THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 LOS ANGELES 
 
 SCHOOL OF LAW 
 GIFT OF 
 
 The American Academy 
 of Public Affairs 
 of Los Angeles
 
 
 c
 
 ELEMENTS OF 
 
 DEDUCTIVE LOGIC 
 
 BY 
 
 NOAH K. DAVIS, PH.D., LL.D. 
 
 if 
 
 PROFESSOR OF MORAL PHILOSOPHY IN THE UNIVERSITY OF VIRGINIA 
 
 AND AUTHOR OF " THE THEORY OF THOUGHT " " KLE- 
 
 MENTS OF INDUCTIVE LOGIC " ETC. 
 
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 irpot Tat Kurd (/n\u<TUf>iuc <-7riaTi,/ia; . AKISTOTLE 
 
 NEW YORK : CINCINNATI : CHICAGO 
 
 AMEKICAN BOOK COMPANY
 
 Copyright, 1893, by HARPER & BROTHERS. 
 
 All riqhtjt reserved. 
 W. P. 2 
 
 -/ v 
 
 /*(
 
 PREFACE 
 
 THIS treatise is designed as a text-book for under- 
 graduates. It comprises the body of approved log- 
 ical doctrine, so that in a limited time a student 
 may acquire a rounded knowledge of the funda- 
 mental forms _o.f thought, be profited by the excel- 
 lent discipline of the study, and prepared for the 
 pursuit of philosophical sciences. 
 
 Those who wish to go beyond the elements of 
 logic will find much additional matter in my larger 
 work, entitled " The Theory of Thought," designed 
 especially for universities. In my "Elements of 
 Psychology " are explained the relation of the idea 
 as a mental image to the notion as a product of 
 thought, and the various mental processes involved 
 in thinking. In both works many references will 
 be found to authorities and to the literature of the 
 subject. 
 
 In the preparation of the present text, I have 
 tried to be clear, simple, and true, and to mitigate 
 the natural severity of the subject by copious illus- 
 tration. The care I have taken, and my experience
 
 IV PREFACE 
 
 of more than twenty years in teaching logic, lead 
 me to hope that my fellow-teachers and their pupils 
 will find the treatise well adapted to their wants, 
 and that it will therefore tend to promote the study 
 of this admirable and invaluable science. 
 
 A special feature is a praxis appended to i.u-h 
 chapter. Many standard exercises have been re- 
 tained, and many new ones introduced. They have 
 been carefully arranged in progressive order, in cor- 
 respondence with the increasing complexity of the 
 subject. }. would suggest that the working of the 
 praxes alone, without any recitation of the text, 
 will insure a more satisfactory knowledge of ele- 
 mentary logic than the closest reproduction of the 
 text, the praxes being omitted. 
 
 In the chapter on Fallacies, I have adhered to the 
 original Aristotelic distribution, believing that it 
 should be well known to every student of logic, and 
 that none better has been proposed. 
 
 No treatment of induction is included in this 
 book. But, deeply impressed with the importance 
 of that branch of logic, especially in its relation to 
 the physical sciences, I have prepared a companion 
 volume, entitled Elements of Inductive Logic, which 
 completes the system. 
 
 NOAH K. DAVIS. 
 UNIVERSITY OP VIRGINIA.
 
 CONTENTS 
 
 INTRODUCTION 
 
 I. DEFINITION OF LOGIC 
 
 Page 
 
 1. The definition. The word. A valued study 1 
 
 2. Science distinguished from art. Logic a science 1 
 
 3. Thought the object-matter of logic 3 
 
 4. Forms of thought. Second intentions 4 
 
 5. Necessity of the forms. Their violability 5 
 
 6. Free treatment adopted 6 
 
 II. PRIMARY LAWS 
 
 7. Their origin and general character 8 
 
 8. The Law of Identity. Rhetorical forms 9 
 
 9. The Law of Contradiction. Rhetorical forma 9 
 
 10. The Law of Excluded Middle 11 
 
 11. Single statements. Co-ordinate and complementary. . 11 
 
 12. Logic only a negative criterion of reality 12 
 
 13. The postulate of logic. Equipollence 13 
 
 14. Praxis on Primary Laws 14 
 
 PART I. CONCEPTION 
 I. THE NOTION 
 
 15. Abstraction. Marks. Concrete and abstract terms. .. 15 
 
 16. Generalization. Classification. Specialization 17 
 
 17. Conception. Individual and general concepts 18 
 
 18. These momenta coexist. Mark and concept 20 
 
 19. Denomination. Common and proper names 20
 
 VI CONTENTS 
 
 Page 
 
 30. Intension and extension of concepts. Correlated 22 
 
 21. Progress towards perfection. Clear and distinct. ... 23 
 22. Praxis on The Notion 25 
 
 II. RELATIONS 
 
 23. The qualitative and quantitative wholes 26 
 
 24. The quantitative whole, integral and collective 27 
 
 25. The qualitative whole, intensive and extensive 28 
 
 26. Coextension of notions 30 
 
 27. Subordination of notions. Genera and species 30 
 
 28. Praxis on Relations 32 
 
 III. DIVISION 
 
 g 29. Co-ordination of notions. Dichotomy 33 
 
 30. Negative notions. Correlative notions 34 
 
 31. Trichotomy and polytomy. Disparate notions 35 
 
 g 32. The ground, process, and kinds of division 36 
 
 33. Rules for division 37 
 
 34. Praxis on Division 39 
 
 IV.- DEFINITION 
 
 35. Intensive view of definition. An explication of marks 41 
 
 g 36. Indefinable notions. Convertibility 41 
 
 g 37. Extensive view. Intersection. Genus and difference . 42 
 
 g 38. Forms approximating definition 43 
 
 g 39. Kinds of definition ; real, nominal, genetic 44 
 
 g 40. Rules for definition 45 
 
 g 41. Praxis on Definition 47 
 
 V. SYSTEM 
 
 g 42. Scheme of intension and extension 49 
 
 g 43. Scheme of first and second intentions 49 
 
 g 44. The summum genus. In science. In talk 50 
 
 g 45. The infima species. In nature not considered 51 
 
 g 46. Individuals, the basis but not parts of a logical system 52 
 g 47. Relation of division and definition in a system 54
 
 CONTENTS Vll 
 
 Page 
 
 48. Expression of a system. Porphyry's tree 56 
 
 49. Praxis on System 57 
 
 VI. PREDICATION 
 
 50. Its form limited only by self-contradiction 59 
 
 51. Quality of judgments or propositions 59 
 
 52. Existence predicated. Relative. Absolute 60 
 
 53. Negative forms. Pure. Infinite. Impure 61 
 
 54. Intensive and extensive forms. A non-predicable 62 
 
 55. The categories of Aristotle. Interpreted 63 
 
 56. The predicates of Aristotle 64 
 
 57. Praxis on Predication 65 
 
 VII. SIMPLE PROPOSITIONS 
 
 58. Propositions of two kinds, categorical and conditional 67 
 
 59. The categorical proposition dissected 68 
 
 60. The copula, its tense, its quality. Negative subject or 
 
 predicate 69 
 
 61. Strict logical order. Rhetorical displacements 70 
 
 62. Quantity of judgments or propositions 71 
 
 63. Individual propositions 72 
 
 64. Universal propositions. Signs of. Ambiguity of all . 72 
 
 65. Partial or indefinite propositions. Signs of 73 
 
 66. Ambiguity of some. Its semi-definite sense 74 
 
 67. Scheme of the propositional forms 75 
 
 68. Complex propositions. Subdivision. Treated as simple 75 
 
 69. Praxis on Simple Propositions 77 
 
 VIII. COMPOUND PROPOSITIONS 
 
 70. First kind, having components obvious 79 
 
 71. Second kind, exponibles. Exclusives and exceptives. 79 
 
 72. Semi-definite propositions 81 
 
 73. Quantified predication. Small letter symbols 82 
 
 74. Two views; compound qualitative, or simple quantita- 
 tive 83 
 
 75. Rule for quantifying the predicate 85 
 
 76. Praxis on Compound Propositions 85
 
 V1U CONTENTS 
 
 PART II. DEDUCTION 
 
 I. IMMEDIATE INFERENCE 
 
 Page 
 
 77. Definition and distribution of judgments 87 
 
 78. Implications distinguished from inferences 88 
 
 79. Rule limiting quantification. Illicit process 89 
 
 80. Determination. Modified forms of 90 
 
 81. Infinitation. Rule for 91 
 
 82. Conversion. Three kinds of. Remarks 91 
 
 83. Opposition. Square of. Rules. Table of relations . 94 
 
 84. Praxis on Immediate Inference 97 
 
 II. THE SYLLOGISM 
 
 85. Reasoning and the syllogism illustrated and defined. . 99 
 86. Dissection of tbe syllogism. Its parts defined. Their 
 
 order 100 
 
 87. Notations, circular and linear, disapproved ; graphic, 
 
 approved 102 
 
 88. Intensive and extensive forms. Rule for converting. 104 
 
 89. This distinction examined, and discarded 105 
 
 90. The syllogistic judgment. Characterized by neces- 
 sity 107 
 
 91. Relative truth or falsity of its several propositions. . . 108 
 
 92. Praxis on Tbe Syllogism 109 
 
 III. CANON AND RULES 
 
 93. The canon. Four forms of, with comments Ill 
 
 94. The eight general rules, with reasons and comments. . 114 
 
 95. Praxis on Canon and Rules 118 
 
 IV. FIGURE AND MOOD 
 
 96. The four figures explained and illustrated 120 
 
 97. Special rules relative to the several figures 121 
 
 98. The nineteen moods, how ascertained 123
 
 CONTENTS IX 
 
 Page 
 
 99. Names of the moods. Two basic forms. The con- 
 clusions 123 
 
 100. Reduction, ostensive. How accomplished. General 
 
 rule 125 
 
 101. Reduction, indirect. How accomplished. Superflu- 
 ous 127 
 
 102. The fourth figure criticised. Superfluous and erro- 
 neous 128 
 
 103. Praxis on Figure and Mood 129 
 
 V. MODIFIED FORMS 
 
 104. The enthymeme. Its four orders illustrated 132 
 
 105. The epichirema. Defined and illustrated 134 
 
 106. The sorites. Its two forms. Five points noted. . . . 134 
 107. Compound and irregular syllogisms, with illustra- 
 tions 136 
 
 108. Seven methods of argumentation. Remarks 139 
 
 109. Praxis on Modified Forms 142 
 
 VI. CONDITIONAL PROPOSITIONS 
 
 110. Conditions, three kinds real, causal, logical 146 
 
 111. General distribution of propositions 147 
 
 112. The conjunctive proposition. Forms of 148 
 
 113. The disjunctive. Contradictory forms of 149 
 
 114. The disjunctive. Modified forms of 150 
 
 115. The conjunctive-disjunctive. Forms of 152 
 
 116. Interpretation of the conjunctive judgment 153 
 
 117. Praxis on Conditional Propositions 155 
 
 VII. CONDITIONAL SYLLOGISMS 
 
 118. Reasonings founded on conditional forms 158 
 
 119. The conjunctive syllogism; axioms, moods, rules. ... 159 
 120. The disjunctive; contradictory, subcontrary, and cop- 
 ulative 161 
 
 121. The conjunctive-disjunctive; double treatment 163 
 
 122. The dilemma; simple and complex forms 163 
 
 123. Criticism and estimate of the forms 165 
 
 124. Praxis on Conditional Syllogisms 168
 
 CONTENTS 
 
 VIII. QUANTITATIVE FORMS 
 
 Page 
 
 125. The quantitative whole. Kind and degree 171 
 
 126. Quantitative notions, common and proper 171 
 
 127. Judgments of equality and inequality 172 
 
 128. Immediate inference 174 
 
 129. Mediate inference. Syllogisms of equivalence 175 
 
 130. Geometrical illustration. Its generality 177 
 
 131. Mediate inference. Syllogisms of inequality 178 
 
 132. Praxis on Quantitative Forms 180 
 
 IX. FALLACIES 
 
 133. Definition. Two remarks. Distribution 183 
 
 134. Paralogisms. Apparent violations 184 
 
 135. Sophisms in diction ambiguities 185 
 
 136. ^Equivocatio. Its importance. Jests 185 
 
 137. Amphibolia. The oracles 186 
 
 138. Compositio et divisio. Another view. Punctuation.. 187 
 
 g 139. Accentus, prosodia. Sarcasm 188 
 
 140. Figura dictionis. Solecisms and paronyms 189 
 
 141. Sophisms in matter. Meaning of this title 190 
 
 142. Accidens. Illustrations 190 
 
 143. Secundum quid. Two forms of 191 
 
 144. Ignoratio elenchi. Enlarged view of 192 
 
 145. Consequens. Two forms of 193 
 
 146. Petitio principii. Five forms of 194 
 
 147. Non causa pro causa. An erroneous view of 196 
 
 148. Plures interrogationes, or cornutus. Varieties of . . . 197 
 
 149. Praxis on Fallacies 198 
 
 INDEX.. . 205
 
 ELEMENTS OP 
 
 DEDUCTIVE LOGIC 
 
 INTRODUCTION 
 I. DEFINITION OF LOGIC 
 
 L. Logic is the science of the necessary 
 forms of thought. The word logic is Greek. 
 Aristotle, the author and finisher of the science, 
 did not give this name to his work, but it was ap- 
 plied by his followers, and has been for many cen- 
 turies its universally recognized title. In the me- 
 diaeval universities, logic was studied as one of three 
 ways to eloquence, and in modern schools it is just- 
 ly held in high esteem as an independent science 
 and an excellent discipline. 
 
 It will be well, at the outset, to have a distinct 
 explication of the several terms used in the forego- 
 ing definition of logic, and to this we now proceed. 
 
 2. A science is a complement of knowledge 
 having, as to form, the character of logieal perfec- 
 tion; as to matter, the character of truth. Log- 
 ical perfection requires primarily that the objects 
 
 1 
 
 I /
 
 2 INTRODUCTION 
 
 of knowledge shall be classified clearly, distinctly, 
 completely, and harmoniously. Truth requires that 
 the objects be real; what is unreal and false cannot 
 constitute a science. Hence, a science is a perfect- 
 ed system of truths; or, science is classified knowl- 
 edge. Few branches have reached this ideal per- 
 fection ; perhaps pure mathematics alone has done 
 so; but others, having made high attainments, are 
 properly called sciences. 
 
 Science and art should be distinguished. A sci- 
 ence teaches us to know, an art to do. Science 
 discovers laws, art gives rules. Science is specu- 
 lative, art practical. The scientist knows the prop- 
 er relations of things, the artisan brings them into 
 these relations. There is a science of civil law, 
 there is an art for the practitioner, Anatomy is a 
 science, surgery an art. But science often leads 
 so directly to art, and art is so dependent on sci- 
 ence, that they are not always clearly distinguish- 
 able. 
 
 Now, logic is not at all an art, but strictly a sci- 
 ence. It tells us how we think when we think cor- 
 rectly, but does not pretend to tell us how to think. 
 It is of great interest to know what are the princi 
 pies and processes of thought, the laws that regulate 
 intellect in the attainment of truth. Yet knowl- 
 edge is power, and when one has mastered this sci- 
 ence there is a practical result in a special cultiva- 
 tion of his faculties ; for whatever process one clear- 
 ly understands, it is manifest he can more efficiently 
 perform. As grammar and rhetoric are helpful to
 
 DEFINITION OF LOGIC 6 
 
 correct and elegant speaking and writing, so logic 
 is helpful to correct and cogent thinking. 
 
 3. The object-matter of logic is thought. Each 
 science has its own object-matter. As .astronomy 
 treats of the stars, geology of the earth's crust, zo- 
 ology of its fauna, botany of its flora, mathemat- 
 ics of quantity, theology of God. philosophy of prin- 
 ciples, psychology of mind, ethics of morals, so logic 
 treats of thought. Thought denotes the acts of the 
 understanding as distinguished from perception, 
 memory, imagination, feeling, desire, and volition, 
 of whose exercises logic takes no notice. Thought 
 is the bringing a notion into or under another. 
 This is to comprehend or understand it. For ex- '] 
 ample, when I say a lily is a flower, I bring my( 
 notion lily under a class-notion flower, and so this' 
 is a thought. Now, we think about all kinds of 
 things, but logic is indifferent to all except one 
 that is, thought itself. In studying logic, we think 
 about thought. As a science, it is the theory of 
 thought. 
 
 Let it not be supposed, however, that logic treats 
 of thought as exercised in scientific pursuits only. 
 It treats of thought universally. Thought as found 
 in all sorts of literature and speech, in common 
 conversation, in silent meditation, all our every-day 
 thinking about the most trivial things at any in- 
 stant, as well as the lofty thought of the philoso- 
 pher or theologian, is of the same nature, proceeds 
 in the same manner, is according to the same laws, is
 
 4 INTRODUCTION 
 
 logical if correct. Logic explains how any human 
 mind thinks correctly at any time about any thing. 
 
 4. It appears, then, that logic has nothing to 
 do with the things we think about. It treats of 
 thought in disregard of its contenfr. Excluding the 
 matter of thought, it discusses the form of thought. 
 The form as distinguished from the matter may be 
 exemplified thus : When I think that the book be- 
 fore me is a folio, the matter of this thought is 
 book and folio, the form is a judgment. Thought 
 is concerned with the relations of objects to each 
 other, and the nomenclature of logic consists of the 
 names of these relations apart from the objects re- 
 lated ; as, judgment, concept and mark, species and 
 genus, subject and predicate, definition, syllogism, 
 dilemma, etc. These are all names of mere forms 
 of thought. 
 
 In mediaeval logic, the matter and form were dis- 
 tinguished as first and second intentions. First in- 
 tentions are names of objects ; as, lily and flower, 
 book and folio. Second intentions are names of 
 relations ; as, species and genus. Hence a second 
 intention is, in modern logic, a form of thought. 
 Logic, then, is ascience of second intentions. Gram- 
 mar, also, is a science of second intentions, treating 
 of the forms of speech ; as, verb, adverb, noun, ad- 
 jective, clause, sentence, etc. Grammar is the sci- 
 ence of second intentions or forms of speech. Log- 
 ic is the science of second intentions or forms of 
 /thought.
 
 DEFINITION OF LOGIC O 
 
 The matter and the form of thought cannot have 
 any actually separate existence. No object is think- 
 able except under some form of thought ; no form 
 of thought can have any existence in consciousness 
 unless there be some object of thought. But by 
 abstraction we can contemplate these apart; we 
 can consider either the object of thought or the 
 manner of thinking it ; we can distinguish the form 
 from the content or matter. Logic,Jtherefore, is i an 
 abstract science, abstracting from all matter the 
 mere form of thought, and considering this only. 
 
 It follows that logic stands in a similar and fun- 
 damental relation to all other sciences, for it consid- 
 ers only what is common to all that is, the forms 
 of thought to which all are subjected making that 
 alone its object-matter. Now, philosophy is the sci- 
 ence of principles, and therefore fundamental in 
 treating of the primary truths that underlie all 
 knowledge. But philosophy proceeds logically or 
 not at all. Hence logic is fundamental even t phi- 
 losophy, in that it exhibits the processes of thought 
 which bind philosophy as well as all other sciences. 
 Moreover, logic itself must proceed logically, and 
 can become a science only by conforming to those 
 laws which it is its province to explicate and ex- 
 hibit. 
 
 5. Logical forms are necessary forms. That is 
 to say, the mind cannot think truly, unless it pro- 
 ceed according to these forms. It must not be 
 understood that logic invents laws to control our
 
 6 INTRODUCTION 
 
 thinking ; it merely discovers and unfolds the strict 
 necessities that exist in the very nature of mind and 
 things, and formulates them as laws of thought. It 
 demonstrates that the mind must proceed accord- 
 ing to these laws or under these forms, if the pro- 
 cess be truly consecutive from one thought to an- 
 other. Any violation of the laws, or deviation from 
 the forms, it shows to be an inconsequence, and 
 therefore futile. 
 
 For these laws are not necessary in the sense that 
 they are inviolable. We may wilfully or ignorantly 
 disregard them ; and, blinded by prejudice or pas- 
 sion or confusion of thoughts, we often do violate 
 them ; but the process is fallacy and error, and the 
 result null and void. All consequent thinking must 
 be legitimate ; that is, it necessarily conforms, con- 
 sciously or unconsciously, to these laws. The con- 
 formity is necessary to valid thought. This is log- 
 ical necessity (not unlike the practical necessity of 
 a certain means to a certain end), and should be dis- 
 tinguished from philosophical necessity and moral 
 necessity. 
 
 6. Such, then, is the definition of Pure Logic, 
 both Deductive and Inductive. Since it excludes 
 the matter of thought, considering only its form, a 
 strict observance of its limits would forbid the use 
 of concrete examples. This would make the treat- 
 ment very narrow, dry, and difficult. We shall 
 therefore transgress the bounds of the definition 
 whenever it seems desirable, and give concrete illus
 
 DEFINITION OF LOGIC 
 
 trations involving matter, hoping to enliven and 
 facilitate the study. The student, however, should 
 constantly keep in mind that logic has nothing to 
 do with the matters thought about, does not at all 
 concern itself with the truth or falsity of any prop- 
 ositions used for illustration, but deals only with 
 the forms in which such matter is expressed.
 
 II. PRIMARY LAWS 
 
 7. An analysis of our thoughts, discharging 
 their matter, discovers that they have definite forms 
 ( 4). These forms, being native and necessary ( 5), 
 are universal; that is, they are in all thoughts, 
 and all thoughts are in them. Since they are uni- 
 versal, we may view them as conforming to laws ; 
 and these, when formulated, are known as the laws 
 of logic. Now, a thorough analysis of the empty 
 forms, rejecting their differences, discloses certain 
 general abstract principles. As the result of com- 
 plete analysis, these are ultimate; as essential in 
 every thought, even in that of themselves, they are 
 necessary; as common to all the forms, they are 
 strictly universal ; as intuitively self-evident, they 
 are axiomatic. These, then, are called Logical 
 Principles, or Primary Laws of Thought. 
 
 This complement of laws is assumed by logic as 
 its punctum saliens, and it proceeds to demonstrate 
 from them as axioms the secondary and special 
 laws that regulate all thinking. The whole of pure 
 logic is only an articulate development of the pri- 
 mary laws and of their applications. Deductive 
 logic posits three laws; inductive logic superadds 
 others.
 
 PRIMARY LAWL 9 
 
 8. The three primary laws are as follows: 
 The first is the LAW OF IDENTITY. It is the princi- 
 ple of affirmation. It is variously stated, but pref- 
 erably thus : Whatever does not contradict a / 
 subject may be affirmed of it. The subject 
 and the attribute are thereby identified ; hence the 
 name of this law. E. g., A is A; 2x3=6 ; The 
 moon is our satellite / Francis Bacon is Lord Veru- 
 lam Saltpetre is nitrate of potassa. In these ex- 
 amples the identity in thought is entire. 
 
 But the law extends to partial identity. E. g., 
 A is a / 6 > 4 ; The moon is spherical / Congress is 
 in session ; Silver is a metal. In this case one term 
 is only a part of the content of the other. The 
 great majority of propositions take this form ( 50). 
 
 Supplementary laws are: Whatever is essential 
 inlT subject InusTHSe affirmed ofjt ; as, The sun is 
 'bright; and, Whatever is not essential in a subject 
 may be denied of it ; as, The sun is not up. 
 
 Strictly logical propositions are always to be con- 
 strued literally, and should be distinguished from 
 rhetorical forms, wherein more is meant than meets 
 the ear. E. g., A man's a man for a* that / What 
 I have written I have written y I am that I am. 
 Such highly significant expressions in rhetorical 
 identity have no meaning when taken literally. 
 
 9. The second is the LAW OF CONTRADICTION. It 
 is the principle of negation. Its statement is : 
 Whatever contradicts a subject must be 
 denied of it. Being in opposition, the subject
 
 10 INTRODUCTION 
 
 and an attribute are thereby set apart. Contradic- 
 tories cannot coexist ; affirmations not self -consist- 
 ent are unintelligible. If we attempt to unite them, 
 the thought is null, it destroys itself. E. g., A is 
 not A, = ; The circle is square ; The larger half ; 
 The laws of chance I expected to be disappointed ; 
 It is certain that nothing is certain. This is the log- 
 ical paradox, or logical absurdity. Also notions 
 that are incongruous, as noisy colors, are essentially 
 contradictory, and cannot coexist. 
 
 According to the law, we must deny contradic- 
 tories of each other. Of two contradictories one 
 must be false. E. g., A is not non-A; 2+ 3 is not 4; 
 No pain is pleasurable What is wrong can never 
 be right ; No lie is of the truth. Let it be observed 
 that A and non-A divide the universe of things, so 
 that whatever is one is not the other; everything 
 is either man or non-man. Such opposition is abso- 
 lute contradiction. But the members of a genus or 
 logical universe, though in themselves mere contra- 
 ries, are contradictory of each other relatively to 
 their limiting genus. Thus, if we take the universe 
 animal, then everything within this universe or 
 genus is either man or non-man, i. e. brute, and so 
 these are contradictories. E. g., A man, is not a 
 brute likewise, A fish is not a reptile A whale is 
 not a fish A vine is not a tree. For similar rea- 
 sons, an attribute incongruous to a subject is to be 
 denied of it; as, A dishonest man is not trust- 
 worthy. Likewise two individuals are denied of 
 each other ; as, fronds Bacon is not Roger Bacon.
 
 PRIMARY LAWS 11 
 
 Rhetorical contradictions are often used to con- 
 vey emphatically a covert meaning. E. g., Sitter 
 Sweet; Festina lente Not to decide is to decide; 
 When I am weak, then am / strong ; Hope that is 
 seen is not hope y In diplomacy ; whatever is is some- 
 thing else Learned ignorance is wiser than pre- 
 sumptuous 'knowledge. Such opposites are like the 
 barbs of an arrow. The invisible point pierces, the 
 barbs cling. This is the rhetorical paradox. 
 
 10. The third is the LAW OF EXCLUDED MIDDLE. 
 It prescribes a necessity in affirmation. A state- 
 ment is: Whatever contradicts a contradic- 
 tory of a subject must be affirmed of it^ Evi- 
 dently, of two absolute contradictories one must 
 be true of any subject. If a genus or logical uni- 
 verse be strictly divided into two species, every- 
 thing within it must be of one or the other kind. 
 In either case no third affirmation is possible, i. e., 
 every middle possibility is excluded; hence the name 
 of this law. E. g., X is either A or non-A ; God ex- 
 ists, or does not exist ; Every animal that is not a 
 man is a brute; Defence being impracticable, we 
 must yield / To be or not to be, that is the question ; 
 If he do not fulfil the agreement, I shall be disap- 
 pointed. The argument called reductio ad absur- 
 dum ( 108) is an application of this law. Of two 
 contradictory alternatives it shows one to be ab- 
 surd, hence the other must be allowed. 
 
 11. The second and third laws are often united
 
 12 INTRODUCTION 
 
 Fin one brief but compound statement ; as, Of two 
 contradictories one must be false, the other true ; 
 or, Any attribute^ must be either denied or affirmed 
 of any subject. 
 
 It has been proposed to reduce the three laws to 
 one simple statement ; as, All thought must be self- 
 consistent. But an analysis of self-consistency will 
 evolve the three laws as its ground. Still contra- 
 diction is obviously their common principle. 
 
 Also the attempt has been made to deduce from 
 one the other two. But neither can be inferred as 
 a second from another as first. In every such at- 
 tempt the inferred law is necessarily presupposed, 
 4 L which is petitio principii, Like the sides of a tri- 
 angle, not only are they not the same, not reduci- 
 ble to unity, but also each gives, in its own exist- 
 ence, the existence of the other two. The three 
 are co-ordinate and complementary T di>t,inp.h yp|. 
 insejDarable. 
 
 12. It has already been said that logic is con- 
 cerned only with the form, not at all with the mat- 
 ter, of thought. Consequently, it furnishes no guar- 
 antee or criterion of the material truth of any 
 proposition. There is no logical fault in our say- 
 ing, for instance, that Spain is an island, or that 
 Theft is justifiable. These false affirmations are in 
 accord with the first law, and so are formally cor- 
 rect. What is conceivable in thought may be quite 
 impossible in fact, and so is merely logically possi- 
 ble ; as, a centaur. For the sphere of thought is
 
 PRIMARY LAWS 13 
 
 far wider than the sphere of reality, and there is 
 no valid inference from the correctest thinking a 
 thing to its actual existence. 
 
 But whatever violates either of these laws we 
 know is impossible, not merely in thought, but in 
 reality. We cannot allow that a thing can differ 
 from itself, or that it can both be and not be, or 
 that it can neither be nor not be. AVe must regard 
 that as false and unreal which these laws condemn. 
 They thus determine the sphere of impossibility, 
 and that not merely in thought, but in reality ; not 
 only logically, but metaphysically. 
 
 While, then, these laws are no criterion of the 
 reality of an object or of the truth of a proposi- 
 tion, they are a strict and universal criterion of 
 non-reality and of falsity. Thus they are related 
 to existence, not positively, but negatively. And 
 this holds equally of all the secondary and special 
 laws of logic. Our science, then, in its relation to 
 other sciences, is not a positive criterion of truth ; 
 it is only _a negative criterion, being conversant 
 with thoughts, and not with things ; with the pos- 
 sibility, and not with the reality, of existence. 
 
 13. Beside the primary laws we place the 
 POSTULATE OF LOGIC: Lgic postulates to states 
 explicitly all that is implicit in a thought. 
 As pure logic has no concern at all with the mat- 
 ter of thought, so it has none with its language. 
 It deals not in words, and must not be bound by 
 them. Now, ordinary speech is often elliptical 
 and rhetorical, much of thought being conveyed
 
 14 INTRODUCTION 
 
 in hints and metaphors. In dealing with it, the 
 logician must be free to strip off all ornament, to 
 supply all lacuna?, and so exhibit the thought 
 naked and entire. This is sometimes difficult to 
 do, thought being so subtile and evasive, and words 
 so meagre and inaccurate. The only limitation is 
 that the thought itself must not be changed. Also, 
 there must be liberty to alter the form, provided, 
 likewise, the thought be not modified. t Expressions 
 |hus translated or transformed are equipllent,and 
 the procedure is by equipollence. 
 
 14. Praxis. What point or points of this chap- 
 ter are obviously exemplified, and in what way 
 illustrated, by each of the following propositions? 
 
 1. George Sand is a woman. He is she. 
 
 2. Courts of justice are worse than useless. 
 
 3. That which survives is the fittest. 
 
 4. When an irresistible force meets as insurmountable 
 
 obstacle, the result is compound stationary motion. 
 
 5. Man is the only being that laughs. 
 
 6. Will is either free or necessitated. 
 
 7. That Herod is a fox, means that he is cunning. 
 
 8. Richard is himself again. 
 
 9. If death be death, these have passed into the past; 
 If death be life, they live, though their semblance dies. 
 
 10. Summum jus. summa injuria. 
 
 11. A man who never makes mistakes, never makes any- 
 
 thing else. 
 
 12. If a man be wise, he is cautious, which is to soy, 
 
 Every wise man is cautious. 
 - 13. His honor rooted in dishonor stood, 
 
 And faith unfaithful kept him falsely true.
 
 PART I. CONCEPTION 
 I. THE NOTION 
 
 15. A notion is either a mark or a concept. 
 In the forming of notions three movements^of , 
 thought may be discerned : abstraction, general- 
 ization, and conception. First of abstraction^ 
 
 When a complex object impresses us, it is appre- 
 hended as possessing qualities. In so far as they 
 are dissimilar, they cause in us a feeling of differ- 
 ence. Now, if attention be fixed on one quality, 
 as the color or the weight, the other qualities be- 
 come obscure, while this one is drawn by attention 
 into vivid consciousness, and so becomes the chief, 
 perhaps the exclusive, object of cognition. This 
 quality is said to have been abstracted, or drawn 
 away from, the others, and the process is called 
 logical abstraction. By it we obtain a clear and 
 distinct knowledge of the qualities, attributes, char- 
 acters, features, etc., that determine an object, or, 
 in general, of its marks. 
 
 Marks considered merely in respect of their form 
 are of several kinds T which may be designatgd_and_ 
 exemplified as follows : 
 
 1st. Positive and negative ; as, rational is a 
 positive, and imperfect a negative, mark of man.
 
 16 CONCEPTION 
 
 2d. Essential or necessary, and accidentaLojLcon- 
 tingent ; as, rational is an essential, and learned an 
 accidental, mark of man. 
 
 3d. Original and derivative; as, rational is an 
 original, and learned a derivative, mark of man, de- 
 rived from his rationality. 
 
 4th. Simple and complex ; as, conscious is a sim- 
 ple mark, it being incapable of analysis, and ani- 
 mal a complex mark of man, this being composed 
 of organized and sentient, 
 
 5th. Common and peculiar ; as, mortal is a mark 
 common to man and brute, risible a mark peculiar 
 to man, found in no other being. A peculiar mark 
 is called a property when viewed apart from the 
 essence as belonging to a certain class of things, 
 and to no other ; as risible is a property of man, 
 and a property of the circle is that the chord of 60 
 is equal to the radius. ^A peculiar mark is called a 
 particular mark when it is found onlyjnasmgle 
 individual : as the mark set upon Cain. 
 
 A mark is very often thought of as though it 
 were itself a substantial thing. Instead of being 
 referred to its original substance, it is completely 
 severed therefrom by thought, and established in 
 an independent but fictitious existence. Marks so 
 treated are called abstractions, and are expressed 
 by abstract terms, very many ending in -ness. E. g., 
 blue is a concrete mark of the sky, of the ocean, of 
 sapphire, etc. ; but Uueness is thought of as some- 
 thing independent of these things and having a 
 real existence apart, which is a mere fiction of
 
 il -L i T 
 
 THE NOTION 17 
 
 thought. Likewise, Aristides is /ws, but we extol 
 justice apart from any person. Here the mark 
 just is thought as concrete in the man, inhering 
 in him ; but justice is thought as abstract and hav- 
 ing independent being. So human is a concrete, 
 humanity an abstract term. A concrete term is 
 the name of an inhering mark ; an abstract term 
 is the name of a mark viewed as an independent 
 and substantial thing. 
 
 16. In observing several objects, we note that 
 they differ in some respects, or produce dissimilar 
 impressions; perhaps we also note that they are 
 alike in some respects, or produce similar impres- 
 sions. The repetition of an impression is precisely 
 what excites attention, and determines the direc- 
 tion of reflection. Thus consciousness is concen- 
 trated naturally on those objects which partially 
 agree, and then on those respects or marks in which 
 they agree. For example, we observe a horse, an 
 ox, a goat, a dog, and we note that each has four 
 feet, in which respect they agree. When marks 
 are^entirely similar the impressions they make on 
 us are indistinguishable. But what we cannot dis- 
 tinguish is to us virtually the same. Accordingly, 
 we consider them to be the same, though really in 
 different objects. This act, to think the similar 
 
 n. We 
 
 think that each of the animals named above has 
 the same mark, four-footed. A plurality is reduced 
 to unity, and the generality of the mark consists 
 2
 
 18 CONCEPTION 
 
 in this, that it may be said of any of the objects. 
 Generalization is a fiction of thought, but without 
 it our limited powers would be unable to grasp the 
 multiplicity of objects about us. 
 
 Generalization is classification, another aspect of 
 the same operation. By thinking a mark as com- 
 mon to several individuals, we thereby group them ; 
 we constitute a class. Thus, the animals named 
 belong to the group or class quadruped. 
 
 Now, in considering this group of quadrupeds 
 we note that the ox and goat each have horns ; so 
 we generalize and call them horned quadrupeds. 
 The horse and dog have no horns ; so we general- 
 ize and make a group of non-horned quadrupeds. 
 This is specialization, correlative to generalization. 
 We have marked off two species, the horned and 
 the non-horned, the A and the non-A, subordinate 
 to the genus or universe quadruped, which is their 
 sum. It is obvious that specialization is the inverse 
 of ^generalization, involves it, and likewise is clas- 
 sification. 
 
 17. A third movement of thought is concep- 
 tion, its product, a, con rapt. JCo__cojiceiYe is to grasp 
 
 together. When a number of marks have been 
 abstracted, they may^be. collected by thought into 
 one notion, and so constitute a concept. A con- 
 cept, then, is a union of marks, or a bundle of 
 marks, thought as belonging to some thing. 
 
 Each object has an indefinite plurality of marks. 
 Many of them may be known to us, but a mental
 
 THE NOTION 19 
 
 representation of an object becomes confused if we 
 attempt to grasp into one or comprehend more 
 than a very few of them. We therefore make a 
 selection of some distinctive and some essential 
 marks to form our concept, and must be content 
 with this partial and inadequate representation. 
 For example, I take the marks Athenian, inquisi- 
 tive, virtuous, moralist, famous, martyr, these and 
 perhaps others, to constitute my notion of Socrates. 
 I may know much more about him, but practically 
 this, or some such limited group of marks, com- 
 prises all I use in representing him. On the sup- 
 position that these marks have not been general- 
 ized, the concept is complex, but not general. Yet 
 a notion thus formed of an individual is potentially 
 general, potentially a class notion. There might 
 be several persons having all the marks here at- 
 tributed to Socrates. We must then add a partic- 
 ular mark, as, Plato's teacher, to the notion and 
 thus secure its individuality. 
 
 When a concept is constituted of marks that 
 have been generalized, that is, of common marks, 
 the notion is then both complex and general. It is 
 a class notion, comprising the objects to which the 
 marks are common. For example, I take the fol- 
 lowing marks, which I have abstracted and general- 
 ized, each of which I have thought as common to 
 a large number of objects : self- luminous, bright, 
 sparkling, celestial, very distant, relatively fixed, etc. ; 
 and, making a unity of this plurality, I form the 
 concept star. This complex notion is applicable to
 
 20 CONCEPTION 
 
 each of a host of distinct objects, in which fact its 
 generality consists ; and the word star, which stands 
 for this bundle of marks, is the common name of 
 many individual things. A general concept^ then, 
 isji combination or reduction to unity in thought 
 of similar marks of objects, thereby constituting a 
 class. 
 
 18. The three momenta we have described are 
 not separate and successive in thinking, but are so 
 distinguished and stated to enable us to compre- 
 hend what is actually an indivisible operation. It 
 is merely a logical analysis of an activity whose 
 movements co-operate and coexist. 
 
