SCIENCE OF LOGIC; 
 
 AN ANALYSIS 
 
 THE LAWS' (^-THOUGHT. 
 
 BY REV. ASA MAUAN, 
 
 AUTHOR OF AN "INTELLECTUAL PHILOSOPHY,' 1 
 "A TREATISE ON THE WILL," ETC. 
 
 ""Words are things; 
 A small drop of ink, falling like dew upon a thought, 
 Produces that which makes thousands, perhaps millions, think." 
 
 NEW YORK: 
 A. S. BARNES & BURR, 
 
 51 & 53 JOHN STREET. 
 
*$" 
 
 ttjW 
 
 Entered according to Act of Congress, in the year 1856, 
 By ASA MAHAN, 
 In the Clerk's Office of the District Court of the United States for the Southern 
 District of New York. 
 
PREFACE. 
 
 Whenever, in the development of any particular science, 
 there has been a misapprehension of its appropriate sphere, and 
 especially when wrong principles have been introduced in its 
 development, a reconstruction of the whole science is of course 
 demanded. The following treatise has been prepared in view 
 of the assumption, that both these defects exist in important 
 forms in the common treatises on this subject treatises of 
 which Dr. Whately's is one of the most prominent representa- 
 tives. Every one is aware, that any given intellectual process 
 having for its object the establishment of truth, may fail of its 
 end for one or more of the three following reasons : 1. The 
 process may be based throughout upon a misconception of the 
 subject treated of. 2. Invalid premises may be introduced as 
 the basis of conclusions deduced. 3. Or there may be a want 
 of connection between the premises and the conclusions de- 
 duced from them. All are equally aware, also, that every valid 
 process is not only free from each of these defects, but pos- 
 sessed of the opposite excellences. In examining any such 
 process, then, three questions are or should be always put, to 
 wit : Has the author rightly apprehended his subject ? Are 
 his premises sound ? Is there a valid connection between his 
 premises and conclusions ? In answering such questions, every 
 one feels the need of valid criteria by which he can determine 
 whether the process is or is not valid in each of these particu- 
 lars, and in one no less than in either of the others. The fol- 
 lowing treatise has been prepared upon the assumption, that 
 the true and proper sphere of logic is to furnish all these dif- 
 ferent criteria, and thus to meet in full the real logical necessi- 
 ties of the human mind. The common treatises are construct- 
 ed upon the assumption that its true and proper sphere is to 
 meet this want in the last particular only, that is, to furnish 
 
4 PREFACE. 
 
 criteria by which we can distinguish valid from invalid deduc- 
 tions from given premises, and that irrespective of the charac- 
 ter of the premises themselves. If we are right in our assump- 
 tion and the question whether we are or are not right, is ful- 
 ly discussed in the Introduction then an enlargement of the 
 sphere of the science beyond what is aimed at in ordinary trea- 
 tises is demanded, and so far the science needs a reconstruction. 
 All such treatises that we have ever heard of with one ex- 
 ception, " Thomson's Laws of Thought," which has never been 
 reprinted in this country have been constructed throughout 
 upon the assumption, that " all negative propositions and no 
 affirmative, distribute the predicate," and that in converting 
 a universal affirmative proposition we must change its form 
 from a universal to a particular ; as, " All men are mortal," 
 " Some mortal beings are men." Let us now suppose that as 
 far as affirmative propositions are concerned, the above princi- 
 ples hold only in respect to a single class, while, in all other 
 cases, such propositions as well as negative ones do, and from 
 the nature of the relations between the subject and predicate 
 must, distribute the predicate as well as the subject. In that 
 case undeniably, a reconstruction of the whole syllogism is de- 
 manded. Now the truth of each of the above statements can 
 be rendered demonstrably evident on a moment's reflection. 
 Why is it, that in the proposition, for example, " All men are 
 mortal," the subject only is distributed, and that its converse 
 is, " Some mortal beings are men ?" The reason is obvious. 
 The term men represents a species of which the term mortal 
 represents the genus. In other words, the former term repre- 
 sents what is called an inferior, and the latter its superior, con- 
 ception. The term mortal being applicable to a larger number 
 of objects than the term men, must be understood, in the above 
 proposition, as representing only a part of its significates. Such 
 proposition, of course, can be converted, but by limitation, that 
 is, changing its form from a universal to a particular. It is only 
 in reference to this one class of propositions, however, that the 
 principles under consideration do or can hold. When the 
 sphere of the subject and predicate are, from the nature of the 
 terms themselves, equal as they are, in all cases but in reference 
 to the single class referred to then affirmative propositions dis- 
 tribute the predicate on the same principles that negative ones 
 do. We will mention here for illustration but a single class of 
 

 PREFACE. 5 
 
 propositions of this kind the mathematical. In every univer- 
 sal affirmative proposition throughout the entire range of this 
 science, the predicate as well as the subject is distributed ; the 
 converse as well as the exposita being universal also. This 
 holds equally in regard to the principles and subsequent deduc- 
 tions of this science. What is the converse, for example, of 
 such propositions as the following ? " Things equal to the 
 same tilings are equal to one another," " The square of the 
 hypothenuse of a right-angled triangle is equal to the sum of 
 the squares of the two sides," "6+4 10," "X = Z," &c. ? 
 The whole science of logic has been constructed upon principles 
 of distribution and conversion, which would utterly mislead 
 us, if applied to any of the universal affirmative propositions 
 throughout the entire range of the science of the mathematics, 
 or to any propositions but one of the single class above named. 
 In respect to the different figures of the syllogism, also, it has 
 been laid down as holding universally, that the second yields 
 only negative, and the third only particular, conclusions. This 
 also holds true when, and only when, the propositions belong 
 to the single class above named. In all other cases, we can ob- 
 tain universal affirmative or negative conclusions, in each and 
 all the figures alike. Take the following as examples : 
 
 FIG. I. FIG. II. FIG. III. 
 
 M=X ; X=M ; M=X ; 
 
 Z = M; Z=M; M=Z ; 
 
 .-. Z = X. .-. Z=X. .-. Z=X. 
 
 Every one will perceive at once that each of the above syllo- 
 gisms is of equal validity, and that the converse of the conclu- 
 sion is in each case universal, as well as the exposita. 
 
 The dictum, too, under which the syllogism has been con- 
 structed will be found to be applicable only to arguments con- 
 structed entirely from the single class of propositions named. 
 These facts being undeniable, every one will perceive that sci- 
 ence demands a reconstruction of the syllogism throughout. 
 This we have attempted to do, and trust we have accomplished 
 to the satisfaction of all who shall acquaint themselves with the 
 following treatise. Before venturing to give our deductions in 
 the important particulars now before us to the public, we sub- 
 mitted them to numbers of scientific men in whose judgment 
 we have great confidence. From these we have received such 
 expressions of approbation as to inspire us with the assurance, 
 
 V 
 
6 PREFACE. 
 
 that these deductions will stand the test of the most rigid scien- 
 tific scrutiny, which is most cordially invited. 
 
 The doctrine of fallacies, treated of in Part II., we have 
 aimed to simplify by proper definitions, logical division, and 
 arrangement of the whole subject, so as to render the doctrine 
 luminous throughout and its principles of ready application in 
 the reader's mind. 
 
 Almost no portion of the treatise does the author regard as 
 of higher importance than the doctrine of method, as eluci- 
 dated in Part III. We judge that the public will perceive 
 that an important scientific want is there met. 
 
 In furnishing the examples presented in Part TV. we have 
 had two special objects in view to present fundamental sug- 
 gestions in regard to important questions in science ; and to 
 furnish examples for criticism of corresponding importance. 
 If, in any case or in all cases, it should turn out that we have 
 erred in reasoning or in any other particular, and the error 
 shall be discovered by the application of the principles previous- 
 ly elucidated, the great end of the work is answered, and the 
 examples will still have their proper place in the work, just as 
 they would if cited from another author as examples of fallacy 
 in reasoning, or of error or defect in any other particular. 
 
 In the perusal of the following treatise the public will per- 
 ceive that we are much indebted to three authors Mr. Thom- 
 son, whose work we had never seen till we had progressed in 
 our own to the very place where important citations from his 
 first appear Kant, whose treatise, in our judgment, excels by 
 far in important respects any other that we have met with 
 and Sir William Hamilton, to whom the science of logic, and 
 the author of this treatise especially, is more indebted than to 
 any other author the father of the science, of course, excepted. 
 It is with the utmost gratification that we would record the 
 fact, that in almost every particular in which we have departed 
 from the beaten track in the development of the science, we 
 are sustained throughout by such high authority as Sir Wil- 
 liam Hamilton. With these suggestions, the following treatise 
 is commended to the careful examination and candid criticism 
 of the public. 
 
CONTENTS. 
 
 PAGE 
 
 Introduction 17 
 
 Necessity of a correct definition of Logic 17 
 
 All things occur according to rules 18 
 
 ' Logic defined 19 
 
 Eelations of Logic to other sciences 19 
 
 The idea of Logic developed in a form still more clear and distinct 20 
 
 Divisions of Logic 21 
 
 Correctness of the ahove definition verified 21 
 
 Logic as distinguished from Esthetics 24 
 
 Accordance of the above conception of Logic with that given by Kant. 25 
 Accordance of the above idea of Logic with that set forth by Sir Wil- 
 liam Hamilton 26 
 
 Inadequate and false conceptions of this science 27 
 
 1. The syllogistic idea 27 
 
 2. Conceptions of Dr. Whately and others 32 
 
 3. The idea that " the adequate object of Logic is language" 33 
 
 General division of topics 35 
 
 PART I. THE ANALYTIC. 
 
 CHAPTER I. Analytic of Conceptions and Terms. - 
 
 Section I. Of Conceptions 37 
 
 Conceptions defined 37 
 
 Origin and constituent elements of Conceptions 37 
 
 Error commences, not with Intuitions, but Conceptions 39 
 
 Universal characteristics of all valid and invalid Conceptions 39 
 
 Spontaneous and Reflective Conceptions 40 
 
 First and second Conceptions 40 
 
 Matter and sphere of Conceptions 41 
 
 Individual, generic or generical, and specific or specifical Conceptions . 42 
 
 Highest genus and lowest species 42 
 
 Empirical and rational Conceptions 43 
 
 Presentative and representative Conceptions 45 
 
8 CONTENTS. 
 
 Abstract and concrete Conceptions 45 
 
 Positive, privative, and negative Conceptions 46 
 
 Conceptions classed under the principle of unity, plurality, and totality 46 
 
 Inferior and superior Conceptions 46 
 
 Concrete and characteristic Conceptions 47 
 
 Laws of thought pertaining to the validity of Conceptions 47 
 
 Particular, general, and abstract Conceptions 48 
 
 Individual, specifical, and generical Conceptions 48 
 
 Presentative and representative Conceptions. 49 
 
 Concrete and characteristic Conceptions 49 
 
 Inferior and superior Conceptions 50 
 
 Empirical and rational Conceptions 50 
 
 Section II. Of Terms 51 
 
 Singular and common Terms. Significates 51 
 
 Eelations of Logic to Terms 51 
 
 CHAPTEK II. Of Judgments. 
 
 Section I. Of Judgments considered as Mental States 52 
 
 Matter and form of Judgments 52 
 
 Quantity of Judgments, universal, particular, individual or singular . 53 
 
 Quality of Judgments, affirmative, negative, indefinite 54 
 
 Relation of Judgments, categorical, hypothetical, and disjunctive 54 
 
 Remarks on these Judgments 55 
 
 Categorical Judgments 55 
 
 Hypothetical Judgments 56 
 
 Disjunctive Judgments 58 
 
 Modality of Judgments, problematical, assertative, contingent, neces- 
 sary (appodictical) Remarks 58, 59 
 
 Theoretical and practical Judgments 60 
 
 Demonstrable, and indemonstrable or intuitive Judgments 61 
 
 Analytical and synthetical Judgments 61 
 
 Criteria of all first Truths 63 
 
 Kant's definition of analytical and synthetical Judgments 63 
 
 Tautological, identical, and implied Judgments 64 .. 
 
 Axioms, Postulates, Problems, and Theorems 65 
 
 Corollarys, Lemmas, and Scholia ( 66 
 
 Criteria of Judgments, or characteristics of all valid Judgments 66 
 
 General Criteria 67 
 
 Particular and special Criteria 67 
 
 Judgments relative to all valid Conceptions 67 
 
 Individual (single), Particular, and Universal Judgments 68 
 
 Individual Judgments (affirmative) 68 
 
 Individual Judgments (negative) 69 
 
CONTENTS. 9 
 
 Universal Judgments (affirmative) 71 
 
 Universal Judgments (negative) 71 
 
 Judgments pertaining to the objects of inferior and superior Concep- 
 tions 72 
 
 Judgments pertaining to the objects of characteristic Conceptions (af- 
 firmative) 73 
 
 Judgments relative to objects of characteristic Conceptions (negative) . . 73 
 
 Hypothetical Judgments 74 
 
 Hypothetical Judgments classed 74 
 
 Criteria of such Judgments 74 
 
 Disjunctive Judgments 76 
 
 Section II. Of Propositions 77 
 
 Quality and Quantity of Propositions, &c 77 
 
 Distribution of Terms 78 
 
 Of Opposition 80 
 
 Of the Conversion of Propositions 82 
 
 Quantification of the Predicate 84 
 
 Parti-partial Negation , 87 
 
 Criteria by which Propositions properly falling under these different 
 
 classes may be distinguished from each other 90 
 
 CHAPTER III. Analytic of Arguments or Syllogisms. 
 
 Section I. Argument defined and elucidated 94 
 
 Diverse Forms of the Syllogism 96 
 
 Section II. The Analytic and Synthetic Syllogism 96 
 
 These distinct forms of the Syllogism elucidated 96 
 
 Section III. Figured and Unfigured Syllogisms 99 
 
 Principles and Laws of the Unfigured Syllogism ., . . . 100 
 
 The Canon of this Syllogism 100 
 
 General Remarks upon this form of the Syllogism 102 
 
 Section IV. The Figured Syllogism 103 
 
 This form defined 103 
 
 Common assumption on the subject 103 
 
 Influence of Assumptions 104 
 
 Principles determining the distribution of the Predicate . 104 
 
 Fundamental mistake in developing the science of Logic '. 106 
 
 Division of the present subject 107 
 
 I. Those forms of the Syllogism which have been commonly treated of 
 as including all forms of the categorical argument, to wit : those 
 forms in which the terms employed are related to each other as 
 
 Inferior and Superior Conceptions 108 
 
 Preliminary Remarks upon this Form of the Figured Syllogism 108 
 
 1* 
 
10 CONTENTS. 
 
 Only proximate conclusions obtained 108 
 
 1. The principle of Extension and Intension, or of Breadth and 
 
 Depth, as applied to the Syllogism 109 
 
 2. Import of Judgments (Extension and Intension Naming) 110 
 
 3. Direct and indirect conclusion. . 112 
 
 4. Character of all the propositions employed in this form of the 
 
 Syllogism 113 
 
 Letters to be employed 113 
 
 Canon and Laws of this Form of the Syllogism Conditions on which 
 we can obtain the different classes of Conclusions above named ; 
 
 that is, A, I, E, 113 
 
 Universal Affirmative Conclusions 113 
 
 Universal Negative Conclusions 114 
 
 Particular Affirmative Conclusions 114 
 
 Particular Negative Conclusions 115 
 
 All valid Conclusions deduced upon principles which accord with those 
 
 above elucidated 116 
 
 Analysis of the above relations 117 
 
 The Canon of this Syllogism 119 
 
 Moods of the Syllogism 120 
 
 Figure of the Syllogism Form defined 121 
 
 Number of figures of the Syllogism 121 
 
 Major and Minor Terms and Premises 122 
 
 Order of the Premises 122 
 
 Final abolishment of the Fourth Figure 123 
 
 Opinions of Logicians upon the subject 123 
 
 Our Eeasons for the abolition of this Figure 124 
 
 Special Characteristics and Canon of each of the three Figures 126 
 
 Figure 1 126 
 
 The Canon illustrated. 127 
 
 Figure II 128 
 
 Canon of this Figure 130 
 
 Figure ni 131 
 
 Canon of this Figure 132 
 
 Absurdity of reducing the Syllogisms of the other Figures to the first. 132 
 
 Nature of the Conclusions obtained in this form of the Syllogism 133 
 
 Kind of arguments which appropriately belong to the different Figures 135 
 
 A more brief view of this subject I 138 
 
 A scientific determination of the real number of Legitimate Moods in 
 
 this form of the Syllogism 138 
 
 Conditions of valid deductions of any kind in this form of the Syl- 
 logism 139 
 
 Universal affirmative conclusions 139 
 
 Particular affirmative conclusions 139 
 

 CONTENTS. 11 
 
 Universal negative conclusions 140 
 
 Particular negative conclusions 141 
 
 The number of Moods 142 
 
 Similar determination of the number of Moods in each Figure 142 
 
 1. Syllogisms allowable in the First Figure 142 
 
 2. Moods or Syllogisms allowable in the Second Figure 143 
 
 3. Allowable Moods in the Third Figure. 144 
 
 II. That department of the Figured Syllogism in which there is, not 
 
 only in Negative but in Affirmative Propositions, the distribution 
 
 of the Predicate as well as of the Subject 145 
 
 Propositions of this kind classified 146 
 
 Additional Syllogisms illustrative of the above classes of Judgments. . . 148 
 
 1. Syllogisms constituted of Substitutive Judgments 149 
 
 2. Quantitive Judgments 149 
 
 3. Correlative Judgments 149 
 
 4. Judgments falling under the principle of likeness and unlikeness 149 
 6. Proportional Judgments 150 
 
 Table of Logical Judgments 150 
 
 Affirmatives 150 
 
 Negatives 151 
 
 Of opposition and conversion of Judgments 151 
 
 Canon of this form of the Syllogism 152 
 
 Special Characteristics of this Form of the Syllogism 152 
 
 III. The two Forms of the Syllogism combined 154 
 
 Table of all the Legitimate Moods in all figures 155 
 
 A mode of Notation 156 
 
 Equivalent Syllogisms 159 
 
 Sir William Hamilton's Scheme of Moods and Figures of Syllo- 
 gisms 161, 162 
 
 Table of Moods 164 
 
 Sum of all the valid Moods in each Figure 165 
 
 Euler's System of Notation 165 
 
 Sir William Hamilton's Special Canons of the different Figures 166 
 
 1. Canon of the First Figure 166 
 
 2. Canon of the Second Figure 166 
 
 3. Canon of the Third Figure 167 
 
 Canons and Diverse Forms of the Figured Syllogism elucidated 167 
 
 Proper sphere and application of Aristotle's dictum 169 
 
 Section V. The Conditional Syllogism 170 
 
 The appropriate sphere of the Conditional Syllogism 172 
 
 Section VI. The Disjunctive Syllogism 175 
 
 Circumstances in which the Disjunctive Syllogism should be used 175 
 
 Section VII. The Dilemma 177 
 
 Circumstances which require the use of this form of the Syllogism 177 
 
12 CONTENTS. 
 
 Section VIII. The Deductive and Inductive Syllogisms 179 
 
 Section IX. Syllogisms of Induction and Analogy 183 
 
 Demonstrative, inductive, and analogical reasoning distinguished. . . . 183 
 
 Canon of the Inductive Syllogism 187 
 
 General Characteristics of all facts or principles which are to be as- 
 sumed as Causes or Laws 187 
 
 Verification of Inductions 193 
 
 Canon of the Syllogism of Analogy 195 
 
 When the Syllogism of Analogy has the greatest force 196 
 
 The Enthymeme 196 
 
 Section X. The Sorites, or Chain Syllogism Term defined 197 
 
 Principles on which this Form of Seasoning depends 197 
 
 The Sorites can have but one particular, and one negative, premise. . . 199 
 
 Forms of this kind of argument 199 
 
 Section XL Syllogism of Chance this Syllogism defined 201 
 
 Principle which governs such calculations 201 
 
 Section XII. Immediate and Mediate Syllogisms 202 
 
 Section XIII. The Prosyllogism and Episyllogism 203 
 
 Section XIV. Syllogism of Classification 204 
 
 Principles and Laws of this Form of the Syllogism 204 
 
 Concluding Explanations 206 
 
 PART n. THE DIALECTIC, OR DOCTRINE OF FAL- 
 LACIES. 
 
 Fallacy defined 209 
 
 Fallacies where found 209 
 
 The ultimate cause and source of Error 210 
 
 CHAPTER I. Invalid Conceptions. 
 
 Sources of Invalid Conceptions , 211 
 
 CHAPTER II. The Dialectic Invalid Judgments. 
 
 Section L Problematical Judgments assumed as First Truths 216 
 
 Assumption that a thing cannot act where it is not 217 
 
 The assumption that our knowledge of matter is exclusively mediate. . 217 
 
 Fundamental and opposite Assumptions of Materialism and Idealism . . 218 
 
 Assumption pertaining to the Origin of our idea of Cause and Effect . . . 220 
 
 "The Eternal Now" of Theology 223 
 
 Assumption pertaining to the Divine Personality, &c 224 
 
 Section II. Invalid Assumptions pertaining to Matters of Fact 226 
 
CONTENTS. 13 
 
 CHAPTER III. The Dialectic Fallacies of Reasoning. 
 
 Fallacies in Reasoning '. 232 
 
 General Characteristics of all Invalid Deductions 233 
 
 Section I. Conclusions deduced from Premises which prove nothing. 233 
 
 Arguing from two Negative or two Particular Premises 233 
 
 Drawing positive conclusions from Problematical Premises 234 
 
 Petitio Principii 234 
 
 Arguing in a Circle 235 
 
 Deducing positive conclusions from Premises known to be invalid in 
 
 themselves 236 
 
 Leap in Logic 238 
 
 Proving too much 240 
 
 Inferring the falsity of the conclusion from that of the premise, or the 
 
 truth of the premise from the truth of the conclusion 240 
 
 Fallacy of References 241 
 
 Fallacies connected with the use of the Middle Term 242 
 
 Conditional Syllogisms whose Conditional Premises are void of Logical 
 
 Consequence 247 
 
 Disjunctive Syllogisms whose Disjunctive Premises are void of Logical 
 
 Consequence 248 
 
 Fallacies arising from the use of Invalid Dilemmas 251 
 
 Conclusions based upon false Analogies , 252 
 
 Section II. Conclusions deduced from Premises which come short of 
 
 proving said Conclusions 253 
 
 Drawing a universal conclusion, where only a particular is allowable. 253 
 Proving a part of aconclusion and then assuming the whole as established 254 
 
 Fallacy of Objections 255 
 
 Assumption of Probabilities 255 
 
 Section III. Conclusions deduced from Premises which prove not those 
 
 really sought to be proved, but certain other and irrelevant ones . . 257 
 
 Ignoratio elenchi, or Irrelevant Conclusion 257 
 
 Suppressing the Conclusion 263 
 
 Argumentum ad hominem 264 
 
 PART EX THE DOCTRINE OF METHOD. 
 
 Terms defined 267 
 
 Means by which the Logical Perfection of Thought may be secured . . . 267 
 
 Conditions on which these ends may be secured 268 
 
 Section I. Logical Perfection of Thought as promoted by proper Defi- 
 nition and Exposition 268 
 
 Design of Definition and Exposition 268 
 
14 CONTENTS. 
 
 Proper objects of Definition and Exposition 268 
 
 Characteristics of all Correct Definitions 269 
 
 Characteristics of Defective Definitions 271 
 
 Elements which enter into, and are excluded ffom, all Perfect Definitions 272 
 
 Characteristic, Generical, Specifical, and Individual Conceptions 272 
 
 Definitions of Propositions 273 
 
 True use of Affirmation and Negation in Definition 273 
 
 Nominal and Real Definitions 274 
 
 Subjective and Objective Definitions 274 
 
 Examples of Perfect and Imperfect Definitions 273 
 
 The term Judgment defined 275 
 
 Moral Action defined 276 
 
 Moral Law defined 277 
 
 A Moral Agent defined : 278 
 
 Ultimate Intuition defined 278 
 
 The term God defined 279 
 
 Section II. Promotion of the Logical Perfection of Thought by means 
 
 of the Logical Division of Conceptions or Subjects Terms defined 280 
 
 Universal Rules for Logical Division 281 
 
 Codivision and Subdivision 282 
 
 The Fragmentary as opposed to the Real Logical Division of Subjects. . 283 
 Section III. The Promotion of the Logical Perfection of Thought by 
 
 means of a proper arrangement of the parts of the Subject treated of 283 
 
 Terms defined Analytic and Synthetic Order of Thought 283 
 
 Canons of Order 284 
 
 Section IV. Miscellaneous Topics bearing upon our present Inquiries 
 
 The Doctrine of Method 285 
 
 Characteristics of every well-conducted Argument 285 
 
 Methods of Proof the Direct and Indirect, and the two united in the 
 
 same Argument 286 
 
 Characteristics of all Forms of Valid Evidence 287 
 
 Forms of Evidence classified 287 
 
 Characteristics of all Forms of Valid Proof 288 
 
 The Mathematical Form 288 
 
 Reasoning from Facts to General Conclusions, or from one Fact to 
 
 another 289 
 
 The True and Proper Method of determining the Character and Validi- 
 ty of any given Argument 298 
 
 Example in illustration 291 
 
 Method or Forms of Proving a given Proposition false 293 
 
 Method or Forms of Refuting any given Argument Terms defined . . . 294 
 
 Objections to a given Hypothesis when valid 295 
 
 Method of Refuting Objections, or the Forms in which they may be re- 
 futed 296 
 
CONTENTS. 
 
 PART IV. APPLIED LOGIC. 
 
 *" The Anglo-Saxon and German Methods of developing Thought 298 
 
 Reasons for this difference 299 
 
 - Illustration 1. Systems of Natural Theology developed according to 
 
 these two Methods 299 
 
 " Illustration 2. Systems of Intellectual Philosophy developed according 
 
 to the Principles of these two Methods 300 
 
 The Character of any System of Intellectual Philosophy which shall 
 
 meet the fundamental wants of the present age ". . . 304 
 
 - Error of Mr. Mill in regard to the Syllogism 305 
 
 Error of Mr. Mill in regard to the Nature of all Forms of Inference 307 
 
 Mr. Mill's position that "the syllogism is not the type of reasoning, 
 
 but a test of it" 309 
 
 Exclusive Condition on which we can legitimately reason from particu- 
 lars to particulars 310 
 
 Relations of the Syllogism to the Discovery of Truth 311 
 
 The Great Problem in Philosophy according to Kant 312 
 
 Kant's Solution of this Problem 313 
 
 Errors of Kant in the solution of this Problem 314 
 
 The Sensational Theory of External Perception 320 
 
 The Great Problem in Philosophy of the Present Age 322 
 
 Proposed solution of this Problem 323 
 
 Distinction between Presentative and Representative Knowledge 323 
 
 The Formulas stated 324 
 
 These Formulas and Test verified 326 
 
 Bearing of these Formulas upon Systems of Ontology 327 
 
 -"Character and claims of Empiricism, Materialism, Idealism, and Real- 
 ism, as systems of philosophy 327 
 
 General Remarks upon these Systems 331 
 
 ^ Dogmatism, Skepticism, Positiveism, and Free-Thinking 333 
 
 Conditions of the Possibility of Science in any Particular Department 
 
 of Thought 334 
 
 Bearings of the Sensational Theory of Perception 335 
 
 Conditions on which the Proposition, "God exists," can legitimately 
 
 take its place as an undeniable Truth of Science 337 
 
 The Theistic Formulas \ . 338 
 
 The Disjunctive Argument for the Theistic Hypothesis 339 
 
 The ultimate principles on which the hypotheses of Theism, Skepti- 
 cism, and Anti-Theism in all its forms, rest 340 
 
 Common Theistic Syllogism and Argument 341 
 
 Influence of the Hypothesis, that there are different kinds of proof of 
 the being of God 349 
 
16 CONTENTS. 
 
 The two Aberdeen prize essays denominated "Christian Theism," 
 
 and " Theism" 351 
 
 Professor Tulloch's Treatise (Theism) v . . 352 
 
 Professor Tulloch's professed Demonstration of his Major Premise 353 
 
 Our Author's Direct and Positive Argument 357 
 
 Mr. Thomson's Treatise (Christian Theism) 364 
 
 The Dogma that our Idea of God is purely Negative 376 
 
 The real Basis of all Valid Scientific Procedures 377 
 
 The Dogma that our Knowledge of Nature is confined to Phenomena, 
 
 and does not pertain to Substances themselves 378 
 
 The Dogma that Individual Conceptions pertain to Objects, and gen- 
 eral ones only to the Mind which forms them 379 
 
 The idea of a " Positive Philosophy' ' 380 
 
 False Methods in Philosophy 386 
 
INTRODUCTION. 
 
 Necessity of a correct definition of Logic 
 
 Every science has a sphere peculiar to itself. Its end or 
 aim also, in the occupancy of that sphere, is equally special 
 and peculiar. The mathematics, for example, have an exclu- 
 sive sphere, end, and aim, and metaphysics others equally 
 special and exclusive. To enter intelligently and with the ra- 
 tional hope of the highest profit, upon the study of any par- 
 ticular science, its peculiar sphere, and special aim in the occu- 
 pancy of the same, must be distinctly apprehended. Now; 
 while the sphere and aim of most of the sciences have been 
 definitely determined, the opposite is most strikingly true in 
 regard to logic. It would be difficult to name any two phi- 
 losophers, with the exception perhaps of Kant and Sir Wil- 
 liam Hamilton, who fully agree in their ideas and definitions 
 of this science. By some it is defined as the art, by others 
 as the science, and by others still, as " the science and art of 
 reasoning.' 1 '' According to Sir William Hamilton, "the laws 
 of thought, and not the laws of reasoning, constitute the ade- 
 quate object of the science." This definition, as the reader 
 will readily perceive, is really identical with the following given 
 by Kant : " This science of the necessary laws of the under- 
 
18 INTRODUCTION. 
 
 standing and of reason in general, or of (what amounts to the 
 same thing) the mere form (laws) of thinking in general, we 
 name logic." These last two definitions, as we apprehend 
 them, we regard as strictly correct, and as presenting the 
 only true and adequate conception of the proper sphere and 
 aim of the science. "We will now proceed to elucidate the 
 ahove definitions as we understand tnem, and to do so by giv- 
 ing our own independent definition of the science. As pre- 
 paratory to this end, we would invite special attention to 
 the following extract from our own work on Intellectual Phi- 
 
 " All things occur according to rules, 
 
 " ' Every thing in nature,' says Kant, and this is one of his 
 most important thoughts, 'as well in the inanimate as in the 
 animate world, happens, or is done, according to rules, though 
 we do not know them. Water falls according to the laws of 
 gravitation, and the motion of walking is performed by ani- 
 mals according to rules. The fish in the water, the bird in 
 the air, move according to rules.' 
 
 " Again : ' There is nowhere any want of rule. When we 
 think we find that want, we can only say that, in this case, the 
 rules are unknown to us.' 
 
 " The exercise of our intelligence is not an exception to the 
 above remark. When we speak, our language is thrown into 
 harmony with rules, to which we conform without, in most in- 
 stances, a reflective consciousness of their existence. Grammar 
 1b nothing but a systematic development of these rules. So 
 also, when we judge a proposition to be true or false, or to be 
 proved or disproved, by a particular process of argumentation, 
 or when we attempt to present to ourselves, for self-satisfac 
 

 INTEODUCTION. 19 
 
 tion, or to others for the purpose of convincing them, the 
 grounds of our own convictions that is, when we* reason, our 
 intelligence proceeds according to fixed rules. When we have 
 judged or reasoned correctly, we find ourselves able, on reflec- 
 tion, to develop the rules in conformity to which we judged and 
 reasoned, without a distinct consciousness of the fact. In the 
 light of these rules we are then able to detect the reason and 
 grounds of fallacious judgments and reasonings. 
 
 "Logic defined. 
 
 " The above remarks have prepared the way for a distinct 
 statement of the true conception of logic. It is a systematic 
 development of those rules in conformity to which the univer- 
 sal intelligence acts, hi judging and reasoning. Logic, accord- 
 ing to this conception, would naturally divide itself into two 
 parts a development of those rules to which the intelligence 
 conforms in all acts of correct judgment and reasoning, and 
 a development of those principles by which false judgments 
 may be distinguished from the true. A treatise on logic, in 
 which the law T s of judging and reasoning are evolved in strict 
 conformity to the above conception, would realize the idea of 
 science, as far as this subject is concerned. Logic, to judging 
 and reasoning, is what grammar is to speaking and writing. 
 Logic pertains not at all to the particular objects about which 
 the intelligence is, from time to time, employed, but to the 
 rules or laws in conformity to which it does act, whatever the 
 objects may be. 
 
 " Relations of Logic to other sciences. 
 
 " In the chronological order of intellectual procedure, logic is 
 preceded by judging and reasoning, just as speaking and writ- 
 
20 INTEODUCTIOST. 
 
 ing precede grammar. ' In the logical order, however, it is 
 the antecedent of all other sciences. In all sciences the in- 
 telligence, from given data, judges in regard to truths resulting 
 from such data : we also reason from such data for the estab- 
 lishment of such truths. Logic develops the laws of thought 
 which govern the action of the intelligence in all such pro- 
 cedures. As a science, it is distinct from all other sciences. 
 Yet, it permeates them all, giving laws to the intelligence in 
 all its judgments and reasonings, whatever the objects may be 
 about which it is employed." 
 
 The idea of Logic developed in a form still more clear and 
 distinct. 
 
 It will readily be perceived, we judge, that the above defini- 
 tions and statements have made a somewhat near approach, to 
 say the least, to the true idea of the science under consideration. 
 To place the subject in a light still more clear and distinct, 
 we -would observe, that there are certain cognitions, certain pro- 
 cesses of thought, which are universally regarded as valid for 
 the truth of what is therein referred to. We examine, for ex- 
 ample, the process of thought (statements and demonstrations) 
 by which we are conducted to the conclusion, that the square 
 of the hypothenuse of a right-angled triangle, is equal to the 
 sum of the squares of its two sides. We affirm that, on ac- 
 count of what is contained in said process, that proposition is 
 to be held as true ; in other words, the process itself is valid 
 for the truth of what is therein referred to. On the other 
 hand, there are other processes which are not thus valid. 
 What is true is sometimes professedly established by pro- 
 cesses not at all valid for its reality, and through other pro- 
 cesses what is not true is often affirmed to have been estab- 
 

 INTRODUCTION. 21 
 
 lished as a reality. All processes of the first class are held as 
 valid, and the two last named are regarded as invalid pro- 
 cedures of the intelligence. In each process alike, the valid, 
 as well as the invalid, the intelligence has acted in accordance 
 with certain fixed laws or principles, which we are able to de- 
 termine. To develop, that is, determine, define, and elucidate 
 these laws, and thus present universal criteria of valid and in- 
 valid procedures of the intelligence, when the object of such 
 procedure is truth, is, as we understand the subject, the true 
 and exclusive sphere and aim of logic as a science. 
 
 Divisions of Logic 
 
 Logic, as a science, consequently divides itself into two parts : 
 1. A systematic development of those principles or laws to 
 which the intelligence accords in all valid intellectual processes, 
 processes whose object is truth. 2. A similar development of 
 those principles to which the intelligence conforms, in all in- 
 valid processes of the class under consideration. Such is logic 
 as a science, in the sense in which we understand the subject 
 and in which we shall attempt to realize the idea. Xo one 
 will dissent from the above conception, but upon a single as-, 
 sumption, to wit, that the sphere assigned to the science is too 
 extensive, that sphere including all that has been commonly re- 
 ferred to the science and some things else supposed not to per- 
 tain to it. That this is the true and proper sphere of the 
 science, we argue from the following considerations. 
 
 Correctness of the above definition verified. 
 
 1. The above definition gives a perfect unity and definiteness 
 to our conceptions of the science, the very unity and definite- 
 
22 INTRODUCTION. 
 
 ness which characterize all correct definitions of any other 
 science. The truth of this statement is self-evident. 
 
 2. While the sphere here assigned to the science possesses 
 not only perfect unity and definiteness, but also exclusiveness, 
 occupying no department properly pertaining to any other 
 science, it also has throughout a fixed and definite relation to 
 all the other sciences, that is, it is what the science of logic 
 should be, the true and proper antecedent to them all. It does 
 not profess to teach what is true or what is false, in any sphere 
 occupied by any one of the sciences ; but it does aim to de- 
 velop those laws and principles, by which we can determine 
 whether any given procedure in the development of any of the 
 sciences, is or is not valid for the truth of what is referred 
 to in such process, and why such procedure is or is not thus 
 valid. This is precisely what no one of the sciences professes, 
 or aims, in any of its appropriate departments, to accomplish. 
 Yet what this science aims to accomplish, is just what is 
 needed, in all the sciences alike, in all intellectual processes 
 having truth for their object and aim. We certainly need 
 criteria by which valid processes may, in all cases, be deter- 
 mined and distinguished from those which are not valid. 
 Hence we remark, 
 
 3. That this idea when realized meets a fundamental want of 
 universal mind, a necessity which no other science does or can 
 meet. The navigator, when abroad upon the ocean, no more 
 needs tables and instruments by which he can determine his 
 latitude and longitude, than does universal mind, educated 
 mind especially, criteria by which it can judge correctly of the 
 character of its own intellectual processes. Logic, as now de- 
 fined, aims to meet this universal want, and when realized, 
 does most fully and perfectly meet it. When its sphere is con- 
 

 INTRODUCTION". 
 
 tracted within narrower limits than is here assigned to it, a fun- 
 damental want of universal mind is so far left unmet, and that 
 when we have no science, which, while moving in its proper 
 sphere, does or can meet that want. 
 
 4. No adequate reason can be assigned, why any department 
 of the sphere of this science, as above defined, should be as- 
 signed to logic, and any other department excluded from it. 
 Nor can any other science be named to which the department 
 excluded, can properly be assigned. We might, with the same 
 propriety, include the latter department in our definition of the 
 science and exclude the former, as to include the former and 
 exclude the latter. 
 
 5. All treatises, or most, at least, attempt to realize the full 
 idea of the science, as above defined, though not nnfrequently 
 in palpable contradiction to the fixed aim of the science, as 
 previously defined in such treatises. The science is sometimes 
 so defined, for example, that the only fallacies properly falling 
 under its cognizance, are those belonging to one class exclu- 
 sively, to wit, inferences deduced from premises whether true 
 or false, with which they (the premises) have no logical con- 
 nection. Yet, when such treatises come to treat of fallacies, 
 they discuss not only this, but eveiy other class of fallacies, and 
 attempt to give us universal criteria by which valid intellectual 
 processes may be distinguished from those which are not valid, 
 the very sphere and aim of logic, as above defined. Hence in 
 these illogical treatises, fallacies are discussed under three 
 classes the strictly logical, that is, those which fall within the 
 proper sphere and cognizance of logic, as defined the semi- 
 logical, those which partly do, and partly do not, belong to the 
 defined sphere of logic and the non-logical, those that logic, 
 as defined, has no business with whatever. It is just as wide a 
 
 ^ffoiXS 
 
24 INTRODUCTION. 
 
 departure from all true principles of scientific procedure, to 
 treat of non-logical fallacies, in a treatise on logic, as it would 
 to include a treatise of arithmetic in a system of geometry. 
 All fallacies are really and truly logical fallacies, or only a cer- 
 tain class of them should be discussed in a treatise on logic. 
 
 Logic as distinguished from Esthetics. 
 
 It may do something to render still more distinct and defi- 
 nite our conceptions of this science to compare its sphere and 
 aim with those of another, the science of esthetics. This last 
 has been commonly defined as the science of the beautiful in 
 nature and art. As pertaining to mind, its appropriate sphere 
 is t/ie creations of the imagination, the object of which is to 
 blend the elements of thought, not in harmony with things as 
 they are, but with the ideas of beauty, grandeur, sublimity, 
 perfection, &c. Esthetics, as a science, aims to develop those 
 laws and principles in conformity to which this faculty must 
 act, in order to realize the end referred to, to show what kind 
 of elements must be blended into a given conception, and how 
 they must be blended, so as to realize these ideas. Thus it 
 presents criteria by which we can distinguish the truly beauti- 
 ful from that which is not, in other words, the valid from the 
 invalid procedures of the imagination. 
 
 The true and proper aim of the understanding and judgment, 
 on the other hand, is to blend the elements of thought given by 
 the primary faculties into conceptions and judgments in harmo- 
 ny with things, not as they might or should exist, but as they 
 do exist. Logic aims to give those criteria by which we can 
 distinguish those procedures of these faculties which are to be 
 held as valid for realities, from those which are to be held as 
 not thus valid. Esthetics might, with some approach to truth. 
 
INTRODUCTION. 25 
 
 be defined as the logic of the imagination, while logic proper 
 has for its sphere the procedures of the understanding and 
 judgment, in all processes the aim of which is to realize in pro- 
 cesses of intuition, conception, judgment, and reasoning, the 
 idea of truth. 
 
 Accordance of the above conception of Logic with that given 
 by Kant. 
 
 The perfect accordance, in all essential particulars, of the con- 
 ception of logic above developed, with that given by Kant, will 
 appear manifest to all who are acquainted with his treatise on 
 this science. To evince that accordance, we need only, in con- 
 nection with his definition of the science above given, cite the 
 following passages from that treatise : " In logic we want to 
 know," he says, " not how the understanding is and thinks, and 
 how it has hitherto proceeded in thinking, but how it shall pro- 
 ceed. It is to teach the right use of the understanding," &c. 
 Further on, after giving precisely similar distinctions between 
 esthetics and logic that we have done, he presents the following 
 division of the latter science, a division which must have its ex- 
 clusive basis in a conception of the science strictly identical, in 
 all essential particulars, if not in all others, with that which we 
 have given : " We shall consequently have two parts of logic : 
 the analytic, which propounds the formal criteria of truth ; and 
 the dialectic, which comprises the marks and the rules, by which 
 we can know, that something does not agree with them. In 
 this sense the dialectic would be of great use as a cathartic of 
 the understanding." He then goes on to show that all other 
 conceptions of the science not accordant with this are "im- 
 proper" and "wrong." 
 
26 INTRODUCTION. 
 
 Accordance of the above idea of Logic with that set forth by 
 Sir William Hamilton. 
 
 In connection with the fact that Sir William Hamilton ac- 
 cords in general with the conception of logic as given by Kant, 
 the accordance of the idea of the former with that which we 
 have presented will be made sufficiently manifest through the 
 following paragraph selected from his article on Logic, found in 
 his Discussion on Philosophy and Literature, p. 136, as pub- 
 lished by the Harpers : 
 
 " We shall not dwell on what we conceive a very partial con- 
 ception of the science, that Dr. Whately makes the process of 
 reasoning not merely its principle, but even its adequate object, 
 those of simple apprehension and judgment being considered 
 not in themselves as constituent elements of thought, but simply 
 as subordinate to argumentation. In this view logic is made 
 controvertible with syllogistic. This view, which may be al- 
 lowed in so far as it applies to the logic contained in the Aristo- 
 telic treatises now extant, was held by several of the Arabian 
 schoolmen ; borrowed from them by the Oxford Crackenthrope, 
 it was adopted by Wallis ; and from Wallis it passed to Dr. 
 Whately. But, as applied to logic, in its own nature, this 
 opinion has been long rejected, on grounds superfluously con 
 elusive, by the immense majority even of the peripatetic dia 
 lecticians ; and not a single reason has been alleged by Dr. 
 Whately to induce us to waver in our belief, that the Imcs of 
 thought, and not the laws of reasoning, constitute the adequate 
 'object of the science. This error, which we cannot now refute, 
 would, however, be of comparatively little consequence, did it 
 not as is notoriously the case, in Dr. Whately 's Elements in- 
 duce a perfunctory consideration of the laws- of those faculties 
 
INTRODUCTION. 27 
 
 of thought ; these being viewed as only subsidiary to the pro- 
 cess of reasoning." 
 
 The object of logic, we repeat, is not to reveal or affirm what 
 is true or what is false in itself, that being the exclusive province 
 of the various special departments of mental operation. Its ex- 
 clusive object, on the other hand, is to develop and elucidate 
 those laws of thought by which we can determine whether any 
 given intellectual process, whatever its object may be, a process 
 which professedly reveals and establishes the truth in respect to 
 the object to which it pertains, is or is not valid 'for its truth, 
 and why it is to be held as thus valid or not valid. 
 
 Inadequate and false conceptions of this science. 
 
 It will add somewhat to the distinctness and definiteness of 
 our conceptions of this science, to compare the conceptions 
 which we have set forth, with certain others which we regard 
 as inadequate or wrong. Among these the following only de- 
 mand special notice. 
 
 The syllogistic idea. 
 
 The first which we adduce is what may not inappropriately be* 
 denominated the syllogistic idea, that which affirms that the ex- 
 clusive object of this science is to develop the laws of reasoning, 
 that is, to state what, in a process of reasoning, are and must be 
 the relations between the premises and conclusion, when the lat- 
 ter does or does not necessarily follow from the former. A 
 very few considerations only are requisite to show how funda- 
 mentally inadequate this idea is to represent the true and ap- 
 propriate sphere of this science. Take, as examples, the follow- 
 ing syllogisms : 
 
Iso INTRODUCTION. 
 
 All men are mortal ; 
 George is a man ; 
 Therefore, he is mortal. 
 
 The conclusion, in this instance, is not only true, hut it results 
 
 as a necessary deduction from the premises. Take now another 
 
 of a different character : 
 
 All mortal beings are men ; 
 Every brute is a mortal being ; 
 Therefore, every brute is a man 
 
 Here we have a false conclusion. It has the same necessary 
 logical connection with the premises, however, that the conclu- 
 sion of the former syllogism has. Again : 
 
 All bipeds are mortal ; 
 All men are mortal ; 
 Therefore, all men are bipeds. 
 
 In this case a true conclusion is deduced from premises with 
 which it has no logical connection. Further : 
 
 All mortal beings are men ; 
 
 All brutes are men ; 
 
 Therefore, all brutes are mortal beings. 
 
 Here, also, we have a conclusion which is true in itself, hut 
 which is deduced from premises, hoth of which are false, and 
 with which it has no logical connection. Again : 
 
 All animals are mortal ; 
 All men are mortal ; 
 Therefore, all men are animals. 
 
 In this syllogism, all the propositions are true ; but the con- 
 clusion has no logical connection with the premises from which . 
 it is deduced. Once more : 
 
 All mortal beings are men ; 
 George is a mortal being ; 
 Therefore, he is a man. 
 

 INTRODUCTION. 
 
 The conclusion in this case is true, and is necessarily con- 
 nected with the premises. Still there is a fallacy in the argu- 
 ment, one premise being false. 
 
 We have in the five last syllogisms, five different kinds of fal- 
 lacies, and it would seem that the science of logic ought to give 
 us principles by which we can determine, in each case alike, 
 what is the nature and character of the fallacy, and why it is to 
 be regarded as such. Yet with the first and last of the five, 
 logic, according to the present definition, has nothing whatever 
 to do. There being, in these cases, a necessary connection be- 
 tween the premises and conclusion, every condition required 
 by the science has been fulfilled, and its mission is at an end in 
 respect to them. At the same time, we have no other science 
 to which it pertains to trace out the source of the fallacy in 
 either case, and tell us where it may be found, and why it 
 should be regarded as a fallacy. Numbers three, four, and 
 five, only, are logical fallacies, according to this definition, and 
 would properly be designated as fallacies in reasoning by the 
 science, as thus defined. 
 
 Of the six syllogisms, in three of them, numbers one, two, 
 and six, the conclusions have a necessary connection with the 
 premises, and the argument throughout, in each case, alike 
 fulfils all the conditions of the science, as now defined : in the 
 other three, though in the last two of them the intellectual pro- 
 cedure is fundamentally fallacious, and the propositions all true 
 in the first, the whole of these syllogisms, we say must be 
 classed together under the same category in a treatise upon 
 this science, a treatise developed in strict consistency with 
 such an idea of its exclusive sphere and design. Now we 
 affirm that logic, when developed according to the true con- 
 ception of its entire and proper domain and adequate aims 
 
30 INTRODUCTION. 
 
 as a science, will not thus confound things which so fundamen- 
 tally dhTer. 
 
 In numbers one and two, each conclusion has the same neces- 
 sary connection with its premises, yet the process of thought 
 is in the first case valid for the truth of the conclusion, and not 
 valid in the last. In the last four syllogisms, there is. the same 
 want of validity, whether the conclusion is true or false. Sup- 
 pose we ask for the reason or grounds of the difference. To 
 answer such an inquiry our investigations must, in every case, 
 take a Avider range than the mere consideration of the logical 
 connection between the premises and the conclusion, and must 
 in all instances take into account the conceptions represented by 
 the various terms of the syllogisms, the judgments represented 
 in the propositions of which the syllogisms are constituted, and 
 the connections between the premises and the conclusion in the 
 same. We will take the first syllogism in illustration. In this 
 syllogism there are three conceptions represented by the terms 
 men, mortal, and George. On examination they will be found 
 to possess certain fundamental characteristics common to all 
 others which appear in judgments really and truly valid for 
 the reality and character of the objects to which they pertain, 
 and which consequently distinguish all conceptions which must 
 be held as true from those which must not, as elements of such 
 judgments, be thus held. Relations equally fundamental and 
 peculiar will be found to obtain between the subject and predi- 
 cate in each of the premises of such a syllogism, and also be- 
 tween the premises themselves and the conclusion deduced 
 from them. The characteristics of the conceptions, on the one 
 hand, and those of the relations between the subject and predi- 
 cate in each of the premises, and between said premises and the 
 conclusion deduced from them, on the other, characteristics and 
 
INTRODUCTION. 
 
 relations which may bo determined and defined, constitute the 
 laws of thought by which all valid judgments and processes of 
 reasoning may be distinguished from those which are not valid, 
 inasmuch as all valid processes do and must possess throughout 
 these identical characteristics, and all not valid must be thus 
 regarded, for the reason that they violate these rules in seme 
 particular or otherj some in the relations affirmed to exist be- 
 tween the premises and conclusion, others, in those existing be- 
 tween the subject and predicate in one or the other of the 
 premises, or in both together, and others because they are con- 
 stituted of invalid conceptions. !N"ow why should it be affirmed 
 that one class of these laws of thought come within the appro- 
 priate sphere of logic, and that either of the others should be 
 excluded from it ? No reason whatever can be assigned for 
 such an assumption. If any individual should accomplish what 
 is needed in regard to any one of these departments, the rela- 
 tions between the premises and conclusion in processes of* rea- 
 soning, for example, he would so far meet one important logical 
 demand of universal mind. If, when he has done thus much, 
 he should put forward the claim, that he has occupied the entire 
 sphere of the science of logic, he would simply reveal the fact 
 that he entertains too limited conceptions of that science. 
 
 Conceptions, judgments, and deductions from judgments pre- 
 sented as premises, these together, Ave repeat, constitute the 
 proper sphere and object of this science. Its object is to de- 
 velop and elucidate those laws of thought by which valid con- 
 ceptions, valid judgments, and valid deductions, can be distin- 
 guished from those which are not valid, and by which it can be 
 shown in what respects and for what reasons any given intel- 
 lectual process is or is not thus valid. 
 
INTRODUCTION". 
 
 of Dr. Whately and others. 
 
 " Logic ' r.ays Dr. Whately, and we will give the definition 
 in full, " k, l\<e most extensive sense which the name can with 
 propriety he made to hear, may be considered as the science, 
 and also as the art, of reasoning. It investigates the principles 
 on which argumentation is conducted, and furnishes rules to se- 
 cure the mind from error in its deductions. Its most appro- 
 priate office, however, is that of instituting an analysis of the 
 process of the mind in reasoning ; and in this point of view, it 
 is, as has been stated, strictly a science/ while, considered in 
 reference to the practical rules above-mentioned, it may be 
 called the art of reasoning. This distinction, as will hereafter 
 appear, has been overlooked, or not clearly pointed out by most 
 writers on the subject ; logic having been in general regarded 
 as merely an art ; and its claim to hold a place among the 
 sciences having been expressly denied." 
 
 *In the above paragraph there are, as shown most indubitably 
 by Sir William Hamilton, at least three important errors. 
 
 The first that we notice is an historical one, the statement, that 
 logicians have generally considered logic as an art, and not a 
 science, whereas in the language of the author just named, " the 
 great majority of logicians have regarded logic as a science, and 
 expressly denied it to be an art. This is the oldest as well as 
 the most general opinion." 
 
 The next error that we notice pertains to the nature of logic 
 itself. It is in fact in no proper sense an art of reasoning, its 
 fundamental aim, as far as reasoning is concerned, being not to 
 teach us how to reason, but to enable us to judge, upon scien- 
 tific principles, of proces'ses of reasoning. We all know that an 
 individual may be an excellent and scientific judge of processes 
 
INTRODUCTION. 33 
 
 f reasoning, and practically a very bad reasoner. Yet science 
 nds to render practice more perfect. In this indirect and 
 secondary sense logic is an art of reasoning. 
 
 The third and last error that we notice, is that of a too lim- 
 ited and inadequate conception of the true sphere and conse- 
 quent full aim of the science. The error to which we now re- 
 fer, consists in the supposition that the laws of reasoning, instead 
 of the laws of thought, constitute the real sphere and object of 
 the science. This error we have already exposed in another 
 connection. Nothing in addition is therefore required on the 
 subject. 
 
 The idea that " the adequate object of Logic is language?'' 
 
 As Dr. Whately proceeds in his elucidation of what he re- 
 gards as the true and proper conception of this science, he has 
 fallen into another important error, an error which has been so 
 fully and so well exposed by Sir William Hamilton, that we 
 will simply present his statement of it together with his exposi- 
 tion of the same, without any additional remarks of our own : 
 
 " But Dr. "Whately is not only ambiguous ; he is contradicto- 
 ry. We have seen that, in some places, he makes the process 
 of reasoning the adequate object of logic ; what shall we think, 
 when we find, that, in others, he states that the total or ade 
 quate object of logic is language ? But, as there cannot be two 
 adequate objects, and as language and the operation of reason- 
 ing are not the same, there is, therefore, a contradiction. ' In 
 introducing,' he says, ' the mention of language, previously to 
 the definition of logic, I have departed from established prac- 
 tice, in order that it may be clearly understood, that logic is 
 entirely conversant about language ; a truth which most wri- 
 ters on the subject, if indeed they were fully aware of it them- 
 
34 INTRODUCTION. 
 
 selves, have certainly not taken due care to impress on their 
 readers' (p. 56). And again: 'Logic is wholly concerned in 
 the use of language' (p. 74). 
 
