Class t£C I^ F Book.. COPYRIGHT DEPOSm NEW REVISED EDITION The Laws of Thought OR FORMAL LOGIC A BRIEF COMPREHENSIVE TREATISE ON THE LAWS AND METHODS OF CORRECT THINKING BY WILLIAM POLAND, S.J. St. Louis University LOYOLA UNIVERSITY PRESS CHICAGO COPYRIGHT, 1921 BY LOYOLA UNIVERSITY CHICAGO, ILL. c « c c c c e c V JUL -5 '21 ©CI.A617567 Al^ \ PREFACE It may not be unwise to preface the following pages with a caution regarding their scope and purpose. Such caution may, indeed, be due not only to the writer lest his aim be misunderstood; but also to the reader, who might otherwise seek in this little book for what it does not contain. This book, then, is not a Psychology. It does not discuss the nature of the soul or of its faculties. It merely enumerates the principal acts of the intellect; and describes them as far as is necessary for the pur- pose of this book, which is to lay down briefly and clearly the process of right thinking. This requires no encroachment upon the field of psychology. Questions which should be discussed later on, in the course of philosophical studies, if introduced into an outline of correct thinking, only retard progress : firstly, because they are distracting; but especially because the mind is not prepared for them. Even after long discussions they are not understood by one who is just entering on the study of philosophy. Many things have been here omitted which would find a fitting place in an exhaustive treatise on Logic. But they are such things as are not necessary to the purpose of this compendious work. Just as there are many curious combinations of numbers which might be 3 4 PREFACE introduced, and sometimes are introduced, into an arith- metic, but which are of no essential service in forming an accurate and rapid accountant; so there are many things — curiosities — which may be introduced into a Logic, but which are in nowise necessary to prepare the mind for accurate and ready thought in the study of philosophy. On the other hand, this book is not intended as a sort of a ''Logic made easy," or ''Logic in twenty lessons without a master." In philosophy less than in other things can we profitably dispense with a master. Finally, attention is called to the fact that terminology is strictly adhered to, both for the sake of brevity, and for the sake of the learner's progress, that he may be obliged to understand each section before passing further. The chief revision in this edition affects Chapter VI, on Method. This Chapter has been re-arranged and has been entirely re-written. CONTENTS CHAPTER I. INTRODUCTORY. Page Article I. Logic. 1. Logic. 2. Formal and Material Logic. 3. Natural Logic. 4. Artificial Logic. 5. Logic as a Science. 6. As an Art 9 Article II. Three Acts of the Mind. 7. Three Acts. 8. Knowledge Representative. 9. Sim- ple Apprehension, Idea. 10. Judgment. 11. Reasoning, Argument. 12. Oral Expression. 13. Term. 14. Propo- sition. 15. Syllogism 11 CHAPTER II. IDEAS— TERMS. Article I. Ways of Classifying Our Ideas. 17. Abstract, Concrete. 18. Clear, Distinct, Complete, Comprehensive. 19. Singular, Particular, Collective, Universal 15 Article II. Classification of Universal Ideas. 20. Form. 21. Reflex Universal. 22. Species. 2Z. Im- portant Observation. 24. Genus. 25. Dijfference. 26. Property. 21 , Accident. 28. Heads of Predicables . 17 Article III. Subordination of Genera. 29. The Same Form Generic and Specific. 30. Dia- gram. 31. Highest Genus, Lowest Species, Subaltern Genera 22 Article IV. Classification and Use of Terms. 32. Real and Logical Terms. ZZ. Univocal, Equivocal, Analogous Terms. 34. Univocal. 35. Equivocal. 36. Analogous. Zl . Supposition or Use; Material, Logical, Real 23 5 6 CONTENTS. CHAPTER III. JUDGMENTS AND PROPOSITIONS. Page Article I. Definitions. Structure of Propositions. 38. Judgment. 39. Proposition. 40. Subject, Copula, Predicate. 41. Logical and Grammatical Predicate . . 27 Article II. Simple and Compound Propositions. 42. Simple. 43. Compound. 44. Various Constructions. 45. Categorical. 46. Conditional. 47. Conjunctive. 48. Disjunctive. 49. Remark 28 Article III. Immediate and Mediate Judgments. 50. All Judgments. 51. Immediate. 52. Mediate. 53. The Process 31 Article IV. Connection Between Subject and Predicate. 54. All Judgments. 55. A Priori. 56. A Posteriori. 57. No Synthetic a Priori 32 Article V. Extension and Comprehension. 58. An Axiom. 59. Extension. 60. Comprehension. 61. Illustration 34 Article VI. Extension of Propsitions. Quantity and Quality. 62. Extension. 63. The Subject. 64. Note. 65. The Predicate. 66. Universal Affirmative. 67. One Excep- tion. 68. Universal Negative. 69. Particular Affirma- tive. 70. Particular Negative. 71. Two Laws. 72. Af- firmative and Negative. 73. Negative Particle. 74. Quantity and Quality 36 Article VII. Related Propositions. 75. Three Relationships. 76. Conversion. 77. Equiva- lence. 7S. Opposition. 79. Diagram 41 CHAPTER IV. REASONING— ARGUMENT. Article I. The Syllogism. 80. Reasoning and Argument. 81. Styles of Argument. 82. The Syllogism. 83. Antecedent, Consequent, Prem- CONTENTS. 7 Page isses. 84. Consequence. 85. Axioms. 86. Analysis o£ Argument. 87. Middle and Extremes 45 Article II. Figures and Moods of the Syllogism. S8. Major, Minor, Middle. 89. First Figure. 90. Second Figure. 91. Third Figure. 92. Moods of the Syllogism 48 Article III. Laws of the Syllogism. 93. Scope of the Laws. 94. First Law: Three Terms. 95. Second Law : Extension of Extremes. 96. Third Law: Extension of Middle Term. 97. Fourth Law: Place of Middle Term. 98. Fifth Law: Affirmative Conclusion. 99. Sixth Law: Negative Conclusion. 100. Seventh Law : No Conclusion. 101. Eighth Law : No Conclusion. 102. Ninth Law : Particular Conclusion. 103. Caution . 54 Article IV. Some Species of Syllogism. 104. Simple and Compound Syllogisms. 105. Condi- tional Syllogisms. 106. Conjunctive Syllogisms. 107. Disjunctive Syllogisms 61 Article V. Other Styles of Argument. 108. Argument Abbreviated. 109. Enthymeme. 110. Sori- tes. 111. Polysyllogism. 112. Epichirem. 113. Dilemma 64 CHAPTER V. TRUTH OF THE PREMISSES. Article I. Formal and Material Logic. 114. The Form. 115. The Matter. 116. Value of the Conclusion 68 Article II. The Demonstration. 117. Two Kinds. 118. Direct. 119. Indirect. 120. Sim- ple, Compound. 121. A Priori. 122. A Posteriori . . 70 Article III. Induction. 123. Deduction and Induction. 124. Complete Induc- tion. 125. Incomplete Induction. 126. Example. 127. Analogy. 128. Caution 72 8 CONTENTS. Page Article IV. Fallacies. 129. Fallacy. 130. Petitio Principii. 131. Evading the Question. 132. Of the Accident. 133. A Dicto Simplici- ter. 134. Of the Consequent. 135. Of the Cause. 136. Of the Question. 137. Of Reference. 138. Of Ob- jections n CHAPTER VI. METHOD. Article I. Scientific Method. 139. Scientific Method. 140. Analysis and Synthesis. . 82 Article II. Parts. 141. Parts: real and logical. 142. Real Parts: accidental, integral, essential. 143. Real Essential Parts: physical and metaphysical. 144. Physical Parts. 145. Meta- physical Parts. 146. Logical Parts 83 Article III. An Illustration. 147. Analysis. 148. Synthesis. 149. The Negative. . . 87 Article IV. Analytic Table. 150. Table. 151. Meaning of Table 90 Article V. Definition. 152. Kinds of Definition. 153. Essential Definition. 154. Some Rules for Definition 92 Article VI. Division. 155. Logical Division. 156. The Simple Rule 95 Article VII. Science. 157. Science. 158. Object of a Science. 159. Material and Formal Object. 160. Logical Character of a Science 97 Outline of Sciences 102 Explanation of Outline 103 Points for Practice 104 Index 107 THE LAWS OF THOUGHT. CHAPTER I. INTRODUCTORY Article I. Logic. ^ Logic — Formal and Material Logic — Natural and Artificial Logic. 1. The name Logic comes from the Greek, Xoyog. Aoyo? signifies reason, thought; also oral speech, a word. But the oral word, oral speech, is merely a sign of what is in the mind, of the mental word, mental speech, thought. Logic, therefore, has to do with thought. 2. Formal Logic is so called in opposition to Material Logic, because it deals solely with the form or structure of thought, of an argument; and not with the matter contained in the structure. In the building of a house there are different persons or sets of persons concerned. Besides the architect there are those who supply and prepare the material, and there are the builders. It is the business of the architect to see that the material is supplied and properly prepared by one set and put together by the other. The builders have not to question the nature, value or strength of the material. They have only to see that the pieces fit. They are concerned only with the shape, the form of the 9 10 THE LAWS OF THOUGHT Structure and of each piece as tending thereto. Now, apply this to the edifice of knowledge. Formal logic has to do with the principles for the correct putting together of the material furnished. The general method of furnishing the material ready prepared is the sub- ject of material logic. Hence in formal logic we have to work at, to study, only the correct form of thought; not minding whether the examples we take to practice upon be true or not: just as one wishing to illustrate the structure of a bridge will take bits of wood, paper, straw, thread, wire or whatever he may find at hand, occupied solely, for the moment, with the form; and not at all concerned about the material. 3. Natural Logic. Natural logic is the innate dispo- sition all men have to think correctly, to follow certain rules in the pursuit of knowledge, of truth. We are all, by nature, logicians. 4. Artificial Logic. However, as sometimes, even with the best intentions, we are liable to think inaccur- ately by reason of complications of notions which arise ?nd defects which are easily overlooked in the process of our thought, there has been invented what is called an artificial logic. Not that there is anything artificial about it in the sense that it is intended to replace real logic; but, in this sense, that it is made an art whose princi- ples we can learn and apply, to ensure correct thinking. The methods which we follow when we think correctly have been closely observed and have been put together as a connected system of rules. By learning to apply them we can acquire the art of logic. 5. Logic as a Science. But logic is not merely an art. It is primarily a science. For these rules are a sys- INTRODUCTORY 11 tematized body of fixed laws regarding the reason of cor- rectness in thought. Hence logic as a science may be defined: "The science of those laws which must rule the acts of the mind in correct thinking.'' 6. Logic as an Art. Logic becomes an art when these laws are presented, or made ready instruments, for use, to ensure right thinking, to detect false reasoning, and to mend faulty argument. Article II. Three Acts of the Mind Simple Apprehension; Judgment; Reasoning — Idea; Judg- ment; Argument — Term; Proposition; Syllogism. 7. Three Acts of the Mind. To find out the rules which we must follow in aiming at a knowledge of truth, we must consider three acts which the mind performs in obtaining knowledge. They are: i. Simple Apprehen- sion; 2. Judgment; 3. Reasoning. 8. Knowledge Representative. All knowledge is representative of something real or possible. It is a mental expression of that something. Hence every act of the mind by which we know may be considered in two ways : either with reference to the degree of activity called forth or with reference to the degree in which it is representative. 9. Simple Apprehension. Simple apprehension is an act by which the mind simply perceives or apprehends something without affirming or denying anything about it. If we consider this act as representative, as a mental expression of that something, it is called an idea (like- 12 THE LAWS OF THOUGHT ness), a concept (the mind conceiving that something in itself, in Hkeness), a notion (the first element of knowl- edge). Thus by the act of simple apprehension we may have a notion, an idea, a concept, of rose, blue, plant, cloth, beauty, justice, etc. Remark that when we perceive or apprehend we do not perceive the idea, but the object which the idea represents. We do not advert, at least not especially, to the act of the mind. It is only by a second act of the mind, called reflection, that we perceive we are per- ceiving. 10. Judgment. Judgment is that act by which the mind, having formed two ideas, affirms or denies identity between their objects. Thus: The rose is a plant. This cloth is not blue. Remark, as for the simple apprehen- sion, that what we affirm or deny is not about the ideas, but about the objects which the ideas represent. This is expressed by saying that we affirm or deny objective identity. The judgment, as the simple apprehension, may be regarded as a certain exercise of the activity of the mind, or as representative of the presence or absence of objective identity. As an act it is called judgment; as representative it is also called a judgment or a declaration. 11. Reasoning. Reasoning is an act or a series of acts by which the mind compares (objectively) two cases pronounced upon in two judgments, and in that comparison perceiving implied the material for a third judgment, thereupon forms explicitly such third judg- ment affirming or denying according to what was per- ceived implicitly through the comparison. This defini- tion will be emade sufficiently clear for present purposes by two examples: INTRODUCTORY 13 First example. The judgment makes two declarations : A man is a living being; Hannibal is a man. The mind compares these two cases and then declares explicitly what it perceives implied, namely: Hannibal is a living being. Second example. The judgment makes two declara- tions : A horse is a quadruped ; This feathered being is not a quadruped. The mind compares these two cases and then declares explicitly what it perceives implied, namely: This feathered being is not a horse. In the first example the mind worked upon the prin- ciple that, in the sense in which tv/o things {living being, Hannibal) are the same as a third thing {man), in the same sense are they the same as one another. In the second example the mind worked upon the principle that, in the sense in which two things {horse, this feathered being) are, the one {horse) the same as a third thing {quadruped) , the other {this feathered being) different from it, in the same sense are they different from one another. As in the simple apprehension and judgment the action of the mind was also regarded as representative, so the act of reasoning may be regarded as carrying in its third judgment a new representation of something perceived through the two prior judgments. Considered as an act it is called reasoning, argumentation, deduc- tion. In the other sense it is called argument, and also sometimes inference, conclusion. 14 THE LAWS OF THOUGHT 12. Oral Expression of Thought. Just as our thoughts are, as it were, mental words expressing certain objects, so in written and spoken words do we express our thoughts as well as the objects represented in our thought. 13. Term. The oral {spoken) or written word ex- pressing an idea is called a term, as, blue, cloth, justice, beauty. 14. Proposition. The terms, oral or written words, expressing a judgment are called a proposition, as, Hannibal is a man. 15. Syllogism. The three propositions expressing an argument are called a syllogism, and also an argu- ment. CHAPTER II. IDEAS, TERMS. 16. We shall now proceed, within the limits of the scope of Formal Logic, to make some considerations upon ideas, judgments, arguments; and upon their respective verbal expressions, terms, propositions, syllo- gisms. We begin with the most elementary, the idea. Article I. Ways of Classifying our Ideas. 17. There are many ways of partitioning off into classes all the ideas we have or may have. 1. Abstract and Concrete. An abstract idea is one which represents its object as independent of, taken asunder from {abstracted from), everything else. A con- Crete idea represents its object as coalescing with, in union with, grown together with {concreted) something else. Our ideas of blueness, wisdom, are abstract. Our ideas of blue, wise, are concrete, because blue, wise, are thought of as concreted in something else : blue sky, wise judge. 18. 2. Clear, Distinct, Complete and Adequate or Comprehensive. According to the degree of perfection with which ideas express the characteristics (called notes) of their object, they are divided into clear, dis- tinct, complete and adequate or comprehensive. A clear idea expresses characteristics or notes suffi- cient to discern the object from others. A distinct idea distinguishes between these notes themselves. A com- 15 16 THE LAWS OF THOUGHT plete idea expresses all the notes that distinguish the object in reality from others. A comprehensive or ade- quate idea expresses all that can be perceived in the object: the human intellect has no such idea of any- thing. I see an object moving in the distance. I have an indefinite, obscure idea of something moving. It ap- proaches. I get an idea of my friend X — just enough to know that it is X without distinguishing any marks — a clear idea. X comes nearer. Yes, there is the walk and build and countenance of X. M,y idea is the walk and build and countenance of X. My idea is becoming distinct. X steps up and shakes hands with me. I know X intimately and thoroughly. I note all the points that distinguish him as X from aught else. My idea is complete. 19. 3. Singular, Particular, Collective, Universal. Ideas may again be divided according to the number of individuals embraced in the idea and the manner of embracing them; that is, according to the extension of the idea. In this way we divide ideas into singidar, par- ticular, collective, universal. When one special individual is expressed in a deter- minate manner, we have a singular idea. Thus : Canada, ''The President," to-day, this hook. When the idea expresses in an indeterminate way some one or other individual or some individuals, it is called particular. Thus: Some man or other, a man, a certain man, some men. When several objects are expressed under one idea or concept, but in such a way that the idea cannot be applied to them individually but only as a collection, the IDEAS, TERMS 17 idea is called collective. Thus: A crowd, a fleet. No individual of the collection is a crowd or a fleet. When several objects are expressed by an idea, but in such a Vv'ay that the idea not only embraces them all, but is applied to them distributively and individually, we have what is called a universal idea. Thus : Man, horse, gold. I can say, Man is a living being, mean- ing that all men are living beings; meaning also that each individual man is a living being. When I say. The horse is a quadruped, I mean that all are quadrupeds, and this horse is a quadruped. When I say. Gold is a metal, I mean that all gold and that this piece of gold is metal. This partition of ideas being made, we have to deal now, in a special manner, with universal ideas. Article II. Classification of Universal Ideas. Species — Genus — Difference — Property — Accident. Heads of Predicables. 20. Form. Universal ideas are classified according to the manner in which the one idea can be applied to many individuals; or, what comes to the same, accord- ing to the manner in which what the idea represents belongs to many individuals. This will explain itself as we proceed. Let us for the purpose of clearness and brevity introduce a new word, form or formality. We shall call form or formality whatever can be the object of an idea. The same thing may have many forms (or determinations) existing in it simultaneously. A ball may contain the forms of wood, roundness, whiteness. 