 Moreover, a mark ^nd concept are commutable. 
 Everyjnark is potentially a concept, and every con- 
 cept potentially a mark. Thus : Man is animal, or 
 Man is an animal. Here animal is first a mark, 
 then a concept. The distinction consists in the use 
 made of the notion. If used connotatively, the no- 
 tion is a mark ; if used denotatively, the notion is a 
 concept. Man is animal means that man has the 
 attributes connoted by the mark animal. Man is 
 an animal means that man is one of the kind of 
 things denoted by the concept animal. 
 
 19. A notion would immediately fall back into 
 the infinitude and confusion from which it has been 
 called out, were there not some especial means to 
 render it permanent. This is accomplished by a 
 word. The notion is fixed and ratified by a verbal
 
 THE NOTION 21 
 
 sign, by means of which it can easily be recalled. 
 Language, even in mere denomination, is a register 
 of thought. 
 
 The name of a general notion is a common noun. 
 Every common noun consists of one or more at- 
 tributes belonging to each of several objects. It 
 stands for a product of thought, and is a factitious 
 unit useful in further thought. A mark is expressed 
 by an adjective noun, a concept by a substantive 
 noun, and an abstract noun is the name of a mark 
 thought as a thing. Let it be observed that many 
 notions, both marks and concepts, are registered in 
 phrases instead of single words; as, for instance, 
 there is no single word to express the notion of 
 morally weak, or of a rainy day. Also, a verb is 
 the naming of an action or passion or mere being. 
 
 A common noun is often used to_designate an 
 individual object or group by prefixing a limiting 
 word ; as, a svng, this world, those books, my house, 
 the king, your friends, these troubles, etc. Such 
 naming designates the object^ thpu^_mdiyidual- 
 ized, as belonging to a class. The terms are con- 
 notative ; they imply marks, and attribute these 
 marks to the object or group they indicate. 
 
 A proper noun, strictly taken, is non-connotative. 
 It denotes an individual, but in itself does not im- 
 ply or indicate any qualities or marks of the indi- 
 vidual. It is an unmeaning sign which we connect 
 in our minds with an object, so that when it meets 
 our eyes or ears it recalls to mind the thing. This 
 is true of names strictly proper. But a name stand-
 
 22 CONCEPTION 
 
 ing for a notion of an individual is evidently a com- 
 plement of marks, as the example in 17 of the 
 notion Socrates. Moreover, names of individuals 
 are often so contrived that they indicate their class; 
 thus, names of persons generally distinguish sex, 
 also family relations; and names of mere things 
 also often have class significance, as Monticello, 
 Charlottesville, Fluvanna. In such cases marks are 
 connoted, and there is a distinct approach to the 
 common noun or class name. 
 
 20. Concepts have a twofold content, intensive 
 and extensive. The intension is determined by the 
 number of marks comprehended by the concept. 
 E. g., Man connotes or comprehends the marks ex- 
 isting, living, sentient, rational. This explication of 
 the connotation of a notion is its determination or 
 definition. The^uantity^pf extension, is determined 
 by the number of specific concepts or of objects 
 contained under the concept. E.g., J/rt* denotes or 
 contains under it the species logician, chemist, trtist, 
 mechanic, etc. This explication of the denotation 
 of a notion is its specification or division. 
 
 If the marks constituting the content of a con- 
 cept be few, it may extend to many things ; if the 
 marks be many and distinctive, the concept extends 
 to few things. Thus the concept bird has few 
 marks, as animal, biped, feathered, winged, etc., 
 but is applicable to, or contains under it, a great 
 variety and number of things; now the concept 
 swan has at least one more mark, web -footed, and
 
 
 THE NOTION 23 
 
 the variety and number of things denoted is less. 
 Hence the LAW: The greater the intension 
 the smaller the extension, and vice versa; 
 or, these contents are in inverse ratio. 
 
 Wo think a predicate either as a mark or as a 
 class ; as, Facts are stubborn, or, facts are stubborn 
 things. The one is thinking in intension, the other 
 in extension. True, these involve each other, are 
 essential correlatives, and are readily convertible ; 
 we do not think the one without, at the same time, 
 thinking the other. But usually one mode is in 
 vivid consciousness, while the other is obscure, and 
 either phase of thinking may become habitual, one 
 person more attentively considering the qualities 
 of a thing, another regarding it as a member of a 
 class. 
 
 21. Progress injnowledge consists chiefly in 
 rendering concepts clear and distinct. Conception 
 is first obscure and then clear. We think a concept 
 clearly when it is distinguished as a whole from 
 other wholes. ^This is accomplished by negative 
 judgments distinguishing of^ setting~~aparT other 
 concepts from this one, especially those which lie 
 nearest to it, or by remarking a specilic dill'erence. 
 E. g., We have a clear knowledge of the faces of our 
 friends, since we readily know one from another. 
 So we have a clear notion of horse when we know 
 that it is not ox, nor ass, nor mule. So, also, our 
 knowledge of justice is clear when we know that it 
 is not truth, nor benevolence, nor wisdom, nor power.
 
 24: CONCEPTION 
 
 Our notion of perfume is cleared by noting its 
 specific difference ; it is something that can be 
 smelled. 
 
 Clear conception is first confused, then distinct. 
 We think a concept distinctly when, viewing it as 
 a plurality, we distinguish the marks or the objects 
 that constitute it. Distinctness is attained by af- 
 firmative judgments. Analytic abstraction pre- 
 cedes, and is followed by a synthesis wherein the 
 mark is affirmed of the thing. Or the notion is ap- 
 plied to its various objects, and in this becomes 
 known by what is contained under it. E. g., An 
 artist knows distinctly the features he has deline- 
 ated. An artisan knows the virtues of his tools, and 
 also their various kinds. It is natural 'and logical, 
 when onejindertakes to explain any obscure matter, 
 to begin by clearing it, especially .of those things 
 tEat lie nearest to_it that/Js^which most nearly re- 
 semble it showing that it is not these, and then 
 proceeding to render it distinct by pointing out 
 what it is in itself, or to what it applii s. 
 
 Distinctness, then, has two modes: one which 
 notes the marks which a notion connotes, distinct- 
 ness in intension ; the other which n0tes the ob- 
 jects it denotes, distinctness in extension. Inten- 
 sive distinctness is attained by logical definition, 
 which enumerates marks. Extensive distinctness 
 is attained by logical division, which discovers 
 kinds. A primitive notion, such as identity, can be 
 cognized only per se. However clear it may be, 
 it has no distinctness, either intensive or extensive.
 
 THE NOTION 25 
 
 22. Praxis. Write answers to the following 
 questions, and make reference to the section and 
 paragraph illustrated : 
 
 1. Name the kinds of these marks of an apple: red 
 (e. g., positive, accidental, original, simple), round, juicy with 
 cider, innocuous, grown on this stem, worth five cents. Also 
 of preachers as they ought to be, these : unselfish, called 
 to this ministry, hortatory, devoted, well informed, spiritu- 
 ally minded, widely sympathetic, all things to all men. 
 
 2. Name which- of the following terms are concrete and 
 which abstract : trnth, truthful, trueness, true, truthful- 
 ness, wisdom, wise, foolish, folly, consciousness, individu- 
 ality, gratitude, homely, straight, a straight line, a circle, 
 a fault, mercy, improved health, a healing balm. 
 
 3. What marks constitute your notion of Caesar ? What 
 denotation has the word? What concept is formed of: 
 small, hard, transparent, brilliant, elementary, precious, 
 ornamental ? 
 
 4. What mark is common to : chair, sofa, stool, bench ? 
 What general marks characterize the concepts : teacher, 
 preacher, doctor, lawyer, author ? What specific mark dis- 
 tinguishes teacher, preacher, and author from the others ? 
 
 5. Change the quality noble into a concept. Distin- 
 guish the notion book from this book. Is Kaiser a com- 
 mon or proper name ? Has the name Mary Jones John- 
 son any meaning? 
 
 6. Give the intension of the concepts: war-ship, hexa- 
 gon, wisdom (see James iii. 17). Give the extension of 
 the concepts: vessel, triangle, wisdom (cf. James iii. 15). 
 
 7. Clear the concept piano-forte ; then render it distinct 
 intensively, then extensively. Make a note on the logical 
 procedure in 1 Cor. xiii.
 
 II. RELATIONS 
 
 23. The relations which notions bear to each 
 
 other need fuller explication. As preliminary, a 
 
 very important and thorough - going distinction 
 
 should be made between two wholes in or under 
 
 which the mind thinks its objects. They are these : 
 
 1st. The Qualitative or Logical Whole. This is 
 
 ' ^f two sorts : 
 
 (a) The intensive whole, whose parts are marks. 
 
 (5) The extensive whole, whose parts are kinds. 
 2d. The Quantitative or Mathematical Whole; 
 of two sorts : 
 
 (a) The integral whole. 
 
 (5) The collective whole. 
 
 These primary forms of the notion, the qualitative 
 and the quantitative, should be carefully observed. 
 Heretofore we have considered solely the former 
 ( 15 sq.). It js entirely subjective, a creation of 
 thought, and its parts are separable only by ab- 
 straction. It is general, and its parts are general. 
 The latter is not so entirely subjective, since it is 
 often determined by, and so corresponds to, aa_ob- 
 jective reality, and its parts are separable only by 
 dissection. It is individual, and its parts are indi-^ 
 vidual.
 
 RELATIONS 27 
 
 The importance of this distinction is seen in that, 
 although both forms intermingle in our thoughts, 
 reasoning in one of these wholes is regulated by 
 principles differing from those regulating it in 
 the other. Radical defects in the common logical 
 theory, as well as many superfluities, are due to a 
 neglect of the distinction. The oversight occurs, 
 probably, because nearly every notion is capable 
 of being viewed in either whole, either as a quali- 
 tative common notion or as a quantitative total; 
 and its transference from one of these aspects or 
 forms of thought to the other is often very facile, 
 taking place almost unconsciously. This does not 
 make it a matter of indifference, but is a reasen- 
 why we should the more carefully note this subtile 
 play of thought, so as not to be misled by it into 
 illogical confusion. 
 
 We shall proceed to discuss the qualitative or 
 logical whole minutely and at length. In the next 
 section, however, and occasionally, we shall make 
 mention of the quantitative whole so far as is need- 
 ful to distinguish it clearly, and to recognize it when 
 it occurs in qualitative propositions Its full dis- 
 cussion is postponed to 125 sq. 
 
 24. The quantitative or mathematical whole, 
 then, is individual; that is, not capable of division 
 into kinds. An individual is indivisum in se, et di- 
 visum ab omnialio^ Formally, it is a unit viewed 
 as a quantity, and consisting of portions severable 
 in thought. These are evolved by cutting" asunder
 
 28 CONCEPTION 
 
 the whole; that is, by partition or section, which 
 must be clearly distinguished from logical division. 
 Such parts are neither marks nor kinds, but merely 
 new individuals. 
 
 First, the integral whole is that in which the 
 whole is before the parts. The sections may be 
 hoinogeneous, as a hexagon severed into similar tri- 
 angles / or heterogeneous, as a human body, con- 
 sisting of head, trunk, and limbs. Anatomy is a sci- 
 ence of partition or dissection. The general notion 
 sword logically divides into the kinds sabre, rapier, 
 etc. ; but each sword consists of and is separated 
 by thought into the sections hilt, blade, etc. 
 
 Second, the collective whole is that in which the 
 parts are before the whole. Such are the notions 
 of an army, a, forest, a town, formed by repetition 
 of the notions of a soldier, a tree, a house. We 
 should not confuse the general notion of 
 
 which is u class notion capable of division into 
 kinds, with the particular notion of some one army, 
 which is an individual, and can only be parted into 
 sections, as regiments. These are not kinds of army, 
 but each is a new individual. 
 
 Quantitative notions occur frequently as the sub- 
 ject of qualitative propositions, but never as the 
 predicate. 
 
 25. In the qualitative^Jntensiye whole, notions 
 are_related as congruent, incongment, an.d~confli.c- 
 tive. Congruent notions are such as may coexist in 
 thought. All identical notions are congruent, as
 
 RELATIONS 29 
 
 achromatic and colorless. Also many that are not 
 identical, as learned and virtuous, beauty and riches. 
 Incongruent notions are such as cannot unite in the 
 same object, as a in nx'iral msr, a !>! n<- Mn<l<ii/. Ar- 
 istotle asks, Is happiness praiseworthy f There is 
 no answer, for the question has no meaning. It is 
 an incongruous jumble. Conflictive notions deny 
 ejichjQthsr, \\.s virtue and via 1 , Ix'autij and d< fortuity, 
 rich and poor. They are in opposition. 
 
 Of congruent notions one involves or compre- 
 hends others when these are marks connoted by it. 
 Thus the notion Socrates involves both famous and 
 Athenian. These are co-ordinate, being both imme- 
 diately comprehended. But Athenian further in- 
 volves Greek ; and Greek, European ; and Europe- 
 an, human. It is evident that these are not equally 
 proximate and immediate in Socrates, and that they 
 are in the relation of part to whole. They are par- 
 tes intra partes ; yet each permeates and informs 
 the whole. So chalk is both white and brittle, and 
 these marks coexist throughout. 
 
 In the qualitative, extensive whole, notions have 
 the relations of coextension, subordination, co-ordi- 
 nation, and intersection. These may be figured 
 thus: 
 
 Globe 
 Coextension 
 
 Animal 
 Subordination
 
 30 
 
 Co-ordination 
 
 Sword Spear 
 
 , n _ r , Protestants 
 
 Intersection 
 
 Irish 
 
 The circular notation needs no explanation. In 
 the linear notation a horizontal line expresses the 
 extension of a notion ; the comparative length and 
 the relative position of two such lines, the relation 
 of two notions. The vertical line indicates affirma- 
 tion ; its absence, negation ( 86, 87). 
 
 26. Two notions are coextensive when they 
 have the same denotation. They may be symbol- 
 ized by two coincident circles. The following are 
 coextensive : globe and sphere, triangle and trilater- 
 al, endogens and monocotyledons, dmihle-refracting 
 and polarising crystals, to conquer one's passions and 
 to become master of one 's self. Either of two such 
 notions may be thought of as contained under the 
 other. Coextension^ shouldjbe_distinguished from 
 equality which expresses quantitative Delation. 
 
 27. One notion or concept is subordinate to or 
 contained under another wTJeri it comprehends the 
 
 same and more marks and extends to fewer objects 
 (20). "TTislTspecies] Thus7raofl- is a species of 
 animal, and sword is a species of weapon. The 
 former is subordinate to the latter; it connotes
 
 RELATIONS 31 
 
 more marks, but it denotes fewer objects. The 
 superior concept, since more objects are contained 
 under it, is the more general notion. It is a genus. 
 Thus animal is the genus of man ; weapon, of sword. 
 Both genera and species are classes, and the ar- 
 rangement of things according to genera and 
 species is classification ( 16). 
 
 It is manifest that these forms of thought are 
 merely relative. A genus may be contained under 
 some higher concept, and then relatively to this 
 higher genus it is a- species. .Thus weapon is a 
 species of the genus mMrwiiwiit. A species may 
 contain under it some lower concept, and then rel- 
 atively to this lower species it is a genus. Thus 
 sword is a genus of the species sabre. A notion 
 that is thus alternately a genus relatively to lower, 
 narrower concepts, and a species relatively to some 
 higher, broader concept, is called a subalternate or 
 subaltern genus. It is characterized as a genus 
 that may^become a species. 
 
 A genus is a universal notion or a universe ( 9), 
 since it turns the many parts into the unity of a 
 whole. This is the logical meaning of universe, ad 
 unum versus, giving e'pluribus unum. It is often 
 called, by way of eminence, a logical whole. A 
 species is a special or specific notion, and since it is 
 but a part of the generic whole it is a particular 
 notion. The species as parts make up the genus 
 as a whole ( 10). These are paries extra paries, 
 since they are distinct groups of objects; as dia- 
 monds and rubies are species of jewels. Hence we
 
 32 CONCEPTION 
 
 can symbolize by circles or lines the relations of 
 concepts in extension, but not of those in intension. 
 
 28. Praxis. Write answers to the following 
 questions, referring to the section and paragraph 
 descriptive of the point in question : 
 
 1. In which whole do we think : the world, the planets, 
 disorder, a flash, thunder, war, King Henry ? Transfer 
 each to the other whole. 
 
 2. What kind of quantity is : a constellation, a tree, a 
 mob, Mt. Blanc, a sphere, a dollar, the ocean, this book ? 
 
 3. What is the intensive relation of : money and mem- 
 ory, simple and complex, magnanimity and stature, an 
 aching void, saint and sinner, sweet and sour, my dwelling- 
 house is built of brick burned with fire ? 
 
 4. What is the relation in extension of : brute and dog, 
 heat and motion, seeing and perceiving, frankness and 
 candor, lyric and hymn, hymn and sacred lyric, gun and 
 cannon, bimana and mankind? Write the circular and 
 linear notation in connection with each pair. 
 
 5. Considering chair, monarchy, and poetry, each as a 
 subaltern genus, what genus is each contained under, and 
 what species is contained under each ? 
 
 6. What paries extra paries constitute the entire logical 
 universe : animal, triangle, doctrine, lake, history, logical 
 whole ?
 
 III. DIVISION 
 
 29. The relation of co-ordination is evolved by 
 logical division ( 25). It has already been seen 
 that by specification we form subordinate groups 
 whose members are co-ordinate. Since pure logic 
 considers only the form, each genus or universal 
 whole can contain only two species, marked with 
 A and non-A. For A being a generic difference, 
 that is, a mark not found in the genus or divisum, 
 but found in some of its members, we know a pri- 
 ori, without any consideration of the matter of 
 thought, that the members are exclusive of each 
 other and exhaustive of the divisum. This is di- 
 vision by dichotomy, and the members are contra- 
 dictories ( 9). For example : languages are Aryan 
 and non-Aryan, animals are vertebrate and inver- 
 tebrate, the ancients were Greeks and 
 barbarians. The^process viewed inten- 
 sively, as thinking marks in ? js determi- 
 nation ; viewed extensively, as distin- 
 guishing^ species, it is specification ( 20). In rela- 
 tion to each other, the two species are co-ordinate, 
 being of equal rank in respect of the divisum ; but 
 we remark that either may be of indefinitely great- 
 er extent or breadth than the other. 
 3
 
 34 CONCEPTION 
 
 30. The negative member of a dichotomy is 
 characterized by the absence of the mark A, or, in 
 other words, by the negative mark non-A. Hence 
 arise negative, privative, or infinitated concepts. 
 Often their sphere is very wide, denoting almost 
 everything, and connoting very little, almost noth- 
 ing positive. E. g., unbounded, insert, apathy, Hind, 
 free, absolute, infinite. In many cases a notion, 
 originally a mere negative of its co-ordinate, has 
 received a positive mark, so that either or both of 
 the members of the dichotomy may be regarded as 
 positive. E. g., happy and unhappy, true and un- 
 true or false, hon-or and dishonor, man and brute, 
 town and country, i. e., the contrary. Notions es- 
 sentially negative, but whose name does not indi- 
 cate this character, are often opposed by terms neg- 
 ative in form, yet positive in fact. Thus temperate, 
 verbally positive, is a negative notion, opposed to 
 the positive intemperate, which is negative in form. 
 So also ease or health and disease, pure and impure. 
 
 Notions strictly correlative originate in dichoto- 
 my. The two always coexist in thought. We 
 may be thinking more of one member of the 
 couple than of the other, but if either exists the 
 other coexists with it in consciousness, if either be 
 expressed the other is implied. For example : pa- 
 rent and child, ruler and subject, cause and effect, 
 heavy and light, up and down, rich and poor, genus 
 and species, positive and negative. This last pair is 
 the origin and generalization of all correlatives. 
 One of the two is usually more or less negative, and
 
 DIVISION 35 
 
 in case a separate name has not been adopted for 
 each, the negative correlative to any positive notion 
 may be expressed by the prefix dis-, un-, or m-, or 
 the suffix -ee or -less. For example : conscious and 
 unconscious, correct and incorrect, truster and trus- 
 tee, godly and godless, A. and non-A. 
 
 31. In divisions not purely logical, but having 
 respect to the matter, it often occurs that we have 
 those that are more than dichotomous; we may 
 have a trichotomy or a polytomy. E. g., doctrines 
 are helpful, harmless, hurtful. This arises from 
 two causes. Either it is an abbreviation, whereby 
 several species, in turn subordinate, are condensed 
 into one co-ordinate statement ; as, angles are right 
 (and non-right, which are) acute and obtuse. Or it 
 arises from the lack of a sharp definition of our 
 concepts. There is often between two opposite 
 thoughts a notion or notions which it is impossible 
 to identify surely with either, and so constituting 
 a tertium quid, a third species, which it is needful 
 to insert in order to exhaust the divisum. Thus 
 we have age distributed as young, middle-age, old; 
 so also, riches, competence, want ; also, white, gray, 
 Hack. For many of these intermediate species we 
 have no name ; as between sick and well, strong and 
 weak, long and short, wise and foolish. 
 
 We have remarked that in a strictly logical dis- 
 tribution the members, A and non-A., are contra- 
 dictories ; no member of that universe can be both, 
 or can be neither ( 9 and 29). In a trichotomy
 
 36 CONCEPTION 
 
 or a polytomy the members are disparate notions. 
 Thus, brook, creek, river are disparates, contained 
 under the genus streams. Any two of such a di- 
 vision, as brook and river, are logical contraries ; a 
 thing of this genus cannot be both, but may_be 
 neither ; it may be the tertium quid. 
 
 Finally, a polytomous division admits of one, 
 and only one, strictly privative or negative notion. 
 Thus, some men lend, some borrow, some do both, 
 some do neither. The intermediate ground, well 
 named the undefined or indifferent part, often 
 takes this negative character ; as, men are very in- 
 dustrious, positively lazy, and neither the one nor 
 the other. 
 
 32. A thoughtful consideration of the preced 
 ing discussion, together with the illustrations, will 
 discover that each division is made with reference 
 to some general character or mark of the genus di- 
 vided. In dividing animals, for example, into ra- 
 tional and irrational, reference is made to their in- 
 telligence. Also in distributing books into folios, 
 quartos, etc., the reference is to their size. This 
 generic mark, or character of the divisum, which 
 reappears in a distinct, modified form as at once a 
 generic and a specific difference, is called the prin- 
 ciple or ground of the division, the fundamentum 
 di/oisionis. 
 
 A strict procedure, then, would be this : "We as- 
 semble representative instances of the objects de- 
 noted by the divisum, and having fixed upon a gen-
 
 DIVISION 37 
 
 eric mark as the principle of division, we select a 
 mark immediately involving this principle to serve 
 as a specific difference. Then we divide the deno- 
 tation by affirming the specific difference of the 
 class which it determines, and denying it of all 
 other contained objects. In subsequent divisions 
 we do likewise, involving in each new specific 
 difference the one immediately preceding, and, of 
 course, the original principle. 
 
 A nominal or artificial division is one made for 
 some transient purpose, or to attain a practical 
 end ; or one tentative and precursory to a real di- 
 vision ; or one popularly accepted and useful, such 
 as the numbers that may be observed on every 
 page, and in every few minutes of conversation. 
 A real or scientific division is one proposing to di- 
 vide notions and things according to their true and 
 essential nature, in order to attain correct objective 
 knowledge of things as they are. Such division 
 develops natural kinds, and is to be looked for in 
 the more refined sciences. The Linna3an artificial 
 divisions of flora were precursory and tentative ; 
 those of Jussieu's natural system are real and 
 more rigidly scientific. 
 
 33. The old saying, Divide et impera, may be 
 freely translated by Classify and conquer. In 
 treating any matter, so great is the practical value 
 of correct logical division, the root of classification, 
 that we now gather up the foregoing principles in 
 the following RULES :
 
 38 CONCEPTION 
 
 1st. The ground of a division should be 
 an essential or at least an important mark 
 of the divisum. The ground or principle select- 
 ed should be essential, if we would attain to real, 
 scientific knowledge. It should be important, im- 
 porting other attributes, if we would evolve an ex- 
 tended and valuable series. The purpose of an 
 artificial division fixes its ground. In civil affairs 
 it would be absurd to divide men into horsemen 
 and footmen, but in military affairs this is impor- 
 tant. In grammar, words are distributed accord- 
 ing to syntactical relations ; in a dictionary, alpha- 
 betically. Medical botany and the florist's manual 
 distribute plants differently, and both differ from 
 Jussieu. We sort our books by size to fit our 
 shelves, by subjects for handy reference, by tending 
 for show. 
 
 2d. The members should, as parts, equal 
 the whole divisum. No one should exhaust the 
 genus; as in sciences are deductive and inductive, 
 whereas all sciences use deduction. Together they 
 should exhaust it ; which is the case in angles are 
 right and oblique, but not in governments are mon- 
 archies and democracies, for there are other kinds. 
 
 3d. The species should emerge immedi- 
 ately from the genus. The genus should be 
 proximate ; as in plants are flowering and flower- 
 less. Thought should not overlook and overleap 
 subaltern genera, and proceed directly to remote 
 species ; as in plants are annual, biennial, and per- 
 ennial. This rule relates chiefly to strict scientific
 
 DIVISION 39 
 
 classification. In other matter the hiatus is quite 
 usual and useful ; as in plants are noxious and in- 
 noxious. 
 
 4th. Only one principle should be used in 
 determining a series. The use of different 
 grounds of division in a series gives rise to the log- 
 ical fault called cross division. Thus: vertebrates 
 are quadrumana, bimana, quadrupeds, and bipeds. 
 Here two grounds of division are used, first num- 
 ber of hands, then of feet. We have, consequently, 
 a cross division, bimana and bipeds are communi- 
 cant species, they overlap in man. 
 
 Such a series is tested by dichotomy. Any cor- 
 rect trichotomy or polytomy may be reduced to a 
 dichotomy by taking any one member as positive, 
 and including the rest under its negative. Thus : 
 Substances are animal, and vegetable, and mineral. 
 Tested: S are a and non-a (=v + m); or v and 
 non-v (=a-\-m); or m and non-m (=a+v). This 
 test applied to the following polytomy will dem- 
 onstrate it to be logically vicious : Religious sects 
 are catholic, calvinist, episcopal, and dissenting. 
 
 34. Praxis. Write answers to the following 
 questions and requisitions : 
 
 1. Which of these are positive, and which are negative 
 notions, and what are the opposites of each : dry, simple, 
 stranger, protestant, atheist, shadow, calm, disorder, sober, 
 living, restless, iniquity, silence, unclean ? 
 
 2. What notions are correlate to : teacher, north, above, 
 useful, right, committee, beggar, payer, pastor ?
 
 40 CONCEPTION 
 
 3. What tertium quid lies between : day and night, hot 
 and cold, love and hate, far and near, joy and sorrow ? 
 What is the logical relation of these notions? 
 
 4. What is the fundamentum divisionis of the follow- 
 ing: conduct is interested and disinterested, animals are 
 herbivorous and carnivorous, sounds are agreeable and dis- 
 agreeable ? 
 
 5. Assign a principle upon which : houses, fruits, his- 
 torical periods, and tariff laws may each be dichotomized. 
 
 6. Criticise the following examples, that is, state whether 
 they are logical divisions or quantitative partitions ( 23). 
 If divisions, state whether they are correct or not ; and if 
 not, what rule or rules are violated : 
 
 (a.) The human hand consists of palm and fingers ; it is 
 flexible and expert ; and known as right and left. 
 
 (b.) Propositions are affirmative, hypothetical, and negative. 
 
 (c.) Logic is deductive and inductive. The former treats of 
 conception, deduction, and fallacy. 
 
 (d.) Imaginative writers are poets, dramatists, and novelists. 
 
 (e.) The seasons of the year are spring, summer, autumn, 
 and winter. 
 
 (f.) Men are rational and fanatic. 
 
 (g.) Religions are Christian and Antichristian. 
 
 (h.) Men are Americans, Europeans, blacks, and pagans. 
 
 Y. Make several divisions of citizens, stating the ground 
 of each, into the species : laity, aliens, peers, natives, clergy, 
 commons. 
 
 8. Divide mankind on the principle of : age, sex, fam- 
 ily relations, color, riches, education, occupation, and dis- 
 position.
 
 IV. DEFINITION 
 
 35. The relation of intersection is discovered 
 in definition ( 25). Now, as division has reference 
 primarily to extension, so definition refers prima- 
 rily to intension. Our thought, having been cleared 
 ( 21), is by these rendered distinct ; the external 
 or extensive distinctness being secured by division, 
 the internal or intensive distinctness by definition. 
 
 A definition is the explication of tbe_essential 
 and original marks of a concept, the definitum. 
 Thus : Man is defined as rational, sentient, living, 
 existing. It is evident, however, that this mode of 
 statement is awkward, and in many cases impracti- 
 cable. Observing, then, that the notion animal in- 
 volves successively sentient, living, existing, we sub- 
 stitute for them that mark, and define summarily : 
 Man is rational and animal. The mark rational, 
 not included in the summation, is distinctive, since 
 of all the notions that we here connote, it belongs 
 to man alone. A logical definition, then, consists 
 of two, and only two, essential and original marks, 
 one being common, the other distinctive. 
 
 36. From the foregoing principles are derived 
 three corollaries, as follows :
 
 42 CONCEPTION 
 
 1st. . Simple notions, having no plurality of marks, 
 are incapable of definition. The notion of a being, 
 since it has only the one mark existing, and no dif- 
 ferential or distinctive character, is indefinable, is 
 an indefinite notion. 
 
 2d. An individual cannot be defined. Practi- 
 cally, we cannot enumerate its essential and orig- 
 inal marks, or sum up all those it has in common 
 with any other notion or thing. It can only be 
 described. 
 
 3d. Since the definitum, or notion defined, con- 
 tains implicitly the marks which its definition con- 
 tains explicitly, they are reciprocating or converti- 
 ble concepts. Thus: A triangle is a polygon of three 
 sides ; and, reciprocally, A polygon of three sides is 
 a triangle. Hence either may replace the other. 
 Thus : Every rectilineal figure may be cut into tri- 
 angles ; or, by replacement, Every rectilineal figure 
 may be cut into polygons of three sides. 
 
 37. Though definition relates primarily to in- 
 tension, it is readily and usually viewed in relation 
 to the extension of a concept. Concepts in exten- 
 sion often intersect; that is, two concepts often 
 have a common part, and each a part not com- 
 mon ( 25). Thus there are Irish Protestants, also 
 there are Irish not Protestants, and Protestants not 
 Irish. The common part is a species which is con- 
 tained under either of the total concepts as a ge- 
 nus. In other words, whenever a certain group of 
 things may be referred as a species to either of two
 
 DEFINITION 43 
 
 genera, these genera intersect, the group being a 
 common part. 
 
 Now, the two portions of a definition may each 
 be viewed as a concept in extension. If so, they 
 will be seen to intersect, and the definitum to be 
 the common part. Thus, the notion 
 rational being intersects the notion 
 animal / man, being both, is the com- 
 mon part. Formally, the definitum 
 may be referred to either concept as a genus ; log- 
 ically, neither has preference; but whichever be 
 chosen, the other serves to mark off or limit the 
 definitum. 
 
 Thus we get the usual form of the logical defi- ? 
 nition. It consists of the genus proximate to the 
 definitum, together with its specific difference. The 
 proximate genus is that class under which the no- 
 tion defined is immediately contained ; as animal 
 is the proximate genus to the concept man. The 
 specific difference is that which thoroughly distin- 
 guishes the notion defined from all other species of 
 that genus ; as rational is the specific difference 
 distinguishing man from all other species contained 
 under animal, as beasts, birds, fishes, etc. Thus we 
 have, Man is a rational animal. Also, Logic is the 
 science (=prox. gen.) of the necessary forms of 
 thought (=spc. dif.). Such is the formal definition 
 per genus et differentiam. 
 
 38. For the sake of clear treatment, it should ^ 
 at once be remarked that any predicate consisting
 
 44 CONCEPTION 
 
 of two or more qualitative notions may be viewed 
 as a genus with a difference. Thus: Negroes are 
 docile (=dif.) creatures (=gen.). Here the genus 
 is not proximate, and the difference is neither es- 
 sential nor thorough-going. So, also : Faith is the 
 assurance of things hoped for, etc. No clear think- 
 ei will mistake these for definitions. 
 
 A description recites constituent parts of a thing, 
 especially such as are of interest and importance and 
 at the same time distinctive, the selection being gov- 
 erned by a purpose. It may approximate definition. 
 
 An accidental mark or a property ( 15) may be 
 used to set a notion clearly apart ; as, Man is a 
 featherless biped ; or, Body only is mobile. This is 
 definite, but not definition. 
 
 A predicate generalizing the conditions, or the 
 consequences, or explicating, not the connotation, 
 but the denotation, is merely a quasi - definition. 
 Thus: Motion is the product of force and time 
 Malaria is feverous air Mind is that which knows 
 and feels, desires and wills. This last is evidently 
 a division rather than a definition. Such forms are 
 often spoken of as definitions a posteriori but a 
 logical definition is strictly a priori. 
 
 39-_A_rfta.1 defini'tint] pyjlu^igs^tjift essence of 
 
 a real object or class, in the forms of its proxi- 
 mate genus and specific difference. It is a priori 
 and analytic. It has the character of a proposi- 
 tion affirming both the reality and the nature of 
 the thing defined. Such are the verified defini-
 
 DEFINITION 45 
 
 tions of science ; as, Table-salt is sodium chloride / 
 Attention is consciousness concentrated on an object. 
 Definitions of abstract notions derived from reali- 
 ties must also be accounted real ; as, A circle is a 
 plane figure whose outline is everywhere equally 
 distant from some point. 
 
 A nominal definition is of the name of an object 
 or class having only an ideal or hypothetical ex : 
 istence ; as, a centaur ; open polar seas. In prac- 
 tice the distinction between the nominal and the 
 real cannot always be clearly applied; for nominal 
 definitions, being often tentative and preliminary, 
 may become real. 
 
 A genetic or causal definition is concerned with 
 the rise or production of a thing, considering it, 
 not as being, but as becoming. Thus : A cone is a 
 solid generated by the revolution of an angle about 
 one of its sides. The notion defkied, not being 
 given but made, this definition is a priori and 
 synthetic. 
 
 40. The original essence being known, help in 
 making or criticising a definition is given by the 
 following practical K.ULES : 
 
 A logically correct definition should J)e : 
 1st. Positive. The definition is always to be 
 affirmed of the definitum. Negative statements 
 serve to render the notion clear, and are important 
 precursors to definition, but they do not render a 
 notion distinct (jj 21). When the subject is a pusi- 
 _tiye notion, which is most frequently the case, the
 
 46 CONCEPTION 
 
 definition predicated of it should consist of positive 
 notions. A definition should tell what a thing is, 
 not what it lacks, or what it is not ; as, A line is 
 length without breadth ; and, Pleasure is the feeling 
 opposed to pain. When, however, a notion is essen- 
 tially negative, as shadow, freedom, gentile, want, 
 then its definition should be negative; as, Inverte- 
 brates are animals destitute of an internal skeleton. 
 
 2d. Adequate. If the genus be not proximate, 
 the definition is too wide ; as, Man is a rational 
 being. If the difference be not thorough-going 
 that is, not common to all members of the class 
 the definition is too narrow ; as, Man is a praying 
 animal. A convenient test of adequacy is con- 
 vertibility ( 36). 
 
 3d. Not tautological. It should not contain 
 the name of the thing defined, nor a synonym, nor 
 a correlative term, for this is to define a thing by 
 itself. Thus : A lawmaker is one who makes law 
 Life is the sum of the vital functions / A cause is 
 that which produces an effect. Reciprocal defini- 
 tions are not allowed ; as, A board is a thin plank, 
 and a plank is a thick board. This is a sort of 
 logical seesaw. It is called defining in a circle, 
 and by the Greeks diallelon (through each other). 
 There is a similar vice in reasoning called by the 
 same name ( 146). 
 
 4th. Precise. It should contain nothing merely 
 accidental ; as, The potato is the food of the Irish. 
 This difference is an accident ( 15). It should con- 
 tain nothing superfluous ; as, A triangle is a figure
 
 DEFINITION 47 
 
 having three sides and three angles. Here is super- 
 fluity. Names of forms should not be included 
 with names of things ; as, The cur is a species of 
 dog, etc. Here species is superfluous. Derivatives 
 being implied by their originals should be excluded 
 as superfluous ; as, Honest dealing is rendering to 
 every one his own property. Here the notion of 
 own, derived from property, is superfluous. 
 
 5th. Perspicuous. It should be intelligible, lit- 
 eral, and brief. A definition proposes to make a 
 notion distinct ; hence the use of notions more ob- 
 scure than the one to be defined violates perspi- 
 cuity ; as, The soul is the first entelechy of an 
 organized body possessing life potentially. Again, 
 all figurative notions should be excluded, for 
 tropes do not indicate what a thing is, but only 
 something similar ; as, Omnipresence is a circle of 
 which the centre is everywhere and the circumfer- 
 ence nowhere. Many expressions, however, origi- 
 nally metaphorical have become literal, and may 
 properly be used in defining. Finally, brevity is 
 certainly a merit, but extreme brevity may be less 
 perspicuous than needless prolixity. 
 
 41. Praxis. Analyze into genus and differ- 
 ence, classify by giving the kind, and criticise by 
 applying the principles and rules, the following 
 questionable definitions "! 
 
 1. Philosophy is the science of principles. 
 
 2. Gratitude is the memory of the heart. 
 
 3. Motion is the change of place of body.
 
 48 CONCEPTION 
 
 4. Motion is the act of potential being up to the meas- 
 
 ure of its potentiality. 
 
 5. Motion is an accidental property of body that effects 
 
 a changing of its place. 
 
 6. Mad call I it ; for, to define true madness, 
 What is't but to be nothing else but mad ? 
 
 7. Green is a color compounded of blue and yellow. 
 
 8. Silence is the entire absence of sound or noise. 
 
 9. Mind is unextended substance. 
 
 10. Mind is conscious substance. 
 
 11. Health is the condition of a living body free from 
 
 disease or pain. 
 
 12. A spheroid is a solid formed by the revolution of an 
 
 ellipse about its diameter. 
 
 13. Opium is a vegetable product which causes sleep. 
 
 14. A dragon is a serpent breathing flame. 
 
 15. A synopsis is a conspectus of the chief points. 
 
 16. Animal is the genus denoting men and brutes. 
 
 17. Psychology is the science of the phenomena of mind. 
 
 18. Logic is the light-house of the understanding. 
 
 19. Dirt is matter in the wrong place. 
 
 20. Pleasure is the reflex of normal activity. 
 
 21. An atom is an ultimate particle of matter incapable 
 
 of division. 
 
