Write briefly on the practical applications of the five methods to the ordinary walks of life. 11. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) Trace the connection between the method of agreement and induction by simple enumeration. (2) Show that Mill's methods may properly be termed "Inductive Methods of Scientific Investigation." (3) How may it be shown by "agreement" that the high cost of living is due to the tendency to spend more than we earn? (4) Assume that you are a member of the Board of Health, and that you desire to ascertain the cause of the diphtheria epidemic by means of the principle of agreement. (5) What is the error involved in coming to the conclusion that to sit at table where there are thirteen, may mean the death of one of the thirteen before the end of the year. (O Indicate how it could be shown, by the method of difference, that the mosquito is responsible for the propagation of yellow fever. (7) "Another experiment similar to this was tried by Plateau, who put some food of which cockroaches are fond on a table and surrounded it with a low circular wall of cardboard. He then put some cockroaches on the table; they evidently scented the food, and made straight for it. He then removed their antennae." (Hibben). Complete and give with explanations the method used. (&} "In some cases it is impossible to remove an element which is supposed to be the cause of an effect under investigation." Explain and illustrate. (9) "Extreme care must be taken that, in the withdrawing of Questions for Original Thought 417 any element, no other element is inadvertently introduced." Tyndale supposed he had proved spontaneous generation, when, after sealing in a jar of boiled water a wisp of baked hay, he found, after many days, indications of life within the bottle. In transferring the hay to the bottle, he carried the former across the room. What element was inadvertently introduced? (10) "The attempt to determine the numerical relations ac- cording to which two phenomena vary, requires the utmost caution as soon as our inference outsteps the limits of our observations." (Fowler). Explain this in connection with the law of concomitant variations. (11) "When the effects of all known causes are estimated with exactness and subducted, the residual facts are constantly ap- pearing in the form of phenomena altogether new, and leading to the most important conclusions." Make clear by illustration this quotation which has reference to the principle of residues. (12) Explain "invariable conjunction of phenomena." (13) Investigate by means of one of the five methods the following problems: (1) "All vegetables which grow to root should be planted during the last two days of the waxing moon." (2) "In this section the south wind is the storm wind." (3) "Mischief is the outcome of misdirected energy." (4) "Bad boys usually receive unjust treatment." (5) "An ounce of prevention is worth a pound of cure." CHAPTER 19. THE AUXILIARY ELEMENTS OF INDUCTION. OBSERVATION EXPERIMENT HYPOTHESIS. 1. THE FOUNDATION OF INDUCTIVE GENERALIZA- TIONS. Induction is the process of universalizing particular facts. The starting point is the fact. Through observa- tion the investigator gathers facts, and then works them over with a view of finding uniformities. The mind cannot build inductive generalizations without facts any- more than a mason can build a brick wall without the bricks. A fact is any particular thing made or done or is that which may be acquired by means of the presentative (perception and imagination) powers of the mind. The state of awareness which results from the observation of facts is an individual notion. This presents another aspect of the inductive process ; namely, "It is a matter of building general notions from individual notions, acquired by the observation of facts." To illustrate: I note that A, B, C and D are honest in their dealings with me, hence I come to the conclusion that some men are honest. A fact is something done, consequently the actual doing of the honest things by A, B, C and D are facts. Each state of awareness of each fact is an individual notion. The mind now discerns a uniformity in these facts and de- rives the general notion that "some men are honest." 418 Observation 419 2. OBSERVATION. Facts are acquired by means of observation. When the mind fixes the attention upon any phenomenon it observes it. The term observation means "to watch for" and may be defined as the act of watching for phenomena as they may occur. The observation may be only casual, or it may be willed or rational. It is the latter aspect which most concerns the logician. In this sense observa- tion means careful, painstaking, systematic perception. It involves the concentration of consciousness upon the case in hand, or the actual giving of attention. The thing observed may be external, when the observation takes the form of sense-perception; or it may be internal, when the observation becomes a matter of introspection. 3. EXPERIMENT. In observation we simply watch the phenomenon; in experiment we make it. In experiment we not only ob- serve, but we manipulate the circumstances so as to pre- sent the phenomenon under the most favorable condi- tions for observation. "In observation," says Mill, "we find an instance in nature suited to our purposes" ; whilst in experiment, by an artificial arrangement of circum- stances, we make an instance suited to our purpose. In observation we watch for causes ; in experiment we work for effects. We may thus define experiment as the act of making phenomena occur for the purpose of watching for effects. In experiment there is much which is merely observation. In fact experiment is observation in which the phenomenon is artificially produced. For the sake 420 The Auxiliary Elements of Induction of definiteness, however, any observation which involves a manipulation of circumstances, may be designated as experimental. 4. RULES FOR LOGICAL OBSERVATION AND EXPERI- MENT. To the uninitiated, the matter of observation seems an easy task, and yet when one hears two honest men swear to diametrically opposite facts which have come to them from observing the same phenomenon, his faith is shaken. "Eyes have they but see not" is a logical truth as well as a moral one. Only the observation of the trained can be depended upon; and yet this should not discourage the layman, for even he, by a little conscien- tious effort towards careful observation, may greatly increase his store of accurate knowledge and add to the joy of living. The attending rules are usually heeded by the trained scientist in matters of observation and experiment: First Rule. The observations should be precise. The time, the place, the surrounding conditions must be ac- curately noted. Many artificial contrivances have been devised because of the desire of the scientist to be pre- cise. Instruments like the balance, the thermometer, the microscope, etc., has he invented, and various devices and methods has he adopted for the sake of precision. A common method is to take an average of observations. For example, to estimate justly the class work of a student, the teacher should not be content with the ratings of one or two recitations, but must average the ratings of Rules for Logical Observation and Experiment 421 many recitations. Again, a child may be led to discover approximately the value of the sum of the interior angles of a triangle by measuring the angles of many triangles and then striking an average; assume that the following results are obtained by such a procedure: (1) 178, (2) 181, (3) 179, (4) 180, (5) 182; adding these and divid- ing by 5 gives 180. Second Rule. The observations should concern only the material circumstances of the case in hand. All the non essentials may be ignored, as they serve only to dis- tract attention. For example, (1) in order to get the "right count" all other sounds must be ignored save that of the fire gong; (2) in finding the depth of the water for the building of a dam, soundings ten miles away from the objective point could be of little value. On the other hand, it is easy to overlook certain lurking essentials. To observe such, it is necessary to resort to what the psy- chologist terms a "preadjustment of attention." We must know with exactness what we are looking for. We must have a mental image of what we wish to see. The astronomer in the discovery of a new planet must know the exact spot where it ought to be, and have a clear mental image of its appearance. This expectant attention is a necessity in the case of the physician who is anxious to make no mistakes in his diagnosis. If he is looking for pneumonia, he must have a very distinct auditory image of the sound of an affected lung. It should be re- marked, however, that this very preadjustment of atten- tion, with the untrained, frequently leads to illusion. We are so anxious to see what we are looking for that nine- 422 The Auxiliary Elements of Induction tenths of what we believe we see is only inference. How easy it is to read into a phenomenon something that is entirely foreign to it; to read between the lines; to see only the reflection of our own ideas. "Verily the mental picture of what we wish to see becomes so vivid that we are positive of the thing being external." Thus the drunkard sees snakes and the superstitious see ghosts. Reading into the external what is only vivdly internal is probably the most common error with the untrained observer. Third Rule. The observed circumstances should be varied as much as possible. To observe a fact from a dif- ferent viewpoint may not only broaden the original no- tion, but it may change it entirely. In order to gain a true notion of the effect of a particular nostrum on the human organism, it becomes necessary to experiment with persons of different ages, living under different environments, and inheriting different constitutions. Those who are noted for pronouncing broad, safe and sane judgments upon momentous questions are those who are "all-angled observers." Fourth Ride. The observed phenomenon should, if possible, be isolated from all interfering phenomena. In studying the action of a drug or a food, all other drugs or foods must be eliminated. The effect of gravita- tion on a body cannot be recorded accurately unless the experiments are made in a vacuum. When studying the deflections of the compass, all magnetic substances must be removed from the field. Common Errors of Observation and Experiment 423 5. COMMON ERRORS OF OBSERVATION AND EXPERI- MENT. The rules for scientific observation have suggested cer- tain common errors which may now be considered. (1) Preconceived ideas. There is not an unholy belief nor an unwholesome theory which cannot be bolstered up by means of ap- parent facts. For example, that monstrosity of Puritan thought known as "Salem Witchcraft" was substantiated by facts honestly observed. Again, having made up his mind that it is going to be "so and so," the statistician goes out into the highways and byways and gathers the facts which vindicate his judgment. Further, the demo- crat finds that the majority of the voters are democrats; while the republican is confident that two-thirds of the voters are for republicanism. Here again is the fallacy springing from a preadjustment of attention. We see what we want to see. Only the highly trained observer is able, with impunity, to make use of preadjusted atten- tion, and even with him, it is not easy to remove from the situation belief and prejudice. The true observer undertakes his work with his mind open to anything which the eye may bring him, though it may topple into the dust his dearest theory and most cherished belief; he proceeds — the mind a "clean white page. }} (2) The "observed" and the "inferred" confused. This error has already received some attention. It may be remarked further, however, that, psychologically con- sidered, observation is a matter of interpreting the new 424 The Auxiliary Elements of Induction by means of the old. Of necessity the interpretation, whatever it may be, will assume the complexion of the particular "old knowledge" which the mind is able to use. In short, a man will see what his previous environ- ment has trained him to see; the conscientious gardener sees the weeds, whilst the artist may see nothing but the flowers. It follows, therefore, that all observation must be largely a matter of inference based on experience. In looking at the moon, for example, all I actually see is a patch of color; the form and distant location of the moon being a matter of experience. The inference referred to in this heading is not that which is necessary for perception, but that which is sug- gested by perception. To illustrate : It is icy ; three men are running for a car; Smith raises his arm; Jones slips to the ground; and Brown testifies, that "Smith knocked Jones down." Brown observed, that Smith assumed the proper attitude and that Jones conveniently went down at the right time ; and then inferred the rest. (3) Ignoring the exceptions. This comes through an over anxiety to prove our theory. With this mental attitude, the observations which are corroborative will so completely fill the mental field, that the exceptions are made to seem of no consequence. This accounts for the superstition attached to thirteen: As a coincidence some one at some time died who had previously eaten at a table where there were thirteen. Perhaps during the life of the superstitious one this hap- pened on two or three occasions, but the fact so im- presses the subject that he ignores the dozen times when Common Errors of Observation and Experiment 425 death did not follow. Other generalizations belonging to this class are (1) people never die at flood tide; (2) there must be three accidents in succession; (3) the first sight of the new moon over the right shoulder is a good omen ; (4) seeds which grow to root do best when planted during the last days of the waxing moon; (5) horse chestnut in pocket guards against sore throat, etc. (4) Sympathy and undue interest. The influence of the heart over the brain is well known. A physician is liable to this error when he attempts to prescribe for one of his own family. Sympathy not only warps the judgment but it may actually interfere with the accuracy of an honest observer's perceptive powers. (5) Inattention and a fallible memory. These short comings are too apparent to demand dis- cussion. 6. THE HYPOTHESIS. Having observed the facts, the mind naturally seeks for explanation of the same. Hence taking the facts as a cue and bringing into play a constructive imagination, a plausible supposition is advanced, which is then proved or disproved. Such a supposition is known as an hypothesis. Definition. An hypothesis is a supposition advanced for purposes of explanation and proof. First illustration. The facts are known that light travels from the sun to the earth, and at the rate of 186 thousand miles per second. These facts suggest the prob- 426 The Auxiliary Elements of Induction lems: (1) How does the light reach the earth? (2) Why this rate of speed ; why so much faster than the rate at which sound travels? To solve these problems, or to explain the facts, the "ether" hypothesis is advanced: viz., "A rare medium called ether pervades space and transmits the light and heat of the sun." This hypothesis has never been conclusively proved. Second illustration. Fact : The child leans forward and squints his eyes, when attempting to read work which has been placed on the black board ; hypothesis : The child is near sighted. 7. INDUCTION AND HYPOTHESIS DISTINGUISHED. Induction is a matter of realizing generalizations from the observation of facts. The product of such is an in- duction, but we know that an hypothesis is likewise a generalization based upon facts. What is the difference ? An induction, as such, is a broader term than hypothesis. As soon as the hypothesis is proved or disproved, it ceases to be an hypothesis, but still remains an induction. An hypothesis, being advanced for purposes of explana- tion ceases to be an hypothesis when, in the last analysis, it fails to explain. Moreover, as soon as the hypothesis is shown to be an undoubted truth, it also loses its dis- tinctive hypothetic marks. An hypothesis is merely a tentative induction. Illustrations : (1) The hypothesis is advanced that the fire started from the coal range in the kitchen. After the incendiary is caught, this supposition ceases to be an hypothesis. Induction and Hypothesis Distinguished 427 (2) It is suspected, that my insomnia is due to the three cups of strong coffee indulged in at the evening meal. As soon as this supposition is proved by experi- mental means (law of difference), it ceases to be an hypothesis and becomes an unpopular inductive truth. 