18 THE LAWS OF THOUGHT elasticity, etc. In man there are the forms of spirit, matter, organism, sensation, etc. 21. Reflex Universal. Any form or formality may become the object of my idea. This idea I may reflect upon, and then regard as applicable not only to the individual form from which I first got it, but as appli- cable to an indefinite number of individual cases, actual or possible, and also as sufficiently representative of the same formality as it exists or may exist in each of those cases. I begin to regard the idea as universal, as applicable to many, by reflecting up it. The idea, as so regarded by reflection, is called a reflex universal idea. Even before I reflected upon it, even as I got it directly from the individual form, it was in itself capable of being applied to the indefinite number of cases. As such, prior to reflection, it is called a direct universal, 22. Species. If a form constitutes, or if combined forms constitute, the whole essence of a class of indi- viduals, so that no individual of the class can be, or be thought, without said form or combination, then such form or combination is said to be specific, and the reflex universal idea representing it is called a specific idea. Thus the combination of rational and animal in man constitutes his essence. The complex idea rational animal regarded as applicable to all possible men is a specific idea. 23. Important Observation. Now here we have something curious to note. The idea rational animal is one idea — complex, but one. Where, when we apply it to all men actual and possible, has it one object? When we speak of the rational animal, of rational ani- mals, of humanity, we find ourselves figuring to our- IDEAS, TERMS 19 selves a certain something outside of us which is neither this man nor that man nor the great collection of all men. Yet is it something which we do put up before us as the object of our universal reflex idea, rational animal, humanity; and we talk of it a^ if it were some- thing, a man in general. We know that what we say of it is true of each case where there exists the rational animal, where there exists humanity. What is it? It is a convenience invented by the ingenuity of the mind for the needs of thought. It is consequent upon the innate tendency of the mind to pursue the most profitable and expeditious modes of thought. It is something we create in possessing ourselves of the reflex universal idea. It is a something that does service for all the individual cases. We call it the species. I know that the expression human species suggests to us the whole collection of men, and that naturalists do use the word species to express collections. But we do not reason upon collections. We should never get through. Neither do we reason, when speaking, for instance, of man, upon this man or that man. When we say man is mortal, we speak of man, in general, taken as a species, in the sense explained. 24. Genus. If the form be something that is found in all the individuals of two or more classes so as to constitute part of the essence of such individuals, or briefly, if the form be found as part of the essence in two or more species, it is called generic, and the reflex universal idea representing it is called a generic idea. Thus man and brute agree in this, that they are both animal; the formality animal is of the essence of the species man and of the species brute. Animal, therefore. 20 THE LAWS OF THOUGHT is generic, and applies to all the individuals of the two species. If now we put before us that certain something which will stand as one for all the individuals possessing animal nature, we shall have what is called a genus. 25. Difference. Now take two species. They agree in something that is common to the essences of both. This, as we have said, is genus. But they differ also in other essentials. All the individuals of one species have a formality which is not in any of the individuals of the other, and which distinguishes all the individuals of one from all those of the other. The reflex universal idea of this formality is called a differential idea ; and as this stands out objectively in the species, it is called a differ- ence or specific difference. Take the genus animal. It embraces the two species, rational animal and irrational animal. Rational and irrational are specific differences. 26. Property or Inseparable Accident. Sometimes there is found a form in all the individuals of a species, which form, though not of their essence, is still neces- sarily connected with the essence and flows from it. The reflex universal idea of a form so considered is said to be the idea of a property. Such form, considered in the species, as we have explained species, is named a property or an inseparable accident. Such may be con- sidered for instance, the powers of speech and of laughter in man. 27. Accident. If, however, a certain form happen to be common to many individuals, but be in nowise of their essence nor necessarily connected therewith, and be such that it can be added or taken away without affecting the essence, such form is said to be simply IDEAS, TERMS 21 accidental. The universal reflex idea representing it as so separable is the idea of an accident. The form itself, in whatever way considered, as thus separable, is called an accident. Thus the forms, blue, green, circular, square, thick, soft, etc., are separable accidents. We dis- tinguish the inseparable accidents by the special name of property, 28. Heads of Predicables. The wide reaching na- ture of the classification which has just been given, will be seen if we consider that whatever we affirm or deny of anything is affirmed or denied as a genus, species, difference, property or accident. That is to say, what- ever we predicate (affirmatively or negatively) we pred- icate (affirmatively or negatively) as the genus, species, etc., of that of which we predicate it. Thus we say man is a rational animal. We predicate rational animal of man. We predicate it as the species. If we say man is rational, we predicate rational as the specific difference. If we say man is an animal, we predicate animal as the genus. If we say the man is white, yellow, strong, we predicate white, yellow, strong as accidental, as ac- cidents. Hence genus, species, difference, property, accident, are called Heads of predicables, because what- ever is pre die able of anything comes under one of these heads. There is a single exception to this general law. The exception is for the form being. Being applies to whatever can exist or be thought of. The idea of being is said to be transcendental. But the predication of be- ing (as also of one, true, good) constitutes on§ of the most subtle discussions of general metaphysics. We need not speak of it here. 22 THE LAWS OF THOUGHT Article III. Subordination of Genera. Highest Genus — Subaltern Genera — Lowest Species — Individuals. 29. The Same Form Generic and Specific. It is to be remarked that there are cases where the same form considered as a universal is capable of being regarded as both genus and species. Take, for instance, the form substance. Since the individuals to which it extends can be divided into two classes, corporal substance (body) and incorporeal substance (spirit), it is genus with reference to them, and they are species embraced by it. But the form corporeal substance (body) is again a genus when regarded as universal, for it extends to individuals that can again be divided into classes, — organic body and inorganic body. These become species under it. Organic body, next taken as a universal, be- comes a genus with reference to the classes sentient or- ganic body (animal) and non-sentient organic body (plant). These are species under it. But animal is also genus with reference to rational animal and irrational animal. 30. Diagram. The following plan will exhibit this to the eye : Substance. I Corporeal Substance or Body. Incorporeal Substance. Organic Body. Inorganic Body. I I I . Sentient Organic Body or Animal. Non-sentient. Rational Animal or Man. Irrational. I I Charles, Frederic, Augustus, etc. 1 IDEAS, TERMS 23 31. Highest Genus, Lowest Species, Subaltern Genera. In this table it is seen that substance is used as genus only. Body, organic body and animal are used both as species and as genus. Man is used as species only. When a genus cannot be considered as a species under a higher genus, it is called highest genus. When a species under one genus cannot be made a genus with reference to individuals under it, that is, when the individuals cannot be classified as species, it is called lowest species. The forms that are predicable both as genus and as species are called subaltern genera. In the table, Substance (supposing it to be incapable of being ranged as species under a higher genus) is highest genus. Man is lowest species. Body, Organic Body, Animal, are subaltern genera. Charles, Frederic, Augustus, etc., are merely individuals of the species man. Article IV. Classification and Use of Terms. Real, Logical — Univocal, Equivocal, Analogous — Supposition. 32. Real and Logical Terms. We may now say a word about terms. Terms are the written or spoken words that stand for ideas or for the objects of ideas. A term is called real when it expresses an object as that object may exist independently of the mind. Thus Lon- don, this man, are real terms. A term is called logical when it expresses an object in that kind of existence which depends entirely on the mind, as man, animal, used in the universal sense to stand for genus or species, v. gr., for animal and man in general. Genus and species 24 THE LAWS OF THOUGHT as we have explained them are mental creations, doing service as representatives for a class, or what is the same, their existence is logical, dependent on the mind. Hence the terms expressing them as such are called logical terms. 33. Univocal, Equivocal, Analogous Terms. Leav- ing the real terms and concerning ourselves solely with the logical, we find that, on account of the defects of language, some terms, doing service as universals, do not always represent the same idea nor apply in the same manner to all the individuals for which we make them stand. We find terms to be not only univocal but also equivocal and analogous. 34. Univocal. That term is called univocal (one word) which is really but one term in meaning as well as in sound. That is to say, the univocal term is always applied with the same signification to each and all of the inferiors (i.e. species or individuals) to which it can be applied. Such are the terms, animal, man. 35. Equivocal. But if the same written or spoken word, the same term, comes, in the complexity of language-growth, to stand for two or more different ideas and objects of ideas, it is called an equivocal term. Thus the term pen is equivocal. It is a word that serves equally to express different ideas and objects of ideas. It stands equally for a writing instrument and a cattle enclosure. The equivocation is sometimes in the sound only, as bow (a reverence) and bough. Sometimes :: is in the writing only, as bow (a reverence) and bow (in archery). IDEAS, TERMS 25 36. Analogous, Again, there are terms that are ap- pHed to different things neither univocally (i.e. in quite the same meaning), nor equivocally (i.e. in quite different meanings), strictly speaking. The same term is used on account of some connection between the objects. The connection is called, in philosophy, analogy. The terms are called analogous terms. When the analogy or connection is merely a likeness between the objects, it is called analogy of proportion. We make this the ground for the use of the metaphor. We will call a man a lion on account of his courage. We merely abbreviate a comparison. There is another analogy where the connection is cl<3ser. We say a healthy man and also (however justly) a healthy climate, a healthy complexion. We affirm of the climate (which is the cause) and of the complexion (which is a natural sign) the attribute which, in its full, original and proper meaning, belongs only to the man. We have here again, strictly speaking, figures of speech. This analogy is closer than the mere similitude. It is called analogy of attribution. However, it is specified as analogy of extrinsic attribution, because the form that is attributed, health, is intrinsic to man only, belongs to man only, and is extrinsic to climate and to complexion, they being but the cause and the sign of man's health. But we have introduced this question only to come to what is called the analogy of intrinsic attribution. And we speak of the analogy of intrinsic attribution only as an aid to the understanding of a later question, the subtle question of the attribution of being, referred to in 28. Therefore — What is attributed may really exist in all the individu- als to which it is attributed, and still not in such a way 26 THE LAWS OF THOUGHT that it can be attributed univocally, i.e. in the very same sense and manner. It exists in one independently of all the others, but in the others only dependently upon this one. Thus being is predicated of God and of created things: of God, independently; of created things, only with dependence upon the Creator. Being is not used univocally. It does not apply in the same sense to Creator and Creation. It cannot be called genus. Under genus the species are independent one of another. But this question will be treated in the General Meta- physics. 37. Supposition. The supposition of a term is what is suh- posed by {put under) the term, what is implied by it or intended to be understood by it. This depends upon the wish of the one who uses the term. We might extend this subject and go back over all the various classification of ideas and their corresponding objects. We shall give but three wide divisions of the supposi- tion and thus close this chapter. The supposition is said to be material when we imply no more than is evident from the mere sound of the term or its appearance as written. Thus, when we say or write, Man is a word of one syllable, our use or sup- position of the term man is material. If we imply that the term is used in the universal sense to stand for genus or species, the supposition is called logical. In the sentence, Man is a rational animal, the supposition of the term man is logical. When we wish the term to stand for a reality, the supposition is called real. In the sentence. This man is temperate, the supposition of the term man is real. CHAPTER III. JUDGMENTS, PROPOSITIONS Article I. Definition and Structure of Propositions. 38. Judgment. The judgment, as we have said, is that act of the mind by which we compare two objects of thought and pronounce upon their identity or agree- ment, affirming or denying. It is an affirmation or a denial. It is not always necessary that any appreciable time should be taken to compare the terms before passing sentence. There may be and there are cases where the verdict is evident at once upon the presentation of the terms. We see at once the identity or the disagree- ment. Our daily thoughts are full of instances in point. 39. Proposition. We have already stated that the judgment as expressed in spoken or written w^ords is called a proposition. 40. Subject, Copula, Predicate. A proposition con- sists of three parts, subject, copula, predicate. The sub- ject is that of which something is affirmed or denied. The predicate is that which is affirmed or denied of the sub- ject. The copula is a word or words expressive of the affirmation or denial, the words, namely, is, are, is not, are not, 27 28 THE LAWS OF THOUGHT SUBJECT. COPULA. PREDICATE. Man is rational. Knowledge is not virtue. Vices are detestable Sinners are not saints. The copula is a convenience of language. It merely stands for the agreement or disagreement that exists in the objects; this agreement or disagreement is perceived by the mind comparing the ideas, and is finally pro- nounced upon in the judgment. 41. Logical and Grammatical Predicate. We must be careful to distinguish between the predicate of the logician and the predicate of the grammarian. In the sentence, Birds fly, the grammarian may tell us that fly is the predicate. The logician will resolve the sentence in such a way as to employ the copula. He will say, Birds are beings-that-fly; and with him the predicate is beings-that-fly. Thus the logician will transform any sentence to put it into logical shape. Article II. Simple and Compound Propositions. Simple — Compound — Copulative — Disjunctive — Conditional — Casual. 42. A Simple Proposition contains but one principal subject and one principal predicate. The ship is sailing, is a simple proposition. We may add circumstances of time and place, adjectives, adverbial and relative clauses, without making it a compound proposition. It will be- come complex, but not compound. The ship that was made last year at New York is sailing amid icebergs that JUDGMENTS, PROPOSITIONS 29 have floated from Greenland to the coast of Newfound- land, is still for the logician a simple sentence though complex. All that belongs to ship goes in as subject. All that belongs to sailing goes in as predicate. 43. A Compound Proposition contains two or more principal subjects and predicates expressed or implied. Paris and Berlin are beautiful is a compound proposi- tion and stands for the two simple propositions Paris is beautiful, Berlin is beautiful. Add another predicate: Paris and Berlin are large and beautiful. Here we have four simple propositions in the compound. 44. Various Constructions. There are various kinds of simple and compound propositions — various as the grammatical constructions invented to secure brevity in language, the sometimes cumbersome vehicle of thought. The propositions receive their names from the construc- tions. We call attention to a few propositions. 45. Categorical. A categorical proposition is one that affirms or denies absolutely and directly. It may be simple or compound. Thus: Man is rational, The soul is not material, Prudence and Justice are virtues, Camels and giraffes are not insects. 46. Conditional. A conditional proposition affirms or denies not absolutely, but on condition. The rain is coming is categorical. But, // the wind is west, the rain^ is coming is a conditional proposition. Remark that this is really a simple proposition. We do not say. The wind is west, the rain is coming. We merely affirm condi- tional connection between the two. The conditional proposition is also called hypothetical. 30 THE LAWS OF THOUGHT 47. Conjunctive. A conjunctive proposition affirms the simultaneous incompatibility between two cases. No man can spend all his money on drink and still sup- port his family. Here we do not affirm or deny the categorical propositions that he spends his money on drink, that he supports his family. We affirm only the incompatibility between the two. The proposition is simple, however complicated in language. The conjunc- tive proposition is reducible to the conditional thus : // a man spends all his money on drink, he cannot support his family. The conjunctive proposition is therefore a species of the hypothetical. It is always negative. It is called conjunctive for the sake of a name, on account of the conjunctive particle and which connects the in- compatible cases. 48. Disjunctive. A disjunctive proposition is made up of two or more categorical propositions connected in such way by a disjunctive particle that no one is declared absolutely, but the acceptance of one implies the rejection of the others. Thus, speaking of a per- son's age, I may say. He is either just fifty or under fifty or past fifty. Suppose I declare categorically that he is just fifty; then the two other parts become he is not under fifty, he is not past fifty. However, the denial of one case does not imply the affirmation of the Ocher two. If I say. He is not just fifty, I may not therefore affirm both that he is under fifty and that he is past fifty. The remaining parts are simply left in the diminished disjunctive proposition. He is either under fifty or past fifty. The disjunctive proposition is a species of the hypothetical, with one part positive and the other part negative. Thus: // he is just fifty, he is JUDGMENTS, PROPOSITIONS 31 neither under fifty nor past fifty. As the example given implies two such conditions, we might class it with the compound propositions; but this matters nothing to our purpose. 