a_class_room_logic
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| - | Transcriber’s Notes</ | ||
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| - | <p> | ||
| - | The cover image was provided by the transcriber and is placed in the public domain.</ | ||
| - | <p> | ||
| - | Punctuation has been standardized.</ | ||
| - | <p class=" | ||
| - | Most abbreviations have been expanded in tool-tips for screen-readers and may be seen by hovering the mouse over the abbreviation.</ | ||
| - | <p> | ||
| - | The under bracket in the original text has been replaced by a standard underline.</ | ||
| - | <p> | ||
| - | This book was written in a period when many words had not become standardized in their spelling. Words may have multiple spelling variations or inconsistent hyphenation in the text. These have been left unchanged unless indicated with a Transcriber’s Note.</ | ||
| - | <p> | ||
| - | Index references have not been checked for accuracy.</ | ||
| - | <p> | ||
| - | Footnotes are identified in the text with a superscript number and have been accumulated in a table at the end of the text.</ | ||
| - | <p> | ||
| - | Transcriber’s Notes are used when making corrections to the text or to provide additional information for the modern reader. These notes have been accumulated in a table at the end of the book and are identified in the text by a dotted underline and may be seen in a tool-tip by hovering the mouse over the underline.</ | ||
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| This cause, however, need not be a < | This cause, however, need not be a < | ||
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| - | <div class=" | + | |
| - | <h1 class=" | + | |
| - | A CLASS ROOM LOGIC</ | + | |
| - | <div class=" | + | |
| - | DEDUCTIVE AND INDUCTIVE</ | + | |
| - | <div class=" | + | |
| - | WITH SPECIAL APPLICATION TO<br /> | + | |
| - | THE SCIENCE AND ART OF TEACHING</ | + | |
| - | <div class=" | + | |
| - | BY</ | + | |
| - | <div class=" | + | |
| - | GEORGE HASTINGS <span | + | |
| - | class=" | + | |
| - | <div class=" | + | |
| - | HEAD OF DEPARTMENT OF LOGIC AND MATHEMATICS, | + | |
| - | <div class=" | + | |
| - | THE ETHLAS PRESS</ | + | |
| - | <div class=" | + | |
| - | FIVE NORTH BROADWAY. NYACK. NEW YORK</ | + | |
| - | <div class=" | + | |
| - | C< | + | |
| - | <div class=" | + | |
| - | G< | + | |
| - | H< | + | |
| - | M< | + | |
| - | <div class=" | + | |
| - | To</ | + | |
| - | <div class=" | + | |
| - | MY WIFE.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <p class=" | + | |
| - | Transcriber’s Notes</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | The cover image was provided by the transcriber and is placed in the public domain.</ | + | |
| - | <p> | + | |
| - | Punctuation has been standardized.</ | + | |
| - | <p class=" | + | |
| - | Most abbreviations have been expanded in tool-tips for screen-readers and may be seen by hovering the mouse over the abbreviation.</ | + | |
| - | <p> | + | |
| - | The under bracket in the original text has been replaced by a standard underline.</ | + | |
| - | <p> | + | |
| - | This book was written in a period when many words had not become standardized in their spelling. Words may have multiple spelling variations or inconsistent hyphenation in the text. These have been left unchanged unless indicated with a Transcriber’s Note.</ | + | |
| - | <p> | + | |
| - | Index references have not been checked for accuracy.</ | + | |
| - | <p> | + | |
| - | Footnotes are identified in the text with a superscript number and have been accumulated in a table at the end of the text.</ | + | |
| - | <p> | + | |
| - | Transcriber’s Notes are used when making corrections to the text or to provide additional information for the modern reader. These notes have been accumulated in a table at the end of the book and are identified in the text by a dotted underline and may be seen in a tool-tip by hovering the mouse over the underline.</ | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h2 class=" | + | |
| - | PREFACE.</ | + | |
| - | <p> | + | |
| - | This treatise is an outgrowth of our class room work in logic.</ | + | |
| - | <p> | + | |
| - | It has been published in the hope of removing some of the difficulties which handicap the average student.</ | + | |
| - | <p> | + | |
| - | We trust that the language is simple and definite and that the illustrative exercises and diagrams may be helpful in making clear some of the more abstruse topics.</ | + | |
| - | <p> | + | |
| - | If a speedy review for examination is necessary, it is recommended that the briefer course as outlined on <a href="# | + | |
| - | <p> | + | |
| - | Only the fundamentals of deductive and inductive logic have received attention. Moreover emphasis has been given to those phases which appear to commend themselves because of their practical value.</ | + | |
| - | <p> | + | |
| - | Further than this we trust that the book may fulfill in some small way the larger mission of inspiring better thinking and, in consequence, | + | |
| - | <p> | + | |
| - | Surely as civilization advances it is with the expectation of giving greater significance to the assumption “that man is a < | + | |
| - | <p> | + | |
| - | I am indebted to a number of writers on logic, notably to Mill, Lotze, Keynes, Hibben, Fowler, Aikins, Hyslop, Creighton and Jevons. I& | + | |
| - | <p> | + | |
| - | For constructive criticism and definite encouragement I& | + | |
| - | title=" | + | |
| - | Gray Shaw of New& | + | |
| - | title=" | + | |
| - | D. Blodgett of the Oneonta Normal School and to <abbr | + | |
| - | title=" | + | |
| - | MacLachlan of the Jamaica Training School for Teachers.</ | + | |
| - | <p class=" | + | |
| - | G. H. McN.</ | + | |
| - | <p class=" | + | |
| - | City Training School for Teachers,< | + | |
| - | Jamaica, <abbr title=" | + | |
| - | October 3, 1914.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <hr class=" | + | |
| - | <h2 class=" | + | |
| - | TABLE OF CONTENTS</ | + | |
| - | <table id=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 1.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Mind.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Logic Related to Other Subjects.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Logic Defined.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Value of Logic to the Student.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 2.</ | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Knowing Mind Compared with the Thinking Mind.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Knowing by Intuition.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Thinking Process.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Notions, Individual and General.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Knowledge and Idea as Related to the Notion.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Logic of the Psychological Terms Involved in the Notion.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Thought in the Sensation and Percept.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Evolution and the Thinking Mind.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Concept as a Thought Product.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Judgment as a Thought Product.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Inference as a Thought Product.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Thinking and Apprehension.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Stages in Thinking.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 3.</ | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Two Fundamental Laws.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Law of Identity.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Law of Contradiction.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Law of Excluded Middle.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Law of Sufficient Reason.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Unity of Primary Laws of Thought.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 4.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Logical Thought and Language Inseparable.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Meaning of Term.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Categorematic and Syncategorematic Words.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Singular Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | General Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Collective and Distributive Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Concrete and Abstract Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Connotative and Non-connotative Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Positive and Negative Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Contradictory and Opposite Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Privative and Nego-positive Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Absolute and Relative Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 5.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Two-fold Function of Connotative Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Extension and Intension Defined.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Extended Comparison of Extension and Intension.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | A List of Connotative Terms Used in Extension and Intension.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Other Forms of Expression for Extension and Intension.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Law of Variation in Extension and Intension.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Important Facts in Law of Variation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Law of Variation Diagrammatically Illustrated.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 6.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Importance.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Predicables.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Nature of a Definition.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Definition and Division Compared.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Kinds of Definitions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | When the Three Kinds of Definitions are Serviceable.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Rules of Logical Definition.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Terms Which Cannot be Defined Logically.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Definitions of Common Educational Terms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 7.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Nature of Logical Division.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Logical Division Distinguished from Enumeration.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Logical Division as Partition.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Four Rules of Logical Division.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Dichotomy.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Classification Compared with Division.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Kinds of Classification.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Two Rules of Classification.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Use of Division and Classification.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 8.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Nature of Logical Propositions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Kinds of Logical Propositions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Four Elements of a Categorical Proposition.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Logical and Grammatical Subject and Predicate Distinguished.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Four Kinds of Categorical Propositions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Propositions which do not Conform to Logical Type.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Propositions not Necessarily Illogical.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Relation between Subject and Predicate.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 9.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Nature of Inference.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Immediate and Mediate Inference.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Forms of Immediate Inference.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | Opposition.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 10.</ | + | |