 " The term logic (as also dialectic) is of ambiguous deriva- 
 tion. It may either be derived from "koyog (ivSia8e<ros), reason, 
 or our intellectual faculties in general ; or, from \6yog (* po-cpopj- 
 xos), speech or language, by which these are expressed. The 
 science of logic may, in like manner, be viewed either 1. As 
 adequately and essentially conversant about the former (the in- 
 ternal Xo'yoff, verbum mentale), and partially and accidentally, 
 about the latter (the external \6yog, verbum oris) ; or, 2. As 
 adequately and essentially conversant about the latter, partially 
 and accidentally about the former. 
 
 " The first opinion has been held by the great majority of lo- 
 gicians, ancient and modern. The second, of which some traces 
 may be found in the Greek commentators of Aristotle, and in 
 the more ancient Nominalists, during the middle ages (for the 
 later scholastic Nominalists, to whom this doctrine is generally, 
 but falsely attributed, held in reality the former opinion), was 
 only fully developed in modern times by philosophers, of whom 
 Hobbs may be regarded as principal. In making the analysis 
 of the operation of reasoning the appropriate office of logic, 
 Dr. Whately adopts the first of these opinions ; in making logic 
 entirely conversant about language, he adopts the second. We 
 can hardly, however, believe that he seriously entertained this 
 last. It is expressly contradicted by Aristotle (Analyt. Part i. 
 10,. 1). It involves a psychological hypothesis in regard to 
 the absolute dependence of the mental faculties on language, 
 once and again refuted, which we are confident that Dr. 
 Whately never could sanction ; and, finally, it is at variance 
 with sundry passages of the Elements, where a doctrine appa- 
 
INTRODUCTION. So 
 
 rently very ditTerent is advanced. But, be his doctrine what 
 it may, precision and perspicuity are not the qualities we should 
 think of applying to it." 
 
 General division of topics. 
 
 We have now sufficiently indicated our own conception of 
 the science under consideration. The way has thus been pre- 
 pared to enter intelligently upon the elucidation of the different 
 departments of our subject, which we shall treat of under the 
 following general arrangement of topics : 
 
 I. The necessary laws of thought to which the intelligence 
 does and must conform in all valid conceptions, judgments, and 
 deductions, or processes of reasoning. This department of the 
 science is denominated by Kant, the Analytic. For the sake 
 of convenience we shall include what we have to say on this 
 topic, under this same general title. 
 
 II. The doctrine of fallacies which the philosopher just named 
 denominates the Dialectic, and which we shall attempt to eluci- 
 date under the same title. 
 
 III. The doctrine of Method, or the rules in conformity to 
 which all scientific procedures should be conducted. 
 
 IV. Certain general and specific applications of the principles 
 elucidated, applications adduced for the purpose of exemplify- 
 ing the importance of the science, and the manner of applying 
 its principles. 
 
 The first two topics embrace the entire field of logic consid- 
 ered as a science. The last two are presented for the purpose 
 of elucidation. 
 
LOGIC. 
 
 PART I. 
 
 THE ANALYTIC. 
 
 CHAPTER I. 
 
 ANALYTIC OF CONCEPTIONS AND TEEMS. 
 
 Section I. Of Conceptions. 
 
 Conceptions defined. 
 
 A conception, or notion, is a mental apprehension of some ob- 
 ject or objects, an apprehension which we express by such terms 
 as George, man, tree, plant, animal, &c. Such apprehensions 
 we represent by the general term conception. 
 
 Origin and constituent elements of Conceptions. 
 
 Knowledge, with the human intelligence, begins not with 
 conceptions but with intuitions, or a direct and immediate per- 
 ception of the reality or qualities of objects. As shown in the 
 Intellectual Philosophy,* and as now generally admitted by phi- 
 losophers, the faculties of intuition, or original perception, are 
 three, Sense, the faculty of external percejrtion, the faculty 
 which perceives the qualities of external material substances 
 Consciousness, the faculty of internal perception, the faculty 
 which perceives and apprehends the operations or phenomena 
 of the mind itself and Reason, which apprehends the logical 
 antecedents of phenomena perceived by Sense and Conscious- 
 
 * A System of Intellectual Philosophy, by Kev. Asa Mahan, j 
 Barnes & Co. 
 
 . 476. New York, A. 8. 
 
ness, to wit, truths necessary and universal, such as space, time, 
 substance, cause, personal identity, the infinite, &c. 
 
 In intuition each particular quality or phenomenon, together 
 with its logical antecedent, is given singly and by itself. From 
 the nature of the case, it cannot be otherwise, the quality being, 
 in all instances, the object of direct and immediate perception 
 or apprehension. By this we would not be understood as affirm- 
 ing that different qualities may not each be the object of simul- 
 taneous perception with others. This we believe. Yet, as each 
 quality is itself individual and single, and is the object of direct 
 and immediate perception, such quality must be originally given 
 singly and by itself. The same holds true of the logical ante- 
 cedent of such quality, as given by reason. Each quality has 
 its special logical antecedent ; and as the quality is originally 
 given singly and by itself, the same must be held equally true 
 of its logical antecedent. The logical antecedent of the reality 
 of the quality of extension, for example, is that of an extended 
 substance, quality necessarily supposing as the condition of its 
 existence, the reality of substance, it being impossible to conceive 
 of the reality of the former, without supposing that of the latter. 
 The same holds true of all other qualities, or phenomena, of 
 every kind. 
 
 The origin and constituent elements of conceptions of every 
 kind now admit of a ready statement and explanation. When 
 a quality is perceived, and its logical antecedent apprehended, we 
 have a secondary operation of the intelligence, an operation in 
 which the apprehension of the quality and that of its logical an- 
 tecedent are united into a conception of a particular object. As 
 other qualities of the same object together with their logical an- 
 tecedents are perceived and apprehended, they are blended into 
 the same conception, which thus becomes more or less complete, 
 as it more or less fully represents its object. Thus if the object 
 is material, for example, a conception of it is formed as a body 
 existing in time and space, and having definite extension, 
 form, color, &c. On the perception of subjective phenomena, 
 we obtain, in a similar manner, the conception of mind, as a 
 substance possessing the powers and susceptibility of thought, 
 

 ANALYTIC OF CONCEPTION 
 
 feeling, and voluntary determination. All the elements which 
 do or can enter into conceptions must be given by the primary 
 faculties referred to, as these are the only original sources of 
 cognition. The function which thus blends the original ele- 
 ments of thought (intuitions) into conceptions, is denominated 
 the understanding ; and logic, so far as it pertains to concep- 
 tions, is the science of the laws of the understanding. 
 
 Error commences, not with Intuitions, but Conceptions. 
 
 As intuition, in all instances, pertains directly, immediately, 
 and singly to its respective object, the fact of such intuitive per- 
 ception must always be held as valid for the reality of its object. 
 A denial of this principle is a formal impeachment of the validi- 
 ty of the intelligence, as a faculty of knowledge, and nullifies all 
 attempts at knowledge of every kind. All forms of scientific 
 procedure also have their basis in the assumed truth of this 
 principle, the validity of intuition for the reality of its objects. 
 Nor can any reasons be assigned for the assumption that any 
 one class of* intuitions should be regarded as thus valid, and 
 others not. No principles, therefore, are required to enable us 
 to distinguish valid from invalid intuitions. 
 
 One universal division of conceptions, however, is that of true 
 and false. Here valid and invalid cognitions first appear in the 
 process of thought, and hence the necessity of valid criteria by 
 which the one class may be distinguished from the other. 
 
 Universal characteristics of all valid and invalid Conceptions. 
 
 The universal characteristics which distinguish all conceptions 
 which should be held as valid for the reality and character of 
 their respective objects, from conceptions which should not be 
 thus held, may now be very readily and distinctly pointed out. 
 
 1. All conceptions which embrace those elements only, which 
 have been really and truly given by intuition relatively to any 
 object, must be held as valid throughout for the reality and 
 character of such object. 
 
40 LOGIC. 
 
 2. All conceptions also must be held as thus valid which em- 
 brace such intuitions exclusively, together with their necessary 
 logical antecedents. If the intuition is thus valid, so must all 
 its necessary logical antecedents and consequents be. Of this 
 there can be no doubt. 
 
 3. All conceptions, on the other hand, which embrace any 
 elements not thus given in respect to the objects of said concep- 
 tions, must be held as not valid for such objects. 
 
 The truth of the above principles is serf-evident. The only 
 question to be determined is, how may we know when a given 
 conception has one or the other of the above characteristics ? 
 To accomplish this end is the object of the following distinctions 
 and elucidations. 
 
 Spontaneous and Reflective Conceptions. 
 
 There are two states in which each conception may be con- 
 templated to wit, as it first appears in the intelligence through 
 the spontaneous action of the understanding ; and as it appears 
 when each element embraced in it has been the qbject of dis- 
 tinct reflection, and the entire conception, with all its constituent 
 elements, is presented in consciousness in a distinct and reflec- 
 tive form. All the elements embraced in the conception, in its 
 reflective, is really found in it when in its spontaneous form. 
 In the latter state, however, each element is given obscurely 
 and indistinctly. In the former, in a form distinct and well 
 defined, as a part of the whole conception. 
 
 First and second Conceptions. 
 
 Another important distinction between conceptions, a distinc- 
 tion for which we are indebted to Sir William Hamilton, and 
 which was first developed, as b states, by Arabian philosophers, 
 is that of first and second conceptions. " A first notion" (con- 
 ception), says the writer above named, " is the concept of a 
 thing as it exists in itself, and independent of any operation of 
 thought, as John, man, animal, &c. A second notion is the 
 

 ANALYTIC OF CONCKPTIONS 
 
 concept, not of an object as it is in reality, but of the mode un- 
 der which it is thought by the mind, as individual, species, ge- 
 nus, &c. The former is the concept of a thing real imme- 
 diate direct ; the latter is the concept of a concept formal 
 mediate reflex." In other words, when a conception is contem- 
 plated as immediately pertaining to its object, as it is in itself, 
 and that without reference to other conceptions, it is denomi- 
 nated a first conception. When it is contemplated in its rela- 
 tion to other conceptions, and as being capable of being classed 
 with, or separated from them, then it is denominated a second 
 conception. When, for example, we contemplate the concep- 
 tions represented by such terms as John, man, animal, &c, not 
 as merely pertaining to some object, or class of objects, but in 
 reference to the mode or form in which they pertain to them, 
 that is, as individual, species, or genus, and consequently as ca- 
 pable of being classed with others which pertain, in a similar 
 manner, to their object, these, we repeat, are denominated 
 second conceptions. It is with conceptions of this class espe- 
 cially that logic, as a science, has to do. Phenomena must be 
 classified, before their laws can be determined. So with con- 
 ceptions. Before the laws of thought can be determined, 
 thought itself must be classified by reflection. 
 
 Matter and sphere of Conception. 
 
 By the matter of the conception is meant, the intuitions ac- 
 tually included in it. By the sphere of a conception, we mean 
 the number of individuals embraced under it. The conceptions 
 represented by the term John, for example, as to its matter, 
 represents all the elements given by intuition, in respect to this 
 individual, and as to its sphere, is limited to this one person, it 
 being applicable to none other. The conception represented 
 by the term man, as to its ma' ir, represents all intuitions, 
 and those only which are common to all individuals of the 
 race ; and as to its sphere, it comprehends every such individual. 
 
 " The matter and sphere of a conception," as Kant observes, 
 " bear to one another a converse relation." The more elements 
 
42 LOGIC. 
 
 (intuitions) a conception embraces, that is, the more it contains 
 so far as its matter is concerned, the less number of individuals 
 does it represent, that is, the narrower is its sphere, and vice 
 versa. 
 
 The greatness or narrowness of the sphere of a conception 
 depends upon the number of individuals which take rank un- 
 der it. 
 
 Individual, generic or generical, and specific or specifical Con- 
 ceptions. 
 
 Conceptions which pertain to individuals are denominated in- 
 dividual conceptions. Those which pertain to kinds which em- 
 brace, not individuals as such, but sorts or classes of individuals 
 (species) under them, are denominated generic or generical con- 
 ceptions. Those, on the other hand, which pertain to the sorts 
 (species) which are contained under the generic or generical 
 conception, are denominated specific or specifical conceptions. 
 The individual conception embraces all the elements given by 
 intuition relatively to the one object to which it (the concep- 
 tion) pertains. The generic conception embraces only the in- 
 tuitions which are common to all the specific conceptions which 
 rank under it, and to all the individuals which rank xmder its 
 various specific conceptions. The specific conception embraces 
 all the elements of intuition belonging to the generic, and also 
 all that belong to the particular class which it represents, and 
 which are not found in the class from which the former is sepa- 
 rated. 
 
 . Highest genus and lowest species. 
 
 It is evident that a conception may be generic relatively to 
 another and lower conception, and itself specifical, relatively to 
 one pertaining to a higher genus. Thus the conception repre- 
 sented by the term man, is generic relatively to those which 
 pertain to different orders of the race, and at the same time, 
 specifical relatively to that of a higher genus represented by 
 such terms as rational beings, including as a genus men, an- 
 gels, &c. 
 

 ANALYTIC OF CONCEPTIONS. 
 
 A genus which is not a species is called the highest genus. A 
 species which is not a genus, is called the lowest species. The 
 following remarks of Kant upon this subject are worthy of 
 special regard : 
 
 " If we conceive of a series of several conceptions subordinate 
 to one another for example, iron, metal, body, substance, thing 
 we may obtain higher and higher genera ; for every species is 
 always to be considered as a genus with regard to its inferior 
 conception. For instance, the conception of a man being ge- 
 nerical with regard to that of a philosopher, till we at last arrive 
 at a genus that cannot be a species again. And one of that sort 
 we must finally reach ; because there must, at last, be a higher 
 conception, from which, as such, nothing can be further ab- 
 stracted without the whole conception vanishing. But in the 
 whole series of species and of genera there is no such thing as 
 a lowest conception of species, under which no other conception 
 or species is contained ; because one of that sort could not pos- 
 sibly be determined. For, if we have a conception, which Ave 
 apply immediately to individuals, specific distinctions, which we 
 do not notice, or to which we pay no attention, may exist in 
 respect to it. There are no lowest conceptions, but compara- 
 tively, for use, which have obtained this signification, as it were, 
 by convention, provided that we are agreed not to go deeper 
 in a certain matter. 
 
 " Relatively to the determination of the specifical and of the 
 generical conception, then, this universal law There is a genus 
 that cannot be any more a species ; but there are no species but 
 what may become genera again holds good." 
 
 Empirical and national Conceptions. 
 
 Intuitions are also classed as empirical and rational. All in- 
 tuitions derived through perceptions external and internal, that 
 is, through the intuitions of sense and consciousness, are called 
 empirical, being derived through experience. Those, on the 
 other hand, which sustain the relation of logical antecedents to 
 empirical intuitions, such, for example, as the intuitions of space, 
 
44 LOGIC. 
 
 time, cause, substance, &c, are denominated rational intuitions, 
 being the intuitions of that faculty or function of the intelligence 
 denominated the reason. 
 
 Now conceptions, the leading elements of which are intuitions 
 of qualities of substances material and mental in the world with- 
 in and around us, qualities which are the objects of perception, 
 external and internal, are called empirical conceptions. All 
 such conceptions are constituted of two classes of elements, the 
 empirical and rational, that is, intuitions of sense and conscious- 
 ness, on the one hand, and of reason on the other, all such ob- 
 jects, for example, being apprehended as substances or causes 
 existing in time and space, &c, and as possessed of certian qual- 
 ities and attributes. The latter class of elements are given by 
 immediate perceptions, external or internal, and the former by 
 the reason. Such conceptions are denominated empirical. 
 
 When the rational intuition becomes itself the object of re- 
 flection and abstraction, and the intelligence apprehends its 
 object in a distinct and reflective form, as it is in itself, and in its 
 relations to objects of empirical conceptions, we then have what 
 is denominated rational conceptions : those of time, as the place 
 of events ; of space, as the place of bodies ; of substances, as the 
 subjects of qualities ; and of causes, as the origin of events, &c. 
 Rational conceptions sustain to the empirical the relations of 
 logical antecedents, the reality of the objects of the latter being 
 conceivable and possible, but upon the condition of that of the 
 objects of the former class. Thus the reality of body is neither 
 conceivable nor possible, but upon the supposition of the reality 
 of space. So of time relatively to succession, of substance rela- 
 tively to qualities, and of cause in respect to events. If there 
 is no space, no time, no substance, or causes, there can be no 
 bodies, succession, qualities, nor events. The conceptions of 
 space, time, substance, cause," &c, are therefore denominated 
 the logical antecedents of those of body, succession, qualities, 
 and events. So in all other instances. ' 
 
ANALYTIC OF CONCEPTIONS. 
 
 Presentative and representative 
 
 Sir William Hamilton has classed all our knowledge under 
 two divisions that which is derived by direct and immediate 
 intuition of the qualities of objects and that which pertains to 
 such qualities mediately, through the consciousness of sensa- 
 tions, for example. Qf the first kind are our intuitions of the 
 primary qualities of matter, those which belong to matter as 
 such for example, extension, form, &c. Our intuitions of the 
 secondary qualities, such as taste, smell, and soimd, are not di r 
 rect and immediate, but indirect and mediate, that is, through 
 the consciousness of sensations. Such intuitions are therefore 
 called representative. Our intuitions of the secundo-primary 
 qualities, on the other hand, those qualities which distinguish 
 one class of material substances from another, such, for example, 
 as gravity, cohesion, &c, are partly presentative and partly rep- 
 resentative. 
 
 Conceptions constituted of presentative intuitions may be 
 called presentative conceptions. Those constituted of the other 
 class would then be denominated representative. The same 
 conception may partake partly of one, and partly of the other 
 character. 
 
 Abstract and concrete Conceptions. 
 
 Conceptions also are properly classed as abstract and con- 
 crete. The former pertain to some single quality given by in- 
 tuition, irrespective of the particular object to which such quali- 
 ty belongs, or to which the intuition pertains conceptions rep- 
 resented by such terms as redness, whiteness, roundness, Tight- 
 ness, &c. 
 
 Concrete conceptions pertain to. their objects as they actually 
 exist, and combine all the elements given by intuition relatively 
 to such objects conceptions expressed by such concrete terms 
 as George, man, animal, &c. 
 
Positive, privative, and negative Conceptions. 
 
 Conceptions which embrace those intuitions only which are 
 actually given by intuition in respect to their objects, and refer 
 to their objects as actually possessed of the qualites which such 
 intuitions embrace, are called positive ; such conceptions, for ex- 
 ample, as are represented by such terms as sound, speech, a 
 man speaking, &c. Conceptions which pertain to their objects 
 as void of certain qualities which might be supposed to have 
 been given by intuition as pertaining to the object, are denomi- 
 nated privative conceptions ; conceptions, for example, ex- 
 pressed by such terms as deafness, dumbness, a man silent, &c. 
 When, on the other hand, the conception pertains to its object, 
 as merely void of certain characteristics, or as by no possibility 
 possessed of them, then it is denominated a negative concep- 
 tion. Such conceptions are represented by such terms as a 
 dumb statue, a lifeless corpse, &c. 
 
 Conception classed under the principle of unity, plurality, and 
 totality. 
 
 . Every conception pertains to its object as numerically one 
 an individual, John ; or as many a multitude ; a number of 
 individuals as John, Thomas, Samuel, &c. ; or as a totality, a 
 whole of which each individual is an integral part a troop of 
 horse, &c. For this reason they are classed under the catego- 
 ries above named. 
 
 Inferior and superior Conceptions. 
 
 When one conception takes rank as a species under another 
 as its genus, as, for example, the conceptions of the various spe- 
 cies of fruit-bearing and forest trees ranked under that of the 
 genus tree, the former class of conceptions are denominated in- 
 ferior, and the latter superior conceptions. 
 
 "The inferior conception," as Kant well observes, "is not 
 contained in the superior, for it contains more in itself than the 
 

 pk 
 
 ANALYTIC OF COXCEPTIONS. 47 
 
 superior, but is contained under it, because the superior contains 
 the ground of the cognition of the inferior." We know the ap- 
 
 Le-tree, as a tree, for example, through the superior conception 
 
 (presented by the term tree. 
 
 Concrete and characteristic Conceptions. 
 
 We commonly have two classes of conceptions relatively to 
 the same object, the one embracing in concrete all the ele- 
 ments given by intuition in respect to the object, and the other 
 embracing those only which peculiarize and distinguish that ob- 
 ject from all others. The former class of conceptions Ave have 
 already designated. The latter may be denominated charac- 
 teristic conceptions. It is through this conception that objects 
 are distinguished one from another, recognized and classified. 
 
 Laics of thought pertaining to the validity of Conceptions. 
 
 We are now prepared to state the general laws of thought 
 pertaining to the validity of conceptions. All conceptions, as 
 we have seen, together with all their logical antecedents and 
 consequents, are to be held as valid for their objects concep- 
 tions which are constituted of real intuitions in respect to such 
 objects. Just so far as any conception is constituted of intui- 
 tions not thus given, it is not thus valid. These are the general 
 laws. A conception, we would further state, is valid when, and 
 only when, all judgments legitimately deduced from it are 
 themselves valid in respect to their object. How often, for ex- 
 ample, when certain judgments are expressed in regard to per- 
 sons or objects do we hear the reply, "You are totally mis- 
 taken in your conception of such person or object ;" or, " That 
 judgment is based upon a total misconception of its object;" or, 
 "You are right in your conception," &c. Wrong conceptions 
 lead to misjudgments. Let us now apply them to particular 
 conceptions and to particular classes of conceptions. 
 
Particular ; general, and abstract Conceptions. 
 
 Particular conceptions are valid when, and only when, such 
 conceptions embrace no elements hut actual intuitions, empiri- 
 cal and rational in respect to such objects. Intuitions with all 
 their necessary or logical antecedents and consequents, being 
 thus valid, the same must be true of conceptions into which 
 such intuitions only enter as constituent elements. This holds 
 true, whether the conception relative to its object is complete 
 or incomplete, that is, whether it represents the whole, or only 
 a, part of the qualities of its object ; for whatever is necessarily 
 implied in the existence of a quality, must be true of all objects 
 to which the quality pertains, and that whether it exists in such 
 objects in connection with other qualities or not. 
 
 For this reason, abstract conceptions, with all their necessary 
 antecedents and consequents, must be valid for their objects. 
 General conceptions are valid, when they embrace those ele- 
 ments only which are common to every particular conception 
 contained under it, and when each of the former embrace those 
 elements only which are actually given by intuition relatively 
 to its object. This for reasons above stated holds true, whether 
 the general conception be complete or incomplete. 
 
 Individual, specifical, and <; 
 
 What has been said of particular, being applicable in all re- 
 spects to all individual conceptions, nothing further need be 
 added in respect to the latter. 
 
 When individual conceptions ranking under the specifical are 
 valid, the latter are also valid for their objects, when they 
 embrace all the elements contained in the generic, together with 
 all those that are common to all the individual conceptions 
 which rank under the specifical. Thus, for example, the specifi- 
 cal conception represented by the term apple-tree is valid, 
 when said conception embraces all the elements contained in 
 the conception represented by the term tree, together with all 
 those common to all valid conceptions pertaining to all apple- 
 

 ANALYTIC OF CONCEPTIONS. 
 
 trees of every kind and sort. So of all other speeifical concep- 
 tions. 
 
 Generical conceptions are valid when they include those ele- 
 ments only strictly common to all valid speeifical ones contained 
 under the former. 
 
 Presentative and representative Conceptions. 
 
 Preventative conceptions, those, for example, which are con- 
 stituted of intuitions pertaining to the primary and secundo- 
 primary qualities of matter, must be valid absolutely for their 
 objects. This is self-evident. All conceptions also, so far forth 
 as they are constituted of such conceptions, are thus valid. 
 
 Representative conceptions, on the other hand, can, from the 
 nature of the case, have only a relative validity. Our knowl- 
 edge of the secondary qualities of matter, for example, is me- 
 diate, through the consciousness of sensations. The subjects of 
 such qualities, therefore, are known to us only as the otherwise 
 unperceived causes of such sensations. Our conceptions of 
 them, therefore, are valid in this sense only, that constituted 
 as our sensibility now is, there is in sixch objects a power thus 
 to affect us. Our presentative conceptions are valid, not for 
 ourselves merely, but for all intelligents. Our representative 
 conceptions are valid only for beings constituted in respect to 
 their sensitivity, as we are, and when in our circumstances, 
 questions which can be resolved only by a reference to general 
 experience. 
 
 The same conceptions are often constituted of presentative 
 and representative intuitions, and are, consequently, in corre- 
 sponding degree absolutely and relatively valid. 
 
 Concrete and characteristic Conceptions. 
 
 Concrete conceptions are valid, when they are constituted 
 exclusively of actual intuitions in respect to their object, and 
 when they embrace all the intuitions thus given, and as given. 
 
 Characteristic conceptions are valid, when they are consfci- 
 
50 LOGIC. 
 
 tuted of such intuitions of those qualities which belong exclu- 
 sively to the object of said conceptions, and which are always 
 connected with them. Let A, for example, represent some ob- 
 ject or class of objects, and B a quality which belongs to no 
 object but A, and is always present as a constituent element 
 of A. The conception represented by the term B, is valid as a 
 valid characteristic conception of A. When the quality repre- 
 sented by the term B appears, the presence of all that are rep- 
 resented by A may be affirmed. 
 
 A conception may often be assumed as valid for ordinary 
 practical purposes, which should not be assumed as the basis of 
 any truly scientific procedure. 
 
 Inferior and superior Conceptions. 
 
 The rules just stated in respect to individual, specifical, and 
 generic conceptions, embrace all that need be said of inferior 
 and superior ones, the latter being only different forms of rep- 
 resenting the former. 
 
 Empirical and rational Conceptions. 
 
 All empirical conceptions fall directly under the laws and 
 rules already defined and elucidated. We have occasion, 
 therefore, to speak only of the latter class, those which sustain 
 to the former the relation of logical antecedents. If any con- 
 ception is to be held as valid for its object, all that is contained 
 and implied in its logical antecedents must be regarded as 
 equally valid for the same object. A fundamental element of 
 our conception of body, for example, is that of a substance con- 
 tained in space, and which occupies space. Whatever, there- 
 fore, is necessarily implied in the conception of the latter, must 
 be absolutely valid for the object of the former conception. 
 The same holds true of all other rational intuitions. All the 
 necessary logical antecedents of a valid intuition must be just 
 as valid as the intuition itself in respect to the object of said in- 
 tuition. The validity of the rational conception, therefore, can 
 
be 
 
 ANALYTIC OF TERMS. 
 
 >e denied but upon one assumption, the absolute objective in- 
 validity of all empirical conceptions, together with that of the 
 intuitions of which the former are constituted. This would be 
 an utter and universal impeachment of the intelligence itself, 
 as a faculty of knowledge, and would annihilate the validity of 
 the impeachment itself. 
 
 All conceptions conforming to the principles above defined 
 are to be held as valid. All violations, in whole or in part, of any 
 of those principles are to be held as in a corresponding degree 
 invalid. How conceptions became thus vitiated, it will be our 
 object to show, when we come to the Dialectic, the inv T estiga* 
 tion of the sources of fallacy. 
 
 Section II. Of Teems. 
 
 Very little is requisite in regard to the subject of the present 
 section, to wit, terms. In logic a conception, or notion, ex- 
 pressed in language is called a term. All that is employed for 
 this purpose, that is, to represent the conception, is included in 
 this definition. 
 
 It is evident from the above definition, that a term may con- 
 sist of one, or many words ; as, man, or a man on horseback, 
 a horseman, or a troop of horse, &c. 
 
 Singular and common Terms. Significatss. 
 
 In the science of logic, terms are divided into two classes, 
 singular and common. All terms which represent individuals, 
 or single objects only, are called singular terms, as George, the 
 Hudson, New York, &c. Those, on the other hand, which 
 represent classes of individuals, as man, river, mountain, &c, 
 are called common terms. The individuals which a common 
 term represents are denominated its significates. 
 
 Relations of Logic to Terms. 
 
 Logic has to do with terms only indirectly, that is, as the 
 representatives of conceptions. What is required in regard to 
 
the term is, that, according to its received import, it shall fully 
 and distinctly represent its conception, and nothing more nor 
 less. It must not, according to received usage, represent more 
 nor less elements than are included in the conception ; for, in 
 such cases wrong, and not the right conceptions are represented. 
 
 CHAPTER II. 
 
 OF JUDGMENTS. 
 
 Section I. Of Judgments considered as Mental States. 
 
 A judgment is an intellectual apprehension in which a certain 
 relation is mentally affirmed to exist between two or more con- 
 ceptions. We have in our mind, for example, the conception 
 of body and space. On reflection, we perceive a necessary re- 
 lation between them, or rather between their oHjects.ia relation 
 of this character, to wit : the existence of the K>rmer|can be 
 conceived of as possible, but upon one condition, the admission 
 of the reality of the latter. The mind then becomes distinctly 
 conscious of the truth, that body supposes space. This mental 
 affirmation is a judgment. We have in our minds also the con- 
 ceptions represented by the terms man, on the one hand, and 
 mortal, on the other ; we perceive that, as a matter of fact, all 
 that is included in the latter conception, holds true of every in- 
 dividual represented by the former. Mortality is, therefore, 
 mentally affirmed of all men. This mental affirmation, also, is 
 a judgment. So in all other instances. Whenever a certain re- 
 lation is affirmed to exist between two or more conceptions, or 
 between the objects of the same, this mental affirmation is a 
 judgment. 
 
 Matter and form of Judgments. 
 
 Logic, as a science, as we have seen, pertains not at all di- 
 rectly to the particular objects about which the thoughts are 
 

 JUDGMENTS. 53 
 
 employed in particular conceptions, judgments, and reasonings, 
 but to the laws of thought itself relating to such objects. So it 
 distinguishes between the matter and form of judgments, and 
 takes cognizance directly only of the latter. The former con- 
 sists of the special notions or judgments relating to their par- 
 ticular objects, one judgment pertaining to one object, or class 
 of objects, and another to another. The latter, the form of the 
 judgment, pertains to its character relative to other judgments, 
 as affirmative or negative, universal or particular, &c. 
 
 Logic, as a science, considers specially the form of the judg- 
 ment, and has to do with the matter thereof, only so far as to 
 give the universal criteria, by which valid may be distinguished 
 from invalid judgments. 
 
 Quantity of Judgment, universal, particular, individual or 
 singular. 
 
 When judgments are contemplated relatively to the num- 
 ber of objects of the class to which they pertain, the number 
 which is embraced in the judgment, we then refer to the quan- 
 tity of judgments, as whether the relation affirmed is conceived 
 of as holding true of all such objects, or of a part of them, or 
 of some one individual. Relatively to quantity, judgments are 
 accordingly classed as universal, particidar, and individual, as 
 in the case of those represented by the propositions, " All men 
 are mortal ; Some men are mortal ; and, George is mortal." In 
 the first case, as the relation is affirmed to hold true universally 
 of all individuals represented by the term man, the judgment is 
 called universal. In the second case, this relation is affirmed 
 relatively to a part only of the individuals represented by this 
 term. The judgment is accordingly called particular. In the 
 last case, the relation is affirmed of one individual only. The 
 judgment is therefore denominated individual. All judgments, 
 as far as the relation of quantity is concerned, may be ranked 
 as universal, particular, or individual. 
 
 According to Kant, particular judgments might more prop- 
 erly be called plurative, because they relate to more than one 
 
individual. In this he is no doubt correct, and equally correct, 
 while he expresses such preference, in adhering to common usage. 
 Individual judgments also are, in logic, treated practically as 
 universal ones, because in the former, equally as in the latter, 
 the relation affirmed holds in regard to the whole subject with- 
 out exception. 
 
 Quality of Judgments, affirmative, negative, indefinite. 
 
 As far as quality is concerned, their own intrinsic characteris- 
 tics, judgments are classed, as affirmative, negative, and indefi- 
 nite. When one conception (the subject) is thought of as coming 
 under the sphere of another (the predicate), as in the judgment, 
 " All men are mortal," all men being in the judgment placed 
 in the sphere, or class of mortal beings, the judgment is called 
 affirmative. When one conception is thought of as excluded 
 from the sphere of another conception, as in the judgment, 
 " Mind is not matter," the former substance being thought of as 
 excluded from the sphere or class of material substances, the 
 judgment in that case is called negative. When, on the other 
 hand, a conception is thought of not only as excluded from the 
 sphere of another conception, but as included indefinitely in 
 one excluded from the latter, we then have what is called an in- 
 definite judgment. Thus in the judgment, " The human soul is 
 not mortal," we separate the subject from the sphere or class of 
 mortal beings, and place it, but indefinitely, in a class excluded 
 from the former, that is, among immortal beings. The distinc- 
 tion between negative and indefinite judgments is important to 
 a correct understanding of the notion of judgments themselves. 
 In logic, however, both are included under one, the negative, 
 and all judgments are classed as affirmative or negative. 
 
 Relation of Judgments, categorical, hypothetical, and disjunc- 
 tive. 
 
 When one conception is directly affirmed or denied of 
 another, as in the judgments, "All men are mortal, and, the 
 soul is not mortal," the judgment is denominated categorical. 
 
Wl 
 
 JUDGME X T S . 
 
 hen conceptions are thought of in respect to one another in 
 the relation of antecedent and consequent, as in the judgment, 
 "If Caesar was a usurper, he deserved death," the judgment is 
 then denominated hypothetical. 
 
 When a conception is thought of as included hi one member 
 of a certain division, as in the judgment, " Caesar was a hero or 
 a usurper," "A is in B, C, or D," the judgment is called dis- 
 junctive. From the nature of the relation of the subject and 
 predicate in judgments, all judgments must be either categori- 
 cal, hypothetical, or disjunctive. 
 
 REMARKS ON THESE JUDGMENTS. 
 
 Categorical Judgments. 
 
 In categorical judgments, as Kant remarks, "the subject and 
 the predicate make up the matter of the judgment ; the form, 
 by which the relation (of agreement or disagreement) between 
 the subject and predicate is determined and expressed, is the 
 Copula," which, when expressed in language, is always is, or is 
 not. Categorical judgments, as Kant further remarks, " make 
 up the matter of other judgments." With the following remark 
 of this great logician we cannot agree : " But from this we must 
 not think, as several logicians do, that hypothetical and disjunc- 
 tive judgments are nothing more than different dresses of cate- 
 gorical ones, and can therefore be all reduced to them. All 
 the three judgments depend upon essentially distinct logical 
 functions of the understanding, and consequently must be dis- 
 cussed according to their specific distinction." On a careful 
 analysis of any hypothetical judgments, it will be found, that, 
 in all cases, it is, as stated in the Intellectual Philosophy, a 
 universal proposition expressed in the form of a particular. 
 The proposition, for example, if Caesar was a 'usurper he de- 
 served death, is nothing more than the universal proposition, 
 " All usurpers deserve death," expressed in a concrete and par- 
 ticular form. A comparison of categorical and hypothetical 
 syllogisms will also show that they are only different forms of 
 the same thing. For example : 
 
All usurpers deserve death ; 
 Caesar was a usurper ; 
 Therefore, he deserved death. 
 
 r If Caesar was a usurper, he deserved death ; 
 He was a usurper ; 
 Therefore, he deserved death. 
 
 The same may be shown to hold true in all the forms which 
 hypothetical judgments assume, and in regard to all the princi- 
 ples and laws pertaining to hypothetical syllogisms. Through- 
 out they are nothing but categorical judgments, or syllogisms 
 stated in a particular form. , 
 
 What has been said in regard to hypothetical judgments be- 
 ing so directly and manifestly applicable to the disjunctive, 
 nothing in addition is required to show that this class also dif- 
 fers only in form from the categorical. 
 
 Hypothetical Judgments. 
 
 In the language of Kant, "the matter of these consists of two 
 judgments, which are connected together as antecedent and 
 consequent. The one of these judgments which contains the 
 ground" (the subject of the universal categorical) " is the ante- 
 cedent ; the other, which stands in the relation of consequence 
 to that" (that is, the predicate of the universal categorical judg- 
 ment), "the consequent." The connection affirmed to exist be- 
 tween them is denominated the consequence. The antecedent 
 and consequent in a hypothetical judgment, answer to the sub- 
 ject and predicate in the categorical, and the consequence in the 
 former to the copula in the latter. A few passing remarks are 
 deemed requisite on the following paragraph from Kant : 
 
 " Some think it easy to transform a hypothetical proposition 
 to a categorical. But it is not practicable ; because they are 
 quite distinct in their very nature. In categorical judgments 
 nothing is problematical, but every thing assertive ; whereas in 
 hypothetical ones, the consequence is only assertive or positive. 
 In the latter we may therefore connect two false judgments 
 together, for in this case the whole affair is the rightnes? in the 
 
C01 
 
 JUDGMENTS. 
 
 nmcction the form of the consequence ; upon which the logi 
 cal truth of these judgments depends. There is an essential dis 
 tinction between these two propositions : ' All bodies are divisi 
 ble, and, if all bodies are composed, they are divisible.' In tl 
 former, the thing is maintained directly : in the latter it is main 
 tained on a problematically expressed condition only." 
 
 In reply, we remark : 
 
 1. That while it is true that "in categorical judgments 
 nothing is problematical, but every thing assertive, whereas 
 in hypothetical ones, the consequence only is assertive," it is 
 equally true, that in both the same thing is asserted, only in 
 different forms. This is manifest, from the fact, that in all hy- 
 pothetical syllogisms, a categorical may be substituted for the 
 hypothetical judgment (premise), and the argument will stand 
 just as it did before. This we shall see hereafter. 
 
 2. Even in those hypothetical judgments which contain " two 
 false judgments," with the connection of necessary consequence 
 between them, a universally valid categorical judgment is al- 
 ways given a judgment which alone renders valid the relation 
 of consequence referred to. In the judgment, for example, "If 
 Washington was a traitor to his country, he deserved death," 
 we have the two false judgments, and the relation of necessary 
 consequence, under consideration. In this very judgment, 
 however, we have, in reality, the universal categorical one, " All 
 traitors to their country deserve death," and upon the validity 
 of this last judgment depends that of the consequence before 
 us. The same holds true in all other instances. 
 
 3. The reason why there is " an essential distinction between, 
 these two propositions, all bodies are divisible, and, if all bodies 
 are composed they are divisible," is not, as Kant affirms, because 
 a hypothetical proposition cannot be transformed into a cate- 
 gorical one, but because the two propositions before us do not 
 in fact belong to the same class. The judgment, therefore, " If 
 all bodies are composed they are divisible," cannot be trans- 
 formed into this, "All bodies are divisible." The former judg- 
 ment, however, may be transformed into this, " All substances 
 which are composed (compounded) :m> divisible," because that, 
 
hi these instances, what is affirmed in one case categorically, is 
 affirmed in the other hypothetically. The examples adduced 
 by our author lay no valid basis for the conclusion which he de- 
 duces from them. 
 
 Disjunctive Judgments. 
 
 A disjunctive judgment, is distinguished from all others by 
 this peculiarity, to wit : it is constituted of a certain number of 
 problematical judgments, all of which together sustain such a 
 relation to a certain judgment known to be true, that the object 
 of this judgment must be in one of the numbers referred to, to 
 the exclusion of all the rest. For example, the judgment, which 
 all will admit cannot but be true, that the final determining 
 cause of the facts of the universe in creation and providence, is 
 either an inhering law of nature, or some power out of and 
 above nature, has its basis in the judgment which also must be 
 true, that for the facts named some ultimate reason or cause 
 must exist. A is known to exist. But it sustains such relations 
 to B, C, and D, that it must be found in one of them, to the ex- 
 clusion of all the rest. Hence the disjunctive judgment. A is 
 in B, C, or D. The same principle obtains in all disjunctive 
 judgments. 
 
 The several problematical judgments constitute the matter of 
 the disjunctive judgments, and are called, as Kant observes, 
 " members of the disjunction or opposition." Their mutual re- 
 lations of disjunction or opposition, that is, the fact that each 
 sustains such relations to all the others, that if it is true, they 
 must be false, and if any of the others be true, each of the rest 
 must be false, constitute the form of such judgments. 
 
 Modality of Judgments, problematical, assertative, contingent, 
 necessary (appodictical). 
 
 When the connection between conceptions is conceived of as 
 possible, that is, Math the conviction that the relation may or 
 may not exist, as in the proposition, " A may be in B," the judg- 
 
JUDGMENTS. 59 
 
 ment is called problematical. When the connection is con- 
 ceived of as not only possible, but as actual, the judgment is 
 called assertative. When the relation is conceived as actual, 
 with the conviction that the facts might possibly have been 
 otherwise, the judgment is denominated contingent ; as in the 
 proposition, "A died on yesterday," it being possible to conceive, 
 while it is asserted, that he did die, at the time named, that he 
 is yet alive, or that he died at some other time. When a rela- 
 tion between conceptions is conceived of as not only actual, but 
 the conception is accompanied with the conviction that the facts 
 can, by no possibility, be otherwise than they are, the judgment 
 is said to be necessary or appodictical, as in the judgment, 
 " Body supposes space, or an event, a cause." The contradic- 
 tory of the problematical is the impossible, a relation which 
 cannot be conceived of as existing. 
 
 Remarks. 
 
 1. A judgment maybe deemed necessary for either of two 
 reasons the nature of the relations between the conceptions, or 
 the nature of the evidence in favor of the actual existence of 
 such relations. Of the first class are the judgments, " Every 
 event has a cause," " Two straight lines cannot inclose a space," 
 &c. Of the second, is the judgment, "That the square of the 
 hypothenuse of a right-angled triangle is equal to the sum of 
 the square of its two sides." Judgments of the former class 
 are called primitive, those of the latter, derivative. 
 
 2. An assertative judgment, while, from the nature of the re- 
 lations between the conceptions themselves, it may be, and is 
 contingent, may, relatively to the evidence of the existence of 
 the relations referred to, be necessary. The judgments, " The 
 world exists, and I exist," are of this character. Relatively to 
 the nature of the relations between the subject and predicate in 
 each of these judgments, the judgments themselves are merely 
 assertative or contingent. Relatively to the nature of the affir- 
 mations of perception and consciousness, we say that these judg- 
 ments must be true. 
 
60 LOGIC. 
 
 3. A judgment necessary, from the nature of the relations 
 between the subject and predicate, is necessary in the absolute 
 sense the judgments, for example, " Body supposes space ; and 
 succession time," &c. A judgment necessary relatively to the 
 perceptions of sense and consciousness, is said to be relatimly 
 necessary ; as, for example, " Phenomenon supposes substance." 
 A necessary form of this judgment is this : " Substances are aa 
 their phenomena." The logical antecedent of the phenomenon 
 of extension is the reality of an extended substance (body). 
 The logical antecedent of the subjective phenomena of thought, 
 feeling, and voluntary determination, is the reality of the self aa 
 possessed of the powers of intelligence, sensibility, and will. 
 The above-named phenomena being given, the judgments, 
 " Body is, and Self exists," are necessary, relatively so. 
 
 4. Assertative judgments, like the appodictical, are divided 
 into two classes primitive and derivative. The judgments, 
 " Body is, and Self exists," are of the first class. The judgment, 
 " All bodies attract each other directly, as their matter, and in- 
 versely as the squares of their mean distances," is of the latter 
 character. 
 
 5. All derivative judgments, as originally given, are prob- 
 lematical, and subsequently become assertative or appodictical, 
 as the case may be ; that is, they are originally given as possibly 
 true or false, and consequently as capable of proof, and as Avant- 
 ing it. 
 
 Theoretical and practical Judgments. 
 
 Theoretical judgments affirm what does .and what does not 
 really belong to their objects. Practical judgments, on the 
 other hand, express those forms or rules of action by which cer- 
 tain ends may be obtained, or those actions which ought or 
 ought not to be performed. 
 
 Practical principles are treated as theoretical ones, when the 
 question to be argued is, whether the former are, in reality, 
 what they are judged to be. As thus contemplated only, 
 would logic have to do with them. 
 

 JUDGMENTS. 
 
 Demonstrable, and indemonstrable or intuitive Judgments. 
 
 A demonstrable judgment is a problematical one, of the class 
 which is capable of being proved. Indemonstrable (intuitive) 
 judgments are those which are immediately certain, and for this 
 reason, incajjable of proof. 
 
 Judgments of the latter class, since every intellectual process 
 properly denominated reasoning commences with them, are 
 sometimes, and Avith unquestionable propriety, denominated 
 primitive judgments. Those of the former, being in fact de- 
 duced from and evinced by the latter, are called derivative 
 judgments. 
 
 Intuitive judgments by which the demonstrable may be 
 evinced, but which cannot be subordinated to others, are called 
 elemental judgments, and also principles, a principle in science 
 being always a judgment which is itself immediately certain, 
 and consequently not evincible through any other judgment. 
 
 A demonstrable judgment, when evinced, may become a 
 principle relative to other demonstrable judgments ; and a judg- 
 ment which is derivative in one science, may be an elemental 
 principle in another. 
 
 Analytical and synthetical Judgments. 
 
 Those judgments whose certainty is immediately evinced 
 from an analysis of, or reflection on the conceptions constituting 
 the subject and predicate of said judgments, are called analyti- 
 cal judgments ; those judgments which are evincible only 
 through other and more elementary ones, are called syntheti- 
 cal judgments. 
 
 On examination it will be found that all analytical judg- 
 ments, that is, all judgments whose validity is immediately cer- 
 tain, divide themselves into two classes, and are and must be 
 all comprehended in one or the other of them. 1. Those in 
 which the predicate represents an essential quality of the sub- 
 ject, as in the judgment, " All bodies have extension." It is 
 impossible for us to conceive of a body which has not exten- 
 
62 LOGIC. 
 
 sion. In the judgment before us, then, the predicate, exten- 
 sion, represents a fundamental element of our necessary concep- 
 tion of body. The judgment has, and must have, immediate 
 certainty, of course. The same holds true in all similar judg- 
 ments. 2. Those in which the conception represented by the 
 predicate, sustains to that represented by the subject, the rela- 
 tion of logical antecedent, that is, when the reality of the object 
 of the latter conception can be admitted but upon the supposi- 
 tion of that of the former. Of this kind is the judgment, 
 "Body supposes space." The reality of the object represented 
 by the term body, can be admitted but upon the condition of 
 admitting that of the object of the conception represented by 
 the term spaca So of the judgments expressed by such propo- 
 sitions as " Succession supposes time ; events a cause ; phe- 
 nomena substance," &c. All judgments of this character can 
 but have, of themselves, immediate intuitive certainty. 
 
 Now if we adduce any known indemonstrable judgment 
 which has immediate certainty, we shall find, on examination, 
 that it does, in fact, belong to one or the other of these classes, 
 and that this is the exclusive ground of its certainty. Take, as 
 an illustration, the axiom, "Things equal to the same things are 
 equal to one another." On reflection, it will be perceived, that 
 the relation of equality among themselves, is the necessary 
 condition of their being equal to the same things. In other 
 words, the conception represented by the words, " equal to one 
 another" (the predicate), is the logical antecedent of that rep- 
 resented by the words, " things equal to the same things" (the 
 subject). Thus we might take up all similar judgments, and 
 all other self-evident ones, and show that they do, in fact, be- 
 long to one or the other of the classes above elucidated. 
 
 Nor is it possible for us to conceive of any other grounds of 
 the immediate certainty of judgments. In any other conceiva- 
 ble or definable case, the relation between the subject and 
 predicate of the judgment would be such that the judgment 
 would be, at the utmost, only problematical. 
 
JUDGMENTS. 63 
 
 Criteria of all first Truths. 
 
 "We have, then, in the relations before us, the fundamental 
 and universal criteria by which first truths may be distin- 
 guished from all others. In all such judgments (first truths) 
 the conception constituting the predicate either exclusively 
 represents elements contained in that represented by the sub- 
 ject, or the former conception sustains to the latter the relation 
 of logical antecedent. There are, and can be, no other first 
 truths but these. The criteria of such truths commonly given, 
 are rather external and circumstantial than intrinsically charac- 
 teristic, as all scientific criteria should be. We refer to those 
 criteria given by Dr. Reid, and concui-red in by philosophers 
 generally, such, for example, as the fact, that all men admit 
 them as a matter of fact in all their reasoning ; that even those 
 who deny their validity act upon them ; and if denied, the va- 
 lidity of all reasoning fails. 
 
 Kant's definition of analytical and synthetical Judgments. 
 
 According to Kant, we have but one class of analytical judg- 
 ments, those in which the relation of identity referred to ob- 
 tains between the predicate and subject. The other class he 
 represents as synthetical judgments, which, according to him, 
 embrace all judgments in which all the elements of the concep- 
 tion represented by the predicate are not embraced in that rep- 
 resented by the subject. He accordingly divides synthetical 
 judgments into two classes, the intuitive and problematical, 
 though he gives us no explanations of the reasons why one 
 class is intuitive and the other not. In the Intellectual Phi- 
 losophy, pp. 336-341, we have stated our objections to our au- 
 thor's definition of these two classes of judgments, the analyti- 
 cal and synthetical, and to the use which he has made of the 
 latter. In this connection, we would simply add, that while 
 our definition is just as plain, and of as ready application, as 
 that of Kant, it presents a much more simple and easily un- 
 derstood classification of judgments. If any one, however, 
 
 IUFI7BESITT 
 
64 LOGIC. 
 
 should prefer the definition of that philosopher, we would re- 
 mind him, that in that case, he must divide synthetical judg- 
 ments into two classes : those in which the conception repre- 
 sented by the predicate is, and those in which it is not, the 
 logical antecedent of that represented by the subject, and that 
 the former class, together with Kant's analytical judgments, are 
 to be ranked together, as first truths, and that no other judg- 
 ments can be classed with them, as such truths. The logical 
 and scientific bearings of each classification will then" be, in 
 all respects, the same, and nothing but a verbal difference 
 
 Tautological, identical, and implied Judgments. 
 
 A tautological judgment is one in which the subject and 
 predicate are identical, either in fact and in form ; as, " John is 
 John, Man is man," &c. ; or, in all respects, in meaning, so that 
 the predicate is, in no respect, even explicative of the subject ; 
 as, " Man is a human being," &c. Such judgments are of no 
 use whatever. 
 
 Identical judgments, as distinguished from tautological, are 
 those in which, while there is an identity in fact, there is such 
 a diversity in form between the subject and predicate, that the 
 latter is really and truly explicative of the former. Of this char- 
 acter are all correct definitions ; as, for example, a triangle is a 
 figure bounded by three straight lines. Of the same character 
 is the class of analytical judgments; in which the predicate rep- 
 resents some element or quality of the subject; as, "All bodies 
 have extension." Such judgments are, by no means, void of 
 consequence, inasmuch as they render clear and distinct our 
 conceptions of their objects. 
 
 An implied judgment is one which is really only another form 
 of another judgment, but which presents some important ele- 
 ment of the latter which was not distinctly expressed before. 
 We often say : If this proposition is true, that is also true, be- 
 cause the latter is really implied in the former, that is, is only a 
 different form of stating the same thing. Implied judgments 
 
JUDGMENTS. 65 
 
 have a very important use ; indeed, a statement of them is 
 often indispensable to the production of conviction. 
 
 Axioms, Postulates, Problems, and Theorems. 
 
 An axiom is an analytical judgment (analytical or intuitive 
 synthetical judgment of Kant) which may be employed as a 
 principle in the sciences in general, that is, a judgment by 
 which other judgments may be evinced. As shown in the In- 
 tellectual Philosophy, pp. 257-8, the axioms which constitute 
 the foundation-principles of each of the sciences are essentially 
 identical with those of every other. 
 
 Postulates are analytical judgments which can be employed 
 as principles only in particular sciences. Thus the axiom, 
 " Things equal to the same things are equal to one another," is 
 really, though often stated in a somewhat different form, iden- 
 tical with that which lies at the basis of every science that can 
 be named ; while the postulate, " That a straight line may be 
 drawn between any two points in space," pertains exclusively 
 to geometry and kindred sciences. 
 
 A problem is a judgment which appears neither true nor 
 false, and requires an answer to the question, Is it, or is it not 
 true ? or presents a number of judgments either of which appa- 
 rently may be true, and but one can be, and requires an answer 
 to the question, Which is true ? or finally affirms that a certain 
 thing may be done, and requires an answer to the question, 
 How may it be done? In problems of the first and second 
 classes above named, an annwer of this kind is most commonly 
 required, to wit, not what is, or what is not true, in the particular 
 cases presented, but how may we determine, what is, and what 
 is not true, in these cases ? In the solution of particular prob- 
 lems, in this form, w r e obtain not only answers to the specific 
 questions presented, but principles by which all other similar 
 questions may be solved. Let us suppose, for example, that an 
 event like the raising of Lazarus from the dead occurs in our 
 presence. The question presents itself, Is this, or is it not a 
 real miracle ? or, Is this event the result of the direct and im- 
 
66 LOGIC. 
 
 mediate interposition of creative power, or of mere natural 
 causes ? In the first form, we have a problem of the first class 
 named, and in the other of the second. Suppose, that we are 
 required not merely to give a direct answer to these questions, 
 but to give criteria by which we may know whether the event 
 is, or is not, a miracle, or whether it was the result of a super- 
 natural interposition of creative power, or of natural causes. 
 In giving the solution in this form, we should not only obtain 
 an answer to the specific questions above stated, but should also 
 obtain criteria by which we can, in all other cases, distinguish 
 events resulting from natural causes from real miracles. Sup- 
 pose, on the other hand, we are required to give a rule, by 
 which a given line may be divided into any specific number of 
 equal parts. We then have a problem of the third class. 
 
 Theorems are theoretical judgments capable of proof, and re- 
 quiring it ; as, for example, the proposition, " All the angles of a 
 triangle are equal to two right angles." 
 
 Corollaries, Lemmas, and Scholia. 
 
 Corollaries are the immediate and intuitive consequences of 
 preceding judgments. 
 
 A lemma is a judgment previously evinced, and now used as 
 a principle in the demonstration of other judgments. In gen- 
 eral it is not native in the paiticular science in which it is presup- 
 posed as evinced, but is taken from some other science, as when 
 some ascertained truth in the science of geology, for example, 
 is employed as a principle in the science of natural theology. 
 