8. HYPOTHESIS AND THEORY. In common parlance hypothesis and theory are used interchangeably. We refer to the "nebular hypothesis" or the "nebular theory" ; to the "hypothesis of the sun's heat" or "the theory of the sun's heat." On the other hand, we say "the theory of gravitation," "the theory of evolution," etc., with certain uniformity. From these observations we may infer that hypothesis and theory may be used interchangeably when the facts are of a low probability; but when the facts have undergone cogent verification, it is more correct to use theory in their designation rather than hypothesis. "A theory is a partially verified hypothesis." It has been remarked that theory has a second signification of being a term which stands for "any body of acquired truth." It is unfor- tunate that its use could not be confined to this latter conception. 9. THE REQUIREMENTS OF A PERMISSIBLE HYPOTHE- SIS. Any hypothesis should be made to conform to the fol- lowing requisites: (1) The hypothesis must be con- ceivable. The hypothetic generalizations of primeval days were mere fancy. For example, the loud noise from the 428 The Auxiliary Elements of Induction clouds on dark days was the angry voice of the God of the skies. Even in this day when a complex situation cannot be explained there comes the temptation to draw entirely upon the imagination, and advance an hypothesis which is absurd in every sense of the word. The per- missible hypothesis demands that there be some ground for the conjecture. A fact or two at least must be used as the foundation for whatever the constructive imagina- tion may build. On the other hand the past has taught us that we cannot afford to be too exacting in the enforce- ment of this rule. The ideas of Copernicus, Newton, Harvey, Darwin, and many another of the world's best thinkers, were looked upon at first as being ridiculous. There is always a bare possibility of a "lurking truth" in the conjecture, and no broad minded and sanely edu- cated man can afford to scoff blindly at something which may seem to him mere fancy. Prejudice and a willful blindness to truth, have ever been imminent stumbling blocks in the path of progress. (2) The hypothesis must be capable of proof or dis- proof. This means, that where it is possible the hypoth- esis should touch, in one form or another, our experi- ence. If the hypothesis is wholly unlike any experience we may have had, it becomes impossible to ascertain, whether it agrees or disagrees with the facts, which it is supposed to explain. A legitimate hypothesis must furnish some opportunity for securing facts to prove or disprove it. For example, to advance an hypothesis rela- tive to the conditions of the next world is hardly per- missible, as "spirit-facts" are entirely without our field The Requirements of a Permissible Hypothesis 429 of experience. Surely, one returning from Heaven could give us no conception of it; because there is nothing in the carnal mind that may be used to interpret the experi- ences that must function in the Celestial City. (3) The hypothesis must be adequate. It should take into consideration all the known facts. It stands to reason that, if one known fact is ignored, the entire pro- cedure is thus vitiated. It would be absurd to suppose the moon to be inhabited without giving heed to the fact of its having no atmosphere. (4) The hypothesis must be as simple as possible. We must, of course, recognize situations which in them- selves are too complex to admit of simple conjectures. The purport of the fourth rule is, that the hypothesis should not be made unnecessarily complex. (5) The hypothesis should not contradict any verified truth. Any conjecture which opposed the law of gravita- tion would be out of place. Of course it is possible to have only apparent conflicts between the new hypothesis and the old law. Further observation should show that no such clash exists. 10. THE USES OF HYPOTHESES. The hypothesis is serviceable mainly in these par- ticulars : (1) As a working basis. When one is confronted with a huge mass of facts it becomes necessary to start somewhere, and with as little waste of time and energy as possible. Almost anything is better than a haphazard floundering which reaches 430 The Auxiliary Elements of Induction "nowhere." So the investigator hazards a tentative theory, which he at once proceeds to verify. If verification fails, then he may discard this first hypothesis for a better one. (2) As a guide to ultimate truth. Much might be said relative to the use of rejected hypotheses. By means of these, science has advanced step by step towards the full light of perfect knowledge. As has been remarked, no true scientist cares to overlook the opportunity for suggestive inspiration which some forsaken hypothesis may afford him. Just as the indi- vidual attains the best success by using his failures as stepping stones, so the true scientific discoverer climbs up to the light on the stairway of discarded hypotheses. By testing and rejecting the false hypotheses, the situation becomes more definite and the problem more accurately defined. "Kepler himself tried no less than nineteen different hypotheses before he hit upon the right one, and his ultimate success was doubtless in no slight degree due to his unsuccessful efforts." (3) As a discoverer of immediate truth. Often, moreover, the hypothesis leads directly to posi- tive verification. The supposition advanced may hit the truth squarely ; and may be of such peculiar nature as to lead easily to clear and conclusive proof. (4) As affording a probable explanation of a problem which will not lend itself to an entirely satisfactory solution. The theory of evolution may illustrate this fourth use ; while the history of the discovery of Neptune illustrates the third. Characteristics Needed by Investigators 431 11. CHARACTERISTICS NEEDED BY SCIENTIFIC INVES- TIGATORS. The hypothesis is referred to "as the great instrument of science." The greatest thinkers of time have possessed the courage and the conscience to step from the known to the unknown; to hazard a guess as to the meaning of what they saw, and then subject their guess to a rigor- ous test. This procedure involves three elements on the part of the investigator : ( 1 ) Power of accurate observa- tion. (2) Constructive imagination. (3) A passion for truth. ( 1 ) An hypothesis formed without an accurate knowl- edge of facts is not only useless, but often it may work positive harm. To advance serviceable suppositions which are not grounded on fact, is as impossible, as it is to build a house without a foundation. The hypothesis is an image of the constructive imagination, but the pedestal of this image must rest on the ground of fact. The investigator who would be scientific must exercise scrupulous care in securing his facts through observation and experiment. The rules and errors involved in such a procedure have received sufficient attention. (2) After the investigator has his facts to build upon ; and these may be few or many — sometimes even a single fact is sufficient — then may he theorize as to a possible explanation of them. Here is where the real work of the born genius tells. To some the facts are nothing but words, to others they mean universal laws and great inventions. Who but a Newton could have seen the law of gravitation in the falling apple? Who 432 The Auxiliary Elements of Induction but an Edison could have seen the phonograph in the sound wave and wax? It must be recognized that this remarkable imaginative insight is inborn in some cases ; and yet this does not preclude the necessity for cultivating this power, though it may be only in a rudimentary state. Here is another opportunity for the school teacher; namely, to train in every legitimate way the constructive imagination. (3) Having once constructed the hypothesis, the hon- est scientific investigator at once proceeds to subject it to a series of most rigorous tests. It is well to see big things in a little fact; to have a mind as fertile in new ideas as a watered garden — this is genius! But is it not more incumbent to have a conscience so keen, that nothing will be allowed to pass for truth which has not received ample verification? Intellectual dishonesty is quite as common as moral dishonesty. Moreover, one must main- tain an open mind, absolute candor, and a willingness to abandon the most cherished theory. Often it is much easier to explain away contradictory facts than it is to forsake a pet theory. 12. OUTLINE. The Auxiliary Elements in Induction — Observation — Experiment — Hypothesis. (1) The Foundation of Inductive Generalizations. (2) Observation. Defined. (3) Experiment. Defined. Compared with Observation. (4) Rules for Logical Observation and Experiment. Their need. Outline 433 First Rule. Second Rule. Third Rule. Fourth Rule. (5) Common Errors of Observation and Experiment. (1) Preconceived Ideas. (2) Confusing the Observed with the Inferred. (3) Ignoring the Exceptions. (4) Sympathy and Undue Interest. (5) Inattention and a Fallible Memory. (6) The Hypothesis. Denned and Illustrated. (7) Induction and Hypothesis Distinguished. (8) Hypothesis and Theory Distinguished. (9) The Requirements of a Permissible Hypothesis. (1) Conceivable, (2) Capable of proof or disproof, (3) Adequate, (4) Simple, (5) Not contra- dictory. (10) Uses of Hypothesis. (1) A working basis, (2) Guide to ultimate truth, (3) Discoverer of immediate truth, (4) Probable explanation. (11) Characteristics Required by Scientific Investigators. (1) Accurate observer, (2) Constructive imagination, (3) Passion for truth. 13. SUMMARY. (1) Facts are the foundation of all inductive generalizations. Induction is largely a matter of building general notions from individual notions derived from the observa ion of facts. (2) Observation is the act of watching the phenomena as they may occur. It involves the voluntary concentration of c mscious- ness on the case in hand. (3) Experiment is the act of making phenomena occur for the purpose of watching for effects. It is in reality a form of observation which necessitates a manipulation of circumstances. 434 The Auxiliary Elements of Induction (4) The average man is not given to careful observation. The rules adopted by scientific observers are: (1) The observa- tion should be precise; (2) should concern only the material circumstances; (3) should be varied; (4) should be isolated. For the sake of precision many instruments have been invented and methods devised; notably instruments for accurate measure- ments, such as the balance and thermometer, and methods like the method of averages. Frequently a situation may be so complicated as to demand a "preadjustment of attention." With the untrained this very pre- adjustment may lead to serious error. An "all-angled observer" is the most trustworthy. (5) Errors in observation come from preconceived ideas; confusing perception with inference; ignoring the exceptions; sympathy; inattention; and a fallible memory. (6) An hypothesis is a supposition advanced for purposes of explanation and proof. (7) An hypothesis is a tentative induction. As soon as it is deprived of its tentative nature it ceases to be an hypothesis. (8) Hypothesis and theory are often used interchangeably when reference is made to phenomena of low probability. Theory should be used only in instances of high probability. (9) A permissible hypothesis must be (1) conceivable; (2) capable of proof or disproof; (3) adequate; (4) simple; (5) must not contradict any verified truth. (10) The hypothesis is especially serviceable in these ioui particulars: (1) as a working basis; (2) as a guide to ultimate truth; (3) as a discoverer of immediate truth; (4) as affording probable explanations. (11) There are certain characteristics which an honest and courageous investigator needs to possess. These are: (1) un- doubted ability as an accurate observer of facts, (2) a con- structive imagination, (3) a passion for truth. To build an acceptable hypothesis without fact is as impossible as it is to build a house without a foundation. The genius, because of his imaginative insight, transforms the simple fact into a complex invention or law. A prevailing "intellectual dishonesty" suggests the need of "a greater passion for truth." Review Questions 435 14. REVIEW QUESTIONS. (1) Show that facts are the raw material of induction. (2) Define and illustrate a fact. (3) Define induction in terms of the notion. (4) Define and illustrate observation. (5) Define and illustrate experiment. (6) Show the difference between observation and experiment. (7) State and exemplify the rules for logical observation and experiment. (8) Illustrate the method of averaging observations. (9) Explain "preadjustment of attention." (10) What is the most common error with the untrained observer? Explain and illustrate. (11) Explain the expression "all-angled observer." (12) State and exemplify the errors of observation and ex- periment. (13) To what error in observation are superstitions generally due? . (14) Define and illustrate hypothesis. (15) Indicate the difference between an hypothesis and an ordinary induction. (16) When may theory and hypothesis be used interchangeably? Illustrate. (17) Show by illustration that the term theory is ambiguous. (18) Summarize the requirements of a permissible hypothesis. Illustrate. (19) Select some school room experience with a view of mak- ing it conform to the requirements of a permissible hypothesis. (20) Explain and illustrate the uses of hypothesis. (21) "The scientific discoverer climbs up to the light on the stairway of discarded hypotheses." Explain. (22) Write a short theme on "Characteristics Required by Scientific Investigators." 15. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) "Land and sea breezes are due to a difference in tem- perature." Is this a fact or a law? Explain your position. 436 The Auxiliary Elements of Induction (2) Give three different definitions of induction. Which one have you adopted? Defend your position. (3) Define and illustrate observation. (4) Distinguish between observation and attention. (5) "In observation we find, in experiment we make" What is meant by this? (6) Give illustrations of falsehood due to careless observa- tion. (7) Argue for and against the use of "expectant attention" in observation. (8) "Nine-tenths of what we see comes from within." Do you believe this? Labor the question. (9) Offer suggestions which, if followed, should lead to scientific observation. (10) "One must be just before he is sympathetic." Relate this to the fine art of accurate observation. (11) Is an hypothesis a generalization? Explain. (12) Give school room examples of hypotheses which lead to injustice. (13) "An hypothesis is merely a tentative induction." Make clear this assertion. (14) Illustrate inconceivable hypotheses by drawing on your knowledge of ancient history. (15) "Prejudice and willful blindness to truth have ever been imminent stumbling blocks in the path of progress." Expatiate upon this. (16) Are the hypotheses advanced concerning communications from the spiritual world capable of proof or disproof? Give reasons. (17) Show by historical examples the use of discarded hypotheses. (18) "Genius is another name for hard work." Do you agree? Defend your position. (19) "The man to whom nothing ever occurs is unlikely to make any important discoveries." Discuss this. CHAPTER 20. LOGIC IN THE CLASS ROOM. 1. THOUGHT IS KING. "Our habits make or unmake us." "In a thoughtless hour a groove is imbedded in the nerve substance, and thereafter, nine-tenths of the life flows through that groove." Habit is, indeed, a most powerful and a most tyrannical master; and yet it has come within the ob- servation and even the experience of many, that thought is even more masterful than habit. Appearing at the psy- chological moment and in a pedagogical way, a thought may be made to possess the mind with force sufficient to break almost any habit. From an ethical point of view, the exceptions to this are due to an inability to arouse thought of sufficient strength. Moreover, mental re- actions which result in habit are originally brought about through some thought process. Speaking in general terms, it may be affirmed that thought makes habit and if sufficiently strong breaks habit. That our habits make or unmake us may be true, but is it not likewise true that our thoughts make or unmake our habits? Thought is king; thought has made man king of the animal kingdom, and if thought has figured so largely in the evolution of the human animal in past ages, may we not assume that it will sway the future ages in like manner? Thought is a product of the class room. Here thoughts which make habits, and thoughts which break 437 438 Logic in the Class Room habits have full sway. As the children of the American schools think to-day, so will the men of American life think on the morrow; and as America thinks so will she ultimately do. This lends vital import to any object which may either inspire or regulate thought. 