r DV# \0l ( a 1: i (J ) I a I P h^i I o s o p hy LIBRARY OF CONGRESS. ^rr-. mp^ iujt^rtBlt lu Shelf ....v.^-^ UNITED STATES OF AMERICA. Digitized by the Internet Arciiive in 2011 with funding from The Library of Congress http://www.archive.org/details/rationalphilosopOOpola RATIONAL PHILOSOPHY THE LAWS OF THOUGHT FORMAL LOGIC A BRIEF, COMPREHENSIVE TREATISE ON THE LAWS AND METHODS OF CORRECT THINKING BY WILLIAM POLAND Professor of Rational Philosophy in St. Louis University SILVER, BURDETT & CO., PUBLISHERS New York BOSTON Chicago 1892 Copyright, 1892, By silver, BURDETT & CO. Typography by J. S. Gushing & Co., Boston. Presswork by Berwick & Smith, Boston. 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. 3 4 ' PREFACE. 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 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. CONTENTS. CHAPTER I. INTRODUCTORY. PAGE Article I. Logic. I. 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. 1 1 . Reasoning, Argu- ment. 12. Oral Expression. 13. Term. 14. Proposition. 15. Syllogism 11 CHAPTER II. IDEAS — TERiMS. Article I. Ways of Classifying our Ideas. 17. Abstract, Concrete. 18. Clear, Distinct, Complete, Comprehensive. 19. Singular, Particular, Collective, Uni- versal 15 Article II. Classification of Universal Ideas. 20. Form. 21. Reflex Universal. 22. Species. 23. Impor- tant Observation. 24. Genus. 25. Difterence. 26. Prop- erty. 27. 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. 33. Univocal, Equivocal, Analogous Terms. 34. Univocal. 35. Equivocal. 36. Anal- ogous. 37. Supposition or Use ; Material, Logical, Real . 23 5 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. Dis- junctive. 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. Il- lustration 34 Article VI. Extension of Propositions. Quantity and Quality. 62. Extension. 63. The Subject. 64. Note. 65. The Pred- icate. 66. Universal Affirmative. 67. One Exception. 68. Universal Negative. 69. Particular Affirmative. 70. Par- ticular Negative. 71. Two Laws. 72. Affirmative and Neg- ative. 73. Negative Particle. 74. Quantity and Quality . 36- Article VII. Related Propositions. 75. Three Relationships. ']^. Conversion, tj. Equiva- lence. 78. 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 of Argument. 87. Middle and Extremes 45 Article II. Figures and Moods of the Syllogism. 88. Major, Minor, Middle. 89. First Figiu'e. 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. loi. Eighth Law: No Conclusion. 102. Ninth Law: Particular Conclusion. 103. Caution . 54 Article IV. Some Species of the Syllogism. 104. Simple and Compound Syllogisms. 105. Conditional Syllogisms. 106. Conjunctive Syllogisms. 107. Disjunc- tive Syllogisms 61 Article V. Other Styles of Argument. 108. Argument Abbreviated. 109. Enthymeme. no. Sori- tes. II I. 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 Induction. 125. Incomplete Induction. 126. Example. 127. Analogy. 128. Caution 72 5 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 . . . yj CHAPTER VI. METHOD. Article I. Scientific Method. 139. Scientific Method. 140. Analysis and Synthesis . . 82 Article II. Definition. 141. Definition. 142. Nominal Definition. 143. Real Defi- nition. 144. Rules for Definition 83 Article III. Division. 145. Scientific Division. 146. Physical and Metaphysical Parts. 147. Actual Union. 148. Integral Parts. 149. Logi- cal Division. 150. Potential Parts. 151. Logical Whole. 152. Importance. 153. How to Divide -87 Article IV. Analysis and Synthesis. 154. The Question. 155. The Answer : Analysis, Synthe- sis. 156. Analysis. 157. Synthesis. 158. Explanation Complete. 159. Singular to Universal, and vice versa. 160. Complex to Simple, and vice versa. 161. Discovery and Instruction. 162. Analytic and Synthetic Sciences. 163. Advice 91 Article V. Science. 164. Science. 165. Object of a Science. 166. Material and Formal Object. 167. A Delusion. 168. Outline of the Sciences. Explanation of Outline 96 Points for Practice 100 Index loi THE LAWS OF THOUGHT. oJOio CHAPTER I. INTRODUCTORY. Article I. Logic. Logic — Formal and Material Logic — Natural and Artificial Logic. 1. The name Logic comes from the Greek, X0709. A0709 signifies reaso7i, 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 fonn of the 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 q,oxxq.qX. 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 inaccurately by reason of complications of notions which arise and 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 system- INTRODUCTORY. ll atized 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 ; 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 Apprehen- sion ; 2. Judgment; 3. Reasoning. 8. Knowledge Representative. All knowledge is repre- sentative 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 likeness), 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, ai^rms or denies identity between their objects. Thus : TJie 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 aji act or a series of acts by which the mind compares (objectively) two cases pro- nounced upon in two judgments, and in that compari- son 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 made sufficiently clear for present purposes by two examples : INTRODUCTORY. I3 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- ^*^" ■ A horse is a quadriiped; 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 two 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 ^ third thing {quadruped), the other {this featJiered 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 some- times 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 express- ing an idea is called a term, as, bhte, cloth, j^istice, 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, 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. I. 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, zvise, are concrete, because bine, wise, are thought of as concreted in something else : blice sky, wise judge. 18. 2. Clear, Distinct, Complete and Adequate or Compre- hensive. 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 suf- ficient to discern the object from others. A distinct l6 THE LAWS OF THOUGHT. idea distinguishes between these notes themselves. A complete idea expresses all the notes that distinguish the object /;/ 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 any- thing. 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. 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 indi- viduals embraced in the idea and the manner of embrac- ing them ; that is, according to the extension of the idea. In this way we divide ideas into singular, 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 book. 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. 1/ idea is called collective. Thus : A cjvivd, 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 way 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 : Ma7i, 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 tJiis 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 r(\2iny forms (or determinations) existing in it simultaneously. A ball may contain the forms of wood, roundness, whiteness, 1 8 THE LAWS OF THOUGHT. elasticity, etc. In man there are the forms of spirit, matter, orgajtism, 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 upon 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 / ^ ^ t-i X t-i 3. Some man is just (Par^. ^^.). 