| - | <span class=" | + | |
| - | (Continued).</td></ | + | |
| - | <tr> | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | | + | |
| - | Immediate Inference by Obversion.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | Immediate Inference by Conversion.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | Immediate Inference by Contraversion.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Epitome of the Four Processes of Immediate Inference.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | & | + | |
| - | Inference by Inversion.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Problems for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 11.</ | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Inference and Reasoning.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Syllogism.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Rules of the Syllogism.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Rules of Syllogism Explained.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Aristotle’s Dictum.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Canons of the Syllogism.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Mathematical Axioms.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 12.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Four Figures of the Syllogism.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Moods of the Syllogism.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Testing the Validity of the Moods.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Special Canons Related.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Mnemonic Lines.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Relative Value of the Four Figures.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 13.</ | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Enthymeme.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Epicheirema.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Polysyllogisms. Prosyllogism—Episyllogism.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Sorites.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Irregular Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 14.</ | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Arguments of Form and Matter.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Order of Procedure in a Formal Testing of Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercise in Testing Arguments which are Complete and whose Premises are Logical.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercise in Testing Completed Arguments, one or both of whose Premises are Illogical.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Incomplete and Irregular Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Common Mistakes of the Student.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 15.</ | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Three Kinds of Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Hypothetical Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Antecedent and Consequent.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Two Kinds of Hypothetical Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Rule and Two Fallacies of Hypothetical Argument.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Hypothetical Arguments Reduced to Categorical Form.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises Testing Hypothetical Arguments of All Kinds.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Disjunctive Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Two Kinds of Disjunctive Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | First Disjunctive Rule.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Second Disjunctive Rule.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Reduction of Disjunctive Argument.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Dilemma.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Four Forms of Dilemmatic Arguments.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | The Rule of Dilemma.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises Testing Disjunctive and Dilemmatic Argument.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Ordinary Experiences Related to Disjunctive Proposition and Hypothetical Argument.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Review Questions.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Questions for Original Thought and Investigation.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | 16.</ | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | A Negative Aspect.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Paralogism and Sophism.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | A Division of the Deductive Fallacies.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | General Divisions Explained.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Fallacies of Immediate Inference.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Fallacies in Language (Equivocation).</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Fallacies in Thought (Assumption).</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Outline.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Summary.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Illustrative Exercises in Testing Arguments in Both Form and Meaning.</ | + | |
| - | < | + | |
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| - | Review Questions.</ | + | |
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| - | Questions for Original Thought and Investigation.</ | + | |
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| - | 17.</ | + | |
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| - | Inductive and Deductive Reasoning Distinguished.</ | + | |
| - | < | + | |
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| - | The “Inductive Hazard.â€</ | + | |
| - | < | + | |
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| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Complexity of the Problem of Induction.</ | + | |
| - | < | + | |
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| - | <a href="# | + | |
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| - | Various Conceptions of<a id=" | + | |
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| - | <a href="# | + | |
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| - | Induction and Deduction Contiguous Processes</ | + | |
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| - | Induction an Assumption.</ | + | |
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| - | Universal Causation.</ | + | |
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| - | Uniformity of Nature.</ | + | |
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| - | Inductive Assumptions Justified.</ | + | |
| - | < | + | |
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| - | <a href="# | + | |
| - | <td class=" | + | |
| - | Three Forms of Inductive Research.</ | + | |
| - | < | + | |
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| - | Induction by Simple Enumeration.</ | + | |
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| - | Induction by Analogy.</ | + | |
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| - | Perfect Induction.</ | + | |
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| - | Traduction.</ | + | |
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| - | Outline.</ | + | |
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| - | Summary.</ | + | |
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| - | Review Questions.</ | + | |
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| - | Questions for Original Thought and Investigation.</ | + | |
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| - | 18.</ | + | |
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| - | Aim of Five Methods.</ | + | |
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| - | Method of Agreement.</ | + | |
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| - | Method of Difference.</ | + | |
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| - | The Joint Method of Agreement and Difference.</ | + | |
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| - | The Method of Concomitant Variations.</ | + | |
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| - | <a href="# | + | |
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| - | The Method of Residues.</ | + | |
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| - | General Purpose and Unity of Five Methods.</ | + | |
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| - | Outline.</ | + | |
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| - | Summary.</ | + | |
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| - | Review Questions.</ | + | |
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| - | Questions for Original Thought and Investigation.</ | + | |
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| - | <a href="# | + | |
| - | 19.</ | + | |
| - | <span class=" | + | |
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| - | Foundation of Inductive Generalizations.</ | + | |
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| - | Observation.</ | + | |
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| - | Experiment.</ | + | |
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| - | Rules for Logical Observation and Experiment.</ | + | |
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| - | Common Errors of Observation and Experiment.</ | + | |
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| - | The Hypothesis.</ | + | |
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| - | Induction and Hypothesis Distinguished.</ | + | |
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| - | Hypothesis and Theory Distinguished.</ | + | |
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| - | The Requirements of a Permissible Hypothesis.</ | + | |
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| - | Uses of Hypothesis.</ | + | |
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| - | Characteristics Needed by Scientific Investigators</ | + | |