4^. Remark. Here we shall leave the complex and compound propositions. We have mentioned the con- ditional, conjunctive and disjunctive, because we shall have occasion to refer to them when treating of the varieties of the syllogism. Henceforth in the present chapter we shall confine our study to the elementary proposition, the simple cate- gorical proposition. Article IH. Immediate and Mediate Judgments. 50. All Judgments. The judgments we form are all necessarily either immediate or mediate. 51. Immediate. An immediate judgment is one that is formed without a process of reasoning. If some one says to me, A whole orange is greater than half an orange, I do not ask him to prove it. I see the truth immediately, and pronounce upon it without having to be led to see it through the medium of other truths better known. Again, if I take a piece of heated iron in my hand, I can and do know and say at once. This iron is hot. I do not have to go through any other judgment to arrive at the knowledge that this iron is hot. The judgment is immediate. 52. Mediate. On the other hand, if some one tells me that the three angles of a triangle are equal to two right angles, I do not see at once that it is so ; I ask him 32 THE LAWS OF THOUGHT to show me that it is so. And he proceeds to put before me other propositions through which I see, until it dawns upon me that what he said at first is true. These other propositions or truths are the medium through which I see that the three angles are equal to two right angles. This judgment is therefore called a mediate judgment. To take another example. I hand a banknote to some one, as payment. He tells me, This banknote is a coun- terfeit. I do not perceive that the note is a counterfeit. He imparts to me some new knowledge, and through the medium of that knowledge, I too can see and say, This note is a counterfeit. My judgment is mediate. 53. The Process. The process by which one judg- ment, proposition, is made evident through the medium of others is called reasoning. This will form the subject of the next chapter. We have still to consider, in this chapter, two other divisions of judgments or proposi- tions. This we shall do in the two following articles. Article IV. Connection between Subject and Predicate. A Priori, A Posteriori — Necessary, Contingent — Absolute, Hypothetical — Metaphysical, Physical — Analytical, Synthetical. 54. All Judgments. If we consider the connection that exists between the predicate and the subject, we can classify all judgments as a priori or a posteriori. 55. A Priori. If the predicate is such that it is al- ways implied in the subject, and in such way that a full understanding of what is meant by the subject and predicate is sufficient, without any experiment upon a JUDGMENTS, PROPOSITIONS 33 particular case, to make us see that the proposition holds in all cases, absolutely, necessarily and without possible exception, the proposition or judgment is called a priori. It is seen to hold prior to any application to a particular case. A whole is greater than any of its parts; no thing can simultaneously exist and not exist, — these are a priori propositions. Such propositions are also called necessary, because an exception is impossible. They are called absolute, because they hold, absolved from, free from, all condi- tion. They are called metaphysical, because their truth does not depend upon the physical, actual order of things existing. They are called analytical, because by analyzing the subject, by taking it asunder into all that it implies, we will finally arrive at the predicate and see that the predicate belongs to the subject. 56. A Posteriori. An a posteriori proposition is one in which the idea of the predicate is not implied in the idea of the subject. Some one says to me. This iron is hot. I may know all that books can teach about the nature of iron and the nature of heat. But all of it will not teach me that this iron is hot. I must have experi- ence of this particular case of iron and heat. After the test, posterior to the experience, I may affirm. This iron is hot. Hence the name a posteriori. Such propositions are also called contingent, as op- posed to necessary, because they may happen to be true or not true. They are called hypothetical, as opposed to absolute, because their truth depends upon a supposition, a hypothesis, which may be wanting. They are called physical, because they represent facts of the actual, physical order. Finally, they are called synthetic, as 34 THE LAWS OF THOUGHT opposed to analytic, because they are made up by the synthesis, the putting together, of two ideas, terms, neither of which is found in the analysis of the other. 57. Synthetic a Priori. We have here to make a re- mark upon an assertion of Emmanuel Kant which has caused a great deal of confusion in philosophy. He asserted that there could be a proposition which would be at once synthetic and a priori, and he called it the synthetic a priori. Kant illustrates his discovery with examples. For instance, he draws upon arithmetical addition. The proposition three and two are five, 3 -J- 2 = 5, is with him synthetic a priori : a priori, be- cause it is absolute ; synthetic, because, he says, the pred- icate five, 5, adds on a new notion over and above three and two, 3 + 2. Let us see if the predicate adds a new idea. We repeat what we said before, that we do not reason with the mere sound of the voice or the mere appearance of marks on paper. What does the subject mean ? 3 means 1 -|- 1 -f- 1.. 2 means 1 + 1. 3 + 2 means 1 + 1 + 1+1+1. 5 means 1 + 1 + 1 + 1 + 1. Now put down the meaning of 3 + 2 =5, and you have 1 + 1 + 1 + 1 + 1=1 + 1 + 1 + 1 + 1. What is there in the predicate that is not in the subject? Article V. Extension and Comprehension. 58. An Axiom. We have delayed to this point a very important consideration on the subject of ideas and terms. We have delayed it on account of its immediate use in the next article. In fact, we do not hesitate to say that the thorough understanding of the subject of JUDGMENTS, PROPOSITIONS 35 the present article is the key to philosophy. There is an old axiom in philosophy which runs thus: The greater the extension, the smaller the comprehension; or The smaller the comprehension, the greater the extension; or Widen the extension, and you diminish the comprehen- sion; or Expand the comprehension, and you narrow the extension. All mean the same thing. But what do they mean? 59. Extension. The extension of an idea or a term refers to the number of individuals to which it can apply. 60. Comprehension. The comprehension of an idea or of a term refers to the number of ideas or terms implied in said idea or term. 61. Illustration. Take the idea, animal It can apply to — that is, it extends to all individuals in which there is animal nature. But combine it with the idea rational, so as to have rational animal, or man. At once you shut out from its application all irrational animals. You cut them off from its extension. You narrow its extension. Why? Because you have ex- panded the comprehension. The idea man comprehends not merely animal but animal -)- rational. If you expand the comprehension by adding the term white, so as to have white man, you will diminish the extension by cutting off all men who are not white. And so on. Every new idea added represents a new requisite in the object that is to correspond. The more you require in the objects, the fewer will they be found. Once more take the term animal. What is its com- prehension? What ideas does it imply? It implies sensitive organic material substance. Diminish the com- prehension. Take away the term sensitive. You have 36 THE LAWS OF THOUGHT left organic material substance. At once you have widened the extension so as to take in the whole vege- table kingdom. Diminish comprehension again. Strike out organic. There remains material substance. The extension is widened so as to take in all that is matter whether organic or not. Diminish the comprehension again. Strike out material. Substance remains. The extension has been increased so as to reach into the spiritual world. Article VI. Extension of Propositions — Quality. Universal — Collective — Particular — Singular. 62. Extension. We have just spoken of extension in the abstract as contrasted with comprehension. In No. 19 we saw that the same idea could be used with varied compass within the entire range of its extension. It may be singular, particular, collective, universal. 63. The Subject. The extension of a proposition depends upon the extension or compass of the subject as used in the proposition. The proposition is named accordingly singular, particular, collective, universal. The following are examples. Singular: This man is virtuous. Particular: Some man is virtuous. Some men are virtuous. Collective: The crowd is orderly. Universal: Angels are spirits. 64. N. B. In speaking of terms and propositions we shall often not make a distinction between singular, col- lective and particular, but shall call them indifferently by the name particular as representing any term or proposition that is not universal. JUDGMENTS, PROPOSITIONS 37 65. The Predicate. To state clearly what we wish to say about the predicate, let us take four propositions, — two universal and two particular, — and let one of each kind be an affirmative proposition ; the other, a negative. This will give us, for instance, the following: 1. Cats are quadrupeds. (Universal Affirmative.) 2. Birds are not quadrupeds. (Universal Negative.) 3. This field is triangular. (Particular Affirmative.) 4. Some roses are not red. (Particular Negative.) 66. Universal Affirmative. The first proposition is universal, because its subject is universal, i.e. taken in its entire extension. As to the predicate, quadruped, we do not directly allude to its extension. We merely assert that the idea quadruped enters into the comprehension of the idea cat. And as cat here is universal, taking in each and every cat, we do state that quadruped is at least coextensive with cat. But we do for a fact know that quadruped has a wider extension than cat, that cat covers only a part of the extension of quadruped. Only some quadrupeds are cats. Hence, when we speak according to our knowledge and say that all cats are quadrupeds, we wish to say that some quadrupeds are cats or the idea, cat, extends to some individuals not to all individuals in the extension of quadruped. Quadruped, therefore, in the discussion of the proposition is to be regarded as a particular term. As these remarks hold good for all universal affirmative propositions (one class excepted), we formulate the law: The Predicate in a universal affirmative proposition is a particular term. 67. One Exception. The one exception is, when the predicate is the exact essential definition of the subject. Thus in the proposition, Man is a rational animal, the 38 THE LAWS OF THOUGHT predicate, rational animal, is the essential definition of the subject, man. It is synonymous with man. Hence it is precisely coextensive with the subject. We can say, Man is a rational animal, or Rational animal is man. But though we say, Cat is quadruped, we cannot say, Quadruped is cat. Quadruped may be tiger or elephant. Rational animal, however, cannot be anything but man. 68. Universal Negative. In the second proposition, Birds are not quadrupeds, the subject is universal, and hence, too, the proposition. By denial we separate the idea quadruped from the comprehension of the idea bird. So that wherever the idea bird is applicable, in its entire extension, there the idea quadruped is excluded. Now, knowing that quadruped can have its own extension, the proposition implies that bird and quadruped extend to two distinct classes of individuals. To say that birds are not quadrupeds is the same as saying that no individual bird is a quadruped. Not one bird can be found in the class quadruped. Not one quadruped can be found in the class bird. If it could, some bird would be a quad- ruped. What is this but to exclude quadrupeds in its entire extension, that is, as a universal, from the entire extension of the subject? As the same remarks hold good for all universal negative propositions, we formu- late the law : The Predicate in a universal negative prop- osition is a universal term. 69. Particular Affirmative. In the third proposi- tion. This field is triangular, the subject is particular. Hence the proposition is particular. Referring to our knowledge of things, we shall find that the predicate, triangular, is used in a particular sense. We do not predicate of this field all that is or may be triangular, the JUDGMENTS, PROPOSITIONS 39 entire extension of triangular; but only this particular case of triangular. This field is one of the things em- braced in the extension of triangular. Triangular, hence, is used in the particular sense. These remarks hold good for every particular affirmative proposition. Hence the law: The Predicate in a particular affirmative proposi- tion is a particular term. 70. Particular Negative. In the fourth proposition, Some roses are not red, the extension of the subject, only some roses, is particular. Hence the proposition is par- ticular. The predicate red, however, is used in the uni- versal sense. We affirm that redness is not found in the comprehension of some certain roses. No one of these some certain roses is to be found in the entire extension of things that are red. We separate the entire extension of things that are red from these some certain roses. Hence, in our denial of red as applicable to some roses, we use it in its entire extension, or as a universal. These remarks hold good for every particu- lar negative proposition. Hence the law: The Predi- cate in a particular negative proposition is a universal term. 71. Two Laws. Now let us put the four laws to- gether and make two of them. The first and third will give us this : The predicate in an affirmative proposition is used as a particular term, i.e. according to part of its extension. The second and fourth law will give us this : The pred- icate in a negative proposition is used as a imiversal term, i.e. according to its entire extension. 72. Affirmative and Negative. We have not thought it necessary to state explicitly heretofore that every 40 THE LAWS OF THOUGHT proposition must be either affirmative or negative. For all needs, up to the present, this was sufficiently implied in the definitions of judgment and proposition. 73. Negative Particle. We call attention now to the fact that, in the negative proposition, the negative particle need not necessarily stand between the subject and the predicate. To say. Birds are not quadrupeds, is the same as saying, No bird is a quadruped. Both are negative and are understood as such. We have not to question the arbitrary constructions of language. Still be it understood that, in order to have a negative proposi- tion, the language must be capable of such construction that the negative particle not may be construed with the copula, is, are, so as to form with it one piece that shall be, not as a link between subject and predicate, but as a wall of separation. This is the case in the example given above. But the following proposition is affirma- tive: Not to complain in adversity is a mark of a great soul We may indeed say. To complain in adversity is not a mark of a great soul; but the two propositions are not identical in meaning, for we turn the predicate from a particular into a universal. However, we may say, A mark of a great soul is not-to-complain-in-adversity. Here the negative particle, though next to the copula, is, does not form one piece with it : it forms a piece of the predicate. The proposition is affirmative. 74. Quantity and Quality. The extension of a proposition, universal, particular, etc., is referred to as its quantity The form, affirmative or negative, is re- ferred to as its quality. JUDGMENTS, PROPOSITIONS 41 Article VII. Related Propositions. Conversion — Equivalence — Opposition. 75. Three Relationships. We now pass on to con- sider the relations that may exist between certain prop- ositions. The relation between two propositions — iwhen there is any relation at all — will be one of convertibility, of equivalence or of opposition. 76. Conversion. A proposition is said to be con- vertible into another when the subject can be made predicate and the predicate subject without loss of truth in the new proposition. Thus the proposition, No man is an angel, is convertible into No angel is a man. There are three ways of converting propositions. We may keep the quantity and quality unchanged; or we may change quantity only; or we may change quality only. The first called simple conversion; the second, conversion per accidens; the third, conversion by contraposition.. Without minding these traditional names, we shall ex- emplify the three conversions. Quantity and quality unchanged. This conversion may take place in propositions where subject and predicate are both universal or both particular — that is, in universal negative and particular affirmative; as also, in propositions where the predicate is the essential defini- tion of the subject, since the two are coextensive. Thus, No man is an angel is convertible into No angel is a man. This field is square is convertible into This square thing is a field. Man is a rational animal is convertible into The rational animal is man. Quantity changed. This kind of conversion may be applied to universal affirmative and universal negative 42 THE LAWS OF THOUGHT propositions. In the universal affirmative, All plants are substances, the predicate is particular. If we make it subject, we have Some substances are plants. The uni- versal negative, No man is an angel, we saw above may be converted into No angel is a man. This being uni- versal, applies to each individual in the extension of the subject; hence we have, This angel is not a man. Quality changed. This kind of conversion may be used upon the universal affirmative and the particular negative. The universal affirmative. Cats are quadrupeds, tells us that cats are altogether within the extension of quadruped. Outside of the extension of quadruped, cats are not to be looked for. Hence the proposition is convertible into What is not quadruped is not a cat. In the particular negative, Some roses are not red, red is universal in its extension. Hence outside of the exten- sion of red there are some roses; or, Some things not red are roses. 