 22. A circle is a curved line returning upon itself, all the 
 
 points of which are equidistant from a given point 
 within called the centre. 
 
 23. A point is position without parts or magnitude. 
 
 24. Time is a measured portion of indefinite duration. 
 
 25. Laws are the expressed will of a ruler ; and a ruler 
 
 is one whose will is expressed in laws.
 
 V. SYSTEM 
 
 42. As preliminary to an examination of logi- 
 cal system, we will present and remark upon the 
 following scheme : 
 
 r Existing Minerals, Plants, Brutes, Men. ~| a 
 
 5 I Existing, living Plants, Brutes, Men. [ | 
 
 j Existing, living, sentient Brutes, Men. f 
 
 B I Existing, living, sentient, rational Men. J w 
 
 The most obvious point here illustrated is the law 
 that as intension increases, extension diminishes, 
 and vice versa ; that the maximum of either is the 
 minimum of the other ; that the two are in inverse 
 ratio ( 20). 
 
 In ascending the series, we think marks out and 
 think things in. This, on the intensive side, is ab- 
 straction ( 15) ; on the extensive side, it is general- 
 ization or generification ( 16). 
 
 In descending the series, we think marks in and 
 think things out in the same mental act. This, on 
 the intensive side, is determination ; on the exten- 
 sive side, it is specialization or specification. 
 
 43. The same matter in a modified form, with 
 some additions, is presented in the following 
 scheme : 
 4
 
 50 
 
 CONCEPTION 
 
 Second Intentions. 
 Concepts of Forms. 
 
 First Intentions. 
 Concepts of 
 Things. 
 
 Intension or Depth. 
 Marks connoted. 
 
 Extension or 
 Breadth. 
 Things denoted. 
 
 Summum Genus 
 Species or Sub-genus 
 Species or Sub-genus 
 Iniima Species 
 
 Being or Thing 
 Organism 
 Animal 
 Man 
 
 Existing 
 Ex., living 
 Ex., lv., sentient 
 Ex., lv., sn., rational 
 
 All Things 
 All Organisms 
 All Animals 
 All Men 
 
 Individual 
 
 Aristotle 
 
 Ditto, Father of Logic One Being 
 
 Here is represented a complete logical system 
 founded on the relation of genus and species. It 
 should be thoughtfully examined by the student of 
 logic, in all its details, some of which we now pro- 
 ceed to discuss. 
 
 44. It is evident that thought, rising from indi- 
 viduals to classes, and by successive generalizations 
 forming wider and wider classes or genera, at each 
 step diminishing the marks connoted, must at last 
 reach a notion of widest generality, connoting but 
 one mark and denoting all things, above which, of 
 course, it cannot rise. This highest, widest notion 
 is the Summum Genus, and is characterized as the 
 genus that cannot~Become a species! ItTis repre- 
 sented in the foregoing scheme by Being or Thing, 
 which are synonymous, comprehending only the 
 mark Existing, and containing under it All Things. 
 
 It is possible to analyze metaphysically and 
 logically the notion being or thing into its constit- 
 uent notions matter and form ( 4). It is therefore 
 referable to the still higher genus matter, and so 
 is definable thus : A iking is matter having form. 
 In this view, matter, taken in its widest, metaphys-
 
 SYSTEM 51 
 
 ical sense, is the true summum genus. We shall, 
 however, for convenience, continue to speak of 'be- 
 ing or thing as the actual summum genus, simple, 
 indefinable, and ultimate. 
 
 In departments of science, it is not usual to make 
 reference to this common genus. For each, its own 
 subject is regarded as summum genus, that notion 
 which is characterized by the mark selected as its 
 fundamentum dimsionis _(_ 32). Thus, in botany, 
 plant is the highest genus considered ; in zoology, 
 animal; in political economy, wealth; in logic, 
 thought form. They leave to metaphysics or ontol- 
 ogy, the science of being, the exploration of the 
 still higher, more rarefied region. Similarly, in 
 more commonplace matters, some subaltern genus 
 ( 27) is usually assumed as ultimate. 
 
 But the frequent use of the word thing shows 
 what constant mental reference is had to the actual 
 summum genus. Indeed, whenever we do not 
 know the proximate or approximate genus of an 
 object, or do not care to be exact, we mount up on 
 eagle wing and call it a thing ; thus : A comet is a 
 curious thing. Likewise it is used as an index of 
 mere existence; as, Evil is an unavoidable thing. 
 Again, if we wish to consider an object relative to 
 some one mark exclusively, we call it a thing ; as, 
 Wine is a hurtful thing, because, etc.; or if we 
 wish to emphasize some mark; as, Cruelty is a 
 hateful thing. 
 
 45. On the other hand, when thought descends L
 
 52 CONCEPTION 
 
 the scale, and by successive specifications forming 
 narrower and narrower classes or species, at each 
 step adding marks and so rejecting things, it must 
 at last reach a class of narrowest generality, con- 
 noting a maximum plurality of common marks, 
 and denoting a minimum plurality of things, below 
 which, of course, it cannot descend. Thisjowest, 
 narro west_class is the Infima Species, and is char- 
 acteri/.'Ml as the species that cannot become a genus. 
 It is represented in the foregoing scheme by Jlan, 
 comprehending many common marks, and contain- 
 ing under it only individual human beings. 
 
 The early logicians consider the infima species 
 as fixed by nature, and expressed in the terms 
 man, horse, etc. Such classes as negro, barb, etc., 
 they do not admit to be species, but merely acci- 
 dental varieties. But the whole question of natural 
 kinds belongs exclusively to the naturalist, and 
 with it the logician has nothing whatever to do. 
 In logical theory, which disregards matter (4), 
 system is restricted only by the primary laws of 
 thought. Hence division into logical kinds pro- 
 ceeds until no mark common to even two individ- 
 uals remains to serve as a specific difference. The 
 species that comprehends all the common marks is 
 theoretically the injmia species, for that alone can- 
 not become a genus by further division. 
 
 46. It is important to observe, clearly and dis- 
 tinctly, what relation individuals bear to the logi- 
 cal system. This system consists of classes only,
 
 SYSTEM 53 
 
 and hence an individual is not a member of it. 
 For an individual is not a kind, is not a logical part 
 ( 24) ; that is, it cannot be evolved by division. It 
 is evident ex vi termini that the infima species has 
 no subordinate. It follows that the objects of which 
 a class is formed cannot in strictness be spoken of 
 as contained under the class, though this expression 
 is used. More properly the class is said to denote, 
 not only its species, but also the objects or things 
 it comprises. 
 
 But individual objects are the basis of all classi- 
 fication ( 16, 32). Now, it is not necessary in 
 generalizing that we should begin with the infima 
 species and thence build up the scale. It is com- 
 petent to begin with any wide class and evolve 
 the system downward and upward. This indicates 
 that any and every genus denotes, not only its sub- 
 ordinate classes, but also all the individual things 
 of which it can be predicated. 
 
 An individual, as the word itself points out, is 
 logically indivisible ( 24). But this is a mark also 
 of infima species. What, then, distinguishes the one 
 from the other? Principally that the latter is a 
 class, the former not. Thus, while the latter con- 
 sists of common marks only, the former possesses 
 also at least one particular mark, represented in 
 the scheme by Father of Logic. This particular 
 mark determines only a numerical, not a specific, 
 difference ; and therefore the individual cannot be 
 defined, yet may be described ( 38). Such is the 
 logical individual ( 17). The real, actual individ-
 
 54 CONCEPTION 
 
 ual possesses also a distinct existence in space or 
 time. It is discriminated by perception, external 
 or internal. It has many numerical differences. 
 
 47. It is apparent that division and definition 
 are correlative forms ( 30). As division is con- 
 cerned with the extension or breadth of a concept, 
 so definition is concerned with its intension or 
 depth. By the one a notion is rendered externally 
 or extensively distinct; by the other it is rendered 
 internally or intensively distinct ( 21). A division 
 explicates or evolves subordinate concepts ; a defi- 
 nition explicates or evolves marks. The one devel- 
 ops the sphere, the other the comprehension. The 
 one analyzes the denotation, the other the conno- 
 tation. To each of the forms herein named is op- 
 posed a correlative. 
 
 In a systemized series of concepts, division looks 
 down, definition up, the scale. When a specific 
 subject is to be treated, we first define it ; we give 
 its proximate genus, the one next above, which in- 
 volves all the marks of the preceding genera, in- 
 cluding the highest ; we also give its specific differ- 
 ence, which sets it apart from co-ordinate notions. 
 Then we proceed downward, dividing and subdi- 
 viding, until we reach and include the lowest 
 species. This exhausts the scale, and the treat- 
 ment is logically complete. Of course it is not 
 necessary that this order should be rigidly ob- 
 served. In the progress of a treatise, definition 
 may often replace division, and one or the other
 
 SYSTEM 55 
 
 will preponderate according to the point in the 
 scale at which a beginning is made, or according to 
 the inclination of the thinker or the nature of his 
 subject. 
 
 But since division and definition are convertible 
 correlatives, a system may be expressed entirely 
 in either, they being, mutatis mutandis, the same 
 form. We may begin with the summum genus, 
 and, descending, exhaust the scale by a series of 
 divisions. Or we may begin with the infima spe- 
 cies, and, ascending, exhaust the scale by a series 
 of definitions. Any specific concept being de- 
 fined, it is requisite to define the proximate genus 
 to which it is referred, and again the proximate 
 genus to which this is referred, and so on until the 
 summum genus is reached. 
 
 Certain sciences, as botany and zoology, are 
 sometimes called classificatory sciences, because 
 they exhibit their matter mostly in the form of 
 divisions. But all sciences are classificatory, and 
 those referred to should rather be called dividing 
 sciences. On the other hand, chemistry is emi- 
 nently a defining science. Having named the ele- 
 ments, it uses few other names, a compound being 
 designated generally by its definition only ; as, 
 potassium iodide, and nitrate of cupric oxide. It 
 would be quite possible, however, to state the rela- 
 tions of chemical substances as genera and species. 
 
 Thus it is that thoughts are elaborated and ren- 
 dered clear and distinct by being co-ordinated and 
 subordinated, by being divided and defined, until
 
 56 CONCEPTION 
 
 they are gradually built into systems, more or less 
 complete and perfect. Let it be particularly re- 
 marked that this is true not merely of scientific 
 thinking, but is equally true of our every-day 
 thinking, and that about the most trivial matters 
 ( 3). It is thus that at all times and about all 
 things we do think, and, governed by the necessary 
 laws of pure thought, it is thus that we must think. 
 Every common noun in a language occupies a place 
 in some of the countless hierarchies of concepts 
 which the human mind is forming or has formed. 
 It is true that in most minds there is much con- 
 fusion and disorder in the fabric of thought ; still, 
 the greater part of the humblest mental life is oc- 
 cupied in generalizing and specializing, in system- 
 atically arranging and correcting the arrangement 
 of thoughts. 
 
 48. A series of definitions may be expressed 
 either directly, from the lowest species upward, 
 or inversely, as in the examples given in the next 
 section. A series of divisions is generally best ex- 
 pressed in the unnamed manner briefly exemplified 
 in 23, in the distribution of Wholes, which should, 
 therefore, be closely considered. The early logi- 
 cians made use of the figure of a logical tree, arbor 
 Porphyriana, erect, horizontal, or inverted, from 
 which comes the familiar phrase "branches of 
 knowledge." Also they used the figure of a scale 
 or ladder (scala, icA7/za, a staircase). These several 
 forms are illustrated in the next section.
 
 SYSTEM 57 
 
 49. Praxis. The following exercises should be 
 written with care, and reference made to the sec- 
 tions illustrated : 
 
 1. Name a number of individuals denoted by the wide 
 notion town. Of these, which are comprised by the nar- 
 rower notion city ? Of which may metropolis he predi- 
 cated? --^Ca. 
 
 2. Criticise the following series : The U. S. domain con- 
 sists of states and territories ; the states are Northern and 
 Southern, the Northern are Eastern and Western, all are 
 divided into counties, and these into townships, ti^*' 
 
 3. Divide and subdivide officers of the U. S. government 
 with reference to their official functions. ^*- -VP- ^ tt ^ r 
 
 4. What is the fundamentum divisionis of the following 
 scala ? Reduce it to a series of definitions, supplying spe- 
 cific differences : 
 
 Mankind 
 
 Theists Atheists 
 
 I 
 
 I 
 Monotheists Polytheists 
 
 I 
 Christians Antichristians 
 
 I 
 
 Papists Protestants 
 
 I 
 
 Jesuits Non-Jesuits 
 
 5. Change the following tree into a scale or ladder : 
 
 Gaseous non-gaseous 
 
 Liquid non-liquid 
 
 Viscid non-viscid 
 
 Solid non-solid 
 
 Matter
 
 58 CONCEPTION 
 
 6. Describe the divisions exhibited in the following 
 horizontal tree in ordinary language (cf. 21) : 
 
 ! Obscure 
 ( Confused \ Inadequate 
 
 Clear -| M Adequate ) 
 
 ( Distinct -j [ Perfect. 
 
 ( j Intuitive ) 
 ( Symbolic 
 
 7. Try to divide and subdivide triangle so as to include, 
 without cross division ( 33), the right-angled, the equi- 
 angular, the obtuse-angled, and the isosceles. 
 
 8. Change the following series of definitions, omitting 
 the specific differences and supplying negative members, 
 into a series of divisions, presenting a scala, as in Ex. 4 : 
 
 A carnivore is a flesh-eating mammal. 
 
 A mammal is a vertebrate suckling its young. 
 
 A vertebrate is an animal having an internal skeleton. 
 
 An animal is a sentient organism. 
 
 An organism is a living being. 
 
 9. Change the following series of definitions, omitting 
 and supplying as above, into a series of divisions, present- 
 ing a horizontal logical tree, as in Ex. 6 : 
 
 Wealth is things useful and agreeable, acquired by labor. 
 Capital is wealth destined to reproductive consumption. 
 Circulating capital is capital consumed in a single use. 
 Wages is circulating capital paid in remuneration of labor. 
 
 10. Exhibit the following logical distribution of the sci- 
 ences in the manner exemplified in 23 : 
 
 All rational knowledge, or philosophy in its widest sense, is 
 either a posteriori and empirical, or a priori and pure. 
 Empirical knowledge gives rise to abstract science, as 
 mathematics ; and to concrete science, as the inductive 
 sciences. Pure knowledge, or philosophy in its restricted 
 sense, is either formal or material. Material philosophy, 
 or metaphysics, has two branches a metaphysic of nature 
 or physics, and a metaphysic of morals or ethics. The 
 chief sciences strictly fgroial are philology and logic.
 
 VI. PREDICATION 
 
 50. To predicate is either to affirm or deny one 
 notion of another. Since pure logic does not at all 
 consider the matter of propositions, but only their 
 form ( 4, 12), it is permissible, according to the 
 Law of Identity, to affirm any notion of any other, 
 provided they be not contradictories ( 8). Thus 
 there is no logical or formal fault in saying : The 
 moon is made of green cheese ; or, The earth is a 
 cube ; or, Every man is dishonest. However false 
 to fact such statements may be, they are not logi- 
 cally absurd ; that is, in themselves essentially con- 
 tradictory. It is possible to entertain the thought. 
 But to speak of a spherical cube, or of something 
 better than the best, or of a complete vacuum,, or of 
 our mutual friend, or of tempting providence, or to 
 say that all men are liars, is logically absurd, since 
 a contradiction is involved, and it is not possible to 
 entertain a thought thus qualified ( 9). In consid- 
 ering predication, then, we are not at all concerned 
 with the material truth or falsity of what is said, 
 but with the form of the saying, which is limited 
 only by self-contradiction. 
 
 51. Predication is either positive or negative. 
 It is the issue of comparison. Two notions com-
 
 60 CONCEPTION 
 
 pared are apprehended as similar or dissimilar, and 
 the judgment pronounces that they agree, or that 
 they disagree. Positive predication affirms or pos- 
 its, by the Law of Identity, that the subject and 
 predicate are in the relation of part and whole, con- 
 tained and containing. Negative predication de- 
 nies or sublates, by the Law of Contradiction, such 
 relation, excluding subject and predicate each from 
 the sphere or comprehension of the other. By the 
 Law of Excluded Middle, no third form of predica- 
 tion is possible ; the relation in question between 
 subject and predicate either does or does not exist, 
 it is yea or nay. The ground of this division of the 
 forms of predication is called their Quality ; that is, 
 judgments, with reference to their quality, are pos- 
 itive and negative. 
 
 52. When one notion is predicated of another, 
 the existence of their objects is neither posited nor 
 sublated. To affirm that sea-water is salty does not 
 posit the existence of sea, or of water, or of salt, or 
 of the mark salty. This is presumed in case of each, 
 the result of prior thought ; or the affirmation is 
 conditioned on their existence, thus : If there be 
 sea-water, it is salty. Obviously to deny one notion 
 of another does not sublate the existence of their 
 objects. So far of absolute existence. Their rela- 
 tive existence is predicated, conditioned on their 
 absolute existence ; that is to say, if they absolutely 
 or really exist, a relation between them is affirmed 
 or denied as existing.
 
 PREDICATION 61 
 
 But very often there is occasion to predicate ab- 
 solute existence. This is accomplished by existen- 
 tial forms of speech or propositions. Thus, I am 
 means / exist, lam existing, or / am a being. The 
 predicate in such case is the summum genus, or its 
 single simple mark. So, also, Chance is not; that is 
 to say, there is no such thing. Existential proposi- 
 tions frequently take an inverted form, the place of 
 the transposed subject being occupied by a mean- 
 ingless particle ; as, It is Jme weather There are 
 not many wise. Some predications may be con- 
 strued as existential or otherwise. Thus the latter 
 example may be construed either as, Not many wise 
 are, or as, The wise are not many. 
 
 53. Negative forms call for special remark. A . 
 negation strictly pure merely denies one notion of 
 another, no more. If we say, Smoke is not vapor, 
 the thought is that these two notions, though lia- 
 ble to be confounded, are so essentially unlike that 
 they should be set entirely apart. This is simply a 
 holding back from error. In other negations there 
 is a thought of a genus which is denied to the sub- 
 ject ; as, Smoke is not a gas ; that is, the genus gas 
 does not contain under it smoke as one of its kinds. 
 Thirdly, there may be a reference of both notions 
 to a containing genus. Thus in Men are not brutes, 
 the thought is limited by the universe animal, un- 
 der which man and brute are specific contradictories 
 ( 9). Lastly, the notions may be disparate, or con- 
 trary, and as such be denied of each other ( 31).
 
 62 CONCEPTION 
 
 A proposition whose predicate is a pure negative 
 is called infinite. If we say, The soul is not mortal, 
 by this denial we merely ward off error. But if we 
 say, The soul is non-mortal, as to logical form we 
 affirm, and thereby place the soul in the infinite 
 sphere of non-mortal beings. This sphere, obtained 
 by the subtraction of mortals from the infinite 
 sphere of beings, though limited thereby, is still 
 infinite. 
 
 Very many notions formally negative have never- 
 theless a positive character ( 30). Each of these is 
 usually thought as a finite mark or universe. Such 
 are the notions helpless, unpleasant, unwell, infa- 
 mous, uneven, immortal. Thus, if we say, The soul 
 is immortal, there is affirmed of it, besides the nega- 
 tive notion of infinity, the positive one of continu- 
 ous existence. This marks a definite genus, quite 
 distinguishable from non-mortal. 
 
 54. Predication is either in the intensive or _in 
 the extensive whole ( 23 sq.). The distinction is 
 grounded on the relation of subject and predicate, 
 as reciprocally whole and part. 
 
 In an intensive judgment, the subject is the whole 
 or major term, the predicate is the part orjninor 
 term. Thus, in the attributive judgment The earth 
 is spherical, the notion earth is an intensive whole 
 consisting of a complement of marks, and the mark 
 spherical attributed to it enters into or is recognized 
 as a part of this whole, it being only one mark out 
 of many that characterize the notion earth. This
 
 PREDICATION 63 
 
 form is conventionally interpreted, The earth com- 
 prehends spherical. 
 
 In an extensive judgment, the predicate is_Jthe 
 whole or major term, the subject is the part_or 
 minorjerm. Thus, in the proposition The earth is 
 a sphere, the notion sphere is an extensive whole, a 
 genus, constituted of many kinds of things, as the 
 other planets, their satellites, the sun, the geomet- 
 rical sphere, globular fruits, rain-drops, etc. Now, 
 the earth is declared to be one of the many things 
 denoted by sphere, to be a part of this whole, a 
 member of the genus. This form is conventionally 
 interpreted, The earth is contained under sphere. 
 
 Consequently, while a qualitative judgment^ may 
 have an individual as its subject, it cannot have an 
 individual predicate. For the predicate in inten- 
 sion is a mark, in extension a genus ( 20) ; an 
 individual cannot be either. We may say, Great 
 is Diana, but this is a rhetorical inversion ; Diana 
 is the subject, and the predicate is great. We may 
 say, The rival of Plato is Aristotle, but this is not 
 qualitative, but a quantitative equivalent proposi- 
 tion. 
 
 55. The ten categories or predicaments of Aris- 
 totle, about which opinions greatly differ, are as 
 follows, illustrated by his own examples : 
 
 1. Substance; it is a man, a horse, etc. 
 
 2. Quantity ; it is two cubits long, three, etc. 
 
 3. Quality ; it is white, grammatical, etc. 
 
 4. Relation ; it is half as large, greater, etc.
 
 64 CONCEPTION 
 
 5. Action ; it cuts, burns, etc. 
 
 6. Passion ; it is cut, is burned, etc. 
 
 7. Place ; it is in the Agora, the Lyceum, etc. 
 
 8. Time ; it is to-day, was yesterday, etc. 
 
 9. Posture ; it is reclining, seated, etc. 
 
 10. Possession ; it is having shoes, armor, etc. 
 
 These may be interpreted as an exhaustive series 
 of summa genera standing next the true summum 
 genus, Being ; metaphysically, a classification of 
 the modes of objective or real existence ; logically, 
 a classification of the most general notions that 
 can be predicated of any subject. That is to say, 
 anything whatever may be said to be a substance, 
 a quantity, or some other one, at least, of these 
 highly generalized notions. In this view they are 
 first intentions or names of things ( 4). 
 
 But it seems clear, both from the title of the list 
 and from his examples, that Aristotle intended to 
 name rather all the possible forms under which 
 things may be represented in thought. Thus, if 
 we say of anything, It is a man, we are thinking 
 it in the category of substance ; or, if we say, It is 
 seated, we are representing it in the predicament of 
 posture ; and so any judgment whatever will fall 
 into one or another of these ten formal categories. 
 In this view they are second intentions or names 
 of forms of thought. 
 
 56. Having settled the category in which a 
 predication places the subject, it may be asked, 
 What kinds of predicates are then possible ; or, in
 
 PREDICATION 65 
 
 other words, what are the second intentions or 
 forms of its possible predicates? The answer is 
 Aristotle's doctrine of the predicables, as follows : 
 Every judgment affirms or denies of its subject one 
 or another of these four relations : 
 
 1. Definition; as, Man is a ra- ) J 
 
 tional animal J > Convertible. 
 
 2. Property ; as, Man is risible. . . . = None of the essence ) 
 
 3. Genus; as, Man is an animal. . = Part of the essence ) 
 
 4. Accident; as, Man is a biped. . = None of the essence \ Inconvert ble - 
 
 It has been proposed to substitute specific differ- 
 ence for definition, since it already contains genus, 
 and to make the number five by adding species as 
 predicable of individuals. But the list would not 
 be improved ; for, as Aristotle himself remarked, 
 both difference and species are of the nature of 
 genus, and interchangeable with it ( 27, 37). 
 
 57. Praxis. Write the quality of each of the 
 following propositions, stating whether the predi- 
 cation is logically permissible or not, and why, and 
 noting existential forms : 
 
 1. I do not just now remember anything I have for- 
 
 gotten. 
 
 2. A national debt is a national blessing. 
 
 3. There is none that doeth good, no, not so much as 
 
 one. Let there be light ; and there was light. 
 
 4. A flying arrow is at rest. 
 
 5. It is impossible to love and be wise. 
 
 6. There is a tide in the affairs of men 
 
 Which, taken at the flood, leads on to fortune. 
 
 7. I think there be six Richmonds in the field. 
 
 5
 
 66 CONCEPTION 
 
 8. Man is not a beast for burdens, nor a reptile for 
 
 bruising. 
 
 9. There is no place like home. 
 
 10. Let us try to amuse ourselves by doing nothing, and 
 
 so making ourselves miserable. 
 
 11. An idiot is irrational. A brute is non-rational. 
 
 Note which is the major term in the following, 
 with the reason : 
 
 12. Pearls are precious. Rubies are stones. 
 
 13. Heresy is sin. Solomon is wise. 
 
 Predicate a categorical class of each of these 
 subjects : 
 
 14. Gold. The wealth of Crcesus. Antiquity. Red. 
 
 Parallelism. A battle. New York. A multitude. 
 Upright. A defeat. 
 
 State to what category and to what predicable 
 each of these judgments belongs : 
 
 15. Snow is frozen mist ; it falls lightly ; is very white ; 
 
 but is easily discolored ; it is colder than water ; 
 lies level ; occurs only in winter ; but not at the 
 equator ; it has minute crystalline forms ; and 
 accumulates in huge masses.
 
 VII. SIMPLE PROPOSITIONS 
 
 58. As a product of thought, a judgment is the 
 result of comparison. Two notions are compared, 
 and the judgment pronounces that they agree or! 
 disagree. In case they disagree, they are set apart' 
 by a denial. In case they agree, they are unified 
 by an affirmation. To judge affirmatively is to 
 bring a notion into or under another. One is 
 thought as determined by the other; for either 
 the latter is brought as a mark into the one, which 
 is thereby determined, or else the one is brought 
 under the other as a class, and thereby determinedi 
 A judgment expressed in words, since it is placed 
 before us for acceptance, is called a proposition. 
 What is subjectively a judgment is objectively a' 
 proposition. 
 
 The prepositional forms with which logic is im- 
 mediately concerned are the conditional and the 
 categorical. A conditional proposition states a 
 comparison so nearly complete that only some pro- 
 vision remains in question. The contingency is 
 expressed as a condition, thus : If air be pure, it is 
 wholesome. Categorical propositions constitute the 
 negative member of the dichotomy. A categorical 
 proposition is one wherein no contingency or condi-
 
 68 CONCEPTION 
 
 tion is expressed. This difference is obviously not 
 essential ; but since the conditional declares rela- 
 tively to some provision, and the categorical names 
 none, the latter is said to declare absolutely. In 
 strictness, however, all propositions, except axioms, 
 are conditioned on prior thoughts, and on the ex- 
 istence of their objects ( 52). The provision may or 
 may not be expressed. While, therefore, we shall 
 give the conditional form special consideration in 
 a subsequent chapter ( 110 sq.), we shall not care 
 to exclude it meantime from view, though our at- 
 tention for the present will be directed chiefly to 
 the categorical form. 
 
 59. The categorical proposition is severed by 
 partition into three portions ( 24). In affirmation 
 these are : 
 
 ' 1st. The notion of something determined, called 
 the Subject. 
 
 2d. The notion of something determining, called 
 the Predicate. 
 
 3d. The part which expresses this relation, called 
 the Copula. 
 
 In the negative proposition there is no determi- 
 nation of one notion by another. But in both forms 
 something is spoken of, which is the Subject ; some- 
 thing is said of it, which is the Predicate ; and that 
 which says this is the Copula. Thus, Snow is Pure, 
 or S is P. In early logic the predicate includes 
 the copula, and this is still the usage of gramma- 
 rians. But logicians now reckon the copula as a
 
 SIMPLE PROPOSITIONS 69 
 
 distinct co-ordinate part. The subject and pred- 
 icate, being the extremes of the partition, are called 
 the Terms of the proposition. It is not at all req- 
 uisite that a term should consist of a single word ; 
 each term may be composed of many words in in- 
 tricate grammatical relations. E. g., 
 
 "With taper light 
 
 To seek the beauteous eye of heaven to garnish (=sulyect) 
 Is (=copula) wasteful and ridiculous excess" (predicate). 
 
 60. A judgment always expresses the relation 
 of two notions now in mind ; therefore the copula 
 must always appear as the present tense of the 
 verb to be : For the mind is its own kingdom, in 
 which an eternal now does always last. Very often 
 in common speech it is absorbed in verb forms, 
 or elided, and a whole proposition may be ex- 
 pressed by a single word. E. g., Stars twinkle, 
 i. e. Stars are things that twinkle ; He loved, i. e. He 
 is one who loved; Cogito, i. e. /am thinking ; Ilium 
 fuit, i. e. Troy was, i. e. Troy is something that for- 
 merly existed (existential) ; Did he say so ? Ans. 
 Yes, i. e. He is one who said so. All verbs are per- 
 haps fundamentally one, the verb to be of the sum- 
 mum genus being, their variety arising from the in- 
 corporation of various temporal and attributive no- 
 tions with this simple verbal element, its own past 
 and future forms being adverbial notions incorpo- 
 rated with its present tense. 
 
 The copula admits of only one qualification, ne- 
 gation. Hence in a negative proposition the nega-
 
 70 CONCEPTION 
 
 tive particle, wherever it may occur, is a part of 
 the copula. E. g., The quality of mercy is not 
 strained; No chastisement is joyous; Not a drum 
 was heard; Not every mistake is culpable; Britan- 
 nia needs no bulwark, i. e. Britannia is not needing 
 a bulwark. 
 
 Let it be observed that affirmative propositions 
 often contain negatives in the subject or in the 
 predicate, and should not be mistaken for negative 
 propositions. E. g., To wonder not is a rare art; 
 Axioms affirm what no one can deny. Also observe 
 that propositions affirmative in form are sometimes 
 negative in thought. E. g., The brute perishes; He 
 is blind; Darkness and silence fall on land and sea. 
 Negative thought may also be conveyed in affirm- 
 ative forms by means of such words and phrases 
 as without, beyond, far from, the reverse _ of \ on the 
 contrary, wanting, deficient in, devoid of, and the 
 like. E. g., We can do without it. 
 
 \ 61. In accordance with its postulate ( 13), 
 logic requires that all propositions shall be trans- 
 formed, as has been shown, so that, without addi- 
 tion or retrenchment or distortion of the thought, 
 the three parts, subject, copula, predicate, shall 
 severally appear. The process is sometimes quite 
 
 . troublesome, and the result awkward, but it is nev- 
 ertheless indispensable. E. g., So he said becomes 
 What has just been said is what he said ; If he 
 should come to-morrow, he will probably stay till 
 Monday becomes The happening of his arrival to-
 
 SIMPLE PROPOSITIONS 71 
 
 morrow is an event from which it may he inferred 
 rt-v ]>robable that he will stay till Monday. 
 
 The proposition often exhibits rhetorical inver- 
 sions, and a displacement of minor parts. E. g., 
 Great is Diana of the Ephesians / Few and short 
 were the prayers we said / Flashed all their sabres 
 bare ; Gold and silver have I none ; but what I 
 have, that give I thee. Herein order must be re- 
 stored, the subject naturally coming first. 
 
 All inversions and displacements corrected, all 
 elisions supplied, and the three parts stated dis- 
 tinctly in their natural order, constitute the re- 
 duction of a proposition to its strict logical form.J 
 Hence every proposition must, for logical purposes, 
 be reduced to one or the other of the two invaria- 
 ble forms, S is P, or S is not P. 
 
 62. It has already been stated that proposi- 
 tions, as to their Quality, are positive and negative 
 ( 51). It is now to be observed that propositions, 
 as to their Quantity, are total and partial. The 
 quantity of a judgment or proposition is determined 
 solely by the quantity of its subject, according as 
 this is definite or indefinite. The following scheme 
 exhibits this division with, subdivisions : 
 
 f Total, definite. f Individual, as, All the world's a stage. 
 
 I Universal, as, All men are players. 
 Propositions J 
 
 . f Divisive, as, Some plav soldier. 
 |^ Partial, indefinite J 
 
 1 Indivisive, as, Some act armies. 
 
 The quantity of the subject, and hence of the prop- 
 osition, is indicated by the predesignation all or
 
 72 CONCEPTION 
 
 some, or its equivalent. These two exhaust the 
 possibilities of predication; that is to say, every 
 possible proposition predicates either concerning 
 all, or concerning some, of its subject. 
 
 It is often the case that no sign of quantity is 
 prefixed. A judgment always has quantity in the 
 mind of the thinker and speaker, but the hearer 
 may be left to surmise the quantity from the mat- 
 ter or the context. E. g., Birds breathe, i. e. all do, 
 the predicate being of the essence ; Birds sing, i. e. 
 some do, the predicate being an accident. On re- 
 ducing such propositions to strict logical form, it is 
 generally needful to designate the quantity by its 
 sign. 
 
 63. Individual propositions are those in which 
 the subject is thought as an indivisible total. The 
 subject may be a proper noun, as in Ccesar is ambi- 
 tious ; or something designated by the definite ar- 
 ticle, or any demonstrative or possessive, as in The 
 world is round, This 'man is crazy, Let your words 
 be few. It may be a collective whole, as in The 
 college of apostles was typified in the twelve tribes 
 ( 24). It may even be a genus, as in The horse is 
 a noble animal. It may be unified by all, as in 
 All Jerusalem went out to meet him. . 
 
 64. TJniEfirsal propositions are those in which 
 the subject is thought as a divisible total. The 
 subject is said to be distributed, because what is 
 said of it as a whole is thought as distributively
 
 SIMPLE PROPOSITIONS 73 
 
 applicable to each part, as in All men are players, 
 i. e. all without exception ; and in Every man is a 
 }>l<njer, i. e. each taken severally. So also in No 
 man is perfect. 
 
 Predesignations or signs of universality or dis- 
 tribution are all, a or an or every, each, both,, neither, 
 not any, none, always, never, whoever, etc. 
 
 It appears that all is ambiguous, meaning either 
 all as an undistributed unity, or all as a distributed 
 plurality, as in Drink ye all of it. The matter 
 generally determines whether the meaning is cu- 
 mular or distributive. 
 
 Names of substances, as water, flesh, flame, iron,' 
 of forces, as gravity, heatj of actions, as to walk, 
 talking; and abstract terms, as charity, are usually 
 universal without predesignation. 
 
 65. Partial or indefinite propositions are those 
 in which the subject is thought as less than the 
 whole denoted by its naked form. We do not 
 think definitely of all, but partially or particularly 
 of some. The indefinite some, as the predesigna- 
 tion of logical quantity in affirmative propositions, 
 means at least some, perhaps all / in negatives, it 
 means at least some not, perhaps none. E. g., Some 
 men play soldier, i. e. at least some, perhaps all, do ; 
 Some men are not pure, i. e. at least some are not, 
 perhaps none are. A subject thus quantified is said 
 to be undistributed. 
 
 Predesignations or signs of particular or indefi- 
 nite propositions are some, a few, a or an or one, two,
 
 74: CONCEPTION 
 
 three, etc., certain, there are that, not all, not every, 
 sometimes, somewhere, etc. E. g., A few are saved, 
 i. e. some, a small number, are, perhaps all ; There 
 are men that practise self-denial, i. e. some exist, at 
 least a few, perhaps many, perhaps all ; All are not 
 here, i. e. some are not here, contradicting All are 
 here Not every step counts, i. e. some steps do not 
 count. The sign any signifies an indifferent some ; 
 the statement is limited to some, but is applicable 
 to every one, as in Anybody can do that. 
 
 There are signs that approximate the total, but 
 being less are still particular, as many, most, almost 
 all, the large majority of, etc. Others are nearly 
 total negatives, as few, very few, hardly or scarcely 
 any, little, small, slight, rare, seldom, etc. E. g., 
 Many are called, hut few chosen, i. e. at least some, 
 nearly all, perhaps all are called, but at least some 
 are not, nearly none, only a few, chosen ; Few are 
 saved, i. e. many are not, perhaps none ; Little reck 
 /, i. e. almost and may be not at all. Let it be 
 remarked that a few and a little are affirmative, 
 and that not all, when cumular, is total. 
 
 66. It appears that some also is ambiguous. 
 Besides the divisive sense just considered, it has an 
 indivisive, undistributed sense. E. g., Some men 
 act armies, means that a portion, a section, wholly 
 indefinite as to extent, do so. It has the same 
 meaning in : Give me some water ; Some time has 
 passed; We have come some distance; Some of the 
 way was rough; Some of the company is in ad-
 
 SIMPLE PROPOSITIONS 75 
 
 vance. The thought is of a mathematical quantity, 
 of a mass, logically indivisible ( 24). 
 
 Besides its indefinite significations, some is often 
 used in a semi-definite sense, meaning some at most, 
 not all, as in Some men seek fame, i. e. some at most 
 do, but not all, for some do not. This form, how- 
 ever, is compound, and will be examined in the 
 next chapter ( 72). 
 
 67. Combining the quality and quantity of 
 propositions, and symbolizing by vowels, we have 
 the following scheme of the four simple proposi- 
 tional forms : 
 
 Quantity. Quality. Symbol. Formula. Example. 
 
 Universal Affirmative, A All S is P All oaks are exogens. 
 
 Universal Negative, E No S is P No oaks are vines. 
 
 Particular Affirmative, I Some S is P Some oaks are trees. 
 
 Particular Negative, Some S is not P. . .Some are not shrubs. 
 
 The examples are in strict logical form. Indi- 
 vidual propositions ( 63), since the subject is def- 
 inite, are treated as universals, and symbolized by 
 A and E. Propositions whose subject is the indi- 
 visive some ( 66), being indefinite, may be symbol- 
 ized by I and O. 
 
 68. A simple proposition comprises only one 
 judgment ; it contains not more than one subject 
 and one predicate. It may, however, consist of 
 many grammatical elements; as, Well - organized 
 and skilfully administered governments are produc- 
 tive of happiness in their subjects.
 
 76 CONCEPTION 
 
 A complex proposition involves witb the princi- 
 pal judgment one or more subordinate judgments. 
 This subordinate element appears as a clause inci- 
 dental to the principal subject or predicate. E. g., 
 A man who is learned is respected ; I am monarch 
 of all / survey ; They that are wise shall shine as 
 the stars (shine). 
 
 A subdivision may be made into explicative and 
 restrictive clauses. The explicative clause merely 
 unfolds the marks connoted by the notion it quali- 
 fies ; as, Man, who is born of woman, is of few days. 
 The restrictive clause limits the notion it qualifies ; 
 as, 111 blows the wind that profits nobody. Not all 
 winds, but all in a limited class, are here spoken of. 
 The concessive clause removes a conceivable re- 
 striction ; as, I will trust him though he slay me. 
 When a restriction is a condition, the categorical 
 may be transformed to a conditional proposition ; 
 thus, A man who is learned is respected, becomes, 
 If a man be learned, he is respected. 
 