2. SPECIAL FUNCTION OF INDUCTION AND DEDUCTION. As commonly treated logic is a regulative subject. This implies the two aspects of direction and correction. Logic directs by means of the laws and forms of thought, and corrects by means of the rules of right thinking. To a certain degree both departments of logic are directive as well as corrective ; but it is worthy of remark that in- ductive logic emphasizes the former, while deductive logic lays stress upon the latter. It is inductive logic which shows how man has acquired new knowledge; inductive logic explains the mode of procedure adopted by the dis- coverer and the inventor. On the other hand, deductive logic is distinctly a science of criticism. Induction directs to new truth; deduction aims to modify and correct new truth. 3. TWO TYPES OF MIND. Though there are many special forms of thought, yet there are but two general forms; namely, induction and deduction. Inductive thought seeks the new; deductive thought corrects the old. Similarly, there are two types of mind : the inductive type and the deductive type. The former reaches out for new things, the latter is satisfied with ordering the old. In politics the man with the in- ductive type of mind becomes a "Liberal" or a "Progress- Two Types of Mind 439 ive"; while the man with the deductive type of mind becomes a "Conservative" or a "Standpatter." It must be conceded that both are needed in the development of the best form of Democracy. We need an unfettered free- dom as advocated by Jefferson; but we also need an ordered freedom as taught by Hamilton. 4. TOO MUCH CONSERVATISM IN SCHOOL ROOM. Since the beginning these two mental types have been in evidence — the liberal who wants to do things, and the conservative who wants to weigh things. With the liberal, it is fight whether or no ; with the conservative, it is fight provided the enemy is not too formidable. The one dares; the other cautions: both are needed to balance the world. Liberalism and conservatism may be fostered in the school room, and to maintain a true balance each must receive its share of attention. Is such the case? The passing of "district-school-individualism and the coming of "graded-school-collectism" has transferred the em- phasis from liberalism to conservatism — from the in- ductive type to the deductive type. In this day it seems to be more important to have the child's work orderly. than to have it original. In the main, examination papers call for correct knowledge and not for thought; in the main, promotions are based on accuracy, not on initiative. The conservative type being in control, the schools are sending out too many "Decluctives," not enough "Inductives." The world needs more Columbuses and Edisons. 440 Logic in the Class Room 5. THE METHOD OF THE DISCOVERER. A change must come. The methods of instruction are too didactic and not sufficiently inspirational. Greater attention must be given to the spirit of discovery and less to the spirit of correction. The teacher must lead less and follow more; must correct less and suggest more; must tell less and direct more. If we are to give greater attention to the training of discoverers, logic may aid in this crusade by calling attention to the common mode of procedure which the discoverers of the past have adopted. This is a legitimate topic for the logician, since induction, deduction, hypothesis, and proof have ever been common tools in the discoverer's workshop. With a view to becoming better acquainted with the common mode of procedure of the man who seeks for new truth, let us study two typical instances : (1) The Discovery of Neptune. The discovery of Neptune was a double one. Early in the present century it was found that Uranus was straying widely from his theoretic positions, and the cause of this deviation was for a long time unsuspected. Two astronomers, Adams in Eng- land and Leverrier in France, the former in 1843 and the latter in 1845, undertook to find out the cause of this perturbation, on the supposition of an undiscovered planet beyond Uranus. Adams reached his result first, and the English astronomers began to search for the suspected planet with their telescopes, by first making a careful map of all the stars in that part of the sky. But Leverrier, on reaching the conclusion of his search, sent his result to the Berlin observatory, where it chanced that an accurate map had just been formed of all the stars in the suspected region. On comparing this with the sky, the new planet, afterward called Neptune, was at once discovered, 23d September, 1846. Too Much Conservatism in School Room 441 (2) Bees are guided in their flight by a knowledge of their surroundings, not by a general sense of direction. "M. Romanes took a score of bees in a box out to sea, where there could be no landmarks to guide the insects home. None of them returned home. Then he liberated a second lot of bees on the seashore and none of these returning, he liberated another lot on the lawn between the shore and the house. None of these returned, although the distance from the lawn to the hive was not more than two hundred yards. Lastly he liberated bees in different parts of the flower garden on either side of the house, and these at once returned to the hive." (Hibben.) A multiplication of instances would only give stronger evidence to the fact that the mode of procedure adopted by the discoverer and inventor conforms to these three general steps: (1) antecedent facts, (2) forming an hypothesis, (3) verification. It will be to our advantage to study somewhat in detail these three steps. (1) Antecedent facts. In the discovery, of Neptune the decisive or crucial fact was the knowledge that Uranus deviated from his true path about the sun. This knowledge was obtained through observation and mathematical calculation. But the hypothesis of the existence of another planet could not have been formed had it not been for the more funda- mental facts of inertia, gravitation, falling bodies, etc. For the sake of definiteness antecedent facts may thus be divided into foundation facts and crucial or decisive facts. The latter are an outgrowth of the former. The foundation fact of the second illustration is Romanes' knowledge of animal instinct; while the crucial fact is, no doubt, the observation that bees fly in a circle before starting for home. In the case of Newton's discovery of 442 Logic in the Class Room the law of gravitation, the falling of the apple was the crucial fact; while his knowledge of terrestrial gravity proved to be the vital foundation fact. A crucial fact is one which leads immediately to the formation of a reasonable hypothesis. It is not to be inferred from this that the same fact becomes a crucial one to all alike. The falling of the apple was only crucial to a genius like Newton. With the average only extraor- dinary facts become crucial; but with the genius any ordinary fact may become crucial. Both the scholar and the genius may have the foundation facts, but only the latter may be able to read into a dry fact or event, a new world of truth. (2) Forming an Hypothesis. From the viewpoint of logical correctness, the matter of hypothesis has received due attention in an antecedent chapter; we need now to look at the subject through the eyes of the discoverer, not the logician. The crucial fact at first creates an intellectual perplexity which is accom- panied with an uneasy, dissatisfied state of mind. This unsatisfied feeling drives the intellect to protracted thought. As a final result some hypothesis is constructed which seems to explain the crucial fact. Here is where analogy functions in a most vital manner. No hypothesis is forthcoming unless it resembles the crucial fact. It has been remarked elsewhere that analogy is the basic element in the forming of hypotheses. So it transpires, that the protracted thought referred to, is virtually a mental ef- fort to detect significant resemblances between the well known crucial fact, and some hypothetical fact which the Too Much Conservatism in School Room 443 imagination may picture. To put it differently: The crucial fact arouses a mental state of unrest which in turn drives the mind to a "still hunt" for relations. The establishment of the hypothesis is simply a makeshift, designed to satisfy this "mental urge." In the discovery of Neptune the crucial fact, the deviation of Uranus, produced a state of uneasiness in the minds of the as- tronomers. Surely something was wrong. This urged them to further meditation, which finally resulted in the hypothesis that there must be an unknown planet beyond the orbit of Uranus. They assumed, of course, that the relation between this supposed planet and Uranus was analogous to the relation between any two of the known planets. In the case of Newton the falling apple stirred his astute mind to the assumption that the same force which pulled the apple, likewise pulled the moon towards the earth. Here we have again (1) the crucial fact, (2) the mental urge, (3) the analogous hypothesis. (3) Verification. Forming an hypothesis only partly fulfills the demands of an unsatisfied intellect. The true discoverer, being possessed with a passion for truth, seeks for "the truth, the whole truth, and nothing but the truth." In conse- quence the hypothesis is subjected to tests which may lead to its confirmation, its rejection, or its modification. The two possible modes of verification are recourse to experience and appeal to reason ; or empirical proofs and rational proofs. In the former the hypothesis is compared with facts by means of further observation and experi- ment. M. Romanes' experience with the bees is a fair 444 Logic in the Class Room illustration of this form. Possibly the student has already noted that Romanes' mode of procedure conforms to the "joint method of agreement and difference." In the case of rational proofs the hypothesis is subjected to deduct- ive demonstration, either of the form of syllogistic argu- ment or mathematical calculation. A fair sample of this kind of verification is Newton's discovery of universal gravitation. When he decided that the moon and the apple might be controlled by the same universal force, he undertook to establish his hypothesis by mathematical calculation. At first his figures seemed to disprove his theory, but after a wait of ten years, new data relative to the diameter of the earth, removed the apparent dis- crepancy. In the case of the discovery of Neptune, the verification was both rational and empirical. Mathe- matical (rational) calculation led to the assumption that the new planet must be at such a point. With this knowl- edge the observer was enabled to turn his telescope to the spot indicated and there, true to the calculations, was Neptune (empirical). To summarize: The method of the discoverer involves a knowledge of certain fundamental facts; the observa- tion of crucial facts; a mental unrest; the constructing of an hypothesis through analogy; and finally verifi- cation by either appeal to experience, or mathematical demonstration. 6. THE REAL INDUCTIVE METHOD OR DISCOVERER'S METHOD NOT IN VOGUE IN CLASS ROOM WORK. It has been remarked elsewhere that there are two gen- eral mind types, the liberal and the conservative. Also Real Inductive Method Not in Vogue 445 that the natural method of thought animating the former k inductive; while the natural method of thought of the latter is deductive. The "liberal" is the apostle of new truth; the "conservative" an apostle of safe truth. Both types are needed ; the one to balance the other. In conse- quence both methods are of service in the class room; here each should be given its proportionate place. That this condition does not obtain may not be apparent, since much attention is being given to certain inductive forms, such as "proceeding from the concrete to the abstract," "from the particular to the general," "from the known to the related unknown," etc. Likewise the courses of study and the various text books, claim to advocate the use of the inductive process. Seemingly these facts point toward a very general observance of the inductive tenets. This is true with one vital exception : Induction is the natural method of the discoverer. With it he acquires knowl- edge; but in the class room induction is used to impart knowledge. In life the discoverer takes the initiative, thinks his own thoughts first hand; but in the school room, above the kindergarten, the child is not allowed to take the initiative, not even in his play. All is planned for him, all doled out, not in the raw, but partially made over. The teacher must impart a certain amount of knowledge in a given time, and consequently she must "set the pace" in this race for second hand facts. To allow the child to lead; to give him the benefit of his own individuality; to permit him to use the God given spirit of discovery which clamors for recognition; would be suicidal according to our present standards. If the 446 Logic in the Class Room plan of the discoverer were followed, the course of study could not be covered; children would fail of promotion; and criticism would be forthcoming from both principal and parent. In the average class room of the day the inductive FORM prevails but the SPIRIT is not in evidence. Like a wolf in sheep's clothing induction has entered the class room to devour that primal force in the child's make-up, which has raised his race above his simian ancestors. Our class room methods, being inductive in form but deductive in spirit, may train the youngster to be a camp follozver but never a leader in thought and action. The call of the day is for more initiative ; for more originality ; for more individuality; for more enthusiasm. There is too much form without the spirit; so much that bespeaks system and refinement without those native impulses and native abilities which mark one child from another. Like the books of a library our children are classified and labeled, and when more come in the others are dusted and placed on the next higher shelf. How many more cen- turies must we wait before the schools will adopt, in spirit as well as in form, the pedagogical principles of life? Will the time ever come when it may be said that all our leaders in thought and action are college graduates ? 7. AS A METHOD OF INSTRUCTION DEDUCTION IS SUPERIOR TO INDUCTION. The inductive method is pre-eminently the method of the discoverer only when it involves both the form, which he follows, and the spirit, which he evinces. The so- Deduction is Superior to Induction 447 called method of the school room is inductive in form, as the procedure is from particular facts to general truths; but deductive in spirit, as it is used to impart knowledge. If it were inductive in spirit, the child would be allowed to acquire knowledge entirely through his own initiative. Deduction is the method of instruction, whereas induction is the method of discovery. That the child of the school is instructed or better "deducted" and not generally allowed to discover, is a situation so ap- parent that we need not labor the point further. Because the inductive process has been made a method of instruction, it has been robbed of its chief advantage over deduction. Indeed, as a method of instruction, deduction is really the superior method. It requires less time, demands greater concentration, often arouses more interest, and creates situations which are less involved. 