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| - | Outline.</ | + | |
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| - | Review Questions.</ | + | |
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| - | Questions for Original Thought and Investigation.</ | + | |
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| - | 20.</ | + | |
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| - | Thought is King.</ | + | |
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| - | Special Functions of Induction and Deduction.</ | + | |
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| - | The Method of the Discoverer.</ | + | |
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| - | Real Inductive Method not in Vogue in Class Room Work</ | + | |
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| - | As a Method of Instruction, | + | |
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| - | Conquest, not Knowledge, the Desideratum.</ | + | |
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| - | Motivation as Related to Spirit of Discovery.</ | + | |
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| - | Discoverer’s Method Adapted to Class Room Work.</ | + | |
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| - | Question and Answer Method not Necessarily One of Discovery.</ | + | |
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| - | Questions for Original Thought and Investigation.</ | + | |
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| - | 21.</ | + | |
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| - | Logic Given a Place in a Secondary Course.</ | + | |
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| - | Man’s Supremacy Due to Power of Thought.</ | + | |
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| - | Importance of Progressive Thinking.</ | + | |
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| - | Necessity of Right Thinking.</ | + | |
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| - | Indifferent and Careless Thought.</ | + | |
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| - | The Rationalization | + | |
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| - | The Rationalization of Business and Political Sophistries.</ | + | |
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| - | The Rationalization | + | |
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| - | A Rationalization of the Attitude Toward Work.</ | + | |
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| - | The Logic of Success.</ | + | |
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| - | CHAPTER 1.<br /><br /> | + | |
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| - | 1. THE MIND.</ | + | |
| - | <p> | + | |
| - | As to the true conception of matter the world is ignorant. Yet when asked, “What does matter do?†the reply is, “Matter moves, matter vibrates.†Moreover, relative to the exact nature of mind, the world is likewise ignorant. But to the question, “What does mind do?†the response comes, “The Mind < | + | |
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| - | 2. LOGIC RELATED TO OTHER SUBJECTS.</ | + | |
| - | <p> | + | |
| - | What the mind < | + | |
| - | <p> | + | |
| - | Though both psychology and logic treat of the knowing aspect of the mind, yet the fields are not identical. The former deals with the < | + | |
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| - | What are the<a id=" | + | |
| - | <p> | + | |
| - | For the logician thought has two sources, his own mind and the mind of others. In the latter case thought becomes accessible through the medium of language. There is in consequence a close connection between logic, the science of thought, and grammar, the science of language. Because of this near relation logic is sometimes called the “grammar of thought.â€</ | + | |
| - | <p> | + | |
| - | To study any science properly one must have thoughts and since logic is the science of all thought the subject may be regarded as the < | + | |
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| - | 3. LOGIC DEFINED.</ | + | |
| - | <p> | + | |
| - | “Logic is the science of thought.†This definition commonly given is too brief to be helpful. Should not a definition of any subject represent a working basis upon which one may build with some knowledge of what the structure is to be? The following, a little out of the ordinary, seems to supply this condition: < | + | |
| - | <p> | + | |
| - | In justification of the latter definition it may be argued that it covers the topics usually treated by logicians. It is said that a science teaches us to know while an art teaches us to do. As a science logic teaches us to know certain laws which underlie right thinking. For example, the law of identity which makes possible all affirmative judgments, such as “Some men are wise, | + | |
| - | <abbr title=" | + | |
| - | Likewise as a science logic acquaints us with certain universal < | + | |
| - | <p> | + | |
| - | A possible profit to the student may result from a study of certain authentic definitions herewith subjoined:</ | + | |
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| - | <span class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | It would seem as if there were as many different definitions as there are books on the subject. This is due partly to the disposition of the older logicians to ignore the < | + | |
| - | </ | + | |
| - | + | ||
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| - | 4. THE VALUE OF LOGIC TO THE STUDENT.</ | + | |
| - | <p> | + | |
| - | Logic is rapidly coming into favor as a major subject in institutions devoted to educational theory. Some of the reasons for this change of attitude are herewith subjoined:</ | + | |
| - | <p> | + | |
| - | (1) < | + | |
| - | <p> | + | |
| - | (2) < | + | |
| - | <p> | + | |
| - | (3) < | + | |
| - | <p> | + | |
| - | (4) < | + | |
| - | <p> | + | |
| - | (5) < | + | |
| - | <p> | + | |
| - | (6) < | + | |
| - | <p id=" | + | |
| - | (7) < | + | |
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| - | (8) < | + | |
| - | </ | + | |
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| - | 5. OUTLINE—</ | + | |
| - | <p class=" | + | |
| - | T< | + | |
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| - | Three aspects.</ | + | |
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| - | Unity of.</ | + | |
| - | <p> | + | |
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| - | <p class=" | + | |
| - | Mental philosophy, psychology, logic.</ | + | |
| - | <p class=" | + | |
| - | Psychology, logic, aesthetics, ethics.</ | + | |
| - | <p class=" | + | |
| - | Two ways of knowing.</ | + | |
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| - | Special province of logic.</ | + | |
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| - | Logic and language.</ | + | |
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| - | A science of sciences.</ | + | |
| - | <p> | + | |
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| - | A general definition.</ | + | |
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| - | A more satisfactory definition.</ | + | |
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| - | A list of authentic definitions.</ | + | |
| - | <p> | + | |
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| - | Eight reasons for its study.</ | + | |
| - | </ | + | |
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| - | + | ||
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| - | 6. SUMMARY.</ | + | |
| - | <p> | + | |
| - | (1) The aspects of the mind are knowing, feeling and willing.</ | + | |
| - | <p id=" | + | |
| - | The mind is a living unit and never knows without feeling in some way and willing to some extent.</ | + | |
| - | <p> | + | |
| - | (2) What the mind < | + | |
| - | <p> | + | |
| - | Psychology treats of the mind as a whole, logic of the mind knowing, aesthetics of the mind feeling and ethics of the mind willing. Ethics answers the question, What is right? Aesthetics, What is beautiful? Logic, What is true?</ | + | |
| - | <p> | + | |
| - | The standpoint of logic is not identical with any particular portion of psychology.</ | + | |
| - | <p> | + | |
| - | The mind knows in two ways: (a) by intuition, (b) by thinking. Thinking is a process—thought a product. Logic deals indirectly with the former and directly with the latter.</ | + | |
| - | <p> | + | |
| - | Generally speaking, logic is a systematic study of thought. For the logician thought has two sources: (a) his own mind and (b) spoken or written language.</ | + | |
| - | <p> | + | |
| - | Because of the ambiguity of language logic has much to do with it as a faulty vehicle of thought.</ | + | |
| - | <p> | + | |
| - | (3) Logic as a science makes known the laws and forms of thought and as an art suggests conditions which must be fulfilled to think rightly. Author.</ | + | |
| - | <p> | + | |
| - | “Logic may be defined as the science of the conditions on which correct thoughts depend, and the art of attaining to correct and avoiding incorrect thoughts.†Fowler.</ | + | |
| - | <p> | + | |
| - | In the fundamentals of logical doctrine present day logicians virtually agree.</ | + | |
| - | <p> | + | |
| - | (4) Logic should stimulate the thought powers; secure correct and clear thinking; aid in the estimation of arguments; inspire definite, systematic procedure; demand lucid, pointed, accurate expression and be especially adapted to general mental discipline.</ | + | |
| - | <p> | + | |
| - | Logic adds to our store of knowledge and develops a passion for the truth.</ | + | |
| - | </ | + | |
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| - | 7. REVIEW QUESTIONS.</ | + | |
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| - | 8. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.</ | + | |
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| - | CHAPTER 2.<br /><br /> | + | |
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| - | 1. THE KNOWING MIND COMPARED WITH THE THINKING MIND.</ | + | |
| - | <p> | + | |
| - | In the preceding chapter we were told that the mind may know in two ways (1) by intuition and (2) by thinking. It is thus implied that the knowing mind includes the thinking mind plus intuition. Thinking always involves knowing, but knowing need not involve thinking, and when some logicians maintain that to know a thing one must think it, there is danger of being misled. They mean by this that in order to know anything in a permanent and highly serviceable way one must think it. All animals know, even such a stupid one as the oyster, and yet one would hardly give an oyster credit for thinking. Only the higher orders of animal life think. Some argue that the power is confined exclusively to the human family. This opinion is debatable. If the claimant means by thinking, reasoning then his ground is well taken. But if he is willing to give to thinking a broader content, then he has little defense for his stand. However, attach as broad a meaning to thinking as the derivation of the word will permit and even then it is a narrower term than knowing. Thinking plus intuition equals knowing, and in intuition there is probably no thinking.</ | + | |
| - | </ | + | |
| - | + | ||
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| - | 2. KNOWING BY INTUITION.</ | + | |