4. Some man is not just (/*ar^.iV>^.). SUBCONTRARY. I and 2 are contraries ; 3 and 4 are subcontraries ; 1 and 4, also 2 and 3, are contradictories ; i and 3, also 2 and 4, are subalterns {i and 2 being called subalternant, 3 and 4 their subalternates). It is clear that if i is true, 3 is true ; and that if 2 is true, 4 is true. But we cannot conclude from 3 to i nor from 4 to 2. I 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 (ii) 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 said, 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 argument. The propositions which, taken together, represent in language the knowl- edge and its process, we also called argument. We shall use the word argument in this latter sense. 81. Styles of Argument. There are indeed many com- binations of propositions which are used as language- representations of the process of reasoning, many styles of argument. Different names are given to them, accord- ing to the variety of structure. We have the Syllogism, 45 4-6 THE LAWS OF THOUGHT. tke Enthymeme, the Sorites, the Polysyllogism, the Epi- chirem, the Dilemma. All, however, are reducible to the syllogism, which is the nearest approach language can make towards exhibiting the working of the mind in reasoning. Not that we alwa,ys, 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 argument made up of three propositions so connected that if the first two be admitted, the third must, likewise, be admitted. Thus, Every jtlant is a substance; But the verbena is a jy^cint. Therefore, The verbena is a substance, 83. Antecedent ; Consequent ; Premisses. The first two propositions taken together are called the antecedent. The third proposition is called the consequent. In the antecedent the evidence is stated. In the consequent the verdict is given. The two propositions of the ante- cedent 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 REASONING, ARGUMENT. 47 in the consequent is a consequence of what was laid down in the premisses. If an argument is proposed to 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 admitted. {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 consequence. 85. Axioms. We repeat here two axioms stated in No. II. They are the bases upon which every argu- ment must rest. If the conclusion is an affirmative proposition the argument rests upon this axiom : /;/ tJie sense in wJiicJi two things are the same as a tJiird thing, in the same sefise are they the same as one another. If the conclusion is a negative proposition, the argument rests upon this axiom : In the sense in ivhich tzvo things arc, 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 argument given above, namely : Antecedent \ ^^'^''>' P'^"^ '^ ^ substance (Major Premiss), i But the verbena is a plant (Minor Premiss). Consequent or ^ Therefore, the verbena is a substance (Conse- CONCLUSION ( quence). 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 the conclusion. 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 premisses, 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 verbetia 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 arti- cle, of major and minor premiss, major and minor ex- treme, 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 attached 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 premiss put first, the major ; that put second, the minor : and we never speak of the extremes as major and minor. This leads us to the question of figures of the syllo- gism. 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. Anhnals 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 bei7igs {va2i]or extreme), and greater extension than lio7is {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 : Ziions 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 outside of the F'irst 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; li'o 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 Figure the term of comparison is the subject of both the first and second premiss. Thus : Therefore, Every plant is substance; Every 2ilfttit 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. 9^ 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. I. 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; Evertjthiuff organic is substance. Therefore, Some siihstance is a tree. This, it will be noticed, is the same as the First Figure with the position of subject and predicate inverted in the conclusion, and the proposition accordingly changed from the universal, Everj/ 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 be three, and only three, terms, and they mitst be only tJu^ee 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) with 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 tvareJiouses, Stores can be eaten, Therefore, Warehouses can he 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 j^^^onoun, 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 Jachson is one of the Presidents ^ Franklin Pierce is one of the Presidents, Therefore, Andretv tfackson is Franklin Pierce, we have four terms, in meaning; because, One-of-the- Prcsidents is taken in two di\'iiQXQXi\. particular senses. 95. Second Law. Extension of Extremes. Neither ex- treme may have a greater extension in the conclusion tJian 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 j)lant, 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 jiniversal. 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 56 THE LAWS OF THOUGHT. meanings for the middle, and hence, four terms. If we say : 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 ajiy 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. In this case, both premisses will have to be affirmative, and the conclusion will be particular. Thus : All fishes are sensitive ; All fishes are shy. Therefore, Some things sensitive are shy. REASONING, ARGUMENT. 5/ In these premisses the extremes are predicates of affir- mative propositions, and hence are particular. There- fore, by the second law, they must have a particular ex- tension in the conclusion. This last example belongs to the Third Figure. 97. Fourth Law. Place of the Middle Term. The mid- dle term must not be found in the eonelusion. 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. Tiuo affirma- tive premisses demand an affirmative eonelusion. 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 affir- mative and one premiss negative demaiid 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 zve can drazv 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 an elephant; No elephant is a tvJieelbarrow. No conclusion. 101. Eighth Law. No Conclusion. F;^^. two particu- lar premisses we can draw no conchLsion. For they will be either, i, 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 conckision 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 w^here both premisses are singular. In this case there may be a conclusion. Thus : Mars is a planet; Mars is uninhabited. Therefore, One planet is uninhahited. 