8. CONQUEST NOT KNOWLEDGE THE DESIDERATUM. In all great inventions, man has taken his cue from nature. In inventing the telescope, his model was the eye; in building his house, his inspiration was the cave. In reality man has accepted nature's suggestions, and then attempted to improve upon them. In this he has met with success. From the crab apple tree, he has de- veloped the northern spy; from the wild hen which laid 2 5 eggs a year, he has evolved the modern hen which produces 225 eggs a year. Moreover, man has attained his greatest successes by enlarging upon the thoughts of nature and not by unmixed substitutions. Burbank, through a long process of years, has changed the color of 448 Logic in the Class Room a flower, but in accomplishing this did he not use some hidden tendency of nature? Burbank, with all his wis- dom, cannot give a flower color unaided by "Dame Nature." When man commenced to study nature's mode of edu- cation, he saw that fearful sacrifices were entailed, both in time and in energy as well as in life itself; and so he evolved a more economical way of leading the child through the experiences of the race. In consequence, he has developed the present splendid system of education. In the evolution of all great institutions, there are in evidence crucial weaknesses, and in the evolution of man's educational system it appears that he has erred in adopt- ing nature's form of education without her spirit of edu- cation. In his anxiety to have the young acquire as much as possible, man has overshot nature's true purpose. For example, the big word in man's educational system is knowledge ; but the big word in nature's educational sys- tem is conquest. Nature gives man knowledge simply to reward him for his effort; but man would give to his fellow the reward without the effort. According to nature, the strongest men are those who overcome most; according to man, the strongest men are those who know most. The common educational principles, such as, "From the concrete to the abstract and from the known to the related unknown," etc., are interpreted by man from the viewpoint of knozvlcdge; whereas nature would teach 'that these are a feasible way to develop power — to grow manhood. It is seen that nature uses knowledge onlv as a means to an end, and therefore when man uses Conquest not Knowledge the Desideratum 449 knowledge as an end only, he is trying to substitute a plan of his own for nature's plan. The best results can be secured only when man co-operates zvith nature in de- veloping, and at the same time regulating, the spirit of conquest. 9. MOTIVATION AS RELATED TO THE SPIRIT OF DIS- COVERY. It has been remarked in this chapter, that the "crucial fact" serves to stir the mind of the natural born dis- coverer to an activity raised to the nth power of effective- ness. Naturally, the intent of such activity is to solve the mysteries which the crucial fact may suggest. This pas- sion of the mind to "know more about it" is appropriately termed "the mental urge." From the viewpoint of the pedagogue, the "mental urge" is simply an intrinsic inter- est in the situation at hand; an interest born of an innate or acquired passion to know the truth. With the average child, the "mental urge" is strong only when the situations appeal to some immediate need or vital experience. The attempt to make the school work concrete and vital; to make it answer the child's natural curiosities and real necessities, is dignified with the name "motivation." It is obvious that this is a new term for an old condition. To motivate the work, means to give to it an attractiveness which any situation might have for the true born discoverer and inventor. // we would use the discoverer's method successfully, we must learn the art of motivating the work. This may be ac- complished by appealing to the play instincts, to the busi- ness instincts, and to the vital interests of every day life. 450 Logic in the Class Room 10. DISCOVERER'S METHOD OR THE REAL INDUCTIVE METHOD ADAPTED TO CLASS ROOM WORK. A revolt has already set in against this insatiate desire to teach knowledge, rather than to teach the child. Many- schools are permitting a study of those topics which vitally concern every day life. Less attention is being given to formal discipline, and more attention to self activity. Gradually will the scheme of education be di- rected toward fitting the school work to the child, rather than fitting the child to the school work. When this new thought in education is fully upon us, then will every device and method be directed toward giving full scope to the spirit of inquiry, which so completely possesses every normal child. It now remains for us to indicate ways in which the spirit of inquiry, or the "discoverer's method," may be adapted to school room work. In the first illustration, we shall outline the topic as it is generally given in the average school where attention is paid to development work. This will then be followed by a second outline which may be suggestive of the discoverer's mode of procedure. First illustration. School Room Method. I. Aim : To teach addition of business fractions. 11. Preparation: (Only type examples given). (1) (2) (3) 3 bushels 3 parts Rule: Only like numbers -j-5 bushels -)-S parts can be added. 8 bushels 8 parts Discoverer's Method 451 III. Presentation : (1) 3 ninths +5 ninths (2) 3/9 +5/9 (3) 2/3= 4/6 l/6=+l/6 (4) 2/3= 8/12 3/4=+9/12 8 ninths 8/9 5/6 17/12 IV. Summary : (1) Only like fractions can be added. (2) Change unlike fractions to like fractions. (3) Add the numerators, placing the sum over the common denominator. V. Application : Examples and problems involving similar and dis- similar fractions. Before undertaking to illustrate the discoverer's method, it may be well to designate in order the evident steps as they would appear to the pedagogue : ( 1 ) Motivate the topic to be presented. (2) Bring to mind appropriate "foundation facts/' (3) Make evident the "crucial fact." (4) Lead to the forming of an hypothesis through analogy. (5) Afford ample opportunity to prove the hypoth- esis. Discoverer's Method Adapted. Lesson Plan. I. Aim : ( 1 ) By playing upon the curiosity or by ex- posing a vital need, create a strong desire to know how to add business fractions. (Motivate the topic.) Curiosity: "We all know what a fraction is and we know, too, how to change fractions to higher or lower 45 2 Logic in the Class Room terms." "Now I wonder how many know how to add fractions, such as 2/5 and 1/5?" "Don't you tell any one, Mary, but just write your answer on a piece of paper and show it to me." (Mary's answer shows that she has thought correctly, but figured incorrectly. John, after having raised his hand, shows his answer to the teacher.) "John has the right answer." "That's fine, but let us keep the secret, John." "I wonder how many others there are in this class who will find the right way?" etc., or Vital need : Discuss with the class the various occupa- tions of life and secure expressions of preference. Some may plan to be real estate agents, others contractors or book keepers, etc. "George, you plan to be a book keeper." "Let us suppose that I have given you the job of book keeper in my factory." "Show that you are worth your wages by adding these numbers: 124 3/4, 647 2/3." "What! can't do it?" "Then I don't want you!" etc. II. Preparation : (2) Bring to the foreground the necessary founda- tional knowledge. Suggestions: 4 bushels 8 parts +3 bushels +2 parts 7 bushels 10 parts III. Presentation : (3) Make evident the crucial fact. Suggestions: Add 2 fifths 3 eighths % + 1 fifth +1 eighth 3 fifths 4 eighths Discoverer's Method 453 (4) Without further suggestion, give the young dis- coverer suitable opportunity for finding the sum of y% and y%. In the act of discovering, an implicit hypothesis takes form in the mind through analogous reasoning. This point marks the climax of the lesson — the supreme moment, when the skill and tact of the teacher is assessed to the limit. Just here the child must have a comfortable environment where perfect concentration is possible. Nothing must be forced; and there should be nothing suggestive of disgrace or shame, if the youthful Colum- bus is unsuccessful. The first attempt should be without books. If more help is needed, access to books may be given. If the investigation is still without definite result, then as a last resort the teacher may, in the presence of the child, add fractions, solving with deliberation example after example, until the child believes he has discovered the process. (5) Stimulate a desire to verify the facts discovered. Suggestions leading to verification: Afford oppor- tunity for mathematical demonstration. Illustrations: The fractions >4 and y% have been added in this way — y 4 = 2/8 5/8 Use is now made of the crucial fact, when the example assumes this form — 2 eighths +3 eighths 5 eighths 454 Logic in the Class Room Or if the class has been trained in the. use of the dia- | gram the following may be the form of proof : *{ H- Explanation from diagram. I see that % equals 2 parts and ^ equals 3 parts; the sum of 3 parts and 2 parts are 5 parts. But the name of the part is eighths; hence the answer 5 parts may be written 5 eighths, or y% Thus the final form is 2 parts +3 P ar ts 5 parts=^ Give opportunity to consult answers in text books as further verification. The summary and application of adding fractions ac- cording to the "discoverer's method," are virtually the same as the corresponding steps in the "school room method." Second Illustration of Discoverer's Method. David P. Page in his Theory and Practice of Teaching well illustrates the discoverer's method in conducting a general exercise in nature study. We cannot do better than to quote from him : ''It is the purpose of the following remarks to give a specimen of the manner of conducting exercises with reference to waking up the mind in the school and also in the district. Let us sup- pose that the teacher has promised that on the next day, at ten j Discoverer's Method 455 minutes past ten o'clock, he shall request the whole school to give their attention five minutes to something that he may have to show them. This very announcement will excite an interest both in school and at home (playing upon the curiosity) ; and when the children come in the morning they will be more wakeful than usual till the fixed time arrives. At the precise time, the teacher gives the signal agreed upon, and all the pupils drop their studies and sit erect. When there is perfect silence and strict attention by all, he takes from his pocket an ear of corn and in silence holds it up before the school. The children smile, for it is a familiar object (foundational knowledge already in hand) ; and they probably did not suspect they were to be fed with corn." Teacher. "Now, children," addressing himself to the youngest, "I am going to ask you only one question about this ear of corn. If you can answer it, I shall be very glad. As soon as I ask the question, those who are under seven years old, and think they can give an answer, may raise their hand. What is this ear of corn for?" Several of the children raise their hands, and the teacher points to one after another in order, and they rise and give their answers. Mary. It is to feed the geese with. John. Yes, and the hens, too, and the pigs. Sarah. My father gives corn to the cows. Laura. It is good to eat. They shell it from the cobs and send it to the mill, and it is ground into meal. They make bread of the meal and we eat it. "I am sorry to tell you that none of you have mentioned the use I was thinking of, though, I confess, I expected it every minute. I shall now put the ear of corn in my desk, and no one of you must speak to me about it till to-morrow. You may now take your studies." The consequence of this would be that various families, father, mother and older brothers and sisters, would resolve themselves into a committee of the whole on the ear of corn : and by the next morning several children would have something further to communicate on the subject. The hour would this day be awaited with great interest and the first signal would produce perfect silence. 456 Logic in the Class Room The teacher now takes the ear of corn from the desk and dis- plays it before the school; and quite a number of hands are instantly raised as if eager to be the first to tell what other use they have discovered for it. The teacher now says pleasantly, "The use I am thinking of you have all observed, I have no doubt; it is a very important use, indeed; but as it is a little out of the common course (crucial facts) I shall not be surprised if you cannot give it. However, you may try." "It is good to boil," says little Susan, almost springing from the floor as she speaks. "And it is for squirrels to eat," says little Samuel. "I saw one carry away a whole mouthful yester- day from the cornfield." Others still mention other uses. Perhaps, however, none will name the one the teacher has in his own mind; he should cordially welcome the answer if perchance it is given. (Suppos- ing that it has not been given.) "I have told you that the answer I was thinking of was a very simple one ; it is something you have all observed and you may be a little disappointed when I tell you. The use I have been thinking of for the ear of corn is this : It is to plant. It is for seed, to propagate that species of plant called corn." (Verification.) Here the children may look disappointed as much as to say, We knew that before. The teacher continues : "And this is a very important use for the corn; for if for one year none should be planted, and all the ears that grew the year before should be consumed, we should have no more corn. The other uses you have named were merely secondary. But I mean to make something more of my ear of corn. My next question is: Do other plants have seed?" Here is a new field of inquiry, etc., etc. From the standpoint of "the greatest amount of knowl- edge in the shortest possible time," this mode of presenta- tion consumes an inexcusable amount of time and is, therefore, "impracticable." But when viewed from the ground of interest, originality, initiative, and conquest — the watchwords of the "new thought in education" ; there is no real waste in either time or energy. The spirit and Discoverer's Method ' 457 method of the discoverer will no doubt be the educational slogan of the future age. Epitome of Discoverer's Method, adapted to the class room: ( 1 ) Motivate the topic to be presented. (2) Bring to mind, if necessary, the "foundational facts." (3) Make evident the "crucial fact." (4) Furnish every opportunity for a first-hand dis- covery of the "lesson-point" (establishing hypothesis through analogy). (5) Let the hypothesis be verified. The entire situation must be one of freedom, zeal, originality, and initiative. 11. THE QUESTION AND ANSWER METHOD NOT NECES- SARILY ONE OF DISCOVERY. No one mode of presentation is more universally used than the "question and answer." The advantages of this mode are many and the teacher who is an adept in the art of questioning, from the standpoint of knowledge, is generally efficient. The common error, however, incident to much questioning, is that of asking "telling questions." By the use of such, the class is forced along the desired channel of thought so rigorously as to have a condition where the spirit of inquiry is entirely wanting. It is pos- sible to conform to the rules of good questioning, and yet rob the class of all originality and initiative. From the teacher's viewpoint, the discoverer's method demands few questions ; it is the method of suggestion rather than 458 Logic in the Class Room one of questions. Avowedly in this method, the children should ask and answer their own questions. Viewed from the ground of discovery there are three modes of presentation which may represent a progressive series. These are (i) the lecture mode, (2) the question and answer mode, (3) the mode by suggestion. In the first there is little of the spirit of the discoverer ; in the second there is a trifle more of the spirit of the discoverer; while in the third there is much of this spirit. The student is advised to select some class room topic with a view to illustrating these three modes of presentation. 