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| - | It has been affirmed that intuition is the process involved when the mind knows <span | + | |
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| - | (1) As I raise my eyes a figure comes to view. My mind knows < | + | |
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| - | Knowledge is anything known. < | + | |
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| - | The intuitions are the beginning and the basis of all knowledge, and knowledge gained by intuition is the basis of all thinking.</ | + | |
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| - | 3. THE THINKING PROCESS.</ | + | |
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| - | It is claimed that < | + | |
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| - | The same idea may be expressed in a variety of ways as the following indicate.</ | + | |
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| - | In the foregoing definitions it is implied that thinking is a connecting or < | + | |
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| - | The thinking process is the digestive process of the mind. Much as the digestive organs assimilate the food stuff of the physical world, so the thinking organ assimilates the food stuff of the mental world.</ | + | |
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| - | (1) The child is unable to explain the meaning of “hocus-pocus†as it occurs in the question, “What hocus-pocus is this? | + | |
| - | <p> | + | |
| - | (2) The teacher holds before the class an Egyptian house god and asks, “What is it?†After a moment of hesitation some child who has seen pictures of “his satanic majesty†avers that the object is a “little devil.†Thus has a connection been established between the idol and pictures of satan.</ | + | |
| - | <p> | + | |
| - | (3) John is unable to solve the following problem as he can discern no connection between the data given and the data required. Problem. | + | |
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| - | of my salary is $900, what is my salary?</ | + | |
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| - | Data. Given: | + | |
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| - | of salary = $900.</ | + | |
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| - | Required: | + | |
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| - | of salary = ?</ | + | |
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| - | In order that John may < | + | |
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| - | Given: 3-fourths = $900</ | + | |
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| - | Required: 4-fourths = ?</ | + | |
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| - | or</ | + | |
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| - | Given: 3 parts = $900</ | + | |
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| - | Required: 4 parts = ?</ | + | |
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| - | John now notes that 4 parts is | + | |
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| - | times 3& | + | |
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| - | of $900, which is $1,200 as the answer. Or he may find the value of 1& | + | |
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| - | + | ||
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| - | 4. NOTIONS, INDIVIDUAL AND GENERAL.</ | + | |
| - | <p> | + | |
| - | <em>A notion is any product of the knowing mind—anything which the mind notes or becomes aware of.</ | + | |
| - | <p> | + | |
| - | But the mind knows in two ways, by intuition and by thinking. In consequence the mind has two kinds of notions, those which are intuitive or < | + | |
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| - | My notion of the pencil with which I& | + | |
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| - | A sure way to determine whether the notion is individual or general is to attempt to divide it into its kinds. Only general notions may be subdivided.</ | + | |
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| - | 5. KNOWLEDGE AND IDEA AS RELATED TO THE NOTION.</ | + | |
| - | <p> | + | |
| - | Knowledge is anything known, while anything of which the mind becomes aware is a notion. Notions are always bits of knowledge, but knowledge is not always a notion. Notions are mental products belonging to the mind which thinks them, while knowledge, though it must first be a mental product of someone’s mind, may not necessarily be a product of yours or mine. Notions are always found in the mind, while knowledge may be found in books, but not necessarily in some individual mind. Knowledge stands for everything < | + | |
| - | <p> | + | |
| - | “Idea, | + | |
| - | </ | + | |
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| - | 6. THE LOGIC OF THE PSYCHOLOGICAL TERMS INVOLVED IN THE NOTION.</ | + | |
| - | <p> | + | |
| - | Concerning the knowing mind the psychologist classifies its activities and their products as follows:</ | + | |
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| - | The notion as < | + | |
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| - | The individual notion which is intuitive includes the sensation, percept and image; the general notion which is<a id=" | + | |
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| - | As we shall have occasion frequently to refer to these psychological terms it may be well to define them.</ | + | |
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| - | A sensation is the first and simplest mental result of the stimulation of an incarrying nerve.</ | + | |
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| - | A sensation is a vague, unlocalized mental product of the knowing mind.</ | + | |
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| - | A percept is a mental product which results from a consciousness of particular material things present to the sense.</ | + | |
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| - | A percept is a consciously localized group of sensations.</ | + | |
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| - | An image is a mental product which results from particular material things not present to the sense.</ | + | |
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| - | An image is a reproduced percept.</ | + | |
| - | < | + | |
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| - | A concept is a representation in our minds answering to a general name.</ | + | |
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| - | A concept is a mental product arising from thinking many notions into one class.</ | + | |
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| - | A judgment is the result of asserting an agreement or disagreement between two ideas.</ | + | |
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| - | A judgment is the mental product arising from conjoining or disjoining notions.</ | + | |
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| - | An inference is a judgment derived from perceiving relations between other judgments.</ | + | |
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| - | An inference is a judgment derived from antecedent judgments.</ | + | |
| - | </ | + | |
| - | <p> | + | |
| - | It is seen that the sensations furnish the raw material. Ignoring the few exceptions we may then say that a percept is a made-over group of sensations; a concept a thought-made group of percepts; a judgment a thought-made group of concepts; an inference a judgment derived from other judgments.</ | + | |
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| - | Speaking figuratively, | + | |
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| - | 7. T< | + | |
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| - | So far in this discussion it has been assumed that there is no thinking involved in the sensation or the percept. There are good authorities, | + | |
| - | <p> | + | |
| - | As the percept is a localized group of sensations then there must be involved in perception a more complex form of thinking, since in grouping sensations there is a recognition of connections.</ | + | |
| - | <p> | + | |
| - | If there is thinking in the sensation which is the simplest and lowest form of the knowing-mind then thinking conditions all knowledge and really is the basic elemental cell of all knowing.</ | + | |
| - | <p> | + | |
| - | On the other hand there are those who maintain that the sensation and percept are mere reflections of consciousness; | + | |
| - | <p> | + | |
| - | It will probably never be settled to the satisfaction of all just when thinking commences. The question is as difficult as some others which have never been solved. For example: Where does life commence? When does the plant merge into the animal? Which was first the egg or the hen? Does the objective world really exist or is it only a mental interpretation of vibrations? | + | |
| - | <abbr title=" | + | |
| - | <p> | + | |
| - | Logically considered the question is immaterial. All will agree that developed thought is involved in the concept, judgment and inference, while, if it appears at all in the percept and sensation, it is more or less undeveloped and consequently lies quite without the province of the logical field.</ | + | |
| - | </ | + | |
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| - | 8. EVOLUTION AND THE THINKING MIND.</ | + | |
| - | <p> | + | |
| - | Speaking in general terms evolution is a development from a lower to a higher state. Thus have come the various species of the vegetable and animal world. The<a id=" | + | |
| - | <p> | + | |
| - | An analogous development is seen in the thinking mind. The little child thinks in < | + | |
| - | <p id=" | + | |
| - | Progress in thinking is measured by progress in discrimination. The skilled thinker divides the large unit into very small units, compares these with each other and then reunites them into a more perfect and unified whole. First there is an analysis and then a synthesis. Like a shuttle the power of thought works in and out; it goes in to separate, it comes out to unify.</ | + | |
| - | <p> | + | |
| - | There is another aspect in the analogy between the life of the physical and mental worlds. Somewhere in the order of progress there is a connecting link between the mineral and vegetable kingdoms, likewise between the vegetable and animal kingdoms. The sensation is as much a state of feeling as an act of knowing and consequently is the connecting link between the < | + | |
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| - | (These are general notions because they admit of a subdivision into kinds. Industry, for instance, may be divided< | + | |
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| - | Thus does the concept stand for a group of all kinds of notions, individual and general, abstract and concrete.</ | + | |
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| - | I see for the first time in my life a pencil. In other words I& | + | |
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| - | An examination of conception makes evident two distinct characteristics.< | + | |
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| - | each individual pencil because of the two common qualities, a thread of lead and an encasement of some kind. This process of the knowing mind whereby it recognizes and affirms connections is called thinking as we have already learned. Here is the < | + | |
