{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_57912/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_57912","id":"gutenberg_57912","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/57912","summary":null,"tags":["Category: Philosophy & Ethics","Category: Teaching & Education","Logic"],"text":"Produced by Richard Hulse and the Online Distributed\nProofreading Team at http://www.pgdp.net (This file was\nproduced from images generously made available by The\nInternet Archive)\n\n\n\n\n\n\n\n\n\n A CLASS ROOM LOGIC\n\n\n DEDUCTIVE AND INDUCTIVE\n\n WITH SPECIAL APPLICATION TO THE\n SCIENCE AND ART OF TEACHING\n\n\n BY\n\n\n GEORGE HASTINGS McNAIR, PH. D.\n\n HEAD OF DEPARTMENT OF LOGIC AND MATHEMATICS,\n CITY TRAINING SCHOOL FOR TEACHERS.\n JAMAICA. NEW YORK CITY\n\n\n THE ETHLAS PRESS\n FIVE NORTH BROADWAY. NYACK. NEW YORK\n\n\n\n\n COPYRIGHT, 1914, BY\n GEORGE HASTINGS McNAIR\n\n\n\n\n To\n MY WIFE.\n\n\n\n\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n \u2502 \u2502\n \u2502 Transcriber\u2019s Notes \u2502\n \u2502 \u2502\n \u2502 \u2502\n \u2502 Punctuation has been standardized. \u2502\n \u2502 \u2502\n \u2502 Characters in small caps have been replaced by all caps. \u2502\n \u2502 \u2502\n \u2502 Non-printable characteristics have been given the following \u2502\n \u2502 transliteration: \u2502\n \u2502 Italic text: --> _text_ \u2502\n \u2502 bold text: --> =text=. \u2502\n \u2502 \u2502\n \u2502 This book was written in a period when many words had \u2502\n \u2502 not become standardized in their spelling. Words may have \u2502\n \u2502 multiple spelling variations or inconsistent hyphenation in \u2502\n \u2502 the text. These have been left unchanged unless indicated \u2502\n \u2502 with a Transcriber\u2019s Note. \u2502\n \u2502 \u2502\n \u2502 The symbol \u2018\u2021\u2019 indicates the description in parenthesis has \u2502\n \u2502 been added to an illustration. This may be needed if there \u2502\n \u2502 is no caption or if the caption does not describe the image \u2502\n \u2502 adequately. \u2502\n \u2502 \u2502\n \u2502 Index references have not been checked for accuracy. \u2502\n \u2502 \u2502\n \u2502 Footnotes are identified in the text with a number in \u2502\n \u2502 brackets [2] and have been accumulated in a single section \u2502\n \u2502 at the end of the text. \u2502\n \u2502 \u2502\n \u2502 Transcriber\u2019s Notes are used when making corrections to the \u2502\n \u2502 text or to provide additional information for the modern \u2502\n \u2502 reader. These notes are not identified in the text, but have \u2502\n \u2502 been accumulated in a single section at the end of the book. \u2502\n \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n\n\n\n\n PREFACE.\n\n\nThis treatise is an outgrowth of our class room work in logic.\n\nIt has been published in the hope of removing some of the difficulties\nwhich handicap the average student.\n\nWe trust that the language is simple and definite and that the\nillustrative exercises and diagrams may be helpful in making clear some\nof the more abstruse topics.\n\nIf a speedy review for examination is necessary, it is recommended\nthat the briefer course as outlined on page 493 be followed and that\nthe summaries closing each chapter be carefully read.\n\nOnly the fundamentals of deductive and inductive logic have received\nattention. Moreover emphasis has been given to those phases which\nappear to commend themselves because of their practical value.\n\nFurther than this we trust that the book may fulfill in some small way\nthe larger mission of inspiring better thinking and, in consequence, of\nleading to a more serviceable citizenship.\n\nSurely as civilization advances it is with the expectation of giving\ngreater significance to the assumption \u201cthat man is a _rational_\nanimal.\u201d\n\nI am indebted to a number of writers on logic, notably to Mill,\nLotze, Keynes, Hibben, Fowler, Aikins, Hyslop, Creighton and Jevons.\nI am likewise under obligation to that large body of students who, by\nfrankly revealing their difficulties, have given me a different point\nof view.\n\nFor constructive criticism and definite encouragement I owe a personal\ndebt of gratitude to Prof. Charles Gray Shaw of New York University,\nto Prof. Frank D. Blodgett of the Oneonta Normal School and to Prin.\nA. C. MacLachlan of the Jamaica Training School for Teachers.\n\n G. H. McN.\n\n City Training School for Teachers,\n Jamaica, N. Y. City.\n October 3, 1914.\n\n\n\n\n TABLE OF CONTENTS\n\n CHAPTER 1.\u2015\u2015THE SCOPE AND NATURE OF LOGIC.\n 1. The Mind.\n 2. Logic Related to Other Subjects.\n 3. Logic Defined.\n 4. The Value of Logic to the Student.\n 5. Outline.\n 6. Summary.\n 7. Review Questions.\n 8. Questions for Original Thought and Investigation.\n\n CHAPTER 2.\u2015\u2015THOUGHT AND ITS OPERATION.\n 1. The Knowing Mind Compared with the Thinking Mind.\n 2. Knowing by Intuition.\n 3. The Thinking Process.\n 4. Notions, Individual and General.\n 5. Knowledge and Idea as Related to the Notion.\n 6. The Logic of the Psychological Terms Involved in the Notion.\n 7. Thought in the Sensation and Percept.\n 8. Evolution and the Thinking Mind.\n 9. The Concept as a Thought Product.\n 10. The Judgment as a Thought Product.\n 11. Inference as a Thought Product.\n 12. Thinking and Apprehension.\n 13. Stages in Thinking.\n 14. Outline.\n 15. Summary.\n 16. Review Questions.\n 17. Questions for Original Thought and Investigation.\n\n CHAPTER 3.\u2015\u2015THE PRIMARY LAWS OF THOUGHT.\n 1. Two Fundamental Laws.\n 2. The Law of Identity.\n 3. The Law of Contradiction.\n 4. The Law of Excluded Middle.\n 5. The Law of Sufficient Reason.\n 6. Unity of Primary Laws of Thought.\n 7. Outline.\n 8. Summary.\n 9. Illustrative Exercises.\n 10. Review Questions.\n 11. Questions for Original Thought and Investigation.\n\n CHAPTER 4.\u2015\u2015LOGICAL TERMS.\n 1. Logical Thought and Language Inseparable.\n 2. Meaning of Term.\n 3. Categorematic and Syncategorematic Words.\n 4. Singular Terms.\n 5. General Terms.\n 6. Collective and Distributive Terms.\n 7. Concrete and Abstract Terms.\n 8. Connotative and Non-connotative Terms.\n 9. Positive and Negative Terms.\n 10. Contradictory and Opposite Terms.\n 11. Privative and Nego-positive Terms.\n 12. Absolute and Relative Terms.\n 13. Outline.\n 14. Summary.\n 15. Illustrative Exercises.\n 16. Review Questions.\n 17. Questions for Original Thought and Investigation.\n\n CHAPTER 5.\u2015\u2015THE EXTENSION AND INTENSION OF TERMS.\n 1. Two-fold Function of Connotative Terms.\n 2. Extension and Intension Defined.\n 3. Extended Comparison of Extension and Intension.\n 4. A List of Connotative Terms Used in Extension and Intension.\n 5. Other Forms of Expression for Extension and Intension.\n 6. Law of Variation in Extension and Intension.\n 6a. Important Facts in Law of Variation.\n 6b. Law of Variation Diagrammatically Illustrated.\n 7. Outline.\n 8. Summary.\n 9. Illustrative Exercises.\n 10. Review Questions.\n 11. Questions for Original Thought and Investigation.\n\n CHAPTER 6.\u2015\u2015DEFINITION.\n 1. Importance.\n 2. The Predicables.\n 3. The Nature of a Definition.\n 4. Definition and Division Compared.\n 5. The Kinds of Definitions.\n 6. When the Three Kinds of Definitions are Serviceable.\n 7. The Rules of Logical Definition.\n 8. Terms Which Cannot be Defined Logically.\n 9. Definitions of Common Educational Terms.\n 10. Outline.\n 11. Summary.\n 12. Illustrative Exercises.\n 13. Review Questions.\n 14. Questions for Original Thought and Investigation.\n\n CHAPTER 7.\u2015\u2015LOGICAL DIVISION AND CLASSIFICATION.\n 1. Nature of Logical Division.\n 2. Logical Division Distinguished from Enumeration.\n 3. Logical Division as Partition.\n 4. Four Rules of Logical Division.\n 5. Dichotomy.\n 6. Classification Compared with Division.\n 7. Kinds of Classification.\n 8. Two Rules of Classification.\n 9. Use of Division and Classification.\n 10. Outline.\n 11. Summary.\n 12. Review Questions.\n 13. Questions for Original Thought and Investigation.\n\n CHAPTER 8.\u2015\u2015LOGICAL PROPOSITIONS.\n 1. The Nature of Logical Propositions.\n 2. Kinds of Logical Propositions.\n 3. The Four Elements of a Categorical Proposition.\n 4. Logical and Grammatical Subject and Predicate Distinguished.\n 5. The Four Kinds of Categorical Propositions.\n 6. Propositions which do not Conform to Logical Type.\n 7. Propositions not Necessarily Illogical.\n 8. The Relation between Subject and Predicate.\n 9. Outline.\n 10. Summary.\n 11. Illustrative Exercises.\n 12. Review Questions.\n 13. Questions for Original Thought and Investigation.\n\n CHAPTER 9.\u2015\u2015IMMEDIATE INFERENCE\u2015\u2015OPPOSITION.\n 1. The Nature of Inference.\n 2. Immediate and Mediate Inference.\n 3. The Forms of Immediate Inference.\n (1) Opposition.\n\n CHAPTER 10.\u2015\u2015IMMEDIATE INFERENCE (Continued).\n (2) Immediate Inference by Obversion.\n (3) Immediate Inference by Conversion.\n (4) Immediate Inference by Contraversion.\n 4. Epitome of the Four Processes of Immediate Inference.\n \u25c6 Inference by Inversion.\n 5. Outline.\n 6. Summary.\n 7. Illustrative Exercises.\n 8. Review Questions.\n 9. Problems for Original Thought and Investigation.\n\n CHAPTER 11.\u2015\u2015MEDIATE INFERENCE\u2015\u2015THE SYLLOGISM.\n 1. Inference and Reasoning.\n 2. The Syllogism.\n 3. The Rules of the Syllogism.\n 4. Rules of Syllogism Explained.\n 5. Aristotle\u2019s Dictum.\n 6. Canons of the Syllogism.\n 7. Mathematical Axioms.\n 8. Outline.\n 9. Summary.\n 10. Illustrative Exercises.\n 11. Review Questions.\n 12. Questions for Original Thought and Investigation.\n\n CHAPTER 12.\u2015\u2015FIGURES AND MOODS OF THE SYLLOGISM.\n 1. The Four Figures of the Syllogism.\n 2. The Moods of the Syllogism.\n 3. Testing the Validity of the Moods.\n 4. Special Canons of the Four Figures.\n 5. Special Canons Related.\n 6. Mnemonic Lines.\n 7. Relative Value of the Four Figures.\n 8. Outline.\n 9. Summary.\n 10. Illustrative Exercises.\n 11. Review Questions.\n 12. Questions for Original Thought and Investigation.\n\n CHAPTER 13.\u2015\u2015INCOMPLETE SYLLOGISMS AND IRREGULAR ARGUMENTS.\n 1. Enthymeme.\n 2. Epicheirema.\n 3. Polysyllogisms. Prosyllogism\u2015\u2015Episyllogism.\n 4. Sorites.\n 5. Irregular Arguments.\n 6. Outline.\n 7. Summary.\n 8. Review Questions.\n 9. Questions for Original Thought and Investigation.\n\n CHAPTER 14.\u2015\u2015CATEGORICAL ARGUMENTS TESTED ACCORDING TO FORM.\n 1. Arguments of Form and Matter.\n 2. Order of Procedure in a Formal Testing of Arguments.\n 3. Illustrative Exercise in Testing Arguments which are Complete\n and whose Premises are Logical.\n 4. Illustrative Exercise in Testing Completed Arguments, one or\n both of whose Premises are Illogical.\n 5. Incomplete and Irregular Arguments.\n 6. Common Mistakes of the Student.\n 7. Outline.\n 8. Summary.\n 9. Review Questions.\n 10. Questions for Original Thought and Investigation.\n\n CHAPTER 15.\u2015\u2015HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS INCLUDING THE\n DILEMMA.\n 1. Three Kinds of Arguments.\n 2. Hypothetical Arguments.\n 3. Antecedent and Consequent.\n 4. Two Kinds of Hypothetical Arguments.\n 5. Rule and Two Fallacies of Hypothetical Argument.\n 6. Hypothetical Arguments Reduced to Categorical Form.\n 7. Illustrative Exercises Testing Hypothetical Arguments of All\n Kinds.\n 8. Disjunctive Arguments.\n 9. Two Kinds of Disjunctive Arguments.\n 10. First Disjunctive Rule.\n 11. Second Disjunctive Rule.\n 12. Reduction of Disjunctive Argument.\n 13. The Dilemma.\n 14. Four Forms of Dilemmatic Arguments.\n 15. The Rule of Dilemma.\n 16. Illustrative Exercises Testing Disjunctive and Dilemmatic\n Argument.\n 17. Ordinary Experiences Related to Disjunctive Proposition and\n Hypothetical Argument.\n 18. Outline.\n 19. Summary.\n 20. Review Questions.\n 21. Questions for Original Thought and Investigation.\n\n CHAPTER 16.\u2015\u2015THE LOGICAL FALLACIES OF DEDUCTIVE REASONING.\n 1. A Negative Aspect.\n 2. Paralogism and Sophism.\n 3. A Division of the Deductive Fallacies.\n 4. General Divisions Explained.\n 5. Fallacies of Immediate Inference.\n 6. Fallacies in Language (Equivocation).\n 7. Fallacies in Thought (Assumption).\n 8. Outline.\n 9. Summary.\n 10. Illustrative Exercises in Testing Arguments in Both Form and\n Meaning.\n 11. Review Questions.\n 12. Questions for Original Thought and Investigation.\n\n CHAPTER 17.\u2015\u2015INDUCTIVE REASONING.\n 1. Inductive and Deductive Reasoning Distinguished.\n 2. The \u201cInductive Hazard.\u201d\n 3. Complexity of the Problem of Induction.\n 4. Various Conceptions of Induction.\n 5. Induction and Deduction Contiguous Processes.\n 6. Induction an Assumption.\n 7. Universal Causation.\n 8. Uniformity of Nature.\n 9. Inductive Assumptions Justified.\n 10. Three Forms of Inductive Research.\n 11. Induction by Simple Enumeration.\n 12. Induction by Analogy.\n 13. Induction by Analysis.\n 14. Perfect Induction.\n 15. Traduction.\n 16. Outline.\n 17. Summary.\n 18. Review Questions.\n 19. Questions for Original Thought and Investigation.\n\n CHAPTER 18.\u2015\u2015MILL\u2019S FIVE SPECIAL METHODS OF OBSERVATION AND\n EXPERIMENT.\n 1. Aim of Five Methods.\n 2. Method of Agreement.\n 3. Method of Difference.\n 4. The Joint Method of Agreement and Difference.\n 5. The Method of Concomitant Variations.\n 6. The Method of Residues.\n 7. General Purpose and Unity of Five Methods.\n 8. Outline.\n 9. Summary.\n 10. Review Questions.\n 11. Questions for Original Thought and Investigation.\n\n CHAPTER 19.\u2015\u2015AUXILIARY ELEMENTS IN INDUCTION.\n OBSERVATION\u2015\u2015EXPERIMENT\u2015\u2015HYPOTHESIS.\n 1. Foundation of Inductive Generalizations.\n 2. Observation.\n 3. Experiment.\n 4. Rules for Logical Observation and Experiment.\n 5. Common Errors of Observation and Experiment.\n 6. The Hypothesis.\n 7. Induction and Hypothesis Distinguished.\n 8. Hypothesis and Theory Distinguished.\n 9. The Requirements of a Permissible Hypothesis.\n 10. Uses of Hypothesis.\n 11. Characteristics Needed by Scientific Investigators.\n 12. Outline.\n 13. Summary.\n 14. Review Questions.\n 15. Questions for Original Thought and Investigation.\n\n CHAPTER 20.\u2015\u2015LOGIC IN THE CLASS ROOM.\n 1. Thought is King.\n 2. Special Functions of Induction and Deduction.\n 3. Two Types of Minds.\n 4. Conservatism in School.\n 5. The Method of the Discoverer.\n 6. Real Inductive Method not in Vogue in Class Room Work.\n 7. As a Method of Instruction, Deduction Superior.\n 8. Conquest, not Knowledge, the Desideratum.\n 9. Motivation as Related to Spirit of Discovery.\n 10. Discoverer\u2019s Method Adapted to Class Room Work.\n 11. Question and Answer Method not Necessarily One of Discovery.\n 12. Outline.\n 13. Summary.\n 14. Review Questions.\n 15. Questions for Original Thought and Investigation.\n\n CHAPTER 21.\u2015\u2015LOGIC AND LIFE.\n 1. Logic Given a Place in a Secondary Course.\n 2. Man\u2019s Supremacy Due to Power of Thought.\n 3. Importance of Progressive Thinking.\n 4. Necessity of Right Thinking.\n 5. Indifferent and Careless Thought.\n 6. The Rationalization of the World of Chance.\n 7. The Rationalization of Business and Political Sophistries.\n 8. The Rationalization of the Spirit of Progress.\n 9. A Rationalization of the Attitude Toward Work.\n 10. The Logic of Success.\n 11. Outline.\n 12. Summary.\n 13. Review Questions.\n 14. Questions for Original Thought and Investigation.\n\n GENERAL EXERCISES IN TESTING CATEGORICAL ARGUMENTS.\n\n GENERAL EXERCISES IN TESTING HYPOTHETICAL, DISJUNCTIVE AND\n DILEMMATIC ARGUMENTS.\n\n EXAMINATION QUESTIONS FOR TRAINING SCHOOLS AND COLLEGES.\n\n BIBLIOGRAPHY.\n\n OUTLINE OF BRIEFER COURSE.\n\n INDEX.\n\n\n\n\n CHAPTER 1.\n\n THE SCOPE AND NATURE OF LOGIC.\n\n\n=1. THE MIND.=\n\nAs to the true conception of matter the world is ignorant. Yet when\nasked, \u201cWhat does matter do?\u201d the reply is, \u201cMatter moves, matter\nvibrates.\u201d Moreover, relative to the exact nature of mind, the world\nis likewise ignorant. But to the question, \u201cWhat does mind do?\u201d the\nresponse comes, \u201cThe Mind _knows_, the mind _feels_, the mind _wills_.\u201d\nThe mind has ever manifested itself in these three ways. Because of\nthis three-fold function it is easy to think of the mind as being\nseparated into distinct compartments, each constituting an independent\nactivity. This is erroneous. The mind is a living unit having three\nsides but never acting one side at a time. When the mind knows it also\nfeels in some way and wills to some extent. To illustrate: Music is\nheard and one _knows_ it to be Rubinstein\u2019s Melody in F. The execution\nbeing good one _feels_ pleasure. That the pleasurable state may be\naugmented one _wills_ a listening attitude. For analytical purposes\nthe psychologists have a way of naming the state of mind from the\npredominating manifestation.\n\n\n=2. LOGIC RELATED TO OTHER SUBJECTS.=\n\nWhat the mind _is_ may in time be answered satisfactorily by\nphilosophy; what the mind _does_ is described by psychology; what the\nmind _knows_ is treated by logic. Again: the mind as a whole furnishes\nthe subject matter for psychology, whereas logic is concerned with the\nmind knowing, aesthetics with the mind feeling, and ethics with the\nmind willing. Ethics attempts to answer the question, \u201cWhat is right?\u201d\naesthetics, \u201cWhat is beautiful?\u201d and logic, \u201cWhat is true?\u201d\n\nThough both psychology and logic treat of the knowing aspect of the\nmind, yet the fields are not identical. The former deals with the\n_process_ of the knowing mind as a _whole_, while the latter is\nconcerned mainly with the _product_ of the knowing mind when it\n_thinks_. To be specific: The mind knows when it becomes aware of\nanything, moreover, this condition of awareness appears in two ways:\nfirst, immediately or by _intuition_; second, after deliberation or by\n_thinking_. For example, one may know immediately or by intuition that\nthe object in the hand is a lead pencil, but when requested to state\nthe length of the pencil there is deliberation involving a comparison\nof the unknown length with a definite measure. It may now finally\nbe asserted that the pencil is six inches long. When we know without\nhesitation the process involved is intuition, whereas when the\nknowledge comes after some sort of comparison the mental act is called\nthinking. It, therefore, becomes the business of psychology to deal\nwith both intuition and thinking while logic devotes its attention\nto thinking only, and even in this field the work of logic is more or\nless indirect. The specific scope of logic is the product of thinking\nor thought.[1] What are the forms of thought? What are the laws of\nthought? Are the several thoughts true? These are the questions which\nlogic is supposed to answer.\n\nFor the logician thought has two sources, his own mind and the mind\nof others. In the latter case thought becomes accessible through the\nmedium of language. There is in consequence a close connection between\nlogic, the science of thought, and grammar, the science of language.\nBecause of this near relation logic is sometimes called the \u201cgrammar\nof thought.\u201d\n\nTo study any science properly one must have thoughts and since logic is\nthe science of all thought the subject may be regarded as the _science\nof sciences_.\n\n\n=3. LOGIC DEFINED.=\n\n\u201cLogic is the science of thought.\u201d This definition commonly given\nis too brief to be helpful. Should not a definition of any subject\nrepresent a working basis upon which one may build with some knowledge\nof what the structure is to be? The following, a little out of the\nordinary, seems to supply this condition: _Logic as a science makes\nknown the laws and forms of thought and as an art suggests conditions\nwhich must be fulfilled to think rightly._\n\nIn justification of the latter definition it may be argued that it\ncovers the topics usually treated by logicians. It is said that a\nscience teaches us to know while an art teaches us to do. As a science\nlogic teaches us to know certain laws which underlie right thinking.\nFor example, the law of identity which makes possible all affirmative\njudgments, such as \u201cSome men are wise,\u201d \u201cAll metals are elements,\u201d etc.\nLikewise as a science logic acquaints us with certain universal _forms_\nto which thought shapes itself, such as definitions, classifications,\ninductions, deductions. Further, logic lays down definite _rules_ which\nlead to right thinking. To wit: Because it is true of a _part_ of a\nclass it should not be assumed that it is true of the _whole_ of that\nclass: or, in short, do not distribute an undistributed term.\n\nA possible profit to the student may result from a study of certain\nauthentic definitions herewith subjoined:\n\n (1) \u201cLogic is the science of the laws of thought.\u201d Jevons.\n\n (2) \u201cLogic is the science which investigates the process of\n thinking.\u201d Creighton.\n\n (3) \u201cLogic as a science aims to ascertain what are the laws of\n thought; as an art it aims to apply these laws to the detection\n of fallacies or for the determination of correct reasoning.\u201d\n Hyslop.\n\n (4) \u201cLogic is the art of thinking.\u201d Watts.\n\n (5) \u201cLogic is the science and also the art of thinking.\u201d Whateley.\n\n (6) \u201cLogic is the science of the formal and necessary laws of\n thought.\u201d Hamilton.\n\n (7) \u201cLogic is the science of the regulative laws of the human\n understanding.\u201d Ueberweg.\n\n (8) \u201cLogic treats of the nature and of the laws of thought.\u201d Hibben.\n\n (9) \u201cLogic may be defined as the science of the conditions on which\n correct thoughts depend, and the art of attaining to correct and\n avoiding incorrect thoughts.\u201d Fowler.\n\n (10) \u201cLogic is the science of the operations of the understanding\n which are subservient to the estimation of evidence.\u201d Mill.\n\n (11) \u201cLogic may be briefly described as a body of doctrines and rules\n having reference to truth.\u201d Bain.\n\nIt would seem as if there were as many different definitions as there\nare books on the subject. This is due partly to the disposition of\nthe older logicians to ignore the _art_ of logic and partly to the\ndifficulty of giving in a few words a satisfactory description of a\nbroad subject. In the fundamentals of logical doctrine present-day\nauthorities virtually agree.\n\n\n=4. THE VALUE OF LOGIC TO THE STUDENT.=\n\nLogic is rapidly coming into favor as a major subject in institutions\ndevoted to educational theory. Some of the reasons for this change of\nattitude are herewith subjoined:\n\n(1) _Logic should stimulate the thought powers._ This is the age of\nthe survival of the thinker. The fact that the man who thinks _best_\nis the man who thinks _much_ and _carefully_ will be accepted by those\nwho believe that practice makes perfect. \u201cOne needs only to observe\nthe average commuter to conclude that a large percent. of our business\nmen read too much and think too little.\u201d \u201cMuch readee and no thinkee\u201d\nwas the reply of a Chinaman when asked his opinion of the doings of\nthe average American. \u201cWe as a people are newspaper mad, reading for\nentertainment, seldom for mental improvement.\u201d\n\n(2) _Logic aims to secure correct thought._ Are not many of the sins\nand most of the failures in this world due to incorrect thinking?\n\n(3) _Logic should train to clear thinking._ It would be difficult to\nestimate the loss of energy to the brain worker because he has not\nthe power to think clearly. Maximum efficiency is impossible with a\nbefogged brain. How discouraging it is to the student to attempt to\nget from the paragraph the thought of the author, who in trying to be\nprofound succeeds in being profoundly abstruse. There is a probable\nneed for broad, deep thoughts, but these when placed in a text book\nshould be sharpened to a point.\n\n(4) _Logic should aid one to estimate aright the statements and\narguments of others._ This is of especial value to the teacher who is\nconstrained to teach largely from text books. Because it is found in a\nbook is not proof positive that it is true. Why should we assume that\nthe book is infallible when we know that the man behind the book is\nfallible?\n\n(5) _Logic insists on definite, systematic procedure._ To be logical\nis to be businesslike. A study of logic would, no doubt, benefit our\nchurches and parliamentary orders as well as our schools.\n\n(6) _Logic demands lucid, pointed, accurate expression._ How we would\nincrease our working efficiency could we but express our thoughts in\nan attractive and interesting manner. To listen to the speeches of some\nof our great and good men who are concerned in directing the \u201cship of\nstate\u201d is sufficient argument that the American schools need more logic.\n\n(7) _Logic is especially adapted to a general mental training._ Despite\nthe swing of the pendulum of public opinion toward the bread-and-butter\nside of life, there are many of high repute who claim that for the\nsake of that mental acumen which distinguished the Greek from his\ncontemporaries we cannot afford to sacrifice everything on the altar\nof commercialism.\n\n(8) _Logic worships at the shrine of truth and adds to our store of\nknowledge._ What has aided the world more in its march onward than this\ndeep-seated passion for truth and what has impeded it more than that\nvain and wanton indifference to truth which brought to the world its\ndarkest age?\n\n\n=5. OUTLINE\u2015\u2015=\n\n THE SCOPE AND NATURE OF LOGIC.\n\n (1) The Mind.\n Three aspects.\n Unity of.\n\n (2) Logic Related to Other Subjects.\n Mental philosophy, psychology, logic.\n Psychology, logic, aesthetics, ethics.\n Two ways of knowing.\n Special province of logic.\n Logic and language.\n A science of sciences.\n\n (3) Logic Defined.\n A general definition.\n A more satisfactory definition.\n A list of authentic definitions.\n\n (4) The Value of Logic to the Student.\n Eight reasons for its study.\n\n\n=6. SUMMARY.=\n\n(1) The aspects of the mind are knowing, feeling and willing.\n\nThe mind is a living unit and never knows without feeling in some way\nand willing to some extent.\n\n(2) What the mind _is_ must be answered by philosophy; what the mind\n_does_ by psychology and what the mind _knows_ by logic.\n\nPsychology treats of the mind as a whole, logic of the mind knowing,\naesthetics of the mind feeling and ethics of the mind willing. Ethics\nanswers the question, What is right? Aesthetics, What is beautiful?\nLogic, What is true?\n\nThe standpoint of logic is not identical with any particular portion of\npsychology.\n\nThe mind knows in two ways: (a) by intuition, (b) by thinking. Thinking\nis a process\u2015\u2015thought a product. Logic deals indirectly with the former\nand directly with the latter.\n\nGenerally speaking, logic is a systematic study of thought. For the\nlogician thought has two sources: (a) his own mind and (b) spoken or\nwritten language.\n\nBecause of the ambiguity of language logic has much to do with it as a\nfaulty vehicle of thought.\n\n(3) Logic as a science makes known the laws and forms of thought and\nas an art suggests conditions which must be fulfilled to think rightly.\nAuthor.\n\n\u201cLogic may be defined as the science of the conditions on which correct\nthoughts depend, and the art of attaining to correct and avoiding\nincorrect thoughts.\u201d Fowler.\n\nIn the fundamentals of logical doctrine present day logicians virtually\nagree.\n\n(4) Logic should stimulate the thought powers; secure correct and clear\nthinking; aid in the estimation of arguments; inspire definite,\nsystematic procedure; demand lucid, pointed, accurate expression and be\nespecially adapted to general mental discipline.\n\nLogic adds to our store of knowledge and develops a passion for the\ntruth.\n\n\n=7. REVIEW QUESTIONS.=\n\n (1) Explain and illustrate the three ways in which the mind may\n manifest itself.\n\n (2) Illustrate the fact that the mind acts in unity.\n\n (3) Show briefly how logic is related to mental philosophy,\n psychology, aesthetics, ethics and grammar.\n\n (4) Illustrate the two ways of knowing.\n\n (5) Distinguish between thinking and thought.\n\n (6) Give a general definition of logic. Why is this definition\n unsatisfactory?\n\n (7) What are the two sources of thought?\n\n (8) Why are logic and language so closely related?\n\n (9) Give that definition of logic which best satisfies you.\n\n (10) Summarize the benefits which you hope to derive from your study\n of logic.\n\n (11) Why should teachers be clear thinkers?\n\n (12) Why should teachers be especially on guard against incorrect\n statements of all kinds?\n\n (13) Show how logic might be of assistance to the business man.\n\n\n=8. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Prove that there is nothing real in the world save the mind\n itself.\n\n (2) \u201cLogic is concerned primarily with how we _ought_ to think and\n only in a secondary way with how we actually think.\u201d Explain this\n quotation.\n\n (3) Prove that there is no such thing as intuitive knowing.\n\n (4) Is there any difference between knowledge and thoughts?\n Illustrate.\n\n (5) Show by illustrations that the English language is ambiguous.\n\n (6) Prove by concrete illustration that this is the age of the\n survival of the thinker.\n\n (7) Which is the more harmful: falsehood mixed with truth or\n unadulterated falsehood? Give reasons.\n\n (8) Give a concrete example of incorrect thinking.\n\n (9) Show that wrong thinking leads to wrong doing.\n\n (10) To be worth while must every subject have a practical value?\n\n (11) \u201cThe 20th century virtue is a passion for truth.\u201d Prove the truth\n of this.\n\n\n\n\n CHAPTER 2.\n\n THOUGHT AND ITS OPERATION.\n\n\n=1. THE KNOWING MIND COMPARED WITH THE THINKING MIND.=\n\nIn the preceding chapter we were told that the mind may know in two\nways (1) by intuition and (2) by thinking. It is thus implied that\nthe knowing mind includes the thinking mind plus intuition. Thinking\nalways involves knowing, but knowing need not involve thinking, and\nwhen some logicians maintain that to know a thing one must think it,\nthere is danger of being misled. They mean by this that in order to\nknow anything in a permanent and highly serviceable way one must think\nit. All animals know, even such a stupid one as the oyster, and yet one\nwould hardly give an oyster credit for thinking. Only the higher orders\nof animal life think. Some argue that the power is confined exclusively\nto the human family. This opinion is debatable. If the claimant means\nby thinking, reasoning then his ground is well taken. But if he is\nwilling to give to thinking a broader content, then he has little\ndefense for his stand. However, attach as broad a meaning to thinking\nas the derivation of the word will permit and even then it is a\nnarrower term than knowing. Thinking plus intuition equals knowing,\nand in intuition there is probably no thinking.\n\n\n=2. KNOWING BY INTUITION.=\n\nIt has been affirmed that intuition is the process involved when the\nmind knows _instantly_.[2]\n\n\n ILLUSTRATIONS:\n\n(1) As I raise my eyes a figure comes to view. My mind knows\n_instantly_ that it is the figure three. (2) The ear catches\n_immediately_ a tune which is being sung in the room below. Without\ndeliberation the mind recognizes the tune as America. The mind may\nthus know by intuition through any one of the five senses. These are\nthe wires of connection between the outer world and the mind within\nand transmission over these wires may be instantaneous or intuitive.\nThis is not all. (3) My mind may center its attention on itself and\nmay recognize there a mental picture or image of a pet dog. Since\nthis activity is without any apparent deliberation the process must\nbe intuitive. To define intuitive knowledge as that which comes to the\nmind through the senses only is incorrect, as it leaves out altogether\nthe knowledge the mind may obtain of its own activity as in\nillustration \u201c(3).\u201d\n\nKnowledge is anything known. _Intuitive knowledge is knowledge which\ncomes to the mind immediately by direct observation._ The field for\nintuitive knowledge may be the external world or the internal world\nthough, of course, the former is the more common ground. It is here\nthat the mind by intuition secures the most of its raw material which,\nthrough the process of thinking, is worked over into a connected,\nunified system of lasting value.\n\nThe intuitions are the beginning and the basis of all knowledge, and\nknowledge gained by intuition is the basis of all thinking.\n\n\n=3. THE THINKING PROCESS.=\n\nIt is claimed that _think_ comes from the same root as _thick_. From\nthis one would conclude that the process of thinking is virtually a\nprocess of thickening. Surely as one thinks he enriches or thickens\nhis knowledge. As one thinks percepts into concepts and concepts into\njudgments he makes richer in meaning the various notions concerned.\nThinking is largely a matter of pressing many into one: of linking\ntogether the disconnected fragments of the conscious field.\n\n\n DEFINITION:\n\n_Thinking is the deliberative process of affirming or denying\nconnections._\n\nThe same idea may be expressed in a variety of ways as the following\nindicate.\n\n (1) \u201cThinking is the conscious adjustment of a means to an end in\n problematic situations.\u201d Miller.\n\n (2) \u201cTo think is to designate an object through a mark or attribute\n or what is the same thing, to determine a subject through a\n predicate.\u201d Bowen.\n\n (3) \u201cThought is the comprehension of a thing under a general notion\n or attribute.\u201d Wm. Hamilton.\n\n (4) \u201cTo think is to make clear through concepts the perceived\n objects.\u201d Dressler.\n\nIn the foregoing definitions it is implied that thinking is a\nconnecting or _thickening_ process. In all forms of thinking from the\nsimplest to the most complex the knowing mind hunts for some basis of\nconnection and having found it _thinks_ the relationship into a unified\nwhole.\n\nThe thinking process is the digestive process of the mind. Much as\nthe digestive organs assimilate the food stuff of the physical world,\nso the thinking organ assimilates the food stuff of the mental world.\n\n\n ILLUSTRATIONS OF THE THINKING PROCESS:\n\n(1) The child is unable to explain the meaning of \u201chocus-pocus\u201d as\nit occurs in the question, \u201cWhat hocus-pocus is this?\u201d The child mind\nis unable to establish any connection between the word and its real\nmeaning. In short, is unable to _think into it a meaning_; it therefore\nbecomes necessary for the teacher to establish some basis of connection\nand this he does by suggesting _nonsense_ as a _synonym_.\n\n(2) The teacher holds before the class an Egyptian house god and asks,\n\u201cWhat is it?\u201d After a moment of hesitation some child who has seen\npictures of \u201chis satanic majesty\u201d avers that the object is a \u201clittle\ndevil.\u201d Thus has a connection been established between the idol and\npictures of satan.\n\n(3) John is unable to solve the following problem as he can discern no\nconnection between the data given and the data required. Problem. 3/4\nof my salary is $900, what is my salary?\n\n Data. Given: 3/4 of salary = $900.\n Required: 4/4 of salary = ?\n\nIn order that John may _think_ a solution the teacher must lead him to\nsee some connection between 3/4 and 4/4. With this in mind the form of\nthe data is changed to\n\n Given: 3-fourths = $900\n Required: 4-fourths = ?\n\nor\n\n Given: 3 parts = $900\n Required: 4 parts = ?\n\nJohn now notes that 4 parts is 4/3 times 3 parts and consequently\nwrites 4/3 of $900, which is $1,200 as the answer. Or he may find the\nvalue of 1 part and then of 4 parts.\n\n\n=4. NOTIONS, INDIVIDUAL AND GENERAL.=\n\n_A notion is any product of the knowing mind\u2015\u2015anything which the mind\nnotes or becomes aware of._\n\nBut the mind knows in two ways, by intuition and by thinking. In\nconsequence the mind has two kinds of notions, those which are\nintuitive or _individual notions_ and those which originally result\nfrom thinking or _general notions_.\n\n_An individual notion is a notion of one thing. A general notion is a\nnotion of a class of things._\n\n_Note._ Here it is necessary to distinguish between a thing and an\nobject. _An object is a thing which occupies space_ such as a pencil\nor a book. \u201c_Thing_\u201d is, therefore, a broader term than \u201c_object_.\u201d\n\u201c_A thing is that which has individual existence._\u201d From the viewpoint\nof logic \u201cthing\u201d includes objects, qualities, relations, spiritual\nentities. Gravitation is a thing but not an object. A tree is both an\nobject and a thing.\n\n\n ILLUSTRATIONS OF NOTIONS.\n\nMy notion of the pencil with which I am writing is an individual\nnotion, but my notion of pencil as a _class name_ is general. My\nyellow dog, the honesty of Lincoln, Albert White, New York City, are\nindividual notions, while dog, honesty, man, city, are general notions.\n\nA sure way to determine whether the notion is individual or general\nis to attempt to divide it into its kinds. Only general notions may be\nsubdivided.\n\n\n=5. KNOWLEDGE AND IDEA AS RELATED TO THE NOTION.=\n\nKnowledge is anything known, while anything of which the mind becomes\naware is a notion. Notions are always bits of knowledge, but knowledge\nis not always a notion. Notions are mental products belonging to the\nmind which thinks them, while knowledge, though it must first be a\nmental product of someone\u2019s mind, may not necessarily be a product of\nyours or mine. Notions are always found in the mind, while knowledge\nmay be found in books, but not necessarily in some individual mind.\nKnowledge stands for everything _known_, the notion, for everything\n_noted_. The Egyptians may have possessed much knowledge of which we\nmay never become aware. Much of their _knowledge_ may never become\n_notions_ of the American people. A notion is an existing state of\nconsciousness. Said notion may be committed to paper, and then it\nmay give way to another notion. It now ceases to be your notion, but\nremains on the printed page, as a bit of knowledge.\n\n\u201cIdea,\u201d because of its ambiguity, really has no place in logic. The\nterm is frequently restricted to a _reproduced percept_. To illustrate:\nWhen the pencil is before me the mental product is a percept, but when\nthe pencil is withdrawn and I try to think of it, then have I an _idea_\nof \u201cpencil.\u201d Probably _idea_ is most commonly associated with _meaning_\nand _belief_. To illustrate: What is your _idea_ as to the meaning of\nhomogeny? or What are your _ideas_ on the tariff?\n\n\n=6. THE LOGIC OF THE PSYCHOLOGICAL TERMS INVOLVED IN THE NOTION.=\n\nConcerning the knowing mind the psychologist classifies its activities\nand their products as follows:\n\n _Activity_ _Product_\n (1) Presentative\n (1) Sensation Sensation\n (2) Perception Percept\n\n (2) Representative\n (1) Imagination } Image\n (2) Memory }\n\n (3) Thinking\n (1) Conception Concept\n (2) Judging Judgment\n (3) Reasoning Inference\n\nThe notion as _any_ product of the knowing mind includes the _six_\nproducts as indicated by the psychologist.\n\nThe individual notion which is intuitive includes the sensation,\npercept and image; the general notion which is a thought product stands\nfor the concept, judgment and inference. To put it mathematically\u2015\u2015\n\n { sensation } }\n Individual notion = { percept } = intuitive products }\n { image } } _notion_\n { concept } }\n General notion = { judgment } = thought products }\n { inference } }\n\nAs we shall have occasion frequently to refer to these psychological\nterms it may be well to define them.\n\n _Psychological Definition._ _Logical Definition._\n\n A sensation is the first and A sensation is a vague,\n simplest mental result of the unlocalized mental product of\n stimulation of an incarrying the knowing mind.\n nerve.\n\n A percept is a mental A percept is a consciously\n product which results from a localized group of sensations.\n consciousness of particular\n material things present to the\n sense.\n\n An image is a mental product An image is a reproduced\n which results from particular percept.\n material things not present to\n the sense.\n\n A concept is a representation A concept is a mental product\n in our minds answering to a arising from thinking many\n general name. notions into one class.\n\n A judgment is the result of A judgment is the mental\n asserting an agreement or product arising from conjoining\n disagreement between two ideas. or disjoining notions.\n\n An inference is a judgment An inference is a judgment\n derived from perceiving derived from antecedent\n relations between other judgments.\n judgments.\n\nIt is seen that the sensations furnish the raw material. Ignoring the\nfew exceptions we may then say that a percept is a made-over group of\nsensations; a concept a thought-made group of percepts; a judgment a\nthought-made group of concepts; an inference a judgment derived from\nother judgments.\n\n_Developed thinking_ is first found in the concept, and as we study the\nthought products, \u201cconcept,\u201d \u201cjudgment\u201d and \u201cinference,\u201d the truth is\nforced upon us that _thinking as a process aims to group the many into\none_. From many percepts is built the one concept, from two concepts\nis built the one judgment and from two judgments is built the one\ninference.[3]\n\nSpeaking figuratively, thinking is a matter of picking up the fragments\nalong the shore of consciousness and tying them into bundles.\n\n\n =7. THOUGHT IN THE SENSATION AND PERCEPT.=\n\n So far in this discussion it has been assumed that there is\n no thinking involved in the sensation or the percept. There\n are good authorities, however, who insist on dignifying the\n sensation, even with a crude form of thinking. To illustrate:\n One may be reading an interesting novel. The mind is being\n entertained and ignores the activities of the objective world,\n yet we cannot say that the mind is dead to the world outside.\n There is a dim consciousness of certain noises without. These\n unlocalized sounds are sensations; but how is the mind able to\n recognize them as sounds or noises? To interpret the noises is\n it not necessary for the mind to affirm a connection between\n them and some past mental experience? Is it possible for\n the mind to know anything without establishing some kind\n of connection between the outside occurrence and an inner\n situation? If this is granted then in sensation there must be\n implicit thinking.\n\n As the percept is a localized group of sensations then\n there must be involved in perception a more complex form of\n thinking, since in grouping sensations there is a recognition\n of connections.\n\n If there is thinking in the sensation which is the simplest and\n lowest form of the knowing-mind then thinking conditions all\n knowledge and really is the basic elemental cell of all knowing.\n\n On the other hand there are those who maintain that the\n sensation and percept are mere reflections of consciousness; the\n sensation being a reflected quality and the percept a reflected\n object. These mental situations come into being instantly\u2015\u2015there\n is no time for thought and we all know that thought requires\n time. (\u201cAs quick as thought\u201d is misleading, since light travels\n more rapidly by many times than the agencies of thought.)\n\n It will probably never be settled to the satisfaction of all\n just when thinking commences. The question is as difficult\n as some others which have never been solved. For example:\n Where does life commence? When does the plant merge into the\n animal? Which was first the egg or the hen? Does the objective\n world really exist or is it only a mental interpretation of\n vibrations? etc.\n\n Logically considered the question is immaterial. All will agree\n that developed thought is involved in the concept, judgment\n and inference, while, if it appears at all in the percept and\n sensation, it is more or less undeveloped and consequently lies\n quite without the province of the logical field.\n\n\n=8. EVOLUTION AND THE THINKING MIND.=\n\nSpeaking in general terms evolution is a development from a lower to\na higher state. Thus have come the various species of the vegetable\nand animal world. The lower orders of life are simple in structure and\nfunction. In the one-celled animate form a single organ performs all of\nthe work needed to maintain life and perpetuate the species. If these\nsimple life-forms are cut in two, life continues in the two parts as\nif nothing had happened. Aside from their simplicity there is little\nof interdependence of function and little of co-ordination of organs\nin the lowest life-forms. In short there is no division of labor; \u201ceach\ncell is a world unto itself.\u201d\n\nAn analogous development is seen in the thinking mind. The little\nchild thinks in _lumps_, and these lumps are only faultily linked\ntogether, but the adult thinks in terms of the _grains_ of the lump,\neach grain having its place, which it must occupy for the sake of all\nthe other grains as well as the entire lump. The child\u2019s thinking is\nvague, general and inaccurate, while the adult\u2019s thinking should be\ndefinite, specialized and accurate. Thinking in the lump means little\ndiscrimination and very faulty integration or unity, while thinking\nin terms of the grains means detailed discrimination and perfect\nintegration. To illustrate: The child sees a dog trotting along the\nside walk which, according to the suggestion of his mother, he learns\nto call \u201cbow-wow.\u201d Later he observes a cat and at once says \u201cbow-wow,\u201d\nbecause all that the child notes is that something with legs, ears\nand a tail is trotting along the side walk. Anything which fits these\ngeneral marks is a \u201cbow-wow.\u201d Similarly when a child first observes\na robin perched on a gate post he fails to distinguish between the\ntwo\u2015\u2015it is _all_ bird from the top of the robin\u2019s head to the bottom\nof the gate post.\n\nProgress in thinking is measured by progress in discrimination. The\nskilled thinker divides the large unit into very small units, compares\nthese with each other and then reunites them into a more perfect and\nunified whole. First there is an analysis and then a synthesis. Like a\nshuttle the power of thought works in and out; it goes in to separate,\nit comes out to unify.\n\nThere is another aspect in the analogy between the life of the\nphysical and mental worlds. Somewhere in the order of progress there is\na connecting link between the mineral and vegetable kingdoms, likewise\nbetween the vegetable and animal kingdoms. The sensation is as much\na state of feeling as an act of knowing and consequently is the\nconnecting link between the _feeling_ mind and the _knowing_ mind. If\nthe percept is the result of thinking as well as intuition then it may\nstand for the dividing line between the _knowing_[4] mind and the\n_thinking_ mind.\n\n\n =9. THE CONCEPT AS A THOUGHT PRODUCT.=\n\n _Conception is the process of thinking many notions into one\n class._ The product of such a process is called a concept.\n (1) The concept may stand for a group of concrete _general_\n notions\u2015\u2015as the concept _man_, which stands for the five general\n notions: Caucasian, Mongolian, Ethiopian, Malay and American\n Indian. (2) The concept may stand for a group of concrete\n _individual_ notions. For example, the same concept _man_\n represents all of the individual men of the world. (3) The\n concept may stand for a group of _abstract general_ notions. To\n wit: Virtue represents such general notions as honesty, justice,\n industry, purity, etc. (These are general notions because they\n admit of a subdivision into kinds. Industry, for instance,\n may be divided into two kinds: mental industry and physical\n industry.) (4) The concept may stand for a group of _abstract\n individual_ notions. To illustrate: Blueness stands for the\n various shades of blue, as sky blue, bird\u2019s egg blue, navy blue,\n etc.\n\n Thus does the concept stand for a group of all kinds of notions,\n individual and general, abstract and concrete.\n\n\n THE PROCESS OF CONCEPTION ILLUSTRATED.\n\n I see for the first time in my life a pencil. In other words I\n become conscious of a localized group of sensations\u2015\u2015this is a\n percept. I am told that the name of that which I see is _pencil_.\n I note that this particular pencil has a thread of black lead\n encased in a cylindrical strip of wood which is brown in color.\n A second object is presented which I recognize as a pencil\n though the shape is prismatic rather than cylindrical and the\n color green rather than brown. But I call it a pencil because\n it has a thread of black lead encased in a strip of wood. The\n notion which I now have in mind stands for two pencils and\n is therefore represented by a class name. As I observe other\n pencils of various shapes, made of wood and paper with threads\n of different colored lead, my notion of pencil broadens till\n finally it stands for all pencils. This is the process of\n conception according to the definition, namely: \u201cThe process of\n thinking many notions into one class.\u201d In this case the notions\n are individual.\n\n An examination of conception makes evident two distinct\n characteristics. First, I may be able to recognize each\n individual pencil because of the two common qualities, a\n thread of lead and an encasement of some kind. This process of\n the knowing mind whereby it recognizes and affirms connections\n is called thinking as we have already learned. Here is the\n _thinking_ aspect of conception. Second, as the instances of\n the observed objects are multiplied, my notion of pencil is\n _broadened_. It is a building process where many are cemented\n into one; like the blocks of a cement wall. Here we find the\n characteristic which enables us to call the process _conception_.\n This is the mark which distinguishes conception from all the\n other thought processes.\n\n\n =10. THE JUDGMENT AS A THOUGHT PRODUCT.=\n\n Judging is the process of conjoining and disjoining notions.\n The product of judging is the judgment and all judgments are\n expressed by means of propositions. A proposition consists of\n one subject and one predicate connected by some form of the verb\n _be_ or its equivalent.\n\n (1) A judgment may conjoin or disjoin two individual notions.\n To wit: Conjoined\u2015\u2015This pencil belongs to Albert White.\n Disjoined\u2015\u2015This pencil does not belong to Mary Smith.\n\n (2) A judgment may conjoin or disjoin two general notions.\n Conjoined\u2015\u2015Some men are virtuous.\n Disjoined\u2015\u2015Some men are not virtuous.\n\n (3) A judgment may conjoin or disjoin a general and an individual\n notion.\n Conjoined\u2015\u2015Abraham Lincoln was virtuous.\n Disjoined\u2015\u2015Edgar Allen Poe was not temperate.\n\n In order that the knowing mind may conjoin notions it must\n recognize some mark of similarity or connection. This is the\n _thinking_ aspect of the judgment. It is likewise to a certain\n degree the judging aspect as the latter is simply a matter of\n affirming or denying connections between notions. But thinking\n is a broader term than judging. There may be connections\n established between a name and a notion. For example in the case\n of the dog which the child sees trotting along the sidewalk and\n which the mother refers to as a \u201cbow-wow\u201d; the term \u201cbow-wow\u201d is\n not a percept and has no meaning independent of its association\n with the dog, hence it is not a notion, yet some connection has\n been made in the child\u2019s mind between \u201cbow-wow\u201d and his notion\n of dog. This is a simple form of thinking, but not of judging,\n as the latter affirms or denies connections between _notions_\n only.\n\n The fact that judging and thinking so closely resemble each\n other has given just cause for some logicians to designate\n judging as the most fundamental element in all thinking. \u201cThe\n simplest form of thinking,\u201d says Creighton, \u201cis judging.\u201d In\n order to think many notions into one class it is necessary to\n conjoin notions. To illustrate: The child who has a general\n notion of man sees for the first time a negro. If he recognizes\n the negro as a colored man he must conjoin his general notion of\n man with this individual notion. In short, a concept is built by\n means of a series of judgments. It may be said further that an\n inference is simply a _made-over judgment_. It is thus evident\n that judging appears in both the thought processes of conception\n and inference and, therefore, as a final conclusion it may be\n affirmed that judging, though perhaps not the simplest form of\n thinking, is the basic element of _developed_ thought.\n\n\n =11. INFERENCE AS A THOUGHT PRODUCT.=\n\n Reasoning is the process of deriving a new judgment from a\n consideration of other judgments. The product of any reasoning\n process may be called an inference, although, as will appear in\n a later chapter, inference is commonly used as indicating the\n process as well as the product.\n\n Often reasoning may assume a syllogistic form with the inference\n as its conclusion. A syllogism is an arrangement of three\n propositions using three different terms. The following are\n syllogisms:\n\n (1) All children should play.\n Mary is a child.\n Hence, Mary should play.\n\n (2) No teacher should judge hastily.\n You are a teacher.\n Hence, you should not judge hastily.\n\n In the second syllogism the inference, \u201cyou should not judge\n hastily,\u201d is derived from the other two judgments by merely\n eliminating the common term teacher and disjoining the remaining\n two terms. The inference is consequently a _new_ judgment.\n Therefore, reasoning is only a matter of judging carried to a\n more complex stage.\n\n To summarize\u2015\u2015_conception_ is largely a matter of conjoining\n a general notion with an individual notion, _judging_ of\n conjoining and disjoining all kinds of notions and _inference_\n of conjoining and disjoining judgments. All three processes\n go to form the larger process of thinking. _The concept, the\n judgment and the inference are products arising from conjoining\n and disjoining notions._\n\n\n=12. THINKING AND APPREHENSION.=\n\nSays Jevons: \u201cSimple apprehension is the act of the mind by which we\nmerely become aware of something, or have an idea or impression of\nit brought into the mind;\u201d while Hyslop states that \u201cThe process of\nknowledge which gives us percepts is apprehension.\u201d It is obvious that\nthe idea of the latter is that _apprehension_ yields individual notions\nonly, while Jevons, in citing the term _iron_ as an illustration of\nhis definition, would infer that the general notion is the product\nof _apprehension_. The term is strikingly ambiguous and will not be\nreferred to often in this treatise. If the student desires a definition\nthis will cover the concensus of opinion on the meaning of apprehension.\n_Apprehension is that process of the knowing mind which yields the\npercept and concept._ Some logicians give to the thinking mind the\nthree aspects of apprehension, judging and reasoning.\n\n\n=13. STAGES IN THINKING.=\n\nIn all thinking there are three steps or stages which may be termed\n_discrimination_, _comparison_, _integration_.\n\nIn the case of the two pencils held in the hand, it is noted that\none is longer than the other. Let us analyze the process which\nmade possible this conclusion. Step one\u2015\u2015Attention is given first\nto one pencil and then to the other. In each case the pencils are\ndistinguished from the hand and the other surrounding objects. This is\ndiscrimination. Step two\u2015\u2015The pencils are _compared_ in length. Step\nthree\u2015\u2015The two notions are united in the judgment, \u201cPencil number _one_\nis longer than pencil number _two_.\u201d This is integration.\n\nAnother illustration. The child is requested to solve this problem: If\n8 tons of hay cost $165, what will 16 tons cost?\n\n Statement: Given: 8 tons cost $165.\n Required: 16 tons cost?\n\nDiscrimination. The child notes that 8 tons cost $165 and at this rate\nhe is required to find the cost of 16 tons.\n\nComparison. The child perceives that 16 tons is twice 8 tons.\n\nIntegration. The child concludes that the cost of 16 tons will be twice\nthe cost of 8 tons or $330.\n\nWhen we think, we first tear to pieces that we may become acquainted\nwith every part. This may be called analysis. Then we put the related\npieces together again. This may be called synthesis. Before, however,\nthe parts are re-united a certain amount of comparison is necessary.\nThe three stages of thought might thus be denominated: (1) analysis,\n(2) comparison, (3) synthesis.\n\nAfter the synthesis or integration it is necessary to name the result,\nconsequently a fourth step is sometimes given, namely denomination.\n\n\n=14. OUTLINE.=\n\n THOUGHT AND ITS OPERATION.\n\n (1) The Knowing Mind Compared with the Thinking Mind.\n\n (2) Knowing by Intuition.\n\n (3) The Thinking Process.\n Defined.\n Other definitions.\n\n (4) Notions.\n Individual.\n General.\n Thing and object distinguished.\n\n (5) Knowledge and Idea as Related to the Notion.\n\n (6) The Logic of Psychological Terms Involved in the Notion.\n\n The sensation }\n The percept } Individual notions.\n The image }\n\n The concept }\n The judgment } General notions.\n The inference }\n\n Terms defined.\n\n (7) Thought and the Sensation and Percept.\n\n (8) Evolution and the Thinking Mind.\n\n (9) The Concept as a Thought Product.\n\n (10) The Judgment as a Thought Product.\n The simplest form of thinking.\n\n (11) Inference as a Thought Product.\n\n (12) Thinking and Apprehension.\n\n (13) Stages in Thinking.\n Discrimination.\n Comparison.\n Integration.\n (Denomination.)\n\n\n=15. SUMMARY.=\n\n(1) Knowing is a broader term than thinking as the former equals the\nlatter plus intuition.\n\n(2) Intuitive knowledge is that which comes to the mind immediately by\ndirect observation.\n\nAlthough intuitive knowledge comes to the mind without thought, yet\nsuch knowledge is _essential_ to all thinking. Intuitive knowledge is\nthe foundation upon which the thinking mind builds.\n\n(3) Thinking is the deliberative process of affirming and denying\nconnections. Thinking is a \u201cthickening process,\u201d the smaller units\nbeing pressed together to make a larger. Thinking is chiefly a matter\nof reducing plurality to unity.\n\n(4) A notion is any product of the knowing mind.\n\nAn individual notion is the notion of one thing.\n\nA general notion is a notion of a class of things.\n\nA thing includes objects, qualities, relations or any existing entity.\nA thing is that which has _individual existence_.\n\n(5) A bit of knowledge must have been a notion of some one\u2019s mind, but\nmay not necessarily be a notion of _your_ mind. Knowledge may be found\nin books, but a notion is a mental product found only in the mind. Idea\nis ambiguous, though its meaning is usually restricted to an image, a\nmeaning or a belief.\n\n(6) The products of the knowing mind are the sensation, the image,\npercept, concept, judgment, inference.\n\nThe sensation, image and percept are individual notions, while the\nconcept, judgment and inference are general notions.\n\nA sensation is a vague, unlocalized product of the knowing mind.\n\nA percept is a consciously localized group of sensations.\n\nAn image is a reproduced percept.\n\nA concept is a mental product arising from thinking many notions into\none class.\n\nA judgment is a mental product arising from conjoining and disjoining\nnotions.\n\nAn inference is a judgment derived from antecedent judgments.\n\nThe developed thought processes are the concept, the judgment and the\ninference.\n\n(7) Just where the simplest form of thinking appears in the various\nactivities of the knowing mind is still an undecided question. It is\nagreed that thinking in its developed and more complex form is found\nin conception, judging and reasoning.\n\n(8) Thinking evolves from the simple to the more complex, just as life\nhas evolved.\n\nThe child thinks in vague, indefinite wholes, while the adult thinks in\nclear, definite parts. The child discriminates very imperfectly while\nthe adult discriminates accurately.\n\nThe sensation seems to be the connecting link between the feeling mind\nand the knowing mind, while the percept links together the knowing mind\nand the thinking mind.\n\n(9) Conception is the process of thinking many notions into one class.\nThe product of such a process is a concept. The concept stands for\ngroups of all kinds of objects.\n\nConception has the two aspects of _affirming connections_ and of\n_building many into one_. The first is the thinking side of the process\nand the second is the mark which distinguishes conception from the\nother thought processes.\n\n(10) Judging is the process of conjoining or disjoining notions.\nJudgment is the product of judging.\n\nJudgments conjoin and disjoin all kinds of notions.\n\nJudging and thinking, though they closely resemble each other, are not\nsynonomous terms. Thinking is a broader term in that connections may be\nestablished between a notion and a name for that notion.\n\nJudging is the most fundamental of all thinking, as the concept is\nbuilt from a series of judgments and an inference is simply a made-over\njudgment.\n\n(11) Inference.\n\nReasoning is the process of deriving a new judgment from a\nconsideration of antecedent judgments. This derived judgment may be\ncalled an inference. Sometimes the term inference denotes the process\nof reasoning as well as the product.\n\nReasoning often takes the form of a syllogism.\n\nThe concept, the judgment and the inference are _products_ arising from\nconjoining and disjoining notions.\n\n(12) Some give to the thinking mind the three aspects, apprehension,\njudging and reasoning. Apprehension is another word for the two\nprocesses, perception and conception.\n\n(13) The three important stages in thinking are discrimination,\ncomparison, integration; or analysis, comparison and synthesis.\n\n\n=16. REVIEW QUESTIONS.=\n\n (1) Show the difference between the knowing mind and the thinking\n mind.\n\n (2) Describe the process known as intuition.\n\n (3) What is intuitive knowledge?\n\n (4) Is the assumption that _think_ comes from the same root as\n _thick_ a feasible one? Explain.\n\n (5) Define thinking in at least two ways.\n\n (6) \u201cInability to think is due to inability to note connections.\u201d\n Show this by making use of some problem in arithmetic.\n\n (7) Distinguish between individual and general notions.\n\n (8) Which is the broader term, object or thing? Explain.\n\n (9) What kind of notions only admit of subdivisions? Illustrate.\n\n (10) What is the difference between knowledge and notions? Explain.\n\n (11) Explain and illustrate the meaning of idea.\n\n (12) Classify the various activities of the knowing mind and define\n each.\n\n (13) Explain by definition and illustration the products of the\n knowing mind.\n\n (14) Relate the general notion to the psychological products of the\n knowing mind.\n\n (15) \u201cThe thinking mind is a unit.\u201d Explain fully.\n\n (16) Trace the analogy between the evolution of the physical world and\n the evolution of thought.\n\n (17) Show that the sensation and the percept may be regarded as\n connecting links between lower and higher states.\n\n (18) Define and illustrate conception.\n\n (19) Show that the concept stands for all kinds of notions.\n\n (20) Point out the thinking aspect of conception as distinguished from\n the activity which gives the process its name.\n\n (21) Define the judgment. Illustrate two kinds.\n\n (22) Show that the concept is built by means of a series of judgments.\n\n (23) Show that judging is the fundamental element in the thought\n products.\n\n (24) Define and illustrate reasoning.\n\n (25) Describe the syllogism.\n\n (26) Explain the use of apprehension.\n\n (27) What are the stages in thinking? Illustrate fully.\n\n (28) Show that thinking is a matter of analysis and synthesis.\n\n\n=17. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Give your argument in favor of the statement, \u201cDogs think, but do\n not reason.\u201d\n\n (2) Show by illustration that thinking would be impossible without\n intuition.\n\n (3) \u201cThinking is the conscious adjustment of a means to an end in\n problematic situations.\u201d Illustrate this.\n\n (4) The class is unable to solve the following problem: \u201cI sell\n my house for $12,000, which is a gain of 25% on the cost. Find\n the cost.\u201d What is the trouble? State the problem so that some\n connection is apparent.\n\n (5) \u201cTwo-thirds of my salary is $2,400. What is my salary?\u201d A child\n solves this by dividing $2,400 by two and multiplying this result\n by three. Illustrate a plan for establishing right connections.\n\n (6) May a judgment express a general notion? Illustrate.\n\n (7) Is a thought a thing? Illustrate.\n\n (8) Show the illogic of dividing notions into individual, general and\n abstract.\n\n (9) Show that goodness is a general notion.\n\n (10) Is the concept an idea? Explain.\n\n (11) Prove that a mental image is always an individual notion.\n\n (12) \u201cIn sensation is there implicit thinking?\u201d Argue both sides of\n the question.\n\n (13) Show that the concept, the judgment and the inference are\n products of the thinking mind.\n\n (14) Show by illustration where perception ceases and conception\n begins.\n\n (15) Is there actually any difference between thinking and judging?\n Illustrate.\n\n (16) \u201cReasoning is controlled thought.\u201d Explain.\n\n (17) Of the three stages in thinking which one most concerns the\n teacher? Illustrate.\n\n\n\n\n CHAPTER 3.\n\n THE PRIMARY LAWS OF THOUGHT.\n\n\n=1. TWO FUNDAMENTAL LAWS.=\n\nThe elemental form of evolved thought is the judgment. The laws\nor axioms of thought may, therefore, be discovered by studying the\njudgment.\n\nJudging is the process of conjoining and disjoining notions.\nWhen these notions are conjoined the judgment is affirmative; when\ndisjoined the judgment is negative. To illustrate: \u201cSome men are\nwise,\u201d is an affirmative judgment, while \u201cSome men are not wise,\u201d is\na negative judgment. All judgments are either affirmative or negative\nand this suggests that there may be but two fundamental laws or axioms\nunderlying judging or all forms of developed thinking. One law would\ncondition the affirmative judgment; the other the negative. Such is\nactually the case. The law which permits the affirmative judgment is\ncalled the _law of identity_, while the law which allows a negative\njudgment is known as the _law of contradiction_. There is a third law\ntermed the _law of excluded middle_, which is in reality a combination\nof the other two.\n\n\n=2. THE LAW OF IDENTITY.=\n\nIn general the law of identity implies a certain permanency throughout\nthe material world. That door is a door and always will be a door till\nthe conditions change. If it were not for this law, that everything is\npermanently identical with itself, it would be impossible to think at\nall. For example: Take away the notion of permanency from the door and\nthought becomes at once ridiculous. Suppose that while we are asserting\nthat the object is a door, it changes to a tree, and while we insist\nthat the object is now a tree, it changes to a cow, etc. We can readily\nsee that it would hardly be worth while to think at all.\n\nThe law of identity may be stated in three ways: (1) Whatever is, is;\n(2) Everything remains identical with itself; (3) The same is the same.\n\n\n ABSOLUTE IDENTITY\u2015\u2015COMPLETE AND INCOMPLETE.\n\nApplying the law of identity to the affirmative judgment expressed in\nthe form of a proposition, we find two kinds of identity, absolute and\nrelative. In the propositions, \u201cSocrates is Socrates,\u201d \u201cdogs are dogs,\u201d\n\u201chonesty is honesty,\u201d the subject is _absolutely_ identical with the\npredicate\u2015\u2015the same in form and meaning. If we were to illustrate the\nsubject and predicate by two circles they would be of the same size and\nshape, the one coinciding with the other point to point.\n\nThis kind of absolute identity which makes possible all truisms we\nmay term, for want of a better name, complete absolute identity. This\nwould imply that there is an incomplete absolute identity and such\nseems to be the case. Examining the definition, \u201cA man is a rational\nanimal,\u201d we observe that the notion _man_ has the same content or\nmeaning as the notion _rational animal_. In meaning, then, the two\nnotions are absolutely identical. The one includes just as many\nobjects or qualities as the other, and if we were to draw two circles\nrepresenting them, they would be of the same size. In form, in mode\nof expression, however, the notions differ and the circles, though\ncoinciding, would need to differ in form, the boundary of one might be\na solid line, the other a dotted. This we may call incomplete absolute\nidentity. All logical definitions illustrate identities of this kind.\n\n\n RELATIVE IDENTITY.\n\nRelative identity is best understood by thinking of it as _partial_\nidentity, just as we may think of absolute identity as _total_ identity.\nIn relative identity the _whole_ of one notion may be affirmed of a\n_part_ of another notion; or a _part_ of one notion may be affirmed\nof a _part_ of another notion. To illustrate: (1) All men are mortal;\n(2) Some men are wise. These and their like are made possible because\nof the law of relative identity. In the first proposition all of the\n\u201c_men_\u201d class is identical with a part of the \u201c_mortal_\u201d class. If\nwe were to represent this relation by circles, the \u201cmen\u201d circle would\nbe made smaller than the \u201cmortal\u201d circle and placed inside it, as in\nFig. 1.\n\n Illustration: Fig. 1.\n\nBe it remembered that circles are surfaces, and in Fig. 1 the men\ncircle is identical with that portion of the mortal circle which is\nimmediately underneath it.\n\nThe same relation may be indicated by a small pad being placed on top\nof a larger pad. Then the whole of the smaller pad could be thought\nof as being identical with that part of the larger pad which is\nimmediately underneath.\n\nIn the case of the second proposition a part of the \u201cmen\u201d class\nis identical with a portion of the \u201cwise\u201d class. The two circles\nindicating this relation must intersect each other so that a portion\nof each may be common ground, as in Fig. 2 where the shaded part\nrepresents the identity.\n\n Illustration: Fig. 2.\n\nThus we see that the law of identity underlies all affirmative\npropositions. Absolute identity making possible the truism and\ndefinition, and relative identity conditioning all the universal and\nparticular affirmative propositions which are neither truisms nor\ndefinitions.\n\nThe three forms may be symbolized as follows:\n\n (1) A is A\u2015\u2015Absolute complete\n\n (2) _A_ is A\u2015\u2015Absolute incomplete\n\n (3) A is B\u2015\u2015Relative.\n\nThe student will note that the \u201cA\u2019s\u201d of absolute incomplete differ in\nform.\n\n\n=3. LAW OF CONTRADICTION.=\n\nThe law of contradiction underlies all negative propositions. It is the\nmission of this law to tear down or to be destructive in nature; while\nthe law of identity builds up or is constructive in nature.\n\nThe law of contradiction may be stated in this way: It is impossible\nfor the same thing to be and not to be at the same time and in the same\nplace. Or better, _it is impossible for the same thing to be itself and\nits contradictory at the same time_. Bringing out a further aspect, no\nthing can have and not have the same attributes at the same time.\n\nThe little word _not_ bisects the universe. All the people in the world\nare either honest or not honest, virtuous or not virtuous. These are\ncontradictory statements and what is comprehended by the one cannot\nbe comprehended by the other at the same time, any more than a man can\nshake his head and nod his head at the same time.\n\nIf we assert the identity between two notions then we cannot in the\nsame breath deny their identity.\n\n\n ILLUSTRATIONS:\n\n (1) A red flower cannot be a red flower and not a red flower at\n the same time.\n\n (2) No man can be guilty and not guilty at the same time.\n\n (3) A boy cannot be working and not working at the same time.\n\nIf I assert that the flower is red, then I cannot affirm in the same\nbreath that the flower is not red.\n\n\n TWO USES OF NOT.\n\nThe word _not_ when used with the copula of a given proposition makes\nthat _proposition_ negative, as (1) \u201cSome men are not wise.\u201d But when\n_not_ is attached to the predicate by a hyphen, the _predicate_ is made\nnegative, not the proposition, as (2) \u201cSome men are not-wise.\u201d Here\nthe predicate _not-wise_ is negative, but the proposition in which it\nappears is affirmative. It is obvious that the proposition \u201cSome men\nare not wise\u201d illustrates the law of contradiction, since the _some\nmen_ referred to are contradicted of all which is wise. Whereas the\nproposition \u201cSome men are not-wise\u201d illustrates relative identity,\nsince the subject \u201csome men\u201d is affirmed of a part of the predicate\n\u201cnot-wise.\u201d The student may be led to see these relations by drawing\ncircles, the one to represent the subject, the other the predicate.\n(See page 141.)\n\n\n FURTHER ILLUSTRATIONS:\n\n Some teachers are wise }\n Some teachers are not-wise } Illustrate the law of identity.\n Some teachers are unwise }\n\n Some teachers are not wise }\n Some teachers are not not-wise } Illustrate the law of contradiction.\n Some teachers are not unwise }\n\nThe student must understand that a term and its contradictory destroy\neach other. If we affirm something of the one, then we must deny it\nof the other, or we undermine the integrity of both. If it is affirmed\nof teachers A, B and C that they are wise, then it must be denied that\nthey are not-wise.\n\n\n ILLUSTRATIONS:\n\n A, B and C are wise. } These are mutually\n A, B and C are not-wise. } destructive.\n\n A, B and C are wise. } These are not mutually destructive,\n A, B and C are not not-wise. } but virtually mean the same thing.\n\n\n SYMBOLIZATION OF THE LAW OF CONTRADICTION.\n\n A is not not-A. A is not B.\n (As A is always A it would or or\n be absurd to say that A is A is not not-B.\n not A.)\n\n\n CONTRADICTORY AND OPPOSITE TERMS.\n\nIt is easy to use opposite terms in a contradictory sense. This\nleads to serious error. \u201cNot-guilty\u201d is the _contradictory_ of\n\u201cguilty,\u201d while \u201cinnocent\u201d is the _opposite_ of \u201cguilty.\u201d We could\nhardly say that the water must either be cold or hot, as it might be\nwarm. \u201cNot-hot\u201d is the only term which contradicts \u201chot.\u201d The law of\ncontradiction has nothing to do with opposites.\n\nFurther, it is dangerous to regard words with the negative prefix as\nbeing contradictory of the affirmative form. For example: Valuable and\ninvaluable are not contradictory. There is likewise some doubt as to\nthe contradictory nature of such words as agreeable and disagreeable,\nthough we are sure that agreeable and not-agreeable contradict each\nother. To use the \u201cnot\u201d with a hyphen is safer than to depend upon some\nprefix which is supposed to mean \u201c_not_.\u201d\n\n\n ILLUSTRATIONS OF CONTRADICTORY AND OPPOSITE TERMS.\n\n _Opposite._ _Contradictory._\n \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n bad good bad not-bad\n soft hard soft not-soft\n cold hot cold not-cold\n rough smooth rough not-rough\n good evil good not-good\n warm cool warm not-warm\n weak strong weak not-weak\n\n\n=4. THE LAW OF EXCLUDED MIDDLE.=\n\nThe law of excluded middle may be considered as a combination of\nidentity and contradiction. Identity gives the proposition, \u201cJohn Doe\nis honest.\u201d Contradiction, \u201cJohn Doe is not honest.\u201d Combine the two\nusing _either_ and _or_ and we have the excluded middle proposition,\n\u201cEither John Doe is honest or he is not honest.\u201d\n\nExcluded middle explains itself. Of the two contradictory notions it\nmust be either the one or the other. There is no \u201cgo-between\u201d notion.\n\nThe law may be stated in many ways, as will be seen by the following:\n(1) Everything must either be or not be. (2) Either a given judgment\nis true or its contradictory is true; there is no middle ground. (3) Of\ntwo contradictory judgments one must be true. (4) Every predicate may\nbe affirmed or denied of every subject.\n\n\n ILLUSTRATIONS:\n\n(1) A man is either mortal or he is not mortal. (2) John Doe is either\nhonest or not-honest. (3) Either you are going or you are not going.\n\n\n SYMBOLIZATION OF EXCLUDED MIDDLE.\n\n A is either A or not-A\n or\n A is either B or not-B.\n\n\n=5. THE LAW OF SUFFICIENT REASON.=\n\nThe law may be stated in this wise. Every phenomenon, event or\nrelation must have a sufficient reason for being what it is. To\nillustrate: (1) If Venus is the evening star, there must be a\nsufficient reason. (2) If the ground is wet, there must be a cause.\nMany logicians argue that this law has no place in logic, its\nfield being that of the physical sciences. The laws of identity,\ncontradiction and excluded middle are, however, universally regarded\nas the Primary Laws of thought.\n\n\n=6. UNITY OF PRIMARY LAWS OF THOUGHT ILLUSTRATED BY SYMBOLS.=\n\n (1) Absolute Symbols Relative Symbols.\n\n Excluded middle.\n A is either A or not-A. A is either B or not-B.\n\n Contradiction.\n A is not not-A. A is not B or A is not not-B.\n\n Identity.\n A is A. A is not-B or A is B.\n\n (2) Propositions made to fit symbols.\n\n Excluded middle.\n A man is either a man or A man is either honest or\n a not-man. not-honest.\n\n Contradiction.\n A man is not a not-man. A man is not honest, or a man\n is not not-honest.\n\n Identity.\n A man is a man. A man is not-honest, or a man\n is honest.\n\nThe \u201cexcluded middle\u201d propositions of the foregoing express\nalternatives which are mutually contradictory. There is no middle\nground. The \u201ccontradictory propositions\u201d contradict the identity of\nthe subject with one alternative, while the \u201cidentity\u201d propositions\naffirm the identity of the subject with the other alternative. This is\nmade possible because of the principle, \u201cOf two mutually contradictory\nterms, if one is true the other must be false.\u201d The foregoing scheme\nshows how closely \u201ccontradictory\u201d and \u201cidentity\u201d propositions are\nrelated to \u201cexcluded middle\u201d propositions. Expressed mathematically:\nexcluded middle = contradiction + identity.\n\n\n=7. OUTLINE.=\n\n PRIMARY LAWS OF THOUGHT.\n\n (1) Two fundamental laws.\n Identity, contradiction.\n\n (2) Law of identity.\n Absolute\u2015\u2015complete, incomplete.\n Relative.\n\n (3) Law of contradiction.\n Two uses of _not_.\n Contradictory and opposite terms.\n\n (4) Law of excluded middle.\n\n (5) Law of sufficient reason.\n\n (6) Unity of primary laws of thought.\n\n\n=8. SUMMARY.=\n\n(1) The elemental forms of evolved thought are the affirmative and\nnegative judgments. This suggests two fundamental laws of thought, the\nlaw of identity and the law of contradiction. The former conditions the\naffirmative judgment, the latter the negative.\n\n(2) The law of identity implies a permanency of being. \u201cEverything\nremains identical with itself,\u201d is a statement of identity.\n\nAbsolute identity may be divided into complete and incomplete identity.\n\nIn complete absolute identity the subject is the same as the predicate\nin both form and meaning. Truisms illustrate this.\n\nIn incomplete absolute identity the subject is identical with the\npredicate in meaning only. Illustrated by definitions.\n\nIn relative identity the whole of the subject may be affirmed of a part\nof the predicate or a part of the subject may be affirmed of a part of\nthe predicate.\n\n(3) \u201cIt is impossible for the same thing to be itself and its\ncontradictory at the same time,\u201d is a statement of the law of\ncontradiction. _Identity_ is _con_structive while _contradiction_\nis _de_structive in nature. To make the proposition negative the word\n_not_ must be used with the copula. \u201c_Not_\u201d attached to the predicate\nwith a hyphen makes the _predicate_ negative, but not the _proposition_.\n\nTo use opposite terms in a contradictory sense leads to serious error.\n\nThe safest way of making a positive term a contradictory negative term\nis to prefix \u201c_not_\u201d with a hyphen or use \u201cnon.\u201d\n\n(4) The law of excluded middle is virtually a combination of identity\nand contradiction. It may be stated as follows: \u201cA thing must either be\nitself or its contradictory.\u201d\n\n(5) \u201cEvery condition must have a sufficient reason for its existence,\u201d\nis the law of sufficient reason. Its distinct province is physical\nscience rather than logic.\n\n(6) The laws may be expressed mathematically: excluded middle =\nidentity + contradiction.\n\n SCHEMATIC STATEMENT OF PRIMARY LAWS.\n\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n \u2502 Name \u2502 Stated \u2502 Symbolized \u2502 Illustrated \u2502\n \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n \u2502 Absolute \u2502 Whatever is, is \u2502 A is A \u2502 Work is work \u2502\n \u2502 identity \u2502 \u2502 \u2502 \u2502\n \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n \u2502 Relative \u2502 The whole is \u2502 All A is B \u2502 Work is a blessing \u2502\n \u2502 identity \u2502 identical with \u2502 Some A is B \u2502 Some play is a \u2502\n \u2502 \u2502 a part or a part \u2502 \u2502 blessing \u2502\n \u2502 \u2502 is identical \u2502 \u2502 \u2502\n \u2502 \u2502 with a part \u2502 \u2502 \u2502\n \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n \u2502 Contra- \u2502 Nothing can both \u2502 A is not not-A \u2502 Work is not \u2502\n \u2502 diction \u2502 be and not be at \u2502 or \u2502 not-work \u2502\n \u2502 \u2502 the same time \u2502 A is not B \u2502 John is not honest \u2502\n \u2502 \u2502 \u2502 or \u2502 Albert is not \u2502\n \u2502 \u2502 \u2502 A is not not-B \u2502 not-honest \u2502\n \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n \u2502 Excluded \u2502 Everything must \u2502 A is either A \u2502 Fair play is \u2502\n \u2502 middle \u2502 either be or not \u2502 or not-A \u2502 either fair play \u2502\n \u2502 \u2502 be \u2502 or \u2502 or not-fair play \u2502\n \u2502 \u2502 \u2502 A is either B \u2502 This man is either \u2502\n \u2502 \u2502 \u2502 or not-B \u2502 educated or \u2502\n \u2502 \u2502 \u2502 \u2502 not-educated \u2502\n \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n\n\n=9. ILLUSTRATIVE EXERCISES.=\n\n(1a) Each of the following propositions is made possible because of the\nexistence of which law of thought?\n\nIn answering this question I summarize in my mind the meaning of each\nlaw of thought. Viz.:\n\n (1) In complete absolute identity the subject and predicate are\n the same in form and meaning.\n\n (2) In incomplete absolute identity the subject and predicate\n are the same in meaning, but not in form.\n\n (3) In relative identity either the whole or a part of the\n subject is identical with a part of the predicate.\n\n (4) The law of contradiction always denies the identity between\n subject and predicate.\n\n (5) Excluded middle conditions all alternative expressions.\n\n\n THE PROPOSITIONS.\n\n (1) \u201cA thief is a thief.\u201d Complete absolute identity.\n\n (2) \u201cThinking is the process of affirming or denying connections.\u201d\n Incomplete absolute identity.\n\n (3) \u201cAll good men are wise.\u201d Relative identity.\n\n (4) \u201cNo triangle has interior angles whose sum is greater than\n two right angles.\u201d Contradiction.\n\n (5) \u201cA stitch in time saves nine.\u201d Relative identity.\n\n (6) \u201cJudging is the process of conjoining and disjoining notions.\u201d\n Incomplete absolute identity.\n\n (7) \u201cYou are either a voter in this district or you are not a\n voter in this district.\u201d Excluded middle.\n\n (8) \u201cSome people do not know how to live.\u201d Contradiction.\n\n (9) \u201cAll is well that ends well.\u201d Incomplete absolute identity.\n\n (10) \u201cSome men teach school.\u201d Relative identity.\n\n (11) \u201cNone of the planets are as large as the sun.\u201d Contradictory.\n\n (12) \u201cAll the trees in this grove are maple.\u201d Relative identity.\n\n(1b) Indicate the law which conditions each of the following\npropositions:\n\n (1) \u201cHe who laughs last laughs best.\u201d\n\n (2) \u201cPerfect is perfect.\u201d\n\n (3) \u201cHe is a wolf in sheep\u2019s clothing.\u201d\n\n (4) \u201cEither your memory is poor or you are telling a deliberate\n falsehood.\u201d\n\n (5) \u201cSome of our greatest teachers thought they were failures.\u201d\n\n (6) \u201cNo man of sense would ever try to get something for nothing.\u201d\n\n (7) \u201cFailure is _not to try_.\u201d\n\n (8) \u201cSuccess is the right man in the right place doing his best.\u201d\n\n (9) \u201cEvery man is insane on some topic.\u201d\n\n (10) \u201cSome pupils are not industrious.\u201d\n\n (11) \u201cYou are either a genius or a successful fakir.\u201d\n\n (12) \u201cHonesty is the best policy.\u201d\n\n\n=10. REVIEW QUESTIONS.=\n\n (1) How many kinds of judgments are there? Illustrate.\n\n (2) Name the fundamental laws of thought and explain how they are\n related to the kinds of judgments.\n\n (3) Show that it would be impossible to think at all were it not for\n the law of identity.\n\n (4) State the law of identity in three ways.\n\n (5) Explain the kinds of absolute identity. Illustrate by\n propositions and by circles.\n\n (6) Explain by word and by diagrammatical illustration relative\n identity.\n\n (7) Symbolize the three forms of identity. Fit words to these\n symbols.\n\n (8) State in three ways the law of contradiction.\n\n (9) Show by illustration that _not_ bisects the world.\n\n (10) Explain the uses of _not_.\n\n (11) Prove that \u201cJohn Doe is not-honest,\u201d illustrates identity and\n not contradiction.\n\n (12) Symbolize in three ways contradiction. Fit words to these\n symbols.\n\n (13) Illustrate contradictory and opposite terms.\n\n (14) Show that words with negative prefixes are not necessarily the\n contradictory of the corresponding affirmative forms.\n\n (15) State and explain the law of excluded middle.\n\n (16) Symbolize the law of excluded middle.\n\n (17) State the law of sufficient reason. Illustrate.\n\n (18) Illustrate the unity of the three primary laws of thought.\n\n\n=11. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Prove that the judgment is the elemental form of evolved thought.\n\n (2) What is meant by evolved thought?\n\n (3) Show that \u201cWhatever is, is\u201d is a statement of complete absolute\n identity only.\n\n (4) State incomplete absolute identity.\n\n (5) By means of _one_ proposition state relative identity.\n\n (6) Show that incomplete absolute identity is a term more or less\n illogical.\n\n (7) Show that these statements are exact expressions of relative\n identity:\n All men are some wise.\n Some men are some wise.\n\n (8) Why is the law of contradiction so named?\n\n (9) Show that space may be bisected by drawing a circle upon the\n black board.\n\n (10) Show that there is a difference in meaning between \u201cYou are not\n honest\u201d and \u201cYou are not-honest.\u201d\n\n (11) Is there any difference in meaning between disagreeable and not\n agreeable?\n\n (12) Which is the stronger term not-just or unjust? Why?\n\n (13) Give a list of words in which the contradictory forms are\n expressed by the ordinary prefixes.\n\n (14) Illustrate by circles the law of excluded middle.\n\n (15) Illustrate by a line-diagram the difference between contradictory\n and opposite terms.\n\n (16) Show that the province of the law of sufficient reason is\n physical science.\n\n\n\n\n CHAPTER 4.\n\n LOGICAL TERMS.\n\n\n=1. LOGICAL THOUGHT AND LANGUAGE INSEPARABLE.=\n\nAny impression upon the mind tends to manifest itself in some form of\nexpression. Impression which arouses thought tends to expression in the\nform of symbols. Thought and symbol go hand in hand. Expression, taking\nthe form of word-symbols, constitutes a word-language.\n\nIt is commonly supposed that language is serviceable mainly in\ncommunicating one\u2019s thoughts to others, but language does service\nin another way which is quite as important. It tends to clarify and\nmake definite all thought. Without a word-language thinking would\nlack continuity; would be vague, loose, illogical. The right use of a\nword-language, therefore, is a necessary adjunct to logical thought.\nThe basic element of a word-language is the logical term.\n\n\n=2. MEANING OF LOGICAL TERM.=\n\nA notion has been referred to as any product of the knowing mind.\nWhen we express these notions in words such expressions may be called\nlogical terms.\n\nDefinition. _A logical term is a word or a group of words denoting\na definite notion._ Illustrations: Honesty, Chicago, tree, walking,\nthe man who was ill, beautiful roses. This is a list of logical terms,\nbecause each word or group of words denotes a _notion_ of some kind.\nIt is now evident that any subject or predicate with its modifiers\nconstitutes a logical term. In the proposition, \u201cThe beautiful red\nhouse on the hill, owned by Mr. Jones, has burned,\u201d the term used\nas the subject consists of eleven words. The reader must not confuse\nlogical terms with grammatical parts of speech. \u201cOf\u201d is a preposition\nbut not a logical term, as no definite notion is indicated.\n\n\n=3. CATEGOREMATIC AND SYNCATEGOREMATIC WORDS.=\n\nThere are some words which, when used alone, denote definite notions,\nsuch as man, tree, dog, justice. On the other hand there are other\nwords which, when used alone, do not stand for a definite notion, such\nas up, beautifully, a, and.\n\nWords like those in the first list are called categorematic words,\nwhile those in the second list illustrate syncategorematic words.\n\n\n DEFINITION.\n\n_A categorematic word is one which forms a logical term unaided by\nother words. A syncategorematic word is one which must be used with\nother words to form a logical term._\n\nAny word or group of words which can be used as either subject or\npredicate of a proposition is a logical term. If the _one_ word in\nquestion can be used as either subject or predicate of a proposition\nthen it must be a categorematic word. If it is impossible to use the\none word as either subject or predicate of a proposition then this is\na sure indication that such a word is syncategorematic. For example,\nthere is no sense in the expressions, \u201c_And_ is honest,\u201d \u201c_Of_ is not\ntrue\u201d; hence _and_ and _of_ are syncategorematic.\n\nWe may conclude from this that nouns, descriptive adjectives and\nverbs may be categorematic words, while adverbs, prepositions and\nconjunctions are syncategorematic words.\n\n\n=4. SINGULAR TERMS.=\n\n_A singular term is a term which denotes one object or one attribute._\n\nProper nouns, when they stand for individuals, are singular terms, such\nas John Adams, Mississippi River, Socrates. Some proper names stand for\na class of objects, as the Caesars, the Mephistopheles, the Napoleons.\nBut when thus used they lose their character as proper names. Such\nnames, therefore, are general terms, not singular.\n\nCommon nouns may be made singular by some modifying word, as the first\nman, the pole star, the highest good, my pet dog, etc.\n\nCertain attributes which imply a _oneness_ or a distinct individuality\nare singular, such as absolute justice, birds-egg blue, perfect\nhappiness, etc.\n\nSome claim that terms like water, air, salt, etc., are singular, as\nthey stand for one thing. This, however, cannot be if such terms admit\nthe possibility of classification as: hard water, soft water, mineral\nwater.\n\n\n=5. GENERAL TERMS.=\n\n_A general term is one which denotes an indefinite number of objects or\nattributes._\n\nClass-names are general terms, such as men, chair, tree, army, nation.\nWords like redness, sweetness, justice, are probably general in that\nthey denote a combination of qualities or may be subdivided into kinds.\n\nThe way the term is employed in the proposition should determine its\nsingular or general nature.\n\n\n=6. COLLECTIVE AND DISTRIBUTIVE TERMS.=\n\n_A collective term is a general term which indicates an indefinite\nnumber of objects as one whole._ Such words as class, crowd, army,\nforest, nation, are collective.\n\n_A distributive term is a general term which indicates an indefinite\nnumber of objects as a whole, and also may be used to refer to each one\nof the group separately._ Such as man, pupil, tree, book.\n\nIt is easy to distinguish collective from distributive terms when we\nattempt to use them in the designation of individuals. Pointing to\na body of troops, one may remark, \u201cThere is the regiment.\u201d But when\npointing to _one man_ in the regiment, he could hardly say, \u201cThere is\nthe regiment.\u201d \u201cRegiment\u201d is therefore collective because it may be\nused with reference to the whole body of troops but cannot be used in\nconnection with any individual of that body. On the other hand in the\nsentence, \u201cMan is mortal,\u201d \u201cman\u201d refers to the whole family of men. It\nalso indicates any one of them. As, \u201cThis man, John Doe, is mortal.\u201d\nThus \u201cman\u201d is distributive. The distributive term, therefore, can be\nused in a two-fold sense; namely, to denote the whole or to denote each.\n\nIt must be noted that, viewed from a different standpoint, some\ncollective terms become distributive in nature. As for example in the\nproposition, \u201cThe army of the world is composed of able bodied men,\u201d\n_army_ is used with reference to all armies. While it may be used to\ndesignate some particular army, as The American army.\n\nCollective terms have been classified as general terms. It must\nbe borne in mind, however, that such may be made singular by some\nmodifying word. For example, _people_ is a general term, but _American\npeople_ is a singular term in that it refers to one people, being thus\nlimited by the word American.\n\n\n=7. CONCRETE AND ABSTRACT TERMS.=\n\n_A concrete term is a term which denotes a thing_; e. g., this man,\nthat tree, John Doe, denote in each case a thing. Man and tree, denote\nmany things. All are concrete.