 Now, be it observed that the complex proposition 
 is treated logically as a simple proposition, the in-- 
 cidental clauses being regarded as mere substan- 
 tive, adjective, or adverbial qualifiers. In reducing 
 to strict logical form, it is needful to subordinate 
 clauses to the principal subject and predicate, and 
 to place them in close connection with the notions 
 they qualify ; as, He who, though he be rich, is sav- 
 ing is one that can share with him who is needy 
 without lessening what is enjoyed ; here the form 
 is simply, S is P. Indeed, the complex proposition
 
 SIMPLE PROPOSITIONS 77 
 
 is often directly reducible to one that is strictly 
 simple ; thus, The man who is learned is respected, 
 becomes, The learned man is respected. 
 
 This account of the complex proposition is given 
 to prevent clauses from being mistaken for princi- 
 pal propositions, and so confusing it with the com- 
 pound proposition. 
 
 69. Praxis. Concerning each of the follow- 
 ing propositions, answer, in their order, these five 
 questions: Is it conditional or categorical? If 
 categorical, what is its strict logical form ? "What 
 is its symbol of quantity and quality ? Is it indi- 
 vidual ? Aside from its form, is it essentially posi- 
 tive or negative? 
 
 1. No man is wiser because of his learning. 
 
 2. The senate has adjourned. Charity affords relief. 
 
 3. If you understand this, you can explain it. 
 
 4. From peak to peak the rattling crags among 
 Leaps the live thunder. 
 
 5. There was a sound of revelry by night. 
 
 6. This to hear 
 Would Desdemona seriously incline. 
 
 7. Not to know me argues yourself unknown. 
 
 8. I implore you, reject not this bill. 
 
 9. The blind are helpless. Richard III. was infamous. 
 10. Men are all sinners. No news is good news. 
 
 .11. Few patriots are disinterested. Diogenes was no fool. 
 
 12. All these claims upon my time overpower me. 
 
 13. Virtue is teachable, if it be knowledge. 
 
 14. Not many, if any, metals are without lustre.
 
 78 CONCEPTION 
 
 15. Not being rich is not always an evil. 
 
 16. Hardly any virtue is safe from passing into vice. 
 
 17. Those here present constitute the class in logic. 
 
 18. There's few or none do know me. That horse won 
 
 the race. A general cry was, No surrender. 
 
 19. There are who ask not if thine eye be on them. 
 
 20. I will not let thee go, unless thou bless me. 
 
 21. The most skilful general was Napoleon. 
 
 22. Little preface is needed. Not every man is honest. 
 
 23. The circle is the figure of greatest area. 
 
 24. Some education is desirable. Some pudding, a slice, 
 
 if you please. Some love to roam. 
 
 25. All honorable conduct is not to be rewarded. 
 
 26. Yonder forest is a covert for outlaws. 
 
 27. Gold is precious. To converse is pleasant. 
 
 Eeduce each of the following propositions to 
 strict logical form, and affix its symbol : 
 
 28. Nothing is harmless that is mistaken for virtue. 
 
 29. One truth is clear, whatever is, is right. 
 
 30. All is not gold that glitters. 
 
 31. He who truly loves most is not he who flatters. >5<7 
 
 32. Though this be madness, yet there's method in it. 
 
 33. Even a fool is counted wise, when he holdeth his 
 
 peace. That I am is no proof that he is. 
 
 34. They strive that they may enter in. 
 
 35. There's a divinity that shapes our ends, 
 Rough-hew them how we will.
 
 VIII. COMPOUND PROPOSITIONS 
 
 70. A compound proposition is one that com- 
 prises two or more judgments, co-ordinate or near- 
 ly so. For logical treatment the components are 
 to be separated, and stated independently. Such 
 propositions are of two kinds, according as the 
 composing elements are more or less obvious. 
 
 The first kind, wherein the components are quite 
 obvious, has received no specific name, and needs 
 only a few illustrations. E. g., Art is long, and 
 time is fleeting' Every man desireth to live long, but 
 no man would be old. In Veni, vidi, vici, there are 
 three propositions. So also in Pompey, Crassus, 
 and Ccesar were triumvirs. It is often the case 
 that a simple proposition has a compound subject 
 or predicate, as in Pompey, Crassus, and Caesar 
 were the triumvirs, for the three are here taken col- 
 lectively as one whole. So Roses and lilies contend 
 for a home in her che-ek is single and simple ; but 
 in Darkness and silence settle on land and sea there 
 are four propositions. 
 
 71. Compound propositions of the second class, 
 having components less obvious, require analysis, 
 and are called exponibles. They are chiefly ex- 
 clusives and exceptives.
 
 80 CONCEPTION 
 
 Exclusives may be formulated and exemplified 
 thus: 
 
 . . . _ ( AisB A or I 
 
 OnlyA,sB = -j NonA . gnotB Qr Q 
 
 ( Faith justifies A 
 
 E. g., Faith alone justifies = -j What is not faith does not ) 
 ( justify f 
 
 It is evident that this proposition may be in- 
 verted and the excluding particle made to appear 
 in the predicate ; thus, Justification is by faith 
 alone, i. e. B is only A. 
 
 Exceptives are exemplified in All but one were 
 saved, which means Nearly all were saved, and One 
 was not saved, I and O. It should be noted that 
 but is sometimes not exceptive, but merely adver- 
 sative, as herein ; also, that it sometimes means 
 that not, as in It cannot be but nature hath some 
 director. 
 
 No useful rule can be given for the resolution of 
 these exponibles. The components differ in quali- 
 ty, and one is direct and the other implied. But 
 the distinction between exclusives and exceptives 
 is of no logical moment, for they are mutually con- 
 vertible, the difference being that what is the di- 
 rect judgment in the one form becomes the indirect 
 in the other. 
 
 The following are some of the exclusivejmd ex- 
 ceptive particles : only, almfe, merely, solely, save, 
 but, etc. These particles, when qualifying a uni- 
 versal subject, quantify the predicate totally; as, 
 God alone is wise, i. e. He is all the wise. When 
 qualifying the entire predicate, they limit the sub-
 
 COMPOUND PROPOSITIONS 81 
 
 ject to that predicate ; as, The sacraments are but 
 two, i. e. there are no more. Sometimes the ex- 
 clusion or exception is in the sense, and not 
 expressed; as, (There is only) one Lord, one faith, 
 one baptism. 
 
 72. Our thoughts are often incompletely ex- 
 pressed. A proposition may be accompanied by 
 another limiting judgment unexpressed, with no 
 sign of implication, yet understood, because of our 
 knowledge of the matter. Thus if we say, Some 
 flowers are fragrant, knowing very well that some 
 are not, the proposition is accompanied by the 
 counter-judgment, Some flowers are not fragrant. 
 If this double thought be completely expressed in 
 a single, grammatically simple proposition, it is, 
 Only some flowers are fragrant. Now, this form! 
 is an exponible, a logical compound, which an- 
 alyzes into the two logically simple propositions : 
 
 Some flowers (I know not how many) are fragrant I 
 
 Some flowers (I know not how many) are not fragrant 
 
 Each of these, considered in itself, entirely apart 
 from the other, is wholly indefinite ; for the mean- 
 ing of some, I know not how many, must in that 
 case be at least some, perhaps all. It is evident, 
 then, that some, in the semi-definite sense of some 
 at most, not all ( 66), is equivalent to only some, 
 and does not occur unless one judgment is thought 
 as limiting another. Therefore, propositions quan- 
 tified by the so-called semi-definite some are com- 
 pound propositions.
 
 82 CONCEPTION 
 
 Since logic proposes to exhibit a thorough anal- 
 ysis of thought, it should in no case stop short 
 of simple forms. It is out of character to present 
 compound forms as the result of analysis, and 
 especially to rank them as co-ordinate with simple 
 forms. Hence the semi-definite proposition must 
 be denied a position among the elementary forms, 
 and assigned a place among the abbreviated, ellip- 
 tical modes of statement, subject to analysis and 
 full, discrete expression. 
 
 73. The predicate of a simple qualitative prop- 
 osition has no quantity whatever. We mean to 
 say, not merely that it may have none, but that it 
 cannot possibly have any. This is quite obvious in 
 case of intensive propositions. E. g., An athlete is 
 strong, cannot mean either all strong or some strong, 
 which is senseless, but simply that the mark strong 
 is found in the subject. In case of negative prop- 
 ositions, both intensive and extensive, the same is 
 true. E. g., Some athletes are not studious, or are 
 not students, means simply to deny the notion 
 studious or students of the subject, without any 
 quantification of students. The subject and predi- 
 cate are merely coexclusive. The same is equally 
 true, though perhaps nofr so clearly evident, in case 
 of affirmative propositions in extension. E. g., AU 
 athletes are sportsmen, or Some athletes are snobs, 
 merely places athletes in a class, without any 
 thought whatever of the quantity of the class; 
 that is, without thinking it as either all or some.
 
 COMPOUND PROPOSITIONS' 83 
 
 The statement that a predicate cannot have 
 quantity is true of simple qualitative propositions 
 only. We can readily, and often do, think quan- 
 tity into the predicate of extensive propositions; 
 but this is to compound our thoughts, the pred- 
 icate becoming for a moment the subject of 
 thought, and then being restored to its place 
 quantified. For example, if we say, All triangles 
 are trilateral, and then think that All trilaterals 
 are triangles, we may express the double thought 
 directly thus: All triangles are all trilaterals. It 
 has already been remarked that an exclusive or an 
 exceptive added to a universal subject quantifies 
 the predicate totally ( 71), and so the same 
 thought may be indirectly expressed by the ex- 
 ponible, Only triangles are trilaterals. In like man- 
 ner predicates of other forms may be quantified. 
 
 A very convenient mode of symbolizing the 
 forms of such propositions has been devised, which 
 we shall have some occasion to use. Let a stand 
 for a total, i for a particular term ; also let f repre- 
 sent the affirmative, and n the negative copula. 
 Then the forms spoken of may be represented 
 thus: 
 
 All triangles are (all) trilaterals all are all afa 
 
 All triangles are (some) figures. . . .all are some afi 
 
 Some men are (all) priests some are aU ifa 
 
 Some men are (some) poets some are some ifi 
 
 Some men are not (any) poets some are not any ina 
 
 No oaks are (any) vines not any are any ana 
 
 74. Two views may be taken of these forms.
 
 84 CONCEPTION 
 
 With reference to their origin, they are compound 
 propositions, formed from components, into which 
 they can be resolved. In this view, they cannot 
 be allowed co-ordinate rank with the four simple 
 forms ( 67), and must be held subject to analysis. 
 
 If viewed in themselves, without reference to 
 their origin, they are seen to be propositions, not 
 in the qualitative, but in the quantitative whole 
 ( 23). For consider the meaning of afa. Take, 
 All men are all bimana. Here the ambiguous all 
 ( 64) has changed from the distributive all, which 
 quantifies the components, to the cumular, indivisi- 
 ble all ( 63). It does not mean, Every man is every 
 bimana, which is nonsense, but All men (taken to- 
 gether as a mass) all bimana (taken together as 
 a mass). The proposition, considered in itself, is 
 therefore a mathematical equation. This is clearly 
 true of the affirmative forms. As to negative forms, 
 any thought into the predicate does not properly 
 quantify it, but serves rather to emphasize the nega- 
 tion, the proposition remaining qualitative ; though, 
 of course, a mass may be denied of a mass, and we 
 may think a negative proposition in either whole. 
 
 While, therefore, a simple qualitative judgment 
 always has a quantified subject T it cannot have a 
 rjuantified predicate. It follows, also, that a system 
 of logic built upon the quantification of the predi- 
 cate is vicious, either by confusing compound with 
 simple forms, or else by unnaturally transferring 
 all thought to the quantitative whole, and so mak- 
 ing logic merely a branch of applied mathematics.
 
 COMPOUND PROPOSITIONS 85 
 
 75. Finally, it is to be observed that in draw- 
 ing inferences, and so transforming thought, it is 
 frequently necessary to make a predicate, for a mo- 
 ment at least, the subject of a judgment to which 
 quantity is assigned. Then this is spoken of as the 
 quantity of the predicate, and must be taken into 
 account in many forms of illation. Now, this so- 
 called distribution of the predicate, ascertained by 
 compounding the thought, and having no verbal 
 sign, depends on the quality of the judgment, and 
 is expressed by the following RULE : Negatives 
 distribute the predicate, affirmatives do not. 
 
 In view of the preceding discussion, it is clear 
 that this statement taken in itself as to simple judg- 
 ments is not true. But taken merely as a derived 
 rule to be applied in illation, tersely and hence im- 
 perfectly expressed, it serves, under the given ex- 
 planation, as an unerring guide in logical processes. 
 
 76. Praxis. Referring to each of the follow- 
 ing propositions by its number, state whether it be 
 simple, complex, or compound. If either of the two 
 former, reduce it to strict logical form, and affix 
 the capital symbol ( 67). If compound, state what 
 kind, then write its components, affixing to each the 
 capital symbol, and noting the semi-definite some. 
 If its predicate have a sign of quantity, symbolize 
 literally ( 73), then state its components with their 
 capital symbols. 
 
 1. None but the brave deserve the fair. 
 
 2. Mercy but murders, pardoning those that kill.
 
 86 CONCEPTION 
 
 3. Men may come, and men may go, 
 But I go on forever. 
 
 4. Length, breadth, and depth are all the dimensions of 
 
 extension. 
 
 5. When I was a boy, I always chose the wrong side. 
 
 6. It is the duty of every man to fear God and honor 
 
 the king. 
 
 7. Jonah sought to evade the God who is omnipresent. 
 
 8. Few, few shall part where many meet, 
 The snow shall be their winding-sheet. 
 
 9. There is no fireside, howsoe'er defended, 
 But has one vacant chair. 
 
 10. Not every one that saith unto me, Lord, Lord, shall 
 
 enter in, but he that doeth the will of my Father. 
 
 11. Some inspired men were all of the apostles. 
 
 12. Brutus, in killing Ca3sar, was merely patriotic. 
 
 13. The moon is only our satellite. 
 /' / 14. The moon is our only satellite. 
 
 1 5. The paths of glory lead but to the grave. 
 
 16. A fool thinks none except himself wise. 
 
 17. Ho ! hearts, tongues, figures, scribes, bards, poets, 
 
 cannot 
 
 Think, speak, cast, write, sing, number hoo ! 
 His love to Antony. 
 
 18. Live how we can, yet die we must. 
 
 19. Some who are poor are nevertheless contented. 
 
 20. All grace is all free favor. Certain gifts are not any 
 
 favor. 
 
 21. All present are some of my friends. 
 
 22. My tasks are all but impossible. 
 
 23. The quarrel toucheth none but us alone. 
 
 24. Whereto serves mercy, but to confront the visage of 
 
 offence ?
 
 PART II. DEDUCTION 
 L IMMEDIATE INFERENCE ; 
 
 77. A judgment either affirms or denies that 
 one notion is in or under another ( 58). A division 
 of judgments, grounded on the process by which 
 they are formed, is as follows : 
 
 ! Intuitions. 
 ( Inductive. 
 Inferences. < ( Immediate. 
 
 ( Deductive, -j 
 
 ( Mediate. 
 
 Intuitions are self-evident, axiomatic judgments. 
 They are the origin of all knowledge, and deter- 
 mine all other judgments; for example, the Pri- 
 mary Laws ( 7 sq.). 
 
 Inferences are enunciations in which from seme- 
 thing laid down and admitted, something distinct 
 from what is laid down follows of necessity. Or, 
 more simply, to infer is to derive a judgment from 
 one or more premised judgments. Both the process 
 and the conclusion are called inferences. 
 
 Inductive inferences are universal judgments de- 
 rived from particular cases, and furnishing premises 
 for subsequent deduction. The general definition 
 of Logic includes them ( 6), but the present work
 
 88 DEDUCTION 
 
 is limited to deductive inferences. Inductive Logic 
 requires a separate treatise. 
 
 Deductive inferences are judgments of equal or 
 less generality than the premises from which they 
 are derived. They are especially the subject of 
 Deductive Logic, and are of two kinds, immediate 
 and mediate. 
 
 When two notions having a given relation are 
 concluded of each other in another relation with- 
 out the introduction of a third notion, the inference 
 is immediate. In this case one judgment is derived 
 directlyfrom another. The conclusion has but one 
 premise, the given judgment. The matter in both 
 is the same ; the relation is modified. 
 
 A mediate inference or a reasoning is accom- 
 plished through a third notion used as a medium of 
 comparison. It has two premises. 
 
 78. Implications should be distinguished from 
 inferences. An implied judgment is one actually 
 coexisting with the given judgment, either merely 
 in thought or involved covertly in the expression. 
 An inferred judgment is one that only potentially 
 exists in the given judgment, and may be derived 
 from it. The statement of the one is nothing new, 
 there is no advance, no progress of thought, but 
 only its full expression ; that of the other contains 
 something new, there is a step forward, a progress 
 of thought. 
 
 The forms extension and intension are hardly to 
 be considered even as implying each other, much
 
 IMMEDIATE INFERENCE 89 
 
 less as inferable one from the other. They are 
 simply different aspects of the thought, which nec- 
 essarily coexist, one having merely accidental pre- 
 ponderance ( 20). 
 
 Correlatives merely imply and are not inferable 
 from one another ( 30). To infer from The cause 
 of the explosion was a spark, that The effect of a 
 spark was the explosion, is a fallacy ( 146). 
 
 The interchange of active and passive forms is 
 not an inference. God made the world, and The 
 world was made by God, imply each other, or rather 
 are equipollent ( 13). 
 
 Incomplete speech implies thought, as in the 
 semi-definite proposition ( 72). Thus if we say, 
 Some men are rich, it is accompanied by the judg- 
 ment that Some men are not rich. But this actually 
 coexistent thought is not inferred. We cannot say 
 that from Some men are rich, it follows that some 
 are not. An exponible contains an implied, indi- 
 rect judgment covertly expressed, as in Only some 
 men are rich. 
 
 Finally, neither the compounding of two or more 
 simple propositions, nor the resolution of a com- 
 pound proposition into its components, should be 
 mistaken for inference. 
 
 79. Also preparatory to an account of the sev- 
 eral kinds of immediate inference for which we 
 shall have subsequent use, we state a prohibition 
 applied to all deductions in the following RULE: 
 The quantification must not be increased.
 
 90 DEDUCTION 
 
 Truly we may deduce all from all, some from some, 
 some from all, but not all from some. It is evident 
 that what is said only of some furnishes no ground 
 for a deduction concerning all. The attempt to 
 make this deduction in violation of the foregoing 
 rule is called the illicit process. The principles 
 of induction license the inference of all from some, 
 and so exhaust the possible processes. 
 
 80. Determination. Immediate inference by 
 determination is one of the four kinds to be noted. 
 The same mark may be added to both terms of a 
 proposition, by which they are more closely deter- 
 mined ( 42). The new judgment thus formed is 
 an immediate inference from the given premise. 
 Thus, from Coal is fuel, it follows that Cheap coal 
 is cheap fuel; if Science be system, then A false 
 science is a false system. We must be on our guard 
 not to use a determinant ambiguously, as in A king 
 is a man, therefore A good Icing is a good man. 
 The narrowing of both subject and predicate by 
 thinking a mark into them is passing from genus 
 to species. We observe that the subtraction of the 
 same mark from both terms is legitimate ; but the 
 remainder is an implicit judgment, not an infer- 
 ence. 
 
 Inverting the foregoing process, the t\vo terms 
 of a proposition may be added as marks to the 
 same concept. Thus, if Science be system, then A 
 scientific arrangement is a systematic arrangement. 
 Also two propositions may be combined, the terms
 
 IMMEDIATE INFERENCE 91 
 
 of one being added as marks to the terms of the 
 other. Thus, if A museum be a collection of speci- 
 mens, then A scientific museum is a systematized 
 collection of specimens. 
 
 81. Inflnitation. This mode of immediate 
 inference passes from the purely negative to the 
 infinite judgment ( 53). It places the subject in 
 the outer, infinite sphere. Thus, if The soul be not 
 mortal, then The soul is non-mortal. These prop- 
 ositions express different thoughts. They are sim- 
 ilar, but not identical. The reverse inference is in- 
 cluded, for the sake of brevity, under the same 
 name. Also purely affirmative and doubly nega- 
 tive propositions are infinitated ; thus, if Man be 
 mortal, then No man is non- mortal, and reversed. 
 Hence the general RULE : Change the quality 
 of the judgment, and also of its predicate. 
 The quantity of the judgment remains unchanged. 
 In using privatives, as in-, un-, dis-, -less, etc., we 
 must be on our guard lest we derive too much. 
 With this precaution, we add the following com- 
 plete series of examples : 
 
 Since All metals are fusible, then No metal is infusible A yields E 
 
 " No miser is happy, " Every miser is unhappy. .E " A 
 
 , . ( Some sins are not un- ) 
 
 " Some sins are pardonable, " { j. . . . I " O 
 
 ( pardonable ) 
 
 u Some men are not gentle, " Some men are ungentle. ..O " I 
 
 82. Conversion. In immediate inference by 
 conversion, the terms are transposed. Besides ob- 
 serving the general rules already given ( 75, 79),
 
 92 DEDUCTION 
 
 we must take heed to make a total transference ; 
 that is, the whole naked subject must be made 
 predicate, and vice versa. By naked is meant with- 
 out the sign of quantity all or some. Thus, from 
 Every old man has been a boy, we cannot infer that 
 Some boy has been an old man, but that Some one 
 who has been a boy is an old man. Hence it is gen- 
 erally needful before converting to reduce the prop- 
 osition to its strict logical form. 
 
 We shall consider only three kinds of illative 
 conversion, and these only so far as our subse- 
 quent need in syllogizing requires, which is that 
 we be able to convert each of the four forms A, E, 
 1,0. 
 
 1st. Simple conversion transposes the terms with- 
 out changing the quantity or the quality of the 
 proposition. It is applied to E, and to I ; thus : 
 
 No one without sympathies is a true poet; E ana 
 
 .'.No true poet is without sympathies E 
 
 Some mathematicians are poor financiers; I ifi 
 
 .'. Some poor financiers are mathematicians ...... I 
 
 2d. Conversion per accidens, or by limitation, jre- 
 duces the quantity without changing the quality 
 of the proposition. It is applied to A, and the con- 
 verse is I ; thus : 
 
 All plane triangles are rectilinear figures; A afi 
 
 ..Some rectilinear figures are plane triangles I 
 
 This is called per accidens because it is not the 
 transfer of a predicate per se, but only of an unes-
 
 IMMEDIATE INFEKENCE 93 
 
 sential or accidental part which that term, viewed 
 universally, includes. 
 
 Observe that the rule in 79 forbids retracing 
 the step, reconverting the I into A, which would 
 be the illicit process. 
 
 If, on subjecting the predicate of A to inquiry, 
 the proposition is recognized as afa, as when a 
 property, a definition, or a division is predicated, 
 then it is convertible simply. 
 
 Also E may be converted per accidens ; but this 
 case is rather simple conversion followed by subal- 
 ternation. 
 
 3d. Conversion by contraposition, or by negation, 
 changes the quality but not the quantity of the 
 proposition. It is applied to O, and the converse 
 is I. To contrapone, we have the following RULE : 
 Inflnitate, and then convert simply. Thus : 
 
 Some pure air is not wholesome; O I ifi 
 
 .'.Some unwholesome air is pure I 
 
 This is evidently a double process. It was devised 
 to convert O, which cannot be converted simply or 
 per accidens, as either would be the illicit process. 
 It is applicable also to A. 
 
 Upon inspection it is obvious that the whole doc- 
 trine of conversion has respect to extension. An 
 intensive judgment cannot be converted. But on 
 changing its predicate to a class notion it becomes 
 extensive, and so convertible. 
 
 Since an individual cannot be a predicate ( 54),
 
 94 DEDUCTION 
 
 it follows .that an individual proposition ( 63), 
 though it be symbolized by A or E ( 67), is in- 
 convertible. We say Juno is a queen, and may say 
 One queen is Juno ; but this apparent conversion 
 per accidens is merely a rhetorical inversion ( 61) ; 
 the subject of thought is still Juno. No mere in- 
 version is a logical conversion. 
 
 83. Opposition. A proposition in any one of 
 the four forms A, E, I, O, is in opposition to the 
 same matter in each of the other three forms. The 
 relations are such that if the given proposition be 
 formally true or false, we can immediately infer 
 the formal truth or falsity of some of the others. 
 Opposition is of four kinds, exhibited thus : 
 
 All Salt is Pure, A s Contrary E No Salt is Pure. 
 
 
 
 P *< ** I 
 
 SQUARE OF ^ * **. ^g OPPOSITION. 
 
 Cj *. rf ^]?* 
 
 Some Salt is Pure, I _ _ Subcontrnry - Q Some Salt is not 
 
 Pure. 
 
 1st. Contradictory opposition exists between A 
 and O, and between E and I, propositions having 
 the same naked or unquantified subject and predi- 
 cate, but which differ in both quantity and quality. 
 RULE : Both cannot be true, and both cannot 
 be false. This is merely a specific statement of 
 the Laws of Contradiction and Excluded Middle 
 ( 11). E, g., If All Salt is Pure be sublated, then
 
 IMMEDIATE INFERENCE 95 
 
 by an immediate inference we can posit Some Salt 
 is not Pure. If Some Salt is Pure be posited, then 
 we can immediately sublate No Salt is Pure, and 
 so on. If it be true that Every man has a con- 
 science, then it cannot be that Some men have no 
 conscience. Such propositions are said to be dia- 
 metrically opposed. Contradiction is pre-eminently 
 logical opposition. Also it is complete ; the other 
 forms are more or less incomplete. 
 
 2d. Contrary opposition exists between A and E, 
 universal propositions differing in quality only. 
 EULE : Both cannot be true, but both may be 
 false. Between A and E there is a tertium quid, 
 namely I and O ( 31). If All S is P be posited, 
 No S is P is sublated, and vice versa. But to deny 
 that All Stars are Planets does not afford the in- 
 ference that No Stars are Planets, for both are false, 
 since some are, and some are not, I and O. 
 
 Contrariety is less logical than metaphysical. 
 Contradiction occurs only in thoughts, and contra- 
 dictory thoughts cannot coexist. It cannot occur 
 in things, i. e. among real, external objects, contra- 
 diction has no place. Contrary thoughts can co- 
 exist indeed always do so as white and Hack, 
 straight and crooked, motion up and down. But 
 these cannot coexist in reality, in external things. 
 Hence contradiction is logical, contrariety physical, 
 opposition. Says Aristotle : Body cannot receive 
 contraries ; mind can receive contraries ; therefore 
 mind is not corporeal. 
 
 3d. Subcontrary opposition exists between I and
 
 96 DEDUCTION 
 
 O, particular propositions differing in quality only. 
 RULE : Both may be true, but both cannot be 
 false. They are compossible. If Some S is P be 
 allowed as true, it may be that Some S is not P is 
 also true. But if I is false, then O must be true, 
 and vice versa. We remark, howWer, that the 
 some in the two propositions must be a different 
 some. If the same some is thought, the proposi- 
 tions are incompossible. Also that if the some is 
 semi-definite, the rule becomes : Both must be true. 
 4th. Subalternate opposition exists between A 
 and I and between E and O, propositions differing 
 in quantity only. RULE: If the universal be 
 true, the particular is true ; if the particular 
 be false, the universal is false. This is not 
 strictly opposition, but rather a specific application 
 of the Law of Identity ( 8). No illustration is 
 needed. 
 
 These formal relations arising from opposition 
 may be tabulated thus : 
 
 Contradictories. Contraries. Subalterns. 
 
 (If A is true, O is false, ---- E false, I true. 
 If E is true, I is false ..... A false ..... O true. 
 -,...,'.. ' , 
 If A is false, O is true. ) m , A , , . . , 
 
 If E is false, I is true. \ The others Determined. 
 C If I is true, E is false. ) Tfae otherg undetermined . 
 
 Particulars^ . f 
 
 If I is false, E is true, ---- O true ..... A false. 
 
 I If O is false, A is true, ---- I true ..... E false. 
 
 Hence by the truth of universals, and by the falsity 
 of particulars, all others are determined ; otherwise 
 only the contradictory.
 
 r IMMEDIATE INFERENCE 97 
 
 Let it be observed that when the proposition is 
 individual ( 63) all the distinctions in opposition 
 are merged in the simple negative, which is com- 
 plete contradiction ; as, Caliban is a man, and Cali- 
 ban is not a man. 
 
 9 
 
 84. Praxis. Draw an immediate inference 
 from each of the following propositions : 
 
 Infer by determination from the three following : 
 
 1. War is an* evil. (Use unprovoked, and welcomed with 
 
 ardor.) 
 
 2. The ignorant are ceremonious. (Use an age, and 
 
 a nation.) 
 
 3. Honesty deserves reward. (Combine this with :) 
 
 Every man whom we meet is a neighbor. 
 
 Infinitate each of t;he following propositions : 
 
 4. Some men's hearts are not in the right place. 
 
 5. It is wrong not to reward the deserving. 
 
 6. In jewels and gold, men never grow old. 
 
 7. There are studies much vaunted, yet of little utility. 
 
 Convert each of the following, and affix the 
 symbols as in 82 : 
 
 8. None are free wb/ do not govern themselves. 
 
 9. With man many things are impossible. 
 
 10. Whoso loveth instruction, loveth knowledge. 
 i\j\\. Fair promises are often not to be trusted. 
 
 Contrapone and then infinitate the following : 
 
 12. Some invisible things are not intangible. 
 
 13. Every unjust action is inexpedient.
 
 98 DEDUCTION 
 
 If the following be true, what opposites are true, 
 and what false ? 
 
 14. By night an atheist half believes a God. 
 
 15. No one is always happy. 
 
 16. Some democracies are unstable. 
 
 17. Some great orators are not statesmen. 
 
 If the following be false, what opposites are 
 false, and what true ? 
 
 18. All self-confident persons have strong will, 
 
 19. No honest men become bankrupt. 
 
 20. Some private vices are public benefits. 
 
 21. Some plants do not produce seed.
 
 II. THE SYLLOGISM 
 
 85. "When we are unable to judge directly the 
 relation of two given notions, resort is had to some 
 third notion as a medium, which, being directly 
 compared with each of the former, enables us to 
 see their agreement or disagreement, and conse- 
 quently to conjoin or disjoin them. This is medi- 
 ate inference or reasoning ( 77). For example, 
 take the notion man, and the notion frefrwilled. On 
 comparing these, we are unable, perhaps, to judge 
 whether or not this mark belongs to that concept. 
 So we seek a medium of comparison. We find the 
 notion responsible, and see directly that man in- 
 volves responsible, likewise that responsible com- 
 prehends free / thus we come to see that man 
 involves /ra?. This is the intensive view. It is 
 formally stated thus : 
 
 Every maiyjs respousible ; 
 Every responsible is iree; 
 . '. Every man is free. 
 
 Again, we are unable to judge, perhaps, whether or 
 not man is contained under the class free agent. 
 But we judge that man is contained under the class 
 responsible agent, and this under the class free agent, 
 and so conclude man to be a, free agent. This is 
 the extensive view. It is formally stated thus :
 
 100 DEDUCTION 
 
 Every responsible agent is a free agent ; 
 Every man is a responsible agent ; 
 .'. Every man is a free agent. 
 
 A mediate judgment thus formally and fully ex- 
 pressed is called a syllogism. What is subjectively 
 a reasoning is objectively a syllogism. Hence the 
 definition :_A syllogism is a reasoning f ully_and 
 regularly expressed in language. What is meant 
 by regularly will more clearly appear hereafter. 
 Another definition is : A syllogism is an inference 
 by which a proposition is derived from two others 
 conjointly, the one being virtually contained in the 
 others. 
 
 86. In dissecting the syllogism we find three 
 propositions, two antecedents or premises, and a 
 consequent or conclusion. To conclude is to shut 
 up together in the last proposition notions which 
 stood apart in the first two. The word syllogism 
 also means a collecting together. The following is 
 an example in extension : - 
 
 All Men are Persons; =M: P = Major Premise; 
 All Slaves are Men ; = S : M = Minor Premise ; 
 /.All Slaves are Persons; = S: P =: Conclusion. 
 
 Here are only three notions or terms, Slaves, 
 Men, Persons. These are in the relation of whole 
 and part, Slaves being contained under Men, and 
 Men under Persons. P, then, is the term of wid- 
 est extent (as in the notations), or the Major Term ; 
 least extent, or the Minor Term ; and M, in this
 
 THE SYLLOGISM 101 
 
 case, of intermediate extent, or the Middle Term. 
 The latter occurs in each of the premises, but not 
 in the conclusion. The two former, called the Ex- 
 tremes, constitute the conclusion. "We may now 
 define as follows : 
 
 The Middle Term. (M) is the one with which 
 each of the extremes is compared in the premises. 
 It is also called the Argument, or the Keason. 
 
 The Major Term (P) is the extreme of greater 
 quantity, or the greater whole. It is always (in 
 extension) the Predicate of the conclusion. 
 
 The Minor Term (S) is the extreme of less 
 quantity, or the lesser whole. It is always (in ex- 
 tension) the Subject of the conclusion. 
 
 The Major Premise is the premise containing 
 the Major Term. It is usually placed first. It is 
 also called the Sumption. 
 
 The Minor Premise is the premise containing 
 the Minor Term. It is usually placed second. It 
 is also called the Subsumption. 
 
 Observe that the middle term is not so called 
 because of intermediate extent, but because it is 
 the medium of comparison. There are many cases 
 in which it has not intermediate extent. 
 
 The order of the propositions, the major premise 
 first, the minor second, and the conclusion last, is 
 arbitrary, and merely agreed upon for the sake of 
 uniformity. Also that there are three distinct 
 propositions. It is easy and accurate to state the 
 reasoning in an inverted order, and in a single 
 proposition ; as, That slaves are persons is an infer-
 
 102 DEDUCTION 
 
 encefrom the judgments that they are men, and that 
 men are persons. 
 
 In the foregoing example all the propositions are 
 universal and affirmative. The following differs in 
 these respects : 
 
 No murmurs are prayers. . .(E) /^ "^ ^ *\ Prayers. 
 Some sighs are murmurs ... (I) 
 
 .'. Some sighs are not prayers . (O) ^ ' : 
 
 In this example one premise is particular, and one 
 negative, yielding a conclusion which is both. 
 
 87. Let us consider the several notations. The 
 circular and linear have already been mentioned 
 ( 25), and on slight inspection are easily under- 
 stood. The circular is objectionable, as allowing a 
 great variety of insignificant arrangement, and also 
 as constantly signifying too much. For instance, 
 in the last example it expresses No S is P, and 
 also that Some S is not M, or the semi -definite 
 some. The linear has the advantage that only 
 those parts of the lines opposite each other are 
 compared. Of what is beyond the limit of com- 
 parison nothing is said, the extension of the line 
 merely serving to show that it is indefinite. For 
 this and other reasons the linear is preferable to 
 the circular. 
 
 These notations are not at all applicable to in- 
 tension, but only to extension. But even as ap- 
 plied to extension they are radically objectionable.
 
 THE SYLLOGISM 103 
 
 Both circles and lines have geometrical extension 
 only, and are quantities ; and therefore when used 
 to figure qualitative notions they transfer thought 
 to the quantitative or mathematical whole ( 23), 
 and so induce confusion. This is favored by the 
 ambiguity of the word extension, and has doubt- 
 less been influential in promoting the unnatural 
 and false view that all propositions are equations, 
 and logic a branch of applied mathematics ( 74). 
 The circular and linear notations are therefore cov- 
 ertly false and misleading. We shall not, however, 
 wholly discard them, for by long and widely ap- 
 proved usage they have become almost an integral 
 part of elementary logic; but we caution the 
 reader by pointing out their essentially erroneous 
 representation. 
 
 Another mode of notation, called graphic nota- 
 tion, is shown in connection with the examples. 
 It needs some explanation. A colon standing next 
 a term indicates that it is distributed ; a comma, 
 that it is undistributed. The positive copula is ex- 
 pressed by a pointed dash ( ), in manuscript a 
 slight pen-stroke ; the negative by the same crossed 
 ( H- ). A peculiar advantage of this device is that it 
 discriminately expresses either extension or inten- 
 sion. Pointing to the predicate, the copula indi- 
 cates an extensive judgment ; thus M : P reads 
 All M is (contained under) P ; P -+ : M reads No 
 M is (contained under) P ; M , S reads Some S 
 is (contained under) M. The long dash is the 
 copula of the conclusion ; thus, P " , S reads
 
 104 DEDUCTION 
 
 Some S is not (contained under) P. Pointing to 
 the subject, the copula indicates an intensive judg- 
 ment ; thus S : M reads All S is (comprehends) 
 M ; S , ^ P reads Some S is not (does not com- 
 prehend) P. When needful, a sign of quantifica- 
 tion ( , or : ) may be added to the predicate also. 
 This admirable method of notation is very elastic, 
 capable of expressing thought relations accurately, 
 and is recommended for constant use. 
 
 88. In the intensive syllogism the predicates 
 are marks. The following is an example, with its 
 graphic notation : 
 
 i Silver is Metallic; = S : M \ 
 Metal is Positive; =M: P V = S: M: P 
 .'.Silver is Positive. = S : P ) 
 
 By positive is meant electro-positive. The same 
 matter transformed yields : 
 
 {All Metals are Positive elements; \ 
 Silver is a Metal ; l=P :M :S 
 
 .'. Silver is a Positive element. 
 
 Here the relative quantity of the extremes is in- 
 verted ; the greater part in extension, P, is the less- 
 er part in intension, and vice versa ( 54). This is 
 in accord with the law that extension and inten- 
 sion are in inverse ratio ( 20). In the example, 
 Silver comprehends Metallic, and this comprehends 
 Positive ; S is obviously the greatest whole, and P 
 the least. Hence, in intension the major term is 
 the subject of the conclusion, and the minor term
 
 THE SYLLOGISM ' 105 
 
 its predicate. And, since it is agreed to place the 
 major premise first, the order of the premises is 
 transposed. Consequently, for changing either form 
 into the other, we have the following RULE: 
 Transpose the premises, and invert the 
 copulas; that is, instead of comprehends, read is 
 contained under, and vice versa. 
 