77. Equivalence or EquipoUence. A proposition is said to be equivalent to (equal in value) or equipollent with (equal in weight) another when it means the same thing as the other, there being no conversion of subject and predicate. A proposition is turned into its equipollent in various ways by the use of the negative particle. Thus, Every man is mortal is equivalent to No man is not mortal, etc. 78. Opposition. To explain what is meant by oppo- sition, let us take the universal affirmative proposition, Every man is just. In order merely to contradict this it would be sufficient to say. Some man is not just. Now take the universal negative proposition. No man is just. To contradict this it is enough to say, Some JUDGMENTS, PROPOSITIONS 43 man is just. We have in both cases an opposition be- tween a universal and a particular, an affirmative and a negative. There is opposition in both quantity and quality. The opposition is one of contradiction. Propo- sitions so related are called contradictories. Eoth cannot be true, simultaneously; nor can both be false, simulta- neously. If it be true that all men are just, then it is false that some man is not just. Opposition in quality only. When two universal prop- ositions are opposed in quality, i. e., one being affirm- ative, the other negative, as, All men are just and No man is just, there is not merely a contradiction of a sweeping statement. There is a sweeping statement to the contrary. The contradiction covers each individual in the extension of the opposite proposition. The oppo- sition is one of contrariety. The propositions are called contraries. Both cannot be true at the same time, be- cause each one contradicts every individual case of the other. However, both may be false. They may both claim too much in opposite directions. The particular propositions implied in these two uni- versal, that is, the particulars. Some man is just and Some man is not just, as opposed to one another in quality, are called sub contraries. Both may be true, since their contradictories, the universals, may both be false, may both assert too much. Both particulars, how- ever cannot be false; for if both were false, then their contradictories, the universals, would both be true. Opposition in quantity only. This is the opposition between a universal and particular affirmative or a universal and particular negative, as. All men are just and Some man is just; or No man is just and Some man is not just. There is in reality no opposition here. 44 THE LAWS OF THOUGHT The particular is implied in the universal. It is a subaltern of the universal. Hence, for the sake of a name, propositions so related, the universal and its implied particular, are called subalterns. If the uni- versal is true, the particular is true. If the universal is false, the particular may still be true. So, the truth of the particular does not imply either the truth or falsity of its universal. But if the particular is false its universal is false. 79. Diagram. Now look at the following diagram: Contrary. 1. All men are just {Univ. Aff.). 2. No man is just {TJniv. Neg.) . C ^' ^ X ^ 3. Some man is jnst {Part. Aff.). 4. Some man is not just {Part. Neg.). SUBCONTRARY. 1 and 2 are contraries; 3 and 4 are subcontraries ; 1 and 4, also 2 and 3, are contradictories ; 1 and 3, also 2 and 4, are subalterns ( 1 and 2 being called subalternant, 3 and 4 subalternate). It is clear that if 1 is true, 3 is true; and that if 2 is true, 4 is true. But we cannot conclude from 3 to 1 nor from 4 to 2. 1 and 4 cannot be both false. One must be true, and the other false. The same is to be said of 2 and 3. 3 and 4 may be both true, or one true and the other false. Both cannot be false. CHAPTER IV. REASONING, ARGUMENT. Article I. The Syllogism. Argument — The Syllogism — Analysis of Argument — Middle and Extremes. 80. Reasoning and Argument. We have seen how the idea is the element of the judgment, and thus the term, the element of the proposition. We have now to see how an argument is constructed out of propositions. We defined Reasoning (11) to be an act, or a series of acts, by which the mind compares the truths expressed by two judgments, and in that comparison perceives implied a third truth, which it accordingly expresses mentally in a third judgment. This process, we s-iid, regarded as mere mental working, is called reasoning. Regarded as knowledge contained in the third judgment, pronounced as having been implied in the two others, we called it inference or argumeni The propjsiiions which, taken together, represent in Ir^nguage the knowl- edge and its process, we also called argument. We shall use the word argument in this latter sense. 18. Styles of Argument. There are indeed many combinations of propositions which are used as language- representations of the process of reasoning, many styles of argument. Different names are given to them, accord- in to the variety of structure. We have the Syllogism, the Enthymeme, the Sorites, the Poly syllogism, the Epi- chirem, the Dilemma. All, however, are reducible to the 45 46 THE LAWS OF THOUGHT syllogism, which is the nearest approach language can make towards exhibiting the working of the mind in reasoning. Not that we always, or usually, argue, in speaking or writing, with completed syllogisms. We abbreviate. However, we must study the syllogism in its completeness. We begin with it. A few words at the end of this chapter will then suffice to explain the other styles of argument. 82. The Syllogism. The syllogism is an argimient made up of three propositions so connected that if the first two be admitted, the third must, likewise, be ad- mitted. Thus, Every plant is a substance ; But the verbena is a plant. Therefore, The verbena is a substance. 83. Antecedent; Consequent; Premisses. The first two propositions taken together are called the ante- cedent. The third proposition is called the consequent. In the antecedent the evidence is stated. In the conse- quent the verdict is given. The two propositions of the antecedent are commonly called premisses (put before). The first is called the major premiss; the second, the minor premiss. For brevity's sake they are styled the major and the minor. The original meaning of major and minor, and the reason for the use of the terms, will be explained in the next article. 84. Consequence. If the consequent does really fol- low from the premisses, we have what is called a conse- quence, by which we mean that the assertion contained in the consequent is a consequence of what was laid down in the premisses. If an argument is proposed to REASONING, ARGUMENT 47 US in which the consequent does not follow as a conse- quence, the argument must be regarded as faulty. Hence, (a) If both the premisses be true, and the argument be rightly constructed, the consequent, called also the conclusion, must be true: the consequent must be ad- mitted. (b) The conclusion, or consequent, may indeed be a true proposition, as stated, and taken by itself ; and still, on account of a flaw in the structure of the argument, it may not really follow from the premisses. In this case we may admit it as an independent proposition. We admit the consequent, but we deny the consequen.ce. 85. Axioms. We repeat here two axioms stated in No. 11. They are the bases upon which every argu- ment must rest. If the conclusion is an affirmative proposition the argument rests upon this axiom: In the sense in which two things are the same as a third thing, in the same sense are they the same as one another. If the conclusion is a negative proposition, the argument rests upon this axiom : In the sense in which two things are, the one the same as a third thing, the other differ- ent from it, in the same sense are they different from one another. ' 86. Analysis of Argument. Now look at the argu- ment given above, namely : A ^ ^^^ fEvery plant is a substance (Major Premiss). Antecedent -<_■:. . . ,\^' t^ • x tBut the verbena is a plant {Minor Fremiss). Consequent or r Therefore, the verbena is a substance (Con- CoNCLUSiON \ sequence). 48 THE LAWS OF THOUGHT You will find 1. That it contains but three terms, — plant, substance, verbena. 2. That one of the terms, plant, occurs twice in the premisses, — once in the major, and once in the minor. 3. That the two other terms, substance, verbena, occur each once in the premisses, one in the major, and one in the minor ; and that they both occur in tlie con- clusion 4. That the term plant is not found in the conclusion. 5. That thus each term occurs twice in the argument. 6. That the term plant, which occurs twice in the premises, is there compared with the two others; with one in the major, with the second in the minor. 7. That a certain relationship having been discovered, in the premisses, between verbena and substance, by means of the aforesaid comparison, this relationship is declared in the conclusion. 87. Middle and Extremes. The term that is used as a standard of comparison between the two others is called the middle term; or for brevity, the middle: the two others are called the extreme terms or the extremes, one the major and the other the minor extreme. We shall have to speak of this subject presently. Article II. Figures and Moods of the Syllogism. Major and Minor Premiss — Major and Minor Extreme — Middle Term. 88. Major; Minor; Middle. We spoke, in the last article, of major and minor premiss, major and minor extreme, and of the middle. We called the first premiss REASONING, ARGUMENT 49 the major, and the second premiss the minor, and we shall continue to call them so. But the first premiss is not always really the major, in the original meaning at- tached to the word; nor in the same original meaning, is the second always the minor. According to the orig- inal use of the words, the major premiss is the premiss in which the middle is compared with the major extreme; and the minor premiss is the one in which the middle is compared with the minor extreme. The major ex- treme is the one whose extension is greater than that of the middle. The minor extreme is the one whose exten- sion is less than that of the middle. This is how the middle came to be called middle; because, its extension is between the extensions of the two other terms. There is only one style of syllogism in which the mid- dle is a real middle, as just explained. This is in the most obvious style of construction of the syllogism (No. 89) ; and it is from this that the names have grown into common use, and are applied to all syllogisms, in the same way, regardless of construction. We call the premises put first, the major; that put second, the minor: and we never speak of the extremes as major and minor. This leads to the question of figures of the syllogism. By Figures are meant merely the various combina- tions of the extremes with the middle, in the premisses. 89. First Figure. The First Figure is the one that we have just spoken of. In this, the middle is made the subject of the premiss containing the major extreme, and this premiss is placed first: it (the middle) is made the predicate of the premiss containing the minor extreme, and this premiss is placed second. Thus : 50 THE LAWS OF THOUGHT Animals are living beings; (Major Premiss.) But lions are animals. (Minor Premiss.) Therefore, Lions are living beings. Here the middle, animals, has less extension than living beings (major extreme), and greater extension than lions (minor extreme). The following squares will show how one is included in the extension of the other, and how easily the argument proceeds on that account. LIVING BEINGS ANIMALS LIONS Minor Extreme Middle Major Extreme As our argument was stated, we proceeded within the extension of living beings to find animals, and then within the extension of animals to find lions; thence to conclude that lions were within the extension of living beings, and that living being could be predicated of lion. The minor premiss might be placed first, and the major premiss second. Thus : Lions are animals; But animals are living beings. Therefore, Lions are living beings. In this, we proceed from the minor extreme up through the middle to the major extreme. REASONING, ARGUMENT 51 90. Second Figure. We remark, again, that out- side of the First Figure, what we call middle is really not a middle, in the true sense, but only in the sense that it is taken as a term of comparison between two other terms. Still we keep the name, middle; and the other terms are called simply the extremes. In what we call the Second Figure, the middle term is used as predicate in both premisses. Thus: Therefore, Every man is mortal; No angel is mortal. No angel is a man. Here mortal is the middle. Man is truly minor with reference to mortal. But we cannot say that Angel is major with reference to mortal. Angel is simply ex- cluded by, and excludes, mortal, and hence, excludes the minor contained in mortal. MORTAL MAN ANGEL 91. Third Figure. In what we call the Third Fig- ure the term of comparison is the subject of both the first and second premiss. Thus: Therefore, Every plant is substance; Every plant is material. Some substance is material. 52 THE LAWS OF THOUGHT Here the term plant has less extension than either of the other two. The meaning of middle is lost. The extremes are both major. i5\ PLANT - \ Both substance and material cover the extension of plant, and hence partly coincide, i.e. at least to the extent of plant. This will suffice on the subject of Figures. What we have to remember is' this, that in practice the premiss which stands first we shall call major ; the premiss that stands second, minor; the term that is used as the standard of comparison, middle; the two other terms, extremes. 92. Moods of the Syllogism. By moods of the Syl- logism are meant the various combinations that may be made in the premisses, of universal, particular, affirma- tive and negative propositions. We should derive no practical utility from a discussion of the sixty-four possible combinations, few of which give a correct REASONING, ARGUMENT 53 argument. For the sake of a completeness, which is not necessary, we subjoin the following remarks on figures and moods. 1. There is a Fourth Figure, which is little used, and which it is well to avoid in argumentation. In it the middle is made predicate of the major proposition and subject of the minor. Every tree is organic ; Everything organic is substance. Therefore, Some substance is a tree. This, it will be noticed, is the same as the First Fgure with the position of subject and predicate inverted in the conclusion, and the proposition accordingly changed from the universal. Every tree is a substance, to the implied particular. 2. If now we take the four kinds of propositions, Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative, and make all the possible combinations of them that can be made in each of the Four Figures, we shall find that there are sixteen possible combinations in each figure, or sixty four in all, — simply regarding the position of the middle and taking no account of the validity of the conclusion. These sixty-four combinations are called the Moods of the Syllogism. If we take into account the validity of the conclusion as proceeding from the premisses, we shall find that only nineteen of the sixty- four combina- tions make correct arguments. These nineteen Moods are thus distributed: 4 in the First Figure; 4 in the Second; 6 in the Third; and 5 in the Fourth. We shall be able to decide upon the correctness of any combination from the laws of the syllogism which follow. 54 THE LAWS OF THOUGHT Article III. Laws of the Syllogism. 93. Scope of the Laws. We are now prepared to formulate the laws which must govern the construction of the correct syllogism. These laws have reference to the number of terms, the extension of terms, the place of the middle term, the quantity and quality of premisses and conclusion. 94. First Law. Three Terms. There must he three, and only three, terms, and they must be only three in meaning. This is evident from what has been said : that the conclusion of a syllogism is simply a declaration of identity or difference between two terms (objectively), which identity or difference was implied by the compari- son of these terms (objectively) w4th a third term in the premisses. It is not enough, therefore, to have the terms three in mere sound or written appearance. They must be three in meaning (objectively). Our reasoning is not upon sounds of the voice or upon printed letters ; it is upon that which is represented both by the idea and by the spoken and written word. If we say : Stores are warehouses, Stores can be eaten, Therefore, Warehouses can be eaten, we have three terms in sound and writing; but we have four in meaning; and thus there is no syllogism. If we say : Eye is the organ of sight, I is a personal prounoun, Therefore, The organ of sight is a personal pronoun, REASONING, ARGUMENT 55 the terms are three in sound, but four in meaning, as in writing. There is no syllogism. If we say: Andrew Jackson is one of the Presidents, Franklin Pierce is one of the Presidents, Therefore, Andrew Jackson is Franklin Pierce, we have four terms, in meaning; because, One-of-the- Presidents is taken in two different particular senses. 95. Second Law. Extension of Extremes. Neither extreme may have a greater extension in the conclusion than it had in the premisses. This is a consequence, or an application, of the first law. For if a term in the conclu- sion embraces more individuals than it did in the prem- isses, it is really a fourth term, because it stands for something not meant in its first use. In the following. Tobacco is a plant. Tobacco is narcotic. Therefore, Plants are narcotic, the term plant, as predicate of an affirmative proposi- tion in the major, is a particular term; whilst, in the conclusion, as subject of the universal proposition, it is taken according to its entire extension. There are four- terms: hence no syllogism. 96. Third Law. Extension of the Middle Term. The middle term must be used once, at least, according to its entire extension, i.e. as universal. The reason : for if it be twice a particular, each use may embrace totally different sets of individuals, totally distinct sections of the entire extension. This would give two different meanings for the middle, and hence, four terms. If we say: 56 THE LAWS OF THOUGHT Tigers are animals, Lions are animals, we may not conclude Therefore, Lions are tigers. The middle term, animals, is twice particular, covering distinct sections of the entire extension, animals. It is really two terms. An objection. How, then, can the middle term be used once universally, and once particularly? Will not this give us four terms? No; because what is said of the term taken universally, i.e. standing for all individ- uals, and for each and every individual in the extension, can also be said of this or that individual taken sepa- rately. An example: Spirit is indivisible; The soul is spirit. Therefore, The soul is indivisible. In the major, spirit is universal. We say that all spirits are indivisible; hence, that each particular spirit is indivisible. In the minor, we simply call one particu- lar spirit by its name. In the major we said any spirit. In the minor we make the choice that has been offered us directly in the major. There are only three terms. Of course the middle may be used twice universally with both premisses affirmative or with one affirmative. Thus: All fishes are sensitive; All fishes are shy. Therefore, Some things sensitive are shy. REASONING, ARGUMENT 57 or, All fishes are sensitive; No fishes are men. Therefore, Some things sensitive are not men. In each case the conclusion is particular. 97. Fourth Law. Place of the Middle Term. The middle term mvist not he found in the conclusion. This is evident from the nature of the syllogism. Two terms are compared, separately in the premisses, with a third term, in order that their identity, or disparity, may be expressed in the conclusion; the middle term being rejected, after its use as a standard of comparison. 98. Fifth Law. Affirmative Conclusion. Two affir- mative premisses demand an affirmative conclusion. For if, in the premisses, we implicitly affirm the identity of the extremes, we cannot deny that identity, explicitly, in the conclusion. 99. Sixth Law. Negative Conclusion. One premiss affirmative and one premiss negative demand a negative conclusion. For, in the premisses, we implicitly deny identity between the extremes, by declaring that one is identical with the middle, and that the other is not. Hence we have but to deny their identity, explicitly, in the conclusion. 100. Seventh Law. No Conclusion. From two negative premisses we can draw no conclusion. If we say, Scipio is not a carpenter, Scipio is not a Russian, there is no conclusion to be drawn. We have done nothing but to place Scipio outside the extension of the 58 THE LAWS OF THOUGHT two extremes; but there is nothing from which to infer whether there be, or be not, Russians among the car- penters, or carpenters among the Russians. All we can Carpenters Russians say is what has been affirmed explicitly, that Scipio is neither a Russian nor a carpenter. The same holds if the premisses are two negative uni- versal propositions. All the terms will be universal. The middle term, in its entire extension, will be outside the entire extension of each extreme. No star is a elephant ; No elephant is a wheelbarrow. No Conclusion. 