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. If one premiss be particular, the conclusion must be particular. Of course, by the eighth law, one premiss must be universal. The possible cases with one premiss universal, and one par- ticular, 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- 6o THE LAWS OF THOUGHT. tive ; or we may take a universal negative and a par- ticular affirmative. 1. Making both premisses affirmative, we shall have, Universal Affirmative (with subject utiiversal 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 {TJm'd 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. 6 1 103. 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 hith- erto, for the sake of clearness, given examples of syllo- gisms composed of simple categorical propositions only. Such syllogisms are, as their component propositions, 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 propose to treat of compound syllogisms. We should never end. Attention is called here to three complexi- ties 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, If tJiey 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 tninds. Or the minor may deny the consequent : TJiey are not training tlieir minds. Then the conclusion denies the condition : They are not studying logic. Note. i. 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 train- ing their minds. 2. Hence affirmation of the consequent does not always necessi- tate 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 incompati- ble propositions are proposed in the major by means of a conjunctive proposition (47). The minor denies one, and the conclusion affirms the other. Example : N'o man can spend all his money on drink and still support his family ; But he spends all his inoney on drink. Therefore, Se does not support his family. REASONING, ARGUMENT. 6^ 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. If a man spends all his money on drink, he is unable to support his fafnily; 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 proposi- tion (48). If the minor makes choice of one, the conclu- sion 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 JBut he is neither under fifty nor 2>nst fifty ; Therefore, He is just fifty : Or But he is not just fifty ; Therefore, He is either under fifty or jyast fifty. In the last case, 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. If he is under fifty, he is neither just fifty nor past fifty. The conjunctive 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 — Polysyllogism — 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 syllo- gism, the argument is called an enthymeme. Example : All liquids will 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-np 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 desjyonds ceases to labor; He who ceases to labor makes no progress ; He who maUes no progress does not reach the end. Therefore, He tvho desponds does not reach the end. It is easy to see that this is an abbreviation of two syllogisms. Thus : He ivho desponds ceases to labor; He who ceases to labor makes no jtrogress. Therefore, He ivho desponds makes no progress. The next syllogism begins with this conclusion as a major : He who desponds m,akes no jrrogress ; He who makes no progress does not reach the end. Therefore, He tvho 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. Polysyllogism. 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 tzvice as above, but once, to be used, simultaneously, as conclusion 66 THE LAWS OF THOUGHT. to the two preceding premisses, and as major to a follow- ing minor, our argument is called a Polysyllogis7n. The preceding example, as a polysyllogism, will be : He who desponds ceases to labor ; He who ceases to labor inaTces no progress. Therefore, He who desjionds makes no jyrogress; He who makes no 2)rogress 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 otice). Example : One who denies the existence of God and a future life cannot be trusted in society ; because he ad- mits no inotive to restrain him frotn evil when he can do the evil without tetnporal 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-inorrow morning it tvill he either raining or not raining. Jf it he raining, I will liave an excuse to stay at home. If it he not raining, I can use my per- mission to take a day at the fair. Therefore, Wliatever the weather may he, 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 quality and quantity of the premisses, and in the exten- sion of middle and extremes, in order that a given conclusion may be taken as lawfully drawn from given premisses. If I say, Every stea^nhoat 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 /(?;''/«(^/ 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 TRUTH OF THE PREMISSES. 69 left out of consideration. And for this reason is it called 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 with 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 2l 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 demonstratioji. Leaving aside the probable argument, we shall treat of the demojistratiou 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 : Tixe soul can thinks flatter cannot think. Therefore, The soul is not matter. TRUTH OF THE PREMISSES. /I 119. Indirect. In the indirect demonstration, instead of drawing our conclusion as coming directly 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 sollogisms 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 special article about a peculiar kind of a posteriori argument, 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, C 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 inco^nplete in- duction, 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 formu- late the laws of gravitation, of equilibrium, of reflection, of refraction, from a very limited number of cases ; and we hold these laws to be applicable, as universal propo- sitions, to cases tried and untried. Is the process law- ful .? 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 of thought m.ay 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 validity 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 hetwetn fore o-oin^ zxi^ fol- lowing, his conclusion is universal only to the extent of ^6 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. It 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. JJ Article IV. Fallacies. Begging the Question — Evading the Question — Accident — A Dicto Simpliciter, etc. — Consequent — 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 circulns vitiosus {vicioiLS circle) is of the same order as Xh^ petitio prmcipii. 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 ftuestion {ignorantia elenchi). Under this head may be ranged all those tricks of argument 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 {argumentmn ad hominem), thus arousing 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 assum- ing as essential what is purely accidental. Thus a man might argue against Christianity because some who pro- fess 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 un- qiialified statement to the same statement qualified, or vice versa. This fallacy pervades daily conversation. 