 89. The distinction between the extensive and 
 intensive syllogism has been discussed because need- 
 ful in order to general definition, and to a complete 
 view of the dissected parts. We are now prepared 
 to make an estimate, briefly and once for all, of the 
 value of the distinction. The grammatical differ- 
 ence, which frequently but not always appears, be- 
 tween substantive and adjective noun forms in the 
 predicate is hardly a logical difference. This apart, 
 the external difference lies wholly in transposed 
 premises. But the order of the premises being 
 merely conventional, any distinction founded there- 
 on is arbitrary and artificial, not real and natural, 
 and so goes for nothing. The other difference 
 named in the rule is the inversion of the copulas. 
 This is not an external difference. Ordinarily the 
 copula is wholly indifferent and ambiguous, and its 
 special meaning is indicated only by unusual sub- 
 stitutions ( 54). 
 
 The difference, then, lies entirely in the thought, 
 in the modes extension and intension, and the con- 
 sequently, reversed relation of part and whole. That 
 this is a difference in kind may be granted, one to
 
 106 DEDUCTION 
 
 be noted in an exposition of mental modes, and in 
 a theory of thought. But it is of very small log- 
 ical consequence. Both forms of the syllogism are 
 mediate inferences through the same medium ; both 
 reach the same conclusion ; the formal expression of 
 both is the same ; the supreme canon ( 93) is essen- 
 tially the same for both ; the general rules ( 94) are 
 the same ; and the special rules ( 97) need for ad- 
 aptation only the interchange of the words major 
 and minor y hence no general modification of the 
 old logical doctrine is called for by introducing the 
 intensive syllogism. 
 
 The practical difference is of no moment. When 
 we consider that one of these modes subjectively, 
 and with the greatest facility, changes to the other, 
 and that without further consequence, we ask: 
 What is the worth of a difference between forms 
 so completely and readily transmutable ? The two 
 always actually coexist in thought as psychological 
 correlatives, one more obscure than the other ( 20), 
 and their convertibility would indicate rather iden- 
 tity, being inconsistent with the opposition which 
 belongs to kinds. Moreover, we very often use 
 both forms in one reasoning. For example : 
 
 All of the metals are positive; Intensive. 
 
 Silver is one of the metals; Extensive. 
 
 .'.Silver is positive Intensive. 
 
 This is formally perfect, calling for no logical mod- 
 ification whatever. 
 
 From these considerations we conclude that it is
 
 THE SYLLOGISM 107 
 
 needless to continue to observe the distinction. Let 
 the reader, then, understand that hereafter we shall 
 view all matter primarily in the form of extension, 
 even when adjective predicates are used, satisfied 
 that at any instant the view can readily be re- 
 versed, and noting expressly the form of intension 
 only in special cases. 
 
 90. Formally stated, a syllogism consists of 
 three propositions. But let it not be understood 
 that a syllogistic judgment or reasoning consists of 
 three judgments. Two judgments are premised; 
 then parts of these are combined. This last alone 
 is the act of mediate comparison, the syllogistic 
 judgment, the reasoning ; and it is a single act of 
 mind, a single thought, only one judgment. Sub- 
 sequently it is formally stated as a third proposi- 
 tion, the conclusion. 
 
 In the definition of inference it is said that some- 
 thing distinct from what is laid down follows of 
 necessity ( 77). Accordingly, the essence of the 
 syllogism is the necessary sequence of the conclu- 
 sion from the premises. This necessity flows from 
 the necessary character of the Primary Laws 
 ( 5> 7), to which the syllogism conforms, and by 
 which alone it is ultimately governed. It is some- 
 times expressed in the conclusion by the addition 
 of must. For example : 
 
 If all metals are fusible, 
 And gold is a metal, 
 Gold must be fusible.
 
 108 DEDUCTION 
 
 The common distinction, then, between demon- 
 strative and moral or probable reasoning lies 
 wholly in the matter, not at all in the form. The 
 form is in all cases demonstrative, apodeictic, nec- 
 essary. 
 
 91. Since logic is not at all concerned with the 
 matter of thought ( 50), it has no regard for the 
 material truth or falsity of syllogistic propositions, 
 but only for the relation of sequence. In view of 
 this fact, it would be an improvement if the prem- 
 ises in logical examples of the syllogism were ex- 
 pressed not categorically, but conditionally, as in 
 the example in the preceding section. The mind 
 of the reader would then be less drawn to the truth 
 or falsity of the propositions, which is not at all in 
 question, and away from the form, which is the 
 sole consideration. For the same reason, illustra- 
 tions whose matter is trite and familiar are to be 
 preferred. 
 
 But some remark upon the relations of the parts 
 of the syllogism with reference to formal truth 
 and falsity is desirable. The antecedents being 
 granted, the consequent must also be allowed. If_ 
 the_antficedents be true, necessarily the consequent 
 is true. Whatever measure of doubt attaches to 
 the antecedents, just that degree of uncertainty- 
 no more, no less belongs to the consequent. Should 
 t/he antecedents be false, it does not follow that 
 ,the consequent is false ; it is merely unproven, and 
 may, perhaps, be established by other antecedents.
 
 THE SYLLOGISM 109 
 
 These antecedents, being false, prove nothing : 
 
 The natives of Italy were Greeks ; 
 The Athenians were natives of Italy; 
 /. The Athenians were Greeks. 
 
 This example shows also that the truth of the con- 
 sequent does not guarantee that of the antece- 
 dents. But if the consequent be false, it follows 
 that at least one of the antecedents is false. These 
 points may be summarized thus : 
 
 Affirming the antecedents, affirms the conse- 
 quent. 
 
 Denying an antecedent, nothing follows. 
 
 Affirming the consequent, nothing follows. 
 
 Denying the consequent, denies an antecedent. 
 
 92. Praxis. Point out the major, minor, and 
 middle terms in the following reasonings, and re- 
 dress them in syllogistic order. Then write the 
 circular, linear, and graphic notation of each : 
 
 1. True poets are men of genius ; but since very un- 
 
 wise men sometimes prove true poets, they must 
 be men of genius. 
 
 2. Whatever is universally believed must be true. This 
 
 may be said of the existence of God, which, there- 
 fore, must be a truth. 
 
 3. No duty involves loss ; hence to give freely does 
 
 not always involve loss, for this is occasionally a 
 duty. 
 
 4. Sensualists are not free ; for they are governed by 
 
 passion, and no one so governed is free. 
 
 Write the graphic notation of each of the fol-
 
 110 DEDUCTION 
 
 lowing syllogisms, then change the extensive to the 
 intensi\ r e form, and vice versa, and write the graphic 
 notation of the result : 
 
 5. All men are liable to err ; 
 
 None liable to err are safe from disaster; 
 /. No man is safe from disaster. 
 
 6. All expedient actions are justifiable actions ; 
 Some wars are expedient actions ; 
 
 .-. Some wars are justifiable actions. 
 
 Answer the questions appended to the following 
 syllogism : 
 
 7. If infants have no language, and if they reason, then 
 
 some reasoning is possible without language. 
 But the sumption is quite doubtful ; therefore, what 
 
 follows ? 
 But the subsumption is not true; therefore, what 
 
 follows ? 
 But the conclusion is not true ; therefore, what 
 
 follows ? 
 But the conclusion surely is true ; therefore, what 
 
 follows? 
 But both of the premises are true ; therefore, what 
 
 follows ?
 
 III. CANON AND RULES 
 
 93. The syllogistic judgment that the antece- 
 dents necessitate the consequent ( 90) is deter- 
 mined by the Primary Laws. Since these, howev- 
 er, because of their wide generality, are not readily 
 applicable, the principle of the syllogism is ex- 
 pressed in a single special CANON which can be used 
 as a direct test of its validity. We select four out 
 of many modes of statement. 
 
 1. Part of a part is part of the whole. As 
 marks are parts of a notion, and species parts of a 
 genus, this is obviously applicable to both exten- 
 sion and intension in the qualitative whole. Also, 
 it applies to the quantitative whole. Its general- 
 ity, brevity, and simplicity render it very useful. 
 It is, however, inadequate, being applicable only 
 to affirmative syllogisms. A modified formula, 
 limited to the qualitative whole, is : What is said 
 distributively of a whole may ~be said of a part. 
 
 Let the reader apply these formulas to any of 
 the foregoing affirmative syllogisms, and the mean- 
 ing will become clear. 
 
 2. Quicquid de omni valet, valet etiam de quibus- 
 dam et singulis. Quicquid de nullo valet, nee de 
 quibusdam nee de singulis valet. These are the
 
 112 DEDUCTION 
 
 famous Dicta de omni et nullo of the schoolmen. 
 They have been often and sharply criticised as 
 senseless, the first being charged with saying 
 merely Whatever is true of each, is true of 'each the 
 second, What is not true of any, is not true of any. 
 
 3. Whatever is discovered or admitted as 
 predicable distributively of a class, must be 
 allowed as predicable of any of its discovered 
 or admitted members. 
 
 This formula, carefully worded to avoid similar 
 reproach, is applicable to syllogisms both positive 
 and negative, but is limited in expression to those 
 in extension. We note : predicable, positively or 
 negatively; discovered, by intuition, by induction, 
 or by testimony ; admitted, by hypothesis, or mere- 
 ly for sake of argument ; of a class, as an undivided 
 whole ; must, necessity ; members, species or indi- 
 viduals. 
 
 4. Any notion may be replaced by its equiv- 
 alent ; or by its undistributed genus ; or, if 
 distributed, by any of its parts. 
 
 This canon of replacement is here proposed as 
 more general than the others, and as more truly 
 expressive of the actual process of thought. It is 
 simple and self-evident. The first clause is appli- 
 cable to coextensive, or equipollent, or mathemati- 
 cal equivalence. For instance : 
 
 A is equal to B ; 
 B is equal to C ; 
 .'.A is equal to C. .(replacing the first B by its equivalent C). 
 
 The several clauses are applicable to the various
 
 CANON AND RULES 113 
 
 forms of immediate inference. For instance, con- 
 version per accidens may be viewed thus : 
 
 All men are men ; ( mere identity). 
 
 Prop. .All men are mortals ; (mortals, genus of men). 
 
 .'.Some mortals are men. .(replacing the first all men 
 by its undistributed genus). 
 
 The view taken in this canon of the qualitative 
 syllogism is peculiar. It considers the sumption 
 as stating a relation between two notions ; the 
 subsumption as stating that some other notion is a 
 part of one of them ; the syllogistic judgment as 
 replacing that one by this part ; and the conclusion 
 as setting forth the result. For instance : 
 
 All men are mortal ; (sumption). 
 
 Socrates is a man ; (he is one, a part of all men), 
 
 :. Socrates is mortal (replacing all men by this part). 
 
 The third clause of the canon applies thus to syllo- 
 gisms of the first and second figure; the second 
 clause, to those of the third figure. Moreover, some 
 natural and very simple forms of reasoning, which 
 it is difficult to put in strict logical form, are directly 
 justified by this canon. For instance, the follow- 
 ing has been accounted a sore logical puzzle : 
 
 The divine law commands us to honor kings ; 
 Louis XIV. is a king ; 
 .'.The divine law commands us to honor Louis XIV. 
 
 Its solution by replacement is easy. In the sump- 
 tion kings is a distributed notion, and in the con- 
 clusion is simply replaced by its part, Louis XIV. 
 This seems to be the actual mental process by 
 which a child would accept this conclusion. 
 8-
 
 1 14 DEDUCTION 
 
 94. The canon in its original and usual form 
 is directly applicable only to syllogisms of the first 
 figure. For this reason, and because its use as a 
 test is, in some cases, rather confusing, logicians 
 have resolved its principle into a series of distinct 
 GENERAL RULES applicable to any figure. All 
 sound reasoning must conform to these rules. Be- 
 ing quite simple and used separately, they render 
 the process of testing a syllogism easy, quick, and 
 sure. They are as follows : 
 
 1. A syllogism has three, and only three, 
 terms. For a reasoning, which it expresses, com- 
 prises three, and only three, notions two compared 
 by means of a third. A good syllogism is a tripod. 
 The following is a quadruped ; verbally it is a triad, 
 but in thought quaternio terminorum, and hence 
 called a quaternion : 
 
 Light is contrary to darkness ; 
 
 Feathers are light ; (light equivocal). 
 
 /. Feathers are contrary to darkness. 
 
 2. A syllogism has three, and only three, 
 propositions. For three terms give three pairs, 
 and three only. Apparently we have more in- 
 All beings that have nerves are sentient A 
 
 All self-moving things have nerves A 
 
 Worms are self-moving A 
 
 .'. Worms are sentient A 
 
 The reasoning is good, the form logical; but we 
 shall find in a subsequent analytical study ( 106) 
 that it is a Sorites, resolving into two syllogisms 
 of three propositions each.
 
 CANON AND RULES 115 
 
 3. One premise at least must be affirmative. 
 
 For if the middle term agrees with neither of the 
 other two, we cannot infer through it whether or 
 not they agree with each other. From the follow- 
 ing negative premises 
 
 No marble is sentient E 
 
 Some statues are not marble O 
 
 we get no conclusion ; for, however true it may 
 be, they do not prove some statues not sentient. 
 But the following yield a conclusion : 
 
 No man is without religious feeling E 
 
 Many men are not true believers I 
 
 .'. Many infidels are not without religious feeling O 
 
 But the minor premise is really affirmative, the 
 negative particle belonging to the predicate, which 
 thereby becomes equivalent to infidels, and consti- 
 tutes the subject of the conclusion. 
 
 4. If one premise be negative, the conclu- 
 sion must be negative. For if one extreme be 
 denied to the middle term, it must be denied final- 
 ly to the other extreme which agrees with the 
 middle term by Rule 3. For example : 
 
 Few men weep O 
 
 All men feel A 
 
 We cannot conclude Some who feel weep. How- 
 ever true it may be, these premises do not yield it. 
 Few is essentially negative ( 65), and gives a nega- 
 tive sumption, yielding a negative conclusion : 
 
 Sumption, Most men do not weep O 
 
 Now subsume, ... All men feel A 
 
 Hence conclude, . .Many who feel do not weep O
 
 116 DEDUCTION 
 
 5. The middle term must be total at least 
 once. For if in each premise it is used in a partial 
 sense, it may in each denote different objects, and 
 so be equivalent to two terms, making four in all, 
 in violation of Rule 1. From these premises 
 
 Some of our students use profane language I 
 
 Some of our students are refined gentlemen I 
 
 we can conclude nothing, for the middle evidently 
 refers to entirely different groups. This is the fal- 
 lacy of undistributed middle. Sometimes it is not 
 quite so obvious ; for example : 
 
 A valid syllogism has three terms A 
 
 This syllogism has three terms A 
 
 .'. This is a valid syllogism A 
 
 Here the middle is in each case the predicate of an 
 affirmative, and is not distributed ( 75), and so the 
 conclusion is unproven. 
 
 If, however, an undistributed middle be so quan- 
 tified that the sum of its portions is more than the 
 whole, a conclusion is competent. This is called 
 the Ultra-total Quantification of the Middle Term- 
 Two thirds of mankind are Asiatics I Asiatics 
 
 Two thirds of mankind are heathen I mankind 
 
 .'. Some heathen are Asiatics I heathen"] 
 
 (At least one half are, perhaps all are.) 
 
 The early logic makes no mention of this appar- 
 ent exception to the rule, which is apparent only, 
 not real, for the reasoning is in the quantitative, 
 rather than in the qualitative, whole. 
 
 6. An extreme, if partial ia a premise, 
 must be so in the comclusiom. For if only some
 
 CANON AND RULES 117 
 
 is premised, we cannot conclude all we cannot 
 argue from part to whole. The violation of this 
 rule is the fallacy of illicit process ( 79). It is 
 illicit major or illicit minor, according to the term 
 to which the fault attaches. For example : 
 
 All birds are winged A 
 
 A bat is not a bird E 
 
 .'. A bat is not winged E 
 
 Here the major term winged is not distributed 
 (i. e. is partial) in the premise, since it is there the 
 predicate of an affirmation ; but it is distributed 
 (i. e. is universal) in the conclusion, since it is there 
 the predicate of a negation. Hence there is an 
 illicit process of the major term. The following is 
 an illicit process of the minor term : 
 
 Persons without imagination are not true poets.. E 
 
 Good logicians are often without imagination I 
 
 .*. Good logicians are not true poets. E 
 
 Illicit major occurs only when the conclusion is 
 negative. Illicit minor occurs only when the con- 
 clusion is universal. 
 
 7. One premise at least must be universal. 
 For if the premises be I I, there is no distributed 
 term for a middle (Rule 5). If they be O O, both 
 premises are negative (Rule 3). If they be I O or 
 O I, there is but one term distributed, the predi- 
 cate of O ; if this be taken for the middle term, 
 then illicit major, since the negative conclusion 
 required by Rule 4 distributes its predicate, the 
 major term ; if it be not so taken, then undistrib- 
 uted middle (Rule 5).
 
 118 DEDUCTION 
 
 8. If one premise be particular, the con- 
 clusion must be so. For a universal following 
 
 A with I would require 2 distributed terms ; there is but 1 ; 
 A " O " " 3 " " " are but 2; 
 
 E " I " "3 " " " . " " 2; 
 
 E " O, both negative (Rule 3). No conclusion whatever. 
 
 95. Praxis. Reduce all propositions to strict 
 logical form ( 61), and arrange them in syllogistic 
 order ( 86). 
 
 Apply the first canon, pointing out the parts 
 and whole, to 
 
 1. The truly virtuous are truly happy. The poor are 
 
 often the one, and therefore the other. 
 
 Apply the third canon, pointing out the class 
 and its member, to 
 
 2. All planetary bodies move in elliptic orbits (by induc- 
 
 tion). Now, if an asteroid be truly a planet (by 
 hypothesis), then the orbit of an asteroid is elliptic. 
 
 Apply the canon of replacement, supplying the 
 conclusion, to 
 
 3. The gospel promises salvation to the faithful ; yet 
 
 many are faithful whom the world condemns. 
 
 Affix the symbol to each proposition, and then 
 point out what rule or rules, if any, are violated 
 in the following examples: 
 
 4. Many who conquer their passions have strong will ; 
 Whoever resists temptation conquers his passions ; 
 
 .. Whoever does not yield possesses powerful will.
 
 CANON AND RULES 119 
 
 5. No sentient being is without a nervous system ; 
 The sensitive mimosa is not sentient ; 
 
 /. The sensitive mimosa has no nervous system. 
 
 6. Whatever causes intoxication should be prohibited ; 
 The use of wine causes intoxication ; 
 
 /. The use of wine should be prohibited. 
 
 7. No one is rich who is not content ; 
 No miser is content ; 
 
 /. No miser is rich. 
 
 8. Few men are entirely unworthy of respect; 
 Most men are unlearned ; 
 
 /. Some unlearned men are worthy of respect. 
 
 9. Some x is y ; every y is not z ; hence some x is not z. 
 
 10. No rose is without thorns ; 
 This bouquet is of roses ; 
 
 .-. This bouquet has thorns. 
 
 11. All rational beings are accountable for their actions; 
 But many that suffer punishment are irrational ; 
 
 /. Many that suffer punishment are not accountable for 
 their actions. 
 
 12. Every man ha* wants; 
 
 All men are rational animals ; . . . afa 
 .-. Every rational animal has wants. 
 
 13. All householders pay taxes ; 
 
 The voters are those that pay taxes ; . . afa 
 /. All householders are voters. 
 
 N. B. With reference to the forms of examples 12 
 and 13, see 146 and 131.
 
 IV. FIGURE AND MOOD 
 
 96. Syllogisms are divided into Figures accord- 
 ing to the position of the middle term. In the 
 First Figure, it is the subject of the major premise, 
 and predicate of the minor. In the Second, it is 
 predicate of both. In the Third, it is subject of 
 both. In the Fourth, it is predicate of the major, 
 and subject of the minor. Thus : 
 
 Fig. 1. Fig. 2. Fig. 3. Fig. 4. 
 
 M~P P~M M~P P-M 
 
 S M S M M S M~ S 
 
 .-.S-P .-.8 P .'.8 P .-.S~P 
 
 tub prce turn pros prat turn tub tub turn prce tub. 
 
 This last line is a useful mnemonic, without any 
 other meaning. 
 
 The first figure serves especially to establish 
 general propositions. The universal affirmative A 
 can be proved only in this figure. It has been 
 sufficiently illustrated in foregoing examples. 
 
 The second figure, whose conclusion is always 
 negative, is especially adapted to proving differ- 
 ences, and so clearing obscure thought ( 21). For 
 example : 
 
 The true apostles were not thieves ; ana 
 
 Judas was a thief; afi 
 
 .'. Judas was not a true apostle ana
 
 FIGURE AND MOOD 121 
 
 The third figure, whose conclusion is always par- 
 ticular, is especially adapted to bringing in exam- 
 ples, and thus proving an exception to some uni- 
 versal statement. For example : 
 
 The apostles sought no temporal reward ; ana 
 
 The apostles were zealous in their work ; af i 
 
 .'.Some zealous persons did not seek temporal reward ina 
 
 This contradicts, and so disproves, All zealous per- 
 sons seek temporal reward. Only in the third fig- 
 ure can the middle term be individual ; for in each 
 of the others the middle term is once at least a 
 predicate, and an individual cannot be predicated 
 ( 54). For example : 
 
 Peter was an inspired man ; af i 
 
 Peter was unlearned ; afi 
 
 .'. Some one unlearned was inspired ifi 
 
 The fourth figure is reserved for subsequent and 
 special examination ( 102). 
 
 97. By deduction from the General Rules of the 
 syllogism ( 94) we obtain, relative to the several 
 figures, certain SPECIAL EULES, as follows : 
 
 Example. Special Rule*. 
 
 Fig. 1 (sub prcs). 
 
 No man is perfect Major premise must be universal. 
 
 (Else undistributed middle.) 
 
 Some saints are men Minor premise must be affirma- 
 tive. (Else illicit major.) 
 .'. Some saints are not perfect . 
 
 Fig. 2 (prceprce). 
 
 No perfect-one is a man Major premise must be universal. 
 
 (Else illicit major.) 
 
 Some saints are men One premise must be negative. 
 
 (Else undistributed middle.) 
 
 .'. Some saints are not perfect . (Hence the conclusion is always 
 
 negative, Rule 4.)
 
 122 DEDUCTION 
 
 Example. Special Kulei. 
 
 Fig. 8 (sub sub). 
 No man is perfect. 
 
 Some men are saints Minor premise must be affirma- 
 tive. (Else illicit major.) 
 .'. Some saints are not perfect . Conclusion must be particular. 
 
 (Else illicit minor.) 
 Fig. 4 (prce sub). 
 
 No perfect-one is a man If either premise be negative, 
 
 major must be universal. 
 (Else illicit major.) 
 
 Some men are saints If major premise be affirmative, 
 
 minor must be universal. 
 (Else undistributed middle.) 
 
 /.Some saints are not perfect. If minor premise be affirmative, 
 
 conclusion must be particular. 
 (Else illicit minor.) 
 
 These rules, and their proof, should be thoroughly 
 examined ; but only those of the first figure need 
 be retained in memory. All have reference to ex- 
 tension. To adapt them to the intensive syllogism, 
 it is needful only to change the word major to 
 minor, and vice versa, wherever they occur. The 
 symbolic notation of the example above is the 
 same for each of the four figures; the graphic 
 notation is different for each of the figures ; thus 
 
 Perfect 
 Men P -H : M , S (Fig. 1.) 
 
 Saints 
 
 98. The four figures of the syllogism are sub- 
 divided into moods, upon the ground of the quan- 
 tity and quality of the premises. The conclusion 
 need not be taken into account, since it is deter- 
 mined by the premises. A method of ascertaining 
 the moods is as follows :
 
 FIGDKE AND MOOD 123 
 
 Relative to quantity and quality, we recognize 
 four propositions, A, E, I, O. These, as premises, 
 taken two at a time, yield sixteen possible combi- 
 nations, exhibited in the following scheme : 
 
 AA Figs. 1, 3, 4. EA Figs. 1, 2, 3, 4. 
 
 AE " 2, 4. [EE] 3d Gen. Rule. 
 
 AI " 1, 3. El Figs. 1, 2, 3, 4. 
 
 AO Fig. 2. [EO] 3d Gen. Rule. 
 
 IA Figs. 3, 4. OA Fig. 3. 
 
 [IE] 6th Gen. Rule. [OE] 3d Gen. Rule. 
 
 [II] 7th " ' [OI] 7th " ' 
 
 [IO] 7th [OO] 3d " " 
 
 But not all these combinations will yield con- 
 clusions, for they do not all represent the premises 
 of valid syllogisms. Those bracketed are to be 
 eliminated as violative of the General Rules. Eight 
 (one half) remain as valid, since they accord with 
 the General Rules. 
 
 Let us now inquire in which of the four figures 
 each of these eight valid combinations may occur. 
 We apply the Special Rules, and find that EA and 
 El accord with all these rules, and therefore can 
 appear in each of the four figures, as indicated in 
 the scheme. The figures in which the others can 
 appear are similarly ascertained and indicated. 
 Upon counting, we find there are nineteen valid 
 moods of the syllogism. 
 
 99. The first figure has the mood A A. Now 
 annex the symbol of the conclusion, and coin a 
 word containing the three vowels consecutively as 
 the name of the mood, thus : Barbara. The several
 
 124 DEDUCTION 
 
 moods are treated in this manner, and the names 
 of the nineteen moods thus coined are arranged in 
 the following mnemonic hexameters : 
 
 Barbara, Celarent, Darii, Ferio queprioris; 
 Cesare, Camestres, Festino, Baroco 1 secundce; 
 Tertia Darapti, Disamis, Datiai, Felapton, 
 Bocardo, 2 Ferison habet. Quarta insuper addit 
 Bramantip, Cameues, Dimaris, Fesapo, Fresison. 
 
 1 or Dokamok, * or Fakofo. 
 
 orFokmafokf. 
 
 These names of the moods are very convenient. 
 By applying its name to any reasoning, we at once 
 indicate its figure, and the quantity and quality of 
 each proposition, and also, as will be seen, its rela- 
 tion to other moods to which it may be reduced, 
 and the method of reduction. Moreover, they 
 serve as a test; for, since these are all the valid 
 moods, when we have a simple syllogistic form to 
 which none of the names is .applicable, we know 
 at once that the reasoning is false. 
 
 From the conclusions it appears that each of the 
 four judgments is proved in Fig. 1. Its four moods 
 are reducible to two, the third and fourth being 
 varieties of the first and second. Thus : 
 
 Barbara or Darii. Celarent or Ferio. 
 
 All M is P ; No M is P ; 
 
 All or some S is M ; All or some S is M ; 
 
 /. All or some S is P. /. No S is P, 
 
 or Some S is not P. 
 
 Here is one positive and one negative form. Since 
 all the other moods may, as we shall find, be re- 
 duced to one or the other of these, they are the 
 two fundamental forms of all reasoning. The evi-
 
 FIGURE AND MOOD 125 
 
 dence of this, furnished by reduction, is perhaps 
 the chief merit of the system. 
 
 Again, on noting the conclusions throughout, it 
 appears that 
 
 A is proved in 1 figure and in 1 mood whose initial letter is B. 
 E " 3 figures " 4 moods " " " C. 
 
 I " 3 figures " 6 moods " " " D. 1 
 
 O " 4 figures " 8 moods " " " F.* 
 
 1 Except Bramantip. a Except Baroco and Bocardo. 
 
 Hence the proposition A is the hardest to estab- 
 lish, and the easiest to overthrow; and O is the 
 easiest to establish, and the hardest to overthrow. 
 
 100. Reduction is of two kinds. First, Osten- . 
 sive Reduction. A syllogism in any other mood 
 may be ostensively reduced to one or another of 
 the first four, and thus brought under the syllogis- 
 tic canon ( 93). The initial consonant of each 
 name is that of the mood in Fig. 1, to which it 
 reduces. Baroco and Bocardo are exceptions, but 
 may be replaced by their alternates. The reduction 
 is accomplished by substituting for one or more of 
 the propositions an immediate inference from it. 
 Other consonants in the name direct us in doing this. 
 s indicates that the proposition symbolized by 
 the vowel that precedes it is to be converted 
 simply. 
 
 p indicates that the preceding proposition is to 
 be converted per accidens. (Except in Bra- 
 mantip, where it shows that, after converting 
 simply, a universal is warranted by the prem- 
 ises. This is the reverse of per accidens.}
 
 126 DEDUCTION 
 
 k indicates conversion by contraposition* 
 
 f indicates infinitation. 
 
 m indicates that the premises are to be trans- 
 posed (mutari). 
 
 The consonants b, d, 1, n, r, t, are not significant, 
 but are inserted merely for the sake of euphony, 
 or for metrical quantity. 
 
 The following examples will sufficiently illus- 
 trate the process : 
 
 Fig. 2, Camestres, reduces to Fig. 1, Celarent. 
 
 AllPisM; No Mis 8; 
 
 NoSisM; AllPisM; 
 
 /.No S is P. /.No P is 8. 
 
 Cam- Every wicked man is discont'd; J I Ce- No discontented man is happy ; 
 
 es- No happy man is discontented; > = < la- Every wicked man is discont'd; 
 tres. .-. No happy man is wicked. ) ( rent. /. No wicked man is happy. 
 
 Fig. 3, Darapti, reduces to Fig. 1, Darii. 
 
 Da- All wits are dreaded; \ | Da- All wits are dreaded; 
 
 rap- All wits are admired; f ~ 1 r '~ Some who are admired are wits; 
 
 tl. .-.Some who are adm'd are dreaded. ) ( i. .-. Some who are adm'd are dreaded. 
 fig. 2, Fakofo, reduces to Fig. 1, Ferio. 
 
 Fak- AH murders are intentional ; \ i Fe- No unintent'l things are murders; 
 
 Of- Some homicides are not intent'l; I = -| rt- Some homicides are unintent'l; 
 
 O. .'.Some homicides are not murders. ) ( o. .'. Some homicides are not murders. 
 
 If in a given syllogism a proposition requiring 
 conversion in order to reduction be an individual 
 proposition, then the reduction is not practicable, 
 for an individual proposition cannot be convert- 
 ed ( 82). 
 
 Moods having the same initial letter conclude 
 the same formal judgment. The only exception is 
 Bramantip, for Baroco and Bocardo have alternates 
 inF. 
 
 Moods having the same initial are equivalent 
 moods, being generally reducible to each other
 
 FIGURE AND MOOD 127 
 
 by the following GENERAL RULE FOB REDUCTION. 
 Cause the propositions to appear as required 
 by any legitimate inference from them, trans- 
 posing, if need be, the premises. 
 
 101. The ostensive reduction just explained 
 could not, it was believed, be applied to the two 
 moods Baroco and Bocardo, having a premise in 
 O. Hence the early logicians devised the Reductio 
 ad impossibile. It is a test of the validity of rea- 
 soning from granted premises in those two moods. 
 
 B, the initial letter, shows, not that the syllogism 
 is reduced to Barbara, but that Barbara is 
 used in making the test. 
 
 c indicates that the proposition preceding it is 
 to be omitted, and the contradictory of the 
 conclusion substituted. This gives premises 
 in Barbara, from Avhich a new conclusion is 
 drawn. E. g. : 
 
 Baroco, tested by Barbara. 
 
 Ba- All murders are intentional; (1) Bar- All murders are intentional; (4, 
 
 roc- Some homicides are not inteut'l; (2)*.jr ba- All homicides are nifrders; (5; 
 
 * .-.Some homicides are not murders. (3) ^^, ra. /.All homicides are intent'l (6; 
 
 Here the conclusion drawn in Barbara (6) is false, 
 because it contradicts a granted premise (2). Hence 
 a premise in Barbara is false ( 91). But one of 
 these (4) having been granted (1), the false one 
 must be the one substituted (5). Now, this false 
 proposition being the contradictory of the origi- 
 nal conclusion (3), that conclusion must be true, 
 and this reasoning in Baroco valid. So also :
 
 128 DEDUCTION 
 
 Bocardo, tested by .Barbara. 
 
 Hoc- Most men do not weep; (2) * * Bar- All who feel weep; (6) 
 
 r- All men feel; (1) V ba- All men feel; (4) 
 
 do. .'. Many who feel do not weep. (3) / \ ra. .-. All men weep. (6) 
 
 It is sufficient to say : If we contradict the con 
 eluding 0, then by plain proof (Barbara) we con- 
 tradict the premised O, which is absurd, being a 
 self-contradiction. 
 
 All the other moods may be tested by the same 
 process. But even in the case of Baroco and Bocar- 
 do it is superfluous. The former can be reduced 
 to Fig. 1 by using its alternate Fakofo; the latter 
 by Dokamok ( 82). But since Bocardo concludes 
 O, it should reduce, not to Darii, but to Ferio. 
 Therefore we propose Fokmafokf as a preferable 
 alternate. 
 
 Viewing reduction as a means of testing the 
 validity of syllogisms, then : 
 
 Ostensive reduction is direct reduction, and indirect test; 
 Reduction ad impossibile is direct test, and indirect reduction. 
 
 102. The fourth figure is open to just and fatal 
 criticism. The general form ( 96) is : 
 
 But observe that, in the affirmative form, P being 
 the major term, the premises are impossible. The 
 greater cannot be contained under the less. But 
 if S be the major term, we directly conclude P S. 
 This is Fig. 1, t. p. Then we may convert the con- 
 clusion per accidens, or else simply, and get Some
 
 FIGURE AND MOOD 129 
 
 6 P. The procedure is evidently compound, 
 which forbids Bramantip and Dimaris taking rank 
 with the simple moods. In thought they are Bar- 
 bara and Darii, with transposed premises, which 
 is arbitrary ( 86), and a subsequently converted 
 conclusion. For similar reasons, Camenes is Ce- 
 larent. 
 
 Fesapo and Fresison are even more faulty. The 
 direct conclusion is illicit major, which is corrected 
 by a conversion per accidens. This passage, through 
 a fallacy, is of course inadmissible. 
 
 Therefore, the moods of the fourth figure should 
 be rejected as not co-ordinate with the others, as 
 superfluous, and in two cases erroneous. 
 
 103. Praxis. Write a detailed proof, based on 
 the General Rules, of the three following points : 
 
 1. Prove that the conclusion in Fig. 3 must be particular. 
 
 2. Prove that the major premise in Fig. 1 must be uni- 
 
 versal. 
 
 3. Prove that from IE no conclusion is valid. 
 
 Name the moods expressed by these notations : 
 
 4. P : M . . S 6. P H , M ; S 8. P -H:M, S 
 
 5. P : M H- : S 7. P, M : . 1' 8 9. P : M -H \ S 
 
 following examples the agreed order of 
 
 the propositions is preserved. Redress each in 
 strict syllogistic form, supplying any lacking prop- 
 osition, and name its mood. Then write its graphic 
 notation. Then, if it be not in Fig. 1, reduce it 
 9
 
 130 DEDUCTION 
 
 thereto. To Baroco and Bocardo apply the test 
 per impossibile. 
 
 10. Whoever possesses prudence possesses all virtue ; 
 Whoever possesses one virtue must possess pru 
 
 dence. 
 
 11. Prudence has for its object the benefit of indi- 
 
 viduals ; 
 But prudence is a virtue. 
 
 12. No good action results in evil ; 
 Some alms-giving results in evil. 
 
 13. All abstract studies strengthen the intellect; 
 Exercises that strengthen the intellect are profitable. 
 
 14. No science is capable of perfection ; 
 All science is worthy of culture. 
 
 15. No vicious conduct is praiseworthy ; 
 All heroic conduct is praiseworthy. 
 
 16. All pride is inconsistent with religion ; 
 Some pride is commended by the world. 
 
 17. All true philosophers account virtue a good in itself ; 
 The Epicureans do not account virtue a good in 
 
 itself. 
 
 18. A fallacious argument is not a legitimate mode of 
 
 persuasion ; 
 A legitimate mode of persuasion sometimes fails to 
 
 convince ; 
 .. Not all those arguments are fallacious that fail. 
 
 19. Every candid man acknowledges merit in a rival; 
 Every learned man does not do s ; 
 
 .*. Every learned man is not candid.
 
 FIGURE AND MOOD 131 
 
 20. A few men at least are truly honorable, yet all have 
 
 imperfections ; hence some are so who have im- 
 perfections. 
 
 21. All expedient acts are conformable to nature ; 
 Nothing conformable to nature is hurtful to society. 
 
 22. Nothing that must be repented of is desirable. Now 
 
 many of our most intense enjoyments constrain 
 repentance. Few of these, then, are truly de- 
 sirable. 
 
 23. There is no growth without sunshine, and these 
 
 flowers, being deprived of it, will not grow. 
 
 24. What is not in Scripture is not binding on con- 
 
 science ; 
 
 Since many ecclesiastical canons are not found there- 
 in, they may be disregarded. 
 
 25. No virtue is a natural quality ; 
 
 Every natural quality has God for its author. 
 
 i 26. Some kinds of anger are not unrighteous ; 
 Every kind of anger is a passion. 
 
 27. Some of our tax-laws are oppressive measures; 
 All oppressive measures should be repealed. 
 
 28. Prejudices are in no case compatible with perfection j 
 Yet some are quite innocent 
 
 29. All wicked men are discontented; 
 Socrates is not discontented.
 
 V. MODIFIED FORMS 
 
 104. The various modes in which reasonings 
 may be expressed are endless. Except in treatises 
 on logic, it is rare that a formal syllogism occurs. 
 In conversation, or even in argumentation, its pres- 
 ence is offensive, for an intelligent hearer does not 
 need complete statement, a hint being often suffi- 
 cient. Unnecessary words do not elucidate, but 
 obscure, thought. It is usual, then, to abbreviate 
 expression. Even essential propositions, if they 
 be obvious, are elided ; often they are compounded 
 or condensed, so that the thought is rarely stated 
 entire, or in strictly logical order. We propose 
 now to illustrate some of these modified forms. 
 
 An Enthymeme is an incomplete syllogism, 
 one or two judgments being unexpressed. There 
 are four orders : 
 
 1st. The major premise unexpressed. This oc- 
 curs most frequently because the sumption is very 
 often a general rule understood and admitted, 
 whereas the subsumption is often a question of 
 fact which needs to be stated and established, in 
 order to be subsumed. E. g., Yonder celestial body 
 has a proper motion among the fixed stars ; there- 
 fore it is a member of the solar system.
 
 MODIFIED FORMS 133 
 
 2d. The minor premise unexpressed. This gives 
 emphasis to the conclusion. E. g., Pra/yers are often 
 sinful j for whatsoever is not of faith is sin. 
 