12. OUTLINE. Logic in the Class Room. (1) Thought is king. (2) Special functions of induction and deduction. (3) Two types of mind. Inductive or liberal. Deductive or conservative. (4) Too much conservatism in school. (5) The method of the discoverer. Three steps ( 1. Foundational 1. Antecedent facts j 2 Crudal „ ^ . , i. . ' ( 1. "Mental urge" 2. Forming hypothesis j 2 Analogy „,_.-. C 1. Empirical 3. Verification j 2 Rational (6) The real inductive method or Discoverer's Method not in vogue in class room work. (7) As a method of instruction, deduction is superior to induction. (8) Conquest, not knowledge, the desideratum. Outline 459 (9) Motivation as related to the spirit of discovery. (10) Discoverer's method or the real inductive method adapted to class room work. School room method. Discoverer's method. Epitome. (11) Question and answer method not necessarily one of dis- covery. 13. SUMMARY. (1) Thought is king in that it is the ruling factor in the making and breaking of habit. This lends import to logic, which is the science of thought. (2) The chief function of induction is to discover new truth ; whereas deduction aims at clarifying and correcting new truth. Inductive logic makes known the special forms of thought which the discoverer uses; while deductive logic tends to show how he verifies the truth thus obtained. (3) Just as there are two general forms of thinking, in- ductive and deductive; so there are two general types of mind, the inductive and the deductive; the former leads to liberalism, the latter to conservatism. Both types are needed to maintain a safe balance. (4) The schools of the day are emphasizing the deductive phase of work to the sacrifice of the inductive. They are neglecting the Columbuses and the Edisons of the class. The course of study makes for a conservatism, which "nips in the bud" any marked tendency to discover and invent. (5) Logic may aid in the crusade against the ultra conserva- tive tendency of class method, by giving emphasis to the method of the discoverer and inventor. An analysis of this method re- veals these three steps : antecedent facts, forming an hypothesis and verification. Antecedent facts may be divided into founda- tional and crucial. A crucial fact leads immediately to the formation of the hypothesis; whereas the foundational facts represent that body of knowledge which makes it possible to interpret the crucial fact. The crucial fact creates an unsatisfied state of mind, which, in turn, urges the discoverer to construct some satisfactory hypothesis. Inference by analogy is the process used in such a construction. The two modes of verification are 460 Logic in the Class Room recourse to experience, or empirical; and appeal to reason, or rational. (6) In the class room, induction is used in form, not in spirit; in consequence we are neglecting the generals for the camp followers. (7) The inductive method is logically the method of dis- covery, while the deductive method is the method of instruction. In the class room, both methods have been devoted to the matter of instruction. Because of this, induction has been robbed of its chief advantage over deduction. (8) Man has attained his greatest success by enlarging upon the thoughts of nature and not by an absolute substitution. In enlarging upon nature's way of educating the child, man has adopted her form of procedure, but has lost her spirit of work. In his scheme of education, man's watchword is knowledge, while nature's is conquest. To seek knowledge without inspiring the spirit of conquest is man's way; whereas nature's way is to encourage the spirit of conquest by using knowledge as a reward. Man must co-operate with nature, if the best results are to be secured. (9) In the case of the true discoverer, it is not necessary to endow the object of his thought with added attractiveness; but with the child enthusiasm may need to be stimulated by "moti- vating" the subject in hand. This may be accomplished by appealing directly to the vital needs, worldly necessities, and f innate cravings of the child mind. (10) A revolt is in evidence against that insatiate desire to teach knowledge, which has been so marked in the past. Already schools are introducing departments of work which look toward conquest rather than knowledge. When adapted to the school room the discoverer's method naturally resolves itself into these five steps: (1) "Motivate" the topic for presentation. (2) Bring to mind "foundational facts." (3) Vividly make evident the "crucial fact." (4) Lead to discovery of "lesson-point." (5) Afford opportunity for verification. (11) The question and answer method of presenting work, Summary 461 does not necessarily give full scope to the spirit of inquiry as emulated by the true born discoverer. As a matter of affording opportunity for the development of the spirit of discovery, there are three modes of presentation which may be arranged in a progressive series : (1) The lecture mode in which there is little opportunity for discovery. (2) The question and answer mode which permits some opportunity for discovery. (3) The mode by suggestion which permits ample opportunity for discovery. 14. REVIEW QUESTIONS. (1) Show that thought may be made to make and break habit. (2) "Induction directs to new truth, deduction aims to modify and correct new truth." Explain and illustrate this. (3) Relate radicalism and conservatism to induction and deduction. (4) Show that in the present day school situations, the spirit of deduction prevails. (5) Describe a discovery which is a typical illustration of the discoverer's method. (6) Indicate with explanation the general steps in the dis- coverer's method. (7) Show by illustration the difference between "founda- tional facts" and "crucial facts." (8) Explain how the "crucial fact" leads to the construction of an hypothesis. (9) Explain and illustrate the two ways of verification. (10) Distinguish between the inductive method as it is used in the class room, and the inductive method as used by the discoverer. (11) Show that in his inventions, man enlarges upon the thoughts of nature. (12) Explain "motivation" and show that it is a new name for an old situation. (13) In adapting the discoverer's method to class work, what are the successive steps to be followed? (14) Show by illustration that the question and answer method is not necessarily one which encourages the spirit of discovery. 462 Logic in the Class Room 15. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTI- GATION. (1) "Our pet thoughts control us." Discuss this. (2) Select some class room experience for the purpose of showing that induction is especially directive in nature, whereas deduction is more or less corrective in nature. (3) "There are just two kinds of people in the world, the Inductives and the Deductives'' Explain. (4) Are the schools sending out too many Deductives? Argue the question. (5) "It is the business of the teacher to teach himself out of the business." Explain. (6) Look up the discovery of the laws of the pendulum, with a view of showing that the event well illustrates the fact of the three general steps in the discoverer's method. (7) "With the average, only extraordinary facts become crucial; but with the genius any ordinary fact may become crucial." Make this clear. (8) Explain "mental urge." Illustrate. (9) Illustrate "empirical proof," also "rational proof." (10) Show by illustration that the inductive method as used in the class room, falls far short of being the method of the discoverer. (11) Indicate by citing historical examples, that conquest rather than knowledge makes for manhood. (12) Show how you would motivate a topic in geography. (13) Outline a plan for teaching some topic in nature accord- ing to the discoverer's method. (14) Select a topic in arithmetic, for the purpose of giving a comparative illustration of the "question and answer mode" of presentation, and the "mode by suggestion." CHAPTER 21. LOGIC AND LIFE. 1. LOGIC GIVEN A PLACE IN A SECONDARY COURSE. "To prepare for complete living" seems to be the ulti- mate aim of education, and any school subject which does not aid to this end must be eliminated from the courses of study. "Knowledge for the sake of knowledge" will not do in this age of practical efficiency. A subject in order to survive must show indications of doing its share in this larger business of man building. If it can be made evident that logic lends itself in no undecided terms to such an aim, then may its incorporation in a secondary course of study be not only justified but more highly appreciated. 2. MAN'S SUPREMACY DUE TO POWER OF THOUGHT. That man is the supreme agent of intelligent progress is due to three factors : First, to the existence of the nat- ural world ; second, to the existence of man himself ; third, to man's ability to think. Given life and the world as a place to evolve that life, and it is barely possible that man might have survived, but without thought he could never have become supreme. Man is king of the animal king- dom because of his power of thought. Let us illustrate : Ages ago when England was a part of the main land ; when there was no North Sea nor English Channel ; we 463 464 Logic and Life are told that there lived in the forest tracts there about b many large and ferocious animals ; such as the elephant, the lion, and the tiger. There lived also in the region a smaller and apparently a weaker animal. This creature had no tusks to hook with, no great jaws to crunch with, \ and no claws to tear with ; and an eye witness would have said "Such a weakling has no possible chance against these | enemies of his; he and his descendants will succumb and 1 the species will become extinct." The region was tropical ; ■ but, of a sudden, a cataclysmic twist changed the tern- 1 perature from a torrid to a frigid state. What happened f The large and ferocious animals either migrated to the '■ south or froze to death; but this weakling put on furs, j built fires, and remained in the jungle as its king. His fe name was man, and though he had no horns to hook with, he possessed a brain to think with; this gave him suprem- acy over the forces of nature. From the beginning the adaptation of the lower animals has been physical; whereas man's has been more or less intellectual. By means of deliberative thought man made \ the bow and arrow which could kill at a distance of 200 ^ yards; then he invented the repeating rifle which may kill a mile away. Thought has taught man to harness the forces of nature in the form of all kinds of invention. Thought has given man the power to build bridges and palaces, to paint pictures, to chisel angels. Thought has pierced the fog of ignorance and brought light to the dark spots of the globe. Thought has build nations and established the spirit of good will on earth. Through the long years, thought has been the one tool of conquest Man's Supremacy Due to Power of Thought 465 which has enabled man to build for himself, out of the furnishings of nature, a heaven on earth. Can you recall a department of life which thought has not embellished ? Can you recall a single factor that has been raised to the nth power of efficiency without thought? Steam and electricity plus thought lights the world, unites the world, feeds and clothes the world. To-day, as in the olden time, men who think are ever at a pre- mium. This holds true from the Shopkeeper to the Magnate of Wall Street; from Basil, the Blacksmith, to Edison, the King Inventor ; from Reuben, the Farmer, to Burbank, the Wizard. 3. IMPORTANCE OF PROGRESSIVE THOUGHT. Man not only thinks but he thinks progressively. The average horse of to-day, for example, is probably no more intelligent than was the average equine of the time of Alexander the Great, whose war horse, Bucephalus, at- tained historical fame. Yet, intellectually, the average man of to-day is far above the average man of Alex- ander's time. "Horse-knowledge" is more or less sta- tionary. Through instinct each generation makes use of the knowledge of its ancestors without any noticeable accretions. But "man-knowledge" is a growing product of progressive thought. Man appropriates all the knowl- edge of his forbears, and then adds to this a bit of his own. By being able to think progressively, man is enabled to stand upon the shoulders of his ancestors and thus to take advantage of a broader vision. We are now led to the conclusion that man's supremacy 466 Logic and Life is due not only to his ability to think, but to his power of progressive thought. 4. NECESSITY OF RIGHT THINKING. In the main, man's thinking has been for his good; that is, in the long run, it has contributed to his general progress. If this had not been so, long since would he have dropped back to the level of the non-thinking animals. Thinking has been defined as the process of affirming or denying connections. Right thinking is, therefore, a matter of affirming the right connections or denying the wrong connections. To put it differently : right thinking is the process of adjusting the best means to a right end; whereas wrong thinking is a matter of overlooking the best means, or directing improper means to a wrong end. Right thinking involves proper adjustment ; wrong think- ing improper adjustment. In the intellectual world as in the physical, improper adjustment means extinction. Illustrations of this : (i) A contractor undertakes to build a skyscraper. In the excavation an old wall is discovered. The thought of the contractor is, "I must make a pot of money out of this job, and since this old wall is in the right spot I will build on it, and thus save me 'five hundred/ " In the course of ten years, without warning, the building top- ■ pies over and fifty women and children are killed. The contractor is convicted and sent to prison for life. If the builder had thought the right thought; namely, "I want to put up a building that will stand for generations," he would have survived the competition of his fellows and I Necessity of Right Thinking 467 entered his long home with success etched upon his soul. (2) Two school teachers, A and B, are working in the same system. A's ambition is to be promoted and she uses "pull" as the means. For a time she succeeds in pulling the wires, and likewise in pulling the "wool" over the eyes of the Board of Education. B aspires to pro- fessional growth, using as the means every opportunity for genuine improvement. In time both are known as they really are, not as they seem to be. A is denominated a "shirk," a politician, a mere school keeper; whereas B is looked up to as the best equipped worker in the building, a real school teacher. There may seem to be many exceptions to this point of view, and yet in the last analysis we find that these ex- ceptions are only apparent. When we maintain that right thinking means survival and wrong thinking ex- tinction, we assume that the standard adopted is genuine efficiency and not a certain money basis. High positions may be secured through wrong thinking, but these cannot be filled creditably without the preponderance of right thinking. 5. INDIFFERENT AND CARELESS THOUGHT. It may be advanced as a plausible hypothesis that man, especially if he is an American, finds much trouble for himself, and makes much trouble for the world because of his indifference to thought. To leap first and look afterwards is the spirit of youth, and America is young. Think twice before you look and look tzvice before you leap is sound logical doctrine. A logically minded man 468 Logic and Life rationalizes every new proposition before he adopts it. He marshals before the mind the favorable points and then bombards them with every conceivable objection. With the steady eye of an honest, earnest, open minded critic, he weighs the unfavorable against the favorable and then accepts the indications of the balance unequiv- ocally. If logic did nothing else save to inspire young people to thus rationalize every doubtful undertaking, it would do its share toward world betterment. 