101. Eighth Law. No Conclusion. From two par- ticular premisses we can draw no conclusion. For they will be either, 1, both negative; or 2, both affirmative; or 3, one affirmative and one negative. First case: both negative. This is settled by the seventh law. Second case: both affirmative. In this case the sub- jects are particular, as we have particular propositions ; and the predicates are particular because the proposi- tions are affirmative (No. 71). Hence the middle term is not taken once universally, and the third law is broken. Third case: one affirmative and one negative. Then, according to the sixth law, the conclusion will have to REASONING, ARGUMENT 59 be negative. The predicate of the conclusion will thus be universal (No. 71). As this predicate is one-of the extremes, it must, by the second law, be universal in the premisses. But in the. premisses there is only one place for a universal term ; that is, as predicate of the negative premiss. The particular affirmative premiss cannot have a universal term, and the subject of the particular nega- tive premiss must be particular. Now if this one place in the premisses where a universal term can be, be taken by one of the extremes, the middle term will not be, cannot be, used universally at all. Hence this third case is an impossibility, and the eighth law holds. We must here make an exception for the case where both premisses are singular. In this case there may be a conclusion. Thus: Mars is a planet; Mars is uninhabited. Therefore, One planet is uninhabited. The reason is that the term. Mars, being applicable to one individual only must be used in its entire exten- sion, and hence, as subject in both premisses, has the value of a universal: so that the two premisses may be treated as universals. 102. Ninth Law. Particular Conclusion. // one premiss be particular, the conclusion must be particular. Of course, by the eighth law, one premiss must be uni- versal. The possible cases with one premiss universal, and one particular, are: 1. With both premisses affirmative; 2. With one premiss affirmative, the other negative; and in the second case we have an alternative. We may take a universal affirmative and a particular nega- 60 THE LAWS OF THOUGHT live; or we may take a universal negative and a par- ticular affirmative. 1. Making both premisses affirmative, we shall have, Universal Affirmative )with subject universal and predicate particular) ; Particular Affirmative (with subject particular and predicate particular). There is but one place for a universal term. This must be for the middle {Third Law), The extremes are both particulars in the premisses. Hence the subject of the conclusion must be particular {Second Law) ; and the conclusion, a particular proposition. 2. Making one premiss negative and one affirmative, we shall have either Universal Affirmative (with subject universal and predicate particular) ; Particular Negative (with subject particular and predicate universal). Or, Universal Negative (with subject universal and predicate universal) ; Particular Affirmative (with subject particular and predicate particular). In either case there are two places for a universal. One place must be for the middle {Third Law). The other place will be for the extreme which is predicate of the conclusion; the conclusion being negative, since one premiss is negative. The subject of the conclusion must therefore be an extreme, used particularly in the premisses. It must be particular in the conclusion {Second Law), and will make the conclusion a particular proposition. REASONING, ARGUMENT 61 103. Caution. Here we leave the laws of the syllo- gism Certain correct syllogisms may be adduced which may seem to contravene the laws. But if the propo- sitions of the syllogisms thus presented be examined, it will be seen that certain propositions, apparently particular, are really universal ; and certain propositions, apparently negative, are really affirmative, or vice versa. But let it be kept in mind that we reason not with mere words as they sound or appear on paper, but with what they stand for; and words, by tricks of grammar, may be made to obscure a thought in the presentation. In the same way, syllogisms with ill-drawn conclusions may be made to appear in keeping with the laws. But study the sense of the propositions. Article IV. Some Species of the Syllogism. Conditional — Conjunctive — Disjunctive. 104. Simple and Compound Syllogisms. We have hitherto, for the sake of clearness, given examples of syllogisms composed of simple categorical propositions only. Such syllogisms are, as their component proposi- tions, called simple. One compound premiss is sufficient to make the syllogism compound and equal to as many simple syllogisms as there are simple categorical propo- sitions compounded into that premiss. We do not pro- pose to treat of compound syllogisms. We should never end. Attention is called here to three complexities in the syllogism, to which we alluded in No. 49. 105. Conditional Syllogisms. In these the major is a conditional proposition (46) ; for instance, this, // they 62 THE LAWS OF THOUGHT are studying logic, they are training their minds. The first member of the conditional proposition is called the condition; the second, the consequent. The minor may affirm the condition categorically: They are studying logic. Then the conclusion must affirm the consequent cate- gorically : They are training their minds. Or the minor may deny the consequent: They are not training their minds. Then the conclusion denies the condition: They are not studying logic. Note. 1. The denial of the condition will not necessitate the denial of the consequent. This (the consequent) may be true for other reasons. In the present instance they might be studying grammar or geometry without logic; and they would still be training their minds. 2. Hence affirmation of the consequent does not always neces- sitate affirmation of the condition. There may, as we said, be other conditions from which it (the consequent) would follow. They may in the present instance be training their minds by studying other matters than logic. 106. Conjunctive Syllogisms. In these, two incom- patible propositions are proposed in the major by means of a conjunctive proposition (47). The minor denies one, and the conclusion affirms the other. Example: No man can spend all his money on drink and still support his family; But he spends all his money on drink. Therefore, He does not support his family. REASONING, ARGUMENT 63 What we said about looking into the meaning of the proposition and not being deceived by tricks of construc- tion is of service here. The conjunctive proposition is really equivalent to a conditional, thus, // a man spends all his money on drink, he is unable to support his family; and with regard to affirmation and denial of condition and consequent must be treated as such. 107. Disjunctive Syllogisms. In these the major puts all the alternatives of a case in the disjunctive prop- osition (48). If the minor makes choice of one, the conclusion will be the denial of all the others. If the minor denies all but one, that one will be affirmed in the conclusion, etc. Example : He is either just fifty or under fifty or past fifty; But he is just fifty; Therefore, He is neither under fifty nor past fifty : Or But he is neither under fifty nor past fifty ; Therefore, He is just fifty : Or But he is not just fifty ; Therefore, He is either under fifty or past fifty. In the last casfe, as we have three possibilities, and the minor denies one only, the two others remain as a dis- junctive proposition in the conclusion. This form of syllogism may also be reduced to the conditional with one member positive and the other negative. // he is under fifty, he is neither just fifty nor past fifty. The disjunctive syllogism is useful in controversy and investigation. But it is, at the same time, capable of treacherous application for the spread of error in history and physical science, by the use of disjunctive majors which are not complete. The disjunction should state 64 THE LAWS OF THOUGHT all the possibilities of the case. The members should have marked lines of division, and not run into one another. All the members may not be true; neither may all be false. Article V. Other Styles of Argument. Enthymeme — Sorites — Polsyllogism — Epichirem — Dilemma. 108. Argument Abbreviated. We said (No. 81) that when we write and speak we do not always, nor even usually, carry on an argumentation with completed syllogisms. We abbreviate. The various methods of abbreviation give us various styles of argument, which have, respectively, their proper names. 109. Enthymeme. If we drop one premiss in the syl- logism, the argument is called an ethymeme. Example: All liquids flow; Therefore, This tar will flow. We have dropped one evident premiss, this tar is liquid, to avoid being tiresome. Enthymeme originally meant a probable argument; but, by a mistake as to its derivation, it came to be applied to the argument where one premiss is kept in the mind. In this sense alone is the word now used. 110. Sorites. (Piled-tip argument.) When we put down three or more premisses and, then, one conclusion following from them, the argument is called a Sorites, It abbreviates by dropping intermediate conclusions. It presumes the evidence of the conclusion after the first two premisses, and adds a third premiss as a minor to REASONING, ARGUMENT 65 the second premiss considered as a major; then a fourth premiss as a minor to the third premiss considered as a major, etc. Thus: He who desponds ceases to labor; He who ceases to labor makes no progress; He who makes no progress does not reach the end. Therefore, He who desponds does not reach the end. It is easy to see that this is an abbreviation of two syllogisms. Thus : He who desponds ceases to labor; He who ceases to labor makes no progress. Therefore, He who desponds makes no progress. The next syllogism begins with this conclusion as a major : He who desponds makes no progress; He who makes no progress does not reach the end. Therefore, He who desponds does not reach the end. As the Sorites involves so much argument, and pro- ceeds so rapidly, we must be cautious with an adversary who uses it. The sorites may be drawn out to any length. Each implied syllogism must observe the laws of the syllogism. 111. Polsyllogism. If we argue with a chain argu- ment, as in the Sorites, but in such a way that we bring out the intermediate conclusions, not explicitly twice as above, but once, to be used, simultaneously, as conclusion 66 THE LAWS OF THOUGHT to the two preceding premises, and as major to a fol- lowing minor, our argument is called a Poly syllogism. The preceding example, as a polysyllogism, will be: He who desponds ceases to labor; He who ceases to labor makes no progress. Therefore, He who desponds makes no progress; He who makes no progress does not reach the end. Therefore, He who desponds does not reach the end. 112. Epichirem. If a premiss, or even each premiss, requires proof, and the proof is attached to it immedi- ately, whether in substance or in full, the argument is called an Epichirem {taking in hand the doubted premiss at once). Example: One who denies the existence of God and a future life cannot be trusted in society; because he ad- mits no motive to restrain him from evil when he can do the evil without temporal inconven- ience. But the atheist denies the existence of God and a future life. Therefore, He cannot be trusted in society. 113. Dilemma. The Dilemma is a double argument in the compass of a single syllogism. It may be even triple, quadruple, etc. The major is a disjunctive prop- osition. The minor takes up each member of the dis- junction, separately, and an equally satisfactory conclu- REASONING, ARGUMENT 67 sion is drawn from whichever member is chosen. Thus a schoolboy might argue, to escape his evening study: To-morrow morning it will be either raining or not raining. If it be raining, I will have an excuse to stay at home. If it be not raining, I can use my per- mission to take a day at the fair. Therefore, Whatever the weather may be, I shall not have to go to school; and hence I need not study my lessons to-night. ^ The Dilemma is sometimes a very useful form of argument for a summary refutation of false theories. CHAPTER V. TRUTH OF THE PREMISSES. Article I. Formal and Material Logic. 114. The Form. We have seen what is required in the quaUty and quantity of the premisses, and in the extension of middle and extremes, in order that a given conclusion may be taken as lawfully drawn from given premises. If I say. Every steamboat is a sunflower, Every sunflower is a violin, Therefore, Every steamboat is a violin, and suppose the premisses to be true, I have to accept the conclusion, inevitably, from the premisses. The conclusion is in perfect accord with all the laws of the syllogism. All that formal logic has shown us to be necessary in quality, quantity and extension has been . — supposing the premisses true — strictly attended to. Yet every proposition in the strange argument is false. This leads us to speak of the matter of the premisses, as affecting the acceptance of the conclusion. We shall say something, therefore, on the truth of the premisses. It may be urged that the subject does not belong strictly to the formal logic. The formal logic has to deal, strictly speaking, only with the form, or structure, of argument necessary to have a conclusion rightly drawn from pre- misses; — the matter, or truth, of the premisses being left out of consideration. And for this reason is it called 68 TRUTH OF THE PREMISSES 69 formal logic. By this is it distinguished from material logic. 115. The Matter. Material logic will teach us what care must be taken in the use of the various means we have of arriving at the truth, that is in the use of our various faculties; and when we may cease examining, and rest reasonably secure in mind as to the truth or falsity of what is expressed in a proposition. So that, if we should meet w4th a syllogism such as the following, Every timepiece is made of brass, All brass is organic matter, Therefore, Every timepiece is made of organic matter, material logic would have to tell us how to use our faculties, — that is, how far to trust the various faculties — in our search for truth in the propositions. It is only when we have decided as to how far we are to admit the propositions that the work of formal logic begins. Nevertheless, we begin the study of philosophy with formal logic, because we have had so much practical experience in the use of our faculties, that we already hold securely that many propositions are true, many others false, and many, again, doubtful; and we want, at once, a safe and systematic rule for arguing from the known to the unknown. Therefore we study formal logic first. However, we shall here make a short consideration upon the truth and falsity of the premisses, and upon the corresponding adhesion of mind which we can give to the conclusion. Yet we shall do this in such a way as not to touch the question of the means we have for arriving at the truth. 70 THE LAWS OF THOUGHT 116. Value of the Conclusion. We cannot hold to the conclusion any more firmly than we hold to the prem- isses. Supposing the form of the syllogism to be correct, if we are certain of the truth of the major and minor, we may be certain of the conclusion. If we have a lingering doubt as to the truth of either major or minor, that doubt will cling to the conclusion. If either major or minor be false, the conclusion is false ; and the argument is called a sophism or a fallacy. Sophism or fallacy is in the matter, not in the form. A defect in the form is called a paralogism. This has been abundantly treated in the preceding chapter (Nos. 80-102). When the major and minor are both truths of which we are certain, the argument is called a demonstration. Leaving aside the probable argument, we shall treat of the demonstration and of fallacies. Article II. The Demonstration. Direct — Indirect — Simple — Compound — A Priori — A Posteriori. 117. Two Kinds. A demonstration is an argument in which the conclusion is drawn from premisses of whose truth we are certain. It may be direct or indirect; and either kind may be a priori or a posteriori. 118. Direct. In the direct demonstration we draw the conclusion we desire, directly from the premisses where we have compared its subject and its predicate with a middle term. Thus: The soul can think; Matter cannot think. Therefore, The soul is not matter. TRUTH OF THE PREMISSES 71 119. Indirect. In the indirect demonstration, in- stead of drawing our conclusion as coming dirctly from premisses in a syllogism, we show that the contradictory cannot be true, by exhibiting the absurd consequences that would follow from such contradictory. The indi- rect demonstration is of frequent use in geometry, where we show absurd consequences that would follow from not admitting the theorem laid down. 120. Simple; Compound. A demonstration is called simple when the whole argumentation is finished clearly and satisfactorily with a single syllogism. If, however, it be necessary to bring forward new syllogisms to prove the major or minor or both — which may not be clear, or may be called in question — and, perhaps, again, new syllogisms to prove the new majors or minors, the demonstration is called compound. All the longer theo- rems in geometry are illustrations in point. 121. A Priori. An argument is called a priori when it advances from premisses which state truths that are prior in the nature of things to the truth stated in the conclusion. Thus we may advance from what we know about the nature of a cause or agent, to establish some conclusion regarding the nature of the effect it may produce. The name a priori is used, also, for an argu- ment where we advance from principles in their wider extension to an application of the same principles in a less wide extension; as, for instance, from principles regarding the whole animal kingdom to conclusions respecting elephants and kangaroos. Likewise, when- ever we advance from principles to facts, as from the general truths about triangles to the exhibition of the truths applied in a particular given triangle. 72 THE LAWS OF THOUGHT 122. A Posteriori. The a posteriori demonstration proceeds in the opposite direction. It advances from what is posterior in the nature of things to what is prior in the nature of things. From the existence of an effect it concludes to the existence of a cause ; from the nature of an effect to the nature of the cause. It rises from a given fact to the principle that must explain the fact. We have an illustrious example of the a posteriori argu- ment in the discovery of the planet Neptune. After a quarter of a century of observations made upon the planet Uranus, discovered by Sir W. Herschel, it was found that its movement did not correspond with the known forces of gravity acting upon it, especially from Jupiter and Saturn. There was a fact: movement. The movement must have a cause. The cause must be a heavenly body. The movement was of such a character, said Leverrier, that if it came from a single heavenly body, that body, at a given time would be found in a given point of the heavens. The telescope is directed, at the given time, to the given point; and there is found the planet Neptune ! Article III. Induction. Complete and Incomplete Induction — Example — Analogy. 