 Scholia are explanatory notes or observations appended to 
 evinced judgments, for the purpose of illustration. 
 
 CEITEEIA OF JUDGMENTS, OE CHABACTEEISTICS OF ALL VALID 
 JUDGMElSrrS. 
 
 We are now prepared to give the universal criteria of judg- 
 ments, or the universal and necessary characteristics of all valid 
 judgments, as distinguished from those which are not valid. 
 
1 
 
 JUDGMENTS. 67 
 
 General Criteria. 
 
 All universally valid judgments must have the following char- 
 acteristics : 
 
 1. The conceptions constituting the subject and predicate of 
 such judgments must be valid according to the criteria devel- 
 oped in the last chapter. 
 
 2. The judgment must be analytical according to the defini- 
 tion above given of such judgments. 
 
 Or, 3. It must be evinced as true, by means of judgments 
 which are analytical. 
 
 All valid primitive judgments have the first two characteris- 
 tics. All valid derivative ones have all the three together. 
 Any judgment wanting these characteristics must be held as 
 not valid. 
 
 Particular and special Criteria. 
 
 As necessarily involved in the above criteria, we present the 
 following particular and special ones. 
 
 Judgments relative to all valid Conceptions. 
 
 1. All judgments must be held as valid in which any ele- 
 ment of any valid conception is affirmed of the object or ob- 
 jects of such conception. Suppose, for example, that the con- 
 ception represented by the term man, be assumed as valid, 
 then any judgment in which any or every element of that con- 
 ception is affirmed of all men or any one individual of the race, 
 must be held as valid. So of all similar judgments relative to 
 all valid conceptions. 
 
 2. All judgments must be held as valid, in which the neces- 
 sary relations between a valid conception and its logical ante- 
 cedent, or between any element of such conception and the log- 
 ical antecedent of that element, are affirmed ; as, for example, 
 the judgments, ".Body supposes space ; succession time ; events 
 a cause ; and phenomena substance," &c. 
 
3. All judgments must be held as valid which affirm the im- 
 mediate and necessary consequence of valid judgments. In 
 other words, when one judgment must be held as valid, all 
 Others immediately implied in it must be held as valid also. If 
 the judgment, " Every event must have a cause," is valid, then 
 the judgment, " Every event must have a cause adequate and 
 adapted to produce that event," must be held as valid also. 
 If the judgment, " Phenomenon or quality supposes substance," 
 is valid, the judgment, " Substances are as their phenome- 
 na or qualities," must be held as valid also. So in all other 
 instances. 
 
 INDIVIDUAL (SINGLE), PARTICULAR, AND UNIVERSAL JUDGMENTS. 
 
 Individual Judgments affirmative. 
 
 In regard to every individual (each particular object), the 
 following judgments must be held as true : 
 
 1. AH judgments which affirm of such object any element of 
 any valid conception pertaining to it. Such judgments, being 
 really analytical, must be valid. 
 
 2. All judgments which affirm of said object that it belongs 
 to any class of objects with which it has common characteris- 
 tics, the characteristics which peculiarize that class. 
 
 3. All judgments which affirm of such object any or all of 
 the elements of the conception which represent that class. 
 
 4. All judgments which affirm of that individual any or all of 
 the elements embraced in any superior conception of that just 
 named. 
 
 The judgment, in the first instance, is really, as said above, 
 analytical, and cannot but be valid. In the second case, we 
 have the universal and immutable law of classification. Each 
 object must take rank with all others with which it has common 
 characteristics. The third case is necessarily involved in the 
 second ; for these are the necessary conditions of an object be- 
 ing entitled to take rank with a certain class. When, there- 
 fore, it is known to belong to a certain class it is, and must be, 
 
JUDGMENTS. 69 
 
 recognized as possessed of all the elements embraced in the con- 
 ception which represents that class, and all judgments which 
 affirm of it any or all of such elements must he valid. The ele- 
 ments embraced in the superior conceptions are embraced in the 
 inferior. When all of the former may be affirmed of an object, 
 of course any or all of the latter may be. All judgments of the 
 fourth class, therefore, must be valid. 
 
 Individual Judgments {negative). 
 
 The following negative judgments in regard to such objects 
 must be held as valid : 
 
 1. All judgments which deny of said object any and all ele- 
 ments and characteristics incompatible with any and all ele- 
 ments of valid conceptions and judgments in regard to it. 
 When a given characteristic may be affirmed of any object, 
 every thing incompatible with that characteristic may of 
 course be denied of it. When, for example, it is admitted that 
 matter has the quality of extension, and it is affirmed that the 
 substance itself, in regard to its ultimate essence, is unknown to 
 us, it may be denied absolutely that there is, or can be, in such 
 substance, any thing incompatible with the idea of extension, 
 and the judgment, that any theory in regard to the nature of 
 that, substance (any ontological conception of it) that affirms 
 that it is not in reality an extended substance, is and must be 
 false, must be held as valid. So in all other cases of the kind. 
 
 2. When it is undeniably true, that if an object does or did 
 possess certain characteristics, those characteristics would ap- 
 pear, that is, would be given in intuition, and they do not ap- 
 pear, and have not appeared (are not given in intuition), then 
 the judgments, which deny such characteristics of such objects, 
 must be held as valid. It is undeniable, for example, that if 
 Washington was under the controlling ambition of possessing 
 monarchical or despotic power, he would, in the circumstances 
 in which he was placed, have attempted to have gained that 
 power over his countrymen, and the fact of such attempt would 
 appear. The absence of the fact, renders valid the judgment, 
 
70 LOGIC. 
 
 that he was not under the control of the principle before us. 
 Again : if spontaneous production and the transmutation of spe- 
 cies are the law of nature, and the order of creation, we should 
 find somewhere in the present or past history of the earth, un- 
 deniable facts indicative of the truth of such theory. The total 
 absence of any such facts within the knowledge of man, since 
 his existence on earth, and the total absence of all abnormal 
 specimens, of any intermediate creations, in the vast laboratory 
 of geological science, render undeniably valid the judgment, 
 " That the theory of spontaneous production and transmutation 
 of species is not, and cannot be true." Very few of the laws of 
 thought are of more importance than that under consideration, 
 when legitimately employed. 
 
 3. All negative judgments are valid, which in matter, though 
 not in form, are identical with valid affirmative ones. If the 
 judgment, "A is mortal," is valid, the judgment, "A is not 
 immortal," is also valid, inasmuch as the two propositions mere- 
 ly affirm one and the same thing. In argument, it is often ex- 
 pedient to state an affirmative judgment in its equivalent nega- 
 tive form. 
 
 A careful examination will show, we judge, that all valid indi- 
 vidual judgments fall under one or the other of the classes 
 above named, and that no judgment not belonging to one or 
 the other of these classes should be held as valid. 
 
 Particular (pluratave) Judgments. 
 
 All particular judgments of the following classes must be held 
 as valid : 
 
 1. All judgments of this class which rank as subaltern judg- 
 ments under universal ones which are valid. What is true of 
 every member of a given class, may of course be affirmed to be 
 true of some members of that class. 
 
 2. When a certain characteristic, or quality, belongs to ajpart, 
 but not to all, of the members of a certain class, particular judg- 
 ments which affirm that some of the members of that class have 
 guch characteristic or quality, must be held as valid. 
 

 JUDGMENTS. 71 
 
 3. In all such cases, the particular negative judgment which 
 denies that characteristic or quality of some member of the class 
 under examination, must he valid also. As wisdom, for exam- 
 ple, pertains to a part, and not the whole, of the human race, 
 the particular judgments, "Some men are wise, and some men 
 are not wise," must be held as valid. So in all similar instances. 
 
 Universal Judgments {affirmative). 
 
 All affirmative universal judgments are valid which have 
 either of the following characteristics, or all of them together : 
 
 1. Those in which any or all of the elements embraced in 
 the conception which represents a class of objects, are affirmed 
 of all the members of that class any judgment, for example, 
 which affirms of all men any or all of the. elements of the con- 
 ception represented by the term man. 
 
 2. All which affirm universally of such a class any or all of 
 the elements embraced in any conception, to which the concep- 
 tion representing that class sustains the relation of an inferior 
 conception, that is, we may affirm of all the objects of a specifi- 
 cal conception, any or all of the elements of any of its superior 
 or generical conceptions. 
 
 3. All judgments which affirm of all the members of a class 
 any or all the elements embraced in the characteristic concep- 
 tion of such class. 
 
 's (negative). 
 
 All negative universal judgments must be admitted as valid 
 which have the following characteristics : 
 
 1. All which deny of all the members of any one class or 
 species any or all of the elements of any opposite specifical con- 
 ception, those elements excepted which belong to superior con- 
 ceptions under which each of the above take rank as inferior 
 ones. 
 
 Thus, if we should deny of the conception represented by the 
 term apple, any or all of the elements of the conception repre- 
 
72 LOGIC. 
 
 sented by the terra peach, with the exception of those embraced 
 in the superior conception represented by the term fruit, the 
 affirmation would be valid, and that for the reason, that species 
 under a genus are formed exclusively on the principle of contra- 
 diction. The same will hold equally true in all other similar cases; 
 
 2. All judgments in which any and all characteristics incom- 
 patible with any or all the elements of any valid conception, are 
 denied of all objects represented by such conceptions. We may 
 affirm absolutely, for example, that no untruth was ever given 
 forth by inspiration of the Almighty. The reason is obvious. The 
 thing denied is incompatible with all valid conceptions of Deity. 
 
 3. All universal negative judgments must be held as valid 
 which are really equivalent to valid affirmative ones. Thus the 
 judgment, " No man, physically considered, is immortal," must 
 be held as valid, because it is in fact equivalent to the universal- 
 ly valid judgment expressed by the proposition, " All men are 
 mortal." It is often of great importance, thus to substitute for 
 a valid affirmative judgment, its equivalent negative one. 
 
 4. When it is undeniable, that a given characteristic, if it did 
 attach to any member of a given class, would be given by intui- 
 tion in connection with some members of the same, and is not 
 given, then the judgment which denies such characteristic of 
 all the members of that class, must be held as valid. Thus the 
 judgment, " No plant is produced but through a seed, and no 
 seed but through a plant," must be held as valid, because it is 
 undeniable, that if the opposite judgments were true, facts cor- 
 roborative of them would appeal*. 
 
 It is believed, that all valid universal negative judgments be- 
 long to one or the other of the classes above defined, and that 
 we have here fundamental criteria by which to determine the 
 validity of such judgments. 
 
 Judgments pertaining to the objects of inferior and superior 
 conceptions. 
 
 All that is required to be said relating to judgments pertain- 
 ing to the objects of inferior and superior conceptions, has al- 
 
JUDGMENTS. 73 
 
 ready been anticipated, and what is added, in this connection, 
 is only for the sake of distinctness. On this subject we would 
 simply add, that all judgments relative to such objects must be 
 held as valid which have the following characteristics : 
 
 1. All judgments in which any object or class of objects hav- 
 ing the elements represented in any conception is ranked or 
 classed under that conception. 
 
 2. All judgments which affirm of any object of an inferior 
 conception, not only any or all of the elements of that particular 
 conception, but any or all of those of any superior one. 
 
 Judgments pertaining to the objects of characteristic concep- 
 tions (affi 
 
 When, an object agrees with a characteristic conception, or 
 possesses the elements embraced in such conception, the follow- 
 ing judgments relative to it must be held as valid : 
 
 1. Any which rank said object with the class to which the 
 conception under consideration pertains. 
 
 2. All judgments which affirm of said object any or all the 
 elements of the conception which represents that class, or all or 
 any of the elements of any superior conception. 
 
 Suppose, for example, that an object is before us, that agrees 
 with the characteristic conception of the class of substances rep- 
 resented by the term gold. For no other reason, we may af- 
 firm, that the object is gold, that it has any or all of the proper- 
 ties of gold. We may affirm, further, that it is a metal, a min- 
 eral ; that it is matter, a substance ; or affirm of it any or all of 
 the elements, of any or of all the conceptions which these terms 
 represent. So in all other instances. 
 
 Judgments relative to objects of characteristic conceptions 
 {negative). 
 
 Of all objects agreeing with characteristic conceptions, the 
 following negative judgments must be held as valid : 
 
 1. All which deny of such objects any or all the elements 
 represented in any opposite specifical conception, those excepted 
 
74 LOGIC. 
 
 which are represented in the common superior conceptions. 
 Thus, for example, if an object has the characteristic elements 
 of gold, we may affirm, from such fact, that such object is not 
 silver, copper, platinum, &c, and deny of it any of the peculiar 
 and specifical qualities of such metals. So in all other instances. 
 
 2. All judgments which deny of such objects any or all of the 
 elements represented by any incompatible conception. Thus, 
 if we should affirm that any act having the undeniable charac- 
 teristics of an act of perjury, did not proceed from an honest 
 intention to speak the truth, the judgment would be valid. 
 
 3. All negative judgments which are equivalent to valid af- 
 firmative ones. In other connections, this principle has received 
 a sufficient elucidation. Nothing, therefore, need be added in 
 respect to it here. 
 
 HYPOTHETICAL JUDGMENTS. 
 
 It is a somewhat remarkable fact, that while all systems of 
 logic treat of hypothetical and disjunctive judgments, in no 
 such treatises do we find, so far as our knowledge extends, even 
 an attempt to give us any criteria by which we may determine 
 the validity of either class of these judgments. We will, there- 
 fore, attempt the accomplishment of this important result. 
 
 Hypothetical Judgments classed. 
 
 All hypothetical judgments may be divided into three classes : 
 1. Those in which the antecedent and consequent have different 
 predicates, and each the same subject ; as, " If A is in B, it is, or 
 is not, in C." 2. Those in which both have the same predicate, 
 and each a different subject : " If A is in B, C is, or is not, in B." 
 3. Those in which both have different subjects, and different 
 predicates : "If A is B, C is, or is not, D." 
 
 Criteria of such Judgments. 
 
 Judgments of the first class are valid, when, and only when, 
 the predicate of the consequent may be affirmed or denied uni- 
 

 JUDGMENTS. 15 
 
 ersally, as the case may be, of the predicate of the antecedent. 
 Thus, the judgment, "If A is in B, it also is' in C," can be valid 
 only when the judgment, " Every B is in C," is valid ; and the 
 former judgment must be valid when the latter is. So, also, we 
 can affirm that, " If A is in B, it is not in C," when, and only 
 when, the judgment, "B is never in C," is valid; and in that 
 case, the former judgment must be true. 
 
 Judgments of the second class' are valid, when, and only 
 when, the subject of the antecedent may be affirmed or denied, 
 as the case may be, universally of the subject of the consequent. 
 Thus, the judgment, "If A is in B, C is in B," can be true but 
 upon the supposition that C is always in A, and must be true in 
 that case. The judgment, in its negative form, can be true, 
 but upon the supposition, that C is never in A, and must, in 
 that case-, be always true. 
 
 Judgments of the third class can be true, but upon the con- 
 dition that the relations between the subject and predicate of 
 the antecedent, are the same as between the subject and predi- 
 cate of the consequent. Equality or similarity of relations is 
 the thing, and the only thing, really affirmed or denied in all 
 such judgments. Unless, therefore, the judgment, "A sustains 
 similar relations to B that C does to D," is valid, the judgment, 
 " If A is B, C is D," cannot be valid. On the other hand, when 
 the former judgment is valid, the latter, of course, must be. 
 These remarks are so manifestly applicable to these judgments 
 when given in the negative form, that nothing is called for on 
 this point. 
 
 "What may be affirmed, when the relations referred to are 
 equal, may be affirmed when the relations are greater in de- 
 gree. If, for example, we may say that A, possessing $100, is 
 able to meet an indebtedness amounting to that sum, we may 
 of course affirm, that B, possessing $10,000, is able to discharge 
 an indebtedness amounting to $1,000. 
 
 
76 
 
 ^Disjunctive Judgments. 
 
 Disjunctive judgments always partake of one or the other of 
 these characteristics. A fact, or a class of facts (A), is known 
 to exist, and their explanation is required. A certain given 
 number of hypotheses, B, C, D, &c, two or more, present them- 
 selves, none others being, from the nature of the case, conceiva- 
 ble or possible, while one of them, to the exclusion of all the 
 others, must be true. Hence we say, " A must be in B, C, or D." 
 A judgment of this class is valid, when the facts A, are known 
 to exist, and when all conceivable demonstrable judgments are 
 specified in the judgment, "A is in B, C, or D," &c, and when, 
 from the character of the facts, A must be found in one of these 
 judgments, B, C, or D, to the exclusion of each of the others. 
 Each judgment must be, in its nature, exclusive, and the whole 
 together must, undeniably, exhaust the subject : for, if any one 
 conceivable hypothesis is not included, the judgment is not 
 valid. 
 
 Or it may be known that there is a cause, X, for a given class 
 of facts, and the inquiry is, what is the nature of this cause ? 
 From the nature of the case, there can be but a certain num- 
 ber of answers to this question, and one of these, to the exclu- 
 sion of each and all the others, must be true. In such a case, 
 we say, " X is A, B, or C." Such a judgment is valid, when it 
 undeniably embraces all conceivable or possible answers, and 
 when each member of the judgment is in such disjunction with, 
 or opposition to each and all of the others, that one of them, to 
 the exclusion of each and all the others, must be true. If any 
 possible answer to the question is omitted, or if each proposi- 
 tion is not, in its nature, exclusive of each and all the others, 
 then the judgment is not valid. For example, All men be- 
 lieve, and must believe, that there is an ultimate reason why 
 the facts of the universe are what they are, and not otherwise. 
 Let X, for example, represent this ultimate or unconditioned 
 cause. Now it is self-evident, that this cause X, must be an in- 
 herent law, or principle of nature, which we will call L, or a 
 power out of and above nature, which we will denominate G, 
 
the 
 
 PROPOSITIONS. 11 
 
 ie god of theism. Hence, the judgment, " X is L or G," must 
 be valid. 
 
 There is one form of the disjunctive judgment which, oJ 
 course, must be valid, to wit : " Every X is A, or not A ;" a 
 form of judgment which hardly differs from the tautological, 
 and requires no elucidation. 
 
 We believe that all disjunctive judgments belong to one 01 
 the other of the above classes, and that we have, in the princi 
 pies above given, universal criteria of their validity. 
 
 Section II. Of Propositions. 
 
 Having treated sufficiently of judgments, it remains to make 
 a few remarks in respect to propositions,. which are judgments 
 expressed in words. Logic treats only of assertative proposi- 
 tions, those which affirm or deny ; as, " A is B, or A is not B." 
 
 Quality and Quantity of Propositions, &c. 
 
 Propositions, when contemplated with reference to their na- 
 ture or substance, are divided into two classes, to wit : categori- 
 cal, those which simply affirm or deny, as, " A is, or is not, B ;" 
 and hypothetical, those which affirm conditionally, as, " If A is 
 B, C is D, &c. 
 
 When contemplated with reference to their quality, they are 
 divided as affirmative : " A is B ;" or negative, "A is not B." 
 
 In regard to the quantity, they are divided into universal, 
 those in which the predicate is affirmed or denied of all the ob- 
 jects represented by the subject ; as, " Every A is B, or no A 
 is B ;" and particular, those in which the predicate is affirmed 
 or denied of a part only of the objects represented by the sub- 
 ject. As affirmative and negative propositions are each divided 
 into two classes, universal and particular, we have four kinds of 
 propositions : the universal affirmative, which is represented by 
 the term, A ; the universal negative, E ; the particular affirma- 
 tive, I ; and the particular negative, O. 
 
IS 
 
 Distribution of Terms. 
 
 When a term stands for all its significates, that is, for every 
 individual of the class which it represents, then it is said to be 
 distributed. When it represents apart only of its significates, 
 then it is said to be not distributed. 
 
 When the subject of a proposition is a common term, its dis- 
 tribution is commonly signified by such terms as " All, every, 
 no," &c. ; and when not distributed, by the term " Some," &c. 
 When no sign is used, the question, whether the subject is to be 
 understood as distributed or not, is always to be determined 
 by the particular circumstances of the case, and not by a refer- 
 ence to the matter of the proposition. The quantity of a propo- 
 sition, when no signs are used to indicate the distribution or 
 non-distribution of terms, " is ascertained," says Dr. Whately, 
 " by the matter, i. e. the nature of the connection between the 
 extremes, which is either necessary, impossible, or contingent. 
 In necessary and impossible matter, an indefinite is understood 
 as a universal ; e. g. * Birds have wings,' i. e. all birds ; ' Birds 
 are not quadrupeds,' i. e. none. In contingent matter (i. e. 
 where the terms partly i. e. sometimes agree, and partly 
 not), an indefinite is understood as a particular; e. g. 'Food 
 is necessary to life,' i. e. some food ; ' Birds sing,' i. e. some 
 do ; ' Birds are not carnivorous,' i. e. some are not, or, all 
 are not." 
 
 Here are two fundamental mistakes relatively to the science 
 of logic, the supposition that this science has any thing to do 
 with the matter of the proposition and the supposition that in- 
 dividuals always conform, in their use of terms, to the rules 
 which our author has laid down ; whereas the opposite is not 
 unfrequently the case, and we should violate all the laws of lan- 
 guage should we interpret their words according to any such 
 rules. 
 
 Apply the principle we have laid down to the cases cited by 
 Dr. Whately, and we shall at once see its validity. Suppose 
 that the question is being argued, whether, as a matter of fact, 
 
aU 
 
 PROPOSITIONS. 79 
 
 birds have wings. The individual maintaining the affirma- 
 tive uses the phrase, " Birds have wings ;" and on the opposite 
 side it is affirmed, " Birds have not wings." The circum- 
 stances of the case require us to understand the first proposition 
 as universal, and the second as particular, that is, the contra- 
 dictory of the first. If, on the other hand, the question was 
 this, " Are any birds quadrupeds ?" and, on one side, it should 
 be affirmed, " Birds are quadrupeds," and on the other, " Birds 
 are not quadrupeds," we should be bound, by the circumstances 
 of the case, to assume the first proposition as particular, and 
 the second as universal. So in all other circumstances. 
 
 Singular propositions, those in which the subject is a proper 
 name, or a common term, with a singular sign, are reckoned in 
 logic as universals, because in such cases the predicate is af- 
 firmed of the whole subject. The following quotation from 
 Dr. Whately presents the rules of distribution pertaining to 
 the subject and predicate of propositions as commonly given, 
 so distinctly, that we give it, without note or comment of 
 our own : 
 
 " It is evident, that the subject is distributed in every univer- 
 sal proposition, and never in a particular (that being the very 
 difference between universal and particular propositions) ; but 
 the distribution or non-distribution of the predicate depends 
 (not on the quantity, but) on the quality of the propositions ; 
 for, if any part of the predicate agrees with the subject, it must 
 be affirmed, and not denied of the subject ; therefore, for an 
 affirmative proposition to be true, it is sufficient that some part 
 of the predicate agrees with the subject ; and (for the same 
 reason) for a negative to be true, it is necessary that the whole 
 of the predicate should disagree with the subject ; e. g. it is 
 true that ' Learning is useful,' though the whole of the term 
 ' useful' does not agree with the term ' learning,' (for many 
 things are useful besides learning) ; but, ' No vice is useful,' 
 would be false, if any part of the term ' useful' agreed with the 
 term ' vice' (i. e. if you could find any one useful thing which 
 was a vice). The two practical rules, then, to be observed re- 
 specting distribution, are : 
 
" 1st. All universal propositions (and no particular) distribute 
 the subject. 
 
 " 2d. All negative (and no affirmative)* the predicate. It 
 may happen, indeed, that the whole of the predicate, in an 
 affirmative, may agree with the subject ; e. g. it is equally true, 
 that ' All men are rational animals ;' and, ' All rational ani- 
 mals are men ;' but this is merely accidental, and is not at all 
 implied in the form of expression, which alone is regarded in 
 logic." 
 
 Of Opposition. 
 
 Propositions are said to be opposed to each other, when the 
 subject and predicate are the same, and they differ in quantity, 
 quality, or both. 
 
 In respect to quantity, A and E are each opposed to I and O. 
 From the nature of this opposition, the following rules, pertain- 
 ing to the validity of propositions, arise : 
 
 1. If the universal is valid, so is the particular; that is, if A is 
 true, I must be true also ; and if E is true, O must be. If the 
 proposition, " All men are mortal," is true, I, which affirms that 
 " Some men are mortal," must be true also. If the proposition, 
 "No birds are quadrupeds," is true, O, which affirms that 
 " Some birds are not quadrupeds," must also be true. 
 
 2. If the particular, I or O, be false, its respective universal, 
 A or E, must be false also ; in other words, the denial of the 
 particular involves a denial of the universal under which the 
 former ranks. If the proposition, " Some men are mortal," is 
 false, A, which affirms that " All men are mortal," cannot, of 
 course, be true. So if the proposition, " Some men are not im- 
 mortal," is false, E, which affirms that " No man is immortal," 
 must be false also. 
 
 3. On the other hand, both the universals (A and E) may be 
 false, and both the particulars (I and O) may be true ; that is, 
 the denial of the universal does not necessitate a denial of the 
 particular. The propositions, " All men are liars," and " No 
 
 * Here, as we shall see hereafter, is a fundamental mistake in the science of logia 
 
PROPOSITIONS. 81 
 
 men are liars," may both be false ; and the propositions, " Some 
 men are liars," and " Some men are not liars," may be true. 
 
 In respect to quality, A and I are each, respectively, opposed 
 to E and O, and vice versa. The two universale are opposed 
 throughout their whole extent ; that is, what one affirms in re- 
 gard to a whole class, the other denies in regard to every indi- 
 vidual of that class. The universal of one is opposed to the par- 
 ticular of the opposite quality, A to O, E to I, simply and ex- 
 clusively, in regard to one point, the question of universality. 
 What the universal affirms as true of every individual of a 
 certain class, the opposite particular denies in regard to some 
 individuals of the same class. What I affirms as also true 
 of some individuals of a given class, O denies, not of all, or 
 of the same, but of some individuals of the same class. From 
 the nature of this opposition, therefore, the following rules or 
 axioms obtain : 
 
 1 . If one universal is true, its opposite universal must be false 
 If "Every A is B," the proposition, "No A is B," must be false 
 throughout. 
 
 2. The fact that one universal is false, does not imply that 
 the opposite is true. The propositions, " Every A is B," and 
 " No A is B," may both be false, and each of the particulars, to 
 wit : " Some of A is B," and " Some of A is not B," may be 
 true. The propositions, " All men are bars," and " No men are 
 liars," are, in fact, both false ; and their respective particulars,, 
 " Some men are liars," and " Some men are not liars," are true. 
 
 3. If either particular is true, its opposite universal is false. 
 If the proposition, " Some men are liars," is true, the proposi- 
 tion, " No men are liars," must be false. So in all other in- 
 stances. 
 
 4. The fact that one particular is true, does not imply that 
 the opposite one is falsa. Both may be, and often are, true. 
 The propositions, " Some men are virtuous," and " Some men 
 are not virtuous," are both true. 
 
 5. If a universal is false, its opposite particular must be true ; 
 and if the particular is false, its opposite universal must be true. 
 If the proposition, " No A is B," is false, the proposition, " Some 
 
A is B," must be true. So if the proposition, " Some 'A is B," 
 is false, the proposition, " No A is B," must be true. 
 
 6. Both particulars can, in no case, be false, because both uni- 
 versals would then be true, which, as we have seen, is impos- 
 sible. 
 
 The above principles will be found to be of very great impor- 
 tance, when understood and duly reflected on.* 
 
 Of the Conversion of Propositions. 
 
 A proposition is said to be converted when, without a change 
 of quality, its terms are transposed; that is, the subject is made 
 the predicate, and the predicate the subject. When nothing 
 more is done, we have what is called simple conversion. The 
 original proposition is called the exposita / when converted, it 
 is denominated the converse. 
 
 Conversion is valid when, and only when, nothing is asserted 
 in the converse which is not affirmed or implied in the exposita. 
 Hence the universal rule of conversion, to wit : " no term must 
 be distributed in the converse which was not distributed in the 
 expositaP Whenever this is done, that is affirmed of the whole 
 class which was before only asserted of a part of it ; that is, 
 more is affirmed in the converse than was implied in the exposi- 
 ta. The following are the necessary applications of this law : 
 . 1. E distributes both terms, and I neither. Each of these 
 classes of propositions may always be converted simply, and the 
 conversion will be illative / that is, the truth of the converse is 
 implied in the truth of the exposita. If the proposition in E, 
 " No virtuous man is a rebel," is true, its converse, " No rebel 
 is a virtuous man," must be true also. If the proposition in I, 
 " Some boasters are cowards," is true, its converse, " Some 
 cowards are boasters," must also be true. 
 
 2. A, the universal affirmative, distributes only the subject.f 
 
 * See Tappan's Logic, pp. 318-320, where most of the above principles are stated and 
 elucidated with great precision and clearness. 
 
 t This proposition, as we shall see, holds when, and only when, the subject represents an 
 Inferior and the predicate a superior conception. 
 
PROPOSITIONS. 83 
 
 Its simple -conversion, therefore, would not be illative. From 
 the fact, that "All men are mortal," we cannot infer, or affirm, 
 that all mortal beings are men. That fact being admitted, 
 however, we can affirm, as necessarily implied in it, the truth of 
 the proposition, that " Some mortal beings are men." Universal 
 affirmatives, then, may always be converted by making the con- 
 verse particular instead of universal. This has been denominated 
 "conversion by limitation," or "per accident." As we are al- 
 ways permitted to affirm a particular, when a universal might be 
 affirmed, the universal negative E can always be thus converted. 
 
 3. The particular negative distributes the predicate instead 
 of the subject. Such propositions, therefore, cannot be con- 
 verted simply ; since, in that case, we should have the predicate 
 distributed in the converse, when it was not distributed in ex- 
 posita. As Professor Tappan has observed : " According to a 
 strict exposition of the form, a particular negative has no con- 
 verse." From the fact, " That some men are not truthful," we 
 cannot affirm, that " Some truthful persons are not men." The 
 proposition is, hi fact, incapable, as it stands, of conversion. It 
 can be converted only by changing its form from a negative to 
 a positive ; that is, by attaching the term of negation to the 
 predicate of the exposita. Take, for example, the proposition, 
 " Some men are not truthful." From such a proposition, we 
 may affirm, that " Some persons who are not truthful are men." 
 This has been named conversion by negation. Since, as Dr. 
 Whately remarks, " it is the same thing to affirm some attri- 
 bute of the subject, as to deny the absence of that attribute," 
 the universal affirmative may always be converted in the same 
 manner. From the fact, for example, that " Every virtuous 
 man is a true patriot," we may infer, that " Every one who is 
 not a true patriot, is not a virtuous man," or, " None but true 
 patriots can be virtuous." 
 
 Thus, as Dr. "Whately states, " in one of these three ways, 
 every proposition may be illatively converted, viz. : E and I 
 simply ; A and O by negation ; A and E by limitation." 
 
 Hardly any department of logic needs to be more thorough- 
 ly studied and reflected upon than the department we have just 
 
passed over, when treating of the laws and principles of opposi- 
 tion and conversion of propositions. When a proposition is ad- 
 mitted as self-evident, or as having been proved true, few per- 
 sons seem to know what use to make of it, and that in conse- 
 quence of not perceiving what is implied in it. 
 
 Quantification of the Predicate. 
 
 What we have said hitherto in regard to propositions, has 
 been based on the assumption, that the quantity of propositions 
 depends icholly upon the relations of the whole predicate to the 
 subject. If the former is affirmed or denied of the ichole sub- 
 ject, the proposition is universal. If it is affirmed or denied 
 only of apart of the subject, the proposition is particular. We 
 have said nothing (for the reason that logic, with the exception 
 about to be .named, has hitherto left the subject untouched) of 
 the quantity of propositions so far as the predicate is concerned. 
 TO Sir William Hamilton the world is indebted for one of the 
 most important attainments in this science which has been 
 made for centuries, to wit : in the quantification of the predi- 
 cate as well as of the subject. In all propositions alike, as he 
 maintains, if we refer to the judgment itself, that is, to what is 
 really thought in the mind, the predicate always has as real a 
 quantity as the subject ; and that, if we refer to the judgment, 
 and not to the words of the proposition expressing it, conver- 
 sion of propositions is always and exclusively simple, the sub- 
 ject and predicate being really, in all instances, definite in their 
 meaning. Why, for example, is the converse of the proposi- 
 tion, " All men are animals," this : " Some animals are men ?" 
 The answer commonly given is : " That the subject and not the 
 predicate is distributed in this proposition." This is true, as far 
 as the mere form of expression is concerned. If we refer to 
 the thought in the mind, however, we shall find that the reason 
 is, that, in the exposita, the subject is universal, and the predi- 
 cate particular. What we really mean, when we say, "All 
 men are animals," is not, that all men are any kind of annuals, 
 but some kind ; rational, for example. The proposition before 
 us, then, is really universal relative to the subject, and particu- 
 
PROPOSITIONS. 85 
 
 lar relative to the predicate. Hence, by simple conversion, we 
 have the converse, " Some animals are men." The propositions, 
 on the other hand, " Men are rational animals," and " All trian- 
 gles are figures bounded by three straight fines," are universal 
 in both particulars ; and their converse would be, not " Some, 
 but all rational animals are men," and not " Some, but all 
 figures bounded by three straight lines are triangles." The 
 proposition, " Men are wine-manufacturing and wine-drinking 
 animals," however, is particular in respect to the subject, and 
 universal in respect to the predicate ; its real meaning being, 
 " Some men are the only animals of this class that do exist," 
 and its converse, " All wine-manufacturing and wine-drinking 
 animals are men." The proposition, finally, " Some rational be- 
 ings are animals," is particular, both in reference to subject and 
 predicate, its real meaning being, " Some rational beings are 
 some (some one class of) animals," and its converse, consequent- 
 ly, " Some animals are rational beings." 
 
 In negative propositions also, there is the same quantification 
 of the predicate as in affirmative ones. In the proposition, 
 for example, " No animal is immortal," the subject and predi- 
 cate are both universal ; the real meaning of the proposition be- 
 ing, " Any animal is not any one immortal being," and its con- 
 verse, " Any immortal ' being is not any (any one) animal." In 
 the proposition, on the other hand, " Money is not all that is 
 valuable," the subject is universal, and the predicate, though 
 universal in form, is particular in fact ; that is, the thought which 
 it represents is particular. The converse, " All that is valuable 
 is not money," really means, " Some things that are valuable 
 are not money." The real meaning of the exposita, then, is, 
 "All of money that exists, is not some valuable things." In 
 the proposition, " Some currency is not metal," the subject is 
 particular, and the predicate universal, its real meaning being, 
 that " Some one kind of currency is not any kind of metal." In 
 the proposition, finally, " Some men are not like other men," 
 both the subject and predicate are particular, the real meaning 
 being, " Some individuals of a class are not like others of a given 
 class." So the proposition, " Some qualities of some individuals 
 
are not like other qualities of the same individual," is equiva- 
 lent to the proposition, " Some of A (the quality B) is not some 
 of A (the quality C)." 
 
 Rightly classified, then, we have eight instead of four classes 
 (A, E, I, 0) of propositions, as far as quantity is concerned, to 
 wit : four classes of affirmative, and four of negative, proposi- 
 tions. Of the affirmative we have : 
 
 1st.) The "Toto-total=A f a," those in which hoth the sub- 
 ject and predicate are universal, as to quality =" All A is all 
 of B." " (All) triangles are (include all) figures bounded by 
 three straight lines." 
 
 2d.) The " Toto-partial=A- f i," the universal affirmative 
 recognized by logicians, those propositions in which the sub- 
 ject is universal, and the predicate particular, "All men are 
 mortal (some mortal beings)" = " All A is some B." 
 
 3d.) The " Parti-total = I f a" = " Some A is all of B." 
 
 4th.) The " Parti-partial = I f i" = "Some A is B," that is, 
 some B the particular affirmative of logicians. 
 
 Of negative propositions, we have : 
 
 5th.) The "Toto-total=A n a" =" Any is not any" =" Any 
 man is not any irrational animal." This is E the universal 
 negative of logicians. 
 
 6th.) "Toto-partial:=A n i"="Any is not some" =" All of 
 A is not B," that is, some of B. "All of money is not all of 
 valuable things," that is, some valuable things. 
 
 7th.) " Parti-total = I n a"="Some is not any"="Some A 
 is not B," that is, any part of B. " Some currency is not 
 coin," that is, any coin. This is the particular negative of logi- 
 cians. 
 
 8tb.) " Parti-partial = I n i" = "Some is not some," that is, 
 "Some of A (B) is not some of A (C)." "Some men are not 
 like some other men." 
 
 This formula, though hitherto, as Sir William Hamilton af- 
 firms, " totally overlooked by logicians, is one of the most im- 
 portant and commonly used of all the others. It lies, indeed, 
 at the basis of all the processes of specification and individuali- 
 zation, that is, the process by which a class (genus or species) is 
 
PROPOSITIONS. 87 
 
 divided into its subject-parts, the counter-process, to wit: of 
 quantification." We have before us, for example, a certain class 
 of objects, we immediately begin to separate them into distinct 
 sub-classes, and these last we individualize, separate, and distin- 
 guish as individuals. How is this done ? It is wholly based 
 upon the perception (judgment), that some portions of the class 
 first named differ from some other portions of the same class ; 
 that is, upon the judgment, that " Some A is not some A." In 
 the sub-classes, we may find, by means of the same formula, 
 other specific differences, and thus continue the process till we 
 have arrived at the lowest species. This last is individualized, 
 as above stated. On the same principle, the qualities of the in- 
 dividual are separated from each other, till we come to elements 
 incapable of division the contradictory of the proposition- - 
 " Some is not some" being the affirmation of absolute indi- 
 viduality, or indivisibility. For the sake of perspicuity and elu- 
 cidation, as well as to bring out more fully the true aims of 
 logic itself, we now give the following lengthy extract from Sir 
 William Hamilton, an extract containing an objection to the 
 formula under consideration, and the author's reply to the same. 
 
 " Parti-partial Negation. 
 
 "To this Mr. do Morgan makes the following objection : 
 " ' Thirdly, the proposition, " Some X's are not some F~'s," 
 has no fundamental proposition which denies it, and not even a 
 compound of other propositions. It is then open to the above 
 objection ; and to others peculiar to itself. It is what I have 
 called (F, L, p. 153) a spurious proposition, as long as either of 
 its names applies to more than one instance. And the denial 
 is as follows : " There is but one A", and but one F, and X 
 is Y." Unless we know beforehand, that there is but one sol- 
 dier, and one animal, and that soldier the animal, we cannot 
 deny " that some soldiers are not some animals.'''' When- 
 ever we know enough of X and Y to bring forward " some 
 X's are not some F~'s," as what could be conceived to have 
 been false, we know more, namely, " no X is F," which, when 
 
88 LOGIC. 
 
 X and Y are singular, is true or false with "some X's are 
 not some Y's.' " 
 
 " Here, also, Mr. de Morgan wholly misunderstands the na- 
 ture and purport of the form which he professes to criticise. 
 He calls it ' a spurious proposition.' /Spurious, in law, means a 
 bad kind of bastard. This is, however, not only a legitimate, 
 for it expresses one of the eight necessary relations of proposi- 
 tion al terms, but, within its proper sphere, one of the most impor- 
 tant of the forms which logic comprehends, and which logicians 
 have neglected. It may, indeed, and that easily, be illogically 
 perverted. It may be misemployed to perform the function 
 which other forms are peculiarly adapted more effectually to 
 discharge ; it may be twisted to sever part of one notion from 
 part of another, the two total notions being already, perhaps, 
 thought as distinct ; and then, certainly, in this relation, it 
 may be considered as useless ; but in no relation can it ever 
 logically be denominated ' spurious.'' For why? Whatever 
 is operative in thought, must be taken into account, and, con- 
 sequently, be overtly expressible in logic ; for logic must be, 
 as it professes to be, an unexclusive reflex of thought, and 
 not merely an arbitrary selection a series of elegant extracts, 
 out of the forms of thinking. Whether the form that it ex- 
 hibits as legitimate, be stronger or weaker, be more or less 
 frequently applied ; that, as a material and contingent con- 
 sideration, is beyond its purview. But, the form in question 
 is, as said, not only legitimate not ' spurious' it is most im- 
 portant. 
 
 " What then is the function which this form is peculiarly 
 is, indeed, alone, competent to perform ? A parti-partial nega- 
 tive is the proposition in which, and in which exclusively, we de- 
 clare a whole of any kind to be divisible. ' Some A is not 
 some A,' this is the judgment of divisibility and of division ; 
 the negation of this judgment (and of its corresponding inte- 
 grant) in the assertion, that " A has no some, no parts," is the 
 judgment of indivisibility, of unity, of simplicity. This form is 
 implicitly at work in all the sciences, and it has only failed in 
 securing the attention of logicians, as an abstract form, because, 
 
PROPOSITIONS. 89 
 
 in actual use, it is too familiar to be notorious, lying, in fact, 
 unexpressed and latescent in every concrete application. Even 
 in logic itself, it is indispensable. In tbat science it constitutes 
 no less than the peculiar formula of the great principle of speci- 
 fication (and individualization), that is, the process by which 
 a class (genus or species) is divided into its subject-parts the 
 counter-process, to wit, of generification. And this great logi- 
 cal formula is to be branded by logical writers as ' spurious !' 
 No doubt, the particularity, as a quantity easily understood, is 
 very generally elided in expression, though at work in thought ; 
 or it is denoted by a substitute. Meaning, we avoid saying 
 ' Some men are not some men.' This we change, perhaps, into 
 'men are not men,' or 'how different are men from men,' or 
 ' man from man,' or ' these from those,' or ' some from other,' 
 &c. Still, ' some is not some,' lies at the root ; and, when we 
 oppose ' other,' ' some other,' &c, to ' some,' it is evident, that 
 ' other' is itself only obtained as the result of the negation, 
 which, in fact, it pleonastically embodies. For ' other than' is 
 only a synonym for ' is not ;' ' other (or some other) A,' is con- 
 vertible with ' not some A ;' while" there is implied by ' this,' 
 ' not that ;' by ' that,' ' not this ;' and by ' the other,' ' neither 
 this nor that ;' and so on. Here we must not confound the 
 logical with the rhetorical, the necessary in thought with the 
 agreeable in expression. 
 
 " Following Mr. de Morgan, in his selected example, and not 
 even transcending his more peculiar science, in the first place, 
 as the instance of division, I borrow his logical illustration from 
 the class ' soldier.' Now in what manner is the generic notion 
 divided into species ? We say to ourselves : ' Some soldier is 
 not some soldier,' for ' some soldier is (all) infantry ; some sol- 
 dier is (all) cavalry,' &c, and ' (any) infantry is not any caval- 
 ry.' A parti-partial negative is the only form of judgment for 
 division, of what kind soever be the whole (and Mr. de Morgan 
 can state for it no other). Again : in the second place, as the 
 example of indivisibility : ' Some of this point is not some of 
 this (same) point.' Such a proposition, Mr. de Morgan, as a 
 mathematician, cannot admit ; for a mathematical point is, ex 
 
hypothesis 'without some without some, and some 1 without 
 parts, same, and other ; it is indivisible. He says, indeed, that 
 a parti-partial negative cannot be denied. But if he be unable 
 to admit, he must be able to deny ; and it would be a curious 
 a singular anomaly, if logic offered no competent form for so or- 
 dinary a negation ; if we could not logically deny that /Socrates 
 is a class that an individual is a universal that the thought 
 of an indivisible unit is the thought of a divisible plurality?'' 
 
 Criteria by which Propositions properly falling under these 
 different classes may be distinguished from each other. 
 
 We will now attempt to give, what our author has not 
 formally done, special criteria, by which we may distinguish 
 propositions which fall under these different classes from one 
 another. The following, we think, will be admitted as univer- 
 sally valid, as such criteria : 
 
 1. When the object of the proposition is to give a correct and 
 full definition of a term or subject or to assert the essential 
 characteristics of an individual or class or finally, to assert a 
 real and perfect identity between the subject and predicate, 
 then the proposition is to be classed as toto-total affirmative. 
 Thus, in the definition, " A triangle is a figure bounded by three 
 straight lines," we mean, all triangles include all such figures. 
 So in all full definitions. When, on the other hand, we affirm 
 that " All equilateral triangles are equiangular," the predicate 
 represents a characteristic conception of the* subject. Of course, 
 it is found only in the subject, and always found in it. The sub- 
 ject and predicate, therefore, stand related ; as, "All A is all of 
 B." Of the same character is the proposition, " A good gov- 
 ernment is one that has the "good of its subjects as its object." 
 When we say, finally, " A Christian is a man who fears God," 
 we mean that there is a real identity between the subject and 
 predicate in this case. The proposition, therefore, like those 
 before mentioned, is equivalent to " All A is all of B." The 
 converse of all such propositions, consequently, is a universal 
 affirmative. 
 
PROPOSITIONS. 91 
 
 2. When the judgment really affirmed in a proposition is, 
 that individuals belong to a certain class, as, " John is a man," 
 or that all the individuals represented by an inferior conception 
 rank specifically under a superior conception, as, "All men are 
 animals," "All men are mortal," &c, then the proposition is 
 " toto-partial," the universal affirmative of logicians ; that is, the 
 subject is universal and the predicate particular ; and the con- 
 verse is a particular affirmative, " Some man is John," " Some 
 mortal beings are men," &c. 
 
 3. When the judgment affirmed in a proposition is, that a qual- 
 ity assumed as attaching exclusively to a certain class, but not to 
 all the members thereof, belongs exclusively to that class as, 
 " Men possess wealth ;" or, that a superior conception embraces 
 under it all the individuals included under an inferior one as, 
 " Some animals are men," " A part of currency is gold coin," 
 then the proposition is parti-total, the exposita being, " Some 
 men possess all of wealth," " Some part of currency is all of 
 gold coin," &o. ; and the converse a toto-partial affirmative, to 
 wit: "All of wealth is possessed by men (some men)," "All 
 gold coin is currency (some part of currency)." 
 
 4. When the judgment affirmed in a proposition is, that some, 
 not all, individuals of one class are like some, not all, individuals 
 of another, as, " Some men are long-lived animals," then the 
 proposition is a parti-partial affirmative, and its converse of the 
 same class, " Some long-lived animals are men." 
 
 5. When the judgment affirmed in a proposition is this, 
 that no individual of one class is a member of another class, 
 " No man is an angel ;" or, that a certain individual is utterly 
 void of given characteristics or class of characteristics, " John 
 possesses no virtue ;" or, that a certain individual does not be- 
 long to a certain class, " A is not an American," then the prop- 
 osition is a toto-total negative, and its converse will be of the 
 same character ; as, " No angel is a man (any man)," " No vir- 
 tue attaches to John," " No American is A," &c. 
 
 6. When one conception is admitted to represent all that 
 another does, and some other things besides, and when the ob- 
 ject of the proposition is to deny that what is embraced in the 
 
92 LOGIC. 
 
 former includes all that is embraced in the latter as, " All of 
 A is not all of B," that is, some of B then the proposition is a 
 toto-partial negative ; and its converse a parti-total negative, 
 " Some B is not A (any of A)". So when the object of a prop- 
 osition is to deny of an individual the totality of characteristics 
 represented by a given conception ; as, " A has not all the 
 vices," that is, some vices. 
 
 7. When the judgment affirmed in a given proposition de- 
 nies that some individuals of a given class have any of the char- 
 acteristics belonging to other individuals of the same class, or 
 to any individual of another class as, " Some members of the 
 university are not studious," " Some Americans are not pa- 
 triots," &c. ; or, that all the individuals embraced under a supe- 
 rior conception are found among those embraced under an infe- 
 rior one as, " Some animals are not brutes ;" the proposition 
 is then parti-total, and its real converse would be a toto-partial 
 negative, " All A is not some of B :" a certain class of studious 
 persons does not include some members of the university, or 
 any studious person is not some member of the university. 
 
 8. When the judgment affirmed in a given proposition de- 
 nies the absolute indivisibility of any object, or the absolute 
 likeness of all its qualities to one another as, " Some A (the 
 quality B) is not some A (the quality C) ;" or, that some mem- 
 bers of a given class are not like other members of the same 
 class as, " Some men are not men," that is, do not belong to 
 the class who properly represent humanity ; then the proposi- 
 tion is a parti-partial negative, and its converse the same. 
 
 Such are the principles of classification of propositions, when 
 respect is had to their sense, and not to the mere language m 
 which the sense is expressed. The rules presented in the pre- 
 ceding section are applicable, when reference is had, not to the 
 sense exclusively, but to the mere words of the propositions 
 themselves. 
 
 Scholia 1. The most philosophical or scientific classification 
 of propositions would be, as Sir William Hamilton observes, into 
 two classes the definite and indefinite. All universal and all 
 individual propositions are definite, affinning or denying in re- 
 
PROPOSITIONS. 93 
 
 gard to each and every individual referred to. The terms, 
 " John, any man, no man," &c., are each alike and equally defi- 
 nite. The term, "Some (some men)," is indefinite. So the 
 propositions, " John is an American," " Every man is mortal," 
 " No man is a brute," &c, are each and all alike definite propo- 
 sitions ; while the proposition, " Some men are learned," is in- 
 definite. As all propositions are either individual, universal, or 
 particular, and as the two classes first named are definite, and 
 the latter class indefinite, all propositions, if strict scientific pre- 
 cision were observed, would be classed as definite or indefinite. 
 
 Scholia 2. Propositions whose subject and predicate are both 
 definite, may properly be called definite-definite ; those whose 
 subject and predicate are both indefinite, might be called indefi- 
 nite-indefinite propositions ; those whose subject is universal 
 and predicate particular, the definite-indefinite ; and, finally, 
 those whose subject is particular and predicate universal, the 
 indefinite-definite. We thus have a complete and exhaustive 
 system of classifying propositions. 
 
 Scholia 3. All conversion of propositions in accordance with 
 the most perfect scientific procedure, is, as Sir William Hamil- 
 ton has affirmed, exclusively simple. Example : " All men are 
 mortal." Why is the converse of this proposition this, " Some 
 mortal beings are men ?" The reason is obvious, the subject of 
 the exposita is, in fact, universal, while the predicate is particu- 
 lar. The converse, on the other hand, as thought, is parti-total, 
 to wit : " Some mortal beings are all of mankind." Hence, we 
 have in reality, if we refer, not to the form, but to the matter 
 of the judgment, that is, to what is given in the thought, but 
 one form of conversion, that is, simple. Unless this principle is 
 kept distinctly in mind, logic, as a science, will not be under- 
 stood. 
 
CHAPTER III. 
 
 ANALYTIC OF ARGUMENTS OR SYLLOGISMS. 
 Section I. Abgument defined and elucidated. 
 
 An argument is an intellectual process in which one judg- 
 ment is deduced from another. All judgments are either intui- 
 tive or inferential, immediate or mediate. When the relation 
 between two objects or conceptions is such, that the mind has, 
 from the nature of said relation, a direct and immediate percep- 
 tion of the same, the judgment affirming such relation is called 
 intuitive or immediate. When, on the other hand, this relation 
 is discerned through other judgments, the judgments affirming 
 such relation is said to be inferential or mediate. 
 
 The characteristics of all valid immediate or intuitive judg- 
 ments have already been given. When the relations between 
 any two objects or conceptions, A and B, are not immediately 
 discernible, it is self-evident that such relations can be discerned 
 but upon one condition that each of those objects sustain 
 known or knowable relations to some one known object, C. 
 Through their discerned relations to this known object, we may 
 infer (discern) their relations to each other. Thus, if A and B 
 are both equal to C, we infer that they must be equal to each 
 other. If, on the other hand, one agrees and the other disa- 
 grees with C, we infer that they must disagree with each other. 
 On this principle, exclusively, all mediate judgments are de- 
 duced. 
 
 The term C, with which the others are compared, is called 
 the middle term. Those compared with it (A and B), are called 
 the extremes. Hence we remark : 
 
 1. That in no given argument can there be more than one 
 middle term. If there was, then the extremes would not be 
 compared with the same thing, and nothing pertaining to their 
 relations to each other could be inferred from the comparison. 
 
ANALYTIC OP SYLLOGISMS. 95 
 
 2. In such argument there must be two extremes, and there 
 can be no more. If there were more than two, there would be 
 a corresponding number of distinct arguments. 
 
 3. There must be, in such argument, when stated at length 
 and in full, three, and no more, and no less, propositions : two 
 called premises, hi one of which, one, and in the other the re- 
 maining extreme, is compared with the middle term, and the 
 conclusion or inference in which the relation of the two terms 
 is affirmed. The truth of this statement is too evident to need 
 any further elucidation. 
 
 Note. The subject of the conclusion is, in logics generally, 
 called the minor term, and the predicate of the conclusion the 
 major term. The premise in which the minor term is compared 
 with the middle, is called the minor premise, and that in Avhich 
 the major term is compared with the middle, is called the ma- 
 jor premise. 
 
 4. When each premise, together with the conclusion, is stated 
 in its proper form and order, the argument is then called a syl- 
 logism ; and this is what is meant by the term syllogism. For 
 
 example : 
 
 Every C is B ; 
 
 Every A is C ; 
 
 <* .-. Every A is B. 
 
 5. From the nature of the syllogism, as above denned and 
 elucidated, it is manifest that the following is, and must be, the 
 universal canon or principle in conformity to which all valid 
 conclusions must be deduced, namely : All conceptions or terms 
 which agree with one and the same third conception or term, 
 agree with each other, and any two conceptions or terms, the 
 one agreeing and the other disagreeing with said common con- 
 ception or term, disagree with each other. The validity of this 
 principle is self-evident. All forms, also, which the syllogism 
 can assume grow out of the diversified applications of this one 
 principle ; and the principle itself, always one and identical, 
 assumes different forms according to the nature of the relations 
 to which it is applied. 
 
 * The 6ign (.*.) will be U6ed to designate the term " therefore," or, the conclusion. 
 
DIVERSE FORMS OF THE SYLLOGISM. 
 
 The syllogism assumes diverse forms, each of which demands 
 especial elucidation. Among these we notice in this connec- 
 tion the following : 
 
 Section II. The Analytic and Synthetic Syllogism. 
 