\n\n_An abstract term is a term which denotes an attribute of a thing_;\ne. g., whiteness, patience, squareness, are abstract terms.\n\nSuch words as red, honest, just, are concrete; while redness, honesty,\njustice, are abstract.\n\nOn first thought it might be inferred that \u201cred\u201d is the name of\nan attribute just as much as \u201credness.\u201d This is a mistaken thought,\nhowever, as when we use the word red we mean red something\u2015\u2015an _object_\nwhich is red in color, not the color itself. For example, in saying\nthe house is red, we refer to the thing that is red, not to the color\nredness.\n\nDescriptive adjectives, because they describe things, are concrete.\nThey do not alone name qualities of things, hence they are not abstract.\n\n\n=8. CONNOTATIVE AND NON-CONNOTATIVE TERMS.=\n\n_A connotative term is one which denotes a subject and at the same\ntime implies an attribute._ (A subject is anything which possesses\nattributes.)\n\nAll concrete general terms are connotative because they denote subjects\nand at the same time stand for certain attributes; e. g., \u201cman\u201d denotes\nmany subjects; in fact, it stands for all the men in the world; it also\nimplies rationality, the power of speech, power of locomotion, etc.\n\u201cTriangle\u201d stands for all plane figures of three sides; it likewise\nstands for the qualities, three-sided, three-cornered, etc. Both \u201cman\u201d\nand \u201ctriangle\u201d are connotative.\n\n_A non-connotative term is one which denotes a subject only, or implies\nan attribute only._ Such words as Boston, Columbus, The Elizabeth\nWhite, denote a subject only. \u201cBlueness,\u201d \u201cjustice,\u201d \u201cwidth,\u201d imply an\nattribute only. All these terms are non-connotative. The words blue,\njust, wide, are connotative. \u201cBlue,\u201d for example, denotes all blue\nthings, as the blue sky, the blue sea; at the same time \u201cblue\u201d implies\nthat something possesses the quality, _blueness_.\n\nGenerally speaking, proper and abstract nouns are non-connotative;\nthough such proper nouns as Mount Washington, Mississippi River, are,\nno doubt, connotative, as they denote an object and imply at least one\nattribute. In the case of Mount Washington an object is surely denoted,\nand the attribute mountainous is implied. Any proper noun which conveys\ndefinite information is connotative. It may be claimed that all proper\nnouns give information. For example, to many _Boston_ indicates not\nonly an object, but the qualities common to a city. In reply it may\nbe said that \u201cBoston\u201d might indicate a boat, or a dog, or almost any\nindividual object.\n\n\n=9. POSITIVE AND NEGATIVE TERMS.=\n\n_A positive term is one which signifies the possession of certain\nattributes_; e. g., metal, man, teacher, happy, honest.\n\n_A negative term is one which signifies the absence of certain\nattributes_; e. g., inorganic, unhappy, non-metallic.\n\nTerms which have the prefix not, non, un, in, dis, etc., or the affix\nless, are usually considered negative. The fact that there are some\nexceptions to this must not be overlooked. For example, unloosed,\ninvaluable, are positive terms.\n\nIn theory every positive term has its corresponding negative; as pure,\nimpure; organic, inorganic; metal, non-metal; good, not-good.\n\nIn some instances the language does not supply the word with the\nnegative prefix because no need of it has been felt. The only way to\nexpress the negative of such words as good, table, etc., is to prefix\n\u201cnot\u201d or \u201cnon.\u201d\n\n\n=10. CONTRADICTORY AND OPPOSITE TERMS. (See page 38).=\n\nPositive terms with their negatives have contradictory meanings and\ntherefore are referred to as contradictory terms. For example, honest\nand not-honest, metallic and non-metallic, perfect and imperfect,\nare contradictory terms. Such terms are mutually destructive. When we\nassert the truth of one we also imply the falsity of the other. If, for\nexample, we assert that Abraham Lincoln was honest, we carry with this\nassertion the implication that Lincoln was not not-honest, or that any\nstatement to the effect that he was not honest is false.\n\nContradictory terms, when used in a sentence, illustrate the law of\nexcluded middle, as in the statements: \u201cJohn\u2019s recitation is either\nperfect or imperfect.\u201d \u201cThis teacher is either just or not-just.\u201d\nThere is no middle ground in such propositions.\n\nWhen contradictory terms are used in classification the whole is\ndivided into but two classes; e. g.:\n\n honest not-honest\n agreeable not-agreeable\n metallic non-metallic\n perfect imperfect\n pure impure\n organic inorganic\n\nAll the men in the world are either honest or not-honest. All the\nsubstances in existence are either organic or inorganic, etc.\n\nIt will also be seen from this list that the contradictory of the\npositive form is not always indicated by using the prefix. Honest\nand dishonest, or agreeable and disagreeable, are not contradictory\nterms. In the case of agreeable and disagreeable, there seems to be\nthe middle ground of absolute indifference. For example: the music of\nthe orchestra is agreeable while the humming of the enthusiast back\nof me is decidedly disagreeable; but as to the noise upon the street,\nit is neither agreeable nor disagreeable as long practice has made me\nindifferent to it.\n\nWhen there is any doubt as to the terms being contradictory, the safest\nplan is to prefix \u201cnot\u201d or \u201cnon\u201d to the positive form.\n\nTerms which oppose each other but do not contradict are said to be\nopposite or contrary terms. The following list illustrate opposite\nterms:\n\n hot cold\n cool warm\n less greater\n wise foolish\n bitter sweet\n soft hard\n tall short\n agreeable disagreeable\n\nAll these terms admit of a medium. In the case of hot or cold, for\nexample, a substance need not necessarily be either. It may be warm or\ncool.\n\nTerms seem to be contradictory when it is a matter of quality, but\nopposite when it is a question of quantity or degree.\n\n\n=11. PRIVATIVE AND NEGO-POSITIVE TERMS.=\n\n_A privative term is one which is positive in form but negative in\nmeaning._ Such words as blind, deaf, dumb, dead, maimed, orphaned, are\nprivative terms, in that there is no negative prefix or suffix and yet\nthey denote the absence of certain qualities. \u201cBlind,\u201d for example, is\npositive in form, but denotes absence of sight.\n\n_A nego-positive term is one which is negative in form but positive\nin meaning._ Such terms as invaluable, unloosed, immoral, indwell, are\nnego-positive because, though they have negative prefixes, yet they\npossess a certain positive meaning. \u201cInvaluable,\u201d for instance, does\nnot mean not-valuable, but very valuable.\n\n\n=12. ABSOLUTE AND RELATIVE TERMS.=\n\n_An absolute term is one whose meaning becomes intelligible without\nreference to other terms._ Automobile, water, tree, house, book, are\nabsolute terms. Any of them may be made clear to a child or a foreigner\nwithout special reference to other terms. For example, the child will\nrecognize from certain common marks the automobile every time he sees\nit. The marks of tree, house, flower, are apparent to every one.\n\n_A relative term is one which derives its meaning from its relation\nto some other term._ Parent, teacher, shepherd, monarch, eldest, cause,\ncommander, are relative terms. For example, in explaining the meaning\nof \u201c_parent_\u201d to a foreigner, reference must be made to \u201c_child_.\u201d\nThe pairs of terms thus associated are spoken of as correlatives.\nParent and child, teacher and pupil, shepherd and flock, monarch and\nsubject, eldest and youngest, cause and effect, commander and army,\nare correlative terms. Either one of each pair is the correlate to the\nother, and every relative term needs its correlate to make its meaning\nclear. To say that a relative term denotes an object which cannot be\nthought of without reference to some other object, is confusing, as it\nis quite impossible to think of any object without calling to mind some\nother object or notion. Fire calls to mind water; tree suggests shade,\netc.\n\n\n=13. OUTLINE.=\n\n LOGICAL TERMS.\n\n (1) Meaning of term.\n\n (2) Categorematic and syncategorematic words.\n\n (3) Kinds of terms.\n Singular terms.\n General terms.\n (a) Collective terms.\n (b) Distributive terms.\n Concrete and abstract terms.\n Connotative and non-connotative terms.\n Positive and negative terms.\n Contradictory and opposite terms.\n Privative and nego-positive terms.\n Absolute and relative terms.\n\n\n=14. SUMMARY.=\n\nA logical term is a word or group of words denoting a definite notion.\n\nA singular term is a term which denotes one object or one attribute.\n\nA general term is a term which denotes an indefinite number of objects\nor attributes.\n\nGeneral terms are collective or distributive.\n\nA collective term is a general term which indicates an indefinite\nnumber of objects considered as _one whole_.\n\nA distributive term is a general term which indicates an indefinite\nnumber of objects as a whole and also may be used to refer to each one\nof the group separately.\n\nA concrete term is a term which denotes a thing.\n\nAn abstract term is a term which denotes the attribute of a thing.\n\nA connotative term is one which denotes a subject and at the same time\nimplies an attribute.\n\nA non-connotative term is one which denotes a subject only or implies\nan attribute only.\n\nA positive term is one which signifies the possession of certain\nattributes.\n\nA negative term is one which signifies the absence of certain\nattributes.\n\nIn theory every positive term has its negative. As related to each\nother positive and negative terms are said to be contradictory. If\none denotes a true notion then the other denotes a false notion.\n\nSome terms oppose each other but do not flatly contradict. As related\nto each other such terms are said to be opposite.\n\nA privative term is one which is positive in form but negative in\nmeaning.\n\nA nego-positive term is one which is negative in form but positive in\nmeaning.\n\nAn absolute term is one whose meaning becomes intelligible without\nreference to other terms.\n\nA relative term is one which derives its meaning from its relation to\nsome other term.\n\n\n=15. ILLUSTRATIVE EXERCISES.=\n\n(1a) The words in italics are categorematic.\n\n (1) \u201c_Honesty_ is the _best policy._\u201d\n\n (2) \u201c_A wise teacher_ never _scolds._\u201d\n\n (3) \u201cThe _woodcock_ has a _long bill_ and _eyes high_ up on the\n _head._\u201d\n\nNOTE\u2015\u2015If there is any doubt as to such words as never, on, etc., being\nsyncategorematic, attempt to use them as subject or predicate of a\nproposition; e. g., John is _never_.\n\n(1b) Underscore the categorematic words in the following:\n\n (1) \u201cSocrates was the greatest teacher of pagan times.\u201d\n\n (2) \u201cPlay is nature\u2019s way of teaching a child how to work.\u201d\n\n (3) \u201cA man may be what he chooses if he is willing to pay the price.\u201d\n\n(2a) In the following, words enclosed in parentheses are logical terms:\n\n (1) (\u201cAll men) are (mortal.\u201d)\n\n (2) (\u201cThe law of identity) is (one of the primary laws of thought.\u201d)\n\n (3) (\u201cJudging) is (the process of conjoining and disjoining\n notions.\u201d)\n\n(2b) Indicate the logical terms in the sentences under 1b.\n\n(3a) The logical characteristics of the term _teacher_ are\n\n (1) general term,\n\n (2) distributive term,\n\n (3) concrete term,\n\n (4) connotative term,\n\n (5) positive term,\n\n (6) relative term.\n\n(3b) The logical characteristics of other terms are as follows:\n\n (1) Goodness\u2015\u2015general, abstract, non-connotative, positive, abstract.\n\n (2) Soft\u2015\u2015general, concrete, non-connotative, positive, \u201chard\u201d is its\n opposite, \u201cnot-soft\u201d is its contradictory, absolute.\n\n (3) Disagreeable\u2015\u2015general, concrete, non-connotative, \u201cagreeable\u201d\n is its opposite, \u201cnot-disagreeable\u201d is its contradictory,\n nego-positive, absolute.\n\n (4) Aristotle\u2015\u2015singular, concrete, non-connotative, positive,\n absolute.\n\n (5) Class\u2015\u2015general, collective, concrete, connotative, positive,\n relative.\n\n(3c) Give the logical characteristics of the following terms: justice,\nAbraham Lincoln, tree, library, America, president, principle, sympathy,\ndumb, nation.\n\n\n=16. REVIEW QUESTIONS.=\n\n (1) What is the connection between logical thinking and language?\n\n (2) Why is _man_ a categorematic word?\n\n (3) Why is _beautifully_ syncategorematic?\n\n (4) Distinguish between singular and general terms.\n\n (5) Show how a collective term may be used in a distributive sense.\n\n (6) Why are the words _tree_ and _book_ distributive?\n\n (7) Distinguish between concrete and abstract terms.\n\n (8) Define and illustrate a non-connotative term.\n\n (9) Why are concrete general terms connotative?\n\n (10) Distinguish between positive and privative terms.\n\n (11) Why is not the word _immoral_ negative?\n\n (12) Give the opposite of \u201chot.\u201d What is the contradictory of \u201chot\u201d?\n\n (13) Distinguish by definition and illustration between relative and\n absolute terms.\n\n (14) What is the correlate of the word _effect_?\n\n\n=17. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Is it possible to think independent of language?\n\n (2) May words be spoken or written without thought? Illustrate.\n\n (3) Are categorematic words always logical terms?\n\n (4) Must all the words of a logical term be categorematic?\n\n (5) Are pronouns and auxiliary verbs categorematic?\n\n (6) Indicate the logical connection between the terms of a\n proposition and the termini of a railroad.\n\n (7) Show that attribute is a broader term than quality.\n\n (8) Is the word _Washington_ general or singular? Give reasons.\n\n (9) Make the word _dog_ a singular term.\n\n (10) Give an illustration where the word _class_ would not be\n collective.\n\n (11) \u201cAll the members of the baseball team are star players.\u201d\n How has the term _star players_ been used, collectively or\n distributively?\n\n (12) Why may the term _New York City_ be connotative to a New Yorker\n and non-connotative to a Patagonian?\n\n (13) So far as your present knowledge of the martyred president\n Abraham Lincoln is concerned, is the term _Abraham Lincoln_\n connotative or non-connotative?\n\n (14) Are non-connotative terms always singular? Illustrate.\n\n (15) Are singular terms always non-connotative?\n\n (16) What is the difference in meaning between immoral and unmoral,\n disagreeable and not-agreeable?\n\n (17) Why is immoral a nego-positive term while unmoral is negative?\n\n (18) What is the contradictory of the opposite of _wise_?\n\n (19) Show that there is some ground for believing all terms to be\n relative.\n\n (20) Is _army_ a relative term? If \u201carmy\u201d were used so as to be\n distributive in nature would it then be general or collective?\n\n (21) Why should the pronoun be ignored by the logician?\n\n (22) Show the difference between thing and subject.\n\n (23) Argue to the effect that no term can be non-connotative.\n\n\n\n\n CHAPTER 5.\n\n THE EXTENSION AND INTENSION OF TERMS.\n\n\n=1. TWO-FOLD FUNCTION OF CONNOTATIVE TERMS. (See page 52.)=\n\nIt has been indicated that a connotative term is one which possesses\nthe double function of signifying a subject as well as an attribute.\nIt may be observed here that an attribute of a notion is any mark,\nproperty or characteristic of that notion. Attribute, then, represents\nquality, relation or quantity. By a subject is meant anything which\npossesses attributes. Most subjects stand for objects and most\nattributes are qualities; consequently, for the sake of simplicity,\nwe may use subject and object interchangeably; likewise, attribute and\nquality.\n\nA connotative term, therefore, denotes an object at the same time\nit implies a quality. To illustrate: The symbol _man_ stands for the\nvarious individual men of the world, such as Lincoln, Washington,\nAlfred the Great, etc., or for certain qualities like rationality,\npower of speech and power of locomotion. The connotative term _teacher_\nmay be used to _denote_ Socrates, Pestalozzi, Thomas Arnold, or\n_connote_ such qualities as ability to instruct, sympathy, and\nscholarship. The term _planet_ stands for such objects as Venus, Earth,\nand Mars, and for such qualities as rotation upon axis, revolution\nabout sun, and opaque or semi-opaque bodies. In each of the three\nillustrations the term is employed in the two-fold sense of denoting\nobjects and of implying qualities.\n\n\n=2. EXTENSION AND INTENSION DEFINED.=\n\nThis double function of connotative terms furnishes an important\ntopic for the student of logic\u2015\u2015the Extension and Intension of Terms.\nIn short, some authorities claim that to master the extension and\nintension of terms is virtually to master the entire subject of\nlogic. Though this position may be an exaggerated one, yet it tends\nto emphasize the importance of the topic.\n\n_A term is used in extension when it is employed with reference to the\nobjects for which the term stands._\n\nWhen the term triangle is used to refer to the objects isosceles\ntriangle, scalene triangle, right triangle, it is employed in extension.\n\n_A term is used in intension when it is employed with reference to the\nattributes for which the term stands._\n\nThe term triangle is employed in intension when we use it to refer to\nthe qualities, three sided and three angled.\n\n\n=3. EXTENDED COMPARISON OF EXTENSION AND INTENSION.=\n\nA connotative term seems to be two dimensional\u2015\u2015it has extent or length\nand intent or depth.\n\n\u201cExtension consists of the things to which the term _ap_plies,\u201d while\n\u201cintension consists of the properties which the term _im_plies.\u201d\n\nExtension is quantitative, while intension is qualitative. An\nextensional use means to point out or number objects, while an\nintensional use means to describe by naming qualities. To name is to\nuse a term in extension\u2015\u2015to describe is to use a term in intension.\n\nTo divide a term into its kinds we must regard it in an extensional\nsense; e. g., the term _man_ may be divided into Caucasian, Mongolian,\nMalay, Ethiopian, American Indian.\n\nTo define a term we must regard it in an intensional sense; e. g., man\nis a rational animal.\n\nEtymologically considered extension means to _stretch out_, intension,\nto _stretch within_. To use a term extensionally one must _look out_.\nTo use a term intensionally one must _look in_.\n\nIn attempting to use a term in extension we may ask ourselves the\nquestion, \u201cWhat are the kinds?\u201d or \u201cTo what objects may the term be\napplied?\u201d While if we would use a term in intension the question should\nbe, \u201cWhat does it mean?\u201d or \u201cWhat are the qualities?\u201d Let us, for\nexample, use the term _metal_ in the two senses, first in extension,\nsecond in intension. Question: To what _objects_ may the term _metal_\nbe applied? Answer: Metal may be applied to the objects silver, gold\nand iron. Thus has metal been employed in extension.\n\nQuestion: What are the _qualities_ of _metal_? Answer: The qualities\nare element, metallic lustre, good conductor of heat and electricity.\nThus has metal been used in _intension_.\n\nNOTE. Since an attribute is anything which _belongs_ to a subject, then\nthe _parts_ of a subject must be classed as attributes. Hence, a term\nis used intensionally when reference is made to its parts.\n\n\n=4. A LIST OF CONNOTATIVE TERMS USED IN EXTENSION AND INTENSION.=\n\n _The Term._ _Extensional Use._ _Intensional Use._\n\n { roots, branches, trunk.\n tree. maple, oak, beech. { or\n { woody-fiber, sap, bark.\n\n house. stone, brick, cement. foundation, frame-work,\n roof.\n\n dog. shepherd, fox terrier, carnivorous, quadruped,\n bull. propensity to bark.\n\n book. textbook, dictionary, cover, leaves, binding.\n encyclopaedia.\n\n quadrilateral. trapezium, trapezoid, four sides, four angles,\n parallelogram. limited plane.\n\n logic. theoretical logic, science of thinking, art of\n applied logic, right thinking, treats of\n educational logic. laws of thought.\n\n star. Sirius, Arcturus, Vega. heavenly body, gives light\n and heat, twinkles.\n\n force. gravitation, molecular, { produces motion\n atomic. { changes motion\n { destroys motion.\n\n term. general, singular, word or group of words,\n non-connotative. definite idea.\n\n government. monarchy, aristocracy, body of people,\n democracy. established form of law,\n banded together for\n mutual protection.\n\n bird. crow, robin, pigeon. biped, feathered, winged.\n\n\n=5. OTHER FORMS OF EXPRESSION FOR EXTENSION AND INTENSION.=\n\n _Extension._ _Intension._\n comprehension content\n extent intent\n breadth depth\n denotation connotation\n application implication\n\nFormerly the words extension and intension were applied to concepts\nwhile denotation and connotation were applied to terms representing the\nconcepts, but now the words are interchangeable. Denotation, the noun,\nand denote, the verb, signify, etymologically, a _marking off_. To\ndenote is to mark off or indicate the objects or classes of objects for\nwhich the term stands. Connotation, the noun, and connote, the verb,\nsignify _to mark along with_. To connote is to mark along with the\nobject, its attributes.\n\nThe terms which should be remembered are\n\n extension } { intension\n or } and { or\n denotation } { connotation\n\n\n=6. LAW OF VARIATION IN EXTENSION AND INTENSION.=\n\nIt has been noted that the intension of a term has reference to its\nqualities while extension considers its application to various objects.\nIt may be wise to experiment with the extension and the intension of\ncertain terms as types with a view of ascertaining how the two ideas\nare related to each other. For the sake of definiteness let us make use\nof the following scheme:\n\n I.\n\n _Intensional_ _Extensional_\n\n (1) four sides }\n (2) parallel sides } common qualities of { (1) squares\n (3) equal sides }\n (4) right angles }\n\n (1) four sides }\n (2) parallel sides } common qualities of { (1) squares\n (3) equal sides } { (2) rhombs\n\n { (1) squares\n (1) four sides } common qualities of { (2) rhombs\n (2) parallel sides } { (3) rectangles\n { (4) rhomboids\n\n { (1) squares\n { (2) rhombs\n (1) four sides } common qualities of { (3) rectangles\n { (4) rhomboids\n { (5) trapezoids\n { (6) trapeziums\n\n\n II.\n\n { (1) nebulae\n { (2) fixed stars\n (1) heavenly body } common qualities of { (3) sun\n { (4) comets\n { (5) meteors\n { (6) moon\n\n { (1) nebulae\n (1) heavenly body } common qualities of { (2) fixed stars\n (2) self-luminous } { (3) sun\n { (4) comets\n\n (1) heavenly body } { (1) nebulae\n (2) self-luminous } common qualities of { (2) fixed stars\n (3) fixed } { (3) sun\n\n (1) heavenly body }\n (2) self-luminous } common qualities of { (1) nebulae\n (3) fixed } { (2) fixed stars\n (4) twinkle }\n\n (1) heavenly body }\n (2) self-luminous }\n (3) fixed } common qualities of { (1) nebulae\n (4) twinkle }\n (5) foggy }\n\nIn considering the first illustration we observe that as the number of\nqualities is decreased, the number of objects increases. While in the\nsecond example as the qualities are increased, the number of objects\ndecreases. It would appear from this that the intension and extension\nof a term are _inversely_ related to each other. As the one increases\nthe other decreases and _vice versa_. It is customary to state this\nrelation in the form of a law known as the law of variation. \u201c_As the\nintension of a term is increased its extension is decreased and vice\nversa_,\u201d or the extension and intension of a term vary in an inverse\nratio to each other. To further illustrate: this _book_ refers to a\nlarge number of objects; add to the qualities of book those of _text\nbook_ and the application is much reduced. In other words as we\nincrease the intension, the extension is diminished. Increase the\nintension further by adding the quality _English_ text book and the\nextension becomes still less.\n\n\n=6a. TWO IMPORTANT FACTS IN THE LAW OF VARIATION.=\n\nIn studying the law of variation two facts are especially evident.\n(1) The law applies only to a series of terms representing notions\nof the same family. The extension and intension of \u201ctext book,\u201d for\nexample, could not be compared with the extension and intension of\n\u201chouse\u201d as they belong to a different class of words, the genus of\n_text book_ being _book_, while the genus of _house_ is _building_.\n\nTo illustrate the law of variation, determine upon any class name,\nthen think of its proximate genus (the next _higher-up_ class to which\nit belongs). Continue this till the series is sufficiently complete\nto illustrate the law. Or proceed in the opposite direction. That\nis, after selecting the class name think of the next lower term in\nthe class and thus continue till series is complete. Illustration:\nThe class name _man_ is determined upon; the proximate genus of man\nis _biped_, the proximate genus of biped is _animal_, and so on. Or\nthinking downward: a proximate species of man is _white man_, of white\nman. _European_, etc.\n\nThus the series:\n\n animal\n biped\n _man_\n white man\n European\n\n(2) As a second fact: the increase and decrease is not a mathematical\none. That is, by doubling the extension the intension is not halved.\nOr if the intension is decreased by one quality the extension is not\nnecessarily increased by one object. Thus \u201cman\u201d stands for one billion\nseven hundred million beings or objects. Decrease the intension of\n\u201cman\u201d by the one quality of rationality and the extension would include\nall bipeds\u2015\u2015many billion objects.\n\n\n=6b. THE LAW OF VARIATION DIAGRAMMATICALLY ILLUSTRATED.=\n\nIn a general way _lines_ may be used to represent the variation\nin extension and intension. For example: we may let a line an inch\nlong represent the extension of _man_, one two inches long represent\nthe extension of _biped_, three inches long represent the extension\nof _animal_, etc. While on the other hand, if a line an inch long\nrepresents the intension of _man_, a line one-half inch long may\nbe used to represent the intension of _biped_, one a quarter of an\ninch long to represent the intension of _animal_, etc. The following\nillustrates this scheme in connection with another series of words:\n\n _Extension_ _Intension_\n \u2015\u2015 barn \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2015\u2015\u2015\u2015 building \u2015\u2015\u2015\u2015\u2015\u2015\n \u2015\u2015\u2015\u2015\u2015\u2015 structure \u2015\u2015\u2015\u2015\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 object \u2015\u2015\n\nIn the foregoing scheme _building_ refers to a greater number of\nobjects than _barn_, hence the line under _extension_ representing\n_building_ should be longer than the line for _barn_. Likewise\n_structure_, referring to a greater number of objects than _building_,\nis represented by a longer line. Thus when the series is viewed\nfrom top to bottom a gradual increase in extension is noted. Giving\nattention to the intensional use of the series we note that _building_\nhas fewer qualities than _barn_, _structure_ fewer than _building_ and\n_object_ fewer than _structure_. Therefore, from top to bottom, the\nintension of the terms gradually decreases.\n\nThe variation may be made still more apparent if triangles are used,\none triangle being placed upon the other, vertex to base, like the\nfollowing:\n\n Illustration: ( \u2021 Intension and Extension )\n\n\u201cBiped\u201d is written near the base or in the broadest part of the\nextension triangle because it denotes the greatest number of objects,\nand is, therefore, broadest in extension. \u201cMan\u201d occupies a narrower\npart of the extension triangle because it refers to fewer objects or\nis narrower in extension than \u201cbiped.\u201d \u201cArnold\u201d occupies the narrowest\npart of the extension triangle because it is the narrowest in extension.\nOn the other hand \u201cArnold\u201d occupies the broadest part of the intension\ntriangle because intensionally it possesses more qualities than\nthe others, while \u201cbiped,\u201d having the least depth in intension or\npossessing the fewest qualities, occupies the narrowest portion of the\nintension triangle.\n\n\n=7. OUTLINE.=\n\n THE EXTENSION AND INTENSION OF TERMS.\n\n 1. Two-fold Function of Connotative Terms.\n\n 2. Extension and Intension Defined.\n\n 3. Extended Comparison of Extension and Intension.\n\n 4. A List of Connotative Terms used in Extension and Intension.\n\n 5. Other Forms of Expression for Extension and Intension.\n\n 6. Law of Variation in Extension and Intension.\n\n 6a. Two Important Facts in the Law of Variation.\n\n 6b. The Law of Variation Diagrammatically Illustrated.\n\n\n=8. SUMMARY.=\n\n1. Connotative terms are used in a two-fold sense: first, to denote\nobjects; second, to imply qualities.\n\n2. A term is used in extension when it is employed with reference\nto the objects for which the term stands. A term is used in intension\nwhen it is employed with reference to the qualities for which the term\nstands.\n\n3. The answer to either of the following questions will lead one to use\nany term in extension: First, what are the kinds? or second, to what\nobjects may the term be applied?\n\nThe answer to either of the following questions will lead to the use\nof any term in intension: First, what does it mean? or second, what are\nthe qualities?\n\n4. To illustrate extension and intension it is best to use the\nclass-names in every day speech.\n\n5. The word denotation is commonly used for extension and connotation\nfor intension.\n\n6. \u201cAs the intension of a term is increased its extension is decreased\nand _vice versa_,\u201d is a statement of the Law of Variation in the\nextension and intension of terms.\n\n6a. The law of variation applies only to a series of terms representing\nnotions of the same class or family, the words being arranged in a\nspecies-genus order. The increase and decrease of the extension and\nintension of a series is not proportional.\n\n6b. The law of variation is best explained by using two triangles, one\nsuper-imposed upon the other vertex to base and base to vertex.\n\n\n=9. ILLUSTRATIVE EXERCISES.=\n\n1a. Employ the following terms in extension\u2015\u2015European, flower, term,\ntruth.\n\n { Russian\n European { Englishman\n { Scotchman\n\n { lily\n flower { rose\n { pansy\n\n { singular\n term { distributive\n { collective\n\n { Truth has no extension.\n truth { Since it refers to a\n { quality only, it is\n { non-connotative.\n\n1b. Employ the following in extension\u2015\u2015grain, rock, soil, precious\nstone.\n\n2a. Use intensionally bird, quadruped, letter, John.\n\n { two feet\n bird { ability to fly\n { feathers\n\n { four feet\n quadruped { back bone\n { hairy covering\n\n { heading\n letter { body\n { complimentary close\n\n { John has no intension.\n John { Since it refers to\n { an object only, it is\n { non-connotative.\n\n2b. Use the following in intension\u2015\u2015word, table, purity, government.\n\n3a. The use of a term in extension follows when attempting to answer\ntwo questions: First, what are the kinds? Second, to what objects may\nthe term be applied? Make application of this with reference to the\nterm _man_.\n\n1. What are the kinds of men? Caucasian, Malay, Mongolian, Ethiopian,\nRedman.\n\n2. To what objects does the term _man_ refer? George Washington, Chas.\nHughes, John Smith.\n\nIn both 1 and 2 the word _man_ is used to denote objects, hence it is\nemployed in extension.\n\n3b. Use the term _vegetable_ in extension by answering the two\nquestions in 3a.\n\n4a. Decrease one by one the qualities of some common object with a\nview of noting how when the intension is decreased the extension is\nincreased.\n\n _Intension_ _Extension_\n\n binding } {\n leaves } {\n cover } { school arithmetic\n printed matter } {\n designed for instruction } {\n instruction in arithmetic } {\n\n binding } {\n leaves } { school arithmetic\n cover } { school grammar\n printed matter } { school speller, etc.\n designed for instruction } {\n\n binding } { school arithmetic\n leaves } { school grammar\n cover } { school speller, etc.\n printed matter } { encyclopaedia\n } { novel\n\n } { school arithmetic\n binding } { school grammar\n leaves } { school speller, etc.\n cover } { encyclopaedia\n } { novel\n } { note book\n\n4b. With a view of noting how when the intension is decreased the\nextension is increased, decrease one by one the common qualities of\n_peach tree_.\n\n5a. In the following series what word could be substituted for \u201cmammal\u201d\nand why? Being, organized being, animal, vertebrate, mammal. Answer:\nFish, reptile, or bird; because there are at least seven classes of\nanimals which belong to the vertebrate family, any one of which could\nbe used to complete the series.\n\n5b. Form a series of which \u201cBaldwin apple\u201d has the narrowest extension.\nWhat terms may be substituted for \u201cBaldwin apple?\u201d\n\n6a. In a series of which \u201cpupil\u201d is a member show that the increase\nand decrease is not proportional. The series: logic pupil, pupil, youth,\nhuman being, being. In decreasing the intension of \u201clogic pupil\u201d by\ndropping the one quality, logic, the extension is made larger by many\nmore than one, as \u201cpupil\u201d represents many more objects than \u201clogic\npupil.\u201d Therefore, the increase is not in proportion to the decrease.\n\n6b. In a series in which \u201cruler\u201d appears, show that the increase and\ndecrease is not proportional.\n\n7. From the following list select the proper words of the series;\narrange them; draw and name the triangles: Caesar, brute, man, Roman,\nAmerican, biped, sensuous being, animal, individual.\n\n\n=10. REVIEW QUESTIONS.=\n\n 1. What is a connotative term? Illustrate.\n\n 2. Which is the broader term, quality or attribute? Why?\n\n 3. When is a term used in extension?\n\n 4. Use the term triangle in intension.\n\n 5. As an aid to using a term in extension or intension what questions\n may one ask himself?\n\n 6. By asking these questions use the term _clock_ in both extension\n and intension.\n\n 7. By experimenting with the qualities of a rectangle show that as\n the intension is decreased the extension is increased.\n\n 8. Write a list of five connotative terms. Prove that they are\n connotative by illustrating their extension and intension.\n\n 9. The term metal { denotes } such qualities as element, metallic\n { connotes }\n lustre, conductor of heat and electricity. In the foregoing which\n of the two words following the brace should be used? Give reasons.\n\n 10. State the law of variation in two ways.\n\n 11. As one studies the law of variation what two facts are especially\n evident? Explain fully.\n\n 12. For the purpose of illustrating the law of variation form a series\n of which _desk_ is a member. Draw and name the triangles.\n\n\n=11. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n 1. Which is the broader term, subject or object? Prove it.\n\n 2. If a term like _Caesar_ is given extension does it become a\n general term? Why?\n\n 3. Using \u201cman\u201d as a member of each, arrange at least three different\n series.\n\n 4. Why may it be said that a connotative term is _two_ dimensional?\n\n 5. Is there a word which has a broader extension than \u201cbeing\u201d? Why?\n\n 6. Prove that _youth_ has less intension than _human being_.\n\n 7. Devise a series of words in which the variation is proportional.\n\n 8. Advance arguments supporting the hypothesis that the term _John_\n has neither extension nor intension.\n\n 9. Suggest arguments to prove that \u201cGeorge Washington\u201d has both\n extension and intension.\n\n\n\n\n CHAPTER 6.\n\n DEFINITION.\n\n\n=1. IMPORTANCE.=\n\nTo be clear, cogent, concise and consistent is to be logical.\nReference has been made to a striking tendency on the part of writers\nand speakers to use words loosely. It is a noticeable fact that\nscholars generally aim to be profound rather than clear, philosophical\nrather than pointed.\n\nIn the use of text books more or less pedagogical these are the common\ncomplaints: \u201cI don\u2019t understand what he means\u201d or \u201cYou have to read so\nmuch to get so little.\u201d This condition gives to the topic of definition\na prominence which cannot be overlooked by those who are seeking the\ntruth; because the definition is the clearest, briefest and altogether\nthe most satisfactory way of describing an idea. Likewise the habit\nof defining any doubtful term reduces to a minimum the possibility of\nmisunderstanding.\n\nThe subject must appeal strongly to the instructor, as he, above all\nothers, should make his work stand for clearness, pointedness and\ncontinuity.\n\n\n=2. THE PREDICABLES.=\n\n_A predicable is a term which can be affirmed or predicated of any\nsubject._ In the proposition, \u201cA man is a rational animal,\u201d the term\n\u201crational animal\u201d is a predicable, because it can be affirmed of the\nsubject _man_.\n\nTo gain a clear knowledge of the definition it is quite necessary\nto understand the _five predicables_ which we shall consider in the\nfollowing order:\n\n 1. Genus.\n\n 2. Species.\n\n 3. Differentia (difference).\n\n 4. Property.\n\n 5. Accident.\n\n(1) _Genus_ and (2) _Species_.\n\nGenus and species are relative terms and can best be defined together.\n\n_A genus is a term which stands for two or more subordinate classes._\n\n_A species is a term which represents one of the subordinate classes._\n\nThe genus may be subdivided into species; the species together form the\ngenus.\n\nTo illustrate: The term _man_ stands for five subordinate classes or\nspecies, as white, black, brown, yellow and red. \u201cMan\u201d is, therefore,\na genus, while \u201cwhite man\u201d and \u201cblack man,\u201d etc., are species. The\nterm \u201cpolygon\u201d is a genus with reference to \u201ctrigon,\u201d \u201ctetragon,\u201d\n\u201cpentagon,\u201d etc., while \u201ctrigon\u201d is a species of \u201cpolygon.\u201d\n\nAny given genus may be a species of some higher class. That is, \u201cman,\u201d\nwhich is a genus with reference to the kinds of men, is a species\nof the higher class \u201cbiped,\u201d while \u201cbiped\u201d is a species of \u201canimal,\u201d\n\u201canimal\u201d a species of \u201corganized being,\u201d \u201corganized being\u201d of \u201cmaterial\nbeing,\u201d \u201cmaterial being\u201d of \u201cbeing.\u201d But here we stop, as there is no\nhigher grade to which \u201cbeing\u201d can be referred. This highest genus takes\nthe name of _summum genus_.\n\nSimilarly any given species may be a genus of some lower class.\n\u201cWhite man,\u201d for example, which is a species of \u201cman,\u201d is a genus of\n\u201cAmerican,\u201d \u201cEnglishman,\u201d \u201cGerman,\u201d \u201cFrenchman,\u201d etc. \u201cAmerican\u201d is\na genus of \u201cNew Yorker,\u201d \u201cCalifornian,\u201d etc., while \u201cNew Yorker\u201d is\na genus of \u201cSmith of Jamaica.\u201d This last term is an individual and\ncannot be subdivided. It represents the lowest possible species and\nis referred to in logic as _infima species_.\n\nIt is obvious that the highest genus cannot become a species, neither\ncan the lowest species become a genus.\n\n\n PROXIMATE GENUS.\n\nThe proximate genus is the next class above. To illustrate: \u201cAnimal\u201d\nis a genus of \u201cman,\u201d but \u201cbiped\u201d is the proximate genus of \u201cman.\u201d\n\u201cQuadrilateral\u201d is the genus of \u201csquare,\u201d but \u201crectangle\u201d is the\nproximate genus. The next class above \u201ctrigon\u201d is _polygon_ not\n_figure_. Hence \u201cpolygon\u201d is the proximate genus of \u201ctrigon.\u201d\n\n\n GENUS AND SPECIES OF NATURAL HISTORY.\n\nIn natural history the following terms are used to denote the\nvarious grades of kinship in any scheme of classification: (1) kingdom,\n(2) class, (3) order, (4) family, (5) genus, (6) species, (7) variety,\n(8) the individual thing. Here \u201cgenus\u201d and \u201cspecies\u201d are absolute not\nrelative and occupy a _fixed_ place in the scheme, while from a logical\nviewpoint any of the grades indicated between the lowest and highest\nwould be the species of the next higher grade or a genus of the next\nlower; e. g., _order_ is a species of \u201cclass,\u201d while it is the genus\nof \u201cfamily.\u201d\n\n\n GENUS, A DOUBLE MEANING.\n\nWe recall that any class name or genus has a double use, extensional\nand intensional. When considered from the standpoint of its extension,\na genus represents a group of objects or is _mathematical_ in its\napplication, but when used in an intensional sense it represents a\ngroup of qualities or is _logical_ in its application.\n\nConsidered extensionally the genus refers to a larger number of objects\nthan the species. But when viewed intensionally the species refers to\nmore qualities than the genus. This was made clear when discussing the\nlaw of variation in the extension and intension of terms.\n\n(3) _Differentia._\n\n_The differentia of a term is that attribute which distinguishes a\ngiven species from all the other species of the genus._\n\nIt has been observed that the species refers to more qualities than\nthe genus. In fact, it represents all the attributes of the genus plus\nthose which distinguish the particular species from the other species\nof the genus. These additional qualities are the differenti\u00e6 of the\nparticular species.\n\n\n TO ILLUSTRATE:\n\nThe attribute which distinguishes man from the other bipeds of the\nworld is his rationality. That which distinguishes the rectangle from\nthe other parallelograms is its four right angles. The attributes\n_rationality_ and _right angles_ are differentiae.\n\n(4) _Property._\n\n_A property of a term is any attribute which helps to make the term\nwhat it is._ Thus \u201cconsciousness\u201d is a property of man, \u201cbinding\u201d a\nproperty of book, \u201cangles\u201d a property of triangle. Deprive the terms\nof these attributes and their true nature is altered.\n\nA differentia is a property according to the foregoing definition.\nHowever, Jevons defines \u201cproperty\u201d as \u201cAny quality which is common to\nthe whole of a class, but is not necessary to mark out the class from\nother classes.\u201d This viewpoint excludes \u201cdifferentia\u201d from the notion\nof property. The difference in opinion is of slight importance.\n\n(5) _Accident._\n\n_An accident of a term is any attribute which does not help to make\nthe term what it is._ It may indifferently belong or not belong to the\nterm. Deprive a term of an accident and the nature of the term remains\nunchanged. Thus, a teacher\u2019s position, a man\u2019s watch, the fact that the\nangle is one of 80\u00b0 are all accidents.\n\nIt is obvious that a property is a _constant_ attribute while an\naccident is variable. This gives to the former a universal validity\nwhile the latter is more or less shifting and uncertain. All triangles\nmust have _three angles_ (property) while the _value of each angle in\ndegrees_ (accident) admits of unlimited variation.\n\nSome logicians divide accidents into separable and inseparable. A man\u2019s\n_hat_ would be a separable accident while his _birthplace_ would be an\ninseparable accident.\n\n\n FIVE PREDICABLES ILLUSTRATED.\n\nIn the following brief descriptions the five predicables are\ndesignated:\n\n (species) (genus) (differentia)\n (1) This \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 is a \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 with \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n rectangle parallelogram four right angles\n (accident)\n its longer sides being \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015.\n ten inches\n\n (species) (differentia) (prox. genus)\n (2) This \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 is a \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 with the\n man rational biped\n (property) (accident)\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 and a \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015.\n power of locomotion ruddy complexion\n\n (species) (genus) (differentia) (property)\n (3) A \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 is a \u2015\u2015\u2015\u2015\u2015\u2015\u2015 of \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 and \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015,\n trigon polygon three sides three angles\n (accident)\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015.\n the sum of the angles being equal to two right angles\n\n\n=3. THE NATURE OF A DEFINITION.=\n\nIt will be remembered that an individual notion is a notion of a single\nthing or attribute, while a general notion is a notion of a class of\nthings or a group of attributes. A term which represents an individual\nnotion is known as a _singular term_, while a term which stands for a\ngeneral notion is referred to as a _general term_.\n\nOne may explain the meaning of a singular term which stands\nfor one thing by enumerating its various attributes. For example,\nsuch attributes as a piercing bark, a yellow color, intelligent,\ncompanionable, a strong liking for sweetmeats, explain the meaning\nof the singular term \u201cFido.\u201d Likewise we may explain the meaning of\na general term by enumerating its attributes. To illustrate: power of\nspeech, rationality, ability to laugh, etc., explain the meaning of\nthe general term _man_. The explanation of the singular term fits only\nFido. There is probably no other dog in the world just like Fido. But\nthe explanation of the general term _man_ may be applied to _all_ men.\n\nA brief enumeration of attributes which may be applied to a _class of\nthings_ often takes the form of a definition. The word definition comes\nfrom the word _definire_, meaning to limit or fix the bounds of.\n\nA definition, then, consists of the enumeration of such attributes\nas distinguish a term from all other terms. In this sense it would\nseem that the singular term _Fido_, as well as the general term\n_man_, admits of definition, but it is usual for logicians to confine\ndefinition to the _general term_. Singular terms may be _described_;\ngeneral terms, _defined_.\n\n\n A DEFINITION OF DEFINITION.\n\n_A definition of a term is a statement of its meaning by enumerating\nits characteristic attributes._\n\nThat the enumeration must be in terms of its distinguishing or\ncharacteristic attributes is implied in the derivation of the term\n_definition_. The attributes must establish limits or bounds, just as a\nline fence limits a land owner\u2019s possessions. To indicate that man is a\ncreature possessing the power of locomotion, sense of sight and ability\nto eat, is surely not a definition, as the marks are not characteristic\nof men only. These attributes set no boundary between man and horse,\nconsequently the statement is a faulty _description_ of man, not\na _definition_. But when the enumeration includes such attributes\nas power of speech, rationality and ability to laugh, then does the\ndescription become a definition. To put it differently: A definition is\na description of a term by means of its distinguishing attributes. This\nstatement may be considered a definition of man, though somewhat faulty:\n\u201cA man is a creature who is rational and who possesses the power of\nspeech and ability to laugh.\u201d\n\n\n=4. DEFINITION AND DIVISION COMPARED.=\n\nWe have learned that general terms when connotative may be used\nextensionally or intensionally.\n\nA definition indicates the _intensional_ nature of a term, while a\nstatement which points out the _extensional_ nature of a term is known\nas logical division. More briefly: A definition is an _intensional_\nstatement of the nature of the term, while logical division is an\n_extensional_ statement of the nature of the term.\n\nTo illustrate: The following statements are definitions:\n\n (1) A dog is a domesticated quadruped of the genus canis and given\n to barking.\n\n (2) A quadrilateral is a rectilinear figure of four sides.\n\n (3) Soil is a substance composed of pulverized rock and decayed\n vegetable matter in which plants will grow.\n\nThe following represent Logical Division:\n\n (1) Dogs are divided into hounds, terriers, bull, etc.\n\n (2) The kinds of quadrilaterals are trapeziums, trapezoids and\n parallelograms.\n\n (3) The various soils are loam, sand, clay, muck, etc.\n\n\n=5. THE KINDS OF DEFINITIONS.=\n\nGenerally speaking there are three kinds of definitions, namely,\n(1) Etymological, (2) Descriptive, (3) Logical.[5]\n\n(1) _An etymological definition is one based upon the derivation of the\nterm._\n\nThis kind of a definition, which gives merely the meaning of the\nsymbol, is sometimes called a _nominal_ or verbal definition; while\na _real_ definition is regarded as one which gives the _meaning\nof the notion_ for which the symbol stands. The modern logician is\ninclined to ignore this classification on the argument that to make a\ndistinction between a symbol and the notion it symbolizes is simply to\nmisunderstand the relation which exists between them. If the definition\ndoes not agree with the thing then it cannot correctly explain the\nterm which represents the thing. Define correctly the term and one has\ndefined correctly the notion signified by the term.\n\nThe attributes of a term may be separated into three classes:\ndifferentia, property and accident. It would appear possible,\ntherefore, to define a term by enumerating the accidents only or by\nenumerating the properties, or, finally, by stating the differentiae.\nBut if the enumeration is confined to accidents the chances are that\nthe statement will be a description, not a definition, as accidents\nare seldom sufficiently characteristic to determine the boundaries of\na term. This leaves open two distinct ways of defining a term: First,\nby naming the properties or properties and accidents only; second,\nby stating the differenti\u00e6 only. The former kind is the so-called\ndescriptive definition, while the latter is the logical.\n\n(2) _A descriptive definition of a term is a description of its nature\nby means of its properties and accidents._\n\n(3) _A logical definition of a term is a description of its nature by\nmeans of its differenti\u00e6._\n\n\n THE THREE KINDS OF DEFINITIONS ILLUSTRATED AND COMPARED.\n\nEtymological Definition of Trigon.\n\n A trigon is a figure of three corners.\n\nDescriptive:\n\n A trigon is a figure which has three sides and three angles, the sum\n of the latter being equal to two right angles.\n\nLogical:\n\n A trigon is a polygon of three angles.\n\nIt is seen that an etymological definition is simply a root-word\nanalysis. In the case of _trigon_, the prefix comes from the Greek,\nmeaning three, while the root-word comes from the Greek meaning corner.\n\nThe descriptive definition of trigon names the properties, \u201cthree\nsides and three angles\u201d (differenti\u00e6) and the accident, \u201cthe sum of\nthe angles of which equals two right angles.\u201d\n\nThe logical definition of trigon simply states the proximate genus,\n\u201cpolygon,\u201d and the differentia, \u201cthree angles.\u201d\n\n\n=6. WHEN THE THREE KINDS OF DEFINITIONS ARE SERVICEABLE.=\n\nThe etymological definition is helpful in furnishing a cue for\nremembering the descriptive and logical definitions. It also leads\nto precision of expression\u2015\u2015the right word in the right place. Here\nis where the knowledge of a foreign language, particularly Latin, is\nhelpful.\n\nThe descriptive definition is best adapted to the child-mind. Children\nthink in the large; are not given to hair-splitting discriminations,\nand, therefore, _many_ characteristic marks must be mentioned in\norder to insure a mastery of the content. With children the logical\ndefinition is often too brief to be clear. For example, it is easy\nto see which of the following definitions would be better adapted\nto the child-mind. _Logical_: A square is an equilateral rectangle.\n_Descriptive_: A square is a figure of four equal sides and four right\nangles.\n\nThe logical definition may be introduced to the student of the\nsecondary school.\n\nFew exercises are better adapted to the development of powers of\ndiscrimination and precision than practice in defining logically the\ncommon terms of every-day life. For example: \u201cA book is a pack of\npaper-sheets bound together.\u201d \u201cA chair is a piece of furniture with\nback and seat, designed for the seating of one person.\u201d \u201cA lead pencil\nis a cylindrical writing implement with lead through the center.\u201d\n\u201cA door is an obstacle designed to swing in and out to open and close\nan entrance.\u201d \u201cAn eraser is an implement made to rub out written or\nprinted characters.\u201d\n\nThese definitions, coming from training school students, are not above\ncriticism, yet they illustrate the point in hand.\n\n\n=7. THE RULES OF LOGICAL DEFINITION.=\n\nFive rules summarize the requirements to which a logical definition\nmust conform.\n\n\n FIRST RULE.\n\n_A logical definition should state the essential attributes of the\nspecies defined._\n\nThis means that a logical definition should contain the species, the\nproximate genus and the differentia. As the terms species, genus and\ndifferentia have been explained, it will be sufficient to briefly\nillustrate this rule.\n\n_Logical According to the First Rule._\n\n species genus differentia\n (1) A \u2015\u2015\u2015\u2015\u2015\u2015\u2015 is a \u2015\u2015\u2015\u2015\u2015 with \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015.\n bird biped feathers\n\n species genus differentia\n (2) A \u2015\u2015\u2015\u2015\u2015\u2015\u2015 is a \u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015.\n mascot person supposed to bring good luck\n\n species genus differentia\n (3) \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 is a \u2015\u2015\u2015\u2015\u2015\u2015 of \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015.\n Religion system faith and worship\n\n species genus differentia\n (4) A \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 is a \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015.\n moonbeam ray of light from the moon\n\n_Illogical According to the First Rule._\n\n (1) A man is a rational animal.\n (\u201cBiped\u201d is the proximate genus, not \u201canimal.\u201d)\n\n (2) A Connotative term always denotes both an object and an attribute.\n (No genus.)\n\n (3) A trigon is a polygon.\n (No differentia.)\n\n (4) It is a term which denotes an indefinite number of objects or\n attributes.\n (No species.)\n\n_The Foregoing Illogical Definitions Made Logical._\n\n (1) A man is a rational _biped_.\n\n (2) A Connotative term is a _term_ which denotes both an object and\n an attribute.\n\n (3) A trigon is a polygon of _three angles_.\n\n (4) A _general term_ is a term which denotes an indefinite number of\n objects or attributes.\n\n\n SECOND RULE.\n\n_A logical definition should be exactly equivalent to the species\ndefined._\n\nThis means that the species must equal the genus plus the differentia\nor the subject and predicate of the definition must be co-extensive\u2015\u2015of\nthe same bigness. The subject must refer to the same number of objects\nas the predicate.\n\nA man upon the witness stand makes the declaration that he will testify\nto the truth, the whole truth and nothing but the truth. A logical\ndefinition must contain _the species, the whole species_ and _nothing\nbut the species_. If the definition does not include all the species,\nit is too narrow; while on the other hand, if it includes other species\nof the genus it is too broad.\n\nAn excellent test of this second requirement is to interchange subject\nand predicate. If the interchanged proposition means the same as the\noriginal then the conditions have been met. To illustrate: Original\u2015\u2015A\ntrigon is a polygon of three angles. Interchanged\u2015\u2015A polygon of three\nangles is a trigon.\n\nThe very best way of making the definition conform to this rule is to\nput to oneself these three questions: 1. Does it include all of the\nspecies? 2. Does it exclude all other species of the genus? 3. Has it\nany unnecessary marks?\n\nTo exemplify: Let us ask the three questions relative to the following\nlogical definitions:\n\n (1) A parallelogram is a quadrilateral whose opposite sides are\n parallel.\n\n (2) A bird is a biped with feathers.\n\n_Questions_:\n\n (1) Does the definition include all the parallelograms? Yes. Does it\n exclude all other quadrilaterals? Yes. Are there any unnecessary\n marks? No.\n\n (2) Does it include all birds? Yes. Does it exclude all other bipeds?\n Yes. Any unnecessary marks? No.\n\n_Illogical According to the Second Rule._\n\n (1) A man is a vertebrate animal.\n\n (Too broad. Does not exclude other species of the genus, such as\n horses, dogs, etc.)\n\n (2) A barn is a building where horses are kept.\n\n (Too narrow. Does not include all of the species, such as cow\n barn.)\n\n (3) An equilateral triangle is a triangle all of whose sides and\n angles are equal.\n\n (Equal angles is an unnecessary mark.)\n\n_The Foregoing Definitions Made Logical._\n\n (1) A man is a rational biped. (Proximate genus.)\n\n (2) A barn is a building where horses and cattle are kept and hay and\n grain are stored.\n\n (3) An equilateral triangle is a triangle all of whose sides are\n equal.\n\n\n THIRD RULE.\n\n_A definition must not repeat the name to be defined nor contain any\nsynonym of it._\n\nA violation of this rule is known as \u201ca circle in defining\u201d (_circulus\nin definiendo_).\n\nThere are some exceptions to this rule, as in the case of compound\nwords and a species which takes its name from its proximate genus. To\nsay that a hobby-horse is a horse, or that an equilateral triangle is a\ntriangle, is not only allowable but necessary, that the proximate genus\nmay be used.\n\n_The following definitions are illogical according to the third rule_:\n\n (1) A teacher is one who _teaches_.\n\n (2) Life is the sum of the _vital_ functions.\n\n (3) A sensation is that which comes to the mind through the _senses_.\n\n\n FOURTH RULE.\n\n_A definition must not be expressed in obscure, figurative or ambiguous\nlanguage._\n\nA violation of this rule is referred to in logic as \u201cdefining the\nunknown by the still more unknown\u201d (_ignotum per ignotius_).\n\nIt is known that the purpose of definition is to make clear some\nobscure term, consequently unless every word used is understood the\nchief aim of the definition has been defeated.\n\nFrom this it must not be inferred that all definitions should be free\nfrom technical terms. Such a restriction would make the defining of\nmany terms unsatisfactory and in a few cases practically impossible.\nTo the student of evolution the following definition by Spencer\nis intelligible while to the uninitiated it would appear obscure:\n\u201cEvolution is a continuous change from an indefinite, incoherent\nhomogeneity to a definite coherent heterogeneity through successive\ndifferentiations and integrations.\u201d\n\nThis rule insists upon simple language when it is possible to use such\nin giving an accurate and comprehensive meaning to the term defined.\n\n_Illogical Definitions According to the Fourth Rule._\n\n (1) \u201cA net is something which is reticulated and decussated, with\n interstices between the intersections.\u201d Dr. Johnson.\n\n (2) \u201cThought is only a cognition of the necessary relations of our\n concepts.\u201d\n\n (3) \u201cThe soul is the entelechy, or first form of an organized body\n which has potential life.\u201d Aristotle.\n\n\n FIFTH RULE.\n\n_When possible the definition must be affirmative rather than negative._\n\nThe fact that there are a considerable number of terms which admit of a\nnegative definition only, takes from the force of this rule. Such terms\nas deafness, inexpressible, infidel and the like can best be defined\nnegatively.\n\nIt likewise happens that when words are used in pairs it is expedient\nto define one affirmatively and the other negatively. Recall, for\nexample, the definitions of relative and absolute terms: \u201cA relative\nterm is one which needs another term to make its meaning clear.\u201d\n\u201cAn absolute term is one which does not need another term to make its\nmeaning clear.\u201d\n\n_Illogical Definitions According to the Fifth Rule._\n\n (1) A gentleman is a man who is not rude.\n\n (2) An element is a substance which is not a compound.\n\n (3) An univocal term is a term which does not have more than one\n meaning.\n\n\n=8. TERMS WHICH CANNOT BE DEFINED LOGICALLY.=\n\nA logical definition insists upon a proximate genus and differentia.\nBut as there is no genus higher than the highest genus (_summum genus_)\nthen surely such cannot be defined logically. The words _being_ and\n_thing_ illustrate terms of this class. Moreover, it is impossible\nto give a satisfactory definition of an individual (_infima species_)\nas no attributes can be mentioned which will distinguish definitely\nand permanently the individual from others of the class. We may\nperceive the attributes but not those that are possessed solely\nby the individual. To say that Abraham Lincoln was a man who was\nsimple and honest is not a definition, as other men have had the\nsame characteristics.\n\nAgain there are a few terms such as life, death, time and space which\ncannot be defined satisfactorily. These terms seem to be in a class by\nthemselves or of their own genus (_sui generis_).\n\nSince a definition of a term is a brief explanation of it by means of\nits attributes, it follows that collective terms and terms standing for\na single attribute are incapable of definition. Such terms as group,\npain, attribute, belong to this class.\n\nWe may say, then, that there are some terms too high, some too low and\nsome too peculiar to come within the province of logical definition.\nIn short, \u201c_summum genus_,\u201d \u201c_infima species_\u201d and \u201c_sui generis_\u201d are\nincapable of definition.\n\n\n=9. DEFINITIONS OF COMMON EDUCATIONAL TERMS.=\n\n (1) _Development_ is the process whereby the latent possibilities\n of an individual are unfolded or the invisible conditions of a\n situation are made apparent.\n\n Development means expansion according to principle, while\n unfolding may or may not involve a principle.\n\n (2) _Education_ is the process employed in developing systematically,\n symmetrically and progressively all of the capabilities of a\n single life; or\n\n (3) _Education_ is the process of modifying experience in order to\n make the life as valuable as it ought to be.\n\n (4) _Teaching_ is the art of occasioning those activities which\n result in knowledge, power and skill.\n\n It is the duty of the true teacher to inspire the child to\n activity along right lines. Through his own activity the child\n shapes his inner world which is sometimes termed _character_.\n\n Knowledge is anything known, power is ability to act, skill is a\n readiness of action.\n\n (5) _Instruction_ is the art of occasioning those activities which\n result in knowledge.\n\n Instruction develops the understanding; teaching develops\n character.\n\n (6) _Training_ is the occasioning of those activities which, by means\n of directed exercise, result in power and skill.\n\n Training and education are not interchangeable. Training implies\n an outside authority, while education, which involves inner\n development, may proceed without supervision.\n\n (7) _Knowledge_ is anything acquired by the act of knowing.\n\n (8) _Learning_ is the act of acquiring knowledge or skill.\n\n (9) Instruction, training, teaching, learning and education all\n involve activity.\n\n Instruction arouses activity which results in knowledge;\n training directs activity which produces power and skill;\n teaching includes both instruction and training. Learning is an\n activity which results in knowledge and skill, while education\n is a developing process which involves all the others.\n\n (10) A _science_ is knowledge classified for the purpose of\n discovering general truths.\n\n (11) _An art_ is a skillful application of knowledge and power to\n practice.\n\n \u201cA science teaches us to know, an art to do.\u201d\n\n (12) A _fact_ is a single, individual, particular thing made or done.\n\n A _truth_ is general knowledge which exactly conforms to the\n facts.\n\n A truth may be a definition, rule, law, or principle.\n\n (13) A _fact_ as opposed to hypothesis is an occurrence which is true\n beyond doubt.\n\n An _hypothesis_ is a supposition advanced to explain an\n occurrence or a group of occurrences.\n\n A _theory_ is a general hypothesis which has been partly verified.\n\n (14) _Theory_ as opposed to practice means _general knowledge_, while\n practice involves the putting into operation one\u2019s theories.\n\n (15) A _fact_ as opposed to phenomenon is something accomplished.\n A phenomenon is something shown.\n\n (16) A _method-whole_ is any subdivision of the matter for instruction\n which leads to a generalization.\n\n (17) _Method_ is an orderly procedure according to a recognized system\n of rules and principles.\n\n As the term is commonly used it includes not only the arrangement\n of the subject matter for instruction but the mode of presenting\n the same to the mind.\n\n (18) _Induction_ is the process of proceeding from the less general to\n the more general.\n\n _Deduction_ is the process of proceeding from the more general to\n the less general.\n\n (19) The terms induction and deduction may have reference to forms of\n reasoning or to methods of teaching.\n\n The _inductive method_ is the method of deriving a general truth\n from individual instances.\n\n The _deductive method_ is the method of applying a general truth\n to individual instances.\n\n The inductive method is objective, while the deductive method is\n subjective. Induction is the method of discovery; deduction is\n the method of instruction.\n\n (20) _Analysis_ is the process of separating a whole into its related\n parts.\n\n _Synthesis_ is the process of uniting the related parts to form\n the whole.\n\n (21) The _analytic method_ is the method of proceeding from the whole\n to the related parts.\n\n The _synthetic method_ is the method of proceeding from the\n related parts to the completed whole.\n\n (22) Analysis and synthesis deal with _single things_, while induction\n and deduction are concerned with _classes of things_.\n\n (23) The _complete method_ consists of three elements: (1) induction,\n (2) deduction, (3) verification or proof.\n\n When the emphasis is placed on the inductive phase, the complete\n method is sometimes termed the development method.\n\n\n=10. OUTLINE.=\n\nDEFINITION.\n\n (1) Importance.\n\n (2) The Predicables.\n Genus\u2015\u2015species\u2015\u2015summum genus\u2015\u2015infima species.\n Proximate Genus.\n Genus and Species of Natural History.\n Genus, Double meaning of\n Differentia.\n Property.\n Accident.\n Separable, Inseparable.\n\n (3) Nature of Definition.\n\n (4) Definition and Division Compared.\n\n (5) The Kinds of Definitions.\n (1) Etymological.\n (2) Descriptive.\n (3) Logical.\n\n\n THREE KINDS ILLUSTRATED AND COMPARED.\n\n (6) When the Three Kinds are Serviceable.\n\n (7) The Rules of Logical Definition.\n (1) _Essentials._\n (2) Same _size_.\n (3) Do not _repeat_.\n (4) _Unambiguous._\n (5) _Language_ affirmative.\n\n (8) Terms Which Cannot be Defined Logically.\n Summum genus.\n Infima species.\n Sui generis.\n Collective terms.\n A single attribute.\n\n\n=11. SUMMARY.=\n\n(1) To be logical one must acquire the habit of accurate definition.\n\nThis topic ought to appeal strongly to the school teacher, who should\nabove all others make his work stand for clearness, pointedness and\ncontinuity.\n\n(2) A predicable is a term which can be affirmed or predicated of any\nsubject.\n\nThe five predicables are Genus, Species, Differentia, Property and\nAccident.\n\n (1) A Genus is a term which stands for two or more subordinate\n classes.\n\n (2) A Species is a term which represents one of the subordinate\n classes.\n\n The _proximate genus_ of a species is the next class above the\n species, while the _summum genus_ is the highest possible class\n in any graded series of terms. The lowest class is the _infima\n species_ of that series. The lowest class may be individual.\n\n In natural history genus and species are not relative terms, but\n absolute, having a fixed place in the series of gradations.\n\n The term genus possesses a double meaning: it may be used to\n represent objects (extensionally) or qualities (intensionally).\n\n (3) The differentia is that attribute which distinguishes a given\n species from all the other species of the genus.\n\n (4) A property of a term is any attribute which helps to make that\n term what it is.\n\n Differentia is a property according to definition. Some logicians\n would not include the differentia in the content of the term\n property.\n\n (5) An accident of a term is any attribute which does not help\n to make it what it is. Some authorities divide accidents into\n separable and inseparable.\n\n(3) A definition of a term is a statement of its meaning by enumerating\nits characteristic attributes.\n\n(4) Definitions explain a term intensionally, while logical division\nexplains a term extensionally.\n\n(5) There are three kinds of definitions: (1) etymological,\n(2) descriptive, (3) logical.\n\nAn etymological definition is based upon the derivation of the term;\na descriptive definition states the characteristic properties and\naccidents of a term, while a logical definition is simply a statement\nof the differentia of a term.\n\n(6) The etymological definition leads to precision of expression, the\ndescriptive definition is best adapted to the child-mind, while the\nlogical definition belongs to the realm of secondary education.\n\n(7) Five rules summarize the requirements to which a logical definition\nmust conform. In a word or two these five rules are: Every logical\ndefinition must (1) state the genus and differentia, (2) be equivalent\nto the species defined, (3) not repeat the name to be defined, (4) not\nbe expressed in obscure language, (5) commonly be affirmative.\n\n(8) Some terms are too high (summum genus), some too low (infima\nspecies), some too peculiar (sui generis) to come within the province\nof logical definition.\n\n\n=12. ILLUSTRATIVE EXERCISES.=\n\n1a. The italicized words in the following propositions are predicables\nbecause they are affirmed of the subject:\n\n (1) \u201cThis man weighs _one hundred fifty pounds_.\u201d\n\n (2) \u201cA bird is a _feathered biped_.\u201d\n\n (3) \u201cThe earnest teacher is an _indefatigable worker_.\u201d\n\n (4) \u201cWalking is the _most beneficial outdoor exercise_.\u201d\n\n1b. Underscore the predicables in the following:\n\n (1) \u201cAll men are rational.\u201d\n\n (2) \u201cTeachers must be just.\u201d\n\n (3) \u201cEvery form of unhappiness springs from a wrong condition of the\n mind.\u201d\n\n (4) \u201cCalmness of mind is one of the beautiful jewels of wisdom.\u201d\n\n2a. To clarify our ideas it is an excellent plan to select a group\nof words belonging to the same genus with a view of defining them as\nsimply and expeditiously as possible. As an illustration _building_\nmay be selected as a genus. The word _kind_ will suggest to us the\nspecies, such as dwelling, church, theatre, school, barn, bird-house,\ngranary and smoke-house. Next it is necessary to discover the basis of\ndistinction. This seems to be the use to which the building is put. Now\nwe are ready for the definitions:\n\n _Species_ _Genus_ _Differentia_\n\n A dwelling is a building where people live.\n A church is a building where people worship.\n A theatre is a building where people act.\n A school is a building where children are taught.\n A barn is a building where domestic animals, hay and\n grain are kept.\n A bird-house is a building designed for birds.\n A granary is a building where grain is stored.\n A smoke-house is a building where meat is smoked.\n\n2b. By selecting _man_ as the genus, define the terms Caucasian,\nMongolian, Ethiopian, Malay and American Indian. Treat the term _chair_\nin the same manner.\n\n3a. One may easily distinguish a property from an accident by asking\nhimself the question, \u201cWould subtracting the attribute from the term\nalter its identity\u201d? For example in the following, I find that the\nwords italicized are properties because subtracting each from the term\nchanges its identity:\n\n _Term_ _Attributes_\n\n man age, _rationality_, possessions.\n book _binding_, _leaves_, size, color, contents.\n radium _emits intense light and heat_, costs a million dollars\n a pound.\n snail _air-breathing mollusk_, moves slowly.\n slush _soft mud and snow_, six inches deep.\n\n3b. Indicate the common attributes of the following terms, underscoring\nthe properties: Tree, teacher, garden, house, river.\n\n4. The rules summarize well the essentials of the subject matter of the\nlogical definition. Therefore, it is highly important for the student\nto have these rules at the \u201ctip of the tongue.\u201d With this in view a\ndevice of this nature may be helpful. Make each letter of the word\nrules stand for the initial letter of a suggestive word in each of the\nfive _rules_. For example: r (repeat), u (unambiguous), l (language\naffirmative), e (essential), s (same size).\n\nWith a little study \u201cr and repeat,\u201d \u201cu and unambiguous,\u201d \u201cl and\nlanguage affirmative,\u201d \u201ce and essential,\u201d \u201cs and same size\u201d may be\nfirmly linked together in the memory. _Repeat_ suggests the third\nrule, do not repeat the name, etc.; _unambiguous_, the fourth rule,\nnot ambiguous language, etc.; _language affirmative_, the fifth rule;\n_essentials_, the first rule; _same size_, the second rule, subject\nand predicate must be of same size. The fact that the rules are not\nrecalled in order of treatment is inconsequential.\n\nIt is the writer\u2019s experience that fifteen minutes of concentrated\nstudy upon this device or one similar to it will indelibly stamp upon\nthe mind these troublesome rules.\n\nThe student may be able to devise a more helpful keyword.\n\n\n=13. REVIEW QUESTIONS.=\n\n (1) Why should the subject of definition appeal strongly to the\n school teacher?\n\n (2) Define a predicable.\n\n (3) Name in order the five predicables.\n\n (4) Define and illustrate the terms genus and species.\n\n (5) Explain the terms summum genus, infima species, sui generis.\n\n (6) Illustrate proximate genus.\n\n (7) Explain the terms genus and species as used in natural history.\n\n (8) Exemplify the double meaning of the genus man.\n\n (9) Define and illustrate differentia.\n\n (10) In what sense is the species a richer term than the genus?\n\n (11) Distinguish between property and accident.\n\n (12) Illustrate separable and inseparable accidents.\n\n (13) Give descriptive definitions of the following, indicating the\n five predicables: logic, general term, non-connotative term,\n obversion.\n\n (14) Define definition; illustrate.\n\n (15) Distinguish between definition and division.\n\n (16) Name, define and illustrate the three kinds of definitions.\n\n (17) Distinguish between real and verbal definitions.\n\n (18) Define in three ways the following: king, government, city, metal.\n\n (19) State the rules of logical definition.\n\n (20) What words may be used as _cues_ to aid in recalling the rules\n for logical definition?\n\n (21) Under what circumstances will the wise teacher make use of each\n of three kinds of definitions?\n\n (22) Relative to the second rule for logical definition what are the\n _three_ questions that one should ask himself?\n\n (23) Explain the exceptions to the third rule.\n\n (24) In connection with the fourth rule what may be said as to the use\n of technical terms?\n\n (25) What facts take from the force of the fifth rule?\n\n (26) What classes of words do not admit of logical definition?\n Illustrate.\n\n (27) Define education, teaching, instruction, training.\n\n (28) Distinguish by illustration between induction and synthesis;\n deduction and analysis.\n\n\n=14. QUESTIONS FOR ORIGINAL THOUGHT\nAND INVESTIGATION.=\n\n (1) Why should the _scholar_ be tempted to speak and write\n illogically?\n\n (2) Name the parts of speech that may be classed as predicables.\n\n (3) Explain the ten categories as given by Aristotle.\n\n (4) Show that genus and species are relative terms.\n\n (5) Why should the definition be needed most in the abstract sciences,\n such as theology, ethics, political economy, juris-prudence and\n psychology?\n\n (6) Define sin, life, wrong, personality, habit, character.\n\n (7) From the viewpoint of natural history find the species in the\n series of terms of which _polygon_ is a member.\n\n (8) What is the plural of differentia?\n\n (9) Why should logic insist upon the proximate genus?\n\n (10) (a) Man is a rational animal.\n (b) Man is a rational biped (proximate genus).\n\n In the case of the immature mind the first definition would be\n clearer. Why?\n\n (11) \u201cA property of a term is any mark or characteristic which belongs\n to that term.\u201d Is this definition logical? Give reasons.\n\n (12) What is the difference between the logical and the popular\n conception of _property_?\n\n (13) Is there any difference between the logical and popular\n conception of accidents?\n\n (14) \u201cThe term _conferentia_ might be used to stand for the essence of\n the genus, as the term differentia represents the essence of the\n species.\u201d[6] Explain this.\n\n (15) John Stuart Mill affirms that there is no such thing as a real\n definition. Discuss this.\n\n (16) In your opinion, of the five rules of logical definition what one\n is violated most by the average teacher? Give reasons.\n\n (17) Distinguish between symbol and content.\n\n (18) Why are descriptive definitions best for young children? What\n educational principle is involved?\n\n (19) From the standpoint of the five rules for logical definition\n criticise the following:\n\n (1) A man is a reasonable vertebrate.\n\n (2) A gentleman is a man with no visible means of support.\n\n (3) A man is an organized entity whose cognitive powers function\n rationally.\n\n (4) A metal is an element with a metallic luster.\n\n (5) A triangle is a figure of three sides.\n\n (6) A teacher is one who imparts knowledge.\n\n (7) Education is the process of drawing out all that is beautiful\n in the body and noble in the soul.\n\n (8) A democrat is a man who believes in free trade.\n\n (9) A government is a commonwealth controlled by direct vote of\n the people.\n\n (20) Write the foregoing definitions in logical form.\n\n (21) Since man is the only animal given to laughter, why is not the\n following a logical definition: \u201cMan is a laughing animal.\u201d\n\n (22) \u201cA logical definition should contain the species, the genus and\n the appropriate differentia.\u201d Is there any reason for using the\n term appropriate?\n\n (23) In connection with genus and species explain subaltern.\n\n (24) Is laughter a property of human being or an accident?\n\n (25) Show how a pedagogue may be an instructor but not a teacher.\n\n (26) Illustrate the complete method.\n\n (27) Show that induction may consist of a series of analyses; also a\n series of syntheses.\n\n\n\n\n CHAPTER 7.\n\n LOGICAL DIVISION AND CLASSIFICATION.\n\n\n=1. NATURE OF LOGICAL DIVISION.=\n\nThe term _genus_ is used for any class name which stands for two or\nmore subordinate classes while the term _species_ is made to stand for\nany one of the subordinate classes.\n\nThe proximate genus of any species is the _next_ class above. For\nexample the proximate genus of man is biped, not animal.\n\n_Logical division is the process of separating a proximate genus into\nits co-ordinate species._\n\n\n ILLUSTRATIONS:\n\n _Genus_ _Species_\n\n { Fixed stars\n { Planets\n (1) Heavenly bodies { Satellites\n { Comets\n { Meteors\n { Nebulae\n\n { Leptocardians\n { Fishes\n (2) Vertebrates { Amphibians\n { Reptiles\n { Birds\n { Mammals\n\n\n { Caucasian\n { Mongolian\n (3) Man { Malay\n { Ethiopian\n { American Indian\n\n { Monarchy\n (4) Government { Aristocracy\n { Democracy\n\n\n=2. LOGICAL DIVISION DISTINGUISHED FROM ENUMERATION.=\n\nWhen the genus is separated at once into _individual objects_ the\nprocess is not logical division, but simple enumeration. Logical\ndivision implies a separating into smaller class terms, each term being\na genus of still smaller subdivisions. This process may be continued\ntill the last division gives individuals as species. Enumeration takes\nplace when the first subdivision results in a list of individuals. To\nillustrate:\n\n _Logical Division._\n\n { Science teacher\n Teacher { Mathematics teacher\n { English teacher\n { Modern language teacher\n\n _Enumeration._\n\n { John J. Brown\n Teacher { H. G. White\n { Mary Jones\n { Alice Smith\n\n\n=3. LOGICAL DIVISION AS PARTITION.=\n\n_Partition is the process of separating an individual thing into its\nparts._\n\nThe partition is quantitative or mathematical when the separation is\nin terms of space or time, but when otherwise the partition becomes\nqualitative or logical. Or to put it in another way, the partition\nis mathematical when the separation gives parts and logical when the\nseparation gives ingredients.\n\nTo illustrate:\n\n { { branches\n { quantitative { leaves\n { or { roots\n { (mathematical) { trunk\n (1) Tree {\n { qualitative { woody fibre\n { or { capillary attraction\n { (logical) { sap\n { { chlorophyll\n\n { quantitative { roof\n { or { frame-work\n { (mathematical) { foundation\n (2) House {\n { qualitative { wood\n { or { iron\n { (logical) { stone\n { { plaster\n\nAn easy way to determine that the separation involves logical division\nproper and not partition is to affirm the connection between a class\nand a sub-class. To wit: A man is a biped; a square is a rectangle;\na Caucasian is a man, etc. If such an affirmation cannot be made then\nthe separation involved is not properly logical division but probably\npartition. For example it cannot be said that a _roof is a house_, or\nthat _sap is a tree_. It is seen, then, that a logical division of any\ngenus may be summarized in the form of a series of judgments of which\na species is the subject and the genus is the predicate. For example,\nby a logical division quadrilaterals may be divided into trapeziums,\ntrapezoids and parallelograms; this process may then be summarized in\na series of three judgments: (1) A trapezium is a quadrilateral; (2) A\ntrapezoid is a quadrilateral; (3) A parallelogram is a quadrilateral.\n\n\n=4. RULES OF LOGICAL DIVISION.=\n\nWhen the logical division of a genus is under consideration there are\nfour rules which should be observed.\n\nFIRST RULE. _There must be but one principle of division (fundamentum\ndivisionis)._ To divide mankind into white man, Australian, yellow man,\nAfrican and red man is a violation of this rule as the _two_ principles\nof color and geographical location are involved. A division in which\nmore than one principle is used is sometimes referred to as _cross\ndivision_ because the various species cross each other. For example in\nthe foregoing there are many white men who are Australians.\n\nThis rule applies only to one division. Where there is a series\nof divisions a new principle may be employed in each division. For\nexample, in dividing triangles into scalene, isosceles and equilateral,\nthe equality of sides is the principle involved, but, in subdividing\nisosceles triangles into right angled and oblique angled, the principle\nemployed concerns the nature of the angle.\n\nSECOND RULE. _The co-ordinate species must be mutually exclusive._\nThere must be no overlapping. The illustration given in the first\nrule is likewise a violation of this rule. Another example in which\nthis second rule is not obeyed may be found in most geometries where\ntriangles are divided into scalene, isosceles and equilateral. Here\nthe second and third classes are not mutually exclusive since all\nequilateral triangles are isosceles according to the usual definition,\n\u201cAn isosceles triangle is a triangle having two equal sides.\u201d All\nequilateral triangles have _two_ equal sides.\n\nTHIRD RULE. _The division must be exhaustive._ That is, the species\ntaken together must equal the whole genus. The sum of the species must\nbe co-extensive with the genus.\n\nDividing man into Caucasian, Ethiopian and Mongolian would be a\nviolation of this rule, as there are at least two other species of man,\nMalay and American Indian.\n\nA distinction should be made between an exhaustive division and\na complete division as the latter is not a logical requirement.\nTo divide government into monarchy, aristocracy and democracy is\nexhaustive but incomplete. Exhaustive because there is no other kind\nof government, all the species are included; but incomplete in that\nmonarchy may be divided into absolute and limited; democracy into pure\nand representative.\n\nFOURTH RULE. _The division must proceed from the proximate genus to the\nimmediate species._ There should be no sudden jumps from a high genus\nto a low species. The division must be gradual and continuous; step by\nstep. To divide government into limited monarchy, absolute monarchy,\npure democracy and representative democracy would be a violation of\nthis rule, as government is the proximate genus of monarchy, not of\nlimited monarchy, therefore one step has been omitted. Such an omission\ninvolves a step from grandfather to grandchild, so to speak, the\ngeneration of father having been left out.\n\nA violation of this rule is most insidious when some of the species\nof a subdivision are immediate while others are not. To wit: dividing\ngovernment into monarchy, aristocracy, pure democracy and republic,\nor dividing quadrilaterals into trapeziums, trapezoids, rectangles,\nsquares, rhomboids and rhombs.\n\n\n=5. DICHOTOMY.=\n\nDichotomy comes from the Greek, meaning _to cut in two_. _Dichotomy\nis a continual division of a genus into two species which are\ncontradictory in nature._\n\nContradictory terms are such as admit of no middle ground. They divide\nthe whole universe of thought into two classes. For example, honest and\nnot-honest, pure and impure, perfect and imperfect, are contradictory\nterms. Dichotomy thus affords an easy opportunity for an exhaustive\ndivision as in the use of contradictories nothing in the universe need\nbe omitted.\n\nAn historical illustration of dichotomy is the \u201cTree of Porphyry\u201d named\nafter Porphyrius, a Neo-Platonic philosopher of the third century.\n\n _Tree of Porphyry._\n\n Substance.\n / \\\n / \\\n Corporeal Incorporeal\n \\\n \\\n Body\n / \\\n / \\\n Animate Inanimate\n \\\n \\\n Living Being\n / \\\n / \\\n Sensible Insensible\n \\\n \\\n Animal\n / \\\n / \\\n Rational Irrational\n \\\n \\\n Man\n / | \\\n / | \\\n / | \\\n Socrates Plato Other Men\n\nThis kind of division is not altogether satisfactory as the negative\nside is too indefinite. On the other hand, if both subdivisions\nare made positive then there is danger of making the opposing terms\ncontrary rather than contradictory. This, of course, would be a\nserious logical fallacy, as contrary terms admit of middle ground while\ncontradictory terms give no choice, it is either the one or the other.\n\nThe use of dichotomy becomes evident in situations where new\nand unexpected discoveries may be made. Without disturbing the\nclassification the new species may be appended to the negative side\nof the division. The following illustrates:\n\n Vertebrates\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n \u2502 \u2502\n Leptocardians Not-leptocardians\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2510\n \u2502 \u2502\n Fish Not-fish\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2510\n \u2502 \u2502\n Amphibians Not-amphibians\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2510\n \u2502 \u2502\n Reptiles Not-reptiles\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2510\n \u2502 \u2502\n Birds Not-birds\n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2510\n \u2502 \u2502\n Mammals Not-mammals\n \u2502\n _The New Species_\n\n\n=6. CLASSIFICATION\u2015\u2015COMPARED WITH DIVISION.=\n\n_Classification is the process of grouping notions according to their\nresemblances or connections._\n\nSo far as results are concerned there is no difference between\nlogical division and classification. Both processes may give us the\nsame orderly scheme of heads and subheads. The difference lies in\nthe process itself. Division is _deductive_ in nature as it proceeds\nfrom the more general genus to the less general species. While\nclassification is _inductive_ as it groups the less general species\nunder the more general genus. Division differentiates unity into\nmultiplicity, while classification reduces multiplicity to unity. It\nfollows that the one is the inverse of the other. The difference in the\nmode of procedure may be illustrated by using the common classification\nor division of triangles. For example:\n\nWithout any knowledge of the kinds of triangles the student discovers\nby examining the various shapes of many triangles that there is a\ngroup in which _none_ of the sides are equal. For the lack of a better\nname he terms these non-equilateral (scalene). Further observation\ndiscloses another group in which two of the sides are equal. These he\nnames bi-equilateral (isosceles). Finally a third group is designated\nas tri-equilateral (equilateral). This process is classification.\nDivision would consist in separating the genus triangle into the three\nkinds\u2015\u2015scalene, isosceles, equilateral.\n\n\n=7. KINDS OF CLASSIFICATION\u2015\u2015ARTIFICIAL AND NATURAL.=\n\n_An artificial classification is one in which the grouping is made on\nthe basis of some arbitrary connection._ Cataloguing alphabetically the\nbooks in a library illustrates this kind of classification. Likewise\nthe arrangement of the names in a directory or a telephone book. The\nconnecting mark being the initial letter of the title or name. The\nreason why Mills and Meyers are put in the same group is that both\nnames happen to commence with the letter _M_.\n\nArtificial classifications are resorted to for some special purpose,\ndesigned by man, not by nature. Consequently artificial classifications\nare sometimes called _special_ or _working_ classifications.\n\n_A natural classification is one in which the grouping is made on the\nbasis of some inherent mark of resemblance._\n\nClassifications in animal and plant life are the best illustrations\nof this kind. Such classifications are suggested by nature and not by\nman, and may, therefore, be called _general_ or scientific. The main\naim of natural classification is to derive general truths and arrange\nknowledge so that it may be easily remembered.\n\n\n=8. TWO RULES OF CLASSIFICATION.=\n\nThe rules of logical division are applicable in the making of a logical\nclassification. In addition to these an artificial classification\nshould be made to conform to the one rule: _The classification must be\nappropriate to the purpose in hand._ Likewise a natural classification\nshould be made to conform to the rule: _Every classification should\nafford opportunity for the greatest possible number of general\nassertions._\n\n\n=9. USE OF DIVISION AND CLASSIFICATION IN THE SCHOOL ROOM.=\n\nIt has been stated that classification and division aim at the\nsame result. Classification reduces multiplicity to unity while\ndivision differentiates unity into multiplicity. In short, division is\n_deductive_ while classification is _inductive_ in mode of procedure.\nTherefore, classification should be used in those situations which\ncall for induction and division in cases where deduction is the better\nmethod.\n\nSpeaking generally, classification should be used with small children\nwhen the essential thing is to present the concrete facts with a view\nof leading the children to discover for themselves the truths contained\ntherein.\n\nWith older pupils division may be used, if the purpose is to set in\norder facts which are already known.\n\n\n=10. TOPICAL OUTLINE.=\n\n LOGICAL DIVISION AND CLASSIFICATION.\n\n (1) Nature of Logical Division.\n Genus\u2015\u2015species.\n Illustrations.\n\n (2) Logical Division Distinguished from Enumeration.\n Illustrations.\n\n (3) Logical Division and Partition.\n Quantitative\u2015\u2015qualitative.\n How summarized.\n\n (4) Four Rules of Logical Division.\n (1) One principle\u2015\u2015cross division.\n (2) Mutually exclusive.\n (3) Exhaustive\u2015\u2015complete.\n (4) Immediate species.\n\n (5) Dichotomy.\n Contradictory terms.\n Tree of Porphyry.\n Use illustrated.\n\n (6) Classification Compared with Division.\n\n (7) Kinds. Artificial\u2015\u2015Natural.\n\n (8) Two Rules of Classification.\n (1) Appropriate.\n (2) Afford many Assertions.\n\n (9) Use of Division and Classification.\n\n\n=11. SUMMARY.=\n\n(1) Logical division is the process of separating a proximate genus\ninto its co-ordinate species.\n\n(2) The first subdivision in a logical division gives class terms,\nwhile the first subdivision in an enumeration gives individual objects.\n\n(3) Partition is the process of separating an individual thing into\nits parts. These parts may be either quantitative or qualitative.\n\nA logical division of any genus may be summarized in a series of\njudgments of which a species is the subject and the genus is the\npredicate.\n\n(4) The four rules of logical division are: the division must (1) be\nbased on one principle, (2) have species mutually exclusive, (3) be\nexhaustive and (4) proceed from proximate genus to immediate species.\n\nA violation of the first rule gives a cross division.\n\nExhaustive division is easily confused with a complete or finished\ndivision.\n\n(5) Dichotomy is a continual division of a genus into two species which\nare contradictory in nature.\n\nAn historical illustration of dichotomy is the Tree of Porphyry.\n\nDichotomy is of service in the field of new and unexpected discoveries.\n\n(6) Classification is the process of grouping notions according to\ntheir resemblances or connections.\n\nClassification is inductive in nature, division deductive.\nClassification unifies, division differentiates.\n\n(7) An artificial classification is made on the basis of some\narbitrary connection; a natural classification, on some inherent mark\nof resemblance.\n\n(8) The rules of logical division are applicable in any classification.