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 direc- tion. An exhibition of some knowledge in a few partic- ular matters is soon made the basis for the conclusion that the exhibitor is "learned." 134. Fallacy of the Consequent. This consists in a misuse of the conditional syllogism. Thus some one says : If the gale is strong to-night, the toiver ivill 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 accompany- ing or preceding circumstance, or at most an occasion. 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 steady 80 THE LAWS OF THOUGHT. business, the administration must be changed. And when the administration is changed, and the same diffi- culties occur, the responsibility is shifted to the opposite, 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 pouring forth a volume of objections, one immediately after TRUTH OF THE PREMISSES. 8 1 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. Supposing the premisses to be true and the form of correct argumentation to be fully- understood and rigorously applied, there are still differ- ent methods which may be followed in the search for conclusions, in the pursuit of truth. Moreover, methods which may have proved most satisfactory to our own minds in the search for, and discovery of truth, we may find less satisfactory for communicating the same truth fully, briefly, and clearly to others. We do not refer here to the mere variations of order in which a number of truths, such as dates of events in history, may be learned or communicated, one after another. But we refer to methods of arriving at the knowledge of even one truth as a conclusion, i.e. in such a way as to possess, together with the truth, also the reasons for it. We speak of scientific methods which give us scientific knowledge. Science. 140. Analysis and Synthesis. There are two kinds of scientific method, the analytic and the synthetic. The analytic proceeds by way of analysis or taking apart ; the synthetic, by way of synthesis or putting together. To take a broad example : the chemist analyzes, when he proceeds to find out the nature and proportions of the 82 METHOD, ^3 various elements in a lump of crude matter brought him from the mines ; he synthetizes, when he puts together various chemical elements for the purpose of discovering some new law of combinations. Thus analysis proceeds from the whole to the parts ; synthesis, from the parts to the whole. Before considering the methods of synthesis and analysis we shall touch upon two other points, — defini- tion and division^ — the understanding of which will enable us to speak more briefly and more clearly about the methods. Article II. Definition. Nominal — Real — Descriptive — Genetic — Essential — Physical — Metaphysical — Rules. 141. Definition. Correct definition is a thing always to be prized in writing and discourse, even for its effec- tiveness in concentrating vague thought and shortening discussion. A universal habit of correct definition would be fatal to false argument and would put an end to much debate that is carried on to tiresome lengths. But the habit of correct definition belongs to the trained master mind. And as most minds are not such, and as most men shirk the search and labor demanded by correct definition, therefore have we so much, in phi- losophy as in other things, that is written all around a subject instead of about it. But here we are called upon to give a definition of a definition. Therefore : A defini- tion is the expression in zvords of the meaning attached to a term ; or, a definition is the expression in zvords of the nature of an object. That is to say, there are two kinds '84 THE LAWS OF THOUGHT. of definition. If we fix our attention on the word, to make it known in its character as a sign, we have the nominal definition. If we fix our attention on the thing, to define what it is, we have the real definition. 142. Nominal Definition. We give a nominal definition, (i) When we make known the sense in which we are using a term for the case in question ; (2) When we make known the meaning usually and generally given to a term ; (3) When we declare the true literal mean- ing of a term according to its derivation. Thus, infinite, from the Latin in (a negative particle) and finis (a limit), means zvitJiout limit. 143. Ileal Definition. This may also be threefold, — descriptive, genetic, essential. The descriptive definition is nothing more than a description. It does not enter into the essence of the object. It gives such a combination of accidental fea- tures, circumstances, etc., as may suffice to make the object recognizable. Its treatment belongs to works on composition and style. The genetic definition (from genesis, origin) gives the process by which a thing is produced. A genetic definition of a circle would be : A plane surface gene- rated by revolving a straight line about one of its extremi- ties fixed. The essential definition names the essential parts of an object ; that is, those without which the object can neither be nor be thought of. According to the way in which we look at an object, we may find it made up of separable essential parts which, taken together, will •give us the whole essence; or of inseparable essential parts which, considered as taken together, will also give METHOD. 85 US the whole essence. Such separable parts are called physical parts, and the enumeration of them is the real essential physical definition. Such non-separable parts are called metaphysical parts, and the enumeration of them is the real essential metaphysical definition. Thus, in man, spiritual soul and organic body are essen- tial parts ; they embrace all that is essential ; they are actually separable; taken together, they give us the essence. Hence to say that man is a being co)nposed of a spiritual soul and an organic body, is to give an essen- tial physical definition of man. Again, in man, animal nature and rational nature are essential parts ; they embrace all that is essential; taken together, they give us the entire essence. But they are not physically, that is actually, separable. Take away rational nature, and you have not animal nature left, but only a dead body ; for the principle of life is gone. Such parts are sepa- rable only in the consideration of the mind ; that is, in an order of things outside the real physical order, — or, in the metaphysical order. They are called metaphysical parts. Hence to say that man is a rational animal, is to give the essential metaphysical definition of man. This is the true definition in logic. It classifies accord- ing to those logical considerations spoken of in Chapter H., Article H. It gives the species by combining the two essentials of proximate genus and final difference; and there is no mistaking a thing thus defined. — It is the perfect definition. 144. Eules for Definition. We may summarize the requisites of a good definition : I. The terms of the definition should convey a more definite idea than the single term expressing the thing 86 THE LAWS OF THOUGHT. defined. This does not mean that every term in the definition should always be at once better known by everybody than the single term. When we define a circle to be a plane stirface luith a single ciwvcd line for a boundary every point of iv hick is equally distant from one fixed point in the surface, our definition is less intelli- gible to an ignorant person than is the term circle. But one who learns the meaning of the terms in the defini- tion will get from it a more definite idea than he had before possessing the definition of a circle. 