 3d. The conclusion unexpressed. Sometimes this 
 is high art. The speaker does not formally com- 
 mit himself, the hearer draws the conclusion, as in 
 the famous speech of Antony over the body of 
 Caesar. E. g., Virtue is always discreet; but there is 
 a zeal without discretion. 
 
 4th. Only one judgment expressed. When we 
 see on a tombstone The memory of the just is 
 Messed, the implied syllogism is manifest. This 
 form often occurs in texts, proverbs, pithy sayings, 
 and in witticisms. If some one, seeing me vexed, 
 should say, The way of the transgressor is hard, 
 I am indignant, for the implied syllogism concludes 
 me a transgressor, and that through an undistrib- 
 uted middle. This was precisely the argument of 
 Job's comforters. Sometimes this form is an in- 
 sinuation, as when Falstaff replies to Prince Hal, 
 Lord, Lord, how this world is given to lying ! The 
 answer to a question is often indirect, merely giv- 
 ing a premise which authorizes the doubtful prop- 
 osition. E. g., Is smuggling a crime ? Ans., What- 
 ever violates the rights of society is a crime. The 
 message to Pilate from his wife may be taken as 
 an instance of a single word hinting premises sup- 
 porting the hortatory conclusion : Have thou noth- 
 ing to do with that JUST man. Finally, when the 
 disciples of John asked our Lord, Art thou he that 
 should come f he replied indirectly, giving them a
 
 134 DEDUCTION 
 
 minor premise, not in words, but in deeds. In that 
 same hour he did many miracles, and bade the dis- 
 ciples tell John what they had seen. 
 
 105. An Epichirema, or reason-rendering syl 
 logism, is one that has attached to either premise, 
 or to both, a supporting reason. That is to say, it 
 is a syllogism having for a premise the conclusion 
 of an enthymeme. This enthymeme may, of course, 
 be expanded into a syllogism. A syllogism whose 
 premise is the conclusion of another is called an 
 Episyllogism. One whose conclusion is the premise 
 of another is called a Prosy llogism. For example : 
 
 Episyllogism. Prosyllogism. 
 
 Vice is odious ; ( Whatever enslaves is a vice ; 
 
 Avarice is a vice ; for it enslaves ; = < Avarice enslaves ; 
 
 /. Avarice is odious. ( .'. Avarice is a vice. 
 
 The propriety of thus, in the progress of an argu- 
 ment, offering some reason or reasons in support 
 of its doubtful propositions is apparent. By so 
 doing we avoid the necessity of returning over the 
 game ground; and by clearing doubts as we go 
 along, we are not so likety to excite in the hearer 
 the disgust that comes of suspense. 
 
 106. A Sorites is a chain of enthymemes, 
 holding throughout the relation of prosyllogism to 
 episyllogism. It is expressed either intensively or 
 extensively. The difference between the two forms 
 as to the order of premises is merely conventional, 
 not essential ( 86).
 
 MODIFIED FOKMS 
 
 135 
 
 SCHEME OP SORITES. 
 
 Progressive form, 
 in intension. 
 
 A^ B 
 
 13 C 
 C D 
 
 I) -H K 
 I .'.A -HE 
 
 Regressive form, 
 in extension. 
 
 Resolution of the progressive form. 
 a is c; 
 C is D; 
 .'. a is d. 
 
 A is B; 
 Bis C; 
 .'. a is c. 
 
 Resolution of the regressive form. 
 D is not E ; c is not e ; 
 
 CisD; BisC; 
 
 ,'.c is not e. .'. b is not e. 
 
 a is d; 
 D is not E ; 
 .'.A is not E. 
 
 b is not e ; 
 A is B; 
 .'.A is not E. 
 
 Example. 
 
 Some who are prosperous are avaricious; 
 The avaricious are intent on gain; 
 The intent on gain are discontented; 
 f he discontented are not happy ; 
 ^ome who are prosperous are not happy. 
 
 Notation in depth. 
 
 Example. 
 
 No discontented men are happy men; 
 All men intent on gain are discont'd men; 
 All avaricious men are men intent on gain 
 Some prosperous men are avaricious men; 
 /.Some prosperous men are not happy men 
 
 Notation in breadth. 
 
 Other notations in breadth. 
 
 D 
 C 
 
 B 
 
 pros 
 
 discontented men 
 
 men intent on gain 
 
 avaricious men 
 
 perous men 
 
 The following points should be carefully noted 
 and analyzed : 
 
 1st. The regular Sorites has as many middle 
 terms, and hence resolves into as many syllogisms, 
 as it has premises, less one. 
 
 2d. The first proposition is the only major prem- 
 ise expressed ; the other premises are minors.
 
 136 DEDUCTION 
 
 . 3d. Each unexpressed major premise is the con- 
 clusion of the preceding syllogism. 
 
 4th. Only one premise may be negative, and 
 this must come last in intension, and first in ex- 
 tension ; else illicit process. 
 
 5th. Only one premise may be particular, and 
 this must come first in intension, and last in exten- 
 sion ; else undistributed middle. 
 
 We also remark that in the scheme all the syllo- 
 gisms are in Fig. 1. A sorites cannot occur in the 
 other figures throughout. One step, however, may 
 be in Fig. 2 or Fig. 3, but only one, and it must be 
 either the first or the last. 
 
 107. Arguments are frequently stated in what 
 at first glance appears to be a single simple syllo- 
 gism, but which a slight inspection discovers to be 
 compound, or to involve some deviation from rule. 
 
 When a conclusion is a compound proposition, 
 it is evident that there must be at least one com- 
 pound premise, and that the statement involves 
 two or more syllogisms. For example : 
 
 The triumvirs were ambitious; 
 Caesar, Pompey, and Crassus were triumvirs; 
 .'.Caesar, Pompey, and Crassus were ambitious. 
 
 Here are obviously three syllogisms involved in 
 one statement. If we substitute for the major 
 term founded the empire, then there is but one, 
 since the change makes all the propositions simple. 
 When the conclusion is simple, a compound prem- 
 ise involves a surplus of matter. For example :
 
 MODIFIED FORMS 137 
 
 Whatever revolves about the earth must present phases, 
 The moon alone revolves about the earth; 
 /.The moon makes phases. 
 
 This compound minor premise resolves into The 
 moon revolves about the earth, from which the con- 
 clusion follows, and What is not the moon does not 
 revolve about the earth, from which no conclusion is 
 competent, since it would give illicit major. Hence 
 more is contained in the premises than can be col- 
 lected in the conclusion. 
 
 But a compound exponible premise in other cases 
 may yield a compound conclusion collecting all 
 that is given. For example : 
 
 .Justification comes by faith alone; 
 Our highest hope is justification; 
 /.Our highest hope comes by faith alone. 
 
 This may be resolved into two simple syllogisms, 
 Barbara and Celarent. But it is not requisite, for 
 we may view comes by faith alone as simply the 
 major term, and the whole as Barbara. 
 
 There is a class of disguised syllogisms in which 
 the premises are irregularly stated. They consist 
 of simple propositions indeed, but require, in order 
 to bring them under logical rule, the substitution 
 of equipollent propositions, or else of one or more 
 subsidiary inferences. In some cases the resolution 
 is obvious. For example : 
 
 The sun is a thing insensible; 
 The Persians worship the sun; 
 .'.The Persians worship a thing insensible. 
 
 Here are five terms; yet the reasoning is evident-
 
 138 DEDUCTION 
 
 ly very good. The canon of replacement is di- 
 rectly applicable, the conclusion being obtained by 
 replacing, in the minor premise, the sun by its un- 
 distributed genus, a thing insensible, as declared in 
 the major premise. But even under the common 
 logical rules the resolution is very simple. From 
 the major premise we may immediately infer, by 
 determination ( 80), They who worship the sun 
 worship a thing insensible, and we then have a per- 
 fectly regular Barbara. 
 
 The following would hardly puzzle a tyro : 
 
 Whoever probes a wound is on the verge of crime ; 
 A wound is probed by the healer ; 
 /.The healer is on the verge of crime. 
 
 For the passive minor, substitute the equipollent 
 active form ( 78), The healer probes a wound, and 
 we have again Barbara. 
 
 An example involving an immediate inference in 
 opposition is as follows : 
 
 That riches are often a bitter curse is true ; 
 And yet it is also true that most men desire riches ; 
 /.It is false to say that no men desire what is often a bit- 
 ter curse. 
 
 The syllogism which is here slightly disguised is the 
 following Darii : 
 
 They who desire riches desire what is often a bitter curse ; 
 Most men desire riches ; 
 /.Most men desire what is often a bitter curse. 
 
 This major premise is immediately inferred by de- 
 termination ; the conclusion, by opposition ; for if 
 E be false, then I is true.
 
 MODIFIED FORMS 139 
 
 108. There are certain modes of procedure in 
 argument which, though strictly belonging under a 
 doctrine of method, may fairly be mentioned here. 
 
 The argumentum ad rem is the direct or osten- 
 sive proof of the thesis, or problem, or main point 
 in question, the qucesitum. 
 
 In order to such procedure, premises must be 
 had. To assume them without proof is to beg the 
 question or principle, petitio principii ( 146). If 
 they be granted argamenti gratia, or allowed as 
 unquestionable, the procedure is legitimate. But 
 whence come unquestionable premises? To say 
 they are conclusions of precedent inferences is in- 
 sufficient, for the question recurs as to these. The 
 answer is that ultimately they are derived from 
 pure intuition or from experience, the two original 
 sources of all knowledge. 
 
 When the ultimate premises are intuitive princi- 
 ples, self-evident truths, axioms, the procedure is 
 a priori. So from the axiom, Two straight lines 
 cannot enclose an area, geometry is evolved ; from 
 the primary laws of thought, logic ; from the mor- 
 al law, ethics. The syllogistic, deductive process 
 a priori is strictly demonstrative, apodeictic ( 90). 
 And since the ultimate premises are necessary 
 truths, the conclusions are necessarily true. 
 
 When the ultimate premises are empirical, or 
 truths of experience, they have been obtained a pos- 
 teriori. Thus induction infers from particular facts 
 of experience truths of empirical universality, and 
 so affords premises for subsequent deduction ( 77);
 
 140 DEDUCTION 
 
 % 
 
 such as All men are mortal, and The volume of a 
 gas is in inverse ratio to the pressure. Hence arise 
 the inductive sciences; as astronomy, geology, 
 physics. Probable or moral reasoning, or dialec- 
 tics, always involves empirical matter, and so falls 
 short of strict demonstration. 
 
 The argumentum a fortiori, which may be taken 
 as one variety of that ad rem, and understood to 
 mean/br a stronger reason, gathers up in the con- 
 clusion an additional force from relations in the 
 premises. The general formula is : If A be con- 
 tained under B, and B under C, then by so much 
 the more is A contained under C. For example : 
 If God so clothe the grass of the field, shall he not 
 much more clothe you f 
 
 When unquestionable premises as a basis for 
 direct probation are not available, resort is often 
 had to one of the three following indirect methods : 
 
 The argumentum ad verecundiam is an appeal 
 to authority, to some venerable institution, to an- 
 tiquity, etc., as when a dictionary is allowed to 
 settle the disputed meaning of a word, or reference 
 is made to an orthodox creed. 
 
 The argumentum adjudicium is an appeal to the 
 judgment or common-sense of mankind. We hear 
 it often in conversation in the phrases Everybody 
 says, and No one thinks, etc. 
 
 The argumentum ad populum is an appeal to 
 principles cherished by the public. It is legiti- 
 mate if the principles be sound. But an appeal to 
 prejudice or passion usually betrays weakness.
 
 MODIFIED FORMS 141 
 
 f 
 
 The argumentum ad impossible or reductio ad 
 absurdum indirectly proves a thesis by showing 
 that its contradictory is absurd, that it is self-con- 
 tradictory, or contradictory of an axiom or other 
 admitted principle, as in 101. For example, In 
 a triangle the sides opposite two equal angles are 
 equal; for if they be not equal, it follows that a 
 part is equal to the whole, which is absurd ( 10). 
 Likewise it is used in disproof ; as, If the foot-tracks 
 were made by the prisoner, he was wearing shoes 
 much smaller than his feet. 
 
 The argumentum ad hominem is arguing from 
 the premises of an opponent merely to defeat him. 
 We accept his principles on which to base a coun- 
 ter-argument, even if believing them false, our ar- 
 gument being directed against him personally, ad 
 hominem. It aims to convict him of ignorance, 
 bad-faith, inconsistency, or illogical reasoning, and 
 so to put him ex curia. Usually it attempts no 
 more. Our Lord often used this method to silence 
 his adversaries, as in Matt. xxii. 41-45. Since the 
 argument proceeds ex concesso, it is formally intro- 
 duced by a concessive proposition ; as, Though one 
 rose from the dead (Luke xvii. 31) ; and, Though, 
 rich, yet not therefore happy, for, etc. Criticism is 
 mostly in the form ad hominem, and should be dis- 
 tinguished from proof of the opposite or contro- 
 versy. 
 
 "We remark, finally and generally, that in disproof 
 the attack may be directly on the thesis, showing
 
 142 DEDUCTION 
 
 it to be false, or upon the argument, showing it to 
 be from a false premise, or else illogical. In the 
 two latter cases the result is merely negative ( 91), 
 but is often sufficient. The onus probandi, or bur- 
 den of proof, rests ordinarily upon the party mak- 
 ing a primary assertion, whether positive or nega- 
 tive. If, however, he can fairly appeal ad verecun- 
 diam or ad judicium, or even ad populum, the 
 logical presumption is in his favor, and the onus 
 falls on the disputant. 
 
 109. Praxis. State of each of the following 
 examples whether it is a simple enthymeme, or an 
 epichirema, or a sorites. Put it in strict logical 
 form, and write out the implied syllogisms, nUming 
 the mood. In case of an epichirema, distinguish 
 the pro- and epi-syllogism : 
 
 1. Blessed are the merciful; for they shall obtain 
 
 mercy. 
 
 2. Cunning cannot be a virtue ; for no virtue degrades. 
 
 3. Every man should be moderate ; for excess will 
 
 cause disease. 
 
 4. Kings, having no equals, have no friends. 
 
 5. Suppose ye that these Galileans were sinners above 
 
 all the Galileans, because they suffered such things ? 
 I tell you nay. 
 
 6. The flesh of ruminants is good for food, and these 
 
 animals, since they have horns and cloven hoofs, 
 belong to that class. 
 
 7. What if a rule never is, and a principle always is, a 
 
 law admitting no exception?
 
 MODIFIED FOKMS 143 
 
 .8. Whatever tends to withdraw the mind from pursuits 
 of a low nature deserves to be promoted. This 
 classical learning does, since it cultivates a taste 
 for intellectual enjoyments. 
 
 9. The Scripture narratives are trustworthy ; because 
 the writers had the means of knowing the facts ; 
 because they evidently were sincere and candid ; 
 and because the narratives are consistent. 
 / 10. All true patriots are friends to religion, religion 
 being the basis of national prosperity ; but, since 
 their lives are not in accordance with its precepts, 
 it follows that some great statesmen are not friends 
 to religion. 
 
 11. Lithium is an element; for it produces an alkali, 
 
 therefore is a metal, and hence an element. 
 
 12. I will not do this act, because it is unjust; I know 
 
 that it is unjust, because my conscience tells me 
 so; and my conscience tells me so, because the act 
 is wrong. 
 
 Put the following logical climax in its opposite 
 form, and write the circular, linear, and graphic 
 notation : 
 
 13. The prudent are temperate ; 
 
 The temperate are constant ; 
 The constant are unperturbed ; 
 
 The unperturbed are without sorrow ; 
 Those without sorrow are happy ; 
 /. The prudent are happy. 
 
 Seneca, Epist. 85. 
 
 Put the following in its opposite form, and write 
 the notation :
 
 144 DEDUCTION 
 
 14. Nothing which is indissoluble is mortal ; 
 
 What has no composition of parts is indissoluble ; 
 A spirit has no composition of parts ; 
 A thinking substance is a spirit ; 
 The mind is a thinking substance ; 
 .-. The mind is not mortal. 
 
 Plato, Phcedo, 78. 
 
 State each of the following as a regular sorites 
 in either form : 
 
 15. A demagogue must hold the people in contempt ; for, 
 
 being a favorite, he must know how to manage 
 them ; therefore he understands their weaknesses, 
 and his contempt must follow. 
 
 16. We must increase the income-tax ; for war has be- 
 
 come a necessity, and we cannot go to war without 
 money, which can be raised only by taxation. 
 But the only tax which the resources of the coun- 
 try can bear is the income-tax, since it will fall on 
 the richer part of the population. 
 
 Write out the syllogisms involved in the follow- 
 ing irregular and compound forms, supplying any 
 inference that may be lacking : 
 
 17. The French once more are endeavoring to establish 
 
 a republic. 
 
 A republic is a representative government ; 
 5 \ The French once more are endeavoring to establish a 
 representative government. 
 
 18. The value of money is merely a purchasing power; 
 Interest on money is only a reward of abstinence ; 
 
 /. Interest on money is not the value of money.
 
 MODIFIED FORMS 145 
 
 19. Gladstone, Argyll, and Disraeli are eminent states- 
 
 men ; but they are also eminent authors ; 
 /. In some cases literary success is not inconsistent 
 with statesmanship. 
 
 20. They are out of the reach of their enemies who can- 
 
 not be robbed of what they love ; 
 He cannot be robbed of what he loves who loves 
 
 God alone ; 
 
 /. They who love God alone are out of the reach of 
 their enemies. 
 
 21. None are happy but the virtuous; 
 
 There are many rich men who are not virtuous ; 
 .*. There are rich men who are not happy. 
 
 22. Every one desires happiness ; but virtue (alone) is 
 
 happiness ; hence every one desires virtue. 
 
 23. The true philosopher places his chief happiness in 
 
 moral and intellectual excellence. 
 But it is false to say that there is an excellence 
 
 without activity ; 
 
 /. His chief happiness is placed by the philosopher 
 in moral and intellectual activity. 
 
 What names mark the following reasonings : 
 
 24. If any objection that can be urged would justify a 
 
 change in the established laws, no laws could 
 reasonably be maintained. 
 
 25. That used in Luke v. 21 ; and its answer. 
 
 26. That used in Luke xiii. 15-16 ; and in John x. 34-36. 
 
 27. Those used by Demetrius in Acts xix. 23-27 ; and 
 
 by the town-clerk in vers. 34-41. 
 
 28. Those used by the barbarians in Acts xxviii. 3-6. 
 
 29. Those used by Paul in Romans v. 7-10. 
 
 30. That used by Eliphaz in Job iv. 17-19. 
 
 10
 
 VI. CONDITIONAL PROPOSITIONS 
 
 110. The word condition is used in at least 
 three several and important senses, as follnffiaj 
 
 1st. A real condition is what must be, that some- 
 thing else may be. Here must indicates conditio 
 sine qua non, or necessitous antecedent/is. E. g., If 
 space is, body may be; or, more fully, Space must 
 be, in order that body may be. So also, Freedom 
 must be, that responsibility may be. This primary 
 meaning has reference to reality in objects, and 
 therefore is metaphysical rather than logical. 
 
 2d. A causal condition is what determines an 
 event. It is causa essendi, an efficient cause of 
 being necessitas consequentis. E. g., If force is, a 
 change is; If industry is, prosperity is. In many 
 specific cases the condition, because of an apparent 
 plurality of causes, is not essential or sine qua non. 
 Likewise an occasion may be a condition. E. g., 
 If repentance is, forgiveness may be; If peace (a 
 negative) is, prosperity may be. Deductive logic is 
 not at all concerned with either real or causal con- 
 ditionals. 
 
 3d. A logical condition is what supports a cog- 
 nition. It is causa cognoscendi, an efficient cause 
 of knowing, a reason necessitas consequentice.
 
 CONDITIONAL PROPOSITIONS 147 
 
 Very often a real or a causal condition or an oc- 
 casion is thought merely as a logical condition. 
 E. g., Tf space is, then (I know that) body may be ; 
 If industry is, then (I know that) prosperity is; If 
 repentance is, (I know that) forgiveness may be. 
 The inverted real and the inverted causal proposi- 
 tions furnish logical conditions. E. g., If body is, 
 (I know) space must be ; If responsibility is, then 
 freedom must be; If prosperity is, surely there is 
 industry. But very often in conditional proposi- 
 tions the logical relation of containing and con- 
 tained, 01 a reason supporting a conclusion, alone 
 is found. E. g., If men are, rational beings are; 
 
 If gold is, metal is; If be a man, he is mortal. 
 
 In simple forms the logical condition is never sine 
 qua non. In compound forms it so occurs. 
 
 In its treatment of conditionals, deductive logic 
 is concerned exclusively with the logical condition, 
 with propositions expressing the relation of reason 
 and consequent. 
 
 111. The distinction between categorical and 
 conditional propositions has already been noted 
 ( 58). The general distribution is as follows : 
 
 (Categorical S is P, and S is not P. 
 ( Conjunctive; If A be B, C is D. 
 tional J Disjunctive; c is either D or non-D. 
 ( Dilemmatic; If A be B, C is either D or non-D. 
 
 Hypothetical is synonymous with conditional, and 
 hypothesis with supposition. The dilemmatic prop- 
 osition, because of its compound character, is also
 
 1 48 DEDUCTION 
 
 called the conjunctive-disjunctive proposition. Con- 
 ditional propositions are always affirmative. 
 
 , 112. A conjunctive proposition expresses the 
 relation between a reason and its consequent. It 
 has two clauses, or members. The subordinate 
 clause expresses the condition, and is called the 
 hypothesis, the supposition, the protasis, the ante- 
 cedent, or the reason. The principal clause ex- 
 presses what is conditioned, and is called the apod- 
 osis, or the consequent. Usually and formally the 
 protasis is written first, but inversions often occur. 
 Existential conjunctives have but two terms; 
 formula, If A is. B is ; examples in 110. Another 
 class having but two terms will be noticed pres- 
 ently ( 116). Conjunctives involving three and 
 four terms are formulated thus : 
 
 1 (a) If A be B, A is C; e. g., If man be responsible, he is free, 
 (b) If Abe B, C is A; e. g., If bliss have no anxieties, igno- 
 rance is not bliss. 
 
 (c) If Abe B, B is C; e. g., If rubies be clay, some clay is 
 
 precious, 
 (d) If Abe B, C isB; e. g.,If metals be fusible, gold is 
 
 fusible. 
 
 2 If A be B, C is D; e. g., If the wise be virtuous, Socrates 
 
 was innocent. 
 
 In each of the first forms there are but three terms, 
 one being common to both members. In the sec- 
 ond there are four. In simple sequence, the con- 
 sequent only or both clauses may be negative and 
 may be particular ; but the consequent in 1 (b) must 
 be negative, and in 1 (c) must be particular,
 
 CONDITIONAL PROPOSITIONS 149 
 
 113. A disjunctive proposition expresses the 
 relation between two alternative clauses in which 
 one must be true. The formula is: Either C is 
 D, or C is non-D, usually abbreviated as in 111. 
 One clause is affirmed on condition that the other 
 be^ denied. In general, then, the condition lies in 
 the opposition of the clauses. The opposed clauses 
 are called the disjunct members, and their relation 
 the disjunction. An inverted formula is: Either 
 D or non-D is C. 
 
 This form of judgment involves the principles, 
 and is subject to the laws of Division ( 29 sq.) and 
 Opposition ( 83). It implies the division of an 
 unnamed genus into co-ordinate species, and affirms 
 identity between an object or a class of the genus 
 and one or the other of the species. For example : 
 Carlo is either a dog or a non-dog ; or, naming the 
 genus, Carlo, being a brute, is either a dog or a 
 non-dog. So also, Cares are either distressing or 
 not, all under the genus feelings Every action is 
 either bond or free ; Either now or later will suit 
 me very well. 
 
 Disjunctive judgments, to be strictly logical, 
 must make a complete disjunction ; that is, the 
 disjunct members must exhaust the divisum, and 
 be exclusive of each other. For example : 
 
 Either all wars are evil, or some wars are not evil. 
 Either the prisoner is guilty, or he is not guilty. 
 
 guilty [ not guilty 
 
 The members are contradictories within the divided 
 genus or logical universe ( 27). The law of con-
 
 150 DEDUCTION 
 
 tradictory opposites is that one must be true and 
 one false ; hence, affirming either denies the other, 
 and denying either affirms the other. 
 
 It follows that a disjunctive resolves into four 
 conjunctives, thus : 
 
 If C be D, it is not non-D; 
 If C be non-D, it is not D; 
 If C be not D, it is non-D ; 
 If C be not non-D, it is D. 
 
 Disjunctive judgments often appear in the form : 
 Either C is D, or M is JX". Here the matter of the 
 opposed clauses is entirely distinct, and the oppo- 
 sition is mediate, evolved thus : 
 
 Either Richard III. was a monster, or he was not a 
 
 monster; 
 
 But If he was not a monster, Shakespeare was wrong; 
 Hence, Either Richard III. was a monster, or Shakespeare was 
 wrong. 
 
 The alternative is declared, not between members 
 directly opposed, but between one of these and a 
 consequence of the other. 
 
 114. When a division is more than dichotomous 
 ( 31), we have a series of disparate terms, exhaust- 
 ive and coexclusive ; thus : 
 
 C is either D, or E, or F, or ,- 
 
 Bodies are solid, or liquid, or aeriform. | sol. | liq. 
 
 Disparates, in logical treatment, must be reduced 
 to contradictories by grouping them into two op- 
 posed members ; thus : 
 
 Bodies are either solid or (liquid or aeriform=) fluid. 
 Less than all the members of a disparate series
 
 CONDITIONAL PROPOSITIONS 151 
 
 will not yield a disjunctive judgment, since they 
 are not exhaustive. We cannot say : 
 
 angles 
 
 Bodies are either solid or aeriform. 
 
 Angles are either acute or obtuse. I acute I obtuse 
 
 Hence it appears that contraries, being any two 
 members of a disparate series ( 31), cannot as 
 such constitute a disjunctive, for both may be false. 
 "We cannot say, Men are either white or black, for 
 some are red, and so the statement is neither true 
 nor logical. When formal contraries are affirmed 
 disjunctively, it is an indirect assertion that a ter- 
 tium does not exist, and so they become contra- 
 dictories ; as, Sheep are either white or black. Also 
 contraries may be stated disjunctively as mere 
 alternatives ; as, Speak briefly, or be silent. A cop- 
 ulative proposition, however, is formed from con- 
 traries ; as, Ye cannot serve God and Mammon. 
 
 In logical strictness, disjunct members must be 
 not only exhaustive, but coexclusive. Yet we often 
 make an imperfect division wherein the species 
 are communicant or intersect, yielding a specific 
 disjunction wherein both may be true. For ex- 
 ample : 
 
 mischiei-maker 
 
 Jack is either a fool or a knave. 
 
 fool 
 
 knave 
 
 That is, he must be one, he may be both. Hence 
 denying one affirms the other ; but affirming one, 
 nothing follows. As this is the principle of sub- 
 contrary opposition, we distinguish the form as 
 subcontrary disjunction. The copulative and this
 
 152 DEDUCTION 
 
 subcontrary proposition are mutually convertible 
 by a sort of contraposition ; thus : 
 
 Either ye do not serve God, or ye do not serve Mammon. . . .subcontrary. 
 Jack is not both smart and good copulative. 
 
 Disjunctive judgments always affirm, are always 
 positive, never negative. In cases where denial is 
 possible, it is done by neither nor, thus : 
 
 C is neither D nor E. charactef 
 
 The boy is neither smart nor good. smart 8 ood 
 
 This, however, is not a disjunctive proposition, but 
 a negative categorical compound, a double denial. 
 In Give me neither poverty nor riches, the implied 
 tertium is sought. While either or are signs of 
 disjunction, neither nor are not at all disjunctive. 
 
 115. A disparate series may be transformed 
 by a supposition, thus : 
 
 An angle is either acute, right, or obtuse; 
 
 If an angle be not acute, it is either right or obtuse. 
 
 Either the doctor is not skilful, or the patient is beyond remedy, 
 
 or he will recover ; 
 If the doctor be skilful, either the patient is beyond remedy, or 
 
 he will recover. 
 
 Either A is not B, or C is D, or C is non-D ; 
 If A be B, C is either D or non-D. 
 
 Such is the genesis of the dilemmatic or con- 
 junctive-disjunctive proposition, which, as this 
 name indicates, is a compound of the two preced- 
 ing forms, and hence involves no new principle. 
 It may be defined as a conjunctive having a dis- 
 junction in the protasis or in the apodosis, or in
 
 CONDITIONAL PROPOSITIONS 153 
 
 both ; or, viewed inversely, as a disjunctive having 
 a conjunction in one or both members. 
 
 Usually its forms are said to be numerous and 
 intricate. But we hold : 
 
 1st. That a difference in the matter or quality 
 of clauses wherein there is partial identity makes 
 them distinct clauses, having a distinct formula. 
 
 2d. That the distinction between contradictory 
 and subcontrary opposition may be disregarded, 
 understanding that each formula represents either. 
 
 3d. That trilemmatic, tetralemmatic, and poly- 
 lemmatic forms are, for logical treatment, to be 
 grouped into dilemmatic contradictory forms. 
 
 These points being allowed, the following for- 
 mulas are exhaustive : 
 
 1, Simple, (a) Either if A be B, C is D; or if A be B, E is F; 
 
 having antecedents identical and conse- 
 quents disjunct, 
 (b) Either if A be B, C is D; or if E be P, C is D; 
 
 having antecedents disjunct and conse 
 quents identical. 
 
 2, Complex, Either if A be B, C is D; or if E be F, G is H. 
 
 having antecedents disjunct and conse- 
 quents disjunct. 
 
 The following are concrete examples of these 
 several forms : 
 
 1 (a) If Socrates was innocent, Anytus was either deceived or perjured. 
 
 (b) If a man be either well or ill deserving, he is a moral agent 
 2 If the accused was deliberate, he was criminal ; or if not, insane. 
 
 1 16. It is now apparent that the conjunctive judg- 
 ment is the basis of the conditional forms. Let us,- 
 then, inquire more particularly into its significance.
 
 154 DEDUCTION 
 
 The conjunctive is sometimes thought as a quali- 
 fied proposition. For example : If air be pure, it 
 is wholesome. This taken from testimony, or ob- 
 tained by induction from experience, does not im- 
 ply any reasoning, though capable of being con- 
 strued syllogistically, but is a simple judgment, 
 equipollent with : Pure air is wholesome. 
 
 More generally, however, a reasoning is implied. 
 Observe that the clauses may be in form either 
 positive or negative, but that in fact they are 
 neither affirmed nor denied. In If A is, B is, it 
 is not said that A is, or that B is. In If virtue be 
 knowledge, it is teachable, it is not said either that 
 virtue is knowledge, or that it is teachable. The 
 clauses are posited not really, but ideally. Observe 
 also that the proposition as a whole is always and 
 only affirmative. What, then, is affirmed ? Merely 
 a relation between the members ; not, however, 
 the relation of containing and contained, but a 
 relation of dependence, the relation of sequence. 
 E. g., If A is, then (or it follows that) is. Or, B 
 is, if (or follows from) A is. Evidently the prota- 
 sis is a logical condition or reason, a premise, and 
 the apodosis is a consequent or conclusion. Sup- 
 plying an unexpressed premise, we have : 
 (All knowledge is teachable ;) 
 If Virtue be knowledge, 
 then Virtue is teachable Barbara. 
 
 The conjunctive proposition, therefore, is an en- 
 thymeme ( 104). Since its matter is ideally stated, 
 it affirms a sequence only ; it is a judgment con-
 
 CONDITIONAL PROPOSITIONS 155 
 
 cerning judgments, expressing in the purest man- 
 ner the syllogistic judgment ( 90). 
 
 All the various forms of inference are implied by 
 conjunctive propositions. Immediate inference by 
 determination ( 80) is affirmed in If coal lefuel, 
 then cheap coal is cheap fuel; conversion per acci- 
 dens, in If triangles be figures, then some figures are 
 triangles, etc. The latter exemplifies a conjunctive 
 form of two terms only. 
 
 Mediate inference is implied by those of three or 
 more terms. Of the forms given in 112, viewing 
 them as ideal enthymemes and supplying the un- 
 expressed premises, 1 (a) yields Barbara, or other 
 moods of Fig. 1 ; 1 (b) yields Cesare ; 1 (c) yields 
 Darapti ; but 1 (d) yields Barbara, confirming the 
 rejection of Fig. 4 ( 102). The form 2, of four 
 terms, yields a sorites, thus : 
 
 (Socrates was wise;) 
 If the wise be virtuous, 
 (And the virtuous be innocent,) 
 then Socrates was innocent. 
 
 117. Praxis. Name each of the following ex- 
 amples in terms of second intention ; designate the 
 section and paragraph it particularly illustrates, 
 explaining how ; and then reply to the special points 
 required. 
 
 Distinguish the four following, and redress as 
 logical conditions : 
 
 1. We may enter, if there be room. 
 
 2. If the moon has passed the meridian, it will soon be 
 
 high tide.
 
 156 DEDUCTION 
 
 3. If the moon has no atmosphere, it has no twilight. 
 
 4. If he happened to be there, you surely met him. 
 
 Are the following seven examples categorical or 
 conditional ? 
 
 5. I will not let thee go, unless thou bless me. 
 
 6. Until the night comes, we must work. 
 
 7. Is any among yon afflicted ? let him pray. 
 
 8. Lear is either at the hut, or at the palace. 
 
 9. Hiawatha left his hut or wigwam. 
 
 10. It has not been decided whether the war will con- 
 
 tinue or not. 
 
 11. Neither flattery nor threats could prevail. 
 
 Having described the following thirteen exam- 
 ples, reduce disparates to contradictories, also sub- 
 contraries to copulatives, and vice versa : 
 
 12. They who slew Caesar are either patriots or parri- 
 
 cides. 
 
 13. Either Caesar was ambitious, or Brutus was criminal. 
 
 14. Either if this be a judgment, it affirms or denies ; 
 
 or if it be a question, it does neither. 
 
 15. The sun moves round the earth, or the earth moves 
 
 round the sun. 
 
 16. A woman either loves or hates ; she never thirds it. 
 
 17. Punishment is intended either to repress crime or to 
 
 reform the criminal. 
 
 18. Your god either is talking, or is pursuing, or is in 
 
 a journey, or peradventure he sleepeth. (From 
 this obtain a conjunctivo-disjunctive.) 
 
 19. Wherever there is smoke, there is fire. 
 
 20. Whenever the moon is on the ecliptic, there is an 
 
 eclipse.
 
 CONDITIONAL PROPOSITIONS 157 
 
 21. There could be no choice, were there no difference. 
 
 22. Day and night are never simultaneous. 
 
 23. Every man is already either justified or condemned. 
 
 ( What genus is here divided? Reduce to conjunc- 
 tives.) 
 
 24. Either my wish is fulfilled, or you have disappointed 
 
 me. (Mediate. Evolve, as in 113.) 
 
 Having designated the names and specific forms 
 of the following examples, reduce the conjunct! vo- 
 disjunctives to disparate disjunctives, and vice versa: 
 
 25. If Caesar live, he will -either rule or ruin. 
 
 26. If we go to war, we must either contract a debt, or 
 
 increase taxation, or indemnify ourselves at the 
 enemy's expense. 
 
 27. If my chess-king be moved, or if he be covered, or 
 
 if I capture the attacking piece, nevertheless I 
 shall be checkmated at the next move. 
 
 28. Either if education be popular, compulsion is un- 
 
 necessary ; or if it be unpopular, compulsion will 
 be resisted ; or if the people be indifferent, com- 
 pulsion will be fruitless. 
 
 29. The mastery of an abstruse science, unless there be 
 
 competent instruction, is hardly possible, or at 
 best is imperfect. 
 
 Complete in syllogistic form the reasonings im- 
 plied in the first four examples in 112. 
 Why must the consequent in 1 (b) be negative? 
 Why must the consequent in 1 (c) be particular ?
 
 VII. CONDITIONAL SYLLOGISMS 
 
 118. The various forms of the conditional prop- 
 osition are used, without regard to their implied 
 reasoning, as premises in further reasoning. A few 
 illustrations shall suffice. 
 
 The following is Barbara, easily solved by re- 
 placement ( 93) : 
 
 ; If the using of credit be a demand for goods, all forms of credit 
 
 affect prices; 
 
 But bills of exchange are a form of credit; 
 .'. If the using of credit be a demand for goods, bills of exchange 
 affect prices. 
 
 The following is Camestres, from a disjunctive 
 premise : 
 
 All sciences are either pure, inductive, or mixed; 
 Astrology is neither; 
 /.Astrology is not a science. 
 
 The following, from a conjunctivo-disjunctive, is 
 Barbara with transposed premises : 
 
 If a ruler make an entirely unselfish use of despotic power, 
 
 he must be either a saint or a philosopher ; 
 But saints and philosophers are rare ; 
 /.Those rulers who so conduct themselves are rare. 
 
 The following is a sorites formed of conjunctives, 
 and resolving into two syllogisms :
 
 CONDITIONAL SYLLOGISMS 159 
 
 If the Scriptures be the word of God, they should be clearly 
 
 explained; 
 If they should be clearly explained, they must be diligently 
 
 studied ; 
 If they must be diligently studied, an order of men must be 
 
 devoted to them; 
 /.If the Scriptures be the word of God, an order of men must 
 
 be devoted to them. 
 
 The foregoing are strictly and properly condi- 
 tional syllogisms, though this title has been usurped 
 by other forms ( 119 sq.). They may be distin- 
 guished from categorical syllogisms, but evidently 
 the difference is not essential ( 58). 
 
 119. Early logicians devised a system of con- 
 ditional forms, using the terminology of the syllo- 
 gistic forms. Of these there are four kinds. 
 
 The so-called conjunctive syllogism has for a 
 major premise a conjunctive proposition, the minor 
 premise and conclusion being the assertion or de- 
 nial of the component clauses. It is governed by 
 the following axioms : 
 
 1. Asserting the reason asserts the conse- 
 quent. 
 
 2. Denying the consequent denies the rea- ; 
 son. 
 
 But denying the reason does not deny the conse- 
 quent, and asserting the consequent does not assert 
 tho_reason_; for the consequent may follow from 
 some other reason ( 91). If the protasis be in fact 
 a sine qua non, it should be expressed by Only if. 
 which is a compound form.
 