 When the conclusion (more properly the theorem or propo- 
 sition to be proved) is stated first, and the propositions by 
 which it is to be proven are subsequently stated, the syllogism 
 is said to be analytic. For example : 
 
 Every A is B 
 
 Because, Every C is B 
 
 And, Every A is C 
 
 " Caesar was a usurper," because, perforce, he seized the reins 
 of government in Rome, and every one who does this is a 
 usurper. On the other hand, when the premises are stated first 
 in their proper order, and the conclusion last, the syllogism is 
 then called synthetic. For example : 
 
 Every C is B ; 
 
 Every A is C ; 
 
 .-. Every A is B. 
 
 Every one who forcibly seizes the reins of government is a 
 usurper. Caesar did this. Therefore, " Caesar was a usurper." 
 The following observations will sufficiently elucidate the nature 
 and relations of these two distinct forms of the syllogism : 
 
 These distinct forms of the Syllogism elucidated. 
 
 1. They differ not at all in thotight, but only in form. A 
 mere inspection of the two forms of syllogisms, as given above, 
 will render this statement self-evident. Each form consequent- 
 ly is equally valid. 
 
 2. The analytic is the most common and natural form of the 
 syllogism, it being a far more common procedure in reasoning 
 
ANALYTIC OF SYLLOGISMS. 97 
 
 to state first the proposition to be proved (conclusion or thesis), 
 and then to present the evidence of its truth, than it is to take 
 the opposite course. 
 
 3. "In point of fact," to quote the language of Sir William 
 Hamilton, to Avhom we would very gratefully acknowledge our- 
 selves indebted for the above . distinction, " the analytic syllo- 
 gism is not only the more natural, it is even presupposed by 
 the synthetic. To express in words, we must analyze in thought 
 the organic whole the mental simultaneity of a simple reason- 
 ing ; and then we may reverse in thought the process, by a syn- 
 thetic return. Further, we may now enounce the reasoning 
 in either order ; but, certainly to express it in the essential, pri- 
 mary, or analytic order, is not only more natural, but more 
 direct and simple, than to express it in the accidental, seconda- 
 ry, or synthetic." 
 
 4. The following citation from the same author wall still fur- 
 ther elucidate the importance of the distinction under consider- 
 ation : 
 
 " This in the first place relieves the syllogism of two one- 
 sided views. The Aristotelic syllogism is exclusively synthetic ; 
 the Epicurean (or Neocletian) syllogism was for it has been 
 long forgotten exclusively analytic ; while the Hindoo syllo- 
 gism is merely a clumsy agglutination of these counter-forms, 
 being nothing but an operose repetition of the same reasoning, 
 enounced, 1st. Analytically ; 2d. Synthetically. In thought 
 the syllogism is organically one ; and it is only stated in an 
 analytic or synthetic form from the necessity of adopting the 
 one order or the other, in accommodation to the vehicle of its 
 expression language. For the conditions of language require 
 that a reasoning be distinguished into parts, and these detailed 
 before and after each other. The analytic and synthetic orders 
 of enouncement are thus only accidents of the syllogistic pro- 
 cess. This is, indeed, shown in practice ; for our best reason- 
 ings proceed indifferently in either order. 
 
 " In the second place this central view vindicates the syllogism 
 from the objection ofpetitio pri?icipii, which professing logical- 
 ly to annul logic, or at least to reduce it to an idle tautology, 
 
defines syllogistic the art of avowing in the conclusion what 
 has been already confessed in the premises. This objection 
 (which has at least an antiquity of three centuries and a half) is 
 only applicable to the synthetic or Aristotelic order of enounce- 
 ment, which the objectors; indeed, contemplate as alone possi- 
 ble. It does not hold against the analytic syllogism ; it does 
 not hold against the syllogism considered aloof from the acci- 
 dent of its expression ; and being proved irrelevant to these, it 
 is easily shown in reference to the synthetic syllogism itself, that 
 it applies 1 only to an accident of its external form."* 
 
 5. As the analytic and synthetic syllogisms differ only in 
 form and are identical in thought, they mutually elucidate each 
 other. Suppose we have argued the ti'uth of some proposition 
 until we have, as we suppose, proved it. The argument has, as 
 is almost universally the case, been conducted wholly in the 
 analytic form. We now wish to test the validity of the argu- 
 ment. The best way to accomplish this will be, in most in- 
 stances, to change the form from the analytic to the synthetic, 
 and see whether the premises necessitate, as an inference, the' 
 truth of the proposition affirmed to have been proven. 
 
 6. For the reasons which have been already stated, the laws 
 and principles which govern these two forms of the syllogism 
 are one and identical. " Every especial variety in the one," to 
 use the language of the author above referred to, " has its cor- 
 responding variety in the other." 
 
 7. The error, we remark in the last place, of modern and 
 most of the ancient logicians, in treating the synthetic as the 
 only and exclusive form of the syllogism, is now sufficiently man- 
 ifest and no additional remarks upon the subject are necessary. 
 
 * The error involved in the above objection, even in its application to the synthetic syllo- 
 gism, may be made manifest by a single illustration. For example : 
 Gold is precious ; 
 This substance is gold ; 
 .'. It is precious. 
 It is very true, that what is here announced in the conclusion, is, in a certain form, 
 fessed in the premises. The object of the syllogism, however, is to announce in form, what 
 has previously been ascertained by investigation. Suppose the conclusion to be denied; 
 tests would then be applied to verify the minor premise. When its truth has been estab- 
 lished, then, and not till then, it logically takes its place as a premise. 
 
 

 ANALYTIC OP SYLLOGISMS. 
 
 Section III. Figured and Unfigured Syllogisms. 
 
 Science is indebted to Sir William Hamilton for another di- 
 vision of syllogisms of fundamental importance to a full and dis- 
 tinct understanding of the doctrine of the syllogism in general, 
 or of the universal process of reasoning. We refer to his dis- 
 tinction between the figured and unfigured syllogism. 
 
 In the figured syllogism, as we shall see hereafter, the terms 
 compared sustain to each other, in the several propositions, the 
 relations of subject and predicate, the figure of the syllogism re- 
 ferring to the situation of the middle term in the premises rela- 
 tively to the extremes. 
 
 In the unfigured syllogism, " the terms compared do not 
 stand to each other in the reciprocal relation of subject and 
 predicate, these being in the same proposition, on the other 
 hand, both subject and predicate." For example : 
 
 All C and some B are equal ; 
 All A and all B are equal ; 
 .-. All C and some A are equal ; or, 
 C and A are unequal. 
 
 Again, a question arises whether C and A were together dur- 
 ing the whole of a given journey taken by the latter. In reply, 
 it is affirmed, that from sources perfectly reliable, it has been 
 ascertained that hi the journey referred to, C and B were in 
 company only part of the distance travelled by the latter, and 
 that from sources equally reliable, it has been ascertained that 
 A and B were in company during the wJtole distance travelled 
 by each. The inference is hence drawn that C travelled but 
 a part of the distance referred to in company with A. This 
 conclusion is perfectly valid, and the form of argumentation 
 by which it is reached is as legitimate as any other, and 
 withal quite as worthy to be elucidated in a treatise on logic ; 
 and that for the obvious reason that it is one of the most com- 
 mon forms of reasoning in almost all departments of thought. 
 Indeed, logic, as a science, will be fundamentally incomplete 
 and imperfect, while it overlooks this one form of the syllogism. 
 
Without further remarks, we shall now proceed to elucidate 
 some of the laws and principles of the unfigured syllogism. 
 
 PRINCIPLES AND LAWS OF THE UNFIGURED SYLLOGISM. 
 
 The Canon of this Syllogism. 
 
 The canon of this syllogism we give in the language of the 
 author above quoted from. " In as far as two notions (notions 
 proper or individuals) either both agreeing, or one agreeing, 
 and the other disagreeing, with a common third notion : just so 
 far those notions do or do not agree with each other." Take 
 the following examples in illustration : 
 
 All C and all or some B are equal ; 
 All A and all B are equal ; 
 .-. All C and all or some A are equal ; 
 And consequently, C and A are, or are not, equal to each other. 
 Again : All C and one-half of B are equal ', 
 All A and all B are equal ; 
 .. All C and one-half of A are equal ; or, 
 C equals one-half of A. 
 Again : A to B, and E to F, are in the same proportional relations ; 
 But, E is three times F ; 
 .-. A is three times B. 
 
 If the minor had been in this case, A is three times B, the 
 conclusion would have been, that E is three times F ; and the 
 former couplet might as properly have been the minor, as the 
 latter. Had the relation above named been that of analogy, 
 the argument would be the same. 
 
 The following present other forms of the same Syllogism. 
 
 All C and some B are equal to Y ; 
 All A and all B are equal to T ; 
 .-. Some C is equal to all A ; or, 
 All A is equal to some C. 
 
 Suppose that it is known that the fortunes of C and B to- 
 gether are larger than that of Y (or all C and some B are equal 
 
ANALYTIC OP SYLLOGISMS. 101 
 
 to Y), while it has been ascertained that the united fortunes of 
 A and B are just equal that of Y (all A and all B are equal to 
 Y). We at once infer that the fortune of C is greater than that 
 of A, for the obvious reason, that when each is added to the 
 same thing the amounts differ as above stated. 
 
 Again : All C and half or all B are equal to Y ; 
 All A and all B are equal to Y ; 
 .-. All C is equal to half or all A. 
 
 So if we should say that C minus, multiplied or divided by 
 B, is equal to Y, and that A similarly related to B is equal to 
 Y, the conclusion would be A=C. If C thus related to B is 
 equal Y, and A thus related is greater or less than Y, we have 
 the conclusion that C is greater or less than A, as the case 
 may be. 
 
 The application of the above examples to negative conclu- 
 sions is so obvious, that little need be said on this topic. In all 
 instances in which the relation of equality between two concep- 
 tions has been proven, that of its absence and also that of 
 greater or less may be denied. So when that of greater or less 
 has been proved, the opposite of what is proven, together with 
 the relation of equality, may be denied. For example : 
 
 All C and all B=Y ; 
 All A and all B do not=Y ; 
 .-. C and A are not equal to each other. 
 
 So, also, when two conceptions pertain to their objects as 
 always coexisting, and neither as existing separate from the 
 other, or as sustaining to each other the relation of universal 
 compatibility, &c, and when the object of a third conception is 
 given as never coexisting, or as being incompatible with the 
 object of either of the others, the same relation between this 
 third and the remaining one may be denied. For example : 
 
 C and B always coexist, or, are universally compatible ; 
 A and B never coexist, or, are wholly incompatible ; 
 .-. C and A never coexist, or, are not compatible. 
 
General Remarks upon this form of the Syllogism. 
 
 The following general remarks upon this form of the syllo- 
 gism are deemed worthy of especial notice : 
 
 1. In it, the order of the propositions is, to use the language 
 of Sir William Hamilton, "perfectly arbitrary." In other 
 words, the unfigured syllogism has no proper major and minor 
 terms or premises. A mere inspection of the above examples 
 will render this statement self-evident. 
 
 2. In this syllogism, also, the terms of the conclusion are so 
 manifestly and formally equivalent and definite, as far as dis- 
 tribution is concerned, that conversion is almost if not quite 
 always simple, both in thought and form. Each term is given 
 as universal or particular. 
 
 3. This syllogism may also, with perfect propriety, be given 
 in the synthetic or analytic form. We may, for example, as 
 properly say, " C and A are equal," because " A and B, on the 
 one hand, and C and B on the other, are equal to Y," as to 
 state the premises first, and then give the conclusion as an in- 
 ference. 
 
 4. While this form of the syllogism had, until Sir William 
 Hamilton presented it, been wholly overlooked by logicians, it 
 presents one of the most common and necessary forms of valid 
 reasoning among all classes of the community, and especially in 
 the inductive sciences. Without this form of the syllogism, 
 therefore, logic, as a science, would be wholly incomplete and 
 limited in its applications.* 
 
 * In justice to myself, and to truth, I would say, that before I had seen what Sir William 
 Hamilton has written upon this subject, or had even heard that he had spoken or written 
 any thing upon it, my own independent investigation had led me to a conception of this 
 form of the syllogism, and to a careful inquiry into its principles and laws ; and at the time 
 when I read what he has written, my mind was employed in a Tain attempt to find a place 
 for it, in some department of the figured syllogism, and that under the apprehension, that 
 what logicians had assumed as true, was so, to wit : that the latter is the only real form of 
 the syllogism itself. I saw clearly, that in many forms of valid reasoning, the terms com- 
 pared did not "stand to each other in the reciprocal relation of subject and predicate, being 
 in the same proposition, either both subjects, or both predicates.'' I saw also, that the ex- 
 tremes in such case?, are not, as is true of the figured syllogism, each singly, and by itself, 
 compared with the middle term; but, that both alike, first one and then the other, stand 
 with the middle, in the common relation of subject and predicate ; and that, in all such 
 
ANALYTIC OF SYLLOGISMS. 103 
 
 Section IV. The Figured Syllogism. 
 
 This form defined. 
 
 We now advance to a special consideration of the figured syl- 
 logism. That which distinguishes this form of the syllogism 
 from every other is this, the fact which we have already stated, 
 that in all the propositions the terms are related to each other 
 
 Common assumption on the subject. 
 
 It has been commonly assumed that the terms employed in 
 the various propositions, stand related to each other as inferior 
 and superior conceptions, the subject being the inferior and the 
 predicate the superior. On this assumption the universal rules 
 of distribution are based, to wit : that while all universal propo- 
 sitions distribute the subject, all negative and no affirmative 
 ones distribute the predicate. The latter principle can be true 
 but upon the supposition, that the predicate is a superior and 
 the subject an inferior conception. In the proposition, "All 
 men are mortal," for example, the term mortal is not distributed, 
 for the reason that it has a wider application than the term men. 
 Suppose we say "X=Z;" then the predicate as well as the 
 subject is distributed, and that for the obvious reason that Z, in 
 this proposition, is a conception in no form or sense inferior 
 or superior to X. The converse of the former proposition is, 
 " Some mortal beings are men," while that of the latter is 
 "Z=X." In this last judgment neither conception is inferior 
 or superior to the other, and, therefore, both terms are m dis- 
 tributed. 
 
 cases, it made no difference as to the order of the premises. Yet I was under the impres- 
 sion, that after all, they "must have a place among the common forms of the syllogism, hav- 
 ing no suspicion that there could he any other legitimate form. From this perplexity I 
 was relieved, by the author referred to, and shall ever esteem it a high privilege to ac- 
 knowledge the obligations which I thereby owe to him. 
 
Influence of Assumptions. 
 
 This fact presents another example of the influence of assump- 
 tions. When they once obtain a place in science as first truths 
 or principles, the assumptions themselves are not examined, be- 
 cause their truth is always taken for granted. How true this is 
 of the case before us ! Since the days of Aristotle the principle 
 has been assumed, that in all propositions, with accidental ex- 
 ceptions, the subject is the inferior and the predicate the supe- 
 rior conception ; and from hence, the principle that no affirma- 
 tive proposition distributes the predicate. "It may happen, 
 indeed," says Dr. Whately, " that the whole of the predicate in 
 an affirmative may agree with the subject ; e. g. it is equally 
 true, that 'All men are rational animals,' and 'All rational 
 animals are men ;' but this is merely accidental, and is not at 
 all implied in the form of expression, which alone is regarded 
 in logic." 
 
 It is true, as Dr. Whately observes, that in cases where the 
 whole predicate in an affirmative proposition agrees with the 
 whole subject, the fact does not appear from the mere form of 
 expression ; and it is equally true, on the other hand, that 
 from the mere form of the expression it does not appear when 
 the whole predicate does not agree with the whole subject. 
 This fact is always to be determined by the nature of the con- 
 ceptions compared, and the nature of the relations between 
 them. 
 
 Principles determining the distribution of the Predicate. 
 
 We are now prepared for a distinct statement of the princi- 
 plesVhich determine the distribution and non-distribution, not 
 only of the subject, but predicate in all judgments employed in 
 reasoning. They are the following : 
 
 1. Whenever the subject and predicate stand related as infe- 
 rior and superior conceptions, then they follow the rules of dis- 
 tribution commonly laid down in treatises on logic, to wit : 
 (1.) All universal propositions (and no particular) distribute 
 
ANALYTIC OF SYLLOGISMS. 105 
 
 the subject : (2.) All negative (and no affirmative) the predi- 
 cate. 
 
 2. Whenever the terms of a proposition belong to the same 
 class, and are compared relatively to the principle of equality 
 and difference, as equal, greater, or less, or when they fall under 
 the relation of proximity or distance in time, or place, &c, then 
 in affirmative and negative propositions alike, the predicate fol- 
 lows the same principles of distribution as the subject. So, 
 when the subject and predicate are correlative terms ; as, 
 " Father and son ; cause and effect," &c, neither, as a con- 
 ception, is superior to the other ; and the predicate, when it 
 as the correlative of the subject becomes by conversion the 
 subject, its quantity is the same as that of the subject was. 
 Finally, when the predicate is used to define the subject, the 
 same principle obtains. The proposition, for example, " A - is 
 the cause of B," when converted becomes, " B is the effect 
 of A." 
 
 That the rules of distribution above stated are applicable uni- 
 versally to all propositions of the first class, is too evident to re- 
 quire much elucidation. In all cases where any class of facts 
 are placed under a universal principle, as, for example, " Murder 
 is criminal," " Such and such actions are right or wrong ;" or, 
 when any individual conception is ranked under a specifical, or 
 one or the other of these under a generical conception, as in the 
 judgments, " John is a man," " All men are mortal," &c. ; in all 
 such cases the predicate has a wider application than the sub- 
 ject, and is hence never distributed in affirmative propositions. 
 Even in negative propositions, the term which has in itself the 
 wider application is most commonly, though not always, the 
 predicate. Thus, in the language of another, it is more natural 
 to say, that " The apostles were no deceivers," than that " No 
 deceivers are apostles." 
 
 Let us now look at propositions of the second class of judg- 
 ments. When we say"X=Z,"for example, the two terms 
 are compared throughout their whole extent, and if one is 
 distributed, the other of course must be, or the equality 
 would not exist. Conversion, in all such cases, is simple, and 
 5' 
 
106 LOGIC, 
 
 never by limitation. If we say " X is greater than Z," the 
 converse holds universally, "Z is less than X;" each term 
 being alike and equally distributed in both cases. If we say, 
 " X is the cause of Z," then in the converse, Z is given equal- 
 ly universally, in the correlative form, as the effect of X. The 
 distribution of the subject and the predicate in both cases is 
 equal. 
 
 The same may be shown to hold true in all the cases which 
 are given as falling under this class. From the nature of the 
 case it cannot be otherwise. We are not here endeavoring to 
 find under what superior conception a given inferior one ranks, 
 or what inferior conception any given superior one includes. 
 We are not inquiring under what general principle any given 
 class of facts are to be classed. But we are inquiring in regard 
 to objects of the same class, and that relatively to the question 
 of their agreement or disagreement ; as, whether they are equal 
 or unequal, which is the greater and which the less, &c. In all 
 such cases it makes no difference whatever which term is the 
 subject and which the predicate ; both, in all cases, being equal- 
 ly distributed. 
 
 Fundamental mistake in developing the science of Logic. 
 
 In all treatises on the science of logic, as far as we know, with 
 the exception of Sir William Hamilton's works, and " Thomp- 
 son's Laws of Thought," the figured syllogism has been consid- 
 ered as covering all forms of the categorical argument. In de- 
 veloping the syllogism it has also been assumed, as we have 
 said, that the terms employed in the syllogism are related as in- 
 ferior and superior conceptions. Now while the science of logic 
 is developed upon such principles, it must remain as one of the 
 most imperfect and unsatisfactory of all the sciences. Take the 
 principle laid down as holding universally, that no affirmative 
 propositions distribute the predicate, and apply it to any of the 
 processes in the mathematics, and we shall find it wholly to fail ; 
 for these almost, if not quite universally, distribute the predicate 
 equally with the subject. The entire science of the mathematics 
 
ANALYTIC 0E SYLLOGISMS. 107 
 
 is based upon illogical principles, if this principle is correct. 
 Every one of its principles is convertible, not by limitation, 
 but simply. So of its subsequent deductions, not one of them 
 accord with the principle, that no affirmative propositions dis- 
 tribute the predicate. Take, as an example, the proposition, 
 " The square of the hypothenuse of a right-angled triangle is 
 equal to the sum of the squares of its two sides." If no affirm- 
 ative propositions distribute the predicate, and the universal 
 affirmative ones can be conveited but by limitation, then the 
 converse of the above proposition would be this : " Some part 
 of the sum of the squares of the two sides of such triangle 
 equals the square of the hypothenuse." But this is not the con- 
 verse of the above proposition ; that converse being universal 
 and not particular, and that for the reason that all universal 
 affirmative propositions of this class distribute the predicate as 
 well as the subject. Nor are such propositions of unfrequent 
 occurrence. We everywhere meet them in almost all depart- 
 ments of human thought, Indeed, it may be questioned which 
 is most numerous, those universal affirmative propositions which 
 do, and those which do not, distribute the predicate as well as 
 the subject, Take another example from common life, to wit : 
 " A resembles or is unlike B." The converse of all such propo- 
 sitions is not a particular but a universal affirmative, to wit : 
 " B resembles or is unlike A." We need not add further illus- 
 trations. 
 
 DIVISION OF THE PRESENT SUBJECT. , 
 
 In further elucidating the figured syllogism, we propose to 
 pursue the following order of investigation : 
 
 1. Those forms of the syllogism which have been commonly 
 treated of as including all forms of the categorical argument, to 
 wit : those forms in which the terms employed are related to 
 each other as inferior and superior conceptions. 
 
 2. Those forms in which affirmative propositions as well as 
 negative distribute the predicate. 
 
 3. We shall then combine the two classes, and endeavor to 
 develop the general laws of the figured syllogism as such. 
 
 
I. Those forms of the syllogism which have been com- 
 
 NONLY TREATED OF AS INCLUDING ALL FORMS OF THE CATE- 
 GORICAL ARGUMENT, TO WIT : THOSE FORMS IN WHICH THE 
 TERMS EMPLOYED ARE RELATED TO EACH OTHER AS INFERIOR 
 AND SUPERIOR CONCEPTIONS. 
 
 In entering upon the investigations which follow, we would 
 request the reader to keep distinctly in mind the kind of judg- 
 ments to he treated of, to wit : those in which the subject and 
 predicate represent respectively inferior and superior concep- 
 tions ; conceptions related to each, as individual, specifical, and 
 generical conceptions. 
 
 PRELIMINARY REMARKS UPON THIS FORM OF THE FIGURED 
 SYLLOGISM. 
 
 Before we proceed further, we would invite special attention 
 to the following preliminary remarks upon the department of 
 the subject before us. 
 
 Only proximate conclusions obtained. 
 
 On a moment's reflection it will appear perfectly evident, 
 that in this form of the syllogism we obtain only conclusions 
 approximating the truth ; that is, we determine not what indi- 
 viduals are in themselves, but with what class or classes they 
 take rank. Take, for example, the following syllogism : 
 
 All men are mortal ; 
 C is a man ; 
 .*. C is mortal, i. e. some mortal being. 
 
 We have here determined not the special characteristics of 
 C, but the particular and special class to which he belongs. 
 This is the character of all conclusions obtained through this 
 form of the syllogism, and from the nature of the case it must 
 be so. 
 
ANALYTIC OF SYLLOGISMS. 109 
 
 The principle of Extension and Intension, or of Breadth and 
 Depth, as applied to the Syllogism. 
 
 In our elucidation of superior and inferior conceptions we 
 showed that, while the matter of the latter is much greater than 
 that of the former, the sphere of the former is in a correspond- 
 ing degree more extensive than that of the latter. In regard 
 to matter, the individual conception embraces more elements 
 than the specifical, and this last more than the generical. At 
 the same time, this last conception is applicable to more objects 
 than the second, and the second to more than the first. The 
 terms extension and intension, breadth and depth, are em- 
 ployed by Sir William Hamilton to represent these two oppo- 
 site principles. In regard to depth (the matter of the concep- 
 tion), the individual is the lowest of all ; that is, includes the 
 greatest number of elements. In regard to breadth, the num- 
 ber of objects which the conception represents, that is, rela- 
 tively to its sphere, the generical conception is the most exten- 
 sive of all others. The two quantities are in relations perfectly 
 reverse to each other. The greater the depth, the less the 
 breadth of a conception ; and the greater its breadth, the less its 
 depth. In regard to breadth, the inferior conception is con- 
 tained under the superior. In regard to depth, the superior is 
 contained in the inferior. 
 
 In this form of the figured syllogism the propositions always 
 refer to one or the other of these principles. In affirmative 
 propositions the subject is an inferior conception, and the predi- 
 cate a superior. When of the two conceptions in a negative 
 proposition one has the greater breadth than the other, this 
 one, as we have before said, is commonly the predicate. 
 
 Now every proposition whose subject is an inferior and pred- 
 icate a superior conception, may be understood relatively to the 
 principle of intension (depth) or extension (breadth), and the 
 meaning of the proposition will be as the principle to which it 
 is referred. Thus the proposition, "All men are mortal," 
 means, in regard to intension, that the quality represented by 
 the term mortal, or mortality, belongs to every individual of 
 
the race ; and in regard to extension, that, all men belong to 
 the class of mortal beings. 
 
 In further elucidation of this very important department 
 of our subject, we "here present the following extract from 
 "Thomson's Laws of Thought." Of the last two examples 
 cited at the close of the extract, we would remark that the 
 term TJ designates toto-total affirmative propositions those in 
 which both subject and predicate are distributed ; and Y parti- 
 total affirmatives those in which the subject is particular and 
 the predicate universal ; as, " Some X is all of Z." 
 
 "Import of Judgments {Extension and Intension Naming). 
 
 " Upon the examination of any judgment which appears to 
 express a simple relation between two terms, we shall find it 
 really complex, and capable of more than one interpretation. 
 ' All stones are hard,' means, in the first place, that the mark 
 hardness is found among the marks or attributes of all stones ; 
 and in this sense of the judgment the predicate may be said to 
 be contained in the subject, for a complete notion of stones con- 
 tains the notion of hardness and something more. This is to 
 read the judgment as to the intention (or comprehension) of its 
 terms. Where it is a mere judgment of exj:>lanation, it will 
 mean, ' the marks of the predicate are among what I know to 
 be among the marks of the subject ;' but where it is the expres- 
 sion of a new step in our investigation of an accession of know- 
 ledge, it must mean, ' the marks of the predicate are among 
 what I now find to be the marks of the subject.' 
 
 " Both subject and predicate, however, not only imply cer- 
 tain marks, but represent certain sets of objects. When we 
 think of ' all stones,' we bring before us not only the set of 
 marks as hardness, solidity, inorganic structure, and certain 
 general forms by which we know a thing to be what we call 
 a stone, but also the class of things which have the marks, the 
 stones themselves. And we might interpret the judgment, 
 ' All stones are hard,' to mean that, ' The class of stones is con- 
 tamed in the class of hard things.' This brings in only the ex- 
 
ANALYTIC OF SYLLOGISMS. Ill 
 
 tension of the two terms according to which, in the example 
 before us, the subject is said to be contained in the predicate. 
 Every judgment may be interpreted from either point of view ; 
 and a right understanding of this doctrine is of great impor- 
 tance. Let it be noticed, against a mistake which has been re- 
 introduced into logic, that all conceptions, being general, repre- 
 sent a class ; and that to speak of a ' general name' which is not 
 the name of a class is a contradiction of terms. But this is very 
 different from asserting that a class of things corresponding . 
 to the conception actually exists in the world without us. The 
 conceptions of ' giants,' ' centaur,' and ' siren,' are all of classes ; 
 but every one knows who realizes them, that the only region in 
 which the classes really exist, is that of poetry and fiction. The 
 mode of existence of the things which a conception denotes is a 
 mark of the conception itself; and would be expressed in any 
 adequate definition of it. It would be insufficient to define 
 ' centaurs' as a set of monsters, half men and half horses, who 
 fought with the Lapithae, so long as we left it doubtful whether 
 they actually lived and fought, or only were feigned to have 
 done so ; and by some phrase, such as ' according to Ovid,' or, 
 'in the mythology,' we should probably express that their 
 actual existence was not part of our conception of them. 
 
 " The judgment selected as our example contains yet a third 
 statement. We observe marks ; by them we set apart a class ; 
 and, lastly, we give a class or name a symbol to save the trou- 
 ble of reviewing all the marks every time we would recall the 
 conception. ' All stones are hard,' means that the name hard 
 may be given to every thing to which we apply the name 
 stones. 
 
 "All judgments, then, may be interpreted according to their 
 intension, their extension, and their application of names or de- 
 scriptions ; as the following examples may help to show : 
 
 "A. ' All the metals are conductors of electricity,' means : 
 
 "Intension. The attribute of conducting electricity belongs to all 
 
 metals. 
 "Extension. The metals are in the class of conductors of electricity. 
 ' Nomenclature. The name of conductors of electricity may be ap- 
 plied to the metals (among other things). 
 
112 LOGIC. 
 
 " E. ' None of the planets move in a circle,' means : 
 
 "Internum. The attribute of moving in a circle does not belong to 
 any planet. 
 
 "Extension. None of the planets are in the class (be it real, or only 
 conceivable) of things that move in a circle. 
 
 " Nomenclature. The description of things that move in a circle can- 
 not be applied to the planets. 
 "I. ' Some metals are highly ductile,' means : 
 
 " Intension. The mark of great ductility is a mark of some metals. 
 
 "Extension. Some metals are in the class of highly ductile things. 
 
 "Nomenclature. The name of highly ductile things may be applied 
 tosome metals. 
 " 0. ' Some lawful actions are not expedient,' means : 
 
 " Intension. The attribute of expediency does not belong to some 
 lawful actions. 
 
 ' : Extension. Some lawful actions do not come into the class of expe- 
 dient things. 
 
 "Nomenclature.- The name of expedient cannot be given to some 
 lawful actions. 
 " U. ' Rhetoric is the art of persuasive speaking,' means : 
 
 "Intension. The attributes of the art of persuasive speaking, and of 
 rhetoric, are the same. 
 
 "Extension. Rhetoric is coextensive with the art of speaking per- 
 suasively. 
 
 "Nomenclature. 'The art of persuasive speaking' is an expression 
 which may be substituted for rhetoric. 
 " T. ' The class of animals includes the polyps,' means : 
 
 " Intension. The attributes of all the polyps belong to some animals. 
 
 " Extension. The polyps are in the class of animals. 
 
 " Nomenclature. The name of polyps belongs to some animals." 
 
 Direct and indirect conclusion. 
 
 All are aware that in every valid syllogism there are two 
 conclusions deducible from the premises laid down. One of 
 these conclusions is direct and immediate, and the other often, 
 though not always, as we shall see, indirect. In the premises, 
 for example, " All M is X, and all Z is M," we have the direct 
 conclusion, that " All Z is X." The converse of this is, " Some 
 X is Z," and this last proposition may be called the indirect 
 conclusion. It is optional, in view of the premises, to draw first 
 the direct conclusion, and then by conversion to obtain the in- 
 
dire' 
 
 ANALYTIC OF SYLLOGISMS. 
 
 rect conclusion, or to assume this last inference as implied in 
 the premises. 
 
 Character of all the propositions employed in this form of the 
 Syllogism. 
 
 The character of all the propositions of this form of the syllo- 
 gism next claims our attention. Every premise and conclusion 
 is either a universal affirmative proposition (A), a proposition 
 with a distributed subject and an undistributed predicate ; a 
 particular affirmative (I) with both the subject and predicate 
 undistributed ; a universal negative with both terms distribu- 
 ted (E) ; or, finally, a particular negative with the subject undis- 
 tributed and the predicate distributed (O). All propositions con- 
 stituted of inferior and superior conceptions must belong to one 
 or the other of these classes. 
 
 Letters to be employed. 
 
 In further prosecuting our investigations we will, in elucida- 
 ting the syllogism, make use of the letters X and Z to represent 
 the extremes, and M to represent the middle term. 
 
 CANON AND LAWS OF THIS FORM OF THE SYLLOGISM CONDI- 
 TIONS O? WHICH WE CAN OBTAIN THE DIFFERENT CLASSES 
 OF CONCLUSIONS ABOVE NAMED; THAT IS, A, I, E, O. 
 
 We now advance to a very important inquiry, to wit : the 
 special relations of the extremes to the middle term, relations in 
 which we can obtain these different classes of conclusions. 
 
 Universal Affirmative Conclusions. 
 
 There is but one conceivable relation of two such terms to a 
 common third term, a relation from which a universal affirm- 
 ative conclusion can be deduced, to wit : when all of the mid- 
 dle is contained hi one extreme, and all of the other extreme is 
 
114 LOGIC. 
 
 itself contained in said term. If all of M is in X and all of Z is 
 M, then, of course, all of Z must be in X. Change the relations 
 of the terms in any form or degree, and it will at once be per- 
 ceived that no such conclusion can then be logically deduced. 
 Stated in form this is the relation referred to : 
 
 All M is X ; 
 All Z is M ; 
 .-. AllZisX. 
 
 Universal Negative Conclusions. 
 
 There are two relations of the extremes to the middle term 
 from which universal negative conclusions arise, namely : 
 
 1. That in which all of the middle term is excluded from one 
 extreme, and all of the other is included in said term. If none 
 of M is in X, and all of Z is in M, then, of course, none of Z is 
 in X. From this relation we have one form of argument ; 
 
 No M is X ; 
 All Z is M ; 
 .-. NoZisX. 
 
 2. When all of one extreme is included in the middle term, 
 and all of the other is excluded from said term. If, for exam- 
 ple, all of X is in M and none of Z is in M, of necessity, none of 
 Z is in X. Here we have two forms, to wit : 
 
 No X is M ; All X is M ; 
 
 All Z is M ; No Z is M ; 
 
 .-. NoZisX. .-. NoZisX. 
 
 Particular Affirmative Conclusions. 
 
 There are three relations of two terms to a common third 
 term, relations from which particular affirmative conclusions 
 may be logically deduced. They are the following : 
 
 1. When all of the middle term is contained in one extreme, 
 and part of the other extreme is contained in said term. So 
 far as this part, which is common to the two extremes, is con- 
 

 ANALYTIC OF SYLLOGISMS. 115 
 
 cerned, they must agree with each other, and a particular affirm- 
 ative conclusion is logically valid. If all of M is in X and a 
 part of Z is in M, then, of course, a part at least of Z must be 
 in X ; and the proposition, " Some Z is X," will be valid. Of 
 this class Ave have one example, to wit : 
 
 All M is X ; 
 Some Z is M ; 
 .-. Some Z is X. 
 
 2. When all of the middle term is contained in each extreme. 
 If all of M is in both X and Z, then, so far as each contains M, 
 they must agree, and the proposition, " Some Z is X," must be 
 logically valid. Of this class, also, we have but one example : 
 
 All M is X ; 
 
 All M is Z ; 
 
 .. Some Z is X. 
 
 3. When all of the middle term is contained in one extreme 
 and part of it in the other. So far as this part, which is com- 
 mon to the two extremes, is concerned, they must agree with 
 each other, and the conclusion, " Some Z is X," must be held as 
 logically valid. Under this division we have two forms of valid 
 argument. For example : 
 
 All M is X ; Some M is X ; 
 
 Some M is Z ; All M is Z ; 
 
 .-. Some Z is X. .-. Some Z is X, 
 
 JParticular Negative Conclusions. 
 
 In the following relations particular negative conclusions are 
 valid. 
 
 1. When some of one extreme is contained in the middle 
 term and the whole of the other is excluded from it. In this 
 case the part of the one extreme contained in the middle must 
 be excluded from the other extreme, all of which is excluded 
 from the middle term, and the conclusion, " Some Z is not X," 
 is valid. We would here remark that a part of one term is 
 contained in another, when the former in the same proposition 
 
116 LOGIC. 
 
 as the latter is the subject of a particular, or the predicate of a 
 universal or particular affirmative proposition. A part of X, 
 for example, is equally contained in M in the propositions, 
 " Some X is M," " All M is X," and " Some M is X." In this 
 relation we have the following forms : 
 
 (1.) (2.) (3.) 
 
 NoMisX; No X is M ; No M is X. 
 
 Some Z is M ; ' Some Z is M ; All M is Z ; 
 
 . . Some Z is not X. . . Some Z is not X. . \ Some Z is not X. 
 
 (4.) (5.) . (6.) 
 
 No M is X ; No X is M ; No X is M ; 
 
 Some M is Z ; All M is Z : Some M is Z ; 
 
 . \ Some Z is not X. . . Some Z is not X. . \ Some Z is not X. 
 
 2. When the whole of one extreme is contained in the mid- 
 dle and a part of the other excluded from it. In this case the 
 part excluded from the middle must, of course, be excluded 
 from the other extreme, all of which is included in the middle 
 term. Of this form we have one example : 
 
 All X is M ; 
 Some Z is not M ; 
 .-. Some Z is not X. 
 
 3. When a part of the middle term is excluded from one ex- 
 treme and all of it contained in the other. In this relation, 
 also, but one single form presents itself, to wit : 
 
 Some M is not X ; 
 All M is Z ; 
 .-. Some Z is not X. 
 
 All valid conclusions deduced upon principles which accord 
 with those above elucidated. 
 
 From a careful examination of the above statements and ex- 
 amples, it will be seen not only that when the above relations 
 do exist between the extremes and the middle term, the dif- 
 ferent forms of conclusions referred to do arise, but that to de- 
 duce any legitimate conclusions of any kind, relatively to infe- 
 
ANALYTIC OF SYLLOGISMS. 117 
 
 rior and superior conceptions related to each other as subject 
 and predicate, these relations must exist. From no conceivable 
 relations of X and Z to M, for example, can we affirm that 
 "Every Z is X," but this, that "All of M is X and all of Z 
 is M." Vary these relations in any form or degree whatever, 
 and it will be seen at once that from such relations no such con- 
 clusion can be deduced. The same holds true in all the other 
 cases named. Let us now analyze these relations for the pur- 
 pose of deducing from them the general laws of the figured syl- 
 logism, especially in the form we are now considering it.* 
 
 Analysis of the above relations. 
 
 1. The fact which Ave first notice is this, that in all these forms 
 of argument we have, at last, one affirmative premise. In all 
 logically valid arguments, then, one premise at least must be 
 affirmative ; in other words, from exclusively negative premises 
 no relations between the extremes can be affirmed or denied. 
 From the fact that two terms disagree with a common third 
 term, we cannot affirm that they agree or disagree with each 
 other, for the reason that while they both do thus disagree with 
 this term, they may either agree or disagree with each other. 
 A and B may differ in size and weight from C, and one be 
 equal or unequal in all particulars to the other. 
 
 2. We notice, also, the fact that when the conclusion is 
 affirmative both premises are affirmative, and that when we 
 have a negative conclusion one of the premises is negative. 
 From the nature of the relations of the extremes to the middle 
 term this must be the case. When the relation of the extremes 
 to the middle term is positive, that is, when both agree with 
 that term, their relations to each other must be positive also. 
 When you affirm of the relation of one extreme to the middle 
 term what you deny of the other, a corresponding disagree- 
 
 * With very few if any exceptions these principles apply to all forms of the syllogism, 
 especially to the figured one. As thus applicable these principles should be studied, as they 
 present the only relations between the extremes and the middle term which authorize in- 
 ferences of any kind. 
 
118 LOGIC. 
 
 ment must be, of course, affirmed of the extremes themselves. 
 Hence the general principle that when both premises are affirm- 
 ative the conclusion must be affirmative, and when one premise 
 is negative such must be the character of the conclusion. 
 
 3. We notice, further, that in all cases one of the premises is 
 universal. From the fact that of the two extremes each partly 
 agrees, or that one in part agrees, and the other similar]}' disa- 
 grees with the middle term, we can 'draw no legitimate infer- 
 ence in regard to their agreement or disagreement with each 
 other ; because the points of agreement or disagreement may 
 not be the same at all, and the extremes, therefore, may not be 
 compared with the same thing. Suppose, for illustration, that 
 M has three, and only three, kinds of currency in his possession, 
 to. wit, gold, silver, and paper ; while X has the first kind and Z 
 the second. Each, in what he possesses, agrees in some respects 
 with M, yet neither agrees with the other. From the fact, then, 
 that two terms mutually agree or disagree in some respects 
 with a third, we cannot legitimately affirm or deny any form of 
 agreement or disagreement between those terms themselves. 
 Suppose, further, that X has gold coin and Z copper ; so far, 
 then, the former agrees and the latter disagrees with M. From 
 this fact, however, we cannot legitimately infer that Z has some- 
 thing (copper coin) which X has not ; for the latter, from aught 
 that appears in the premises, may have copper as well as gold 
 coin, and thus agree with Z as well as M. In all legitimate 
 forms of argument, therefore, one premise at least must be 
 universal. In other words, from particular premises we can 
 infer nothing. 
 
 4. From a careful examination of the above relations it will 
 also be seen, that in every case the middle term is given as the 
 subject of a universal, or the predicate of a negative proposition. 
 In all legitimate forms of argument this condition is, and must 
 be, fulfilled. From the fact that all X and all Z are in M, we 
 cannot logically conclude that any part of Z is in X ; for Z, 
 from any thing presented in the premises, may be in one part of 
 M and X in another, and neither have any form* of agreement 
 or disagreement with the same thing. So from the fact that 
 

 ANALYTIC OF SYLLOGISMS. 119 
 
 all X is in M and some of M is not in Z, we cannot legitimately 
 affirm that some part of Z is not in X ; for all of Z may, notwith- 
 standing what is affirmed in the premises, be in the part of M in 
 which X is. In all forms of argument, logically correct forms,' 
 which we are now speaking of, and which are included in the 
 sphere of the figured syllogism, the middle term must he the 
 subject of a universal or the predicate of a negative proposition ; 
 that is, must be distributed, at least, once in the premises. Nor 
 is it needful, as will appear from an analysis of the above cases, 
 that it be distributed more than once ; for if the whole of this 
 term is compared, as it is in the relations supposed, with one ex- 
 treme and a part only of it with the other, so far they must be 
 compared with the same thing, and so far, therefore, their rela- 
 tions to each other may from hence be determined. 
 
 5. In all the cases before us, we remark again, that the terms 
 of the conclusion are definite or indefinite ; that is, distributed 
 or not distributed just as they were in the premises. This is a 
 universal law of the figured syllogism, and hence the rule : no 
 term must be distributed in the conclusion which was not dis- 
 tributed in the premises. Where this rule is violated (the vio- 
 lation being called an illicit process of the term thus employed), 
 something is affirmed universally in the conclusion which was 
 only affirmed partially in the premises. 
 
 Note. It is not necessary that every term which was dis- 
 tributed in the premises should be distributed in the conclusion, 
 though such a use may always be made of it ; but when a uni- 
 versal conclusion is valid, the particular which comes under it is 
 valid also. 
 
 TJie Canon of this Syllogism. 
 
 "We are now prepared to state definitely the universal canon 
 of this form of the figured syllogism, a canon which to be valid 
 must embrace all of the principles above elucidated. As such 
 a canon, we present the following, to wit : Whatever relations 
 of subject and pi'edicate exist bettceen two terms and a com- 
 mon distributed third term, to which one at least of the former 
 is positively related, exist between the terms themselves. This 
 
120 LOGIC. 
 
 axiom will be found to include all eases which fall under this 
 form of the figured syllogism, inasmuch as it implies all the rela- 
 tions above adduced. 
 
 Moods of the Syllogism. 
 
 Every proposition must, as we have seen, be universal or par- 
 ticular, affirmative or negative. When we have designated the 
 propositions of a syllogism in order according to their respective 
 quantity and quality, we have determined its mood. Thus, if 
 all the propositions are universal affirmatives, we have the mood 
 A, A, A, &c. The following extract from Dr. Whately ex- 
 presses all that need be added on this subject with the excep- 
 tion subsequently stated : 
 
 " As there are four kinds of propositions and three proposi- 
 tions in each syllogism, all the possible ways of combining these 
 four (A, E, I, O) by threes, are sixty-four. For any one of 
 these four may be the major premise, each of these four 
 majors may have four different minors, and of these sixteen 
 pairs of premises each may have four different conclusions, 
 4X4(=16) x4 = 64. This is a mere arithmetical calculation 
 of the moods without any regard to the logical rules ; for many 
 of these moods are inadmissible in practice from violating some 
 of those rules ; e. g. the mood E E E must be rejected as hav- 
 ing negative premises ; IOO for particular premises ; and 
 many others for the same faults ; to which must be added 
 I E O for an illicit process of the major in every figure. By 
 examination then of all, it will be found that of the sixty-four 
 there remain but eleven moods which can be used in a legiti- 
 mate syllogism, viz. : AAA; AAI; AEE; AEO; All; 
 AOO; EAE; EAO; EIO; IAI; OAO." 
 
 Dr. Whately states that the mode I E involves " an illicit 
 process of the major in every figure." This must be admitted 
 if we grant that each figure alike has its proper major and mi- 
 nor terms and premises, which, as we shall hereafter see, is not 
 the case. That, on the other hand, must be regarded as an 
 allowable mood in which the conclusion necessarily results from 
 
ANALYTIC OF SYLLOGISMS. 121 
 
 the premises as presented. If we test the mood under consider- 
 ation by this principle, we shall find that it has the same claim 
 to be regarded as allowable as any of the others. That a legiti- 
 mate and valid conclusion may be deduced from such an ar- 
 rangement of the terms and premises, will be evident on a mo- 
 ment's reflection. For example : 
 
 Some X is M ; 
 
 No Z is M ; 
 .-. No Z is some X. 
 Converse : Some X is not Z. 
 
 No one can deny that both of the above conclusions directly, 
 immediately, and necessarily result from the premises. This, 
 tb*en, is an allowable mood, and we have twelve instead of 
 " eleven moods which can be used in a legitimate syllogism." 
 
 FIGUKE OF THE SYLLOGISM. 
 
 Form defined. 
 
 The figure of the syllogism is determined by the relations of 
 the middle term to the extremes, and the number of the figures 
 will be as the number of the relations which the terms admit. 
 
 Number of figures of the Syllogism. 
 
 A moment's reflection will convince any one that there are 
 three, and only three, such relations conceivable, to wit : 
 
 1. When the middle term is the subject of one extreme and 
 the predicate of the other. 
 
 2. When it is the predicate of both extremes. 
 
 3. When it is the subject of both. 
 
 We conclude, then, that there are three, and only three, fig- 
 ures of the syllogism, and they are numbered according to the 
 order above stated. We will give them in their order : 
 
 I. II. III. 
 
 MX; X M ; MX; 
 
 Z M ; Z M ; M Z ; 
 
 Z X ; Z X ; Z X. 
 
Major and Minor Terms and Premises. 
 
 On a consideration of the relation of the extremes to the mid- 
 dle term in the first figure, it will be seen at once, that the ex- 
 treme which is the predicate of the middle term, is, of all the 
 terms employed, of the widest extension, including first the mid- 
 dle term and then the other extreme, as included in the middle. 
 The term, therefore, which thus includes both the others is 
 properly called the major term ; and that which is determined 
 first by the middle term, and through it by the major, is called 
 the minor term. The premise which contains the major term is 
 called the major, and that which contains the minor term is 
 called the minor, premise. On examining the other figures', it 
 will be seen that in each alike the middle term sustains precise- 
 ly the same relation to the extremes. In neither of these fig- 
 ures, therefore, is either extreme given as a conception superior 
 or inferior to the other. In the second figure the middle term 
 is given as alike superior, and in the third, as alike inferior to 
 each of the extremes. In these figures, therefore, we have no 
 proper major or minor terms or premises. To place one as the 
 major and the other as the minor term or premise is a mere ar- 
 bitrary arrangement, and tends to obscure rather than throw 
 light upon the subject. 
 
 Order of the Premises. 
 
 In the first figure it is more natural to place the major premise 
 first, and then the minor ; though this is by no means univer- 
 sally the case. The following extract from " Thomson's Laws 
 of Thought" is worthy of very special attention on this subject : 
 " Although an invariable order for the two premises and con- 
 clusion, namely, that the premise containing the predicate of 
 the conclusion is first and the conclusion the last, is accepted by 
 logicians, it must be regarded as quite arbitrary. The position 
 of the conclusion may lead to the false notion that it never oc- 
 curs to us till after the full statement of the premises ; whereas 
 in the shape of the problem or question it generally precedes 
 
ANALYTIC OF SYLLOGISMS. 123 
 
 them, and is the cause of their being drawn up. In this point 
 the Hindoo syllogism is more philosophic than that which we 
 commonly use. The premises themselves would assume a dif- 
 ferent order according to the occasion. It is as natural to be- 
 gin with the fact and go on to the law, as it is to lay down the 
 law and then mention the fact. 
 
 " I have an offer of a commission ; now to bear a commission 
 and serve in war is (or is not) against the divine law ; therefore 
 I am offered what it would (or would not) be against the divine 
 law to accept. 
 
 " This is an order of reasoning employed every day, although 
 it is the reverse of the technical ; and we cannot call it forced 
 or unnatural. The two kinds of sorites to be described below, 
 are founded upon two different orders of the premises ; the one 
 going from the narrowest and most intensive statement up to 
 the widest, and the other from the widest and most extensive 
 to the narrowest. The logical order cannot even plead the 
 sanction of invariable practice. Neither the school of logicians 
 who defend it, nor those who assail it, take a comprehensive 
 view of the nature of inference. Both orders are right, because 
 both are required at different times ; the one is analytic, the 
 other synthetic ; the one most suitable to inquiry, and the other 
 to teaching." 
 
 In the second and third figures, no order whatever of the 
 premises is suggested by the relations of the extremes to the 
 middle term ; nor does the validity of the conclusion depend at 
 all upon their order ; either order is to be employed, as occasion 
 requires. 
 
 FINAL ABOLISHMENT OF THE FOURTH FIGURE. 
 
 Opinions of Logicians upon the subjett. 
 
 Logicians have commonly made four instead of three syllo- 
 gistic figures, to wit : that in which the middle term is the sub- 
 ject of the major premise, and the predicate of the minor ; that 
 in which it is predicate of both extremes; that in which it is 
 
124 LOGIC. 
 
 the subject of both ; finally, that in which it is the predicate of 
 the major premise and the subject of the minor. 
 
 When we met with the statement of Sir William Hamilton, 
 that science requires the " final abolition of the fourth figure," a 
 statement for which he gives no reasons in any of his writings 
 that we have met with, we at first supposed that we had fallen 
 upon the statement of an unnecessary attempt, if nothing more, 
 at simplification in the science of logic. A careful examination 
 of the figure, however, together with that of the possible rela- 
 tions of the extremes to the middle term, has convinced us of the 
 truth and importance of this statement. We fully agree with 
 this author that there can be, upon scientific principles, but 
 " three syllogistic figures," and will proceed to give our reasons 
 for that conviction, reasons for which we are alone responsible, 
 as they are to us the exclusive result of our own investigations. 
 Our reasons, among others, are the following : 
 
 Our reasons for the abolition of this Figure. 
 
 1. The relations which we have given embrace, as we have 
 said, all conceivable relations which a single term can, as subject 
 and predicate, sustain to two others in two given propositions, 
 to wit : the subject of one extreme and the predicate of the 
 other; the subject of both ; and the predicate of both extremes. 
 As but three relations are conceivable, science permits but three 
 syllogistic figures. 
 
 2. The premises of the fourth figure are in fact nothing but 
 those of the first transposed, such transposition being allowable 
 and always understood as implying no change of the figure of 
 the syllogism. For example : 
 
 All M is X ; All X is M ; 
 
 All Z is M. All M is Z. 
 
 In the first example we have the premises of Barbara in the 
 first figure, and in the second of Brumantip of the fourth. Let 
 X in the latter case take the place of Z and Z of X, and every 
 one Mall perceive that we have nothing but the premises of Bar- 
 

 ANALYTIC OP SYLLOGISMS. 125 
 
 bara changed. This is the case in all instances in the fourth 
 figure. It is contrary to all the laws of science, therefore, to 
 Buppose a new figure to meet the case of a mere change of the 
 order of the premises. 
 
 3. In the fourth figure, as given by logicians who retain it, 
 the scientific major term is given as the minor and the minor as 
 the major; so of the premises. Take Brumantip as an illus- 
 tration : 
 
 All X is M ; 
 
 All M is Z ; 
 
 .-. Some Zis X. 
 
 Who does not perceive that Z is here the superior, M the inter- 
 mediate, and X the inferior conception ? Z, in the first in- 
 stance, as the superior conception contains M as its inferior con- 
 ception, and then M as the superior contains X as its inferior 
 conception. Z, then, according to all the laws of science, is the 
 superior conception, and the consequent only proper major 
 term. X is the proper minor ; and Z the proper major term. 
 The same holds true of all the moods of this figure. 
 
 4. In this figure, as given by logicians, the indirect is, in all 
 instances, substituted for the direct conclusion. The direct con- 
 clusion from the premises of Brumantip, for example, is "All 
 X is Z," and not " Some Z is X." If all X is in M and all of 
 M in Z, then all of X must be in Z ; and this is the direct, and 
 only direct, conclusion. The proposition, " Some Z is X," is 
 but the converse of the inference which the premises directly 
 yield. The same holds true of every mood in this so called 
 figure. No reasons whatever, then, exist for retaining it ; all 
 the laws and principles of true science, on the other hand, de- 
 mand its "final abolition." It may be often convenient to 
 change the order of the premises of the first figure, and to state 
 its indirect conclusion as immediately evident from the premises, 
 which is often done. For this reason, however, we should not 
 confuse the principles of science by supposing a new figure. 
 
 
SPECIAL CHARACTERISTICS AND CANON OF EACH OF THE THREE 
 FIGURES. 
 
 On a careful examination of the three remaining figures, we 
 shall perceive that in consequence of the peculiar relations of 
 the middle term to the extremes in each, that each must have 
 its peculiar and special characteristics, and be governed by laws 
 equally special and peculiar. We will take them up in the 
 order in which they are numbered : 
 
 FIGURE I. 
 