2. Make the definition such that it may be convert- ible by simple conversion (No. 76) with the term express- ing the object defined. Thus: if a circle is a plane surface . . . etc., then a plane surface . . . etc. (as above) is a circle. 3. Do not define by a negation, by saying what a thing is not. However, sometimes a negative term comes up for definition. In this case separate it into its negative and positive parts, and define the positive part. For instance, injustice is the absence of justice. Now ^Q.'ax\.Q, justice, and you shall have defined injustice. 4. Use words in their exact literal meaning ; and when there is a choice of words, use such as are most commonly understood. 5. In philosophical matters insist upon the essential metaphysical definition. It may sometimes be useful to begin with or to work upon the physical definition ; but never lose sight of the metaphysical. METHOD. 87 Article III. Division. 145. Scientific Division. Definition, the perfect logical definition, regards the comprehension of a term (Chapter III., Article V.). Division, the perfect logical division, regards the extension. This difference we must exam- ine into as being of serious importance in all scientific study. A few words, however, first, upon division in general and on certain divisions which are precisely the inverse of the essential definition whether physical or metaphysical. 146. Parts, Physical and Metaphysical. We saw that essential definition (No. 143) is the enumeration of the essential parts, as taken together to form the zvJwle. Division, in general, is a separation of zuJiatever may be regarded as a ivJiole, a unit, into its parts. If we regard an essence as a whole, a unit, made up of the parts enumerated in the essential physical definition, we have what is called a physical whole, which is divisible by physical, actual division into physical parts. Thus man, considered as a physical whole, is divisible actually into the physical parts, spiritual soul and organic body. If, however, we regard an essence as a whole, a unit, made up of the parts enumerated in the essential metaphysical definition, we have what is called a metapJiysical whole, which is divisible by metaphysical, mental division into metaphysical parts. Thus 7nan, considered as a meta- physical whole, is divisible into the metaphysical parts, animal nature and rational nature. 147. Actual Union. The union of parts in both cases is an actual union. The physical parts, however, are really separable ; the metaphysical parts, only mentally. 88 THE LAWS OF THOUGHT. 148. Integral Parts. Parts which are really separable but which are not essential, i.e. not absolutely necessary for the existence of the whole, though belonging to its integrity or entirety, are called integral parts. A hand or a foot is an integral part of man. To summarize, therefore : A whole, regarded in its essence as made up of real parts actually existing, may be considered as made up of physical parts, really sepa- rable ; or of metaphysical parts not really separable. Physical parts which, though belonging to the normal state of the whole, to its integrity, yet can be separated without destroying the essence, are called integral. Thus : a hand or a foot in man. 149. Logical Division. To return now to logical divis- ion : the parts we are especially concerned with, in this article, and which we are to get at by logical division, are not such as are bound together in actual union by an actual bond of unity, so as to make a real, actual something. We are concerned with another kind of parts, those, namely, which are embraced by, and go to make up the extension of an idea or term, not those which are found in comprehension. We said that the perfect definition was the enumeration of notions con- tained in the comprehension. The perfect division is the enumeration of, the partitioning off of what can be reached by the extension of a term. This logical divis- ion is therefore the enumeration, the dividing up, of species under genus, or of individuals under species. A genus is a logical whole ; the species under it and their subdivisions are logical parts. A species is a logical whole ; the individuals it extends to are logical parts. METHOD. 89 The following diagram will explain better than words the precise distinction between logical definition and logical division. To define animal, we go upwards, Substance A Material Organic A Sentient A ANIMAL = ■pefinition Rational (Man). I Irrational. I Charles, Frederic, Augustus, Hannibal, Scipio, etc. | | Vertebrata, Articulata, MoUusca, Radiata. I \ ^,_J ^ taking in the various notions in the comprehension : sentient, organic, material, substance. To divide animal, we go downwards, classifying all that can be reached by the extension of the term. 150. Potential Parts. Every term taken in the reflex universal sense (Nos. 21, 23) expresses a whole which is divisible by this kind of division into the parts of its extension. As thus divisible it is called a potential whole, because it extends not only to what really exists, but also to what exists only in potcntia; that is, to what- ever of the same kind may exist. All the birds in the universe might be destroyed, still bird would express a potential whole embracing all birds past and all birds possible in the present and the future though they shall not all exist, — embracing them all as potential parts 90 THE LAWS OF THOUGHT. into which it {bird^ is capable of being divided by logi- cal division. 151. Logical Whole. This kind of whole, then, is the logical whole ; because, being the object of a reflex uni- versal idea, it does not exist as a unit in reality, but only by consideration of the mind. Thus man, consid- ered as the object (Nos. 21, 23) of the reflex universal idea, is not a one something that can actually be torn asunder into separate men ; nor can substance, taken as the object of a reflex universal idea, be really split up into material and immaterial substance. Yet in the mysterious process of thought, man, substance, do logi- cally embrace all men, all substances, actual and possible. 152. Importance of Division. It is the logical division which we must be careful to have special regard for, in philosophizing. Philosophy deals with the universal. It is from beginning to end a combination and correla- tion of the comprehension and extension of ideas. The advantage of correct logical division in the study of a subject is evident. It maps out the whole question before us, at the start ; and saves us from time-losing, wandering discussions, as well as from incomplete treat- ment of the matter in hand. 153. How to Divide. To divide correctly : 1. Let the sum of the parts be exactly equal to the whole. 2. Therefore see that no single member of the divis- ion is equal to the whole. A bad division of plants would be into those that grow and those that bear fruit. The first member is equal to the whole. METHOD. 