\nIn addition to these a classification should (1) be appropriate and\n(2) afford opportunity for the greatest possible number of assertions.\n\n(9) Classification should be the mode of procedure in the lower grades,\ndivision in the higher grades.\n\n\n=12. REVIEW QUESTIONS.=\n\n (1) Define and illustrate logical division.\n\n (2) What is the meaning of proximate genus?\n\n (3) How does logical division differ from enumeration? Illustrate.\n\n (4) Distinguish between logical division, and physical division or\n partition.\n\n (5) Illustrate a quantitative partition; a qualitative partition.\n\n (6) Illustrate how a logical division may be summarized in the form\n of a series of judgments.\n\n (7) State and explain the rules of logical division.\n\n (8) State the rules violated in the following divisions, explaining\n in full:\n\n { Primary\n { Secondary\n (1) Education { Collegiate\n { Technical\n { Scientific\n { Professional\n\n { Infancy\n (2) Life { Childhood\n { Youth\n { Old age\n\n { Caucasian\n { Ethiopian\n (3) Man { Malay\n { Mongolian\n { American\n\n { Cement\n { Frame\n (4) Buildings { Stone\n { Dwellings\n { Barns\n { Churches\n\n (9) Show the difference between contradictory and opposite terms.\n\n (10) Define dichotomy.\n\n (11) Illustrate the Tree of Porphyry and indicate its use to\n scientists.\n\n (12) Illustrate the difference between classification and division.\n\n (13) Why should classification be the mode of procedure when dealing\n with immature minds?\n\n (14) Illustrate the difference between an artificial and a natural\n classification.\n\n (15) State and explain the two rules of classification.\n\n (16) Show which of the following divisions are logical and which are\n not:\n (1) The manifestations of the mind into knowing, thinking and\n feeling.\n (2) Books into mathematical and non-mathematical.\n (3) Students into those who are industrious, athletic and\n shiftless.\n (4) Flowers into roses, carnations and lilies.\n (5) Planets into those which are larger than the earth and\n those which are smaller.\n\n\n=13. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Analyze by mathematical partition the terms world, plant, book.\n\n (2) Analyze by logical partition the terms granite, water, air.\n\n (3) What rule is violated if the logical division is applied to the\n genus rather than the proximate genus?\n\n (4) Divide logically the following terms: school, religion, book,\n vegetable, life.\n\n (5) \u201cEach new subdivision may adopt a new principle of division.\u201d\n Illustrate this.\n\n (6) Explain and illustrate the meaning of the terms super-ordinate,\n sub-ordinate and co-ordinate.\n\n (7) Define and illustrate metaphysical division and verbal division.\n\n (8) Give a definition of an isosceles triangle which will make\n logical the division of triangles into scalene, isosceles and\n equilateral.\n\n (9) \u201cThe evolution of all truth develops progressively through three\n stages.\u201d \u201cThe first is the thesis; the second is the antithesis;\n the third is the synthesis.\u201d Explain this in terms of trichotomy.\n\n (10) Illustrate the difference between a complete division and an\n exhaustive division.\n\n (11) Show in what ways, if any, the following divisions violate the\n rules of logical division.\n\n\n { 1 Memory (History)\n Human Learning { 2 Imagination (Poetry)\n (by Bacon) { 3 Reason (Philosophy)\n { or (the Sciences)\n\n { 1 Mathematics\n { 2 Astronomy\n Sciences { 3 Physics\n (by Comte) { 4 Chemistry\n { 5 Biology\n { 6 Sociology\n { 7 Morals\n\n\n\n\n CHAPTER 8.\n\n LOGICAL PROPOSITIONS\n\n\n=1. THE NATURE OF LOGICAL PROPOSITIONS.=\n\nJudging has been defined as the process of conjoining or disjoining\nnotions. This may be put in another way: \u201cJudging is the process of\nasserting or denying the agreement between two notions.\u201d The product\nof the act of judging is a judgment and when judgments are put in\nword-form such expressions are called logical propositions.\n\nDefinition: _A logical proposition is a judgment expressed in words._\nJust as percept and concept notions are expressed by means of logical\nterms so judgment notions may be expressed by logical propositions.\n\nTo illustrate: The terms _the squirrel_ and _cracking a nut_ express\ntwo notions, and when an agreement between them is asserted and the\nproduct is expressed in word form, then such an expression becomes the\nlogical proposition, \u201cThe squirrel is cracking a nut.\u201d\n\nThe following being _expressed_ judgments are logical propositions:\n\n (1) All men are mortal.\n\n (2) Some men are wise.\n\n (3) No men are immortal.\n\n (4) Some men are not wise.\n\n (5) No sane person is a lover of vice.\n\n (6) Some good orators are not good statesmen.\n\n (7) Every man is fallible.\n\n (8) If it rains, I shall not go.\n\n (9) He is either sane or insane.\n\n\n=2. KINDS OF LOGICAL PROPOSITIONS.=\n\nThere are three kinds of logical propositions; namely, categorical,\nhypothetical and disjunctive.\n\n_A categorical proposition_ is one in which the assertion is made\nunconditionally. _An hypothetical proposition_ is one in which the\nassertion depends upon a condition. _A disjunctive proposition_ is\none which asserts an alternative.\n\n\n THE THREE KINDS ILLUSTRATED:\n\n (1) \u201cEvery dog has his day.\u201d Categorical.\n\n (2) \u201cIf you do your best, success will reward you.\u201d Hypothetical.\n\n (3) \u201cHe is either stupid or indolent.\u201d Disjunctive.\n\n (4) \u201cAll vices are reprehensible.\u201d Categorical.\n\n (5) \u201cEither you are very talented or very industrious.\u201d Disjunctive.\n\n (6) \u201cIf capital punishment does not aid society, it should be\n abolished.\u201d Hypothetical.\n\n (7) \u201cYou may go provided your teacher is willing.\u201d Hypothetical.\n\n (8) \u201cNo intelligent man can ignore the practice of temperance.\u201d\n Categorical.\n\nBy studying the illustrations it will be observed that the categorical\npropositions are direct, bold, assertive statements, whereas the\nhypothetical are limited by conditions which make them less forceful.\nIn the second proposition, for example, \u201csuccess will reward you,\u201d\nis limited by the condition, \u201cIf you do your best.\u201d The disjunctive\nmay be regarded as categorical in form, but hypothetical in meaning,\nbecause in such a proposition as, \u201cHe is either, stupid or indolent,\u201d\na direct assertion is made which suggests the categorical, and yet it\nmay be implied that, if he is stupid then he is not indolent; this is\nindicative of the hypothetical.\n\nSome logicians classify propositions as categorical and conditional,\nthe conditional being subdivided into hypothetical and disjunctive. The\nfirst classification seems preferable, however, as it conforms to the\nthree modes of reasoning.\n\nThe common word-signs of the categorical proposition are _all_,\n_every_, _each_, _any_, _no_ and _some_, while those of the\nhypothetical are _if_, _even if_, _unless_, _although_, _though_,\n_provided that_, _when_, or any word or group of words denoting a\ncondition. The disjunctive symbols are _either\u2015\u2015or_.\n\n\n=3. THE FOUR ELEMENTS OF A CATEGORICAL PROPOSITION.=\n\nEvery categorical proposition should have four elements; namely,\nthe quantity sign, the logical subject, the copula and the logical\npredicate. In the foregoing categorical propositions the quantity signs\nare respectively, _every_, _all_ and _no_. In any case the quantity\nsign is always attached to the subject and indicates its breadth or\nextension. For example, in the two propositions, \u201cAll men are mortal\u201d\nand \u201cSome men are wise,\u201d the quantity sign _all_ makes the term _man_\nmuch broader than does the quantity sign _some_.\n\nThe logical subject of a categorical proposition is the term of which\nsomething is affirmed or denied, whereas the logical predicate of a\ncategorical proposition is the term which is affirmed or denied of\nthe subject. In the two propositions, \u201cAll men are mortal\u201d and \u201cNo men\nare immortal,\u201d the term about which something is affirmed or denied is\n_men_, while the terms which are affirmed and denied of the subject are\nrespectively _mortal_ and _immortal_. \u201cMen\u201d is, therefore, the logical\nsubject of each proposition, while \u201cmortal\u201d is the logical predicate\nof the first and \u201cimmortal\u201d the logical predicate of the second. The\ncopula is the connecting word between the logical subject and predicate\nand denotes whether or not the latter is affirmed or denied of the\nformer. The copula is always some form of \u201c_to be_\u201d or its equivalent.\nWhen the predicate is _denied_ of the subject, \u201c_not_\u201d may be used with\nthe copula and considered a part of it. To illustrate: in the logical\nproposition, \u201cSome men are not wise,\u201d \u201c_are not_\u201d may be regarded as\nthe copula.\n\nThe four elements are indicated in the following categorical\npropositions:\n\n _Quantity\n sign_ _Logical subject_ _Copula_ _Logical predicate_\n\n All fixed stars are self-luminous\n\n No wise man is going to steal\n\n Some quadrupeds are domestic animals\n\n Some glittering things are not gold\n\n Some boys are not discreet\n\n A few men are multi-millionaires\n\n Every citizen is duty-bound to vote\n\nThe student must ever keep in mind the fact that to be absolutely\nlogical all categorical propositions must be expressed in terms of\nthe _four elements_. However, life is too short and man is too busy to\nspeak always in terms of the four elements. Moreover, to be logical may\noften compel an awkwardness of expression and a lack of euphony which\ncould hardly be tolerated. For these reasons the utterances in ordinary\nconversation are frequently illogical so far as the four elements are\nconcerned, though not necessarily illogical in meaning. When it is\ndesired to test the validity of any series of statements leading up to\nsome generalization, it may become necessary to express the statement\nin terms of the four elements. The student should gain some facility\nin this, otherwise he may be readily led into fallacious reasoning.\n\nThe following statements taken at random from newspapers are given in\nthe original and then expressed in terms of the four elements:\n\n _The Original_ _In Terms of the Four Elements_\n\n (1) You came too late. (1) The person is one who came too\n late.\n\n (2) I saw the swell turnout (2) The man was one who saw the swell\n coming along. turnout coming along.\n\n (3) All of the men walked. (3) All of the men were those who\n walked.\n\n (4) The robbers cut a hole (4) All the robbers were the ones who\n in this floor. cut a hole in this floor.\n\n (5) Some of these flew away. (5) Some birds were those which\n flew away.\n\n (6) The rain interfered with (6) The rain was that which interfered\n the attendance. with the attendance.\n\n (7) Our habits make or (7) All our habits are forces which\n unmake us. make or unmake us.\n\n (8) We all had a fine time. (8) All the party were those who had\n a fine time.\n\nIn argumentative discourse it is often sufficient to \u201cthink the\nproposition\u201d in terms of the four elements without taking the time to\nactually express it.\n\n\n=4. LOGICAL AND GRAMMATICAL SUBJECT AND PREDICATE DISTINGUISHED.=\n\nThe grammatical subject is _one_ word while the logical subject is the\ngrammatical subject with all its modifiers except the quantity sign.\nFor example: in the proposition, \u201cAll white men are Caucasians,\u201d _men_\nis the grammatical subject, while _white men_ is the logical subject.\n_All_ being the quantity sign simply indicates the extension of _men_\nand is not a part of the logical subject.\n\nThe grammatical predicate is the verb-form together with any predicate\nnoun or adjective, while the logical predicate is the predicate word\nor words and all its modifiers. The grammatical predicate includes\nthe copula, but the logical predicate never includes the copula. The\ngrammatical predicate does not include the object, while the logical\npredicate always includes what is equivalent to the object and all\nits modifiers. To illustrate: in the proposition, \u201cSome men are wise,\u201d\n_are wise_ is the grammatical predicate, while _wise_ is the logical\npredicate. And in the proposition, \u201cHe burned the red house on the\nhill,\u201d _burned_ is the grammatical predicate, while _the one who burned\nthe red house on the hill_ is the logical predicate.\n\n\n=5. THE FOUR KINDS OF CATEGORICAL PROPOSITIONS.=\n\nCategorical propositions are divided according to their _quantity_\ninto _Universal_ and _Particular_ and according to their _quality_ into\n_Affirmative_ and _Negative_.\n\n_A universal proposition is one in which the predicate refers to the\nwhole of the logical subject._\n\n\n ILLUSTRATIONS:\n\n (1) All men are mortal.\n\n (2) All civilized men cook their food.\n\n (3) No dogs are immortal.\n\n (4) Every man was once a boy.\n\nConsidering the first proposition, \u201c_mortal_,\u201d the logical predicate,\nrefers to the whole of the logical subject \u201c_men_.\u201d Similarly \u201c_cook\ntheir food_\u201d refers to the whole of the term \u201c_civilized men_\u201d;\n\u201c_immortal_\u201d to the whole of the term \u201c_dogs_,\u201d and \u201c_once a boy_\u201d\nto the whole of the term \u201c_man_.\u201d\n\nIn considering the definition of a universal proposition it is\nnecessary to keep in mind the distinction between a logical and a\ngrammatical subject, as in the second proposition the logical predicate,\n\u201ccook their food,\u201d refers to only a part of the grammatical subject,\n_men_, and, therefore, the proposition might fallaciously be termed a\nparticular proposition rather than a universal.\n\n_A particular proposition is one in which the predicate refers to only\na part of the logical subject._\n\n\n ILLUSTRATIONS:\n\n (1) Some men are wise.\n\n (2) Some animals are not quadrupeds.\n\n (3) Most elements are metals.\n\n (4) Many children are mischievous.\n\nIn the foregoing propositions _some_, _most_ and _many_ are quantity\nsigns and, therefore, must not be considered as a part of the logical\nsubjects. Considering the logical subjects and predicates in order,\nthe term _wise_ refers to only a part of the _men_ in the world,\n_quadrupeds_ to only a part of the _animals_, _metals_ to only a part\nof the _elements_ and _mischievous_ to only a part of the _children_.\n\n_An affirmative proposition is one which expresses an agreement between\nsubject and predicate._\n\n_A negative proposition is one which expresses a disagreement between\nsubject and predicate._\n\nAffirmative propositions conjoin terms, negative propositions disjoin\nterms. In the first the agreement is affirmed; in the second the\nagreement is denied.\n\n\n ILLUSTRATIONS:\n\n None of the captives escaped. Negative.\n\n Some teachers are just. Affirmative.\n\n All trees grow towards heaven. Affirmative.\n\n Some people are not companionable. Negative.\n\n No person is above criticism. Negative.\n\nDividing both universal and particular propositions as to quality,\ngives four kinds; namely, universal affirmative, universal negative,\nparticular affirmative and particular negative. No topic in logic\ndemands greater familiarity than these four types, as every proposition\nmust be reduced to one of the four before it can be used as a basis of\nreasoning.\n\nFor the sake of brevity the symbols A, E, I and O are used to\ndesignate respectively the universal affirmative, the universal\nnegative, the particular affirmative and the particular negative. A and\nI, symbolizing the affirmative propositions, are the first and second\nvowels in _Affirmo_, while E and O, symbolizing the negatives, are the\nvowels in _Nego_. The common sign of the universal affirmative, or the\nA proposition is _all_; of the universal negative, or E proposition\n_no_; of the particular affirmative, or I proposition _some_; of the\nparticular negative, or O proposition _some_ with _not_ as a part of\nthe copula. The accompanying classification summarizes these facts,\nS and P being used to symbolize the terms \u201c_subject_\u201d and \u201c_predicate_.\u201d\n\n _Illustrations_\n\n { { Affirmative-A All S is P\n Categorical { Universal { Negative-E No S is P\n Propositions {\n { { Affirmative-I Some S is P\n { Particular { Negative-O Some S is not P\n\nHenceforth the symbols A, E, I, O will be used to designate the four\nkinds of categorical propositions. The propositions have other quantity\nsigns aside from the ones used above. These may be summarized:\n\n { A\u2015\u2015all, every, each, any, whole.\n { E\u2015\u2015no, none, all-not.\n Quantity signs of { I\u2015\u2015some, certain, most, a few, many, the\n { greatest part, any number.\n { O\u2015\u2015some - - not, few.\n\n\n=6. PROPOSITIONS WHICH DO NOT CONFORM TO THE LOGICAL TYPE.=\n\nIt has been observed that all expressed judgments must be reduced to\none of the four logical types A, E, I or O, before they can be used\nargumentatively. Logic insists upon definiteness and clearness\u2015\u2015there\nmust be no ambiguity, no opportunity for a wrong interpretation. From\nthis viewpoint the four types fulfill every requirement. Their meaning\ncannot be misunderstood. To any one with normal intelligence their\nsignificance may be made perfectly clear. Any argument when once put in\nterms of the four types may be spelled out with mathematical precision.\nIn consequence it is of prime importance that the four types not only\nbe well understood, but that a certain facility be gained in reducing\nordinary conversation to some _one_ of these types.\n\n(1) Indefinite and Elliptical Propositions.\n\nIt is known that every logical proposition must be expressed in terms\nof the four elements\u2015\u2015_quantity sign_, _logical subject_, _copula_ and\n_logical predicate_, consequently the four types A, E, I and O which\nepitomize every form of logical proposition, are expressed in terms\nof these four elements. But in common conversation often the quantity\nsign, as well as the copula, is omitted. See section 3.\n\nPropositions without the quantity sign are called _indefinite_,\nwhile those with the suppressed copula may be termed _elliptical_\npropositions. Both may be made logical as the attending illustrations\nwill indicate:\n\n _Illogical_ _Logical_\n\n _Indefinite_\n Men are fighting animals. _All_ men are fighting animals.\n (A)\n\n Lilies are not roses. _No_ lilies are roses. (E)\n\n Good is the object of moral _All_ good is the object of moral\n approbation. approbation. (A)\n\n Perfect happiness is _In all cases_ perfect happiness\n impossible. is impossible. (A)\n\n _Elliptical_\n Fashion rules the world. _All_ fashions _are_ ruling the\n world. (A)\n\n Trees grow. _All_ trees _are plants which_\n grow. (A)\n\n Children play. _All_ children _are_ playful. (A)\n\n Some men cheat. Some men _are persons who_ cheat.\n (I)\n\nHere it is noted that the logical form of some propositions is not\nalways the most forceful. Often the logical form gives an awkward\nconstruction and should be resorted to only for purposes of logical\nargument.\n\nThe reduction of either kind to the logical form must be determined\nby the meaning of the proposition. As a usual thing the indefinite is\n_universal_ (either an A or an E) in meaning, while the problem of the\nelliptical is to give it in terms of the _copula_, expressed with as\nlittle awkwardness as possible.\n\nGeneral truths, because attended with no quantity sign, might be\nclassed as indefinite propositions, though their universality is so\napparent that they may be unhesitatingly classed as universals.\n\n\n ILLUSTRATIONS:\n\n \u201cThings equal to the same thing are equal to each other.\u201d\n\n \u201cTrees grow in direct opposition to gravity.\u201d\n\n \u201cHonesty is the best policy.\u201d\n\n \u201cA stitch in time saves nine.\u201d\n\nBecause the indefinite proposition is so frequently of a general\nnature, it is sometimes classed as _general_ rather than _indefinite_.\n\nSir William Hamilton would class the indefinite as an _indesignate\nproposition_.\n\n(2) Grammatical Sentences.\n\nThe grammarian divides sentences into five kinds; namely, declarative,\ninterrogative, imperative, optative, exclamatory. But logic recognizes\nonly the declarative, as it has already been seen that the four logical\ntypes are declarative in nature. A logical proposition, then, is always\na sentence, but all sentences are not logical propositions. The four\nkinds of sentences which are not logical propositions may be usually\nreduced to one of the four types as the attending illustrations will\nindicate:\n\n _Illogical_ _Logical_\n\n Interrogative. Do men have The question is asked, Do men have\n the power of reason? the power of reason?[7] (A)\n\n Imperative. \u201cThou shalt not All men are commanded not to\n steal.\u201d steal, or you are one who should\n not steal. (E)\n\n Optative. \u201cI would I had a I am one who desires a million\n million.\u201d dollars. (A)\n\n Exclamatory. \u201cOh, how you You are one who frightened me. (A)\n frightened me!\u201d\n\n(3) Individual Propositions.\n\n_An individual proposition is one which has a singular subject_; e. g.,\n_Abraham Lincoln_ was an honest man. _Peter the Great_ was Russia\u2019s\ngreatest ruler. _The maple tree in my yard_ is dying of old age. These\npropositions, having a singular term as subject, are individual or\nsingular in nature. As the predicate refers to the whole of the logical\nsubject, individual propositions are classed as _universal_.\n\n(4) Plurative Propositions.\n\nPlurative propositions are those introduced by \u201cmost,\u201d \u201cfew,\u201d \u201ca few,\u201d\nor equivalent quantity signs. For example, \u201c_Most_ birds are useful to\nman\u201d; \u201c_Few_ men know how to live\u201d; \u201c_A few_ of the prisoners escaped,\u201d\nare plurative propositions. \u201cMost\u201d means more than half, while \u201cfew\u201d\nand \u201ca few\u201d mean less than half. In either case the proposition is\nparticular. Stated logically, the illustrative propositions would take\nthe form of \u201cSome birds are useful to man\u201d; \u201cSome men do not know how\nto live\u201d; \u201cSome of the prisoners escaped.\u201d\n\nThe reader will observe the difference in significance between _few_\nand _a few_. The former is negative in character and when introducing\na proposition makes it a particular negative (O). The latter always\nintroduces a particular affirmative (I).\n\n(5) Partitive Propositions.\n\nPartitive propositions are particulars which imply a complementary\nopposite. These arise through the ambiguous use of _all-not_, _some_\nand _few_. _All-not_ may sometimes be interpreted as _not all_ and\nsometimes as _no_. To illustrate: The proposition, \u201cAll men are\nnot mortal,\u201d is distinctly a universal negative or an E, while the\nproposition, \u201cAll that glitters is not gold,\u201d is a particular negative\nor an O. The logical form of the first is, \u201cNo men are mortal,\u201d and\nof the second, \u201cSome glittering things are not gold.\u201d When used in the\n\u201cnot-all\u201d sense, the proposition is partitive because if the O-meaning\nis intended the I is implied. For example, \u201cAll that glitters is not\ngold,\u201d is partitive because the statement implies that some glittering\nthings _are_ gold (I) as well as the complement, \u201cSome glittering\nthings _are not_ gold\u201d (O). A knowledge of both the affirmative and\nnegative aspects is taken for granted in the statement of either the\none or the other.\n\n\u201cAll-not,\u201d then, is negative in any case, but universal when it\nmeans _no_ and particular when it means _not all_. Any proposition is\npartitive in nature when the quantity sign is _not all_, or _all-not_\ninterpreted as the equivalent of _not all_.\n\nIt may be observed here that _all_ has two distinct uses. First, it\nmay be used in a collective sense; second, in a distributive sense. For\nexample: _All_ is used in the _collective_ sense in such propositions\nas, \u201cAll the members of the football team weighed exactly one ton,\u201d or\n\u201cAll the angles of the triangle are equal to two right angles.\u201d Using\n_all_ in the distributive sense would make true these: \u201cAll the members\nof the football team weigh more than 140 pounds\u201d; \u201cAll the angles of\na triangle are less than two right angles.\u201d _All_ is used collectively\nwhen reference is made to an aggregate, but distributively when\nreference is made to each.\n\nThe quantity sign _some_ is likewise ambiguous, as it may mean (1) some\nonly\u2015\u2015some, but not all, or (2) some at least\u2015\u2015some, it may be all or\nnot all. When \u201csome\u201d is used as the quantity sign of any particular\nproposition which has been accepted as logical, the second meaning,\n\u201csome at least,\u201d is always implied. This interpretation of \u201c_some_\u201d\nwill be explained more in detail in a succeeding section.\n\nWhen _some_ is used in the sense of _some only_, the partitive nature\nof the proposition is apparent, as both I and O are implied. For\nexample, with reference to the human family, to say that \u201csome only are\nwise\u201d necessitates an investigation, which leads to the discovery that\nsome are wise, while others are not wise. If the proposition be an I,\nthen its complementary O is implied, or if it be an O, the I is implied.\n\n_Few_ given as a sign of a plurative proposition also serves as a sign\nof the partitive. The plurative aspect is prominent when it is said\nthat \u201cFew men can be millionaires\u201d and emphasis is placed upon the\nmeaning that \u201cMost men cannot be millionaires.\u201d But when emphasis is\ngiven to \u201cfew,\u201d as meaning _few only_ rather than the _most are not_,\nthen the I and the O are both implied; e. g., _Some men become\nmillionaires, but the most do not_.\n\nTo put it in a word, \u201call-not,\u201d \u201csome\u201d and \u201cfew\u201d introduce\npartitive propositions when the meaning implies both an I and an O.\nWhen treating such in logic the meaning which seems to be given the\ngreater prominence must be accepted. Surely in the statement, \u201cAll that\nglitters is not gold,\u201d the O-interpretation is the one intended; namely,\n\u201cSome things which glitter are not gold.\u201d\n\n\n ILLUSTRATIONS:\n\n (1) \u201c_All_ men are not honest.\u201d\n\n (2) \u201c_Few_ men live to be a hundred.\u201d\n\n (3) \u201c_Some_ men are consistent.\u201d\n\nThe first proposition with the emphasis placed upon _all_ suggesting\nthat _some men are not honest_, is the intended proposition while _some\nmen are honest_ is the implied. In reducing it to the logical form the\nintended proposition is the one which should be used.\n\nWith the emphasis upon _few_ and _some_, the second and third\npropositions may be interpreted as follows: (2) Intended proposition,\n_Some men do not live to be a hundred_. Implied proposition, _Some\nmen do live to be a hundred_. (3) Intended proposition, _Some men are\nconsistent_. Implied proposition, _Some men are not consistent_.\n\n(6) Exceptive Propositions.\n\nThese are introduced by such signs as _all except_, _all but_,\n_all save_. To wit: (1) \u201c_All except_ James and John may be excused\u201d;\n(2) \u201c_All but_ a few of the culprits have been arrested\u201d; (3) \u201c_All_\nbirds _save_ the English sparrow are serviceable to man\u201d are exceptive\npropositions.\n\nExceptive propositions are universal when the exceptions are mentioned.\nUniversal propositions necessitate a subject more or less definite, as\nthe predicate of such must refer to the whole of a _definite_ subject.\nIt follows that in exceptive statements definiteness is secured when\nthe exceptions are mentioned, therefore it becomes clear how all\nsuch propositions must be universal. Of the illustrations, the first\nand third propositions are universal. Any exceptive proposition is\nparticular when the exceptions are referred to in general terms or\nwhen the subject is followed by _et cetera_. The second illustrative\nproposition is particular.\n\n(7) Exclusive Propositions.\n\nOf all propositions which vary from the logical form the exclusive\nis the most misleading. Exclusives are accompanied by such words as\n\u201conly,\u201d \u201calone,\u201d \u201cnone but,\u201d and \u201cexcept.\u201d Their peculiarity rests\nin the fact that reference is made to the _whole_ of the predicate,\nbut only to a _part_ of the subject. For example, in the exclusive\nproposition, \u201cOnly elements are metals,\u201d _metals_ is referred to as\na whole while _elements_ is considered only in part. The true meaning\nis \u201cSome elements are all metals,\u201d or to put it in logical form, \u201cAll\nmetals are elements.\u201d _The easiest way to deal with an exclusive is\nto interchange subject and predicate (convert simply) and call the\nproposition an A._\n\n\n PROCESS ILLUSTRATED:\n\n _Exclusive Proposition_ _Reduced to Logical Form_\n\n 1. None but high school All who enter Training School\n graduates may enter must be high school graduates.\n Training School.\n\n 2. Only first-class All parlor cars are for\n passengers are allowed in first-class passengers.\n parlor cars.\n\n 3. Residents alone are All who are licensed to teach are\n licensed to teach. residents.\n\n 4. No admittance except on All who have business may be\n business. admitted.\n\n 5. Only bad men are not-wise. All who are not-wise are bad men.\n\n 6. Only some men are wise. All who are wise are men.\n\nIt is claimed by good authority that the real nature of the exclusive\nis best expressed by _negating_ the subject and calling the proposition\nan E; e. g., exclusive: \u201cOnly elements are metals\u201d; logical form: \u201cNo\nnot-elements are metals\u201d (E). In a succeeding chapter it is explained\nhow an E admits of first simple conversion and then obversion. The\nfollowing illustrate these two processes:\n\n _Original E_: \u201cNo not-elements are metals.\u201d\n\n _Simple conversion_: \u201cNo metals are not-elements.\u201d\n\n _Obversion_: \u201cAll metals are elements.\u201d\n\nFrom this it may be seen that the statement, \u201cThe easiest way to deal\nwith an exclusive is to interchange subject and predicate and call the\nproposition an A,\u201d is substantially correct.\n\n(8) Inverted Propositions.\n\nThe poet often employs the inverted proposition, illustrated by\nthe following: \u201cBlessed are the merciful;\u201d \u201cGreat is this man of\nwar.\u201d An interchanging of subject and predicate makes these poetical\nconstructions logical; e. g., \u201cAll the merciful are blessed;\u201d \u201cThis man\nof war is great.\u201d\n\nNOTE.\u2015\u2015The student should not be misled by the relative clause. Often\nit may be interpreted as a part of the predicate rather than the\nsubject. To wit: \u201cNo man is a friend who betrays a confidence\u201d; clearly\nthe logical subject is _no man who betrays a confidence_.\n\n\n=7. PROPOSITIONS WHICH ARE NOT NECESSARILY ILLOGICAL.=\n\n(1) _Analytic and Synthetic Propositions._\n\n_An analytic proposition is one in which the predicate gives\ninformation already implied in the subject._ Thus, \u201c_Fire burns_,\u201d\n\u201c_Water is wet_,\u201d \u201c_A triangle has three angles_\u201d are analytic\npropositions because the predicates do not give added information\nto one who has any conception of the subjects. Because the attribute\nmentioned by the predicate is an essential one, analytic propositions\nare sometimes termed _essential_ propositions. Other names for the same\nkind of proposition are _verbal_ and _explicative_.\n\n_A synthetic proposition is one in which the predicate gives\ninformation not necessarily implied in the subject. \u201cFire protects men\nfrom the wild animal.\u201d \u201cA cubic foot of water weighs 62\u00bd lbs.\u201d \u201cThe sum\nof the interior angles of a triangle is equal to two right angles.\u201d_\nThese are synthetic because a common conception of the meaning of\nthe subject would not need to include the information given by the\npredicate. Other names for synthetic propositions are _accidental_,\n_real_ and _ampliative_.\n\nThe distinction between analytic and synthetic propositions is not\nso clear as would on first thought appear. \u201c_Fire burns_\u201d might give\nadded information to the child or savage who knows only of the light\nemitted by fire. To them, then, the proposition would be synthetic. The\ndistinction must be based upon the assumption that the same words mean\nabout the same thing to people in general.\n\nThis analytic-synthetic division of propositions finds a significance\nin the domain of philosophy. To the logician the distinction is of\nslight importance save in the so-called verbal disputes, viz.: disputes\nwhich turn on the meaning of words.\n\n(2) _Modal and Pure Propositions._\n\n_A modal proposition states the mode or manner in which the predicate\nbelongs to the subject._ The signs of modal propositions are the\nadverbs of time, place, degree, manner. Illustrations: \u201cJames is\nwalking _rapidly_.\u201d \u201cHonesty is _always_ the best policy.\u201d \u201cAristotle\nwas _probably_ the greatest thinker of ancient times.\u201d\n\n_A pure proposition simply states that the predicate belongs, or\ndoes not belong, to the subject._ Illustrations: \u201cJames is walking.\u201d\n\u201cHonesty is the best policy.\u201d \u201cAristotle was the greatest thinker of\nancient times.\u201d\n\nSome logicians refer to modal propositions as being such as indicate\n_degrees_ of belief. Such words as \u201cprobably,\u201d \u201ccertainly,\u201d etc., would\nindicate their modality.\n\nAs logic has to do with the pure proposition and not the modal, the\ndifference of opinion is of little import.\n\n(3) _Truistic Propositions._\n\n_A truistic proposition is one in which the predicate repeats the words\nand the meaning of the subject._ Illustrations: \u201cA man is a man,\u201d \u201cA\nbeast is a beast,\u201d \u201cA traitor is a traitor,\u201d \u201cWhat I have done I have\ndone.\u201d\n\nThe truistic proposition is of little importance except in cases\nwhere the subject is used extensionally while the predicate is used\nintensionally. In the illustration, \u201cA man is a man,\u201d the subject\nmerely stands for a member of the man family, while the predicate may\nindicate certain manly qualities. Against such ambiguities the logician\nmust be on guard.\n\n\n=8. THE RELATION BETWEEN SUBJECT AND PREDICATE.=\n\nIn Chapter 5 the extension and intension of terms was explained. The\nstudent recalls, for instance, that the term \u201cman\u201d may be used to\ndenote objects, as \u201cwhite man,\u201d \u201cblack man,\u201d \u201cred man,\u201d etc. In this\nsense the term \u201cman\u201d is used _extensionally_. But when made to stand\nfor the attributes \u201crationality,\u201d \u201cpower of speech,\u201d etc., the term\n\u201cman\u201d is used intensionally.\n\nIn considering the relation between subject and predicate it is\ncustomary to employ the terms in an extensional sense only, since such\na restriction serves the purpose of syllogistic reasoning and\nconversion.\n\nLet us, then, give attention to the _extension_ of the subject and\npredicate of the categorical propositions A, E, I, O.\n\n(1) _The Universal Affirmative or A Proposition._\n\n_All S is P symbolizes the A proposition._ This may be interpreted as\nmeaning that all of the subject belongs to a part of the predicate, or\nthat all of the subject belongs to all of the predicate. The first\ninterpretation is the usual one and may be illustrated by the following\npropositions:\n\n 1. \u201cAll men are mortal.\u201d\n\n 2. \u201cAll trees grow.\u201d\n\n 3. \u201cAll metals are elements.\u201d\n\nIt is obvious that the subjects of these propositions include every\nspecimen of the particular class mentioned. For example: The subject\n_all men_ includes every specimen of the human family; _all trees_\nincludes every object of that class; _all metals_ covers everything\nwhich the scientist classes as such. In the three propositions, then,\nreference is made to the _whole_ subject but to only a _part_ of the\npredicate, as other beings beside men, such as the horse, are mortal;\nand other plants aside from trees, such as the sun flower, grow; other\nsubstances, namely oxygen, are elements.\n\nFor the sake of making the logical meaning of the four propositions\nclearer, recourse may be made to Euler\u2019s diagrams, so named because\nthe Swiss mathematician and logician, Leonhard Euler, first used them.\n\nThe first illustration of the A proposition, \u201cAll men are mortal,\u201d\nmay be represented by two circles, a larger circle standing for the\npredicate, _mortal_, and a smaller circle entirely inside the larger\nrepresenting the subject, _men_. Thus:\n\n Illustration: FIG. 1.\n\nIt is evident that all of the smaller circle belongs to the larger.\nThis diagram will then fit any proposition where it may be said that\nall of the subject belongs to a part of the predicate, or which may\nbe symbolized as \u201cAll S is some P.\u201d (All the subject is some of the\npredicate.)\n\nThe student knows that circles are plane surfaces and when such a\nstatement as \u201cAll men are mortal\u201d is given, reference is made to only\nthat part of the \u201cmortal\u201d circle which is _directly underneath_ the\n\u201cmen\u201d circle. Nothing has been said relative to the remaining part of\nthe \u201cmortal\u201d circle.\n\n\u201c_A_\u201d propositions which may be interpreted as meaning \u201cAll S is\nall P\u201d are called co-extensive A\u2019s because the subject and predicate\nare exactly equal in extension. Such propositions are best illustrated\nby definitions; e. g.:\n\n 1. \u201cA man is a rational biped.\u201d\n\n 2. \u201cA trigon is a polygon of three sides.\u201d\n\n 3. \u201cTeaching is the art of occasioning those activities which result\n in knowledge, power and skill.\u201d\n\nTo represent the meaning of the co-extensive A by the Euler diagram,\ntwo circles of the same size may be drawn, one coinciding at every\npoint with the other. If the first circle is drawn heavily in black and\nthe second dotted in red, it will make clear to the eye that there are\ntwo circles.\n\n(2) _The Universal Negative or E Proposition._\n\n_\u201cNo S is P\u201d best symbolizes the E proposition_, though sometimes the\nuniversal negative is written \u201cAll S is not P.\u201d This latter form, as\nhas been explained, is ambiguous and therefore illogical.\n\n\u201cNo S is P\u201d surely means that no part of the subject belongs to any\npart of the predicate and no part of the predicate belongs to any part\nof the subject. The subject and predicate are mutually exclusive.\n\nThe following illustrate the E proposition:\n\n 1. \u201cNo man is immortal.\u201d\n\n 2. \u201cNo true teacher works for money.\u201d\n\n 3. \u201cNo thorough student can remain unwise.\u201d\n\n The E proposition may be represented by two circles, the\none entirely without the other as in Fig. 2:\n\n Illustration: FIG. 2.\n\n(3) _The Particular Affirmative or I Proposition._\n\n_This may be symbolized as \u201cSome S is P,\u201d_ and considered as meaning\nthat a _part_ of the subject belongs to a _part_ of the predicate. It\nhas already been noted that \u201csome\u201d is ambiguous and that its logical\nsignification is \u201csome at least_.\u201d (It may be all or it may not be\nall.) For example, the only logical interpretation which can be placed\non \u201cSome men are wise\u201d is, that the investigation has resulted in\nfinding only a _part_ of the man family wise. Whether or not all are\nwise is unknown as the entire field has not received attention. In no\ncase can it be assumed that all the others are _not_ wise.\n\nThe I proposition illustrated:\n\n 1. \u201cSome men are wise.\u201d\n\n 2. \u201cSome animals are vertebrates.\u201d\n\n 3. \u201cSome teachers are inspiring.\u201d\n\nThe meaning of the I proposition may be represented by two circles\nintersecting each other:\n\n Illustration: FIG. 3.\n\nThe significant feature of the diagram is the shaded part which\nrepresents a part of the \u201cmen\u201d circle as belonging to a part of the\n\u201cwise\u201d circle. The unshaded part of each circle is the unknown field.\n\n(4) _The Particular Negative or O Proposition._\n\n_The common symbolization of the O is \u201cSome S is not P.\u201d_ Put in\nstatement form: Some of the subject is excluded from the whole of the\npredicate. Here, as in the I, the same logical import must be given to\n_some_; e. g., in the proposition, \u201cSome men are not wise,\u201d our\nknowledge is confined to the group who are not wise. Whether or not the\nothers are wise or not-wise is unknown.\n\nIllustrations of the O proposition:\n\n 1. \u201cSome men are not wise.\u201d\n\n 2. \u201cSome laws are not just.\u201d\n\n 3. \u201cSome novels are not helpful.\u201d\n\nThe significance of the O proposition may be shown by two intersecting\ncircles as in Fig. 4:\n\n Illustration: FIG. 4.\n\nA similar diagram represents the I proposition, the only difference\nbeing in the _part shaded_. In the O proposition the investigated field\nis all of the \u201cmen\u201d circle _outside_ of the \u201cwise\u201d circle, while in the\nI proposition the known field is that part of the \u201cmen\u201d circle _inside_\nthe \u201cwise\u201d circle.\n\nIn comparing the four diagrams the student will note that the\naffirmative propositions are _inclusive_, while the negative\npropositions are _exclusive_.\n\n(5) _The Distribution of Subject and Predicate._\n\n_A term is said to be distributed when it is referred to as a definite\nwhole._\n\nIn the proposition, \u201cAll men are mortal,\u201d the subject _all men_ is\nconsidered as a whole. \u201c_All_ men\u201d stands for every specimen of the\nhuman race; not a single one has been left out. Again, _the whole_ is\ndefinite; any one, if he were given the time and opportunity, could\nascertain by actual count just how many \u201call men\u201d represented.\n\nIt should be observed that if the word _definite_ is not incorporated\nin the definition of a distributed term, there is afforded an\nopportunity for error. The attending illustrations will make this clear:\n\n 1. \u201cAll the students except John and James are dismissed.\u201d\n\n 2. \u201cAll the students except John, James, etc., are dismissed.\u201d\n\nThe subject of the first proposition is distributed, while the subject\nof the second is undistributed. Reasons: The first subject, \u201cAll the\nstudents except John and James,\u201d is referred to as a whole and that\nwhole is definite, therefore, it is distributed; the second subject,\n\u201cAll the students except John, James, etc.,\u201d is referred to as a whole,\nbut as the whole is not definite, the term is not distributed. Because\n_all_ is the quantity sign of the second subject the casual observer\nmight easily be misled in designating it as a distributed term.\n\nHere it may be well to explain that when reference is made to subject\nor predicate the _logical_ subject or predicate is meant. Unless this\nis constantly kept in mind error results; e. g., in the proposition,\n\u201cAll white men are Caucasians,\u201d the logical subject is \u201cwhite men,\u201d\nnot \u201cmen.\u201d If the subject were \u201cmen,\u201d it would be undistributed, as\nthe whole of the man family is not considered, but the actual subject,\nbeing \u201cwhite men,\u201d _is_ distributed because the predicate refers to\n_all_ white men.\n\nRecurring to the illustration, \u201cAll men are mortal,\u201d we have concluded\nthat the subject \u201call men\u201d is distributed. The predicate, \u201cmortal,\u201d\nhowever, is undistributed, as reference is made to it only in part;\ni. e., there are other beings aside from men that are mortal, such as\n\u201ctrees,\u201d \u201chorses,\u201d \u201cdogs,\u201d etc. _In all A propositions of the type of\n\u201call men are mortal,\u201d the subject is distributed while the predicate\nis undistributed._ This relation is clearly shown by the diagrammatical\nillustration, Fig. 1. Here _all_ of the \u201cmen\u201d circle is identical with\nonly a part of the \u201cmortal\u201d circle. In other words, the _whole_ of the\n\u201cmen\u201d circle is considered, while reference is made to only a _part_ of\nthe \u201cmortal\u201d circle.\n\n_In the case of the co-extensive A both subject and predicate are\ndistributed._ Relative to the co-extensive \u201cAll men are rational\nanimals,\u201d it could likewise be said that \u201call rational animals are\nmen,\u201d or that \u201call men are all of the rational animals.\u201d Reference is\nthus made to _all_ of the definite predicate as well as to all of the\ndefinite subject.\n\nIn the E propositions, such as \u201cNo men are immortal,\u201d the whole of the\nsubject is excluded from the whole of the predicate. This makes evident\nthe fact that _both terms are distributed_. See Fig. 2.\n\nThe I proposition, such as \u201cSome men are wise,\u201d concerns itself with\nonly a part of the subject and only a part of the predicate,\n_consequently neither subject nor predicate is distributed_. This\nrelation is verified by the representation, Fig. 3.\n\n_In the O proposition the subject is undistributed, while the predicate\nis distributed._ For example, in the proposition, \u201cSome men are not\nwise,\u201d \u201csome men\u201d would indicate that only a part of the logical\nsubject is under consideration. But the predicate is distributed\nbecause \u201csome men\u201d is denied of the _whole_ of the predicate, \u201cwise.\u201d\nThis may become clear by studying Fig. 4. Here all of the shaded part\nwhich stands for the subject, \u201csome men,\u201d is excluded from the whole\nof the \u201cwise\u201d circle. But all of the shaded part is only a part of the\nentire \u201cmen\u201d circle, consequently the subject which the shaded part\nrepresents (some men) is undistributed. The predicate, \u201cwise,\u201d however,\nis distributed, as the subject is excluded from every part of it. It is\nwell to remember that _not_, when used with the copula, distributes the\npredicate which follows it.\n\nIf the student is to succeed in testing the value of arguments, he must\never have \u201cat the tip of his tongue\u201d his knowledge of the distribution\nof the terms of the four logical propositions. With this in view the\nfollowing schemes are offered:\n\n I.\n\n _Subject_ _Predicate_\n\n A distributed undistributed\n\n E distributed distributed\n\n I undistributed undistributed\n\n O undistributed distributed\n\n II.\n\n A distributed undistributed\n\n O undistributed distributed\n\n E distributed distributed\n\n I undistributed undistributed\n\n III.\n\n A All S is P\n \u2514\u2500\u2518\n E No S is P\n \u2514\u2500\u2518 \u2514\u2500\u2518\n I Some S is P\n\n O Some S is not P\n \u2514\u2500\u2518\n\nReferring to scheme II it may be observed that A and O contradict each\nother; i. e., where A is distributed O is undistributed and vice versa.\nA similar relation exists between E and I.\n\nIn scheme III the bracket \u2514\u2500\u2518 under the symbol indicates the term which\nis distributed.\n\nIV. As a fourth scheme a \u201ckey word\u201d might be adopted. Any of these\nthree might be used: (1) saepeo, or (2) asebinop, or (3) uaesneop.\nThe significance of \u201csaepeo\u201d is this: \u201c_s_\u201d stands for _subject\ndistributed_, \u201c_p_\u201d for _predicate distributed_, \u201c_a_\u201d \u201c_e_\u201d \u201c_o_\u201d\nfor the _logical propositions_ where any distribution occurs. Putting\nthe letters together gives this: subject distributed of propositions\nA and E, predicate distributed of propositions E and O.\n\nSimilarly, \u201casebinop\u201d stands for this: \u201c_as_,\u201d _a_ distributes its\n_s_ubject; \u201c_eb_\u201d _e_ distributes _b_oth; \u201c_in_,\u201d _i_ distributes\n_n_either; \u201c_op_,\u201d _o_ distributes the _p_redicate.\n\nIn the coined word \u201c_uaesneop_\u201d appear six letters which compose\n\u201csaepeo,\u201d and the letters have the same significance. The two\nadditional letters, u and n, stand for universal and negative. The\ninterpretation of the entire word, therefore, is this: \u201c_uaes_,\u201d\nthe _u_niversals _a_ and _e_ distribute their _s_ubjects; _neop_,\nthe _n_egatives _e_ and _o_ distribute their _p_ redicates.\n\nIt seems to me that the last word is the most helpful as it emphasizes\nthe two facts which are the most used; namely, (1) Only the universals\ndistribute their subjects; (2) Only the negatives distribute their\npredicates.\n\nIf the student will visualize \u201c_uaesneop_\u201d so thoroughly as never\nto forget it, he will not experience difficulty in determining the\ndistribution of the terms of the four logical propositions.\n\n\n=9. OUTLINE.=\n\n LOGICAL PROPOSITIONS.\n\n (1) The nature of logical propositions.\n\n (2) Kinds of logical propositions.\n Categorical\n Hypothetical\n Disjunctive\n\n (3) The four elements of a categorical proposition.\n\n (4) Logical and grammatical subject and predicate distinguished.\n\n (5) The four kinds of categorical propositions.\n Universal affirmative A\n Universal negative E\n Particular affirmative I\n Particular negative O\n\n (6) Propositions which do not conform to the logical type.\n Indefinite and elliptical\n Grammatical sentences\n Individual\n Plurative\n Partitive\n Exceptive\n Exclusive\n Inverted\n\n (7) Propositions not necessarily illogical.\n Analytic and synthetic\n Modal and pure\n Truistic\n\n (8) The relation between subject and predicate of the four logical\n propositions.\n Euler\u2019s diagrams\n Distribution of subject and predicate\n Uaesneop\n Asebinop\n Saepeo\n\n\n=10. SUMMARY.=\n\n(1) A logical proposition is a judgment expressed in words.\n\n(2) The three kinds of logical propositions are categorical,\nhypothetical, disjunctive.\n\n A categorical proposition is one in which the assertion is made\n unconditionally.\n\n A hypothetical proposition is one in which the assertion depends\n upon a condition.\n\n A disjunctive proposition is one which asserts an alternative.\n\nThe most common word-signs of the categorical proposition are \u201call,\u201d\n\u201cno,\u201d \u201csome\u201d and \u201csome-not,\u201d of the hypothetical, \u201cif\u201d and of the\ndisjunctive, \u201ceither-or.\u201d\n\n(3) Every logical categorical proposition has the four elements:\nquantity sign, subject, copula and predicate.\n\nThe quantity sign indicates the extension of the proposition; the\nlogical subject is that of which something is affirmed or denied;\nthe logical predicate is the term which is affirmed or denied of the\nsubject; the copula is always some form of \u201cto be\u201d and is used to\nconnect subject and predicate. \u201c_Not_\u201d is sometimes used with the\ncopula.\n\nThe statements of ordinary conversation are usually not expressed in\nterms of the four elements, but must be, before they can be used in\ntesting arguments.\n\n(4) One word usually constitutes the grammatical subject while\na word with all its modifiers goes to make up the logical subject.\nThe verb with any predicate word is the grammatical predicate. The\nlogical predicate is all which follows the copula\u2015\u2015it may include the\npredicate-word and all its modifiers as well as the modified object.\n\n(5) Categorical propositions are divided into four kinds; universal\naffirmative (A), universal negative (E), particular affirmative (I),\nparticular negative (O). For the sake of brevity these four are\nrespectively denoted by the vowels A, E, I, O.\n\n An A proposition is one in which the predicate affirms something of\n _all_ of the logical subject.\n\n An E proposition is one in which the predicate denies something of\n _all_ of the logical subject.\n\n An I proposition is one in which the predicate affirms something of\n a part of the logical subject.\n\n An O proposition is one in which the predicate denies something of\n a part of the logical subject.\n\nEvery proposition must be reduced to one of the four types before it\ncan be used as a basis of argumentation.\n\nIt is incumbent on the student to recognize these four types with\nprecision and accuracy.\n\n(6) There are a few proposition types which are recognized as being\nillogical in form. These may be defined as follows:\n\n (1) An indefinite proposition is one without the quantity sign. It\n usually may be classed as universal.\n\n (2) An elliptical proposition is one in which the copula is\n suppressed.\n\n (3) An individual proposition is one which has a singular subject.\n It is universal in content.\n\n (4) Plurative propositions are those introduced by \u201cmost,\u201d \u201ca few\u201d\n or some equivalent quantity sign. These are particular in meaning.\n\n (5) Partitive propositions are particulars which imply a\n complementary opposite. These arise through the ambiguous use of\n \u201call-not,\u201d \u201csome\u201d and \u201cfew.\u201d\n\n\u201cAll-not\u201d sometimes means \u201c_no_,\u201d while at other times it may mean\n\u201c_not-all_.\u201d If the quantity sign means the latter, then it introduces\na partitive proposition.\n\n\u201c_Some_\u201d may mean \u201c_some only_,\u201d or \u201c_some at least_.\u201d The latter is\nthe logical meaning. The former interpretation makes the proposition\npartitive. When \u201cfew\u201d means \u201cfew only,\u201d it is partitive in nature.\n\n (6) Exceptive propositions are those introduced by such signs as\n \u201call except,\u201d \u201call but,\u201d \u201call save,\u201d etc. They are universal\n only when the exceptions are mentioned.\n\n (7) Exclusive propositions are those introduced by such words as\n \u201conly,\u201d \u201calone,\u201d \u201cnone but\u201d and \u201cexcept.\u201d In an exclusive the\n predicate and not the subject is distributed. Consequently\n the easiest way to make an exclusive logical is to interchange\n subject and predicate and call it an A.\n\n (8) An inverted proposition is one where the predicate precedes the\n subject. Interchanging them gives the logical form.\n\nOf the grammatical sentences only the declarative is logical.\n\nThe relative clause, though out of place, must be used with the word it\nmodifies.\n\n(7) There are other propositions, though not illogical, to which the\nlogician usually gives some attention. These may be defined as follows:\n\n (1) An analytical proposition is one in which the predicate gives\n information already implied in the subject.\n\n (2) A synthetic proposition is one in which the predicate gives\n information not implied in the subject.\n\n (3) A modal proposition is one which states the manner in which the\n predicate belongs to the subject. The adverbs of time, place,\n degree and manner are the signs of the modal proposition.\n\n (4) A pure proposition simply states that the predicate belongs or\n does not belong to the subject.\n\n (5) A truistic or tautologous proposition is one in which the\n predicate repeats the words and meaning of the subject.\n\n(8) In considering the relation which may exist between subject and\npredicate, the two terms are employed in extension only, as this use\nbest serves the interests of inference.\n\nThe extensional relation between subject and predicate of the four\nlogical propositions may be stated as follows:\n\n Ordinary A\u2015\u2015All of the subject belongs to a part of the predicate.\n\n Co-extensive A\u2015\u2015All of the subject belongs to all of the predicate.\n\n E\u2015\u2015None of the subject belongs to any part of the predicate.\n\n I\u2015\u2015Some of the subject belongs to some of the predicate.\n\n O\u2015\u2015Some of the subject is excluded from the whole of the predicate.\n\nIn general it may be said that the affirmative propositions are\n_in_clusive while the negatives are _ex_clusive.\n\nA term is said to be distributed when it is referred to as a definite\nwhole.\n\n\u201cA\u201d distributes the logical subject only, \u201cE\u201d both logical subject and\nlogical predicate, \u201cI\u201d neither logical subject nor logical predicate,\n\u201cO\u201d the logical predicate only. The co-extensive \u201cA\u201d distributes both\nsubject and predicate.\n\nIt is essential that the student know by heart the distribution of\nthe terms of the logical propositions. Some keyword like _uaesneop_\nmay be used as an aid to the memory. This means the _u_niversals _A_\nand _E_ distribute their _s_ubjects, while the _n_egatives _E_ and _O_\ndistribute their _p_redicates.\n\n\n=11. ILLUSTRATIVE EXERCISES.=\n\n(1a) Examine the following list of propositions with a view to\nclassifying them as \u201cA\u2019s,\u201d \u201cE\u2019s,\u201d \u201cI\u2019s\u201d or \u201cO\u2019s.\u201d\n\n _E_ 1. \u201cNone of the inmates voted.\u201d\n\n _A_ 2. \u201cBenj. Franklin was the best educated American.\u201d\n\n _I_ 3. \u201cSome doctors deem it right to lie to their patients.\u201d\n\n _A_ 4. \u201cAll earnest teachers need to observe the teaching of others.\u201d\n\n _I_ 5. \u201cSome politicians are honest.\u201d\n\n _A_ 6. \u201cFools rush in where angels fear to tread.\u201d\n\n _O_ 7. \u201cSome proverbs are not true to life.\u201d\n\n _E_ 8. \u201cNo man should infringe upon the rights of others.\u201d\n\nI recall that an affirmative proposition in which the predicate refers\nto the whole of the subject is an A, while one where the predicate\nrefers to only a part of the subject is an I. Further, a negative\nproposition where the predicate refers to the whole of the subject is\nan E, while one in which the predicate refers to only a part of the\nsubject is an O. With these facts in mind, I classify the propositions\nas indicated.\n\n(1b) In a similar manner classify as to quantity and quality the\nfollowing:\n\n (1) \u201cAll worthy workers grow to look like their work.\u201d\n\n (2) \u201cEvery dog has his day.\u201d\n\n (3) \u201cSome of the presidents were not popular.\u201d\n\n (4) \u201cNo unskilled laborer can afford to own an automobile.\u201d\n\n (5) \u201cSome of the \u2018election prophets\u2019 were sadly mistaken.\u201d\n\n(2a) Classify the following propositions and make the illogical,\nlogical:\n\n (1) \u201cOnly first-class passengers may ride in parlor cars.\u201d\n\n (2) \u201cHaste makes waste.\u201d\n\n (3) \u201cFew men know how to act under stress.\u201d\n\n (4) \u201cAll which seems to ring true is not true.\u201d\n\n (5) \u201cMembers alone are admitted.\u201d\n\n (6) \u201cNone but men of integrity need apply.\u201d\n\n (7) \u201cHorses trot.\u201d\n\n (8) \u201cBlessed are they which are persecuted for righteousness sake.\u201d\n\nThe first proposition is an exclusive and may be made logical by\nconverting and calling it an A, viz.: \u201cAll who ride in parlor cars are\nfirst-class passengers.\u201d (A)\n\nThe second is indefinite and elliptical and is made logical by\nprefixing the universal quantity sign and expressing in terms of the\nfour elements. The logical form is, \u201cAll who make haste are those who\nare wasteful.\u201d (A)\n\nThe third is plurative in nature and means, \u201cMost men do not know how\nto act under stress.\u201d It would be classed as an O.\n\nThe fourth is partitive in nature because of the ambiguous use of\n\u201call\u2015\u2015not.\u201d It means, \u201cSome who seem to ring true are not true.\u201d (O)\n\nThe fifth is an exclusive. By converting and changing to an A the\nproposition takes the logical form, \u201cAll who are admitted are members.\u201d\n\nThe sixth is likewise an exclusive, the logical form being, \u201cAll who\napply must be men of integrity.\u201d\n\nThe seventh is an elliptical proposition. Logical form: \u201cAll horses are\ntrotting animals.\u201d\n\nThe eighth is an inverted or poetical proposition. It is made logical\nby interchanging subject and predicate. Logical form: \u201cThose who are\npersecuted for righteousness sake are blessed.\u201d\n\n(2b) Classify the attending propositions and change to the logical form,\nif necessary:\n\n (1) \u201cOnly truthful men are honest.\u201d\n\n (2) \u201cThe stokers alone were saved.\u201d\n\n (3) \u201cAll who run do not think.\u201d\n\n (4) \u201cHonesty is the best policy.\u201d\n\n (5) \u201cThey laugh that win.\u201d\n\n (6) \u201cThe good alone are happy.\u201d\n\n (7) \u201cKnowledge is power.\u201d\n\n (8) \u201cOnly the actions of the just smell sweet and blossom in the\n dust.\u201d\n\n\n=12. REVIEW QUESTIONS.=\n\n (1) Define and illustrate logical propositions.\n\n (2) Define and exemplify the three kinds of logical propositions.\n\n (3) What are the usual quantity signs of the four kinds of\n propositions?\n\n (4) Name and define the four elements of a logical proposition.\n\n (5) Select from the printed page five propositions which are not\n expressed in terms of the four elements, and so express them.\n\n (6) Distinguish between logical and grammatical subject; likewise\n between logical and grammatical predicate.\n\n (7) Define and illustrate the four kinds of categorical propositions.\n\n (8) What makes an understanding of the four logical propositions so\n important?\n\n (9) Give the unusual quantity signs of the logical propositions.\n\n (10) What should guide one in making an indefinite proposition logical?\n\n (11) How are general truths usually classified?\n\n (12) Change _birds fly_ to the logical form.\n\n (13) How many and what kinds of grammatical sentences are logical?\n\n (14) How would the logician deal with interrogative sentences?\n\n (15) Give illustrations of individual propositions. How are they\n usually classified?\n\n (16) Explain the logical mode of dealing with the plurative\n proposition.\n\n (17) Exemplify the ambiguity of \u201call-not,\u201d \u201csome\u201d and \u201cfew.\u201d\n\n (18) Why are propositions introduced by \u201call-not,\u201d \u201csome\u201d and \u201cfew\u201d\n called partitive?\n\n (19) Use \u201c_all_\u201d in both a partitive and collective sense. Which\n signification has logic adopted?\n\n (20) When are exceptive propositions universal and when particular?\n\n (21) What is an exclusive proposition?\n\n (22) Explain by circles the exclusive.\n\n (23) Tell in full how to change an exclusive to logical form.\n\n (24) Tell how the logician would deal with such poetical expressions\n as \u201cBlessed are the pure in heart,\u201d \u201cTell me not in mournful\n numbers,\u201d \u201cStrenuous is the man of state.\u201d\n\n (25) What distinction does the logician make between analytic and\n synthetic propositions?\n\n (26) Illustrate the difference between the so-called modal and pure\n propositions.\n\n (27) Explain and illustrate the truistic proposition.\n\n (28) Show by circles the relation existing between the subject and\n predicate of all the logical propositions.\n\n (29) State in good English the relation between the subject and\n predicate of all the logical propositions.\n\n (30) Relative to the distribution of terms apply the words \u201cuaesneop\u201d\n and \u201casebinop.\u201d Which one is the more serviceable?\n\n (31) Distinguish between the grammatical and logical subject.\n\n (32) Explain by circles the distribution of the terms of the four\n logical propositions.\n\n (33) The statement, \u201cA part of the subject is excluded from the whole\n of the predicate,\u201d describes which proposition? Explain how it\n indicates that the predicate is distributed.\n\n\n=13. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Show that a judgment may be an individual notion as well as a\n general notion.\n\n (2) Many logicians classify logical propositions in this wise:\n\n { Categorical\n Proposition {\n { Conditional { Hypothetical\n { Disjunctive\n\n Give arguments for and against such a classification.\n\n (3) \u201cAll men are bipeds\u201d is a judgment of extension, while \u201cMan is\n wise\u201d is a judgment of intension. Explain.\n\n (4) \u201cTo be logical is to be pedantic.\u201d Discuss this.\n\n (5) Why is the proposition, \u201cHe runs,\u201d illogical? Make it logical.\n\n (6) Point out the reasons for calling, \u201cWhite men are Caucasians,\u201d\n a particular proposition.\n\n (7) What makes it necessary to change the propositions of ordinary\n conversation to those of the four logical types?\n\n (8) Some would call the individual proposition particular. Argue the\n question.\n\n (9) Make a list of five propositions in common speech and show how\n their partitive implication may mislead.\n\n (10) Explain by circles _some only_ and _some at least_.\n\n (11) Explain how \u201c_et cetera_\u201d may change a universal to a particular\n proposition.\n\n (12) \u201cThe real nature of an exclusive is best shown by negating the\n subject and calling the proposition an E.\u201d Give arguments for\n and against this statement.\n\n (13) Show that with the immature mind all propositions must be\n synthetical.\n\n (14) Explain how a proposition may be truistic in form but not in\n meaning.\n\n (15) Show by the Euler diagram how easy it is for the careless student\n to think that an \u201cO\u201d does not distribute its predicate.\n\n (16) Explain by the use of two pads (a small yellow one and a large\n white one) the distribution of terms.\n\n (17) When the logician makes reference to the subject of a\n proposition, show that he should exercise care in designating it\n as the _logical_ subject.\n\n\n\n\n CHAPTER 9.\n\n IMMEDIATE INFERENCE\u2015\u2015OPPOSITION.\n\n\n=1. THE NATURE OF INFERENCE.=\n\n_Inference is the thought process of deriving a judgment from one or\ntwo antecedent judgments._\n\nThe process is simply a matter of expressing explicitly in a final\njudgment, a truth that was implied in one or two previous judgments. To\nexemplify: From the antecedent truth, that \u201cAll teachers should be fair\nminded,\u201d one may derive a consequent truth that \u201cThis teacher, Albert\nWhite, should be fair minded.\u201d Or from the statement, \u201cAll men are\nmortal,\u201d one may derive the judgment, \u201cNo men are immortal.\u201d Because\nthe ground is wet we conclude that it has rained. If _all_ dogs are\nquadrupeds then surely _some_ dogs are quadrupeds. Finally from the two\npropositions, \u201cAll training school students are high school graduates,\u201d\nand \u201cMary Jones is a training school student,\u201d we are led to conclude\nthat \u201cMary Jones is a high school graduate.\u201d\n\n\n=2. IMMEDIATE AND MEDIATE INFERENCE.=\n\nIt has been noted that a truth may be derived from a consideration\nof _one_ or _two_ antecedent judgments. To illustrate further: From\nthe judgment, \u201cAll men are fallible,\u201d we may derive the conclusion\nthat \u201cNo men are infallible\u201d; or, from the two judgments, \u201cAll men\nare fallible,\u201d and \u201cSocrates was a man,\u201d we may readily infer that\n\u201cSocrates was fallible.\u201d These two modes of inference take the names\nof _immediate_ inference and _mediate_ inference. Let us express these\ntwo kinds in equation form:\n\n\n I.\n\n _Equation Form,\n _Ordinary Form._ Using Initial\n Letters._\n\n Antecedent judgment: All men are fallible. All m are f\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n Conclusion: No men are infallible. No m are i\n\n\n II.\n\n First antecedent judgment: All men are\n fallible. All m are f\n\n Second antecedent judgment: Socrates was\n a man. S was m\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\n Conclusion: Socrates was fallible. \u2234 S was f\n\nGiving attention to the antecedent judgments of the second argument\nit is noted that the terms \u201c_f_\u201d and \u201c_S_\u201d are referred to the common\nterm \u201c_m_.\u201d In logic this common term is known as the _middle term_.\nAs there is but one antecedent judgment in the first argument there can\nbe no common or middle term. The first argument is an illustration of\n_immediate_ inference; the second of _mediate_ inference. This suggests\nthe definitions:\n\n_Immediate inference is inference without the use of a middle term._\n\n_Mediate inference is inference by means of a middle term._\n\n\n=3. THE FORMS OF IMMEDIATE INFERENCE.=\n\nMany logicians recognize four forms of immediate inference. These\nfour forms are (1) _opposition_, (2) _obversion_, (3) _conversion_,\n(4) _contraversion._[8]\n\n(1) _IMMEDIATE INFERENCE BY OPPOSITION._\n\nWe have learned that to be logical all categorical assertions must\nbe reduced to some one of the four propositions, A, E, I, O. If these\nfour logical propositions be given the _same subject and predicate_,\ncertain definite relations will become evident; therefore, _Opposition\nis said to exist between propositions which are given the same subject\nand predicate, but differ in quality, or in quantity, or in both_.\n\nThe following illustrative outline will make this clear:\n\n 1.\n _Original Proposition._\n I. All men are mortal. (A)\n II. No men are immortal. (E)\n III. Some men are wise. (I)\n IV. Some men are mortal. (I)\n V. Some men are not wise. (O)\n VI. Some men are not immortal. (O)\n\n 2.\n _Opposite in Quantity._\n I. Some men are mortal. (I)\n II. Some men are not immortal. (O)\n III. All men are wise. (A)\n IV. All men are mortal. (A)\n V. No men are wise. (E)\n VI. No men are immortal. (E)\n\n 3.\n _Opposite in Quality._\n I. No men are mortal. (E)\n II. All men are immortal. (A)\n III. Some men are not wise. (O)\n IV. Some men are not mortal. (O)\n V. Some men are wise. (I)\n VI. Some men are immortal. (I)\n\n 4.\n _Opposite in Both._\n I. Some men are not mortal. (O)\n II. Some men are immortal. (I)\n III. No men are wise. (E)\n IV. No men are mortal. (E)\n V. All men are wise. (A)\n VI. All men are immortal. (A)\n\nGranting the truth of the propositions in the first column, it follows\nthat those in the second column differ in quantity. That is, in \u201cSome\nmen are mortal\u201d a _smaller_ number of men is referred to than in \u201cAll\nmen are mortal.\u201d A similar variation in quantity obtains with the\nother propositions in the second column. Moreover, the propositions\nin the third column are the negative of the corresponding ones in the\nfirst; while the fourth column propositions differ from the first in\n_both_ quantity and quality. Thus opposition exists to a greater or\nless degree between all. We may now ask ourselves the question, \u201cWhen\nthe propositions are related to each other in opposition which ones are\ntrue and which ones are false?\u201d Giving attention to the propositions\nin row \u201cI,\u201d we note that if the universal affirmative, \u201cAll men are\nmortal,\u201d is true, then the particular affirmative, \u201cSome men are\nmortal,\u201d is likewise true; because of the principle, \u201cWhat is true\nof the whole of the class is true of a part of that class.\u201d But the\nuniversal negative, \u201cNo men are mortal,\u201d and the particular negative,\n\u201cSome men are not mortal,\u201d are both false. Briefly stated: If A is\ntrue, then I is true, but, both E and O are false.\n\nRegarding row \u201cII\u201d we may conclude that if E is true, then O is\nlikewise true, but both A and I are false.\n\nAs to rows \u201cIII\u201d and \u201cIV,\u201d granting the truth of the I propositions,\n\u201cSome men are wise\u201d and \u201cSome men are mortal,\u201d we are able to assert\nthat of the two A propositions, \u201cAll men are wise,\u201d and \u201cAll men are\nmortal,\u201d the first is false while the second is true. A is, therefore,\nindeterminate, or doubtful. Of the O propositions, \u201cSome men are not\nwise,\u201d is true while, \u201cSome men are not mortal,\u201d is false. Therefore,\nO is doubtful. Both of the E propositions are false. Hence, the\nconclusion relative to rows \u201cIII\u201d and \u201cIV\u201d is: If I is true, A and O\nare doubtful, while E is false.\n\nConcerning rows \u201cV\u201d and \u201cVI\u201d it will be seen without further\nexplanation that if O is true, then E and I are doubtful and A is false.\n\n\n THE SCHEME OF OPPOSITION.\n\nThe conditions of opposition are easily comprehended and remembered\nwhen recourse is made to the following scheme:\n\n A E I O\n If A be true true false true false\n If E be true false true false true\n If I be true doubt false true doubt\n If O be true false doubt doubt true\n\nTo use the above scheme, read horizontally from left to right. For\nexample: If A be true, then all in the row opposite obtains; that\nis, A is true, E is false, I is true, and O is false. (We take it for\ngranted that the student will see that the first column belongs to A,\nthe second to E, the third to I, and the fourth to O.) If E be true,\nthen A is false, E is true, I is false, O is true, etc.\n\nThe whole of opposition is comprehended in _two facts_ which are based\nupon _one principle_. This is the principle: _Whatever may be said of\nthe entire class may be said of a part of that class._ To put it in\nanother way: Whatever is affirmed of all may be affirmed of some, or,\nWhatever is denied of all may be denied of some. To illustrate:\n\n Accepted truth: All planets rotate. (A)\n Accepted inference: Some planets rotate. (I)\n or\n Accepted truth: No planet is a sun. (E)\n Accepted inference: Some planets are not suns. (O)\n\nThese are the two facts: First, _a particular affirmative may be\nderived from a universal affirmative_. Second, _a particular negative\nmay be derived from a universal negative_. Or, more briefly: _An I may\nbe derived from an A, and an O from an E_.\n\n\n SQUARE OF OPPOSITION.\n\n Illustration: ( \u2021 Square of Opposition)\n\nAristotle represented the relations of the four logical propositions by\nwhat is termed the _square of opposition_. Viewed from the standpoint\nof the square, the relations may be summed up as follows:\n\n1. _Contrary Propositions._\n\n_Why so named._\n\nAs related to each other, A and E are said to be contrary because they\nseem to express _contrariety_ to the greatest degree.\n\n_Relation stated._\n\nIf one is true, the other must be false, but both may be false.\n\n_Illustrations._\n\n(1) If one is true, the other must be false; e. g., if A is true, as\n\u201cAll metals are elements,\u201d then E is false, as \u201cNo metals are elements.\u201d\nOr, if E is true, as \u201cNo birds are quadrupeds,\u201d then A is false, as\n\u201cAll birds are quadrupeds.\u201d\n\n(2) Both may be false. If A is false, as \u201cAll men are wise,\u201d then E may\nbe false, as \u201cNo men are wise.\u201d\n\n2. _Subcontrary Propositions._\n\n_Why so named._\n\nPropositions I and O are said to be related to each other in a\nsubcontrary manner because they are contrary as to each other and\n\u201c_under_\u201d their universals A and E.\n\n_Relation stated._\n\nIf one is false, the other must be true, or, both may be true.\n\n_Illustrations._\n\n(1) If one is false, the other must be true.\n\nIf I is false, as \u201cSome metals are compounds,\u201d then, O is true, as\n\u201cSome metals (at least) are not compounds.\u201d Or, if O is false, as \u201cSome\nmetals are not elements,\u201d then I is true, as \u201cSome metals are elements.\u201d\n\n(2) Both may be true.\n\nIf I is true, as \u201cSome men are wise,\u201d then O also may be true, as \u201cSome\nmen are not wise.\u201d\n\n3. _Subalterns._\n\n_Why so named._\n\nEtymologically considered subaltern means _under the one_, thus\nproposition I is under A, and O is under E.\n\n_Relation stated._\n\n_First Relation._\n\nSubalterns are related to each other as are the universals and\nparticulars; hence,\n\n(1) If the universal is true, the particular under it is also true;\nwhile if the particular is true, the corresponding universal may, or,\nmay not, be true.\n\n_Illustrations._\n\n(a) If the universal is true, the particular under it is true.\n\nIf A is true, as \u201cAll metals are elements,\u201d then I is true, as \u201cSome\nmetals are elements.\u201d Or, if E is true, as \u201cNo metals are compounds,\u201d\nthen, O is also true, as \u201cSome metals (at least) are not compounds.\u201d\n\n(b) If the particular is true, the corresponding universal may, or, may\nnot, be true.\n\nIf I is true, as \u201cSome men are wise,\u201d or, \u201cSome men are mortal,\u201d then A\nmay be false, as \u201cAll men are wise,\u201d or, A may be true, as \u201cAll men are\nmortal.\u201d Or, if O is true, as \u201cSome men are not wise,\u201d or, \u201cSome men\nare not immortal,\u201d then E may be false, as \u201cNo men are wise\u201d; or, true,\nas \u201cNo men are immortal.\u201d\n\n_Second Relation._\n\n(2) If the universal is false, the particular under it may or may not\nbe true, but, if the particular is false, the universal above it must\nbe false.\n\n_Illustrations._\n\n(a) If the universal is false, the particular under it may or may not\nbe true.\n\nIf A is false, as \u201cAll metals are compounds,\u201d or \u201cAll men are wise,\u201d\nthen I may be false, as \u201cSome metals are compounds,\u201d or, I may be true,\nas \u201cSome men are wise.\u201d Or, if E is false, as \u201cNo men are mortal,\u201d or,\n\u201cNo men are wise,\u201d then O may be false, as \u201cSome men are not mortal,\u201d\nor, O may be true, as \u201cSome men are not wise.\u201d\n\n(b) If the particular is false, the universal above it must be false.\n\nIf I is false, as \u201cSome men are trees,\u201d then A is false, as \u201cAll men\nare trees.\u201d Or, if O is false, as \u201cSome men are not bipeds,\u201d then E is\nalso false, as \u201cNo men are bipeds.\u201d\n\n4. _Contradictory Propositions._\n\n_Why so named._\n\nThe propositions A and O, likewise E and I, are called contradictory\npropositions because they oppose each other in both quantity and\nquality. They are mutually opposed to each other or _absolutely_\ncontradictory.\n\n_Relation stated._\n\nIf one is true the other must be false.\n\n_Illustrations._\n\n(1) A and O compared.\n\nIf A is true, as \u201cAll metals are elements,\u201d then, O is false, as \u201cSome\nmetals are not elements.\u201d Or, if O is true, as \u201cSome metals are not\ncompounds,\u201d then A is false, as \u201cAll metals are compounds.\u201d\n\n(2) E and I compared.\n\nIf E is true, as \u201cNo birds are quadrupeds,\u201d then I is false, as \u201cSome\nbirds are quadrupeds.\u201d Or, if I is true, as \u201cSome birds are bipeds,\u201d\nthen E is false, as \u201cNo birds are bipeds.\u201d\n\nThe chief value of the square of opposition springs from the\ncontradictory propositions. The square shows conclusively that any\nuniversal affirmative assertion (an A) may best be contradicted by\nproving a particular negative (an O). For example: To satisfactorily\nrefute the statement that, in this section, all birds migrate to the\nsouth in winter, it would be sufficient to prove that the English\nsparrow and starling do _not_ migrate to the south. The square likewise\nmakes evident that any universal negative (an E) may be conclusively\ndenied by establishing the truth of a particular affirmative (an I).\nTo illustrate: The easiest way to prove the falsity of \u201cNo trusts are\nhonest\u201d is to present facts showing that at least trusts A and B _are_\nhonest.\n\n_The Individual Proposition._\n\nAn individual proposition is one with an individual subject such\nas \u201cAristotle was wise.\u201d In logic, the individual proposition is\nclassed as a universal. This seems to be a bit irregular, as with the\nindividual proposition there is no particular, while, the strictly\n_logical_ universal _always_ implies a particular. Because of this\nvariation from the true logical form the relations, as indicated by\nthe square of opposition, do _not_ apply to the individual proposition.\nFor example: According to the square A and E are contrary, but, when\nindividual, A and E contradict each other, as \u201cAristotle was wise\u201d\n(A)\u2015\u2015\u201cAristotle was not wise\u201d (E).\n\n\n\n\n CHAPTER 10.\n\n IMMEDIATE INFERENCE (CONTINUED)\u2015\u2015OBVERSION,\n CONVERSION, CONTRAVERSION AND INVERSION.\n\n\n(2) _IMMEDIATE INFERENCE BY OBVERSION._\n\n_Obversion is the process of changing a proposition from the\naffirmative form to its equivalent negative or from the negative form\nto its equivalent affirmative._\n\nSome authorities refer to this process as \u201cInference by Privitive\nConception,\u201d but Obversion seems to be a better term.\n\nObversion is based upon the principle that _two negatives are\nequivalent to one affirmative_. With this double negative principle in\nmind let us experiment with the four logical propositions, A, E, I, O.\n\n_The A Proposition._\n\nExample: \u201cAll thoughtful men are wise.\u201d Insert the double negative and\nthe proposition reads: \u201cAll thoughtful men are not not-wise.\u201d Changed\nto the logical form this becomes: \u201cNo thoughtful men are not-wise.\u201d\nSimplified and we have, finally: \u201cNo thoughtful men are unwise.\u201d\nThus by the process of obversion we have passed from the original\nproposition, \u201cAll thoughtful men are wise,\u201d to \u201cNo thoughtful men\nare unwise.\u201d In the first proposition the subject \u201c_thoughtful men_\u201d\nis denied of the predicate \u201c_unwise_.\u201d Assuming that \u201cunwise\u201d is the\ncontradictory of \u201cwise,\u201d then: \u201cWhat is affirmed of a predicate may\nbe denied of its contradictory.\u201d Recourse to circles will make this\nclearer. In the previous chapter it has been suggested that _not_\nbisects the world. For example: What can _not_ be included in the\n_wise_ class may be placed under the not-wise or _unwise_ class.\nLikewise a circle bisects space\u2015\u2015there is the space inside the circle\nand the space outside the circle. Let the space inside the circle\nrepresent all wise beings, then the space outside the circle would\nrepresent all not-wise or unwise beings; e. g.,\n\n Illustration: FIG. 5.\n\nNow representing _thoughtful men_ by a smaller circle and placing it\ninside the larger we have,\n\n Illustration: FIG. 6.\n\nReferring to Fig. 6 we note that all of the smaller circle belongs\nto the larger or that none of the smaller circle belongs to the space\noutside of the larger. Hence the two propositions: \u201cAll thoughtful men\nare wise\u201d (A), and \u201cNo thoughtful men are unwise\u201d (E) have virtually\nthe same meaning though the same subject is related to different\npredicates.\n\nThe use of the positive or negative form depends upon circumstances.\nOften the negative puts the thought in a more forceful way.\n\nIn passing from, \u201cAll thoughtful men are wise,\u201d to \u201cNo thoughtful\nmen are unwise,\u201d it was necessary to prefix _not_ to the predicate\n_wise_ and substitute for _not_ its equivalent _un_. If the original\npredicate were unwise or not-wise, then the reverse order of dropping\nthe _un_ or _not_ could be followed. This process of prefixing the\n_not_ to an affirmative predicate or of dropping the _not_ from a\nnegative predicate is referred to as _negating the predicate_. Before\nsubstituting _in_, _im_, _un_, etc., for _not_, one must make sure\nthat the substitution really gives the contradictory; there are some\nlogicians who claim that unwise, for instance, is not the contradictory\nof wise.\n\nIn comparing the first proposition with the second it is observed that\nthe first is an A, while the second is an E, also that the predicate of\nthe first was _negated_ to form the predicate of the second. Thus the\nrule: Negate the predicate and change A to E.\n\n_To sum up_:\n\n The obversion of an A proposition.\n\n1. Principle:\n\n Two negatives are equivalent to one affirmative.\n\n2. Rule:\n\n Negate the predicate and change the A to an E by using the sign\n _no_ instead of _all_.\n\n3. Process illustrated.\n\n _The Original Proposition (A)_ _The Obverse (E)_\n\n All men are mortal. No men are immortal.\n\n All maples are trees. No maples are not-trees.\n\n All teachers should be No teacher should be\n sympathetic. un-sympathetic.\n\n All pain is unpleasant. No pain is pleasant.\n\n All men are imperfect. No men are perfect.\n\n All birds are feathered No birds are non-feathered\n animals. animals.\n\n All men are not-trees. No men are trees.\n\n All scalene triangles are No scalene triangles are\n non-equilateral. equilateral.\n\n_The E Proposition._\n\nIt is obvious that the process of obverting an E is simply the reverse\nof obverting an A. Consequently, the same principle obtains; whereas\nthe _process_ may be illustrated by reading the foregoing illustrations\nreversely.\n\nThe rule for obverting E is: _Negate the predicate and change the E to\nan A by changing the sign no to all._\n\n_The I Proposition._\n\nLet us note the result when the double negative principle is applied to\nthe I proposition.\n\nOriginal: \u201cSome men are wise.\u201d\n\nAdding two negatives: \u201cSome men are not not-wise.\u201d\n\nThe foregoing simplified: \u201cSome men are not unwise.\u201d\n\nIn comparing the first proposition with the last it is observed that\nthe first is an I while the last is an O; it is also observed that the\npredicate of the first was _negated_ in order to form the predicate\nof the last. Thus the rule: \u201cNegate the predicate and change the I to\nan O.\u201d\n\nThe use of circles may make this clearer:\n\n Illustration: FIG. 7.\n\nThe significant part of Fig. 7 is that which is inked. Here we have\nrepresented the part of the \u201cmen\u201d circle which is common to the \u201cwise\u201d\ncircle. Thus the inked part represents \u201cSome men are wise.\u201d If the\ninked part is entirely inside of the \u201cwise\u201d circle, no part of it can\nbelong to the \u201cunwise\u201d space without. Thus the obverse, \u201cSome men are\nnot unwise.\u201d\n\n_Summary._\n\nThe obversion of an I proposition.\n\n1. Principle:\n\n Same as with A.\n\n2. Rule:\n\n Negate the predicate and change the I to an O.\n\n3. Process illustrated.\n\n _The Original Proposition (I)_ _The Obverse (O)_\n\n Some water is pure. Some water is not impure.\n\n Some curves are perfect. Some curves are not imperfect.\n\n Some friends are loyal. Some friends are not disloyal.\n\n Some men are true. Some men are not not-true.\n\n Some precious stones are Some precious stones are not\n imperfect. perfect.\n\n Some plants are not-trees. Some plants are not trees.\n\n Some boys are not-honest. Some boys are not honest.\n\nIt must be borne in mind that when \u201c_not_\u201d is used without the hyphen\nit makes the proposition negative, because when \u201c_unhyphened_,\u201d \u201c_not_\u201d\nmust be thought of in connection with the copula and not in connection\nwith the predicate; while \u201c_not_\u201d attached to the predicate with\na hyphen simply makes the predicate negative without affecting the\nquality of the proposition; e. g., \u201cSome plants are not trees\u201d is\na negative proposition, while \u201cSome plants are not-trees\u201d is an\naffirmative proposition with a negative predicate.\n\nIt may not be clearly seen how it is possible, by following the rule\ngiven, to pass from such a proposition as \u201cSome plants are _not-trees_,\u201d\nto \u201cSome plants are _not trees_.\u201d Let us illustrate the steps:\n\n 1. The original: \u201cSome plants are not-trees.\u201d\n\n 2. Negating predicate: \u201cSome plants are trees.\u201d\n\n 3. Changing to an O: \u201cSome plants are not trees.\u201d\n\nDropping the not from \u201c1\u201d and then adding it again to \u201c2\u201d is simply\nputting into operation the double negative idea, so that there is no\nviolation of the principle.\n\n_The O Proposition._\n\nO bears the same relation to I that E bears to A. The principle\ninvolved is the same. The process is illustrated by reading reversely\nthe scheme of illustrations under I. The rule is as follows: _To obvert\nan O negate the predicate and change the O to an I by eliminating the\nnot._\n\n_Summary of Obverting the Four Logical Propositions._\n\n1. Principle:\n\n Two negatives are equivalent to one affirmative.\n\n2. Rules:\n\n { (1) A to E\n Negate the predicate { (2) E to A\n and change { (3) I to O\n { (4) O to I\n\n\n(3) _IMMEDIATE INFERENCE BY CONVERSION._\n\n_Conversion is the process of inferring from a given proposition\nanother which has, as its subject, the predicate of the given\nproposition, and, as its predicate, the subject of the given\nproposition._ It is simply a matter of transposing subject and\npredicate. The original proposition is called the _convertend_ while\nthe derived proposition is named the _converse_.\n\nThe process of conversion is limited by two rules. First rule. No term\nmust be distributed in the converse which is not distributed in the\nconvertend. Second rule. The quality of the converse must be the same\nas that of the convertend. More briefly: (1) _Do not distribute an\nundistributed term._ (2) _Do not change the quality._\n\nWe recall that a term is distributed when it is referred to as a\n_definite whole_. An undistributed term is referred to only _in part_.\nThe principle underlying rule \u201c1,\u201d therefore, is the one which forms\nthe basis of inference by opposition; namely, \u201c_Whatever may be said of\nthe entire class may be said of a part of that class_.\u201d The converse of\nthis is _not true_, that is, \u201cWhat is said of part of a class cannot be\nsaid of the whole of that class.\u201d When we distribute an undistributed\nterm we are saying of the _whole_ class what was said only of a _part_\nof that class. This is fallacious. On the other hand, we may say of a\npart what was said of the whole, or \u201cundistribute\u201d a distributed term.\n\nWe recall that the conclusion of the whole matter of inference by\nopposition was, that only an I could be inferred from an A and only an\nO from an E, or to put it in another way: Only an affirmative from an\naffirmative and only a negative from a negative. This establishes the\ntruth of the second rule in conversion: \u201cDo not change the quality.\u201d\n\nLet us apply the two rules to the four logical propositions.\n\n_Converting an A proposition._\n\nTake as a type, \u201cAll horses are quadrupeds.\u201d Here the subject\n\u201c_horses_\u201d is distributed, but the predicate \u201c_quadrupeds_\u201d is\nundistributed. In transposing subject and predicate we cannot\ndistribute the term \u201cquadrupeds,\u201d according to the rule which says, \u201cDo\nnot distribute an undistributed term.\u201d Hence in interchanging subject\nand predicate we cannot say, \u201cAll quadrupeds are horses,\u201d but must\nlimit the assertion to, \u201c_Some_ quadrupeds are horses.\u201d Logicians call\nthis process _Conversion_ by _Limitation_.\n\n_Conversion by Limitation Exemplified Further._\n\n _Convertend._ _Converse._\n\n All metals are elements. Some elements are metals.\n\n All bees buzz. Some buzzing insects are bees.\n\n All men are fallible. Some fallible beings are men.\n\n All good teachers are Some sympathetic persons are good\n sympathetic. teachers.\n\nThe conclusions from the foregoing are these: First, the usual mode of\nconverting an A is to interchange subject and predicate, limiting the\nlatter by the word \u201c_some_\u201d or a word of similar significance. Second,\nthis mode is called _conversion by limitation_. Third, the converse of\nan _A_ is an _I._\n\n_The Co-extensive A._\n\nIn the conversion of A propositions there is the one exception of\n\u201cco-extensive A\u2019s,\u201d such as truisms and definitions. It will be\nremembered that with these both subject and predicate are distributed;\nhence, they may be interchanged without limiting the predicate by\n\u201csome.\u201d To illustrate: The converse of the truism, \u201cA man is a _man_.\u201d\nis \u201cA _man_ is a man,\u201d while the converse of the definition, \u201cA man\nis a rational animal,\u201d is \u201cA rational animal is a man.\u201d This mode\nof interchanging subject and predicate without limiting the latter\nis called _Simple Conversion_. The ordinary A proposition is thus\n_converted_ by _limitation_, while the co-extensive A is _converted\nsimply_.\n\n_Converting an E proposition._\n\nAs both terms of the E proposition are distributed it is not possible\nto violate the rule of distribution. It is to be remembered that no\nfallacy is committed by \u201cundistributing\u201d a term which is already\ndistributed.\n\n_Illustrations._\n\n\n _Convertend._ _Converse._\n\n No men are immortal. No immortals are men. Simply.\n\n No birds are quadrupeds. No quadrupeds are birds. Simply.\n\n No metals are compounds. No compounds are metals. Simply.\n\n No men are immortal. Some immortals (at least) are not\n men. Limitation.\n\n No birds are quadrupeds. Some quadrupeds are not birds.\n Limitation.\n\n No metals are compounds. Some compounds are not metals.\n Limitation.\n\nThree facts are evident relative to the converting of an E. First: An E\nproposition may be converted either _simply_ or by _limitation_. Second:\nE may be converted into either _E_ or _O_. Third: If the converse is\nan O then is the inference a _weakened_ one, being _particular_ when it\ncould just as well be _universal_.\n\n_Converting an I proposition._\n\nWith an I proposition neither term is distributed. Thus care must be\nused lest an undistributed term in the convertend be distributed in the\nconverse. _Illustrations_:\n\n _Convertend._ _Converse._\n\n Some men are wise. Some wise beings are men.\n\n Some teachers scold. Some who scold are teachers.\n\n Some high school graduates Some who enter college are high\n enter college. school graduates.\n\n Some Americans live simply. Some who live simply are Americans.\n\nFrom the foregoing we conclude first, that I is _converted simply_;\nsecond, that I is converted _into I_.\n\n_The O Proposition._\n\nWith an O proposition the subject is _undistributed_ while the\npredicate is distributed. This condition presents a peculiar\ndifficulty. Consider, for example, the O proposition, \u201cSome men are\nnot wise.\u201d Convert this into, \u201cSome wise beings are not men,\u201d and the\n_undistributed_ subject of the convertend, which is \u201cmen,\u201d becomes the\n_distributed_ predicate of the converse. _Thus the O proposition cannot\nbe converted without violating the rule for distribution._\n\n_A Summary of How the Four Logical Propositions May be Converted._\n\n 1. _A._ The ordinary A proposition may be converted by _limitation_\n only. The co-extensive A may be converted _simply_.\n\n 2. _E._ The E proposition is converted _simply_. The E may also be\n converted by _limitation_, but the inference thus obtained is\n _weakened_.\n\n 3. _I._ The I proposition may be converted _simply_ only.\n\n 4. _O._ The O proposition _cannot be converted_.\n\n\n(4) _INFERENCE BY CONTRAVERSION._ (Contraposition).\n\nThis mode of inference is usually referred to as inference by\n_contraposition_, but contraversion, indicating more definitely the\nnature of the process, is a better term. Contraversion involves _two_\nsteps: First, _obversion_; second, _conversion_. The same principles\nand rules evident in these _two_ processes obtain in inference by\ncontraversion. The following scheme, therefore, ought to be sufficient\nto make the matter clear:\n\n_Inference by Contraversion._\n\n 1. _The Given Proposition._ 2. _Obverted._\n\n A. All men are mortal. No men are immortal.