The laws of thought; or, Formal logic; a brief, comprehensive treatise on the laws and methods of correct thinking

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 purpose 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

4 PREFACE

introduced, and sometimes are introduced, into an arithmetic, 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.

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. Simple Apprehension, Idea. 10. Judgment. 11. Reasoning, Argument. 12. Oral Expression. 13. Term. 14. Proposition. 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. Important 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. Diagram. 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

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 Exception. 68. Universal Negative. 69. Particular Affirmative. 70. Particular Negative. 71. Two Laws. 72. Affirmative and Negative. 73. Negative Particle. 74. Quantity and Quality 36

Article VII. Related Propositions.

75. Three Relationships. 76. Conversion. 77. Equivalence. 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. Conditional Syllogisms. 106. Conjunctive Syllogisms. 107. Disjunctive Syllogisms 61

Article V. Other Styles of Argument.

108. Argument Abbreviated. 109. Enthymeme. 110. Sorites. 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. Simple, Compound. 121. A Priori. 122. A Posteriori . . 70

Article III. Induction.

123. Deduction and Induction. 124. Complete Induction. 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 Simpliciter. 134. Of the Consequent. 135. Of the Cause. 136. Of the Question. 137. Of Reference. 138. Of Objections 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. Metaphysical 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

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 subject 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 disposition 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 inaccurately 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 principles 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 correctness 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; Judgment; 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 Apprehension; 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 (likeness), a concept (the mind conceiving that something in itself, in Hkeness), a notion (the first element of knowledge). 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 perceiving.

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 apprehension, 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 judgment affirming or denying according to what was perceived implicitly through the comparison. This definition 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 declarations :

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 principle 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, deduction. In the other sense it is called argument, and also sometimes inference, conclusion.

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 expressing 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 argument.

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, syllogisms. 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, distinct, complete and adequate or comprehensive.

A clear idea expresses characteristics or notes sufficient to discern the object from others. A distinct idea distinguishes between these notes themselves. A complete idea expresses all the notes that distinguish the object in reality from others. A comprehensive or adequate idea expresses all that can be perceived in the object: the human intellect has no such idea of anything.

I see an object moving in the distance. I have an indefinite, obscure idea of something moving. It approaches. 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, particular, collective, universal.

When one special individual is expressed in a determinate 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 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, meaning 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, according 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.

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 applicable 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 individuals, 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 animals, of humanity, we find ourselves figuring to ourselves 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 something, 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.

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 difference 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 necessarily 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 considered 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 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 distinguish the inseparable accidents by the special name of property,

28. Heads of Predicables. The wide reaching nature 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, whatever we predicate (affirmatively or negatively) we predicate (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 accidents. Hence genus, species, difference, property, accident, are called Heads of predicables, because whatever 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 being (as also of one, true, good) constitutes on§ of the most subtle discussions of general metaphysics. We need not speak of it here.

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, becomes a genus with reference to the classes sentient organic 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

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 London, 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 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. Leaving 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.