 160 DEDUCTION 
 
 The double axiom gives rise to two so-called 
 moods. The forms of the conjunctive syllogism 
 in these moods are as follows : 
 
 MODUS ( If A be B ; then C is D ; \ MODUS 
 
 PONENS -J But A is B ; But C is not D ; >- TOLLKNS 
 
 (constructive). ( .'. C is D. ! .'. A is not B. ) (dettructive). 
 
 If the people are industrious, wealth is increasing ; 
 
 Wealth is not increasing ; 
 
 .'. Wealth is increasing ; 
 
 PONENS. They are industrious : 
 
 TOLLENS. 
 
 .'. The people are not industrious. 
 
 The sumption affirms, though one or both clauses 
 be negative. It alone is conditional, the rest are 
 categorical. There may be four terms, as above ; 
 all occur in the sumption. Hence the subsumption 
 has no new term, and the conclusion may have 
 nothing in common with it. 
 
 From the axioms two RULES are derived serving 
 to guide and test. They are as follows : 
 
 1. In Ponens the subsumption and conclusion 
 must each agree with its correspoiding clause in 
 both quantity and quality. 
 
 2. In Tollens the subsumption and conclusion 
 must each disagree with its corresponding clause in 
 both quantity and quality. 
 
 Conclusive deviations from these rules will, on 
 inspection, be found to lack logical accuracy. The 
 double disagreement in Tollens is because logical 
 denial is only by contradiction. When the subject 
 is individual, or a generic total, as above, its quan- 
 tity being fixed, contradiction is merely a change of 
 quality.
 
 CONDITIONAL SYLLOGISMS. 
 
 161 
 
 The following example illustrates the rules : 
 
 If any nation prosper, all are benefited ; 
 
 Some are prospering ; 
 . or This one prospers ; 
 .-.All are benefited. 
 
 Some are not benefited ; 
 or That one is not ; TOLLENS. 
 ..None are prospering. 
 
 Negative clauses, one or both, conform strictly to 
 the rules. Thus : 
 
 If A be not B, then C is not D ; 
 
 PONENS, asserts. A. is not B; | C is D; TOLLENS, denies. 
 .-.CisnotD. : .\AisB. 
 
 On contraponing the sumption that is, taking the 
 negative of each clause and then transposing them 
 we find that the moods are mutually reducible. 
 
 In reductio ad absurdum it is usual to state the 
 argument hypothetically ; then the tollent mood is 
 often so obvious that it is not expressed ; e. g., If 
 we say we have not sinned, we make God a liar. 
 
 The disjunctive syllogism has for its ma- 
 jor premise a disjunctive proposition whose dis- 
 junction is resolved in the minor premise and 
 conclusion. It is governed by the axioms of con- 
 tradiction and excluded middle ( 9, 10). The 
 disjunct members being contradictory, affirming 
 one denies the other, and vice versa. This yields 
 two moods, each double, thus : 
 
 \ MODUS 
 
 > PONENDO 
 
 ) TOLLENS. 
 
 MODUS c C is either D o 
 TOLLENDO < C is not D ; 
 PONENS. ( /. C is E* 
 
 r E (=non-D); 
 CisD; 
 /.C is not E. 
 
 or 
 " C is not E; 
 .-.CisD. 
 
 or 
 Cis E; 
 /.Cis not D. 
 
 11
 
 162 DEDUCTION 
 
 Either all men are justified, or some are condemned ; 
 
 TOLLENDO Some are not justified;! All are justified; PONENDO 
 PONENDS. /. Some are condemned. | .. None are condemned. TOLLENS. 
 
 " None are condemned ; | Some are condemned ; " 
 
 u .'. All are j ustified. ] /.Some are not justified. " 
 
 The sumption always affirms. The conclusion has 
 the same quantity as the subsumptkm^but_the 
 opposite quality. 
 
 When the disjunction is subcontrary ( 114), _we 
 maff proceed in the ponent moods, but not in the 
 tqllent. For example : 
 
 All afflictions are either punitive, or tentative, 
 
 or disciplinary; 
 To. PONENS. Job's afflictions were neither punitive nor dis- 
 
 ciplinary ; 
 
 .'. They were tentative. 
 " David's were not tentative; 
 
 .'. They were either punitive or disciplinary (per- 
 haps both). 
 
 _siihlate__lbe 
 
 other, for both may be true. 
 
 A copulative proportion involving^ contraries 
 ( 114) yields conclusions in the tollent nmods^Jbut 
 
 not in the ponent. For example : 
 
 Ye cannot serve God and Mammon ; 
 Po. TOLLENS. Ye serve Mammon ; 
 /.Ye do not serve God. 
 
 Sublating one contrajy_jdQje^_nnLp_osit the other. 
 for both may be false. As the subcontrary dis- 
 junctive and the copulative propositions contra- 
 pone into each other, so likewise these syllogistic 
 forms are mutually convertible.
 
 CONDITIONAL SYLLOGISMS 163 
 
 121. The dilemmatic proposition, being a com- 
 pound form ( 115), furnishes a double process. 
 Viewing it as a conjunctive, according to its first 
 definition, and taking the disjunct members as a 
 single clause, we proceed as in 119 ; thus : 
 
 If A be B, either C is D, or E is F ; 
 
 PONENS. But A is B; 
 
 /. Either C is D, or E is F. 
 
 Neither C is D, nor _ ToLLEN8> 
 
 E isF; 
 /. A is not B. 
 
 If the apostles taught falsely, they were either deceivers or deceived. 
 
 POSTBNS They did teach falsely ; 
 .'.They were either de- 
 ceivers or deceived. 
 
 They were neither de- 
 ceivers nor deceived ; 
 /.They did not teach falsely. 
 
 TOLLEN8. 
 
 On the other hand, viewing it as a disjunctive, 
 according to its second definition, we proceed as 
 in 120 ; thus : 
 
 If A be B, either C is D, or E is F; 
 To. PONENS. But C is not D ; 
 /.If AbeB, E isF. 
 
 If Socrates was innocent, Anytus was either deceived or 
 
 perjured; 
 
 But Anytus was not deceived ; 
 /.If Socrates was innocent, Anytus was perjured. 
 
 By denying Anytus was perjured, we have another 
 To. Ponens. The disjunct members being contra- 
 dictories under the stated condition, yield also two 
 forms in Po. Tollens. 
 
 Observe that neither of these forms of the con- 
 junctive-disjunctive syllogism, though involving 
 each a dilemmatic proposition, treated first con- 
 junctively, then disjunctively, is a dilemma. 
 
 122. The dilemma is a conditional syllogism
 
 164: DEDUCTION 
 
 having a double conjunctive premise and a dis- 
 junctive premise. Either may be taken as the 
 sumption, but it is usual to write the double con- 
 junctive first. None of its propositions is dilem- 
 matic. It has three forms, as follows : 
 
 1. Simple constructive : If A be B, C is D ; and if E be F, C is D ; 
 
 PON ENS. But either A is B, or E is F ; 
 
 .'.CisD. 
 
 2. Complex constructive : If A be B, C is D ; and if E be F, G is H ; 
 
 PONENS. But either A is B, or E is F; 
 
 .'. Either C is D, or G is H. 
 
 3. Complex destructive : If A be B, C is D ; and if E be F, G is H ; 
 
 TOLLENS. But either C is not D, or G is not H ; 
 
 /. Either A is not B, or E is not F. 
 
 A single concrete example from Demosthenes de 
 Corona must suffice. It is in the complex con- 
 structive form, as follows : 
 
 If ^Escbines joined in the public rejoicings, he is inconsistent ; 
 
 if he did not, he is unpatriotic ; 
 But either he did, or he did not ; 
 .'. Either he is inconsistent, or he is unpatriotic. 
 
 The form of the sumption in this example may be 
 expressed thus : 
 
 If A be B, A is C; and if A be not B, A is D. 
 Here the first term of each of the clauses is the 
 same, and the antecedents differ only by the nega- 
 tive. Yet the form is complex, for the clauses dif- 
 fer either in matter or in quality ( 115). 
 
 There cannot be both a simple constructive and 
 a simple destructive dilemma. Denying the con- 
 sequents in No. 1 gives : 
 
 If A be B, C is D; and if E be F, C is D; 
 But C is not D; 
 .'.A is not B; and E is not F.
 
 , CONDITIONAL SYLLOGISMS 165 
 
 This, however, is merely a double conjunctive syl- 
 logism in Tollens. The simple destructive form, 
 corresponding to No. 1, is : 
 
 If A be B, C is D; and if A be B, E is F; 
 Hut either C is not D, or E is not F; 
 .".A is not B. 
 
 But this is merely No. 1 contraponed, and then 
 treated in Tollens. It is therefore essentially the 
 same, and should not be enumerated apart. 
 
 123. Let us briefly inquire into the nature of 
 the forms presented in the three foregoing sections. 
 Are they truly inferences ? We recall that deduc- 
 tive inference is of two kinds, mediate and imme- 
 diate. In mediate inference we determine the rela- 
 tion of two notions through a third, the middle or 
 medium. A syllogism is the formal expression of 
 this mediate process, and hence a middle term is its 
 essential feature. Now, hypothetical or conditional 
 syllogisms, so called, contain no middle term. .There- 
 fore they are not syllogisms, not expressive of rea- 
 soning at all. Inspect the following : 
 
 C If law prevails, our rights are 
 
 MODUS I secure ; Major Premise. 
 
 PONENS. j But law does prevail ; Minor Premise. 
 
 [_ .'. Our rights are secure Conclusion. 
 
 There is no term here with which the two terms 
 found in the conclusion are compared in the prem- 
 ises. There are in all four terms, and all found in 
 the so-called major premise. The so-called minor 
 introduces no new matter, and has nothing in com- 
 mon with the conclusion, as in a true syllogism
 
 166 
 
 DEDUCTION 
 
 Are they immediate inferences ? An immediate 
 inference from a given judgment infers directly 
 that is, without a medium a different judgment. 
 Let us inspect the same example presented in a 
 slightly varied form : 
 
 If Law prevails, then our rights are secure. 
 Law prevails, then our rights are secure. 
 
 Now, here is an absolute iteration of thought, stated 
 first as supposititious, then as assertorial. The sub- 
 ject is the same. The predication is the same. The 
 second judgment, then, is not different logically 
 from the first, and therefore this cannot be an im- 
 mediate inference. In the tollent mood and in the 
 disjunctive syllogism an immediate inference by 
 opposition ( 83) is indirectly involved. 
 
 These forms express primarily the passage of 
 thought from the ideal to the real, from the ques- 
 tionable to the true, some unexpressed ground hav- 
 ing been discovered. The process is therefore 
 metaphysical rather than logical ( 91). Ought 
 not, then, these conditional forms, these pseudo- 
 syllogisms, to be banished from logic ? By no 
 means ; for they are true, natural, and very com- 
 mon modes of expressing thought, and hence call 
 for logical analysis and treatment. Nothing is 
 more common than for a reasoner at the outset to 
 state hypothetically his premise and conclusion. 
 This he does for the sake of clearness, and to show 
 whither he is tending. For example : 
 
 If the prisoner was sane, then he is responsible for his act. 
 His first argument may be to show the necessity of
 
 CONDITIONAL SYLLOGISMS 167 
 
 the sequence herein declared. As accusing counsel, 
 he next endeavors to establish this antecedent minor, 
 perhaps by showing the deliberation of the agent, 
 his consistency, his motives, etc. ; and, it may be, 
 he brings in the testimony of medical experts. 
 When the argument is complete, he closes by de- 
 claring categorically : 
 
 The prisoner was sane, therefore he is responsible for his act. 
 
 Again, many of these conditional forms present 
 exceedingly condensed expressions through which 
 thought darts with rapidity ; and unless the thinker 
 is familiar with their analysis, he is in danger of 
 paralogism, or of being imposed upon by sophism. 
 On the other hand, their condensation gives to a 
 just argument weight, and logical and rhetorical 
 force. They should, then, be discussed'not only as 
 subjects of analysis, but also because of the practi- 
 cal advantages resulting from their close examina- 
 tion. 
 
 It is clear, however, that their nomenclature 
 ought to be changed. The unfortunate misappli- 
 cation of the terms syllogism, major and minor 
 premise, mood, etc., and the attempt to enunciate 
 rules and methods of reduction parallel to, but dis- 
 tinct from, those of the true syllogism, have filled 
 logic for centuries with confusion and error. But 
 so deeply rooted in logical literature and so widely 
 spread are this false system and terminology that 
 the needed correction can be made only by the 
 highest authority.
 
 168 DEDUCTION 
 
 124. Praxis. In what moods are the follow- 
 ing three syllogistic forms? 
 
 1. Every body is solid, liquid, or aeriform; 
 Solid, liquid, and aeriform bodies are elastic; 
 
 /.Every body is elastic. 
 
 2. Memory is either circumstantial or philosophic; 
 Also it is either voluntary or spontaneous; 
 
 /.In this case, what is either voluntary or spontaneous is also 
 either circumstantial or philosophic. 
 
 3. Desires are either spontaneous or voluntary; 
 But whatever is voluntary has moral quality; 
 
 /.Desires are either spontaneous, or they have moral quality. 
 
 Describe each of the examples in terms of second 
 intention ; redress in strict form ; if inaccurate, say 
 w herein ; then reply to specific points. 
 
 4. Mohammed was either an enthusiast or an impostor ; 
 But he was an enthusiast, and therefore not an im- 
 postor. (Is the disjunction contradictory ?) 
 
 5. Unless matter can move itself, its first motion must 
 
 have been given it by a spiritual being. But mat- 
 ter cannot move itself ; therefore, etc. 
 
 6. If man cannot make progress towards perfection, we 
 
 must believe him to be either an incapable brute, 
 or already divine. (Ad abs.) 
 
 7. Whether logic be regarded as a means of mental dis- 
 
 cipline or as a practical guide in reasoning, it ought 
 to be studied. But it is both. Hence (what ?) 
 
 8. The ancients were in genius either superior to the 
 
 moderns, or inferior, or equal. (How many syllo- 
 gisms may be based on this?) 
 
 9. If all testimony to miracles is to be admitted, the
 
 CONDITIONAL SYLLOGISMS 169 
 
 mediaeval legends are to be believed ; but they are 
 
 not to be believed, and therefore no testimony to 
 
 miracles is to be admitted. 
 10. There are two things we ought not to fret about: 
 
 what we can help, and what we cannot. (From 
 
 this form a dilemma.) 
 21. The greater angle of a triangle is subtended by the 
 
 greater side. 
 
 If b > c, then B > C. 
 
 For if not, then either B= C, 
 
 orB<C. -" 
 
 But B = C is not true, for then b = c (I., 5), 
 
 which is against the hypothesis ; 
 Nor is B < C true, for then b < c (I. , 18), 
 
 which also is against the hypothesis ; 
 :.B>C. Q. E. D. Euclid, Book I., Proposition 19. 
 
 12. If the world existed from eternity, there would be 
 
 records prior to the Mosaic ; and if it were pro- 
 duced by chance, it would not bear marks of de- 
 sign. But there are no records prior to the Mosaic, 
 and the world does bear marks of design. /. The 
 world neither existed from eternity, nor is it the 
 work of chance. 
 
 13. A government cannot be at the same time despotic 
 
 and the licenser of a free press ; 
 But the English government permits a free press ; 
 /. The English government is not despotic. 
 
 14. If the books in the Alexandrine Library be in con- 
 
 formity with the doctrines of the Koran, there is no 
 need of them ; if adverse, then also they should 
 be burned. 
 
 15. If pain be severe, it will be brief; and if it last long, 
 it will be slight ; hence it should be borne patiently.
 
 170 DEDUCTION 
 
 16. If a man cannot be virtuous, he must be either una- 
 
 ble to know what is right, or unable to will what is 
 right. But he is not unable to know what is right, 
 for he is intelligent ; nor unable to will what is 
 right, for he is free. 
 
 17. We must either gratify our vicious propensities or 
 
 resist them ; the former course will involve us in 
 sin and misery, the latter requires self-denial ; there- 
 fore we must either fall into sin and misery, or 
 practise self-denial.
 
 VIII. QUANTITATIVE FORMS 
 
 125. The distinction between the qualitative 
 or logical whole and the quantitative or mathe- 
 matical whole has already been indicated ( 23), 
 and some note made of the latter ( 24). It is 
 now needful to examine the quantitative forms of 
 thought more particularly, because of their essen- 
 tial difference, and because, though constantly oc- 
 curring, logicians commonly either neglect them 
 altogether, or else confound them with the co-ordi- 
 nate qualitative forms. 
 
 In the qualitative whole the thought is funda- 
 mentally of marks ; in the quantitative, of magni- 
 tudes. A quantity, as distinguished from a quality, 
 is measurable by some standard or unit of measure, 
 real or ideal. Magnitudes differ in kind, and when 
 thought as kinds the notion is qualitative; but 
 magnitudes of the same kind differ in degree, and 
 the notion of degree is quantitative, is measurable, 
 is mathematical. The distinction between kind 
 and degree is fundamental and thorough-going in 
 all thinking, and differentiates the two wholes. 
 
 126. From its name alone, a common noun, it 
 is often impossible to decide whether a notion is
 
 172 DEDUCTION 
 
 qualitative or quantitative. Thus mankind in its 
 form is a class, and the human race is a mass, an 
 individual, having no species, and can be partitioned 
 only into sections ; but population may be thought 
 either as a class or as a mass. So being or thing is 
 a class including all kinds of existences, and the 
 Universe is a mass, a mathematical whole, a col- 
 lection of all things into a unit, the only one not a 
 part of any other, and is capable only of dissection ; 
 but, as herein said, things may be thought as a col- 
 lective whole. Again, animals may be thought as 
 divisible into kinds, or as the individual sum total 
 of many individuals, severable only, as the part 
 saved in the ark, and the part destroyed by the 
 deluge. The ambiguity of the predesignations all 
 and some has been noted ( 64, 66) ; hence these 
 do not serve to determine which whole is thought. 
 Generally, if not determined by the context, it is 
 quite ambiguous, the thought readily taking either 
 form, and requiring introspection to ascertain which 
 of the two is thought. So far of general names. 
 Proper names, and common names deprived of 
 their generality by demonstratives, possessives, and 
 the like, designate individuals ( 63), and the thought 
 is quantitative. 
 
 127. Degrees are formally of two sorts, equal 
 and unequal. Hence quantitative judgments or 
 judgments of degree are two, both being mathe- 
 matical comparisons. 
 
 First, in the judgment of equality the ambigu-
 
 QUANTITATIVE FORMS 173 
 
 ous copula is ( 54) means is equal to (=), and 
 when this is so expressed the proposition is unam- 
 biguously quantitative. For example: A is B ; 
 The population of London is double that of New 
 York ; X= Y, or X is equal to Y, often expressed : 
 X and Y are equal. 
 
 Second, the judgment of inequality conforms to 
 the axiom, A whole is greater than a part, and so 
 has the copula is a part of, or its obverse contains, 
 or else is greater than (>), or its obverse is less 
 than (<). When these are expressed, the judg- 
 ment is unambiguously quantitative. For exam- 
 ple : A is a part of B, or contains A / Maine is 
 a part of New England, or conversely ; or else A 
 is greater than B, or B < A / The earth is greater 
 than the moon, or converse! y. This simple relation 
 is often compounded with other notions ; as in in- 
 cluded by, longer and shorter, better and worse, strong- 
 er, more repulsive, most attractive, highest, etc. Thus 
 degrees of comparison are quantitative. For exam- 
 ple : Men are stronger than boys means The strength 
 of men is greater than the strength of boys ; Iron is 
 not as heavy as lead means The specific gravity of 
 iron is less than that of lead Lias lies above coal 
 means The height (in the geological scale) of Lias 
 is greater than that of coal ; Women love best means 
 The love of women is greater than any other. 
 
 In the qualitative whole an individual cannot 
 become a predicate, and therefore the individual 
 proposition is inconvertible ( 54, 82). In the 
 quantitative whole an individual is often the pred-
 
 174 DEDUCTION 
 
 icate, and all quantitative propositions are always 
 and only simply convertible, the copula in the sec- 
 ond class being changed to its obverse. 
 
 When the predicate is an individual, or when it 
 is qualified numerically or by some term of meas- 
 ure, or when it is quantified as all or some, directly 
 or indirectly ( 74), the proposition is quantitative. 
 E. g., Aristotle is the father of logic ; Thou art the 
 man; This is our home; A legion is (=) ten co- 
 horts ; His reasons are as two grains of wheat hid 
 in two bushels of chaff; It weighs a pound ; All 
 men are all reasoners ; Here only thieves (generic 
 total, not every one) are to be dreaded, or all (the 
 sum total) that is to be dreaded ; The committee 
 (collective) consists of some (a portion or section) 
 of our wisest men ; The population of London is 
 more than (>) a million. Generally the character 
 of the predicate determines in which whole the 
 proposition lies. 
 
 The complete generality of many quantitative 
 forms should be observed. Several of the fore- 
 going examples are cases. Pure mathematics, the 
 science of quantity, treats almost exclusively of 
 such abstract generalities; as 6=8x3; o?y t = 
 (x + y) (xy)'-, Triangles on the same base, and be- 
 tween the same parallels, are equal. 
 
 128. Inference in the quantitative whole is im- 
 mediate and mediate. Immediate inference from 
 equivalent propositions conforms to the CANON: 
 Equals affected by equals are equal. This is
 
 QUANTITATIVE FORMS 175 
 
 a general statement of four of the logical axioms 
 (icotvai twoiai) of Euclid, that if equals be added 
 to, or taken from, or multiplied by, or divided by 
 equals, the results are equal. The process corre- 
 sponds to Determination ( 80). E. g., As from A 
 horse is an animal, and What is young is strong, 
 we may immediately infer that A young horse is a 
 strong animal, so from a=b, and c=d, we may im- 
 mediately infer that a + c=b + d. The principle, 
 in a modified form, applies to propositions of ine- 
 quality. E. g., Ifa>l>, then 
 
 129. Mediate inference from equivalent propo- 
 sitions conforms to the CANON : Quantities equal 
 to the same thing are equal to each other. 
 This is Euclid's first logical axiom. The general 
 formula is : 
 
 If A = B; A is not equal to B; 
 
 and B = C ; Negatively : B is equal to C ; 
 
 then A = C. /.Aw not equal to C. 
 
 This may be called the jsyllogism of equivalence. 
 Obviously it is a specific application of the Primary 
 Law of Identity ( 8), which is the ultimate prin- 
 ciple involved in both the foregoing canons. The 
 first clause of the canon of replacement ( 93) also 
 justifies the process, and is even more general. A 
 concrete example in this form is as follows : 
 
 The density of the human body is the density of water; 
 The density of water is the density of air taken 817 times; 
 .'.The density of the human body is 817 times the density of air. 
 
 It will be observed that the middle term here is
 
 1 76 DEDUCTION 
 
 a standard of measure. And this gives occasion to 
 remark the logical function of standards of meas- 
 ure of all sorts. They furnish the media through 
 which we are enabled to compare quantities which 
 cannot be immediately compared. The yard, the 
 bushel, the pound, the atomic weight of hydrogen, 
 the thermometer, barometer, electrometer, etc., sup- 
 ply us with middle terms through which to reason 
 in our calculations. The metric system furnishes a 
 common middle term, the metre, by which to com- 
 pare its various standards with each other. 
 
 In the syllogism of equivalence the order of prem- 
 ises is obviously indifferent. The order of subject 
 and predicate is also indifferent ; that is, either term 
 may be made the subject of thought, and the other 
 the predicate, without other change. The distinc- 
 tion of major and minor terms, and consequently 
 that of major and minor premises, does not exist, 
 the terms being equivalent. The equivalent prop- 
 osition is always and only simply convertible. The 
 doctrine of Conversion, then, has no place relative 
 to this syllogism. It follows, also, that Figure is 
 of no moment, and is to be disregarded. Moods 
 are reduced to two, the positive and the negative ; 
 for the quantification of every term is always total. 
 Hence questions concerning distribution and non- 
 distribution cannot arise. 
 
 These eliminations render the logical treatment 
 of this syllogism exceedingly simple. Perhaps from 
 this simplicity it is, as well as from its clear intui- 
 tive exactness, that elementary mathematics is with-
 
 QUANTITATIVE FORMS 177 
 
 in the grasp of immature minds, even children 
 often being able to apprehend it quite thoroughly ; 
 whereas reasoning in the logical whole, with the 
 qualitative syllogism as the unit form, requires 
 more mental discipline and maturity. 
 
 130. A geometrical example (Euclid, I., 32) con- 
 forming to the canon of mediate inference may be 
 stated as follows : 
 
 The three interior angles of a triangle are equal to two right 
 
 angles; 
 For the interior angles are equal to the adjacent exterior and 
 
 interior angles ; 
 And these are equal to two right angles. 
 
 The expression is rendered more facile by the use 
 of a lettered figure, the letters taking the place of 
 a verbal description of a part ; but the processes are 
 identical. 
 
 Let us exhibit a slightly varied and redressed 
 proof of the same proposition by aid of a lettered 
 figure ; thus : 
 
 Through the apex of an angle b draw a line parallel to 
 the opposite side. Then : 
 
 a=a' Prop. 29. 
 
 b=b Identity. 
 
 c=c' Prop. 29. 
 
 +b+c =a'+b + c'. Canon of immediate inference. 
 
 a'+b+c'=2L Prop. 13. 
 
 .'.a +b+c =2 L Canon of mediate inference. 
 
 This last equation may of course be translated into 
 words. 
 
 I, It is needful to remark particularly that whether 
 the proposition be expressed in symbols or in words, 
 12
 
 178 DEDUCTION 
 
 both have the same, and indeed a complete, gener- 
 ality. Also that the passing from one to the other 
 is not at all a logical process, but simply a trans- 
 lation of expression. Changing the symbols into 
 words is often spoken of as a generalization or an 
 induction, but it is neither. Nor is the reverse a 
 deduction ; yet the following, for instance, is some- 
 times laid down as a syllogism : 
 
 All radii of a circle are equal ; 
 AC and BC are radii of a circle; 
 .'.AC and BC are equal. 
 
 But there is here no progress of thought, no change 
 of thought whatever, only of expression. AC and 
 BC stand for any radii of any circle; hence the 
 simulated conclusion is as completely general as 
 the verbal proposition which simulates a major 
 premise, and nothing whatever is proved. 
 
 131. Mediate inference from propositions of 
 inequality conform to Euclid's 9th logical axiom, 
 A whole is greater than a part. This, modified, 
 furnishes the CANON : A part of a part is part 
 of the whole ( 93). Syllogisms in conformity 
 with this canon may be called partitive syllogisms. 
 A single example, and the converse form, shall suf- 
 fice for illustration : 
 
 A minute is apart oj & degree; A contains B; 
 
 A degree is a part qf& circle ; Converse : B contain* C ; 
 
 ,'. A minute a part of a circle. /.A contains C.
 
 QUANTITATIVE FORMS 179 
 
 Another modification of the axiom furnishes the 
 CANON: A greater than a greater is greater 
 still than the thing. Syllogisms conforming to 
 this canon may be called comparative syllogisms. 
 The formula is : 
 
 A > B ; B is less than A ; A 
 
 B > C ; Conversely : C is lest than B ; B 
 
 .'. A > C. .'.CM less than A. C 
 
 E. g The planet Jupiter is greater than the- earth; 
 
 The earth is greater than the moon ; 
 .'. The planet Jupiter is greater than the moon. 
 
 Logicians sometimes distinguish between the in- 
 ferences a minore ad majus and a majore ad minus; 
 but the distinction is superficial, since one is sim- 
 ply convertible into the other. 
 
 Observe that the premises authorize a pregnant 
 conclusion, one a fortiori ( 108), usually expressed 
 thus: 
 
 /.By so much the more is A greater than C; or: 
 
 .'.C is still less than A; or: 
 
 .'.A fortiori the planet Jupiter is greater than the moon. 
 
 The following example is followed by its re- 
 dressed form : 
 
 The tree is higher than the man; 
 The spire is higher than the tree; 
 .'.The spire is still higher than the man. 
 
 The height of the tree is greater than the height of the man; 
 The height of the spire is greater than the height of the tree; 
 .'. The height of the spire is still greater than that of*the man. 
 
 The following (Euclid, I., 20, redressed) exhibits 
 a variation in respect of its symbolic statement ;
 
 180 DEDUCTION 
 
 Any two sides of a triangle are greater than the third. 
 
 Extend the side A until C'=C. Then : 
 
 c'=c Prop. 5. 
 
 a + c'>c' Ax. 9. 
 
 .\a + c'>c Mediate inference. 
 
 Then A + C'>B Pro'p. 19. 
 
 A + C'=A+C....Ax.2. 
 .'.A + C >B Mediate inference. 
 
 Not only do both kinds of judgments of degree 
 occur in the same reasoning, as in the foregoing 
 demonstration, but qualitative judgments also often 
 combine with quantitative. For example : 
 
 Regulus is a star of the first magnitude; 
 Sirius is as bright or brighter than Regulus; 
 . '.Sinus is a star of the first magnitude. 
 
 A proposition whose terms are not merely equiv- 
 alent, but in strict and entire identity ( 8), that is, 
 in what has been called the sibi-relation, cannot 
 serve as a premise in a proper syllogism ; for such 
 terms, differing merely as to words, are one in 
 thought, and consequently we should have a pseudo- 
 syllogism of only two terms, begging the question 
 ( 146). Of. 26 ; 95, Ex. 12 ; and 130. 
 
 Quantitative relations may be expressed also in 
 the several forms of the so-called conditional syl- 
 logism. For an instance, see 124, Ex. 11. 
 
 132. Praxis. State whether the following prop- 
 ositions are qualitative or quantitative. If the lat- 
 ter, redress with the copula : 
 
 1. It is the duty of every man to serve God and honor 
 the king. Only birds are feathered.
 
 / \ . 
 
 I v , , 
 
 QUANTITATIVE FORMS 181 
 
 2. George Eliot is Mrs. Lewes. Arrows are swifter 
 
 than eagles. 
 
 3. God alone is good. We are all sinners. 
 
 4. Every sly act is nothing less than dishonest. 
 
 5. The container contains the contained. That man 
 
 is my father. 
 
 6. None but Aryans are capable of the highest civil- 
 C- 
 
 ization. 
 
 Can the deduced formula Circ. = %irR, or this 
 vis viva mV, be generalized? 
 
 Name the class to which each of the following 
 reasonings belongs. Supply any lacking proposi- 
 tion. Kedress, if need be, exhibiting the copulas. 
 Construe the first as qualitative also : 
 
 7. Wisdom is more precious than rubies, and rubies 
 
 than gold ; hence wisdom is of yet higher value 
 than gold. 
 
 8. The author of Athalie was the greatest French 
 
 dramatist ; 
 But Racine was the author of Athalie. 
 
 9. The market value of my cloke is $15 ; 
 
 A sword will cost me $10. (Luke xxii. 36.) 
 
 10. John knew more than Peter, and Peter than Mark; 
 /. John knew more than Mark. 
 
 11. Aristotle lived after Plato, and Plato after Socrates ; 
 /. Aristotle lived after Socrates. 
 
 12. Virginia is one of the Southern States; 
 
 The Southern States are a part of the Union ; 
 /. Virginia is a part of the Union. 
 
 13. Lias lies above Red Sandstone ; 
 Red Sandstone lies above Coal; 
 
 .. Lias lies above Coal. 
 
 " 
 
 J 

 
 182 DEDUCTION 
 
 14. The orbit of Venus is within that of the Earth ; 
 And this within that of Jupiter ; 
 
 .-. The orbit of Venus is within that of Jupiter. 
 
 15. The dome is under the sky, and the altar under the 
 
 dome ; therefore the altar is under the sky. 
 
 16. Behold, the heaven and heaven of heavens cannot 
 
 contain thee ; how much less this house that I 
 have builded ! 
 
 17. It were better to have no opinion of God at all than 
 
 such an opinion as is unworthy of him ; for the 
 one is unbelief, the other is contumely ; and cer- 
 tainly superstition is the reproach of the Deity. 
 
 Prove the following proposition (Euclid, I., 15), 
 first in words only, then by the figures and letters, 
 as in 130 : 
 
 18. If two straight lines intersect, 
 
 the vertical angles are equal. 
 
 Eedress the following demonstration (Euclid, I., 
 18) as in 131 : 
 
 19. The greater angle of a tri- 
 
 angle is opposite the 
 greater side. 
 
 Let A C be greater than A B ; take A D equal to A B, 
 
 and join B D. 
 Then since ADB is the exterior angle of the triangle 
 
 B D C, it is greater than the interior opposite angle 
 
 D C B. Prop. 16. 
 But since the side A D is equal to the side A B, the angle 
 
 A D B is equal to the angle A B D. Prop. 5. 
 Therefore the angle A B D also is greater than the angle 
 
 ACB. 
 Much more then is the angle ABC greater than the angle 
 
 ACB. Ax. 9. q. K. D.
 
 IX. FALLACIES 
 
 133. Any violation of logical law is a fallacy. 
 Logical forms are determined originally by the 
 nature of intellect as expressed in the primary laws 
 of thought, from which are derived by deduction 
 the laws of special forms. Hence any essential de- 
 viation from a form is a violation of its law, and so 
 a fallacy. Under this wide definition come illog- 
 ical predications, generalizations, definitions, divi- 
 sionsj etc., as well as illogical inferences^ 
 
 Two remarks are needful. First, that Jogical 
 forms, though necessary, as stated in the definition 
 of logic ( 1), are nevertheless violable ( 5). They 
 are necessary to knowledge of truth, and cannot be 
 violated without risk of error, folly, falsity ; just 
 as a violation of the laws of health risks disorder, 
 disease, death. Second, that what does not violate 
 logical law, however false in matter, js not fallacy. 
 Our science does not take into consideration the 
 material truth or falsity of judgments ( 4, 50). 
 Therefore, in case of inference, the truth or falsity 
 of the premises and conclusion is disregarded, the 
 form alone being considered ( 91). Many logi- 
 cians, overlooking this, include among fallacies syl- 
 logisms correct in form, but having false premises.
 
 184 DEDUCTION 
 
 These, however, are not fallacies. For example, if 
 some one argues from the distress of a country 
 that the government is tyrannical, we must sup- 
 pose him to assume that Every distressed country 
 is under tyranny, which, though false, leads logi- 
 cally to his conciasion, and there is no fallacy ; or 
 that Every country under a tyranny is distressed, 
 which may be true, but the inference from this, 
 the middle being undistributed, is a non sequitur, 
 a fallacy. 
 The distribution of fallacies is as follows : 
 
 ( Paralogisms 
 
 MaC ' eS Sophisms jl0>>- 
 ( In matter. 
 
 The differences- here indicated will be explained in 
 the progress of the discussion. 
 
 134._Ajaralogism is a violation of a law of 
 jgrny manifest' without regard to the diction or 
 matter! Of this we have already had many inci- 
 dental examples. When the form of a proposition 
 is obviously the logical paradox, A=non-A, as To 
 do wrong is sometimes right ; or when there is an 
 inference from All A is B, to All B is A, as To 
 possess a large amount of money is to be wealthy, 
 hence To be wealthy is to possess a large amount of 
 money ; or an inference through an undistributed 
 middle ; or an inference involving the illicit proc- 
 ess these and the like are paralogisms. 
 
 Sometimes, however, law is only apparently, not 
 really, violated. For example :
 
 FALLACIES 185 
 
 No rose is without thorns; 
 This bouquet is ef roses ; 
 .'.This bouquet has thorns. 
 
 Here seems to be an affirmative conclusion from 
 a negative premise, violating General Itule 4. But 
 on looking into the diction of the major premise, 
 it is seen to yield by infinitation Every rose has 
 thorns, and then the form is Barbara. 
 
 135. ^ophisms in diction, in voce, are such as 
 require an inspection of the expression in order to 
 detect the formal fault. They all arise from am- 
 biguities of language. A term repeated ambigu- 
 ously, though identical to eye and ear, must be 
 counted twice, for it represents two notions. A 
 syllogism containing such a term is therefore, in 
 thought, quaternio terminorum, a quaternion, a log- 
 ical quadruped ( 94). This is the common vice 
 of sophisms in diction. Aristotle distinguishes six 
 species, which we proceed to examine. 
 
 136. ,2Equivocati.o is. the use of a term in two 
 different senses. If it be the middle term, it is 
 called the fallacy of ambiguous middle, as in : 
 
 Designing persons are untrustworthy; 
 Everybody forms designs; 
 .'. Nobody can be trusted. 
 
 Likewise an ambiguous major or minor term pro- 
 duces a quaternion. 
 
 Perhaps no fallacy is so prolific as this. Living 
 languages abound in ambiguities, and no procedure
 
 V 
 
 186 *' DEDUCTION 
 
 ' 
 
 is safe that does not keep close watch upon them. 
 Many important words, as nature, state, representa- 
 tion, moral, inconceivable, and even money, are quite 
 * ambiguous. There are at least five distinct senses 
 in which the word law is habitually used. The 
 only security is in exact definition and consistent 
 usage. As by attrition crystals become pebbles, 
 so words in common use lose their sharp meaning. 
 Like coins defaced by much handling, current words 
 are no longer clear. Science, to be accurate, takes 
 refuge in a barbarous terminology. 
 
 The paranomasia or pun is the sophism of equiv- 
 ocation. Here is a time -honored example: Two 
 men ate oysters for a wager ; one ate ninety-nine, but 
 the other ate two more, for he ate a hundred and 
 won. This affords occasion for the general obser- 
 vation that jests are usually mock logic, and often 
 in absurd form let fly a sharp dart of truth. The 
 " bull " is a palpable self-contradiction, generally 
 an unconscious blunder, but sometimes on purpose ; 
 as, Do you believe in ghosts f No indeed, I've seen 
 too many of them or, as when my wife said to me, 
 / hope I shall not live to see you a frisky widower. 
 
 137. ^Amphibolia differs from equivocation 
 in that the ambiguity is in the construction of a 
 sentence rather than in a term. Examples of am- 
 phiboly are : How much is twice two and three f 
 I will go and return to-morrow. See Quince's pro- 
 logue in Midsummer- Night's Dream, act v., sc. i. 
 In the Nicene Creed, the words "by whm all
 
 FALLACIES 187 
 
 things were made" are grammatically referable 
 either to the Father or to the Son. Amphiboly 
 was the trick of the oracles. Thus the prophecy 
 of the Spirit in Henry 71., pt. ii., act i., sc. iv. : 
 
 The duke yet lives that Henry shall depose, 
 But him outlive, and die a violent death. 
 
 But this, says York, is just the response of the ora- 
 cle to Pyrrhus : 
 
 Aio te, ^Eacida, Romanos vincere posse; 
 Ibis redibis nuuquam in bello peribis. 
 