\n\n All trees are plants. No trees are not-plants.\n\n E. No men are infallible. All men are fallible.\n\n No men are trees. All men are not-trees.\n\n I. Some men are wise. Some men are not not-wise.\n\n O. Some water is not pure. Some water is impure.\n\n Some houses are not white. Some houses are not-white.\n\n3. _Converted; giving the contraverse of the original proposition._\n\n No immortals are men.\n\n No not-plants are trees.\n\n Some fallible beings are men.\n\n Some not-trees are men.\n\n An O cannot be converted, consequently the contraversion of an\n I is impossible.\n\n Some impure liquids are water.\n\n Some not-white buildings are houses.\n\nIt is indicated in the foregoing scheme that \u201cI\u201d cannot be contraverted.\nThis is due to the fact that the obverse of an I is an O, and it will\nbe remembered that \u201cO\u201d cannot be converted. All the other propositions\nadmit of contraversion.\n\n\n=4. EPITOME OF THE FOUR PROCESSES OF IMMEDIATE INFERENCE IN CONNECTION\n WITH THE FOUR LOGICAL PROPOSITIONS.=\n\n [*]\u2502Proposition\u2502Name of \u2502Inference \u2502Principle\n \u2502symbolized \u2502Process \u2502symbolized \u2502involved\n \u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n A \u2502All S is \u2502Opposition \u2502Some S is \u2502What is said of _all_ may\n \u2502 P[\u2020] \u2502 \u2502 P (I) \u2502 be said of _some_.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Obversion \u2502No S is \u2502Two negatives are\n \u2502 \u2502 \u2502 not-P (E)\u2502 equivalent to one\n \u2502 \u2502 \u2502 \u2502 affirmative.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Conversion by\u2502Some P is \u2502An undistributed term\n \u2502 \u2502 Limitation \u2502 S (I) \u2502 cannot be distributed.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Contraversion\u2502No not-P \u2502Same principles which\n \u2502 \u2502 \u2502 is S (E) \u2502 obtain in obverting\n \u2502 \u2502 \u2502 \u2502 A and converting E.\n \u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n E \u2502No S is P \u2502Opposition \u2502Some S is \u2502What is said of _all_ may\n \u2502 \u2502 \u2502 not P (O)\u2502 be said of _some_.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Obversion \u2502All S is \u2502Two negatives are\n \u2502 \u2502 \u2502 not-P (A)\u2502 equivalent to one\n \u2502 \u2502 \u2502 \u2502 affirmative.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Simple \u2502No P is S \u2502Distribution not\n \u2502 \u2502 Conversion \u2502 (E) \u2502 affected.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Contraversion\u2502Some not-P \u2502An undistributed term\n \u2502 \u2502 \u2502 is S (I) \u2502 cannot be distributed.\n \u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n I \u2502Some S is P\u2502Opposition \u2502Doubtful \u2502None.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Obversion \u2502Some S \u2502Two negatives are\n \u2502 \u2502 \u2502 is not \u2502 equivalent to one\n \u2502 \u2502 \u2502 not-P (O)\u2502 affirmative.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Conversion \u2502Some P is \u2502Distribution not\n \u2502 \u2502 \u2502 S (I) \u2502 affected.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Contraversion\u2502Impossible \u2502None.\n \u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n O \u2502Some S is \u2502Opposition \u2502Doubtful \u2502None.\n \u2502 not P \u2502 \u2502 \u2502\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Obversion \u2502Some S is \u2502Two negatives are\n \u2502 \u2502 \u2502 not-P (I)\u2502 equivalent to one\n \u2502 \u2502 \u2502 \u2502 affirmative.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Conversion \u2502Impossible \u2502None.\n \u2502 \u2502 \u2502 \u2502\n \u2502 \u2502Contraversion\u2502Some not-P \u2502Same as in obversion of\n \u2502 \u2502 \u2502 is S (I) \u2502 O and conversion of I.\n\n * \u2013 Name of proposition\n \u2020 \u2013 \u201cS\u201d represents any subject and \u201cP\u201d any predicate.\n\n\n INFERENCE BY INVERSION.\n\nSome logicians treat of a form of immediate inference known as\ninversion though it is of small importance and of little practical\nvalue.\n\nThe process can be applied only to propositions A and E. In the one\ncase the _contradictory subject_ is limited by \u201c_some_\u201d and then denied\nof the predicate, whereas, in the other case, the contradictory subject\nis merely affirmed of the predicate.\n\n_Illustrations._\n\n _The Given Proposition._ _The Inverse._\n\n I. All S is P. (A) Some not-S is not P. (O)\n All planets rotate. Some not-planets do not rotate.\n\n II. No S is P. (E) Some not-S is P. (I)\n No men are immortal. Some not-men are immortal.\n\n\nFrom the foregoing we are able to conclude _that the inverse of \u201cA\u201d is\nfound by negating the subject and changing to an \u201cO\u201d; while the inverse\nof \u201cE\u201d is found by negating the subject and changing to an \u201cI.\u201d_\n\n\n=5. OUTLINE.=\n\n IMMEDIATE INFERENCE\u2015\u2015OPPOSITION\u2015\u2015OBVERSION, CONVERSION,\n CONTRAVERSION AND INVERSION.\n\n 1. The Nature of Inference.\n\n 2. Immediate and Mediate Inference.\n\n 3. The Forms of Immediate Inference.\n (1) Opposition.\n (a) Scheme of Opposition.\n (b) Square of Opposition.\n (2) Obversion.\n (3) Conversion.\n (a) Simply.\n (b) By Limitation.\n (4) Contraversion.\n Inversion.\n\n\n=6. SUMMARY.=\n\n1. Inference is the thought process of deriving a judgment from one or\ntwo antecedent judgments.\n\n2. Immediate inference is inference without the use of a middle term.\nMediate inference is inference by means of a middle term.\n\n3. The four common forms of immediate inference are (1) opposition,\n(2) obversion, (3) conversion, (4) contraversion.\n\n(1) The name _opposition_ stands for certain definite relations which\nexist between the logical propositions when they are given the same\nsubject and predicate. The one principle underlying opposition is:\nWhatever is said of the entire class may be said of a part of that\nclass. The two statements which sum up opposition are first, an I may\nbe derived from an A; and second, an O may be derived from an E.\n\nThe crucial fact made obvious by the square of opposition is that A and\nO are mutually contradictory; likewise E and I.\n\n(2) Obversion is the process of passing from an affirmative to its\nequivalent negative or from a negative to its equivalent affirmative.\n\u201cTwo negatives are equivalent to one affirmative,\u201d is the basic\nprinciple of obversion.\n\nThe proposition A may be obverted by negating the predicate and\nchanging to an E. \u201cE\u201d is obverted by negating the predicate and\nchanging to an A. \u201cI\u201d is obverted by negating the predicate and\nchanging to an O. \u201cO\u201d is obverted by negating the predicate and\nchanging to an I.\n\n(3) Conversion is the process of inferring from a given proposition\nanother which has as its subject the _predicate of the given\nproposition_ and as its predicate the _subject of the given\nproposition_.\n\nConversion is limited by the two rules, (1) do not distribute an\nundistributed term; (2) do not change the quality.\n\nTo convert an A interchange subject and predicate, limiting the latter\nby _some_, or a word of like significance. This is called conversion by\nlimitation.\n\nThe co-extensive A may be converted without limiting the predicate.\nThis is called simple conversion.\n\nAn E proposition may be converted either simply or by limitation. When\nconverted by limitation the inference is a _weakened_ one.\n\nAn I proposition is converted simply only.\n\nThe O proposition does not admit of conversion.\n\n(4) Immediate inference by contraversion is a process involving first\n_obversion_ and then _conversion_.\n\n\u201cA,\u201d \u201cE\u201d and \u201cO\u201d may be contraverted; \u201cI\u201d cannot be contraverted.\n\n\n=7. ILLUSTRATIVE EXERCISES.=\n\n(1a) From the antecedent judgment, \u201cAll weeds are plants,\u201d I am able\nto derive by immediate inference these judgments: (1) \u201cAll weeds are\nnot not-plants,\u201d or \u201cNo weeds are not plants.\u201d (2) \u201cNo not-plants are\nweeds.\u201d (3) \u201cSome plants are weeds.\u201d (4) \u201cSome weeds are plants.\u201d\n\n(1b) \u201cAll vertebrates have a backbone.\u201d From the foregoing judgment\nderive immediately five different conclusions.\n\n(2a) \u201cAll good citizens try to vote,\u201d\n\n \u201cAlbert White is a _good citizen_,\u201d\n Hence, \u201cAlbert White will try to vote.\u201d\n\nI know that the above is an example of mediate inference because the\ntwo antecedent judgments make use of the middle term, \u201c_good citizen_.\u201d\n\n(2b) Why is the following illustrative of mediate inference?\n\n \u201cAll wise men are close observers,\u201d\n \u201cAll wise men are thoughtful,\u201d\n Hence, \u201cSome thoughtful men are close observers.\u201d\n\n(3a) Derive immediate inferences by opposition from the following:\n\n (1) \u201cGood men are wise.\u201d\n\n (2) \u201cNo teacher can afford to be unjust.\u201d\n\n (3) \u201cAll birds fly.\u201d\n\n (4) \u201cNone of the inner planets are as large as the earth.\u201d\n\nI first determine that \u201c1\u201d and \u201c3\u201d are A propositions, while \u201c2\u201d and\n\u201c4\u201d are E\u2019s. Then I recall that by opposition an I may be derived from\nan A and an O from an E. Hence, the inferences are:\n\n (1) \u201cSome good men are wise.\u201d\n\n (2) \u201cSome teachers cannot afford to be unjust.\u201d\n\n (3) \u201cSome birds fly.\u201d\n\n (4) \u201cSome of the inner planets are not so large as the earth.\u201d\n\n(3b) Derive by opposition inferences from the following:\n\n (1) \u201cNo true woman will neglect her home for society.\u201d\n\n (2) \u201cAll patriotic men love the flag.\u201d\n\n (3) \u201cFools rush in where angels fear to tread.\u201d\n\n(4a) Obvert the following:\n\n (1) \u201cAll earnest teachers are diligent students.\u201d\n\n (2) \u201cNo self-respecting man can afford to be careless in his personal\n appearance.\u201d\n\n (3) \u201cSome of the great teachers of the past did not practice what\n they preached.\u201d\n\n (4) \u201cSome weeds are beautiful.\u201d\n\nI determine first the logical character of each proposition, finding\nthe first to be an A, the second an E, the third an O and the fourth an\nI. Then I recall that in obversion the predicate must always be\n_negated_ and an A must be changed to an E or an E to an A; also an I\nmust be changed to an O or an O to an I. Hence, the obverse of each\nproposition is:\n\n (1) \u201cNo earnest teacher is a not-diligent student.\u201d\n\n (2) \u201cAll self-respecting men can afford to be not-careless (careful)\n in their personal appearance.\u201d\n\n (3) \u201cSome of the great teachers of the past did not-practice (failed\n to practice) what they preached.\u201d\n\n (4) \u201cSome weeds are not not-beautiful.\u201d\n\n(4b) Infer by obversion from the following:\n\n (1) \u201cAll roses are beautiful.\u201d\n\n (2) \u201cNone of the members of the stock exchange are dishonest.\u201d\n\n (3) \u201cSome pupils are not industrious.\u201d\n\n (4) \u201cSome teachers are tactful.\u201d\n\n(5a) Convert the following:\n\n (1) \u201cAll that glitters is not gold.\u201d\n\n (2) \u201cAll good men are wise.\u201d\n\n (3) \u201cSome books are to be chewed and digested.\u201d\n\n (4) \u201cNo man is perfectly happy.\u201d\n\nIt is first necessary to determine the logical character of each\nproposition. Carelessness might lead one to call the first proposition\nan A because it is introduced by the quantity sign \u201c_all_.\u201d But on\nsecond thought we note that the meaning is to the effect that _some\nglittering things are not gold_; this is an O. It is clear that\nthe second is an A, the third an I and the fourth an E. It is now\nexpedient to recall the rules regarding conversion. These are, (1) do\nnot distribute an undistributed term; (2) do not change the quality.\nWe may now attempt to interchange the subject and predicate of each\nproposition, with the following results:\n\n (1) Conversion impossible.\n\n (2) \u201cSome wise men are good men.\u201d\n\n (3) \u201cSome things to be chewed and digested are books.\u201d\n\n (4) \u201cNo perfectly happy being is a man.\u201d\n\nWhen attempting to convert proposition (1), I find that the subject\nwhich is undistributed becomes distributed, hence the rule pertaining\nto distribution is violated. This conclusion is verified by recalling\nthe fact that an O proposition cannot be converted. The second\nproposition, being an A, is converted by limitation; while the third\nand fourth are converted simply, as is the natural procedure with all\nI\u2019s and E\u2019s.\n\n(5b) Convert these propositions:\n\n (1) \u201cBlessed are the meek.\u201d (All the meek are blessed.)\n\n (2) \u201cNone but material bodies gravitate.\u201d (All gravitating bodies are\n material.)\n\n (3) \u201cGold is not a compound substance.\u201d\n\n (4) \u201cUsually cruel men are cowards.\u201d\n\nNOTE.\u2015\u2015_The first proposition is poetical while the second is an\nexclusive._\n\n(6a) Contravert the following propositions:\n\n (1) \u201cAll virtue is praiseworthy.\u201d\n\n (2) \u201cSome teachers are not tactful.\u201d\n\n (3) \u201cA man who lies is not to be trusted.\u201d\n\nContraversion consists in obverting first, and then converting;\nconsequently, the contraverse of the three propositions is as follows:\n\n (1) \u201cNo unpraiseworthy deed is virtue.\u201d\n\n (2) \u201cSome not-tactful persons are teachers.\u201d\n\n (3) \u201cSome untrustworthy men are those who lie.\u201d\n\n(6b) Write the contraverse of the following:\n\n (1) \u201cAll honest men pay their debts.\u201d\n\n (2) \u201cAll men are rational.\u201d\n\n (3) \u201cNearly all the troops have left the town.\u201d\n\n (4) \u201cSome teachers are not patient.\u201d\n\n(7a) The attending scheme indicates the logical process and rule\ninvolved in passing from one proposition to another:\n\n A. \u201cAll men are imperfect.\u201d\n Process: Obversion.\n Rule: Negate predicate and change to E.\n\n E. \u201cNo men are perfect.\u201d\n Process: Simple Conversion.\n Rule: Interchange subject and predicate.\n\n E. \u201cNo perfect beings are men.\u201d\n Process: Contraversion.\n Rule: Obvert and then convert.\n\n I. \u201cSome not-men are perfect beings.\u201d\n\n(7b) Treat in a manner similar to the above the proposition, \u201cAll\nhorses are quadrupeds.\u201d\n\n\n=8. REVIEW QUESTIONS.=\n\n (1) What is inference?\n\n (2) What is the meaning of antecedent?\n\n (3) Define (1) judging, (2) a judgment.\n\n (4) All roses are beautiful,\n This flower is a rose,\n This flower is beautiful.\n\n Write this example of mediate inference in equation form. Name\n the middle term.\n\n (5) Define immediate inference. Illustrate.\n\n (6) Define mediate inference. Illustrate.\n\n (7) Name the five forms of immediate inference.\n\n (8) What principle is involved in inference by opposition?\n\n (9) Draw the scheme of opposition.\n\n (10) Make use of this scheme in deriving inferences from the following\n propositions:\n (a) \u201cGood men are wise.\u201d\n (b) \u201cNo king is infallible.\u201d\n (c) \u201cCattle are ruminants.\u201d\n (d) \u201cAll who cheat the railroads are not honest.\u201d\n\n (11) What are contradictory propositions? Illustrate.\n\n (12) What would be the simplest way of disproving the statement that\n \u201cNo great religious teacher has been consistent?\u201d\n\n (13) Why are A and E said to be contrary propositions?\n\n (14) Define obversion.\n\n (15) By what other name is obversion known?\n\n (16) State the basic principle of obversion.\n\n (17) Illustrate the process known as _negating the predicate_.\n\n (18) State the rule for obverting an A proposition.\n\n (19) Obvert the following:\n (1) \u201cAll the boys in my room are industrious.\u201d\n (2) \u201cHonesty is the best policy.\u201d\n (3) \u201cOnly the industrious are truly successful.\u201d\n\n (20) First state the rule and then obvert the following:\n (1) \u201cSome plants are biennial.\u201d\n (2) \u201cPlanets are not suns.\u201d\n (3) \u201cBlessed are the merciful.\u201d\n (4) \u201cThese samples are not perfect.\u201d\n\n (21) Define conversion.\n\n (22) State and illustrate the rules which condition the process of\n conversion.\n\n (23) Convert, if possible, the following:\n (1) \u201cSome men practice sophistry.\u201d\n (2) \u201cFew men know how to live.\u201d\n (3) \u201cSome of the inhabitants are not civilized.\u201d\n (4) \u201cAll the world is a stage.\u201d\n (5) \u201cNone of my pupils failed.\u201d\n (6) \u201cExperience is a hard taskmaster.\u201d\n\n (24) Why may co-extensive propositions be converted simply?\n\n (25) Describe the process of inference by contraversion.\n\n\n=9. PROBLEMS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) What ground is there for the belief that immediate inference, so\n called, is merely a matter of the interpretation of propositions?\n\n (2) Is there any difference between reasoning and inference?\n\n (3) When the conclusion is reached that two rooms are of the same\n width, because each is five yards wide, what is the middle term?\n\n (4) Put in equation form:\n All teachers instruct,\n John Jones is a teacher,\n John Jones instructs.\n\n Show that the equations are not _absolutely true_.\n\n (5) Indicate the true relation between the subjects and predicates\n of the foregoing by using the algebraic signs > and <.\n\n (6) Why cannot an A be derived from an I?\n\n (7) Why cannot an O be derived from an A?\n\n (8) The basic principle of obversion is \u201cTwo negatives are equivalent\n to one affirmative.\u201d Show by means of circles that this is not\n absolutely true; take as an illustrative proposition, \u201cNo men are\n not mortal.\u201d\n\n (9) Show that agreeable and disagreeable are not contradictory terms.\n\n (10) Why should the logician class individual propositions as\n universal?\n\n (11) Show by circles that there is a difference in signification\n between, \u201cSome men are _not wise_\u201d and \u201cSome men are _not-wise_.\u201d\n\n (12) Show by circles that the O proposition cannot be converted.\n\n (13) \u201cThe I proposition cannot be contraverted.\u201d Make this clear.\n\n (14) Is there any difference in meaning between, \u201cAll illogical work\n is unscholarly\u201d and \u201cNo illogical work is scholarly?\u201d Explain by\n circles.\n\n (15) State the logical process involved in passing from each\n proposition to its succeeding one:\n\n (1) \u201cAll men are imperfect.\u201d\n\n (2) \u201cNo men are perfect.\u201d\n\n (3) \u201cNo perfect beings are men.\u201d\n\n (4) \u201cSome not-men are perfect beings.\u201d\n\n (5) \u201cSome perfect beings are not-men.\u201d\n\n (6) \u201cSome perfect beings are not men.\u201d\n\n (16) It is sometimes said that in sub-contraries there is really no\n opposition. Do you agree? Give arguments.\n\n\n\n\n CHAPTER 11.\n\n MEDIATE INFERENCE. THE SYLLOGISM.\n\n\n=1. INFERENCE AND REASONING.=\n\nInference has been defined as both a product and a process. When\nused to indicate a process the term inference becomes synonomous with\nreasoning. If logicians could agree to confine inference to the product\nand reasoning to the process, it would remove an ambiguity which is\nmore or less misleading. But since this has not become the custom, we\nshall use inference as indicating the process as well as the product.\n\n_Definitions\u2015\u2015Middle Term Explained._\n\nInference is the thought process of deriving a judgment from one or two\nantecedent judgments.\n\n_Mediate inference is inference by means of a middle term._\n\nReasoning of this nature involves three terms, two of which are\ncompared with a third or middle term, and then related to each other\nto form a new judgment. The middle term is the common unit, or the\n_standard_ by which the other terms are measured. To illustrate: If\nJohn and James are each six feet tall, then plainly, they are of the\nsame height. The standard, or _middle_ term, is \u201c_six feet tall_.\u201d\n\n\n=2. THE SYLLOGISM.=\n\nJust as the judgment is expressed by means of the proposition, so\nmediate inference is best expressed by means of the syllogism.[9] The\nfollowing are syllogisms:\n\n (1) James is six feet tall,\n John is six feet tall,\n Hence James is as tall as John.\n\n (2) All true teachers are just,\n You are a true teacher,\n Hence you are just.\n\n (3) All men are mortal,\n You are a man,\n Hence you are mortal.\n\n\n=3. THE RULES OF THE SYLLOGISM.=\n\nAll syllogistic reasoning is conditioned by the following eight rules:\n\n (1) A syllogism must have three, and only three, different terms.\n\n (2) A syllogism must have three, and only three, propositions.\n\n (3) The middle term must be distributed at least once.\n\n (4) No term must be distributed in the conclusion which is not also\n distributed in a premise.\n\n (5) No conclusion can be drawn from two negative premises.\n\n (6) If one premise be negative, the conclusion must be negative; and\n conversely, to prove a negative conclusion, one of the premises\n must be negative.\n\n (7) No conclusion can be drawn from two particular premises.\n\n (8) If one premise be particular, the conclusion must be particular.\n\nThese rules are exceedingly important, as their observance is necessary\nin all mediate reasoning. The student needs, not only to understand\nthe meaning of these rules, but he needs to commit them to memory so\nthoroughly that they may be recalled without hesitation or mistake. To\naid the memory, the eight rules may be divided into these four groups:\n\n I. Rules one and two relate to the _composition of the syllogism_.\n\n II. Rules three and four pertain to the _distribution of terms_.\n\n III. Rules five and six have reference to _negative premises_.\n\n IV. Rules seven and eight concern _particular premises_.\n\n\n=4. RULES OF THE SYLLOGISM EXPLAINED.=\n\n(1) _A syllogism must have three and only three terms._\n\nIt is common to represent the various syllogistic forms by symbols,\nthe same symbols always standing for the same terms. In this treatment\nwe shall let capital G stand for the major term, as \u201cmajor\u201d means\n_greater_; capital S for the minor term, as \u201cminor\u201d means _smaller_,\nand capital M for the middle term. G, S and M, the initial letters\nof greater (major), smaller (minor) and middle, will be the constant\nsymbols for these terms; just as A, E, I and O are used as the constant\nsymbols for the four logical propositions.\n\n_Illustration._\n\n Syllogism written in full:\n All men are mortal,\n Socrates is a man,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n (Therefore) Socrates is mortal.\n\n Syllogism symbolized:\n All M is G\n S is M\n \u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 S is G\n\n_The major term is always the predicate and the minor term the\nsubject of the conclusion._ The conclusion of the foregoing syllogism\nis, \u201cSocrates is mortal.\u201d Since G stands for the predicate of every\nconclusion, then it stands for \u201c_mortal_,\u201d the predicate of the above\nconclusion. For a similar reason, S stands for the subject, namely,\n\u201c_Socrates_\u201d; while M represents the middle term, \u201c_man_.\u201d\n\nSince every syllogism must have three propositions, and since it takes\ntwo terms to form a proposition, then it follows that every syllogism\nmust contain _six terms_. But, as no syllogism can have _more_ than\nthree _different_ terms, we conclude that each term of the syllogism\nmust be used _twice_. In the foregoing example, G thus appears,\nnot only in the last proposition, or conclusion, but in the first\nproposition also. Similarly, both S and M occur twice. Every logical\nsyllogism, then, contains first, _a major term_, which is always the\n_predicate_ of the conclusion and appears _once_ in the premises;\nsecond, a _minor term_, which is always the _subject_ of the conclusion\nand appears _once_ in the premises; and third, a _middle term_ to which\nthe other two terms are referred.\n\nThere are two ways of locating the middle term; first, it is the term\nwhich is used in _both_ the premises; second, it is the term which\n_never appears in the conclusion_. Likewise, there are two ways of\nlocating the major and minor terms; first, the major term is always\nthe _predicate_ and the minor term the _subject_ of the conclusion;\nsecond, the major term is usually the _broader_ and the minor term the\n_narrower_ of the two. If the major and minor terms seem to be of about\nthe same extension or breadth, then the term in the first proposition,\nwhich is not the middle term, is the major.\n\nIn the attending syllogisms the three terms are designated:\n\n (middle) (major)\n | |\n (1) All true teachers are sympathetic,\n\n (minor) (middle)\n | |\n You are a true teacher,\n\n (minor) (major)\n | |\n \u2234 You are sympathetic.\n\n (major) (middle)\n | |\n (2) No shell fish are vertebrates,\n\n (minor) (middle)\n | |\n All trout are vertebrates,\n\n (minor) (major)\n | |\n \u2234 No trout are shell fish.\n\nThe necessity of having but _three_ different terms in any syllogism\nmay be understood by supposing that there are four different terms;\nthen it would follow that there could be _no standard_ or common link.\nIn the axiom, \u201cThings equal to the same thing are equal to each other,\u201d\nthe _same thing_ is the common standard or link. Two things which equal\ntwo different things are not equal to each other.\n\nThe impossibility of reasoning from four terms may be shown by circles.\n\n All men are mortal.\n All trees grow.\n\n Illustration: FIG. 8.\n\nThese circles show that no connection can be established between either\ngroup. Using four terms in any syllogism is known as the _fallacy of\nfour terms_.\n\n(2) _A syllogism must have three and only three propositions._ The\nproposition containing the major term is called the _major premise_,\nwhile the one containing the minor term is called the _minor premise_.\nIn a strictly logical syllogism the major premise is written first,\nthe minor premise second and the conclusion third. In common parlance,\nhowever, the minor premise or even the conclusion may appear first.\n\nThe conclusion of a syllogism is always preceded by _therefore_, or\nits equivalent, which may be written or understood. The premises always\nanswer the question, Why is the conclusion true? The premises are often\npreceded by such words as _for_ and _because_.\n\nThe attending irregular syllogisms are arranged logically and the\npremises and conclusions indicated:\n\n(1a) _Illogical._\n\n\u201cYou must take an examination because all who enter the school are\nexamined and you, as I understand it, are planning to enter.\u201d\n\n(2a) \u201cSome of these books are not well bound, for they are going to\npieces as no well bound book would do.\u201d\n\n(1b) _Logical._\n\n All who enter this school are examined, Major premise.\n You are planning to enter this school, Minor premise.\n You must be examined. Conclusion.\n\n(2b)\n\n No well bound book goes to pieces, Major premise.\n Some of these books are going to pieces, Minor premise.\n Some of these books are not well bound. Conclusion.\n\nThe fact that all syllogisms must have three and only three premises\nfollows from rule \u201c1.\u201d One premise must compare the middle term with\nthe \u201cmajor\u201d; another premise must compare the middle term with the\n\u201cminor\u201d; while the conclusion links together the \u201cmajor\u201d and the\n\u201cminor.\u201d\n\n(3) _The middle term must be distributed at least once._ The rule is\nusually given in this way, \u201cThe middle term must be distributed once at\nleast, and must not be ambiguous.\u201d In this treatment the last part of\nthe rule has been omitted because it must be apparent to the student\nthat a middle term used in two senses is virtually equivalent to _two\ndifferent terms_; such an \u201cambiguous middle\u201d would, in consequence,\ngive a syllogism of _four terms_.\n\nRules 3 and 4 are of greater importance than the others because they\nare more frequently violated. If the middle term is not distributed\nat least once, the fallacy is referred to as \u201c_undistributed middle_.\u201d\nIf the distributed major term of the conclusion is not distributed\nin the major premise, then the fallacy is called, \u201c_illicit process\nof the major term_\u201d; and finally, if the distributed minor term of\nthe conclusion is not distributed in the minor premise the fallacy is\ndenominated an \u201c_illicit process of the minor term_.\u201d These two illicit\nprocesses may be abbreviated to illicit major and illicit minor.\n\nRecall that any term is distributed when it is referred to as a\ndefinite whole. Unless the whole of the middle term is considered it\nfails to become a common standard of comparison. This becomes clear\nwhen recourse is made to the circles.\n\n_Illustration._\n\nSyllogism in which the middle term is not distributed:\n\n All men are mortal,\n All trees are mortal,\n \u2234 All trees are men.\n\nAll the propositions are A\u2019s and consequently the predicates of each\nare undistributed, as A distributes the subject _only_. Therefore the\nmiddle term, \u201c_mortal_,\u201d is not distributed in either of the premises\nand thus the fallacy.\n\nFallacy shown by circles:\n\n Illustration: FIG. 9.\n\nThese circles indicate the correct meaning of the two premises. By them\nit is seen that all of the \u201cmen\u201d circle belongs to the \u201cmortal\u201d circle\nand all of the \u201ctree\u201d circle belongs to the \u201cmortal\u201d circle, but in\nthis case there is no connection between the \u201cmen\u201d and \u201ctree\u201d circles.\nThus, to say that \u201c_All trees are men_,\u201d is fallacious. We have no\nright to either affirm or deny the connection between men and trees.\nIf \u201cmortal\u201d were distributed we would have this right as the following\nwill make clear:\n\n All men are mortal,\n No stones are mortal,\n \u2234 No stones are men.\n\n Illustration: FIG. 10.\n\nHere the middle term _mortal_ is distributed in the second premise\nas in it the subject \u201c_stones_\u201d is _excluded_ from the entire mortal\nterritory. This conclusion is verified by the formal statement that \u201cE\u201d\ndistributes both subject and predicate. Since all of the \u201cmen\u201d circle\nbelongs to the \u201cmortal\u201d circle and none of the \u201cstones\u201d circle belongs\nto the \u201cmortal\u201d circle then none of the \u201cstones\u201d circle can belong to\nthe \u201cmen\u201d circle.\n\n(4) _No term must be distributed in the conclusion which is not also\ndistributed in its premise._\n\nIt has been affirmed that a term is distributed when it is referred to\nas a definite whole. To put it in another way, a term is distributed\nwhen it is employed in its fullest sense. It is obvious that we should\nnot employ a term in its fullest sense in the conclusion when it has\nbeen used only in a partial sense in its premise. What is said of the\npart cannot necessarily be said of the whole. For example: Because\n_some_ men are honest it does not follow that _all_ men are honest. Of\ncourse the converse of this is true, namely, if it could be proved that\nall men are honest then surely it would follow that some of the men are\nhonest. To put it briefly: What is true of _all_ is true of _some_ but\nwhat is true of _some_ is not necessarily true of _all_.\n\nTo distribute a term in the conclusion when it is not distributed in\nthe premise where it occurs is equivalent to saying, \u201cwhat is true of\nsome is true of all.\u201d This error which violates rule \u201c4\u201d leads to the\ntwo fallacies of illicit process of the major and minor terms. The\nfollowing illustrate the two fallacies.\n\nSyllogism illustrating illicit major:\n\n All trees grow,\n No men are trees,\n \u2234 No men grow.\n\nThe first premise is an A and consequently its subject is distributed.\nThe second premise and conclusion being E\u2019s have both subject and\npredicate distributed. Thus _grow_, as used in the conclusion, is\ndistributed, but, as used in the major premise, it is not distributed.\nFallacy shown by circles:\n\n Illustration: FIG. 11.\n\nHere all of the \u201ctree\u201d circle belongs to the \u201cgrow\u201d circle and none\nof the \u201cmen\u201d circle belongs to the \u201ctree\u201d circle, hence the diagram\ncorrectly represents the meaning of the two premises and shows the\nfallacy of concluding that _no men grow_. The \u201cmen\u201d circle, being\nentirely within the \u201cgrow\u201d circle, indicates that _all men grow_.\nSyllogism illustrating illicit minor:\n\n All true teachers are just,\n All true teachers are sympathetic,\n \u2234 All the sympathetic are just.\n\nEach proposition being an A distributes its subject. But the subject of\nthe conclusion which is \u201c_the sympathetic_\u201d is not distributed in the\nminor premise, as an A proposition distributes its subject only. Hence\nthe fallacy of illicit minor.\n\nFallacy shown by circles:\n\n Illustration: FIG. 12.\n\nThe diagram correctly represents the two premises since all of the\n\u201ctrue teacher\u201d circle belongs to both the \u201cjust\u201d and \u201csympathetic\u201d\ncircles. But all of the \u201csympathetic\u201d circle does not belong to the\n\u201cjust\u201d circle. Hence the fallacy.\n\n(5) _No conclusion can be drawn from two negative premises._\n\nWhen two terms are both denied of a third term, it is quite impossible\nto draw any conclusion relative to the two terms, as the absolute\nexclusion of the third term eliminates any possibility of a common link\nor standard.\n\nThe circles will make this apparent:\n\n No men are immortal,\n No trees are immortal,\n\n Illustration: FIG. 13.\n\n\u201cNo trees are men\u201d is the conclusion represented by Fig. 13.\n\nOther possible conclusions are, \u201c_All trees are men_,\u201d \u201c_All men are\ntrees_\u201d and \u201c_Some men are trees_.\u201d\n\nIt is thus seen that no definite conclusion can be drawn. It may now\nbe said that when the major and minor terms are used in two negative\npremises the connection between them is _indeterminate_. This violation\nof rule \u201c5\u201d may be termed the fallacy of _two negatives_.\n\n(6) _If one premise be negative the conclusion must be negative; and\nconversely, to prove a negative conclusion one of the premises must be\nnegative._\n\nReferring to the first part of this rule, it may be said of two terms\nthat if one is affirmed and the other denied of a third term, then the\ntwo terms must be denied of each other. The attending syllogism and its\n\u201ccircled\u201d representation will throw light upon this:\n\n No men are immortal,\n All Americans are men,\n \u2234 No Americans are immortal.\n\n Illustration: FIG. 14.\n\nSince none of the \u201cmen\u201d circle belongs to the \u201cimmortal\u201d circle and all\nof the \u201cAmerican\u201d circle is inside the \u201cmen\u201d circle, it is evident that\nnone of the \u201cAmerican\u201d circle can belong to any part of the \u201cimmortal\u201d\ncircle. Thus it is manifest that an affirmative conclusion like, \u201cAll\nAmericans are immortal,\u201d is invalid.\n\nThe converse of rule 6, \u201cTo prove a negative conclusion, one of the\npremises must be negative,\u201d may be explained by the general principle\nin logic that when two terms are known to disagree, one must agree with\na third term while the other must disagree. If both agreed with a third,\nthen the conclusion would of necessity be affirmative. If both\ndisagreed no conclusion could be drawn. A violation of rule 6 may be\ncalled the fallacy of _negative conclusion_.\n\n(7) _No conclusion can be drawn from two particular premises._ Proof:\n\n (1) All the possible combinations of the two particular premises\n I and O are, (1) IO, (2) OI, (3) II, (4) OO.\n\n \u201cIO\u201d considered.\n\n (2) Since O is a negative premise the conclusion would have to be\n negative according to rule 6. (If one premise is negative, the\n conclusion must be negative.)\n\n (3) If the conclusion is negative, then its predicate, which is\n the major term, must be distributed. (All negative propositions\n distribute their predicates.)\n\n (4) If the major term is distributed in the conclusion, it must\n be distributed in the major premise, rule 4. (No term must be\n distributed in the conclusion, which is not also distributed in\n one of the premises.)\n\n (5) Hence two terms must be distributed in the premises, the major\n term according to (4) and the middle term according to rule 3.\n\n (6) But I distributes neither term and O distributes its predicate\n only; I and O together, then, distribute but _one_ term.\n\n (7) To draw a negative conclusion the premises must distribute two\n terms, the middle and the major, according to the foregoing.\n\n (8) Hence a conclusion from I and O is untenable. The same may be\n said of \u201cOI.\u201d\n\n \u201cII\u201d considered.\n\n (1) The I proposition distributes neither subject nor predicate,\n hence the premises \u201cII\u201d would distribute no term.\n\n (2) But the middle term must be distributed at least once according\n to rule 3.\n\n (3) Therefore no conclusion can be drawn from \u201cII.\u201d\n\n A valid conclusion from \u201cOO\u201d is impossible according to rule 5.\n\n(8) _If one premise be particular the conclusion must be particular._\nProof: The possible combinations conditioned by rule 8 are AI, AO, EI,\nEO, IO, II, OO.\n\n \u201cAI\u201d considered.\n\n (1) Proposition A distributes its subject, proposition I neither;\n hence \u201cAI\u201d together distribute but one term.\n\n (2) According to rule 3 this one term must be the middle term.\n\n (3) The minor term must, therefore, be undistributed in the minor\n premise, and in consequence undistributed in the conclusion.\n\n (4) But this undistributed minor term is the subject of the\n conclusion; hence said conclusion must be particular, as only\n particulars have an undistributed subject.\n\n \u201cAO\u201d and \u201cEI\u201d considered.\n\n Proof:\n\n (1) \u201cAO\u201d distribute two terms; so do \u201cEI.\u201d\n\n (2) Both \u201cAO\u201d and \u201cEI\u201d must have negative conclusions according to\n rule 6.\n\n (3) A negative conclusion distributes its predicate which is the\n major term.\n\n (4) The major term and the middle term must be distributed in the\n premises. Rules 4 and 3.\n\n (5) Thus the third term, which is the minor, cannot be distributed\n in the minor premise and, consequently, the minor cannot be\n distributed in the conclusion.\n\n (6) This necessitates a particular conclusion.\n\nPremises EO and OO, being negative, cannot yield a conclusion according\nto rule 5; similarly, neither can the particulars IO and II because of\nrule 7.\n\n\n=5. THE DICTUM OF ARISTOTLE.=\n\nAristotle gives an axiom on which all syllogistic inference is\nbased. Indeed from this fundamental principle the significant rules\nof the syllogism could be derived. The dictum is stated in this wise:\n\u201cWhatever is predicated, whether affirmatively or negatively, of\na term distributed may be predicated in the manner of everything\ncontained under it.\u201d The following statements represent various ways\nof explaining this dictum:\n\n (1) Whatever is said of a term used in its fullest sense may likewise\n be said of that term when used only in a partial sense.\n\n (2) What is true of the whole is true of the part.\n\n (3) \u201cWhat pertains to the higher class pertains also to the lower.\u201d\n Since this dictum is the basic principle underlying the important\n rules of the syllogism, it is unnecessary to dwell longer\n upon it; because an explanation of the rules is, virtually, an\n explanation of the dictum.\n\n\n=6. CANONS OF THE SYLLOGISM.=\n\nThe dictum of Aristotle is ostensibly a self-evident truth, and some\nlogicians have put this truth in the form of three axiomatic statements\nwhich are known as the _canons of the syllogism_. These are as follows:\n\n (1) \u201cTwo terms agreeing with one and the same third term agree with\n each other.\u201d\n\n (2) \u201cTwo terms of which one agrees and the other does not agree with\n one and the same third term, do not agree with each other.\u201d\n\n (3) \u201cTwo terms both disagreeing with one and the same third term may\n or may not agree with each other.\u201d\n\nMaking use of the symbols as explained on a previous page of this\nchapter, it will be seen that the first canon conforms to this\nsyllogistic type:\n\n All M is G\n All S is M\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 All S is G\n\nThe two terms are S and G, while M is the third term.\n\nThe attending symbolizations illustrate, respectively, the second and\nthird canons:\n\n No M is G\n All S is M\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 No S is G\n\n No M is G\n No S is M\n Conclusion indeterminate.\n\n\n=7. THREE MATHEMATICAL AXIOMS.=\n\nAnalogous to the three canons treated in \u201c6,\u201d there are certain\nmathematical axioms which are here stated:\n\n (1) \u201cThings equal to the same thing are equal to each other.\u201d\n\n (2) \u201cOne thing equal to and the other thing not equal to the same\n third thing are not equal to each other.\u201d\n\n (3) \u201cThings not equal to the same thing may or may not equal each\n other.\u201d\n\nIllustrations of the three axioms:\n\n (1) If x equals 5, and y equals 5, then x equals y.\n\n (2) If x equals 5, and y does not equal 5, then x does not equal y.\n\n (3) If x does not equal 5, and y does not equal 5, then x may or may\n not equal y.\n\n\n=8. OUTLINE.=\n\n MEDIATE INFERENCE.\n\n (1) Inference and reasoning.\n Definitions. Middle term explained.\n\n (2) The analogy between the judgment and the syllogism.\n\n (3) Rules of the syllogism given. Eight in number.\n\n (4) Rules of the syllogism explained:\n\n Rule 1. Syllogistic symbols.\n Major, minor, and middle terms; how found.\n Fallacy of four terms.\n\n Rule 2. Major and minor premises and conclusion, how determined.\n Logical arrangement.\n Reason for three propositions.\n\n Rule 3. Reason for omitting \u201cambiguous middle\u201d from rule.\n Undistributed and distributed middle explained.\n\n Rule 4. Illicit major and minor explained and illustrated.\n\n Rule 5. Fallacy of two negatives.\n\n Rule 6. Fallacy of negative conclusion.\n\n Rule 7. Fallacy of two particulars.\n\n Rule 8. Fallacy of particular conclusion.\n\n (5) Aristotle\u2019s dictum.\n\n (6) Canons of the syllogism.\n\n (7) Mathematical axioms.\n\n\n=9. SUMMARY.=\n\n(1) Inference is a term used to denote a process as well as a product.\nAs a process reasoning and inference are in reality synonomous terms.\n\nInference is a thought process of deriving a judgment from one or two\nantecedent judgments.\n\nMediate inference is inference by means of a middle term. Mediate\ninference makes use of three terms, two of which are compared with a\nthird term as a standard. This third term is called the middle term.\n\n(2) The syllogism is the common mode of expression for mediate\ninference.\n\n(3) Valid syllogistic reasoning is conditioned by eight rules. The\nfirst and second relate to the composition of the syllogism; the\nthird and fourth to the distribution of terms; the fifth and sixth\nto negative premises; the seventh and eighth to particular premises.\n\n(4) All syllogisms must have three terms: the major, the minor, and the\nmiddle. The middle term occurs twice in the premises but never appears\nin the conclusion. The minor term is always the subject, and the major\nterm the predicate of the conclusion. The major term is usually broader\nthan the minor.\n\nNo conclusion can be drawn from four terms. To attempt this gives rise\nto the fallacy of four terms.\n\nAll syllogisms must have three propositions, the major and the\nminor premises, and the conclusion. The major premise first and the\nminor second is the more logical arrangement, although the common\nconversational form is to use the minor premise first.\n\nAmbiguous middle amounts to the fallacy of four terms.\n\nUnless the middle term is distributed at least once in the syllogism,\nit fails to become a common standard.\n\nDistributing a term in the conclusion, without its being distributed in\nits premise, is equivalent to asserting that, \u201cWhat is true of a part\nis true of the whole.\u201d This error results in the fallacies of illicit\nmajor and minor.\n\nA conclusion from two negatives is impossible, because of the total\nexclusion of the middle term.\n\nOf two terms, if one is affirmed and the other denied of a third term,\nthen they must be denied of each other; and, conversely, if two terms\nare to be denied of each other, one must be affirmed and the other\ndenied of a given third term. This fundamental principle necessitates\nderiving a negative conclusion from two premises when one is negative.\nIt, likewise, compels the converse of this.\n\nA valid conclusion from two particulars is untenable because of the\ntwo negative fallacies, or some fallacy relative to the distribution\nof terms.\n\nOne particular premise forces a particular conclusion because of the\nfallacies of two negatives, two particulars, and illicit minor.\n\n(5) Aristotle\u2019s dictum simplified means, \u201cWhat is true of the whole is\ntrue of the part.\u201d\n\n(6) The canons of the syllogism, three in number, are:\n\n (1) \u201cTwo terms agreeing with one and the same third term agree with\n each other.\u201d\n\n (2) \u201cTwo terms of which one agrees and the other does not agree with\n one and the same third term do not agree with each other.\u201d\n\n (3) \u201cTwo terms both disagreeing with one and the same third term may\n or may not agree with each other.\u201d\n\n(7) The foregoing canons may be stated as mathematical axioms.\n\n\n=10. ILLUSTRATIVE EXERCISES.=\n\n(1a) Make use of the proper symbols and indicate the three terms of\neach of the attending syllogisms:\n\n (1) All fixed stars twinkle,\n Vega is a fixed star,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 Vega twinkles.\n\n (2) All men are rational beings,\n No tree is a rational being,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 No trees are men.\n\n (3) All good citizens are law abiding,\n All good citizens vote,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 Some who vote are law abiding.\n\nI recall that the three terms are the middle, the major and the minor,\nand that the \u201cmiddle\u201d does not occur in the conclusion, whereas the\n\u201cmajor\u201d is always the predicate and the \u201cminor\u201d the subject of the\nconclusion. The symbols M, G and S being the initial letters of middle,\ngreater and smaller, I make use of these in designating the three terms,\nas the following will illustrate:\n\n M G\n (1) All fixed stars twinkle,\n\n S M\n Vega is a fixed star,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n S G\n \u2234 Vega twinkles.\n\n\u201cTwinkles\u201d being the predicate of the conclusion is designated as being\nthe major term by putting the letter G above it. Then \u201cG\u201d is placed\nabove the term \u201ctwinkle\u201d in the first premise.\n\n\u201cS\u201d is placed above the subject of the conclusion to indicate that it\nis the minor term. \u201cS\u201d is also placed above \u201cVega,\u201d the minor term, as\nfound in the second premise.\n\nThe remaining term, \u201cfixed stars,\u201d must be the middle term, therefore\nI place \u201cM\u201d above it. The fact that \u201cfixed star\u201d does not occur in the\nconclusion verifies this.\n\nUsing only the symbols, the syllogism takes this form:\n\n All M is G\n S is M\n \u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 S is G\n\nUsing the symbols to represent the other syllogisms, we have\n\n (2) All G is M\n No S is M\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 No S is G\n\n (3) All M is G\n All M is S\n \u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 Some S is G\n\n(1b) Indicate by symbols the three terms of the following syllogisms:\n\n (1) No trees are men,\n All rational beings are men,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 No rational being is a tree.\n\n (2) All men have the power of speech,\n You are a man,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 You have the power of speech.\n\n (3) Some men are wise,\n All men are rational,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 Some rational beings are wise.\n\n(2a) Illustrate by syllogism the fallacy of undistributed middle. An\neasy way is to use _the middle term as the predicate of two A premises_.\nThis yields the fallacy because an A proposition does not distribute\nthe predicate.\n\nThe illustration: distributed terms underscored.\n\n All true teachers are students,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n All scholars are students,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 All scholars are true teachers.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n(2b) Give two illustrations of undistributed middle.\n\n(3a) Give syllogistic illustrations of the fallacies of illicit major\nand minor.\n\n_Illicit Major._\n\n_Use the middle term as the subject of an A proposition, and then as\nthe predicate of an E proposition._ This would necessitate a negative\nconclusion in which the major term is distributed. But the major term\nis not distributed in the major premise, hence the fallacy.\n\nIllustration in which the distributed terms are underscored:\n\n All men are mortal,\n \u2015\u2015\u2015\n No trees are men,\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 No trees are mortal.\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\n\n_Illicit Minor._\n\nTo illustrate this fallacy one may use _the middle term as the subject\nof two A premises_. This would give an A conclusion in which the\nsubject is distributed. But this same term is not distributed in its\npremise because here it is used as the predicate of an A. Illustration:\n\n All earnest students study,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n All earnest students desire to succeed,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n \u2234 All who desire to succeed study.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n\n=11. REVIEW QUESTIONS.=\n\n (1) Distinguish between inference and reasoning.\n\n (2) Define inference. Mediate inference.\n\n (3) Illustrate the difference between mediate and immediate\n inference.\n\n (4) Explain by illustration the use of the middle term.\n\n (5) Exemplify the syllogism.\n\n (6) State the rules of the syllogism.\n\n (7) From the attending syllogisms select the three terms:\n\n (1) All patriotic citizens vote,\n You are a patriotic citizen,\n \u2234 You should vote.\n\n (2) No honest man would misrepresent,\n (but) John Smith did misrepresent,\n \u2234 John Smith is not honest.\n\n (8) Symbolize the foregoing syllogisms.\n\n (9) Illustrate by syllogisms the fallacy of four terms.\n\n (10) Indicate by circles that a valid conclusion cannot be drawn from\n four terms.\n\n (11) Why must a syllogism have three and only three propositions?\n\n (12) Indicate how the three propositions of an argument may be\n designated. What is the logical arrangement?\n\n (13) Show that an ambiguous middle amounts to a fallacy of four terms.\n\n (14) Explain and illustrate undistributed middle, illicit major,\n illicit minor.\n\n (15) Exemplify the fallacies of question \u201c14\u201d by using circles.\n\n (16) Explain by circles why a conclusion cannot be drawn from two\n negatives.\n\n (17) Make clear that a negative conclusion must follow, if one premise\n be negative.\n\n (18) State and explain the principle which underlies the rule, \u201cIf the\n conclusion is negative one premise must be negative.\u201d\n\n (19) Prove by the process of elimination that no conclusion can be\n drawn from two particulars.\n\n (20) In a way similar to that of question \u201c19\u201d show that if one\n premise be particular the conclusion must be particular.\n\n (21) State and explain Aristotle\u2019s dictum.\n\n (22) State the canons of the syllogism.\n\n (23) Symbolize and explain by circles the three canons.\n\n (24) Illustrate the three mathematical axioms which the canons\n suggest.\n\n\n=12. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Give an illustration of a valid conclusion being drawn from four\n terms.\n\n (2) Explain by circles the foregoing.\n\n (3) From three different business transactions, select the middle\n term of comparison.\n\n (4) Why should not those who are given to much which is argumentative,\n speak in syllogistic terms?\n\n (5) \u201cHe is a man of high ideals, and you know him to be strictly\n honest, therefore you have no excuse for not voting for him.\u201d\n Recast this quotation with a view of making a logical syllogism.\n\n (6) Show by circles that there may be a vital difference between a\n _syllogism_ of three terms and an _equation_ of three terms.\n\n (7) Indicate by illustration that in conversational argumentation the\n minor premise naturally comes first.\n\n (8) Show by circles the meaning of \u201cindeterminate conclusion.\u201d\n\n (9) Rule five states that no conclusion can be drawn from two\n negatives. Defend this rule in connection with the following\n syllogism, which seems to contain a valid conclusion:\n\n Any statement which is not true cannot be accepted,\n This statement is not true,\n \u2234 It cannot be accepted.\n\n (10) If the conclusion is particular, must one premise be particular?\n Explain.\n\n\n\n\n CHAPTER 12.\n\n FIGURES AND MOODS OF THE SYLLOGISM.\n\n\n=1. THE FOUR FIGURES OF THE SYLLOGISM.=\n\nBy a figure of a syllogism is meant some particular arrangement of the\nthree terms in the two premises. The conclusion is eliminated from this\ndiscussion, because in it the arrangement of the terms is constant, the\nmajor term always being used as the predicate of the conclusion and the\nminor as the subject. Using the symbols M, G and S, we find that there\nare four possible arrangements and, therefore, but _four figures_.\nThese may be represented as follows:\n\n First Second Third Fourth\n figure figure figure figure\n M \u2015 G G \u2015 M M \u2015 G G \u2015 M\n S \u2015 M S \u2015 M M \u2015 S M \u2015 S\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n S \u2015 G S \u2015 G S \u2015 G S \u2015 G\n\nNo matter what the syllogism, if it is to be proved \u201c_logical_,\u201d it\nshould be made to fit one of the four figure-types. To be sure, it may\nfit the figure without being logical, but it cannot be strictly logical\nwithout fitting the figure. The following valid syllogisms conform to\nthe four figures as will be seen by the symbolized terms:\n\n M G\n First figure: All men are mortal,\n\n S M\n Socrates is a man,\n\n S G\n \u2234 Socrates is mortal.\n\n M \u2015 G\n S \u2015 M\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n G M\n Second figure: All good citizens love their country,\n\n S M\n No criminal loves his country,\n\n S G\n \u2234 No criminal is a good citizen.\n\n G \u2015 M\n S \u2015 M\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n M G\n Third figure: All good citizens are law abiding,\n\n M S\n All good citizens vote,\n\n S G\n \u2234 Some who vote are law abiding.\n\n M \u2015 G\n M \u2015 S\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n G M\n Fourth figure: Some teachers are fair minded,\n\n M S\n All who are fair minded are just,\n\n S G\n \u2234 Some just persons are teachers.\n\n G \u2015 M\n M \u2015 S\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\nHere, then, are the types that represent all the syllogisms which\nmediate inference may use. _Logic recognizes no other._ Since every\nsuccessful student of logic must be familiar with the four figures, the\nfollowing may be used as a suggestive aid to reproducing the figures at\nwill:\n\nFirst. It is easy for any one to remember this syllogism:\n\n All men are mortal,\n Socrates is a man,\n \u2234 Socrates is mortal.\n\nIn fact, it comes down to us from the time of Aristotle, and is\ntherefore a patriot of many generations to whom the faithful should\ntouch their hats. Let us, then, be ready to reproduce this syllogism\nwith automatic precision, since it will enable us to know at once the\n_position of the terms_ in the first figure. Second. Converting the\nterms of the _major premise_ of the first figure gives the second\nfigure, as, e. g.:\n\n First figure. Second figure.\n M \u2015 G (Convert) G \u2015 M\n S \u2015 M S \u2015 M\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n S \u2015 G S \u2015 G\n\nThird. Converting the terms of the _minor premise_ of the first figure\ngives the third figure, as, e. g.:\n\n First figure. Third figure.\n M \u2015 G M \u2015 G\n S \u2015 M (Convert) M \u2015 S\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n S \u2015 G S \u2015 M\n\nFourth. Converting the terms of _both the major and minor premises_ of\nthe first figure gives the fourth, as, e. g.:\n\n First figure. Fourth figure.\n M \u2015 G (Convert) G \u2015 M\n S \u2015 M (Convert) M \u2015 S\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n S \u2015 G S \u2015 G\n\nTo summarize: _The second, third and fourth figures may be derived from\nthe first. Converting the major premise of the first figure gives the\nsecond figure; converting the minor premise gives the third figure; and\nconverting both premises gives the fourth figure._\n\n\n=2. THE MOODS OF THE SYLLOGISM.=\n\nBy the mood of a syllogism is meant some particular arrangement of\nthe propositions which compose the syllogisms. \u201c_Mood_\u201d stands for\nan arrangement of the _propositions_, while \u201c_figure_\u201d represents an\narrangement of the _terms_ in any syllogism.\n\nCombining any three of the four logical propositions gives a mood, as,\ne. g.,\n\n (1) E (2) A (3) E\n A I I\n E I O\n\nare moods. The first one has an E proposition for the major premise, an\nA for the minor and an E for the conclusion. This syllogism represents\nthe first mood given above:\n\n E No men are trees,\n A All Americans are men,\n E \u2234 No Americans are trees.\n\nIt would not be difficult to determine by actual experiment, just how\nmany moods could be formed, and of these, how many would admit of valid\nconclusions. It may be seen that there are sixty-four permutations of\nthe four logical propositions, taken three at a time. These are in part:\n\n (1) (2) (3) (4) (5) (6) (7) (8)\n A A A A A A A A\n A A A A E E E E\n A E I O A E I O\n\n (9) (10) (11) (12) (13) (14) (15) (16)\n A A A A A A A A\n I I I I O O O O\n A E I O A E I O\n\nAnd so the permutations could be continued. Substituting E for the\nmajor premise of the above group would give another group of sixteen,\nwhile a like substitution of I and O would result in two more groups,\nsixteen in each. This gives sixty-four in all.[10]\n\n\n=3. TESTING THE VALIDITY OF THE MOODS.=\n\nIn order to put the moods to good use, it is necessary to ascertain\nwhich ones yield a valid conclusion in any figure. If each were valid\nin all of the four figures, there would be 256. But it is obvious that\nsuch is not the case.\n\nReferring to the sixteen permutations given above, we find that the\n_\u201cnegative-conclusion\u201d rule_ makes invalid 2, 4, 5, 7, 10, 12, 13 and\n15; whereas the rule for particulars throws out 9 and 14. This leaves\nthe following as the probable valid moods in one or more of the figures:\n1, 3, 6, 8, 11, 16. But to be certain of this the investigation must be\n A\ncontinued. The mood A has stood the test of the rules for negative and\n A\nparticular conclusions; now let us test this mood from the standpoint\nof the distribution of terms, using it in all four figures:\n\n\n _First_ _Second_ _Third_ _Fourth_\n A M \u2015 G G \u2015 M M \u2015 G G \u2015 M\n \u2015 \u2015 \u2015 \u2015\n A S \u2015 M S \u2015 M M \u2015 S M \u2015 S\n \u2015 \u2015 \u2015 \u2015\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\n A S \u2015 G S \u2015 G S \u2015 G S \u2015 G\n \u2015 \u2015 \u2015 \u2015\n\nAs an A proposition distributes its subject only, we underscore the\nsubject of each proposition in all the figures. (This underscoring is\na simple way to indicate distribution.)\n\nWe now find that the mood is valid in the first figure, because the\nmiddle term is distributed at least once; namely, in the major premise,\nand there is no term distributed in the conclusion which is not already\ndistributed in the premise where it occurs. On the other hand, the mood\nA\nA is invalid in the second, because of \u201c_undistributed middle_,\u201d and\nA\ninvalid in the third and fourth, because S is distributed in the\nconclusion but not distributed in the premise where it occurs (illicit\nminor).\n\nLet us try AII in the four figures:\n\n A M \u2015 G G \u2015 M M \u2015 G G \u2015 M\n \u2015 \u2015 \u2015 \u2015\n I S \u2015 M S \u2015 M M \u2015 S M \u2015 S\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n I S \u2015 G S \u2015 G S \u2015 G S \u2015 G\n\nWe underscore the subject of the A proposition in each of the four\nfigures. As I distributes neither subject nor predicate, no other term\n A\nshould be underscored. It is now evident that I is not valid in figures\n I\ntwo and four, because in both figures the middle term is undistributed\n(undistributed middle).\n\nIn a like manner all the other moods might be tested. Logicians, who\nhave done this, have found 24 to be valid. Five of these have weakened\nconclusions; i. e., a particular conclusion when it could just as well\n A\nbe universal. E illustrates this as the conclusion _could be E_. This\n O\n\nsyllogism exemplifies the weakened conclusion:\n\n A All trees grow,\n E No sticks are trees,\n O \u2234 Some sticks do not grow.\n\nThis conclusion is true, since \u201csome\u201d means \u201csome at least.\u201d Yet the\nconclusion is weak, because there is nothing to interfere with the\nbroader and stronger conclusion that, \u201cNo sticks grow.\u201d There are,\ntherefore, only 19 valid and serviceable moods. These are as follows:\n\n (1) (2) (3) (4) (5) (6)\n { A E A E \u2015 \u2015 }\n First figure { A A I I \u2015 \u2015 } 4\n { A E I O \u2015 \u2015 }\n\n { E A A E \u2015 \u2015 }\n Second figure { A E O I \u2015 \u2015 } 8\n { E E O O \u2015 \u2015 }\n\n { A I A E O E }\n Third figure { A A I A A I } 14\n { I I I O O O }\n\n { A A I E E \u2015 }\n Fourth figure { A E A A I \u2015 } 19\n { I E I O O \u2015 }\n\n A\nOf these nineteen moods it is not much of a tax to remember that A is\n A\n E\nvalid only in the first figure; whereas A is valid in the first and\n E\n A E\nsecond figures; I in the first and third; while I is valid in all. This\n I O\nknowledge, however, should be used only as one would employ the answers\nin arithmetic. Testing the validity of a mood in the four figures is an\nexceedingly valuable thought-exercise, which a knowledge of the final\nresult might easily vitiate. It is, no doubt, best to test the value\nof any mood without such knowledge, and then compare the result by\nreferring to the foregoing list of valid moods. It is not always wise\nto work with the answer in mind, yet it is most satisfying to know of\na _certainty_ that one\u2019s reasoning has led to a truth which others have\nverified.\n\n\n=4. SPECIAL CANONS OF THE FOUR FIGURES.=\n\nAs a deductive exercise in clear, logical thought, the indirect proof\ninvolved in establishing certain principles underlying the four figures,\nis of immense value. On no account should this section be omitted. The\nmere fact that it appears to be a difficult section is proof positive\nthat the student is in need of just such exercises.\n\n_Canons of the first figure._\n\n (1) The minor premise must be affirmative.\n\n (2) The major premise must be universal.\n\n_Problem: The minor premise must be affirmative._\n\n_Data_: Given the form of the first figure, which is,\n\n M \u2015 G\n S \u2015 M\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) If the minor premise is not affirmative then it must\nbe negative; because affirmative and negative propositions, being\ncontradictory in nature, admit of no middle ground.\n\n(2) If the minor premise is negative, the conclusion must be negative;\nfor the reason that a negative premise necessitates a negative\nconclusion.\n\n(3) If the conclusion is negative then its predicate, G, must be\ndistributed; since all negatives distribute their predicates.\n\n(4) If the predicate of the conclusion, which is the major term, is\ndistributed, then it must be distributed in the premise where it occurs,\nwhich is the major premise; for any term which is distributed in the\nconclusion must be distributed in the premise where it occurs.\n\n(5) If the major term, which is the predicate of the major premise,\nis distributed, then the major premise must be negative; because only\nnegatives distribute their predicates.\n\n(6) The result of this argument, then, gives _two_ negative premises,\nand we know from rule 3 that a conclusion from two negatives is\nuntenable.\n\n(7) Since the minor premise cannot be negative, it must be affirmative.\n\n_Problem: To prove that the major premise must be universal._\n\n_Data_: Given the form of the first figure:\n\n M \u2015 G\n S \u2015 M\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) The predicate of the minor premise, M, which is the middle\nterm, is undistributed; because no affirmative proposition distributes\nits predicate.\n\n(2) The middle term must be distributed in the major premise; since in\nany syllogism the middle term must be distributed at least once.\n\n(3) As the middle term, M, used as the subject of the major premise,\nmust be distributed, then the major premise must be universal; because\nonly universals distribute their subjects.\n\n_Epitome._\n\n_In the first figure, the minor premise must be affirmative, since\nmaking it negative necessitates making the major premise negative also;\nthe major premise must be universal in order to distribute the middle\nterm at least once._\n\n_Special canons of the second figure._\n\n(1) One premise must be negative.\n\n(2) The major premise must be universal.\n\n_Problem: To prove that one premise must be negative._\n\n_Data_: Given the form of the second figure:\n\n G \u2015 M\n S \u2015 M\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) The middle term, M, is the predicate of both premises.\n\n(2) The middle term must be distributed at least once, according to\nrule 3.\n\n(3) Hence one premise must be negative; since only negatives distribute\ntheir predicates.\n\n_Problem: To prove that the major premise must be universal._\n\n_Data_: Given the form of the second figure:\n\n G \u2015 M\n S \u2015 M\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) As one premise must be negative, it follows that the\nconclusion must be negative according to rule 6.\n\n(2) If the conclusion is negative, then its predicate, G, the major\nterm, must be distributed; since all negatives distribute their\npredicates.\n\n(3) When distributed in the conclusion, the major term, G, must also be\ndistributed in the major premise, where it is used as the subject. See\nrule 4.\n\n(4) Hence the major premise must be universal; for only universals\ndistribute their subjects.\n\n_Epitome._\n\n_In the second figure one premise must be negative in order to\ndistribute the middle term at least once; and the major premise must be\nuniversal that the major term, which is distributed in the conclusion,\nmay be distributed in the premise where it occurs._\n\n_Canons of the third figure._\n\n(1) The minor premise must be affirmative.\n\n(2) The conclusion must be particular.\n\n_Problem: To prove that the minor premise must be affirmative._\n\n_Data_: Given the form of the third figure, which is,\n\n M \u2015 G\n M \u2015 S\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) Suppose the minor premise were negative, then the\nconclusion would have to be negative, and this would distribute the\npredicate G.\n\n(2) A distributed predicate would necessitate its being distributed in\nthe major premise.\n\n(3) But G, being the conclusion of the major premise, could be\ndistributed only by a negative proposition.\n\n(4) This would result in two negatives; therefore no conclusion could\nbe drawn, if the minor premise were negative.\n\n_Problem: To prove that the conclusion must be particular._\n\n_Data_: Given the form of the third figure:\n\n M \u2015 G\n M \u2015 S\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) The minor term, which is the predicate of the affirmative\nminor premise, is undistributed; because no affirmative distributes its\npredicate.\n\n(2) If undistributed in the premise, then the minor term must remain\nundistributed in the conclusion, where it is used as the subject.\n\n(3) The conclusion must, then, be particular; since all universals\ndistribute their subjects.\n\n_Epitome._\n\n_In the third figure, unless the minor premise be affirmative, there\ncan be no conclusion; since a negative minor would necessitate a\nnegative major. An affirmative minor compels a particular conclusion,\nin order that the minor term, in the conclusion, may remain\nundistributed._\n\n_Canons of the fourth figure._\n\n(1) If the major premise is affirmative, the minor premise must be\nuniversal.\n\n(2) If the minor premise is affirmative, the conclusion must be\nparticular.\n\n(3) If either premise is negative, the major must be universal.\n\n_Problem: To prove that if the major is affirmative, the minor must be\nuniversal._\n\n_Data_: Given the form of the fourth figure:\n\n G \u2015 M\n M \u2015 S\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) If the major premise is affirmative, then its predicate\nwhich is the middle term, M, is undistributed; for no affirmative\ndistributes its predicate.\n\n(2) The middle term must then be distributed in the \u201cminor\u201d according\nto rule 3.\n\n(3) Then the \u201cminor\u201d must be universal; since only universals\ndistribute their subjects.\n\n_Problem: To prove that if the minor is affirmative, the conclusion\nmust be particular._\n\n_Data_: Given the form of the fourth figure:\n\n G \u2015 M\n M \u2015 S\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) If the minor premise be affirmative, then S, its\npredicate, must be undistributed; because no affirmative distributes\nits predicate.\n\n(2) Since S is undistributed in the minor premise, it must remain\nundistributed in the conclusion where it is used as the subject.\n\n_Problem: To prove that if either premise is negative, the major must\nbe universal._\n\n_Data_: Given the form of the fourth figure:\n\n G \u2015 M\n M \u2015 S\n \u2015\u2015\u2015\u2015\u2015\n S \u2015 G\n\n_Proof_: (1) If one of the premises is negative, then the conclusion\nmust be negative according to rule 6.\n\n(2) If the conclusion is negative, then the predicate, G, must be\ndistributed.\n\n(3) If G is distributed in the conclusion, it must be distributed in\nthe major premise.\n\n(4) The major premise must be universal; as G is used as its subject,\nand only universals distribute their subjects.\n\n_Epitome._\n\n_In the fourth figure, if the \u201cmajor\u201d is affirmative, the \u201cminor\u201d must\nbe universal in order to distribute the middle term. If the minor is\naffirmative, the conclusion must be particular; otherwise the fallacy\nof illicit minor would result. If either premise is negative, the major\nmust be universal to avoid the fallacy of illicit major._\n\n\n=5. SPECIAL CANONS RELATED.=\n\nAfter a particular mood has been tested in the regular way, it has been\nintimated that the student may refer to the tabulated list of valid\nmoods to ascertain, with a certainty, the validity of his reasoning.\nThis is equivalent to referring to the answers in arithmetic; for\nif the student is unable to find the mood in the figure in which he\nhas proved it valid, then he knows that he has made some mistake in\nhis reasoning. A second check, though not absolute, is to recall the\nspecial canons of section four. If, for example, our reasoning has led\n A\nus to believe that E is valid in the first figure, we may recall that\n E\nthe minor premise of the first figure must be affirmative and therefore\nAEE cannot be valid.\n\nA few suggestions relative to memorizing the special canons may not\nbe out of place. The two canons of the first figure must be committed,\nand then it may be remembered that the _second figure is the negative\nfigure of logic_. Other figures _may_ yield a negative conclusion,\nbut the second _must_ yield a negative conclusion. Since a negative\nconclusion necessitates a negative premise, it follows that the second\nfigure must always appear with one premise negative. The other canon\nwhich pertains to the major premise is the same as the \u201cmajor premise\u201d\ncanon of the first figure.\n\n_The third figure is the particular figure of logic._ Other figures may\nyield particular conclusions, but the third _must_ do so. This helps us\nto remember the canon that the conclusion of the third figure must be\nparticular. The other canon which relates to the minor premise is the\nsame as the \u201cminor premise\u201d canon of the first figure. The canons of\nthe fourth figure are in reality a summary of the canons of the other\nthree figures.\n\n\n=6. MNEMONIC LINES.=\n\nAs a device for remembering the 19 valid moods, the logicians of an\nearlier day originated a combination of coined words which, though\nrather unscientific, may be easily committed to memory. Since, however,\nit is of much more value to test the moods by means of the general\nrules of the syllogism than it is to try to remember these moods, the\nmnemonic lines are of slight value. They are treated here merely as an\nitem of historical interest.\n\n(1) _Barbara_, _Celarent_, _Darii_, _Ferio_que prioris;\n\n(2) _Cesare_, _Camestres_, _Festino_, _Baroko_, secund\u00e6;\n\n(3) Tertia, _Darapti_, _Disamis_, _Datisi_, _Felapton_, _Bokardo_,\n_Ferison_, habet; Quarta insuper addit\n\n(4) _Bramantip_, _Camenes_, _Dimaris_, _Fesapo_, _Fresison_.\n\nThe only letters in these lines which mean nothing are l, n, r, t and\nsmall b and d; all the others have a signification. For example, the\n_vowels_ of the italicized words signify the various valid moods, as\ne. g., the first line indicates the moods AAA, EAE, AII, EIO. The Latin\nwords, printed in ordinary type, are intended to make evident that the\nmoods indicated by the artificial italicized words of the first line,\nbelong to the _first_ figure; that the moods of the next four words,\nbelong to the _second_ figure; while the _third_ figure includes the\nnext six, and the _fourth_ figure the last five. It is now seen that\nFestino, for example, stands for that mood of the second figure which\nhas an E for its major premise, an I for its minor premise, and an O\nfor its conclusion.\n\nThe first figure was called by Aristotle the _perfect figure_, whereas\nthe second and third were the _imperfect figures_. The fourth figure\nwas given no place in the works of Aristotle; its discovery is credited\nto Galen, a celebrated teacher of medicine of the second century.\nAccording to Aristotle, the first figure is the most serviceable and\nthe most convincing and, therefore, as a final test of their validity,\nthe moods of the other figures should be changed to the _first_.\nThis process in logic is termed _Reduction_. In this reduction of\nthe imperfect figures to the perfect, the _capital letters_ of the\nartificial words, together with s, p, m, and k, have a definite meaning.\nThe capital letters indicate that certain moods of the imperfect\nfigures can be reduced to the corresponding moods of the first figure;\ne. g., Festino (eio) of the second figure, Felapton (eao) of the third\nfigure, and Fesapo (eao) of the fourth figure may all be reduced to\nFerio (eio) of the first figure. This is known because _F_ is the\ninitial letter of each word. _s_ signifies that the proposition denoted\nby the preceding vowel is to be converted simply. To illustrate: _s_\n E\nin Fesapo means that the major premise E of the mood A of the fourth\n O\nfigure must be converted _simply_ in order to change the mood to Ferio\nof the first figure. _p_ indicates that the proposition represented\nby the vowel which precedes p must be converted by _limitation_ (per\naccidens). _m_ (mutare) makes evident that the premises are to be\ninterchanged, the major of the old becoming the minor of the new,\nand the minor of the old becoming the major of the new. _k_ denotes\nthat the mood, such as Baroko, must be reduced by a special process\nknown as _indirect reduction_. These directions may now be followed\nas illustrative of the process of reduction.\n\n A\n(1) _Given: A syllogism in Darapti_ A\n I\n M G\n A All true teachers are just,\n M S\n A All true teachers are sympathetic,\n S G\n I \u2234 Some sympathetic persons are just.\n\n A\nThe symbols indicate that the mood is A or is in Darapti and that this\n I\nmood is used in the third figure.\n\n A\n_Problem_: To reduce A of the third figure to some mood of the first\n I\nfigure.\n\n_Process_: D, being the initial letter of Darapti, suggests that its\nmood must be reduced to one indicated by a word of the first figure\n A\nwhose initial letter is D. This mood is in Darii, or is I.\n I\n\nThe _p_ in Darapti indicates that the proposition represented by the\npreceding vowel must be converted by limitation. This proposition is\nthe minor premise; converting it by limitation gives: \u201cSome sympathetic\npersons are true teachers.\u201d As there are no other significant letters\nthe reduction is complete and we have this:\n\n M G\n A All true teachers are just,\n\n S M\n I Some sympathetic persons are true teachers,\n\n S G\n I \u2234 Some sympathetic persons are just.\n\n A\nThe symbolization indicates that the mood is I of the first figure, or\n I\nis in Darii.\n\n A\n(2) _Given: A syllogism in Camestres_ E\n E\n G M\n A All true teachers are just,\n\n S M\n E No one who shows partiality is just,\n\n S G\n E \u2234 No one who shows partiality is a true teacher.\n\nThe symbols show that the mood is AEE of the second figure or in\nCamestres. Judging from the initial letter C, the mood in Camestres\n E\nmust be reduced to the mood in Celarent A.\n E\n\n\nThe letter m between a and e indicates that the major and minor\npremises of the given syllogism must be interchanged. The letters\nfollowing both e\u2019s suggest that the minor premise and the conclusion\nof the syllogism must be converted simply.\n\nThis is the resulting syllogism:\n\n M G\n E No just person shows partiality,\n\n S M\n A All true teachers are just persons,\n\n S G\n E \u2234 No true teacher shows partiality.\n\n E\nHere, then, is the A of the first figure or the mood in Celarent.\n E\n\nAccording to the ancient theory, reduction is necessary as a matter of\n_final_ and _absolute proof_ that the conclusion follows from the given\npremises. But, as this claim has been satisfactorily refuted by modern\nlogicians, we need not give more space to the process. The meaning of\nk, as related to \u201c_indirect reduction_,\u201d is explained in most of the\nearlier works on logic. See Hyslop, page 193.\n\n\n=7. RELATIVE VALUE OF THE FOUR FIGURES.=\n\n_The first figure._\n\nThe first figure is known as the _perfect_ figure; because it is the\nonly one which proves _all_ of the four logical propositions. Recalling\nthe moods of the first figure makes this evident:\n\n A E A E\n A A I I\n _A_ _E_ _I_ _O_\n\nIt is likewise the more natural figure; because it is the only one\nwhich uses both the subject and predicate of the conclusion in the same\nrelative places as they appear in the premises. Symbolizing the figure\nmakes this apparent:\n\n M \u2015 _G_\n _S_ \u2015 M\n _S_ \u2015 _G_\n\nThe first figure, being the only figure which proves a \u201cuniversal\naffirmation\u201d (A), is used most by the _scientist_; as the object of\nscience is to establish _universal affirmative_ truths.\n\n_The second figure._\n\nAs the second figure conditions negative conclusions only, it is called\nthe figure of _disproof_, or the exclusive figure. It is easy to see\nhow negative conclusions may be used to narrow the inquiry down to one\ndefinite theory. For example, suppose it is desired to ascertain which\nboy of the five broke the window; by a series of deductions the teacher\nmay be able to prove that the culprit is not A, not B, not C and not D;\nhence the guilty one must be E. This figure is virtually the one used\nin diagnosing most diseases.\n\n_The third figure._\n\nThe third figure admits of particular conclusions only, and in\nconsequence is of little value to the scientist. Since, however, the\neasiest way to contradict a universal affirmative (A) or a universal\nnegative (E), is to prove the truth, respectively, of a particular\nnegative (O) and a particular affirmative (I), it follows that the\nthird figure serves a purpose.\n\n_The fourth figure._\n\nThis figure is so nearly like the first that it is of little value; in\nfact, it may be changed to the first by simply interchanging the major\nand minor premises. Some authorities refuse to recognize the fourth\nfigure.\n\n\n=8. OUTLINE.=\n\n FIGURES AND MOODS OF THE SYLLOGISM.\n\n (1) The four figures of the syllogism.\n Definition\u2015\u2015symbolization.\n Illustrations\u2015\u2015device for remembering.\n\n (2) The moods of the syllogism.\n _Twenty-four_ valid.\n\n (3) Testing the validity of the moods.\n Application of the general rules of the syllogism.\n Weakened conclusion\u2015\u2015five.\n _Nineteen_ useful moods.\n A thought exercise.\n\n (4) Special canons of the four figures.\n Proof of the two canons of the first figure.\n Proof of the two canons of the second figure.\n Proof of the two canons of the third figure.\n Proof of the three canons of the fourth figure.\n\n (5) Special canons related.\n Used as checks.\n\n (6) Mnemonic lines.\n Their use explained.\n Reduction.\n\n (7) Relative value of the four figures.\n\n\n=9. SUMMARY.=\n\n(1) By a syllogistic figure is meant some particular arrangement of the\nthree terms in the two premises.\n\nThis arrangement yields four figures which are designated by the\nposition of the middle term.\n\nTo be logical, any syllogism must conform to _one_ of the four figures.\nThe first figure is suggested by the position of the terms of the\n\u201cSocrates is mortal\u201d syllogism. The second is derived by converting\nthe _major premise_ of the first; while the third figure results\nfrom converting the _minor premise_ of the first, and the fourth by\nconverting _both_ major and minor of the first.\n\n(2) By a mood of a syllogism is meant some particular arrangement of\nthe propositions which compose it.\n\nThere are 64 moods but only 24 are valid.\n\n(3) The validity of the various moods may be tested by applying to them\nthe rules of the syllogism. No mood is valid if it violates any one of\nthe eight rules.\n\nA \u201cweakened conclusion\u201d is a particular conclusion which could just as\nwell be universal.\n\nOf the 24 valid moods five have weakened conclusions. This leaves but\n19 useful moods.\n\nTesting the validity of the various moods in the four figures is a most\nvaluable thought exercise.\n\n(4) The deductive exercise involved in establishing certain special\ncanons of the four figures is of immense value and should not be\nomitted.\n\nIn the first figure it may be proved (1) that the minor premise must\nbe affirmative; since making it negative necessitates making the major\npremise negative, and no conclusion can be drawn from two negatives;\n(2) that the major premise must be universal in order to distribute the\nmiddle term at least once.\n\nIn the second figure it may be proved (1) that one premise must be\nnegative in order to distribute the middle term; (2) that the major\npremise must be universal in order to distribute its subject, which\nis distributed in the negative conclusion where it appears as the\npredicate.\n\nIn the third figure it may be proved (1) that the minor premise must\nbe affirmative in order to prevent the \u201ctwo negative\u201d fallacy; (2) that\nan affirmative minor necessitates a particular conclusion, because the\nminor term in the conclusion must remain undistributed.\n\nIn the fourth figure it may be proved (1) that if the major is\naffirmative, the minor must be universal in order to distribute the\nmiddle term; (2) that if the minor is affirmative, the conclusion must\nbe particular in order to avoid committing the fallacy of illicit minor;\n(3) that if either premise is negative, the major must be universal to\navoid the fallacy of illicit major.\n\n(5) A knowledge of the special canons is helpful in that it may be used\nto check fallacious reasoning.\n\n(6) Certain mnemonic lines were used by the Schoolmen as an aid in\nrecalling the nineteen valid moods, and also as a suggestive device to\naid in the process known as Reduction.\n\nThe process of reduction is merely a matter of changing to the first\nfigure the moods of the other figures. This process is no longer\nthought to be necessary.\n\n(7) The first figure, called the perfect figure, is the one used\nmost by scientists, as it is the only figure which proves a universal\naffirmative truth. The second figure is the negative, or figure of\ndisproof, and is used mainly for the purpose of eliminating all the\nconditions of the inquiry save _one_. The third figure serves a purpose\nin affording an easy way to contradict a universal assertion; this is\nthe figure of particulars. The fourth figure, because it so closely\nresembles the first, is of little value.\n\n\n=10. ILLUSTRATIVE EXERCISES.=\n\nQuestion 1a. By making use of the rules for negatives and particulars,\n O A A\ntest the validity of the following moods: I I A\n A A I\n\nAnswer: The first mood has the negative O as its major premise, and\nthe affirmative A as its conclusion; the mood is thus invalid; because\na negative premise necessitates a negative conclusion according to\nrule 6.\n\nThe second mood contains the particular proposition I as its minor\npremise, and thus should have a particular conclusion according to\nrule 8. But the conclusion A is universal and, therefore, the mood is\ninvalid.\n\nThe premises of the third mood are universal and the conclusion\nparticular. The mood, however, is valid, because rule 8 does not work\nboth ways, as does rule 6. When a universal can just as well be drawn,\nthen the particular becomes a weakened conclusion.\n\n(1b) Using the rules for negatives and particulars, test the validity\n A E E\nof the following: A O A\n E O O\n\n(2a) Paying no regard to \u201cfigure,\u201d derive as many conclusions as\npossible from the following sets of premises: E A\n I E\n\nAnswer: _E_. The major premise of this mood, being negative,\n _I_\n\nnecessitates a negative conclusion, according to rule 6, and the minor\npremise, being particular, compels a particular conclusion, according\nto rule 8. Since the conclusion must be negative and particular, then\n E\nO is the only one which can be drawn. The completed mood is I.\n O\n\n_A_. This mood must have a negative conclusion, because the minor\n_E_\npremise is negative; this would necessitate either E or O; but O\nas a conclusion would be, in this case, a _weakened_ one; since E\ndistributing both terms would necessarily distribute the minor; which\nfact would permit the minor to be distributed in the conclusion. Thus\nthe conclusion could just as well be universal as particular. The\n A\ncompleted mood is E.\n E\n\n(2b) From the following sets of premises derive as many conclusions as\npossible paying no attention to figure: E A O\n A A A\n\n(3a) Making use of all the general rules of the syllogism, test the\n A\nvalidity of the following mood in all the figures: A.\n I\n\nAnswer: 1 2 3 4\n A M \u2015 G G \u2015 M M \u2015 G G \u2015 M\n \u2015 \u2015 \u2015 \u2015\n A S \u2015 M S \u2015 M M \u2015 S M \u2015 S\n \u2015 \u2015 \u2015 \u2015\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n I S \u2015 G S \u2015 G S \u2015 G S \u2015 G\n\nAn underscored symbol indicates a distributed term. Since A distributes\nits subject, the subjects of both premises are underscored in all the\nfigures. No term is underscored in the conclusions; since I distributes\nneither term. In the first figure the middle term is distributed in the\nmajor premise, and no term is distributed in the conclusion. Since both\npremises are affirmative, the rules for negatives are not applicable;\nand as a particular may be drawn from two universals, if there is no\nviolation of the rules for distribution, this mood seems to be valid in\nthe first figure. It is, however, a _weakened_ conclusion; since an A\ncould just as well be drawn. The mood is invalid in the second figure\nbecause of undistributed middle, but valid in both the third and fourth;\nsince in both cases the middle term is distributed at least once.\n\n(3b) Determine the validity of the attending moods in all the figures\n I A E\ngiving reasons: A O A.\n I O O\n\n\n=11. REVIEW QUESTIONS.=\n\n (1) Define a logical figure and illustrate by means of some ordinary\n syllogistic argument.\n\n (2) Symbolize the four figures and give suggestions for remembering\n them.\n\n (3) Write syllogisms which illustrate each of the four figures.\n\n (4) Define mood as it is used in logic. Illustrate.\n\n (5) How many moods are valid?\n\n (6) Explain by illustration a \u201cweakened conclusion.\u201d\n\n A E\n (7) Test the validity of E in the third figure; of I in the third.\n E O\n\n (8) Independent of all helps, prove the truth of the canons of the\n first figure.\n\n (9) In a similar way prove the canons of the second, third and fourth\n figures.\n\n (10) So far as testing arguments is concerned, what use may be made\n of the special canons of the syllogism?\n\n (11) Offer a few suggestions for remembering the special canons.\n\n (12) Why did Aristotle attach so much importance to reduction in\n logic?\n\n (13) Justify calling the first figure the \u201cperfect figure,\u201d and the\n others the \u201cimperfect figures.\u201d\n\n (14) Treat of the relative value of the four figures.\n\n (15) Show by illustration that the second figure is the exclusive\n figure.\n\n E O I\n (16) Test the following moods in all the figures: I A A\n A O I\n\n A E E A A E A A A\n E I A E I E O A I.\n O O O O E I I I I\n\n\n=12. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Give an illustration of a syllogism in the fourth figure which\n might just as well be written in the first figure.\n\n (2) May a syllogism, which is invalid in the fourth figure, be made\n valid by writing it in the form of the first figure? Prove it.\n\n (3) Show why it is impossible to apply all the rules of the ***\n\n (4) Show the difference between a direct and an indirect proof.\n\n A\n (5) Show that A is valid in the first figure when the major premise\n O\n (A) is co-extensive.\n\n (6) The third figure is known as the figure of particular\n conclusions. Why should not the second canon of that figure be,\n \u201c_One premise_ must be particular\u201d rather than \u201cThe conclusion\n must be particular?\u201d\n\n (7) Show that there is some ground for thinking that, as a final\n test, moods in the other figures should be reduced to the first.\n\n (8) Illustrate the fact that the second figure is the figure of\n disproof; whereas the third is the figure of contradictions.\n\n (9) \u201cTo be logical a syllogism must conform to one of the four\n figures, but this does not mean, necessarily, that _all\n arguments_ must conform to some figure.\u201d Explain this.\n\n\n\n\n CHAPTER 13.\n\n INCOMPLETE SYLLOGISMS AND IRREGULAR ARGUMENTS.\n\n\n=1. ENTHYMEME.=\n\n_An enthymeme is a syllogism in which one of the three propositions is\nomitted._\n\nSuppressing the major premise gives an enthymeme of the _first order_;\nwhereas if the minor premise be suppressed, the enthymeme becomes one\nof the _second order_; while omitting the conclusions gives an\nenthymeme of the _third order_.\n\n_Illustrations_:\n\n Complete syllogism.\n All true teachers are just,\n You are a true teacher,\n (Hence) You are just.\n\n Enthymeme of _first order_; major premise omitted.\n ..........................\n You are a true teacher,\n (Hence) You are just.\n\n Enthymeme of _second order_; minor premise omitted.\n All true teachers are just,\n ..........................\n (Hence) You are just.\n\n Enthymeme of the _third order_; conclusion omitted.\n All true teachers are just,\n (And) You are a true teacher,\n ..........................\n\nTo argue in terms of the complete syllogism is the _unusual_, not the\n_usual_ method. We have a way of abbreviating our remarks; expressing\nonly the necessary and leaving the obvious to be taken for granted.\nThus the enthymeme becomes the natural form of expression. But the mere\nfact that a part of the argument is omitted, makes it more essential\nfor the student to think clearly and with careful continuity, that no\nerror may intrude itself.\n\nProbably the most common enthymemes are those of the first order.\nThis may be explained by the fact that the major premise is usually the\nmost universal of the three propositions, and, in consequence, the one\nwhich would be the most generally understood. The following represent\nenthymemes of this order, gleaned from the ordinary conversation of\nordinary people:\n\n (1)\u2002\u201cYour beets won\u2019t grow, because you are planting them in the\n wrong time of the moon.\u201d\n\n (2) \u201cYou, being a member of the Sunday School, should be ashamed of\n such language.\u201d\n\n (3) \u201cBeing the son of your father, you ought to have some pride in\n this matter.\u201d\n\n (4) \u201cWe are going to have an open winter, because I have observed\n that the hornets\u2019 nests are near the ground.\u201d\n\n (5) \u201cYou had better put in lots of coal, for I have noticed that the\n squirrels have gathered in more nuts than usual.\u201d\n\nJudging from these enthymemes, it would seem to be more natural to\nassert the conclusion and follow this by a reason in the form of a\nminor premise, leaving the _major_ to the intelligence of the auditor.\n\nThe enthymeme of the second order occurs only infrequently, since\nit seems to be an unnatural mode of expression, though sometimes it\nappears to lend emphasis to the conclusion; e. g., \u201cAll untrustworthy\nboys come to a bad end, and I predict that you will come to a bad end.\u201d\n\nEnthymemes of the third order are commonly used for the sake of\nemphasis, as the following make evident:\n\n (1) \u201cNo business man wants an indolent boy, and you are indolent.\u201d\n\n (2) \u201cAll successful teachers are interested in their work, and you\n plan to be a successful teacher.\u201d\n\n (3) \u201cHumility is a sign of greatness, and Lincoln possessed this\n quality.