91 3. Do not make one member to include another or part of another. This would happen if substance were divided into inunatcrial, material, living and organic. Living enters into material and immaterial. Organic enters into living and material. 4. Divide first into proximate and immediate mem- bers, and then, if possible, subdivide. The meaning of this is that we should first seek the widest general grand divisions and then see if we cannot regard these as new wholes to be subdivided, etc. 5. In scientific matters prefer the logical division. See if the whole may not be regarded as a genus. Mark off the species. See, again, if any species, thus found, may be regarded, in its turn, as a genus (Chapter II., Article III.) ; and do not go on to divide into indi- viduals until a species cannot be regarded as a new genus. (See Diagram No. 30). Article IV. Analysis and Synthesis. 154. The Question Put. We may now go on to the explanation of the methods referred to above (Nos. 139, 140). A proposition is presented to us in study, reflec- tion, reading, conversation, debate. Is it true or false .-* We make an assertion. We do not doubt the truth of our proposition, but how shall we proceed to place it in evidence, by means of demonstration .'' An adversary advances a false statement. How shall we prove it to be false } A single object of thought is offered us for investigation. What propositions shall we formulate regarding it } What shall we predicate of it .-' Of what may it be predicated .■* 92 THE LAWS OF THOUGHT. 155. The Answer : Analysis and Synthesis. Our inves- tigation of any single object of thought must begin by- analysis or synthesis, and must advance by one or the other, either purely by analysis or purely by synthesis, or by changing about, as circumstances may prompt, from one to the other. Let the object of thought pre- sented for investigation be animal. We must begin by trying to make animal the subject or the predicate of a proposition. If we begin by making it a subject, we are using analysis ; we are beginning by the analytic method. If we begin by trying to use it as a predicate, we are using synthesis ; we are beginning by the synthetic method. Again, an entire proposition is presented to us : Animal is substance, or Animal is not mineral. We have to test the truth of the proposition. We must begin by studying the subject or the predicate. If we begin with the subject, we are using analysis ; if with the predicate, we are using synthesis. The meaning of all this and the reasons for the terminology will best be seen in the case of a complete proposition. 156. Analysis. Take the propositions, Animal is sub- stance, Animal is not mineral. Are they true t We know that in an affirmative proposition the form (No. 2o) of the predicate is included in the comprehension of the subject (No. 66) ; and that in the negative propo- sition the form of the predicate is excluded from the comprehension of the subject (No. 68). Suppose we begin by a study of the subject. To see whether the forms, substance, mineral, are comprehended in a?timal, we must take animal apart into all the forms implied in its comprehension. We must analyze it. We do this by taking it as a metaphysical ivhole, proceeding upward METHOD. 93 (No. 149) from the metaphysical whole, rt'wm^/, through all the forms, parts, of its comprehension. There we find substance embraced in the comprehension, but not viiueral. Hence animal is substance, animal is not mi)icraL The process is nothing more than logical definition. 157. Synthesis. On the contrary, if we begin by the study of the predicate, since we know that in an affir- mative proposition the predicate expresses some form that is contained in the comprehension of the subject, we shall — if the predicate be not merely the essential definition of the subject (No. 66) — we shall have to keep adding on to it what is compatible with it until we shall have gathered together all the forms embraced in the comprehension of the subject. Thus (No. 149) we keep on adding material, organic, sentient, one after another, to substatice, until we get a combination that gives us animal. This is synthesis. The process is that of logical division. In the case of a negative proposi- tion, — if it be true, — we may keep on adding to the predicate forever, and we shall never find a combination giving us the subject. This proves that the negative proposition is true. If in an affirmative proposition we fail to find the subject, this shows the proposition to be false. 158. The Explanation Complete. These few words cover all the essentials of synthesis and analysis as sci- entific methods. The words analysis and synthesis are sometimes used in ways that are apt to confuse the mind. Reduce every mode of expression back to that of comprehension, remembering that it varies inversely with extension, and the confusion will disappear. 94 THE LAWS OF THOUGHT. 159. Singular to Universal, and Vice Versa. It is said that analysis proceeds from the singular, or particular, or less universal, to the more universal ; and that synthesis proceeds from the more universal to the less universal. This would seem to contradict all that we have been saying. But remember that reference is here made to the extension, which varies inversely, with the com- prehension. When we proceed from animal up to substance, we go from the less universal to the more universal in exteitsion, though from the wider to the less wide comprehension. Hence there is analysis in both cases. 160. Complex to Simple, and Vice Versa. It is said that analysis goes from the complex to the simple ; synthesis, from the simple to the complex. Understand this of comprehension. This manner of expression is applied to the process from particular concrete facts to the universal law, for analysis; and to the process from the law to particular applications, for synthesis. But how is the single fact complex and the universal law simple .-' You will see it in an illustration. You argue from the par- ticular concrete facts regarding matter, to a universal law regarding matter. The single fact is complex. The matter you have is this or that kind of matter, organic, inorganic, vegetable, animal, mineral, gaseous, liquid, etc. You have a complex comprehension. You have to analyze the separate cases, and cut away from the comprehension, until you arrive at the simpler form, matter, simpler in comprehension, more universal in extension, to make your general law about all matter, without specifying this or that particular kind of matter. Induction is analytic. Deduction is synthetic. METHOD. 95 161. Discovery and Instruction. The modern growing natural sciences groiv by analysis. The sciences that have been explored to satisfaction and present a com- plete whole, as also growing sciences, — botany, chemis- try, etc., — so far as they have been explored and classified, are best taught by the synthetic method. Analysis is best for discovery. Synthesis is, in general, more satisfactory for instruction. The two methods may be used alternately, in the same treatment of the same subject. A change is sometimes useful in the treatment to rouse attention. 