123. Deduction and Induction. We add here a spe- cial article about a peculiar kind of a posteriori argu- ment, which, by custom, has been allowed to appropriate, as it were, the name Induction. Every a posteriori argu- ment is, indeed, an induction, as opposed to the a priori argument, which is a deduction. Deduction means the TRUTH OF THE PREMISSES 73 drawing out of a particular proposition or conclusion from the universal premiss. Induction, on the contrary, is a leading back to the universal from the particular. Every process of thought from the particular to the universal is inductive. We wish to speak of induction, in the usual and limited acceptation of the word, as signifying an argument which passes from a uniform experience of several individual cases to a universal conclusion covering them all. The induction may be, as it is termed, complete or incomplete. 124. Complete Induction. The induction is called complete when after having really made an examination of all the cases of which there is question, and having found that the same proposition, varying only the sub- ject, is applicable to each case individually, we draw a conclusion in which we include them all in a single universal proposition. If, for instance, I, an American, step into a railway car and finding there five men. A, B. C, D, E, I discover gradually that A is an Ameri- can, that B is an American, that each of the five is an American, and conclude that all the men in the car are Americans, I go through the process of a complete induction. The complete induction is the exact reverse of a detailed deduction, in which, from the universal, that all the men in the car are Americans, I would conclude: A is an American, B is, G is, D is, E is, I am an American. We may sometimes think we have a complete induc- tion when, in reality, we have not. We are liable to overlook particular cases. Moreover, sometimes even when the greatest care is taken in the observation of facts in certain branches of the natural sciences, when 74 THE LAWS OF THOUGHT all the known facts have been classified under a general proposition, some new discovery will show that the general proposition is untrue, and that the induction was not as complete as it was believed to be. 125. Incomplete Induction. It is to the incomplete induction, which bears the name in the strictest sense, that we wish to call particular attention. It is a process by which, from experience of a limited number of cases, we pass on to formulate a universal law. Thus we formulate the laws of gravitation, of equilibrium, of re- flection, of refraction, from a very limited number of cases; and we hold these laws to be applicable, as universal propositions, to cases tried and untried. Is the process lawful? We inquire more particularly into the matter because some modern logicians, of the school of experimentalists, make the study of induction the chief business of logic. The process ef thought may be accepted as lawful, — the experiments having been rightly conducted, — but, upon one condition. The condition is, that we admit the reality of such a thing as cause. This very condition, which is absolutely necessary to the valility of the process of induction, is not accepted by the great champion of induction among the experimentalists, Mr. J. Stuart Mill. The process, then, is lawful if we admit true causality; namely, that whatever begins to be, depends for its exist- ence upon some real influence exercised by something else in bringing it about. In other words. Every effect demands a cause. Recognizing this, we may set to work with experiment and observation at the process of induction. If we find, by repeated test, that the same consequent follows the TRUTH OF THE PREMISSES 75 same antecedent constantly and uniformly in whatsoever circumstances or adjuncts of time, place, quality or rela- tion the antecedent may be tried, and in all the variations of circumstances by composition, opposition, etc. ; if we find, on the other hand, that, suppressing the one ante- cedent in question, whilst leaving all the circumstances and adjuncts the same, the said consequent does not make its appearance in any of the cases when the ante- cedent is so suppressed; if, again, varying the antece- dent, in the various cases, in quantity, intensity, direction, etc., we find that the consequent varies proportionally in quantity, intensity, direction, etc. ; in other words, if we find that said consequent follows said antecedent only, but always, and in regular proportion, — we are bound to recognize as really existing in said antecedent a certain power whereby it brings into existence the said conse- quent; and, also, in said consequent, a certain real dependence for its existence upon the antecedent. We perceive the two to be related as cause and effect. But yet more. We perceive that the antecedent is cause by reason of something inherent to its very nature ; for we have made our observations, tests, experiments, abstract- ing from it everything but its essential, inherent nature. But the essential, inherent nature of that thing must be present always where that thing is; the same yesterday, to-day, to-morrow. Hence we conclude that the same thing will produce the same effect to-morrow as to-day. We formulate a universal law which reaches to the future. Mr. J. Stuart Mill has, of all writers, written best upon the manner of making the tests for an induc- tion. But as he does not recognize the reality of cause, as he puts no real connection between foregoing and fol- lowing, his conclusion is universal only to the extent of 76 THE LAWS OF THOUGHT the tests actually made. What he builds up with one hand he tears down with the other. 126. Example. Allied to induction is what is some- times called the argument from example. It concludes to the universal from a few cases ; and, even, it may be, from a single case, without the tests and observations prescribed for induction. Its value is rather in discovery than in proof. A superior, well trained and vigilant mind will often suspect, and even detect, the universal law in a single case; but it will be necessary to go through the various tests, to make the law acceptable to the ordinary intelligence. In general use it is an argu- ment weak in point of logic. Logically, it suggests at most the possibility of a case. Jt is resorted to in ora- torical discussion. The orator has the advantage of forcing his listeners on without giving them time to examine, and urges them to act under the impression of a possibility. 127. Analogy. The argument from analogy is still less reliable, logically, than the argument from example. It is a pure figure of rhetoric, a parallel between two cases of quite different orders. It is useful to persuade an audience that cannot listen to dry argument, but can listen very well to a story, and then follow out the appli- cation of the story, in all its details, to the question under treatment. 128. Caution. In philosophical argument be wary in the use of example and analogy. It is so easy to give illustrations and to make comparisons. Therefore have we so many self-styled ''scientists," to-day, setting them- selves up as professional discoverers, and flying to con- clusions which the slow, careful processes of induction do not warrant. TRUTH OF THE PREMISSES 77 Article IV. Fallacies. Begging the Question — Evading the Question — Accident — A Dicto Simpliciter, etc., — Consequence — Cause — Question — Reference — Objections. 129. Fallacy. We have distinguished the Fallacy or Sophism from the Paralogism. The paralogism is an argument with a flaw in the form. A conclusion, true in itself, may be found in a syllogism which is faulty in the form. The conclusion may be true, indeed, but it has not been proved. We have previously considered arguments, with regard to the correctness of the form (Laws of the Syllogism). This article has reference to the matter of the conclusion. Any argument with a false conclusion is a fallacy. The word, however, is applied, in its special sense, to falsely concluding argu- ments which have so much the appearance of correct- ness as easily to deceive the unwary or to silence those whose limited knowledge or intelligence does not enable them to detect the deceit. We shall not consider any fallacy which is an evident violation of the laws of the syllogism. Every equivocation is such, since it uses a word in two senses, and thus gives us four terms in the syllogism. We subjoin some fallacies arising from the matter. 130. Petitio Principii or Begging the Question. This is to insert cleverly and covertly into the premisses the very thing that has to be proved. This is a favorite fallacy of demagogues haranguing listeners whose hearts are already in the conclusion. Communistic gatherings echo with arguments like this: 78 THE LAWS OF THOUGHT "All men are born into the world, equal, with equal rights to live, equally, upon the earth and to enjoy an equal share of the spontaneous productions of the earth. So that by Nature herself are they justified in asserting their equality against all comers. ''But all the existing laws of society are in open con- flict with the equal rights of men and are framed only to increase the inequality. ''Therefore, as we cannot get the rights of our equal- ity from society, we are by Nature herself justified in overturning governments and helping ourselves.'' Here, you see, the right to plunder is assumed covertly in order to justify plunder. The circulus vitiosus (vicious circle) is of the same order as the petitio principii. We prove, for instance, the fall of the apple from the tree by gravitation; and, later on, we establish gravitation by the fall of the apple. 131. Evading the Question (ignorantia elenchi). Under this head may be ranged all those tricks of argu- ment by which one tries to make the best of his case without offering proof; or to shirk an objection without showing it to be invalid. This may be done by assuming for proof or disproof something similar or analogous to the point in question; or by attacking an opponent on the ground that he is not to be regarded as an authority on the subject (argumentum ad hominem), thus arous- ing prejudice against his argument; or by appealing to the passions of the reader or listener; or by trying to shame an opponent out of the debate by citing against him authorities that have the respect of the listeners. This is an utterly illogical way of proceeding, but it may be followed with great effect. TRUTH OF THE PREMISSES 79 132. Fallacy of the Accident. This consists in as- suming as essential what is purely accidental. Thus a man might argue against Christianity because some who profess it are not exemplary in their conduct. However, evil-doers are never such by reason of Christianity ; they may be, in spite of it. 133. A Dicto Simpliciter ad Dictum Secundum Quid, and vice versa. This is the fallacy of arguing from an unqualified statement to the same statement qualified, or vice versa. This fallacy pervades daily con- versation. From the unqualified statement that a man is learned the popular mind jumps to the conclusion that he is learned in particular matters to which, perhaps, he has never given any attention. How many a man truly ''learned" has had to pay for his name as ''learned'' by being consulted as though he were an encyclopaedia? This fallacy works with equal success in the opposite direction. An exhibition of some knowledge in a few particular matters is soon .made the basis for the con- clusion that the exhibitor is "learned." 134. Fallacy of the Consequent. This consists in a misuse of the conditional syllogism. Thus some one says : // the gale is strong to-night, the tower will fall. In the morning the tower is found to have fallen. The fallacy infers that the gale was strong. The truth is that the tower may have fallen under other agencies. 135. Fallacy of the Cause. This lies in assuming as the cause of something that which is merely an accom- panying or preceding circumstance, or at most an occa- sion. Thus we sometimes read in the newspapers that the political principles of a party in power are the cause of all the fluctuations in trade. Therefore, to secure 80 THE LAWS OF THOUGHT Steady business, the administration must be changed. And when the administration is changed, and the same difficulties occur, the responsibiUty is shifted to the op- posite principles of the new party in power. Or we read that the cause of a bank robbery was the insecure system of bolts put on by a certain safe company, thus shifting the responsibility from the want of vigilance on the part of the authorities, and from that education of the head without the education of the heart, so prolific in evil- doers. 136. Fallacy of the Question. This consists in asking a number of questions all of which are evidently to be answered in the same way, by yes or no ; and then very deftly inserting one question whose answer should be the opposite, but which is made to pass along with the others, as answerable in the same way. Thus the com- munistic orator: ''Are we poltroons Shall we reject the equality nature has bestowed upon us? Shall we see the products of the earth, which nature intended for all, piled up for the use of a few? Can we, as nature's freemen, refuse to vindicate our equality? Is there anything to prevent us from destroying? They refuse us a share in their millions. Shall we refuse them a share in our poverty? etc. Therefore, etc.'' 137. Fallacy of Reference. This is untruth — the inventing of false references for the support of a propo- sition. People do not usually verify references, and hence may be easily deceived by a long array of author- ities [ ?] cited at the foot of the page. 138. Fallacy of Objections. This consists in pour- ing forth a volume of objections, one immediately after TRUTH OF THE PREMISSES 81 another before giving opportunity for reply. The adver- sary's time may be more than taken up in trying to answer one of them. Even then his long, careful answer may not be as effective with the audience (or reader) as the terse, captious objection; and besides, the other objections will be carried away unanswered. CHAPTER VI. METHOD. Article I. Scientific Method. 139. Scientific Method. When an object of thought is presented to us for investigation our task will be to discover v^hat propositions we may formulate regarding it. What may we predicate of it? Of what may it be predicated? When a proposition is presented to us in study, reflection, reading, conversation, debate, we may be concerned to know whether it is true or false. How shall we find out? When we make an assertion, having no doubt of its truth, how shall we proceed, if called upon, to place it in evidence by means of a demonstra- tion? When we are provided with certain truths and we wish to see if they can be made available for research or for the establishment of what we have been accepting as true or for the rejection of what we have been pre- suming to be false, how shall we proceed? The answer to all this is to be found in the application of the laws of thought to the matter in hand. And this is what is meant by scientific method, the means of arriving at scientific knowledge, science. It is an inquiry into the connection or opposition of ideas, of terms. 140. Analysis and Synthesis. Scientific method is ultimately reducible to two processes, analysis and synthesis. Analysis (greek, dvd^ixrtg ) means taking apart. Synthesis (greek, oirv&EOig ) means putting to- 82 METHOD 83 gether. Hence we have the names, analytic m,ethod and synthetic method. The two processes are often inter- woven and the name will then indicate the process that prevails in an investigation. Analysis and synthesis have to do strictly with parts, being the taking asunder and putting together of parts to see what use may be made of such parts, separate or conjoined, as subjects or predicates in true propositions. We may form a general idea of the meaning of the words, analysis and synthesis, from the work of the chemist. When the lump of crude matter is brought to him with the request that he find out what is in it, he separates it into its elements. He analyzes. His process is analysis. On the other hand, when he puts together chemical elements to get a chemical combina- tion, he synthetizes. His process is synthesis. But, as we said, one main process may be supplemented by the other. To be sure of the character of something found in the analysis the chemist may test it by synthesis, that is, by observing whether it will combine with some known element to form some known compound. Article H. Parts. 141. Parts: Real and Logical Parts. In general the word, part, is used to indicate anything that enters in any way into any combination real or fanciful which is considered as a unit. That combination, taken as a unit, is called a whole in reference to such parts. Parts are either real or logical. The whole made up respect- ively of such parts is called a real or logical whole. 84 LAWS OF THOUGHT Real parts are those that really exist in some whole which may have a real existence. A house is a real whole and the foundation and roof are real parts. Log- ical parts do not exist really inside the logical whole. The logical whole is simply a general idea and the logical parts are all the things to which that idea applies. The idea, tree, is a logical whole; and everything it ap- plies to whether existing or not is a logical part. The entire construction is mental, logical. 142. Real Parts: Accidental, Integral, Essential. Real parts are accidental if they can be removed, re- stored, modified, without interfering with what we re- gard as the identity of the unit as a whole. Such, for instance are the shape or hardness of an identical lump of wax. But we must remark that there may be parts which can, indeed, be removed without interfering with the identity of the unit, yet which are always under- stood to belong to its natural completeness, and these are called integral parts. Thus a man may lose a finger and still retain his indentity as the same man, but there will be something wanting to his completeness. Essen- tial parts are those which must all be present in order to have the given unit whole. There are two kinds of real essential parts. 143. Real Essential Parts: Physical and Meta- physical. Real essential parts are those that must be really, actually, in the unit in order that it may exist or even be thought of. Now we may look at these essentials in two different ways, so that for the same unit whole we shall get two sets of essential parts, each set, however, by itself constituting the whole. These two sets are called respectively physical parts and meta- METHOD 85 physical parts, and the whole as looked at in the one or other way is called correspondingly, a physical whole or a metaphysical whole. 144. Physical Parts. Real essential physical parts are essential parts into which the real whole is physically separable. They can be actually separated and if one is disjoined there is an end to the unit whole. For in- stance if an animal be cut in two so that the brain be in one piece and the heart in another, there will be a sepa- ration of essential physical parts. The animal will cease to exist. 145. Metaphysical Parts. We can consider that same animal as a unit whole made up of real essential parts which are physically inseparable from one an- other. Still these parts are real and actually existing in the whole, and as so combined they constitute the whole in its essential unity. We can think of them separately, but we cannot take them asunder physically as we would the brain and heart of the animal. They are named metaphysical parts. The prefix meta (greek, fietd ) in- dicates that they are aside from the physical condition of separability. Of all the real parts mentioned it is only these metaphysical parts that we take account of in scientific method, in analysis and synthesis. These metaphysical parts are simply those requisites which answer to the several ideas that go to make up the comprehension of the idea of the unit whole. Take for instance the object, animal. The idea of this object as a unit whole will be the idea, animal. What is compre- hended in the idea, animal? That idea implies or com- prehends the idea of substance, the idea of something material (matter), the idea of something organic (organ- 86 LAWS OF THOUGHT ism), the idea of sentient power (feeling, sensation). These ideas make up the entire comprehension. No one may be omitted. Each one answers to something that is real in the object. xA.ll these realities in the object as combined constitute the essentials of the object unit whole. They are therefore real essential parts. But they cannot be taken asunder. They are beyond the possibility of physical separation. The power of feeling in the animal cannot be detached from the substance, nor organism from the matter. These metaphysical parts are the real essential parts we have to take account of in analysis and synthesis. 