\u201d\n\n\n=2. EPICHEIREMA.=\n\n_An epicheirema is a syllogism in which one or both of the premises is\nan enthymeme._ To put it in another way: An epicheirema is a syllogism\nin which one or both of the premises is supported by a reason.\n\nWhen one premise is an enthymeme the syllogism is termed a _single_\nepicheirema; whereas when both premises are enthymemes it becomes a\n_double_ epicheirema.\n\n_Single epicheirema._\n\n All men are mortal, _because all men die_,\n Socrates was a man,\n \u2234 Socrates was mortal.\n\n_Double epicheirema._\n\n All men are mortal, _because all men die_,\n Socrates was a man, _because he was a rational animal_,\n \u2234 Socrates was mortal.\n\nIt is obvious that supporting each premise with a reason lends strength\nto the argument. This justifies the use of the epicheirema.\n\n\n=3. POLYSYLLOGISM.=\n\n_A polysyllogism is a series of syllogisms in which the conclusion of\na preceding syllogism becomes a premise of a succeeding one._\n\nThe syllogism in the series whose conclusion becomes a premise of the\nsucceeding syllogism is termed a _prosyllogism_; while the syllogism\nwhich uses as one of its premises the conclusion of the preceding\nsyllogism is called an _episyllogism_.\n\n_Illustrations._\n\n { A quadruped is an animal, }\n { A dog is a quadruped, } _Prosyllogism_\n _Polysyllogism_ {\u2234 A dog is an animal. } }\n { Fido is a dog, } _Episyllogism_\n {\u2234 Fido is an animal. }\n\n { All who libel an associate }\n { are unprofessional, }\n { This teacher has libelled } _Prosyllogism_\n { her associate, }\n _Polysyllogism_ {\u2234 This teacher is } }\n { unprofessional. } }\n { All who are unprofessional } _Episyllogism_\n { should be disciplined, }\n {\u2234 This teacher should be }\n { disciplined. }\n\n\n=4. SORITES.=\n\n_A sorites is a series of syllogisms in which all of the conclusions\nare omitted except the last one._\n\nJust as the epicheirema is a combination of enthymemes of the _first_\nand _second orders_, so the sorites is a combination of enthymemes of\nthe _third order_. If each conclusion were written, the sorites would\ntake the form of prosyllogisms and episyllogisms. Two forms of the\nsorites are recognized by logicians. These are the _progressive_ or\nAristotelian, and the _regressive_ or Goclenian.\n\n_Illustrations._\n\n _Progressive_\n\n _Symbolized._ _Put in Word Form._\n All A is B Thomas Arnold was a teacher,\n All B is C A teacher is a man,\n All C is D A man is a biped,\n All D is E A biped is an animal,\n Hence all A is E Hence Thomas Arnold was an animal.\n\n _Regressive_\n\n All A is B A biped is an animal,\n All C is A A man is a biped,\n All D is C A teacher is a man,\n All E is D Thomas Arnold was a teacher,\n Hence all E is B Hence Thomas Arnold was an animal.\n\nWhen regarded from the viewpoint of extension, the progressive sorites\nproceeds from the smaller to the larger while the regressive is the\nconverse of this. The point may be illustrated by circles:\n\n Illustration: FIG. 15.\n\n Circle 1 stands for Thomas Arnold.\n Circle 2 stands for teacher.\n Circle 3 stands for man.\n Circle 4 stands for biped.\n Circle 5 stands for animal.\n\nThe progressive sorites proceeds from the smaller circle to the larger,\nthus:\n\n All of circle 1 belongs to 2\n All of circle 2 belongs to 3\n All of circle 3 belongs to 4\n All of circle 4 belongs to 5\n Hence, All of circle 1 belongs to 5\n\nThe regressive sorites proceeds from the larger to the smaller; i. e.:\n\n All of circle 4 belongs to 5\n All of circle 3 belongs to 4\n All of circle 2 belongs to 3\n All of circle 1 belongs to 2\n Hence, All of circle 1 belongs to 5\n\nOther differences become apparent when the omitted conclusions are\nexpressed.\n\n _Progressive_\n\n _Symbolized_ _Word Form_\n All A is B T. Arnold was a teacher, (_A_)\n All B is C A teacher is a man, (_A_)\n \u2234 All A is C \u2234 T. Arnold was a man. (_A_)\n All C is D A man is a biped, (_A_)\n \u2234 All A is D \u2234 T. Arnold was a biped. (_A_)\n All D is E A biped is an animal, (_A_)\n \u2234 All A is E \u2234 T. Arnold was an animal. (_A_)\n\nIn the three completed syllogisms it becomes evident that the\nprogressive sorites uses the minor as its first premise and in\nconsequence takes the form of the fourth figure, though the reasoning\nis according to the first figure.\n\nThe progressive sorites must conform to the following rules:\n\n (1) The first premise may be universal or particular, all the others\n _must_ be universal.\n\n (2) The last premise may be affirmative or negative; all the others\n _must_ be affirmative.\n\nA violation of the first rule would result in undistributed middle;\nwhereas a violation of the second rule would give illicit major. These\nrules may be illustrated by giving attention to the symbols of the\nforegoing completed syllogisms.\n\nThe first completed syllogism of the sorites is:\n\n All A is B\n All B is C\n \u2234 All A is C\n\nSecuring a logical arrangement by interchanging the major and minor\npremises gives:\n\n (M) (G)\n (A) All B is C (First premise universal)\n \u2015\n\n (S) (M)\n (A) All A is B\n\n (S) (G)\n (A) \u2234 All A is C\n \u2015\n\nApplying the rules we find this syllogism valid, or we may recall that\nA\nA is valid in the first figure.\nA\n\nLet us now make the first premise of the sorites _particular_ and test.\n\n Some A is B\n All B is C\n \u2234 Some A is C\n\n_Arranged logically_:\n\n (M) (G)\n (A) All B is C\n \u2015\n\n (S) (M)\n (I) Some A is B\n\n (S) (G)\n (I) \u2234 Some A is C\n\n_Proof_:\n\nSince one premise is particular the conclusion must be particular.\n(Rule 7) As there are no negatives in the argument, only one conclusion\nis possible; namely, a particular affirmative (I). Thus, instead of\nthe conclusion, \u201cAll A is C,\u201d which is an (A), it must be, \u201cSome A\nis C,\u201d or an (I). Underscoring the distributed term, it is seen that\nthe middle term is distributed in the major premise and that no term\nis distributed in the conclusion. Thus the mood is valid. This is\n\u201cchecked\u201d when we recall that AII is always valid in the first figure.\nWe have now shown that the first premise of a progressive sorites may\nbe _universal_ or _particular_. Let us further proceed to prove that\nall the other premises must be universal.\n\n_Data_: Given the first completed syllogism of the sorites:\n\n All A is B\n All B is C\n \u2234 All A is C\n\n_Proof_: Let any other premise, such as the second, be particular; this\ngives the following:\n\n All A is B\n Some B is C\n \u2234 Some A is C\n\n_Arranged logically_: Mood, figure, and distribution indicated.\n\n (M) (G)\n (I) Some B is C\n\n (S) (M)\n (A) All A is B\n \u2015\n\n (S) (G)\n (I) \u2234 Some A is C\n\nWe note at once that the middle term is undistributed, hence the\n I\nmood A is invalid in the first figure; reference to the valid moods in\n I\nfigure _one_ \u201cchecks\u201d this conclusion. Since no premise, other than the\nfirst, can be particular, then all save the first must be universal.\n\nThe truth of the first rule has been demonstrated, and now we may\nfollow a similar plan to prove the truth of the second rule.\n\n_Problem_: To prove that the last premise may be negative.[11]\n\n_Data_: Given the _last_ completed syllogism:\n\n { All A is D\n { All D is E\n { \u2234 All A is E\n\nLet us make the last premise negative (E) and test the result. (As all\nbut the first must be universal we cannot use an O.)\n\n All A is D\n No D is E\n \u2234 No A is E\n\n_Arranged logically and symbolized_:\n\n (M) (G)\n (E) No D is E\n \u2015 \u2015\n\n (S) (M)\n (A) All A is D\n \u2015 \u2015\n\n (S) (G)\n (E) \u2234 No A is E\n \u2015 \u2015\n\n_Proof_: Negative premise; negative conclusion. No particulars. Middle\nterm distributed in major premise. No term distributed in conclusion\nwhich is not distributed in premise where it occurs. Syllogism valid.\nWe must now prove that all the other premises must be affirmative.\n\n_Problem_: To prove that no other premise can be negative, or that all\nothers must be affirmative.\n\n_Data_: Given last syllogism of sorites with the first premise negative.\n(Any other may be taken.)\n\n No A is D\n All D is E\n \u2234 No A is E\n\n_Arranged logically and symbolized_:\n\n (M) (G)\n (A) All D is E\n \u2015\n\n (S) (M)\n (E) No A is D\n\n (S) (G)\n (E) \u2234 No A is E\n \u2015 \u2015\n\n_Proof_: \u201cG\u201d is distributed in the conclusion but not in the major\npremise. Fallacy of illicit major. Hence no other premise can be\nnegative.\n\nWe may now consider the completed syllogisms of the _regressive_\nsorites.\n\n All A is B\n All C is A\n \u2234 All C is B\n All D is C\n \u2234 All D is B\n All E is D\n \u2234 All E is B\n\nBy examining the foregoing it becomes apparent that the regressive\nsorites, both in form and in the reasoning, adapts itself to the first\nfigure.\n\nThe rules of the regressive sorites are just the reverse of the\nprogressive. These are:\n\n (1) The first premise may be negative; all the others must be\n affirmative.\n\n (2) The last premise may be particular; all the others must be\n universal.\n\nIt would be a valuable exercise for the student to test these rules\naccording to the plan pursued in treating the progressive sorites.\n\n\n=5. IRREGULAR ARGUMENTS.=\n\nIt has been intimated that a syllogistic argument, in order to be\nlogical, should be made to conform to the _rules of the syllogism_. It\nmust not be inferred from this, however, that all deductive reasoning\nis included by the logical forms here treated. There seem to be\narguments which yield valid conclusions, and yet which are not logical\nin the strict sense of the word. The following illustrate some of these\nforms:\n\n(1) _ Quantitative Arguments._\n\n John is taller than James,\n Albert is taller than John,\n \u2234 Albert is taller than James.\n\nHere, apparently, is a fallacy of four terms: these four terms are\n(1) John, (2) taller than James, (3) Albert, (4) taller than John. Yet\nwe know that the argument is valid. There is not a particle of doubt in\nthe mind relative to the truth of the conclusion that \u201cAlbert is taller\nthan James.\u201d We are consequently forced to the inference that such\nquantitative arguments lie outside the field of syllogistic reasoning.\nThe argument involves this new principle, \u201cWhatever is greater than a\n_second thing_ which is greater than a _third thing_ is itself greater\nthan a third thing.\u201d\n\nThere are many other arguments similar to this which are not\nsyllogistic in nature. To wit: A equals B, B equals C, C equals D;\nA equals D. A is a brother of B, B is a brother of C, C is a brother\nof D; A is a brother of D. A is west of B, B is west of C, C is west\nof D; A is west of D.\n\n(2) _Plurative Arguments._\n\nThese are arguments in which the propositions are introduced by _more_\nor _most_; e. g.:\n\n Most (more than half) of the team are seniors,\n Most (at least half) of the team are under twenty,\n \u2234 Some students under twenty are seniors.\n\n I\nHere we have an I which is evidently valid. No term distributed and yet\n I\nthe conclusion is unquestionably true. This is due to the fact that the\npropositions are so worded as to force an overlapping of the major and\nminor terms. The student may illustrate this relation by circles.\n\n\n=6. OUTLINE.=\n\n INCOMPLETE SYLLOGISMS AND IRREGULAR ARGUMENTS.\n\n (1) Enthymeme.\n First, second and third orders.\n Natural form.\n\n (2) Epicheirema.\n Single, double.\n\n (3) Polysyllogism.\n Prosyllogism, episyllogism.\n\n (4) Sorites.\n Progressive, regressive.\n Two rules of each.\n\n (5) Irregular Arguments.\n Quantitative, plurative.\n\n\n=7. SUMMARY.=\n\n(1) An enthymeme is a syllogism in which one of the three propositions\nis omitted. Suppressing the major premise gives an enthymeme of the\n_first_ order; omitting the minor gives one of the _second_ order;\nwhile omitting the conclusion gives one of the _third_ order.\n\nThe enthymeme is really the natural form of expression. Enthymemes of\nthe first order are the most _common_ while those of the third order\nare the most _emphatic_.\n\n(2) An epicheirema is a syllogism in which one or more of the premises\nis an enthymeme. An epicheirema is said to be _single_ when but one\npremise is an enthymeme, and _double_ when both premises are enthymemes.\n\n(3) A polysyllogism is a series of syllogisms in which the conclusion\nof the _preceding_ syllogism becomes a premise of the _succeeding_ one.\nThe one of the series whose conclusion becomes a premise is termed a\nprosyllogism; while the one which uses the conclusion as a premise is\ncalled an episyllogism.\n\n(4) A sorites is a series of syllogisms in which all the conclusions\nare omitted except the last one.\n\nThe two kinds of sorites are the progressive and regressive. The\nprogressive uses the \u201cminor\u201d as its first premise and adopts the form\nof the _fourth_ figure, whereas the regressive uses the \u201cmajor\u201d as its\nfirst premise and adopts the form of the _first_ figure.\n\nThe two rules of the progressive sorites are, (1) \u201cThe first premise\nmay be particular, all the others must be universal\u201d; (2) \u201cThe last\npremise may be negative, all the others must be affirmative.\u201d\n\nThe two rules of the regressive are, (1) \u201cThe first premise may be\nnegative, all the others must be affirmative\u201d; (2) \u201cThe last premise\nmay be particular, all the others must be universal\u201d.\n\n(5) Irregular arguments are such as yield valid conclusions and yet do\nnot conform to the syllogistic rules.\n\nThe quantitative argument expresses quantity and contains four terms.\nThis argument is based on the principle, \u201cWhat ever is greater than a\nsecond thing which is greater than a third thing is itself greater than\na third thing.\u201d\n\nPlurative arguments are introduced by \u201cmore\u201d or \u201cmost\u201d and give in\nconsequence a valid conclusion from two particulars. This is due to the\noverlapping of the major and minor terms.\n\n\n=8. REVIEW QUESTIONS.=\n\n (1) Define and illustrate an enthymeme.\n\n (2) Illustrate the enthymemes of the three orders and point out their\n distinct uses.\n\n (3) Why should the enthymeme demand closer thought than the ordinary\n syllogism?\n\n (4) Define and illustrate the epicheirema.\n\n (5) Of what use is the epicheirema? Illustrate.\n\n (6) Define and illustrate a prosyllogism and an episyllogism.\n\n (7) Why are polysyllogisms so called?\n\n (8) Define and illustrate the sorites.\n\n (9) Relate the sorites and the epicheirema to the enthymeme.\n\n (10) Illustrate the two forms of sorites.\n\n (11) Explain the two forms of sorites by means of a diagram.\n\n (12) Prove the truth of the two rules of the progressive sorites.\n\n (13) Illustrate two kinds of irregular arguments and show that they\n are valid.\n\n (14) Complete the five enthymemes of page 248 and indicate their mood\n and figure.\n\n\n=9. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Why should enthymemes of the second order be less common than\n those of the first?\n\n (2) You desire to make it evident to a child that a small beginning\n often leads to a momentous ending; do so in terms of the\n enthymeme of the first order.\n\n (3) Show that prosyllogism and episyllogism are relative terms.\n\n (4) When the common premise of the \u201cpro\u201d and \u201cepi\u201d syllogism is\n omitted what abbreviated form results?\n\n (5) From the viewpoint of your definition criticise this: \u201cA sorites\n is a series of prosyllogisms and episyllogisms in which all of\n the conclusions are suppressed except the last.\u201d\n\n (6) Prove the truth of the two rules of the regressive sorites.\n\n (7) Show that the prosyllogism and the episyllogism may be\n progressive or regressive.\n\n (8) \u201cReasoning from cause to effect\u201d\u2015\u2015is such progressive or\n regressive? Explain.\n\n (9) Which is inductive in nature, the progressive form of reasoning\n or the regressive? Explain.\n\n (10) Test the validity of the enthymemes on pages 248 and 249.\n\n (11) \u201cA sorites is at least as immediately convincing as the chain of\n syllogisms into which it can be decomposed.\u201d Discuss this.\n\n\n\n\n CHAPTER 14.\n\n CATEGORICAL ARGUMENTS TESTED ACCORDING TO FORM.\n\n\n=1. ARGUMENTS OF FORM AND MATTER.=\n\nThe matter relative to the syllogism treated in chapters 11, 12\nand 13 is given primarily to enable the reader to test the validity\nof categorical arguments. Such arguments must be viewed from the\ntwo standpoints of _form_ and _matter_, since it is one of the chief\npurposes of logic to enable the student to detect fallacious reasoning,\nno matter how subtly it may be concealed. Therefore, that one may gain\nmarked facility in this kind of work, it becomes necessary to proceed\nwith _thoroughness_ and _confidence_. The _meaning_ of arguments and\nthe various _material_ fallacies may be treated later; but we are now\nequipped with sufficient knowledge and experience to test the validity\nof arguments from the viewpoint of _form_.\n\n\n=2. ORDER OF PROCEDURE IN THE FORMAL TESTING OF ARGUMENTS.=\n\nIn testing categorical arguments _three_ things are essential; first,\n_to follow a definite plan_; second, _to give reasons_; third, _to give\nthe author the benefit of the doubt_. In view of these essentials, we\nsuggest this outline which may be helpful to the inexperienced:\n\n (1) Arrange logically and complete the syllogism.\n\n (2) Determine the figure and mood by using symbols.\n\n (3) Apply the rules for negatives and particulars.\n\n (4) Indicate the distribution by underscoring the terms distributed.\n\n (5) Apply the rules for distribution.\n\n (6) Name fallacies, if any, giving reasons.\n\nWe recall that to be strictly logical any categorical argument must\ntake this form: first, major premise; second, minor premise; third,\nconclusion. Often in common conversation either the minor premise or\nconclusion is given first. Illustrations of this: (1) \u201cHe cannot be a\ngentleman (conclusion); for no gentleman would do such a thing (major\npremise), and there is no doubt but that he did it\u201d (minor premise).\n(2) \u201cHe has the making of a good teacher (conclusion); because he not\nonly knows, but he knows how to impart what he knows (minor premise),\nand this is a sure sign of a good teacher\u201d (major premise). When the\nargument appears in this illogical form, the first duty of the student\nis to arrange it logically. To do this he must be able to recognize\nreadily the premises and the conclusion. To this end these facts may\nbe of assistance:\n\n (1) A premise always answers the question \u201cWhy\u201d, and is often\n introduced by such words as \u201c_for_,\u201d \u201c_because_,\u201d \u201c_since_,\u201d\n and the like.\n\n (2) The conclusion is usually introduced by \u201c_therefore_,\u201d \u201c_hence_,\u201d\n \u201c_it follows_,\u201d etc.\n\n (3) When there are no word-signs those mentioned in the foregoing may\n be inserted with a view of determining which is the conclusion,\n and which are the premises.\n\n_Suggestions relative to completing abbreviated arguments:_\n\n(1) If the conclusion is to be supplied, select the term used twice in\nthe premises; this, the middle term, must not appear in the conclusion.\nThe other two terms may now be connected (copulated) to form the\nconclusion, the _narrower_ term (minor) being used as the subject,\nunless it occurs in what clearly seems to be the major premise. (2) If\neither premise is to be supplied, unite the middle term with the\n_subject_ of the conclusion for the minor premise, and with the\n_predicate_ of the conclusion for the major premise. (3) In supplying\nany missing proposition, care should be taken to make the argument\n_valid_, if this can be done in conformity with good English, good\nsense, and the rules of logic.\n\nAs regards the determination of the figure it is well to locate the\nmiddle term first, placing above it the symbol M. Then \u201cG\u201d (greater)\nmay be placed above the major term and \u201cS\u201d (smaller) above the minor.\n\n\n=3. ILLUSTRATIVE EXERCISES IN TESTING ARGUMENTS WHICH ARE ALREADY\n COMPLETE, REGULAR, AND LOGICALLY ARRANGED.=\n\n M G\n (1) A All dogs are quadrupeds,\n \u2015\u2015\u2015\u2015\n\n S M\n A All greyhounds are dogs,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n A \u2234 All greyhounds are quadrupeds.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n { A\nThis argument is in the first figure, the mood being { A. All\n { A\nthe propositions are affirmative and universal, consequently the\nrules pertaining to negatives and particulars are inapplicable. \u201cA\u201d\ndistributes the subject only, hence all the subjects are underscored.\nThe middle term \u201c_dog_\u201d is distributed in the major premise, and the\nminor term \u201c_greyhound_,\u201d which is distributed in the conclusion, is\nlikewise distributed in the minor premise. The argument is, therefore,\nvalid in _form_. This may be verified by referring to a list of valid\nmoods in the first figure.\n\n G M\n (2) E No prejudiced person is open to conviction,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A\u2002 All fair minded persons are open to conviction,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 No fair minded person is prejudiced.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n { E\nThe argument is in the second figure; mood { A. There is one\n { E\nnegative premise and the conclusion is negative; no particulars.\n\u201cE\u201d distributes both terms, \u201cA\u201d the subject only. The middle term\nis distributed in the major premise. Both major and minor terms are\ndistributed in the conclusion, but they are likewise distributed in\nthe premises where they are used. The argument is, therefore, valid.\nReference to the valid moods of the second figure confirms this\nconclusion.\n\n M G\n (3) A All good citizens vote,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n M S\n A All good citizens obey the law,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n A \u2234 All who obey the law vote.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n { A\nThe mood is { A used in the third figure. All the propositions are\n { A\nA\u2019s, hence the negative and particular rules are inapplicable. \u201cA\u201d\ndistributes its subject. The middle term is distributed in both\npremises. \u201cAll who obey the law\u201d is distributed in the conclusion but\nnot in the premise where it is used. Therefore the argument is invalid.\n { A\nThe fallacy being _illicit minor_. { A is not found in the third\n { A\nfigure\u2019s list of valid moods.\n\n M G\n (4) A All good citizens vote,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n E No criminal is a good citizen,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 No criminal votes.\n\n { A\nThe mood of this argument is { E used in the first figure. One premise\n { E\n\nnegative; conclusion negative; no particulars. \u201cA\u201d distributes the\nsubject only; \u201cE\u201d both subject and predicate. The middle term, \u201cgood\ncitizens,\u201d is distributed in both premises. The major term, \u201cvotes,\u201d is\ndistributed in the conclusion but not in the premise where it is used.\n { A\nThe argument is invalid, the fallacy being _illicit major_. { E is not\n { E\nfound in the first figure\u2019s list of valid moods.\n\n G M\n (5) A All true teachers are sympathetic,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A All lovers of children are sympathetic,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n A \u2234 All lovers of children are true teachers.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n { A\nThe mood of this argument is { A used in the second figure. There are\n { A\nno negatives and no particulars. \u201cA\u201d distributes its subject only. The\nmiddle term, \u201csympathetic,\u201d is distributed in neither premise, hence\nthe argument is invalid. Fallacy of _undistributed middle_. Referring\n { A\nto the list of valid moods, we do not find { A in the second figure.\n { A\n\n M G\n (6) A All thoughtful men are humane,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A All good citizens are thoughtful men,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n I \u2234 Some good citizens are humane.\n\n { A\nThe mood is { A in the first figure. No negatives; no particulars. \u201cA\u201d\n { I\ndistributes its subject only; \u201cI\u201d distributes neither term. Middle term,\ndistributed in the major premise; no term distributed in the conclusion.\nThe argument is, therefore, valid. The conclusion is _weakened_ as it\n { A\ncould just as well be an A. The mood { A in the first figure is valid,\n { I\nbut of little value because of the weakened conclusion.\n\n\n=4. ILLUSTRATIVE EXERCISE IN TESTING COMPLETED ARGUMENTS, ONE OR BOTH\n PREMISES BEING ILLOGICAL.=\n\n_Arguments containing exclusive propositions._\n\n (1) Only first class passengers may ride in the parlor car,\n All these are first class passengers,\n \u2234 They may ride in the parlor car.\n\nPropositions introduced by such words as _only_, _none but_,\n_alone_ and their equivalents are _exclusive_ propositions. Since these\ndistribute their predicates, but do not distribute their subjects, the\nmost convenient way of dealing with them is to _interchange subject\nand predicate_ and then regard them as _\u201cA\u201d propositions_. As the\nfirst proposition of the argument is an exclusive, we must deal with\nit accordingly. Interchanging subject and predicate and introducing it\nwith _all_ places the argument in this form:\n\n G M\n A (All) The parlor car is reserved for first class passengers,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A All these are first class passengers,\n \u2015\u2015\u2015\u2015\u2015\n\n S G\n A \u2234 All these may ride in the parlor car.\n \u2015\u2015\u2015\u2015\u2015\n\n { A\nThe mood of this argument is { A in the second figure. No negatives;\n { A\nno particulars. \u201cA\u201d distributes its subject only; the middle term is\nthus undistributed. The argument is invalid, the fallacy being that of\n_undistributed middle_.\n\n(2) \u201cNo one but a thief would take these books without asking for them,\nand it has been proved that you took the books; that is the reason I\nhave called you a thief.\u201d\n\nIt is clear that \u201c_no one but_\u201d is equivalent to \u201c_only_.\u201d Thus the\nfirst proposition of the argument is an exclusive, and may be made\nlogical by interchanging subject and predicate and calling it an \u201cA.\u201d\nAs a result of this the argument takes the following form:\n\n M G\n A (All) These books were taken by a thief,\n \u2015\u2015\u2015\u2015\u2015\n\n S M\n A You took these books,\n \u2015\u2015\u2015\n\n S G\n A \u2234 You are a thief.\n \u2015\u2015\u2015\n\nWe have now had sufficient experience to recognize the validity of mood\nAAA in the first figure.\n\n (3) \u201cNone but the brave deserve the fair,\n And you are not fair.\u201d\n\nMaking the exclusive logical and completing gives:\n\n M G\n A (All) The fair deserve the brave,\n \u2015\u2015\u2015\u2015\n\n S M\n E You are not fair,\n \u2015\u2015\u2015\n\n S G\n E \u2234 You do not deserve the brave.\n \u2015\u2015\u2015\n\n { A\nThe mood of this argument is { E used in the first figure. There\n { E\nis a negative premise, also a negative conclusion; no particulars.\nThe middle term is distributed twice. The major term \u201c_brave_\u201d is\ndistributed in the conclusion but not in the major premise; hence\nthe argument is invalid, the fallacy being _illicit major_.\n\nNOTE.\u2015\u2015There may be some doubt in the student\u2019s mind as to the\nproposition \u201cNone but the brave deserve the fair,\u201d really meaning\n\u201cAll the fair deserve the brave.\u201d This doubt may be better satisfied by\ntreating the exclusive in the second way as indicated on page 137, to\nwit: Negate the subject of the exclusive, then give it the form of the\nregular \u201cE.\u201d This results in \u201cNo not-brave persons deserve the fair,\u201d\nwhich, after first converting and then obverting becomes, \u201cAll the fair\ndeserve the brave.\u201d\n\n_Arguments Containing Individual Propositions._\n\n (4) \u201cGeorge Washington never told a lie, but you, when tempted,\n yielded with no qualms of conscience.\u201d\n\nCompleting, and arranging logically gives:\n\n E George Washington never told a lie,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n A You _did_ tell a lie,\n \u2015\u2015\u2015\n\n E \u2234 You (in this respect) are not like George Washington.\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nTreated properly this argument proves to be valid; the student, however,\nis apt to deal with such in this wise:\n\n O George Washington never told a lie,\n \u2015\u2015\u2015\n\n I You did tell a lie,\n \u2015\u2015\u2015\n\n O \u2234 You (in this respect) are not like George Washington.\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nWhen placed in this mood the argument is invalid; since the major\nterm, which is distributed in the conclusion, is not distributed in\nthe premise where it occurs (_illicit major_). It is the tendency on\nthe part of students to classify as particular, a proposition which\nhas as its subject a _singular term_. Such propositions we have learned\nto call _individual_. The cause of this tendency is easily explained:\nConsider the propositions, (1) \u201cThis man is mortal\u201d; (2) \u201cSome men are\nmortal\u201d; (3) \u201cAll men are mortal.\u201d In the first instance \u201c_mortal_\u201d\nrefers to the subject \u201c_man_\u201d which is narrower in significance than\n\u201c_some men_\u201d to which \u201cmortal\u201d of the second proposition refers.\nIn consequence, it is very natural to infer that if, \u201c_Some men are\nmortal_,\u201d is particular, then, \u201c_This man is mortal_,\u201d is likewise\nparticular. The error springs from a wrong conception of particular\nas used in logic; the content of the term has little to do with\n_extension_, but is chiefly concerned with _indefiniteness_. A\nparticular proposition is one in which the predicate refers to only\na part of an _indefinite_ subject. If the subject is referred to as\na whole, and this whole is more or less definite, then the proposition\nis universal. Since \u201cmortal\u201d refers to the _whole_ of the definite term\n\u201c_this man_,\u201d as positively as it refers to the whole of \u201c_all men_,\u201d\nthere is as much justification in calling the _first_ proposition\nuniversal as there is in calling the _third_ universal. _It may be\nremembered, then, that logicians class as universal all individual\npropositions._\n\n_Arguments Containing Partitive Propositions._\n\n (5) All that glitters is not gold,\n Tinsel glitters,\n \u2234 Tinsel is not gold.\n\nThe quantity sign \u201c_all_\u201d when used with \u201c_not_\u201d is ambiguous; it may\nmean \u201c_no_\u201d or \u201c_some-not_.\u201d The only way to determine which meaning is\nintended is to try both these quantity signs, selecting the one which\nseems to fit best the author\u2019s meaning. When \u201call-not\u201d means \u201csome-not\u201d\nthe proposition which it introduces is called a _partitive_ proposition;\nsince such always suggests a complementary proposition. (See page 133.)\nFor example, \u201cSome glittering things are _not_ gold,\u201d suggests its\ncomplement, \u201cSome glittering things _are_ gold.\u201d In testing the\nforegoing argument it is clear that \u201c_All that glitters is not gold_\u201d\ndoes not mean \u201c_No glittering thing is gold_,\u201d so much as it implies\n\u201c_Some glittering things are not gold_.\u201d Thus the argument takes this\nform:\n\n M G\n O Some glittering things are not gold,\n \u2015\u2015\u2015\u2015\n\n S M\n A Tinsel glitters,\n \u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 Tinsel is not gold.\n \u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\n\n { O\nThe mood is { A in the first figure. There is one negative premise\n { E\n(O), and the conclusion is negative. There is one particular premise\n(O), but the conclusion is _not_ particular. This makes the argument\ninvalid according to rule 8; viz.: \u201cA particular premise necessitates\na particular conclusion.\u201d Carrying the test still further it will be\nseen that there is likewise the fallacy of _undistributed middle_.\n\n_Other arguments where one of the premises is partitive._\n\n\u201cAll scholars are not wise and, therefore, Aristotle was not wise.\u201d\n\u201cAll democrats are not free-traders, but most of the men of this\nparticular club are democrats, and hence they are of a different faith\n(not free-traders).\u201d\n\n\u201cAll the members of the club are not good players, and James belongs to\nthe club.\u201d\n\n\u201cAll educated men do not write good English; therefore, you ought not\nto express surprise when informed that X, though an educated man, uses\npoor English.\u201d\n\nThe major premise in each of the foregoing is partitive in nature and\nshould be changed to the following form before the argument is tested;\ntaking these in order we have: \u201cSome scholars are not wise\u201d; \u201cSome\ndemocrats are not free-traders\u201d; \u201cSome of the members of the club are\nnot good players\u201d; \u201cSome educated men do not write good English.\u201d Let\nus test the validity of the last one:\n\n (6) O Some educated men do not write good English,\n \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\n A X is an educated man,\n \u2014\n\n E \u2234 X does not write good English (uses poor English).\n \u2014 \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\nLike the first one of the list, this is invalid inasmuch as a\nparticular premise should yield a particular conclusion, not one which\nis universal. The argument also contains the fallacy of _undistributed\nmiddle_.\n\n_Arguments Containing Inverted Propositions._\n\n(7) \u201cBlessed are the merciful: for they shall obtain mercy.\u201d The first\nproposition, being poetical in construction, is typical of the inverted\nform. These are usually made logical by _simple conversion_. Since\npremises usually follow \u201c_for_,\u201d or equivalent word-signs, it is easy\nto see that \u201cfor they shall obtain mercy\u201d is one of the premises; while\nthe other, the broader of the two, is understood.\n\nArranged logically the argument assumes this form:\n\n M G\n A Those who obtain mercy are blessed,\n \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\n S M\n A The merciful shall obtain mercy,\n \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\n S G\n A \u2234 The merciful are blessed.\n \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n\n { A\nHere we have the mood { A in the first figure, which we know to be\n { A\nvalid.\n\n_Other arguments where one of the propositions is inverted._\n\n\u201cBlessed are the pure in heart: for they shall see God.\u201d\n\n\u201cTo thine own self be true, and it must follow, as the night the day,\nthou canst not then be false to any man.\u201d\n\n\u201cA king thou art and, therefore, thy commands shall be, yea, _must_ be\nobeyed.\u201d\n\nTaking the inverted propositions in order and making each logical, the\nfollowing is the result: \u201cThe pure in heart are blessed\u201d; \u201cYou be true\nto yourself, and....\u201d; \u201cYou are a king, therefore....\u201d\n\n\n=5. ARGUMENTS WHICH ARE INCOMPLETE AND MORE OR LESS IRREGULAR.=\n\n (1) \u201cHe must be a star player; for he played fullback on the team\n which won the championship.\u201d\n\n (2) \u201cThe man is not to be trusted; because he served a term of\n 90 days in jail.\u201d\n\n (3) \u201cOnly material bodies gravitate, and ether does not gravitate.\u201d\n\n (4) \u201cIf only fools despise knowledge, this man cannot be a fool.\u201d\n\n (5) \u201cA charitable man has no merit in relieving distress; because he\n merely does what is pleasing to himself.\u201d\n\n (6) \u201cIt is evident that all who get justice buy it; since only the\n rich get it.\u201d\n\nThe above arguments thrown into logical form and validity or invalidity\nstated: (The student should test these in detail.)\n\n M\n (1) A All belonging to the team which won the championship were\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n G\n star players,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A He played with the team which won the championship,\n \u2015\u2015\n\n S G\n A \u2234 He is a star player. _Valid in form._\n \u2015\u2015\n\n M G\n (2) E One who serves a term of 90 days in jail is not to be trusted,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A This man served a term of 90 days in jail,\n \u2015\u2015\u2015\n\n S G\n E \u2234 This man is not to be trusted. _Valid in form._\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n M G\n (3) A All gravitating bodies are material,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n E Ether does not gravitate,\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 Ether is not material. _Illicit major._\n \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n M G\n (4) A All who despise knowledge are fools,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n E This man does not despise knowledge,\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 This man is not a fool. _Illicit major._\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\n\n M\n (5) E No one who merely does what is pleasing to himself has\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n G\n merit in relieving distress,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A A charitable man merely does what is pleasing to himself,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 No charitable man has merit in relieving distress. _Valid\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n in form._\n\n M G\n (6) A All the rich buy justice,\n\n S M\n A All who get justice are rich,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n A \u2234 All who get justice buy it. _Valid in form._\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nIn supplying suppressed premises the critic is duty bound to give\nthe author the benefit of the doubt, if by so doing no principle in\nlogic is violated and the proposition conforms to good English and good\nsense. Often it is not easy to perceive in the abbreviated argument\nthe meaning intended; in such instances all legitimate effort should be\ndirected to making the argument valid. To illustrate: In supplying the\nmajor premise of argument \u201c6\u201d it would be easy to make it, \u201cAll justice\nis bought by the rich\u201d; in consequence the critic could pronounce the\nargument invalid as the middle term would be undistributed.\n\nBefore asserting that an argument is fallacious because it has four\nterms rather than three, the student must make sure that there are\nno synonyms or equivalents used. In argument \u201c4,\u201d for instance, there\nare apparently the four terms: (1) \u201cfoolish,\u201d (2) \u201cdespise knowledge,\u201d\n(3) \u201cman,\u201d (4) \u201cfool\u201d; but to regard \u201c_foolish_\u201d and \u201c_fool_\u201d as\nsynonyms does not seem like undue liberty. The following arguments\nfurther illustrate this need of _recognizing synonyms_:\n\n\u201cHuman beings are accountable for their conduct; brutes, not being\nhuman, are therefore _free from responsibility_.\u201d (Not accountable for\ntheir conduct.)\n\n\u201cNot all educated men spell correctly; because one often finds mistakes\nin the writings of _college graduates_.\u201d (Educated men.)\n\n\u201cModern education is not popular in this state; for it increases the\ntax rate, and the popularity of everything, which _touches the pocket_\nof these frugal Yankees, (increases the tax rate) is very short lived.\u201d\n(Not popular.) In common parlance the use of synonyms is so prevalent\nthat ready ability to substitute equivalents in word, phrase, and\nclause form is needed by him who would be skillful in testing all kinds\nof arguments.\n\nIt has already become apparent to the student that the _number_ of the\nnoun or the _tense_ of the verb is of small logical consequence. A very\nlarge proportion of the formal fallacies in argumentation concern the\nrules of distribution which are summarized in the dictum \u201cWhat may be\nsaid of the whole may be said of part of that whole.\u201d\n\n\n=6. COMMON MISTAKES OF STUDENTS IN TESTING ARGUMENTS.=\n\nThe most common mistakes made by the student when testing arguments\nare as follows: (1) Using the exclusive as an \u201cA\u201d without interchanging\nsubject and predicate; e. g., interpreting the proposition, \u201cOnly\nhigh school graduates may enter the training school,\u201d as meaning \u201cAll\nhigh school graduates may enter the training school.\u201d (2) _Calling\nindividual propositions particular_; e. g., interpreting \u201cSocrates is\nmortal\u201d as an \u201cI\u201d rather than an \u201cA.\u201d (3) Signifying that partitive\npropositions are \u201cA\u2019s\u201d rather than \u201cO\u2019s\u201d; e. g., \u201cAll that glitters is\nnot gold\u201d interpreted as meaning that \u201cAll glittering things are gold,\u201d\nrather than \u201cSome glittering things are not gold.\u201d (A). (4) Concluding\nthat a fallacy of four terms has been committed when two terms are\nsynonomous. (5) Failing to interchange the subject and predicate of\ninverted propositions.\n\n\n=7. OUTLINE.=\n\n CATEGORICAL ARGUMENTS TESTED ACCORDING TO FORM.\n\n (1) Arguments of form and matter.\n\n (2) Order of procedure in the formal testing of arguments.\n The outline.\n Determining premises and conclusion.\n Completing abbreviated arguments.\n\n (3) Illustrative exercises in testing arguments which are complete\n and whose premises are logical.\n\n (4) Illustrative exercises in testing completed arguments, one or\n both of whose premises are illogical.\n Exclusive premises, individual premises, partitive premises,\n inverted premises.\n\n (5) Incomplete and irregular arguments.\n\n (6) Common mistakes of the student.\n\n\n=8. SUMMARY.=\n\n(1) In determining their validity, arguments must be tested from the\ntwo viewpoints of _form_ and _matter_.\n\n(2) In testing categorical arguments it is quite necessary to be\ndefinite, to give reasons, and to give the author the benefit of the\ndoubt.\n\nWith this in view the attending outline is suggestive:\n\n 1. Arrange logically and complete.\n 2. Determine the figure and mood.\n 3. Apply rules for negatives and particulars.\n 4. Indicate distribution.\n 5. Apply rules for distribution.\n 6. Name fallacies, if any, giving reasons.\n\nThe logical arrangement of syllogistic arguments is\n\n 1. Major premise.\n 2. Minor premise.\n 3. Conclusion.\n\nAny proposition in a syllogism which answers the question \u201c_Why?_\u201d\nis a premise, whereas the conclusion follows \u201c_therefore_\u201d, or its\nequivalent either written or understood. If a conclusion is to be\nsupplied, unite the two terms which are used but _once_ in the premises,\nusing the \u201cminor premise term\u201d as the subject. If a premise is to be\nsupplied, unite the middle term with the \u201cminor\u201d to form the minor\npremise and with the \u201cmajor\u201d to form the major premise.\n\n(3) Arguments which are regular, complete, and logically arranged,\nmay be tested by symbolizing the mood and figure, underscoring the\ndistributed terms, and then applying the general rules of the syllogism.\n\n(4) Arguments with illogical premises may not be tested with impunity\ntill the faulty premises are made logical. The exclusive, an illogical\nproposition introduced by only, alone, none but, and the like, may be\nmade logical by interchanging subject and predicate and calling the\nproposition an A. The individual proposition is one with a singular\nsubject. In testing, individual propositions are classed as universal.\nPropositions introduced by \u201call-not\u201d are usually given the significance\nof \u201csome-not\u201d. These are called partitive propositions, which in the\ntesting, should be denominated \u201cO\u2019s\u201d.\n\nInverted propositions when subjected to the test for validity must be\nconverted _simply_ and then classified. (Usually as A\u2019s.)\n\n(5) In supplying propositions which are taken for granted, the aim\nshould be to make the argument valid, provided this can be done without\nviolating the rules of logic, English, and common sense.\n\nAbility to _substitute_ equivalent words, phrases, or clauses is\ndemanded of the student of logic, inasmuch as such substitution is\nfrequently needed in the testing of arguments.\n\nNumber and tense have little significance in dealing with arguments.\n\n(6) The common mistakes of students made in testing arguments concern\nexclusive, partitive and inverted propositions, and an inability to\nrecognize expressions equivalent in meaning.\n\n\n=9. REVIEW QUESTIONS.=\n\n (1) Name and explain the two standpoints from which all arguments\n must be viewed.\n\n (2) Give an outline of procedure which may be serviceable in the\n testing of categorical arguments.\n\n (3) Give illustrations showing that the logical order of categorical\n arguments is not the usual mode of procedure in common parlance.\n\n (4) Offer suggestions which may aid in designating a premise; a\n conclusion.\n\n (5) How would you proceed in forming any one of the three\n propositions of a syllogism when the other two are given?\n\n (6) Designate the premises and the conclusion in the following,\n supplying any proposition which may be omitted, also arrange\n logically and test the validity.\n\n (1) \u201cThe people of this country are suffering from an overdose\n of prosperity; consequently a period of hard times will be\n a valuable lesson.\u201d (The conclusion should be recast so as\n to read, \u201cA period of hard times will cure the people of\n this country.\u201d The minor premise is, \u201cThose who suffer from\n an overdose of prosperity may be cured by a period of hard\n times.\u201d)\n\n (2) \u201cI am a teacher; you are not what I am; hence you are not\n a teacher.\u201d\n\n (3) \u201cTo kill a man is murder, therefore war is murder.\u201d\n\n (4) \u201cYou have not adopted the best policy since honesty has\n always been and will always be the best policy.\u201d\n\n (5) \u201cSince the road is criminally mismanaged, why should not\n the authorities be indicted as criminals?\u201d\n\n (6) \u201cEarly to bed and early to rise makes a man healthy,\n wealthy and wise. I am none of these; hence my sleeping\n hours have been wrong.\u201d\n\n (7) Illustrate a weakened conclusion.\n\n (8) Explain the exclusive proposition and indicate how the logician\n should treat it.\n\n (9) Arrange logically and test the following:\n\n (1) Only weak men become intemperate, and Edgar Allen Poe was\n surely intemperate.\n\n (2) No admittance except on business; hence you cannot be\n admitted.\n\n (3) Virtuous acts are praiseworthy, and indiscriminate giving\n is not a virtuous act.\n\n (10) Explain why individual propositions are classed as universal.\n\n (11) Write an argument whose major premise is a partitive proposition;\n arrange logically and test validity.\n\n (12) Arrange and test this argument: \u201cBlessed are the poor in spirit:\n for theirs is the kingdom of heaven.\u201d\n\n (13) Complete, arrange and test.\n\n (1) \u201cThe object of war is to settle disputes; hence soldiers\n are the best peacemakers.\u201d\n\n (2) \u201cThe various species of brutes being created to prey upon\n one another proves that man is intended to prey upon them.\u201d\n\n (3) \u201cThe end of everything is its perfection; death being the\n end of life is its perfection.\u201d\n\n (4) \u201cAll the trees of the yard make a thick shade and this is\n one of them.\u201d\n\n (5) \u201cMinds of moderate caliber ordinarily condemn everything\n which is beyond their range, and his is such a mind.\u201d\n\n (6) \u201cThe best of all medicines are fresh air and sleep, and you\n are sorely in need of both.\u201d\n\n (7) \u201cEvery hen comes from an egg; every egg comes from a hen;\n therefore every egg comes from an egg.\u201d\n\n (8) \u201cHe cannot have been there\u2015\u2015otherwise I should have seen\n him.\u201d\n\n (14) \u201cIt is fair to give the author the benefit of the doubt when we\n set ourselves up as censors worthy of the name.\u201d Explain this.\n\n (15) Illustrate by citing arguments the need of detecting terms which\n are equivalents in signification.\n\n (16) How does the logician look upon number and tense as treated in\n grammar?\n\n (17) Illustrate and test an argument in which one of the premises is\n elliptical.\n\n (18) Summarize the most common mistakes made by students in the\n testing of categorical arguments; illustrate these mistakes and\n then write in logical form.\n\n\n=10. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Give illustrations of arguments which are valid in form but\n invalid in meaning. Explain.\n\n (2) May an argument be valid in meaning but invalid in form?\n Exemplify.\n\n (3) Put a simple problem in arithmetic in syllogistic form and show\n that the minor premise naturally comes first.\n\n (4) In the practice of law is there any custom analogous to giving\n the author the benefit of the doubt in logical argumentation?\n\n (5) Test in detail the following arguments:\n\n (1) \u201cAll wise presidents strive to give heed to the demands of\n the people, but this president has not done so.\u201d\n\n (2) \u201cThe existence of God is not universally believed, hence it\n cannot be true.\u201d\n\n (3) \u201cThe institution has prospered under the present r\u00e9gime\n therefore why change it?\u201d\n\n (4) \u201cThe man is guilty because seven out of the nine witnesses\n so testified.\u201d\n\n (5) \u201cI know three men who cleared not less than ten thousand\n dollars in this business; and why cannot I do as much?\u201d\n\n (6) \u201cOnly members may vote and, since you are not a member, you will\n not be allowed to vote.\u201d Change the exclusive in this argument in\n the two ways suggested in Chapter 8, page 126. Test the argument\n in both cases.\n\n (7) Show by illustration that the quantity sign \u201c_all_\u201d when used\n with \u201c_not_\u201d may in some cases mean \u201c_no_\u201d and in others\n \u201c_some-not_\u201d.\n\n (8) Make two selections from some poet of authority representing\n arguments with an inverted premise.\n\n (9) Select from news papers three arguments which seem to illustrate\n the fallacy of four terms but which in reality do not. Explain.\n\n (10) Wherein could the elliptical proposition lead to error?\n\n (11) Put the following in syllogistic form and test:\n\n (1) \u201cThat persons may reason without language is proven by the\n circumstances that infants reason and yet have no language.\u201d\n\n (2) \u201cThe scriptures cannot come from God because they contain\n some things which cannot be comprehended by man.\u201d\n\n (3) \u201cWhen Columbus was sailing the ocean in search of a new\n world, he fell in with a flock of land birds and concluded\n that he could not be far from land.\u201d\n\n (4) \u201cBolingbroke in arguing against the truth of the Christian\n religion shows that the Christian religion has bred\n contentions.\u201d \u201cBurke answered him by showing that civil\n government had bred contentions.\u201d\n\n\n\n\n CHAPTER 15.\n\n HYPOTHETICAL ARGUMENTS, AND DISJUNCTIVE ARGUMENTS\n INCLUDING THE DILEMMA.\n\n\n=1. THREE KINDS OF ARGUMENTS.=\n\nThe proposition, constituting the basic unit of the argument, would\nof necessity be indicative of the nature of said argument; therefore\nthe three general kinds of propositions, categorical, hypothetical and\ndisjunctive, suggest the three kinds of arguments which are in turn\ncategorical, hypothetical and disjunctive. Categorical arguments are\nthose in which all of the propositions are categorical. Since this kind\nhas been treated, it remains for us to consider the other two.\n\n\n=2. HYPOTHETICAL ARGUMENTS.=\n\nWe have observed that a hypothetical proposition is one in which the\nassertion depends on a condition; for example, in the proposition, \u201cIf\nit is pleasant, I will call on you to-morrow,\u201d the _calling_ depends\non the state of the weather. \u201cI will call on you to-morrow,\u201d is the\n_assertion_ which is limited by the _condition_, \u201cIf the weather is\npleasant.\u201d Definition:\n\n_The hypothetical argument or syllogism is one in which the major\npremise is hypothetical and the minor premise categorical._\n\n ILLUSTRATION:\n\n If the people are right more than half of the time, the world will\n progress;\n\n And the people _are_ right more than half of the time,\n\n Hence the world will progress.\n\nIn contradistinction to _disjunctives_, hypothetical propositions and\nhypothetical syllogisms are frequently referred to as \u201c_conjunctive_.\u201d\n\n\n=3. THE ANTECEDENT AND CONSEQUENT.=\n\nFacility in detecting the antecedent and consequent of hypotheticals\nis required in order to deal intelligently with the argument. The\nhypothetical proposition has been defined as one in which the assertion\nis limited by a condition. The _consequent_ is the assertion and\nusually follows (though not always) the _antecedent_ which is the\nlimiting condition. _First the antecedent and then the consequent is\nthe logical order_ as the derivative meaning of the words antecedent\nand consequent would indicate. The antecedent is introduced by such\nwords as \u201cif,\u201d \u201cthough,\u201d \u201cunless,\u201d \u201csuppose,\u201d \u201cgranted that,\u201d \u201cwhen,\u201d\netc.\n\n\n ILLUSTRATIONS:\n\n _Antecedent._ _Consequent._\n 1. If you study, you will pass.\n 2. If it rains, it is cloudy.\n 3. If two is added to three, the result is five.\n 4. If you are temperate, you will live to a ripe old age.\n\n _Consequent._ _Antecedent._\n 5. I will go, unless you wire me to the\n contrary.\n 6. I will pay you, when you present your bill.\n 7. I shall make the trip in granted that I have no accidents.\n ten hours,\n 8. My overcoat would not have if the door had been locked.\n been stolen,\n\n\n=4. TWO KINDS OF HYPOTHETICAL ARGUMENTS.=\n\nThe two kinds of hypothetical syllogisms are the _constructive_ and\n_destructive_.\n\n_A constructive hypothetical syllogism is one in which the minor\npremise affirms the antecedent._\n\n_A destructive hypothetical syllogism is one in which the minor premise\ndenies the consequent._\n\nThe constructive hypothetical is sometimes referred to as the \u201c_modus\nponens_\u201d; whereas the destructive hypothetical is called the \u201c_modus\ntollens_.\u201d\n\n\n ILLUSTRATIONS:\n\n _Constructive_ Hypothetical Syllogisms.\n\n _Symbols._ _Words._\n\n If A is B, C is D If you are diligent, you will succeed;\n A is B And you _are_ diligent,\n \u2234 C is D Therefore you will succeed.\n\n _Destructive_ Hypothetical Syllogisms.\n\n If A is B, C is D If you had been diligent, you would have\n succeeded;\n C is not D But you did not succeed,\n \u2234 A is not B Therefore you were not diligent.\n\n\n=5. THE RULE AND TWO FALLACIES OF THE HYPOTHETICAL ARGUMENT.=\n\nFrom a given hypothetical proposition it is possible to construct\n_four_ different hypothetical syllogisms, as the attending\nillustrations make evident:\n\nConsider the hypothetical proposition \u201cIf it has rained, the ground is\ndamp.\u201d\n\n (1) Minor premise affirms antecedent.\n If it has rained, the ground is damp;\n It has rained,\n Therefore the ground is damp.\n\n (2) Minor premise denies antecedent.\n If it has rained, the ground is damp;\n It has not rained,\n Therefore the ground is not damp.\n\n (3) Minor premise affirms consequent.\n If it has rained, the ground is damp;\n The ground is damp,\n Therefore it has rained.\n\n (4) Minor premise denies the consequent.\n If it has rained, the ground is damp;\n The ground is not damp,\n Therefore it has not rained.\n\nWithout any knowledge of the rules of the hypothetical syllogism let\nus strive to determine how many of the foregoing are valid. Relative to\nthe first, it would be impossible for any rain to fall without making\nthe ground somewhat damp; a few drops would be sufficient. In short,\nif the antecedent happens, the consequent _must_ follow. It seems,\ntherefore, that the first argument is _valid_. Considering the second:\nrain is not the only cause for the dampness of the ground, as it might\nresult from the falling of dew, or from a dense fog; _no rain_ does not\nnecessarily mean _no dampness_. It is clear that if the antecedent does\nnot happen, the consequent may or may not follow. Thus it appears that\nthe second argument is _invalid_. Attention to the third makes evident\na condition similar to the second: the ground may be made damp by\nagencies other than rain, such as fog and dew. Thus the third argument\nis likewise _invalid_. But in the fourth argument it is obvious that\nif the ground is not damp, then there could have been neither rain, nor\nfog, nor dew. No dampness shuts out _all_ of the conditions, including\nthe rain. Therefore the fourth argument is _valid_.\n\nThis investigation suggests a rule for hypothetical arguments. Since\nonly the first and fourth arguments are valid, this is the rule which\nmust obtain: _The minor premise should either affirm the antecedent or\ndeny the consequent._\n\nAny violation of this rule would result in the fallacies of _denying\nthe antecedent_ or _affirming the consequent_.\n\nThere is one exception to this rule which must not be overlooked;\nviz.: If the antecedent and consequent of the hypothetical proposition\nare _co-extensive_ then both may be either affirmed or denied.\n\n\n ILLUSTRATIONS:\n\n (1) If the rectangle is equilateral, then it is a square;\n The rectangle is equilateral,\n \u2234 It is a square.\n\n (2) If the rectangle is equilateral, then it is a square;\n The rectangle is not equilateral,\n \u2234 The rectangle is not a square.\n\n (3) If the rectangle is equilateral, then it is a square;\n It is a square,\n \u2234 The rectangle is equilateral.\n\n (4) If the rectangle is equilateral, then it is a square;\n It is not a square,\n \u2234 The rectangle is not equilateral.\n\n\n=6. HYPOTHETICAL ARGUMENTS REDUCED TO THE CATEGORICAL FORM.=\n\nThe hypothetical syllogism so closely resembles the categorical that\nit may be changed to it by a slight alteration in the wording. After\ntesting the hypothetical by its own rule, it may be expedient to reduce\nthe argument to the categorical form, and subject it to a second test\nin which the categorical rules are applied. This reduction usually\nnecessitates two steps; first, _change the propositions which represent\nthe antecedent and consequent to a subject term and a predicate term\nrespectively and then unite them to form the major premise_; second,\n_supply a new minor term, if necessary_.\n\nIllustrations of Reduction; and Comparison of Hypothetical and\nCategorical Fallacies:\n\n_Hypothetical Form_:\n\n (1) If it has rained, the ground is damp;\n It has rained,\n \u2234 The ground is damp.\n\n_Categorical Form_:\n\n M G\n A The falling rain makes the ground damp,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A In this case rain has fallen,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n A \u2234 In this case the ground is damp ground.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nIt is seen that the argument in the hypothetical form is valid as the\nminor premise affirms the antecedent. Reducing to the categorical gives\n { A\nto the argument the mode { A in the first figure which we know to be\n { A\nvalid.\n\n_Hypothetical_:\n\n (2) If one were wise, he would study;\n But you will not study,\n \u2234 You are not wise.\n\n_Categorical_:\n\n G M\n A A wise person would study,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n E \u2234 You will not study,\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 You are not wise.\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\n\nIn the hypothetical form the argument is valid since the minor premise\n { A\ndenies the consequent. Reducing to the categorical gives mood { E in\n { E\nthe second figure. This is valid.\n\n_Hypothetical_:\n\n (3) If the wind blows from the south, it will rain;\n But the wind is not blowing from the south,\n Hence it is not going to rain.\n\n_Categorical_:\n\n M G\n A South wind brings rain,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n E This wind is not a south wind,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 This wind will not bring rain.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nHypothetically considered, the minor premise denies the antecedent and\nconsequently the argument is invalid. Reducing to the categorical form,\nit is found that the major term is distributed in the conclusion, but\nis not distributed in the major premise; hence the fallacy of _illicit\nmajor_ is committed.\n\n_Hypothetical_:\n\n (4) If a man is just, he will obey the golden rule;\n This judge has obeyed the golden rule,\n Hence he is just.\n\n_Categorical_:\n\n G M\n A A just man will obey the golden rule,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A This judge has obeyed the golden rule,\n \u2015\u2015\u2015\u2015\u2015\n\n S G\n A \u2234 This judge is a just man.\n \u2015\u2015\u2015\u2015\u2015\n\nHypothetically considered, the minor premise affirms the consequent\nand thus the argument is fallacious; when changed to the categorical\nwe find the fallacy of _undistributed middle_. If other examples were\ntaken, it could be proved that the hypothetical fallacy of _denying\nthe antecedent_ is usually equivalent to the categorical fallacy of\n_illicit major_; whereas the hypothetical fallacy of _affirming the\nconsequent_ amounts to _undistributed middle_.\n\nIn reducing some hypotheticals it is necessary to make use of such\nexpressions as, \u201c_the case of_\u201d or \u201c_the circumstances that_.\u201d The\nattending argument will illustrate this:\n\n If Jefferson was right, man was created free and equal;\n (but) Man was not created free and equal,\n \u2234 Jefferson was not right.\n\n_Reduced to the categorical_:\n\n G\n The case of Jefferson being right is the case of man being created\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n M\n free and equal;\n\n S M\n Man was not created free and equal,\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n \u2234 Jefferson (this man) was not right.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n\nThe argument is valid in both cases.\n\n\n=7. ILLUSTRATIVE EXERCISE TESTING HYPOTHETICAL ARGUMENTS OF ALL KINDS.=\n\nThe following brief outline may be followed in testing hypothetical\narguments:\n\n 1. Arrange logically.\n 2. Determine antecedent and consequent.\n 3. Apply the hypothetical rule; name fallacies giving reasons.\n 4. Reduce to categorical form.\n 5. Apply the categorical rules, giving fallacies with reasons.\n\n (1) If a man is properly educated, he will not despise manual labor;\n therefore I conclude that you have not been properly educated,\n since you dislike to work with your hands.\n\n_Arranged logically and antecedent and consequent indicated_:\n\n If a man is properly educated (antecedent), he will not despise\n manual labor (consequent);\n You despise manual labor (dislike to work with your hands),\n \u2234 You have not been properly educated.\n\nThe minor premise denies the consequent, hence the argument is valid\naccording to the rule, \u201cThe minor premise must affirm the antecedent\nor deny the consequent.\u201d The student should note that the consequent is\nnegative and therefore its denial must be an affirmative proposition.\n\n_Reduced to the categorical_:\n\n G M\n E A properly educated man will not despise manual labor;\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A You despise manual labor,\n \u2015\u2015\u2015\n\n S G\n E \u2234 You have not been properly educated.\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nRegarded categorically this is valid. Why?\n\n(2) \u201cIf one believes in the tenets of the democratic party, then he\nshould vote for its candidates; and since A does believe in them I have\nasked him to vote for me.\u201d\n\n_Arranged, and antecedent and consequent indicated._\n\n If one believes in the tenets of the democratic party (antecedent),\n then he should vote for its candidates (consequent);\n And A does believe in these tenets,\n \u2234 He should vote for its candidates (I have asked him to vote for\n me).\n\nThe minor premise affirms the antecedent and thus the argument is valid\naccording to rule.\n\n_Reduced to the categorical_:\n\n M\n A One who believes in the tenets of the democratic party should\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n G\n vote for its candidates,\n\n S M\n A A believes in these tenets,\n \u2015\n\n S G\n A \u2234 A should vote for its candidates.\n \u2015\n\n { A\nReduced to the categorical gives mood { A in the first figure and this\n { A\nwe know to be valid.\n\n(3) \u201cIf the weather had not been pleasant, I could not have come; but\nas the weather is pleasant, here I am.\u201d\n\n_Arranged and antecedent and consequent indicated_:\n\n If the weather had not been pleasant (antecedent), I could not have\n come (consequent);\n The weather is pleasant,\n \u2234 I have come (here I am).\n\nThe minor premise _denies_ the antecedent and consequently the argument\nis invalid according to the rule. (An affirmative minor premise denies\na negative antecedent.)\n\n_Reduced to the categorical_:\n\n E Unpleasant weather would not permit me to come,\n E This weather is not unpleasant,\n A \u2234 This weather enabled me to come.\n\nFallacy of two negative premises.\n\n(4) \u201cIf one pays his debts, he will not be \u2018black-listed\u2019; but since\nyou are \u2018black-listed,\u2019 I conclude that you have not paid your debts.\u201d\n\n_Arranged logically and antecedent and consequent indicated_:\n\n If one pays his debts (antecedent), he will not be \u201cblack-listed\u201d\n (consequent);\n You are \u201cblack-listed,\u201d\n \u2234 You have not paid your debts.\n\nThe minor premise denies the consequent hence the argument is valid.\n\n_Reduced to categorical form_:\n\n G M\n E No one who pays his debts is black listed,\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n A You are black listed,\n \u2015\u2015\u2015\n\n S G\n E \u2234 You have not paid your debts.\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n { E\nThe mood { A in the second figure is valid.\n { E\n\n(5) \u201cMen would do right for the sake of themselves, if they appreciated\nthe law of retribution; but they never think of that.\u201d\n\n_Arranged, completed, and tested_:\n\n If they appreciated the law of retribution (antecedent), men would\n do right for the sake of themselves (consequent);\n But they do not appreciate the law of retribution (never think of\n that),\n Hence they do not do right for the sake of themselves.\n\nFallacy of denying the antecedent.\n\n_Reduced to the categorical_:\n\n M\n A The case of men appreciating the law of retribution, is the case\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n G\n of men doing right for the sake of themselves;\n\n S M\n E But men do not appreciate the law of retribution,\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S G\n E \u2234 Men do not do right for the sake of themselves.\n \u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nFallacy of illicit major.\n\n(6) \u201cIf an animal is a vertebrate, then it must have a backbone; but\nthe books say that this animal is not a vertebrate, hence it cannot\nhave a backbone.\u201d\n\nSince the minor premise denies the antecedent it would appear that the\nargument is invalid; yet common knowledge and common sense dictate that\nthe conclusion is true. Surely no invertebrate can have a backbone. As\na matter of fact the antecedent and consequent are _co-extensive_ and\ntherefore the hypothetical rule is not applicable.\n\n_Reduced to the categorical_:\n\n M G\n A Vertebrates must have a backbone (Co-extensive),\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n S M\n E This animal is not a vertebrate,\n \u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\n E \u2234 This animal cannot have a backbone.\n \u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n\nAs co-extensive A\u2019s distribute their predicates the possibility of\nthere being a fallacy of illicit major is forestalled.\n\nCategorically considered the argument is likewise valid.\n\n\n=8. DISJUNCTIVE ARGUMENTS.=\n\nIt has been observed that a disjunctive proposition is one which\nexpresses an alternative. _A disjunctive syllogism is one in which the\nmajor premise is a disjunctive proposition._\n\n\n ILLUSTRATION:\n\n The boy is either honest or dishonest,\n He is honest,\n \u2234 He is not dishonest.\n\n\n=9. THE TWO KINDS OF DISJUNCTIVE ARGUMENTS.=\n\nThe two forms of disjunctive arguments are _the one which by affirming\ndenies_ and _the one which by denying affirms_. The former is known by\nthe Latin words \u201c_modus ponendo tollens_\u201d; while the latter is termed\nthe \u201c_modus tollendo ponens_.\u201d\n\n\n ILLUSTRATIONS:\n\n (1) By affirming denies.\n\n The defendant is either guilty or innocent,\n He is guilty,\n \u2234 He is not innocent.\n\n or\n\n The defendant is either guilty or innocent,\n He is innocent,\n \u2234 He is not guilty.\n\n (2) By denying affirms.\n\n The defendant is either guilty or innocent,\n He is not guilty,\n \u2234 He is innocent.\n\n or\n\n The defendant is either guilty or innocent,\n He is not innocent,\n \u2234 He is guilty.\n\n\n=10. THE FIRST RULE OF DISJUNCTIVE ARGUMENTS.=\n\nIt may be said that disjunctive arguments depend on _two_ rules. This\nis the first: _The major premise must assert a logical disjunction._\nA logical disjunction involves two requisites; first, the alternatives\nmust be _mutually exclusive_; second, the _enumeration_ must be\n_complete_.\n\n_Illustrations of illogical major premise._\n\n _Terms not mutually exclusive_:\n\n This boy is either inattentive or indolent,\n He is not inattentive,\n \u2234 He is indolent.\n\nIt is obvious that the boy might be _both_ inattentive and indolent.\nExperience teaches that the qualities are usually concurrent, and to\nassume that the boy must be either one or the other is a clear case of\n\u201cbegging the question.\u201d\n\nSome logicians maintain that \u201c_either\u2015\u2015or_\u201d signify that both\nalternatives _cannot be false_, but that both _may be true_. If this\nviewpoint were adopted, the major premise of the illustration would\n_not_ be a case of begging the question. It is unnecessary to argue the\npoint, if it is made perfectly clear which view is to obtain in this\ndiscussion. Briefly stated the two points are these. First opinion:\n\u201c_Either\u2015\u2015or_\u201d when used logically, mean that if the first alternative\nis false the second must be true, or if the first alternative is true\nthe second must be false. Second opinion: \u201c_Either\u2015\u2015or_\u201d when used\nlogically mean that if the first alternative is false, the second must\nbe true; but if the first alternative is true, the other may or may\nnot be true. _This treatise adopts the first opinion._ With us all\nalternative arguments to be logical must be mutually contradictory;\ni. e., _when one is false, the other must be true and when one is true\nthe other must be false; both_ cannot be false, neither can _both_\nbe true. When it is intended that this implication should not obtain,\nthen the expressed alternative will take this form, \u201cThe boy is either\ninattentive or indolent or _both_.\u201d\n\nOther examples where the terms of the disjunctive may not be mutually\nexclusive:\n\n (1) \u201cLord Bacon was either exceedingly studious or phenomenally\n bright.\u201d (Undoubtedly he was both.)\n\n (2) \u201cThis teacher is a graduate either of Harvard or of Yale.\u201d\n (Perhaps both.)\n\n (3) \u201cThe defendant is either a liar or a thief.\u201d (The one often\n leads to the other.)\n\n (4) \u201cTo succeed one must either seize the opportunity as it passes\n or make his own.\u201d (The best success results from doing both.)\n\n\n_Incomplete enumeration_:\n\n The cause of the disease was either the water or the milk,\n It was not the milk,\n \u2234 It was the water.\n\nWhen such an argument as this is advanced, it must be with the\nknowledge that every other alternative has received satisfactory\ninvestigation. Without this assurance one could justly claim that the\ndisease might have been caused by the _meat_ or _fish_ supply. Complete\nenumeration means that the investigation has narrowed the facts to\nthe boundary of the field covered by the alternatives. The fallacy\nof incomplete enumeration is also one of \u201cbegging the question.\u201d\n\nOther examples of a possible incomplete enumeration:\n\n (1) \u201cJones lives either in Boston or New York.\u201d\n\n (2) \u201cMary is studying either algebra or geometry.\u201d\n\n (3) \u201cHe either committed suicide or was lynched.\u201d\n\n (4) \u201cEither the Giants or the Boston Americans will win the pennant.\u201d\n\n\n=11. SECOND RULE OF DISJUNCTIVE ARGUMENTS.=\n\nThe second rule is made so self evident by the first that there is\nlittle need of a detailed discussion concerning it. The rule is this:\n_When the minor premise affirms or denies one of the alternatives of\na logical disjunction, the conclusion must, in order, deny or affirm\nall of the others._ To put it differently: When the \u201cminor\u201d affirms,\nthe conclusion must deny every other alternative, and vice versa.\nWhen there are but two alternatives reference to any of the foregoing\ndisjunctive arguments will make the rule clear. There may be, however,\n_more_ than two alternatives. In such a case, if the first rule is\nobserved then the second becomes applicable.\n\n\n ILLUSTRATIONS:\n\n (1) John Doe lives either in Boston, Albany, or New York;\n He lives in New York,\n \u2234 He does not live in either Boston or Albany.\n\n or\n\n He does not live in New York,\n \u2234 He lives in either Boston or Albany.\n\n (2) The season must have been either summer, or autumn, or winter,\n or spring;\n It was neither autumn, nor winter, nor spring,\n \u2234 It must have been summer.\n\n or\n\n It was either autumn, or winter, or spring,\n \u2234 It could not have been summer.\n\n\n=12. REDUCTION OF THE DISJUNCTIVE ARGUMENT TO THE HYPOTHETICAL AND\n THEN TO THE CATEGORICAL.=\n\nIt would seem that the laws of the disjunctive contradict those of the\ncategorical syllogism; for we apparently derive from two affirmatives a\nnegative conclusion, and we also derive an affirmative conclusion when\none premise is negative. This objection is seen to be nugatory when the\ndisjunctive is reduced to the categorical form. The reduction involves\nthe two steps of first changing the disjunctive to the hypothetical\nform and then to the categorical form. The following illustrations will\nsuffice to make the matter clear:\n\n (1) _Disjunctive._\n A is either B or C\n A is B\n \u2234 A is not C\n\n _Hypothetical._\n If A is B, then A is not C\n A is B\n \u2234 A is not C\n\n _Categorical._\n The case of A being B is the case of A not being C\n In this case A is B\n \u2234 A is not C\n\n (2) _Disjunctive._\n The defendant is either guilty or innocent;\n He is not innocent,\n \u2234 He is guilty.\n\n _Hypothetical._\n If the defendant is guilty, then he is not innocent;\n But he is guilty,\n \u2234 He is not innocent.\n\n _Categorical._\n The case of the defendant being guilty is the case of the\n defendant not being innocent,\n In this case the defendant is guilty,\n \u2234 In this case the defendant is not innocent.\n\n\n=13. THE DILEMMA.=\n\nThe majority of us are acquainted with the dilemma as related to the\nactivities of life. One is in a dilemma when there are two courses open\nto him but neither is particularly enticing. One is placed in a dilemma\nwhen he is forced to choose the lesser of two evils. For example, one\nmay, without the proper equipment, be overtaken by a heavy rain storm;\nhe seeks the shelter of a wayside shed; the rain continues so that\nhe is forced either to miss his train, or to endure the discomfort of\na drenching. Thus the logical dilemma limits one to a choice between\nalternatives, either one of which might well be avoided.\n\n_Definition._\n\n_The dilemma is a syllogism in which the major premise consists of\ntwo or more hypothetical propositions, while the minor premise is a\ndisjunctive proposition._\n\nIt being a combination of hypothetical and disjunctive propositions\nthe dilemma is sometimes appropriately referred to as the\n\u201chypothetico-disjunctive\u201d argument. The order of the premises is\nindifferent, yet it seems to be more natural to use the hypothetical\nfirst; thus the definition.\n\n\n=14. FOUR FORMS.=\n\nThe four forms of the dilemma are the _simple constructive_, the\n_simple destructive_, the _complex constructive_, and the _complex\ndestructive_. The following symbolizations illustrate these four kinds:\n\n_Simple Constructive Dilemma._\n\n If A is B, W is X; and if C is D, W is X,\n But either A is B or C is D,\n Hence W is X.\n\nThis is termed a simple dilemma because there is but _one_\nconsequent; namely, W is X. The conclusion being affirmative makes it\n_constructive_.\n\n_Simple Destructive Dilemma._\n\n If A is B, W is X; and if A is B, Y is Z,\n But either W is not X or Y is not Z,\n Hence A is not B.\n\nThis is simple because there is but one antecedent, A is B, and\ndestructive because the conclusion is _negative_.\n\n_Complex Constructive Dilemma._\n\n If A is B, W is X; and if C is D, Y is Z,\n But either A is B or C is D,\n Hence either W is X or Y is Z.\n\nThis is complex because there are two antecedents and two consequents;\nconstructive, inasmuch as the conclusion is affirmative.\n\n_Complex Destructive Dilemma._\n\n If A is B, W is X; and if C is D, Y is Z,\n But either W is not X or Y is not Z,\n Hence either A is not B or C is not D.\n\nThis is complex because there are two antecedents as well as two\nconsequents, and destructive because the conclusion is negative.\nBriefly: (1) A simple dilemma is one where either the antecedent or\nconsequent is repeated; whereas if neither is repeated the dilemma is\ncomplex. (2) A constructive dilemma contains an affirmative conclusion;\nwhile a destructive dilemma uses a negative conclusion. (3) A simple\ndilemma has as its conclusion a categorical proposition; whereas the\nconclusion of a complex dilemma is always disjunctive.\n\nIf the number of antecedents and consequents be increased, a trilemma,\ntetralemma, etc., may result.\n\n\n ILLUSTRATION\u2015\u2015_Trilemma._\n\n If A is B, W is X; and if C is D, Y is Z; and if E is F, U is V,\n But either A is B, or C is D, or E is F,\n Hence either W is X, or Y is Z, or U is V.\n\nSome authorities define a dilemma as a syllogism in which the\n\u201cmajor-hypothetical\u201d has _more than one antecedent_ while the \u201cminor\u201d\nmust be disjunctive. This viewpoint necessarily _excludes_ the second\nform or the simple destructive dilemma. The weight of authority,\nhowever, appears to favor the classification here recommended.\n\n\n=15. THE ONE RULE INVOLVED IN DILEMMATIC ARGUMENTS.=\n\nSince the major premise of the dilemma is hypothetical, the rule for\ntesting such would of necessity be the hypothetical rule; namely, \u201cThe\nminor premise must either affirm the antecedent or deny the consequent.\u201d\nAs this rule and the fallacies incident to it have been treated in\ndetail, further discussion is unnecessary.\n\n\n=16. ILLUSTRATIVE EXERCISE TESTING DISJUNCTIVE AND DILEMMATIC\n ARGUMENTS.=\n\n (1) If the arithmetic contains useful facts, it will help to good\n citizenship; and if it trains the powers of reason, it will\n help to good citizenship,\n But the arithmetic either contains useful facts or trains the\n powers of reason,\n Hence it will help to good citizenship.\n\nThis is a simple constructive dilemma in which the minor premise\naffirms the antecedents. The argument is, therefore, valid since it\nconforms to the rules of the hypothetical syllogism. The fact that the\nminor premise may not be a perfect disjunctive does not invalidate the\nconclusion, inasmuch as it is perfectly obvious that if the arithmetic\nfulfilled both the requirements of the antecedents, the conclusion\nwould still obtain. It may, therefore, be inferred that if the dilemma\nconforms to the rules of the hypothetical argument, it is valid, though\nthe disjunctive proposition which it contains may not be strictly\nlogical.\n\n(2) A man is either temperate or intemperate; and, as I have seen you\ndrunk several times, I conclude that you are intemperate.\n\n_Arranged logically._\n\n A man is either temperate or intemperate,\n You are not temperate,\n \u2234 You are intemperate.\n\nIt would seem that the major premise is a logical disjunctive, since\ntemperate and intemperate indicate that the alternatives are _mutually\nexclusive_ and the _enumeration complete_. And since the minor premise\ndenies one alternative while the conclusion affirms the other, we may\ninfer that the argument is valid.\n\n(3) If a man is honest, he will either pay his debts or explain; but\nthis fellow paid no heed to the repeated notifications.\n\n_Arranged logically._\n\n If a man is honest, he will pay his debts; and if he is honest, he\n will explain in case he cannot pay,\n This man neither paid his debt, nor explained,\n \u2234 This man is not honest.\n\nThis is a simple destructive dilemma, and since the minor premise\ndenies the consequents it is valid.\n\n(4) A voter must either favor protection or free trade; and since you\ndo not favor protection, you must be a free trader. The disjunctive is\nnot logical as one might believe in universal reciprocity. The argument\nis, therefore, invalid. _Why?_\n\n(5) If a man were loyal, he would not be unduly critical; and if he\nwere wise, he would not be too loquacious; but I find this clerk has\nbeen both unduly critical and too loquacious; hence I consider that he\nhas been not only unwise but strikingly disloyal.\n\nThis complex dilemma is valid since the minor premise denies the two\nconsequents.\n\n\n=17. ORDINARY EXPERIENCES RELATED TO THE DISJUNCTIVE PROPOSITION AND\n HYPOTHETICAL ARGUMENT.=\n\n(1) One desires to take a certain trip which involves various routes;\ninformation from time tables reveals the fact that there are three\nroutes A, B, and C. Concerning the conditions of the journey the most\nimportant factor is the _matter of comfort_. Further investigation\nmakes evident that route B will be the most comfortable one, and\nconsequently is the route selected. Putting this ordinary experience\nin argumentative form gives the following:\n\n The route is to be either A, or B, or C;\n I will take route A; if it is the most comfortable; (co-extensive)\n A is not the most comfortable route,\n Hence I will not take route A.\n If B is the most comfortable route, I will take it;\n B is the most comfortable route,\n Hence I will take route B.\n\n(2) The symptoms suggest either malarial or typhoid fever; the\nphysician is undecided till a blood test makes evident that it is not\ntyphoid.\n\n_Considered argumentatively._\n\n This disease is either malarial or typhoid fever;\n If it is typhoid, the blood will reveal certain evidences;\n But the blood does not reveal these evidences,\n Hence the disease is not typhoid.\n\n(3) The natural bent of the youth suggests the profession of either the\nministry or teaching. He finally decides to follow the one in which he\ncan best serve his fellows. This, after mature deliberation, appears to\nhim to be the work of the teacher. Thrown into the form of an argument\nthe following results:\n\n I am best fitted for either the pulpit or the schoolroom;\n If the schoolroom furnishes the richest field for helping my fellows,\n I will choose that work;\n The schoolroom _does_ appear to furnish such a field,\n Hence I will choose the work of the teacher.\n\nIt would appear from these ordinary experiences that frequently we\nare brought face to face with a choice of alternatives which are not\nunattractive, as in the case of the dilemma. Moreover, some condition\nsuggests itself which, if proved or disproved, will lead to a choice\nof _one_ of these alternatives. Such circumstances when thrown into\nthe form of an argument present a _disjunctive proposition_ followed\nby a _hypothetical argument_. To put it differently: Often in our daily\naffairs a most prominent limiting condition induces us to select one\nout of several alternatives. These alternatives are _not_ dilemmatic\nin nature.\n\n\n=18. OUTLINE.=\n\n HYPOTHETICAL ARGUMENTS, AND DISJUNCTIVE ARGUMENTS INCLUDING THE\n DILEMMA.\n\n (1) Three kinds of arguments\n Categorical, hypothetical, disjunctive.\n\n (2) Hypothetical arguments\n Defined, illustrated.\n\n (3) Antecedent and consequent.\n How determined, illustrations.\n\n (4) Two kinds of hypothetical arguments\n Constructive, destructive, illustrations.\n\n (5) Rule and two fallacies of the hypothetical argument.\n Illustrations and application of rules.\n Fallacy of denying antecedent.\n Fallacy of affirming consequent.\n Co-extensive hypotheticals.\n\n (6) Hypothetical arguments reduced to the categorical form.\n Rule, illustrations.\n Hypothetical and categorical arguments compared.\n\n (7) Illustrative exercises testing hypothetical arguments of all\n kinds.\n\n (8) Disjunctive arguments.\n Defined, illustrated.\n\n (9) Two kinds of disjunctive arguments.\n By \u201caffirming denies,\u201d by \u201cdenying affirms.\u201d Illustration.\n\n (10) First rule.\n Stated, illustrated.\n\n (11) Second rule\n Stated, illustrated.\n\n (12) Reduction of disjunctive argument\n Two steps.\n\n (13) The dilemma\n Definition.\n\n (14) Four forms of dilemmatic arguments\n Simple constructive, simple destructive,\n Complex constructive, complex destructive.\n Illustrations.\n\n (15) The rule.\n\n (16) Illustrative exercises testing disjunctive and dilemmatic\n arguments.\n\n (17) Ordinary experiences related to the disjunctive proposition and\n hypothetical argument.\n\n\n=19. SUMMARY.=\n\n(1) Just as there are three kinds of propositions so there are three\nkinds of arguments; namely, categorical, hypothetical, disjunctive.\n\n(2) Categorical syllogistic arguments are those in which all of the\npropositions are categorical.\n\nHypothetical syllogistic arguments are those in which the major premise\nis hypothetical.\n\nIn contradistinction to disjunctives, hypothetical arguments may be\nreferred to as \u201c_conjunctive_\u201d.\n\n(3) The hypothetical proposition is composed of antecedent and\nconsequent; the former being the limiting condition; while the latter\nis the direct assertion. As the words indicate the antecedent usually\nprecedes the consequent. The signs of the antecedent are \u201cif,\u201d \u201cthough,\u201d\n\u201cunless,\u201d \u201csuppose,\u201d \u201cgranted that,\u201d \u201cwhen,\u201d etc.\n\n(4) The two kinds of hypothetical syllogisms are the constructive and\ndestructive; the former is involved when the minor premise affirms the\nantecedent; the latter when the minor premise denies the consequent.\nThese two kinds are sometimes referred to as \u201c_modus ponens_\u201d and\n\u201c_modus tollens_\u201d respectively.\n\n(5) Out of the four possible hypothetical syllogisms only _two_ are\nvalid as investigation proves this rule: _The minor premise must affirm\nthe antecedent or deny the consequent._ In the case of the hypothetical\nproposition being _co-extensive_, the rule does not apply.\n\n(6) Hypothetical arguments may be reduced to the categorical by\ncontracting the antecedent of the hypothetical proposition to form\nthe subject-term, and by contracting the consequent of the hypothetical\nproposition to form the predicate-term of the major premise of the\ncategorical syllogism. If it is necessary, supply a new minor term.\n\nDenying the antecedent is a matter of illicit major; whereas affirming\nthe consequent is equivalent to undistributed middle.\n\n(7) Hypothetical arguments may be tested by following this outline:\n\n (1) Arrange logically.\n (2) Determine antecedent and consequent.\n (3) Apply hypothetical rule.\n (4) Reduce to categorical form.\n (5) Apply categorical rules.\n\n(8) A disjunctive syllogism is one in which the major premise is a\ndisjunctive proposition.\n\n(9) The two kinds of disjunctives are those which \u201c_by affirming deny_\u201d\nand those which \u201c_by denying affirm_.\u201d\n\n(10) In testing disjunctive arguments there are _two_ rules involved:\n_First_, \u201cThe major premise must assert a _logical disjunction_.\u201d This\nnecessitates the two requisites \u201c_the alternatives must be mutually\nexclusive_\u201d and the \u201c_enumeration must be complete_.\u201d The two opinions\nrelative to the nature of an alternative assertion are, first, if one\nis false, the other must be true and vice versa; and second, if one\nis false, the other must be true, but _both_ may be true. The first is\nadopted in this discussion.\n\n_Second._ The second rule involved is \u201cWhen the minor premise affirms\nor denies _one_ of the alternatives of a logical disjunctive the\nconclusion must deny or affirm all of the others.\u201d\n\n(11) Subjecting the disjunctive arguments to the categorical test\ngives evidence to the close relation existing between the two forms.\nA logical disjunctive proves to be logical when reduced to the\ncategorical. The reduction entails the two steps, first, reduce to\nthe hypothetical; second, reduce to the categorical.\n\n(12) The logical meaning of the dilemma is suggested by the popular\nconception. One is said to be in a dilemma when two courses are open\nto him, neither of which is specially attractive.\n\nA logical dilemma presents two alternatives either one of which might\nwell be avoided.\n\nThe major premise of the dilemma is hypothetical; while the minor is\ndisjunctive.\n\n(13) The four forms of the dilemma are the simple constructive,\nthe simple destructive, the complex constructive and the complex\ndestructive.\n\n(14) The dilemma is subject to the hypothetical rule which is, \u201cThe\nminor premise must either affirm the antecedent or deny the consequent.\u201d\n\n(15) The minor premise need not be a logical disjunctive provided the\nmajor conforms to the hypothetical rule.\n\n(16) Frequently when ordinary experiences are reduced to augmentative\nform they present a disjunctive proposition followed by a hypothetical\nargument.\n\n\n=20. REVIEW QUESTIONS.=\n\n (1) Relate the three kinds of arguments to the three general kinds\n of propositions.\n\n (2) Define and illustrate the hypothetical argument.\n\n (3) Explain the term conjunctive with reference to hypothetical\n arguments.\n\n (4) Explain and illustrate antecedent and consequent in hypothetical\n arguments.\n\n (5) Select from the following the antecedent and consequent:\n\n (1) \u201cI usually succeed when I try.\u201d\n (2) \u201cI will not undertake it unless you guarantee half of the\n sum needed.\u201d\n (3) \u201cThough I speak with the tongues of men and of angels,\n and have not charity, I am become as sounding brass or a\n tinkling cymbal.\u201d\n\n (6) Illustrate the two kinds of hypothetical syllogisms which are\n valid.\n\n (7) State and explain the rule to which hypothetical arguments must\n conform.\n\n (8) State and exemplify the one exception to the hypothetical rule.\n\n (9) Explain how hypothetical arguments may be reduced to the\n categorical form. Illustrate.\n\n (10) Show by illustration that denying the antecedent is equivalent\n to _illicit major_, while affirming the consequent is equivalent\n to _undistributed middle_.\n\n (11) Reduce to the categorical form and test:\n\n \u201cIf Napoleon had possessed more of the spirit of Washington, he\n would have been less famous but a better man than he was; but\n he did not possess the spirit of the \u2018Father of His Country.\u2019\u201d\n\n (12) Test according to outline the following hypothetical arguments:\n\n (1) \u201cIf it be a good thing to have faith, then certainly he who\n believes in the bible of a pagan has faith and must have a\n good thing.\u201d\n (2) \u201cIf a 10-inch charge burst inside of a tank, there would\n be nothing left of the tank. It would be blown into small\n pieces.\u201d\n (3) \u201cIf the plate found had been originally on the outside of\n the ship, I should have judged that there must be green\n paint on it, but I could not find green paint on that part\n of the ship.\u201d\n (4) \u201cIf I mistake not, you are the man who did not pay me for\n that pair of shoes. I am sure that you are the man as I\n never forget a face.\u201d\n (5) \u201cIf the maxim \u2018Early to bed and early to rise makes one\n healthy, wealthy and wise\u2019 were true, I would have been a\n millionaire long ago.\u201d\n\n (13) Define and illustrate a disjunctive argument.\n\n (14) Exemplify the two kinds of disjunctive arguments.\n\n (15) What is meant by a logical disjunction?\n\n (16) \u201cThe alternatives must be mutually exclusive.\u201d Explain this,\n illustrating fully.\n\n (17) Cite cases where the enumeration is not complete.\n\n (18) State in complete form both of the rules to which all disjunctive\n arguments must conform.\n\n (19) Show by illustration how the disjunctive syllogism may be reduced\n to the categorical.\n\n (20) Define and illustrate the dilemma.\n\n (21) Give examples, using symbols, of the four dilemmatic forms.\n Explain why these forms are so named.\n\n (22) Why does the hypothetical rule apply to the dilemmatic syllogism?\n\n (23) Test the validity of the following: Give reasons.\n\n (1) \u201cIf a substance is solid it possesses elasticity and\n so also it does if it be a liquid or gaseous; but all\n substances are either solid, liquid or gaseous; therefore,\n all substances possess elasticity.\u201d\n (2) \u201cIf men were prudent, they would act morally for their own\n good; if benevolent, for the good of others. But many men\n will not act morally, either for their own good or that of\n others; such men, therefore, are not prudent or benevolent.\u201d\n (3) \u201cIf the majority of those who use public houses are\n prepared to close them, legislation is unnecessary; but if\n they are not prepared for such a measure, then to force it\n upon them by outside pressure is both dangerous and unjust.\u201d\n (4) \u201cThe man is either a liar or a fool and in either case he\n is beneath my attention.\u201d\n (5) \u201cEither he is sincere or else he is the most astute\n impostor the world has ever produced; for me I prefer to\n think him sincere.\u201d\n\n (24) Explain the relation that many experiences appear to bear toward\n an argument introduced by a disjunctive proposition and followed\n by a hypothetical syllogism. Illustrate.\n\n\n=21. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) May both premises of a hypothetical argument be hypothetical\n propositions? Explain. See Fowler p. 115.