6. THE RATIONALIZATION OF THE WORLD OF CHANCE. Man seems to be a natural born gambler. He loves to "take a chance" and herein lies much of his unhappiness. Without discussing the evils of the stock exchange, the horrors of the gambling den, and the unbusiness like procedure of the race track, we may merely attempt here to show how the rationalization of the conception of chance may be instrumental in dimming the glare of gambling to the average youth. (i) The meaning of the term chance. The term chance implies an inability to find a cause for jl any particular event. Whenever we trust to luck, we do so through ignorance. In reality every thing in this world is ordered according to law, and if we possessed infinite knowledge concerning these laws, then, for us, the word "chance" would have no meaning. One accomplishment f of knowledge has been to rationalize superstition and chance. "Not a grain of sand lies upon the beach, but infinite knowledge would account for its lying there ; and the cause of every falling leaf is guided by the same prin- j: The Rationalization of the World of Chance 469 ciples of mechanics as rule the motions of the heavenly bodies." — Jevon's Prin. of Science, vol. I, p. 225. That chance is a literal confession of ignorance, is a wholesome truth for all to bear in mind. If we were not so ignorant of atmospheric conditions, we would never be caught in the rain without an umbrella; if we knew per- fectly the laws of mechanics, we would not speed our car and trust to luck that the car would hold together. (2) Chance mathematically considered. The principle of the "calculation of chances" has been discussed elsewhere. It will be sufficient here to illus- trate the principle from a mathematical point of view. Suppose that a jeweller desires to dispose of a ten- dollar watch by a raffle. He may place a hundred num- bers in a box, one of which corresponds to the number on the watch. My chance of drawing the right number is one out of a hundred and may be expressed by the 1 fraction . The fact that I may draw the right num- 100 ber on the first trial or on the last trial is immaterial. The real meaning of the ratio "one out of a hundred" is, that in the long run, I shall lose 99 times where I gain but once. This implies, that if I pay 25 cents for each draw, I shall in the end pay 99 times 25 cents for the watch, or I will have paid $24.75 f° r a ten dollar watch. (3) Chance and gambling. In all forms of gambling no wealth is produced. What one man gains the other man loses. In addition to this the institution which projects the gambling scheme must 470 Logic and Life be supported. In consequence, more money must be lost than can possibly be gained. This leads to the conclusion that on the basis of averages he who would gamble must terminate his career "behind the game." Statistics verify this conclusion. (4) Chance and investments. Interest, which is money paid for the use of money, is high when the demand for money exceeds the supply and low when the supply equals or exceeds the demand. The fact that the supply is short is largely due to the lack of confidence on the part of the investor. This means that he is unwilling to take the risk. Thus the principle: "High rate of interest, great risk; lozv rate of interest, little risk." 7. THE RATIONALIZATION OF POLITICAL AND BUSI- NESS SOPHISTRIES. "Win right or wrong" is a nut shell statement of modern sophistry. Corollaries to this are such aphorisms as "Of two evils choose the lesser"; "Do evil that good may come," etc. Armed with these platitudes the modern business and political octopus will play the bully and squeeze the life out of the little fellow in the name of economy ; will pay for editorials to elect the "right man" ; will evade bad laws so-called ; institute lobbies ; buy votes ; and perpetrate a thousand other immoral deeds in the name of "good business" or of "party loyalty." Half truths are the most atrocious of all kinds of fallacies in that they are the most misleading. "Do evil that good may come" is but half of the whole truth "Do The Rationalization of Sophistries 471 evil that good may come, provided there is no other way open." Again, "Of two evils choose the lesser, if a com- plete enumeration has shown that there is not a third course" A development of a finer ability of discernment under right influence should lead the common citizen to see through these various sophistries practiced by corporate greed, and should enable him by means of the ballot to "blaze a better way." The "public is a blunderbuss" because the average man either cannot, or will not, think his own thoughts. By developing greater skill and arousing greater interest in the thinking process, the crowd of camp followers will be reduced; selfish bossism will die; and a truer and more efficient democracy will reign supreme. 8. THE RATIONALIZATION OF THE SPIRIT OF PROGRESS. Genuine progress comes through a happy combination of the old with the new. A love for the old only, means ultra conservatism; whereas a love for the new only, means ultra radicalism; a love for both means rational liberalism. That people love the old way may be attributed to two forces which will receive attention here. (1) Race instinct. It may be said that "life is a brief space between two eternities — a path between infinity and infinitude." "Man is a pedestrian who perambulates along the way." The eternities concern him not so much as the path which 47 2 Logic and Life stretches between them. In a former day, one of the striking characteristics of the western plain was the beaten path stretching out along the table-land like an elongated, dust colored serpent; and often following this path would be a herd of buffalo winding its way in single file around boulder and ant hill till shut from view by the distant horizon. Thus has man travelled along the beaten path, following the "foot prints of the ages." Here and there and everywhere do we see signs of those who have gone on before; father, grandfather, great grandfather; yes, even to the toe marks of those primeval ancestors of ours who shambled along the way, nobody knows how many years ago. From the dark recesses of the cave, have our forbears thrown a lasso of blood about our necks, and it seems as if we must follow the old, old way. "Being acorns of the ancestral oak," we grow similar oak tree tendencies, living over again the life of our progen- itors. "There lies in every soul the history of the universe." (2) Imitation. But there is another reason for this ultra conserva- tive spirit and it is that nature's chief mode of instruction is by means of imitation. To every living thing of wood or field nature seems to say, "Your parents are always right, do as they do for this is the best way to learn the lessons of life." A man thinks, feels and wills his way through life in a certain manner largely because his father did likewise. Moreover, we not only imitate those who have gone on before, but we counterfeit each other ; fashion is another name for world wide mimicry. We The Rationalisation of the Spirit of Progress 473 imitate our friends and those whom we admire; we talk like them, we walk like them, we live like them. It now appears that we are held to the path of the past by means of race instinct and the power of imitation, and we are thus prone to believe that the old way is good enough. It is evident that to get out of the beaten path is dangerous. The wild animal that deserts the habits of the race dies a premature death, and the man who pos- sesses the temerity to struggle through the thicket of new things must, of necessity, shorten his span of life. To follow the "same old rut" is easiest for the teacher ; to be loyal to the "grand old party" is safest for the politician. But to the contrary, if every man of every generation had followed the beaten path blindly — without deviation, the human race would now be a horde of simians. Be- cause man has possessed the power of progressive thought, he has developed the spirit of radicalism and has thereby made himself supreme. "The old way anyway — the old way right or wrong" has been the world's biggest stumbling block. Every innovation must fight for its life. Every good thing has to be condemned in its day and generation. It is Huxley who suggests three stages for the course of a new idea : First, it is revolutionary ; second, it will make little differ- ence; third, / have always believed in it. On the other hand, the new way anyway; "we must have a change whether or no"; "we must have something different despite the cost," have ever been the slogans of waste and destitution. The wars which have not resulted from the prejudice of ultra conservatism have been brought about 474 Logic and Life through the thoughtlessness of ultra radicalism. The revolutionist, the freak and the anarchist, products of impulse and the spirit of discontent, spring from an unwise love of change. The world needs conservatism and radicalism not so much as it needs rationalism. It needs men who can hold to the good of the old and adopt the best of the new; men who neither "rust out" nor "waste out"; but wear out. That rational progress may obtain, there must be a perfect dovetailing of the old with the new. Man must leave the beaten path not altogether, but at times. He needs to blaze out a new way not so much as he needs to straighten the bends, tunnel through the mountains, and fill in the swamps of the old way. A rational "liberal- ism" implies a willingness to follow the old path with a view to improving the imperfections thereof. 9. A RATIONALIZATION OF THE ATTITUDE TOWARD WORK. On the assumption that true happiness is the ultimate aim of life, we may conclude that anything which does not contribute to this end functions as a curse and not as a blessing. Happiness involves physical comfort and mental joy. To have comfort of the body implies moderate means. The poor cannot be happy because of bodily want. When "physical-man" is not given proper nourishment for healthy growth, then does he goad "spiritual-man" with the pricks of appetite and pain till his wants are appeased. This is a law of nature. On the other hand happiness is not attained through acquisition; A Rationalization of the Attitude Toward Work 475 neither the millionaires, nor the scholars, nor the famous are the happiest. This is a fact apparent to all. Over worry and over excitement follow closely the heels of much money and high position. Too little brings un- happiness through want; too much brings unhappiness through worry. Therefore man is cursed by his work when the remuneration is not enough for comfort of body, or when the income is too much for poise of mind. Unless the organs of the body are used they atrophy. Every cell of the physical makeup demands exercise. Work which is not drudgery; work which causes the organs of the body and the powers of the mind to func- tion normally ; work which gives comfort without luxury ; work which forces one to the highest actualization of his physical and spiritual powers is man's greatest blessing. In and through such work will man attain his highest state of happiness. 10. THE LOGIC OF SUCCESS. We may now hope to show that material aggrandize- ment, the adopted standard of success, is one of the illogical factors of modern life. The tree of the forest always grows toward the light. It pushes its way through the darkness of the soil into the shadow of the underbrush and finally out into the unobstructed light of the sun. This parallels the progress of the race. From the darkness of savagery into the shadow of barbarism, and finally out into the full light of civilization. Thus has man grown steadily and con- tinually toward better things. But "better things" is a 476 Logic and Life relative term and has changed with the development of the race. "A good healthy idea may not live longer than twenty years." In consequence growth toward the light has been in accordance with man's conception of a higher and a better life; which conception is ever changing. Moreover, growth toward the best is always rewarded by real happiness. It therefore follows that the right road to real happiness extends along the way of better things as conceived by the traveller, man. Any force which tends to lift the world up toward more light is a blessing, and any personality which con- tributes to this end is a success. When one drops a pin it falls down toward the earth, at the same time the earth comes up to meet the pin. This is according to the uni- versal law of gravitation. It is true that the earth moves the pin through a much greater space than the pin moves the earth, and yet the fact remains that the pin does move the earth. The extent to which the smaller body is able to move the larger, depends on the two factors of weight and relative position. If the pin were lighter or farther away it would influence the earth so much the less. In like manner does the "pin-man" influence the "human- world." The extent of this influence is controlled by man's weight, or his "lifting power," and the position which he occupies; just as the attraction of the pin for the earth is controlled by weight and position. The facts of history have proved that man's power to lift depends not so much upon what he has as upon what he is. In short, lifting power is directly in proportion to personal worth. Moreover, man's ability to draw human- A Rationalization of the Attitude Toward Work 477 ity up may be increased or decreased by the position which he occupies. Such a position must function for the best good of the world, and at the same time must elicit the highest development of the man. To Summarize: Individual success involves these three elements : First — A man of personal worth. Second — A position which draws out the best in the man. Third — A work which definitely contributes to the uplift of the world. A definition is now in order : Success is the right man in the right place doing his best for the highest good of the world. 11. OUTLINE. Logic and Life. (1) Logic given a place in a secondary course. (2) Man's supremacy due to power of thought (3) Importance of progressive thinking. (4) Necessity of right thinking. (5) Indifferent and careless thought. (6) The rationalization of the world of chance. (1) Meaning of the term chance. (2) Chance mathematically considered. (3) Chance and gambling. (4) Chance and investments. (7) The rationalization of business and political sophistries. (8) The rationalization of the spirit of progress. (9) A rationalization of the attitude toward work. (10) The logic of success. 478 Logic and Life 12. SUMMARY. (1) To justify its having a place in any course of study, logic must lend itself to character building. (2) Man is king of the animal kingdom because of his power of thought. From the beginning his adaption has been more or less intellectual and his chief weapon of conquest has ever been his thinking brain. (3) Man's supremacy has been due not only to his ability to think, but also to his power of progressive thought. (4) Right thinking is the process of adjusting the best means to a right end. Wrong thinking involves improper adjustment, which in turn results in extinction. (5) A "logically-minded" man rationalizes every new propo- sition before he adopts it. That is, he analyzes with the utmost care and with unprejudiced frankness all the favorable and un- favorable situations; he then throws them into the balance of honest judgment and adopts the indications of said balance, unequivocally. (6) Chance is a confession of ignorance. If man possessed infinite knowledge, the term chance would have no place in his vocabulary. The games of chance are money making schemes supported by the gambling fraternity. On the basis of averages, the gam- bler, in the long run, must terminate his career "behind the game." High rate of interest implies great risk; low rate of interest little risk. (7) "Win right or wrong" epitomizes the teachings of mod- ern sophistry. With the coming of better thinking, a more efficient democracy will obtain. (8) Rational progress combines the best of the old with what seems to be the best of the new. Blind love for the old, or ultra conservatism, is due to the two forces of race instinct and power of imitation. An adherence to the "old way anyway" may mean retrogres- sion; whereas following the new way, simply because of its newness, may involve unnecessary waste. Summary 479 (9) Work which is not drudgery; work which causes the organs of the body and the powers of the mind to function normally; work which gives comfort without luxury; work which forces one to the highest actualization of his physical and spiritual powers is man's greatest blessing. (10) Logically considered personal aggrandizement is not a true standard of success. Success involves personal worth rather than personal holding. Success is measured by man's ability to help the world on toward better things. Success is the right man in the right place doing his best for the highest good of the world. 