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| - | Judging is the process of conjoining and disjoining notions.< | + | |
| - | <p> | + | |
| - | (1) A judgment may conjoin or disjoin two individual notions.</ | + | |
| - | <p class=" | + | |
| - | To wit: Conjoined—This pencil belongs to Albert White.</ | + | |
| - | <p class=" | + | |
| - | Disjoined—This pencil does not belong to Mary Smith.</ | + | |
| - | <p> | + | |
| - | (2) A judgment may conjoin or disjoin two general notions.</ | + | |
| - | <p class=" | + | |
| - | Conjoined—Some men are virtuous.</ | + | |
| - | <p class=" | + | |
| - | Disjoined—Some men are not virtuous.</ | + | |
| - | <p> | + | |
| - | (3) A judgment may conjoin or disjoin a general and an individual notion.</ | + | |
| - | <p class=" | + | |
| - | Conjoined—Abraham Lincoln was virtuous.</ | + | |
| - | <p class=" | + | |
| - | Disjoined—Edgar Allen Poe was not temperate.</ | + | |
| - | <p> | + | |
| - | In order that the knowing mind may conjoin notions it must recognize some mark of similarity or connection. This is the < | + | |
| - | <p> | + | |
| - | The fact that judging and thinking so closely resemble each other has given just cause for some logicians to designate judging as the most fundamental element in all thinking. “The simplest form of thinking, | + | |
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| - | 11. I< | + | |
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| - | <span class=" | + | |
| - | <p> | + | |
| - | Reasoning is the process of deriving a new judgment from a consideration of other judgments. The product of any reasoning process may be called an inference, although, as will appear in a later chapter, inference is commonly used as indicating the process as well as the product.</ | + | |
| - | <p> | + | |
| - | Often reasoning may assume a syllogistic form with the inference as its conclusion. A& | + | |
| - | <p> | + | |
| - | (1) All children should play.</ | + | |
| - | <p class=" | + | |
| - | Mary is a child.</ | + | |
| - | <p class=" | + | |
| - | Hence, Mary should play.</ | + | |
| - | <p> | + | |
| - | (2) No teacher should judge hastily.</ | + | |
| - | <p class=" | + | |
| - | You are a teacher.</ | + | |
| - | <p class=" | + | |
| - | Hence, you should not judge hastily.</ | + | |
| - | <p> | + | |
| - | In the second syllogism the inference, “you should not judge hastily, | + | |
| - | <p> | + | |
| - | To summarize—< | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 12. THINKING AND APPREHENSION.</ | + | |
| - | <p> | + | |
| - | Says Jevons: “Simple apprehension is the act of the mind by which we merely become aware of something,< | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 13. STAGES IN THINKING.</ | + | |
| - | <p> | + | |
| - | In all thinking there are three steps or stages which may be termed < | + | |
| - | <p> | + | |
| - | In the case of the two pencils held in the hand, it is noted that one is longer than the other. Let us analyze the process which made possible this conclusion. Step one—Attention is given first to one pencil and then to the other. In each case the pencils are distinguished from the hand and the other surrounding objects. This is discrimination. Step two—The pencils are < | + | |
| - | <p> | + | |
| - | Another illustration. The child is requested to solve<a id=" | + | |
| - | <p> | + | |
| - | Statement: Given: 8 tons cost $165.</ | + | |
| - | <p class=" | + | |
| - | Required: 16 tons cost?</ | + | |
| - | <p> | + | |
| - | Discrimination. The child notes that 8& | + | |
| - | <p> | + | |
| - | Comparison. The child perceives that 16& | + | |
| - | <p> | + | |
| - | Integration. The child concludes that the cost of 16& | + | |
| - | <p> | + | |
| - | When we think, we first tear to pieces that we may become acquainted with every part. This may be called analysis. Then we put the related pieces together again. This may be called synthesis. Before, however, the parts are re-united a certain amount of comparison is necessary. The three stages of thought might thus be denominated: | + | |
| - | <p> | + | |
| - | After the synthesis or integration it is necessary to name the result, consequently a fourth step is sometimes given, namely denomination.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 14. OUTLINE.</ | + | |
| - | <p> | + | |
| - | T< | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | Defined.</ | + | |
| - | <p class=" | + | |
| - | Other definitions.</ | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | Individual.</ | + | |
| - | <p class=" | + | |
| - | General.</ | + | |
| - | <p class=" | + | |
| - | Thing and object distinguished.</ | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | <span class=" | + | |
| - | The sensation< | + | |
| - | The percept< | + | |
| - | The image</ | + | |
| - | <img | + | |
| - | class=" | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <span class=" | + | |
| - | Individual< | + | |
| - | notions.</ | + | |
| - | <p class=" | + | |
| - | <span class=" | + | |
| - | The concept< | + | |
| - | The judgment< | + | |
| - | The inference</ | + | |
| - | <img | + | |
| - | class=" | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <span class=" | + | |
| - | notions.</ | + | |
| - | <p class=" | + | |
| - | Terms defined.</ | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | The simplest form of thinking.</ | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | Discrimination.</ | + | |
| - | <p class=" | + | |
| - | Comparison.</ | + | |
| - | <p class=" | + | |
| - | Integration.</ | + | |
| - | <p class=" | + | |
| - | (Denomination.)</ | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 15. SUMMARY.</ | + | |
| - | <p> | + | |
| - | (1) Knowing is a broader term than thinking as the former equals the latter plus intuition.</ | + | |
| - | <p> | + | |
| - | (2) Intuitive knowledge is that which comes to the mind immediately by direct observation.</ | + | |
| - | <p> | + | |
| - | Although intuitive knowledge comes to the mind without thought, yet such knowledge is < | + | |
| - | <p> | + | |
| - | (3) Thinking is the deliberative process of affirming and denying connections. Thinking is a “thickening process, | + | |
| - | <p> | + | |
| - | (4) A notion is any product of the knowing mind.</ | + | |
| - | <p> | + | |
| - | An individual notion is the notion of one thing.</ | + | |
| - | <p> | + | |
| - | A general notion is a notion of a class of things.</ | + | |
| - | <p id=" | + | |
| - | A thing includes objects, qualities, relations or any existing entity. A& | + | |
| - | <p> | + | |
| - | (5) A bit of knowledge must have been a notion of some one’s mind, but may not necessarily be a notion of < | + | |
| - | <p> | + | |
| - | (6) The products of the knowing mind are the sensation, the image, percept, concept, judgment, inference.</ | + | |
| - | <p> | + | |
| - | The sensation, image and percept are individual notions, while the concept, judgment and inference are general notions.</ | + | |
| - | <p> | + | |
| - | A sensation is a vague, unlocalized product of the knowing mind.</ | + | |
| - | <p> | + | |
| - | A percept is a consciously localized group of sensations.</ | + | |
| - | <p> | + | |
| - | An image is a reproduced percept.</ | + | |
| - | <p> | + | |
| - | A concept is a mental product arising from thinking many notions into one class.</ | + | |
| - | <p> | + | |
| - | A judgment is a mental product arising from conjoining and disjoining notions.</ | + | |
| - | <p> | + | |
| - | An inference is a judgment derived from antecedent judgments.</ | + | |
| - | <p> | + | |
| - | The developed thought processes are the concept, the judgment and the inference.</ | + | |
| - | <p> | + | |
| - | (7) Just where the simplest form of thinking appears in the various activities of the knowing mind is still an undecided question. It is agreed that thinking in its developed and more complex form is found in conception, judging and reasoning.</ | + | |
| - | <p> | + | |
| - | (8) Thinking evolves from the simple to the more complex, just as life has evolved.</ | + | |
| - | <p> | + | |
| - | The child thinks in vague, indefinite wholes, while the adult thinks in clear, definite parts. The child discriminates very imperfectly while the adult discriminates accurately.</ | + | |
| - | <p> | + | |
| - | The sensation seems to be the connecting link between the feeling mind and the knowing mind, while the percept links together the knowing mind and the thinking mind.</ | + | |
| - | <p> | + | |
| - | (9) Conception is the process of thinking many notions into one class. The product of such a process is a concept. The concept stands for groups of all kinds of objects.</ | + | |
| - | <p> | + | |
| - | Conception has the two aspects of < | + | |
| - | <p> | + | |
| - | (10) Judging is the process of conjoining or disjoining notions. Judgment is the product of judging.</ | + | |
| - | <p> | + | |
| - | Judgments conjoin and disjoin all kinds of notions.</ | + | |
| - | <p> | + | |
| - | Judging and thinking, though they closely resemble each other, are not synonomous terms. Thinking is a broader term in that connections may be established between a notion and a name for that notion.</ | + | |
| - | <p> | + | |
| - | Judging is the most fundamental of all thinking, as the concept is built from a series of judgments and an inference is simply a made-over judgment.</ | + | |
| - | <p> | + | |
| - | (11) Inference.</ | + | |
| - | <p> | + | |
| - | Reasoning is the process of deriving a new judgment from a consideration of antecedent judgments. This derived judgment may be called an inference. Sometimes the term inference denotes the process of reasoning as well as the product.</ | + | |
| - | <p> | + | |
| - | Reasoning often takes the form of a syllogism.</ | + | |
| - | <p> | + | |
| - | The concept, the judgment and the inference are < | + | |
| - | <p> | + | |
| - | (12) Some give to the thinking mind the three aspects, apprehension, | + | |
| - | <p> | + | |
| - | (13) The three important stages in thinking are discrimination, | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 16. REVIEW QUESTIONS.</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
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| - | <p id=" | + | |
| - | <span class=" | + | |
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| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 17. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
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| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <hr class=" | + | |
| - | <h2 class=" | + | |
| - | CHAPTER 3.<br /><br /> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 1. TWO FUNDAMENTAL LAWS.</ | + | |
| - | <p> | + | |
| - | The elemental form of evolved thought is the judgment. The laws or axioms of thought may, therefore, be discovered by studying the judgment.</ | + | |
| - | <p> | + | |
| - | Judging is the process of conjoining and disjoining notions. When these notions are conjoined the judgment is affirmative; | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 2. THE LAW OF IDENTITY.</ | + | |
| - | <p> | + | |