 In the first figure, the middle term, as the subject of the ma- 
 jor term, is determined by said term, while it (the middle), as 
 the predicate of the minor, itself determines the same, and in 
 the immediate conclusion the determining extreme stands as 
 the predicate, and the determined as the subject. In this figure 
 consequently we have, from the relations of the terms to each 
 other, our proper major and minor terms and equally proper 
 major and minor premises. From these facts the proper order 
 of the premises, as well as the relations of the extremes as sub- 
 ject and predicate in the conclusion, become perfectly manifest. 
 In this figure, also, for the reasons just stated, we have one, and 
 only one, direct, immediate, and proximately definite conclu- 
 sion ; and, mediately, the converse of the same. As an illustra- 
 tion of the above statement let us take, as an example, the 
 mood Barbara : 
 
 All M is X ; 
 
 All Z is M ; 
 .-. AllZisX. 
 Converse : Some X is Z. 
 
 Here it will be seen that we pass from one extreme (X) to 
 the other (Z), through the middle term (M) ; X being given as 
 containing all of M, that is, as determining it, and M in a simi- 
 lar manner as determining Z. In the conclusion, also, each 
 term sustains to the other the identical relation which it did to 
 the middle in the premises in which it appears. X contains Z, 
 that is, determines it, as it did M in the major premise ; and Z 
 
ANALYTIC OF S.YLLOGISMS. 127 
 
 is contained in X, that is, is determined by it, as the former 
 was by M in the minor premise. The relations of the extremes 
 to each other in the conclusion, also, are necessarily determined 
 by their relations to the middle term in the premises ; no other 
 order than that which gives X as the predicate and Z as the 
 subject of the conclusion, being permitted by their relations in 
 the premises to the middle term, through which their relations 
 to each other, as expressed in the conclusion, are determined. 
 It is by no arbitrary arrangement, therefore, that X is given as 
 the major term, and the premise containing it as the major 
 premise ; and Z as the minor term, and the premise containing 
 it as the minor premise. From the nature of the relations of 
 the terms in the premises, also, but one conclusion, Z is X, is 
 directly and immediately given, and this conclusion is a proxi- 
 mately definite one. 
 
 Similar remarks are equally applicable, as a careful examina- 
 tion will show, to all the other moods of this syllogism. This 
 figure, therefore, has a special canon which is the following, 
 to wit : 
 
 Whatever relations of determining predicate and of deter- 
 mined subject exist between two terms and a common dis- 
 tributed third term, to which one at least is positively related, 
 that relation said terms immediately, that is, directly, hold 
 to each other ; and mediately, that is, indirectly, its converse. 
 
 The Canon illustrated. 
 
 We will now, as a means of illustrating this canon, examine 
 each of the moods in this figure. Barbara has already been suf 
 ficiently elucidated. We will, therefore, simply give an exam- 
 ple of reasoning in this mood, without the use of letters. The 
 case we present is cited from Dr. Whately, and presents the 
 celebrated argument of Aristotle' (Mh., sixth book), to prove 
 that the virtues are inseparable, viz. : 
 
 " He who possesses prudence possesses all virtue ; 
 He who possesses one virtue must possess prudence ; 
 Therefore, he who possesses one possesses all." 
 
128 i^ogic. 
 
 We will give Celarent in both forms, to wit, with and with- 
 out the letters : 
 
 No M is X ; 
 Every Z is M ; 
 
 .-. NoZisX. 
 Converse : No X is Z. 
 
 Whatever is conformable to nature is not hurtful to society ; 
 
 Whatever is expedient is conformable to nature ; 
 Therefore : Whatever is expedient is not hurtful to society ; 
 Converse : Whatever is hurtful to society is never expedient. 
 
 In both these examples alike there is a perfect conformity to 
 the canon above given. The term included in or determined 
 by the middle is the subject, and the one excluded from, and 
 thus determining the middle, is the predicate of the conclusion. 
 This determines the character and relations of the extremes and 
 of the premises also. We will now consider the two remaining 
 moods, Darii and Ferio. 
 
 All M is X ; No M is X ; 
 
 Some Z is M ; Some Z is M ; 
 
 .'. Some Z is X. .-. Some Z is not X. 
 
 Converse : Some X is Z. Converse : Some not X is Z ; 
 
 Or better, perhaps : No X is some Z. 
 
 The remarks made above are so obviously applicable to these 
 two moods, that we need add nothing in particular with respect 
 to them. From an inspection of the four moods above given, it 
 will appear that they present the only possible combinations of 
 the premises according to the immutable laws of this figure. 
 In this figure alone, also, can all of the four classes of proposi- 
 tions A, E, I, and O, be proven. 
 
 FIGTJKE II. 
 
 In elucidating the second figure, we will first present all its 
 allowable moods, as given in the common treatises on logic. 
 The letters prefixed will indicate the quantity of the propo- 
 sitions : 
 
ANALYTIC OF SYLLOGISMS. 
 
 
 Cesare. 
 
 Camestres. 
 
 Fesiino. 
 
 
 Baroko. 
 
 E. 
 
 XisM; 
 
 A. XisM; 
 
 E. XisM; 
 
 
 A. XisM; 
 
 A. 
 
 ZisM; 
 
 E. ZisM; 
 
 I. ZisM; 
 
 
 0. ZisM; 
 
 .-. E. 
 
 Z is X, or, 
 
 .-.E ZisX, or, 
 
 .-.0. ZisnotX, 
 
 or, 
 
 .-.0 ZisnotX, or, 
 
 E. 
 
 XisZ. 
 
 E. XisZ. 
 
 I. not X is Z, 
 
 or, 
 
 I. not X is Z, or, 
 
 
 
 
 No X is some 
 
 Z. 
 
 No X is some Z. 
 
 In this figure, as will be readily perceived, we have in neither 
 extreme a determining predicate as we have in the first. We 
 have in each extreme alike, on the other hand, nothing but de- 
 termined subjects. As a consequence we have no proper major 
 or minor terms or premises, each extreme sustaining in these 
 respects precisely similar relations to the middle term. The va- 
 lidity of the conclusion in no sense depends upon the order of 
 the premises. In the first two moods, for example, we have by 
 one order of the premises, Cesare, and by a simple change of 
 the order we have Camestres. Nor can any reason be assigned 
 why Z instead of X should be held as the minor term, or why 
 the premise containing it should be considered as the minor 
 premise. In the premises sometimes one and sometimes the 
 other term is given as in part or wholly included in, and the 
 ofher, in each case, as in whole or in part excluded from, one 
 and the same term. By what law of intellectual procedure 
 should one of the extremes be called the major term and its 
 premise the major premise, and the other the minor term and 
 its premise the minor premise ? For the same reason we have 
 no fixed law of subordination for the extremes in the conclusion. 
 We have, on the other hand, in all instances two conclusions, 
 each connected with the same distinctness and immediateness 
 with the premises, to wit : " No Z is X, or, no X is Z ;" " Some 
 Z is not X, or, some not X is Z." A mere reference to the 
 moods of this figure as above given, is all that is requisite to 
 verify the above statement. In Camestres, for example, X sus- 
 tains the precise relation to M that Z does in Cesare, and vice 
 versa. The inference, then, " No X is Z," is just as directly 
 and immediately deducible from the premises, as its converse 
 "No Z is X." The same remarks are equally applicable to the 
 conclusions, " Some Z is not X," and " Some not X is Z," ob- 
 
 ftnrivaEsiTT] 
 
130 LOGIC. 
 
 tained in Festino and Baroko. If, for example, " All X is in 
 M," and " Some Z is not in M," the conclusion, " Some not X is' 
 Z," as immediately follows as its converse, " Some Z is not X." 
 The difference here lies not in the connection of the conclusion 
 with the premises, hut in the fact that in one case we have an 
 apparently affirmative conclusion when we have a negative 
 premise. The conclusion, however, is, as far as mere conven- 
 tional form is concerned affirmative, while in reality it is nega- 
 tive. So far, then, as this kind of affirmative propositions are 
 concerned we may have in this, as we shall see in Figure III., 
 an affirmative conclusion when we have one negative premise. 
 What we desire to call especial attention to, is the fact, that this 
 conclusion is as directly and immediately deducible from the 
 premises, as its negative converse " Some Z is not X." In this 
 figure, then, the premises always yield with the same distinct- 
 ness and immediateness two conclusions. In consequence of the 
 fact, that we have no proper major or minor premises in this 
 figure, we have, by a change of the order of the premises in the 
 cases of Festino and Baroko, two additional allowable moods, 
 making its real number six instead of four. 
 
 Canon of this Figure. 
 
 The following, then, is the special canon of this figure, to wit : 
 Whatever relations of determined subject is held by two notions 
 to a common distributed thirfl, with which one is positively and 
 one distributively, that is, negatively, related, that relation these 
 conceptions hold indifferently to each other. 
 
 In illustrating this canon we will first take the case of Cames- 
 tres. In this syllogism X is given as wholly agreeing, and Z 
 as wholly disagreeing, with a common distributed third term, 
 M, to which both stand related as determined subjects. In 
 other words they, as determined subjects, wholly disagree in 
 their relations to a common distributed third term. Similar re- 
 lations of subject and predicate must they sustain to each other ; 
 and the propositions, " No X is Z," and " Xo Z is X," must be 
 held as logically valid. In Cesare X is positively and Z nega- 
 
ANALYTIC OF SYLLOGISMS. 131 
 
 tively related to M. In all other respects, therefore, their rela- 
 tions to each other must be as in Camestres. In the other syl- 
 logisms of this figure. X is given as wholly agreeing or wholly 
 disagreeing with M, and Z as undistributed, and as such as sus- 
 taining in each case opposite relations to M. In other words, 
 in these syllogisms these terms as determined subjects partially 
 disagree in their relations to M. In their relations as subject 
 and predicate to each other, therefore, they are given as partial- 
 ly disagreeing with each other. The canon includes every case 
 that can fall under this figure. 
 
 FIGURE III. 
 
 The following are 
 
 the syllogisms of this 
 
 figure as commonb 
 
 given, namely : 
 
 
 
 Darapti. 
 
 JDimmis. 
 
 Datisi. 
 
 A. MisX; 
 
 I. MisX; 
 
 A. MisX; 
 
 A. MisZ; 
 
 A. MisZ; 
 
 I. MisZ; 
 
 .-. I. ZisX, or, 
 
 .-. I. ZisX, or, 
 
 .-. I. ZisX, or, 
 
 I. XisZ. 
 
 I. XisZ. 
 
 I. XisZ. 
 
 Felapton. 
 
 Bokardo. 
 
 Ferison. 
 
 E. MisX; 
 
 0. MisnotX; 
 
 E. MisX; 
 
 A. MisZ; 
 
 A. MisZ; 
 
 I. MisZ; 
 
 .-. 0. ZisnotX, or 
 
 , . . 0. Z is not X, or, 
 
 .-. 0. ZisnotX, or, 
 
 I. not X is Z. 
 
 I. not X is Z. 
 
 I. not XisZ. 
 
 In this figure the middle is in both premises alike the deter- 
 mined subject, and not the determining predicate, as in the 
 second. As one extreme determines the middle in the precise 
 form that the other does, we have here, also, no proper major 
 and minor terms or premises. The order of the premises being 
 indifferent, equally so is that of the terms in the conclusion. 
 As each premise may stand indifferently as major or minor, so 
 each extreme may be indifferently the subject or predicate of 
 the conclusion. In.other words, as in the second figure, so in 
 this, the premises always yield with equal distinctness and im- 
 mediateness two conclusions, one in which one extreme, and 
 
 
another in which the other extreme, is the subject. A careful 
 examination of each of the above moods will 'perfectly evince 
 the truth of all these statements, and will also show that, by a 
 simple change of the order of the propositions in the case of the 
 three last-named moods, we have three more allowable ones in 
 this figure. 
 
 Canon of this Figure. 
 
 The following, then, is the special canon of this figure, to wit : 
 Whatever relations of determining predicate any two terms 
 sustain to a common distributed third term, to which one, at 
 least, of the former is positively related, those relations these 
 terms sustain indifferently to each other. The application of 
 this canon is too obvious to require any special elucidation. 
 
 Note. In giving to each figure an especial canon, we have 
 followed the example of Kant and of Sir William Hamilton. 
 Our statement of these canons differs, not in thought but in 
 form, from that found in the writings of these authors. 
 
 Absurdity of reducing the Syllogisms of the other Figures to 
 the first. 
 
 In the Intellectual Philosophy, page 320-1, we stated years 
 ago our objections to a practice common to almost all treatises 
 on logic, of reducing the syllogisms of the other figures to the 
 first. We are quite happy to find our objections sustained by 
 such authority as that of Sir William Hamilton. At the time 
 we stated these objections we had never read or heard of his 
 thoughts upon the subject, and he, of course, has never met 
 with ours. Our objections to this practice, among others, are 
 the following : 
 
 1. The laws of thought may be fully elucidated without any 
 reference to figure. This we have already sufficiently shown in 
 determining, wholly independent of any reference to the figure, 
 the conditions on which all valid conclusions can be deduced. 
 
 2. Figure itself, as Sir William Hamilton observes, is "an 
 unessential variation in syllogistic form." The middle term is 
 
ANALYTIC OF SYLLOGISMS. 133 
 
 just as really and truly compared with the extremes, and the 
 conclusions thence deduced are just as valid, in one figure as in 
 any other. Not a solitary ray of light is thrown upon the sub- 
 ject by the reduction. This we have already shown in the pas- 
 sage in the Philosophy above referred to. 
 
 3. The science of reasoning is, consequently, rather obscured 
 than elucidated by the process. The pupil expects light and 
 finds none ; the disappointment obscures rather than illumines 
 his vision of the principles of the science. 
 
 4. The pupil, we remark finally, is actually deceived by the 
 process. He is made to think that the validity of one syllogism 
 depends, not upon the relations of the extremes to the middle 
 term, relations found in the syllogism itself, but upon that of 
 other relations found in a syllogism of another and different 
 figure, whereas the reverse of all this is in fact true. The va- 
 lidity of the process, in each syllogism alike, depends exclusively 
 upon the relations to each other of the terms found in it. 
 These considerations are abundantly sufficient to justify us in 
 totally disregarding the custom under consideration. 
 
 Nature of the conclusions obtained in this form of the Syllo- 
 gism. 
 
 We have already stated that in this form of the syllogism, 
 there is in reality but an approach towards the truth, that is, 
 the whole truth pertaining to the objects of inquiry. It may 
 be a matter of no little interest and importance to consider, for 
 a few moments, the nature of the conclusions which we do ob- 
 tain. What then is the nature of the agreement or disagree- 
 ment between the subject and predicate really affirmed in said 
 conclusions ? Suppose that in the first figure we have obtained 
 the conclusion, " All or some Z is X." That answer may be 
 considered relatively to the principle of intension or extension. 
 In reference to the former, the conclusion affirms that Z pos- 
 sesses the elements represented by the superior conception X. 
 In reference to the latter, it affirms that all or some of the indi- 
 viduals represented by the individual or specifical conception Z, 
 
 
do belong to the class represented by the specifical or generical 
 conception X. What pertains to Z in other respects is not 
 affirmed or denied. So in the negative conclusion, "All or 
 some Z is not X," we simply ascertain, that in so far as the 
 qualities represented by the conception M are ever concerned, 
 they differ, one having, and the other not having, them. How 
 far they may or may not agree in other respects, is not ascer- 
 tained. 
 
 In the second figure, from the fact that one extreme does, and 
 the other does not, rank in whole or in part under a given supe- 
 rior conception, we infer that they therefore so far disagree. 
 This disagreement pertains simply and exclusively to the quali- 
 ties or class represented by said superior conception. How far 
 they agree or disagree in other particulars is not ascertained. 
 Suppose, for example, that it has been ascertained that A is, 
 and B is not, guilty of murder ; m other words, that A is not B. 
 In very many particulars, such as taking life and intentionally 
 doing it, and doing it with the same weapons, they may agree. 
 What has been ascertained is, that relatively to the peculiar 
 elements ^represented by the term murder, the act of one does, 
 and that of the other does not, involve said elements. . This is 
 the real character of the conclusions obtained in this figure. 
 
 In the third figure, in affirmative propositions, we ascertain, 
 from the fact that certain elements represented by a certain 
 conception M belong to a part of each of the classes represented 
 by two conceptions Z and X, each superior to M, that some in- 
 dividuals ranking under each of these superior conceptions have, 
 either both the whole, or one all, and the other a part, of the 
 qualities represented by M, and, therefore, that they so far 
 agree. The agreement ascertained pertains exclusively to the 
 qualities referred to. In negative conclusions, from the fact 
 that the elements referred to do belong to a part of one class 
 and not to a part of another class, it is affirmed that so far por- 
 tions of these classes do not agree with each other. The disa- 
 greement is always specific, and pertains exclusively to the ele- 
 ments represented by the inferior conception M. 
 
 Such is the character of all the conclusions obtained through 
 
ANALYTIC OF SYLLOGISMS. 135 
 
 this form of the syllogism. They are always in themselves spe- 
 cific and definite, but pertain only to a part of what really is 
 true. 
 
 Kind of arguments which approp-iately belongs to the dif- 
 ferent Figures. 
 
 It may be important to occupy some time in considering the 
 forms of argument which most properly belong to the different 
 figures of the syllogism. 
 
 All cases in which the principle of extension on the one hand, 
 and comprehension on the other, are in equilibrium, belong, as 
 we have seen, exclusively to the first figure ; and the question, 
 whether in any given case these relations do obtain ? may, in 
 all instances, be very readily resolved. In this figure the minor 
 as a determined subject ranks under another term, the middle ; 
 while said middle, as such a subject, ranks under, or is excluded 
 from, the major term. This one peculiarity distinguishes all 
 arguments in this figure from all which pertain to the others. 
 Suppose, for example, the question to be argued is, Whether A 
 in a certain act, taking the life of B, was guilty of murder, the 
 fact of taking the life referred to being admitted. The advo- 
 cate sustaining the charge first lays down the general principle, 
 that, in the language of Coke and Blackstone, unlawfully killing 
 a human being with premeditated malice, by a person of sound 
 mind, is murder (All M is X), affirms and attempts to show, 
 that A killed B in these very circumstances (All Z is M), and 
 hence infers that A, in the act.referred to, was guilty of murder 
 (All Z is X). This is an argument in the mood Barbara. On 
 the other hand, let us suppose that the advocate on the other 
 side, after laying down the principle that taking life in self- 
 defence is not murder (Xo M is X), affirms and attempts to 
 prove that A took the life of B in self-defence (All Z is M), and 
 hence concludes that the act referred to was not murder (Xo Z 
 is X). We have in such a case an argument in the mood Ce- 
 larent. The application of the above illustration to particular 
 conclusions, affirmative and negative, belonging to this mood, 
 are too obvious to require elucidation. 
 
 
Let us suppose, now, that it is claimed or is likely to be, that 
 two cases (X and Z) rank under one and the same principle or 
 superior conception (M), and that we wish to disprove that 
 assertion. In accomplishing this object, Ave first show that, on 
 the principle of intension, X contains all of M, that is, as an in- 
 ferior X is contained under M, as the superior conception (All 
 X is M) ; we then show that Z has none of these elements, that 
 is, as an inferior conception does not rank under M as its supe- 
 rior (No Z is M) ; we hence deduce the conclusion, " No Z is 
 X," that is, X and Z do not rank under the same principle. In 
 this case the argument is in the second figure, in the mood 
 Camestres. If, on the other hand, it was argued that X is 
 wholly void of certain fundamental characteristics which Z pos- 
 sesses, and that, therefore, X and Z do not belong to the same 
 class, or that no Z is X, the argument would be in the same 
 figure, but in the mood Cesare. On the same principle, in Fes- 
 tino and Barako a partial disagreement is disproved. Supposs 
 it to be maintained, for example, that the miracles recorded in 
 the Bible (X), and those claimed in behalf of other religions (Z), 
 are in all essential characteristics alike, and, therefore, alike un- 
 worthy of credit ; that is, the miracles recorded in the Bible are 
 of the same essential characteristics as those claimed in behalf 
 of other religions. The latter class are wholly unworthy of 
 credit. Such, therefore, must be the character of the miracles 
 chronicled in the Bible, an argument in the'mood Barbara. In 
 opposition to this, we show, that the latter class of events have 
 all of them certain infallible marks of credibility (All X is M), 
 that none of the former class, in fact, have any one of these char- 
 acteristics (No Z is M), and hence deduce the conclusion, that 
 these two classes of events do not belong to the same class at 
 all (No Z is X). This, also, would be an argument in the 
 second figure ; the figure whose special province is such kind of 
 refutations. Suppose once more that we wish to prove that 
 certain individuals of each of two different classes have certain 
 common characteristics, that is, that each class as the superior 
 conception contains under it, in Avhole or in part, a common 
 conception, and that there is consequently a partial resemblance 
 
ANALYTIC OF SYLLOGISMS. 137 
 
 between the classes themselves; or, that while part of one class 
 has these characteristics, portions at least of the other class 
 have them not, and that, consequently, there is this partial disa- 
 greement between these classes. Let us suppose, further, that 
 it is asserted that all of these classes have these characteristics, 
 or that all of one class and none of the other have them, and 
 that we wish to disprove these propositions in their universal 
 form. In all the above-named cases we naturally use some ot 
 the modes of the third figure. The argument will, in the first 
 instance, stand thus : All of these characteristics do belong to 
 one extreme, and all or a part of the same do or do not belong 
 to the other, and, therefore, some of one class are or are not 
 like some of the other ; that is, " All of M is in X," and " All 
 or some of it is or is not in Z," and, therefore, all or some of Z 
 is or is not in X. When we desire to prove the contradictory 
 of a universal proposition, whether affirmative or negative, we 
 prove that some of the one, at least, are, and some of the other 
 are not, in the state referred to, and that, therefore, the univer- 
 sal proposition cannot be true. In opposition to the universal 
 affirmative proposition we show, that no or some M is not in X, 
 and that all or some M is in Z, and, therefore, some Z is not 
 in X. In opposition to the universal negative proposition we 
 show, that all M is in X, and that all or some M is in Z, and, 
 therefore, some Z is in X. In all such positive arguments, and 
 in all replies like "those under consideration, the reasoning is 
 commonly in the third figure ; for example, " Prudence has for 
 its object the benefit of individuals; but prudence is virtue, 
 therefore, some virtue has for its object the benefit of indi- 
 viduals." This argument is in Darapti, and its object is to 
 establish a fact or principle. . Its form would be the same if its 
 object was to refute the principle, that no form of real virtue 
 has for its object the benefit of individuals. Suppose, for the 
 sake of still further elucidation, that it is argued that a certain 
 doctrine cannot be true, and that on account of a certain diffi- 
 culty (M) which it involves. The argument hi full stands thus : 
 No doctrine involving this difficulty (M) can be true (X), or, 
 " No M is X." This doctrine (Z) does involve this difficulty 
 
138 LOGIC. 
 
 (M), or, "All Z is M," therefore this doctrine (Z) cannot be 
 true, or, " No Z is X." To refute this argument we have only 
 to show, that some one doctrine which cannot be denied in- 
 volves this very difficulty. The argument in reply is in Da- 
 rapti, and stands, when stated in full, thus : This doctrine (M) 
 involves this very difficulty (X), or " All M is X." This doc- 
 trine (M) is true (Z), or, "All M is Z." Therefore, some doc- 
 trine which is true involves this very difficulty, or " Some Z is 
 X ;" in other words, this objection is of no force against any 
 doctrine. By carefully reflecting upon the above illustrations 
 the pupil will be able to judge correctly in regard to the figure 
 into which any particular argument is, or should be, thrown. 
 
 A more brief view of this subject. 
 
 To state the matter in still fewer words : when the middle 
 term stands intermediate between the extremes, being inferior 
 to one and superior to the other, then the argument is in the 
 first figure. This we believe is generally the case when one 
 premise is a general or universal principle. In this figure we 
 always advance from the minor term through the middle to the 
 major or superior conception. On the other hand, when the 
 middle term is superior to each extreme, then the argument is 
 in the second ; and when it is in the relation of an inferior con- 
 ception to each extreme, then the argument is in the third 
 figure. 
 
 A SCIENTIFIC DETERMINATION OF THE REAL NUMBER OF LE- 
 GITIMATE MOODS IN THIS FORM OF THE SYLLOGISM. 
 
 Hitherto, in treatises on logic, the number of legitimate moods 
 has been given as the result of mere experiment. Science de- 
 mands that it shall be shown that, from the relations of the ex- 
 tremes to the middle term, there must be a certain number of 
 legitimate moods, and that there can by no possibility be any 
 more. This is what we now propose to accomplish. 
 
ANALYTIC OF SYLLOGISMS. 139 
 
 Conditions of valid deductions of any kind in this form of 
 the Syllogism. 
 
 The following, it must be borne in mind, are the immutable 
 conditions of any valid conclusions in the syllogism as thus far 
 elucidated: 1. The middle term must be distributed at least 
 once in the premises. 2. No term must be distributed in the 
 conclusion which Avas not distributed in the premises. 3. One 
 premise at least must be universal. 4. When the conclusion 
 is universal both premises must be of the same character 
 5. One premise, also, must be affirmative. 6. When the con 
 elusion is affirmative both premises must be affirmative, and 
 when one premise is negative the conclusion must be negative. 
 From these laws, which, as we have already seen, cannot but 
 be valid, we must have a certain definite number of legitimate 
 moods, and by no possibility can we have any more. This we 
 will now proceed to show. 
 
 Universal affirmative conclusions. 
 
 Let us, in the first place, take a universal affirmative conclu- 
 sion. To have such a conclusion, each premise must be both 
 universal and affirmative. Unless X and Z are both given in 
 the premises as agreeing universally Avith M, the former cannot, 
 from their mutual relations to the latter, be affirmed to agree 
 universally with each other. Such an agreement as legitimates 
 such a conclusion does exist, as Ave have already seen, when the 
 whole of one extreme is contained in the middle term, and the 
 whole of said term is contained in the other extreme. AAA, 
 then, is an allowable mood. 
 
 Particular affirmative conclusions. 
 
 To have a particular affirmative conclusion both premises 
 must be affirmative, and one universal, of which the middle 
 term is the subject, this being the condition of its being dis- 
 tributed in an affirmative proposition. Now there are but 
 
140 LOGIC. 
 
 three possible forms in which these conditions can -be fulfilled, 
 to wit : when both premises are universal affirmatives when 
 the first premise is a universal, and the second a particular, 
 affirmative and, when the first is a particular, and the second 
 a universal, affirmative. There can, then, be but three moods 
 yielding such a conclusion, and there may be just this number. 
 When the middle term, for example, is the subject of two uni- 
 versal affirmative propositions we may have a particular affirm- 
 ative conclusion, and in such a case we can have nothing more ; 
 because neither of the extremes are distributed in the premises, 
 and, consequently, must not be in the conclusion. If all of M 
 is in X and Z alike, then, " Some Z must be in X." A A I, 
 therefore, is an allowable mood. So if all of M is in X, and 
 some of Z in M, some of Z must be in X, and from the relations 
 supposed nothing more can be inferred. These conditions may 
 undeniably be fulfilled when the first premise is universal (A), 
 and the second particular (I), and vice versa. All and I A I 
 are, therefore, allowable moods. We have, then, four allowa- 
 ble affirmative moods and can have no more, to wit : A A A ; 
 A A I; All; I A I. 
 
 Universal negative conclusion. 
 
 To have a universal negative conclusion both premises must 
 be universal, and one of them affirmative and one negative ; 
 that is, one extreme must be given as agreeing, and the other 
 as disagreeing, universally with the middle term. This is possi- 
 ble on two conditions only, to wit : when the first premise is 
 affirmative and the second negative and vice versa. On these 
 conditions, also, we may have a logically valid universal nega- 
 tive conclusion ; for if all of X and none of Z, or none of X 
 and all of Z, are in M, in either case none of Z can be in X. 
 The moods E A E and A E E are allowable ; and this gives us 
 six allowable moods four affirmative and two negative. 
 
ANALYTIC OF SYLLOGISMS. 141 
 
 Particular negative conclusions. 
 
 A particular negative conclusion requires that one premise be 
 affirmative and the other negative, and that one at least shall 
 be universal. These conditions are fulfilled: 1. "When both 
 premises are universal, and the first is affirmative and the 
 second negative, and vice versa ; that is, A E O and E A O are 
 possible moods. 2. When the first premise is a universal af- 
 firmative and the second a particular negative, and vice versa, 
 to wit : A O and O A O. 3. When the first premise is a 
 universal negative and the second a particular affirmative, and 
 vice versa ; that is, E I O and I E O. These it will be seen are 
 the only possible arrangements of the premises consistent with 
 the necessary conditions before us, and present the only possi- 
 ble number of moods when the conclusion is a particular nega- 
 tive. The only question which now arises is this : Are all of 
 these allowable moods ? We affirm that they are, and will now 
 proceed to verify this affirmation. 
 
 Every one Avill perceive that when both premises are univer- 
 sal, one affirmative and the other negative, and one extreme is 
 the predicate of the affirmative premise, and consequently not 
 distributed, that this term must be in the conclusion the subject 
 of a particular proposition. Otherwise we should have an illicit 
 process of said term. In such a case, however, such a conclu- 
 sion (a particular negative) must be logically valid ; because, 
 when none of M is in X and all of M is in Z, the part of Z con- 
 taining M cannot be in X, and the proposition " Some Z is not 
 X," will hold true ; and this conclusion is equally valid, what- 
 ever the order of the premises may be. A E O and E A O, 
 therefore, are valid moods. 
 
 For equally obvious reasons, the moods A O O and O A O 
 must be valid. If all X is in M and some of Z is not in M, then 
 some of Z, the part not contained in M, cannot be in X ; and 
 this will hold equally true, whether the affirmative or negative 
 premise be stated first, that is, A O O and A O are allowable 
 or valid moods. 
 
 The validity of the mood E I O is self-evident. If none of M 
 
142 LOGIC. 
 
 is in X and some of M is in Z, then the part of Z containing 
 this part of M cannot be in X, and the proposition, " Some Z is 
 not X," is valid. That is, the mood E I O is, and must be, 
 allowable. The same conclusion, as we have before shown, fol- 
 lows, when the order of the premises is reversed, and I E 
 must also be held as an allowable mood. 
 
 The number of Moods. 
 
 We have, then, twelve allowable moods, and we can have no 
 more, to wit, four affirmative and eight negative ones. We 
 will now give them in their proper order : AAA; A A I ; 
 All; IAI; AEE; EAE; AEO; EAO; AOO; 
 OAO;EIO; IEO. 
 
 SIMILAR DETERMINATION OF THE NUMBER OF MOODS IN EACH 
 FIGURE. 
 
 We will now attempt a similar determination of the number 
 of legitimate syllogisms in each figure, keeping distinctly in 
 view the six conditions above stated, of deducing any valid in 
 ferences of any kind. 
 
 /Syllogisms allowable in the first Figure. 
 
 To have affirmative conclusions of either kind in the first 
 figure, the major premise must be a universal affirmative. 
 Otherwise the middle term would not be distributed at all. 
 The minor premise, also, must be affirmative, and consequently 
 a universal or particular affirmative. If the minor premise is 
 universal, the conclusion must, as we have already seen, be uni- 
 versal also. If it is particular, the conclusion is particular, and 
 no other is allowable. We have then, in this figure, two allow- 
 able syllogisms with affirmative conclusions, to wit, Barbara and 
 Darii, and we can have no more. 
 
 To have a universal negative conclusion both premises must 
 be universal, one affirmative an 1 the other negative, and both 
 
ANALYTIC OF SYLLOGISMS. 143 
 
 terms distributed in the premises, both being distributed in the 
 conclusion also. These conditions can be fulfilled only when the 
 major premise is a universal negative proposition, and the minor 
 a universal affirmative. If the major premise was affirmative, 
 the major term would be undistributed, and we would have no 
 negative conclusion at all. We can have, then, in this figure, 
 but one syllogism whose conclusion is a universal negative one, 
 to wit, Celarent. 
 
 To have a particular negative conclusion in this figure, the 
 major premise must be a universal negative, and the minor a 
 particular affirmative. If the major premise was not negative, 
 the major term would not be distributed, and we should have 
 an illicit process of that term in the conclusion. If said premise 
 was not universal, the middle term would not be distributed, and 
 we could have no conclusion of any kind. If the minor premise 
 was not a particular affirmative proposition, the conclusion would 
 be universal, and not particular. But one syllogism having a 
 particular negative conclusion is possible in this figure, to wit, 
 Ferio. In the first figure, then, there are four, and only four, 
 allowable moods, to wit, Barbara, Darii, Celarent, and Ferio. 
 
 MOODS OR SYLLOGISMS ALLOWABLE IN THE SECOND FIGURE. 
 
 The second figure yields none but negative conclusions. To 
 have a universal negative conclusion one premise must be a uni- 
 versal affirmative, and the other a universal negative, proposi- 
 tion. When we have such propositions, the middle term will 
 be distributed in the negative premise, and each extreme in its 
 own premise, the extremes being the subjects of universal prop- 
 ositions. As these conditions are fulfilled, whatever the order of 
 the premises may be, we have two moods of this kind, to wit : 
 one when the major is affirmative and the minor negative, and 
 one when this order is reversed ; that is, Cesare and Camestres 
 
 We have a particular negative conclusion when the affirma- 
 tive premise is particular, viz., Festino and Fisteno, according 
 to the order of the premises. So, also, when the affirmative 
 premise is universal and the negative particular we have two 
 
moods, according to the order of the premises, to wit : Baroko 
 and Borako. 
 
 There are, then, in this figure, six allowable moods ; two with 
 universal, and four with particular negative, conclusions. 
 
 ALLOWABLE MOODS IN THE THIRD FIGURE. 
 
 The third figure, as we have already seen, yields only partic- 
 ular conclusions. To have affirmative conclusions, one of the 
 premises must be universal ; else the middle would not be dis- 
 tributed. Now there are but three conceivable relations of the 
 premises which will yield an affirmative conclusion, to wit : 
 when both premises are universal affirmatives (dArAptl) ; 
 when the first premise is a universal, and the second a par- 
 ticular, affirmative (dAtlsI) ; and, when the first is a particu- 
 lar, and the second a universal, affirmative (dlsAmls). All 
 these are legitimate moods, because that in these the middle 
 is distributed, and no term is distributed in the conclusion, and 
 none were distributed in the premises. 
 
 We may have particular negative conclusions on the follow- 
 ing conditions : when both premises are universal, one negative 
 and the other affirmative (fElAptOn and fAlEptOn) ; when one 
 premise is a universal affirmative and the other a particular neg- 
 ative (bOkArdO and bAkOrA) ; and, when one premise is a 
 universal negative and the other a particular affirmative (Ferison 
 and Fireson). This gives us nine moods in this figure, making 
 just nineteen in the three figures. If we subtract those which 
 result from merely a change of the order of the premise, and in 
 which the extreme in the first premise is made the subject of 
 the conclusion moods, consequently, which must be regarded 
 as in themselves valid, but practically useless the number will 
 be reduced to fourteen, five affirmative and nine negative syllo- 
 gisms, all of which are expressed in the following fines : 
 
 " Fig. 1. bArbArA, cElArEnt, dArll, fErlO que, prioris. 
 Fig. 2. cEsArE, cAmEstrEs, fEstlnO, bArOkO, secundas. 
 Fig. 3. Tertia, dArAptl, dlsAmls, dAtlsI, fElAptOn, bOkArdO, 
 fErlsO, habet." 
 
ANALYTIC OF SYLLOGISMS. 145 
 
 Note. The conclusions resulting from the moods fEstlnO 
 and bArOkO in the second, and from fElAptOn, fErlsO, and 
 bOkArdO in the third figure, by a change of the order of the 
 premises, may be given in a still different form, to wit : 
 
 Some X is M ; Some X is not M ; 
 
 No Z is M ; All Z is M ; 
 
 .-. No Z is some X ; or, .-. No Z is some X ; or, 
 Some X is not Z. Some X is no Z. 
 
 All M is X ; All M is X ; 
 
 . No M is Z ; Some M is not Z ; 
 
 .. No Z is some X ; or, .\ No Z is some X ; or, 
 Some X is not Z. Some X is no Z. 
 
 Feriso has been given before. The form given in this note 
 will be seen to be the preferable one. 
 
 II. That department of the figured syllogism in which 
 
 THERE IS, NOT ONLY IN NEGATIVE BUT IN AFFIRMATIVE 
 PROPOSITIONS, THE DISTRIBUTION OF THE PREDICATE AS 
 WELL AS OF THE SUBJECT. 
 
 We now advance to a consideration of the second depart- 
 ment of our present subject, the figured syllogism, to wit : that 
 department of it in which there is, or may be, not only in nega- 
 tive, but equally in affirmative propositions, a distribution of the 
 predicate as well as of the subject. The reason why universal 
 negative propositions distribute both terms is the fact, that in 
 such propositions the terms are compared throughout their 
 whole extent. Whenever such comparison occurs in affirmative 
 propositions, and from the nature of the case, must be so, then 
 there is the same distribution of subject and predicate in one 
 class of propositions as in the other. Now there is an exceed- 
 ingly numerous class of propositions in which such distribution 
 occurs, and, from the character of the relations of the subject 
 and predicate, must occur ; relations which can readily be des- 
 ignated, and thus presented as criteria to distinguish this class 
 from those in which no such distribution obtains. The reason, 
 7 
 
146 LOGIC. 
 
 and only reason, why the predicate as well as siibject is not 
 always distributed in universal affirmative propositions is the 
 fact that, in a large part of them, those which we have consid- 
 ered, the predicate is a superior and the subject an inferior con- 
 ception ; the sphere of the latter being less than that of the 
 former. In all cases, therefore, where the terms of the proposi- 
 tion are not thus related, there we should expect to find both 
 alike distributed, and that upon the same principles. "We will 
 now, though at the expense of repeating something already 
 presented in another connection, proceed to classify the propo- 
 sitions, which, whether affirmative or negative, distribute the 
 predicate as well as the subject. 
 
 Among these we notice the following : 
 
 Propositions of this kind classified. 
 
 1. Substitutive judgments, those in which the predicate, by 
 another set of words defines the subject ; as, for example, 
 "Common salt is chloride of lime," "A triangle is a figure 
 bounded by three straight lines," &c. The converse of such 
 propositions is, " Chloride of lime is common salt," and, " A 
 figure bounded by three straight lines is a triangle." And the 
 reason why conversion is simple in such cases is, that both terms 
 alike are distributed. 
 
 2. Quantitive judgments of that class in which the subject 
 and predicate are compared quantities with reference to the 
 ideas of equality and difference, and in which one is affirmed to 
 be equal to, greater, or less than the other. If X = Z, Z=X. 
 If X is greater or less than Z, Z is correspondingly less or 
 greater than X. In all such relations both the subject and 
 predicate are alike distributed, and from the nature of the rela- 
 tions it must be so. 
 
 3. Numerical judgments, those in which the subject and 
 predicate are numerically compared with each other ; as in the 
 judgments, 6+4 = 10, X numerically =Z, &c. In all such 
 judgments the same laws of distribution govern both subject 
 and predicate. 
 
ANALYTIC OF SYLLOGISMS. 147 
 
 4. Correlative judgments, those in which the subject and 
 predicate are correlative terms, and affirm such correlation ; as, 
 " Cause and effect," *" Parent and child," <fcc. In all such judg- 
 ments, also, the same laws of distribution obtain. If X is the 
 cause of Z, Z is the effect of X. If X is the father of Z, Z is 
 the child of X, both terms being equally distributed in the ex- 
 posita and converse. 
 
 I 5. All judgments, in which the subject and predicate are com- 
 pared with reference to the idea of likeness or unlikeness, fol- 
 low the same law of distribution in respect to the subject and 
 predicate both. The converse of the proposition X resembles 
 Z, for example, is not some Z resembles X, but Z resembles X, 
 and that for the reason, that in such propositions, both terms 
 are alike distributed, and the conversion of a universal affirma- 
 tive as well as negative proposition is consequently simple. 
 
 6. Proportional judgments, also, follow the same law. For 
 example, " Exertions of certain individuals are proportional to 
 their strength ;" " The velocity of a moving body, its matter be- 
 ing given, is in proportion to the impelling force ;" " Momentum, 
 velocity being given, is proportional to the quantity of matter-;" 
 "A is to B as C is to D," &c. In all such judgments the subject 
 and predicate are compared throughout their wdiole extent, and 
 therefore, in universal affirmatives as well as negatives, both 
 terms are alike distributed and conversion is always simple. 
 
 7. "We notice but one other class of judgments as falling 
 under the same law of distribution relatively to the predicate, 
 those in which the subject is a generical (superior), and the 
 predicate a specifical (inferior) conception, and the object of the 
 judgment is to affirm, that the former class includes the latter. 
 For example, "Animals are men," that is, "Some animals = all 
 men," " Creatures (some creatures) are animals (all the species 
 called animals)." In such propositions the subject is particular 
 and the predicate universal. The syllogism, whose premises 
 are of this character, would, when stated in full, read thus : 
 
 Some animals are men (all the race of men) ; 
 Some creatures are men (all the race of men) ; 
 . \ Some creatures are (some) animals. 
 
Here is a valid syllogism with two affirmative particular prem- 
 ises as far as the subject is concerned. The syllogism is valid 
 because the predicate is distributed and the extremes are mu- 
 tually compared with the same thing. For the same reasons 
 we may have from similar premises a particular negative con- 
 clusion which must be held as valid. Example : 
 
 Some animals are (all) men ; 
 Some creatures are not men ; 
 Some creatures are not (some) animals. 
 
 The classification above given will, we doubt not, be admit- 
 ted to be valid as far as it goes. Whether it includes all judg- 
 ments of the class before us must be determined by future in- 
 vestigation. Our object has been to indicate the existence and 
 character of the class itself, and then to determine the laws of 
 the syllogism when constituted in whole or in part of such 
 propositions. 
 
 ADDITIONAL SYLLOGISMS ILLTTSTEATIVE OF THE ABOVE CLASSES 
 OF JUDGMENTS. 
 
 We will now present a few additional syllogisms illustrative 
 of the above classes of judgments. We shall give our examples 
 generally in the second and third figures, in which, in affirmative 
 propositions, either the middle term or the extremes are always 
 undistributed in propositions whose subjects are inferior and 
 predicates superior conceptions. For the sake of convenience 
 we will use the following signs adopted by Sir William Hamil- 
 ton, to indicate the nature of the propositions : A colon (:) 
 placed before a term indicates its distribution, and a comma (,) 
 its non-distribution. Thus, : A means all A, and , A means 
 some A. The followingsign (=) placed between two terms in- 
 dicates their equality, and consequently the fact that both terms 
 are distributed ; as, : A=B, means all A equals all B. This 
 sign > placed between two terms indicates that one is greater 
 than ;the other, and that the one towards which the convergent 
 is directed is the less, and that towards which the divergent is 
 
ANALYTIC OP SYLLOGISMS. 149 
 
 directed is the greater. Thus: A>B means A is greater than 
 B, and A<B means A is less than B. Addition, subtraction, 
 multiplication, division, and proportion will be indicated by the 
 usual mathematical signs employed to express such relations. 
 Let us now consider the following illustrative examples : 
 
 1. Syllogisms constituted of Substitutive Judgments. 
 
 U. A triangle is a figure bounded by three straight lines ; 
 U. A is a figure bounded by three straight lines ; 
 C .*. A is a triangle. 
 
 
 2. Quantitive Judgments. 
 
 (1.) 
 
 (2.) (3.) 
 
 X=M; 
 
 M=X; X>M; 
 
 Z=M; 
 
 M=Z ; Z=M ; 
 
 Z=X. 
 
 .-. Z=X .-. Z is lees than X. 
 
 (4.) 
 
 (5.) (6.) 
 
 M<X; 
 
 One half X=M ; M=X ; 
 
 M=Z; 
 
 Z=M; M=onehalfZ; 
 
 Z is less than X. .-. Z is one half X .-. Z=twice X, 
 
 
 3. Correlative Judgments. 
 
 
 (1.) 
 
 
 M is the cause of X ; 
 
 
 M is the cause of Z ; 
 
 
 ,\ Z is an effect of the same cause as X. 
 
 
 (2.) 
 
 
 X is the son of M ; 
 
 
 Z is the son of M ; 
 
 
 .-. The father of Z is the father of X. 
 
 4. Judgments falling under t/ie principle of likeness and un- 
 
 (1-) (2.) 
 
 X resembles M ; M resembles X ; 
 
 Z resembles M ; M resembles Z ; 
 
 . Z resembles X. .*. Z resembles X. 
 
5. ProportionaUud 
 
 (1-) (2.) 
 
 A:B::C:D; C : D : : A : B; 
 
 A is one half B ; A is one half B ; 
 
 .-. C is one half D. .*. C is one half D. 
 
 Those judgments in which the subject is a generical and the 
 predicate a specifical conception have already been sufficiently 
 elucidated. The validity of the above syllogisms will not be 
 questioned. Their validity, however, depends wholly upon the 
 fact that, in judgments of the above-named classes, the predi- 
 cate as well as the subject is distributed. 
 
 Table of Logical Judgments. 
 
 In the Analytic of Judgments we showed, that in addition to 
 the number of judgments given in the common treatises on 
 logic, to wit, the universal affirmative (A), the particular affirm- 
 ative (I), the universal negative (E), and the particular nega- 
 tive (0), we have four additional ones the toto-total affirma- 
 tive, in which both subject and predicate are distributed (U) ; 
 the parti-total affirmative, in which the subject is undistributed 
 and the predicate distributed (Y) ; the parti-partial negative, in 
 which both terms are undistributed (w) ; and the toto-partial 
 negative, in which the subject is universal and the predicate 
 particular (?)). We have employed, in accordance with the 
 usage of Sir William Hamilton, the letters IT, Y, and the Greek 
 letters w (omega), and r\ (eta), to express these last four propo 
 sitions. This gives us eight instead of four logical judgments 
 which may enter into different processes of reasoning. We 
 will give this table of judgments, prefixing their respective signs. 
 
 SIGN. 
 
 XL All X is all Z, or X=Z ; 
 A. All X is some Z, or all X is Z ; 
 I. Some X is some Z, or some X is Z ; 
 Y. Some X is all Z, or some X=Z 
 

 ANALYTIC OP SYLLOGISMS. 151 
 
 Negatives. 
 
 SIGN. 
 
 E. No X is Z, that is, any Z ; 
 u. Some X is not some Z ; 
 r,. No X is some Z ; 
 0. Some X is no Z, not any Z. 
 
 Mr. Thomson, in his " Laws of Thought," while he adopts 
 all the other classes of judgments, rejects ij and w as useless, 
 though valid in themselves. In the Analytic of Judgments we 
 have indicated fully our views of these judgments, and have 
 there given sufficient reasons for retaining them. 
 
 Of opposition and conversion of Judgments. 
 
 In the common treatises on logic, treatises in which all forms 
 of judgments are included under the four propositions A, E, I, 
 and O, E is given as the contrary of A, and O as its contra- 
 dictory, and I as its subaltern. A, of course, is given as the 
 contrary of E, and I as its contradictory, and O as its subaltern, 
 while I and O are given as sub-contraries. By increasing the 
 classes of judgments we have multiplied the forms of opposition. 
 A has the same number of contraries as before, with the addi- 
 tion of *j and w, while U and Y are both alike inconsistent 
 with A. The proposition, for example, "AH X is Z," cannot 
 be true, if any of these propositions are true, to wit : " No X 
 is Z," " Some X is not Z," " No X is some Z," or, " Some X is 
 not some Z." The proposition, also, "All X is Z," that is, 
 " some Z," the real universal affirmative represented by A, is 
 inconsistent with the proposition, " All X is all Z," that is, (U) 
 and some X is all Z (Y). E now has, for its contradictory, as 
 before, I, and for its contraries A, U, and Y. O has for its sub- 
 contrary not only I but Y also, and I is the subaltern not only 
 of A, but also of Y. These are sufficient to indicate the forms 
 of opposition which obtain among the eight classes of judgments 
 now admitted as real and valid. 
 
 In regard to conversion, E, TJ, I, and w are each convertible 
 into itself, that is, the converse has the same form as the ex- 
 
152 LOGIC. 
 
 posita. A is converted into Y and Y into A. O is converted 
 into y\ and >] into O. A careful inspection of the above table of 
 judgments will clearly evince the truth of all these statements. 
 
 Canon of this form of the Syllogism. 
 
 We now advance to a consideration of the canon of the form 
 of the syllogism under consideration. It is this : Every concep- 
 tion or term, agreeing with a certain common conception or 
 term, agrees with all others that agree with said conception or 
 term, and disagrees with all that disagrees with said concep- 
 tion or term. If A, for example, equals M, it equals all other 
 objects that are equal to 31. The agreement or disagreement 
 of the extremes will always be as their relations to the common 
 or middle term. 
 
 SPECIAL CHARACTERISTICS OF THIS FORM OF THE SYLLOGISM. 
 
 It would readily be anticipated that forms of the syllogism, 
 the terms of whose premises are exclusively constituted of infe- 
 rior and superior conceptions, would diner essentially from those 
 constituted of premises in which, even in affirmative proposi- 
 tions, the predicate as well as subject is distributed. Let us 
 consider some of the peculiarities of this second class of forms 
 of the syllogism, as compared with those of the other class. 
 Among these we notice the following : 
 
 1. In the former class a universal affirmative can be proved 
 only in the first figure, while the second gives us only negative, 
 and the third only particular, conclusions. When the premises 
 are composed of propositions which distribute not only the sub- 
 ject but predicate also, then we have toto-total affirmative con- . 
 elusions in all figures alike ; that is, U may be proven in each 
 of the three figures. We will give a syllogism of this class in 
 each figure : 
 
 TJ. : M is : X, i. e. M=X ; 
 
 U. : Z is : M, " Z=M ; 
 
 U. .-. : Z is : X, " .-. Z=X. 
 

 ANALYTIC OF SYLLOGISMS. 153 
 
 Here the syllogism is in the first figure. Let us now see how 
 the argument will appear in the other figures : 
 
 Fig. 2. Fig. 3. 
 
 : X is : M, or X=M ; : M is : X, or M=X ; 
 
 : Z is : M, or Z=M ; : M is : Z, or M=Z ; 
 
 .-. : Z is : X, or Z=X. .-. : Z is : X, or Z=X. 
 
 Every condition requisite to a valid conclusion, it will readily be 
 perceived, is as fully met, in the above examples, in one figure 
 as in the other. We might add here that in each figure we 
 may also have particular affirmative conclusions, U I I and 
 I U I, for example. 
 
 2. Another peculiarity of this form of the syllogism is, that 
 from apparently particular premises we can have valid conclu- 
 sions ; as, for example : 
 
 Some stones do not resist the action of the acids ; 
 Some metals resist the action of the acids ; 
 .-. Some metals are not some stones ; or better, 
 
 Some metals differ in their relations to the acids from some stones. 
 
 This certainly is a valid argument, and arises from the fact 
 that the middle term, though the predicate of an affirmative 
 conclusion, is distributed. The predicate of the conclusion, as 
 well as the subject, is particular, though the predicate of a nega- 
 tive conclusion. 
 
 3. Another peculiarity of this form of the syllogism is this, 
 that when the subject of one premise is- particular we may still 
 have a universal negative conclusion. Take as an illustration 
 the following mood in Y E E : 
 
 Some M is all X ; 
 No Z is M ; 
 .-. NoZisX. 
 
 Every condition requisite to a valid argument is fulfilled in the 
 above syllogism. 
 
 4. We mention but one other peculiarity, the fact that we 
 can have in all figures alike, not only universal affirmative con- 
 clusions, but also universal negatives. UEE and EUE are 
 
moods alike valid in all the figures. It will be noticed that in 
 each of the propositions of each of these moods, both terms are 
 distributed. In the mathematics and other kinds of reasoning, 
 the above forms of argument are continually occurring. 
 
 III. The two forms of the syllooism combined. 
 
 It is evident that the propositions of the same syllogism may 
 be constituted partly of propositions of the first and partly of 
 those of the second class above elucidated. In other words, 
 one proposition may be constituted of. inferior and superior con- 
 ceptions, and another of the class in which, in affirmative and 
 negative propositions alike, the predicate as well as subject may 
 be distributed. In syllogisms of the first class of affirmative 
 propositions, the middle term must be the subject of a univer- 
 sal proposition, else it is not distributed. When we have a 
 premise of the second class, the middle, though the predicate of 
 an affirmative proposition, may be distributed, and the argu- 
 ment still be valid. When all the propositions are constituted 
 of the first class of conceptions we have one kind of syllogisms. 
 When they are constituted of the second class we have still 
 another kind of arguments. When the two classes of concep- 
 tions are combined and enter into the same argument, still 
 another class of syllogisms arises. The following extract from 
 " Thomson's Laws of Thought" contains all that need be said 
 under this head. We feel at liberty to make use of this extract 
 for two reasons especially, to wit : 1. It contains three sys- 
 tems of notation taken very properly from other authors. 
 2. The system of notation of which Sir William Hamilton is 
 the author, together with his classifications of the moods of the 
 syllogism, was furnished by that author for the special benefit 
 of the science of logic. We might describe the systems of no- 
 tation in our own language. This, however, would be needless, 
 as we should only say the same things through a new selection 
 of words. The difference in the arrangement of the moods by 
 Mr. Thomson and Sir William Hamilton, consists only in the 
 omission of those syllogisms which arise from the use of the 
 
ANALYTIC OF SYLLOGISMS. 155 
 
 judgments u and v\ by the latter author, and their rejection by 
 the former. Our reasons for agreeing with the latter have al- 
 ready been given. All persons who would attain both to a 
 theoretical and practical knowledge of the science of logic, 
 should render themselves perfectly familiar with the moods, 
 syllogisms, and systems of notation presented in this extract. 
 What has gone before has fully prepared the way for an intelli- 
 gent acquaintance with the subject here presented. 
 
 " Table of all the Legitimate Moods in all Figures. 
 
 The following table is an index of the moods in which a 
 good inference can be drawn* It is arranged according to the 
 order in which the vowels occur in the alphabet, so that, when 
 any mood has been omitted, as not available for inference, the 
 eye can detect and supply it, and the mind examine the reason 
 for its omission. 
 
 Some of these moods exemplify different special rules and 
 theorems of logical writers, of which a few are subjoined. 
 
 FIG. I. FIG. II. FIG. III. 
 
 AAA AAI 
 
 AEE 
 
 All All 
 
 AOO 
 
 ADA AUY AUA 
 
 AYI AYY A YA 
 
 EAE EAE EAO 
 
 EIO EIO ElO 
 
 EI?E EUE EUE 
 
 EYO EYO EYE 
 
 IAI 
 
 IUI IUI IUI 
 
 IYI IYI , 
 
 OAO 
 
 OUO OUO 
 
 OYO 
 
 UAA UAA UAY 
 
 * Another table is given below, with such additional moods as contain the doubtful nega- 
 tive judgments n and u. 
 