146. Logical Parts. The other kind of parts which are taken account of in scientific method are the logical parts. Take that same idea animal as representing the real animal, a metaphysical whole. We may look at that idea as a universal idea which is applicable to many cases. The idea thus taken in its universal sense is called a logical whole and all the things to which it ap- plies, of which it can be predicated, are its logical parts. These things, these parts, may exist or they may not exist. The greater number will never exist. The idea embraces all in the universality of its application. It embraces all possibilities. For this reason logical parts are also called potential parts. Hence, these parts are not things that have a real existence within the logical whole. The logical whole is only a general idea, and the logical parts are the things possible or actual to which that idea can apply. The logical whole represents the entire comprehension of the idea animal, all that it im- plies; and the logical parts will make up the extension of the idea, everything to which it applies. METHOD 87 The construction is altogether mental. The logical whole is an idea. The logical parts are the things pos- sible of which it may be predicated. It embraces them all in its meaning, in its extension. The one same idea, animal, representing a real metaphysical whole, is re- garded in its uuniversal logical sense as being applicable to all animals thinkable in the past, present or future. To conclude, therefore, the parts that must be consid- ered in scientific work are the metaphysical parts which are the parts of comprehension, and the logical parts which are the parts of extension. Article III. An Illustration. 147. Analysis. We are not treating of any partic- ular science but only of method. We are, therefore, using the same example throughout in order to avoid confu- sion; and we are using only so much of the example as is necessary to our purpose. Analysis and synthesis have to do strictly with parts. The investigation of any object of thought must begin by analysis or synthesis; and it must advance either continuously by the process first used, or by changing from one process to the other as circumstances may prompt. A simple example will serve to illustrate the mental movement in either process. Let us suppose, for instance, that we wish to know something about animal. What is animal? This ques- tion is an express wish to use the term, animal, as the subject of a proposition. We wish to predicate some- thing of it. We wish to predicate of it all that must necessarily be predicated of it. To do this we must sep- 88 LAWS OF THOUGHT arate it mentally into its real, essential, metaphysical parts. We shall then have everything that must neces- sarily be predicated of animal. This separation may be begun variously in as much as one mind may give first attention to one characteristic, and another mind to an- other. The actual knowledge of the investigator will be of service to him in helping him to pick out the char- acteristics in the best order. To begin, then, we may presume that our attention is first attracted by the fact that animal has the power of sensation. We find this everywhere in what is called animal, and nowhere outside of what is called animal. It is an essential character, an essential part. We say, therefore, that animal is sentient. We ask what does this sense power imply, what does this act of sensation imply? We find by investigation that amid all varia- tions it implies some kind of general organism of the being and a particular instrument or organ for each dif- ferent kind of sensation. We say, therefore, that organ- ism is an essential character in animal, a metaphysical part. Animal is organic. We see readily that organism is always matter. Hence we say that animal is material. We know that matter is substance, sornething underlying the material accidents of color, shape, etc. Hence, ani- mal is substantial. Do we see anything beyond? No. We have mentally separated the real metaphysical whole into its real metaphysical parts. Animal is sentient, or- ga7iic, material substance. The process has been analy- sis. The process is always analysis when we proceed from the subject. 148. Synthesis. If we start from what is to be used as a predicate the process will always be synthesis. If METHOD 89 we wish to discover, for instance, what subjects sub- stance may be predicated of, what things may be called substance, or, to keep the same example, whether sub- stance may be predicated of animal, our process will be synthesis. We take this idea, substance, as a logical whole and we try to find out whether in its extension it reaches to animal as one of its logical parts. We experi- ment by adding to substance other ideas that will com- bine with it in order to see if we can arrive at a combi- nation that will give us all the essential parts of animal so that the idea, animal, as representing the metaphysical whole may be considered to be a logical part in the ex- tension (the application, the classification) of substance. The process is nothing more than that of going back mentally through the analysis and predicating succes- sively of the whole the parts that belong to it and into which it has been separated. Now, of course, we all know that animal is substance. This knowledge belongs to our most primary perceptions. But if we did not know, how should we find out by starting from substance ? We should have to add to sub- stance notions compatible with it to see if we might reach a combination which a competent person would recognize as constituting animal. Beginning, then, ac- cording to our knowledge, we say that substance must be material or immaterial, one or the other. Let us go first in the direction of matter. We find that matter must be either organic or inorganic. Let us go in the direction of organic matter. We find that organic matter is again of two kinds, sentient or non-sentient. We choose to go by way of sentient. Here we are told to stop for we have reached animal. Animal is sentient, organic, mate- rial substance. 90 LAWS OF THOUGHT 149. The Negative. What we have said applies also to the negative proposition. We must start from the sub- ject by analysis and we must start from the predicate by synthesis. May we say, animal is mineral? In the essen- tial metaphysical parts of animal we do not find min- eral. Hence, from the analysis of the subject we must say, animal is not mineral. If we try the predicate for a synthesis we may add to mineral all that is compatible with it but we shall never get the combination that gives animal, hence, again, animal is not mineral. Finally, in a proposition we cannot reverse subject and predicate unless subject and predicate have both exactly the same comprehension and the same extension, that is to say, unless they indicate exactly the same thing, no more no less, in different words. What we have been saying will be seen plainly indi- cated in the following table. Article IV. Analytic Table. 150. ■: Cable. Substance. 1 1 Material. 1 Immaterial. | 1 Organic. Inorganic. | 1 Acid. Salt. Base. | 1 Sentient (Animal). 1 Non-Sentient ( Plant ).| 1 i Vertebrate. Articulate. Molluscan. Radiate. | 1 Flowering. Flowerless. | I Mammal. Bird. Reptile. Amphibian. Fish. 151. Meaning of Table. A term, written or spoken, stands for idea and for thing, that is, for the logical METHOD 91 and the real whether whole or part. What then do the terms as they lie on the table indicate? They show that comprehension and extension are opposites. The com- prehension of a term takes in everything above it, — mov- ing upward always but never past the middle and down again. The extension of a term takes in everything below it, that is, on every side always moving downwards. Start at any term on the table. We may look at it as a metaphysical whole and as a logical whole. We get its metaphysical parts, its comprehension, going upwards. We get its logical parts, its extension, going downwards. Hence everything on the table if considered as a meta- physical whole will have substance as an essential part in its comprehension. At the same time substance, as a logical whole, will have everything on the table as a log- ical part in its extension. Comprehension, going up- ward, gives us all that enters into the essential meaning of the term. Extension, going downward, gives us a classified arrangement of all that the term can apply to. As we go up the table, from term to term, comprehen- sion diminishes because at each step a requisite is elimi- nated. At the same time the extension increases with each step upward, the field of application below becom- ing wider and wider. Contrariwise, as we go down the table the extension diminishes because we are cutting off from the field of application. At the same time compre- hension increases because at each step down we are add- ing a new requisite (above), a new essential part. We may here call attention to a statement which may be confusing if not rightly construed. It is said that analysis proceeds from the less universal to the more uni- versal at the same time that it proceeds from the com- plex to the simple. There is no contradiction. The first 92 LAWS OF THOUGHT part of the statement refers to extension and the second part refers to comprehension. Anaylzing, for instance, animal, we shall find that any one of the essentials will have a wider extension, application, than the extension of all the essentials taken together. The extension of animal is not so wide as that of substance. On the other hand considering comprehension the combination of es- sentials in animal is something more complex than any one essential which is necessarily more simple in its make-up. In actual study and inquiry, then, comprehension will give us what the term necessarily means, no more no less. It will provide us with the essential definition of our subject. Extension will give us a classified arrange- ment of the field covered by the term. It will give us the exhaustive logical division of our subject. Article V. Definition. 152. Kinds of Definition. Correct definition, exact, precise, definition should always be aimed at. Insistence on exact definition is the only way to security and clear- ness in argument. There are various kinds of explana- tions which are called definitions. There is but one kind with which we are here concerned. This is the real, essential, metaphysical definition. This table will show the various kinds of definition. Definition. I 1 Nominal. Real. I Descriptive. Genetic. Essential.] I Physical. Metaphysical. METHOD 93 A nominal definition is an expression in words of the meaning which for any reason whatsoever happens to be attached to a term whether arbitrarily by the speaker or by common though incorrect use or by the agreement of the best writers and lexicographers, etc. The definition is nominal also when the literal meaning of a word is given according to its derivation. Thus we say that in- finite, from the Latin in (a negative particle) and finis (a limit), means without limit. The word is looked at from the viewpoint of grammar, etymology, etc. A real definition is the expression in words of the nature of an object. The attention is fixed upon the object which is to be definitely represented in words. Such definition may be descriptive, genetic or essential. A descriptive definition is nothing more than what is named description in treatises on literary composition. It does not enter into the essence of the object. It merely presents, at the choice of the writer, such combination of salient features as may make the object recognizable, and fix it in the imagination. It is thus variable accord- ing to the mind of the writer and its purport is not scientific. A genetic definition (from genesis, origin) is the expression in words of the manner in which an object is produced. A genetic definition of a circle would be : a plane surface generated by revolving a line about one of its extremities. It does not enter into the essence. 153. Essential Definition. An essential definition names in combination all the essential parts of an object. It has been noted (No. 143) that the same object may be regarded as made up of separable essential parts, called physical parts, or as made up of inseparable essential parts, called metaphysical parts. . The enumeration of 94 LAWS OF THOUGHT these physical parts will give us the physical definition. The enumeration of these metaphysical parts will give us the metaphysical definition. This real essential meta- physical definition is the one to be aimed at in logical dis- course. It is the perfect scientific definition. It gives all that is in the comprehension of the thing; hence, a thoroughly comprehensive definition. To formulate this metaphysical definition it is not nec- essary to make explicit mention of each of the meta- physical parts. Two will be sufficient. We have seen (Table, No. 150) how each term implies all the terms above. Hence we will take one term to indicate the gen- eral class to which the thing to be defined immediately belongs and we will qualify this term, by a term in the row immediately below, thus excluding all the other terms in the row. If we take organic as a general class (genus) and sentient as special class (species) to exclude all the other species in the row, we shall have a defini- tion by proximate genus and ultimate difference. This is the metaphysical definition of animal. An animal is a sentient organic being. 154. Some Rules for Definition. 1. In philo- sophical matters insist on the essential metaphysical defi- nition. It may sometimes be useful to begin with another kind of definition; but never lose sight of the meta- physical. 2. The terms of any kind of definition should convey a more definite idea than the single term expressing the thing defined. This does not mean that every term in the definition should be at once better known by every- body than the single term. When we define a circle to be a plane surface with a single curved line for a boun- METHOD 95 dory, every point of which is equally distant from one fixed point on the surface, our definition may be less intelligible to some persons than is the term circle. But one who learns the meaning of the terms in the defini- tion will find that his idea of circle has become more definite. 3. Try to so word the definition that it may be con- vertible by simple conversion (No. 76) with the term ex- pressing the object defined. Thus: if a circle is a plane surface . . . etc., then a plane surface . . . etc. (as above) is a circle. 4. Do not define by a negation, by saying what a thing is not. However, a negative term may sometimes call for definition as, for instance, the term injustice. It is made up of a negative particle, in, and a positive part which is excluded by the negative. We define the posi- tive part justice. The definition will represent the posi- tive part as excluded. 5. Use words in their exact meaning; and when there is a choice of words use such as may be most readily understood by the persons immediately addressed. Article VI. Division. 155. Logical Division. As the scientific definition of a term or subject is given by combining the meta- physical parts of comprehension, so the scientific division is made by indicating the logical parts of extension. When we define we look at the term as a metaphysical whole. When we divide we look at it as a logical whole. Take any term on the Table (No. 150). If we combine 96 LAWS OF THOUGHT it with what is above we have the definition of some- thing. When we consider it as taken asunder into the parts below we have the logical, the scientific division of the same something. The logical division is made by first placing the term in question as genus, as highest genus. (See No. 29 to No. 31.) We may, for instance, wish to divide matter. As genus it will be divided into species. This is done by separating it into kinds according to qualifying dif- ferences that do not overlap. These differences are called specific differences and the kinds so qualified are called species. The differences should be chosen as furnishing the fewest immediate divisions of the whole genus. Matter is thus divided into organic matter and inorganic matter. After such division is made it may be found that each species can serve as a genus and be divisible into its own species. Perhaps one species will serve as a genus and another will not. But we go on dividing in the same manner in every direction until no new species can be made a new genus divisible into spe- cies or kinds. Each species will then be found to be divisible only into individuals all of one kind having the same specific difference. 156. The Simple Rule. In every correct division the parts must be found to be precisely equal to the whole. In a logical division, therefore, the sum of the species must cover precisely the field that is covered by the genus. This implies that there must be no over- lapping. We may not place as species anything that covers the whole genus ; and each species in a division must be characterized by a difference which separates it totally as a part from each of the other species. If METHOD 97 plants were to be divided into growing plants and food plants the first member would cover the genus since all plants grow. If animals were to be divided into wild, vertebrate, dangerous and tropical there would not be a complete division and there would be some overlapping. The advantage of correct logical division in the study of any matter is evident. It maps the subject in a way that insures both order and completeness. It can be applied in any study. Though other divisions may have to be resorted to as temporarily expedient and in lack of detail, the logical division should be kept in mind. In this chapter we have been using a single example as summarized in the Table (No. 150) in order to fix in the memory the respective distinctions between, meta- physical and logical whole; metaphysical and logical parts; comprehension and extension; analysis and syn- thesis; definition and division. In the readiness of our knowledge of these distinctions we shall find the best test of our knowledge of the principles that underlie the laws of thought. Article VII. Science. 157. Science. What we have learned about the ways of correct thought will be valuable to us in any kind of study. Every perception of truth is knowledge. If this perception be through a demonstration it is scientific knowledge. A complete body of related truths regard- ing a given object as presented by demonstration is called a science. The knowledge of that body of truths as so related and demonstrated is the knowledge of the science. 98 LAWS OF THOUGHT 158. Object of a Science. By the name, object of a science, we mean not an end or purpose, but the thing, the object that is studied. And the same thing as a gen- eral groundwork or object of study may provide us with the particular object of more than one science. It may be considered under aspects that are quite distinct one from the other, and we may thus get distinct sets of con- nected truths — each set being in itself complete. In other words, we may consider separate characters which are found to affect the totality of the same general object. 