| - | In general the law of identity implies a certain permanency throughout the material world. That door is a door and always will be a door till the conditions change. If it were not for this law, that everything is<a id=" | + | |
| - | <abbr title=" | + | |
| - | We can readily see that it would hardly be worth while to think at all.</ | + | |
| - | <p> | + | |
| - | The law of identity may be stated in three ways: (1)& | + | |
| - | <p class=" | + | |
| - | A< | + | |
| - | I< | + | |
| - | class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | Applying the law of identity to the affirmative judgment expressed in the form of a proposition, | + | |
| - | <p> | + | |
| - | This kind of absolute identity which makes possible all truisms we may term, for want of a better name, complete absolute identity. This would imply that there is an incomplete absolute identity and such seems to be the case. Examining the definition, “A& | + | |
| - | <p class=" | + | |
| - | R< | + | |
| - | <p> | + | |
| - | Relative identity is best understood by thinking of it as < | + | |
| - | <a href="# | + | |
| - | title=" | + | |
| - | <div class=" | + | |
| - | <img | + | |
| - | class=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <p class=" | + | |
| - | <abbr title=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | Be it remembered that circles are surfaces, and in | + | |
| - | <a href="# | + | |
| - | title=" | + | |
| - | the men circle is identical with that portion of the mortal circle which is immediately underneath it.</ | + | |
| - | <p id=" | + | |
| - | The same relation may be indicated by a small pad being placed on top of a larger pad. Then the whole of the smaller pad could be thought of as being identical with that part of the larger pad which is immediately underneath.</ | + | |
| - | <p> | + | |
| - | In the case of the second proposition a part of the “men†class is identical with a portion of the “wise†class. The two circles indicating this relation must intersect each other so that a portion of each may be common ground, as in | + | |
| - | <a href="# | + | |
| - | title=" | + | |
| - | where the shaded part represents the identity.</ | + | |
| - | <div class=" | + | |
| - | <img | + | |
| - | class=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <p class=" | + | |
| - | <abbr title=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | Thus we see that the law of identity underlies all affirmative propositions. Absolute identity making possible the truism and definition, and relative identity conditioning all the universal and particular affirmative propositions which are neither truisms nor definitions.</ | + | |
| - | <p> | + | |
| - | The three forms may be symbolized as follows:</ | + | |
| - | <p class=" | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | The student will note that the “A’s†of absolute incomplete differ in form.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 3. LAW OF CONTRADICTION.</ | + | |
| - | <p> | + | |
| - | The law of contradiction underlies all negative propositions. It is the mission of this law to tear down or to be destructive in nature; while the law of identity builds up or is constructive in nature.</ | + | |
| - | <p> | + | |
| - | The law of contradiction may be stated in this way: It is impossible for the same thing to be and not to be at the same time and in the same place. Or better, < | + | |
| - | <p> | + | |
| - | The little word < | + | |
| - | <p> | + | |
| - | If we assert the identity between two notions then we cannot in the same breath deny their identity.</ | + | |
| - | <p class=" | + | |
| - | I< | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | If I assert that the flower is red, then I& | + | |
| - | <p class=" | + | |
| - | T< | + | |
| - | N< | + | |
| - | <p> | + | |
| - | The word < | + | |
| - | <a href="# | + | |
| - | <p class=" | + | |
| - | F< | + | |
| - | <table id=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | Illustrate the law of identity.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | Illustrate the law of contradiction.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | The student must understand that a term and its contradictory destroy each other. If we affirm something of the one, then we must deny it of the other, or we undermine the integrity of both. If it is affirmed of teachers A, B and C that they are wise, then it must be denied that they are not-wise.</ | + | |
| - | <p class=" | + | |
| - | I< | + | |
| - | <table class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | These are mutually destructive.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | These are not mutually destructive, | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | S< | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | <table class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | (As A is always A it would be absurd to say that A is not A.)</ | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | C< | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | It is easy to use opposite terms in a contradictory sense. This leads to serious error. “Not-guilty†is the < | + | |
| - | <p> | + | |
| - | Further, it is dangerous to regard words with the negative prefix as being contradictory of the affirmative form. For example: Valuable and invaluable are not contradictory. There is likewise some doubt as to the contradictory nature of such words as agreeable and disagreeable, | + | |
| - | <p class=" | + | |
| - | I< | + | |
| - | <span class=" | + | |
| - | < | + | |
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| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 4. THE LAW OF EXCLUDED MIDDLE.</ | + | |
| - | <p> | + | |
| - | The law of excluded middle may be considered as a combination of identity and contradiction. Identity gives the proposition, | + | |
| - | <p> | + | |
| - | Excluded middle explains itself. Of the two contradictory notions it must be either the one or the other. There is no “go-between†notion.</ | + | |
| - | <p> | + | |
| - | The law may be stated in many ways, as will be seen by the following: (1)& | + | |
| - | <p class=" | + | |
| - | I< | + | |
| - | <p> | + | |
| - | (1) A man is either mortal or he is not mortal. (2)& | + | |
| - | <p class=" | + | |
| - | S< | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | A is either A or not-A<br /> | + | |
| - | or<br /> | + | |
| - | A is either B or not-B.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 5. THE LAW OF SUFFICIENT REASON.</ | + | |
| - | <p> | + | |
| - | The law may be stated in this wise. Every phenomenon, event or relation must have a sufficient reason for being what it is. To illustrate: (1)& | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 6. UNITY OF PRIMARY LAWS OF THOUGHT ILLUSTRATED BY SYMBOLS.</ | + | |
| - | <table id=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | (2) Propositions made to fit symbols.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | <td class=" | + | |
| - | A man is not honest, or a man is not | + | |
| - | <span class=" | + | |
| - | <tr id=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | A man is | + | |
| - | <span class=" | + | |
| - | or a man is honest.</ | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | The “excluded middle†propositions of the foregoing express alternatives which are mutually contradictory. There is no middle ground. The “contradictory propositions†contradict the identity of the subject with one alternative, | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 7. OUTLINE.</ | + | |
| - | <p> | + | |
| - | P< | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | Identity, contradiction.</ | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | Absolute—complete, | + | |
| - | <p class=" | + | |
| - | Relative.</ | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | Two uses of < | + | |
| - | <p class=" | + | |
| - | Contradictory and opposite terms.</ | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 8. SUMMARY.</ | + | |
| - | <p> | + | |
| - | (1) The elemental forms of evolved thought are the affirmative and negative judgments. This suggests two fundamental laws of thought, the law of identity and the law of contradiction. The former conditions the affirmative judgment, the latter the negative.</ | + | |
| - | <p> | + | |
| - | (2) The law of identity implies a permanency of being. “Everything remains identical with itself, | + | |
| - | <p> | + | |
| - | Absolute identity may be divided into complete and incomplete identity.</ | + | |
| - | <p> | + | |
| - | In complete absolute identity the subject is the same as the predicate in both form and meaning. Truisms illustrate this.</ | + | |
| - | <p> | + | |
| - | In incomplete absolute identity the subject is identical with the predicate in meaning only. Illustrated by definitions.</ | + | |
| - | <p> | + | |
| - | In relative identity the whole of the subject may be affirmed of a part of the predicate or a part of the subject may be affirmed of a part of the predicate.</ | + | |
| - | <p> | + | |
| - | (3) “It is impossible for the same thing to be itself and its contradictory at the same time, | + | |
| - | <p> | + | |
| - | To use opposite terms in a contradictory sense leads to serious error.</ | + | |
| - | <p> | + | |
| - | The safest way of making a positive term a contradictory negative term is to prefix “< | + | |
| - | <p> | + | |
| - | (4) The law of excluded middle is virtually a combination of identity and contradiction. It may be stated as follows: “A& | + | |
| - | <p> | + | |
| - | (5) “Every condition must have a sufficient reason for its existence, | + | |
| - | <p> | + | |
| - | (6) The laws may be expressed mathematically: | + | |
| - | <p class=" | + | |
| - | S< | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <span class=" | + | |
| - | <span class=" | + | |
| - | <table class=" | + | |
| - | < | + | |
| - | <th class=" | + | |
| - | <th class=" | + | |
| - | <th class=" | + | |
| - | <th class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | The whole is identical with a part or a part is identical with a part</ | + | |
| - | <td class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <td class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | Nothing can both be and not be at the same time</ | + | |
| - | <td class=" | + | |
| - | <div class=" | + | |
| - | A is not <span class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <span class=" | + | |
| - | <td class=" | + | |
| - | <div class=" | + | |
| - | <span class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | Everything must either be or not be</ | + | |
| - | <td class=" | + | |
| - | <div class=" | + | |
| - | <span class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <span class=" | + | |
| - | <td class=" | + | |
| - | <div class=" | + | |
| - | <span class=" | + | |
| - | <div class=" | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 9. ILLUSTRATIVE EXERCISES.</ | + | |
| - | <p> | + | |
| - | (1a) Each of the following propositions is made possible because of the existence of which law of thought?</ | + | |
| - | <p> | + | |
| - | In answering this question I& | + | |
| - | <abbr title=" | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | T< | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | (1b) Indicate the law which conditions each of the following propositions:</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 10. REVIEW QUESTIONS.</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 11. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | All men are some wise.</ | + | |