UEE 
 
 LOGIC. 
 
 uee*: 
 
 UEE 
 
 UII 
 
 UII 
 
 UII 
 
 U ....... 
 
 U ... 
 
 uoo 
 
 u u u ...... . 
 
 uuu 
 
 uuu 
 
 U Y Y.. 
 
 UYY 
 
 U Y A 
 
 
 YAA 
 
 Y A Y 
 
 YEE 
 
 
 YEE 
 
 
 YII 
 
 
 YOO 
 
 
 
 YUY 
 
 YU A 
 
 YUY 
 
 YYY 
 
 YYI 
 
 
 Fiq. I. A A A and A A I are the only moods to -which the dictum de 
 omni directly applies 'Whatever is said of a class may he said" of a con- 
 tained part of the class.' 
 
 Fig. I. A U A is a formula into which a ' perfect induction' might fall, 
 where we affirm something of a whole class, because we have found it true 
 of all the individuals or species which the class contains. Thus : 
 x y and z are P ; 
 S=x y and z ; 
 .-. Sis P. 
 
 Leibnitz gives the formula ' Cui singula insunt, etiam ex ipsis constitu- 
 tum inest.' 
 
 Fig. I. E A E and E I are the only moods to which the dictum de nullo 
 applies. ' What is denied of a class must be denied of any part of the class.' 
 E U E and U E E in all figures. ' Si duorum qua? sunt eadem inter se 
 unum diversum sit a tertio, etiam alterum ab eo erit diversum.' Leibnitz. 
 
 Figs. I. and II. U A A. ' Quod inest uni coincidentium, etiam alteri 
 inest.' Leibnitz. 
 
 M=P; 
 All S is M ; 
 .-. All Sis P. 
 
 U U U in all figures. ' Qua? sunt eadem uni tertio, eadem sunt inter se.' 
 
 A mode of Notation. 
 
 To be able to represent to the eye by figures the relation 
 which subsists in thought between conceptions, tends so greatly 
 to facilitate logical analysis, that many attempts have been 
 made to attain it. Of two important schemes, that of Euler, 
 and that which Sir William Hamilton has by improving made 
 his own, an account will be given hereafter. The scheme now 
 
ANALYTIC OF SYLLOGISMS. 157 
 
 to be explained is that which Lambert makes use of in his 
 Neues Organon. 
 
 A distributed term is marked by a horizontal line, with the 
 letter S, P, or M attached, to denote that it is the subject, 
 predicate, or middle term of the syllogism : 
 
 An undistributed term is marked, not by a definite line, but by 
 a row of dots, to show its indefiniteness, thus : 
 
 These are the two forms of quantity in which separate concep- 
 tions may occur. But when two conceptions are joined in a 
 judgment, another power as to quantity must be represented 
 also. Let the judgment be, 'All plants are organized,' and let 
 the lower line represent the subject and the upper the predi- 
 cate ; will this representation convey the whole truth ? 
 
 P ... 
 
 S - 
 
 In one point it is inadequate, that the term ' organized' is not 
 wholly indefinite. We mean, indeed, by it, only some organ- 
 ized things ; but then one part of it is made definite by affirm- 
 ing it of plants. We do not know how many, or what, indi- 
 viduals, come into the conception ' Some organized things' by 
 itself; but when it occurs in this judgment, we are certain of 
 some individuals in it, viz., those which are ' all plants.' This 
 we are able to express by a line pavtly definite, partly undeter- 
 mined, thus : 
 
 P 
 
 Every affirmative judgment may be represented by a fine drawn 
 under another, the lower being always the subject. Negative 
 judgments, which express that one conception cannot be con- 
 tained under another, are represented by two lines drawn apart 
 from each other, the predicate being a little higher than the 
 subject, thus : 
 
158 LOGIC 
 
 But in a syllogism there are three terms, so that we require 
 three lines to represent their relations ; and the diagram thus 
 drawn will supply some important illustrations of the nature of 
 inference. Suppose the premises are, 'All matter undergoes 
 change, and the diamond is a kind of matter,' the relations of 
 the three terms may be thus exhibited : 
 
 P .... 
 
 From this notation, besides the two premises given, 
 
 1. All M is P, 
 
 2. All S is M, 
 
 we may by reading downwards gather that 
 
 3. Some P is M, and 
 
 4. Some M is S, 
 
 which are in fact immediate inferences by conversion from each 
 of the premises respectively. But further, from knowing that 
 M stands under P, and S under M, we have learned that S 
 stands also under P, and this we may express, leaving M alto- 
 gether out of our statement, 
 
 5. All S is P, 
 
 6. Some P is S, 
 
 the former being the proper conclusion from our premises, and 
 the latter the converse of the conclusion. 
 
 Where our premise is negative, and by the canon of syllo- 
 gism one only can be of that quality, the notation will be 
 
 P 
 
 M 
 
 which would be read thus : 
 
 No M is P ; 
 
 All S is M ; 
 .-. No Sis P. 
 
 Finally, every universal judgment of substitution, or U, may 
 be expressed by two equal lines : 
 
ANALYTIC OF SYLLOGISMS. 159 
 
 p __ 
 
 s __ 
 
 But when such a judgment expresses a logical division, as ' Or- 
 ganized beings are either plants, brutes, or men,' the divided 
 character of the predicate may be expressed by breaking up the 
 line which represents it, thus : 
 
 P x y z 
 
 which would be read, ' All S is either x y or z.' The contrary 
 process, of logical composition, which is used to express induc- 
 tion, as ' Plants, brutes, and men are the only organized beings,' 
 would appear as : 
 
 and be read ' x y z make up the sum of P.' The reader will 
 find great advantage in comprehending the rules of syllogism, 
 from figuring the syllogisms to which they happen to apply, 
 according to these directions.* 
 
 Equivalent Syllogisms. 
 
 Though the reduction of syllogisms, from a so-called imper- 
 fect, to the perfect, figure, is no longer requisite, now that the 
 power of the dictum de omni et nullo is confined to the proper 
 limits, the relations of three conceptions can be expressed, com- 
 monly, in more than one syllogism of the same figure, and al- 
 ways in different figures. And the advantage of any adequate 
 system of notation is, that it not only represents to us the syllo- 
 gism itself, which is one way of stating the mutual bearing of 
 three conceptions, but, in making that mutual bearing visible, 
 it furnishes the means of stating it in other syllogisms. An ex- 
 ample will illustrate this : 
 
 ' No agent more effectually imitates the natural action of the 
 nerves, in exciting the contractility of muscles,' than electricity 
 
 * This scheme of notation has likewise heen improved by Sir William Hamilton, but the 
 view in the text is quite sufficient for our present purpose. 
 
160 LOGIC. 
 
 transmitted along their trunks, and it has been hence supposed, 
 by some philosophers, that electricity is the real agent by which 
 the nerves act upon the muscles. But there are many objec- 
 tions to such a view ; and this very important one among the 
 rest : that electricity may be transmitted along a nervous trunk 
 which has been compressed by a string tied tightly round it, 
 whilst the passage of ordinary nervous power is as completely 
 checked by this process, as if the nerve had been divided.''* 
 This argument may be thrown into the following syllogism, as 
 the most direct form of statement : 
 
 Electricity will travel along a tied nerve ; 
 The nervous fluid will not travel along a tied nerve ; 
 .-. The nervous fluid is not electricity. 
 
 This is a syllogism in the second figure, and of the mood 
 A E E, which will be found in the table in the preceding sec- 
 tion, and is therefore a valid mood. The middle term is the 
 conception ' travelling along a tied nerve ;' and one of the other 
 terms is under it, and the other not, so that they cannot agree ; 
 and this mutual relation may be conceived by the following 
 
 lines : 
 
 M 
 
 The question now is : Whether having obtained this relation, 
 we cannot find other moods, besides A E E, Fig. II., in which 
 to express it ? 
 
 As the physiologist is most engaged with the parts and func- 
 tions of the animal economy, to him ' the nervous fluid' would be 
 the most prominent term, the subject of thought, and therefore 
 would very properly be the subject of the whole syllogism. But 
 the same three conceptions would be the grounds for arguing : 
 
 The nervous fluid will not travel along a tied nerve ; 
 Electricity will travel along a tied nerve ; 
 .. Electricity is not the nervous fluid. 
 
 This is E A E, Fig. II., which is also a valid mood ; and it 
 would best suit one who was examining electricity. It is the 
 
 * Carpenter, Animal'Physiology, p. 437. 
 
ANALYTIC OF SYLLOGISMS. 161 
 
 same as the last statement, except that the present is the con- 
 verse of the former conclusion. Again, though somewhat less 
 naturally, we may state it, 
 
 Nothing that travels along a tied nerve can be the nervous fluid ; 
 Electricity travels along a tied nerve ; 
 .. Electricity cannot be the nervous fluid. 
 
 This is E A E of the first figure. From what has been said we 
 see that the relations between any three conceptions in our 
 mind are permanent, that the mode of statement is not perma- 
 nent, but may appear now as one mode of syllogism, now as 
 another ; that the conditions which determine us to one form 
 as more natural than another are, partly, the difference of ex- 
 tension in the conceptions, where it is ascertainable, partly the 
 greater prominence 'of one conception in our thoughts at the 
 time, which entitles it to be the subject ; that any one of the 
 syllogisms founded on the conceptions is sufficient to ascertain 
 their relations ; and that by a scheme of notation we may rep- 
 resent, not merely one of the cognate syllogisms, but the ground 
 of all of them, from which they can afterwards be drawn out 
 separately. 
 
 Sir William Hamilton's Scheme of Moods and Figures of 
 Syllogisms. 
 
 A mode of notation proposed by Sir William Hamilton is, 
 beyond doubt, one of the most important contributions to pure 
 logic which has ever been made since the science was put forth ; 
 and I am fortunate in being permitted to annex it. Its excel- 
 lencies are : that it is very simple ; that it shows the equivalent 
 syllogisms in the different figures at a glance ; that it shows aa 
 readily the convertible syllogisms in the same figure ; that it 
 enables us to read each syllogism Avith equal facility according 
 to extension and intension, the logical and the metaphysical 
 whole. Many of the different elements of the notation are not 
 new, but the novelty lies in the completeness and simplicity of 
 the whole scheme. 
 
SIR WILLIAM HAMILTON'S SCHEME OF NOTATION. 
 
 Fig. i. Fig. it. Fic. hi. 
 
 I X:^ m . M: m :Z X__^f ; ^*.Z X .-af-^^.-Z 
 
 [JI X,^ m:M: ZX ^C ^fX ^ ^ 
 
 [Iff X_. M . _,Z X^ _. M; ^_ ,Z ** M.^ ^ 
 
 ^<~ ^^ ^^ 
 
 Y X.^ M> :Z X : :Mt Z X: :M> :Z 
 
 . ^^ ' ^<~ , "^^ 7 
 
 Z 
 
 
 r 23T X:^. .j^; .,Z X__ -jj;- IMJ E X__ .flf, ** 
 
 ~x~ :s: , "^~ 
 
 z 
 
 XL T } _. Jr z X^^ZZZiZ X,^-.m. -Z 
 XffX:- 
 
 ~^<" ^^~ ^>^" 
 
 tf X^Tm. \.,z X: jM; Z X ^ z 
 
 X Balanced Middle; Unbalanced Extremes. B. Unbalanced Middle; Balanced Ex 
 tremes. O. Unbalanced Middle and Extremes. 
 
ANALYTIC OF SYLLOGISMS. 163 
 
 In this table M denotes the middle term ; and X and Z the 
 two terms of the conclusion. A colon ( : ) annexed to a term 
 denotes that it is distributed, and a comma (,) that it is undis- 
 tributed. Where the middle term has a : on the right side, 
 and a , on the left, we understand that it is distributed when 
 it is coupled in a judgment with the term on the right, and un- 
 distributed when coupled with the other. 
 
 The syllogisms actually represented are all affirmatives, be- 
 ing twelve in each figure ; and the affirmative copula is the 
 line wm , the thick end denoting the subject, and the thin 
 the predicate, of extension. Thus: 'X : es-, M,' would 
 signify ' All X is (some) M.' In reading off" the intension, the 
 thin end denotes the subject. 
 
 But from each affirmative can be formed two negative syl 
 logisms, by making each of the premises negative in turn. 
 The negation is expressed by drawing a perpendicular stroke 
 through the affirmative copula; thus: Mseww.. . In the nega- 
 tive moods the distribution of terms will remain exactly the 
 same as it was in the affirmatives from which they were respec- 
 tively formed, with some few exceptions in which the conclusion 
 has a term distributed Avhich was not when it was affirmative. 
 
 The line beneath the three terms is the copula of the conclu- 
 sion ; and in the second and third figures, as there may be two 
 conclusions indifferently, a line is also inserted above, to express 
 the second of them. 
 
 The mark v-*->^-w under a mood denotes that when the 
 premises are converted, the syllogism is still in the same mood. 
 
 But a "^^^^^^ between two moods signifies that when the 
 premises 01 either are converted, the syllogism passes into the 
 other. 
 
 The middle is said to be balanced when it is distributed in 
 both premises alike. The extremes or terms of the conclusion 
 are balanced when both alike are distributed, unbalanced when 
 one is and the other is not. 
 
 According to this scheme there are 12 affirmative moods in 
 each figure, and 24 negatives, or 36 altogether. All the possi- 
 ble moods of syllogism are here exhibited ; but the value of the 
 
164 
 
 LOGIC. 
 
 inference in some of them is so small that they would never 
 actually be employed. For example, by making negative the 
 first premise of No. vii. Fig. II. we have such a syllogism as : 
 
 Some stones do not resist the action of acids ; 
 
 Some metals resist the action of acids ; 
 . . Some metals are not some stones ; 
 where there is undeniably an inference, but one which can 
 scarcely be said to add to our knowledge of the subject of it. 
 To facilitate a comparison of this table with the former one 
 (p. 155), its moods are translated into equivalent letters; and 
 an examination will prove that every mood not containing the 
 vowel i) or w, occurs in both tables, which, after deducting the 
 disputed moods so marked, coincide in all respects. 
 
 FIG. 
 
 Aff 
 -U u u. . 
 
 I. 
 
 Neg. 
 ..EUE.. 
 
 Table of M 
 
 FIG 
 
 Aff 
 U U TJ.. 
 
 "oods. 
 ii. 
 
 Neg. 
 ..EUE.... 
 UEE 
 ,0Y 
 
 FIG. 
 
 Aff. 
 
 ....uuu.. 
 
 ....A A I.. 
 
 m. 
 
 Neg. 
 ..EUE 
 
 -A Y I.. 
 
 UEE 
 . .v Y #.. 
 
 Y Y I.. 
 
 UEE 
 
 ..n A m 
 
 -U T Y. . 
 
 AO 
 . .E YO.. 
 
 TJYY.. 
 
 YO * 
 .E YO 
 
 U A Y.. 
 
 ..EAO 
 
 -A U A. . 
 
 UOO 
 
 ,.,u? 
 
 YTJA.. 
 
 UOO 
 .0 U , 
 
 ....ADA.. 
 
 U ,0 
 ..v U n 
 
 -U A A. . 
 
 AE, 
 . .E AE.. 
 
 TJA A.. 
 
 YE, 
 .E AE 
 
 ....UYA.. 
 
 AE, 
 ..EYE 
 
 -Y TJ Y. . 
 
 TJ v v 
 ..OTJO.. 
 
 YEE 
 .., I .. 
 
 ATJY.. 
 
 Y I 1.. 
 
 U , , 
 
 .,uo 
 
 mi.. 
 
 UOO 
 ..OUO 
 
 -All.. 
 
 AEE 
 .0 I <*.... 
 
 Yu. 0, 
 
 .m Y ..., 
 
 10. 
 .E I 0.... 
 
 . U .... 
 I E v 
 .0 A i? 
 
 ....A I I.. 
 ....I A I.. 
 ....U I I.. 
 ....I U I.. 
 A YA.. 
 
 YEE 
 
 ..n I o 
 
 -I Y I.. 
 
 A w m 
 
 ..<* Y .. 
 
 I Y I. . 
 
 ..U A 0, 
 
 -TJ I I.. 
 
 ..E I 0.. 
 
 .....TJ I I.. 
 
 I , * 
 ..E I 
 
 IUI.. 
 
 TJa, 
 
 .. TJ &>.. 
 
 I U I.. 
 
 Uo.0 
 
 ..0) U u> 
 
 -AAA.. 
 
 IE, 
 
 YA A.. 
 
 IE, 
 .., Y , 
 
 -Y Y Y. . 
 
 A , , 
 . .0 YO.. 
 
 .. AYY . 
 
 Y v n 
 ,Y0 
 
 ....Y A Y.. 
 
 A , 
 ..0 AO 
 
 
 TOO.. 
 
 
 AOO 
 
 
 Y,0 
 
ANALYTIC OF SYLLOGISMS. 
 
 Sum of all the valid Moods in each Figure. 
 
 THIS TABLE. FORMER. TABLE. 
 
 i. 36 (=12aff.4-24neg.) 14 weak neg .= 22. 
 ii. 36 (=12aff.+24neg.) 16 weak neg.=20. 
 in. 36 (=12aff.+24neg.) 15 weak neg.=21. 
 
 Euler^s System of Notation. 
 
 Perhaps the most celebrated plan of notation is that of Eu- 
 ler, as described in his Lettres a une princesse d? Allemagne'. 
 But, as it only represents the extension of the terms, and not 
 the opposite capacity, of intension, it is far inferior to that which 
 
has just been described. The sphere of a conception is repre- 
 sented by a circle ; an affirmative judgment by one circle whol- 
 ly or partly contained in another ; and a negative by two sepa- 
 rate circles. The judgment that ' All men are mortal' has the 
 effect of including men in the class of mortal beings, which 
 would be represented by a small circle for ' men,' in a large one 
 for 'mortal.' The annexed diagram exhibits (I) the mood 
 AAA, (II) E A E, (III) All, and (IV) E I O, all of the 
 first figure." 
 
 SIR WILLIAM HAMILTON'S SPECIAL CANONS Or THE DIFFERENT 
 FIGURES. 
 
 We have, as we have seen, a general canon for the syllogism 
 in all its forms, and, at the same time, a special one for each 
 special form, and, also, for each particular figure. The follow- 
 ing are the forms adopted by Sir William Hamilton, and com- 
 municated by him for the benefit of the science of logic, the 
 form adapted to each special figure in all its various modifica- 
 tions, to wit : 
 
 " Canon of the First Figure. 
 
 " In as far as two notions are related, either both positively, 
 or the one positively and the other negatively, to a third notion 
 to which the one is subject and the other predicate, they are 
 related positively or negatively to each other as subject and 
 predicate. 
 
 " Canon of the Second Figure. 
 
 " In as far as two notions, both subjects, are, either each posi- 
 tively, or the one positively, the other negatively, related to a 
 common predicate notion, in so far are those notions positively 
 or negatively subject and predicate of each other. 
 
1 
 
 ANALYTIC OF SYLLOGISMS. 
 
 " Canon of the Third Figure. 
 
 " In as far as two notions, both predicates, are, either each 
 positively, or the one positively and the other negatively, related 
 to a common subject notion, in so far are those notions, positive- 
 ly or negatively, subject and predicate of each other." 
 
 CANONS AND DIVERSE FORMS OF THE FIGURED SYLLOGISM ELU- 
 CIDATED. 
 
 We will now proceed to elucidate somewhat the canons and 
 diverse forms of the figured syllogism, by the induction of a 
 few examples. We will commence with the mood U U U : 
 
 X is : M, or X=M ; 
 Z is : M, or Z=M ; 
 Z is : X, or Z=X. 
 Converse. : X is : Z, or X=Z. 
 
 It will be perceived on reflection, that in the premises each 
 extreme, together with the middle term, is distributed. Both 
 extremes are, consequently, as required by the canon, distribu- 
 ted in the conclusion. For the same reasons the converse of the 
 conclusion, like the exposita, is a toto-total affirmative proposi- 
 tion, " : X is : Z." We give the mood in the second figure. 
 We might have given it in the first or third, and the same re- 
 marks would be equally applicable. Contrast with the above 
 an example in the mood Barbara : 
 
 : M is X, that is, some X ; 
 : Z is M, that is, some M ; 
 .. : Z is X, that is, some X. 
 Converse, Some X is Z, or : Z. 
 
 In the major premise X, being the predicate of a toto-partial 
 affirmative proposition, is undistributed. Z and M being the 
 subjects of such propositions are both distributed. The pre- 
 mises, therefore, permit only a toto-partial conclusion, whose 
 converse is a particular proposition, or, rather, a parti-total one, 
 " Some X is Z, that is, : Z." Let us next consider the mood 
 
168 LOGIC. 
 
 Y Y Y, which, for reasons hereafter to be stated, is allowable 
 only in the first figure : 
 
 , M is : X ; 
 , Z is : M ; 
 .-. , Z is : X. 
 Converse, : X is , Z. 
 
 In this mood M and X, as the predicates of parti-total affirma- 
 tive propositions, are both distributed ; the latter in the major, 
 and the former in the minor premise. Z, as the subject of a 
 parti-total proposition, is undistributed. In the conclusion, 
 then, Z should be undistributed and X distributed, while Z is 
 the proper minor and X the proper major term. The former, 
 then, as the subject of the conclusion, should be particular, and 
 the latter, as the predicate of the same, distributed. In other 
 words, the premises yield a parti-total affirmative conclusion, 
 " Some Z is all of X," with its converse, " All X is Z, that is, 
 some Z." The mood Y Y Y is allowable only in the first 
 figure for these reasons, that in the second figure both of the 
 extremes, and in the third the middle term, would be undis- 
 tributed. Let us now contemplate some of the negative syl- 
 logisms. We will first notice the iYw: 
 
 No M is some X ; 
 
 Some Z is all of M ; 
 
 . \ Some Z is not some X. 
 
 In this syllogism, while M is distributed in both premises, 
 neither extreme is distributed at all. In the conclusion, conse- 
 quently, Ave have, on account of the fact that one premise is 
 negative, but a parti-partial conclusion, and that conclusion is 
 authorized by the premises. So, while in the first figure we 
 can have no syllogism in the mood A O O, we may have a valid 
 one in A O cj. Example : 
 
 : M is X ; 
 
 , Z is not M ; 
 .. , Z is not , X. 
 
 The middle term is here distributed in both premises, and 
 neither of the extremes in either of the premises. For this rea- 
 
(Fig, 1.) 
 
 (Fig. 2.) 
 
 Some M is X (some X) ; 
 
 Some X is M ; 
 
 No Z is M ; 
 
 No Z is M ; 
 
 No Z is some X. 
 
 No Z is some X 
 
 ANALYTIC OF SYLLOGISMS. 169 
 
 son we have, one premise being negative, a valid parti-partial 
 negative conclusion, to wit : " Some Z is not some X." 
 
 In the first figure we have no valid syllogism in the mood 
 I E O. In each alike, however, we have one in I E *j : 
 
 (Fig. 3). 
 Some M is X ; 
 No M is Z ; 
 No Z is some X 
 
 In all these examples M is distributed, being either the subject 
 of a universal or the predicate of a negative proposition. For 
 the same reasons Z is distributed, while X, being the subject of 
 a particular or the predicate of an affirmative proposition, is not 
 distributed. The laws of deduction, therefore, authorize a toto- 
 partial negative conclusion. These examples are sufficient for 
 purposes of elucidation, and will prepare the way for a distinct 
 understanding of the whole subject as given in the above table 
 from Sir William Hamilton. 
 
 Proper sphere and application of Aristotle's dictum. 
 
 In almost all treatises on logic the dictum of Aristotle, the 
 dictum de omni et de nullo, has been assumed as the universal 
 canon of the syllogism in all its forms. The dictum is this : 
 "Whatever is predicated of any term distributed, whether 
 affirmatively or negatively, may be predicated, in like manner, 
 of any thing contained under it." "This rule," says Dr. 
 Whately, "may be ultimately applied to all arguments, and 
 their validity ultimately rests on their conformity thereto." In 
 reply, we would remark, that this canon is applicable to argu- 
 ments of the following class only: 1. Something must be af- 
 firmed of a class of objects; as, for example, "All men are 
 mortal." 2. Some individual or individuals must be given as 
 contained under this class ; as, " John is a man." 3. The quali- 
 ty affirmed in the first proposition of the whole class must, as 
 a conclusion, be affirmed of this individual ; as, " John is mor- 
 tal." In all such cases, the terms are arranged according to 
 
the canon of the first figure. On examination it will be found 
 that the dictum is applicable to arguments only as they are re- 
 duced to this figure ; and on one condition then, that the terms 
 represent inferior and superior conceptions. It is not applicable 
 to the second and third figures at all, nor to any form of argu- 
 ment in which the terms do not represent such conceptions. 
 Because an argument belongs to this figure, it does not follow 
 from hence that the terms are subordinated one to another, as 
 above stated. For example : 
 
 : M= : X; 
 
 : Z= : M ; 
 .-. : Z= : X. 
 In this syllogism neither term is given as in any form subordi- 
 nated to the other. Nothing, in the first instance, is affirmed 
 of a class of objects, and no individuals are there given as in- 
 cluded under this class ; nor in the conclusion is something 
 affirmed, as required by the dictum, of individuals which had 
 been previously affirmed of the class. Each term, on the other 
 hand, is equal to every other. The argument is valid, and in 
 the first figure. Yet the dictum is not applicable to it. What 
 then is the exclusive and proper sphere and application of this 
 dictum f We answer : 1. The dictum de omni is applicable to 
 the affirmative moods of this figure, when the terms, as repre- 
 senting inferior and superior conceptions, are subordinated, as 
 such, the one to the other, that is, Barbara and Darii. 2. The 
 dictum de nullo is applicable only to Celarent and Ferio. Thus 
 a dictum which has hitherto been considered as the basis of all 
 valid reasoning, is found to be of quite limited application. 
 
 Section Y. The Conditional Syllogism. 
 
 A conditional syllogism is one whose major proposition is con- 
 ditional, and whose minor together with the conclusion is cate- 
 gorical. Example : 
 
 If the scriptures are not wholly false they are entitled to respect ; 
 They are not wholly false ; 
 .. They are entitled to respect. 
 
ANALYTIC OF SYLLOGISMS. 171 
 
 When the reasoning does not turn upon the hypothesis, but a 
 hypothetical conclusion is drawn from a hypothetical premise, 
 then the reasoning is categorical. Example : 
 
 If the Scriptures come from God they are entitled to faith and obedience ; 
 If they are not an imposture they came from God ; 
 
 If, therefore, they are not an imposture they are entitled to faith and obe- 
 dience. 
 
 The reasoning here is throughout categorical. In the first 
 example, however, the case is different. The reasoning in this 
 instance turns upon the hypothesis, and consequently, a cate- 
 gorical answer is deduced from a hypothetical premise. This is 
 what is meant by a hypothetical or conditional syllogism. The 
 major premise in such syllogisms consists of two categorical 
 ones, related to each other as antecedent and consequent, and 
 so connected that the truth of the latter necessarily follows 
 from that of the former. The nature of such propositions and 
 the conditions of their validity have been already explained. 
 Nothing, therefore, need be added in this connection on this 
 subject. In the minor premise the truth of the antecedent is 
 affirmed, and in the conclusion the truth of the consequent in- 
 ferred, or, the truth of the consequent is denied in said premise 
 and that of the antecedent denied in the conclusion. 
 
 If we should affirm the consequent or deny the antecedent, no 
 conclusion could from hence be deduced. The reason is ob- 
 vious. The truth of the antecedent does not, in any sense, de- 
 pend upon that of the consequent. It may be true that if A, 
 for example, has a certain amount of real estate he is rich. 
 From the fact that he is rich, however, we cannot infer that he 
 has any real estate at all, for many individuals who are rich 
 have, or may have, no such possessions. So the truth of the 
 consequent does not depend upon that of the antecedent. It 
 is true, that if A has a fever he is sick. He may have no fever, 
 however, and yet be sick from some other form of disease. 
 Hence the rule of this form of the syllogism, that from the af- 
 firmation or admission of the truth of the consequent or the de- 
 nial of the antecedent, we can infer nothing. 
 
172 LOGIC. 
 
 The case is very different, however, where we grant the truth 
 of the antecedent or deny that of the consequent. In the first 
 case the latter must be true, and in the second the former must 
 be false. Let, for example, the following proposition be admit- 
 ted as true, to wit : " If A is B, C is D." Suppose we admit the 
 truth of the antecedent and affirm A is B, then, undeniably, we 
 must admit the truth of the consequent C is ~D. Suppose, on 
 the other hand, that we deny the consequent, and affirm C is 
 not D. In this case we must deny the antecedent, it being 
 originally granted that if A is B, C must be D. Hence the. 
 two principles, that when we admit the relation of consequence 
 between the antecedent and consequent in a conditional propo- 
 sition, the following conclusions must be held as valid in regard 
 to the deductions of conclusions in this form of the syllogism, to 
 wit: 
 
 1. If we admit the antecedent the consequent may be inferred 
 or affirmed. 
 
 2. If we deny the consequent we may deny the antecedent. 
 The former is called the constructive or direct, and the latter 
 
 the destructive or indirect form of reasoning. 
 
 THE APPROPRIATE SPHERE OP THE COISTDITIONAL SYLLOGISM. 
 
 The question which now demands- attention, is the appro- 
 priate sphere of the conditional syllogism. In all instances, as 
 we have seen, a universal proposition may in such syllogism be 
 substituted for the hypothetical premise, and the conclusion 
 would be perfectly the same and equally valid. The question 
 is, Under what circumstances is the hypothetical form of argu- 
 mentation to be preferred to the categorical ? Among these 
 we notice, as of special importance, the following : 
 
 1. When a question is being argued under circumstances in 
 which there is a strong reluctance to admit the conclusion which 
 we wish to reach, and in which, consequently, there is a strong 
 likelihood that the evidence, unless most distinctly apprehended 
 in its nature and bearing, will be resisted. In such circum- 
 stances it is altogether best to state the case, first of all, in the 
 
ANALYTIC OP SYLLOGISMS. 173 
 
 conditional form, to wit : if such is the state of the case, such or 
 such a conclusion or consequent must he admitted. When the 
 relation between the antecedent and consequent is too evident 
 to be denied, and the evidence to be pi-esented is equally con- 
 clusive in itself, the hypothetical form of argument is the most 
 conclusive of all. 
 
 2. When such prejudice does not exist, but the force or bear- 
 ing of the evidence, though perfectly conclusive in itself, is not 
 likely to be distinctly perceived, then, also, first of all, to state 
 the case in the hypothetical form is most likely to secure the re- 
 sult desired. Any one can see, the speaker may state, that, if 
 such and such things are shown to be true, the conclusion must 
 be admitted, and this is precisely what I design to accomplish. 
 This, of all things, is often best adapted to secure a distinct ap- 
 prehension of the nature and bearing of the evidence to be pre- 
 sented. 
 
 3. When we wish to test the bearing of an argument which 
 comes under a general principle, it is often best to state it hy- 
 pothetically relatively to the specific case under consideration. 
 Instead of presenting the subject in the universal form, "All 
 who do so and so are guilty of such and such crimes," for exam- 
 ple, we had better state the subject in the hypothetical form, to 
 wit : If these individuals have perpetrated such and such spe- 
 cific acts, and done so from such and such motives, such and 
 such is the character of those acts. The bearing of the argu- 
 ment will, in such circumstances, be most distinctly seen. 
 
 4. But one of the most important uses of the hypothetical 
 syllogism consists in its judicious employment for the refutation 
 of false propositions, by showing that if their truth be admitted, 
 that of others whose truth none will have the effrontery to ad- 
 mit, must be admitted also. The argument of Sir William 
 Hamilton in favor of the validity of external perception for the 
 reality of its object, presents an admirable example of this use of 
 the conditional syllogism. The object of the author is to show 
 that the opposite doctrine involves a universal impeachment of 
 consciousness itself on all subjects alike, and a consequent denial 
 of the possibility of real knowledge on any subject. The real 
 
174 LOGIC. 
 
 argument presented is this, If the validity of the testimony of 
 consciousness is denied in this specific case, it is to he denied 
 universally. The dogma under consideration does deny its va- 
 lidity in this case, and, therefore, impeaches it universally. 
 With these remarks special attention is invited to the extract 
 referred to : 
 
 " In perception, consciousness gives as an ultimate fact, a be- 
 lief of the knowledge of the existence of something different 
 from self As ultimate this belief cannot be reduced to a 
 higher principle ; neither can it be truly analyzed into a double 
 element. We only believe that this something exists, because 
 we believe that we knoxc (are conscious of) this something as 
 existing ; the belief of the existence is necessarily involved in 
 the belief of the knowledge of the existence. Both are origi- 
 nal, or neither. Does consciousness deceive us in the latter, it 
 necessarily deludes us in the former ; and, if the former, though 
 a fact of consciousness, be false, the latter, because a fact of con- 
 sciousness, is not true. The beliefs contained in the two propo- 
 sitions : 
 
 " 1st. I believe that a material world exists, 
 
 " 2d. I believe that I immediately know a material world 
 existing, (in other words,) I believe that the external reality it- 
 self is the object of which I am conscious in perception, though 
 distinguished by philosophers, are thus virtually identical." In 
 another place, he adds, " In our perceptive consciousness there 
 is revealed as an ultimate fact, a self and a not-self each given 
 as independent each known only in antithesis to the other. 
 No belief is more intuitive, universal, immediate, or irresistible, 
 than that this antithesis is real and known to be real ; no belief, 
 therefore, is more true. 
 
 " If the antithesis be illusive, self and not-self subject and ob- 
 ject, Zand thou, are distinctions without a difference; and con- 
 sciousness, so far from being ' the internal voice of our Creator,' 
 is shown 1 1 be, like Satan, ' a bar from the beginning.' " 
 
ANALYTIC OF SYLLOGISMS. 175 
 
 Section VI. The Disjunctive Syllogism. 
 
 A disjunctive syllogism is one whose major premise is a dis- 
 junctive, and whose minor together with the conclusion is a 
 categorical, proposition. 
 
 A disjunctive proposition or judgment has already heen de- 
 fined, as a proposition made up of two or more categorical ones, 
 one at least of which must be true, and the others false. We 
 have also presented the characteristics of all valid judgments of 
 this kind. On these topics nothing more need he added in tliis 
 connection. 
 
 In disjunctive syllogisms we argue in either of two directions : 
 from the truth of one member of the disjunction to the falsity of 
 the others ; or, from the falsity of all but one, to the truth of 
 that one. For example, A is either B, C, or D. It is B, and, 
 therefore, not C or D. Or, A is B, C, or D. It is not C nor D, 
 it is, therefore, B. 
 
 When the proposition to be argued is a very important one, 
 it may be wise to adopt both forms of argumentation above 
 stated ; that is, first show by one process that the one member 
 is true, and the others, consequently, false, and then, by another 
 process, that these are false, and that the one under considera- 
 tion, consequently, must be true. When the major proposition 
 in such syllogism is valid, either of the forms of argument above 
 mentioned must be valid also. 
 
 Circumstances in which the Disjunctive Syllogism should be 
 used. 
 
 The following, at least, are circumstances where the disjunc- 
 tive syllogism may be most successfully employed : 
 
 1. When we wish to ascertain or prove the motives of an in- 
 dividual in a certain act or course of conduct, and but a certain 
 number of motives, two or more, are conceivable from the na- 
 ture of the case, and when one of these to the exclusion of 
 the others, must be the real one. In such circumstances, it is 
 often indispensable to full conviction, and always most favorable 
 
176 LOGIC. 
 
 to the ascertainment and establishment of the truth, to state dis- 
 tinctly these different hypotheses, and to show that one of them 
 must, and but one can, be true. The argument may, then, take 
 either of the two courses above named, or both united, and that 
 with the greatest prospect of a satisfactory issue. A, we will 
 suppose, has taken the life of B under circumstances which ren- 
 der it certain that this was done in sell-defence, and the act is, 
 consequently, no legal crime whatever ; or, with malice pre- 
 pense, and is, therefore, to be regarded as murder. How im- 
 portant to a correct judgment of the facts, is a distinct appre- 
 hension of the case in the light of these two hypotheses. The 
 disjunctive syllogism alone has place in such cases. 
 
 2. Suppose that the question to be argued pertains to the in- 
 quiry, What is the cause or law of a given class of facts ? and 
 that, from the nature of the case, but a certain number of hy- 
 potheses are conceivable, one of which, and but one, to the ex- 
 clusion of all the others, must be true. In all such- cases, it is of 
 the utmost importance to state distinctly these different hypoth- 
 eses, and to show their real relations as members of the disjunc- 
 tion. In other words, in all such cases, the disjunctive syllogism 
 has place and must be employed, if we would argue with any 
 reasonable hope of success. 
 
 3. Suppose that the question to be argued pertains to the 
 meaning of a certain document or passage. When the words ad- 
 mit of different constructions, or when various constructions are 
 conceivable, here, too, such constructions should be presented 
 as members of the disjunction ; that is, it should be shown that 
 such and such constructions alone are conceivable, and that one 
 only can be true, and that this one, to the exclusion of the 
 others, must be true. We are, then, best prepared to state the 
 argument in favor of one, and against the other, hypothesis. 
 In all cases, in short, where a case to be argued admits of dif- 
 ferent constructions, and when different constructions are put 
 upon it, it is of the greatest importance to state definitely in the 
 outset how many such are conceivable, and to show that one, 
 to the exclusion of the others, must be true. Here is the ap- 
 propriate sphere of the disjunctive syllogism, and within its 
 
ANALYTIC OF SYLLOGISMS. 177 
 
 sphere no other form of argument can well be substituted in its 
 place. 
 
 Sectioh VII. The Dilemma. 
 
 A dilemma is a form of the syllogism in which the major 
 premise is a conditional, and the minor a disjunctive, proposi- 
 tion. Of this form of the syllogism there are three kinds : 
 
 1. Where there are in the major different antecedents, all 
 having the same consequent, while in the minor these ante- 
 cedents are disjunctively affirmed, and in the conclusion the 
 common consequent is affirmed. For example : If A is B, A is 
 X ; and if A is C, A is X ; and if A is D, A is X. But, either 
 A is B, A is C, or A is D ; therefore, A is X. 
 
 2. Where we have the same antecedent and different conse- 
 quents, one of which must be false, and when in the minor 
 premise we disjunctively deny the consequents, and in the con- 
 clusion deny the antecedents. If A is B, C is D ; and if A is B, 
 E is F ; and if A is B, G is H. But, either one or the other of 
 these consequents must be false ; thex-efore, A is not B. 
 
 3. When we have several antecedents, and each a different con- 
 sequent, and when in the minor premise we disjunctively deny 
 the consequents, and in the conclusion disjunctively deny the 
 antecedents, or similarly affirm the antecedents and consequents. 
 If A is B, C is D ; and if E is F, G is II. But, either C is not 
 D, or G is not H ; and, therefore, either A is not B, or E is not 
 F ; or A is B, or E is F ; therefore, either C is D, or G is H. 
 
 When we affirm the antecedent, and as a consequence infer 
 the consequent, we have what is called the constructive, and 
 when we deny the consequent, and, therefore, deny the ante- 
 cedent, we have what is called the destructive, dilemma. 
 
 Circumstances which require the use of this form of the Syl- 
 logism. 
 
 We now notice the circumstances in which this form of the 
 syllogism may be employed to the greatest advantage : 
 
178 LOGIC. 
 
 1. When several consequents are necessarily connected with 
 a particular dogma which we desire to disprove, consequents so 
 related to said dogma that if it be true, all these must be ad- 
 mitted, but some at least of which are so undeniably self-con- 
 tradictory and absurd, that no one will have the effrontery to 
 maintain them. In such circumstances no form of argument 
 can have such force as the syllogism under consideration. So, 
 also, when the conduct of an individual is such, that it can be ex- 
 plained in consistency only with one of two or more intentions, 
 each of which is equally dishonorable to himself and available 
 in argument to his conviction ; here, also, we have a case for 
 the dilemma, a case coming under the same principle as that 
 above specified. In illustration, take the dogma of infidelity, 
 that the miraculous events recorded in the Scriptures never oc- 
 curred. If this dogma is true, then those who professed to per- 
 form these miracles must have known that they were deceiving 
 the world in such pretensions, and Christ, the prophets, and 
 apostles must have been gross impostors and deceivers. If this 
 dogma is true, those, also, who narrated these events must have 
 known the falsehood they were palming upon the w T orld, and 
 they, too, must be held as deliberate deceivers of the grossest 
 character. Once more : if this dogma is true, the enemies of 
 Christ, his own murderers and crucifiers among others, must 
 have united with his disciples and Christians generally in deceiv- 
 ing the world in regard to these events ; for they all alike ad- 
 mitted the fact of their occurrence. But Some of these neces- 
 sary consequences of this dogma must be false, and the dogma 
 itself cannot be true. In this case none of the consequences re- 
 ferred to can be true. All that is requisite to the destruction of 
 the antecedent, however, is a disjunctive denial of these conse- 
 quents. 
 
 2. .When we have a number of facts or principles, some of 
 'which must be admitted as real or true, and while each alike 
 stands necessarily connected with a conclusion which we desire 
 to establish, so connected, that if any one of the series be admit- 
 ted, .the common consequent must be admitted also. Here, too, 
 no form of .argument can take the place of this one form of the 
 
ANALYTIC OF SYLLOGISMS. 179 
 
 syllogism. In many instances it may happen that all the facts 
 referred to are true. Yet if the argument is made to turn upon 
 such a broad claim, it may happen that the conclusion would 
 thereby he esteemed doubtful. When there can be no doubt 
 that some must be, and while it is undeniable that if any are, 
 true, the conclusion must be valid, the disjunctive syllogism 
 should always be employed. 
 
 3. It not unfrequently happens that the advocate of a certain 
 dogma may be necessitated to take one of two distinct positions, 
 and when each is connected necessarily with consequents abso- 
 lutely ruinous to his cause. A distinct statement of these posi- 
 tions, together with the necessary consequents of each, will often 
 render the truth demonstratively evident. An individual some- 
 times, also, may be placed in circumstances where he must act 
 in one of two or more specific directions, and when action in 
 either direction would be inconsistent with his principles or pro- 
 fessions. In nil such cases we have the appropriate sphere of 
 the dilemma. For example, "If this man were wise he would 
 not speak irreverently of the Scriptures in jest; and, if he were 
 good, he Avould not do so in earnest ; but he does so either in 
 jest or in earnest, therefore, he is not wise or not* good." "If 
 ^Echines joined in the public rejoicings he is inconsistent ; if he 
 did not join he is Unpatriotic ; but he either did or did not join, 
 therefore he is either inconsistent or unpatriotic." 
 
 Section VIII. The Deductive and Inductive Syllogisms. 
 
 The inductive and deductive syllogisms are commonly repre- 
 sented as distinguished from each other by the following par- 
 ticulars. In the first, we reason from the particular to the gen- 
 eral, from the individual to the whole class ; whereas in the lat- 
 ter, w r e reason from the general to the particular, from the class 
 to the individual. This view of the subject has evidently arisen 
 from confounding the laws of investigation with those of reason- 
 ing. In the former process individual facts are investigated as 
 preparatory to illation or induction proper. We thus investi- 
 
180 LOGIC. 
 
 .gate such facts, for the purpose of ascertaining their character 
 as parts of a given whole. When we have satisfied ourselves on 
 this subject, we then reason from the parts to the whole, and 
 we reason thus : What belongs to the individuals constituting 
 'a given class belongs to the class itself. This characteristic be- 
 longs to such individuals ; it, therefore, belongs to the class itself. 
 This is the inductive syllogism. When this process is com- 
 pleted we then reverse it, and reason from the whole to its con- 
 stituent parts, thus : All of this class have this characteristic ; 
 A belongs to tliis class ; therefore he has this characteristic. 
 This is the deductive syllogism. The two have a fixed relation 
 to each other, the latter always presupposing and depending 
 for its validity upon the former. 
 
 In adducing individual facts in a process of investigation, we 
 do not even then conclude from the particular to the general, 
 but from individuals to individuals. One individual, for exam- 
 ple, in a course of experiments upon a mass of matter called 
 gold discovers some new property in it. The mass before him* 
 he calls gold, because it presents all the elements of the concep- 
 tion represented by the term under consideration. When the 
 new fact appears, his first and great inquiry is, Whether it arises 
 from. the essential properties of the substance itself, or from 
 some foreign substance accidentally connected with it ? When 
 this question is resolved and the new fact is found to be the re- 
 sult of the essential elements of this substance, it is assumed as 
 itself an essential element of our conception of this substance. 
 On what groimds ? Because we. have reasoned from the indi- 
 vidual to the class ? By no means ; but because it, with the 
 other elements referred to, now enters into our fundamental 
 conceptions of the substance itself, and no individual mass want- 
 ing this characteristic can take rank under this conception. If 
 it should be found that this fact characterized some masses and 
 not others reckoned as gold, this would occasion a separation of 
 such masses into ,two species, one having, and the other not hav- 
 ing, this characteristic. When we have formed a general con- 
 ception, an individual to take rank under it, must represent all 
 the elements included in the conception. The conception does 
 
ANALYTIC OF SYLLOGISMS. 181 
 
 not represent a mass of individuals whose character we do not 
 know, and in respect to each of whom, without having obtained 
 such knowledge, we reason from the general conception. On 
 the other hand, it represents a class which we do know, and 
 from which, consequently, we reason to said individuals. We 
 first know the individuals, and from the elements common to 
 them all abstracted, we form the general conception, and when 
 we reason back from the conception to the individuals, Ave do 
 not reason from the known to the unknown, but from the 
 known to the known. I would here invite very special atten- 
 tion to the following lengthy extract from Sir William Hamil- 
 ton, as presenting all that need be added upon this subject : 
 
 " Logic does not consider things as they exist really and in 
 themselves, but only the general forms of thought under which 
 the mind conceives them ; in the language of the schools, logic 
 is conversant, not about first, but about second, notions. Thus 
 a logical inference is not determined by any objective relation 
 of causality subsisting between the terms of the premises and 
 conclusion, but solely by the subjective relation of reason and 
 consequent under which they are construed to the mind in 
 thought. The notion conceived as determining is the reason ; 
 the notion conceived as determined is the consequent ; and the 
 relation between the two is the consequence. Now, the mind 
 can think two notions under the formal relation of consequence 
 only in one or other of tAvo modes. Either the determining 
 notion must be conceived as a whole, containing (under it), 
 and, therefore, necessitating the determined notion conceived 
 as its contained part or parts ; or, the determining notion must 
 be conceived as the parts constituting, and, therefore, necessi- 
 tating the determined notion conceived as their constituted 
 whole. Considered, indeed, absolutely and in themselves, the 
 whole and all the parts are identical. Relatively, however, to 
 us they are not, for in the order of thought (and logic is only 
 conversant with the laAvs of thought), the whole may be con- 
 ceived first, and then, by mental analysis, separated into its 
 parts ; or, the parts may be conceived first, and then, by men- 
 tal synthesis, collected into a Avhole. Logical inference is thus 
 
182 LOGIC. 
 
 of two, and only of two, kinds ; it must proceed, either from the 
 whole to the parts, or from the parts to the whole ; and it is 
 only under the character of a constituted or containing whole, 
 or, of a constituting or contained part, that any thing can he- 
 come the term of a logical argumentation. 
 
 Before proceeding we must, however, allude to the nature of 
 the whole and part, ahout which logic is conversant. These 
 are not real or essential existences, hut creations of the mind 
 itself in secondary operation on the primary ohjects of its know- 
 ledge. Things may be conceived the same, inasmuch as they 
 are conceived the street of the same attribute or collection of 
 attributes (i. e. of the same nature) ; inasmuch as they are con- 
 ceived the same, they must be conceived as the parts constituent 
 of, and contained under, a whole ; and as they are conceived 
 the same only as they are conceived to be the subject of the 
 same nature, this common nature must be convertible with that 
 ichole. A logical or universal whole is called a genus when its 
 parts are thought as also containing wholes or species ; a spe- 
 cies when its parts are thought as only contained parts or indi- 
 viduals. Genus and species are each called a class. Except 
 the highest and the lowest, the same class may thus be thought 
 either as a genus or as a species. 
 
 Such being the nature and relations of a logical whole and 
 parts, it is manifest what must be the conditions under which 
 the two kinds of logical inference are possible. The one of 
 these, the process from the whole to the parts, is deductive rea- 
 soning (or syllogism proper) ; the other, the process from the 
 parts to the whole, is inductive reasoning. The former is gov- 
 erned by the rule : What belongs {or does not belong) to the 
 containing whole, belongs {or does not belong) to each and all 
 of the contained parts. The latter by the rule : What belongs 
 {or does not belong) to all the constituent parts, belongs {or does 
 not belong) to the constituted whole. These rules exclusively 
 determine all formal inference ; whatever transcends or vio- 
 lates them, transcends or violates logic. Both are equally abso- 
 lute. It would be not less illogical to infer by the deductive 
 syllogism, an attribute belonging to the whole of something it 
 
ANALYTIC OF SYLLOGISMS. 183 
 
 was not conceived to contain as a part, than by the inductive, 
 to conclude of the whole what is not conceived as a predicate 
 of all its constituent parts. In either case the consequent is not 
 thought as determined by the antecedent ; the premises do not 
 involve the conclusion. 
 
 The deductive and inductive processes are elements of logic 
 equally essential. Each requires the other. The former is only 
 possible through the latter ; and the latter is only valuable as 
 realizing the possibility of the former. As our knowledge com- 
 mences with the apprehension of singulars, every class or uni- 
 versal whole is consequently only knowledge at second-hand. 
 Deductive reasoning is tlms not an original and independent 
 process. The universal major proposition, out of which it de- 
 velops the conclusion, is itself necessarily the conclusion of a 
 foregone induction, and, mediately or immediately, an infer- 
 ence ; a collection from individual objects of perception or self- 
 consciousness. Logic, therefore, as a definite and sell-sufficient 
 science, must equally vindicate the formal purity of the ana- 
 lytic illation by which it ascends to its wholes, as of the syn- 
 thetic illation by which it re-descends to their parts." 
 
 Section IX. Syllogisms of Induction and Analogy. 
 
 Demonstrative, inductive, and analogical reasoning distin- 
 guished. 
 
 There are three kinds of conclusions deduced from different 
 kinds of premises : what is commonly called the demonstrative, 
 in which, in general, we obtain necessary truths, truths whose 
 opposites are inconceivable and impossible ; truths of induction, 
 truths which are real, but whose opposites are conceivable, and 
 therefore, in themselves, possible ; and deductions of analogy, 
 deductions based upon such remote relations as to claim our 
 regard only as probably true. Syllogisms which yield the first 
 class of truths are denominated by Kant, and with perfect pro- 
 priety, " syllogisms of reason." Those which yield the last two 
 kinds of conclusions he calls syllogisms of the understanding, this 
 
latter class being divided into two species, those of induction 
 and those of analogy. The distinction between syllogisms of 
 reason and of the understanding is perfectly obvious. To the 
 former pertain all mathematical truths and those of a kindred 
 nature. To the latter belong all truths in respect to matters 
 of fact, and deductions from the same relative to the universe 
 of matter and spirit. The distinction between arguments of in- 
 duction and analogy, however, is not so obvious, excepting in 
 their extreme relations. Perhaps the following statements will 
 render this distinction as clear and distinct, as is practicable 
 from the point of observation from which the subject is gen- 
 erally viewed. When facts are adduced which can be really or 
 professedly explained, but upon a given hypothesis relative to 
 the cause or law of their occurrence, and when the object for 
 which said facts are adduced is to establish such hypothesis, the 
 reasoning is inductive. On the other hand, .suppose that in 
 connection with a certain object A, we find certain qualities 
 X Y Z and also M, while no causal connection is perceived be- 
 tween M and the other qualities named. All that is given is 
 the fact of coexistence in this case. In another object B, we 
 perceive the qualities X Y Z, and are not able from our rela- 
 tions to B to determine immediately whether it has also the 
 quality M or not. From the fact that this characteristic is 
 found connected with X Y Z in A, we conclude that it exists, 
 also, in connection with the same qualities in B. In this case 
 our reasoning is wholly analogical. In analogical reasoning we 
 infer from the fact of coexistence in one case mere coexistence 
 in another. In induction we argue, from certain facts of coex- 
 istence, the relation of cause and effect,, or of law, &c, in all 
 cases of the same kind. An inductive inference is valid when 
 all the facts can be explained by the hypothesis presented, and 
 by no other conceivable one, and each inference has greater or 
 less claims to validity according to its relations to this one prin- 
 ciple. An argument from analogy to have force must possess 
 the following characteristics: 1. The quality M must not be 
 known to be connected with X Y Z, nor to be unconnected 
 with them. If M were shown to be the result of some cause in 
 
ANALYTIC OF SYLLOGISMS. 185 
 
 A which has no connection with X Y Z, then the argument is 
 vi. no force at all. 2. It must be seen that the relation of ante- 
 cedence and consequence of some kind may exist between them, 
 a relation followed by that of uniform coexistence. 3. .The 
 characteristics must be so related to each other as to favor the 
 supposition of such a relation. 4. This supposition must not be 
 overbalanced by stronger facts of an opposite nature. When 
 all these circumstances combine in the same case, they present 
 a very strong argument from analogy. 
 
 When Sir Isaac Newton, for example, adduced facts to prove 
 the principle or law, that all bodies attract each other in pro- 
 portion directly as the amount of matter which they contain, 
 and inversely as the squares of their mean distance, his argu- 
 ment was inductive. When, on the other hand, from having 
 observed that objects which are combustible have the power of 
 refracting light, .he inferred that the diamond and water are 
 both combustible, because both alike possess the refracting 
 power in proportion to their density, he reasoned from analogy. 
 The following extract from "Mills' Logic" presents another 
 illustration of this form of argument : 
 
 " For example, I might infer that there are probably inhabi- 
 tants in the moon, because there are inhabitants on the earth, 
 in the sea, and in the air, and this is the evidence of analogy. 
 The circumstance of having inhabitants is here assumed not to 
 be an ultimate property, but (as it is reasonable to suppose) a 
 consequence of other properties ; and depending, therefore, in 
 the case of our earth, upon some of its properties as a portion 
 of the universe, but upon which of those properties we know 
 not. Now, the moon resembles the earth in being a solid, . 
 opaque, nearly spherical substance ; containing active volca- 
 noes ; receiving heat and light from the sun in about the same 
 quantity as our earth ; revolving on its axis, whose materials 
 gravitate, and which obey all the various laws resulting from 
 that property. And I think no one will deny that if this were 
 all that was known of the moon, the existence of inhabitants in 
 that luminary would derive from these various resemblances to 
 the earth, a greater degree of probability than it would other- 
 
wise have, although the amount of the augmentation it would 
 be ridiculous to attempt to estimate. 
 