162. Analjrtic and Synthetic Sciences. A science is called analytic or synthetic from the method chiefly used in its development. If, however, both methods enter very largely on account of the nature of the subject-matter, we have the mixed method, properly so called. Logic and geometry are synthetic. The vari- ous branches that make up the modern physics are analytic. Civil engineering, taken as a whole, is mixed ; it implies the synthetic mathematics and also the result of analytic observation on material to be used, as well as climatic conditions, etc. — In this little book we have mingled analysis whenever it seemed useful for clear- ness or interest. 163. Advice. With what has been said, the student will be enabled to follow up the complete working of synthesis and analysis by attention to the processes pursued in standard treatises on the various sciences. If you find yourself confronted with the burden of proof or investigation, observe the following : 1. Work cautiously. 2. Consult your actual knowledge. The general out- 96 THE LAWS OF THOUGHT. line of your actual knowledge may determine your method. Particulars may be so scanty that you will see your way to lie only through general principles, by syn- thesis. Or facts may be in such abundance that you may set to work at once by analysis. 3. Beware of being unconsciously betrayed into a fallacy. 4. Be on the alert for the moment when you can formulate a definition of terms. 5. In distributing and classifying, keep in view the logical division. 6. When you have found something by analysis, go over it again by synthesis. This will map it out in your memory. Article V. Science. 164. Science. With a clear understanding of what is required for correct thought, and with some insight into methods of procedure, we may go in pursuit of knowl- edge. Every perception of any truth is knowledge. If this perception be through a demonstration, it is called scientific knowledge. The perception, through demon- stration, of a complete body of related truths regarding a given object, is called science. 165. Object of a Science. The same object may be the object of more than one science. For we may con- sider the same object under different aspects; and obtain, regarding it, different sets-of-connected-truths — each set complete without the other. In other words, we may consider different forms, or formalities, found in the totality of the comprehension of the object. METHOD. 97 166. Material and Formal Object. The object, taken in the totahty of its comprehension, is called the mate- rial object of a science. The particular formality consid- ered, or this formality as affecting the material object — abstraction made from all the other formalities compre- hended — is called the fonnal object of the science. The whole corporeal universe is the material object v.gr. 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 chemis- try is the substantial distinction between elements of matter and their respective capacities for substantial union with one another. Again, various things, even of different orders, may be united into one science by reason of a formality running through them all. Thus, spirit, matter, substance, accident, all contain in their comprehension, the formality of beitig ; and can be taken all together as the material object of the science of being. They can all be considered in the same science, under the aspect of being, and this will give us the science of Ontology. 167. A Delusion. Knowledge acquired by scientific processes is scientific knowledge. The possession of such knowledge is the possession of science. No other knowledge has a right to the name. Children in pri- mary schools who are obliged to memorize a few facts about rocks or animals or flowers, are often instructed to a false acceptation of the word by being told that they are " studying science " ! ! Thus they come to regard geology, zoology, botany, any and every science, as merely a list of facts, and the acquisition of a science to be an affair of memory and not of reason. « -«•« ■^>^ ■f S)§| o •- 1 V — ■■C rt -. ^ > M rt 09 CO a o > .a t30 H S .a H s.a J z< Zw — (U 1) 1.4 c4 a o _Z 2 J u •£<5 < I-' 1) ^ i o m 2 § OT ^ Method of Materi; ork. Formal work, ogic or Laws rial Lo of Thought. Trul Thou o 03 d z_ . z^ o 73 _o ;-• o o H O -Si 173 — a fc ao '0 r! 00 P "(3 ^o PhO 3? M tn O ^ 0) CO ° Sep ^ 1— W.iJ P «a .So o 73 -P O cil J>„bfl 3 tuO 1-1 4: lU O n " > _ 5 o '^ c 'S < S So "3 cJ ? fe (= G ^.2.2 §^" - o o 73 CL, ze. <'^ .'(? —"o < > > Ph O 35 ffl 2 u 3 Z ^^ W hJ(/3 <-S ^b zl^ 98 <^ EXPLANATION OF OUTLINE. 99 In the preceding table or "Outline of the Sciences" we have advanced from the term of least comprehension and greatest extension, namely, the term, Being. That which is represented by the term or concept Being supplies the subject- matter for Ontology, 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-matter of the science called, in philosophy, Natural Theology. Continuing with Finite Being, increasing comprehension and diminishing ex- tension, we have, in a perfect division, Substantial Finite Being and Acciden- tal 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 Material Substan- tial 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 M.-\tekial, etc., we find that range of sciences which treat of inanimate, inorganic matter : Physics, etc. We leave the Inanimate; and we divide the Animate, by adding to the com- prehension, into the Rational and the Irrational. 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 science of Man in general, or Anthropology. From this point forward we are engaged solely with Man. We can no longer divide into species. W^e 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 general principles, we refer over to Sensation. Soul is the subject-matter of the Science, Psychology. Psychology will treat of the Nature of the Soul and the Fo'cvers of the Soul. The Powers of the Soul, we group under three headings : Fozuer of actuating sense-perception, etc. ; Intellect ; Free- Will. Intellect, we consider in its A'ature ; its Method of Work; its Supply of Material. The Method of Work constitutes the object (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 a7id Nature of Free Will; of the Norma or Rule of the Free Act; and oi Practical Morality. 77ie 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 A^orma 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 study- ing, we begin upon the lowest line with Formal Logic. Next, we take up Material Logic. Thus equipped, we go back to Ontology, and follow do^n 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 conclusions 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 alto- gether upon the skill acquired in readily discerning the comprehen- sion and extension of terms. The Laws of the Syllogism — Definition, Division, Synthesis, and Analysis — are all to be learned by the care- ful study of Extension and Comprehension. 