\n\n (2) Which of the two is valid? Explain.\n\n (1) If A is B, C is D\n If A is B, E is F\n \u2234 If C is D, E is F\n\n (2) If A is B, C is D\n If C is D, E is F\n \u2234 If A is B, E is F\n\n (3) Show by circles that two of the possible four hypothetical\n arguments are invalid.\n\n (4) What categorical rules does the hypothetical argument seem to\n violate? Explain.\n\n (5) Originate a hypothetical syllogism whose antecedent and\n consequent are both negative. Test its validity.\n\n (6) Originate a co-extensive hypothetical argument and show that four\n valid syllogisms may be derived from it.\n\n (7) Explain by word and illustration the two meanings which may be\n attached to \u201ceither-or.\u201d\n\n (8) If we accepted the opinion that both alternates of a disjunctive\n may be true, which kind of disjunctive argument would it\n invalidate?\n\n (9) In a logical disjunction what law of thought is involved?\n Explain.\n\n (10) Why do the laws of the disjunctive seem to contradict the\n categorical rules? Explain fully.\n\n (11) Show by drawing on common experience that a logical dilemma is\n closely related to the popular conception of dilemma.\n\n (12) Illustrate by symbols and then place in good English a pentalemma.\n\n (13) State a definition of a dilemma which excludes the simple\n destructive form.\n\n (14) Give a common experience which, when thrown into argumentative\n form, results in a disjunctive proposition followed by a\n hypothetical syllogism. Coin a name for such a combination.\n\n\n\n\n CHAPTER 16.\n\n THE LOGICAL FALLACIES OF DEDUCTIVE REASONING.\n\n\n=1. A NEGATIVE ASPECT.=\n\nIt has been remarked that \u201cLogic as a science makes known the laws\nand forms of thought and as an art suggests conditions which must\nbe fulfilled to think rightly.\u201d In recent chapters we have discussed\nthe second aspect of the definition; in these we have attempted to\nanswer the question, \u201cWhat _rules_ must be followed in order to reason\ncorrectly?\u201d We are now ready to treat the same aspect from a negative\npoint of view namely, what _errors_ must be avoided in order to reason\ncorrectly? What are the fallacies which we must strive to avoid in our\n_own_ thinking, and attempt to correct in the thinking of _others_?\n\n\n=2. PARALOGISM AND SOPHISM.=\n\n\u201cFallacy\u201d comes from the Latin _fallacia_, meaning deceptive or\nerroneous, and therefore _a fallacy in logic is any error in reasoning\nwhich has an appearance of correctness_. If the writer or speaker is\n_himself_ deceived by the fallacy, then such is called a _Paralogism_;\nbut if the fallacy is committed by him for the expressed purpose of\ndeceiving others, then such becomes a _Sophism_. During the time of the\nSchoolmen the Sophism was in such high repute that it required even a\nSocrates to puncture this ignominious bubble of vain trickery. In fact,\nSocrates, the greatest of all pagan educators, _led_ the crusade which\nhas relegated to the \u201clogical dust bin\u201d the notion that _skill in the\nart of framing sophisms is a scholarly accomplishment_. Many believe\nmodern sophistry to be the chief social and commercial evil of the\nday, and to Socrates must be given the credit for teaching us to look\nupon those who would practice sophism with righteous indignation and\npronounced disgust. However, paralogism and not sophism is the more\nlegitimate field for the student of logic; his problem being, \u201cWhat\nare the common errors which I, as a writer and speaker, must strive to\navoid?\u201d\n\n\n=3. A DIVISION OF THE DEDUCTIVE FALLACIES.=\n\nThe mistakes of induction will occupy our attention in a later\nchapter. We are now concerned with the fallacies of deduction. Any\nclassification or division of the deductive fallacies must of necessity\nbe faulty. Even the labors of Aristotle in this regard are now\npronounced crude and unsatisfactory. This is due to the divergence of\nopinion as to the signification of some of the fallacies, as well as\nto the fact that no division is free from the fault of an _overlapping_\nof the species. As a result of this lack of unanimity in definition and\nlack of ability in making the species mutually exclusive, any division\nof the deductive fallacies must be more or less illogical.\n\nAristotle divides the fallacies of deduction into two groups:\n(1) Fallacies _in dictione_, or formal fallacies. (2) Fallacies _extra\ndictionem_, or material fallacies. This division has received universal\napproval and though many distinctions made by him have been abandoned,\nyet most logicians retain his phraseology. Since many of the technical\nterms which Aristotle used have lived through the generations under\nthe conventional meaning which he assigned to them, it becomes less\nconfusing to adhere as closely as possible to these terms. Therefore,\nin the attending division only those changes have been made which\nprogress and experience have forced upon us. What remains of this\nchapter will be devoted to explaining these fallacies as they appear\nin this division. For the sake of clearness and definiteness it is\nstrongly recommended that the student study the outline extensively\nenough to be able to reproduce it.\n\n _Fallacies._\n\n _Formal_ (_In dictione_)\n\n { 1. Opposition\n 1. Immediate { 2. Obversion\n inference { 3. Conversion\n { 4. Contraversion\n\n { 5. Four terms\n { 6. Undistributed middle\n 2. Categorical { 7. Illicit major\n arguments { 8. Illicit minor\n { 9. Negative premises\n { 10. Particular premises\n\n 3. Hypothetical { 11. Denying the antecedent\n arguments { 12. Affirming the consequent\n\n 4. Disjunctive { 13. Illogical disjunction\n arguments {\n\n _Material_ (_In dictionem_)\n\n { 1. Ambiguous middle\n { 2. Amphibology\n 1. In Language { 3. Accent\n Equivocation { 4. Composition\n { 5. Division\n { 6. Figure of speech\n\n { 1. Accident\n { 2. Converse accident\n 2. In Thought { 3. Irrelevant conclusion\n Assumption { 4. Non sequitur\n { 5. False cause\n { 6. Complex question\n { 7. Begging the question\n\n\n=4. GENERAL DIVISIONS EXPLAINED.=\n\nThe _formal fallacies_ are those which concern the _form_ of the\nargument rather than the meaning. These fallacies arise from an\nimproper use of words as arbitrary signs of thought, not from any\ninconsistency in the thought itself. To commit a formal fallacy we\nmust violate one of the specific rules of logic. For this reason the\nformal fallacies are easier of comprehension. Moreover, because of this\ndefiniteness logicians are better able to come to some agreement as to\ntheir content and import. Classing the fallacies of immediate inference\nas formal is somewhat of an innovation; but since they occur because of\nthe breaking of certain definite rules, and since immediate inference\nis a matter of changing the form without altering the meaning, we\nbelieve there is some justification for this position. Some would class\n\u201cimmediate inference\u201d fallacies with the material fallacies of language.\n\nThe _material fallacies_ are fallacies of meaning and not of form. They\nare those arising from inconsistency in thought, and from imperfect\nways of interpreting this thought as it appears in language. No very\nspecific rules of logic are violated by them and for this reason there\nare those who would entirely eliminate the material fallacies from the\nfield of logic. But since _thought_ is even more subtle than _form_ in\nits deceitful machinations, we believe that the material fallacy calls\nfor special attention on the part of the logician.\n\nMaterial fallacies are divided into two kinds. First, those which have\nreference to wrong thinking, or fallacies _in thought_; and, second,\nthose which are due mainly to an incorrect interpretation of words,\nor fallacies _in language_. The former result from inconsistency and\nunreasonableness in thought, whereas the latter come from lack of\nprecision in expression.\n\n\n=5. FALLACIES OF IMMEDIATE INFERENCE.=\n\nFallacies of immediate inference arise from some violation of the rules\nwhich this topic enunciates.\n\n(1) _Opposition._\n\nAmong other statements opposition posits these two: (1) When the\nparticular is true its opposing universal is indeterminate; (2) A\nuniversal negative does not necessarily contradict a universal\naffirmative.\n\nThese signify that neither an A nor an E must be assumed to be true\nwhen the corresponding I or O is true, and that E may not always\ncontradict A, nor O contradict I.\n\n\n ILLUSTRATIONS OF FALLACIES OF OPPOSITION.\n\n(1) Since some men are wise, then I may conclude that all men are wise.\n(2) I have contradicted his statement \u201call men are honest\u201d by proving\nthat _no men are honest_.\n\nThere is little difference between fallacies like (1) and fallacies of\nconverse accident. Concerning illustration (2), _both_ statements are\nfalse; but to contradict we know that if one is false, the other must\nbe true.\n\n(2) _Obversion._\n\n\u201cTwo negatives are equivalent to one affirmative,\u201d is the principle\nunderlying obversion. The most common fallacy in obversion springs from\nusing one negative instead of two.\n\n\n ILLUSTRATIONS OF FALLACIOUS OBVERSION.\n\n(a) Original: Some men are not wise. Obverse: (incorrect) Some men are\nwise.\n\n(b) Original: All true teachers are just. Obverse: (incorrect) All true\nteachers are not just.\n\n(3) _Conversion._\n\nConversion involves the interchanging of the subject and predicate\nof a proposition without affecting the distribution; in consequence\nthe usual fallacy incident to this interchange is _distributing_ an\nundistributed term.\n\n\n ILLUSTRATIONS OF FALLACY OF CONVERSION.\n\n(a) Original: All fixed stars are heavenly bodies. Converted:\n(incorrectly) All heavenly bodies are fixed stars.\n\n(b) Original: Some men are not wise. Converted: (incorrectly) Some wise\nbeings are not men.\n\n(4) _Contraversion._\n\nAs this process involves the two steps of obversion and conversion,\nfallacies appertaining to contraversion would relate to these two steps.\n\n\n ILLUSTRATIONS OF FALLACIES OF CONTRAVERSION.\n\n(a) Original: No honest man fails to pay his debts. Contraverted:\n(incorrectly) Some who do not pay their debts are honest men.\n\n(b) Original: Some animals are quadrupeds. Contraverted: (incorrectly)\nSome not-quadrupeds are not animals.\n\nThe formal fallacies of categorical, hypothetical, and disjunctive\narguments have received detailed treatment in chapters 11, 14 and 15;\nwe may, therefore, devote our attention to the material fallacies\nwithout further delay.\n\n\n=6. FALLACIES OF LANGUAGE. (Equivocation.)=\n\nThese are the fallacies of _double meaning_. It is known that an\nequivocal term is one which permits two or more interpretations;\nsimilarly a _proposition_ which admits of two or more interpretations\nmay be denominated equivocal. Thus the term equivocation has come to\nstand for all errors in language resulting from a possibility of more\nthan one interpretation. This justifies the position of referring to\nall of the six fallacies in language as fallacies also of equivocation.\n\n(1) _Ambiguous middle._\n\nAmbiguous middle explains itself. _It is the fallacy of giving to the\nmiddle term a double meaning._ In form the argument may contain but\nthree terms, yet in meaning there are in reality four terms. For this\nreason ambiguous middle and the fallacy of four terms appear to be\nabout one and the same thing; but in this treatment we shall regard\nthem as mutually exclusive, and this is the distinction:\n\nInvalid arguments of \u201cambiguous middle\u201d have only _three_ terms in form\nbut _four_ terms in meaning. This signifies that the middle term though\nidentical in _form_ is given a _double meaning_.\n\nInvalid arguments of \u201cfour terms\u201d always have four terms in both _form_\nand _meaning_; they are \u201clogical quadrupeds\u201d in every sense of the word.\n\n\n ILLUSTRATIONS.\n\n_Ambiguous middle._\n\n (a) \u201c_Necessity_ is the mother of invention,\u201d\n Bread is a _necessity_,\n \u2234 Bread is the mother of invention.\n\n (b) \u201c_Nothing is_ better than wisdom,\u201d\n Dry bread is better than _nothing_,\n \u2234 Dry bread is better than wisdom.\n\n (c) A _church_ is a force for good in any community,\n A slate roof is good for a _church_,\n \u2234 A slate roof is a force for good in any community.\n\n_Fallacies of four terms._\n\n (a) All _true teachers_ are just,\n John Doe is an _educator_,\n \u2234 John Doe is just.\n\n (b) _Milk_ is nourishing,\n This substance is a _white fluid_,\n \u2234 This substance is nourishing.\n\n (c) _Thieves_ should be imprisoned,\n This man _has taken what does not belong to him_,\n \u2234 This man should be imprisoned.\n\nIn the \u201cfour-term\u201d fallacies, observe that the four terms occur in\nthe _premises_. When a fourth term is introduced in the conclusion,\nthe material fallacy of _non sequitur_ has been committed.\n\n(2) _Amphibology_ (_or amphiboly_).\n\nAmphibology is a fallacy resulting from an ambiguous proposition\nrather than from the ambiguity of any particular term. _The fallacy of\namphibology is committed when the spoken or written proposition conveys\nmore than one meaning._ The ancient oracles indulged in this sort of\nfallacy, the reason for such indulgence being obvious; the oracles\nwere not too positive as to the outcome of their prognostications, and\ntherefore were especially careful to cover _every emergency_.\n\nA careless use of relative clauses and prepositional phrases often\nresults in the fallacy of amphibology.\n\n\n ILLUSTRATIONS OF THE FALLACY OF AMPHIBOLOGY.\n\n (a) \u201cYou the enemy will slay.\u201d\n\n (b) \u201cThe Duke yet lives that Henry shall depose.\u201d\n\n (c) \u201cWanted a piano by a young lady made of mahogany.\u201d\n\n (d) \u201cYou your father will punish.\u201d\n\n(3) _Accent._\n\n_This fallacy springs from placing undue emphasis on some word or group\nof words._ Naturally such accentuation may convey a meaning entirely\nforeign to the author\u2019s intent. Newspapers are guilty of this fallacy\nwhen they select a few words from a speech and use them as headlines\nwithout further explanation. A politician may quote a sentence uttered\nby an opponent and fail to relate it to what preceded or followed.\nA cartoonist may arouse the prejudice of public opinion by giving\nridiculous emphasis to some idiosyncracy possessed by the subject of\nhis attack.\n\n\n ILLUSTRATIONS OF FALLACIES OF ACCENT.\n\n (a) \u201cThou shalt not bear false witness against thy _neighbor_.\u201d\n\n By giving undue emphasis to _neighbor_, the notion is clearly\n conveyed that one may bear false witness against all who are\n _not_ neighbors.\n\n (b) \u201cYou must not crib when taking _my_ examinations.\u201d\n\n (c) _What the \u201cSpellbinder\u201d said._\n\n \u201cI may say, as a side remark, that the labor unions are guilty of\n developing a nation of shirks, when they prohibit a phenomenally\n efficient workman from doing his best.\u201d \u201cI do not wish to be\n misunderstood in this.\u201d \u201cI believe in labor unions but in this\n particular they are dead wrong.\u201d\n\n _What the newspaper reported._\n\n (Headline) \u201cThe Labor Union Scored as a Training School for\n Shirks.\u201d \u201c\u2015\u2015\u2015\u2015 said in his speech in \u2015\u2015\u2015\u2015 Hall that the Union was\n responsible for the development of a nation of shirks.\u201d \u201cA good\n man,\u201d said he, \u201cis not permitted to do his best work.\u201d\n\n(4) _Composition._\n\n_The fallacy of composition is committed when it is assumed that what\nis true distributively is likewise true collectively._ A term is used\nin a distributive sense when it is applied to _each individual_ of\nthe class; whereas a term is used in a collective sense when it is\napplied to the class considered as _one whole_. \u201cAll\u201d meaning _each\none considered separately_ and \u201call\u201d meaning _the whole_ furnishes a\nfrequent pitfall for this fallacy.\n\n\n ILLUSTRATIONS OF THE FALLACY OF COMPOSITION.\n\n (a) \u201cEvery member of the team is a star player; hence I expect that\n the entire aggregation will be a winner.\u201d\n\n (b) \u201cAll the men of the jury are fair minded; therefore we have good\n reason for supposing that the jury\u2019s verdict will be in accord\n with the rules of justice.\u201d\n\n (c) \u201cThirteen and twenty-three are odd numbers; thirty-six is equal\n to thirteen and twenty-three; hence thirty-six is an odd number.\u201d\n\n (d) \u201cAll the angles of a triangle are less than two right angles;\n hence the angles X, Y and Z are less than two right angles.\u201d\n\n (e) In governmental affairs the assumption, that a law which benefits\n one section will benefit all, is a fallacy of composition.\n\n(5) _Division._\n\n_The fallacy of division is committed when it is assumed that what is\ntrue collectively is true distributively._ Division is the converse of\ncomposition. Composition is a fallacious procedure from a distributive\nto a collective use; while division is a fallacious procedure from\na collective to a distributive use. The fallacy of division may\nbe illustrated by giving the converse of the illustrations under\ncomposition:\n\n (a) \u201cThe team is a star playing team; and since Smith is the \u2018first\n baseman\u2019 of the team, he must be a star player.\u201d\n\n (b) \u201cThe jury rendered a just decision; hence the foreman is a fair\n minded man.\u201d\n\n (c) Thirty-seven is an odd number,\n Nine and twenty-eight are thirty-seven,\n \u2234 Nine and twenty-eight are odd numbers.\n\n (d) All the angles of a triangle are equal to two right angles,\n A is an angle of a triangle,\n \u2234 A is equal to two right angles.\n\n(6) _Figure of Speech._\n\n_This fallacy results from assuming that words of the same root have\nthe same meaning._ Since the same root-word may be used as a noun,\nverb, adjective, etc., it does not follow that in these various forms\nit retains a common meaning. \u201cAddress\u201d as a noun and \u201caddress\u201d as a\nverb convey two distinct meanings.\n\nThe following are examples of this fallacy:\n\n (a) No _designing_ person should be trusted,\n This architect is a _designer_,\n \u2234 This architect should not be trusted.\n\n (b) Justifiable _investigation_ is wise,\n This man is a just _investigator_,\n \u2234 This man is wise.\n\nThese fallacies are not classed as those of \u201cfour terms\u201d because two\nterms so _closely resemble_ each other in _form_, and yet they are\nnot fallacies of ambiguous middle; since the middle terms are _not\nidentical_ in form.\n\n\n=7. FALLACIES IN THOUGHT.=\n\nThe fallacies in thought arise through a tendency to assume as true\nthat which demands further proof. Any one who is more anxious to\nbe _right_ than to _win_ will make sure that nothing has been taken\nfor granted which should receive further investigation, or that no\ntruth has been given a presumptuous twist in order to make it fit the\nparticular case under discussion. Because these errors in thought may\nbe attributed chiefly to undue assumptions, we may denominate them as\nthe fallacies of assumption.\n\n(1) _Accident._\n\n_The fallacy of accident occurs when one reasons from a general truth\nto an accidental case._ Doctrinaires and theoretic enthusiasts are\npartial to this fallacy. It is so easy to lay down a general formula or\nremedy and then attempt to apply it to every accidental circumstance.\nGrandmother with her catnip tea and mustard plaster, however we may\ncherish the memory of the dear old soul, was nevertheless guilty of\nthe fallacy of accident. Applying maxims and proverbs to particular\ninstances is still another way of committing the fallacy.\n\n\n EXAMPLES OF FALLACIES OF ACCIDENT.\n\n (a) \u201cHonesty is the best policy,\u201d thinks the physician as he reveals\n the cold, hard truth to his patient and thus shortens the\n patient\u2019s life.\n\n (b) Spirituous liquor in excess acts as a poison, and therefore\n should not be used to resuscitate an extreme case.\n\n (c) \u201cWhat is bought in the market is eaten; raw meat is bought in the\n market; therefore it is eaten.\u201d\n\n (d) \u201cEarly to bed and early to rise makes one healthy, wealthy and\n wise.\u201d I shall practice this for ten years and by that time hope\n to be healthy, wealthy and wise.\n\n (e) John has earned the enviable (?) reputation of being the \u201cworst\n boy in school,\u201d hence he is going to be the worst boy in \u201cmy\n grade.\u201d\n\n (f) Mary is an inveterate whisperer; and since I know that some one\n is whispering, I am sure that that some one is Mary.\n\n (g) Being a convict, he is not to be trusted.\n\n(2) _Converse Accident._\n\n_As the title implies this is the fallacy of reasoning from an\naccidental case to a general truth._ Illustrations:\n\n (a) \u201cJohn has been a bad boy to-day; and hence he is going to make\n trouble during the entire term.\u201d\n\n (b) \u201cThis food is good for hens; and hence it is good for all\n domestic fowls.\u201d\n\n (c) \u201cI know of several men who have been phenomenally serviceable\n to mankind, and none of these men were college trained; hence\n I conclude that college education is not essential to the\n attainment of the highest state of efficiency.\u201d\n\nRelative to both accident and converse accident, it may be said that\nthey obtain because all general truths, such as rules, principles,\ndefinitions, maxims, etc., have their _exceptions_; and it is through\nthese exceptions that the two fallacies are made possible.\n\n_Accident and Converse Accident Distinguished from Division and\nComposition._\n\nThe fallacy of accident, we have learned, occurs when one reasons\nfrom a _general truth_ to an _accidental case_; whereas the fallacy\nof division obtains when one reasons from a _collective_ use of a\nterm to a _distributive_ use; in both cases the procedure is from a\n_larger unit_ to a _smaller unit_. Moreover, with converse accident and\ncomposition, the movement is from the _smaller unit_ to the _larger_.\nBecause of this similarity there is danger of confusing the two kinds\nof fallacies. As a matter of distinction between the fallacies of\naccident, and composition and division the attending comparative\n_r\u00e9sum\u00e9_ may be of value:\n\n (1) _Division_ is similar in movement to _accident_, while\n _composition_ resembles _converse accident_.\n\n (2) A valuable cue for remembering which way division and accident\n move, is to recall that division in arithmetic is a procedure\n from the larger unit to the smaller, and therefore that division\n in logic would have the same signification.\n\n (3) Division and composition pertain to _mathematical_ wholes; while\n accident and converse accident relate to _logical_ wholes.\n\n (4) The aggregates of division and composition may be counted or\n enumerated easily; while the accident and converse accident\n aggregates (or generals) are not easily enumerated.\n\n (5) Division and composition relate to logical _terms_, whereas\n accident and converse accident relate to general _truths_.\n\n (6) Division and composition use a _term_ in a _collective_ sense\n and then in a separate or _distributive_ sense, or vice versa;\n accident and converse accident use a _thought_ in a _general_\n and then in an _accidental_ sense, or vice versa.\n\n_Irrelevant Conclusion_ (_Ignoratio Elenchi_).\n\n_The fallacy of irrelevant conclusion results when the argument does\nnot squarely meet the point at issue._ It is the fallacy of arguing to\nthe wrong point either purposely or through ignorance. One in defense,\nwho has a weak case, may be tempted to divert attention from the point\nin hand, realizing that a close analysis of the matter in dispute\nwill tend to his undoing. In such instances (1) the lawyer will abuse\nthe plaintiff, (2) the demagogue will tell humorous stories, (3) the\nteacher will take advantage of the ignorance of the pupil, (4) the\nscholar will refer to authority and (5) the magnate will fall back\nupon the power of position and wealth. These forms of \u201c_rhetorical\nthinking_\u201d are as harmful as they are popular, and furnish one of the\nchief reasons for giving to the common people a better understanding\nof \u201chow to think\u201d as well as \u201chow _not_ to think.\u201d\n\nDefinite names have been given to the various forms of irrelevant\nconclusion which may be summarized as follows:\n\n_Argumentum ad populum._\n\nThis is the fallacy of appealing to the feelings, passions and\nprejudices of an audience rather than to their good sense and powers of\nreason. It is probably the most common of the group. To excite sympathy,\nthe lawyer for the defense may speak feelingly of the _suffering_\nthat an unfavorable verdict will bring to the wife and children of the\naccused.\n\n_Argumentum ad hominem._\n\nHere the character of the opponent is defamed with a view of\ndiscrediting him with the court or audience. \u201cMud throwing\u201d in times of\npolitical agitation is a good example of this fallacy.\n\n_Argumentum ad ignorantiam._\n\nThis fallacy comes from taking advantage of the ignorance of the\nopponent; the fallacy assumes that the original supposition has been\nproved if one is unable to prove the _contradictory_ of the original.\nIllustration: Mars is inhabited because no one is able to prove that\nMars is not inhabited.\n\n_Argumentum ad baculum._\n\nIn this all argumentation is made to give way to the forces of personal\nopposition and to the power of money. Illustration: A political\ncommittee seating those delegates only, who will vote _their_ way; and,\ndoing this, not from the merits of the case, but because said committee\nhappen to have a sufficient number of votes to \u201cput the thing through.\u201d\n\n_Argumentum ad verecundiam._\n\nThis fallacy comes from supposing that the whole thing may be settled\nby citing some noted authority who apparently substantiates the\nargument advanced.\n\n_Epitome of five forms of Irrelevant Conclusion_:\n\n (1) Appealing to the audience.\n\n (2) Defaming the character of the opponent.\n\n (3) Inability to prove the contradictory.\n\n (4) Gaining the point by force.\n\n (5) Citing authority.\n\n_Non Sequitur (False Consequent)._\n\n_This is the fallacy of deriving a conclusion which does not follow\nfrom the premises._ The fallacy obtains whenever material appears in\nthe conclusion, which has no bearing on the case under discussion.\n\u201c_Irrelevant conclusion_\u201d pertains to the establishment of the premises\nwhile \u201c_non sequitur_\u201d is concerned with the conclusion only. We know\nthat a logical thinker constructs the conclusion from material already\npresented by the premises; \u201c_Non sequitur_\u201d uses material in the\nconclusion which is found in neither premise.\n\n\u201c_Non sequitur_\u201d differs from the fallacy of four terms in that the\nlatter uses the fourth term in the premises while the former introduces\nthe fourth term in the conclusion, and in a form so well obscured that\nit sometimes escapes notice. Illustration:\n\n All men are thinking animals,\n Socrates was a man,\n \u2234 Socrates was a scholar.\n\nIt does not follow that because a man is a thinking animal that he will\nbecome scholarly.\n\n_False Cause._\n\n_This is the fallacy of assuming that because two happenings have\noccurred together several times, the one is the cause of the other._\nThis very common fallacy is due to lack of discrimination, and to the\nexaggerations incident to fear and superstition. Illustrations:\n\n (a) Planting vegetables which grow down, such as the beet, during\n the last two days of the waxing moon in order to have a larger\n yield. So far as we know the moon has no influence over growing\n vegetables.\n\n (b) Thirteen seated at a table is an indication that one of the\n number will die during the year. This is one of the most absurd\n fallacies that has ever been visited upon an intelligent people.\n\nIt is seen that \u201cFalse Cause\u201d is closely related to \u201c_Non Sequitur_.\u201d\n\n_Complex Question_ (_Double Question_).\n\n_This fallacy obtains when an assumption is put in the form of a\nquestion._\n\n\n ILLUSTRATIONS:\n\n (a) A wise father who did not want to tempt beyond the yielding\n point his three-year-old son, asked, pointing to the scratches on\n the new mahogany piano, \u201cFreddie, did you do that last night or\n this morning?\u201d\n\n (b) What caused you to desist from slandering your neighbors; New\n Year\u2019s resolutions or the preaching of Dominie X?\n\n (c) A daily paper anecdote:\n\n \u201cCharles Bradlaugh, the noted English free-thinker, once engaged\n in a discussion with a dissenting minister. He insisted that\n the minister should answer questions by a simple yes or no,\n asserting that every question should be replied to in that\n manner.\u201d The reverend gentleman arose and said, \u201cMr. Bradlaugh,\n will you allow me to ask you a question on these terms?\u201d\n \u201cCertainly,\u201d said Mr. Bradlaugh. \u201cThen, may I ask, have you\n given up beating your wife?\u201d\n\n_Begging the Question_ (_Petitio Principii_).\n\nThis is a fallacy _of deriving a conclusion from notions which in\nthemselves demand proof_.\n\nThe fallacy is not committed when the assertion is self-evident. It\nis easy to claim that our opponent is begging the question as soon as\nwe see that he is getting the better of us. One may himself beg the\nquestion by being too ready to charge others with begging the question.\nWhen the opponent adopts premises which are commonly accepted, he does\nnot beg the question. One commits the fallacy when he _seems to prove_\nthe conclusion more satisfactorily than he really does. This he may\naccomplish by covertly taking for granted the truth of notions which\nhave not the stamp of universal approval. The fallacy of begging the\nquestion assumes three forms:\n\n(1) _The assumption of an unproved premise_ (_assumptio non probata_).\n\nIn this either the major or the minor premise, or both may demand\nmore substantial proof. It must be borne in mind, however, that the\ndisputant must not ask for further proof after he has once accepted the\npremises, or after the opponent has met his demands to the satisfaction\nof commonly accepted authority.\n\n_Examples of begging the question by assuming unproved premises_:\n\n (a) All patriotic citizens are honest at heart,\n This man charged with graft is a patriotic citizen,\n \u2234 This man charged with graft is honest at heart.\n\n \u201cAll patriotic citizens are honest at heart,\u201d is not an accepted\n truth and thus demands proof.\n\n (b) A famous sophism of the Greek philosopher by which he proved that\n motion was impossible, is an excellent illustration of an assumed\n premise:\n\n \u201cIf motion is possible, a body must move either in the place\n where it is, or in the place where it is not;\n But a body cannot move in the place where it is; and of course\n it cannot move where it is not,\n Therefore, motion is impossible.\u201d\n\n Referring to this, De Morgan claims \u201cMovement is change, and so a\n body requires _two_ places in order to move.\u201d _A body cannot move\n in the place where it is, but must be moved from place to place._\n The major premise being assumed, this sophism illustrates the\n fallacy of begging the question.\n\n (c) The most subtle form of begging the question is an enthymeme\n where the suppressed premise is the one assumed; e. g., \u201cYou,\n being a teacher, should not do as other people do.\u201d\n\n Completed and arranged the argument becomes:\n\n No teacher should do as other people do,\n You are a teacher,\n \u2234 You should not do as other people do.\n\n Surely the major premise demands proof.\n\n\n(2) _Reasoning in a Circle_ (_Circulus in probando_).\n\nThis form of begging the question occurs, \u201cWhen a conclusion is based\nupon a premise which in an earlier stage of the argument was itself\nbased upon this very conclusion.\u201d To put it in another way: Reasoning\nin a circle involves proving the truth of a conclusion by using a\nparticular premise, and then proving the truth of the particular\npremise by using the conclusion. From premise to conclusion and from\nconclusion to premise completes the circle.\n\n_Examples of begging the question by reasoning in a circle_:\n\n (a) It is wrong because my conscience pricks me, and my conscience\n pricks me because it is wrong.\n\n (b) \u201cThe effeminate walk shows a lack of force; because no forceful\n man walks that way.\u201d\n\n (c) Says Hamilton, \u201cPlato, in his _Phoedo_, demonstrates the\n immortality of the soul from its simplicity; and in the\n _Republic_, he demonstrates its simplicity from its immortality.\u201d\n\n(3) _Question Begging Epithets and Appellations._\n\nThis is the fallacy of assuming the point at issue by means of a\ncarefully selected epithet.\n\nScientists sometimes assume to clarify an inexplicable phenomenon by\ngiving it a technical name. Politicians are exceedingly free with their\nepithets and appellations, and the records of religious disputes prove\nthat the theologian often resorted to this device.\n\n_Examples of begging the question by using epithets and appellations_:\n\n (a) We must attribute the disease to _heredity_.\n\n (b) The candidate for governor is an _animated feather duster_.\n\n (c) They call him _Blue Charlie_.\n\n (d) It is the policy of the _big stick_.\n\n (e) The _muck-raker_ seldom makes an efficient servant of the people.\n\nIt is seen that the use of these epithets and appellations is simply a\nrhetorical device for the purpose of creating either a favorable or\nunfavorable impression.\n\n\n=8. OUTLINE.=\n\n THE LOGICAL FALLACIES OF DEDUCTIVE REASONING.\n\n (1) A negative aspect of definition of logic.\n\n (2) Paralogism and sophism.\n Distinguished. Mission of Socrates.\n\n (3) A division of the deductive fallacies.\n More or less faulty. Aristotle\u2019s phraseology retained.\n Division given.\n\n (4) General divisions explained.\n Formal and material. Material fallacies in _language_ and in\n _thought_.\n\n (5) Fallacies of immediate inference.\n Opposition, obversion, conversion, contraversion.\n\n (6) Fallacies in language (also fallacies of equivocation).\n Ambiguous middle\u2015\u2015distinguished from four terms.\n Amphibology.\n Accent.\n Composition\u2015\u2015\u201call\u201d a pitfall.\n Division.\n Figure of speech.\n\n (7) Fallacies in thought\u2015\u2015(also fallacies of assumption).\n Accident.\n Converse accident. Made possible by exceptions.\n Accident and converse accident distinguished from composition\n and division.\n Comparative r\u00e9sum\u00e9.\n Irrelevant conclusion (_ignoratio elenchi_).\n _Argumentum ad populum._\n _Argumentum ad hominem._\n _Argumentum ad ignorantiam._\n _Argumentum ad baculum._\n _Argumentum ad verecundiam._\n _Non sequitur_ (false consequent).\n False cause.\n Complex question.\n Begging the question (_petitio principii_).\n Assumption of premise.\n Reasoning in a circle.\n Question begging epithets and appellations.\n\n\n=9. SUMMARY.=\n\n(1) Logic as a science makes known the laws and forms of thought and as\nan art suggests conditions which must be fulfilled in order to think\nrightly.\n\nA discussion of the second phase of the definition would be incomplete\nwithout a consideration of the negative aspect as well as the positive.\nSuch a viewpoint makes evident the question \u201cWhat errors must be\navoided in order to reason correctly?\u201d An answer to this question is\ngiven under the caption of Logical Fallacies.\n\n(2) A logical fallacy is any error in reasoning which has the\nappearance of correctness.\n\nA fallacy which deceives the writer or speaker himself is termed\na paralogism, whereas a fallacy formed for the express purpose of\ndeceiving another is denominated a sophism.\n\nIt was the pagan teacher Socrates who taught modern thought to frown\nupon all forms of sophism; these exist to-day much as they did in the\nolden time.\n\n(3) Because of disagreement as to definition, and because of inability\nto prevent an overlapping of species, any logical division of the\ndeductive fallacies must be faulty.\n\nIn the division of the deductive fallacies, this treatise retains the\nphraseology and form worked out by Aristotle, so far as such retention\nis consistent with the changes incident to the advances of time.\n\n(4) Formal fallacies occur because of careless and improper use of\nwords as arbitrary signs. Formal fallacies are definite and easy of\ncomprehension.\n\nThe material fallacies are due to certain inconsistencies in thought\nand to imperfect ways of interpreting language. They are more subtle\nand thus more difficult of comprehension than the formal fallacies.\n\nThere are material fallacies in thought and material fallacies in\nlanguage; the former are due to _looseness in thinking_ and the latter\nto _lack of precision in expression_.\n\n(5) Fallacies of opposition result most frequently from deriving\nuniversals from their corresponding particulars, and from assuming\nto contradict affirmative universals by negative universals and\naffirmative particulars by negative particulars.\n\nThe common fallacy in the process of obversion consists in using one\nnegative instead of two, whereas the ordinary error of conversion is a\nmatter of distributing an undistributed term.\n\nFallacies of contraversion must involve either those of obversion or\nconversion since the process is a combination of the two.\n\n(6) Fallacies in language, because they result from permitting\nmore than one interpretation, may be also denominated fallacies of\nequivocation.\n\n (1) Ambiguous middle is the fallacy of giving to the middle term a\n double meaning.\n\n The fallacy of four terms, as the name signifies, exists when\n the argument has four terms in both form and meaning. Ambiguous\n middle is a matter of four terms in meaning but only three in\n form.\n\n (2) The fallacy of amphibology is committed when the given\n proposition conveys more than one meaning. In order to maintain\n their prestige the ancient oracles made use of this fallacy.\n\n (3) The fallacy of accent springs from placing undue emphasis on some\n word or group of words. Newspaper and demagogues are prone to\n this error, that they may thus create an unfavorable impression\n towards those whom they oppose.\n\n (4) The fallacy of composition is committed when it is assumed that\n what is true _distributively_ is likewise true _collectively_.\n \u201cAll\u201d meaning _each one_ and \u201call\u201d meaning the _whole class_\n often leads to the fallacy of composition.\n\n (5) The fallacy of division is committed when it is assumed that what\n is true _collectively_ is true _distributively_.\n\n Division is the converse of composition.\n\n (6) The fallacy of figure of speech is occasioned by assuming that\n words of the same root have the same meaning.\n\n(7) Fallacies in thought are likewise called fallacies of assumption,\nbecause of the tendency to assume as true something which demands\nfurther proof.\n\n (1) The fallacy of accident occurs when one reasons from a general\n truth to an accident case. It is the favored fallacy of the\n doctrinaire, the reformer and the vender of \u201ccure-alls.\u201d\n\n (2) The fallacy of converse accident occurs when one reasons from an\n accidental case to a general truth.\n\nBoth accident and converse accident are made possible because rules,\ndefinitions, maxims, etc., have _exceptions_. It is easy to confuse\ndivision and composition with the fallacies of accident. Division and\ncomposition are concerned with the _collective and distributive use of\nterms_, whereas the fallacies of accident involve the use of notions\nin a _general and accidental sense_. The former represent notions which\nmay be _counted or enumerated_ while the latter concern notions which\nare _logical_ rather than numerical. Composition and division involve\n\u201cnumber of,\u201d accident, \u201cmeaning of.\u201d\n\n (3) The fallacy of irrelevant conclusion results when the argument\n does not squarely meet the point at issue. It is the fallacy of\n arguing to the wrong point either purposely or ignorantly. This\n may be accomplished by (1) appealing to sympathy of audience,\n (2) defaming character of opponent, (3) assuming that the fact is\n true because of inability to prove the contradictory, (4) gaining\n point by force, (5) citing authority.\n\n (4) \u201c_Non sequitur_\u201d is the fallacy of deriving a conclusion which\n does not follow from the premises. It involves introducing new\n material in the conclusion.\n\n (5) \u201cFalse cause\u201d is the fallacy of assuming that because two\n happenings have occurred together several times the one is\n the cause of the other. The fallacy is due largely to the\n exaggerations of fear and superstition.\n\n (6) The fallacy of complex question consists in putting an assumption\n in the form of a question.\n\n (7) Begging the question is the fallacy of deriving a conclusion from\n notions which in themselves demand proof.\n\n This fallacy takes the three forms of (1) the assumption of an\n unproved premise, (2) reasoning in a circle, (3) question begging\n epithets and appellations.\n\n\n=10. ILLUSTRATIVE EXERCISES IN THE TESTING OF ARGUMENTS IN BOTH FORM\n AND MEANING.=\n\n (1a) He who wilfully takes the life of another should be\n electrocuted, This sharp shooter has wilfully taken the life\n of another, Hence he should be electrocuted.\n\n { A\nIn form we know this argument to be valid since it is in mood { A of\n { A\nthe first figure. But as the conclusion does not meet with our approval,\nwe are forced to the belief that there must be a material fallacy.\nSuch proves to be the case. In the first instance, \u201cWilfully takes\nthe life of another\u201d is used in a personal, individual, selfish sense,\nwhereas in the second instance the expression is used in a general,\n\u201cservant-of-the-government\u201d signification. The argument is, therefore,\ninvalid, the fallacy being ambiguous middle.\n\n(1b) From the viewpoint of both _form_ and _meaning_ test the following:\n\u201cEvents which are not probable happen almost every day; but what\nhappens every day are very probable events; therefore events which are\nnot probable are very probable.\u201d\n\n (2a) The planets have those attributes needed in the support of life,\n Mars is a planet,\n Hence Mars has those attributes needed in the support of life.\n\n { A\nThis is valid in form { A in the first figure. The major premise posits\n { A\na fact which has not been proved; the argument is therefore invalid in\nmeaning, the fallacy being that of _begging the question_.\n\n(2b) \u201cThe end of a thing is its perfection; death is the end of life,\ntherefore death is the perfection of life.\u201d\n\nIndicate the fallacy in the foregoing, giving reasons.\n\n (3a) The countries of Europe abound in beggars,\n France is a country in Europe,\n \u2234 France abounds in beggars.\n\n\u201cThe countries of Europe\u201d in the major premise is used in a collective\nsense, while the same expression in the minor premise is used in a\ndistributive sense. The argument is, therefore, invalid in meaning;\n_fallacy of division_.\n\n(3b) State and explain the material fallacy in the following:\n\nThe states believe in the income tax principle; hence Vermont\u2019s vote\nwill be favorable to this.\n\n(4a) \u201cOn general principles I believe that one is better off when he\nabstains from both tea and coffee; and this is the reason why I offer\nyou a cup of hot water.\u201d\n\nThe individual to whom the hot water was offered might have been\nin great need of a mild stimulant. Here, then, is an exception to\nthe general principle and the fallacy committed is clearly that of\n_accident_.\n\n(4b) \u201cBooks are a source both of instruction and amusement; a table of\nlogarithms is a book; therefore it is a source both of instruction and\namusement.\u201d Jevons.\n\nDesignate with explanations the fallacy in the above argument.\n\n(5) \u201cTwice have I started out on Friday and both times I had tire\ntrouble.\u201d Fallacy of _false cause_.\n\n(6) \u201cWhere do you spend your vacation, in Palestine or Rome?\u201d Fallacy\nof _complex question_.\n\n(7) \u201cOf all the men of that department he seemed to be the most\ntrustworthy, and I pride myself on my ability to judge men in this\nregard; but now even the police cannot find him.\u201d\n\nThe fact that the police cannot find him has nothing to do with the\nargument. The fallacy is that of _non sequitur_.\n\n(8) \u201cYou must not whisper in _my_ classes.\u201d Fallacy of _accent_.\n\n(9) \u201cI am a Progressive because I believe in progress.\u201d Fallacy of\n_figure of speech_.\n\n(10) \u201cI know it is true because I found it in our text book.\u201d Fallacy\nof _irrelevant conclusion_.\n\n\n=11. REVIEW QUESTIONS.=\n\n (1) Give the negative aspect of the second part of the definition of\n logic.\n\n (2) Define and illustrate the term fallacy as it is used in logic.\n\n (3) Distinguish between a paralogism and a sophism.\n\n (4) Tell of the mission of Socrates.\n\n (5) What reasons may be given for such a divergence of opinion on a\n proper classification of the fallacies of deduction?\n\n (6) Give a complete outline, without explanation, of the deductive\n fallacies.\n\n (7) Distinguish between formal and material fallacies.\n\n (8) Explain the two kinds of material fallacies.\n\n (9) Illustrate the fallacies of immediate inference.\n\n (10) Why should the fallacies in language be likewise termed fallacies\n of equivocation?\n\n (11) Explain and illustrate ambiguous middle.\n\n (12) Illustrate the fallacy of amphibology.\n\n (13) Explain by illustration the fallacy of accent.\n\n (14) Explain and exemplify the fallacies of composition and division.\n\n (15) Illustrate the fallacy of figure of speech.\n\n (16) Give reasons for denominating the fallacies in thought as\n fallacies also of assumption.\n\n (17) Define and illustrate the fallacies of accident and converse\n accident.\n\n (18) Distinguish between the fallacies of composition and division and\n the two fallacies of accident.\n\n (19) \u201cEvery rule has its exception,\u201d what has this to do with the\n fallacies of accident?\n\n (20) Explain and illustrate the fallacy of irrelevant conclusion.\n\n (21) Name the various ways in which irrelevant conclusion may be\n committed.\n\n (22) Illustrate the fallacy of _non sequitur_.\n\n (23) Explain the fallacy of false cause.\n\n (24) Give examples of the complex question.\n\n (25) How may the teacher use the complex question to advantage?\n\n (26) Explain the fallacy of begging the question.\n\n (27) Illustrate the three forms of begging the question.\n\n (28) From the viewpoint of form and meaning, test the validity of the\n following:\n\n (1) \u201cNo soldiers should be brought into the field who are not\n well qualified to perform their part; none but veterans are\n well qualified to perform their part, therefore, none but\n veterans should be brought into the field.\u201d Whately.\n\n (2) \u201cFor the proverb is true, \u2018That light gains make heavy\n purses;\u2019 for light gains come thick, whereas great gains come\n but now and then.\u201d Bacon.\n\n (3) \u201cWhatever is given on the evidence of sense may be taken as a\n fact; the existence of God, therefore, is not a fact, for it\n is not evident to sense.\u201d St. Andrew. 1896.\n\n (4) \u201cAll the trees in the park make a thick shade; this is one of\n them, therefore this tree makes a thick shade.\u201d Jevons.\n\n (5) \u201cWhat we eat grew in the field; loaves of bread are what we\n eat; therefore loaves of bread grew in the fields.\u201d Jevons.\n\n (6) \u201cWho is most hungry eats most; who eats least is most hungry;\n therefore who eats least eats most.\u201d Jevons.\n\n (7) \u201cGreat talkers should be cropped, for they have no need of\n ears.\u201d Franklin.\n\n (8) \u201cLove your enemies, for they tell you your faults.\u201d Franklin.\n\n (9) \u201cAll the works of Shakespeare cannot be read in a day;\n therefore the play of Hamlet, being one of the works of\n Shakespeare, cannot be read in a day.\u201d Jevons.\n\n (10) \u201cLogic as it was cultivated by the schoolmen proved a\n fruitless study; therefore logic as it is cultivated at the\n present day must be a fruitless study likewise.\u201d Jevons.\n\n\n=12. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Is there any difference in content between error and fallacy?\n Illustrate.\n\n (2) In what ways do trusts indulge in sophisms?\n\n (3) May the sophism be used conscientiously by the country doctor?\n Explain.\n\n (4) Give in substance Aristotle\u2019s classification of fallacies.\n\n (5) Select the fallacies which could with justice be called fallacies\n of interpretation. See Creighton.\n\n (6) Explain in full the popular conception of equivocation.\n\n (7) Indicate the marks which distinguish the following: Ambiguous\n middle, fallacy of four terms, non sequitur, figure of speech.\n\n (8) \u201cWhy should Jeremy Bentham employ a person to read to him who\n habitually read in a monotonous tone of voice?\u201d Jevons\u2015\u2015Hill.\n\n (9) Originate a sentence of about ten words and through the fallacy\n of accent secure as many different meanings as possible.\n\n (10) Show that the fallacy of figure of speech might be classed as a\n fallacy of four terms.\n\n (11) To what fallacies, in your opinion, are teachers especially\n given?\n\n (12) Show that the fallacy of accident could be classed as one of\n ambiguous middle.\n\n (13) \u201cWhen the Puritan settlers in New England passed their three\n famous resolutions\u2015\u2015Resolved, _first_, that the earth is the\n Lord\u2019s and the fullness thereof; _secondly_, that he hath given\n it to his Saints; _thirdly_, that we are his Saints. What fallacy\n did the Puritan Fathers commit?\u201d Ryland.\n\n (14) A Dutchman afflicted with pneumonia arises at midnight and eats\n a large quantity of sauerkraut. The Dutchman gets well, whereat\n his physician writes in his little book on remedies, \u201c_Sauerkraut\n sure cure for pneumonia_.\u201d The physician was guilty of what\n fallacy? Why?\n\n (15) De Morgan quotes from Boccaccio this: \u201cA servant who was roasting\n a stork for his master was prevailed upon by his sweetheart to\n cut off a leg for her to eat. When the bird came upon the table\n the master desired to know what had become of the other leg. The\n man answered that storks never had more than one leg. The master,\n very angry, but determined to strike his servant dumb before\n he punished him, took him next day into the fields where they\n saw storks, standing each on one leg, as storks do. The servant\n turned triumphantly to his master; on which the latter shouted,\n and the birds put down their other legs and flew away. Ah, sir,\n said the servant, you did not shout to the stork at dinner\n yesterday; if you had done so he would have shown his other leg.\u201d\n What fallacy does this quotation from Boccaccio illustrate?\n\n (16) Why should begging the question and irrelevant conclusion be\n classed as fallacies of the \u201cforgotten issue?\u201d\n\n (17) From the standpoint of both form and meaning test the validity of\n the following:\n\n (1) \u201cVirtue is the child of knowledge and vice of ignorance;\n therefore education, periodical literature, traveling,\n ventilation, drainage and the arts of life, when fully\n carried out, serve to make a population moral and happy.\u201d\n Hibben.\n\n (2) \u201cThe civil power has the right of ecclesiastical jurisdiction\n and administration, therefore parliament may impose articles\n of faith on the church or suppress dioceses.\u201d Hibben.\n\n (3) \u201cSeeing that abundance of work is a sure sign of industrial\n prosperity, it follows that fire and hurricane benefit\n industry, because they undoubtedly create work.\u201d\n St. Andrews\u2015\u20151895.\n\n (4) \u201cRiches are for spending, and spending for honor and good\n action; therefore, extraordinary expense must be limited by\n the worth of the occasion.\u201d Bacon.\n\n (5) \u201cAnd let a man beware how he keepeth company with choleric\n and quarrelsome persons; for they will engage him into their\n own quarrels.\u201d Bacon.\n\n (6) \u201cHe that resteth upon gains certain, shall hardly grow to\n great riches; and he that puts all upon adventures, doth\n oftentimes break and come to poverty. It is good, therefore,\n to guard adventures with certainties that they may uphold\n losses.\u201d Bacon.\n\n\n\n\n CHAPTER 17.\n\n INDUCTIVE REASONING.\n\n\n=1. INDUCTIVE AND DEDUCTIVE REASONING DISTINGUISHED.=\n\nIt has been remarked that inference is the process of deriving a\njudgment from one or two antecedent judgments, and that mediate\ninference is inference by means of a middle term. But to reason by\nmeans of a middle term necessitates two judgments; hence mediate\ninference might be defined as the process of deriving a judgment from\n_two_ antecedent judgments. In this treatment mediate inference and\nreasoning have been used interchangeably. This, then, becomes our\ndefinition for reasoning: _Reasoning is the process of deriving a\njudgment from two antecedent judgments._\n\nThe syllogism results when the process of reasoning is formally\nclothed in words. Moreover, the conclusion of the syllogism may be\n_more_ general than the premises or _less_ general. This suggests the\ntwo important kinds of reasoning; namely, inductive and deductive.\nInductive reasoning is reasoning from less general premises to a more\ngeneral conclusion. Deductive reasoning is reasoning from more general\npremises to a less general conclusion.\n\n\n ILLUSTRATION:\n\n _Inductive Syllogism._ _Deductive Syllogism._\n\n The robin, crow, sparrow, All birds have wings,\n etc. have wings, The robin, crow, sparrow,\n The robin, crow, sparrow, etc. are birds,\n etc. are birds, \u2234 The robin, crow, sparrow,\n \u2234 All birds have wings. etc. have wings.\n\n Iron, silver, gold, etc. are All metals are elements,\n elements, Iron, silver, gold, etc. are\n Iron, silver, gold, etc. are metals,\n metals, \u2234 Iron, silver, gold, etc. are\n \u2234 All metals are elements. elements.\n\n Boston, New York, Chicago, All large cities have fine\n etc. have fine harbors, harbors.\n Boston, New York, Chicago, Boston, New York, Chicago, etc.\n etc. are large cities, are large cities,\n \u2234 All large cities have fine \u2234 Boston, New York, Chicago, etc.\n harbors, have fine harbors.\n\nThe student who is sufficiently familiar with the canons of the\ndeductive syllogism will at once detect the fallacy of _illicit\nminor_ in the foregoing inductive syllogisms; i. e., \u201c_birds_\u201d when\nused as the predicate of the minor premise of the first syllogism\nis undistributed, but as the subject of the conclusion \u201c_birds_\u201d is\ndistributed. The same might be said concerning the terms \u201c_metals_\u201d\nand \u201c_large cities_.\u201d A portion of this chapter will be devoted to\nanswering this criticism. At this point it may be stated that _the\ninductive syllogism is not supposed to conform perfectly to the canons\nof the deductive syllogism_.\n\n\n=2. THE INDUCTIVE HAZARD.=\n\nReferring to the first inductive syllogism of section _one_, it is\nassumed that the robin, crow and sparrow are representative birds, and\nthat we are thus justified in concluding that if these _type_ birds\nhave wings, then _all_ birds must have wings. Of course this is more\nor less of a conjecture or \u201ca hazard\u201d; since birds without wings may\nexist in some undiscovered corner of the globe. However, inasmuch\nas the generalization concerns a representative quality, we deem the\nassumption fairly well founded. The logical right to take this \u201cleap\ninto the unknown\u201d will be discussed later. It will profit us at this\ntime to realize more fully how essential the \u201cinductive hazard\u201d is\nto the progress of the world. When the Schoolmen of medi\u00e6val time\nrefused to venture, they failed to progress, and thus came the dark\ndays. Whenever man has ignored this God given instinct which leads to\ndiscovery, the world has stood still. _This willingness to \u201ctake a leap\ninto the dark\u201d with the hope of finding, in the shadow, truth which\nwould enhance man\u2019s power and increase his serviceableness, has given\nto the world about all that is worth while._ It was the spirit of the\n_hazard_ which pushed Columbus to the discovery of a new world; which\ngave Newton the secrets of the motions of the universe; which enabled\nEdison to harness a multitude of lurking forces; and Morse and Bell to\nreduce distance to its lowest terms. In ordinary affairs with ordinary\nmen those succeed _best_ who manifest _most_ a safe, steady, persistent\nspirit of discovery. _Here, then, in the \u201cinductive hazard\u201d have we a\nmost important phase of school life which, in this day of making the\nwork easy, is being sadly neglected._ On the other hand, an unregulated\nand insane spirit of venture may result in a great waste of energy, and\nin the development of low ideals of recklessness and inaccuracy. The\n\u201cinductive hazard\u201d must be cultivated; yet it must be regulated as well,\nand, as the reader already realizes, logic needs to concern itself\nmainly with this _regulative_ aspect.\n\n\n=3. THE COMPLEXITY OF THE PROBLEM OF INDUCTION.=\n\nThe problem of induction is much more complex than that of deduction\nbecause of these reasons: First. Deduction as a process of reasoning\nwas the only kind discussed by the logicians for _two thousand years_.\nAristotle is called the father of deductive logic and this Intellectual\nGiant, the greatest of ancient time and possibly of all time, so\nperfected the form of deductive reasoning that, up to the time of\nFrancis Bacon, no scholar possessed the temerity to gainsay its\nsupremacy in the field of logical reasoning. For twenty centuries\nAristotle\u2019s Deductive Logic was the _Logicians\u2019 Bible_. On the other\nhand, inductive reasoning, though it was briefly discussed by Aristotle,\nreceived little attention till the versatile Francis Bacon placed it\nupon the stage of the thinking world. This makes deduction nearly two\nthousand years older than induction. Time, by eliminating the personal\nequation and exposing in various ways fallacious thinking, tends to\nunify and universalize truth. Hence, logicians are agreed so far as the\nfundamentals of deductive logic are concerned, but are still at odds\nover the true conception and use of inductive logic.\n\nA second reason for this confused status in the field of inductive\nlogic is the fact of its being more closely related to the events of\nevery day living. Induction is the natural method of childhood; the\npopular method of the school room; and the most used method of common\nlife. In consequence its ramifications are so varied and multitudinous,\nthat it will take centuries of thinking to reduce the doctrine of\ninduction to that uniformity and definiteness which so distinguishes\ndeduction.\n\n\n=4. THE VARIOUS CONCEPTIONS OF INDUCTION.=\n\nThe attending quotations will give the student a fair idea of the\nleading conceptions concerning induction:\n\n(1) \u201cInduction is the process by which we conclude that what is true\nof certain individuals of a class is true of the whole class, or that\nwhat is true at certain times will be true under similar circumstances\nat all times.\u201d \u201cInduction, as above defined, is a process of inference;\nit proceeds from the known to the unknown.\u201d \u201cAny process in which what\nseems the conclusion is no wider than the premises from which it is\ndrawn, does not fall within the meaning of the term.\u201d\u2015\u2015J. S. Mill, A\nSystem of Logic, 1892, p. 175.\n\n(2) \u201cAn induction is a generalization or an inference based upon\npropositions that state observed facts.\u201d \u201cThe truth inferred may be\ngeneral or particular, but it must be one which we cannot perceive in a\nsingle act of observation.\u201d\u2015\u2015Ballentine\u2019s Inductive Logic, 1896, p. 14.\n\n(3) \u201cInduction is the process of inference by which we get at general\ntruths from particular facts or cases.\u201d\u2015\u2015Ryland\u2019s Logic, 1900, p. 148.\n\n(4) \u201cInduction may be defined as the legitimate inference of the\ngeneral from the particular, or, of the more general from the less\ngeneral.\u201d\u2015\u2015Fowler, 1905, p. 10, Vol. 2.\n\n(5) \u201cThe term induction has been used by logicians to denote this\nleap of the mind from the limitations of its positive knowledge\nto belief in universal laws.\u201d \u201cIn pedagogy, however, the term\nis applied to the whole process of arriving at general truths or\nprinciples.\u201d\u2015\u2015Salisbury\u2019s Theory of Teaching, p. 156.\n\n\n=5. INDUCTION AND DEDUCTION CONTIGUOUS PROCESSES.=\n\nIf there is one thing above another which modern logic is emphasizing\nit is the _unity of the mind_ and the _contiguity of thinking_.\nInduction and deduction are _dove-tailed processes_ which characterize\nall thinking worthy of the name. Where induction ceases, deduction\ncommences, and vice versa. It becomes the function of inductive\nthinking to establish a connection between what has been experienced\nand what has not been experienced. Therefore, the conclusion of an\ninduction must always contain more than is implied in the premises. The\npremises denote facts which have been observed; whereas the conclusion\ndenotes the observed facts of the premises plus analogous facts which\nhave _not been observed_. Inductive thought ventures into the unknown,\nand attempts to establish a bond of connection between it and something\nalready known. Induction seeks new knowledge, and does so by taking\nthat \u201cleap into the dark\u201d already referred to as the \u201cinductive hazard.\u201d\n\nAs soon as the mind reaches a universal truth, it sets to work to\nclarify this truth. Such is accomplished by reference to other facts\nwhich the universal is supposed to include; and this application of the\ngeneral to the particular is _deduction_. _Induction discovers_ the new\nknowledge while _deduction clarifies_ it.\n\n\n=6. INDUCTION AN ASSUMPTION.=\n\nIn this treatment induction as a general process has been subdivided\ninto induction as a mode of inference and induction as a method.\n_Induction as a mode of inference is the process of reasoning from less\ngeneral premises to a more general conclusion; whereas induction as a\nmethod is a procedure from the observation of individual facts to a\nrealization of a universal truth._ In either case the conclusion of an\ninductive process always implies more than is contained in the premises.\nThis gives to the conclusion an uncertainty. No induction is absolutely\nfree from doubt except the so-called perfect induction, which form will\nreceive attention in a later section.\n\n\n =7. UNIVERSAL CAUSATION.=\n\n All inductive assumptions are made possible because of two\n laws\u2015\u2015_universal causation_ and _uniformity of nature_.\n\n The law of universal causation may be stated in this wise:\n _Nothing can occur without a cause and every cause has its\n effect._ \u201cIt is a universal truth, that every fact which has\n a beginning has a cause.\u201d\u2015\u2015Mill.\n\n\n SIMPLE ILLUSTRATIONS OF UNIVERSAL CAUSATION.\n\n The sun rises in the east. The boy throws a stone through the\n window. A democratic wave sweeps the country. Prices of food\n stuff are high. The bullet, shot out into space, finally falls\n to the earth. Each one of these occurrences has a cause.[12]\n\n That universal causation is a fundamental condition of all\n induction may be further illustrated. The astronomer notes that\n the stars in the vicinity of Vega seem to be moving outward\n _from_ a common center; whereas in the opposite part of the sky\n the stars seem to be moving inward _toward_ a common center.\n Having observed this phenomenon, the astronomer at once looks\n for a cause. Finally he decides that the phenomenon is due to\n the fact that the sun, with his attending family, is moving\n towards Vega. Arranged, the argument may take this form:\n\n The stars in the vicinity of Vega seem to be moving outward\n from a common center, whereas in the opposite part of the sky\n the stars seem to be moving inward, When descending a mountain\n the trees at the foot seem to move outward from, and those at\n the top inward toward, a common center, When riding on the train\n the ties in front seem to move outward while those in the rear\n seem to move inward. From this we conclude that the sun with\n the Earth and other planets is moving toward a spot in the sky\n near Vega. Were it not for the assumption that the phenomenon\n relative to the stars _had a cause_ there could have been no\n induction. Moreover, any investigation concerning \u201cdemocratic\n waves,\u201d \u201cprices of food stuffs,\u201d etc., must assume as a starting\n point that these phenomena have causes.\n\n It would appear that the mind is not satisfied with a mere\n passive observation of the occurrences of the world but is\n inclined to reach out for the \u201cwhys and wherefores.\u201d Due partly\n to this reason, \u201cuniversal causation\u201d is often referred to as\n an _a priori_ law; meaning that it is a law which cannot be\n _proved_, but must be _assumed_ in all thinking.\n\n\n =8. THE LAW OF THE UNIFORMITY OF NATURE.=\n\n Law stated: _The same antecedents are invariably followed by the\n same consequents._ \u201cThat the course of nature is uniform is the\n fundamental principle of induction.\u201d\u2015\u2015Mill. \u201cIt is not enough to\n feel assured that nothing can happen without a cause (causation);\n I must also feel assured that the same cause will invariably be\n followed by the same effect.\u201d\u2015\u2015Fowler.\n\n Referring to the observed phenomenon of the outward movement\n of the stars about Vega, the astronomer might advance as an\n hypothesis the fact of the solar system\u2019s movement toward\n Vega. Having done this he could then experiment with a view of\n verifying this hypothesis. In this experiment he would attempt\n to introduce the same cause surrounded by similar circumstances,\n and then watch for the same effect. To make it concrete: suppose\n the astronomer paints the side of a barn dark blue and bedecks\n this with stars of white. Then taking a position as far removed\n from the blue surface as his eyesight will permit, he runs\n toward the barn watching the apparent movement of the artificial\n stars. A similar experiment could be performed by substituting\n for the _starred_ barn, the stumps on a side hill. In both\n experiments he assumes that like conditions will be followed by\n constant results. That is, in these particular cases, advancing\n toward a group of objects is always followed by an apparent\n separation of said objects.\n\n This law of uniformity of nature not only underlies inductive\n thinking but it really conditions all thinking. It implies\n that the universe is a rational system functioning in a uniform\n manner. Moreover, it suggests that the interpretations of the\n mind are likewise uniform and whenever the mind proves a fact\n to be a universal truth, this truth will _always_ remain a\n truth unless the conditions change. In fact were it not for the\n uniformity of nature, all activity whatsoever would be rendered\n nugatory. Because of this law we have a right to assume that\n grinding a knife under right conditions will always tend\n to sharpen it; that surrounding a live seed with a proper\n environment will result in growth; that water at the same\n altitude will boil at a constant temperature, etc., etc.\n\n The student will discern the close connection between these two\n laws and the laws of thought. There is really no distinctive\n mark between the law of causation and the law of sufficient\n reason, while \u201cuniformity of nature\u201d includes identity as\n one of its distinctive features. The laws differ, however,\n in their application, \u201ccausation\u201d and \u201cuniformity of nature\u201d\n conditioning inductive thinking, while the others are concerned\n with deductive thinking.\n\n Because \u201cuniformity of nature\u201d expresses facts of experience, it\n is regarded as an _empirical_ law, as contrasted with the law of\n causation, which is supposed to be based upon an innate mental\n conception or is an _a priori_ law.\n\n\n=9. INDUCTIVE ASSUMPTION JUSTIFIED.=\n\nThe function of induction seems to be to universalize particulars. The\nmind of man has ever been engaged in establishing connections among the\nconcrete experiences of daily life. This ability of his to generalize\nhis individual experiences has been one of the chief agencies in\nelevating him to the position of \u201cKing of the animal world.\u201d In this\ndisposition to generalize man has taken it for granted that nature is\nhonest; that what she tells him under given conditions, she will tell\nhim again under identical conditions. To put it in logical terms man\ncan depend upon the _invariability_ of nature\u2019s activities, or _upon\nthe uniformity of nature_. Here, then, is one of the most fundamental\nlaws not only of induction but of all activity. But this law implies a\nsecond quite as fundamental. If every cause is invariably followed by\nthe same effect under like conditions, then it is thereby implied that\nevery cause has an affect and every event is due to some cause. This,\ntoo, is invariable. In consequence of these facts man is justified\nin thinking that nature is not only honest and therefore \u201cshe\ngives me _confidence_, but her every activity _means something_ and\ntherefore she arouses my _curiosity_.\u201d \u201cUniformity of nature\u201d engenders\nconfidence, \u201cuniversal causation\u201d inspires the spirit of discovery\nand with these two weapons man is willing to venture into the jungle\nof the unknown. _Why is man eager to undertake the \u201cinductive hazard?\u201d\nBecause, through the laws of universal causation and uniformity\nof nature, his curiosity is aroused, and he is given confidence in\nnature\u2019s activities._\n\n\n=10. THREE FORMS OF INDUCTIVE RESEARCH.=\n\nInduction is a matter of universalizing less universal experiences.\nIn this the process may assume any one of three forms, namely:\n(1) Induction by simple enumeration; (_inductio per enumerationem_);\n(2) Induction by analogy; (3) Induction by analysis.\n\n\n THREE FORMS ILLUSTRATED:\n\n(1) _Simple enumeration._\n\nHaving observed a few instances the generalization is, \u201cAll birds have\nwings.\u201d The certitude of this may now be strengthened by observing more\nbirds and finding without exception that each has wings.\n\n(2) _Analogy._\n\nBy noting on Mars geometric markings which resemble canals, the\ngeneralization is vouchsafed that Mars is inhabited by human beings.\nOther similarities in atmospheric conditions, existence of land and\nwater, etc., tend to make this generalization more plausible.\n\n(3) _Analysis._\n\nBy analyzing water taken from a certain spring, it is found to contain\nhydrogen and oxygen in the proportion of 1 to 8; in consequence a\ngeneralization to this effect is posited. Analyses of specimens from\nother sources yield similar results and thus the generalization is\ngiven greater certitude.\n\nAs a usual thing the particular form which the induction assumes\ndepends on the nature of the topic under investigation and also on\nthe mental make-up of the investigator. The general statement that\nall birds have wings could hardly be derived by means of analogy or\nanalysis, but is a matter of a casual observation of many instances.\nMoreover, that mind given to accurate observation, but not inclined to\nnote resemblances or to carry on experiments, would naturally follow\nthe first inductive type. On the other hand, simple enumeration would\nbe impossible in questions like the habitability of Mars, and would\nyield no results in cases requiring definite scientific experimentation\nlike electrolysis.\n\nIt is worthy of note that some topics lend themselves to all three\nmodes of procedure. To wit: (1) Enumeration. Without being taught the\nrule the child is given a list of examples involving the dividing of\na decimal by a decimal and is asked to solve them. By comparing his\nanswers with those in the book, he somewhat accidentally discovers\nwhat seems to be the correct rule for pointing off in the quotient.\nBy following this rule and each time comparing answers he establishes\nthe truth. (2) Analogy. If .24 \u00f7 .6 is the first example, the child\nmay resort to the well known process of dividing a common fraction by a\n ( 24 60 24 4 )\ncommon fraction, ( \u2015\u2015\u2015 \u00f7 \u2015\u2015\u2015 = \u2015\u2015 = \u2015\u2015, ) then, because of their close\n ( 100 100 60 10 )\nresemblance, he may reason that decimal fractions should yield the same\nresult. (3) Analysis. Here the child reasons that since division of\ndecimals is the inverse of multiplication of decimals, the rule for\npointing off might be the inverse of the multiplication rule. By trying\nthis out and proving his answer in each example, he becomes convinced\nof the correctness of his reasoning.\n\n\n=11. INDUCTION BY SIMPLE ENUMERATION.=\n\nAs its name implies this type of inductive research consists\n_in observing many instances which may exemplify the particular\nuniformity under consideration_. The process is quantitative rather\nthan qualitative, the certitude of the generalization depending on\nthe _mass of facts collected_ rather than on any striking resemblance\nor any detailed analysis. The aim is to observe, accurately if not\nscientifically, instance after instance until all doubt is removed.\nThe outcome of such observation may be three fold. (1) The enumeration\nmay be complete. This gives the so-called \u201cperfect induction\u201d which\nwill receive attention later. (2) The enumeration may be incomplete\nand _without exceptions_; generalizing in this way from uncontradicted\nexperience gives what are termed \u201c_empirical_\u201d truths. (3) The\nenumeration may be incomplete _with_ exceptions. It is obvious that\nthis type of induction could give no valid generalization; but the\nresult may be put in the form of a ratio between the uniformities and\nthe exceptions. Such a procedure is a mere \u201c_calculation of chances_\u201d\nand the result simply an expressed probability.\n\n\n THE THREE KINDS OF SIMPLE ENUMERATION ILLUSTRATED.\n\nThe subject to receive investigation is a _school examination_.\n\n (1) Complete enumeration. Every paper is read and marked; this leads\n to the generalization, \u201cAll the class have passed.\u201d\n\n (2) Incomplete enumeration with no exceptions. Representative\n papers are read and marked in which no failures are found.\n Generalization, \u201cProbably all of the class have passed.\u201d\n\n (3) Incomplete enumeration with exceptions. Representative papers are\n read and marked in which there are 20 failures out of the hundred\n papers examined. Generalization, \u201cProbably about 80% of the class\n have passed.\u201d\n\nBriefly, simple enumeration may take the form of (1) _a perfect\ninduction_, (2) _a probable induction_, (3) _a mere calculation of\nchances_. The first necessitates completed experience, the second\nuncontradicted experience and the third contradicted experience.\n\n\n=12. INDUCTION BY ANALOGY.=\n\n_Induction by analogy assumes that if two (or more) things resemble\neach other in certain respects, they belong to the same type, and,\ntherefore, any fact known of the one may be affirmed of the other._\n\n\n THE TYPE.\n\nAs the definition implies, analogy involves an extensive use of types;\nlet us, therefore, become better acquainted with them as instruments\nin analogical inductions. A type is _one_ of a group which embodies the\n_essential characteristics_ of that group. How easy and natural it is\nto dismiss a complex topic with the citing of an example which may be\nregarded as a type; how common is the use of examples in the school\nroom! On second thought it becomes apparent that analogical induction\nby example or type is the most common of all forms of induction either\nas a method or a mode of inference. _Analogy by example (or type)\nassumes that if two or more things are of the same type, they resemble\neach other in every essential property._\n\nIllustrations of analogical inductions by example or type.\n\n(1) _Mathematics._\n\n Example: a + b\n a + b\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n a\u00b2 + ab\n + ab + b\u00b2\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n a\u00b2 + 2ab + b\u00b2\n\nInductive Inference: The square of the sum of two quantities is equal\nto the square of the first, plus twice the first by the second, plus\nthe square of the second.\n\n(2) _Nature._\n\nThis corn sent me as a sample produced heavy, full ears, and many of\nthem; hence (inductive inference), if I plant corn _like this sample_\nunder like conditions, I will receive in return heavy, full ears, and\nmany of them.\n\n(3) _Geography._\n\nCities like New York, located on the coast, possess a larger foreign\nelement than the inland cities like Philadelphia.\n\n(4) _Grammar._\n\nA noun is the name of anything, as the examples, \u201cGeorge Washington\u201d\nand \u201chouse\u201d would indicate.\n\nIn deriving a generalization from one or two examples the prime\nessential is to select types which are _truly representative_.\nOften the example used is a special type and in consequence does not\nexemplify all of the essential characteristics of the group. To teach\nthe nature of a parallelogram by using a rectangle only, is an easy way\nto commit this error; or one may affirm that the class can easily cover\nthe work, when the judgment is based entirely on knowledge concerning\nthe _brightest_ one of the grade.\n\nType work when judicially used is a positive time saver and a very\npresent help in times of perplexity. Let the skillful teacher use types\nand examples extensively yet cautiously.\n\n\n THE MARK OF SIMILARITY.\n\nAs opposed to analogy by type there is a second form; namely, _analogy\nby one or more similar marks or qualities_. This form is best described\nby the definition: _When two things resemble each other in a few marks\nor qualities they resemble each other in other marks or qualities._\n\nIllustrations of analogy by marks.\n\n (1) Noting that two students have the same surname, I infer that they\n are brothers.\n\n (2) A man with a book under his arm rings the door bell and asks to\n see \u201cthe lady of the house.\u201d At once the conclusion is drawn that\n the caller is a book agent.\n\n (3) Two automobiles, resembling each other in shape of body, force\n one to the conclusion that the machines are of the same make.\n\n\n THE ERRORS OF ANALOGY BY MARKS OF SIMILARITY.\n\nIt follows that analogy by example gives generalizations of much\ngreater certitude than analogy by one or two marks of resemblance.\nHere is a field bespattered from boundary to boundary with erroneous\nthinking. The principle of resemblance being an innate tendency, this\nform of error is most common with the immature. The child reasons\nby analogy when he invests the poodle with the despised cognomen of\n\u201ckitty\u201d; or honors every man who wears glasses with \u201cpapa.\u201d In the\nchildhood of the race natural events were interpreted by means of\nanalogy. The wind blowing through the trees made sounds much like the\nhuman voice; hence these noises were attributed to spirits. Primeval\nman was led to believe by analogy that everything which moved was alive.\nWe may, therefore, think of our revered forbear as engaged in the\nundignified task of running after his shadow, or chasing a leaf around\na stump.\n\n\n THE VALUE OF ANALOGY.\n\nAnalogy being rich in its suggestions is the favored process of the\nscientist and inventor. Newton reasoned by analogy when he tentatively\naffirmed of the moon what he positively knew of the apple. Franklin\u2019s\nreasoning was analogical when he discovered the identity of the\nelectric spark and lightning. Because this form of induction so often\nleads to error and at best involves a degree of probability far below\ninduction by analysis, some logicians are inclined to ignore its\ngeneralizations altogether. Others deem this a mistake because of these\nreasons: First. Analogy is serviceable to a high degree in suggesting\nhypotheses which may be advanced either for the purpose of explanation\nor verification. It has already been indicated that analogy is the\ncommon instrument used by the inventor and discoverer. Second. The\nprinciple of analogy, in reality, lies at the basis of classification;\nbecause in this, things are grouped according to their resemblances.\nThird. Analogical induction affords valuable training in originality\nand initiative. A mind which easily and naturally discerns analogies\nis \u201cfertile in new ideas.\u201d\n\n\n REQUIREMENTS OF A TRUE ANALOGY.\n\nIt has been remarked that the certitude of an induction by simple\nenumeration depends upon the number of uncontradicted instances. In\nanalogy the case is different as the process emphasizes the _weight_\nof the points of resemblance rather than the _number_. In substance\nthe requirements of a logical analogy are three.\n\nFirst. _The points of resemblance must be representative and not\nexceptional._ For example: The argument that Mars is inhabited because\nit has two moons is of little worth, since we have no proof that\nmoonshine is essential to life; this point of resemblance is not\nrepresentative. On the other hand, if the basis of argument is the\nfact that Mars has an atmosphere, the conclusion carries some weight;\nas air seems to be essential to life.\n\nSecond. _The points of resemblance must outweigh the points of\ndifference._ That is, the ratio of probability must always be in\nfavor of the resembling instances. Since it is not a matter of numbers\nbut of weight, a numerical proportion like this would be misleading:\nResemblances: Differences = 10:6. It is obvious that the six\ndifferences might more than outweigh the ten resemblances. The safer\nway, if it were possible, would be to attach a _value_ to each point of\nresemblance or difference, and then express the proportion in terms of\nthe sums of these values.\n\nThird. _There must be no difference which is absolutely incompatible\nwith the affirmation which we wish to prove._ For example, the fact\nthat the moon has no atmosphere renders nugatory any attempt to prove\nthe habitability of the moon.\n\n\n=13. INDUCTION BY ANALYSIS.=\n\nThis, the third form of inductive research, is by far the most\nimportant. Simple enumeration, because it depends upon the number of\nobserved instances, consumes much time; while we have already noted how\neasy it is for analogy to lead to error. At the best, the conclusion\nof these methods must be subjected to analytic investigation, if we are\nseeking universal validity. Induction by analysis is superior to the\nother forms because it secures a _higher degree of probability_ and is\na _positive time saver_.\n\nDefined. We have learned that analysis is the process of separating\na whole into its related parts. We thus define induction by analysis\nas _the process of separating a whole into its parts with a view of\nderiving a generalization relative to the nature and causal connection\nof these parts_.\n\n\n ILLUSTRATIONS:\n\n(1) Concerning the generalization that \u201call birds have wings,\u201d it\nbecomes possible to observe in detail the nature of the wings and\nadvance the hypothesis that these wings are designed for a\u00ebrial\nnavigation. This hypothesis may then be strengthened by observing that\nthe entire structure of the bird is adapted to flying.\n\n(2) If it were possible to analyze the atmosphere, water, and soil of\nMars, and should such analysis reveal a composition similar to that of\nthe earth, it would illustrate well not only the _method_ of analysis\nbut also its superiority over the other methods of investigation.\n\n(3) The physician, in diagnosing a \u201ccase,\u201d observes that the symptoms\nresemble those of typhoid; but to be positive of the truth of his\ndiagnosis, he takes a blood test. Noting the resemblances is induction\nby analogy; but the blood test involves induction by analysis.\n\nInduction by analysis concerns hypothesis, observation, and experiment,\nincluding Mill\u2019s experimental methods. These topics will receive due\nattention in the chapters which follow. It will be sufficient to close\nthis discussion with a brief treatment of perfect induction, and\ntraduction.\n\n\n=14. PERFECT INDUCTION.=\n\nAs has been indicated under simple enumeration, _a perfect induction\nis one in which the premises enumerate all the instances denoted by the\nconclusion_.\n\n\n ILLUSTRATIONS:\n\n (1) A, B, C, D, and E are all Reactionaries,\n (All) The members of the committee are A, B, C, D, and E,\n \u2234 (All) The members of the committee are Reactionaries.\n\n (2) John, James, Albert, and Peter all have perfect eyesight,\n John, James, Albert, and Peter are all the boys of my family,\n \u2234 All the boys of my family have perfect eyesight.\n\n (3) The first, second, and third groups are up to grade,\n The first, second, and third groups include all of the children\n in my room,\n Hence all the children in my room are up to grade.\n\nBecause the conclusion of a perfect induction gives nothing\nnew\u2015\u2015nothing but what is found in the premises, some claim that\nthe process is practically valueless. From the viewpoint of the\ndiscoverer this position is well taken; yet to universalize particular\nobservations puts the knowledge in compact, usable form, and saves\none the trouble of returning each time to the consideration of each\nparticular. Thus as a process which leads to verified universals,\nperfect induction is a _time saver_. In the second place it was the\nmethod used by Socrates when he desired to lead up to a definition or\nsome other general truth. The Sophists were given to a careless use\nof the \u201cinductive hazard\u201d; they were prone to generalize from one\nor two particulars, or what is worse, to establish a generalization\nand then attempt to fit the particular instances to it. This led to a\nsuperficiality which the Great Pagan Educator abhorred. The fact that\nperfect induction was the method used by Socrates to counteract the\nteachings of the Sophists, is sufficient vindication for its use in\ndiscouraging the indefensible assumptions of to-day, and in inspiring\nwarrantable generalizations based on accurate observation.\n\nIn the school room with classes addicted to careless, inaccurate work,\nto accept nothing but a perfectly induced generalization, when this\nis feasible, is a most valuable lesson. For example, the teacher may\nnot accept the generalization that all of the \u201cfirst class\u201d cities\nof the U. S. are located on navigable waterways, until the pupils\nhave investigated the waterway conditions of every city belonging\nto the class. On the other hand, there may be individual cases of\n\u201ccocksureness\u201d which need attention. The teacher can do little for the\n\u201cknow-it-all youngster\u201d until he pricks the bubble of conceit. This may\nbe accomplished by allowing the youth to draw a generalization, which\nseems to meet all the requirements of truth arrived at by means of\nan _imperfect induction_; then without warning let the teacher give\nan instance which will show the generalization to be _false_. This\ninvolves what Socrates termed the \u201ctorpedo\u2019s shock.\u201d To illustrate:\nConsider the \u201cprime number\u201d formula given by Jevons. In deriving this,\ndirect the class to add 2 to its square, and to this sum add 41. Give\nsimilar directions relative to numbers 3, 4, 7 and 10. Indicating the\nwork as directed, would give the following:\n\n (1) 2 + 2\u00b2 + 41 = 47\n (2) 3 + 3\u00b2 + 41 = 53\n (3) 4 + 4\u00b2 + 41 = 61\n (4) 7 + 7\u00b2 + 41 = 97\n (5) 10 + 10\u00b2 + 41 = 151\n\nA question or two will make apparent the fact that all the results\nare prime numbers, and then the generalization may be drawn; namely,\nX + X\u00b2 + 41 = prime number. Now without warning, but under the\nassumption that you desire to test deductively the general formula,\nlet X = 40. This gives (40 + 40\u00b2 + 41) 1681, which is the square of\n41 and is, therefore, not a prime number.\n\n\n=15. TRADUCTION.=\n\nIt may have been noted by the student that \u201cperfect induction\u201d is\nnot induction at all according to the definition; viz.: Inductive\nreasoning is reasoning from less general premises to a more general\nconclusion. Referring to the first illustration of the previous section\nit is apparent that the conclusion is no broader than the premises.\nOstensibly, the conclusion is a mere summary, or a generalization\nof the facts mentioned in the premises. Moreover perfect induction\ndoes not readily conform to the definition of deductive reasoning,\nas in this the movement must be from the more general to the less.\nWe are thus forced to the conclusion that perfect induction is a form\nof a third type of reasoning which is known under the cognomen of\n_traduction_. This is from the Latin _trans_, and _ducere_ meaning\nto lead across. Definition: _Traductive reasoning is reasoning to a\nconclusion which is neither less general nor more general than the\npremises._\n\nAside from the case of perfect induction there are other types\nwhich well illustrate traduction. These are: First. _Reasoning from\nparticular_ (_or individuals_) to _particular_ (or individuals).\n\n\n ILLUSTRATION:\n\n Highland Street is the longest street in Jamaica,\n Highland Street is not so long as Broadway of New York City,\n \u2234 The longest street of Jamaica is not so long as Broadway of\n New York City.\n\nSecond. _Reasoning from general to general._\n\n\n ILLUSTRATION:\n\n All growing things die,\n All living things are growing things,\n \u2234 All living things die.\n\nIt may be observed that all of the propositions in traduction are\nco-extensive \u201cA\u2019s\u201d or \u201cE\u2019s\u201d; hence all the terms are distributed. This\neliminates any possibility of committing fallacies of distribution.\nFurther, the propositions may be interchanged at will, without\ninvalidating the particular conclusion selected. To illustrate we may\nchange the last argument to this:\n\n All growing things are living things,\n All things that die are growing things,\n \u2234 All things that die are living things.\n\nFrom the viewpoint of authenticity traduction is the most, and\ninduction the least dependable; whereas the certitude of deductive\nreasoning lies somewhere between the two. On the other hand, when\nlooked at from the ground of serviceableness the order is reversed,\ninduction being the most useful form of inference and traduction the\nleast.\n\n\n=16. OUTLINE.=\n\n INDUCTIVE REASONING.\n\n (1) Inductive and Deductive Reasoning Distinguished.\n\n (2) The \u201cInductive Hazard.\u201d\n Essential in world\u2019s progress.\n Cultivated and regulated in school.\n\n (3) Complexity of the Problem of Induction.\n\n (4) Various Conceptions of Induction.\n Quotations from prominent authorities.\n\n (5) Induction and Deduction Contiguous Processes.\n\n (6) Induction an Assumption.\n A mode of inference; A method.\n\n (7) Universal Causation.\n Law stated and illustrated.\n Conditions all induction.\n\n (8) Uniformity of Nature.\n Defined and illustrated.\n Conditions all induction.\n Empirical.\n\n (9) Inductive Assumptions Justified.\n\n (10) Three Forms of Inductive Research.\n (1) Enumeration (2) Analogy (3) Analysis.\n Illustrated.\n Conditions determine form followed.\n\n (11) Induction by Simple Enumeration.\n Defined and illustrated.\n Outcome threefold\u2015\u2015these illustrated.\n\n (12) Induction by Analogy.\n Two conceptions.\n Analogy by type or example. Illustrations representative.\n Error of analogy.\n Suggestiveness of analogy.\n Value of analogy.\n Requirements of a true analogy. Three.\n\n (13) Induction by Analysis.\n Importance.\n Defined and illustrated.\n\n (14) Perfect Induction.\n Defined and illustrated.\n Its use.\n Method of Socrates.\n\n (15) Traduction.\n Defined and illustrated.\n Three methods compared.\n\n\n=17. SUMMARY.=\n\n(1) Reasoning is the process of deriving a judgment from two antecedent\njudgments. The syllogism is a common form of expressing the process of\nreasoning.\n\nInductive reasoning is reasoning from less general premises to a more\ngeneral conclusion.\n\nDeductive reasoning is reasoning from more general premises to a less\ngeneral conclusion.\n\nThe inductive syllogism is not supposed to conform to the canons of the\ndeductive syllogism.\n\n(2) Positing in the conclusion more than is indicated in the premises\ninvolves what is known as the \u201c_inductive hazard_.\u201d\n\nThe inductive hazard which is another expression for the spirit of\ndiscovery, should be fostered in the school room since it has been one\nof the great forces in human progress; but this venturesome spirit must\nbe regulated by rules, principles, and systematic procedure, or low\nideals of recklessness and inaccuracy will result.\n\n(3) The problem of induction is more complex than that of deduction;\nbecause the former is a comparatively new subject, and also is more\nclosely related to the activities of life.\n\n(4) The opinion relative to the exact nature of induction, though\nvaried, may be summed up in the thought of its being the process which\nleads to general truths, derived from the observation of individual\nfacts.\n\n(5) Induction and deduction are contiguous processes which go to\nmake up the more general process of thinking. Where induction ceases,\ndeduction naturally commences; induction discovers new knowledge,\ndeduction clarifies it.\n\n(6) Induction as a general process may be treated as a mode of\ninference or as a method. In either case the conclusion comprehends\nmore than is contained in the premises.\n\nSince no imperfect induction is absolutely free from doubt, on what\nground are we justified in making any inductive assumptions? The answer\nfollows:\n\n(7 and 8) \u201cNothing can occur without a cause and every cause has\nits effect,\u201d is the law of universal causation; while the law of the\nuniformity of nature is \u201cthe same antecedents are universally followed\nby the same consequents.\u201d These two laws justify inductive assumptions,\nand, in a sense, condition all thinking.\n\n(9) Uniformity of nature gives man confidence, while universal\ncausation arouses his curiosity. With these two weapons he is willing\nto \u201cmarch into the unknown.\u201d\n\n(10) As the process of universalizing individual experiences, induction\nassumes the three forms of simple enumeration, analogy and analysis.