 " If, however, every resemblance proved between B and A, in 
 any point not known to be immaterial with respect to M, forms 
 some additional reason for presuming that B has the attribute 
 M, it is clear, contra, that every dissimilarity which can be 
 proved between them furnishes a counter-probability of the 
 same nature on the other side. It is not, hideed, impossible 
 that different ultimate properties may, in some particular in- 
 stances, produce the same derivative property ; but on the 
 whole it is certain that things which differ in their ultimate 
 properties, will differ at least as much in the aggregate of their 
 derivative properties, and that the differences which are un- 
 known will on the average of cases bear some proportion to 
 those which are known. There will, therefore, be a competi- 
 tion between the known points of agreement and the known 
 points of difference in A and B ; and according as the one or 
 the other are deemed to preponderate, the probability derived 
 from analogy will be for or against B's having the property M. 
 The moon, for instance, agrees with the earth in the circum- 
 stances already mentioned ; but differs in being smaller, in hav- 
 ing its surface more unequal, and apparently volcanic through- 
 out ; having no atmosphere sufficient to refract light ; no clouds, 
 therefore (it is inferentially concluded) no water. These differ- 
 ences, considered merely as such, might perhaps balance the re- 
 semblances, so that analogy would afford no presumption either 
 way. But considering that some of the circumstances which 
 are wanting on the moon are among those which, on our earth, 
 are found to be indispensable conditions of animal life, we may 
 conclude that if that phenomenon does exist in the moon, it 
 must be as the effect of causes totally different from those on 
 which it depends here ; as a consequence, therefore, of the 
 moon's differences from the earth, not of their points of agree- 
 ment. Viewed in this light, all the resemblances Avhich exist 
 become presumptions against, or in favor of, her being inhabit- 
 ed. Since life cannot exist there in the manner in which it 
 exists here, the greater the resemblance of the lunar world to 
 
ANALYTIC OF SYLLOGISMS. 187 
 
 the terrestrial in all other respects, the less reason we have to 
 believe that it can contain life." 
 
 Canon of the Inductive Syllogism. 
 
 The canon of the inductive syllogism is this : When many- 
 facts of a given class have common essential characteristics, this 
 resemblance arises from a common ground or cause, and that 
 hypothesis which not only accords with the facts, but alone ex- 
 plains them all, must be assumed as such ground. 
 
 General characteristics of all facts ov principles which are to 
 be assumed as causes or laws. 
 
 The following lengthy extract from "Thomson's Laws of 
 Thought," contains the tests laid down by Sir John Herschel 
 of all tacts and principles of this kind. To this is added, from 
 the same author, an account of some important experiments in 
 natural science ; experiments made by Sir Humphrey Davy. 
 We give these experiments in illustration of the general pro- 
 cess of induction in the natural sciences : 
 
 " In order to constitute any tact or principle the cause of 
 other facts, it should possess the following characters : * 
 
 A. ' Invariable connection, and, in particular, invariable an- 
 tecedence of the cause and consequence of the effect, unless 
 prevented by some counteracting cause.' 
 
 B. 'Invariable negation of the effect with absence of the 
 cause, unless some other cause be capable of producing the 
 same effect.' The application of this principle has been called 
 the Method of Difference. 
 
 C. 'Increase or diminution of the effect, with the increased 
 or diminished intensity of the cause, in cases which admit of 
 increase and diminution.' 
 
 D. ' Proportionality of the effect to its cause in all cases of 
 direct unimpeded action.' 
 
 E. ' Reversal of the effect with that of the cause.' The ap- 
 
 * Sir John HerschePs Preliminary Discourse, p. 151. 
 
188 LOGIC. 
 
 plication of the three last principles constitutes the Method of 
 Concomitant Variations. 
 
 From these principles follow some practical rules for ascer- 
 taining causes ; such as : 
 
 1. The cause of a given effect may be the same as we know 
 to produce some similar effect in another case better known 
 to us. 
 
 , For example, Berzelius records that a small bubble of the 
 gas called seleniuretted hydrogen, inspired by accident through 
 the nose, deprived him for some hours of the sense of smell, and 
 left a severe catarrh which lasted for fifteen days. Dr. Prout 
 suggests that the corresponding effects in influenza may be 
 traceable to the same cause as undoubtedly produced them 
 here, to the admixture, namely, of this or some similar sub- 
 stance with the air we breathe ; and as a suggestion or antici- 
 pation this is perfectly legitimate, and may prove highly valua- 
 ble. Its inadequacy as a proof may be shown by throwing it 
 into syllogistic form : 
 
 The case of inspiring seleniuretted hydrogen is a case in which loss of smell 
 
 and severe catarrh follow ; 
 Cases of influenza exhibit these effects ; 
 Therefore, cases of influenza are cases in which the said gas has been inspired. 
 
 This is the mood AAA, Fig. II., invalid because it does not 
 distribute the middle term. 
 
 2. 'If in any of the facts we have to account for, there be 
 even one in which a particular character is wanting, that char- 
 acter cannot be the cause in question ; for the true cause can 
 never be absent.' 
 
 3. 'As the laws of nature are uniform, and never capricious, 
 we are entitled to expect that a cause which in several cases 
 produces a given effect will always do so ; and if it appeal's to 
 be otherwise, we should either search for some counteracting 
 causes, or suspect the accuracy of our observations.' 
 
 4. ' Causes will very frequently become obvious by a mere 
 arrangement of our facts in the order of intensity in which 
 some peculiar quality subsists ; though not of necessity, because 
 
ANALYTIC OF SYLLOGISMS. 189 
 
 counteracting or modifying causes may be at the same time in 
 action.' 
 
 ' For example, sound consists in impulses communicated to 
 our ear by the air. If a series of impulses of equal force be 
 oommunicated to it at equal intervals of time, at first in slow 
 succession, and by degrees more and more rapidly, we hear at 
 first a rattling noise, then a low murmur, and then a hum, 
 which by degrees acquires the character of a musical note, 
 rising higher and higher in acuteness, till its pitch becomes too 
 high for the ear to follow. And from this correspondence be- 
 tween the pitch of the note and the rapidity of succession of the 
 impulse, we conclude that our sensation of the different pitches 
 of musical notes originates in the different rapidities with 
 which these impulses are communicated to our ears.' To make 
 such an arrangement, however, we must have a presage, and 
 no uncertain one, of the cause of our phenomena ; and, there- 
 fore, it is rather useful for verification, than for suggestion, of a 
 theory. 
 
 5. 'If we can either find produced by nature, or produce de- 
 signedly for ourselves, two instances which agree exactly in all 
 but one particular, and differ in that one, its influence in pro- 
 ducing the phenomenon, if it have any, must thereby be ren- 
 dered sensible. If that particular be present in one instance, 
 and wanting altogether in the other, the production or non- 
 production of the phenomenon will decide whether it be or be 
 not the only cause ; still more evidently, if it be present contra- 
 riwise in the two cases, and the effect be thereby reversed. But 
 if its total presence or absence only produces a change in the 
 degree or intensity of the phenomenon, we can then only con- 
 clude that it acts as a concurrent cause or condition with some 
 other to be sought elsewhere. In nature, it is comparatively 
 rare to find instances pointedly differing in one circumstance 
 and agreeing in every other ; but when we call experiment to 
 our aid, it is easy to produce them ; and this is, in fact, the 
 grand application of experiments of inquiry in physical re- 
 searches. They become more valuable, and their results 
 clearer, in proportion as they possess this quality (of agreeing 
 
190 LOGIC. 
 
 exactly in all their circumstances but one), since the question 
 put to nature becomes thereby more pointed, and its answer 
 more decisive.' 
 
 6. ' Complicated phenomena, in which several causes concur- 
 ring, opposing, or quite independent of each other, operate at 
 once, so as to produce a compound effect, may be simplified 
 by subducting the effect of all the known causes, as well as 
 the nature of the case permits, either by deductive reasoning 
 or by appeal to experience, and thus leaving, as it were, a 
 residual phenomenon to be explained. It is by this process, 
 in fact, that science, in its present advanced state, is chiefly 
 promoted.' 
 
 ' A very elegant example may be cited, from the explanation 
 of the phenomena of sound. The inquiry into the cause of 
 sound had led to conclusions respecting its mode of propaga 
 tion, from which its velocity in the air could be precisely calcu- 
 lated. The calculations were performed ; but, when compared 
 with fact, though the agreement was quite sufficient to show 
 the general correctness of the cause and mode of propagation 
 assigned, yet the whole velocity could not be shown to arise 
 from this theory. There was still a residual velocity to be ac- 
 counted for. At length La Place struck on the happy idea, 
 that this might arise from the heat developed in the act of that 
 condensation which necessarily takes place at every vibration 
 by which sound is conveyed. The matter was subjected to 
 exact calculation, and the result was at once the complete ex- 
 planation of the residual phenomenon.' 
 
 These are specimens of the methods according to which re- 
 searches into causes are conducted. I add one example, com- 
 bining the 4th, 5th, and 6th rules, and exhibiting Proportionali- 
 ty of cause and effect, Experiment, and Residual Phenomena 
 in one set of inquiries. Beyond this, the limits I have pre- 
 scribed myself do not suffer mc to go. 
 
 In Sir Humphrey Davy's experiments upon the decomposi- 
 tion of water by galvanism, it was found that, besides the two 
 components of water, oxygen and hydrogen, an acid and an 
 alkali were developed at the two opposite poles of the machine. 
 
ANALYTIC OF SYLLOGISMS. 191 
 
 As the theory of the analysis of water did not give reason to 
 expect these products, they were a residual phenomenon, the 
 cause of which was still to be found. Some chemists thought 
 that electricity had the power of producing these substances of 
 itself; and if their erroneous conjecture had been adopted, suc- 
 ceeding researches would have gone upon a false scent, consid- 
 ering galvanic electricity as a producing rather than a decom- 
 posing force. The happier insight of Davy conjectured that 
 there might be some hidden cause of this portion of the effect ; 
 the glass vessel containing the water might suffer partial <le- 
 composition, or some foreign matter might be mingled with the 
 water, and the acid and alkali be disengaged from it, so that 
 the water would have no "share in their production. Assuming 
 this, he proceeded to try whether the total removal of the camse 
 (B. p. 187) would destroy the effect, or at least the diminution 
 of it cause a corresponding change in the amount of effect pro- 
 duced (C. p. 187). By the substitution of gold vessels for the 
 glass without any change in the effect, he at once determined 
 that the glass was not the cause. Employing distilled water, 
 he found a marked diminution of the quantity of acid and alkali 
 evolved ; still there was enough to show that the cause, what- 
 ever it was, was still in operation. Impurity of the water was 
 not the sole, but a concurrent cause. He now conceived that 
 the perspiration from the hands, touching the instruments, 
 might affect the case, as it would contain common salt, and an 
 acid and an alkali would result from its decomposition under 
 the agency of electricity. By carefully avoiding such contact, 
 he reduced the quantity of the products still further, until no 
 more than slight traces of them were perceptible. What re 
 mained of the effect might be traceable to impurities of the at 
 mosphere, decomposed by contact with the electrical apj^aratus 
 An experiment determined this ; the machine was placed undei 
 an exhausted receiver, and when thus secured from atmospheric 
 influence, it no longer evolved the acid and the alkali. 
 
 A formal analysis of these beautiful experiments will illus- 
 trate the method of applying the rules of pure logic in other 
 
192 LOGIC. 
 
 I. Statement of the case, the residual cause being still undiscovered : 
 
 ' The decomposition of water by electricity, produces oxygen and 
 hydrogen, with an acid and an alkali. ' 
 II. Separation of the residual from the principal cause : 
 
 a. ' The decomposition of water produces oxygen and hydrogen.' 
 
 b. ' The production of an acid and alkali in the decomposition of 
 water may be caused by action on the glass vessel containing the 
 water.' (Problematical judgment, A.) 
 
 HI. The latter judgment (b) disproved by a syllogism in mood E A 0, 
 Fig. III., with a conclusion that contradicts it : 
 
 ' A case in which I employ a vessel of gold cannot involve any de- 
 composing action on a glass vessel ;' 
 ' A case in which I employ a gold vessel still gives the acid and 
 
 the alkali ;' 
 ' Therefore, cases of the production of the acid and alkali are not 
 always cases in which glass is decomposed.' 
 
 IV. Another attempt to suggest the residual cause : 
 
 'The acid and alkali are produced by the decomposition of impu- 
 rities in the water employed.' . 
 
 Syllogism in A A I, Fig. III., tending to prove this. 
 
 ' An experiment with distilled water must admit less impurity ;' 
 
 'An experiment with distilled water gives less acid and alkali ;' 
 
 ' Therefore, sometimes with less impurity we have less acid and 
 alkali.' 
 V. 'The contact of moist hands' may be an additional cause of the re- 
 sidual phenomenon : 
 
 Improved syllogism in A A I, Fig. III., to include this concurrent 
 cause. 
 
 'An experiment with distilled water, and apparatus kept from 
 contact of hands will admit still less impurity ;' 
 
 'An experiment, &c, results in the production of still less acid 
 and alkali ;' 
 
 ' Therefore, sometimes with still less impurity we have stiy. less 
 acid and alkali.' 
 VI. Amended syllogism A A A, Fig. Ill : 
 
 ' A case where we use these precautions in vacuo is a case of no im- 
 purity ;' 
 
 ' A case where we use, &c. , in vacuo is a case of no acid and alkali ;' 
 
 ' Therefore, a case of no impurity is a case of no acid and alkali.' 
 VII. Immediate inference from last conclusion : 
 
 'Cases of no-impurity are cases of non-production of acid and 
 
ANALYTIC OF SYLLOGISMS. 193 
 
 'Therefore' (according to the example in p. 219, Division II., of 
 inference from A), 
 
 ' All cases of production of acid and alkali are cases of some impu- 
 rity ;' 
 
 which was to he proved. 
 
 An example like this brings into a strong light many of the 
 characteristics of inductive reasoning. Forms usually consid- 
 ered to be deductive are here freely employed. The later steps 
 tend to confirm the earlier, on which, however, they themselves 
 depend ; so that a mutual confirmation is obtained from setting 
 them together. When the chemist substituted gold vessels for 
 the glass, and inferred from the continuance of the effect under 
 this change that the glass could have nothing to do with its 
 production, it was formally possible in the then state of know- 
 ledge that the glass might be the cause in the one experiment, 
 and the decomposition of the gold in the other. But the later 
 steps, which showed that the effect varied with the variations 
 in a circumstance wholly distinct from the decomposition of 
 glass or gold, reduced the possibility of maintaining such a 
 view to the very lowest amount. Even the premises of par- 
 ticular syllogisms in the chain are sometimes tested and cor- 
 rected by the conclusion, although formally the conclusion 
 should entirely depend upon the premises. The experimenter 
 expected to find that the use of distilled water would exclude 
 all impurity ; and he intended that his premise (see No. IV.) 
 should assert as much ; but when it turned out in the conclu- 
 sion that the supposed products of the impurity were still 
 present, he was reduced to the choice between abandoning 
 that cause and re-casting his premise so as to admit that the 
 cause was still present : ' the use of distilled water gives less 
 impurity.' " 
 
 VERIFICATION OF INDUCTIONS. 
 
 When such inductions have been made we may wish to veri- 
 fy them. On this topic we are also indebted to Mr. Thomson 
 for the following extract from the " Quarterly Review," an ex- 
 tract upon which our author remarks : " I transcribe this from 
 9 
 
the Quarterly Review ; as I despair of expressing its purport 
 in words of mine, half so clearly and elegantly." For similar 
 reasons relative to ourselves, we give the extract as it is : 
 
 " Verification of Inductions. 
 
 " It is of great moment to distinguish the characters of a 
 sound induction. One of them is its ready identification with 
 our conception of facts, so as to make itself a part of them, to 
 engraft itself into language, and by no subsequent effort of the 
 mind to be got rid of. The leading term of a true theory once 
 pronounced, we cannot fall back even in thought to that help- 
 less state of doubt and bewilderment in which we gazed on the 
 facts before. The general proposition is more than a sum of 
 the particulars. Our dots are filled in and connected by an 
 ideal outline which we pursue even beyond their limits, assign 
 it a name, and speak of it as a thing. In all our propositions 
 this new thing is referred to, the elements of which it is formed 
 forgotten ; and thus we arrive at an inductive formula, a gen- 
 eral, perhaps a universal, proposition. 
 
 " Another character of sound inductions is that they enable 
 us to predict. We feel secure that our rule is based upon the 
 realities of nature, when it stands us in the stead of more expe- 
 rience ; when it embodies facts, as an experience wider than 
 our own would do, and in a way that our ordinary experience 
 would never reach ; when it will bear, not stress, but torture, 
 and gives true results in cases studiously different from those 
 which led to its discovery. The theories of Newton and Fres- 
 nel are full of such cases. In the latter, indeed [the theory of 
 polarization], this test is carried to such an extreme, that theory 
 has actually remanded back experiment to read her lesson anew, . 
 and convicted her of blindness and error. It has informed her 
 of facts so strange as to appear to her impossible, and showed 
 her all the singularities she would observe in critical cases she 
 never dreamed of trying. 
 
 " Another character which is exemplified only in the greatest 
 theories, is the consilience of inductions, where many and wide- 
 
ANALYTIC OF SYLLOGISMS. 195 
 
 ly different lines of experience spring together into one theory 
 which explains them all, and that in a more simple manner than 
 seemed to be required for either separately. Thus in the infi- 
 nitely varied phenomenon of physical astronomy, when all are 
 discussed and all explained, w T e hear from all quarters the con- 
 sentaneous echoes of but one word, ' gravitation.' And so in 
 optics ; each of its endless classes of complex and splendid phe- 
 nomena being interpreted by its own conception ; when these 
 conceptions are assembled and compared, they all turn out to 
 be translated into their peculiar language of the single phrase, 
 ' transverse undulation.' Mr. Whewill has given us, as exam- 
 ples of the logic of induction, what he terms deductive tables 
 of each of these noble generalizations which enable us to trace, 
 as in a map, the separate rills of discovery flowing at first 
 each in its OAvn narrow basin, thence confluent into important 
 streams, which, uniting into one grand liver, bear downwards 
 to an ocean of truth beyond our tracing." 
 
 CANON OF THE SYLLOGISM OF ANALOGY. 
 
 There are two classes of objects to Avhich the argument from 
 analogy is applied, to wit, similarity of ratios or relations and 
 similarity of attributes. Mandeville, for example, uses this ar- 
 gument against popular education, that, " If the horse knew 
 enough he would throw his rider," intending thereby to imply 
 two pairs of related terms, to wit, "As the horse is to the 
 rider, so is the people to its rulers," and to assert that, since 
 one relation depends upon the continuance of ignorance in the 
 horse, the other depends upon the continuance of ignorance 
 among the people. Here is an argument from analogy de- 
 pending upon assumed similarity of relations. The argument, 
 in this case, is fallacious, because no such similarity exists. 
 When, on the other hand, it is argued from certain similarity 
 of attributes, that the moon as well as the earth is inhabited, 
 the argument is based upon the second class of characteristics 
 named above. The argument in the second case depends 
 upon the principle or canon, that the " same attributes may be 
 
 V 
 
assigned to distinct, but similar things, provided they can be 
 shown to accompany the points of resemblance in the things, 
 and not the points of difference." The argument in the first 
 case rests on this principle, to wit : " When any thing resem- 
 bles another in known particulars, it will resemble it in the un- 
 known." " They must not," in the language of Mr. Thomson, 
 " be of the same kind, but only of a similar one ; otherwise the 
 argument is a mere case of example. Neither must the usual 
 tests be applied to prove that the known particulars invariably 
 accompany the unknown, otherwise, as Mr. Mills observes, 
 we trench upon the ground of induction. In venturing thus to 
 assign attributes to a thing, because other things of a different 
 class have them, we show our dependence upon the regularity 
 and consistency of creation." 
 
 The above remarks are sufficient to elucidate the distinction 
 between the argument from induction and .analogy, and to pre- 
 sent a distinct view of the object of our investigations. 
 
 When the Syllogism of Analogy has the greatest force. 
 
 The syllogism of analogy has the greatest force when em- 
 ployed in answering objections to given systems of truth. 
 Suppose that it is urged, that a certain system of doctrine can- 
 not be true, because a certain element (M) is involved in it. 
 In reply, it is shown, that M does, in fact, exist in connection 
 with another system which must be admitted to be true. This 
 reply, if valid, totally annihilates the objection under considera- 
 tion. 
 
 THE ENTHYMEME. 
 
 The common definition of the enthymeme is this, " a syllo- 
 gism with one premise suppressed," or, more properly, " a syl- 
 gjsm with but one premise expressed." Some have doubted 
 the correctness of this definition. Whether the form of the 
 syllogism here defined be properly called the enthymeme, or 
 not, one thing is certain, that it requires no special elucidation, 
 
ANALYTIC OP SYLLOGISMS. 197 
 
 it being the very form in which, in ordinary writing and speak- 
 ing, all kinds of argument are exp'ressed. The syllogism mere- 
 ly presents what is really implied in the argument, and not 
 what is always, in form, expressed. 
 
 Section X. The Sokites, ok Chain Syllogism. 
 Term defined. 
 
 The sorites is a series of propositions of two kinds or classes : 
 
 1. That in which the predicate of the first proposition is 
 made the subject of the second ; and so on till, in the conclu- 
 sion, the predicate of the last proposition is affirmed or denied 
 of the subject of the first. For example : 
 
 Every A is B ; 
 
 Every B is C ; 
 
 Every C is D ; 
 
 .-. Every A is D. 
 
 2. When the subject of the first is made the predicate of the 
 second, and so on till, in the conclusion, the predicate of the 
 first premise is predicated of the subject of the last. For 
 example : 
 
 Every B is A ; 
 Every C is B ; 
 Every D is C ; 
 Every E is D ; 
 .-. Every E is A. 
 
 It is self-evident, that each of the above processes has equal 
 and absolute validity. 
 
 Principles on which this Form of Reasoning depends. 
 
 The following are the principles on which this form of rea- 
 soning depends : 
 
 1. When the terms are related as inferior and superior con- 
 ceptions, then this principle for affirmative conclusions obtains, 
 
to wit : Any conception ranks under (as X is Z) any other con- 
 ception under which any of. its (the former's) superior concep- 
 tions rank ; and, for negative conclusions, any conception disa- 
 grees with any other conception, which disagrees with any of 
 its (the former's) superior conceptions ; and, also, with any 
 which agree with any conceptions with which it disagrees. 
 We will illustrate the above principles by a few examples. 
 
 In regard to affirmative conclusions we need only refer to 
 the two examples given above. In the first, A is given as an 
 inferior conception, ranking under B as its superior ; and B, as 
 in a similar manner, included under C, and C under D, and D 
 under E. E, therefore, in the line of extension, stands as the 
 superior conception of A ; as such, A is said to be E. In the 
 second example, A is given, in the sense explained, as superior 
 to B, B to C, C to D, and D to E. To each alike, therefore, 
 A sustains the relation of a superior conception, and the propo- 
 sition, " Every E is A," must hold as logically valid. Let us 
 now consider examples of the present form of argument yield- 
 ing negative conclusions : 
 
 Every A is B ; Every A is B ; 
 
 Every B is C ; No B is C ; 
 
 Every C is D ; Every D is C ; 
 
 No D is E ; Every E is D ; 
 
 .-. No A is E. .-. No A is E. 
 
 In the first example, E is given as excluded from D, which, 
 as a superior conception, includes A as its inferior. A, then, 
 must be excluded from E. In the second example, E is given 
 as included in C, which is wholly, as not included in B, ex- 
 cluded from A. A, therefore, is wholly excluded from E, and 
 the principles above stated must hold universally. 
 
 2. When the terms of the propositions are not constituted of 
 inferior and superior conceptions, but are related as equal or 
 unequal, &c, then the principle which controls all deductions 
 may be thus stated : Any term agreeing with a given term 
 agrees with all that the latter does, and disagrees with all that 
 disagrees with it ; and when a term disagrees with a given 
 term, it disagrees with all that agree with the latter term. 
 
ANALYTIC OF SYLLOGISMS. 199 
 
 Thus, if A agrees with B, B with C, C with D, and D with E, 
 then A must agree with E, agreeing as the former does with 
 terms which agree with E. If, on the other hand, A agrees 
 with B, C, and D, and the latter disagrees with E, A, of 
 course, must disagree with E. On the other hand still, if A 
 disagrees with B, and any term agrees with the latter, A, of 
 course, disagrees with it. 
 
 The Sorites can have but one particular, and one negative, 
 premise. 
 
 From the nature of th^ sorites it is manifest, that all of the 
 premises, the first excepted, must be universal, and but one of 
 them negative. If we should say, Some A is B, and some B 
 is C, no relation coufd from hence be inferred between A and 
 C, for the reason, that the part of B which is in C may be the 
 part of the former which does not contain A. So, if we should 
 say, All A is B and no B is C, and no C is D, we could not 
 from hence argue, that A either agrees or disagrees with D ; 
 and that because D is given as disagreeing with some thing 
 which disagrees with A, and which, therefore, from aught that 
 appears to the contrary, may either agree or disagree with A. 
 
 Forms of this ki?id of argument. 
 
 There are four distinct forms of the argument under consid- 
 eration : 
 
 1. When all the premises are universal affirmatives, and in 
 the conclusion the predicate of the last is affirmed of the sub- 
 ject of the first : All A is D. 
 
 2. When the last premise is negative, and in the conclusion 
 the subject of the first is denied of the predicate of the last; as, 
 No A is D. If the first premise was particular, such also would 
 be the conclusion, to wit : Some A is not D. 
 
 3. When the first premise is negative, and each successive 
 conception is given as included in the predicate of this first 
 premise, and in the conclusion the subject of the first is denied 
 
200 LOGIC. 
 
 of the subject of the last premise. For example : No A is in 
 B ; all C is in B, and all D is in C ; therefore, no A is in D. 
 
 4. When some intermediate premise is given as negative, 
 and in all the subsequent ones each successive conception is 
 given, as included in or agreeing with the predicate of. the 
 negative one, and in the conclusion the subject of the first is 
 denied of the subject of the last premise. Example : 
 
 All A is B 
 All B is C 
 No C is D 
 All E is D 
 All F is E 
 All G is F 
 .-. No A is G. 
 
 Here all G is given as included in F, wliich, by the previous 
 conditions, is excluded from A. For the same reason, there- 
 fore, that we argue that no A is in D,"we conclude that no A 
 is G. The two last classes have been entirely overlooked by 
 logicians generally. They are as valid, however, as any others, 
 and perhaps as frequently employed in argument* In all cases 
 of the negative sorites, it should be borne in mind, that when 
 the first premise is particular the conclusion will be particular 
 also. 
 
 The sorites has commonly been treated as a compound syllo- 
 gism, which may be drawn out into as many separate ones as 
 there are intermediate propositions between the first and the 
 last. This is true. The manner in which we have treated the 
 subject, however, will be seen, we judge, to be much more sim- 
 ple than this, and quite as accordant with the principles of 
 science. If the pupil should choose to reduce the sorites in the 
 manner indicated, he will bear in mind that his first syllogism, 
 in the language of Dr. Whately, " will have for its major the 
 second, and for its minor the first, proposition of the sorites." 
 
ANALYTIC OP SYLLOGISMS. 201 
 
 Section XI. Syllogism of Chance. 
 
 This Syllogism defined. 
 
 The term chance refers to the probability that one of two or 
 more uncertain events will occur. In induction and analogy 
 we have positive evidence, of greater or less weight, in favor 
 of a given proposition, in distinction from all others. The doc- 
 trine of chance has place where, of a given number of events, 
 some one must occur, and to us there is the absence of all posi- 
 tive evidence that one, in distinction from the others, will occur. 
 The object of the syllogism jDf chance is to announce the degree 
 of probability that such an event will occur. 
 
 Principle which governs such calculations. 
 
 n" The probability that a wholly uncertain event will happen, 
 is," as Mr. Thomson states, " as the number of cases in which 
 it can, to the number of those in which it cannot, occur." 
 
 The simplest case that can be given, is that in which one, 
 and but one, of two events must occur, and there is an equal 
 uncertainty which. In that case the probabilities are equally 
 balanced, and the probability that either, in distinction from 
 the other, will occur, is as one to one. As the number of pos- 
 sible events is increased, the probability that any one will occur 
 is correspondingly diminished. Suppose, on the other hand, 
 that there are three cases, in each of which one of two given 
 events must occur, and in each case each is equally probable. 
 The probability that one of these events will occur in one of the 
 three cases, is as seven to one ; and that it will not occur in 
 each case successively, as one to seven. Suppose, further, that 
 there are six events, each of which is equal to each of the 
 others on the score of probability, and that one of these, to the 
 exclusion of each of the others, must occur. The probability 
 that in any given case any one will occur, is as one to five. 
 The probability that in six successive cases any one will occur, 
 at least once, is as one to one. The probability that any one 
 
 
 
will occur in each of the six successive cases, is as one to forty- 
 four thousand six hundred and fifty-six. The application of the 
 above examples to cases in which one of two or more events 
 must occur, and there is a greater probability that one will 
 occur than there is that the other will, is so obvious, that 
 nothing need be added on the subject. 
 
 The syllogism of chance is, also, often applied in determining 
 the probable cause of given events. Suppose that some event, 
 X, has occurred, and that it is known that one of two causes, 
 A or B, must have produced the event referred to. Suppose 
 that the probabilities in favor of each, equal those in favor of 
 the other ; then, the probability that A is such is one-half, or as 
 one to one. Suppose that there are two, three, or four proba- 
 bilities in favor of A to one in favor of B ; the case would then 
 stand two, three, four, &c, to one, in favor of A as compared 
 with those in favor of B. 
 
 In some instances the syllogism of chance gives a conclusion 
 amounting to almost absolute certainty in favor of the occur- 
 rence of a given event. Suppose that there are six distinct 
 causes, either of which, if present, will produce a given event, 
 and that in reference to each, there is a perfect equality of 
 probabilities of its presence and absence ; then the probability 
 that said event will occur is as forty-four thousand six hundred 
 and fifty-one to one. 
 
 We have stated the above cases to indicate the manner of 
 applying the principle above presented. The application of the 
 principle will be as the nature and degree of the probabilities 
 and improbabilities to be taken into the account. 
 
 Section XII. Immediate and Mediate Syllogisms. 
 
 All syllogisms, of course, are either immediate or mediate. 
 " An immediate syllogism," in the language of Kant, " is the 
 deduction of one judgment from another without any inter- 
 mediate judgment. A syllogism, where, besides the concep- 
 tion which a judgment contains, other conceptions are used, 
 
ANALYTIC OF SYLLOGISMS. 203 
 
 for the purpose of deriving a cognition from them, is me- 
 diate." 
 
 The principle on which all immediate syllogisms rest, is this : 
 Whatever is necessarily implied in an admitted judgment, must 
 also be admitted. If, for example, we admit the judgment 
 A=B, as valid, we must admit that A and B both exist; 
 that they belong to the same class of objects ; have the same 
 fundamental characteristics; that all objects with which one 
 agrees or disagrees, the other agrees or disagrees with, in a 
 similar manner, &c, &c. 
 
 Nothing is of greater importance in reasoning, than a cor- 
 rect use of the immediate .syllogism. Many individuals, when 
 they have established a given conclusion, do not know what 
 use to make of it, because they do not perceive what is implied 
 in it. The mediate syllogism has already been elucidated. 
 
 Section XIII. The Peosyllogism and Episyllogism. 
 
 A process of reasoning which consists of but one syllogism is 
 simple. When it consists of several syllogisms, as in the sorites 
 already treated of, it is compound. A compound syllogism, in 
 which the various syllogisms are in subordination, the first to 
 its successors or the reverse, is called a concatenation of syllo- 
 gisms. Of this class of compound syllogisms we need only 
 allude to two kinds, in addition to those already considered : 
 the prosyllogism and the episyllogism. 
 
 When, in a chain of reasoning, one of the premises of the 
 main argument is the conclusion of another syllogism, the lat- 
 ter is called the prosyllogism. When, on the other hand, the 
 conclusion of the main argument is made the premise of a sup- 
 plementary one, this last is called the episyllogism. The fol- 
 lowing illustration of these two forms of the syllogism we take 
 from " Thomson's Laws of Thought :" " Let us take the syllo- 
 gism which a coroner's jury might have to go through. The 
 questioais, ' Has A B been poisoned ?' and the syllogism is, 
 A man who has taken a large quantity of arsenic has been 
 
 
204 LOGIC. 
 
 poisoned ;' and A B is found to have done so ; therefore, he is 
 poisoned :" with the addition of a prosyllogism and episyllo- 
 gism the reasoning would run : " A man who has taken ar- 
 senic has heen poisoned ; and A B has taken arsenic, for the 
 application of Marsh's and Reinsch's tests discover it (pro- 
 syllogism) ; therefore, A B has been poisoned, and, therefore, 
 we cannot return a verdict of death from natural causes (epi- 
 syllogism)." 
 
 Section XIV. Syllogism of Classification. 
 
 Classification, to a greater or less extent, enters into all the 
 sciences, and constitutes the exclusive basis of some of them ; 
 such as mineralogy, zoology, and botany. The science of logic, 
 therefore, would be incomplete, did it not include a develop- 
 ment of the principles and laws of this one department of the 
 laws of thought. 
 
 principles and laws of this form of the syllogism. 
 
 Two questions, entirely distinct the one from the other, enter 
 into all investigations in this department of science, to wit, the 
 conditions on which any individuals may take rank as members 
 of any given class ; and what may be validly affirmed and de- 
 nied of them, in consequence of the ascertained fact, that they 
 belong to said class. In regard to the first question, we would 
 remark, that each class has its special tests or marks, that is, 
 characteristic conception. Any individual must, as a title to 
 admission into the class, reveal, as possessed by himself, the 
 elements represented in this one conception. In this depart- 
 ment the syllogism of classification may be thus represented : 
 
 Every individual having these characteristics belongs to this class ; 
 
 A has these characteristics ; 
 
 A, therefore, belongs to this class. 
 
 Then every class is represented by a specifical or generical con- 
 ception, as the case may be ; a conception which includes all 
 
ANALYTIC OP SYLLOGISMS. 205 
 
 the elements embraced in the characteristic conception, and all 
 others strictly common to every individual of the class referred 
 to. When it has been ascertained, through the characteristic 
 conception, that an individual belongs to a certain class, then 
 we may reason from this fact to his general characteristics as a 
 member of such class, and may affirm of him any elements em- 
 braced in the specifical conception of that class, or in any of its 
 superior or generical conceptions. In this department, the syl- 
 logism of classification runs thus : 
 
 All members of this class have these characteristics ; 
 
 A is a member of this class ; 
 
 A, therefore, has these characteristics. 
 
 Take, in illustration, the case of the coroner's inquest referred 
 to in another connection. An individual has died in circum- 
 stances which indicate the fact, that he was poisoned. On a 
 post-mortem examination, a certain substance, which resembles 
 in external appearance arsenic, is found in his stomach. Tests 
 are applied to determine the nature of that substance. The re- 
 sult is the inference, that it is arsenic. The form of the syllo- 
 gism yielding this deduction was this : 
 
 Every substance answering certain tests is arsenic ; 
 This substance answers these tests ; 
 It is, therefore, arsenic. 
 
 This fact being thus ascertained, the verdict is now rendered 
 in accordance with this syllogism : 
 
 Every individual with a given amount of arsenic in his stomach is poisoned ; 
 This individual was in that state ; 
 Therefore, he was poisoned. 
 
 The syllogism through which the properties of this substance 
 is inferred, the fact that it is arsenic having been ascertained, 
 may be thus expressed : 
 
 Arsenic is poison ; 
 
 This substance is arsenic ; 
 
 Therefore, it is poison. 
 
 Kote. The correctness of the above view of the syllogism 
 
of classification will not be doubted. Yet this view frees the 
 syllogism, in all its forms, from an objection of pelitio principii 
 and idle tautology already referred to, which has been urged 
 against it, the above being the only form against which the ob- 
 jection even apparently holds. The objection is this, that in the 
 conclusion nothing is asserted but what had, in form, been pre- 
 viously asserted in the premises. The objection overlooks the 
 fact, that the minor premise, as in the case last given (the form 
 in which the syllogism is commonly stated), is the conclusion of 
 a prosyllogism in which the truth of this premise is affirmed, 
 and that as the result of investigation. 
 
 CONCLUDING EXPLANATIONS. 
 
 The following extract from Dr. Whately contains some im-- 
 portant explanations demanding especial attention, and with 
 this extract we conclude our analytic of the syllogism : 
 
 " There are various other abbreviations commonly used, 
 which are so obvious as hardly to call for explanation : as 
 where one of the premises of a syllogism is itself the conclusion 
 of an enthymeme which is expressed at the same time ; e. g. 
 ' All useful studies deserve encouragement ; logic is such {since 
 it helps us to reason accurately), therefore it deserves encour- 
 agement ;' here the minor premise is what is called an enthyme- 
 matic sentence. The antecedent in that minor premise (i. e. 
 that which makes it enthymematic) is called by Aristotle the 
 prosyllogism. 
 
 " It is evident that you may, for brevity, substitute for any 
 term an equivalent ; as in the last example, ' itf for ' logic ;' 
 ' such,'' for ' a useful study,' &c. The doctrine of conversion 
 furnishes many equivalent propositions, since each is equiva- 
 lent to its illative converse. The division of nouns also sup- 
 plies many equivalents ; e. g. if A is the genus of B, B must 
 be a species of A ; if A is the cause of B, B must be the effect 
 of A. 
 
 " And many syllogisms, which at first sight appear faulty, 
 will often be found, on examination, to contain correct reason- 
 
ANALYTIC OF SYLLOGISMS. 207 
 
 ing, and, consequently, to be reducible to a regular form ; e. g. 
 when you have, apparently, negative premises, it may happen, 
 that by considering one of them as affirmative, the syllogism 
 will be regular : e. g. ' No man is happy who is not secure ; 
 no tyrant is secure; therefore, no tyrant is happy,' is a syl- 
 logism in Celarent* Sometimes there will appear to be too 
 many terms ; and yet there will be no fault in the reason- 
 ing, only an irregularity in the expression : e. g.. ' No irra- 
 tional agent could produce a work which manifests design ; 
 the universe is a work which manifests design ; therefore, no 
 irrational agent could have produced the universe.' Strictly 
 speaking, this syllogism has five terms ; but if you look to the 
 meaning, you will see, that in the first premise (considering it 
 as a part of this argument) it is not, properly, ' an irrational 
 agent' that you are speaking of, and of which you predicate 
 that it could not produce a work manifesting design ; but 
 rather it is this ' work,' &c. of which you are speaking, and of 
 which it is predicated that it could not be produced by an irra- 
 tional agent ; if, then, you state the propositions in that form, 
 the syllogism will be perfectly regular. 
 
 " Thus, such a syllogism as this, ' Every true patriot is disin- 
 terested ; few men are disinterested ; therefore, few men are 
 true patriots ;' might appear at first sight to be in the second 
 figure, and faulty ; whereas it is in Barbara, with the premises 
 transposed / for you do not really predicate of ' feAV men,' that 
 they are ' disinterested,' but of ' disinterested persons] that they 
 are ' few.' Again : ' None but candid men are good reasoners ; 
 few infidels are candid ; few infidels are good reasoners.' In 
 this it will be most convenient to consider the major premise as 
 being, ' all good reasoners are candid' (which, of course, is pre- 
 cisely equipollent to its illative converse by negation) ; and the 
 
 * If this experiment be tried on a syllogism which has really negative premises, the only 
 effect will be to change that fault into another, viz., an excess of terms, or (which is sub- 
 stantially the same) an undistributed middle; e. g. "an enslaved people is not happy; the 
 English are not enslaved ; therefore, they are happy ;'' if " enslaved" be regarded as one of 
 the terms, and "not enslaved" as another, there will manifestly be four. Hence you may 
 Bee how very little difference there is in reality between the different faults which are enu- 
 merated. 
 
208 LOGIC. 
 
 minor premise and conclusion may, in like manner, be fairly ex- 
 pressed thus : ' Most infidels are not candid ; therefore, most 
 infidels are not good reasoners ;' which is a regular syllogism 
 in Camestres* Or, if you would state it in the first figure, 
 thus : ' Those who are not candid (or uncandid) are not good 
 reasoners ; most infidels are not candid ; most infidels are not 
 good reasoners.' " 
 
 * The reader is to observe that the term employed as the subject of the minor premise, 
 and of the conclusion, is " most-infidels ;" he is not to suppose that " most" is a sign of dis- 
 tribution ; it is merely a compendious expression for " the greater port of." 
 
PART II. 
 
 THE DIALECTIC, OR DOCTRINE OF FALLACIES. 
 
 Fallacy defined. 
 
 A fallacy, as the term is generally understood, " is any un- 
 sound mode of arguing which appears to demand conviction, 
 and to be decisive of the question hi hand, when in fairness it is 
 not." In the present treatise the term fallacy will be employed 
 to represent any intellectual process held as valid for the truth 
 to which it pertains, but which is, in fact, not thus valid. We 
 know well, that what is not true may be defended by arguments 
 apparently sound or unsound, and truth itself may be defended 
 by invalid arguments. In our treatment of this subject, it will 
 be our object to develop the characteristics of such invalid pro- 
 cedures, characteristics by which they are distinguished from 
 processes which must be received as valid. 
 
 Fallacies where found. 
 
 If we take any argument which is not valid, it is self-evident 
 that the defect in it must consist in the conceptions themselves, 
 in the relations affirmed to exist between such conceptions in 
 the premises ; in a want of connection between such premises 
 and the conclusions deduced from them ; or, in two or more of 
 these defects combined. Every valid process, as we have al- 
 ready shown, has the following characteristics, to wit : the con- 
 ceptions are constituted exclusively of real intuitions relating 
 to the objects of such conceptions ; the premises present nothing 
 
but real relations existing between the conceptions themselves ; 
 and the conclusion is the necessary consequent of the relations 
 given in the premises. 
 
 The question to be determined is, How does error enter into 
 one or the other department of such process, or into two or 
 more of them together ? When this question is resolved, the 
 object of the dialectic will be accomplished. 
 
 The ultimate cause and source of Error. 
 
 Were man a pure intelligence, with no sensibility or Avill, 
 error to him would be impossible. Every intellectual move- 
 ment would be determined by fixed and immutable laws, and 
 would always accord with the facts presented. Knowledge 
 would be limited, but free from error. The real source of error 
 is false assumption. This we have, as we judge, fully estab- 
 lished in the treatise on the will. As pure intelligents we can- 
 not affirm, without adequate evidence, that things are or are 
 not so and so. In the absence of such evidence, however, we 
 may assume that they are, and act accordingly. Similar 
 assumptions may be made in regard to all the antecedents 
 and consequents of the one assumption referred to. Thus long 
 trains of error may be introduced into all our intellectual pro- 
 cedures. Without further preliminary observations, Ave will 
 now proceed in our exposition of the doctrine of fallacies, and 
 will begin with the phenomena of thought in which error first 
 appears, to wit, conceptions. 
 
DOCTRINE OF FALLACIES. 211 
 
 CHAPTER I. 
 
 INVALID CONCEPTIONS. 
 
 A conception, as we have seen, is valid when, and only 
 when, it is constituted of elements really given by intuition 
 Relatively to its object, that is, such conceptions only can be em- 
 ployed as subjects and predicates of valid judgments. Take, as 
 an illustration, the proposition or judgment, " Every A is B." 
 This judgment can be valid but upon the condition, that the 
 conceptions represented by these terms are constituted of 
 nothing but real intuitions relative to their respective objects. 
 If elements not thus given have been introduced into these 
 conceptions, that fact may wholly vitiate the judgment under 
 consideration. 
 
 Almost, if not quite, universally, permit us to remark further, 
 conceptions are constituted of some elements really given by 
 intuition. A conception, none of whose elements were thus 
 given, can hardly be found. They become vitiated only by 
 the introduction into them of elements not thus given. At the 
 basis of such conceptions, also, whether they are really valid or 
 not, there is an assumption that they represent their objects as 
 they are, or rather that such conceptions are constituted ex- 
 clusively of elements given by intuition relatively to their 
 objects. 
 
 The question to be determined is, How do invalid elements 
 come to be intermingled with valid ones, in conceptions as- 
 sumed as valid throughout, for their objects ? We are now 
 prepared to resolve this question. Among the most fruitful 
 causes of vitiated conceptions we notice the following : 
 
 SOURCES OF INVALID CONCEPTIONS. 
 
 1. The action of the Imagination in peculiar circumstances. 
 We meet, for example, a stranger ; some incident connected 
 
with him makes a very pleasing impression upon our minds. 
 Through the action of the associating principle every other ele- 
 ment that is pleasing in character is suggested to our minds, 
 and these elements, by the action of the imagination, are all 
 Wended into one conception, which we thus assume as truly 
 representing the real character of this individual. This con- 
 ception now becomes the basis of an endless diversity of judg- 
 ments relative to the individual referred to. In view of the 
 diverse elements of the conception, we rank the individual with 
 the noble, the honorable, the truthful, the generous, &c, of the 
 race, and separate him from all classes of an opposite character, 
 denying of him all characteristics incompatible with the ele- 
 ments of the conception thus formed of him. 
 
 If the incident referred to happens to be a displeasing one, 
 by the action of the principle named, an opposite conception is 
 formed, a characteristic conception, which becomes the basis 
 of corresponding judgments, affirmative and negative. 
 
 Now, if we go back and analyze this conception, we shall 
 find that but one element in it was really given by intuition, to 
 wit, the single incident referred to. So far only is said con- 
 ception, whether it happens to correspond with its object or 
 not, valid, relatively to us, as the basis of judgments in respect 
 to the individual referred to. On an endless diversity of sub- 
 jects are invalid and vitiated conceptions introduced into the 
 mind, through the action of the principle under consideration. 
 Science itself is not free, in many of its departments, from such 
 conceptions. 
 
 Desire, also, fear, and other kindred affections, often operate 
 in connection with the same principle to induce invalid concep- 
 tions. Such states of mind, through the action of the asso- 
 ciating principle, suggest all elements of thought which accord 
 with the existing state of consciousness, and those elements, 
 through the action of the imagination, are blended into corre- 
 sponding conceptions. These are assumed as valid, and as such 
 become the determining causes of corresponding judgments 
 and deductions. When we come to examine such processes 
 we find them invalid, because the main elements of the concep- 
 
DOCTRINE OP FALLACIES. 213 
 
 tions which lay at the foundation of the whole procedure were 
 not intuitions, as they should have been. 
 
 2. False conceptions are often induced through the action of 
 the suggestive and conceptive principle, in connection with our 
 own internal experience, or in connection with the facts of our 
 own consciousness. 
 
 Suppose that in our experience certain acts or courses of 
 conduct have, in fact, been connected with and induced by 
 certain mental states, motives, or intentions. When we per- 
 ceive the same acts performed by others, we naturally conceive 
 of them as acting from the same motives, and as naturally 
 assume this to be true in fact. Hence all our judgments and 
 deductions in regard to them are determined by such concep- 
 tions. A man whose external acts are honorable, benevolent, 
 and virtuous, and who is conscious of acting from correspond- 
 ing intentions, naturally conceives of all others whose acts, as 
 known to him, are of a similar character, as acting from similar 
 intentions. The man whose motives, even in acts- honorable in 
 themselves, are corrupt, naturally conceives of all others as be- 
 ing, like himself, corrupt and hypocritical, even in such acts, 
 and reveals his own want of moral principle in his inrpeachment 
 of the motives of others. How often do we find ourselves to- 
 tally misled by conceptions thus formed, and assumed as valid 
 relative to their objects. The facts given by intuition are in 
 no sense necessarily connected with those presented by the 
 associating principle, yet a large portion of our practically gov- 
 erning conceptions are thus formed. 
 
 3. Similar conceptions often arise as the result of external 
 experience and observation. Suppose that in our experience 
 certain antecedents or consequents have uniformly happened to 
 attend certain occurrences, though the connection between 
 them is in no form necessary in itself, or thus uniform in the 
 experience of others. Such an experience often induces the 
 conception of these events as sustaining the relations to each 
 other of cause and effect, that is, as necessarily connected. It 
 is thus, consequently, that they are subsequently employed as 
 the basis of judgments and deductions. So when certain quali- 
 
214 LOGIC. 
 
 ties have, in our observation and experience, been found con- 
 nected with certain others, they come often to be related in our 
 conceptions as parts of given wholes. Hence when any of these 
 qualities are perceived, the rest are conceived as present also, 
 that is, the presence of the wholes referred to is apprehended 
 and inferred. Yet, on investigation, these qualities are found 
 to have no necessary connection, and their connection in our 
 observation and experience to have been merely accidental. 
 
 4. Public rumor and opinion often become the sources of 
 false conceptions. We find a certain conception religious, so- 
 cial, political, or scientific, taken for granted in the circle in 
 which Ave are accustomed to move. How often, without being 
 investigated at all, does it assume a similar place in our minds, 
 and thus determine/ our judgments and deductions in all such 
 departments of thought ! So when an individual has attained to 
 a certain reputation, good or bad, with the public, individuals, 
 without a knowledge of the facts, receive that reputation as the 
 determining standard of their judgments in regard to him. 
 Yet subsequent facts may show that the conception thus in- 
 duced is wholly false. On questions of importance, no person is 
 safe in relying upon conceptions thus derived as the basis of 
 judgments and deductions. 
 
 5. The results of false information or scientific deductions 
 often are embodied subsequently as elements of conceptions, 
 and thus lay the foundation of false judgments and deductions 
 on the most important subjects. At one time it was a received 
 deduction of science, for example, that the earth is the centre 
 of the solar system the centre around which the sun, and stars, 
 and planets, all revolve. The conception of the universe thus 
 deduced determined, while thus received, all subsequent judg- 
 ments and deductions in the science of astronomy. How long 
 did the sensational theory, the theory of Locke, given as the re- 
 sult of scientific deduction, determine the judgments and de- 
 ductions of philosophers and theologians too ; and that in refer- 
 ence to the universe, God, duty, and immortality. Of two dis- 
 tinct and opposite conceptions pertaining to the human will, the 
 one or the other of which, that of liberty or necessity, must be 
 
DOCTEINE OF FALLACIES. 215 
 
 true, the one which we do receive will and must determine the 
 character of all our subsequent judgments and deductions, in the 
 whole field of mental and theological science. Suppose that our 
 conceptions on this subject are the result of false deductions, 
 while this result remains it will be impossible for us to reason 
 correctly on the most important questions in the most impor- 
 tant of all sciences, that of God, duty, and immortality. We 
 refer to such examples simply in illustration of the principle un- 
 der consideration, the influence of false deductions in science in 
 determining the character of conceptions which lie at the foun- 
 dation of subsequent judgments and reasoning. 
 
 6. We mention but one other cause of false conceptions, 
 wrong interpretations of authoritative documents, such as the 
 sacred Scriptures, the constitution and laws of our government, 
 &g. A certain exposition, false in itself, we will suppose has 
 been given, and subsequently comes to be received as the valid 
 conception of the real meaning' of the document. Whenever 
 thought is subsequently turned to said document, the concep- 
 tion under consideration will stand between the mind and the 
 document, and the mind will see nothing in the latter but what 
 previously existed in the former. All subsequent applications 
 of the principles of the document will also be determined by 
 this conception. Thus it often happens, that truth as it is in 
 itself, is, for ages, veiled from the human mind by false concep- 
 tions induced as above stated. In the above classification we 
 have simply indicated the sources and influence of false concep- 
 tions, and will leave the reader to complete what has here been 
 commenced. 
 
216 
 
 CHAPTER I. 
 
 THE DIALECTIC INVALID JUDGMENTS. 
 
 We now advance to a consideration of invalid judgments or 
 propositions. "We have already given the criteria of valid judg- 
 ments. Invalid judgments are exclusively assumptive, and con- 
 sist of problematical judgments assumed as already established 
 as true, or, of judgments false in themselves, and assumed as 
 true. We shall endeavor to indicate the sources of such judg- 
 ments. Among these we adduce the following as deserving 
 especial notice : 
 
 Section I. Problematical Judgments assumed as First 
 Truths. 
 
 The first that we notice is a certain class of assumptions in 
 which mere problematical judgments, those which are neither 
 self-evident nor yet established as true by valid evidence, are 
 ranked among primary and necessary intuitions. Hitherto we 
 have had no very definite and decisive criteria of first truths, 
 those commonly given being rather accidents than fundamental 
 characteristics of such truths. The criteria given in the Ana- 
 lytic of Judgments will enable the student, we judge, readily to 
 distinguish such truths from assumptions which have no claims 
 to be ranked among primary intuitions. The criteria to which 
 we refer, it will be recollected, is this, " All valid primary intui- 
 tions or first truths are, exclusively, analytical judgments]'' 
 judgments in which the conception represented by the predi- 
 cate is an essential element of that represented by the subject ; 
 as in the proposition; " All bodies are extended ;" or in which 
 the conception represented by the former term is the logical 
 antecedent of that represented by the latter, as in the principle, 
 " Body supposes space, succession, time," &c. Now nothing is 
 more common than for mere problematical judgments which 
 
DOCTRINE OF FALLACIES. 21V 
 
 have no such characteristics, and which are even false, in fact, 
 to be assumed as first truths of science, and to be used as such 
 in the formation of systems and the explanation of facts. We 
 will give a few examples in illustration. 
 
 Assumption that a thing cannot act where it is not. 
 