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 simple apprehension or of the idea. (10) Give examples of judgments. (11) Upon what two principles does the mind work in reasoning? (13-15) What is a term, a proposition, a syllogism? (17-19) Give three classifications of ideas. (19) Examples of singular, particular, collective, universal ideas. (20) How are universal ideas classi- fied? What is meant by form, formality, or determination, in reference to ideas? (21-27) Examples of species, genus, difference, property, 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) Exam- ples 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 subject, copula, and predicate. (41) Examples showing the difference between the logical and the grammatical predicate. (42) Examples of simple. (43) Com- pound. (45, 46) Categorical, conditional. (47, 48) Conjunctive and dis- junctive propositions. Show how they are reducible to the conditional. (54, 55) Examples of a priori and a posteriori judgments. Show why the a priori are called necessary, absolute, metaphysical, analytical; and the a /cij^,?re'(7r2, contingent, hypothetical, physical, synthetical. (59-61) What is meant by the extension and comprehension of terms or ideas? (62-63) What does the extension of a proposition depend upon? Examples of the four extensions of propositions. (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. (78) 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. (i 14-122) Difference between formal and material logic; between direct and indirect demonstration; between simple and com- pound; between the a priori and the a posteriori. (124) Example of complete induction. (125) What is required for the validity of the incom- plete induction? (129-138) Examples of various fallacies. (145) What is the essential distinction between logical definition and logical division? (146) What is meant by physical and metaphysical parts? (149-153) What is a logical whole? logical division? What are logical parts? 100 ALPHABETICAL INDEX. Numbers refer to Paragraphs. Abstract idea, 17. Accident, inseparable and separable, 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, 33, 36. Analysis, 140, 155, 156. explanation of terminology in regard to, 159, 160. in discovery and instruction, 161. Antecedent in syllogism, 83. Apprehension, simple, 9. as an act, 9. as representative, 9. A prion demonstration, 117, 121. judgment, 55. A posteriori demonstration, 117, 122. judgment, 56. Argument, 11, 15, 80. analysis of, 86. basis of, II, 85. styles of, 81. Argumentation, 11. Axioms, for extension and compre- hension of terms, 58. for argument, 11, 85. Begging the question, 130. Being, predication of, 28, 36. science of, 166. 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 regarding, 58. of idea and term, 60, 61. in analysis and synthesis, 156, 157. Comprehensive idea, 18. Concept, 9. Conclusion, 11, 86. value of, 116. Concrete idea, 17. Consequence, S4. Consequent, fallacy of, 134. in syllogism, 83. Conversion of propositions, 76. Declaration, 10. Deduction, 11, 123. Definition, 141. nominal, 142. real, descriptive, genetic, essential, physical, metaphysical, 143. logical, 143, 156. logical, diagram of, 149. logical and division, difference be- tween, 145. rules for, 144. Delusion, a, 167. loi 102 ALPHABETICAL INDEX. Demonstration, ii6. direct, 117, 118. indirect, 117, 119. simple and compound, 120. a priori and a posteriori, 117, 121, 122. Determination or form, 20. Diagram of figures in syllogism, 89, 90, 91. of genus, species, etc., 30. of logical definition and division, 149. of propositions, 79. of sciences, 168. of seventh law for syllogism, 100. Difference, specific, 25. Differential idea, 25. Dilemma, 81, 113. Direct demonstration, 117, 118. universal idea, 21. Discovery by analysis and synthesis, 161. Distinct idea, 18. Division, 145. physical, metaphysical, mental, 146. logical, 150, 151, 156. logical, diagram of, 149. importance of, 152. rules for, 153. Elenchi, ignorantia, 131. Enthymeme, 81, 109. Epichirem, 81, 112. Equipollence of propositions, 77. Equivalence of propositions, 77. Equivocal terms, 33, 35. Example, argument from, 126. Extension of terms and ideas, 59, 61. of terms, axiom, 58. of predicate, 66, 71. Extremes, extreme major term, ex- treme minor term, 87, 88. Evading the question, 131. Fallacies, 130-138. Fallacy, 116, 129. Figures of syllogism, 88-91. Form (formality or determination), 20. specific, 22. generic, 24. accidental, 27. v/hen both generic and specific, 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, 38. as an act, 10. as representative, 10. immediate, 51. mediate, 52. a priori, necessary, absolute, meta- physical, analytical, 55. a posteriori, contingent, hypotheti- cal, physical, synthetical, 56. synthetic a priori, 57. ALPHABETICAL INDEX. 103 Kant, 57. Knowledge, representative, 8. Laws of extension of predicate, 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, i. Logical and grammatical predicate, 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, advice regarding, 163. analytic, 154-162. mi.\ed, 162. scientific, 139. synthetic, 154-162. Mill, J. Stuart, 125. Mind, three acts of, 7. Minor extreme, 87, 88. premiss, 83, 88. Moods of syllogism, 92. Negative particle, 73. proposition, 72. Notion, 9. Object of a science, 165, 166. material, 166. formal, 166. Objections, fallacy of, 138. Objective, identity, 10. Ontology, 166. Opposition of propositions, 78. Oral expression of thought, 12. Paralogism, ri6. Particular idea, 19. proposition, 63. Parts, physical, metaphysical, separa- ble, inseparable, integral, union of, 146-148. potential, 150. Petitio principii, 130. Polysyllogism, 81, iir. Predicables, heads of, 28. Predicate of a proposition, 40, 65. logical and grammatical, 41. laws of extension, 66-71. Premisses in syllogism, 83. major, 83. minor, 83. Principii petitio, 130. Property, 26. Proposition, 14, 39. simple, complex, 42 ; compound, 43- possible varieties of, 44. categorical, 45. conditional or hypothetical, 46. conjunctive, 47. disjunctive, 48. extension of, singular, particular, collective, universal, 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 equipollence, opposition, 75-78. Question, begging the, 130. fallacy of the, 136. Real supposition of terms, 37. 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, 23. I04 ALPHABETICAL INDEX. Science, 164. object of a, 165. material and formal object, 166. Simple apprehension, 9. demonstration, 120. Singular idea, 19. proposition, 63. Sophism, 116. Sorites, 81, no. 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, material, logical, 37. Syllogism, 15, 81, 82. antecedent, major and minor prem- iss, consequent in, 83, consequence in, 84. figures of, 88-91. moods of, 92. laws of, 93-102. simple, compound, conditional, con- junctive, disjunctive, 104-107. Synthesis, 140, 155, 157. explanation of terminology in re- gard to, 159, 160. in discovery and instruction, 161. Synthetic a priori judgment, 57. Term, 13. classification and use, 32. univocal, equivocal, analogous, 33- 36. comprehension and extension, 59- 61. extreme, extreme major, extreme minor, middle, 87. supposition of, real, material, logi- cal, 37. Thought, form of, 2. material of, 2. oral expression of, 12. Universal idea, 19. idea, direct, 21. idea, reflex, 21. idea, reflex, object of, 23. proposition, 63. Univocal terms, 33, 34. Whole, logical, 151. metaphysical, 146, 156. physical, 146. LIBRARY OF CONGRESS 020 207 203 3