13. REVIEW QUESTIONS. (1) What is the ultimate aim of education?. Show that logic contributes to this end. (2) Prove that man's power of thought has ever been his best weapon of conquest. (3) Exemplify the distinction between non-progressive and progressive thinking. (4) Define right thinking. Illustrate. (5) "A logically-minded man rationalizes every new project before undertaking it." Give a concrete instance in explanation of this. (6) "Chance is a literal confession of ignorance." Demon- strate this. (7) Give a mathematical illustration proving that schemes of chance are simply money making devices for the benefit of those who project them. (8) The average gambler must terminate his career behind the game. Prove this. (9) Why should high rate of interest imply great risk? (10) Show that a half truth is a most misleading fallacy. (11) Illustrate a business sophistry. Explain. (12) Write a brief theme on "The Rationalization of the Spirit of Progress." 480 Logic and Life (13) Under what conditions may work become man's greatest blessing? (14) Define success. Illustrate. (15) In the light of your definition of success discuss the following: "The. only failure is not to try." 14. QUESTIONS FOR ORIGINAL THOUGHT AND INVES- TIGATION. (1) "To prepare for complete living" is the end of educa- tion. Interpret and discuss this quotation from Spencer. (2) Mention some discovery or invention which represents the power of progressive thought. » (3) "Man's adaptation has been largely intellectual while the adaptation of the camel has been physical." Explain. (4) Interpret the expression, "The son stands upon the shoulders of the father." (5) Illustrate instances where man's thinking has not been for his best interests. (6) Indicate how wrong thinking led to the Civil War. (7) Distinguish between legitimate speculation and gambling. (8) Name and explain the logical elements involved in a low rate of interest. (9) How may training in right thinking lead to more efficient citizenship ? (10) "There lies in every soul a history of the universe/' Show the truth of this. (11) Show by illustration that imitation is one of nature's chief modes of instruction. (12) Explain the meaning of drudgery. (13) Mention instances where work is a curse. (14) Is success possible when the right man is found doing his best in the wrong place? (15) Whom do you consider the most successful American? Give reasons. General Exercises 481 GENERAL EXERCISES IN TESTING THE VALIDITY OF CATEGORICAL ARGUMENTS. Let the student give attention to the fallacies in meaning as well as to the fallacies in form. 1. None but those who are contented with their lot in life can justly be considered happy. But the truly wise man will always make himself contented with his lot in life, and, therefore he may justly be considered happy. Keynes. 2. Suffering is a title to an excellent inheritance; for God chastens every son whom he receives. Keynes. 3. No young man is wise; for only experience can give wisdom, and experience comes only with age. Keynes. 4. Dr. Johnson remarked that "a man who sold a penknife was not necessarily an 'iron-monger." Against what logical fallacy was this remark directed? Explain. Keynes. 5. This pamphlet contains seditious doctrines, the spread of which may be dangerous to the state; hence the pamphlet must be suppressed. Keynes. 6. Good workmen do not complain of their tools: my pupils do not complain of their tools; therefore, my pupils are probably good workmen. Keynes. 7. Knowledge gives power; consequently, ,since power is de- sirable, knowledge is desirable. Keynes. 8. Some who are truly wise are not learned; but the virtuous alone are truly wise; the learned, therefore, are not always virtuous. Keynes. 9. The spread of education among the lower orders will make them unfit for their work; for it has always had that effect on those among them who happen to have acquired it in previous times. Keynes. 10. Slavery is a natural institution and therefore ought not to be abolished. Russell. 11. The yardstick of success is the dollar, and you have made your millions. 482 General Exercises 12. "All who talk well are not necessarily intelligent, and A is certainly a spell-binder." 13. Gold and silver are the wealth of a country; consequently, the diminution of gold and silver by exportation must mean the diminution of the wealth of a country. Russell. 14. A miracle is unbelievable, because it fails to conform to known laws of nature. 15. Improbable events happen every day; now, what happens every day is a probable event; therefore, improbable events are probable events. 16. What fallacy did Columbus commit when he made the egg stand on end by breaking one end? 17. Some holder of a ticket is sure to draw the prize; and, as I am a ticket holder, I am sure to draw the prize. Russell. 18. All the members of the jury are just men, hence you may trust the foreman. 19. Select the star players of the country and you will have a team which cannot be beaten. 20. All the houses on this street present a pretty picture; this house, therefore, which is on this street, will make a fine picture. 21. What is the good of all your teaching, for every day we hear of wrong doing made possible by education. 22. You are not what I am; I am a teacher; hence you are not a teacher. 23. The student of history is compelled to admit the law of progress, for he finds that society has never stood still. Russell. 24. This bill must have been designed to bleed the people be- cause it is supported by the grafters of the state. 25. "To close the saloons on Sunday is contrary to the wishes of the people of the city; hence those 'farmer legislators' should keep hands off." 26. Success is the right man in the right place doing his best, and you are working to the limit. 27. Early to bed and early to rise, makes one healthy, wealthy and wise. It is, therefore, easy enough to get rich. 28. Honesty being the best policy, I must tell the truth to my General Exercises 483 patient, though to tell him that he cannot live will shorten his life many days. 29. A stitch in times saves nine, hence an ounce of prevention is worth a pound of cure. 30. The richest man I know used to sweep his office every morning, hence it pays to commence at the bottom. 31. Cramming is an injurious habit, since it makes the building of logical memories practically impossible. 32. A strong will means a trained will ; struggle is an indication of weakness. 33. There is no such thing as a national or state conscience; therefore, no judgments can fall upon a sinful nation. Hibben. 34. The principles of justice are variable; the appointments of nature are invariable; therefore, the principles of justice are no appointment of nature. Aristotle. 35. Intelligence and not sex should be the standard; therefore, let the women have their way. 36. "War by killing off the men of the country gives the living a better opportunity to succeed because of reduced competition." 37. Since you deem yourself a misfit, in the name of common sense, why do you not change your occupation? 38. The conquest of America by Europeans has been a good thing for the world; since no eminent historian doubts it. 484 General Exercises GENERAL EXERCISES IN TESTING THE VALIDITY OF HYPOTHETICAL, DISJUNCTIVE AND DILEMMATIC ARGUMENTS. The student must remember to give attention to the fallacies in meaning as well as to the fallacies in form. 1. If I speak at length, he is bored; if I speak briefly, he is offended; therefore I will not speak at all. 2. If virtue is involuntary, vice is also involuntary, but vice is voluntary, hence virtue is also. 3. If a man cannot make progress toward perfection, he must either be a brute or a divinity; but no man is either; therefore every man is capable of such progress. Fowler. 4. If education is popular, compulsion is unnecessary; if unpopular, compulsion will not be tolerated. Fowler. 5. If you are to recover from this illness, then you will. If you are not to recover, then you will not, hence what is the use of calling in a physician? 6. If your act was right, your conscience will approve it; if wrong, your conscience will prick you. Either your act was right or wrong, so you can depend upon your conscience. 7. If he is intoxicated then he is not responsible but he acts like a sober man. 8. If the Elixir of Life is of any value, those who take it will improve in health; now my friend who has been taking it has improved in health, and therefore the elixir is of value as a curative agent. Hyslop. 9. If you will settle down to business, you may still win out, because I am confident it is not too late for hard work to be effective. 10. If the end justifies the means then money used for any object of charity may be secured in any way. 11. If might is right then money talks, but I find that occa- sionally money proves ineffective. 12. If the majority of those who use public houses are pre- ! General Exercises 485 pared to close them, legislation is unnecessary, but if they are not prepared for such a measure, then to force it on them by outside pressure is both dangerous and unjust. Hyslop. 13. If the conscience is infallible in matters of right and wrong, then sin is just one thing; namely, doing that which is contrary to one's conscience. We believe that an educated conscience is infallible. 14. If the earth were of equal density throughout, it would be about 2 l / 2 times as dense as water; but it is about S l / 2 times as dense; therefore the earth must be of unequal density. Hyslop. 15. The end of human life is either perfection or happiness; death is the end of human life, therefore death is either perfec- tion or happiness. Creighton. 16. That chauffeur either lost his head or was drunk because no sane man would deliberately run down an innocent child. 17. If you argue on a subject which you do not understand, you will prove yourself a fool; for this is a mistake which fools always make. Keynes. 18. If you are a man of your word, you will live up to your agreement, or if you have any self respect, you will do the manly thing. Now your neighbors tell me that you are a man in the habit of making good your promises. 486 Examination Questions SETS OF EXAMINATION QUESTIONS FOR TRAINING SCHOOLS AND COLLEGES. Answer ten questions. Time, 2 hours. Set I. 1. Define and illustrate obversion and state the principle which conditions the process. 2. Give directions for making the following propositions logical: (1) Only first class passengers may ride in parlor cars. (2) All who claim to be pious are not pious. (3) "Blessed are the merciful." 3. Write a theme of 200 words on "Logic and Life." 4. Put into syllogistic form and test the validity of this argument. "We are going to have an open winter because the hornets' nests are near the ground." 5. Justify the teaching of logic in an institution which offers courses in Educational Theory. 6. Correct the following definitions, stating the rules violated: (1) A man is an organized entity whose cognitive powers function rationally. (2) A bird is an animal that flies. (3) A scholar is an educated man with scholarly attain- ments. 7. Prove that in the first figure the minor premise must be affirma- tive. 8. Investigate a case of habitual tardiness by making use of the canon of difference. Examination Questions 487 9. Describe with illustrations the various ways of begging the question. 10. Why should classification rather than logical division be the mode of procedure in the case of small children? Illustrate. 11. Illustrate the following: (1) non connotative- term, (2) un- distributed middle, (3) fallacy of accident. Set II. Answer ten questions. Time, 2 hours. Throw the following into the form of a syllogism and criti- cise, giving reasons: 1. "I do not know how to teach school as I have had no experience." 2. "Only the honest should be in business and you are not honest." 3. Why should all teachers study logic? Give arguments in full. 4. Describe Mill's methods of induction and illustrate one. 5. Give and explain the rules of logical definition. 6. Explain the distribution of terms and illustrate by circles the meaning of the four logical propositions. 7. Define the following: (1) teaching, (2) extension of terms, (3) obversion, (4) hypothesis, (5) relative term. 8. Give a class room illustration of the Complete Method. 488 Examination Questions Distinguish between (1) distributive and collective terms, (2) analysis and deduction, (3) logical division and classification. 10. Illustrate the following: (1) contradictory proposition, (2) analogy, (3) law of identity, (4) singular term, (5) univocal term. 11. Convert, if possible, the following: (1) Some men are honest. (2) All that glitters is not gold. (3) All kings are fallible. Set III. Time, 2 hours. 1. Investigate by the Joint Method of Induction this question : "Why is John absent so often?" 2. Explain and illustrate: (1 contradictory propositions, (2) illicit middle, (3) obversion, (4) contraversion, (5) synthesis. 3. State and exemplify the rules of logical division. 4. Write a theme of at least 150 words on one of the following: (1) Induction as the Discoverer's Method. (2) A Rational View of Success. 5. Define logically: (1) teaching, (2) deduction, (3) education, (4) analysis, (5) money. 6. Distinguish between the extension and intension of terms. 7. Exemplify: (1) an absolute term, (2) the complete method, (3) non connotative terms, (4) fallacy of accident, (5) hy- pothesis. Examination Questions 489 8. "Educated among savages, he could not be expected to know the customs of polite society." Is this valid? Reasons. 9. The signs indicate that you are either stupid or unprepared; but the past proves that you are not the former." Test the validity. 10. Discuss comprehensively one of the following topics: (1) The Fallacies. (2) Thinking. (3) Abbreviated Arguments. Set IV. Answer ten questions. Time, 2 hours. 1. Exemplify: (1) the law of variation in the extension and intension of terms, (2) a distributed predicate. 2. Indicate with explanation the logical errors: (1) A teacher assumes that the "bad boy of the school" is going to cause trouble in her room. (2) All the men of the Commission are fair minded men, hence they will render a fair decision. 3. What experimental method of induction is the most positive in its conclusion? Illustrate this method. 4. State and illustrate the rules of logical definition. 5. Obvert each of the four logical propositions. Explain the principle involved. Test the validity of the following arguments : 6. "Horses, not being human, cannot reason." 7. "Only the industrious deserve to succeed and you have never done a hard day's work in your life." 8. "If you had been wise, you would have refused to stoop to the methods of the firm, but you were not wise." 490 Examination Questions 9. From this premise construct a valid syllogism: "All large cities owe their size to some commercial advantage." 10. Define and illustrate the following: analogy, hypothesis, think- ing, connotative term, relative term. 11. Distinguish between: (1) Analysis and deduction. (2) Logical division and classification. (3) Relative and absolute identity. Set V. Time, 2 hours. Test the validity, giving reasons : 1. All successful teachers are industrious, but you are not indus- trious because you are not successful. 2. John was a troublesome boy in the first and second grades, therefore he is going to make trouble for the third grade teacher. 