\nThe form adopted is not always elective but is controlled largely by\nthe exigency of the case. Some topics lend themselves to all three\nmodes.\n\n(11) Induction by simple enumeration consists in observing many\ninstances which exemplify the uniformity under consideration.\n_Complete_ enumeration gives the so called perfect inductive inference;\n_incomplete but uncontradicted_ enumeration leads to empirical truths;\nwhile _incomplete_ and _contradictive_ enumeration involves a mere\ncalculation of chances.\n\n(12) Induction by analogy assumes that if two (or more) things resemble\neach other in certain respects, they belong to the same type, and,\ntherefore, any fact known of the one, may be affirmed of the other.\n\nA most common form of analogy is reasoning by type or example. In\nthis it is assumed that if two or more things are of the same type,\nthey resemble each in every essential property. The type must be truly\nrepresentative. A second form of analogy is reasoning by marks of\nresemblance. This second form often leads to egregious error.\n\nAnalogy is especially valuable in suggesting hypotheses and in giving\ntraining in originality and initiative.\n\nA true analogy demands that the points of resemblance be representative;\nthat they outweigh the points of difference, and that no disagreement\nbe incompatible.\n\n(13) Induction by analysis is the process of dividing a whole into its\nparts with a view of deriving a generalization relative to the nature\nand causal connection of these parts.\n\nInduction by analysis makes use of the hypothesis, of observation and\nexperiment, including Mill\u2019s five methods.\n\n(14) A perfect induction is one in which the premises enumerate all of\nthe instances denoted by the conclusion. It is serviceable in inspiring\ncare and accuracy in the establishment of generalizations.\n\n(15) Traduction is the process of reasoning to a conclusion which is\nneither less general nor more general than the premises.\n\nTraduction includes reasoning from particular to particular or from\ngeneral to general. Perfect induction is in reality a form of\ntraduction.\n\nInduction, though the most useful form of inference, is the most\nuntrustworthy; whereas traduction is just the reverse of this.\n\n\n=18. REVIEW QUESTIONS.=\n\n (1) Define and illustrate reasoning.\n\n (2) Distinguish by definition and illustration between inductive and\n deductive reasoning.\n\n (3) Explain the \u201cinductive hazard\u201d and show its use to man.\n\n (4) \u201cFor twenty centuries Aristotle\u2019s Deductive Logic was the\n logician\u2019s bible.\u201d Explain this.\n\n (5) Show that induction and deduction are contiguous processes.\n\n (6) Distinguish between induction as a mode of inference and\n induction as a method.\n\n (7) State and explain the law of universal causation. Illustrate\n fully.\n\n (8) Make evident that a cause may involve many antecedents.\n\n (9) State and explain by illustration the law of uniformity of\n nature.\n\n (10) Verify by illustration the notion that the \u201cfact of causation\u201d\n conditions all induction.\n\n (11) Which of the two laws is empirical, \u201ccausation\u201d or \u201cuniformity\u201d?\n Why?\n\n (12) Show that induction is a form of thinking.\n\n (13) Why should the law of uniformity of nature convince man that\n nature is honest? Illustrate.\n\n (14) Show that the law of universal causation stirs the spirit of\n discovery.\n\n (15) Name and illustrate the three forms of induction.\n\n (16) Why is it that the tendencies of the investigator often determine\n the inductive form which he adopts?\n\n (17) Explain by illustration the three-fold outcome of induction by\n simple enumeration.\n\n (18) Selecting some class room experience, illustrate analogy by\n example or type.\n\n (19) Define and exemplify types as used in logic.\n\n (20) Remark upon the errors incident to analogy.\n\n (21) Summarize the advantages which induction by analogy offers.\n\n (22) State and exemplify the requirements of true analogies.\n\n (23) Indicate the superiority of induction by analysis over the other\n two forms. Illustrate.\n\n (24) Define and illustrate perfect induction.\n\n (25) Under what circumstances is perfect induction justified?\n\n (26) Define and illustrate traduction.\n\n (27) Indicate the various forms of traduction.\n\n\n=19. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Show the connection between illicit minor and the \u201cinductive\n hazard.\u201d\n\n (2) Show by illustration that time tends to universalize truth.\n\n (3) \u201cInduction and not deduction is the natural method of the child\n mind.\u201d Prove the correctness of this statement.\n\n (4) \u201cInduction is the process of inference by which we get at general\n truths from particular facts or cases.\u201d Prove that this is not\n strictly correct according to definition.\n\n (5) As related to establishing general truths, what are the special\n functions of induction and deduction?\n\n (6) Show that an inductive inference must of necessity be more or\n less uncertain.\n\n (7) Is there any distinction between the laws of universal causation\n and sufficient reason? Hyslop\u2019s Elements of Logic, page 329.\n\n (8) Show that universal causation and uniformity of nature are\n complementary laws. Hyslop, p. 330.\n\n (9) Relate the \u201cfact of causation\u201d to the laws of thought.\n\n (10) Distinguish between empirical and \u201ca priori\u201d laws.\n\n (11) When Harvey discovered the circulation of the blood, what form\n of induction did he use?\n\n (12) What form of reasoning did Columbus follow in proving that the\n earth is spherical?\n\n (13) \u201cIt is said that the greatness of Darwin was due largely to his\n habit of never ignoring an exception.\u201d Justify by illustration\n the truth of this assertion.\n\n (14) In analogical reasoning by example, under what conditions would\n _one_ illustration be as convincing as _many_?\n\n (15) \u201cConsidering the similarities and differences, the weight of the\n argument favors Mars\u2019 habitability.\u201d Suppose the proportion of\n probability were something like this\u2015\u2015Resemblances: Differences\n = 8:7; wherein might the conclusion be erroneous?\n\n (16) Mention a mark or characteristic which would make the\n habitability of Mars incompatible?\n\n (17) Select a topic for investigation which is peculiarly adapted to\n enumeration; to analogy; to analysis.\n\n (18) \u201cThe uniformities we expect to find in the world take two\n main aspects, one of which is indicated by the term _thing_ and\n the other by the term _circumstance_.\u201d Aikin\u2019s Principles of\n Logic, 1905; p. 233. In the light of the two fundamental laws\n of universal causation and uniformity of nature explain and\n illustrate the quotation.\n\n (19) Explain the principle of teleology as related to analogy. Hibben,\n 1908; p. 317.\n\n\n\n\n CHAPTER 18.\n\n THE FIVE SPECIAL METHODS OF OBSERVATION AND EXPERIMENT.[13]\n\n\n=1. THE AIM OF THE FIVE METHODS.=\n\nThe primary forms of induction have been divided into _simple\nenumeration_, _analogy_ and _analysis_ . Conditioning these forms are\nthe two laws, _uniformity of nature_ and _universal causation_. Since\nthese laws are always concerned with causes, we may refer to them as\ntogether expressing the fundamental \u201c_fact of causation_.\u201d Wherever\nthere is a causal connection, no matter how slight, these laws obtain.\n\nThough \u201cthe fact of causation\u201d probably conditions all forms of\ninduction, it is most conspicuous in the third form; namely, Analysis.\nHere the main aim is to establish a causal connection of some kind; an\naim which may be accomplished through the medium of observation and\nexperiment. Incident to this notion, John Stewart Mill formulated five\nexperimental methods of induction. These are known according to the\nfollowing distinctive titles:\n\n 1. The Method of Agreement.\n\n 2. The Method of Difference.\n\n 3. The Joint Method of Agreement and Difference.\n\n 4. The Method of Concomitant Variations.\n\n 5. The Method of Residues.\n\n\n=2. METHOD OF AGREEMENT.=\n\n(1) Principle stated. As stated by Mill the principle of the Method of\nAgreement is this: \u201cIf two or more instances of the phenomenon under\ninvestigation have only one circumstance in common, the circumstances\nin which alone all the instances agree is the cause (or effect) of the\ngiven phenomenon.\u201d\n\nThis notion is given in clearer terms by Jevons and Creighton. Viz.:\n\u201c_The sole invariable antecedent of a phenomenon is probably its\ncause_\u201d; and \u201c_The sole invariable consequent of a phenomenon is\nprobably its effect_.\u201d\n\nIt is known that an antecedent is anything which _precedes_; while a\nconsequent is anything which _follows_. To be regarded as a cause, an\nantecedent must be _invariable_, and to be regarded as an effect, a\nconsequent must likewise be _invariable_. Antecedents and consequents\nwhich are in no way constant could hardly have any causal connection.\n\n(2) Method symbolized. Let P\u2081, P\u2082, P\u2083, P\u2084, etc., represent the\nphenomenon as it may appear the first, second, third, fourth, etc.,\ntimes, and let A, B, C, etc., stand for the various antecedents, or the\nvarious consequents as the case may demand. These two forms may now be\nused to illustrate the two statements which summarize Agreement:\n\nFirst statement.\n\n _Antecedents._ _Consequents._\n A B C D \u2015\u2015 P\u2081\n A D E F \u2015\u2015 P\u2082\n A L M N \u2015\u2015 P\u2083\n A O P Q \u2015\u2015 P\u2084\n\nSecond statement.\n\n P\u2081 \u2015\u2015 A B C D\n P\u2082 \u2015\u2015 A D E F\n P\u2083 \u2015\u2015 A L M N\n P\u2084 \u2015\u2015 A O P Q\n\nIn the first case, the sole invariable antecedent is A, and, therefore,\nwe infer that A is probably the cause of P. In the second case, the\ninvariable consequent being A, is probably the effect of P.\n\n(3) Concrete examples illustrating first statement.\n\n_The Problem_: Cause of John\u2019s tardiness.\n\nOn investigation the various _antecedents_ are these: (1) John has\nhis breakfast at _seven_; (2) after breakfast he carries his father\u2019s\n_dinner_ to him and (3) feeds the hens; and then (4) goes to school by\nthe _path through the woods and around the mill pond_.\n\n_Phenomenon as a consequent._ John is tardy. Determining to do away\nwith the tardiness, the teacher brings about a variation in the\nantecedents, varying _one at a time_ taken in the order indicated above.\n\n To wit: (1) Varying the first antecedent.\n John breakfasts at 6:30;\n Other antecedents the same;\n (_Phenomenon_) But John is tardy.\n\n (2) Varying the second antecedent.\n The younger brother carries the dinner;\n Other antecedents the same;\n (_Phenomenon_) John is tardy.\n\n (3) Varying the third antecedent.\n Another brother cares for the hens;\n Other antecedents the same;\n\n (_Phenomenon_) John is still tardy.\n\nThe teacher is now quite certain that the tardiness is due to the route\nthrough the woods and around the pond.\n\nUsing, as symbols, the initial letters of the italicized \u201ckey-words\u201d\nof the antecedents as stated above, the case of tardiness may be\nsymbolized as follows:\n\n _Key words_ _Symbols_\n\n seven s\n dinner d\n hens h\n woods w\n tardy t\u2081, t\u2082, t\u2083\n\n _Antecedents_ _Phenomenon_\n s d h w t\u2081\n e d h w t\u2082\n s b h w t\u2083\n s d a w t\u2084\n\n\u201cw\u201d standing for route through the woods, is seen to be the invariable\nantecedent.\n\n(4) Concrete example illustrating the second statement.\n\n_The Problem_: To determine the effect of direct primaries.\n\n _First trial._\n\n _Antecedent_ _Consequents_\n\n { 1. Greater expense to candidate,\n Direct { 2. Greater interest shown,\n primary { 3. Better men nominated,\n { 4. \u201cBumper\u201d crops.\n\n _Second trial._\n\n { 1. Greater expense to candidate,\n Direct { 2. Greater interest shown,\n primary { 3. Better men nominated,\n { 4. Crops below average.\n\n _Third trial._\n\n { 1. No greater expense,\n Direct { 2. Greater interest shown,\n primary { 3. Better men nominated,\n { 4. Crops average.\n\n _Fourth trial._\n\n { 1. No greater expense,\n Direct { 2. No greater interest,\n primary { 3. Better men nominated,\n { 4. Crops average.\n\nIt is seen that the invariable consequent is, \u201cBetter men nominated.\u201d\nWe may, therefore, conclude that this is a probable effect of \u201cDirect\nprimaries.\u201d\n\n(5) Distinguishing features of method of agreement. The essential\ncharacteristics of the method of agreement are three:\n\n First, _The phenomenon always occurs_.\n Second, _There is at least one invariable antecedent_.\n Third, _The other antecedents vary_.\n\nGiving attention to the attending symbolized illustrations it may be\nnoted that \u201cP,\u201d the phenomenon, always happens; while in the case of\nthe first symbolization, \u201cD\u201d is the invariable antecedent and \u201cA, B, C,\nE, G, L, M, F, I\u201d are the variable antecedents. \u201cK\u201d is the invariable\nantecedent of the second and \u201cH, I, L, T, M, W, X, Y, Z, S\u201d are the\nvariable antecedents.\n\n _Antecedents_ _Consequents_\n\n 1. A B C D E \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2081\n A B C D G \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2082\n L B C D M \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2083\n A F G D M \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2084\n L B C D I \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2085\n\n 2. H I K L T \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2081\n K L M T W \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2082\n M T L K W \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2083\n X H K Y Z \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2084\n T W L K S \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 P\u2085\n\n(6) A Matter of Observation and Experiment.\n\nOn studying the problem relative to the tardiness of John, it appears\nthat in obtaining the various antecedents the work would be largely\na matter of _observation_. Carrying the father\u2019s dinner, the route\nthrough the woods, etc., are facts which observation would make evident.\nHowever, when it becomes necessary to vary these antecedents with a\nview to finding the invariable one, the procedure is experimental as\nwell as a matter of casual observation. Moreover, in connection with\nthe direct primary problem the question would be largely a matter of\nexperiment; though observation would obtain as a subsidiary condition.\nWe may conclude from this that the method of agreement involves _both\nobservation and experiment_; and since the student will discover\nthat the other methods impose similar demands, we are justified\nin designating these five special methods of induction as those of\nobservation as well as of experiment.\n\n(7) Advantages and Disadvantages of the Method of Agreement.\n\nThe concrete cases given to illustrate the method of agreement present\na simple combination of antecedents and consequents. In life, however,\nsuch simplicity does not usually obtain and in consequence the method\nof agreement gives rise to a few serious difficulties. These may be\nsummarized as (a) Plurality of causes; (b) Immaterial antecedents;\n(c) Complexity of phenomena; (d) Uncertainty of conclusion.\n\n(a) Plurality of causes is mentioned by Mill as constituting the\n\u201ccharacteristic imperfection\u201d of the method of agreement. As the term\nsignifies, plurality of causes represents a condition where a given\nphenomenon has more than one cause, or where different causes produce\nthe same effect. For example, \u201cA poor crop\u201d may be due to drought,\nneglect, pests, etc.; heat may be caused by friction, electricity,\ncombustion. Unfavorable home conditions; ill health; dislike for\nteacher\u2015\u2015any one of these might be followed by irregular attendance.\n\n(b) Immaterial antecedents are those which precede a given phenomenon\nand yet, under the most favorable situations, have no causal connection\nwith said phenomenon. For example, the various antecedents of the\nheavy rain may have been a south wind, forgetting to take an umbrella,\nmissing the car and having to walk, etc. Clearly these antecedents,\nwith the exception of the first, are immaterial.\n\n(c) The law of agreement demands that _all the material antecedents_\nreceive consideration, but often the situation is too complex to\nmake this possible; a fair illustration of such would be an attempt\nto ascertain all of the antecedents of \u201cthe high cost of living.\u201d\n\n(d) The law of agreement never precludes the possibility of error; as\nit is quite impossible to carry the analysis to the point of absolute\ncertainty. Of all the methods, \u201cagreement\u201d is the least reliable.\nDespite the foregoing objections, however, the method is of positive\nvalue because of its suggestiveness; opening the door to plausible\nhypotheses it gives the investigators a _working basis_.\n\n\n=3. METHOD OF DIFFERENCE.=\n\n(1) Principle stated.\n\nSays Mill, \u201cIf an instance in which the phenomenon under investigation\noccurs, and an instance in which it does not occur, have every\ncircumstance in common save one, that one occurring only in the former;\nthe circumstance in which alone the two instances differ is the effect\nor the cause of an indispensable part of the cause, of the phenomenon.\u201d\n\nTo put this in simple terms: _Whatever is invariably present when the\nphenomenon occurs and invariably absent when the phenomenon does not\noccur, other circumstances remaining the same, is probably the cause\nor the effect of the phenomenon._\n\n(2) Method symbolized.\n\nUsing the same symbols as were used in \u201cAgreement.\u201d\n\n _Antecedents_ _Consequents_\n A B C D P\n \u2012 B C D \u2012\n\n or\n\n P A B C D\n \u2012 \u2012 B C D\n\nIn the first instance A is probably the cause of the phenomenon, since\nit is present when the phenomenon occurs and absent when it does not\noccur. For a similar reason, A is the effect in the second case.\n\n(3) Concrete illustrations.\n\n(A) A wise teacher in ascertaining the cause of John\u2019s tardiness would\nhave suggested at once a change of route. Using as symbols the initial\nletters of the key-words of the antecedents in the case, the following\nresults:\n\n s d h w t\n s d h \u2212 \u2012\n\n(B) _First trial._\n\n_Problem_: Unprepared home work.\n\n _Antecedents_ _Consequents_\n\n 1. Length of lesson, }\n 2. Definiteness of lesson, } Work _not_ properly\n 3. Amount of interest shown, } prepared.\n 4. Physical condition the same. }\n\n_Second trial._\n\n 1. _Length_ of lesson the same, }\n 2. _Lesson made more definite_, } Work _properly_ prepared.\n 3. _Interest_ the same, }\n 4. Physical _condition_ the same. }\n\nThe foregoing symbolized:\n\n L D I C W\n L \u2012 I C \u2012\n\nIt is seen that indefiniteness of lesson assignment is the cause of the\nunprepared home work.\n\n(4) Advantages and disadvantages of the Method of Difference.\n\nThe main difficulty attending the use of the method of difference is\nthe _complexity_ of phenomenon. The very nature of the method insists\nas an essential requirement that _only one material antecedent shall\nbe varied at a time_. In life the variations are more or less confused,\nand it is often not only impossible to observe cases of a single\nvariation, but frequently error comes through _overlooking_ antecedents\nwhich are material to the case under investigation. For these reasons\nthe Method of Difference is more a method of _experiment_ than it is\na method of observation. By controlling the circumstances it becomes\npossible to vary but _one_ antecedent at a time, and also to bring into\nprominence _all_ of the _material_ antecedents.\n\nBacon claims that _all \u201ccrucial instances\u201d_ are merely applications of\nthe Method of Difference. By crucial instance he means any fact which\nwill enable us to determine _at once_ which supposition is the correct\none. For example, the physician may not know whether it is malaria or\ntyphoid fever till he takes a blood test; such a test typifies \u201ccrucial\ninstances.\u201d The various tests in chemistry are likewise cases of\ncrucial instances, and, in consequence, this science makes use of\n\u201cDifference\u201d more than any other method.\n\n(5) Characteristic features of Method of Difference.\n\nThere are three distinguishing marks of the Method of Difference: these\nare, (1) The phenomenon does not always happen; (2) _One_ antecedent is\nvariable; (3) The other antecedents are more or less invariable.\n\nThe following symbolizations will make these three characteristics\nevident:\n\n _Antecedents_ _Consequents_\n\n (1) A B C P\n A \u2012 C \u2012\n (2) \u2012 B C \u2012\n X B C P\n (3) L M T K P\n L M \u2012 K \u2012\n\n\n AGREEMENT AND DIFFERENCE COMPARED.\n\n(a) The methods of Agreement and Difference are complementary as may\nbe discerned by comparing their characteristic features: In Agreement\nthe phenomenon _always occurs_; in Difference the phenomenon _does\nnot always occur_: In Agreement there is one _invariable_ antecedent;\nwhereas in Difference there is one _variable_ antecedent: In Agreement\nthe other antecedents are more or less _variable_; but in Difference\nthe other antecedents are more or less _invariable_.\n\n(b) According to Mill the Method of Agreement insists that what _can\nbe eliminated_ is _not_ connected; whereas the Method of Difference\nimplies that what _cannot be eliminated is_ connected.\n\n(c) The Method of Agreement is more a method of observation, since\nit is chiefly concerned with the _discovery of causes_. The Method of\nDifference is distinctly a method of experiment, because its usual aim\nis to _discover effects_.\n\n(d) The Method of Agreement is so called because the object is to\ncompare several instances to determine in what respect they _agree_;\nbut in the case of Difference instances are compared to determine in\nwhat respects they _differ_.\n\n(e) The conclusions of the Method of Difference involve greater\ncertainty than those of Agreement and, therefore, the former method\nshould be adopted when there is a choice.\n\n\n=4. THE JOINT METHOD OF AGREEMENT AND DIFFERENCE.=\n\n(1) Principle stated.\n\nThe uncertainty of the conclusions of Agreement and the impossibility\nat times of employing directly the Method of Difference, give rise to\nthe use of the combination of Agreement and Difference known as the\nJoint Method. As stated by Mill, the principle conditioning the Joint\nMethod is this: \u201cIf two or more instances in which the phenomenon\noccurs have only one circumstance in common, while two or more\ninstances in which it does not occur have nothing in common save the\nabsence of that circumstance, the circumstance in which alone the two\nsets of instances differ is the effect or the cause or an indispensable\npart of the cause, of the phenomenon.\u201d More briefly the notion may\nbe stated in this wise: _Among many instances, if one circumstance is\ninvariably present when the phenomenon occurs, and invariably absent\nwhen the phenomenon does not occur this circumstance is probably the\ncause or the effect of the phenomenon._\n\nThis principle differs from the one underlying the Method of Difference\nin that the instances considered are more varied and more numerous. The\nprinciple of Difference requires but _two_ sets of instances, while the\nJoint Method demands at least three; _two_ when the phenomenon occurs\nand _one_ when it does not occur. A study of the symbolizations and\nillustrations will clarify this distinction.\n\n(2) Joint Method symbolized.\n\nIf we use circumstances and phenomenon in place of antecedents and\nconsequent, then one symbolization may be made to stand for\nascertaining either the invariable antecedent, or the invariable\nconsequent.\n\n _Circumstances_ _Phenomenon_\n\n 1. A B C D P\u2081\n 2. A D E F P\u2082\n 3. A L M N P\u2083\n 4. A O P Q P\u2084\n 5. O P Q \u2015\n 6. L M N \u2015\n 7. D E F \u2015\n 8. B C D \u2015\n\nIt is obvious that the first, second, third and fourth groups of\ninstances illustrate the principle of Agreement; whereas the first and\neighth, the second and seventh, the third and sixth, and the fourth and\nfifth illustrate in each case, the principle of Difference.\n\n(3) Concrete Examples illustrating Joint Method.\n\n_The problem_: Too much whispering.\n\n _Antecedents_ _Consequent_\n\n 1. Insufficient work, }\n Lack of interest, } Much whispering.\n _Seated near a friend._ }\n\n 2. More work, }\n Lack of interest, } Much whispering.\n _Seated near a friend._ }\n\n 3. More work, }\n More interest, } Much whispering.\n _Seated near a friend._ }\n\n 4. More work, }\n More interest, } Not much whispering.\n _Not seated near a friend._ }\n\n 5. More work, }\n Lack of interest, } Not much whispering.\n _Not seated near a friend._ }\n\n 6. Insufficient work, }\n Lack of interest, } Not much whispering.\n _Not seated near a friend._ }\n\nFrom this it may be concluded that the undue amount of whispering is\ncaused by seating particular friends near each other.\n\n_The problem_: Poor recitations.\n\n _Antecedents_ _Consequent_\n\n 1. Long lesson, }\n Faulty assignment of lesson, } Poor recitation.\n _Fear of teacher._ }\n\n 2. Lesson made shorter, }\n Faulty assignment of lesson, } Poor recitation.\n _Fear of teacher._ }\n\n 3. Lesson made shorter, }\n A more careful assignment, } Poor recitation.\n _Fear of teacher._ }\n\n 4. Lesson made shorter, }\n A more careful assignment, } Good recitation.\n _Removal of fear of teacher._ }\n\n 5. Lesson made shorter, }\n Faulty assignment, } Good recitation.\n _No fear of teacher._ }\n\n 6. Lesson long, }\n Faulty assignment, } Good recitation.\n _No fear of teacher._ }\n\nFear of teacher is the cause of the poor recitation.\n\n(4) Distinguishing features.\n\nBeing a combination of Agreement and Difference the Joint Method\npossesses the characteristics of _each_, though more or less modified.\nThe distinguishing marks may be summarized as follows:\n\n (1) Of the first group of instances:\n (1) The phenomenon must always occur,\n (2) One antecedent must be invariable,\n (3) The other antecedents must be more or less variable.\n\n (2) Of the second group of instances:\n (1) The phenomenon must never occur,\n (2) One antecedent must be variable,\n (3) The other antecedents must be more or less invariable.\n\nBriefly, the one principle concerned is this: There must be an\ninvariable conjunction between the phenomenon involved and the\nantecedent suspected of being the cause.\n\n(5) Advantages and Disadvantages of the Joint Method.\n\nSince the Joint Method permits a consideration of the negative aspect\nof the question as well as the affirmative, the opportunities for\ntesting the many instances concerned are doubled. In consequence, the\nconclusions of the Joint Method are more positive than those of the\nother methods. It follows that this same opportunity to multiply the\ninstances would tend to lessen the other objections raised against the\nMethod of Agreement; viz., plurality of causes, immaterial antecedents,\ncomplexity of phenomenon.\n\nThe student must regard the given illustrative symbolizations and\nconcrete examples as being of the simplest form; in life such are the\nexceptions rather than the rule. When investigating questions, like\nthe cause of the high cost of living, the effect of high tariff, the\nreason for the typhoid epidemic, etc., there is often a confusion of\ncircumstances which makes the Joint Method unsatisfactory, even though\nit furnishes a larger opportunity for the multiplication of instances.\n\nThe strongest case which the Joint Method is able to present is when\nthe negative instances repeat the positive in every detail, with the\none exception of the variable antecedent. To wit:\n\n _Strong Argument_:\n\n _Circumstances_ _Phenomenon_\n A B C P\u2081\n A L M P\u2082\n \u2012 L M \u2015\n \u2012 B C \u2015\n\n _Weak Argument_:\n A B C P\u2081\n A L M P\u2082\n \u2012 R S \u2015\n \u2012 T K \u2015\n\nDespite the disadvantages, the conditions of the Joint Method are more\nor less ideal; since the positive branch of the argument _suggests_\nthe hypothesis, while the negative branch _proves_ the accuracy or\ninaccuracy of such.\n\n\n=5. METHOD OF CONCOMITANT VARIATIONS.=\n\n(1) Principle stated.\n\nMill\u2019s statement is this: \u201cWhatever phenomenon varies in any manner\nwhenever another phenomenon varies in a particular manner, is either a\ncause or an effect of that phenomenon, or is connected with it through\nsome fact of causation.\u201d\n\nTo put it differently: _If when one phenomenon varies alone, another\nalso varies alone, the one is either the cause or the effect of the\nother._\n\n(2) Concomitant Variations symbolized.\n\n Circumstances Phenomenon\n A P\n A + a P + p\n (A + a) \u2212 a (P + p) \u2212 p\n\nIt is evident from this that little \u201ca\u201d is the cause or the effect of\nlittle \u201cp.\u201d To put it in concrete form:\n\nLet A = X number of calories of heat,\n\nAnd P = 68\u00b0 F., the original temperature of room,\n\nAnd a = candle burning in room for \u00bd hour,\n\nAnd p = 2\u00b0 F.\n\nThen\n\n _Antecedents_ _Consequent_\n\n X no. of cal. of heat in room = 68\u00b0 F. temp. of room\n X no. of cal. of heat + burning candle = 68\u00b0 + 2\u00b0 = 70\u00b0\n X (no. of cal. of heat + burning candle) = (68\u00b0 + 2\u00b0) \u2212 2\u00b0 = 68\u00b0\n \u2212 burning candle\n\nAs large \u201cA\u201d is increased and decreased by little \u201ca\u201d so large \u201cP\u201d\nappears to be increased and decreased by little \u201cp.\u201d This strongly\nsuggests a causal connection between little \u201ca\u201d and little \u201cp.\u201d\n\n(3) Other concrete illustrations.\n\n_Problem_: To ascertain nature of sound.\n\n _Antecedent_ _Consequent_\n\n Bell rung when within a glass jar filled Loud sound.\n with air,\n Some of the air pumped out of the jar, Sound not so loud.\n More air pumped into jar again, Sound louder again.\n\nThe conclusion must be that air has something to do with the production\nof sound.\n\n_Problem_: To find best feed for egg production.\n\n 100 lbs. beef scraps, }\n 100 lbs. wheat, } 30 doz. eggs.\n 100 lbs. oats, }\n 100 lbs. corn, }\n\n 50 lbs. beef scraps, }\n 100 lbs. wheat, } 27 doz. eggs.\n 100 lbs. oats, }\n 100 lbs. corn, }\n\n 90 lbs. beef scraps, }\n 100 lbs. wheat, } 28 doz. eggs.\n 100 lbs. oats, }\n 100 lbs. corn, }\n\nSince the variation in the amount of beef scraps is accompanied by a\nlike variation in the number of eggs produced, it may be assumed that\nbeef scraps are essential to large egg production.\n\n(4) Distinguishing features.\n The phenomenon always occurs but in varying degrees;\n One antecedent varies in degree;\n The other antecedents are invariable.\n\n(5) Advantages and disadvantages.\n\nConcomitant Variations is applicable in cases when it is impossible\nto use Difference. Recourse is made to the latter when the phenomenon\ncan be made to appear or disappear at will, but there are times when\nit is impossible to cause the phenomenon to disappear altogether. For\nexample, in the case of the varying degrees of heat in the room it\nwould be scientifically impossible to take _all_ of the heat out of\nthe room; or in experimenting with gravitation, to do away with its\ninfluence entirely, is beyond the power of man. It is thus evident that\nConcomitant Variations may be used in cases where the conditions forbid\ndoing away entirely with the phenomenon.\n\nThe special function of Concomitant Variations seems to be to establish\nthe exact quantitative relation between the varying cause and the\nvarying effect. To illustrate: As a general law it is known that bodies\nattract each other in varying degrees according to their distances\napart and according to their relative sizes; by Concomitant Variations\nthis law has been given definite quantitative value and reads like\nthis: \u201cBodies attract each other directly as the product of their\nmasses, and inversely as the square of the distance between them.\u201d\nThis illustration suggests that the variation between antecedent and\nconsequent may be _direct_ or _inverse_.\n\nThe error most common in this method is the assumption that the\nquantitative relation between two varying phenomena will always be\naccording to a _constant ratio_. For example, when being reduced\nfrom a high temperature to 39\u2155\u00b0 F., water steadily contracts; but at\n39\u2155\u00b0 F. it commences to expand until it becomes ice. Thus the ratio\nof contraction of water is constant only within certain limits. In any\nevent the established ratio of variation can with absolute safety be\napplied only to the _instances investigated_. Another disadvantage\nincident to this method, is the situation of two elements varying\ntogether constantly, and yet having no causal connection whatever.\n\n\n=6. THE METHOD OF RESIDUES.=\n\n(1) Principle stated.\n\nAs stated by Mill the principle of residue is this: \u201cSubtract from\nany phenomenon such part as is known by previous inductions to be the\neffect of certain antecedents, and the residue of the phenomenon is the\neffect of the remaining antecedents.\u201d\n\nIn simpler form the notion is this: _Subtract from any phenomenon those\nparts of it which are known to be the effect of certain antecedents,\nand what is left of the phenomenon is the effect of the remaining\nantecedents_.\n\n(2) Principle symbolized.\n\n _Antecedent_ _Consequent_\n\n A x\n B y\n C z\n\nThe total cause of the phenomenon xyz is ABC. But it is known that\nthe cause of x is the antecedent A; whereas the cause of y is the\nantecedent B; hence it is concluded that the cause of z is the\nantecedent C.\n\n(3) Concrete illustrations.\n\n_Problem_: To find the weight of coal.\n\n _Antecedents_ _Consequents_\n\n Weight of driver, }\n Weight of wagon, } = 4200 lbs.\n Weight of coal. }\n\n Weight of driver, } = { 200 lbs. } = 2200 lbs.\n Weight of wagon, } { 2000 lbs. }\n\nHence we may conclude that the weight of coal is 4200 lbs. \u2212 2200 lbs.,\nor 2000 lbs.\n\nPerhaps the most noted instance in history of the application of\nthis method, was the one which resulted in the discovery of Neptune.\nIn calculating the orbit of Uranus, it was found that the combined\nattractions of the sun and the known planets did not account for the\npath which Uranus took. There was some unknown influence at work.\nAssuming that this unaccountable attraction was due to the presence of\nanother planet beyond the orbit of Uranus, an Englishman by the name\nof Adams, and later the Frenchman Leverrier, were able to indicate by\nthe principle of Residues, the spot where this planet should be. By\ndirecting the telescope toward this point, Neptune was discovered.\n\n(4) Distinguishing features:\n The phenomenon always occurs,\n The antecedents are usually invariable,\n Some of the antecedents are known to be the cause of a part of\n the phenomenon.\n\n(5) Advantages and disadvantages.\n\nThe Method of Residues gives three distinct results: First, it tells\n_what_ is left over after all the other parts of the phenomenon have\nbeen explained. Second, it tells _how much_ is left over, and third,\nit calls attention to the _unexplained parts_ of the phenomenon. For\nexample, in the first concrete illustration, by subtracting the known\nquantities from the total quantity, what is left over is found to be\ncoal; not only so but we are able to calculate the exact amount of\ncoal. This illustrates the first and second results of the Method of\nResidues. (Like concomitant variations it is seen that residues is\nserviceable in given _definite quantitative values_.) The discovery of\nNeptune illustrates well the third result of this method; i. e., after\naccounting for every other force, it was found that there was yet a\nforce at work which had never been explained. It is this third feature\nof _unexplained residues_ which has placed \u201cScience in its present\nadvanced state.\u201d \u201cMost of the phenomena which nature presents are\ncomplicated; and when the effects of all known causes are estimated\nwith exactness, and subducted, the residual facts are constantly\nappearing in the form of phenomena altogether new, and leading to the\nmost important conclusions.\u201d So says John Herschel. Almost all of the\ndiscoveries in astronomy have come about in this way. If a heavenly\nbody does not behave as it should according to the established theory,\nthen either the theory is wrong or there is some _residual phenomenon_\nwhich needs to be explained. Its suggestiveness is, therefore, the most\nimportant function of this method, though this very feature is the one\nwhich makes evident its greatest disadvantage. The unexplained residual\nphenomenon may be very complex and, therefore, a careless observer is\napt to overlook a lurking element which in reality is the true cause.\n\n\n=7. THE GENERAL PURPOSE AND UNITY OF THE FIVE METHODS.=\n\nThinking has been defined as the deliberative process of affirming\nand denying connections. It is obvious that these five methods are a\nmatter of affirming and denying connections between antecedents and\nconsequents. As soon as the looked for connections are established,\nthe antecedents and consequents are known to be related to each other\nas causes and effects. In this attempt to find and prove connections\nthe Method of Agreement is chiefly valuable in suggesting workable\nhypotheses, and the method of difference in verifying, through\nexperiment, the correctness or incorrectness of these hypotheses.\n\nIn substance the principle conditioning both methods is this: \u201c_If\na single antecedent is invariably present when the phenomenon is\npresent and invariably absent when the phenomenon is absent then this\nantecedent is the cause of the phenomenon._\u201d To put it still more\nbriefly: _Between two phenomena there is a causal connection, if the\nconjunction between the two is invariable._ It is the business of\nAgreement to _single out the one antecedent_ and of Difference to\nshow, by presenting the negative as well as the affirmative side of the\ncase, that the _conjunction of the one antecedent and the particular\nphenomenon is invariable_. The Joint Method is merely a combination\nof Agreement and Difference carried into more varied and complex\nsituations. The methods of Concomitant Variations and Residues are\nmerely modifications of Difference; the former being used when the\n_chief feature is the fluctuation_ of the phenomenon, and the latter\nwhen it is desired to find _what is left over_.\n\n_Agreement suggests the hypothesis, \u201cdifference\u201d proves it; the\njoint method is \u201cdifference\u201d more or less complicated, concomitant\nvariations is \u201cdifference\u201d applied to fluctuating phenomena, residues\nis \u201cdifference\u201d used to find what and how much is left over._\n\nAgreement is the method of observation and belongs to the physician\nand nature student. Difference and the Joint Method are experimental\ndevices which are used by the physicist and chemist. Concomitant\nVariations is the method of unstable phenomena and naturally attaches\nitself to the economist and statistician. Residues is the method of\n\u201clurking exceptions\u201d and is favored by the astronomer and mathematician.\nResidues, being the method of \u201cwhat is left over,\u201d is the most common\nin daily affairs.[14]\n\n_All the five methods are forms of inductive thinking which lead to the\nestablishment of causal connections by means of the principle of the\ninvariable conjunction of phenomena._\n\n\n=8. OUTLINE.=\n\n THE FIVE SPECIAL METHODS OF OBSERVATION AND EXPERIMENT.\n\n (1) Aim of Five Methods.\n Fundamental fact of causation.\n\n Aim of analysis.\n { agreement\n { difference\n Methods of { joint\n { concomitant variations\n { residues\n\n (2) Method of Agreement.\n Principle stated\n Method symbolized\n Method illustrated\n Distinguishing features of method\n A matter of observation and experiment\n Advantages and disadvantages\n\n (3) Method of Difference.\n Principle stated\n Method symbolized\n Method illustrated\n Advantages and disadvantages\n Characteristic features\n Agreement and Difference compared\n\n (4) The Joint Method of Agreement and Difference\n Principle stated\n Method symbolized\n Concrete illustrations\n Distinguishing features\n Advantages and disadvantages\n\n (5) Method of Concomitant Variations\n Principle stated\n Method symbolized\n Concrete illustrations\n Distinguishing features\n Advantages and disadvantages\n\n (6) The Method of Residues\n Principle stated\n Method symbolized\n Concrete illustrations\n Distinguishing features\n Advantages and disadvantages\n\n (7) General Purpose and Unity of Five Methods\n One fundamental principle\n\n\n=9. SUMMARY.=\n\n(1) The fundamental fact of causation underlies the three forms of\ninduction, but is most conspicuous in the method of analysis and may\nbe ascertained by recourse to one of the experimental methods.\n\n(2) The principle of the method of agreement may be summed up in the\ntwo statements: The sole invariable antecedent of a phenomenon is\nprobably its cause and the sole invariable consequent of a phenomenon\nis probably its effect. These two statements may be symbolized and\nillustrated.\n\nThe essential characteristics of the method of agreement are the\nphenomenon always occurs; there is at least one invariable antecedent;\nthe other antecedents vary.\n\nThe method of agreement together with the other four methods may justly\nbe termed methods of experiment as well as methods of observation.\n\nThe difficulties of the method of agreement are in the main plurality\nof causes, immaterial antecedents, complexity of phenomenon and\nuncertainty of conclusion. These difficulties may be summarized as\ninvolving a phenomenon which may have several causes; may be preceded\nby conditions of no causal consequence; may be so involved as to\nprevent exhaustive examination; and may give unreliable conclusions.\n\nAgreement is valuable chiefly in furnishing to the investigator\nplausible hypotheses.\n\n(3) The principle of difference is this: \u201cWhatever is invariably\npresent when the phenomenon occurs and invariably absent when the\nphenomenon does not occur, other circumstances remaining the same,\nis probably the cause or the effect of the phenomenon.\u201d\n\nLike agreement, difference admits of symbolization and illustration by\nconcrete examples.\n\nThe chief difficulties attending difference are: in nature varying\n_one_ antecedent at a time is infrequent, and it is easy to overlook\nantecedents which are closely related to the case under investigation.\n\nDifference is the most common method of the experimental sciences.\nThe characteristic features of difference are, the phenomenon does\nnot always occur, one antecedent is variable, while the others are\ninvariable.\n\nThe methods of agreement and difference are complementary processes.\nAgreement attempts to eliminate all the antecedents but one, while\ndifference aims to eliminate one only. Agreement is a method of\nobservation, while difference is a method of experiment. The conclusion\nof the method of difference gives greater certainty than that of the\nmethod of agreement.\n\n(4) The joint method may be stated in this way: Among many instances if\none circumstance is invariably present when the phenomenon occurs and\ninvariably absent when the phenomenon does not occur, this circumstance\nis probably the cause or the effect of the phenomenon.\n\nThe instances of the joint method are more numerous and more varied\nthan those of either agreement or difference.\n\nThe joint method has the distinguishing characteristics of both\nagreement and difference.\n\nBecause it furnishes greater opportunities for multiplying and varying\nthe instances involved, the joint method presents fewer objections than\neither of the two separate methods.\n\nThe positive branch of the joint method suggests the hypothesis, while\nthe negative branch proves it. This makes the method somewhat ideal.\n\n(5) The principle of concomitant variations may be stated as follows:\nIf when one phenomenon varies alone, and another also varies alone,\nthe one is either the cause or the effect of the other. This is the\nmethod of fluctuation, and is used when it is impossible to make\nthe phenomenon disappear altogether, as in the case of difference.\n\nThe chief function of concomitant variations is to establish exact\nquantitative relations between cause and effect.\n\n(6) The principle of residues is this: Subtract from any phenomenon\nthose parts of it which are known to be the effect of certain\nantecedents, and what is left of the phenomenon is the effect of the\nremaining antecedent.\n\nThe most valuable feature of residues is its suggestiveness; an\nattempt to explain the \u201cresidual phenomenon\u201d has led to many important\nscientific discoveries.\n\n(7) The five methods are concerned with the establishment of causal\nconnections between phenomena. Agreement _suggests_ the connection\nwhile difference _proves it_. The other methods are modified\napplications of difference, necessitated by some peculiar form which\nthe phenomenon may take. A statement of the one principle involved is:\n\u201cIf the conjunction between two phenomena is _invariable_ then there is\na causal connection.\u201d\n\nAll of the methods are forms of inductive thinking.\n\n\n=10. REVIEW QUESTIONS.=\n\n (1) Explain \u201cthe fundamental fact of causation.\u201d\n\n (2) Show that the fact of causation is most conspicuous in induction\n by analysis.\n\n (3) Name the five special inductive methods of observation and\n experiment.\n\n (4) State, symbolize, and illustrate the method of agreement.\n\n (5) Give examples of antecedents which do not function as causes.\n\n (6) Show that the \u201cspecial methods\u201d are a matter of both observation\n and experiment.\n\n (7) Give the distinguishing features of the method of agreement;\n illustrate by reference to the symbols.\n\n (8) Exemplify the plurality of causes; immaterial antecedents;\n complexity of phenomenon.\n\n (9) Show that the conclusions of agreement are largely hypothetical.\n\n (10) State, symbolize, and illustrate the method of difference.\n\n (11) Show by illustration that, in the method of difference, only one\n antecedent should be varied at a time.\n\n (12) Show that difference is naturally a method of experiment.\n\n (13) Explain Bacon\u2019s use of the term \u201ccrucial instances.\u201d\n\n (14) Name and explain the characteristic features of the method of\n difference.\n\n (15) Show that agreement and difference are complementary.\n\n (16) Explain and illustrate the joint method.\n\n (17) What inference may be drawn from the following instances:\n\n _Antecedents_ _Consequents_\n\n A L M T p q r g\n B L M E z q r x\n B C M E r z x y\n A M T H p q g o\n\n (18) \u201cMr. Darwin, in his experiment on cross and self fertilization\n in the vegetable kingdom, placed a net about one hundred flower\n heads, thus protecting them from the bees. He at the same time\n placed one hundred other flower heads of the same variety of\n plant where they would be exposed to the bees. He obtained\n the following result: The protected flowers failed to yield\n a single seed. The others yielded about 2,720 seeds. Thus\n cross-fertilization was proved.\u201d (Hibben).\n\n What method did Darwin employ? Symbolize the experiment.\n\n (19) Summarize the distinguishing marks of the joint method.\n\n (20) Show that the joint method is more ideal than either agreement\n or difference.\n\n (21) State and give concrete illustrations of the law of concomitant\n variations.\n\n (22) What is the chief function of concomitant variations? Illustrate.\n\n (23) Give instances where it would be impossible to use difference,\n but easy to use concomitant variations.\n\n (24) Explain this: \u201cThe quantitative variation between antecedent and\n consequent may be either direct or inverse.\u201d\n\n (25) State and explain by illustration the method of residues.\n\n (26) What are the advantages and disadvantages of the principle of\n residues?\n\n (27) State the principle which virtually sums up the five methods.\n\n (28) Write briefly on the practical applications of the five methods\n to the ordinary walks of life.\n\n\n=11. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) Trace the connection between the method of agreement and\n induction by simple enumeration.\n\n (2) Show that Mill\u2019s methods may properly be termed \u201cInductive\n Methods of Scientific Investigation.\u201d\n\n (3) How may it be shown by \u201cagreement\u201d that the high cost of living\n is due to the tendency to spend more than we earn?\n\n (4) Assume that you are a member of the Board of Health, and that you\n desire to ascertain the cause of the diphtheria epidemic by means\n of the principle of agreement.\n\n (5) What is the error involved in coming to the conclusion that to\n sit at table where there are thirteen, may mean the death of\n _one_ of the thirteen before the end of the year.\n\n (6) Indicate how it could be shown, by the method of difference, that\n the mosquito is responsible for the propagation of yellow fever.\n\n (7) \u201cAnother experiment similar to this was tried by Plateau, who put\n some food of which cockroaches are fond on a table and surrounded\n it with a low circular wall of cardboard. He then put some\n cockroaches on the table; they evidently scented the food, and\n made straight for it. He then removed their antennae.\u201d (Hibben).\n Complete and give with explanations the method used.\n\n (8) \u201cIn some cases it is impossible to remove an element which is\n supposed to be the cause of an effect under investigation.\u201d\n Explain and illustrate.\n\n (9) \u201cExtreme care must be taken that, in the withdrawing of any\n element, no other element is inadvertently introduced.\u201d Tyndale\n supposed he had proved _spontaneous generation_, when, after\n sealing in a jar of boiled water a wisp of baked hay, he found,\n after many days, indications of life within the bottle. In\n transferring the hay to the bottle, he carried the former across\n the room. What element was inadvertently introduced?\n\n (10) \u201cThe attempt to determine the numerical relations according to\n which two phenomena vary, requires the utmost caution as soon as\n our inference outsteps the limits of our observations.\u201d (Fowler).\n Explain this in connection with the law of concomitant variations.\n\n (11) \u201cWhen the effects of all known causes are estimated with\n exactness and subducted, the _residual facts_ are constantly\n appearing in the form of phenomena altogether new, and leading\n to the most important conclusions.\u201d Make clear by illustration\n this quotation which has reference to the principle of residues.\n\n (12) Explain \u201cinvariable conjunction of phenomena.\u201d\n\n (13) Investigate by means of one of the five methods the following\n problems:\n\n (1) \u201cAll vegetables which grow to root should be planted during\n the last two days of the waxing moon.\u201d\n\n (2) \u201cIn this section the _south_ wind is the _storm_ wind.\u201d\n\n (3) \u201cMischief is the outcome of misdirected energy.\u201d\n\n (4) \u201cBad boys usually receive unjust treatment.\u201d\n\n (5) \u201cAn ounce of prevention is worth a pound of cure.\u201d\n\n\n\n\n CHAPTER 19.\n\n THE AUXILIARY ELEMENTS OF INDUCTION.\n\n OBSERVATION\u2015\u2015EXPERIMENT\u2015\u2015HYPOTHESIS.\n\n\n=1. THE FOUNDATION OF INDUCTIVE GENERALIZATIONS.=\n\nInduction is the process of universalizing particular facts. _The\nstarting point is the fact._ Through observation the investigator\ngathers _facts_, and then works them over with a view of finding\n_uniformities_. The mind cannot build inductive generalizations without\nfacts any more than a mason can build a brick wall without the bricks.\n\nA fact is any particular thing _made_ or _done_ or is that which may\nbe acquired by means of the presentative (perception and imagination)\npowers of the mind. The state of awareness which results from the\nobservation of facts is an individual notion. This presents another\naspect of the inductive process; namely, \u201cIt is a matter of building\ngeneral notions from individual notions, acquired by the observation\nof facts.\u201d To illustrate: I note that A, B, C and D are honest in their\ndealings with me, hence I come to the conclusion that some men are\nhonest. A fact is something done, consequently the actual doing of the\nhonest things by A, B, C and D are facts. Each state of awareness of\neach fact is an individual notion. The mind now discerns a uniformity\nin these facts and derives the general notion that \u201csome men are\nhonest.\u201d\n\n\n=2. OBSERVATION.=\n\nFacts are acquired by means of observation. When the mind fixes the\nattention upon any phenomenon it _observes_ it. The term observation\nmeans \u201cto watch for\u201d and may be defined _as the act of watching for\nphenomena as they may occur_. The observation may be only casual,\nor it may be _willed_ or rational. It is the latter aspect which\nmost concerns the logician. In this sense observation means careful,\npainstaking, systematic perception. It involves the concentration of\nconsciousness upon the case in hand, or the actual giving of attention.\nThe thing observed may be external, when the observation takes the\nform of _sense-perception_; or it may be internal, when the observation\nbecomes a matter of _introspection_.\n\n\n=3. EXPERIMENT.=\n\nIn observation we simply _watch_ the phenomenon; in experiment we\n_make_ it. In experiment we not only observe, but we _manipulate_ the\ncircumstances so as to present the phenomenon under the most favorable\nconditions for observation. \u201cIn observation,\u201d says Mill, \u201cwe _find_ an\ninstance in nature suited to our purposes\u201d; whilst in experiment, by an\nartificial arrangement of circumstances, we _make_ an instance suited\nto our purpose. In observation we watch for causes; in experiment we\nwork for effects. We may thus define experiment as _the act of making\nphenomena occur for the purpose of watching for effects_. In experiment\nthere is much which is merely observation. In fact experiment _is_\nobservation in which the phenomenon is artificially produced. For\nthe sake of definiteness, however, any observation which involves a\n_manipulation of circumstances_, may be designated as _experimental_.\n\n\n=4. RULES FOR LOGICAL OBSERVATION AND EXPERIMENT.=\n\nTo the uninitiated, the matter of observation seems an easy task, and\nyet when one hears two honest men swear to diametrically opposite facts\nwhich have come to them from observing the same phenomenon, his faith\nis shaken. \u201cEyes have they but see not\u201d is a logical truth as well as\na moral one. Only the observation of the trained can be depended upon;\nand yet this should not discourage the layman, for even he, by a little\nconscientious effort towards careful observation, may greatly increase\nhis store of accurate knowledge and add to the joy of living.\n\nThe attending rules are usually heeded by the trained scientist in\nmatters of observation and experiment:\n\n_First Rule. The observations should be precise._ The time, the place,\nthe surrounding conditions _must_ be accurately noted. Many artificial\ncontrivances have been devised because of the desire of the scientist\nto be precise. Instruments like the balance, the thermometer, the\nmicroscope, etc., has he invented, and various devices and methods\nhas he adopted for the sake of _precision_. A common method is to take\nan _average of observations_. For example, to estimate justly the\nclass work of a student, the teacher should not be content with the\nratings of one or two recitations, but must average the ratings of many\nrecitations. Again, a child may be led to discover approximately the\nvalue of the sum of the interior angles of a triangle by measuring the\nangles of many triangles and then striking an average; assume that the\nfollowing results are obtained by such a procedure: (1) 178, (2) 181,\n(3) 179, (4) 180, (5) 182; adding these and dividing by 5 gives 180.\n\n_Second Rule. The observations should concern only the material\ncircumstances of the case in hand._ All the non essentials may be\nignored, as they serve only to distract attention. For example, (1) in\norder to get the \u201cright count\u201d all other sounds must be ignored save\nthat of the _fire gong_; (2) in finding the depth of the water for the\nbuilding of a dam, soundings ten miles away from the objective point\ncould be of little value. On the other hand, it is easy to overlook\ncertain lurking essentials. To observe such, it is necessary to resort\nto what the psychologist terms a \u201c_preadjustment of attention_.\u201d We\nmust know with exactness what we are looking for. We must have a mental\nimage of what we wish to see. The astronomer in the discovery of a\nnew planet must know the exact spot where it ought to be, and have\na clear mental image of its appearance. This _expectant attention_\nis a necessity in the case of the physician who is anxious to make no\nmistakes in his diagnosis. If he is looking for pneumonia, he must have\na very distinct auditory image of the sound of an affected lung. It\nshould be remarked, however, that this very preadjustment of attention,\nwith the untrained, frequently leads to illusion. We are so anxious to\nsee what we are looking for that nine-tenths of what we believe we see\nis only inference. How easy it is to read into a phenomenon something\nthat is entirely foreign to it; to read between the lines; to see only\nthe reflection of our own ideas. \u201cVerily the mental picture of what we\nwish to see becomes so vivid that we are positive of the thing being\nexternal.\u201d Thus the drunkard sees snakes and the superstitious see\nghosts. _Reading into the external what is only vividly internal is\nprobably the most common error with the untrained observer._\n\n_Third Rule. The observed circumstances should be varied as much as\npossible._ To observe a fact from a different viewpoint may not only\nbroaden the original notion, but it may change it entirely. In order to\ngain a true notion of the effect of a particular nostrum on the human\norganism, it becomes necessary to experiment with persons of different\nages, living under different environments, and inheriting different\nconstitutions. Those who are noted for pronouncing broad, safe and\nsane judgments upon momentous questions are those who are \u201call-angled\nobservers.\u201d\n\n_Fourth Rule. The observed phenomenon should, if possible, be isolated\nfrom all interfering phenomena._\n\nIn studying the action of a drug or a food, all other drugs or foods\nmust be eliminated. The effect of gravitation on a body cannot be\nrecorded accurately unless the experiments are made in a vacuum. When\nstudying the deflections of the compass, all magnetic substances must\nbe removed from the field.\n\n\n=5. COMMON ERRORS OF OBSERVATION AND EXPERIMENT.=\n\nThe rules for scientific observation have suggested certain common\nerrors which may now be considered.\n\n(1) Preconceived ideas.\n\nThere is not an unholy belief nor an unwholesome theory which cannot be\nbolstered up by means of apparent facts. For example, that monstrosity\nof Puritan thought known as \u201cSalem Witchcraft\u201d was substantiated by\nfacts honestly observed. Again, having made up his mind that it is\ngoing to be \u201cso and so,\u201d the statistician goes out into the highways\nand byways and gathers the facts which vindicate his judgment. Further,\nthe democrat finds that the _majority_ of the voters are democrats;\nwhile the republican is confident that _two-thirds_ of the voters\nare for republicanism. Here again is the fallacy springing from\na preadjustment of attention. _We see what we want to see._ Only\nthe highly trained observer is able, with impunity, to make use of\npreadjusted attention, and even with him, it is not easy to remove\nfrom the situation _belief_ and _prejudice_.\n\nThe true observer undertakes his work with his mind open to _anything_\nwhich the eye may bring him, though it may topple into the dust his\ndearest theory and most cherished belief; he proceeds\u2015\u2015_the mind a\n\u201cclean white page.\u201d_\n\n(2) The \u201cobserved\u201d and the \u201cinferred\u201d confused.\n\nThis error has already received some attention. It may be remarked\nfurther, however, that, psychologically considered, observation is a\nmatter of interpreting the new by means of the old. Of necessity the\ninterpretation, whatever it may be, will assume the complexion of the\nparticular \u201cold knowledge\u201d which the mind is able to use. In short, a\nman _will_ see what his previous environment has _trained_ him to see;\nthe conscientious gardener sees the weeds, whilst the artist may see\nnothing but the flowers. It follows, therefore, that all observation\nmust be largely a matter of inference based on experience. In looking\nat the moon, for example, all I actually see is a patch of color; the\nform and distant location of the moon being a matter of experience.\n\nThe inference referred to in this heading is not that which is\n_necessary_ for perception, but that which is _suggested_ by perception.\nTo illustrate: It is icy; three men are running for a car; Smith raises\nhis arm; Jones slips to the ground; and Brown testifies, that \u201cSmith\nknocked Jones down.\u201d Brown _observed_, that Smith assumed the proper\nattitude and that Jones conveniently went down at the right time; and\nthen _inferred_ the rest.\n\n(3) Ignoring the exceptions.\n\nThis comes through an over anxiety to prove our theory. With this\nmental attitude, the observations which are corroborative will so\ncompletely fill the mental field, that the exceptions are made to\nseem of no consequence. This accounts for the superstition attached\nto _thirteen_. As a coincidence some one at some time died who had\npreviously eaten at a table where there were thirteen. Perhaps during\nthe life of the superstitious one this happened on two or three\noccasions, but the fact so impresses the subject that he ignores\nthe _dozen_ times when death did not follow. Other generalizations\nbelonging to this class are (1) people never die at flood tide;\n(2) there must be three accidents in succession; (3) the first sight\nof the new moon over the right shoulder is a good omen; (4) seeds which\ngrow to root do best when planted during the last days of the waxing\nmoon; (5) horse chestnut in pocket guards against sore throat, etc.\n\n(4) Sympathy and undue interest.\n\nThe influence of the heart over the brain is well known. A physician\nis liable to this error when he attempts to prescribe for one of his\nown family. Sympathy not only warps the judgment but it may actually\ninterfere with the accuracy of an honest observer\u2019s perceptive powers.\n\n(5) Inattention and a fallible memory.\n\nThese short comings are too apparent to demand discussion.\n\n\n=6. THE HYPOTHESIS.=\n\nHaving observed the facts, the mind naturally seeks for explanation\nof the same. Hence taking the facts as a cue and bringing into play a\nconstructive imagination, a plausible supposition is advanced, which is\nthen proved or disproved. Such a supposition is known as an hypothesis.\n\nDefinition. _An hypothesis is a supposition advanced for purposes of\nexplanation and proof._\n\nFirst illustration. The facts are known that light travels from the\nsun to the earth, and at the rate of 186 thousand miles per second.\nThese facts suggest the problems: (1) How does the light reach the\nearth? (2) Why this rate of speed; why so much faster than the rate at\nwhich sound travels? To solve these problems, or to explain the facts,\nthe \u201cether\u201d hypothesis is advanced: viz., \u201cA rare medium called ether\npervades space and transmits the light and heat of the sun.\u201d This\nhypothesis has never been conclusively proved.\n\nSecond illustration. Fact: The child leans forward and squints his eyes,\nwhen attempting to read work which has been placed on the black board;\nhypothesis: The child is near sighted.\n\n\n=7. INDUCTION AND HYPOTHESIS DISTINGUISHED.=\n\nInduction is a matter of realizing generalizations from the observation\nof facts. The product of such is an induction, but we know that an\nhypothesis is likewise a generalization based upon facts. What is the\ndifference? An induction, as such, is a _broader_ term than hypothesis.\nAs soon as the hypothesis is proved or disproved, it ceases to be\nan hypothesis, but still remains an induction. An hypothesis, being\nadvanced for purposes of explanation ceases to be an hypothesis\nwhen, in the last analysis, it fails to explain. Moreover, as soon as\nthe hypothesis is shown to be an undoubted truth, it also loses its\ndistinctive hypothetic marks. _An hypothesis is merely a tentative\ninduction._\n\n\n ILLUSTRATIONS:\n\n(1) The hypothesis is advanced that the fire started from the coal\nrange in the kitchen. After the incendiary is caught, this supposition\nceases to be an hypothesis.\n\n(2) It is suspected, that my insomnia is due to the three cups\nof strong coffee indulged in at the evening meal. As soon as this\nsupposition is proved by experimental means (law of difference), it\nceases to be an hypothesis and becomes an unpopular inductive truth.\n\n\n=8. HYPOTHESIS AND THEORY.=\n\nIn common parlance hypothesis and theory are used interchangeably.\nWe refer to the \u201cnebular hypothesis\u201d or the \u201cnebular theory\u201d; to the\n\u201chypothesis of the sun\u2019s heat\u201d or \u201cthe theory of the sun\u2019s heat.\u201d On\nthe other hand, we say \u201cthe theory of gravitation,\u201d \u201cthe theory of\nevolution,\u201d etc., with certain uniformity. From these observations we\nmay infer that hypothesis and theory may be used interchangeably when\nthe facts are of a _low probability_; but when the facts have undergone\n_cogent verification_, it is more correct to use theory in their\ndesignation rather than hypothesis. \u201c_A theory is a partially\nverified hypothesis._\u201d It has been remarked that theory has a second\nsignification of being a term which stands for \u201cany body of acquired\ntruth.\u201d It is unfortunate that its use could not be confined to this\nlatter conception.\n\n\n=9. THE REQUIREMENTS OF A PERMISSIBLE HYPOTHESIS.=\n\nAny hypothesis should be made to conform to the following\nrequisites: (1) _The hypothesis must be conceivable._ The hypothetic\ngeneralizations of primeval days were mere fancy. For example, the\nloud noise from the clouds on dark days was the angry voice of the\nGod of the skies. Even in this day when a complex situation cannot\nbe explained there comes the temptation to draw entirely upon the\nimagination, and advance an hypothesis which is absurd in every sense\nof the word. The permissible hypothesis demands that there be some\nground for the conjecture. A fact or two at least must be used as the\nfoundation for whatever the constructive imagination may build. On\nthe other hand the past has taught us that we cannot afford to be too\nexacting in the enforcement of this rule. The ideas of Copernicus,\nNewton, Harvey, Darwin, and many another of the world\u2019s best thinkers,\nwere looked upon at first as being ridiculous. There is always a bare\npossibility of a \u201clurking truth\u201d in the conjecture, _and no broad\nminded and sanely educated man can afford to scoff blindly at something\nwhich may seem to him mere fancy_. Prejudice and a willful blindness to\ntruth, have ever been imminent stumbling blocks in the path of progress.\n\n(2) _The hypothesis must be capable of proof or disproof._ This\nmeans, that where it is possible the hypothesis should touch, in one\nform or another, our experience. If the hypothesis is wholly unlike\nany experience we may have had, it becomes _impossible_ to ascertain,\nwhether it agrees or disagrees with the facts, which it is supposed\nto explain. A legitimate hypothesis must furnish some opportunity\nfor securing facts to prove or disprove it. For example, to advance\nan hypothesis relative to the conditions of the next world is hardly\npermissible, as \u201cspirit-facts\u201d are entirely without our field of\nexperience. Surely, one returning from Heaven could give us no\nconception of it; because there is nothing in the carnal mind that\nmay be used to interpret the experiences that must function in the\nCelestial City.\n\n(3) _The hypothesis must be adequate._ It should take into\nconsideration all the known facts. It stands to reason that, if _one_\nknown fact is ignored, the entire procedure is thus vitiated. It would\nbe absurd to suppose the moon to be inhabited without giving heed to\nthe fact of its having no atmosphere.\n\n(4) _The hypothesis must be as simple as possible._ We must, of\ncourse, recognize situations which in themselves are too complex to\nadmit of simple conjectures. The purport of the fourth rule is, that\nthe hypothesis should not be made _unnecessarily_ complex.\n\n(5) _The hypothesis should not contradict any verified truth._ Any\nconjecture which opposed the law of gravitation would be out of place.\nOf course it is possible to have only apparent conflicts between the\nnew hypothesis and the old law. Further observation should show that\nno such clash exists.\n\n\n=10. THE USES OF HYPOTHESES.=\n\nThe hypothesis is serviceable mainly in these particulars:\n\n(1) As a working basis.\n\nWhen one is confronted with a huge mass of facts it becomes necessary\nto start somewhere, and with as little waste of time and energy as\npossible. Almost anything is better than a haphazard floundering which\nreaches \u201cnowhere.\u201d So the investigator _hazards_ a tentative theory,\nwhich he at once proceeds to verify. If verification fails, then he may\ndiscard this first hypothesis for a better one.\n\n(2) As a guide to ultimate truth.\n\nMuch might be said relative to the use of rejected hypotheses. By\nmeans of these, science has advanced step by step towards the full\nlight of perfect knowledge. As has been remarked, no true scientist\ncares to overlook the opportunity for suggestive inspiration which\nsome forsaken hypothesis may afford him. Just as the individual attains\nthe best success by _using his failures as stepping stones_, so the\ntrue scientific discoverer _climbs up to the light on the stairway of\ndiscarded hypotheses_. By testing and rejecting the false hypotheses,\nthe situation becomes more definite and the problem more accurately\ndefined. \u201cKepler himself tried no less than nineteen different\nhypotheses before he hit upon the right one, and his ultimate success\nwas doubtless in no slight degree due to his unsuccessful efforts.\u201d\n\n(3) As a discoverer of immediate truth.\n\nOften, moreover, the hypothesis leads directly to positive verification.\nThe supposition advanced may hit the truth squarely; and may be of such\npeculiar nature as to lead easily to clear and conclusive proof.\n\n(4) As affording a probable explanation of a problem which will not\nlend itself to an entirely satisfactory solution.\n\nThe theory of evolution may illustrate this fourth use; while the\nhistory of the discovery of Neptune illustrates the third.\n\n\n=11. CHARACTERISTICS NEEDED BY SCIENTIFIC INVESTIGATORS.=\n\nThe hypothesis is referred to \u201cas the great instrument of science.\u201d The\ngreatest thinkers of time have possessed the courage and the conscience\nto step from the known to the unknown; to hazard a guess as to the\nmeaning of what they saw, and then subject their guess to a rigorous\ntest. This procedure involves three elements on the part of the\ninvestigator: (1) Power of accurate observation. (2) Constructive\nimagination. (3) A passion for truth.\n\n(1) An hypothesis formed without an accurate knowledge of facts\nis not only useless, but often it may work positive harm. To\nadvance serviceable suppositions which are not grounded on fact,\nis as impossible, as it is to build a house without a foundation.\nThe hypothesis is an image of the constructive imagination, but\nthe pedestal of this image must rest on the ground of fact. The\ninvestigator who would be scientific must exercise scrupulous care in\nsecuring his facts through observation and experiment. The rules and\nerrors involved in such a procedure have received sufficient attention.\n\n(2) After the investigator has his facts to build upon; and these may\nbe few or many\u2015\u2015sometimes even a single fact is sufficient\u2015\u2015then may he\ntheorize as to a possible explanation of them. Here is where the real\nwork of the born genius tells. To some the facts are nothing but words,\nto others they mean universal laws and great inventions. Who but a\nNewton could have seen the law of gravitation in the falling apple?\nWho but an Edison could have seen the phonograph in the sound wave and\nwax? It must be recognized that this remarkable imaginative insight is\ninborn in some cases; and yet this does not preclude the necessity for\n_cultivating_ this power, though it may be only in a rudimentary state.\nHere is another opportunity for the school teacher; namely, to train in\nevery legitimate way the _constructive imagination_.\n\n(3) Having once constructed the hypothesis, the honest scientific\ninvestigator at once proceeds to subject it to a series of most\nrigorous tests. It is well to see big things in a little fact; to\nhave a mind as fertile in new ideas as a watered garden\u2015\u2015this is\ngenius! But is it not more incumbent to have a conscience so keen,\nthat nothing will be allowed to pass for truth which has not received\nample verification? Intellectual dishonesty is quite as common as moral\ndishonesty. Moreover, one must maintain an _open mind, absolute candor,\nand a willingness to abandon the most cherished theory_. Often it is\nmuch easier to _explain away_ contradictory facts than it is to forsake\na _pet theory_.\n\n\n=12. OUTLINE.=\n\n THE AUXILIARY ELEMENTS IN INDUCTION\u2015\u2015OBSERVATION\u2015\u2015EXPERIMENT\u2015\u2015\n HYPOTHESIS.\n\n (1) The Foundation of Inductive Generalizations.\n\n (2) Observation. Defined.\n\n (3) Experiment. Defined.\n Compared with Observation.\n\n (4) Rules for Logical Observation and Experiment.\n Their need.\n First Rule.\n Second Rule.\n Third Rule.\n Fourth Rule.\n\n (5) Common Errors of Observation and Experiment.\n (1) Preconceived Ideas.\n (2) Confusing the Observed with the Inferred.\n (3) Ignoring the Exceptions.\n (4) Sympathy and Undue Interest.\n (5) Inattention and a Fallible Memory.\n\n (6) The Hypothesis.\n Defined and Illustrated.\n\n (7) Induction and Hypothesis Distinguished.\n\n (8) Hypothesis and Theory Distinguished.\n\n (9) The Requirements of a Permissible Hypothesis.\n (1) Conceivable,\n (2) Capable of proof or disproof,\n (3) Adequate,\n (4) Simple,\n (5) Not contradictory.\n\n (10) Uses of Hypothesis.\n (1) A working basis,\n (2) Guide to ultimate truth,\n (3) Discoverer of immediate truth,\n (4) Probable explanation.\n\n (11) Characteristics Required by Scientific Investigators.\n (1) Accurate observer,\n (2) Constructive imagination,\n (3) Passion for truth.\n\n\n=13. SUMMARY.=\n\n(1) Facts are the foundation of all inductive generalizations.\nInduction is largely a matter of building general notions from\nindividual notions derived from the observation of facts.\n\n(2) Observation is the act of watching the phenomena as they may occur.\nIt involves the voluntary concentration of consciousness on the case in\nhand.\n\n(3) Experiment is the act of making phenomena occur for the purpose\nof watching for effects. It is in reality a form of observation which\nnecessitates a manipulation of circumstances.\n\n(4) The average man is not given to careful observation. The rules\nadopted by scientific observers are: (1) The observation should\nbe _precise_; (2) should concern only the material circumstances;\n(3) should be varied; (4) should be isolated.\n\nFor the sake of _precision_ many instruments have been invented and\nmethods devised; notably instruments for accurate measurements, such as\nthe balance and thermometer, and methods like the method of averages.\n\nFrequently a situation may be so complicated as to demand a\n\u201cpreadjustment of attention.\u201d With the untrained this very\npreadjustment may lead to serious error.\n\nAn \u201call-angled observer\u201d is the most trustworthy.\n\n(5) Errors in observation come from preconceived ideas; confusing\nperception with inference; ignoring the exceptions; sympathy;\ninattention; and a fallible memory.\n\n(6) An hypothesis is a supposition advanced for purposes of explanation\nand proof.\n\n(7) An hypothesis is a tentative induction. As soon as it is deprived\nof its tentative nature it ceases to be an hypothesis.\n\n(8) Hypothesis and theory are often used interchangeably when reference\nis made to phenomena of low probability. Theory should be used only in\ninstances of high probability.\n\n(9) A permissible hypothesis must be (1) conceivable; (2) capable of\nproof or disproof; (3) adequate; (4) simple; (5) must not contradict\nany verified truth.\n\n(10) The hypothesis is especially serviceable in these four particulars:\n(1) as a working basis; (2) as a guide to ultimate truth; (3) as a\ndiscoverer of immediate truth; (4) as affording probable explanations.\n\n(11) There are certain characteristics which an honest and courageous\ninvestigator needs to possess. These are: (1) undoubted ability as\nan accurate observer of facts, (2) a constructive imagination, (3) a\npassion for truth.\n\nTo build an acceptable hypothesis without fact is as impossible as it\nis to build a house without a foundation.\n\nThe genius, because of his imaginative insight, transforms the simple\nfact into a complex invention or law.\n\nA prevailing \u201c_intellectual dishonesty_\u201d suggests the need of \u201c_a\ngreater passion for truth_.\u201d\n\n\n=14. REVIEW QUESTIONS.=\n\n (1) Show that facts are the raw material of induction.\n\n (2) Define and illustrate a fact.\n\n (3) Define induction in terms of the notion.\n\n (4) Define and illustrate observation.\n\n (5) Define and illustrate experiment.\n\n (6) Show the difference between observation and experiment.\n\n (7) State and exemplify the rules for logical observation and\n experiment.\n\n (8) Illustrate the method of averaging observations.\n\n (9) Explain \u201cpreadjustment of attention.\u201d\n\n (10) What is the most common error with the untrained observer?\n Explain and illustrate.\n\n (11) Explain the expression \u201call-angled observer.\u201d\n\n (12) State and exemplify the errors of observation and experiment.\n\n (13) To what error in observation are superstitions generally due?\n\n (14) Define and illustrate hypothesis.\n\n (15) Indicate the difference between an hypothesis and an ordinary\n induction.\n\n (16) When may theory and hypothesis be used interchangeably?\n Illustrate.\n\n (17) Show by illustration that the term theory is ambiguous.\n\n (18) Summarize the requirements of a permissible hypothesis.\n Illustrate.\n\n (19) Select some school room experience with a view of making it\n conform to the requirements of a permissible hypothesis.\n\n (20) Explain and illustrate the uses of hypothesis.\n\n (21) \u201cThe scientific discoverer climbs up to the light on the stairway\n of discarded hypotheses.\u201d Explain.\n\n (22) Write a short theme on \u201cCharacteristics Required by Scientific\n Investigators.\u201d\n\n\n=15. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) \u201cLand and sea breezes are due to a difference in temperature.\u201d\n Is this a fact or a law? Explain your position.\n\n (2) Give three different definitions of induction. Which one have you\n adopted? Defend your position.\n\n (3) Define and illustrate observation.\n\n (4) Distinguish between observation and attention.\n\n (5) \u201cIn observation we _find_, in experiment we _make_.\u201d What is\n meant by this?\n\n (6) Give illustrations of falsehood due to careless observation.\n\n (7) Argue for and against the use of \u201cexpectant attention\u201d in\n observation.\n\n (8) \u201cNine-tenths of what we see comes from within.\u201d Do you believe\n this? Labor the question.\n\n (9) Offer suggestions which, if followed, should lead to scientific\n observation.\n\n (10) \u201cOne must be just before he is sympathetic.\u201d Relate this to the\n fine art of accurate observation.\n\n (11) Is an hypothesis a generalization? Explain.\n\n (12) Give school room examples of hypotheses which lead to injustice.\n\n (13) \u201cAn hypothesis is merely a tentative induction.\u201d Make clear this\n assertion.\n\n (14) Illustrate inconceivable hypotheses by drawing on your knowledge\n of ancient history.\n\n (15) \u201cPrejudice and willful blindness to truth have ever been imminent\n stumbling blocks in the path of progress.\u201d Expatiate upon this.\n\n (16) Are the hypotheses advanced concerning communications from the\n spiritual world capable of proof or disproof? Give reasons.\n\n (17) Show by historical examples the use of discarded hypotheses.\n\n (18) \u201cGenius is another name for hard work.\u201d Do you agree? Defend your\n position.\n\n (19) \u201cThe man to whom nothing ever occurs is unlikely to make any\n important discoveries.\u201d Discuss this.\n\n\n\n\n CHAPTER 20.\n\n LOGIC IN THE CLASS ROOM.\n\n\n=1. THOUGHT IS KING.=\n\n\u201cOur habits make or unmake us.\u201d \u201cIn a thoughtless hour a groove is\nimbedded in the nerve substance, and thereafter, nine-tenths of the\nlife flows through that groove.\u201d Habit is, indeed, a most powerful and\na most tyrannical master; and yet it has come within the observation\nand even the experience of many, that _thought is even more masterful\nthan habit_. Appearing at the psychological moment and in a pedagogical\nway, a thought may be made to possess the mind with force sufficient to\nbreak almost any habit. From an ethical point of view, the exceptions\nto this are due to an inability to arouse thought of sufficient\nstrength. Moreover, mental reactions which result in habit are\noriginally brought about through some thought process. Speaking in\ngeneral terms, it may be affirmed that thought _makes habit_ and if\nsufficiently strong _breaks habit_. That our habits make or unmake\nus may be true, but is it not likewise true that our thoughts make or\nunmake our habits?\n\nThought is king; thought has made man king of the animal kingdom, and\nif thought has figured so largely in the evolution of the human animal\nin past ages, may we not assume that it will sway the future ages in\nlike manner? Thought is a product of the class room. Here thoughts\nwhich _make_ habits, and thoughts which _break_ habits have full sway.\nAs the children of the American schools think to-day, so will the men\nof American life think on the morrow; and as America _thinks_ so will\nshe ultimately _do_. This lends vital import to any object which may\neither inspire or regulate thought.\n\n\n=2. SPECIAL FUNCTION OF INDUCTION AND DEDUCTION.=\n\nAs commonly treated logic is a _regulative_ subject. This implies the\ntwo aspects of _direction_ and _correction_. Logic directs by means\nof the _laws_ and _forms_ of thought, and corrects by means of the\n_rules_ of right thinking. To a certain degree both departments of\nlogic are directive as well as corrective; but it is worthy of remark\nthat inductive logic emphasizes the former, while deductive logic\nlays stress upon the latter. It is inductive logic which shows how\nman has acquired _new_ knowledge; inductive logic explains the mode\nof procedure adopted by the discoverer and the inventor. On the other\nhand, deductive logic is distinctly a science of criticism. Induction\n_directs_ to new truth; deduction aims to _modify_ and _correct_ new\ntruth.\n\n\n=3. TWO TYPES OF MIND.=\n\nThough there are many _special_ forms of thought, yet there are but\ntwo _general_ forms; namely, induction and deduction. Inductive thought\nseeks the new; deductive thought corrects the old. Similarly, there\nare two types of mind: the inductive type and the deductive type.\nThe former _reaches out for new things_, the latter is satisfied with\n_ordering the old_. In politics the man with the inductive type of\nmind becomes a \u201cLiberal\u201d or a \u201cProgressive\u201d; while the man with the\ndeductive type of mind becomes a \u201cConservative\u201d or a \u201cStandpatter.\u201d It\nmust be conceded that _both are needed in the development of the best\nform of Democracy_. We need an _unfettered_ freedom as advocated by\nJefferson; but we also need an _ordered_ freedom as taught by Hamilton.\n\n\n=4. TOO MUCH CONSERVATISM IN SCHOOL ROOM.=\n\nSince the beginning these two mental types have been in evidence\u2015\u2015the\nliberal who wants to _do_ things, and the conservative who wants to\n_weigh_ things. With the liberal, it is fight whether or no; with the\nconservative, it is fight provided the enemy is not too formidable. The\none _dares_; the other _cautions_: both are needed to balance the world.\n\nLiberalism and conservatism may be fostered in the school room, and\nto maintain a true balance each must receive its share of attention.\nIs such the case? The passing of \u201cdistrict-school-individualism\u201d and\nthe coming of \u201cgraded-school-collectism\u201d has transferred the emphasis\nfrom liberalism to conservatism\u2015\u2015from the inductive type to the\ndeductive type. In this day it seems to be more important to have\nthe child\u2019s work _orderly_, than to have it _original_. In the main,\nexamination papers call for correct knowledge and not for thought;\nin the main, promotions are based on _accuracy_, not on _initiative_.\nThe conservative type being in control, the schools are sending out\ntoo many \u201cDeductives,\u201d not enough \u201cInductives.\u201d The world needs more\nColumbuses and Edisons.\n\n\n=5. THE METHOD OF THE DISCOVERER.=\n\nA change must come. The methods of instruction are too didactic and\nnot sufficiently inspirational. Greater attention must be given to the\nspirit of discovery and less to the spirit of correction. _The teacher\nmust lead less and follow more; must correct less and suggest more;\nmust tell less and direct more._ If we are to give greater attention to\nthe training of discoverers, logic may aid in this crusade by calling\nattention to the common mode of procedure which the discoverers of the\npast have adopted. This is a legitimate topic for the logician, since\n_induction_, _deduction_, _hypothesis_, and _proof_ have ever been\ncommon tools in the discoverer\u2019s workshop. With a view to becoming\nbetter acquainted with the common mode of procedure of the man who\nseeks for new truth, let us study two typical instances:\n\n (1) The Discovery of Neptune.\n\n The discovery of Neptune was a double one. Early in the present\n century it was found that Uranus was straying widely from his\n theoretic positions, and the cause of this deviation was for\n a long time unsuspected. Two astronomers, Adams in England and\n Leverrier in France, the former in 1843 and the latter in 1845,\n undertook to find out the cause of this perturbation, on the\n supposition of an undiscovered planet beyond Uranus. Adams\n reached his result first, and the English astronomers began\n to search for the suspected planet with their telescopes, by\n first making a careful map of all the stars in that part of the\n sky. But Leverrier, on reaching the conclusion of his search,\n sent his result to the Berlin observatory, where it chanced\n that an accurate map had just been formed of all the stars\n in the suspected region. On comparing this with the sky, the\n new planet, afterward called Neptune, was at once discovered,\n 23d September, 1846.\n\n (2) Bees are guided in their flight by a knowledge of their\n surroundings, not by a general sense of direction.\n\n \u201cM. Romanes took a score of bees in a box out to sea, where\n there could be no landmarks to guide the insects home. None of\n them returned home. Then he liberated a second lot of bees on\n the seashore and none of these returning, he liberated another\n lot on the lawn between the shore and the house. None of these\n returned, although the distance from the lawn to the hive was\n not more than two hundred yards. Lastly he liberated bees in\n different parts of the flower garden on either side of the house,\n and these at once returned to the hive.\u201d (Hibben.)\n\nA multiplication of instances would only give stronger evidence\nto the fact that the mode of procedure adopted by the discoverer\nand inventor conforms to these three general steps: (1) antecedent\nfacts, (2) forming an hypothesis, (3) verification. It will be to our\nadvantage to study somewhat in detail these three steps.\n\n(1) Antecedent facts.\n\nIn the discovery of Neptune the _decisive_ or _crucial fact_ was the\nknowledge that Uranus deviated from his true path about the sun. This\nknowledge was obtained through observation and mathematical calculation.\nBut the hypothesis of the existence of another planet could not\nhave been formed had it not been for the _more fundamental facts_ of\ninertia, gravitation, falling bodies, etc. For the sake of definiteness\nantecedent facts may thus be divided into _foundation_ facts and\n_crucial or decisive_ facts. The latter are an outgrowth of the former.\nThe _foundation_ fact of the second illustration is Romanes\u2019 knowledge\nof animal instinct; while the _crucial fact_ is, no doubt, the\nobservation that bees fly in a circle before starting for home. In\nthe case of Newton\u2019s discovery of the law of gravitation, the falling\nof the apple was the crucial fact; while his knowledge of terrestrial\ngravity proved to be the vital foundation fact.\n\n_A crucial fact is one which leads immediately to the formation of\na reasonable hypothesis._ It is not to be inferred from this that\nthe same fact becomes a crucial one to _all_ alike. The falling of\nthe apple was only crucial to a genius like Newton. With the average\nonly _extraordinary_ facts become crucial; but with the genius any\n_ordinary_ fact may become crucial. Both the scholar and the genius may\nhave the foundation facts, but only the latter may be able to read into\na dry fact or event, a new world of truth.\n\n(2) Forming an Hypothesis.\n\nFrom the viewpoint of logical correctness, the matter of hypothesis\nhas received due attention in an antecedent chapter; we need now\nto look at the subject through the eyes of the discoverer, not the\nlogician. The crucial fact at first creates an intellectual perplexity\nwhich is accompanied with an uneasy, dissatisfied state of mind. This\nunsatisfied feeling drives the intellect to protracted thought. As a\nfinal result some hypothesis is constructed which seems to explain the\ncrucial fact. Here is where analogy functions in a most vital manner.\nNo hypothesis is forthcoming unless it resembles the crucial fact. It\nhas been remarked elsewhere that analogy is the basic element in the\nforming of hypotheses. So it transpires, that the protracted thought\nreferred to, is virtually a mental effort to detect significant\nresemblances between the well known crucial fact, and some hypothetical\nfact which the imagination may picture. To put it differently: The\ncrucial fact arouses a mental state of unrest which in turn drives\nthe mind to a \u201cstill hunt\u201d for _relations_. The establishment of the\nhypothesis is simply a makeshift, designed to satisfy this \u201cmental\nurge.\u201d In the discovery of Neptune the crucial fact, the deviation of\nUranus, produced a state of uneasiness in the minds of the astronomers.\nSurely something was wrong. This urged them to further meditation,\nwhich finally resulted in the hypothesis that there must be an unknown\nplanet beyond the orbit of Uranus. They assumed, of course, that the\nrelation between this supposed planet and Uranus was analogous to the\nrelation between any two of the known planets. In the case of Newton\nthe falling apple stirred his astute mind to the assumption that the\nsame force which pulled the apple, likewise pulled the moon towards the\nearth. Here we have again (1) the crucial fact, (2) the mental urge,\n(3) the analogous hypothesis.\n\n(3) Verification.\n\nForming an hypothesis only partly fulfills the demands of an\nunsatisfied intellect. The true discoverer, being possessed with a\npassion for truth, seeks for \u201cthe truth, the whole truth, and nothing\nbut the truth.\u201d In consequence the hypothesis is subjected to tests\nwhich may lead to its confirmation, its rejection, or its modification.\n\nThe two possible modes of verification are recourse to experience\nand appeal to reason; or _empirical_ proofs and _rational_ proofs. In\nthe former the hypothesis is compared with facts by means of further\nobservation and experiment. M. Romanes\u2019 experience with the bees is\na fair illustration of this form. Possibly the student has already\nnoted that Romanes\u2019 mode of procedure conforms to the \u201cjoint method\nof agreement and difference.\u201d In the case of rational proofs the\nhypothesis is subjected to deductive demonstration, either of the\nform of syllogistic argument or mathematical calculation. A fair\nsample of this kind of verification is Newton\u2019s discovery of universal\ngravitation. When he decided that the moon and the apple might be\ncontrolled by the same universal force, he undertook to establish his\nhypothesis by mathematical calculation. At first his figures seemed to\ndisprove his theory, but after a wait of ten years, new data relative\nto the diameter of the earth, removed the apparent discrepancy.\nIn the case of the discovery of Neptune, the verification was both\nrational and empirical. Mathematical (rational) calculation led to\nthe assumption that the new planet must be at such a point. With this\nknowledge the observer was enabled to turn his telescope to the spot\nindicated and there, true to the calculations, was Neptune (empirical).\n\nTo summarize: The method of the discoverer involves a knowledge\nof certain fundamental facts; the observation of crucial facts; a\nmental unrest; the constructing of an hypothesis through analogy; and\nfinally verification by either appeal to experience, or mathematical\ndemonstration.\n\n\n=6. THE REAL INDUCTIVE METHOD OR DISCOVERER\u2019S METHOD NOT IN VOGUE\n IN CLASS ROOM WORK.