 138. Compositio et divisio are conjoining 
 what should be disjoined, and disjoining what 
 should be conjoined. Thus, He well knows the al- 
 phabet he had to learn ; In some things we off end all ; 
 Moses was the daughter of Pharaohs son ; Paul 
 returned to his master one Simus (Onesimus). Aris- 
 totle's example of composition is : A man sitting 
 can walk (i. e.. can walk sitting) ; of division, he 
 gives : 5 is % and ?, loth even and odd. He treats 
 them as distinct species, which seems unnecessary, 
 since the distinction between them generally de- 
 pends merely on which of the propositions, involved 
 in the ambiguous statement, is granted, the affir- 
 mation of the other being the fallacy. Whately 
 construes the above as F. Compositionis, thus : 
 
 Two and three (distributively) are even and odd; 
 Two and three (collectively') are five; 
 .'.Five is even and odd. 
 
 This is clear and correct, although it transposes 
 the titles.
 
 188 DEDUCTION 
 
 The distinction between fallacies of this class 
 and amphibolia is not altogether clear. In many 
 cases we hesitate. Perhaps to either may be re- 
 ferred ambiguities wrongly resolved by punctua- 
 tion. A notable example is found in the United 
 States Constitution, Art. 1, 8. After the word 
 " excises " a semicolon is frequently printed, where- 
 as in the original draft, and in the authorized edi- 
 tion of March 3, 1877, it is followed by a comma. 
 Alexander Hamilton held that the items of the rest 
 of the section are additional powers ; Madison, that 
 they are limitations. The semicolon enlarges fed- 
 eral authority ; the comma favors state-rights. 
 
 This gives occasion for the general observation 
 that it should not be inferred from the trifling 
 character of many of the examples used to illus- 
 trate fallacies, that the fallacies themselves are un- 
 important. In a brief trifle a point is often clearly 
 exposed which, lurking in a body of weighty mat- 
 ters, may be fatal. 
 
 139. Accentus, prosodia, resolves an ambi- 
 guity by a stress of voice so as to mislead, gen- 
 erally by an implication. The early rabbis laid 
 emphasis on the word neighbor in Thou shalt love 
 thy neighbor (Lev. xix. 18) ; hence their gloss, and 
 hate thine enemy (corrected in Matt. v. 43 sq.). By 
 emphasis on against in the ninth commandment, 
 it is implied that one may bear false witness in 
 favor of another, which was Jeanie Deans's temp- 
 tation. The phrase If you were' brave differs from
 
 FALLACIES 189 
 
 If you were brave'. So also Not the least difference 
 may mean no difference at all, or by varying the 
 stress, a very considerable, perhaps the greatest 
 difference. Some words, ambiguous to the eye, 
 are resolved by accent, as to con'jure, to practise 
 magic, and to conjure', to entreat earnestly. Mere- 
 ly the tone may make all the difference between 
 truth and falsehood. 
 
 Sarcasm is generally indicated by the circumflex 
 accent, and unless this or certain tones are used, 
 the meaning is perverted ; as, It cannot be that a 
 prophet perish out of Jerusalem. For other exam- 
 ples of divine irony, see 1 Kings xviii. 27 ; Job xii. 
 2 ; Psa. ii. 10 ; 2 Cor. xii. 13. 
 
 140. Figura dictionis occurs when a meta- 
 phor or other figure of speech is construed liter- 
 ally, or vice versa, as : 
 
 A fox is a quadruped ; 
 Herod is a fox; 
 /.Herod is a quadruped. 
 
 This seems very trifling. But let it be observed 
 that figurative expressions abound, that new mat- 
 ter can hardly be spoken of except metaphorically, 
 that the history of the mental sciences shows how 
 difficult it is to avoid being misled by material con- 
 ceptions which are only remotely comparative, and 
 that in debate illustrations are constantly mistaken 
 for arguments, and often are more convincing than 
 good logic. These considerations make it evident 
 that this is a very subtile and ruinous form of fal-
 
 190 DEDUCTION 
 
 lacy. Hamilton speaks of it with great contempt, 
 unaware that his famous argument for immediate 
 perception is invalidated by this very sophism. 
 
 It is usual to include in this class errors arising 
 from solecisms ; as, George Eliot deserves his fame. 
 Also those from paronyms ; as, Being touched with 
 pity, his behavior was pitiful A phenomenon is that 
 which appears^ and therefore is merely apparent. 
 
 141. Sophisms in matter, in re, are such as re- 
 quire an inspection of the matter in order to detect 
 the formal fault. They are quite commonly called 
 " material fallacies," and described as those whose 
 fault is not in form or diction, but in matter, mean- 
 ing that the form is correct, but the matter, espe- 
 cially the premised matter, is false. If so, they, 
 being logically faultless, are not fallacies ( 133). 
 But not so, for these sophisms are logically, for- 
 mally faulty, only it is requisite to look beyond the 
 diction and examine the matter in order to discover 
 the fault. Of this genus Aristotle distinguishes 
 seven species, which we proceed to examine. 
 
 142. Accidens arises from equating subject 
 and accident, or whenever it is assumed that sub- 
 ject and accident have all their attributes in com- 
 mon. By accident here is meant any subordinate 
 part of a general notion, as in conversion j^r acci- 
 dens ( 82). For example : Men (subject) are bipeds; 
 Birds are (an accident of) bipeds ; hence (equating 
 subject and accident), Men are birds, or Birds are
 
 FALLACIES 191 
 
 men. But it is fallaciously assumed that men and 
 birds have all other attributes in common. Obvi- 
 ously undistributed middle. Again : Since Coriscus 
 is not Socrates, and Socrates is a man, it does not 
 follow that Coriscus is not a man, because Socrates, 
 who is denied of Coriscus, is merely an accident 
 of man. Obviously illicit major. Again : 
 
 The Greeks produced masterpieces of art; 
 The Spartans were Greeks ; 
 /.The Spartans produced masterpieces of art. 
 
 Here the Greeks, the subject in the major premise, 
 is the name of a genus taken as an undivided whole 
 ( 63), of which the Spartans is merely an acci- 
 dent. It is fallaciously assumed that whatever is 
 attributable to the genus as such, may be attributed 
 to an accidental member. Obviously ambiguous 
 middle, and hence a quarternion. 
 
 143. Secundum quid occurs in an inference 
 a dicto secundum quid ad dictum simpliciter, and 
 vice versa. It is the confusion of an absolute state- 
 ment with one limited by time, manner, or some 
 accidental relation. 
 
 The first infers from a statement made under an 
 unessential restriction (secundum quid) to one made 
 without restriction (simpliciter). 
 
 Whatever is pernicious ought to be forbidden; ' 
 The use of wine is pernicious; 
 .'.The use of wine ought to be forbidden. 
 
 Here the minor premise refers to wine used im- 
 moderately ; the conclusion, to wine however used.
 
 192 DEDUCTION 
 
 This is the time-honored jspphism of arguing against 
 a thing from the abuse of it. 
 
 The second infers from a statement made with- 
 out limitation to one limited, proceeding from what 
 is essential to what is accidental. 
 
 The meat you bought yesterday you ate to-day ; 
 You bought raw meat yesterday; 
 .'. You ate raw meat to-day. 
 
 Here is inferred, in the conclusion, of meat with 
 the accidental quality of rawness added, what in 
 the major is said of it simply, that is, of the essen- 
 tial substance, regardless of accidental qualities. 
 
 The first of these cases, when we look into the 
 matter, may evidently be construed as illicit minor ; 
 for what is premised of some, a certain use of wine, 
 is concluded of all use of wine. The second case 
 is plainly a quaternion, having an ambiguous mid- 
 dle ; for The meat you bought yesterday is used in 
 two different senses first, simply or essentially 
 only ; secondly, with its accident. 
 
 144. Ignoratio elenchi is ignoring the refu- 
 tation, answering to the wrong point, proving some- 
 thing not the contradictory (elenchus) of the thesis 
 which one intends to overthrow. This supposes a 
 disputant, an attempt at confutation. It is usual 
 to_ take a wider view, and, under the title of Irrel- 
 evant Conclusion, or mistaking the issue, to include 
 all cases where the attempt is to establish a thesis 
 by a proof of something not sustaining it, or of 
 something which may be mistaken for it. This
 
 FALLACIES 193 
 
 might well be termed Ignoratio or Mutatio con- 
 dusionis. Formally the fault is either in estab- 
 lishing something that is not the required contra- 
 dictory of the thesis, or else establishing something 
 that is not the required thesis. 
 
 145. Consequens is to infer that the conclu- 
 sion is false because a premise is false, or the argu- 
 ment unsound ; also, to infer the truth of a premise 
 from that of the conclusion. Thus, if some one 
 argues for the existence of a God from its being 
 universally believed, another may perhaps be able 
 to refute the argument by producing an instance 
 of a nation destitute of such belief, thus contra- 
 dicting the minor premise ; the argument ought 
 then to go for nothing. But many think that this 
 refutation disproves the existence of a God, in 
 which they are guilty of illicit major ; thus : 
 
 Whatever is universally believed must be true ; 
 The existence of a God is not universally believed; 
 .'.The existence of a God is not true. 
 
 Others, again, from being already convinced of the 
 truth of the first conclusion, the existence of a God, 
 would infer the truth of the premise, which would 
 be the fallacy of undistributed middle ; thus : 
 
 What is universally believed is true ; 
 The existence of a God is true; 
 /.The existence of a God is universally believed. 
 
 If these two fallacies be put in hypothetical form, 
 the one shall proceed from the denial of the ante- 
 cedent to the denial of the consequent ; the other 
 13
 
 194 DEDUCTION 
 
 from affirming the consequent to the affirmation 
 of the antecedent ( 91, 119). These two condi- 
 tional fallacies, therefore, are thus identified respec- 
 tively with those of illicit process and undistrib- 
 uted middle. 
 
 146. Petitio principii, or petition, or begging 
 the question, is the assumption, as a ground of 
 proof, of a proposition that is not proved, or not 
 granted, or not self-evident. It may occur in any 
 one of five ways : 
 
 1st. When the question itself, the qucesitum, the 
 very thing to be proved, is assumed. This may be 
 concealed by using synonyms, or a name and its 
 definition, either directly, or in a circumlocution. 
 Thus there are two varieties. 
 
 Hysteron proteron, or the last first, does not ex- 
 tend beyond an epithet or a single proposition or 
 inference. Thus: rebel, or bigot. Thus, synony- 
 mously : The doctrine is heretical, for has it not, 
 I leg, caused a schism in the Church ? Again : 
 
 A rectilinear figure of three sides has its angles equal to two 
 
 right angles; 
 
 A triangle is a rectilinear figure of three sides; 
 .'. A triangle has its angles equal to two right angles. 
 
 Here the minor premise is a name and its defini- 
 tion. These being strictly identical notions ( 35), 
 differ, not in thought, but only in words ; therefore 
 the conclusion is assumed, or the question is begged 
 by the major premise ( 130). The formal fault 
 of hysteron proteron, when syllogistic, is that there
 
 FALLACIES 195 
 
 are but two terms a logical biped ( 94). Typi- 
 cal forms are : 
 
 A is B B is B 
 
 A is A and A is B 
 
 /.A is B .'.A is B 
 
 The conclusion is already in a premise, and nothing 
 is proved. Of. 95, Ex. 12 ; and 131 near end. 
 
 Diallelon, or a logical circle, occurs when a prem- 
 ise is repeated in a more remote conclusion. The 
 form may be represented as a pro- and epi-syllo- 
 gism, thus : 
 
 A is B C is B 
 
 A is C then A is C 
 
 /.C is B .'.A is B 
 
 In this case the pro-syllogism has an illicit process, 
 or else the epi-syllogism an undistributed middle. 
 Of course any number of syllogisms, or a hiatus, 
 may intervene, and more effectually conceal the fal- 
 lacy. Plato, in the " Phaedo, 1 ' proves the immortal- 
 ity of the soul from its simplicity, and, in the " Re- 
 public," proves its simplicity from its immortality. 
 2d. When a particular is to be proved and a uni- 
 versal is assumed without warrant. Thus: The 
 king is tyrannical, for are not all Icings more or 
 less sof This is not properly a fallacy, for the 
 form is faultless ( 133). Yet the major premise, 
 being unproven, begs the question. It would be 
 petitio principii to prove to a Mohammedan the 
 divinity of Christ from New Testament texts, for 
 he does not admit the authority of the Bible ; but 
 it would be a valid argumentum ad hominem ( 108)
 
 196 DEDUCTION 
 
 to prove to him from the Koran the prophetic 
 mission of Jesus, for the authority of the Koran 
 he acknowledges. 
 
 3d. When a universal is to be proved and a par- 
 ticular contained under it is assumed. Thus : The 
 knowledge of contraries is one, for is not the knowl- 
 edge of black and white (or good and evil, or any 
 other pair of particular contraries) one and the 
 same? This begs the question, but only in part. 
 A deduction to all would be the illicit process ( 79). 
 
 4th. When the problem to be proved is divided 
 and its parts assumed in detail. Thus: Medicine 
 is the science of health and disease. For is it not 
 the science of health f And also of disease f 
 
 5th. When two facts are reciprocally implicated, 
 and one is assumed to prove the other. Correla- 
 tives imply and are not inferred from each other 
 ( 78). Thus it is petition to say : Alexander was 
 the son of Philip, and therefore Philip was the 
 father of Alexander; or, A spark caused the ex- 
 plosion, therefore the explosion was caused by a 
 spark; or, therefore the explosion was the effect of 
 a spark. 
 
 147. Non causa pro causa assumes a premise 
 which is not the cause to be the cause of an absurd 
 conclusion. The conclusion may be a proper se- 
 quence, and its absurdity justify the contradiction 
 of a premise, but not of the one assumed. Thus : 
 If the prisoner was one of the burglars, and made 
 the foot-tracks under the window, then he was wear-
 
 FALLACIES 197 
 
 ing shoes half the size of his feet / but this is im- 
 possible j therefore he was not one of the burglars. 
 This reductio ad absurdum ( 108) authorizes the 
 denial of the second part of the protasis, but not 
 of the first, with which the conclusion is not con- 
 nected by any middle term, and so with the first 
 part makes a quaternion. To detect the fallacy, 
 examine whether the suppression of the contra- 
 dicted premise would invalidate the sequence. 
 
 Evidently this sophism relates to causa cogno- 
 scendiy or reason only, not at all to causa essendi 
 ( 110). But treatises on logic quite commonly 
 ignore the true sense, though the fallacy is by no 
 means rare, and, misled by the usus loquendi of 
 cause, say that it is " to mistake for a cause what 
 is not a cause," meaning causa essendi. Thus : A 
 change of the moon causes a change in the weather, 
 Cometa fulsit, ergo bellum erit. This fallacy is the 
 Cum hoc, vel post^Jioc^ ergo propter hoc. It is an 
 important fallacy of induction, but has no place in 
 
 deduction. 
 
 ^ ^ A 
 
 148. Plures interrogationes is the call for a 
 single answer to plural questions asked in one. 
 Thus : Was Pisistratus the tyrant and scourge of 
 Athens? As he was the one but not the other, 
 either a yea or a nay would commit the respondent 
 to a false position. Avoiding one horn, he is caught 
 on the other,' and hence this sophism is sometimes 
 called the Cornutus. A safe answer is, Yes and no. 
 A variation in form is : Are you the only rogue in
 
 198 DEDUCTION 
 
 your family f Such forms are much used in teasing, 
 and lawyers badger unsophisticated witnesses in this 
 way. To some compound question they demand 
 what they call " a categorical answer," meaning a 
 simple yea or nay, when either will entrap the wit- 
 ness in a damaging admission, or in a self-contra- 
 diction or other falsity. Again : Why is a violin- 
 cello player always fat f But we should inquire 
 an sit? before cur sit? The ancient example, 
 Have you cast your horns f may be stated : Either 
 you have cast your horns, or you have them, still 
 which ? But there is a tertium omitted : or you 
 have never had horns. In this case it is the fallacy 
 of incomplete disjunction ( 114). All this seems 
 quite frivolous, but it is not always so. Nor is the 
 form necessarily fallacious. It is used by our Lord 
 to entangle his adversaries (Matt. xxi. 24-27), in 
 which case the disjunction is complete. 
 
 149. Praxis. Designate and describe the par- 
 alogisms occurring in many, yet not in every one, 
 of the following examples : 
 
 1. All plants come from seed, therefore all seeds come 
 
 from plants. 
 
 2. The French Academy defined a crab as a small 
 
 red fish that walks backwards. Very good, said 
 Cuvier, only a crab is not a fish, is not red, and 
 does not walk backwards. 
 
 8. A legitimate argument may fail to win assent ; 
 No fallacy is a legitimate argument ; 
 
 /. No fallacy can fail to win assent.
 
 FALLACIES 199 
 
 4. A monse is an animal, therefore (by determination, 
 
 80) a very large mouse is a very large animal. 
 
 5. Every one desires happiness ; but virtue secures 
 
 happiness ; therefore every one desires virtue. 
 
 6. Only give me the luxuries of life, and I will dis- 
 
 pense with the necessaries. 
 
 7. None but whites are civilized; the ancient Ger- 
 
 mans were whites ; hence they were civilized. 
 
 8. None but whites are civilized ; the East Indians 
 
 are not whites ; hence they are not civilized. 
 
 9. No good doctor ever takes ,f_ees, ;^all good doctors 
 
 are also lawyers ; hence lawyers never take fees. iTuJ 
 
 10. A little girl studying arithmetic, and coming to a 
 
 " sura " in which oranges were exchanged for 
 eggs, refused to try it, saying nobody would be 
 such a fool. /_/ ^y^ 
 
 11. J. S. Mill's introduction to his " Political Economy " 
 
 is entitled " Preliminary Remarks," which pro- 
 poses a prospective review. 
 
 12. A spaniel is defined as a species of the proximate 
 
 genus dog. 
 
 13. Can you mention anything that is comjnon prop- 
 
 erty ? 
 
 14. All that glitters is not gold; tinsel glitters; there- 
 
 fore tinsel is not gold. 
 
 15. Never do anything you need to be ashamed of, and 
 
 then you need never be ashamed of anything 
 you do. 
 
 16. All do not strive ; but all wish to "succeed ; hence 
 
 not all strive who wish to succeed. . 
 
 17. Some possible cases are improbable ; 
 /. Some probable cases are impossible. 
 
 \ 
 
 a
 
 200 DEDUCTION 
 
 18. Liberty is a negation (absence of constraint); 
 We cannot be conscious of a negative ; 
 
 /. We cannot be conscious of liberty. 
 
 19. Shakespeare knew little Latin and less Greek. 
 
 20. Touchstone says to Corin : Why, if thou never 
 
 wast at court, thou never saw'st good manners ; 
 if thou never saw'st good manners, then thy 
 manners must be wicked ; and wickedness is sin, 
 and sin is damnation. Thou art in a parlous 
 state, Shepherd ! !. 
 
 21. If some men are strong, it follows that some are weak. . 
 
 22. An agnostic is one who holds that it is impossible 
 
 to know anything with certainty. 
 
 23. There is no rule without exceptions ; 
 
 This statement is itself a rule ; 
 
 ^] 
 
 :. This statement has exceptions, or 
 There are rules without exceptions. 
 
 24. If a wife be beautiful, she excites jealousy ; . 
 If she be ugly, she excites disgust ; 
 Therefore it is best not to marry. 
 
 25. Whatever represses the liberties of mankind ought 
 
 to be resisted ; but among the things that do so, 
 there are governments ; 
 .. Governments ought to be resisted. 
 
 26. Nothing is better than wisdom ; 
 Dry bread is better than nothing; 
 
 /. Dry bread is better than wisdom. 
 
 27. Those to whom the Gospel promises come are the 
 
 faithful ; 
 
 Many whom the world condemns are faithful ; 
 /.The Gospel promises come to many whom the 
 world condemns.
 
 FALLACIES 201 
 
 Designate and describe the sophisms in diction 
 occurring in many of the following examples : 
 
 28. Whoever necessarily goes or stays is not a free agent ; 
 But every one necessarily either goes or stays ; 
 
 /. No one is free. 
 
 29. Whatever a man walks on he tramples on ; 
 This man walks on the whole day ; 
 
 /. He tramples on the day. 
 
 30. The prophet spake to his sons, saying, Saddle me 
 
 the ass ; and they saddled him. 
 
 31. All criminal actions should be punished by law ; 
 Prosecutions for theft are criminal actions ; 
 
 /. Prosecutions for theft should be punished by law. 
 
 32. No moral principle is an animal impulse ; 
 
 But some animal impulses are principles of action ; 
 /. Some principles of action are not moral principles. 
 
 33. A member of Congress, charged with having called 
 
 another a liar, apologized thus : Jtt is quite true, 
 and I am sorry for it. 
 
 34. Our consciousness testifies to the external reality 
 
 of objects of sense-perception, but is its witness 
 true ? Of course, for your assertion, literally taken, 
 means only this, that we are conscious of external 
 reality. A reply to Hamilton. 
 
 35. Thou shalt not bear false witness against thy 
 
 neighbor. 
 
 36. The planets are seven ; Mercury and Venus are 
 
 planets ; 
 /. Mercury and Venus are seven. 
 
 37. Finis rei est illius perfectio ; 
 Mors est finis vitae ; 
 
 .-. Mors est vitae perfectio.
 
 202 , DEDUCTION 
 
 s 38. Either animal or vegetable food may be altogether 
 
 dispensed with ; 
 
 All food is either animal or vegetable ; 
 /. All food may be altogether dispensed with. 
 
 39. Philip saith to the eunuch, Tu'wo-mc a avayivuaKtiq ; 
 
 40. Pilate saith to the Jews, Behold your King ! 
 And they cried, Hail, King of the Jews ! 
 
 Designate and describe the sophisms in matter 
 occurring in many of the following examples : 
 
 4' , The gods, say the Epicureans, must be invested with 
 the human form, because this form is most beau- 
 tiful ; and everything beautiful must be found in 
 them. 
 
 42. To pray for rain is to ask for a miracle ; but mira- 
 - cles have ceased. It is replied, first, that prayer 
 for rain has often been followed by rain ; secondly, 
 that men have succeeded in causing rain, and to 
 say God cannot do what men can do is impious. 
 + . 43. Prayer may be regarded as useful, if, indeed, we 
 can regard our prayers as announcing to Deity 
 what he does not know, or as effectual in chang- 
 ing his purposes ; 
 
 But we cannot tell the Omniscient what he does 
 not already know, nor effect a change in his eter- 
 nal purposes; ^ _^ 
 .*. Prayer is useless. 
 
 ; ' 
 
 44. The right of the government to command is un- 
 
 questionable ; therefore we ought to obey it. 
 
 45. Unless logic profess to be an instrument of inven- 
 
 tion, the reproach that it discovers nothing is 
 unfounded ; but it does not make this profes- 
 sion, and hence this reproach is unfounded.
 
 n.e. 
 
 
 
 FALLACIES 203 
 
 46. Either God wills to remove evils and cannot; or 
 
 he can and will not ; or he neither will nor can ; 
 or he both will and can. If he will and cannot, 
 then he is weak, which is not true of God. If 
 he can and will not, then he is malicious, which 
 also is foreign to the nature of God. If he nei- 
 ther will nor can, then he is both malicious and 
 weak, and therefore cannot be God. If he both 
 can and will, which alone is consistent with the 
 nature of God, then whence arc evils, or why 
 does he not remove them ? 
 
 47. To allow every man freedom of speech must always 
 
 be, on the whole, for the good of the state ; for 
 it is highly conducive to the interests of the 
 community that each individual should enjoy a 
 liberty, perfectly unlimited, of expressing his 
 sentiments on its affairs. 
 
 48. Mental effort promotes intellectual vigor, but wearies 
 
 the brain ; hence what wearies strengthens ; but 
 hard study is wearisome, and therefore strength- 
 ens the mind. 
 
 49. Whatever is true 1 of John, Peter, etc., is true of all 
 
 mankind ; 
 
 Mortality is true of John, Peter, etc. ; 
 .. Mortality is true of all mankind. 
 
 Whately's " inductive syllogism" approved 
 as such by Mill, Logic, bk. iii., ch. iii. 
 
 50. This, that, and the other magnet attract iron ; 
 This, that, and the other magnet represent all 
 
 magnets ; 
 .-. All magnets attract iron. 
 
 Hamilton's " inductive syllogism," Logic, 62.
 
 204 DEDUCTION 
 
 51. What is not an uncommon occurrence may reason- 
 
 ably be expected ; 
 
 To gain a high prize in a lottery is not an uncom- 
 mon occurrence ; 
 
 /. To gain a high prize in a lottery may reasonably 
 be expected. 
 
 52. He who calls you a man speaks truly ; 
 
 He who calls you a knave calls you a man ; 
 .-. He who calls you a knave speaks truly. 
 
 53. Every effect is caused ; 
 The world is an effect ; 
 
 .. The world is caused. 
 
 54. Why does a ball, when dropped from the mast-head 
 
 of a ship in full sail, fall not exactly at the foot 
 of the mast, but nearer to the stern of the vessel ? 
 
 55. Who is most hungry eats most ; 
 Who eats least is most hungry ; 
 
 .-. Who eats least eats most. 
 
 56. Omne animal rationale est risibile ; 
 Omnis homo est animal rationale ; 
 
 .. Omnis homo est risibilis. 
 
 57. We are forbidden to kill ; 
 
 Inflicting capital punishment is killing; 
 .-. We are forbidden to inflict capital punishment. 
 
 58. He that is of God heareth the words of God : for 
 
 this cause ye hear them not, because ye are not 
 of God. John viii. 47. 
 
 b- t -a '
 
 INDEX 
 
 (T7ie number refers to the page.) 
 
 Abstraction, its process, 15. 
 Accentus, prosodia, fallacy of, 188. 
 Accidens, conversion per, 92. 
 
 fallacy of, 190. 
 Accident, the mark, 16, 44. 
 ^Equivocatio, fallacy of, 185. 
 Ambiguity of aJ/andof some, 73, 74. 
 Ambiguous terms, fallacies of, 185. 
 Ampliibolia, fallacy of, 186. 
 Analysis of conjunctives, 153, 165. 
 Antecedents, affirmed or denied, 
 
 109. 
 Argurnentum ad rem, 139. 
 
 a fortiori, 140, 179. 
 
 ad verecundiam, 140. 
 
 ad judicium, 140. 
 
 ad populum, 140. 
 
 ad absurdum, impossibile, 11, 
 141. 
 
 ad hominem, 141. 
 Aristotle, categories of, 63. 
 
 predicables of, 64. 
 
 Art distinguished from science, 2. 
 Axioms of inequality, 173,178, 179. 
 
 of reason and con seq., 109, 159. 
 
 Begging the question, forms of, 194. 
 Biped, the logical, 195. * 
 Bulls, self-contradiction, 186. 
 
 Canon of mediate inference, 111, 
 175. 
 
 of replacement, 112. 
 
 of immediate inference, 174. 
 
 of partitive syllogisms, 178. 
 
 of comparative syllogisms, 1 79. 
 
 Categorical propositions, 67. 
 Categories or predicaments, (M. 
 Causae, essendi, coguoscendi, 146, 
 
 197. 
 
 Circle, the logical, 195. 
 Circular notation, 29, 100, 135. 
 
 criticised, 102. 
 Classification, 18. 
 Clauses, of two kinds, 76. 
 Clearness and distinctness, 23. 
 Coextensive notions, 29, 30. 
 Collective whole, 26, 28. 
 Comparative syllogisms, 179. 
 Complex propositions, 76. 
 Com positio, fallacy of, 187. 
 Compound proposition.", 79. 
 Concept and mark cominutable, 20 
 Conception, its modes, 18. 
 Concrete and abstract terms, 17. 
 Conditio sine qua non, 146, 159. 
 Condition, its kinds, 146. 
 Conditional propositions, 67, 148. 
 
 syllogisms, 158. 
 
 analyzed and criticised, 165. 
 Congruent notions, 29. 
 Conjunctive propositions, 148. 
 
 analysis of, 153. 
 
 syllogisms, 160. 
 Conjunctivo-disjunctives, 152. 
 
 syllogisms, 163. 
 Connotation and denotation, 20, 22. 
 Consequens, fallacy of, 108, 159, 
 
 193. 
 Consequents, affirmed or denied, 
 
 109. 
 Contradiction, law of, 9, 59, 60, 94,
 
 206 
 
 INDEX 
 
 Contradiction, rule for, 94. 
 Contraposition, 93. 
 Contrariety, 36, 95, 151. 
 Conversion, inference by, 91. 
 Co-ordination of notions, 30, 33. 
 Copula, how qualified, 69. 
 Copulative proposition, 151. 
 
 syllogism, 162. 
 Cornutus, fallacy of, 197. 
 Correlation not inference, 196. 
 Correlative notions, 34, 89. 
 Cross division, test of, 39. 
 
 Deductive inference, 88. 
 Definition of logic, 1. 
 
 of science, 1. 
 
 of marks, 17. 
 
 of concept, 18, 20. 
 
 of individual, 27. 
 
 constituents of, 41. 
 
 a priori and real, 44. 
 
 a posteriori, 44. 
 
 nominal, 45. 
 
 genetic or causal, 45. 
 
 rules for, 45. 
 
 correlated with division, 54. 
 Denotation and connotation, 20, 
 
 22. 
 
 Determination, inference by, 90. 
 Diallelon, the circle, 195. 
 Dichotomy, division by, 33. 
 Dicta de omni et nullo, 111. 
 Dilemma, its forms, 163. 
 Dilemmatic propositions, 152. 
 Disjunctive propositions, 149. 
 
 syllogisms, 161. 
 Disparate notions, 36, 150. 
 Distinctness, two modes of, 24. 
 Divisio, fallacy of, 187. 
 Division by dichotomy, 33. 
 
 ground of, 36. 
 
 kinds of, 37. 
 
 rules for, 38. 
 
 correlated with definition, 54 
 
 Enthymeme, four orders of, 132. 
 Epichirema, analyzed, 134. 
 Equipollence, 14. 
 Exclusives and exceptive*, 80. 
 Existential forms, 60, 148. 
 
 Exponible propositions, 79. 
 Extension and intension, law of. 
 22. 
 
 illustrated, 49, 62. 
 
 Fallacies, distribution of, 184. 
 
 in diction, 185. 
 
 in matter, 190. 
 
 False matter not fallacy, 183. 
 Figura dictionis, fallacy of, 189. 
 Figures, the four, 120. 
 Form and matter distinguished, 4. 
 Fourth figure criticised, 128. 
 Fundamentum divisionis, 36. 
 
 General rules of syllogism, 114. 
 Generalization, process of, 17. 
 Genetic or causal definition, 45. 
 Genus and species, 31, 33. 
 Geometrical illustration, 177. 
 Graphic notation, 103, 135. 
 Ground of division, 36. 
 
 Hypothetical propositions, 148. 
 
 syllogisms, 160. 
 
 Hysteron proteron, fallacy of, 194. 
 
 Ignoratio elenchi, fallacy of, 192. 
 Illicit process, 90. 
 
 major and minor, 116. 
 Implications not inferences, 88. 
 Inconjrruent notions, 28. 
 Indefinable notions, 42. 
 Indefinite propositions, 73. 
 Individual propositions, 72. 
 Individuals, concepts of, 19, 27. 
 
 indefinable, 42. 
 
 how related to system, 52. 
 
 as predicates, 63, 174. 
 Inference defined and divided. 87. 
 Infima species, 51. 
 Infirrttation, inference by, 91. 
 Infinite propositions, 62. 
 Integral whole, 26, 28. 
 Intension and extension, law of, 
 
 22. 
 
 illustrations of, 49. 
 
 predication of, 62. 
 
 syllogisms of, 99, 104. 
 
 differences estimated, 105.
 
 INDEX 
 
 207 
 
 Intentions, first and second, 4. 
 Intersection of notions, 30, 39, 42. 
 
 Judgment, defined, 67. 
 
 distributed, 87, 147. 
 
 the syllogistic, 107. 
 
 Law of identity, 9, 59, 60. 
 
 of contradiction, 9, 59, 60, 94. 
 
 of excluded middle, 11, 59, 60. 
 
 of intension and extension, 23. 
 Linear notation, 29, 100, 135. 
 
 criticised, 102. 
 Logic, definition of, 1. 
 
 a science, not an art, 2. 
 
 an abstract science, 5. 
 
 a fundamental science, 5. 
 
 a negative criterion, 12. 
 
 a postulate of, 13. 
 
 Logical or qualitative whole, 26,28. 
 
 partition or section, 28. 
 
 division, 33. 
 
 definition, 43. 
 
 tree or ladder, 56. 
 
 Many questions, fallacy of, 197. 
 Marks, kinds of, 15. 
 
 definition of, 17. 
 
 and concepts commutable, 20. 
 Material fallacies, 190. 
 Mathematical whole, 26, 27, 171. 
 
 syllogisms, 175, 177. 
 Matter and form, 4, 8, 50. 
 Mediate inference, 88. 
 Mnemonic hexameters, 124. 
 Moods, how ascertained, 123. 
 Mutatio conclusionis, 193. 
 
 Necessity of logical form, 5. 
 
 in what sense violable, 6, 183 
 Negative species, 34, 36. 
 
 predication, 61, 70. 
 Nominal definition, 45 
 
 Non causa pro causa, fallacy of, 
 
 196. 
 Notations, 29, 100, 122, 135. 
 
 geometric criticised, 102. 
 
 graphic explained, 103. 
 Notions,individual and general, 18. 
 Nouns, common and proper, 21. 
 
 Onus probandi, 142. 
 Opposition, inference by, 94, 96. 
 Oracles, the trick of, 187. 
 Order, strict logical, 7<>. 
 Ostensive reduction, 125. 
 
 Paradox, logical, rhetorical, 10, 11. 
 Paralogism, 1 84. 
 Paranomasia or pun, 186. 
 Paronyms, fallacy of, 190. 
 Particular propositions, 73. 
 Partitive syllogisms, 178. 
 Per accidens, conversion, 92. 
 Petitio principii, fallacy of, 194. 
 Plures interrogationes, fallacy of, 
 
 197. 
 
 Polytomy, its origin, 35. 
 Porphyry's tree, 56. 
 Postulate of logic, 13. 
 Predesignations of quantity, 73, 74 
 Predicables of Aristotle, 64. 
 Predicaments or categories, 63. 
 Predicates, quantification of, 82 
 
 rule for distribution of, 85. 
 Predication, its limits, 59. 
 
 of existence, 60. 
 
 of negative notions, 61. 
 Premises, definition of, 101. 
 Primary laws, 8, 59, 60. 
 
 reduction to unity of, 12 
 Privative notions, 36. 
 Propositions, existential, 6C 
 
 negative, 61. 
 
 infinite, 62. 
 
 definition of, 67 
 
 logical parts of, 68. 
 
 distribution of, 71, 147 
 
 individual, 72. 
 
 universal, 72. 
 
 particular or indefinite, 7e 
 
 simple, scheme of, 75. 
 
 symbols of, 76, 83 
 
 conditional, 146. 
 
 of equality and inequality, 172. 
 Prosodia, accentus, fallacy of, 188. 
 Proximate genus, 43. 
 Punctuation, fallacy of, 188. 
 Punning, fallacy of, 186. 
 
 Quadruped, the logical, 114, 186
 
 208 
 
 INDEX 
 
 Qualitative whole, 26, 28. 
 Quantified predicates, 82. 
 
 symbols of, 83. 
 Quantitative whole, 26, 27, 171. 
 
 propositions, 171. 
 
 syllogisms, 175. 
 Quaternions, 114, 185. 
 
 Reason and consequent, 147. 
 
 axioms of, 109, 159. 
 Reasoning, 88, 99, 100, 107, 132. 
 
 conditional forms of, 154, 158 
 
 criticism of, 165. 
 
 quantitative forms of, 175, 178. 
 Reductio ad absurdum, 11, 141. 
 Reduction of syllogisms, 125. 
 
 ad impossibile, 127. 
 Replacement, canon of, 112. 
 Rhetorical identity, 9. 
 
 contradiction, 11. 
 
 inversions, 71 
 
 Rule for distribution of predi- 
 cates, 85. 
 
 for quantity inferred, 89. 
 
 for infinitation, 91. 
 
 for contraposition, 93. 
 
 for contradictory oppos., 94. 
 
 for contrary opposition, 95. 
 
 for subcontrary opposition, 96.' 
 
 for subalternate opposition, 96. 
 
 for intensive syllogism, 105. 
 
 for reduction, general, 127. 
 Rules for division, 38. 
 
 for definition, 45. 
 
 for syllogism, general, 114. 
 
 for syllogism, special, 121. 
 
 for syllogism, conjunctive, 160. 
 
 Science, definition of, 1. 
 Secundum quid, fallacy of, 191 
 Self-contradiction, 186. 
 Semi-definite some, 75, 81, 89. 
 Signs of quantity, 73. 
 Simple notions indefinable, 42. 
 Some, ambiguity of, 74. 
 
 Some, semi-definite, 75, 81, 89. 
 Sophisms in diction, 185. 
 
 in matter, 190. 
 Sorites, scheme of, 136. 
 Special rules for syllogism, 121, 
 Specialization, process of, 18. 
 Species and genus, 31, 33. 
 Specific difference, 43. 
 Square of opposition, 94. 
 Subalternate opposition, 96. 
 Subcontrary opposition, 96. 
 
 propositions, 151. 
 
 syllogisms, 162. 
 Subordinate notions, 29, 30. 
 Summum genus, 60. 
 Syllogism, definition of, 100. 
 
 necessity of, 107. 
 
 truth and falsity of, 108. 
 
 conditional forms of, 108, 151 
 
 compound, 136. 
 
 disguised, 137. 
 
 conjunctive, 160. 
 
 disjunctive, 161. 
 
 copulative, 162. 
 
 analyzed and criticised, 165 
 
 of equivalence, 176. 
 
 partitive, 178. 
 
 comparative, 179. 
 Symbols of propositions, 76, 88 
 
 Terms, definition of, 101. 
 Thought, the matter of logic, 8 
 Tree, the logical, 56. 
 Trichotomy, its origin, 36. 
 True and false matter, 108, 18c 
 
 Ultra-total quantification, 116. 
 Undistributed middle, 116. 
 Universe, the logical, 10, 31. 
 Universal propositions, 72. 
 
 Violation of logical law, 13, 18S 
 
 Wholes, of two kinds, 26. 
 Wdrds, signs of thoughts, 20. 
 
 FINIS
 
 
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