3. Teaching is the art of imparting knowledge. Criticise, giving reasons. Define correctly, pointing out the essentials. 4. Explain the extensional and intensional use of terms and illus- trate the law of variation. 5. Describe Mill's experimental methods of induction. Symbolize the joint method. G. Define the following: analysis, law of identity, obversion. 7. Illustrate the laws of thought. 8. Write on one of the following topics: (1) Complete Method, (2) Right Thinking. 9. "The science of logic never made a man reason rightly." Dis- cuss this question. Examination Questions 491 10. Explain and illustrate the enthymeme. Set VI. Answer ten questions. Time, 2 hours. 1. Exemplify the following: (1) illicit minor, (2) begging the question, (3) law of excluded middle, (4) inductive method. 2. Write a short theme on one of these topics: (1) Thinking. (2) Logical Terms. Test the validity of the "attending arguments, giving reasons : 3. "He who talks much usually says little and you are certainly a great talker." 4. "You must be industrious, since only such truly succeed." 5. Illustrate and give the characteristic marks of the joint method of induction. 6. Summarize the benefits to be derived from a study of logic. 7. State and illustrate the rules of logical definition. 8. Distinguish between (1) extension and intension, (2) opposite and contradictory terms, (3) analysis and synthesis. 9. Define and illustrate hypothesis, obversion, sorites, hypothetical argument. 10. Explain and illustrate the three forms of induction. 11. Distinguish logically between a teacher and an instructor. 492 Bibliography BIBLIOGRAPHY. Aikins. The Principles of Logic. Henry Holt and Co., New York. 1905. Bain. Logic, Inductive and Deductive. Longmans, Green and Co. 1902. Bosanquet. The Essentials of Logic. The MacMillan Co., London. 1910. Bradley. The Principles of Logic. London. 1886. Creighton. Introductory Logic. The MacMillan Co., New York. 1905. Dewey. Studies in Logical Theory. The University of Chicago Press. 1903. Fowler. The Elements of Deductive and Inductive Logic. Oxford. 1905. Hibben. Logic, Deductive and Inductive. Chas. Scribner's Sons, New York. 1906. Hyslop. Elements of Logic. Chas. Scribner's Sons, New York. 1905. Jevons-Hill. Elements of Logic. American Book Co., New York. 1883. Keynes. Formal Logic. The MacMillan Co., London. 1906. Lotze. Logic. Translated by B. Bosanquet, 2 vols. Oxford. 1888. McCosh. Laws of Discursive Thought. Chas. Scribner's Sons. 1906. Mill. A System of Logic, 2 vols. Longmans, Green and Co., London. 1904. Russell. Elementary Logic. The MacMillan Co., New York. 1908. Ryland. Logic. George Bell and Sons, London. 1900. Sigwart. Logic. Translated by Helen Dendy, 2 vols. The MacMillan Co. 1895. Swinburne. Picture Logic. Longmans, Green and Co., London. 1904. Taylor. Elementary Logic. Chas. Scribner's Sons, New York. 1911. Venn. The Logic of Chance. The MacMillan Co., New York. Outline of Briefer Course 493 OUTLINE OF BRIEFER COURSE. Subject. Page I. THOUGHT AND ITS LAWS Logic Defined 3 The Thinking Process . . . .12 Stages in Thinking 25 Law of Identity 32 Law of Contradiction 35 Law of Excluded Middle . . . -39 II. LOGICAL TERMS All of Chapter 4 47 III. EXTENSION AND INTENSION OF TERMS All of Chapter 5 62 IV. DEFINITION All of Chapter 6 . • JJ V. LOGICAL DIVISION AND CLASSIFICATION All of Chapter 7 105 VI. LOGICAL PROPOSITIONS All of Chapter 8 Except Section 7 . . 120 VII. IMMEDIATE INFERENCE All of Chapter 10 170 VIII. MEDIATE INFERENCE All of Chapter 11 Except Section 8 . . 192 494 Outline of Briefer Course Subject. Page IX. FIGURES AND MOODS The Four Figures of the Syllogism . . 218 The Moods of the Syllogism . . .221 Testing the Validity of the Moods . . 223 X. INCOMPLETE SYLLOGISMS Enthymeme 247 Polysyllogisms 250 Sorites 251 XI. CATEGORICAL ARGUMENTS TESTED All of Chapter 14 263 XII. HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS All of Chapter 15 Except Sections 13, 14, 15 and 17 ....... 288 XIII. THE LOGICAL FALLACIES All of Chapter 16 . . . . . 322 XIV. INDUCTIVE REASONING All of Chapter 17 Except Sections 3, 4., 7, 8 and 9 355 XV. MILL'S METHODS OF OBSERVATION AND EXPERIMENT All of Chapter 18 386 XVI. OBSERVATION, EXPERIMENT AND HYPOTHESIS All of Chapter 19 418 INDEX Absolute Terms, 56. Abstract Terms, 51. Accent, Fallacy of, 330. Accident, 81 ; Fallacy of, 334. Affirmative Proposition, 127. Agreement, Method of, 387. All — not, Some, Few, Logical Significance of, 133. Ambiguous Middle, 328. Amphibology, 329. Analogy, 368. Analysis, Definition of, 97; As a Method, 97; Induction by, 373. Analytic Propositions, 138; Method, 97. Antecedent, 289. Apprehension and Thinking, 24. Arguments, Irregular, 258; Testing of Categorical, 263 ; Incomplete, 247; General Ex- ercises, 481 ; Mistakes of Stu- dents in Connection with, 281; Hypothetical, 288; Dis- junctive, 302; Dilemmatic, 308. Argumentum ad populum, 338; ad hominem, 338; ad igno- rantiam, 338; ad baculum, 338; ad verecundiam, 339. Aristotle's Dictum, 208. Art, Definition of, 96. Auxiliary Elements of Induc- tion, 418. B Bain Quoted, 12. Ballentine Quoted, 359. Barbara, Celarent, etc., 234. Begging the Question, 341. Bibliography, 492. Bowen Quoted, 12. Briefer Course, Outline of, 493. Canons of Syllogism, 209; of Four Figures, 226. Categorematic Words, 48. Categorical Arguments, 263 ; Tested, 263; General Exer- cises, 481. Categorical Propositions De- fined, 121 ; Four Elements, 122; Four Kinds, 126; Classi- fication of, 128. Cause, Fallacy of False, 340. Chance, Rationalization of, 468. Child, Thinking of, 20. Circulus in Probando, 343. Classification Compared with Division, 112; Kinds, 113; Rules of, 114; Use, 114. Co-extensive Propositions, 142. Collective Terms, 50. Comparison, Stages in Think- ing, 25. Complete Method, Three Ele- ments, 97. Composition, Fallacy of, 331. Concept, Definition of, 17; a Thought Product, 21. Concomitant Variations, 402. Concrete Terms, 51. Connotative Terms, Two-fold Function of, 62; Definition of, 52 ; a List of, 65. Conquest the Desideratum, 447. Consequent, 289; Fallacy of False, 339. Contradiction, Law of, 35. Contradictory Terms, 53 ; Prop- ositions, 167. Contrary Propositions, 165. Contraversion, 181 ; Fallacies of, 327. Converse Accident, Fallacy of, 335. Conversion, 176; by Limitation, 178; Simply, 179; Fallacies of, 327. 496 Index Copula, 123. Creighton Quoted, 4, 387, 485. D Deduction, Denned, 96; as a Method, 97; Special Func- tion of, 438. Definition, Importance of, 77; the Predicates, 77; Nature of, 82; Definition of, 83; Compared with Division, 84; Kinds of, 85; When Service- able, 87; Rules of. 88; Terms which Cannot be Defined, 93 ; of Common Educational Terms, 94. Denomination, Stages in Thought, 26. Denotation and Connotation of Terms, 66. Descriptive Definition, 86. Development, Definition of, 94. Dichotomy, 110. Difference, Method of, 393. Differentia, 80. Dilemma, 308. Discoverer's Method, 440. Disjunctive Arguments, 302; Rules of, 303; Logical Dis- junction, 303; Reduction of, 307. Distribution of Subject and Predicate of Propositions, 145 ; Schemes for Remember- ing, 148. Division, Definition of Logical, 105; As Partition, 107; Com- pared with Definition, 84 Distinguished from Enu meration, 106; Rules of, 108 Compared with Classifica tion, 112; Use of, 114 Fallacy of, 332. Dressier Quoted, 12. Education, Defined, 94; Com- pared with Instruction, 95. Educational Terms Defined, 94. Elements of the Logical Prop- osition, 123. Elliptical Propositions, 129. Enthymeme, 247. Epicheirema, 249. Episyllogism, 250. Epithets, Question Begging, 343. Essential Attributes of Defini- tion, 88. Etymological Definition, 85. Euler's Diagrams, 141. Evolution and the Thinking Mind, 19. Examination Questions, 486. Exceptive Propositions, 135. Excluded Middle, Law of, 39. Exclusive Propositions, 136. Exercises, Testing Arguments, 481. Experiment as an Element in Induction, 419. Extension and Intension of Terms, Defined, 63 ; Com- pared, 63; Used in Compari- son, 65 ; Other Forms of Ex- pression for, 66; Law of Variation in, 66. Fact, Defined, 96. Fallacies, of Deductive Reason- ing, 322; Paralogism and Sophism, 322; Division of, 323; of Immediate Infer- ence, 326; in Form, 194, 199; Hypothetical, 291; Disjunc- tive, 303; of Language, 328; in Thought, 334. False Cause, 340. False Consequent, Fallacy of, 339. Figure of Speech, Fallacy of, 333. Figures of Syllogism, 218; Special Canons of, 226; Per- fect and Imperfect, 235 ; Re- duction, 235; Relative Value of, 239. Index 497 Formal Fallacies, 197, 324. Four Terms, Fallacy of, 329. Fowler Quoted, 4, 360. Fundamentum Divisionis, 108. General Exercises in Testing Arguments, 481. General Terms, 49. Genus and Species, 78. Grammatical Subject and Pred- icate, 125. Grammatical Sentences, 131. H Hamilton Quoted, 4, 12, 131. Hibben Quoted, 4, 441. Huxley Quoted, 473. Hypothetical Arguments, 288; Kinds, 290; Rules and Falla- cies, 291 ; Reduced to Cate- gorical, 293; Illustrative Ex- ercise in Testing, 297; Gen- eral Exercises, 484. Hypothesis, Defined, 96, 425; and Theory, 427; Require- ments of, 427; Uses of, 429. Identity, Law of, 32; Absolute, 33; Complete and Incom- plete, 33; Relative, 34. Illicit Major and Minor, 199; Illustration of, 215. Image, Definition of, 17. Immediate Inference, 159; by Obversion, 170; by Opposi- tion, 161 ; by Conversion, 176 ; t by Contraversion, 181 ; Epitome of Four Processes, 182 ; by Inversion, 183 ; Falla- cies of, 326. Imperfect Induction, 361. Indefinite Propositions, 129. Individual Proposition, Nature of, 132; in Opposition, 168. Induction, Defined, 96; as a Method, 97; Reasoning, 355; and the Hazard, 356; the Three Forms of, 365; Per- fect, 375; Special Function of, 438. Inference, Definition of, 18; a Thought Product, 24; Imme- diate, 159; Mediate, 192. Infima Species, 79. Instruction Defined, 95. Intension of Terms, 63. Integration, a Stage in Thought, 26. Inversion, 183. Inverted Proposition, 137. Irregular Arguments, 258. Irrelevant Conclusion, 337. Jevons Quoted, 4, 25, 387, 468. Joint Method of Agreement and Difference, 397. Judgment, Definition of, 17; a Thought Product, 22; Most Fundamental Element in Thinking, 23. K Keynes Quoted, 481, 485. Kinds of Definitions, 85. Knowing, by Intuition and by Thinking, 2; Knowing and Thinking Compared, 10; by Intuition, 11; Habitual, 11. Knowledge, Defined, 95; Intui- tive, 11. Language and Thought Insep- arable, 47. Law of Variation in Exten- sion and Intension, Stated, 66; Two Important Facts in, 69 ; Diagrammatically Illus- trated, 70, 71. 498 Index Laws of Sufficient Reason, 40; of Universal Causation, 361 ; of Uniformity of Nature, 362. Laws of Thought, 32 ; Unity of, 40; Schematic Statement of, 43. Learning, Defined, 95. Logic, Defined, 3; Authentic Definitions of, 4; Grammai of Thought, 3; Science of Sciences, 3; the Value of to the Student, 5; Related to Other Subjects, 1; Specific Scope, 2. Logic in the Class Room, 437. Logic and Life, 463. Logic of Success, 475. Logical Definition, 85, 88. Logical Disjunction, 303. Logical Subject and Predicate, 125. M Major Term, 196. Material Fallacies, 323, 324, 325, 328. Mediate Inference, 192; the Syllogism, 192; Rules of Syllogism, 193. Method Defined, 96; Inductive and Deductive, 97; Complete, 97. Method- Whole Defined, 96. Middle Term, 192, 193, 196. Mill Quoted, 5, 359, 361, 387, 393, 397, 402, 406. Mill's Experimental Methods, 386. Miller Quoted, 12. Mind, the Unity of, 1 ; Know- ing and Thinking Compared, 10. Minor Term, 196. Mnemonic Lines, 234. Modal Proposition, 139. Modus Ponendo Tollens, etc., 302. Moods of Syllogism, 221 ; Test- ing Validity of, 223. Motivation as Related to Spirit of Discovery, 449. N Negative Proposition, 127. Negative Terms, 53. Nego-positive Terms, 55. Non-connotative Terms, 52. Non Sequitur, Fallacy of, 339. Not, Bisects the World, 36; Two Uses of, 36. Notion, Definition, 14; Indi- vidual, 14; General, 14; Dis- tinguished from Knowledge, 15; Distinguished from Idea, 16; Psychological Terms In- volved in, 16. O Observation, 419; Rules of, 420; Errors of, 423. Obversion, Definition of, 170; Fallacies of, 326. Opposite Terms, 53. Opposition, Nature of, 161; Scheme of, 163; Square of, 164. Outline of Briefer Course, 493. P Page Quoted, 453. Particular Propositions, 126; Affirmative, 143 ; Negative, 144. Partition, 107. Partitive Propositions, 133. Percept, Definition of. 17; Re- lated to Thought, 18. Perfect Induction, 375. Petitio Principii, 341. Plurative Propositions, 132. Polysyllogism, 250. Pornhyry, Tree of, 111. Positive Terms, 53. Predicables. Defined, 77; Named, 78; Illustrated, 82. Predicate, Grammatical and Logical, 125; Distribution of, 145. Index 499 Primary Laws of Thought, 32. Privative Terms, 55. Progressive Thought, 465. Property, 81. Propositions, Definition of Log- ical, 120. Prosyllogism, 250. Proximate Genus, 79. Pure Proposition, 139. Q Quantity Signs, 123. Quantity and Quality of Prop- ositions, 126. Question and Answer, not a Method of Discovery, 457. Question Begging Epithets, 343. Question, Complex, 340. R Rationalization, of Chance, 468 ; of Political and Business Sophistries, 470 ; of the Spirit of Progress, 471 ; of the At- titude toward Work, 474. Reasoning, Defined, 24, 355; Inductive, 355 ; Deductive, 355. Reduction of Figures, 235. Relation between Subject and Predicate, 140. Relative Terms, 56 Residues, Method of, 406. Right Thinking, 466. Rules, of Logical Definition, 88; of Logical Division, 108; of Classification, 114; of the Syllogism, 193; of the Hy- pothetical Argument, 291; of the Disjunctive, 303. Russell Quoted, 481, 482. Ryland Quoted, 481, 482. Salisbury Quoted, 360. Science, Defined, 95. Sensation, Defined, 17; Re- lated to Thought, 18. Simple Conversion, 179. Simple Enumeration, 367. Singular Terms, 49. Socrates, 322. Sorites, 251. Species, 78. Square of Opposition, 164. Subaltern Propositions, 164. Subcontrary Propositions, 164. Subject, Logical, 123; Gram- matical and Logical Dis- tinguished, 125; Distribution of, 145. Success, Logic of, 475. Sufficient Reason, Law of, 40. Summum Genus, 79. Syllogism, a Product of In- ference, 24; Nature of, 192; Rules of, 193; Undistributed Middle, 199; Illicit Major, 199; Illicit Minor, 199; Aris- totle's Dictum, 208; Canons of, 209; Mathematical Axi- oms of, 210 ; Four Figures of, 218; Moods of, 221; Incom- plete, 247. Syncategorematic Words, 48. Synthesis, Defined, 97; as a Method, 97. Synthetic Proposition, 138. T Teaching, Defined, 94; Com- pared with Instruction and Education, 95. Terms, Extension and Inten- sion of, 63; Used in Exten- sion and Intension, 65 ; which Cannot be Defined, 93; Con- tradictory and Opposite, 38; Logical, 47; Singular and General, 49; Collective and Distributive, 50; Concrete and Abstract. 51 : Connota- tive and Non-connotative, 52; Positive and Negative, 53; Contradictory and Oppo- site, 53; Privative and Nego- positive, 55; Absolute and Relative, 56. 5oo Index Theory Defined, 96. Thinking, Definition of, 12; II lustration of Process, 13 Compared with Knowing, 10 Compared with Intuition, 2 the Process, 12 ; Groups Many Into One, 18; in the Sensa- tion and Percept, 18; Evolu- tion and Thinking Mind, 19; of the Child, 20; of the Adult, 20; and the Concept, 21 ; and the Judgment, 22 ; and Apprehension, 24; Stages in, 25; in the Inference, 24; Laws of, 32; Unity of Laws, 40; Progressive, 465; Right, Necessity of, 466; Indiffer- ent and Careless, 467. Thought and Language, 47. Thought is King, 437. Traduction, 377. Training, Definition of, 95. Tree of Porphyry, 111. Truistic Proposition, 139. Truth Defined, 96. U Uberweg Quoted, 4. Undistributed Middle, 199; Il- lustration of, 214. Uniformity of Nature, 362. Universal Affirmative Proposi- tion, 140. Universal Causation, 361. Universal Negative Proposi- tion, 142. Universal Propositions, 126. Variations, Method of Con- comitant, 402. W Watts Quoted, 4. Weakened Conclusion, 224. Whately Quoted, 4. Word-signs of Categorical Propositions, 122. 6 7 p^* * 8 4 4* * 8 I -V * * > ... I V P> *<< °o & - " r * 9 1 <£* Deacidified using the Bookkeeper proce Neutralizing agent: Magnesium Oxide -1 Treatment Date: Sept. 2004 PreservationTechnologic A WORLD LEADER IN PAPER PRESERVATI 111 Thomson Park Drive Cranberry Township, PA 16066 ■*>• (79&\ 77Q.91 1 1 -f V- o V ,\ v V N i -n* x°^. '^0^ ^ ^ *P LIBRARY OF CONGRESS