=\n\nIt has been remarked elsewhere that there are two general mind types,\nthe liberal and the conservative. Also that the natural method of\nthought animating the former is inductive; while the natural method\nof thought of the latter is deductive. The \u201cliberal\u201d is the apostle of\n_new_ truth; the \u201cconservative\u201d an apostle of _safe_ truth. Both types\nare needed; the one to balance the other. In consequence both methods\nare of service in the class room; here each should be given its\nproportionate place. That this condition does not obtain may not be\napparent, since much attention is being given to certain inductive\nforms, such as \u201cproceeding from the concrete to the abstract,\u201d \u201cfrom\nthe particular to the general,\u201d \u201cfrom the known to the related unknown,\u201d\netc. Likewise the courses of study and the various text books, claim\nto advocate the use of the inductive process. Seemingly these facts\npoint toward a very general observance of the inductive tenets. This\nis true with one vital exception: Induction is the natural method of\nthe discoverer. With it he _acquires_ knowledge; but in the class room\ninduction is used to _impart_ knowledge. In life the discoverer takes\nthe initiative, thinks his own thoughts first hand; but in the school\nroom, above the kindergarten, the child is not allowed to take the\ninitiative, not even in his play. All is planned for him, all doled\nout, not in the raw, but partially made over. The teacher must impart\na certain amount of knowledge in a given time, and consequently she\nmust \u201cset the pace\u201d in this race for _second hand facts_. To allow the\nchild to lead; to give him the benefit of his own individuality; to\npermit him to use the God given spirit of discovery which clamors for\nrecognition; would be suicidal according to our present standards. If\nthe plan of the discoverer were followed, the course of study could not\nbe covered; children would fail of promotion; and criticism would be\nforthcoming from both principal and parent.\n\n_In the average class room of the day the inductive FORM prevails\nbut the SPIRIT is not in evidence._ Like a wolf in sheep\u2019s clothing\ninduction has entered the class room to devour that primal force in the\nchild\u2019s make-up, which has raised his race above his simian ancestors.\nOur class room methods, being inductive in form but deductive in spirit,\nmay train the youngster to be a _camp follower_ but never a _leader_\nin thought and action. The call of the day is for more initiative; for\nmore originality; for more individuality; for more enthusiasm. There\nis too much form without the spirit; so much that bespeaks system and\nrefinement without those native impulses and native abilities which\nmark one child from another. Like the books of a library our children\nare classified and labeled, and when more come in the others are dusted\nand placed on the next higher shelf. How many more centuries must we\nwait before the schools will adopt, in spirit as well as in form, the\npedagogical principles of life? Will the time ever come when it may be\nsaid _that all our leaders in thought and action are college graduates_?\n\n\n=7. AS A METHOD OF INSTRUCTION DEDUCTION IS SUPERIOR TO INDUCTION.=\n\nThe inductive method is pre-eminently the method of the discoverer only\nwhen it involves both the _form_, which he follows, and the _spirit_,\nwhich he evinces. The so-called method of the school room is _inductive\nin form_, as the procedure is from particular facts to general truths;\nbut _deductive in spirit_, as it is used to _impart_ knowledge. If\nit were inductive in spirit, the child would be allowed to _acquire\nknowledge entirely through his own initiative_. Deduction is the method\nof _instruction_, whereas induction is the method of _discovery_. That\nthe child of the school is _instructed_ or better \u201cdeducted\u201d and _not\ngenerally allowed to discover_, is a situation so apparent that we need\nnot labor the point further.\n\nBecause the inductive process has been made a method of instruction,\nit has been robbed of its chief advantage over deduction. Indeed, as\na method of instruction, deduction is really the superior method. It\nrequires less time, demands greater concentration, often arouses more\ninterest, and creates situations which are less involved.\n\n\n=8. CONQUEST NOT KNOWLEDGE THE DESIDERATUM.=\n\nIn all great inventions, man has taken his cue from nature. In\ninventing the telescope, his model was the eye; in building his house,\nhis inspiration was the cave. In reality man has accepted nature\u2019s\nsuggestions, and then attempted to improve upon them. In this he\nhas met with success. From the crab apple tree, he has developed the\nnorthern spy; from the _wild_ hen which laid 25 eggs a year, he has\nevolved the modern hen which produces 225 eggs a year. Moreover, man\nhas attained his greatest successes by _enlarging_ upon the thoughts\nof nature and not by _unmixed substitutions_. Burbank, through a\nlong process of years, has changed the color of a flower, but in\naccomplishing this did he not use some hidden tendency of nature?\nBurbank, with all his wisdom, cannot give a flower color unaided by\n\u201cDame Nature.\u201d\n\nWhen man commenced to study nature\u2019s mode of education, he saw that\nfearful sacrifices were entailed, both in time and in energy as well\nas in life itself; and so he evolved a _more economical way_ of leading\nthe child through the experiences of the race. In consequence, he has\ndeveloped the present splendid system of education.\n\nIn the evolution of all great institutions, there are in evidence\ncrucial weaknesses, and in the evolution of man\u2019s educational system\nit appears that he has erred in adopting nature\u2019s _form of education_\nwithout her _spirit of education_. In his anxiety to have the young\nacquire as much as possible, man has overshot nature\u2019s true purpose.\nFor example, the big word in man\u2019s educational system is _knowledge_;\nbut the big word in nature\u2019s educational system is _conquest_. Nature\ngives man knowledge simply to reward him _for his effort_; but man\nwould give to his fellow the reward _without the effort_. According\nto nature, the strongest men are those who _overcome_ most; according\nto man, the strongest men are those who _know_ most. The common\neducational principles, such as, \u201cFrom the concrete to the abstract\nand from the known to the related unknown,\u201d etc., are interpreted\nby man from the viewpoint of _knowledge_; whereas nature would teach\nthat these are a feasible way to develop _power\u2015\u2015to grow manhood_.\nIt is seen that nature uses knowledge only as a means to an end, and\ntherefore when man uses knowledge as an end only, he is trying to\nsubstitute a plan of his own for nature\u2019s plan. _The best results can\nbe secured only when man co-operates with nature in developing, and at\nthe same time regulating, the spirit of conquest._\n\n\n=9. MOTIVATION AS RELATED TO THE SPIRIT OF DISCOVERY.=\n\nIt has been remarked in this chapter, that the \u201ccrucial fact\u201d serves to\nstir the mind of the natural born discoverer to an activity raised to\nthe nth power of effectiveness. Naturally, the intent of such activity\nis to _solve the mysteries_ which the crucial fact may suggest. This\npassion of the mind to \u201cknow more about it\u201d is appropriately termed\n\u201cthe mental urge.\u201d From the viewpoint of the pedagogue, the \u201cmental\nurge\u201d is simply an intrinsic interest in the situation at hand; an\ninterest born of an innate or acquired passion to know the truth.\n\nWith the average child, the \u201cmental urge\u201d is strong only when the\nsituations appeal to some immediate need or vital experience. The\nattempt to make the school work concrete and vital; to make it answer\nthe child\u2019s natural curiosities and real necessities, is dignified\nwith the name \u201c_motivation_.\u201d It is obvious that this is a new term\nfor an old condition. To motivate the work, means to give to it an\nattractiveness which _any_ situation might have for the true born\ndiscoverer and inventor. _If we would use the discoverer\u2019s method\nsuccessfully, we must learn the art of motivating the work._ This may\nbe accomplished by appealing to the play instincts, to the business\ninstincts, and to the vital interests of every day life.\n\n\n=10. DISCOVERER\u2019S METHOD OR THE REAL INDUCTIVE METHOD ADAPTED TO\n CLASS ROOM WORK.=\n\nA revolt has already set in against this insatiate desire to teach\n_knowledge_, rather than to teach the _child_. Many schools are\npermitting a study of those topics which vitally concern every day\nlife. Less attention is being given to formal discipline, and more\nattention to self activity. Gradually will the scheme of education\nbe directed toward fitting the school work to the child, rather\nthan fitting the child to the school work. When this new thought\nin education is fully upon us, then will every device and method be\ndirected toward giving full scope to the _spirit of inquiry_, which\nso completely possesses every normal child.\n\nIt now remains for us to indicate ways in which the spirit of inquiry,\nor the \u201cdiscoverer\u2019s method,\u201d may be adapted to school room work. In\nthe first illustration, we shall outline the topic as it is generally\ngiven in the average school where attention is paid to development work.\nThis will then be followed by a second outline which may be suggestive\nof the discoverer\u2019s mode of procedure.\n\nFirst illustration. _School Room Method._\n\nI. Aim: To teach addition of business fractions.\n\nII. Preparation: (Only type examples given).\n\n (1) (2) (3)\n 3 bushels 3 parts Rule: Only like numbers\n + 5 bushels + 5 parts can be added.\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n 8 bushels 8 parts\n\nIII. Presentation:\n\n (1) (2) (3) (4)\n 3 ninths 3/9 2/3 = 4/6 2/3 = 8/12\n + 5 ninths + 5/9 1/6 = + 1/6 3/4 = + 9/12\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n 8 ninths 8/9 5/6 17/12\n\nIV. Summary:\n\n (1) Only like fractions can be added.\n\n (2) Change unlike fractions to like fractions.\n\n (3) Add the numerators, placing the sum over the common denominator.\n\nV. Application:\n\nExamples and problems involving similar and dissimilar fractions.\n\nBefore undertaking to illustrate the discoverer\u2019s method, it may be\nwell to designate in order the evident steps as they would appear to\nthe pedagogue:\n\n (1) Motivate the topic to be presented.\n\n (2) Bring to mind appropriate \u201cfoundation facts.\u201d\n\n (3) Make evident the \u201ccrucial fact.\u201d\n\n (4) Lead to the forming of an hypothesis through analogy.\n\n (5) Afford ample opportunity to prove the hypothesis.\n\n_Discoverer\u2019s Method Adapted._\n\nLesson Plan.\n\nI. Aim: (1) _By playing upon the curiosity or by exposing a vital need,\ncreate a strong desire to know how to add business fractions._\n(Motivate the topic.)\n\nCuriosity: \u201cWe all know what a fraction is and we know, too, how to\nchange fractions to higher or lower terms.\u201d \u201cNow I wonder how many know\nhow to _add_ fractions, such as 2/5 and 1/5?\u201d \u201cDon\u2019t you tell any one,\nMary, but just write your answer on a piece of paper and show it to\nme.\u201d (Mary\u2019s answer shows that she has thought correctly, but figured\nincorrectly. John, after having raised his hand, shows his answer to\nthe teacher.) \u201cJohn has the right answer.\u201d \u201cThat\u2019s fine, but let us\nkeep the secret, John.\u201d \u201cI wonder how many others there are in this\nclass who will find the right way?\u201d etc., _or_\n\nVital need: Discuss with the class the various occupations of life\nand secure expressions of preference. Some may plan to be real estate\nagents, others contractors or book keepers, etc. \u201cGeorge, you plan to\nbe a book keeper.\u201d \u201cLet us suppose that I have given you the job of\nbook keeper in my factory.\u201d \u201cShow that you are worth your wages by\nadding these numbers: 124\u00be, 647\u2154.\u201d \u201cWhat! can\u2019t do it?\u201d \u201cThen I don\u2019t\nwant you!\u201d etc.\n\nII. Preparation:\n\n(2) Bring to the foreground the necessary _foundational knowledge_.\nSuggestions:\n\n 4 bushels 8 parts\n + 3 bushels + 2 parts\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n 7 bushels 10 parts\n\nIII. Presentation:\n\n(3) Make evident the _crucial fact_. Suggestions:\n\n Add 2 fifths 3 eighths 3/8\n + 1 fifth + 1 eighth + 1/8\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015 \u2015\u2015\u2015\u2015\u2015\n 3 fifths 4 eighths\n\n(4) Without further suggestion, give the young discoverer suitable\nopportunity for finding the sum of 3/8 and 1/8. In the act of\ndiscovering, an implicit _hypothesis_ takes form in the mind through\nanalogous reasoning. This point marks the climax of the lesson\u2015\u2015the\nsupreme moment, when the skill and tact of the teacher is assessed\nto the limit. Just here the child must have a comfortable environment\nwhere perfect concentration is possible. Nothing must be forced;\nand there should be nothing suggestive of disgrace or shame, if the\nyouthful Columbus is unsuccessful. The first attempt should be without\nbooks. If more help is needed, access to books may be given. If the\ninvestigation is still without definite result, then _as a last resort_\nthe teacher may, in the presence of the child, _add fractions_, solving\n_with deliberation_ example after example, until the child believes he\nhas discovered the process.\n\n(5) Stimulate a desire to _verify the facts discovered_.\n\nSuggestions leading to verification: Afford opportunity for\nmathematical demonstration. Illustrations: The fractions 1/4 and 3/8\nhave been added in this way\u2015\u2015\n\n 1/4 = 2/8\n 3/8 = + 3/8\n \u2015\u2015\u2015\n 5/8\n\nUse is now made of the crucial fact, when the example assumes this\nform\u2015\u2015\n\n 2 eighths\n + 3 eighths\n \u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\u2015\n 5 eighths\n\n_Or_ if the class has been trained in the use of the diagram the\nfollowing may be the form of proof:\n\n { \u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\n 1/4 { \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n { \u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\n \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n \u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\n { \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 3/8 { \u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\n { \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n { \u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\n\nExplanation from diagram. I see that 1/4 equals 2 parts and 3/8 equals\n3 parts; the sum of 3 parts and 2 parts are 5 parts. But the name of\nthe part is eighths; hence the answer 5 parts may be written 5 eighths,\nor 5/8. Thus the final form is\n\n 2 parts\n + 3 parts\n \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 5 parts = 5/8\n\nGive opportunity to consult answers in text books as further\nverification.\n\nThe _summary_ and _application_ of adding fractions according to the\n\u201cdiscoverer\u2019s method,\u201d are virtually the same as the corresponding\nsteps in the \u201cschool room method.\u201d\n\n_Second Illustration of Discoverer\u2019s Method._\n\nDavid P. Page in his Theory and Practice of Teaching well illustrates\nthe discoverer\u2019s method in conducting a general exercise in nature\nstudy. We cannot do better than to quote from him:\n\n \u201cIt is the purpose of the following remarks to give a specimen\n of the manner of conducting exercises with reference to _waking\n up the mind_ in the school and also in the district. Let us\n suppose that the teacher has promised that on the next day,\n at ten minutes past ten o\u2019clock, he shall request the whole\n school to give their attention five minutes to something that\n he may have to show them. This very announcement will excite an\n interest both in school and at home (playing upon the curiosity);\n and when the children come in the morning they will be more\n wakeful than usual till the fixed time arrives. At the precise\n time, the teacher gives the signal agreed upon, and all the\n pupils drop their studies and sit erect. When there is perfect\n silence and strict attention by all, he takes from his pocket\n an ear of corn and in silence holds it up before the school.\n The children smile, for it is a familiar object (foundational\n knowledge already in hand); and they probably did not suspect\n they were to be fed with corn.\u201d\n\n Teacher. \u201cNow, children,\u201d addressing himself to the youngest,\n \u201cI am going to ask you only one question about this ear of corn.\n If you can answer it, I shall be very glad. As soon as I ask the\n question, those who are under seven years old, and think they\n can give an answer, may raise their hand. _What is this ear of\n corn for?_\u201d\n\n Several of the children raise their hands, and the teacher\n points to one after another in order, and they rise and give\n their answers.\n\n Mary. It is to feed the geese with.\n\n John. Yes, and the hens, too, and the pigs.\n\n Sarah. My father gives corn to the cows.\n\n Laura. It is good to eat. They shell it from the cobs and send\n it to the mill, and it is ground into meal. They make bread of\n the meal and we eat it.\n\n \u201cI am sorry to tell you that none of you have mentioned the use\n I was thinking of, though, I confess, I expected it every minute.\n I shall now put the ear of corn in my desk, and no one of you\n must speak to me about it till to-morrow. You may now take your\n studies.\u201d\n\n The consequence of this would be that various families, father,\n mother and older brothers and sisters, would resolve themselves\n into a committee of the whole on the ear of corn: and by the\n next morning several children would have something further to\n communicate on the subject. The hour would this day be awaited\n with great interest and the first signal would produce perfect\n silence.\n\n The teacher now takes the ear of corn from the desk and displays\n it before the school; and quite a number of hands are instantly\n raised as if eager to be the first to tell what other use they\n have discovered for it.\n\n The teacher now says pleasantly, \u201cThe use I am thinking of you\n have all observed, I have no doubt; it is a very important use,\n indeed; but as it is a little out of the common course (crucial\n facts) I shall not be surprised if you cannot give it. However,\n you may try.\u201d\n\n \u201cIt is good to boil,\u201d says little Susan, almost springing from\n the floor as she speaks. \u201cAnd it is for squirrels to eat,\u201d says\n little Samuel. \u201cI saw one carry away a whole mouthful yesterday\n from the cornfield.\u201d\n\n Others still mention other uses. Perhaps, however, none\n will name the one the teacher has in his own mind; he should\n cordially welcome the answer if perchance it is given.\n (Supposing that it has not been given.) \u201cI have told you\n that the answer I was thinking of was a very simple one; it\n is something you have all observed and you may be a little\n disappointed when I tell you. The use I have been thinking of\n for the ear of corn is this: _It is to plant._ _It is for seed_,\n to propagate that species of plant called corn.\u201d (Verification.)\n Here the children may look disappointed as much as to say, We\n knew that before. The teacher continues: \u201cAnd this is a very\n important use for the corn; for if for one year none should be\n planted, and all the ears that grew the year before should be\n consumed, we should have no more corn. The other uses you have\n named were merely secondary. But I mean to make something more\n of my ear of corn. My next question is: _Do other plants have\n seed?_\u201d Here is a new field of inquiry, etc., etc.\n\nFrom the standpoint of \u201cthe greatest amount of knowledge in the\nshortest possible time,\u201d this mode of presentation consumes an\ninexcusable amount of time and is, therefore, \u201cimpracticable.\u201d But\nwhen viewed from the ground of interest, originality, initiative, and\nconquest\u2015\u2015the watchwords of the \u201cnew thought in education\u201d; there is\nno real waste in either time or energy. _The spirit and method of the\ndiscoverer will no doubt be the educational slogan of the future age._\n\nEpitome of Discoverer\u2019s Method, adapted to the class room:\n\n (1) Motivate the topic to be presented.\n\n (2) Bring to mind, if necessary, the \u201cfoundational facts.\u201d\n\n (3) Make evident the \u201ccrucial fact.\u201d\n\n (4) Furnish every opportunity for a first-hand discovery of the\n \u201clesson-point\u201d (establishing hypothesis through analogy).\n\n (5) Let the hypothesis be verified.\n\n_The entire situation must be one of freedom, zeal, originality, and\ninitiative._\n\n\n=11. THE QUESTION AND ANSWER METHOD NOT NECESSARILY ONE OF DISCOVERY.=\n\nNo one mode of presentation is more universally used than the \u201cquestion\nand answer.\u201d The advantages of this mode are many and the teacher who\nis an adept in the art of questioning, from the standpoint of knowledge,\nis generally efficient. The common error, however, incident to much\nquestioning, is that of asking \u201ctelling questions.\u201d By the use of such,\nthe class is forced along the desired channel of thought so rigorously\nas to have a condition _where the spirit of inquiry is entirely\nwanting_. It is possible to conform to the rules of good questioning,\nand yet rob the class of all originality and initiative. From the\nteacher\u2019s viewpoint, the discoverer\u2019s method demands few questions;\nit is the method of _suggestion_ rather than one of questions.\nAvowedly in this method, the children should ask and answer their own\nquestions. Viewed from the ground of discovery there are three modes\nof presentation which may represent a progressive series. These are\n(1) the lecture mode, (2) the question and answer mode, (3) the mode\nby suggestion. In the first there is _little_ of the spirit of the\ndiscoverer; in the second there is a trifle more of the spirit of\nthe discoverer; while in the third there is _much_ of this spirit.\nThe student is advised to select some class room topic with a view\nto illustrating these three modes of presentation.\n\n\n=12. OUTLINE.=\n\n LOGIC IN THE CLASS ROOM.\n\n (1) Thought is king.\n\n (2) Special functions of induction and deduction.\n\n (3) Two types of mind.\n Inductive or liberal.\n Deductive or conservative.\n\n (4) Too much conservatism in school.\n\n (5) The method of the discoverer.\n Three steps\n\n 1. Antecedent { 1. Foundational\n facts { 2. Crucial\n\n 2. Forming { 1. \u201cMental urge\u201d\n hypothesis { 2. Analogy\n\n 3. Verification { 1. Empirical\n { 2. Rational\n\n (6) The real inductive method or Discoverer\u2019s Method not in vogue in\n class room work.\n\n (7) As a method of instruction, deduction is superior to induction.\n\n (8) Conquest, not knowledge, the desideratum.\n\n (9) Motivation as related to the spirit of discovery.\n\n (10) Discoverer\u2019s method or the real inductive method adapted to\n class room work.\n School room method.\n Discoverer\u2019s method.\n Epitome.\n\n (11) Question and answer method not necessarily one of discovery.\n\n\n=13. SUMMARY.=\n\n(1) Thought is king in that it is the ruling factor in the making and\nbreaking of habit. This lends import to logic, which is the science of\nthought.\n\n(2) The chief function of induction is to discover new truth; whereas\ndeduction aims at clarifying and correcting new truth. Inductive logic\nmakes known the special forms of thought which the discoverer uses;\nwhile deductive logic tends to show how he verifies the truth thus\nobtained.\n\n(3) Just as there are two general forms of thinking, inductive and\ndeductive; so there are two general types of mind, the inductive\nand the deductive; the former leads to liberalism, the latter to\nconservatism. Both types are needed to maintain a safe balance.\n\n(4) The schools of the day are emphasizing the deductive phase of\nwork to the sacrifice of the inductive. They are neglecting the\nColumbuses and the Edisons of the class. The course of study makes for\na conservatism, which \u201cnips in the bud\u201d any marked tendency to discover\nand invent.\n\n(5) Logic may aid in the crusade against the ultra conservative\ntendency of class method, by giving emphasis to the method of the\ndiscoverer and inventor. An analysis of this method reveals these\nthree steps: antecedent facts, forming an hypothesis and verification.\nAntecedent facts may be divided into foundational and crucial.\nA crucial fact leads immediately to the formation of the hypothesis;\nwhereas the foundational facts represent that body of knowledge\nwhich makes it possible to interpret the crucial fact. The crucial\nfact creates an unsatisfied state of mind, which, in turn, urges the\ndiscoverer to construct some satisfactory hypothesis. Inference by\nanalogy is the process used in such a construction. The two modes of\nverification are recourse to experience, or empirical; and appeal to\nreason, or rational.\n\n(6) In the class room, induction is used in form, not in spirit; in\nconsequence we are neglecting the generals for the camp followers.\n\n(7) The inductive method is logically the method of discovery, while\nthe deductive method is the method of instruction. In the class room,\nboth methods have been devoted to the matter of instruction. Because of\nthis, induction has been robbed of its chief advantage over deduction.\n\n(8) Man has attained his greatest success by _enlarging_ upon the\nthoughts of nature and not by an _absolute substitution_. In enlarging\nupon nature\u2019s way of educating the child, man has adopted her form of\nprocedure, but has lost her spirit of work. In his scheme of education,\nman\u2019s watchword is _knowledge_, while nature\u2019s is _conquest_. To\nseek knowledge without inspiring the spirit of conquest is man\u2019s way;\nwhereas nature\u2019s way is to encourage the spirit of conquest by using\nknowledge as a reward. Man must co-operate with nature, if the best\nresults are to be secured.\n\n(9) In the case of the true discoverer, it is not necessary to endow\nthe object of his thought with added attractiveness; but with the child\nenthusiasm may need to be stimulated by \u201cmotivating\u201d the subject in\nhand. This may be accomplished by appealing directly to the vital needs,\nworldly necessities, and innate cravings of the child mind.\n\n(10) A revolt is in evidence against that insatiate desire to teach\nknowledge, which has been so marked in the past. Already schools are\nintroducing departments of work which look toward _conquest_ rather\nthan _knowledge_.\n\nWhen adapted to the school room the discoverer\u2019s method naturally\nresolves itself into these five steps:\n\n (1) \u201cMotivate\u201d the topic for presentation.\n\n (2) Bring to mind \u201cfoundational facts.\u201d\n\n (3) Vividly make evident the \u201ccrucial fact.\u201d\n\n (4) Lead to discovery of \u201clesson-point.\u201d\n\n (5) Afford opportunity for verification.\n\n(11) The question and answer method of presenting work, does not\nnecessarily give full scope to the spirit of inquiry as emulated by the\ntrue born discoverer.\n\nAs a matter of affording opportunity for the development of the spirit\nof discovery, there are three modes of presentation which may be\narranged in a progressive series:\n\n (1) The lecture mode in which there is little opportunity for\n discovery.\n\n (2) The question and answer mode which permits some opportunity for\n discovery.\n\n (3) The mode by suggestion which permits ample opportunity for\n discovery.\n\n\n=14. REVIEW QUESTIONS.=\n\n (1) Show that thought may be made to make and break habit.\n\n (2) \u201cInduction directs to new truth, deduction aims to modify and\n correct new truth.\u201d Explain and illustrate this.\n\n (3) Relate radicalism and conservatism to induction and deduction.\n\n (4) Show that in the present day school situations, the spirit of\n deduction prevails.\n\n (5) Describe a discovery which is a typical illustration of the\n _discoverer\u2019s method_.\n\n (6) Indicate with explanation the general steps in the discoverer\u2019s\n method.\n\n (7) Show by illustration the difference between \u201cfoundational facts\u201d\n and \u201ccrucial facts.\u201d\n\n (8) Explain how the \u201ccrucial fact\u201d leads to the construction of an\n hypothesis.\n\n (9) Explain and illustrate the two ways of verification.\n\n (10) Distinguish between the inductive method as it is used in the\n class room, and the inductive method as used by the discoverer.\n\n (11) Show that in his inventions, man enlarges upon the thoughts of\n nature.\n\n (12) Explain \u201cmotivation\u201d and show that it is a new name for an old\n situation.\n\n (13) In adapting the discoverer\u2019s method to class work, what are the\n successive steps to be followed?\n\n (14) Show by illustration that the question and answer method is not\n necessarily one which encourages the spirit of discovery.\n\n\n=15. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) \u201cOur pet thoughts control us.\u201d Discuss this.\n\n (2) Select some class room experience for the purpose of showing that\n induction is especially _directive_ in nature, whereas deduction\n is more or less _corrective_ in nature.\n\n (3) \u201cThere are just two kinds of people in the world, the\n _Inductives_ and the _Deductives_.\u201d Explain.\n\n (4) Are the schools sending out too many _Deductives_? Argue the\n question.\n\n (5) \u201cIt is the business of the teacher to teach himself out of the\n business.\u201d Explain.\n\n (6) Look up the discovery of the laws of the pendulum, with a view\n of showing that the event well illustrates the fact of the three\n general steps in the discoverer\u2019s method.\n\n (7) \u201cWith the average, only extraordinary facts become crucial; but\n with the genius any ordinary fact may become crucial.\u201d Make this\n clear.\n\n (8) Explain \u201cmental urge.\u201d Illustrate.\n\n (9) Illustrate \u201cempirical proof,\u201d also \u201crational proof.\u201d\n\n (10) Show by illustration that the inductive method as used in the\n class room, falls far short of being the method of the discoverer.\n\n (11) Indicate by citing historical examples, that conquest rather than\n knowledge makes for manhood.\n\n (12) Show how you would motivate a topic in geography.\n\n (13) Outline a plan for teaching some topic in nature according to the\n discoverer\u2019s method.\n\n (14) Select a topic in arithmetic, for the purpose of giving a\n comparative illustration of the \u201cquestion and answer mode\u201d of\n presentation, and the \u201cmode by suggestion.\u201d\n\n\n\n\n CHAPTER 21.\n\n LOGIC AND LIFE.\n\n\n=1. LOGIC GIVEN A PLACE IN A SECONDARY COURSE.=\n\n\u201cTo prepare for complete living\u201d seems to be the ultimate aim of\neducation, and any school subject which does not aid to this end must\nbe eliminated from the courses of study. \u201cKnowledge for the sake of\nknowledge\u201d will not do in this age of practical efficiency. _A subject\nin order to survive must show indications of doing its share in this\nlarger business of man building._ If it can be made evident that\nlogic lends itself in no undecided terms to such an aim, then may its\nincorporation in a secondary course of study be not only justified but\nmore highly appreciated.\n\n\n=2. MAN\u2019S SUPREMACY DUE TO POWER OF THOUGHT.=\n\nThat man is the supreme agent of intelligent progress is due to three\nfactors: First, to the existence of the natural world; second, to the\nexistence of man himself; third, to man\u2019s ability to think. Given life\nand the world as a place to evolve that life, and it is barely possible\nthat man might have _survived_, but without _thought_ he could never\nhave become _supreme_. _Man is king of the animal kingdom because of\nhis power of thought._ Let us illustrate:\n\nAges ago when England was a part of the main land; when there was no\nNorth Sea nor English Channel; we are told that there lived in the\nforest tracts there about many large and ferocious animals; such as\nthe elephant, the lion, and the tiger. There lived also in the region a\n_smaller_ and apparently a _weaker_ animal. This creature had no tusks\nto hook with, no great jaws to crunch with, and no claws to tear with;\nand an eye witness would have said \u201cSuch a weakling has no possible\nchance against these enemies of his; he and his descendants will\nsuccumb and the species will become extinct.\u201d The region was tropical;\nbut, of a sudden, a cataclysmic twist changed the temperature from\na torrid to a frigid state. What happened? The large and ferocious\nanimals either migrated to the south or froze to death; _but this\nweakling put on furs, built fires, and remained in the jungle as its\nking_. His name was man, and though he had no horns to hook with, he\npossessed a _brain to think with_; this gave him supremacy over the\nforces of nature.\n\nFrom the beginning the adaptation of the lower animals has been\nphysical; whereas man\u2019s has been more or less intellectual. By means\nof deliberative thought man made the bow and arrow which could kill\nat a distance of 200 yards; then he invented the repeating rifle which\nmay kill a mile away. _Thought_ has taught man to harness the forces\nof nature in the form of all kinds of invention. _Thought_ has given\nman the power to build bridges and palaces, to paint pictures, to\nchisel angels. _Thought_ has pierced the fog of ignorance and brought\nlight to the dark spots of the globe. _Thought_ has build nations and\nestablished the spirit of good will on earth. Through the long years,\n_thought_ has been the _one tool of conquest_ which has enabled man\nto build for himself, out of the furnishings of nature, _a heaven on\nearth_.\n\nCan you recall a department of life which thought has not embellished?\nCan you recall a single factor that has been raised to the nth power\nof efficiency without thought? Steam and electricity _plus thought_\nlights the world, unites the world, feeds and clothes the world. To-day,\nas in the olden time, men who think are ever at a premium. This holds\ntrue from the Shopkeeper to the Magnate of Wall Street; from Basil,\nthe Blacksmith, to Edison, the King Inventor; from Reuben, the Farmer,\nto Burbank, the Wizard.\n\n\n=3. IMPORTANCE OF PROGRESSIVE THOUGHT.=\n\nMan not only thinks but he thinks _progressively_. The _average horse_\nof to-day, for example, is probably no more intelligent than was the\naverage equine of the time of Alexander the Great, whose war horse,\nBucephalus, attained historical fame. Yet, intellectually, the _average\nman_ of to-day is _far_ above the average man of Alexander\u2019s time.\n\u201cHorse-knowledge\u201d is more or less stationary. Through instinct\neach generation makes use of the knowledge of its ancestors without\nany noticeable accretions. But \u201cman-knowledge\u201d is a growing product\nof progressive thought. Man appropriates all the knowledge of his\nforbears, and then adds to this a bit of his own. By being able to\nthink progressively, man is enabled to _stand upon the shoulders of\nhis ancestors_ and thus to take advantage of a broader vision.\n\nWe are now led to the conclusion that man\u2019s supremacy is due not only\nto his ability to think, but to his power of _progressive_ thought.\n\n\n=4. NECESSITY OF RIGHT THINKING.=\n\nIn the main, man\u2019s thinking has been for his good, that is, in the\nlong run, it has contributed to his general progress. If this had not\nbeen so, long since would he have dropped back to the level of the\nnon-thinking animals.\n\nThinking has been defined as the process of affirming or denying\nconnections. Right thinking is, therefore, a matter of affirming\nthe right connections or denying the wrong connections. To put it\ndifferently: right thinking is the process of adjusting the best means\nto a right end; whereas wrong thinking is a matter of overlooking the\nbest means, or directing improper means to a wrong end. Right thinking\ninvolves _proper adjustment_; wrong thinking _improper adjustment_. In\nthe intellectual world as in the physical, _improper adjustment_ means\nextinction. Illustrations of this:\n\n(1) A contractor undertakes to build a skyscraper. In the excavation\nan old wall is discovered. The thought of the contractor is, \u201cI must\nmake a pot of money out of this job, and since this old wall is in the\nright spot I will build on it, and thus save me \u2018five hundred\u2019.\u201d In\nthe course of ten years, without warning, the building topples over and\nfifty women and children are killed. The contractor is convicted and\nsent to prison for life. If the builder had thought the right thought;\nnamely, \u201cI want to put up a building that will stand for generations,\u201d\nhe would have survived the competition of his fellows and entered his\nlong home with success etched upon his soul.\n\n(2) Two school teachers, A and B, are working in the same system. A\u2019s\nambition is to be promoted and she uses \u201cpull\u201d as the means. For a time\nshe succeeds in pulling the wires, and likewise in pulling the \u201cwool\u201d\nover the eyes of the Board of Education. B aspires to professional\ngrowth, using as the means every opportunity for genuine improvement.\nIn time both are known as they really are, not as they seem to be. A\nis denominated a \u201cshirk,\u201d a politician, a _mere school keeper_; whereas\nB is looked up to as the best equipped worker in the building, a _real\nschool teacher_.\n\nThere may seem to be many exceptions to this point of view, and yet\nin the last analysis we find that these exceptions are only apparent.\nWhen we maintain that right thinking means survival and wrong thinking\nextinction, we assume that the standard adopted is _genuine efficiency_\nand not a _certain money basis_. High positions may be _secured_\nthrough wrong thinking, but these cannot be _filled creditably_ without\nthe preponderance of right thinking.\n\n\n=5. INDIFFERENT AND CARELESS THOUGHT.=\n\nIt may be advanced as a plausible hypothesis that man, especially if he\nis an American, finds much trouble for himself, and makes much trouble\nfor the world because of his indifference to thought. To leap first and\nlook afterwards is the spirit of youth, and America is young. _Think\ntwice before you look and look twice before you leap_ is sound logical\ndoctrine. A logically minded man _rationalizes_ every new proposition\nbefore he adopts it. He marshals before the mind the favorable points\nand then bombards them with every conceivable objection. With the\nsteady eye of an honest, earnest, open minded critic, he weighs the\nunfavorable against the favorable and then accepts the indications of\nthe balance unequivocally. If logic did nothing else save to inspire\nyoung people to thus rationalize every doubtful undertaking, it would\ndo its share toward world betterment.\n\n\n=6. THE RATIONALIZATION OF THE WORLD OF CHANCE.=\n\nMan seems to be a natural born gambler. He loves to \u201ctake a chance\u201d\nand herein lies much of his unhappiness. Without discussing the\nevils of the stock exchange, the horrors of the gambling den, and the\nunbusiness like procedure of the race track, we may merely attempt here\nto show how _the rationalization of the conception of chance_ may be\ninstrumental in dimming the glare of gambling to the average youth.\n\n(1) The meaning of the term chance.\n\nThe term chance implies an inability to find a cause for any\nparticular event. Whenever we trust to luck, we do so through ignorance.\nIn reality every thing in this world is ordered _according to law_,\nand if we possessed infinite knowledge concerning these laws, then,\nfor us, the word \u201cchance\u201d would have no meaning. One accomplishment\nof knowledge has been to rationalize superstition and chance. \u201cNot a\ngrain of sand lies upon the beach, but infinite knowledge would account\nfor its lying there; and the cause of every falling leaf is guided by\nthe same principles of mechanics as rule the motions of the heavenly\nbodies.\u201d\u2015\u2015Jevon\u2019s Prin. of Science, vol. I, p. 225.\n\nThat chance is a literal confession of ignorance, is a wholesome truth\nfor all to bear in mind. If we were not so ignorant of atmospheric\nconditions, we would never be caught in the rain without an umbrella;\nif we knew perfectly the laws of mechanics, we would not speed our car\nand trust to luck that the car would hold together.\n\n(2) Chance mathematically considered.\n\nThe principle of the \u201ccalculation of chances\u201d has been discussed\nelsewhere. It will be sufficient here to illustrate the principle from\na mathematical point of view.\n\nSuppose that a jeweller desires to dispose of a ten-dollar watch\nby a raffle. He may place a hundred numbers in a box, one of which\ncorresponds to the number on the watch. My chance of drawing the right\nnumber is one out of a hundred and may be expressed by the fraction\n1/100. The fact that I may draw the right number on the first trial or\non the last trial is immaterial. The real meaning of the ratio \u201cone out\nof a hundred\u201d is, that in the long run, I shall _lose 99 times_ where\nI gain but once. This implies, that if I pay 25 cents for each draw,\nI shall in the end pay 99 times 25 cents for the watch, or I will have\npaid $24.75 for a ten dollar watch.\n\n(3) Chance and gambling.\n\nIn all forms of gambling no wealth is produced. What one man gains the\nother man loses. In addition to this the institution which projects the\ngambling scheme must be supported. In consequence, _more money must be\nlost than can possibly be gained_. This leads to the conclusion that\non the basis of averages he who would gamble must terminate his career\n\u201cbehind the game.\u201d Statistics verify this conclusion.\n\n(4) Chance and investments.\n\nInterest, which is money paid for the use of money, is high when the\ndemand for money exceeds the supply and low when the supply equals or\nexceeds the demand. The fact that the supply is short is largely due\nto the lack of confidence on the part of the investor. This means that\nhe is unwilling to take the risk. Thus the principle: \u201c_High rate of\ninterest, great risk; low rate of interest, little risk._\u201d\n\n\n=7. THE RATIONALIZATION OF POLITICAL AND BUSINESS SOPHISTRIES.=\n\n\u201cWin right or wrong\u201d is a nut shell statement of modern sophistry.\nCorollaries to this are such aphorisms as \u201cOf two evils choose the\nlesser\u201d; \u201cDo evil that good may come,\u201d etc. Armed with these platitudes\nthe modern business and political octopus will play the bully and\nsqueeze the life out of the little fellow in the name of economy;\nwill pay for editorials to elect the \u201cright man\u201d; will evade bad laws\nso-called; institute lobbies; buy votes; and perpetrate a thousand\nother immoral deeds in the name of \u201cgood business\u201d or of \u201cparty\nloyalty.\u201d\n\nHalf truths are the most atrocious of all kinds of fallacies in that\nthey are the most misleading. \u201cDo evil that good may come\u201d is but half\nof the whole truth \u201cDo evil that good may come, _provided there is\nno other way open_.\u201d Again, \u201cOf two evils choose the lesser, _if a\ncomplete enumeration has shown that there is not a third course_.\u201d\n\nA development of a finer ability of discernment under right influence\nshould lead the common citizen to see _through_ these various\nsophistries practiced by corporate greed, and should enable him by\nmeans of the ballot to \u201cblaze a better way.\u201d\n\nThe \u201cpublic is a blunderbuss\u201d because the average man either cannot,\nor will not, think his own thoughts. By developing greater skill and\narousing greater interest in the _thinking process_, the crowd of camp\nfollowers will be reduced; selfish bossism will die; and a truer and\nmore efficient democracy will reign supreme.\n\n\n=8. THE RATIONALIZATION OF THE SPIRIT OF PROGRESS.=\n\nGenuine progress comes through a happy combination of the old with the\nnew. A love for the old only, means _ultra conservatism_; whereas a\nlove for the new only, means _ultra radicalism_; a love for both means\n_rational liberalism_.\n\nThat people love the old way may be attributed to two forces which will\nreceive attention here.\n\n(1) Race instinct.\n\nIt may be said that \u201clife is a brief space between two eternities\u2015\u2015a\npath between infinity and infinitude.\u201d \u201cMan is a pedestrian who\nperambulates along the way.\u201d The eternities concern him not so much as\nthe _path_ which stretches between them. In a former day, one of the\nstriking characteristics of the western plain was the _beaten path_\nstretching out along the table-land like an elongated, dust colored\nserpent; and often following this path would be a herd of buffalo\nwinding its way in single file around boulder and ant hill till shut\nfrom view by the distant horizon. Thus has man travelled along the\nbeaten path, following the \u201cfoot prints of the ages.\u201d Here and there\nand everywhere do we see signs of those who have gone on before; father,\ngrandfather, great grandfather; yes, even to the toe marks of those\nprimeval ancestors of ours who shambled along the way, nobody knows how\nmany years ago. From the dark recesses of the cave, have our forbears\nthrown a lasso of blood about our necks, and it seems as if we _must_\nfollow the old, old way. \u201cBeing acorns of the ancestral oak,\u201d we\ngrow similar oak tree tendencies, living over again the life of our\nprogenitors. \u201cThere lies in every soul the history of the universe.\u201d\n\n(2) Imitation.\n\nBut there is another reason for this ultra conservative spirit and it\nis that nature\u2019s chief mode of instruction is by means of _imitation_.\nTo every living thing of wood or field nature seems to say, \u201cYour\nparents are always right, do as they do for this is the best way\nto learn the lessons of life.\u201d A man thinks, feels and wills his\nway through life in a certain manner largely because his father did\nlikewise. Moreover, we not only imitate those who have gone on before,\nbut we counterfeit each other; fashion is another name for world wide\nmimicry. We imitate our friends and those whom we admire; we talk like\nthem, we walk like them, we live like them.\n\nIt now appears that we are held to the path of the past by means of\n_race instinct_ and the _power of imitation_, and we are thus prone\nto believe that the old way is good enough. It is evident that to get\nout of the beaten path is dangerous. The wild animal that deserts the\nhabits of the race dies a premature death, and the man who possesses\nthe temerity to struggle through the thicket of new things must, of\nnecessity, shorten his span of life. To follow the \u201csame old rut\u201d\nis easiest for the teacher; to be loyal to the \u201cgrand old party\u201d is\nsafest for the politician. But to the contrary, if every man of every\ngeneration had followed the beaten path blindly\u2015\u2015without deviation, the\nhuman race would now be a horde of simians. Because man has possessed\nthe power of progressive thought, he has developed the spirit of\nradicalism and has thereby made himself supreme.\n\n\u201cThe old way anyway\u2015\u2015the old way right or wrong\u201d has been the world\u2019s\nbiggest stumbling block. Every innovation must fight for its life.\nEvery good thing has to be condemned in its day and generation. It is\nHuxley who suggests three stages for the course of a new idea: First,\nit is revolutionary; second, it will make little difference; third, _I\nhave always believed in it_. On the other hand, the new way anyway; \u201cwe\nmust have a change whether or no\u201d; \u201cwe must have something different\ndespite the cost,\u201d have ever been the slogans of waste and destitution.\nThe wars which have not resulted from the prejudice of ultra\nconservatism have been brought about through the thoughtlessness of\nultra radicalism. The revolutionist, the freak and the anarchist,\nproducts of impulse and the spirit of discontent, spring from an unwise\nlove of change.\n\nThe world needs conservatism and radicalism not so much as it needs\n_rationalism_. It needs men who can hold to the _good of the old_ and\nadopt the _best of the new_; men who neither \u201crust out\u201d nor \u201cwaste\nout\u201d; but _wear out_. That rational progress may obtain, there must\nbe a perfect dovetailing of the old with the new. Man must leave the\nbeaten path not altogether, but at times. He needs to blaze out a _new_\nway not so much as he needs to straighten the bends, tunnel through\nthe mountains, and fill in the swamps of the _old_ way. _A rational\n\u201cliberalism\u201d implies a willingness to follow the old path with a view\nto improving the imperfections thereof._\n\n\n=9. A RATIONALIZATION OF THE ATTITUDE TOWARD WORK.=\n\nOn the assumption that true happiness is the ultimate aim of life,\nwe may conclude that anything which does not contribute to this\nend functions as a curse and not as a blessing. Happiness involves\nphysical comfort and mental joy. To have comfort of the body implies\nmoderate means. The poor cannot be happy because of bodily want. When\n\u201cphysical-man\u201d is not given proper nourishment for healthy growth,\nthen does he _goad_ \u201cspiritual-man\u201d with the pricks of appetite and\npain till his wants are appeased. This is a law of nature. On the\nother hand happiness is not attained through acquisition; neither\nthe millionaires, nor the scholars, nor the famous are the happiest.\nThis is a fact apparent to all. Over worry and over excitement follow\nclosely the heels of much money and high position. Too little brings\nunhappiness through want; too much brings unhappiness through worry.\nTherefore man is _cursed by his work_ when the remuneration is not\nenough for comfort of body, or when the income is too much for poise\nof mind.\n\nUnless the organs of the body are used they atrophy. Every cell of\nthe physical makeup demands exercise. Work which is not drudgery;\nwork which causes the organs of the body and the powers of the mind to\nfunction normally; work which gives comfort without luxury; work which\nforces one to the highest actualization of his physical and spiritual\npowers is _man\u2019s greatest blessing_. In and through such work will man\nattain his highest state of happiness.\n\n\n=10. THE LOGIC OF SUCCESS.=\n\nWe may now hope to show that material aggrandizement, the adopted\nstandard of success, is one of the illogical factors of modern life.\n\nThe tree of the forest always grows toward the light. It pushes its way\nthrough the darkness of the soil into the shadow of the underbrush and\nfinally out into the unobstructed light of the sun. This parallels the\nprogress of the race. From the darkness of _savagery_ into the shadow\nof _barbarism_, and finally out into the full light of _civilization_.\nThus has man grown steadily and continually toward better things. But\n\u201cbetter things\u201d is a relative term and has changed with the development\nof the race. \u201cA good healthy idea may not live longer than twenty\nyears.\u201d In consequence growth toward the light has been in accordance\nwith man\u2019s _conception_ of a higher and a better life; which conception\nis ever changing.\n\nMoreover, growth toward the best is always rewarded by real happiness.\nIt therefore follows that the _right road to real happiness_ extends\nalong the way of _better things_ as conceived by the traveller, _man_.\n\nAny force which tends to lift the world up toward more light is a\nblessing, and any personality which contributes to this end is a\nsuccess. When one drops a pin it falls _down_ toward the earth, at\nthe same time the earth comes _up_ to meet the pin. This is according\nto the universal law of gravitation. It is true that the earth moves\nthe pin through a much greater space than the pin moves the earth, and\nyet the fact remains that the pin _does move the earth_. The extent to\nwhich the smaller body is able to move the larger, depends on the two\nfactors of _weight_ and _relative position_. If the pin were lighter\nor farther away it would influence the earth so much the less. In like\nmanner does the \u201cpin-man\u201d influence the \u201chuman-world.\u201d The extent of\nthis influence is controlled by man\u2019s _weight_, or his \u201clifting power,\u201d\nand the _position_ which he occupies; just as the attraction of the pin\nfor the earth is controlled by _weight_ and _position_.\n\nThe facts of history have proved that man\u2019s power to lift depends not\nso much upon what he _has_ as upon what he _is_. In short, lifting\npower is directly in proportion to _personal worth_. Moreover, man\u2019s\nability to draw humanity up may be increased or decreased by the\nposition which he occupies. Such a position must function for the\nbest good of the world, and at the same time must elicit the highest\ndevelopment of the man.\n\n\n TO SUMMARIZE:\n\nIndividual success involves these three elements:\n\nFirst\u2015\u2015_A man of personal worth._\n\nSecond\u2015\u2015_A position which draws out the best in the man._\n\nThird\u2015\u2015_A work which definitely contributes to the uplift of the world._\n\nA definition is now in order:\n\n_Success is the right man in the right place doing his best for the\nhighest good of the world._\n\n\n=11. OUTLINE.=\n\n LOGIC AND LIFE.\n\n (1) Logic given a place in a secondary course.\n\n (2) Man\u2019s supremacy due to power of thought.\n\n (3) Importance of progressive thinking.\n\n (4) Necessity of right thinking.\n\n (5) Indifferent and careless thought.\n\n (6) The rationalization of the world of chance.\n (1) Meaning of the term chance.\n (2) Chance mathematically considered.\n (3) Chance and gambling.\n (4) Chance and investments.\n\n (7) The rationalization of business and political sophistries.\n\n (8) The rationalization of the spirit of progress.\n\n (9) A rationalization of the attitude toward work.\n\n (10) The logic of success.\n\n\n=12. SUMMARY.=\n\n(1) To justify its having a place in any course of study, logic must\nlend itself to character building.\n\n(2) Man is king of the animal kingdom because of his power of thought.\nFrom the beginning his adaption has been more or less intellectual and\nhis chief weapon of conquest has ever been his thinking brain.\n\n(3) Man\u2019s supremacy has been due not only to his ability to think, but\nalso to his power of _progressive_ thought.\n\n(4) Right thinking is the process of adjusting the best means to a\nright end. Wrong thinking involves improper adjustment, which in turn\nresults in extinction.\n\n(5) A \u201clogically-minded\u201d man _rationalizes_ every new proposition\nbefore he adopts it. That is, he analyzes with the utmost care and with\nunprejudiced frankness all the favorable and unfavorable situations;\nhe then throws them into the balance of honest judgment and adopts the\nindications of said balance, unequivocally.\n\n(6) Chance is a confession of ignorance. If man possessed infinite\nknowledge, the term chance would have no place in his vocabulary.\n\nThe games of chance are money making schemes supported by the gambling\nfraternity. On the basis of averages, the gambler, in the long run,\nmust terminate his career \u201cbehind the game.\u201d\n\nHigh rate of interest implies great risk; low rate of interest little\nrisk.\n\n(7) \u201cWin right or wrong\u201d epitomizes the teachings of modern sophistry.\nWith the coming of better thinking, a more efficient democracy will\nobtain.\n\n(8) Rational progress combines the best of the old with what seems to\nbe the best of the new.\n\nBlind love for the old, or ultra conservatism, is due to the two forces\nof race instinct and power of imitation.\n\nAn adherence to the \u201cold way anyway\u201d may mean retrogression; whereas\nfollowing the new way, simply because of its newness, may involve\nunnecessary waste.\n\n(9) Work which is not drudgery; work which causes the organs of the\nbody and the powers of the mind to function normally; work which\ngives comfort without luxury; work which forces one to the highest\nactualization of his physical and spiritual powers is man\u2019s greatest\nblessing.\n\n(10) Logically considered personal aggrandizement is not a true\nstandard of success. Success involves personal worth rather than\npersonal holding.\n\nSuccess is measured by man\u2019s ability to help the world on toward better\nthings.\n\nSuccess is the right man in the right place doing his best for the\nhighest good of the world.\n\n\n=13. REVIEW QUESTIONS.=\n\n (1) What is the ultimate aim of education? Show that logic\n contributes to this end.\n\n (2) Prove that man\u2019s power of thought has ever been his best weapon\n of conquest.\n\n (3) Exemplify the distinction between non-progressive and progressive\n thinking.\n\n (4) Define right thinking. Illustrate.\n\n (5) \u201cA logically-minded man rationalizes every new project before\n undertaking it.\u201d Give a concrete instance in explanation of this.\n\n (6) \u201cChance is a literal confession of ignorance.\u201d Demonstrate this.\n\n (7) Give a mathematical illustration proving that schemes of chance\n are simply money making devices for the benefit of those who\n project them.\n\n (8) The average gambler must terminate his career behind the game.\n Prove this.\n\n (9) Why should high rate of interest imply great risk?\n\n (10) Show that a half truth is a most misleading fallacy.\n\n (11) Illustrate a business sophistry. Explain.\n\n (12) Write a brief theme on \u201cThe Rationalization of the Spirit of\n Progress.\u201d\n\n (13) Under what conditions may work become man\u2019s greatest blessing?\n\n (14) Define success. Illustrate.\n\n (15) In the light of your definition of success discuss the following:\n \u201cThe only failure is not to try.\u201d\n\n\n=14. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=\n\n (1) \u201cTo prepare for complete living\u201d is the end of education.\n Interpret and discuss this quotation from Spencer.\n\n (2) Mention some discovery or invention which represents the power\n of progressive thought.\n\n (3) \u201cMan\u2019s adaptation has been largely intellectual while the\n adaptation of the camel has been physical.\u201d Explain.\n\n (4) Interpret the expression, \u201cThe son stands upon the shoulders of\n the father.\u201d\n\n (5) Illustrate instances where man\u2019s thinking has not been for his\n best interests.\n\n (6) Indicate how wrong thinking led to the Civil War.\n\n (7) Distinguish between legitimate speculation and gambling.\n\n (8) Name and explain the logical elements involved in a low rate of\n interest.\n\n (9) How may training in right thinking lead to more efficient\n citizenship?\n\n (10) \u201cThere lies in every soul a history of the universe.\u201d Show the\n truth of this.\n\n (11) Show by illustration that imitation is one of nature\u2019s chief\n modes of instruction.\n\n (12) Explain the meaning of drudgery.\n\n (13) Mention instances where work is a curse.\n\n (14) Is success possible when the right man is found doing his best\n in the wrong place?\n\n (15) Whom do you consider the most successful American? Give reasons.\n\n\n\n\n GENERAL EXERCISES IN TESTING THE\n VALIDITY OF CATEGORICAL ARGUMENTS.\n\n\n_Let the student give attention to the fallacies in meaning as well as\nto the fallacies in form._\n\n 1. None but those who are contented with their lot in life can\n justly be considered happy. But the truly wise man will always\n make himself contented with his lot in life, and, therefore he\n may justly be considered happy. Keynes.\n\n 2. Suffering is a title to an excellent inheritance; for God\n chastens every son whom he receives. Keynes.\n\n 3. No young man is wise; for only experience can give wisdom, and\n experience comes only with age. Keynes.\n\n 4. Dr. Johnson remarked that \u201ca man who sold a penknife was not\n necessarily an iron-monger.\u201d Against what logical fallacy was\n this remark directed? Explain. Keynes.\n\n 5. This pamphlet contains seditious doctrines, the spread of\n which may be dangerous to the state; hence the pamphlet must\n be suppressed. Keynes.\n\n 6. Good workmen do not complain of their tools: my pupils do not\n complain of their tools; therefore, my pupils are probably good\n workmen. Keynes.\n\n 7. Knowledge gives power; consequently, since power is desirable,\n knowledge is desirable. Keynes.\n\n 8. Some who are truly wise are not learned; but the virtuous alone\n are truly wise; the learned, therefore, are not always virtuous.\n Keynes.\n\n 9. The spread of education among the lower orders will make them\n unfit for their work; for it has always had that effect on those\n among them who happen to have acquired it in previous times.\n Keynes.\n\n 10. Slavery is a natural institution and therefore ought not to be\n abolished. Russell.\n\n 11. The yardstick of success is the dollar, and you have made your\n millions.\n\n 12. \u201cAll who talk well are not necessarily intelligent, and A is\n certainly a spell-binder.\u201d\n\n 13. Gold and silver are the wealth of a country; consequently,\n the diminution of gold and silver by exportation must mean the\n diminution of the wealth of a country. Russell.\n\n 14. A miracle is unbelievable, because it fails to conform to known\n laws of nature.\n\n 15. Improbable events happen every day; now, what happens every day\n is a probable event; therefore, improbable events are probable\n events.\n\n 16. What fallacy did Columbus commit when he made the egg stand on\n end by breaking one end?\n\n 17. Some holder of a ticket is sure to draw the prize; and, as I am\n a ticket holder, I am sure to draw the prize. Russell.\n\n 18. All the members of the jury are just men, hence you may trust the\n foreman.\n\n 19. Select the star players of the country and you will have a team\n which cannot be beaten.\n\n 20. All the houses on this street present a pretty picture; this\n house, therefore, which is on this street, will make a fine\n picture.\n\n 21. What is the good of all your teaching, for every day we hear of\n wrong doing made possible by education.\n\n 22. You are not what I am; I am a teacher; hence you are not a\n teacher.\n\n 23. The student of history is compelled to admit the law of progress,\n for he finds that society has never stood still. Russell.\n\n 24. This bill must have been designed to bleed the people because it\n is supported by the grafters of the state.\n\n 25. \u201cTo close the saloons on Sunday is contrary to the wishes of the\n people of the city; hence those \u2018farmer legislators\u2019 should keep\n hands off.\u201d\n\n 26. Success is the right man in the right place doing his best, and\n you are working to the limit.\n\n 27. Early to bed and early to rise, makes one healthy, wealthy and\n wise. It is, therefore, easy enough to get rich.\n\n 28. Honesty being the best policy, I must tell the truth to my\n patient, though to tell him that he cannot live will shorten his\n life many days.\n\n 29. A stitch in times saves nine, hence an ounce of prevention is\n worth a pound of cure.\n\n 30. The richest man I know used to sweep his office every morning,\n hence it pays to commence at the bottom.\n\n 31. Cramming is an injurious habit, since it makes the building of\n logical memories practically impossible.\n\n 32. A strong will means a trained will; struggle is an indication of\n weakness.\n\n 33. There is no such thing as a national or state conscience;\n therefore, no judgments can fall upon a sinful nation. Hibben.\n\n 34. The principles of justice are variable; the appointments of\n nature are invariable; therefore, the principles of justice are\n no appointment of nature. Aristotle.\n\n 35. Intelligence and not sex should be the standard; therefore, let\n the women have their way.\n\n 36. \u201cWar by killing off the men of the country gives the living a\n better opportunity to succeed because of reduced competition.\u201d\n\n 37. Since you deem yourself a misfit, in the name of common sense,\n why do you not change your occupation?\n\n 38. The conquest of America by Europeans has been a good thing for\n the world; since no eminent historian doubts it.\n\n\n\n\n GENERAL EXERCISES IN TESTING THE VALIDITY OF HYPOTHETICAL,\n DISJUNCTIVE AND DILEMMATIC ARGUMENTS.\n\n\n_The student must remember to give attention to the fallacies in\nmeaning as well as to the fallacies in form._\n\n 1. If I speak at length, he is bored; if I speak briefly, he is\n offended; therefore I will not speak at all.\n\n 2. If virtue is involuntary, vice is also involuntary; but vice is\n voluntary, hence virtue is also.\n\n 3. If a man cannot make progress toward perfection, he must either\n be a brute or a divinity; but no man is either; therefore every\n man is capable of such progress. Fowler.\n\n 4. If education is popular, compulsion is unnecessary; if unpopular,\n compulsion will not be tolerated. Fowler.\n\n 5. If you are to recover from this illness, then you will. If you\n are not to recover, then you will not, hence what is the use of\n calling in a physician?\n\n 6. If your act was right, your conscience will approve it; if wrong,\n your conscience will prick you. Either your act was right or\n wrong, so you can depend upon your conscience.\n\n 7. If he is intoxicated then he is not responsible, but he acts like\n a sober man.\n\n 8. If the Elixir of Life is of any value, those who take it will\n improve in health; now my friend who has been taking it has\n improved in health, and therefore the elixir is of value as a\n curative agent. Hyslop.\n\n 9. If you will settle down to business, you may still win out,\n because I am confident it is not too late for hard work to be\n effective.\n\n 10. If the end justifies the means then money used for any object of\n charity may be secured in any way.\n\n 11. If might is right then money talks, but I find that occasionally\n money proves ineffective.\n\n 12. If the majority of those who use public houses are prepared\n to close them, legislation is unnecessary, but if they are not\n prepared for such a measure, then to force it on them by outside\n pressure is both dangerous and unjust. Hyslop.\n\n\n 13. If the conscience is infallible in matters of right and wrong,\n then sin is just one thing; namely, doing that which is contrary\n to one\u2019s conscience. We believe that an educated conscience is\n infallible.\n\n 14. If the earth were of equal density throughout, it would be about\n 2\u00bd times as dense as water; but it is about 5\u00bd times as dense;\n therefore the earth must be of unequal density. Hyslop.\n\n 15. The end of human life is either perfection or happiness; death\n is the end of human life, therefore death is either perfection\n or happiness. Creighton.\n\n 16. That chauffeur either lost his head or was drunk because no sane\n man would deliberately run down an innocent child.\n\n 17. If you argue on a subject which you do not understand, you will\n prove yourself a fool; for this is a mistake which fools always\n make. Keynes.\n\n 18. If you are a man of your word, you will live up to your\n agreement, or if you have any self respect, you will do the manly\n thing. Now your neighbors tell me that you are a man in the habit\n of making good your promises.\n\n\n\n\n SETS OF EXAMINATION QUESTIONS FOR\n TRAINING SCHOOLS AND COLLEGES.\n\n\n_Answer ten questions._ Time, 2 hours.\n\n Set I.\n\n 1. Define and illustrate obversion and state the principle which\n conditions the process.\n\n 2. Give directions for making the following propositions logical:\n (1) Only first class passengers may ride in parlor cars.\n (2) All who claim to be pious are not pious.\n (3) \u201cBlessed are the merciful.\u201d\n\n 3. Write a theme of 200 words on \u201cLogic and Life.\u201d\n\n 4. Put into syllogistic form and test the validity of this argument.\n \u201cWe are going to have an open winter because the hornets\u2019 nests\n are near the ground.\u201d\n\n 5. Justify the teaching of logic in an institution which offers\n courses in Educational Theory.\n\n 6. Correct the following definitions, stating the rules violated:\n (1) A man is an organized entity whose cognitive powers\n function rationally.\n (2) A bird is an animal that flies.\n (3) A scholar is an educated man with scholarly attainments.\n\n 7. Prove that in the first figure the minor premise must be\n affirmative.\n\n 8. Investigate a case of habitual tardiness by making use of the\n canon of difference.\n\n 9. Describe with illustrations the various ways of begging the\n question.\n\n 10. Why should classification rather than logical division be the\n mode of procedure in the case of small children? Illustrate.\n\n 11. Illustrate the following:\n (1) non connotative term,\n (2) undistributed middle,\n (3) fallacy of accident.\n\n\n Set II.\n\n_Answer ten questions._ Time, 2 hours.\n\nThrow the following into the form of a syllogism and criticise, giving\nreasons:\n\n 1. \u201cI do not know how to teach school as I have had no experience.\u201d\n\n 2. \u201cOnly the honest should be in business and you are not honest.\u201d\n\n 3. Why should all teachers study logic? Give arguments in full.\n\n 4. Describe Mill\u2019s methods of induction and illustrate one.\n\n 5. Give and explain the rules of logical definition.\n\n 6. Explain the distribution of terms and illustrate by circles the\n meaning of the four logical propositions.\n\n 7. Define the following:\n (1) teaching,\n (2) extension of terms,\n (3) obversion,\n (4) hypothesis,\n (5) relative term.\n\n 8. Give a class room illustration of the Complete Method.\n\n 9. Distinguish between\n (1) distributive and collective terms,\n (2) analysis and deduction,\n (3) logical division and classification.\n\n 10. Illustrate the following:\n (1) contradictory proposition,\n (2) analogy,\n (3) law of identity,\n (4) singular term,\n (5) univocal term.\n\n 11. Convert, if possible, the following:\n (1) Some men are honest.\n (2) All that glitters is not gold.\n (3) All kings are fallible.\n\n\n Set III.\n\n_Answer ten questions._ Time, 2 hours.\n\n 1. Investigate by the Joint Method of Induction this question: \u201cWhy\n is John absent so often?\u201d\n\n 2. Explain and illustrate:\n (1) contradictory propositions,\n (2) illicit middle,\n (3) obversion,\n (4) contraversion,\n (5) synthesis.\n\n 3. State and exemplify the rules of logical division.\n\n 4. Write a theme of at least 150 words on one of the following:\n (1) Induction as the Discoverer\u2019s Method.\n (2) A Rational View of Success.\n\n 5. Define logically:\n (1) teaching,\n (2) deduction,\n (3) education,\n (4) analysis,\n (5) money.\n\n 6. Distinguish between the extension and intension of terms.\n\n 7. Exemplify:\n (1) an absolute term,\n (2) the complete method,\n (3) non connotative terms,\n (4) fallacy of accident,\n (5) hypothesis.\n\n 8. \u201cEducated among savages, he could not be expected to know the\n customs of polite society.\u201d Is this valid? Reasons.\n\n 9. \u201cThe signs indicate that you are either stupid or unprepared; but\n the past proves that you are not the former.\u201d Test the validity.\n\n 10. Discuss comprehensively one of the following topics:\n (1) The Fallacies.\n (2) Thinking.\n (3) Abbreviated Arguments.\n\n\n Set IV.\n\n_Answer ten questions._ Time, 2 hours.\n\n 1. Exemplify:\n (1) the law of variation in the extension and intension of\n terms,\n (2) a distributed predicate.\n\n 2. Indicate with explanation the logical errors:\n (1) A teacher assumes that the \u201cbad boy of the school\u201d is going\n to cause trouble in her room.\n (2) All the men of the Commission are fair minded men, hence\n they will render a fair decision.\n\n 3. What experimental method of induction is the most positive in its\n conclusion? Illustrate this method.\n\n 4. State and illustrate the rules of logical definition.\n\n 5. Obvert each of the four logical propositions. Explain the\n principle involved.\n\n Test the validity of the following arguments:\n\n 6. \u201cHorses, not being human, cannot reason.\u201d\n\n 7. \u201cOnly the industrious deserve to succeed and you have never done\n a hard day\u2019s work in your life.\u201d\n\n 8. \u201cIf you had been wise, you would have refused to stoop to the\n methods of the firm, but you were not wise.\u201d\n\n 9. From this premise construct a valid syllogism: \u201cAll large cities\n owe their size to some commercial advantage.\u201d\n\n 10. Define and illustrate the following: analogy, hypothesis,\n thinking, connotative term, relative term.\n\n 11. Distinguish between:\n (1) Analysis and deduction.\n (2) Logical division and classification.\n (3) Relative and absolute identity.\n\n\n Set V.\n\n_Answer ten questions._ Time, 2 hours.\n\nTest the validity, giving reasons:\n\n 1. All successful teachers are industrious, but you are not\n industrious because you are not successful.\n\n 2. John was a troublesome boy in the first and second grades,\n therefore he is going to make trouble for the third grade\n teacher.\n\n 3. Teaching is the art of imparting knowledge. Criticise, giving\n reasons. Define correctly, pointing out the essentials.\n\n 4. Explain the extensional and intensional use of terms and\n illustrate the law of variation.\n\n 5. Describe Mill\u2019s experimental methods of induction. Symbolize the\n joint method.\n\n 6. Define the following: analysis, law of identity, obversion.\n\n 7. Illustrate the laws of thought.\n\n 8. Write on one of the following topics:\n (1) Complete Method,\n (2) Right Thinking.\n\n 9. \u201cThe science of logic never made a man reason rightly.\u201d Discuss\n this question.\n\n 10. Explain and illustrate the enthymeme.\n\n\n Set VI.\n\n_Answer ten questions._ Time, 2 hours.\n\n 1. Exemplify the following:\n (1) illicit minor,\n (2) begging the question,\n (3) law of excluded middle,\n (4) inductive method.\n\n 2. Write a short theme on one of these topics:\n (1) Thinking.\n (2) Logical Terms.\n\n Test the validity of the attending arguments, giving reasons:\n\n 3. \u201cHe who talks much usually says little and you are certainly a\n great talker.\u201d\n\n 4. \u201cYou must be industrious, since only such truly succeed.\u201d\n\n 5. Illustrate and give the characteristic marks of the joint method\n of induction.\n\n 6. Summarize the benefits to be derived from a study of logic.\n\n 7. State and illustrate the rules of logical definition.\n\n 8. Distinguish between\n (1) extension and intension,\n (2) opposite and contradictory terms,\n (3) analysis and synthesis.\n\n 9. Define and illustrate hypothesis, obversion, sorites,\n hypothetical argument.\n\n 10. Explain and illustrate the three forms of induction.\n\n 11. Distinguish logically between a teacher and an instructor.\n\n\n\n\n BIBLIOGRAPHY.\n\nAikins. The Principles of Logic. Henry Holt and Co., New York. 1905.\n\nBain. Logic, Inductive and Deductive. Longmans, Green and Co. 1902.\n\nBosanquet. The Essentials of Logic. The MacMillan Co., London. 1910.\n\nBradley. The Principles of Logic. London. 1886.\n\nCreighton. Introductory Logic. The MacMillan Co., New York. 1905.\n\nDewey. Studies in Logical Theory. The University of Chicago Press.\n 1903.\n\nFowler. The Elements of Deductive and Inductive Logic. Oxford. 1905.\n\nHibben. Logic, Deductive and Inductive. Chas. Scribner\u2019s Sons, New\n York. 1906.\n\nHyslop. Elements of Logic. Chas. Scribner\u2019s Sons, New York. 1905.\n\nJevons-Hill. Elements of Logic. American Book Co., New York. 1883.\n\nKeynes. Formal Logic. The MacMillan Co., London. 1906.\n\nLotze. Logic. Translated by B. Bosanquet, 2 vols. Oxford. 1888.\n\nMcCosh. Laws of Discursive Thought. Chas. Scribner\u2019s Sons. 1906.\n\nMill. A System of Logic, 2 vols. Longmans, Green and Co., London. 1904.\n\nRussell. Elementary Logic. The MacMillan Co., New York. 1908.\n\nRyland. Logic. George Bell and Sons, London. 1900.\n\nSigwart. Logic. Translated by Helen Dendy, 2 vols. The MacMillan Co.\n 1895.\n\nSwinburne. Picture Logic. Longmans, Green and Co., London. 1904.\n\nTaylor. Elementary Logic. Chas. Scribner\u2019s Sons, New York. 1911.\n\nVenn. The Logic of Chance. The MacMillan Co., New York.\n\n\n\n\n OUTLINE OF BRIEFER COURSE.\n\n\n Subject\n\n =I. THOUGHT AND ITS LAWS=\n \u2b58 Logic Defined\n \u2b58 The Thinking Process.\n \u2b58 Stages in Thinking\n \u2b58 The Law of Identity\n \u2b58 The Law of Contradiction\n \u2b58 The Law of Excluded Middle\n\n =II. LOGICAL TERMS=\n \u2b58 All of Chapter 4\n\n =III. EXTENTSION AND INTENSION OF TERMS=\n \u2b58 All of Chapter 5\n\n =IV. DEFINITION=\n \u2b58 All of Chapter 6\n\n =V. LOGICAL DIVISION AND CLASSIFICATION=\n \u2b58 All of Chapter 7\n\n =VI. LOGICAL PROPOSITIONS=\n \u2b58 All of Chapter 8 Except Section 7\n\n =VII. IMMEDIATE INFERENCE=\n \u2b58 All of Chapter 10\n\n =VIII. MEDIATE INFERENCE=\n \u2b58 All of Chapter 11 Except Section 8\n\n =IX. FIGURES AND MOODS=\n \u2b58 The Four Figures of the Syllogism\n \u2b58 The Moods of the Syllogism\n \u2b58 Testing the Validity of the Moods\n\n =X. INCOMPLETE SYLLOGISMS=\n \u2b58 Enthymeme\n \u2b58 Polysyllogisms\n \u2b58 Sorites\n\n =XI. CATEGORICAL ARGUMENTS TESTED=\n \u2b58 All of Chapter 14\n\n =XII. HYPOTHETICAL AND DISJUNCTIVE ARGUMENTS=\n \u2b58 All of Chapter 15 except Sections 13,14, 15 and 17\n\n =XIII. LOGICAL FALLACIES=\n \u2b58 All of Chapter 16\n\n =XIV. INDUCTIVE REASONING=\n \u2b58 All of Chapter 17 Except Sections 3, 4, 7, 8 and 9\n\n =XV. MILL\u2019S METHODS OF OBSERVATION AND EXPERIMENT=\n \u2b58 All of Chapter 18\n\n =XVI. OBSERVATION, EXPERIMENT AND HYPOTHESIS=\n \u2b58 All of Chapter 19\n\n\n\n\n INDEX\n\n\n A\n\n Absolute Terms, 56.\n\n Abstract Terms, 51.\n\n Accent, Fallacy of, 330.\n\n Accident, 81;\n Fallacy of, 334.\n\n Affirmative Proposition, 127.\n\n Agreement, Method of, 387.\n\n All\u2015\u2015not, Some, Few, Logical Significance of, 133.\n\n Ambiguous Middle, 328.\n\n Amphibology, 329.\n\n Analogy, 368.\n\n Analysis, Definition of, 97;\n As a Method, 97;\n Induction by, 373.\n\n Analytic Propositions, 138;\n Method, 97.\n\n Antecedent, 289.\n\n Apprehension and Thinking, 24.\n\n Arguments, Irregular, 258;\n Testing of Categorical, 263;\n Incomplete, 247;\n General Exercises, 481;\n Mistakes of Students in Connection with, 281;\n Hypothetical, 288;\n Disjunctive, 302;\n Dilemmatic, 308.\n\n Argumentum ad populum, 338;\n ad hominem, 338;\n ad ignorantiam, 338;\n ad baculum, 338;\n ad verecundiam, 339.\n\n Aristotle\u2019s Dictum, 208.\n\n Art, Definition of, 96.\n\n Auxiliary Elements of Induction, 418.\n\n\n B\n\n Bain Quoted, 12.\n\n Ballentine Quoted, 359.\n\n Barbara, Celarent, etc., 234.\n\n Begging the Question, 341.\n\n Bibliography, 492.\n\n Bowen Quoted, 12.\n\n Briefer Course, Outline of, 493.\n\n\n C\n\n Canons of Syllogism, 209;\n of Four Figures, 226.\n\n Categorematic Words, 48.\n\n Categorical Arguments, 263;\n Tested, 263;\n General Exercises, 481.\n\n Categorical Propositions Defined, 121;\n Four Elements, 122;\n Four Kinds, 126;\n Classification of, 128.\n\n Cause, Fallacy of False, 340.\n\n Chance, Rationalization of, 468.\n\n Child, Thinking of, 20.\n\n Circulus in Probando, 343.\n\n Classification Compared with Division, 112;\n Kinds, 113;\n Rules of, 114;\n Use, 114.\n\n Co-extensive Propositions, 142.\n\n Collective Terms, 50.\n\n Comparison, Stages in Thinking, 25.\n\n Complete Method, Three Elements, 97.\n\n Composition, Fallacy of, 331.\n\n Concept, Definition of, 17;\n a Thought Product, 21.\n\n Concomitant Variations, 402.\n\n Concrete Terms, 51.\n\n Connotative Terms, Two-fold Function of, 62;\n Definition of, 52;\n a List of, 65.\n\n Conquest the Desideratum, 447.\n\n Consequent, 289;\n Fallacy of False, 339.\n\n Contradiction, Law of, 35.\n\n Contradictory Terms, 53;\n Propositions, 167.\n\n Contrary Propositions, 165.\n\n Contraversion, 181;\n Fallacies of, 327.\n\n Converse Accident, Fallacy of, 335.\n\n Conversion, 176;\n by Limitation, 178;\n Simply, 179;\n Fallacies of, 327.\n\n Copula, 123.\n\n Creighton Quoted, 4, 387, 485.\n\n\n D\n\n Deduction, Defined, 96;\n as a Method, 97;\n Special Function of, 438.\n\n Definition, Importance of, 77;\n the Predicables, 77;\n Nature of, 82;\n Definition of, 83;\n Compared with Division, 84;\n Kinds of, 85;\n When Serviceable, 87;\n Rules of, 88;\n Terms which Cannot be Defined, 93;\n of Common Educational Terms, 94.\n\n Denomination, Stages in Thought, 26.\n\n Denotation and Connotation of Terms, 66.\n\n Descriptive Definition, 86.\n\n Development, Definition of, 94.\n\n Dichotomy, 110.\n\n Difference, Method of, 393.\n\n Differentia, 80.\n\n Dilemma, 308.\n\n Discoverer\u2019s Method, 440.\n\n Disjunctive Arguments, 302;\n Rules of, 303;\n Logical Disjunction, 303;\n Reduction of, 307.\n\n Distribution of Subject and Predicate of Propositions, 145;\n Schemes for Remembering, 148.\n\n Division, Definition of Logical, 105;\n As Partition, 107;\n Compared with Definition, 84;\n Distinguished from Enumeration, 106;\n Rules of, 108;\n Compared with Classification, 112;\n Use of, 114;\n Fallacy of, 332.\n\n Dressler Quoted, 12.\n\n\n E\n\n Education, Defined, 94;\n Compared with Instruction, 95.\n\n Educational Terms Defined, 94.\n\n Elements of the Logical Proposition, 123.\n\n Elliptical Propositions, 129.\n\n Enthymeme, 247.\n\n Epicheirema, 249.\n\n Episyllogism, 250.\n\n Epithets, Question Begging, 343.\n\n Essential Attributes of Definition, 88.\n\n Etymological Definition, 85.\n\n Euler\u2019s Diagrams, 141.\n\n Evolution and the Thinking Mind, 19.\n\n Examination Questions, 486.\n\n Exceptive Propositions, 135.\n\n Excluded Middle, Law of, 39.\n\n Exclusive Propositions, 136.\n\n Exercises, Testing Arguments, 481.\n\n Experiment as an Element in Induction, 419.\n\n Extension and Intension of Terms, Defined, 63;\n Compared, 63;\n Used in Comparison, 65;\n Other Forms of Expression for, 66;\n Law of Variation in, 66.\n\n\n F\n\n Fact, Defined, 96.\n\n Fallacies, of Deductive Reasoning, 322;\n Paralogism and Sophism, 322;\n Division of, 323;\n of Immediate Inference, 326;\n in Form, 194, 199;\n Hypothetical, 291;\n Disjunctive, 303;\n of Language, 328;\n in Thought, 334.\n\n False Cause, 340.\n\n False Consequent, Fallacy of, 339.\n\n Figure of Speech, Fallacy of, 333.\n\n Figures of Syllogism, 218;\n Special Canons of, 226;\n Perfect and Imperfect, 235;\n Reduction, 235;\n Relative Value of, 239.\n\n Formal Fallacies, 197, 324.\n\n Four Terms, Fallacy of, 329.\n\n Fowler Quoted, 4, 360.\n\n Fundamentum Divisionis, 108.\n\n\n G\n\n General Exercises in Testing Arguments, 481.\n\n General Terms, 49.\n\n Genus and Species, 78.\n\n Grammatical Subject and Predicate, 125.\n\n Grammatical Sentences, 131.\n\n\n H\n\n Hamilton Quoted, 4, 12, 131.\n\n Hibben Quoted, 4, 441.\n\n Huxley Quoted, 473.\n\n Hypothetical Arguments, 288;\n Kinds, 290;\n Rules and Fallacies, 291;\n Reduced to Categorical, 293;\n Illustrative Exercise in Testing, 297;\n General Exercises, 484.\n\n Hypothesis, Defined, 96, 425;\n and Theory, 427;\n Requirements of, 427;\n Uses of, 429.\n\n\n I\n\n Identity, Law of, 32;\n Absolute, 33;\n Complete and Incomplete, 33;\n Relative, 34.\n\n Illicit Major and Minor, 199;\n Illustration of, 215.\n\n Image, Definition of, 17.\n\n Immediate Inference, 159;\n by Obversion, 170;\n by Opposition, 161;\n by Conversion, 176;\n by Contraversion, 181;\n Epitome of Four Processes, 182;\n by Inversion, 183;\n Fallacies of, 326.\n\n Imperfect Induction, 361.\n\n Indefinite Propositions, 129.\n\n Individual Proposition, Nature of, 132;\n in Opposition, 168.\n\n Induction, Defined, 96;\n as a Method, 97;\n Reasoning, 355;\n and the Hazard, 356;\n the Three Forms of, 365;\n Perfect, 375;\n Special Function of, 438.\n\n Inference, Definition of, 18;\n a Thought Product, 24;\n Immediate, 159;\n Mediate, 192.\n\n Infima Species, 79.\n\n Instruction Defined, 95.\n\n Intension of Terms, 63.\n\n Integration, a Stage in Thought, 26.\n\n Inversion, 183.\n\n Inverted Proposition, 137.\n\n Irregular Arguments, 258.\n\n Irrelevant Conclusion, 337.\n\n\n J\n\n Jevons Quoted, 4, 25, 387, 468.\n\n Joint Method of Agreement and Difference, 397.\n\n Judgment, Definition of, 17;\n a Thought Product, 22;\n Most Fundamental Element in Thinking, 23.\n\n\n K\n\n Keynes Quoted, 481, 485.\n\n Kinds of Definitions, 85.\n\n Knowing, by Intuition and by Thinking, 2;\n Knowing and Thinking Compared, 10;\n by Intuition, 11;\n Habitual, 11.\n\n Knowledge, Defined, 95;\n Intuitive, 11.\n\n\n L\n\n Language and Thought Inseparable, 47.\n\n Law of Variation in Extension and Intension, Stated, 66;\n Two Important Facts in, 69;\n Diagrammatically Illustrated, 70, 71.\n\n Laws of Sufficient Reason, 40;\n of Universal Causation, 361;\n of Uniformity of Nature, 362.\n\n Laws of Thought, 32;\n Unity of, 40;\n Schematic Statement of, 43.\n\n Learning, Defined, 95.\n\n Logic, Defined, 3;\n Authentic Definitions of, 4;\n Grammar of Thought, 3;\n Science of Sciences, 3;\n the Value of to the Student, 5;\n Related to Other Subjects, 1;\n Specific Scope, 2.\n\n Logic in the Class Room, 437.\n\n Logic and Life, 463.\n\n Logic of Success, 475.\n\n Logical Definition, 85, 88.\n\n Logical Disjunction, 303.\n\n Logical Subject and Predicate, 125.\n\n\n M\n\n Major Term, 196.\n\n Material Fallacies, 323, 324, 325, 328.\n\n Mediate Inference, 192;\n the Syllogism, 192;\n Rules of Syllogism, 193.\n\n Method Defined, 96;\n Inductive and Deductive, 97;\n Complete, 97.\n\n Method-Whole Defined, 96.\n\n Middle Term, 192, 193, 196.\n\n Mill Quoted, 5, 359, 361, 387, 393, 397, 402, 406.\n\n Mill\u2019s Experimental Methods, 386.\n\n Miller Quoted, 12.\n\n Mind, the Unity of, 1;\n Knowing and Thinking Compared, 10.\n\n Minor Term, 196.\n\n Mnemonic Lines, 234.\n\n Modal Proposition, 139.\n\n Modus Ponendo Tollens, etc., 302.\n\n Moods of Syllogism, 221;\n Testing Validity of, 223.\n\n Motivation as Related to Spirit of Discovery, 449.\n\n\n N\n\n Negative Proposition, 127.\n\n Negative Terms, 53.\n\n Nego-positive Terms, 55.\n\n Non-connotative Terms, 52.\n\n Non Sequitur, Fallacy of, 339.\n\n Not, Bisects the World, 36;\n Two Uses of, 36.\n\n Notion, Definition, 14;\n Individual, 14;\n General, 14;\n Distinguished from Knowledge, 15;\n Distinguished from Idea, 16;\n Psychological Terms Involved in, 16.\n\n\n O\n\n Observation, 419;\n Rules of, 420;\n Errors of, 423.\n\n Obversion, Definition of, 170;\n Fallacies of, 326.\n\n Opposite Terms, 53.\n\n Opposition, Nature of, 161;\n Scheme of, 163;\n Square of, 164.\n\n Outline of Briefer Course, 493.\n\n\n P\n\n Page Quoted, 453.\n\n Particular Propositions, 126;\n Affirmative, 143;\n Negative, 144.\n\n Partition, 107.\n\n Partitive Propositions, 133.\n\n Percept, Definition of, 17;\n Related to Thought, 18.\n\n Perfect Induction, 375.\n\n Petitio Principii, 341.\n\n Plurative Propositions, 132.\n\n Polysyllogism, 250.\n\n Porphyry, Tree of, 111.\n\n Positive Terms, 53.\n\n Predicables. Defined, 77;\n Named, 78;\n Illustrated, 82.\n\n Predicate, Grammatical and Logical, 125;\n Distribution of, 145.\n\n Primary Laws of Thought, 32.\n\n Privative Terms, 55.\n\n Progressive Thought, 465.\n\n Property, 81.\n\n Propositions, Definition of Logical, 120.\n\n Prosyllogism, 250.\n\n Proximate Genus, 79.\n\n Pure Proposition, 139.\n\n\n Q\n\n Quantity Signs, 123.\n\n Quantity and Quality of Propositions, 126.\n\n Question and Answer, not a Method of Discovery, 457.\n\n Question Begging Epithets, 343.\n\n Question, Complex, 340.\n\n\n R\n\n Rationalization, of Chance, 468;\n of Political and Business Sophistries, 470;\n of the Spirit of Progress, 471;\n of the Attitude toward Work, 474.\n\n Reasoning, Defined, 24, 355;\n Inductive, 355;\n Deductive, 355.\n\n Reduction of Figures, 235.\n\n Relation between Subject and Predicate, 140.\n\n Relative Terms, 56.\n\n Residues, Method of, 406.\n\n Right Thinking, 466.\n\n Rules, of Logical Definition, 88;\n of Logical Division, 108;\n of Classification, 114;\n of the Syllogism, 193;\n of the Hypothetical Argument, 291;\n of the Disjunctive, 303.\n\n Russell Quoted, 481, 482.\n\n Ryland Quoted, 481, 482.\n\n\n S\n\n Salisbury Quoted, 360.\n\n Science, Defined, 95.\n\n Sensation, Defined, 17;\n Related to Thought, 18.\n\n Simple Conversion, 179.\n\n Simple Enumeration, 367.\n\n Singular Terms, 49.\n\n Socrates, 322.\n\n Sorites, 251.\n\n Species, 78.\n\n Square of Opposition, 164.\n\n Subaltern Propositions, 164.\n\n Subcontrary Propositions, 164.\n\n Subject, Logical, 123;\n Grammatical and Logical Distinguished, 125;\n Distribution of, 145.\n\n Success, Logic of, 475.\n\n Sufficient Reason, Law of, 40.\n\n Summum Genus, 79.\n\n Syllogism, a Product of Inference, 24;\n Nature of, 192;\n Rules of, 193;\n Undistributed Middle, 199;\n Illicit Major, 199;\n Illicit Minor, 199;\n Aristotle\u2019s Dictum, 208;\n Canons of, 209;\n Mathematical Axioms of, 210;\n Four Figures of, 218;\n Moods of, 221;\n Incomplete, 247.\n\n Syncategorematic Words, 48.\n\n Synthesis, Defined, 97;\n as a Method, 97.\n\n Synthetic Proposition, 138.\n\n\n T\n\n Teaching, Defined, 94;\n Compared with Instruction and Education, 95.\n\n Terms, Extension and Intension of, 63;\n Used in Extension and Intension, 65;\n which Cannot be Defined, 93;\n Contradictory and Opposite, 38;\n Logical, 47;\n Singular and General, 49;\n Collective and Distributive, 50;\n Concrete and Abstract, 51;\n Connotative and Non-connotative, 52;\n Positive and Negative, 53;\n Contradictory and Opposite, 53;\n Privative and Nego-positive, 55;\n Absolute and Relative, 56.\n\n Theory Defined, 96.\n\n Thinking, Definition of, 12;\n Illustration of Process, 13;\n Compared with Knowing, 10;\n Compared with Intuition, 2;\n the Process, 12;\n Groups Many Into One, 18;\n in the Sensation and Percept, 18;\n Evolution and Thinking Mind, 19;\n of the Child, 20;\n of the Adult, 20;\n and the Concept, 21;\n and the Judgment, 22;\n and Apprehension, 24;\n Stages in, 25;\n in the Inference, 24;\n Laws of, 32;\n Unity of Laws, 40;\n Progressive, 465;\n Right, Necessity of, 466;\n Indifferent and Careless, 467.\n\n Thought and Language, 47.\n\n Thought is King, 437.\n\n Traduction, 377.\n\n Training, Definition of, 95.\n\n Tree of Porphyry, 111.\n\n Truistic Proposition, 139.\n\n Truth Defined, 96.\n\n\n U\n\n Uberweg Quoted, 4.\n\n Undistributed Middle, 199;\n Illustration of, 214.\n\n Uniformity of Nature, 362.\n\n Universal Affirmative Proposition, 140.\n\n Universal Causation, 361.\n\n Universal Negative Proposition, 142.\n\n Universal Propositions, 126.\n\n\n V\n\n\n Variations, Method of Concomitant, 402.\n\n\n W\n\n Watts Quoted, 4.\n\n Weakened Conclusion, 224.\n\n Whately Quoted, 4.\n\n Word-signs of Categorical Propositions, 122.\n\n\n\n\n Footnotes.\n\n\n 1 \u2013 NOTE. Sometimes thinking and thought are used\n interchangeably. This is confusing. Properly, \u201cthinking\u201d\n is always a process of the knowing mind while \u201cthought\u201d\n is the product of this process, just as the flour of the\n gristmill is the _product_ of the grinding _process_.\n\n\n 2 \u2013 Intuitive knowing might be termed habitual knowing.\n\n 3 \u2013 Mediate Inference.\n\n 4 \u2013 Intuitive Knowing.\n\n 5 \u2013 Hyslop\u2019s Elements of Logic (1901), page 100.\n\n 6 \u2013 Hyslop.\n\n 7 \u2013 Men do have the power of reason.\n\n 8 \u2013 Sometimes called contraposition.\n\n 9 \u2013 From the Greek meaning _to reason with_.\n\n 10 \u2013 The student may be sufficiently interested to complete the\n list.\n\n 11 \u2013 The student should prove that the last premise may be\n affirmative.\n\n 12 \u2013 This cause, however, need not be a _single_ antecedent, in\n fact it seldom is. \u201cThis cause, philosophically speaking,\n is the sum total of the conditions, positive and negative,\n taken together.\u201d\u2015\u2015Mill. The cause of the price of food stuff\n being high, involves many conditions, or antecedents, so\n interwoven that it is impossible to designate any one as\n being the chief factor concerned.\n\n 13 \u2013 Those might be named the Five Special Methods of Induction\n by Analysis.\n\n 14 \u2013 All cases of finding the net proceeds are examples of the\n law of residue.\n\n\n\n\n Transcriber\u2019s Notes.\n\n\n The following corrections have been made in the text:\n\n Page 22:\n Sentence starting: First, I may be....\n \u2013 \u2018recignize\u2019 replaced with \u2018recognize\u2019\n (able to recognize each)\n\n Page 61, Question 16:\n Sentence starting: What is the difference....\n \u2013 \u2018differenece\u2019 replaced with \u2018difference\u2019\n (the difference in meaning)\n\n Page 61, Question 23:\n Sentence starting: Argue to the effect....\n \u2013 \u2018non-contotative\u2019 replaced with \u2018non-connotative\u2019\n (can be non-connotative.)\n\n Page 86:\n Sentence starting: A logical definition....\n \u2013 \u2018digerenti\u00e6\u2019 replaced with \u2018differenti\u00e6\u2019\n (by means of its differenti\u00e6.)\n\n Page 144:\n Sentence starting: Here, as in the I,...\n \u2013 \u2018comfined\u2019 replaced with \u2018confined\u2019\n (knowledge is confined to)\n\n Page 204:\n Sentence starting: (6) _If one premise....\n \u2013 \u2018nagtive\u2019 replaced with \u2018negative\u2019\n (one premise be negative)\n\n Page 240:\n Sentence starting: Since, however, the easiest....\n \u2013 \u2018affirmavite\u2019 replaced with \u2018affirmative\u2019\n (and a particular affirmative)\n\n Page 246:\n Sentence starting: (3) Show why it is....\n \u2013 Printer error: lost end of point (3) and duplicated part of\n point (4)\n\n Page 276:\n Sentence starting: Other arguments where....\n \u2013 \u2018agruments\u2019 replaced with \u2018arguments\u2019\n (Other arguments where)\n\n Page 286:\n Sentence starting: (4) In the practice....\n \u2013 \u2018analagous\u2019 replaced with \u2018analogous\u2019\n (custom analogous to giving)\n\n Page 286:\n Sentence starting: (4) \u201cThe man is guilty....\n \u2013 \u2018(4)\u2019 missing from text\n ((4) \u201cThe man is guilty)\n\n Page 325:\n Sentence starting: These fallacies arise from....\n \u2013 \u2018abitrary\u2019 replaced with \u2018arbitrary\u2019\n (words as arbitrary signs)\n\n Page 326:\n Sentence starting: There is little difference....\n \u2013 \u2018fallicies\u2019 replaced with \u2018fallacies\u2019\n (and fallacies of converse)\n\n Page 371:\n Sentence starting: (1) Noting that two....\n \u2013 \u2018sirname\u2019 replaced with \u2018surname\u2019\n (have the same surname,)\n\n Page 376:\n Sentence starting: In the school room....\n \u2013 \u2018generalziation\u2019 replaced with \u2018generalization\u2019\n (perfectly induced generalization,)\n\n Page 382:\n Sentence starting: _Complete_ enumeration gives....\n \u2013 \u2018uncontradiced\u2019 replaced with \u2018uncontradicted\u2019\n (_incomplete but uncontradicted_)\n\n Page 405:\n Sentence starting: It is thus evident that....\n \u2013 \u2018prenomenon\u2019 replaced with \u2018phenomenon\u2019\n (entirely with the phenomenon.)\n\n Page 422:\n Sentence starting: _Reading into the external....\n \u2013 \u2018vivdly\u2019 replaced with \u2018vividly\u2019\n (what is only vividly internal)","title":"A Class Room Logic: Deductive and Inductive, with Special Application to the Science and Art of Teaching","tradition":"philosophy-ethics","translated_text":null,"word_count":117368}