| - | <p class=" | + | |
| - | Some men are some wise.</ | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <hr class=" | + | |
| - | <h2 class=" | + | |
| - | CHAPTER 4.<br /><br /> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 1. LOGICAL THOUGHT AND LANGUAGE INSEPARABLE.</ | + | |
| - | <p> | + | |
| - | Any impression upon the mind tends to manifest itself in some form of expression. Impression which arouses thought tends to expression in the form of symbols. Thought and symbol go hand in hand. Expression, taking the form of word-symbols, | + | |
| - | <p> | + | |
| - | It is commonly supposed that language is serviceable mainly in communicating one’s thoughts to others, but language does service in another way which is quite as important. It tends to clarify and make definite all thought. Without a word-language thinking would lack continuity; would be vague, loose, illogical. The right use of a word-language, | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 2. MEANING OF LOGICAL TERM.</ | + | |
| - | <p> | + | |
| - | A notion has been referred to as any product of the knowing mind. When we express these notions in words such expressions may be called logical terms.</ | + | |
| - | <p> | + | |
| - | Definition. <em>A logical term is a word or a group of words denoting a definite notion.</ | + | |
| - | <abbr title=" | + | |
| - | has burned, | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 3. CATEGOREMATIC AND SYNCATEGOREMATIC WORDS.</ | + | |
| - | <p> | + | |
| - | There are some words which, when used alone, denote definite notions, such as man, tree, dog, justice. On the other hand there are other words which, when used alone, do not stand for a definite notion, such as up, beautifully, | + | |
| - | <p> | + | |
| - | Words like those in the first list are called categorematic words, while those in the second list illustrate syncategorematic words.</ | + | |
| - | <p class=" | + | |
| - | D< | + | |
| - | <p> | + | |
| - | <em>A categorematic word is one which forms a logical term unaided by other words. A syncategorematic word is one which must be used with other words to form a logical term.</ | + | |
| - | <p> | + | |
| - | Any word or group of words which can be used as either subject or predicate of a proposition is a logical term. If the < | + | |
| - | <p> | + | |
| - | We may conclude from this that nouns, descriptive adjectives and verbs may be categorematic words, while adverbs, prepositions and conjunctions are syncategorematic words.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 4. SINGULAR TERMS.</ | + | |
| - | <p> | + | |
| - | <em>A singular term is a term which denotes one object or one attribute.</ | + | |
| - | <p> | + | |
| - | Proper nouns, when they stand for individuals, | + | |
| - | <p> | + | |
| - | Common nouns may be made singular by some modifying word, as the first man, the pole star, the highest good, my pet dog, | + | |
| - | <abbr title=" | + | |
| - | <p> | + | |
| - | Certain attributes which imply a < | + | |
| - | <p> | + | |
| - | Some claim that terms like water, air, salt, | + | |
| - | <abbr title=" | + | |
| - | are singular, as they stand for one thing. This, however, cannot be if such terms admit the possibility of classification as: hard water, soft water, mineral water.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 5. GENERAL TERMS.</ | + | |
| - | <p> | + | |
| - | <em>A general term is one which denotes an indefinite number of objects or attributes.</ | + | |
| - | <p id=" | + | |
| - | Class-names are general terms, such as men, chair, tree, army, nation. Words like redness, sweetness, justice, are probably general in that they denote a combination of qualities or may be subdivided into kinds.</ | + | |
| - | <p> | + | |
| - | The way the term is employed in the proposition should determine its singular or general nature.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 6. COLLECTIVE AND DISTRIBUTIVE TERMS.</ | + | |
| - | <p> | + | |
| - | <em>A collective term is a general term which indicates an indefinite number of objects as one whole.</ | + | |
| - | <p> | + | |
| - | <em>A distributive term is a general term which indicates an indefinite number of objects as a whole, and also may be used to refer to each one of the group separately.</ | + | |
| - | <p> | + | |
| - | It is easy to distinguish collective from distributive terms when we attempt to use them in the designation of individuals. Pointing to a body of troops, one may remark, “There is the regiment.†But when pointing to < | + | |
| - | <p id=" | + | |
| - | It must be noted that, viewed from a different standpoint, some collective terms become distributive in nature. As for example in the proposition, | + | |
| - | <p> | + | |
| - | Collective terms have been classified as general terms. It must be borne in mind, however, that such may be made singular by some modifying word. For example, < | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 7. CONCRETE AND ABSTRACT TERMS.</ | + | |
| - | <p> | + | |
| - | <em>A concrete term is a term which denotes a thing</ | + | |
| - | <abbr title=" | + | |
| - | this man, that tree, John Doe, denote in each case a thing. Man and tree, denote many things. All are concrete.</ | + | |
| - | <p> | + | |
| - | < | + | |
| - | <p> | + | |
| - | Such words as red, honest, just, are concrete; while redness, honesty, justice, are abstract.</ | + | |
| - | <p> | + | |
| - | On first thought it might be inferred that “red†is the name of an attribute just as much as “redness.†This is a mistaken thought, however, as when we use the word red we mean red something—an < | + | |
| - | <p id=" | + | |
| - | Descriptive adjectives, because they describe things, are concrete. They do not alone name qualities of things, hence they are not abstract.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 8. CONNOTATIVE AND NON-CONNOTATIVE TERMS.</ | + | |
| - | <p> | + | |
| - | <em>A connotative term is one which denotes a subject and at the same time implies an attribute.</ | + | |
| - | <p> | + | |
| - | All concrete general terms are connotative because they denote subjects and at the same time stand for certain attributes; | + | |
| - | <abbr title=" | + | |
| - | “man†denotes many subjects; in fact, it stands for all the men in the world; it also implies rationality, | + | |
| - | “Triangle†stands for all plane figures of three sides; it likewise stands for the qualities, three-sided, | + | |
| - | <abbr title=" | + | |
| - | Both “man†and “triangle†are connotative.</ | + | |
| - | <p> | + | |
| - | <em>A non-connotative term is one which denotes a subject only, or implies an attribute only.</ | + | |
| - | <p> | + | |
| - | Generally speaking, proper and abstract nouns are non-connotative; | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 9. POSITIVE AND NEGATIVE TERMS.</ | + | |
| - | <p> | + | |
| - | <em>A positive term is one which signifies the possession of certain attributes</ | + | |
| - | metal, man, teacher, happy, honest.</ | + | |
| - | <p> | + | |
| - | <em>A negative term is one which signifies the absence of certain attributes</ | + | |
| - | inorganic, unhappy, non-metallic.</ | + | |
| - | <p> | + | |
| - | Terms which have the prefix not, non, un, in, dis, | + | |
| - | <abbr title=" | + | |
| - | or the affix less, are usually considered negative. The fact that there are some exceptions to this must not be overlooked. For example, unloosed, invaluable, are positive terms.</ | + | |
| - | <p> | + | |
| - | In theory every positive term has its corresponding negative; as pure, impure; organic, inorganic; metal, non-metal; good, not-good.</ | + | |
| - | <p> | + | |
| - | In some instances the language does not supply the word with the negative prefix because no need of it has been felt. The only way to express the negative of such words as good, table, | + | |
| - | <abbr title=" | + | |
| - | is to prefix “not†or “non.â€</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 10. CONTRADICTORY AND OPPOSITE TERMS.< | + | |
| - | (See <a href="# | + | |
| - | <p> | + | |
| - | Positive terms with their negatives have contradictory< | + | |
| - | <p> | + | |
| - | Contradictory terms, when used in a sentence, illustrate the law of excluded middle, as in the statements: “John’s recitation is either perfect or imperfect.†“This teacher is either just or not-just.†There is no middle ground in such propositions.</ | + | |
| - | <p> | + | |
| - | When contradictory terms are used in classification the whole is divided into but two classes; | + | |
| - | <abbr title=" | + | |
| - | <table class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | All the men in the world are either honest or not-honest. All the substances in existence are either organic or inorganic, | + | |
| - | <abbr title=" | + | |
| - | <p> | + | |
| - | It will also be seen from this list that the contradictory of the positive form is not always indicated by using the prefix. Honest and dishonest, or agreeable and disagreeable, | + | |
| - | <p> | + | |
| - | When there is any doubt as to the terms being contradictory, | + | |
| - | <p> | + | |
| - | Terms which oppose each other but do not contradict are said to be opposite or contrary terms. The following list illustrate opposite terms:</ | + | |
| - | <table class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | All these terms admit of a medium. In the case of hot or cold, for example, a substance need not necessarily be either. It may be warm or cool.</ | + | |
| - | <p> | + | |
| - | Terms seem to be contradictory when it is a matter of quality, but opposite when it is a question of quantity or degree.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 11. PRIVATIVE AND NEGO-POSITIVE TERMS.</ | + | |
| - | <p> | + | |
| - | <em>A privative term is one which is positive in form but negative in meaning.</ | + | |
| - | <p> | + | |
| - | <em>A nego-positive term is one which is negative in form but positive in meaning.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 12. ABSOLUTE AND RELATIVE TERMS.</ | + | |
| - | <p> | + | |
| - | < | + | |
| - | <p> | + | |
| - | <em>A relative term is one which derives its meaning from its relation to some other term.</ | + | |
| - | mind water; tree suggests shade, | + | |
| - | <abbr title=" | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 13. OUTLINE.</ | + | |
| - | <p class=" | + | |
| - | L< | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | Singular terms.</ | + | |
| - | <p> | + | |
| - | General terms.</ | + | |
| - | <p class=" | + | |
| - | <span class=" | + | |
| - | <p class=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | Concrete and abstract terms.</ | + | |
| - | <p> | + | |
| - | Connotative and non-connotative terms.</ | + | |
| - | <p> | + | |
| - | Positive and negative terms.</ | + | |
| - | <p> | + | |
| - | Contradictory and opposite terms.</ | + | |
| - | <p> | + | |
| - | Privative and nego-positive terms.</ | + | |
| - | <p> | + | |
| - | Absolute and relative terms.</ | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 14. SUMMARY.</ | + | |
| - | <p> | + | |
| - | A logical term is a word or group of words denoting a definite notion.</ | + | |
| - | <p> | + | |