159. Material and Formal Object. The thing in general which furnishes the material for study is called the material object of a science. The particular char- acter, the formality, studied, or this formality as affect- ing the material object, is called the formal object of the science. We may say for instance that the whole cor- poreal universe is the material object of both astronomy and chemistry. But the formal object of the science of astronomy is the mass, magnitude, distance, co-ordinated motions, etc., of the various masses of matter, called heavenly bodies, which make up the corporeal universe; whilst the formal object of chemistry is the substantial distinction between the elements of matter and their respective capacities for substantial union with one another. Things even the most varied and of different orders miay be brought together as the material object of one science by reason of a same formality or characteristic running through them all and making the formal object of the science. Thus spirit, matter, substance, accident, and whatsoever is or can be, and whatsoever can be thought of as ''something," will make up the material METHOD 99 object of the science of Ontology. Ontology is the science of being (greek, oiv, ov, ovtog ). The character, "being," "something," runs through not only what exists but also through whatever can be thought of. It is the formal object of the science of Ontology. 160. Logical Character of a Science. Looked at in their purely logical aspect, and considered solely in re- gard to the kind of mental work dominating, sciences are distinguished as belonging to one or another of two classes, the analytic or the synthetic. Again, in the log- ical aspect, they are distinguished as being either in- ductive or deductive. Moreover the analytic are spoken of as inductive, and the synthetic as deductive. This does not mean that induction is the same as analysis, nor that deduction is the same as synthesis. Analysis and synthesis refer strictly to the mental work on terms with the view of getting propositions. Induction and deduc- tion refer strictly to the mental work on propositions with the view of getting conclusions. The explanation of analysis and synthesis has been given in this chapter. The explanation of induction and deduction is given in Chapter V. A science is logically characterized by the kind of mental work with which it begins and which pre- vails in the building up of the body of related truths (No, 157). Some sciences grow by analysis and induction: first by analysis of terms to get particular propositions, then by induction to gather (induct) concordant propositions into a general law. All purely experimental sciences are established in this way. Thus beginning with particular objects, we observe, analyze, note agreements, and finally formulate general propositions which represent what we 100 LAWS OF THOUGHT call laws, for instance, of motion, light, heat, equilib- rium, etc. Other sciences grow by synthesis and deduction. In these we begin with known general laws from which we draw (deduce) consequences. Using each new evidence gained we go on to draw more remote consequences. In this way, for instance, starting from a few recognized general truths regarding lines and angles we go on by the search for relations and combinations to build up the science of geometry. The synthesis consists in the put- ting together of ideas, terms, until there is found a valid combination in a logical conclusion. Analysis is the way of discovery. It reveals, lays open, discovers the invariability of a given truth in ever vary- ing circumstances. This truth is then certified to as a general truth, as a law, by the argument of induction. Synthesis is the way of invention. Starting with the general truth, the general proposition, it joins one of the terms to a new term to get a minor which will serve with the first proposition used as a major. It then joins the extremes for a consequence. It thus finds an applica- tion of the general law. The application is also certified to by the argument of deduction. Further discussion of this matter would be confusing. In an analytic science it may frequently be of service to have recourse to synthesis; and in the synthetic science, to analysis. The student will find an aid to methodical thought in looking over the tables of contents in standard text-books of various sciences. It must be noted, how- ever, that in the teaching of the purely experimental (analytic, inductive) sciences the tedious process of growth from which they take their name is not strictly followed. It would be an interminable work for the stu- METHOD 101 dent were he obliged to hear the story of the experi- mentation that was needed to discover each general law. When the general law has been fully established it is much simpler in teaching to present the law first and then to show its generality by chosen illustrations which will suffice to indicate the ground for a valid induction. 102 CO o u CO O 2 H D O vo o I— I O w H .M 52; 1— 1 ►:? fe <1C iz; H ?s 1— 1 IDE acci O"" P Q P-H H < H s 1 "izi , ''^ m ° t— 1 1-5 ?i P4 ^gi (tn the , includir visible Se rse) Co P iJ ^ ^ ?> m § o go l§ .-J Qi ^ 2 2s ® ti_i too© OGQ O <5 > tt ^ bO <» o <;:) O -a P4 O a® o 02 o >» o O m o m O — _ o GQ So ;. . M 03 t EXPLANATION OF OUTLINE. In the preceding table or "Outline of the Sciences" we have advanced from the term of least comprehension and greatest ex- tension, namely, the term, Being. That which is represented by the term or concept Being supplies the subject-matter for On- tology, the Science of Being. We go on trying to increase the comprehension and diminish the extension by adding the terms, Finite and Infinite, to Being. The division is not one of genus into species, as we have seen when speaking of analogy (Nos. 28, 36), yet it serves us for this very broad outline. Infinite Being is the subject-mat- ter of the science called, in philosophy, Natural Theology. Continuing with Finite Being, increasing comprehension and diminishing extension, we have, in a perfect division, Substan- tial Finite Being and Accidental Finite Being. Ontology extends thus far, defining the notions of Infinite and Finite, and treating of Substance and of all that is not Substance, that is of Accident; quantity, quality, action, time, space, etc. It is general philosophy. Again dividing, and increasing comprehension, we have Ma- terial Substantial Finite Being and Spiritual Substantial Finite Being. We do not treat of bodiless spirit under the Finite, in philosophy. But taking the Material, in the wide sense of the term, we have the subject-matter of the science, Cosmology. Increasing the comprehension, again, by adding Animate and Inanimate, we get in the Animate Material, etc., the subject- matter of the science. Biology, as general science of life. If we take the other subdivision, Inanimate Material, etc. ,we find that range of sciences which treat of inanimate, inorganic mat- ter: Physics, etc. We leave the Inanimate; and we divide the Animate, by adding to the comprehension, into the Rational and the Irra- tional. The Irrational divided by adding to comprehension, gives us Sensitive and Non-Sensitive (the brute and the plant), with the sciences, Sensation, etc., Vegetation, etc. Returning to Rational Animate, etc., we find here the sci- ence of Man in general, or Anthropology. From this point forward we are engaged solely with Man. We can no longer divide into species. We use such divisions as will give us a complete and clear view of the subject, Man. By actual physical essential division (No. 146) we can divide Man into Soul and Animal Body. The Animal Body, for 103 104 LAWS OF THOUGHT general principles, we refer over to Sensation. Soul is the sub- ject-matter of the Science, Psychology. Psychology will treat of the Nature of the Soul and the Powers of the Soul. The Powers of the Soul, we group nder three headings : Power of actuating sense-perception, etc.; Intellect; Free-Will. Intellect, we consider in its Nature; its Method of Work; its Supply of Material. The Method of Work constitutes the ob- ject (or subject-matter) of the Science, Formal Logic. The Supply of Material for true thought gives us the object of the Science, Material Logic. Under the heading of Free Will we treat of the Existence and Nature of Free Will ; of the Norma or Rule of the Free Act; and of Practical Morality. The Existence and Nature of Free Will, we may readily refer to the treatise on the Powers of the Soul. In this way, accepting Free Will from Psychology, we have, left, the Norma of Free Act and Practical Morality. These last two. Norma and Practice, taken together, form the subject-matter of the Science, Ethics. This is one presentation of the philosophical and subsidiary sciences. In studying, we begin upon the lawest line with Formal Logic. Next, we take up Material Logic. Thus equipped, we go back to Ontology, and follow down through the Finite until we reach the border line of Ethics. Here, we turn back to take up the study of Natural Theology, which we had omitted and for which we are now prepared. At length, with what philosophy can teach us of God and man and of the wide universe about us, we study, in Ethics, the practical con- clusions to be drawn from the whole, to guide the actions of the free, intelligent being, Man. POINTS FOR PRACTICE. — The practical utility of Formal Logic, and the mental training to be derived from it, depend altogether upon the skill acquired in readily discerning the comprehension and extension of terms. The Laws of the Syllogism — Definition, Division, Synthesis, and Analysis — are all to be learned by the careful study of Extension and Com- prehension. Special attention should be given to these two correlated points. Original illustrations should be sought for as a proof that those in the book have been understood. (9) Name objects of the single apprehension or of the idea. (10) Give examples of judgments. (11) Upon what two prin- ciples does the mind work in reasoning? (13-15) What is a term, a proposition, a syllogism? (17-19) Give three classifica- tions of ideas. (19) Examples of singular, particular, collective, universal ideas. (20) How are universal ideas classified? What is meant by form, formality, or determination, in reference to idea? (21-27) Examples of species, genus, difference, property, POINTS FOR PRACTICE 105 accident. (29) Name some forms that may be used both as generic and specific. (30) Give illustrations of highest genus, lowest species, subaltern genera. Tables of contents in scientific works will furnish examples. (32) Examples of real and logical terms. (33-35) Univocal and equivocal terms. (36) What is an analogous term? and why is the question of analogy introduced here? (37) Examples of the material, logical, real supposition of terms. (40) Examples of propositions, pointing out the sub- ject, copula, and predicate. (41) Examples showing the differ- ence between the logical and the grammatical predicate. (42) Examples of simple. (43) Compound. (45, 46) Categorical, conditional. (47, 48) Conjunctive and disjunctive propositions. Show how they are reducible to the conditional. (54, 55) Ex- amples of a priori and a posteriori judgments. Show why the a priori are called necessary, absolute, metaphysical, analytical; and the a posteriori, contingent, hypothetical, physical, synthet- ical. (59-61) What is meant by the extension and comprehension of terms or ideas? (62-63) What does the extension of a propo- sition depend upon? Examples of the four extensions of propo- sitions. (65-70) Explain the laws which declare the extension of the predicate in universal and particular propositions, both affirmative and negative. Name and illustrate the one exception for the universal affirmative. (73) State what is absolutely necessary that a proposition may have the force of a negation. (76) Examples of the conversion of propositions, retaining and changing quantity and quality. (7S) Of opposition in quantity and quality. (84) Explain the difference between consequent and consequence. (86) Give the analysis of an (original) argument. (88) Explain the true, primary meaning of Middle Term. (92) What is meant by the Moods of the Syllogism? (94-102) Nine Laws of the Syllogism. Compose faulty arguments or syllogisms, and show how each law may be violated. (104-107) Examples of syllogisms. Show how the conjunctive and disjunctive are reduced to the conditional. (108-113) Examples of enthymeme, sorites, polysyllogism, epichirem, dilemma. (114-122) Difference between formal and material logic; between direct and indirect demonstration; between simple and compound; between the a priori and the a posteriori. (124) Example of complete induc- tion. (125) What is required for the validity of the incomplete induction? (129-138) Examples of various fallacies. (139-160) Material for the practical study of Method will be found in ordinary reading. Are the definitions comprehensive? Are the divisions logical, complete? Where is there analysis, synthesis, induction, deduction? ALPHABETICAL INDEX Numbers refer to Paragraphs, Abstract idea, 17 Accident, inseparable and sep- arable, 26, 27. fallacy of, 132. Accidental form, 27. Adequate idea, 18. A dicto simpliciter, fallacy, 133. Affirmative proposition, 72. Analogy, argument from, 127. Analogous terms, 2>2>^ 36. Analysis, 140. illustration of, 147. and the negative proposition, 149. and discovery, 160. Antecedent in syllogism, 83. Apprehension, simple, 9. 'as an act, 9. as representative, 9. A priori demonstration, 117, 121. judgment, 55. A posteriori demonstration, 117, 122. judgment, 56. Argument, 11, 15, 80. analysis of, 86. basis of, 11, 85. styles of, 81. Argumentation, 11. Axioms, for extension and comprehension of terms, 58. for argument, 11, 85. Begging the question, 130. Being, predication of, 28, 36. science of, 166. 107 Cause, fallacy of the, 135. Caution, 103. Clear idea, 18. Collective idea, 19. Collective proposition, 63. Complete idea, 18. Compound demonstration, 120. Comprehension and extension of terms, axiom, regard- ing, 58. of idea and term, 60, 61. and metaphysical parts, 145. explanation^ of, 151. and definition, 153. Comprehensive idea, 18. Concept, 9. Conclusion, 11, 86. value of, 116. Concrete idea, 17. Consequence, 84. Consequent, fallacy of, 134. in syllogism, 83. Conversion of propositions, 76. Declaration, 10. Deduction, 11, 123. Definition, nominal, real, de- scriptive, genetic, essen- tial, 152. physical, metaphysical, 153. and comprehension, 153. some rules for, 154. Demonstration, 116. direct, 117, 118. indirect, 117, 119. simple and compound, 120. a priori and a posteriori, 117, 121, 122. 108 LAWS OF THOUGHT Determination or form, 20. Diagram of figures in syl- logism, 89, 90, 91. of genus, species, etc., 30. of definition and division, 150. of propositions, 79. of sciences, 161. of seventh law for syllogism, 100. Difference, specific, 25. Differential idea, 25. Dilemma, 81, 113. Direct demonstration, 117, 118. universal idea, 21. Distinct idea, 18. Division, made into logical parts, 155. into genus and species, 155. simple rule, 156. Elenchi, ignorantia, 131. Enthymeme, 81, 109. Epichirem, 81, 112. Equipollence of propositions, Equivalence of propositions, n. Equivocal terms, 33, 35. Example, argument from, 126. Extension of terms and ideas, 59, 61. axiom, 58. of predicate, 66, 71. and logical parts, 146. explanation of, 151. Extremes, extreme major term, extreme minor term, 87, 88. Evading the question, 131. Fallacies, 130-138. Fallacy, 116, 129. Figures of syllogism, 88-91. Form (formality or determi- nation), 20. specific, 22. generic, 24. accidental, 27. when both generic and spe- cific, 29. Formal logic, 2, 114, 115. Genera, subaltern, 31. Generic, 24. idea, 24. and specific, the same form, 29. Genus, 24. highest, 31. Grammatical predicate, logical and, 41. Herschel, Sir W., 122. Highest genus, 31. Idea, 9. characteristics of, 18. classifications of ideas, 17-19. comprehension of, 60, 61. differential, 25. extension of, 59, 61. generic, 24. object of universal reflex, 23. specific, 22. Ignorantia elenchi, 131. Indirect demonstration, 117, 119. Induction, 123. complete, 124. incomplete, 125. Inference, 11. Judgment, 10, Z^, as an act, 10. as representative, 10. immediate, 51. mediate, 52. a priori, necessary, absolute, metaphysical, analytical, 55. a posteriori, contingent, hy- pothetical, physical, syn- thetical, 56. synthetic a priori^ 57. ALPHABETICAL INDEX 109 Kant, 57. Knowledge, is representative, 8. scientific knowledge, 139, 157. Laws of extension of predi- cate, 71. of syllogism, 93-102. Leverrier, 122. Logic, artificial, 4. as an art, 6. as a science, 5. formal, 2, 114, 115. material, 2, 114, 115. natural, 3. the name, 1. Logical and grammatical pred- icate, 41. supposition of terms, 37. Lowest species, 31. Major extreme, 87, 88. premiss, 83, 88. Material logic, 2, 114, 115. Material supposition of terms, 37. Method, scientific, 139. two processes, analysis and synthesis, 140. Mill, J. Stuart, 125. Mind, three acts of, 7. Minor extreme, %7, 88. premiss, SZ, 88. Moods of syllogism, 92. Negative particle, 72>. proposition, 72. Notion, 9. Object of a science, 158, 159. material, 159. formal, 159. Objections, fallacy of, 138. Objective, identity, 10. Ontology, 159. Opposition of propositions, 78. Oral expression of thought, 12. Paralogism, 116. Particular idea, 19. proposition, 63. Parts, real and logical, 141. accidental, integral, essen- tial, 142. physical, 143, 144. metaphysical, 143, 145. logical, 146. potential, 146. and comprehension, 145. and extension, 146. in scientific work, 146. and division, 155. Petitio principii, 130. Polysyllogism, 81, 111. Predicables, heads of, 28. Predicate of a proposition, 40, 65. logical and grammatical, 41. laws of extension, 66-71. Premisses in syllogism, 83. major, S2», 88. minor, 83, 88. Principii petitio, 130. Property, 26. Proposition, 14, 39. simple, complex, 42; com- pound, 43. possible varieties of, 44. categorical, 45. conditional or hypothetical, 46. conjunctive, 47. disjunctive, 48. extension of, singular, par- ticular, collective, univer- sal, 62, 63. use of name "particular," 64. extension of predicate in, 66-71.^ affirmative, negative, 72. quality and quantity of, 74. relations of, conversion, equivalence or equipol- lence, opposition, 75-78. no LAWS OF THOUGHT Question, begging the, 130. fallacy of the, 136. Real supposition of terms, yi. Reasoning, 11, 80. as an act, as representative, two working principles, 11. process of, 53. Reference, fallacy of, 137. Reflex universal idea, 21. object of, 2Z, Science, 139, 157. object of a, 158. material and formal object, 159. logical character of a, 160. analytic, synthetic, inductive, deductive, 160. Simple apprehension, 9. demonstration, 120. Singular idea, 19. proposition, 63. Sophism, 116. Sorites, 81, 110.- Species, 22, 23. Specific, 22. difference, 25. idea, 22. and generic, the same form, 29. Subaltern genera, 31. Subject of a proposition, 40. Supposition of terms, real, ma- terial, logical, Zl . Syllogism, 15, 81, 82. antecedent, major and minor premiss, consequent in, 83. consequence in, 84. figures of, 88-91. moods of, 92. laws of, 93-102. simple, compound, condition- al, conjunctive, disjunctive, 104-107. Synthesis, 140. illustration of, 148. and the negative proposition, 149. and invention, 160. Synthetic a priori judgment, 57. Table, analytic, 150. meaning of, 151. Terms, 13. classification and use, 32. univocal, equivocal, analo- gous, 33-36. comprehension and exten- sion, 59-61. extreme, extreme major, ex- treme minor, middle, 87. supposition of, real, materi- al, logical, 7)1, Thought, form of, 2. material of, 2. oral expression of, 12. Universal idea, 19. idea, direct, 21. idea, reflex, 21. idea, reflex, object of, 2Z. proposition, 63. Univocal terms, 33, 34. 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