| - | A singular term is a term which denotes one object or one attribute.</ | + | |
| - | <p> | + | |
| - | A general term is a term which denotes an indefinite number of objects or attributes.</ | + | |
| - | <p> | + | |
| - | General terms are collective or distributive.</ | + | |
| - | <p> | + | |
| - | A collective term is a general term which indicates an indefinite number of objects considered as < | + | |
| - | <p> | + | |
| - | A distributive term is a general term which indicates an indefinite< | + | |
| - | <p> | + | |
| - | A concrete term is a term which denotes a thing.</ | + | |
| - | <p> | + | |
| - | An abstract term is a term which denotes the attribute of a thing.</ | + | |
| - | <p> | + | |
| - | A connotative term is one which denotes a subject and at the same time implies an attribute.</ | + | |
| - | <p> | + | |
| - | A non-connotative term is one which denotes a subject only or implies an attribute only.</ | + | |
| - | <p> | + | |
| - | A positive term is one which signifies the possession of certain attributes.</ | + | |
| - | <p> | + | |
| - | A negative term is one which signifies the absence of certain attributes.</ | + | |
| - | <p> | + | |
| - | In theory every positive term has its negative. As related to each other positive and negative terms are said to be contradictory. If one denotes a true notion then the other denotes a false notion.</ | + | |
| - | <p> | + | |
| - | Some terms oppose each other but do not flatly contradict. As related to each other such terms are said to be opposite.</ | + | |
| - | <p> | + | |
| - | A privative term is one which is positive in form but negative in meaning.</ | + | |
| - | <p> | + | |
| - | A nego-positive term is one which is negative in form but positive in meaning.</ | + | |
| - | <p> | + | |
| - | An absolute term is one whose meaning becomes intelligible without reference to other terms.</ | + | |
| - | <p> | + | |
| - | A relative term is one which derives its meaning from its relation to some other term.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 15. ILLUSTRATIVE EXERCISES.</ | + | |
| - | <p> | + | |
| - | (1a) The words in italics are categorematic.</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | N< | + | |
| - | being syncategorematic, | + | |
| - | <abbr title=" | + | |
| - | John is < | + | |
| - | <p id=" | + | |
| - | (1b) Underscore the categorematic words in the following:</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | (2a) In the following, words enclosed in parentheses are logical terms:</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | (2b) Indicate the logical terms in the sentences under 1b.</ | + | |
| - | <p> | + | |
| - | (3a) The logical characteristics of the term < | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | (3b) The logical characteristics of other terms are as follows:</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | (3c) Give the logical characteristics of the following terms: justice, Abraham Lincoln, tree, library, America, president, principle, sympathy, dumb, nation.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 16. REVIEW QUESTIONS.</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 17. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.</ | + | |
| - | <div class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | class=" | + | |
| - | title=" | + | |
| - | in meaning between immoral and unmoral, disagreeable and not-agreeable?</ | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p> | + | |
| - | <span class=" | + | |
| - | <p id=" | + | |
| - | <span class=" | + | |
| - | title=" | + | |
| - | class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <hr class=" | + | |
| - | <h2 class=" | + | |
| - | CHAPTER 5.<br /><br /> | + | |
| - | <span class=" | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 1. TWO-FOLD FUNCTION OF CONNOTATIVE TERMS.< | + | |
| - | (See <a href="# | + | |
| - | <p> | + | |
| - | It has been indicated that a connotative term is one which possesses the double function of signifying a subject as well as an attribute. It may be observed here that an attribute of a notion is any mark, property or characteristic of that notion. Attribute, then, represents quality, relation or quantity. By a subject is meant anything which possesses attributes. Most subjects stand for objects and most attributes are qualities; consequently, | + | |
| - | <p> | + | |
| - | A connotative term, therefore, denotes an object at the same time it implies a quality. To illustrate: The symbol < | + | |
| - | <abbr title=" | + | |
| - | or for certain qualities like rationality, | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 2. EXTENSION AND INTENSION DEFINED.</ | + | |
| - | <p> | + | |
| - | This double function of connotative terms furnishes an important topic for the student of logic—the Extension and Intension of Terms. In short, some authorities claim that to master the extension and intension of terms is virtually to master the entire subject of logic. Though this position may be an exaggerated one, yet it tends to emphasize the importance of the topic.</ | + | |
| - | <p> | + | |
| - | <em>A term is used in extension when it is employed with reference to the objects for which the term stands.</ | + | |
| - | <p> | + | |
| - | When the term triangle is used to refer to the objects isosceles triangle, scalene triangle, right triangle, it is employed in extension.</ | + | |
| - | <p> | + | |
| - | <em>A term is used in intension when it is employed with reference to the attributes for which the term stands.</ | + | |
| - | <p> | + | |
| - | The term triangle is employed in intension when we use it to refer to the qualities, three sided and three angled.</ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 3. EXTENDED COMPARISON OF EXTENSION AND INTENSION.</ | + | |
| - | <p> | + | |
| - | A connotative term seems to be two dimensional—it has extent or length and intent or depth.</ | + | |
| - | <p> | + | |
| - | “Extension consists of the things to which the term | + | |
| - | <span class=" | + | |
| - | while “intension consists of the properties which the term | + | |
| - | < | + | |
| - | <p> | + | |
| - | Extension is quantitative, | + | |
| - | describe is to use a term in intension.</ | + | |
| - | <p> | + | |
| - | To divide a term into its kinds we must regard it in an extensional sense; | + | |
| - | <abbr title=" | + | |
| - | the term < | + | |
| - | <p> | + | |
| - | To define a term we must regard it in an intensional sense; | + | |
| - | <abbr title=" | + | |
| - | man is a rational animal.</ | + | |
| - | <p> | + | |
| - | Etymologically considered extension means to < | + | |
| - | <p> | + | |
| - | In attempting to use a term in extension we may ask ourselves the question, “What are the kinds? | + | |
| - | <p> | + | |
| - | Question: What are the < | + | |
| - | <p> | + | |
| - | N< | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 4. A LIST OF CONNOTATIVE TERMS USED IN EXTENSION AND INTENSION.</ | + | |
| - | < | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | carnivorous, | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | textbook, dictionary, encyclopaedia.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | trapezium, trapezoid, parallelogram.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | four sides, four angles, limited plane.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | theoretical logic, applied logic, educational logic.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | science of thinking, art of right thinking, treats of laws of thought.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | heavenly body, gives light and heat, twinkles.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | gravitation, | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <span class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | word or group of words, definite idea.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | monarchy, aristocracy, | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | body of people, established form of law, banded together for mutual protection.</ | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 5. OTHER FORMS OF EXPRESSION FOR EXTENSION AND INTENSION.</ | + | |
| - | < | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | <p class=" | + | |
| - | Formerly the words extension and intension were applied to concepts while denotation and connotation were applied to terms representing the concepts, but now the words are interchangeable. Denotation, the noun, and denote, the verb, signify, etymologically, | + | |
| - | <p> | + | |
| - | The terms which should be remembered are</ | + | |
| - | < | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
| - | src=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td class=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 6. LAW OF VARIATION IN EXTENSION AND INTENSION.</ | + | |
| - | <p> | + | |
| - | It has been noted that the intension of a term has reference to its qualities while extension considers its application to various objects. It may be wise to experiment with the extension and the intension of certain terms as types with a view of ascertaining how the two ideas are related to each other. For the sake of definiteness let us make use of the following scheme:</ | + | |
| - | <table id=" | + | |
| - | < | + | |
| - | <th class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <td colspan=" | + | |
| - | <td class=" | + | |
| - | < | + | |
| - | <td class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <div class=" | + | |
| - | <td class=" | + | |
| - | <img | + | |
| - | style=" | + | |
| - | alt="" | + | |
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| - | In considering the first illustration we observe that as the number of qualities is decreased, the number of objects increases. While in the second example as the qualities are increased, the number of objects decreases. It would appear from this that the intension and extension of a term are < | + | |
| - | </ | + | |
| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 6a. TWO IMPORTANT FACTS IN THE LAW OF VARIATION.</ | + | |
| - | <p> | + | |
| - | In studying the law of variation two facts are especially evident. (1)& | + | |
| - | <p> | + | |
| - | To illustrate the law of variation, determine upon any class name, then think of its proximate genus (the next < | + | |
| - | <abbr title=" | + | |
| - | <p> | + | |
| - | Thus the series:</ | + | |
| - | <p class=" | + | |
| - | animal< | + | |
| - | biped<br /> | + | |
| - | < | + | |
| - | white man<br /> | + | |
| - | European</ | + | |
| - | <p class=" | + | |
| - | (2) As a second fact: the increase and decrease is not a mathematical one. That is, by doubling the extension< | + | |
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| - | + | ||
| - | <div class=" | + | |
| - | <h3 class=" | + | |
| - | 6b. THE LAW OF VARIATION DIAGRAMMATICALLY ILLUSTRATED.</ | + | |
| - | <p> | + | |
| - | In a general way < | + | |
| - | <abbr title=" | + | |
| - | While on the other hand, if a line an inch long represents the intension of < | + | |
| - | <abbr title=" | + | |
| - | The following illustrates this scheme in connection with another series of words:</ | + | |
| - | < | + | |
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a_class_room_logic.1603418934.txt.gz · Last modified: by briancarnell