 Let us first notice the following assumption of Sir Isaac New- 
 ton, and presented by this great philosopher as a primary intui- 
 tion : " It is inconceivable that inanimate brute matter should, 
 without the mediation of something else which is not material, 
 operate upon and affect ottter matter Avithout mutual contact." 
 The opposite supposition he affirms to be " too great an absur- 
 dity" to be believed by any one " who, in philosophical matters, 
 has a competent faculty of thinking." Whence this assump- 
 tion ? Is it, like extension, an essential element of our concep- 
 tion of this substance ? Or, is it the logical antecedent of our 
 conception of that substance, or of any element of that concep- 
 tion ? By no means. It has not a shadow of a right to a place 
 among the first truths of science. Nor is its truth even remote- 
 ly indicated by any of the known phenomena of this substance. 
 It is nothing but a mere assumption, unauthorized by any form 
 of evidence, mediate or immediate. 
 
 The assumption that our knowledge of matter is 
 mediate. 
 
 Let us next contemplate the assumption, that all our know- 
 ledge of matter is exclusively mediate or representative, being 
 derived through the consciousness of sensation, and not in any 
 form or respect immediate or presentative. How did this as- 
 sumption ever obtain a place in science ? Not as the result of 
 logical deduction from the facts of consciousness. This none 
 will affirm. , We know of no professed logical demonstration of 
 its truth. It has always, when received, been assumed as a 
 first truth, and has, as such an assumption, taken its place as a 
 principle in science. What claim has this assumption to this 
 10 
 
high position ? We certainly cannot find it by any analysis of 
 our fundamental conceptions of matter, on the one hand, or of 
 mind, on the other. ~No man can affirm, a priori, from what he 
 knows of this substance, that the former cannot be to the latter 
 the object of immediate or presentative knowledge. Nor can 
 we affirm it, in a similar manner, from the fact of the mind's 
 present connection with the body. Nor is its truth the logical 
 antecedent of any elements of our conceptions of mind and mat- 
 ter, or of any of the facts of consciousness. On the other hand, 
 if we are conscious of any thing, we are conscious of a direct and 
 immediate or presentative knowledge of this substance. The 
 most that can be said of this judgment is, that it is a mere pro- 
 blematical judgment, wholly incapable, from the nature of the 
 case, of proof. Yet, as a first truth, whole systems of physical, 
 mental, and theological science have been founded upon and 
 determined, in all their fundamental characteristics, by it. All 
 that we now are called upon to do is, in the name of science, to 
 challenge the right of this assumption to the place which it has 
 so long occupied, to wit, that of a first truth or principle in 
 science. To such a position it has no claims. When, as a theo- 
 rem, its truth has been demonstrated, then, and not before, can 
 it have any legitimate place in science. 
 
 Fundamental and opposite Assumptions of Materialism and 
 Idealism. 
 
 We now refer to two distinct and opposite assumptions, the 
 first of which lies at the basis of Materialism, and the second at 
 that of Idealism. Materialism rests exclusively upon the as- 
 sumption, that all our knowledge is derived exclusively through 
 sensation or external perception, and that, consequently, nothing 
 but the external universe, with its laws, can be to us an object 
 of knowledge, and this whole system must be false, unless the 
 validity of this assumption be granted. Idealism, in all its 
 forms, on the other hand, rests upon the exclusive assumption, 
 that nothing can, by any possibility, be to the mind an object of 
 real knowledge, but its own operations, and this system, in all 
 
DOCTRINE OF FALLACIES. 219 
 
 its forms, must stand or fall with that assumption. Now 
 neither of these assumptions finds a place among the principles 
 of science from any a posteriori evidence or demonstration of 
 its validity. In opposition to the first assumption, that of mate- 
 rialism, we find ourselves in consciousness just as able to distin- 
 guish one mental state from another, thoughts from feelings and 
 acts of will, for example, or one strong feeling or act of will from 
 bother, as we are to distinguish one external object from 
 another. We can as readily distinguish a thought from a sen- 
 sation, emotion, or act of will, as Ave can an elephant from a man, 
 or a mountain from a molehill. We are just as conscious of the 
 fact of perceiving our own* mental states, as we are of having 
 similar perceptions of external objects. In opposition to the 
 assumption of idealism, it cannot be denied that we are just as 
 conscious of the fact of perceiving external material objects, as 
 we are of a knowledge of our own mental states. In opposition 
 to both assumptions, we have precisely the same evidence of the 
 power in ourselves to know one class of phenomena as the 
 other. There can be, we repeat, no possible a posteriori proof 
 of the truth or validity of either of these assumptions. Nor is 
 the validity of either of them self evident ; nor can either of 
 them be shown to sustain the relations of logical antecedents 
 to any facts of consciousness, nor to any elements of our valid 
 conceptions of matter, on the one hand, or of mind on the 
 other. To the high position of first truths or' principles in 
 science, they have not a shadow of a claim in any form what- 
 ever. How can we decide a priori that the human intelligence 
 may not, and does not, possess the power of real external and 
 internal perception both, and that one class of these perceptions 
 may not be, and is not, just as valid for the real character of its 
 objects as the other ? Not a solitary valid characteristic of 
 a first truth or principle of science, can be shown to attach to 
 either of these assumptions ; yet, as first truths, they have for 
 ages lain at the basis of systems of universal ontology, meta- 
 physics, and theology. Now, in the name of science, we chal- 
 lenge the right of each of these assumptions to the place in 
 science which has, for ages, been claimed for them. We affirm 
 
that they are mere assumptions pushed forward, as self-evident 
 primary intuitions, into the sphere of science. Till their validi- 
 ty has been clearly demonstrated, we deny the validity of any 
 deductions which may have been drawn from them, as princi- 
 ples in science. 
 
 ASSUMPTION PERTAINING TO THE ORIGIN OP OUR IDEA OP 
 CAUSE AND EFPECT. 
 
 There is an assumption pertaining to the origin of our idea 
 of causation, an assumption originally set forth by M. de Biron, 
 of France, which has since been pushed forward with great 
 zeal and ability into the sphere of science, by his successor in 
 the chair of philosophy, Victor Cousin, and which is now exert- 
 ing not a little influence in philosophy an assumption, conse- 
 quently, which claims some special notice in this connection. 
 We refer to the assumption, that we originally derived the idea 
 of cause from the consciousness of our own acts of will as causes. 
 We give the theory in the language of Prof. Tulloch in his 
 " Theism :" " This statement is that of a distinguished French 
 philosopher, M. de Biron, who has certainly the eminent merit 
 of having, in the most elaborate manner, fixed attention on the 
 theory of causation under discussion. It is to this effect : ' I 
 will to move my arm, and I move it.' This complex fact gives 
 us on analysis : 1. The consciousness of an act of will. 2. The 
 consciousness of motion produced. 3. The consciousness of the 
 relation of the motion to the volition. This relation is in no 
 respect a simple relation of succession. The motion not merely 
 follows our will, or appears in conjunction with it, but is con- 
 sciously produced by it. The idea of power or cause is thus 
 evolved." 
 
 There are two facts here asserted : 1st. That we have a direct 
 and intuitive consciousness of the fact, that the motion referred 
 to is caused by the act of will. 2d. That it is intuitively im- 
 plied in this fact, that in and through the consciousness of our 
 acts of will as causes, Ave originally obtained the idea of cause 
 itself. Hence this theory of causation is being pushed forward 
 
DOCTEINE OF FALLACIES. 221 
 
 into the sphere of science as a first truth, an intuitive princi- 
 ple. In reply, we remark : 
 
 1. That we have here, in the first place, an undeniable psy- 
 chological error. We are not conscious, as a matter of fact, of 
 any relation of cause and effect between the act of the will and 
 the successive physical motions of our bodies. We are simply 
 and exclusively conscious of the act of will itself, and of nothing 
 else. The motion of the physical organization which follows 
 the act, is as exclusively an object of external perception. 
 " Between the overt fact of corporeal movement which we per- 
 ceive," says Sir William Hamilton, " and the internal act of will 
 to move, of which we are self-conscious, there intervenes a series 
 of intermediate agencies, of which we are wholly unaware ; con- 
 sequently, we can have no consciousness, as this hypothesis men- 
 tions, of any causal connection between the external links of this 
 chain, that is, between the volition to move and the arm mov- 
 ing." There cannot be a more manifest psychological error 
 named, than this dogma presents. 
 
 2. We have precisely the same evidence, that other mental 
 states are causes proper of .certain physical effects, that we have, 
 or can have, that our acts of will are such causes. Suppose that 
 through some thought or apprehension, a state of intense men- 
 tal excitement is induced, a state which is immediately followed 
 by a corresponding agitation of the physical system, and that 
 not only independent of, but in opposition to, our acts of will. 
 Now we have just as much evidence that this agitation of the 
 physical system, the flush or paleness upon the cheek, the trem- 
 bling of limbs, and the quickening of the pulsation, is caused by 
 the state of the sensibility referred to, as we have, or can have, 
 that any movement of the muscular system is caused by voli- 
 tion ; and we might, with the same propriety, affirm, that our 
 idea of causation was originally derived through one of these 
 sources, as through the other. For ourselves, if compelled to 
 select between these two hypotheses, w r e should take the first ; 
 for we believe that, as a matter of fact, the infant has percep- 
 tions of physical effects as connected with states of the sensibili- 
 
222 logic. 
 
 ty long before it has any knowledge of them, as connected with 
 acts of will. 
 
 3. Not the least indication of such an origin can be found in 
 the principle of causality itself, as that principle exists in the 
 universal intelligence, the principle, that " Every event must 
 have a cause." Let any one most carefully analyze this principle, 
 and he will find in it no indication whatever of any such origin. 
 What connection can there be found between the primary prin- 
 ciple, that " Every event must have a cause," and the conscious- 
 ness of an act of will, and the perception of a successive muscu- 
 lar movement, to indicate, that the conception of the principle 
 originated in the intelligence, from the act of consciousness and 
 perception before us ? 
 
 4. We remark, finally, that we need nothing but the percep- 
 tion of an event by the mind, without any perception or appre- 
 hension of its particular or specific cause, to account for the ori- 
 gin of this principle just as it now exists in the human intelli- 
 gence. The idea of Cause exists in the intelligence as the logi- 
 cal antecedent of that of an event, and we find in the intelli- 
 gence this general power to conceive, when any fact is given, of 
 the logical antecedent of that fact. The same function of the 
 intelligence which, on the perception of body, succession, and 
 phenomena, gives us the logical antecedents of such perceptions, 
 the idea of space, time, and substance, may, and from its nature, 
 must, on the perception of any event whatever, give us its logi- 
 cal antecedent, the idea of cause. 
 
 It is just as absurd to refer the origin of this idea to the per- 
 ception of some one specific event, as it would be to refer the 
 origin of the idea of space to the perception, not of any exter- 
 nal substance, whatever it may be, but of some specific body, a 
 mountain, for example. Given in the intelligence any event 
 whatever, and the idea of a cause must, from the nature of the 
 reason, be originated. The inference deduced from this idea of 
 the origin of the principle of causality in the mind, will be con- 
 sidered in another connection. All that we wish now to estab- 
 lish is the fact, that while the assumption under consideration 
 relative to the origin of the idea of causation, has no claim to 
 
DOCTRINE OF FALLACIES. 223 
 
 the place of a first truth or principle in science, its validity has 
 not yet been established by any process of demonstration or 
 proof, and consequently, that any deductions based upon it are 
 without any claims to our regard as truths of science. 
 
 "the eternal now" of theology. 
 
 We will now consider an assumption which has long held a 
 place as an intuitive truth in the science of theology, and which 
 has had not a little influence in the construction of theological 
 systems. We refer to the assumption, that it is only to finite 
 beings that events are, or appear to be, successive ; that with 
 God, the Infinite and Perfect, there is no past, present, or fu- 
 ture, but all is alike present, " one eternal now." If this is true 
 of God, it must be so, because events are not really or truly suc- 
 cessive, or because he wants the power to know them as they 
 are. Shall we conclude that there is no such thing as real suc- 
 cession ? and if so, by what evidence is the truth of the fact 
 to be established ? We cannot know such a fact by intuition. 
 By what process of argument, then, can its truth be established ? 
 No one, we are quite sure, will attempt to prove such a dogma. 
 Shall we admit that events are really and truly successive, and 
 then limit and debase our conception of the Most High by 
 the assumption, that he wants the power to know events as 
 they are ? 
 
 Further, if events are not really and truly successive, then the 
 universal finite intelligence is a lie, and God stands convicted of 
 deception in thus constructing it ; for it affirms absolutely the 
 reality of succession. If succession is real, and our intelligence 
 is not a lie, and God cannot, as this theory affirms, distinguish 
 the real past from the real present, or either from the real fu- 
 ture, then his intelligence is so far less perfect than ours. One 
 question more here. By what process of intuition or deduc- 
 tion have the advocates of this dogma attained, first, to the 
 stand-point from which the finite intelligence views events, and 
 then to that from which the Infinite and Perfect views the 
 same, so that they can inform us how the same things appear to 
 
 vw J.HJS -<-^ 
 
 fUJflVSRSITy 
 
 m^ 
 
each ; and especially be able to affirm, that while to the former 
 there is real and absolute succession of events, to the latter, 
 "all is one eternal now?" Among first truths or valid intui- 
 tions, this dogma surely has no place. It enters not as an essen- 
 tial element into our idea of the Infinite and Perfect, nor can it 
 be shown to sustain the relation of logical antecedent to that 
 idea, or to any element of it. It certainly exists not as a truth 
 of inspiration. This no one will pretend. Nor can it be logi- 
 cally deduced from any fact yet known relatively to matter or 
 spirit, to the finite or the infinite/ As a principle in the science 
 of theology, it has no place by virtue of its claims as an intuitive 
 truth, or a valid deduction of science. This is all that we wish 
 to now say of it. So far as it has had influence in theology, 
 that science has rested upon no valid basis. The question for 
 its advocates to answer is this : By what authority do they 
 claim for this dogma a place among the valid deductions of 
 science ? It is especially as an assumed truth of intuition, how- 
 ever, that we would now challenge its validity. 
 
 Assumption pertaining to the Divine Personality, <&c. 
 
 We now notice another assumption which is being pushed 
 forward into the field of science, as a first truth or principle. It 
 is affirmed that personality and self-consciousness cannot either 
 of them be affirmed of God, and that for this reason : they both 
 alike imply limitation in their subject, and consequently can 
 be affirmed only of the finite. God is infinite and perfect, and 
 therefore these attributes which imply limitation must be de- 
 nied of him. On what ground can such a dogma as this be ad- 
 mitted ? Not surely as a self-evident truth, that is, as a first 
 truth or principle in science. We certainly cannot intelligently 
 affirm a priori that there may not be, and is not, a personality 
 really and truly infinite and perfect in all his attributes, who is 
 distinctly conscious of his own perfections and relations as in- 
 finite and perfect, and who does possess a knowledge similarly 
 perfect of all other beings and objects. It is certainly, and that 
 in the most emphatic sense, limiting the Most High to affirm 
 
DOCTRINE OF FALLACII 
 
 the opposite of him. To affirm that he is not, and cannot be, 
 absolutely conscious of his own perfections, is to limit his know- 
 ledge to the circle of the finite. Indeed, it is to exclude the 
 Infinite and Perfect from the realm of intelligents, and to con- 
 fine, that is, limit him within the circle of non-intelligents ; and 
 this is the exclusive object of those who are pushing this assump- 
 tion into the sphere of science. Under a professed veneration 
 and zeal for the honor of God, that is affirmed of him which 
 utterly disrobes him of every attribute on account of which he 
 can bo to us an object of real esteem or veneration. The Infi- 
 nite and Perfect is held up before us as characterized by in- 
 finite ignorance, instead of 'absolute knowledge. When the 
 advocates of this assumption have demonstrated its truth and 
 validity, however, we will admit it. To a place among first 
 truths or principles of science, the place which its advocates 
 claim for it, it has no claims whatever. It cannot be shown to 
 possess a solitary accidental or scientific characteristic of any 
 such truth or principle. 
 
 We have presented the above assumptions as examples in 
 illustration of the principle under consideration, to wit : the 
 error of assuming mere problematical judgments, as first truths 
 or intuitive principles of science, and then constructing systems 
 of knowledge upon the basis of such assumptions. Others of a 
 similar character might be adduced. Not one of those which 
 we have adduced bears a single characteristic of the class of 
 truths among which they have all been ranked by those who 
 have constructed theories upon them. The reader should con- 
 tinuously bear in mind the fact, that no proposition can have 
 any claims to be regarded as a first truth or valid principle in 
 science which is not strictly according to the definition given 
 an analytical proposition, a proposition in which the predicate 
 represents an essential element of the subject, as in the proposi- 
 tion, " All bodies are extended ;" or in which the predicate rep- 
 resents the logical antecedent of the conception represented by 
 the subject, as in the proposition, " Body sivpposes space." It 
 is only by usurpation or invalid assumption, that any other prin- 
 ciple or class of principles can be pushed forward into the sphere 
 10* 
 
226 logic 
 
 of science as a first truth. We are -also to reject as utterly in- 
 valid, all deductions resting upon any principles not undeniably 
 possessed of one or the other of the characteristics above named. 
 One of the highest demands of science at the present time, is a 
 fundamental examination of principles used as first truths in the 
 construction of systems of knowledge, an examination in which 
 there shall be a most rigid application of the characteristics 
 which distinguish all real and valid intuitions from unauthorized 
 assumptions, and in which all principles not having these char- 
 acteristics shall be rejected as utterly invalid. Till this is done 
 the most visionary and pernicious theories will continue to be 
 palmed upon the world, and held, by even scientific minds, as 
 embodying the highest forms and developments of wisdom and 
 knowledge. 
 
 Section II. Invalid Assumptions pertaining to Matters 
 of Fact.* 
 
 Invalid assumptions pertaining to matters of fact next claim 
 our attention. Among these we notice the following : 
 
 1. False assumptions relatively to the authorized quantity or 
 quality of propositions. Suppose that it has been ascertained 
 that a certain characteristic does, or does not, belong to certain 
 individuals of a given class, and that this is the extent of our in- 
 duction. The truth of the subaltern proposition I or O, and 
 that only, has been established, that is, we have obtained au- 
 thority for the judgment, " Some Z is X, or some Z is not X," 
 and nothing more. Under such circumstances, however, it is 
 perfectly common to assume the truth of the universal judg- 
 ment A or E, as the case may be ; that is, the truth of the judg- 
 ment, " All Z is X, or no Z is X," and to use such judgments 
 as premises in reasoning. So when the universal A or E has 
 
 * The special object of this and the preceding section and chapter, is to furnish criteria by 
 which we may judge correctly, first, of conceptions employed in processes of reasoning, and 
 then of the judgments presented as premises. Upon all these attention must be definitely 
 fixed, and that in the light of valid criteria, if we would judge correctly of the validity of 
 different processes of reasoning. 
 
DOCTRINE OF FALLACIES. 227 
 
 been ascertained to be untrue, it is perfectly common to assume 
 the truth of the contrary judgment. We have, for example, 
 examined some individuals of a given class, and have ascertained 
 that they do, or do not, possess certain characteristics. All 
 that such induction really authorizes, is the assumption of the 
 truth of the contradictory propositions I or O. It does not au- 
 thorize a denial of the subaltern judgment, and a consequent 
 assumption of the truth of the contrary. From the mere fact, 
 that A (All Z is X) is false, Ave are not authorized to judge 
 that I (Some Z is X) is also false, and that, consequently, E (No 
 Z is X) is true. Yet just such judgments are perfectly com- 
 mon. The common assumption, that in the process of indue* 
 tion we reason from the particular to the general, instead of from 
 all the parts to the whole, is, we believe, the fruitful source of 
 this class of invalid judgments, judgments presented as premises 
 for the deduction of conclusions. 
 
 2. Another class of invalid assumptions is this : the assump- 
 tion that a mere accident is an essential characteristic, and 
 hence affirming it as a general or universal characteristic of the 
 individual or class to which it pertains. One substance is found, 
 for example, in certain circumstances combined with another. 
 A necessary, and consequent universal connection, is from 
 hence assumed. Yet the connection, in the circumstances sup- 
 posed, may be perfectly accidental. A., under certain provoca- 
 tions, became angry. It is hence assumed, that he is an irrita- 
 ble man. Y r et his general character may be the total opposite 
 of that assumption. The error here described really falls under 
 that first stated. It is presented in this form, for the sake of 
 distinctness. * 
 
 3. Another source of false judgments is found in the too 
 common practice of assuming the relation of invariable or uni- 
 form sequence from mere casual coincidence, and of cause and 
 effect from mere accidental antecedence and consequence. Mere 
 coincidence does not authorize the assumption of a necessary 
 connection, nor mere sequence that of real cause and effect. 
 Yet such relations are quite commonly assumed in the presence 
 of such facts. The relation of cause and effect can be properly 
 
assumed but in vjew of the fact of invariable antecedence and 
 consequence. This is the lowest condition on which such an 
 assumption can be aiithorized. Another condition should be 
 uniformly required an inability to account for the connection 
 referred to, on any other supposition than the relation of cause 
 and effect. 
 
 4. The very common practice of assuming, that what may 
 be true, is true, is another fruitful source of false judgments. 
 A. may have acted from given motives in such and such circum- 
 stances. From hence it is assumed, that he did then act from 
 these identical motives. Such an assumption is valid but upon 
 one supposition that no other motives but those assigned can 
 originate such acts. A certain class of facts are perceived to 
 consist with a certain hypothesis, that is, it is perceived that 
 this hypothesis may be true. It is hence assumed that that hy- 
 pothesis is, and must be, true, an assumption which is valid but 
 upon one condition the perception that these facts can be ex- 
 plained on no other supposition. 
 
 5. We now refer to another equally fruitful source of false 
 assumptions. A fact or class of facts, equally consistent with 
 two or more distinct and opposite hypotheses is assumed as 
 affirming the truth of one in opposition to that of the others. 
 It is a universal law of all valid intellectual processes, that facts 
 which equally consist with two or more hypotheses, prove 
 neither in distinction from the others. Yet such facts are often 
 made the basis of judgments, that one hypothesis is true and all 
 the others false. The same error is very common in the cita- 
 tion of proof-texts and authorities. No judgment is affirmed 
 by any facts 6*r texts, or any form of authority, which not only 
 does not affirm the truth of this one judgment, but in reality 
 denies all judgments of an incompatible or opposite nature. 
 
 6. Assuming that facts which are equally common to two 
 classes of objects, really and truly pertain to one class in dis- 
 tinction from the other, is still another common source of in- 
 valid judgment. Suppose that the question is, Which is to be 
 preferred, A or B ? Suppose that it is affirmed, that A is the 
 fetter of the i wo. The reason assigned is, that the element C 
 
 
DOCTRINE OF FALLACIES. 229 
 
 is found in A. Such reason has real weight hut upon the sup- 
 position, that C is of decisive value, and is possessed by A, and 
 not by B. If it belongs to each alike, it presents no ground for 
 the judgment, "A is better than B." Yet the form of false 
 judgments under consideration is perfectly common in the 
 world, and not uncommon in scientific deduction. 
 
 7. Affirming a certainty, when the facts presented authorize 
 .only the assertion of a probability \ is still another common form 
 of invalid assumption. How often do we hear individuals say- 
 ing, " I felt certain that the case was so and so, and yet I found 
 myself mistaken." A recurrence to the facts known, would 
 show clearly, that a certainty had been assumed, when only 
 probability, or it may be, a bare possibility, was truly indicated. 
 
 8. Denying the manifest bearing and fundamental charac- 
 teristics of facts, when their admission would contradict some 
 favorite theory, is another source of invalid assumptions. In 
 such cases, which often occur, not only in common life but even 
 in the sphere of science, we have nothing but assumption in op- 
 position to valid evidence. This kind of assumption involves a 
 violation of the principle of sufficient reason. 
 
 9. Refusing to place facts under the principle or class to 
 which they manifestly belong, and arbitrarily placing them un- 
 der a class to which they do not belong, is a form of invalid 
 assumption which we often meet with. Facts are often pre- 
 judged in accordance with some favorite theory or assumption, 
 and then obstinately classed accordingly. Hence the best ac- 
 tions, for example, are attributed to the worst motives, and vice 
 versa ; and all this by an arbitrary act of will or assumption. 
 
 10. Assuming that facts are not real when their reality is 
 affirmed by valid evidence, or, that they are real when not thus 
 affirmed, and this because of the undeniable bearing of the facts 
 granting their occurrence, presents forms of invalid assumption, 
 which should not be overlooked in this connection. No degree 
 of evidence can induce, in some instances, the admission of cer- 
 tain facts, and any form of evidence will be readily admitted 
 for the occurrence of others. The reason is obvious. The lat- 
 ter class affirm a proposition, the truth of which is an object of 
 
230 LOGIC. 
 
 strong desire, and the former affirm one, the admission of which 
 is an object of corresponding aversion. We find, in all such 
 cases, nothing but assumption assumption opposed to valid 
 evidence. 
 
 11. We mention another additional source of invalid assump- 
 tion : assuming that a mere hypothesis, consistent throughout 
 with a given class of facts, but which, for aught that appears, 
 may or may not be true, is the necessary law of their occur- 
 rence. An hypothesis which must be held as law, not only con- 
 sists with the class of facts referred to it, but is necessarily sup- 
 posed by the facts. An hypothesis which cannot properly be 
 held as law, though consistent with the facts, may or may not, 
 for aught presented in them, be true. There may be classes of 
 facts, and there are many such, the law of whose existence, and 
 action may as yet be wholly unknown. Suppose that an hy- 
 pothesis presents itself, an hypothesis consistent with all that is 
 known of the facts, but not necessarily supposed by them. How 
 readily may this problematical hypothesis be assumed as the 
 ascertained truth ! 
 
 12. Assumptions which violate the principles of identity and 
 contradiction are often introduced as premises into processes of 
 reasoning, or presented as valid in themselves. The principle 
 first named is this : that " conceptions which agree can in thought 
 be united or affirmed of the same subject at the same time." 
 The second is this : " The same attribute cannot be at the same 
 time affirmed and denied of the same subject ;" nor can incom- 
 patible attributes be at the same time affirmed of the same sub- 
 ject. The principle first named is the complement of the latter. 
 We often meet with judgments which violate each of these prin- 
 ciples. Conceptions which agree are often denied, and those 
 which disagree are as often affirmed, of each other. A., for ex- 
 ample, takes the life of B., under circumstances which most 
 manifestly characterize the act as murder. Yet the personal 
 friends of A. will resolutely refuse to place the act under the 
 category referred to, and will rank it under an opposite one. 
 A characteristic attaches to a leading dogma of a particular sect, 
 a characteristic which most manifestly marks said dogma as un- 
 
 
DOCTRINE OF FALLACIES. 231 
 
 true, or self-contradictory and absurd. Yet every member of 
 that sect will refuse to place that dogma under such category, 
 and as arbitrarily subsume it under an opposite idea or princi- 
 ple. A mystery is often rejected as an absurdity and a mani- 
 fest absurdity as often embraced under the assumption, that it 
 is n >t an absurdity but a mystery. In all such cases one or the 
 other of the principles under consideration is violated. 
 
 13. We notice, in the last place, a class of assumptions which 
 violate the principle of implied judgments the principle that 
 whatever is manifestly implied in an admitted judgment, must 
 also be admitted. In opposition to this principle, judgments 
 manifestly implied in admitted ones are often denied, and the 
 opposite ones assumed as true, while others not thus implied are 
 assumed as implied. In all theories of the universe, for exam- 
 ple, it is affirmed that creation is progressive in one fixed direc- 
 tion from the less towards the more perfect. At the same 
 time, in systems of skeptical philosophy, it is assumed that the 
 order of nature had no beginning, but is self-subsisting and eter- 
 nal. Now progression from the less towards the more perfect, 
 necessarily implies a commencement, a beginning in time. Thus 
 the principle of implied judgments is violated. 
 
 In the above classification we have aimed to give as full a de- 
 velopment of the sources of invalid assumptions, as the present 
 state of scientific investigation will permit. That some of such 
 sources may have been overlooked, is most probable. What 
 has been indicated, however, is deemed sufficient to give a 
 right direction to the investigations of the inquirer upon this 
 important department of the laws of thought, and also to pre- 
 pare the way for the requisite elucidation of the department of 
 our subject next in order, to wit : invalid deductions from judg- 
 ments assumed as true, and presented as the basis for such de- 
 ductions. 
 
 A careful investigation, also, of the above classes of assump- 
 tions, together with the criteria of valid judgments given in the 
 Analytic, will enable the inquirer to determine what judgments 
 may be denied, and the grounds of such denial. 
 
CHAPTER III. 
 
 THE DIALECTIC. 
 
 Fallacies in Reasoning. 
 
 It now remains to consider the third and last source of falla- 
 cies, to wit : that which especially, hut not exclusively, pertains 
 to the connection between the premises and conclusion in a pro- 
 cess of reasoning. In examining any such process, three dis- 
 tinct inquiries present themselves: the validity of the concep- 
 tions themselves ; that of judgments laid down as premises ; 
 and the connection between said premises and the conclusions 
 deduced from them. In every valid reasoning process, the con- 
 ceptions on the one hand, and the premises on the other, have 
 all the characteristics of validity developed in the Analytic ; and 
 the conclusion in accordance with laws of deduction elucidated 
 in the same, necessarily results from the premises from which it 
 is deduced. In every invalid process there is, either the want 
 of the characteristics of validity referred to in the conceptions 
 or premises, and the consequent presence in one or both of the 
 characteristics of invalidity developed in the preceding chapters 
 of the Dialectic, or a want of valid connection between the 
 premises and the conclusion, or the presence of all these defi- 
 ciencies in the same process. The object of the present chapter 
 is to develope the characteristics of one source of fallacy in rea- 
 soning the want of valid connection between the premises and 
 the conclusion deduced from them. Other sources of fallacy 
 connected with this will also be developed. The inquirer can- 
 not be too often reminded of the fact, that it is perfectly com- 
 mon in reasoning to lay down invalid premises as the basis of 
 conclusions, and of the consequent necessity of rigidly testing 
 the validity both of premises and jf the conclusions and terms 
 used. Our present inquiries, however, lie in a different direc- 
 tion, the source of invalid deductions. 
 
DOCTKINE OF FALLACIES 
 
 GENERAL CHARACTERISTICS OF ALL INVALID DEDUCTIONS. 
 
 All invalid conclusions are, of course, either assumed a* 
 proved by premises which prove nothing, which fail to provt 
 the conclusion deduced from them, or which prove not this, bul 
 some other and irrelevant conclusion. There are various 
 forms in which one or the other of these kinds of fallacy appear 
 We will notice them under the different classes above stated. 
 
 Section I. Conclusion^ deduced from Premises which 
 
 PROVE NOTHING. 
 
 It would hardly be expected, that even intelligent thinkers 
 would draw inferences from premises which really authorize no 
 conclusions of any kind. Such facts, however, are of perfectly 
 frequent occurrence. We will direct attention to a few of them. 
 
 Arguing from tioo Negative or two Particular Premises. 
 
 One of the most obvious forms of this error appears when 
 conclusions are deduced from two negative or two particular 
 premises. Such premises, as we have already seen, authorize 
 no conclusions whatever. When two terms are excluded from 
 a third, which is true where we have two negative premises, 
 nothing whatever can, from hence, be inferred in regard to the 
 relations of the terms to one another. When we have two 
 particular premises, one extreme may be compared with one 
 part of the middle term, and the other with another part ; so 
 that no ground for an inference of any kind is present, the ex- 
 tremes not being compared with the same thing. Yet we fre- 
 quently meet with precisely such deductions as these. We are 
 often, for example, met with the inference, that two entire 
 classes are alike or unlike, on the ground that some individuals 
 of said classes agree or disagree in the particulars referred to. 
 
Drawing positive conclusions from problematical 
 
 The common practice of drawing positive inferences from 
 problematical premises, is another common fallaey which belongs 
 to the class under consideration. A problematical judgment is 
 one which is capable of being proved or disproved, and needs 
 proof. Till proved, it cannot properly be employed as the basis 
 of any conclusions of any kind. Yet it is perfectly common for 
 individuals to lay down a doubtful proposition and one really 
 known to be such, as presenting an ascertained or well-known 
 truth, and then make use of such proposition as the basis of the 
 conclusions which they desire to reach. A problematical propo- 
 sition, it should be borne in mind, is utterly void of all logical 
 force. It authorizes no inferences whatever. This error in 
 logic is one form of the so-called petitio principii, or begging 
 the question, more commonly called the fallacy of undue as- 
 sumption. This fallacy most frequently occurs in this form. 
 Two premises are laid down, which together, if both are admit- 
 ted, necessitate the conclusion deduced from them ; premises, 
 one of which is admitted, and the other doubted or denied, 
 while both alike are assumed as admitted. Thus the conclu- 
 sion is begged instead of proved, no conclusion whatever being 
 authorized by the premises as presented. 
 
 Petitio Principii. 
 
 The proper petitio principii, however, occurs when an infer- 
 ence is deduced from a proposition which is really identical with 
 the inference itself, or in which the latter is directly and imme- 
 diately implied. While the conclusion itself is problematical, 
 the same must be true of every judgment identical with or im- 
 mediately implying it. The former, therefore, is utterly void 
 of all valid logical force, and to argue from it as a valid basis for 
 inferences, is to draw conclusions from premises which pi-ove 
 nothing. Attempting to prove the being of God from the tes- 
 timony of Scriptures to the fact of his being and perfections, is 
 
DOCTRINE OF FALLACIES. 235 
 
 an example of this kind, the conclusion to be reached being im- 
 plied in the premises froni which it is deduced. 
 
 Arguing in a Circle. 
 
 Arguing in a circle, that is, assuming the truth of the conclu- 
 sion from the assumption that the premise is true, and then 
 affirming the truth of the latter from that of the former, is 
 another example of deduction from premises which prove 
 nothing. In such cases, both the premise and the conclusion 
 are in turn given as admitted and problematical judgments. 
 Neither, therefore, can be-valid as the basis of valid deductions 
 of any kind. Arguing the authority of the Church from the 
 truth and divine authority of the Scriptures, and then affirming 
 the latter from the former, is an obvious and commonly adduced 
 example of this kind. One of the main arguments to J prove the 
 doctrine of necessity, as presented by some of our ablest and 
 most worthy theological metaphysicians, is another very striking 
 example of this kind. The will, it is affirmed, must be subject 
 to this law, because its determinations are always, as a matter of 
 fact, in accordance with the strongest motive. The strongest 
 motive is then defined to be that to which said determination 
 is conformed, and the proof that this motive is the strongest is 
 affirmed to be the fact, that this determination is conformed to it. 
 If this motive was not the strongest, it is replied, the will would 
 not have folloAved it. Now here are the three logical vices 
 which we have just considered : reasoning in a circle ; begging 
 the question ; and, employing as a premise a problematical, in- 
 stead of an ascertained, judgment. In the first place, the truth 
 of the doctrine is inferred from that of the premise, and then, 
 the validity of the premise from the truth of the doctrine. The 
 doctrine, it is inferred, is true, because the will is always as the 
 strongest motive, " the greatest apparent good ;" and then the 
 motive which the will does follow is affirmed to be the strongest, 
 because the will must follow the strongest motive that is, be- 
 cause the doctrine first deduced from the assumed validity of 
 the premise is true. Then the question at issue is begged in 
 
the assumption, that the motive to which the will conforms its 
 determinations is the strongest. This assumption, too, is used 
 as an ascertained, while it is, in fact, nothing but a problemati- 
 cal, judgment. 
 
 Deducing positive conclusions from Premises known to be in- 
 valid in t 
 
 The practice of deducing conclusions as valid from premises, 
 not only wanting the characteristics of validity elucidated in 
 the analytic, but possessing the positive characteristics of inva- 
 lidity elucidated in the dialectic of judgments, should not be 
 overlooked in this connection. 
 
 A problematical or invalid judgment may have validity as 
 the antecedent or consequent of a conditional, but never in itself, 
 nor as a premise. A premise void of the characteristics of va- 
 lidity or possessed of those of an opposite character, is utterly 
 void of all valid logical force, and can 'authorize no inference 
 whatever. Yet it is perfectly common for premises of this kind 
 to be employed, as the basis of the most important conclusions, 
 sometimes ignorantly, and sometimes intentionally. One of the 
 common forms of this fallacy is, to ask a question in which the 
 false judgment is tacitly assumed as known to be true, and so 
 asked, that the attention is diverted from this assumption. We 
 have, for example, seen individuals quite embarrassed by the 
 question, " Who was the father of Zebedee's children ?" Thus * 
 the Royal Society was imposed upon by the question, " How 
 shall the fact be accounted for, that a vessel of water receives 
 no addition to its weight when a live fish is put into it ?" At- 
 tention was thus directed, by the form of the question, from the 
 fact to its cause. The moment attention was directed from the 
 cause to the fact, the false assumption was corrected. The fal- 
 lacy under consideration is perhaps of most frequent occurrence 
 in this form : the laying down, as a premise, a universal propo- 
 sition, when only a particular one is allowable, and then de- 
 ducing the conclusion which the former would, if admitted, au- 
 thorize, instead of that authorized by the truly allowable one. 
 
DOCTEINE OF FALLACIES. 23? 
 
 Hume's celebrated argument against miracles is of this char- 
 acter. " It is contrary to experience," he says, " that the laws 
 of nature should be suspended, while it accords with experience 
 that testimony should prove false. Miracles, therefore, which 
 imply a suspension or violation of the laws of nature, cannot be 
 established by testimony." Now the minor premise being that 
 which affirms, that it accords with experience that testimony 
 -should prove false, is unallowable ; because its contradictory 
 to wit, some forms of testimony never prove false is an ascer- 
 tained and universally admitted truth. The Christian syllogism 
 upon the subject is this : some kinds of testimony never, as a 
 matter of fact, do prove false. The testimony which affirms the 
 truth of the miracles of the Bible is exclusively of this charac- 
 ter. The major premise of this syllogism none will dare deny. 
 Mr. Hume, then, in assuming the contradictory of this as true, 
 has laid down premises which prove nothing whatever. His 
 major premise, also, is unallowable for the very reason that the 
 minor is, and also contains the fault of begging the question at 
 issue. The real meaning of his major is this : it is contrary to 
 universal experience, that is, to the experience of all finite in- 
 telligences, that the laws of nature should be suspended. This, 
 to say the least, is not an ascertained truth, and therefore is 
 utterly void of all logical consequence till proven. The only 
 major that he was authorized to lay down, was, that it is con- 
 trary to the experience of some men, that the laws of nature 
 should be violated or suspended. In using the universal in- 
 stead of the particular, he has not only rendered his argument 
 utterly void of valid logical consequence, but has begged the 
 whole question at issue, to wit : Whether it does accord with 
 the experience of some individuals, that the laws of nature 
 should be suspended. 
 
 We might adduce other examples in illustration of the same 
 principles. These are sufficient, however, for illustration, and 
 by fixing attention upon the fact, that an unallowable premise 
 is void of all logical consequence, to induce, as we hope, the 
 habit, in examining processes of reasoning, of carefully examin- 
 ing the character and validity of the premises laid down. The 
 
above classes of fallacies, also, is commonly elucidated under the 
 title of undue assumption. 
 
 Leap in Logic. 
 
 What is called" a leap (saltus) in logic may as properly be 
 elucidated in this connection as in any other, as it falls, in fact, 
 to say the least, under the principle before us. Literally there 
 is a leap in logic, when the conclusion is conjoined with one 
 premise, and the other omitted. This may always be legiti- 
 mately done, when any person may readily supply the sup- 
 pressed premise, but not when this is not the case. The fallacy 
 which goes under the above title is this : A conclusion is con- 
 joined with a premise with which it has a very remote, and no 
 form of logical, connection at all, or with one authorizing no 
 conclusion of any kind. And all this under the assumption, 
 that the suppressed premise legitimizes said connection. The 
 passage across the chasm which really separates the expressed 
 premise and conclusion, assumed as logically resulting from it, 
 is called a leap (saltus), in logic. The dogma of the Romish 
 Church, that because Christ gave to Peter " the keys of the 
 kingdom of heaven," that therefore his assumed successor in 
 Rome holds the same, is a striking example of this form of fal- 
 lacy. The syllogism stated in full is this : The authority con- 
 ferred upon Peter vests in his assumed successor in Rome ; the 
 present pope is such successor ; therefore, the authority con- 
 ferred upon Peter vests in said pope. Any one can see, in a 
 moment, that the major premise here is totally void of all va- 
 lidity. There is not a shadow of evidence anywhere of its truth. 
 On the other hand, we have the most positive evidence of its 
 invalidity. The language of Christ to Peter is exclusively per- 
 gonal and applicable to him alone : " I give to thee the keys," 
 &c. ; " Whatsoever thou shalt bind on earth," &c. Where is 
 the foundation for the inference, that what was thus conferred 
 upon Peter vests in his assumed successor? We will give 
 another example of the fallacy before us an example from the 
 productions of modern infidelity : "Of the origin of the Booka 
 
DOCTRINE OF FALLACIES. 239 
 
 of Moses," says Prof. Robert Hare, of Philadelphia, " no higher 
 evidence exists, according to the testimony of the Bible itself, 
 than that of an obscure priest and a fanatical king." What 
 evidence is adduced by this author to sustain this broad and 
 sweeping assertion ? Simply the following statement found in 
 the 24th chap, of 2 Chronicles and the 22d of 2 Kings: "And 
 when they brought out the money that was brought into the 
 house of the Lord, Hilkiah the priest found a book of the law 
 of the Lord given by Moses," together with the subsequent 
 statement that "Hilkiah delivered the book to Shaphan," 
 " and Shaphan read it before the king ;" and finally, that the 
 king subsequently " read*to all the men of Judea and the in- 
 habitants of Jerusalem," &c, " all the words of the book of the 
 covenant that was found in the house of the Lord." After 
 citing the account given by Josephus of the same facts, an ac- 
 count identical, in all respects, with that given in the chapters 
 referred to, with the exception, that Josephus states what is not 
 affirmed in these chapters, nor implied in any of its statements, 
 that all of the " sacred Books of Moses" were found at that time, 
 our author makes the following statement : " If the Pentateuch 
 had been previously known to the Jews, it is incredible that it 
 could have become obsolete and forgotten prior to the alleged 
 discovery of it in the temple in the reign of Josiah." From 
 these simple statements the Professor deduces such conclusions 
 as the following : 1. The books here found were all the Books 
 of Moses. 2. These entire writings were, and had been, up 
 to that time wholly unknown to the whole Jewish nation. 
 3. Moses never wrote these books. 4. They are gross forgeries 
 palmed upon the nation and the world by this " obscure priest 
 and fanatical king," &o. Now what a leap in logic is here. 
 Not one of the conclusions has the remotest connection with 
 the facts adduced to prove them. For aught that appears in 
 the Bible, but one of the five books of Moses was then found ; 
 and for aught that appears or is implied in the facts stated, mul- 
 titudes of copies might have existed among the ten tribes then 
 in captivity, and even in Judea itself. The fact, that a copy of 
 these writings was found in this place, and that the king was 
 
240 LOGIC. 
 
 deeply moved by the parts subsequently read to him, affords 
 not the shadow of evidence that these writings were utterly un- 
 known to all the tribes of that nation, and that no other copies 
 then existed among them. Then the universal reception of 
 these writings, not only by the individuals of Judea, but also 
 by the hostile tribes then in captivity, shows clearly that these 
 writings could not have been unknown to the nation. 
 
 Proving too much. 
 
 Sometimes a premise is laid down with which the conclusion 
 sought has a necessary connection, but with which, also, a con- 
 clusion, known to be false, has a connection equally necessary. 
 In such a case the argument is said to prove too much, and in 
 doing so, to prove, not the conclusion sought to be established 
 by it, but its own utter invalidity as the basis of any valid con- 
 clusion whatever ; for a proposition connected by necessary an- 
 tecedence with a consequent known to be false, must itself be 
 false, and therefore utterly void of all valid logical consequence. 
 If, for example, an individual should adduce the infinity and 
 perfection of Deity, as proof of the non-perpetuity of moral and 
 physical evil in the universe, the proper reply would be, that 
 this argument proves too much, being equally conclusive against 
 the present as well as perpetual existence of these evils, while 
 their present existence is a known fact. That which now exists, 
 notwithstanding the attributes referred to, may, for aught that 
 can be deduced from the same, exist forever. 
 
 Inferring the falsity of the conclusion from that of thepremise, 
 or the truth of the premise from the truth of the conclusion. 
 
 As belonging to the same general class under consideration, 
 we now refer to the very common error of inferring the falsity 
 of the conclusion from that of the premise, and the truth of the 
 former from that of the latter. To prove a proposition false is, 
 as we have already shown, to show that it is, as a premise, void 
 of all valid logical consequence. We have not thereby touched 
 
DOCTRINE OF FALLACIES. 241 
 
 the question, whether the conclusion deduced from it is in itself 
 true or false, any more than we have determined the character 
 of the consequent in a conditional proposition, when we have 
 merely denied the antecedent. 
 
 So when we have admitted a conclusion deduced from certain 
 premises, and admitted it as true in itself, we have thus deter- 
 termined nothing whatever relatively to the truth or falsity of 
 the premise itself, any more than the admission of the conse- 
 quent determines the truth or falsity of the antecedent in a con- 
 ditional judgment. Yet no forms of fallacy are more common 
 than the two now under consideration, and from this fact two 
 evils of very great magnitifde arise to wit, that by unsound 
 arguments adduced in support of truth, truth itself is often be- 
 trayed into the hands of its enemies ; and that the most obvious 
 and important truths are so often defended by invalid argu- 
 ments. When the truth of any given doctrine or principle is 
 very obvious, its advocates are very apt to assume that any 
 form of argument for its truth must be valid, and for this rea- 
 son to defend it with very feeble and even unsound arguments ; 
 while the refutation of such arguments induces a doubt of the 
 truth itself. 
 
 Fallacy of References. 
 
 There is still another form of fallacy falling under the present 
 division of our subject, a fallacy quite common in theological 
 writings especially, that of references, which is set forth with 
 much distinctness by the following extract from Dr. Whately : 
 I It is, of course, a circumstance which adds great weight to any 
 assertion, that it shall seem to be supported by many passages 
 of Scripture ; now when a writer can find few or none of these 
 
 . that distinctly and decidedly favor his opinion, he may at least 
 find many which may be conceived capable of being so under- 
 stood, or which, in some way or other, remotely relate to the 
 subject ; but if these texts were inserted at length, it would be 
 
 I at once perceived how little they bear on the question : the 
 
 usual artifice, therefore, is, to give merely references to them, 
 
 11 
 
trusting that nineteen out of twenty readers, will never take the 
 trouble of turning to the passages, hut, taking for granted that 
 they afford, each, some degree of confirmation to what is main- 
 tained, will he overawed by seeing every assertion supported, 
 as they suppose, by five or six Scripture-texts." References 
 however numerous, it should be borne in mind, prove nothing 
 whatever unless they are to the point ; and if they are to the 
 point, one, as far as real proof is concerned, is as good as a 
 thousand. 
 
 Fallacies connected with the use of the Middle Term. 
 
 We now refer to another class of fallacies, which should be 
 treated of in the present connection those which arise from an 
 illogical use of the middle term. Among these we notice the 
 following classes : 
 
 1. The undistributed middle. Premises in which the middle 
 term is not distributed are, as we have before shown, void ut- 
 terly of all logical consequence. When any conclusion is de- 
 duced from such premises, it is deduced from premises which 
 authorize no conclusion whatever. 
 
 The form in which this fallacy most commonly appears, is 
 when the middle term, as the subject of a proposition really 
 particular, is used without any qualifying terms, which imply 
 distribution or non-distribution, and when, consequently, it will 
 be likely to be understood as distributed when it is not. For 
 example : 
 
 Food is necessary to life.; 
 
 This article is food ; 
 
 Therefore, it is necessary to life. 
 
 The fact of non-distribution is most likely not to be noticed, 
 when the fact stated is generally, though not universally, true 
 of the whole class referred to. 
 
 2. The ambiguous middle -This fallacy consists in employ- 
 ing as a middle term a word or phrase which has two significa- 
 tions, and employing it in one sense in one premise, and in 
 another in the other ; while in the conclusion the extremes, on 
 
DOCTKINE OF FALLACIES. 243 
 
 account of their relations to the middle, are affirmed to agree 
 or disagree with each other, as the case may be. In seme in- 
 stances the word or phrase may be ambiguous in itself. Thus 
 the term "know" sometimes means a mere intellectual appre- 
 hension, as in the Bible statement, "When they knew God, 
 they glorified him not as God ;" or such apprehension accom- 
 panied with a corresponding state of the heart or internal expe- 
 rience, as in the phrase, "And this is life eternal, that they 
 might know thee, the only true God, and Jesus Christ, whom 
 thou hast sent." A proposition might be true or false accord- 
 ing to the special sense in which it is employed in any given 
 case. If any such term is employed in one sense in one premise, 
 and in another in the other, then we have really two middle 
 terms instead of one, and the extremes are not at all compared 
 with the same thing. " It is worth observing," says Dr. Whate- 
 ly, "that the words whose ambiguity is 'the most frequently 
 overlooked, and is productive of the greatest amount of confu- 
 sion of thought and fallacy, are among the commonest, and are 
 those of whose meaning the generality consider there is the 
 least room to doubt. It is, indeed, from these very circum- 
 stances that the danger arises ; words in very common use are 
 both the most liable, from the looseness of ordinary discourse, 
 to slide from one sense into another, nwl also the least likely to 
 have that ambiguity suspected." 
 
 The middle term may also be ambiguous for J. 3 reason thut 
 it is employed in one premise distributive^, ixnii m th-, other 
 collectively. This is called the fallacy of divisor vtuk 'ytznpo** 
 tion. For example : 
 
 Five is one number ; 
 Three and two are five ; 
 .. Three and two are one number. 
 
 Three and two are two numbers ; 
 Five is three and two ; 
 .. Five is two numbers. 
 
 The first of the above examples belongs to what is called 
 "fallacy of division," and the second to those of composition. 
 
Any one will perceive, on reflection, that in the second premise 
 of the first example, the phrase " three and two" is taken col- 
 lectively, and means, that taken together, these numbers are 
 equal in quantil y to the number five ; while in the conclusion 
 the same phrase is taken distributively, the meaning being, that 
 " three and two," -as an inferior, rank under the superior con- 
 ception represented by the words " one number." Similar re- 
 marks are applicable to the second example. 
 
 This form of fallacy is so well elucidated by Dr. Whately, 
 that we will conclude what we have to say upon it with the fol- 
 lowing lengthy extract from him : 
 
 " To this head may be referred the fallacy by which men 
 have sometimes been led to admit, or pretend to admit, the 
 doctrine of necessity : e. g. ' he who necessarily goes or staya 
 (i. e. in reality, ' who necessarily goes or who necessarily stays') 
 is not a free agent ; you must necessarily go or stay (i. e. ' you 
 must necessarily take the alternative'') ; therefore, you are not a 
 free agent.' Such, also, is the fallacy which probably operates 
 on most adventurers in lotteries : e. g. ' the gaining of a high 
 prize is no uncommon occurrence ; and what is no uncommon 
 occurrence may reasonably be expected ; therefore, the gaining 
 of a high prize may reasonably be expected :' the conclusion, 
 when applied to the individual (as in practice it is), must be un- 
 derstood in the sense of ' reasonably expected by a certain indi- 
 vidual /' therefore, for the major premise to be true, the mid- 
 dle term must be understood to mean, ' no uncommon occur- 
 rence to some one particular person ;' whereas for the mmor 
 (which has been placed first) to be true, you must understand 
 it of 'no uncommon occurrence to some one or other f and 
 thus you will have the fallacy of composition." 
 
 There is no fallacy more common, or more likely to deceive, 
 than the one now before us ; the form in which it is most usual- 
 ly employed is, to establish some truth separately concerning 
 each single member of a certain class, and thence to infer the 
 same of the whole collectively : thus some infidels have labored 
 to prove concerning some one of our Lord's miracles, that it 
 niight have been the result of an accidental conjunction of natu- 
 
DOCTRINE OF FALLACIES. 245 
 
 ral circumstances ; next they endeavor to prove the same con- 
 cerning another and so on ; and thence infer that all of them 
 might have been so. They might argue, in like manner, that 
 because it is not very improbable one may throw sixes in any 
 one out of a hundred throws, therefore it is no more improba- 
 ble that one may throw sixes a hundred times running. 
 
 This fallacy may often be considered as turning on the ambi- 
 guity of the word " all ;" which may easily be dispelled by sub- 
 stituting for it the word " each" or " every," where that is its 
 signification : e. g. " All these trees make a thick shade," is 
 ambiguous, meaning, either " every one of them," or " all to- 
 gether." 
 
 This is a fallacy with which men are extremely apt to deceive 
 themselves ; for when a multitude of particulars are presented 
 to the mind, many are too weak or too indolent to take a com- 
 prehensive view of them ; but confine their attention to each 
 single point by turns ; and then decide, infer, and act, accord- 
 ingly : e. g. " The imprudent spendthrift, finding that he is able 
 to afford this, or that, or the other, expense, forgets that all of 
 them togetJier will ruin him." 
 
 To the same head may be reduced that fallacious reasoning, 
 by which men vindicate themselves to their own conscience 
 and to others, for the neglect of those undefined duties, which, 
 though indispensable, and therefore not left to our choice 
 whether we will practise them or not, are to our discretion as 
 to the mode and the particular occasions of practising them : 
 e. g. " I am not bound to contribute to this charity in particu- 
 lar ; nor to that ; nor to the other." The practical conclusion 
 which they draw is, that all charity may be dispensed with. 
 
 As men are apt to forget that any two circumstances (not 
 , naturally connected) are more rarely to be met with combined 
 than separate, though they be not at all incompatible ; so also 
 they are apt to imagine, from finding that they are rarely com- 
 bined, that there is an incompatibility : e. g. " If the chances 
 are ten to one against a man's possessing strong reasoning 
 powers, and ten to one against exquisite taste, the chances 
 against the combination of the two (supposing them neither 
 
246 LOGIC. 
 
 connected nor opposed) will be a h mdred to one." Many, 
 therefore, from finding them so rarely united, will infer that 
 they are in some measure incompatible ; which fallacy may 
 easily be exposed in the form of the undistributed middle : 
 " Qualities unfriendly to each other are rarely combined ; ex- 
 cellence in the reasoning powers and in taste are rarely com- 
 bined ; therefore, they are qualities unfriendly to each other." 
 
 The argument for the Divine Infinity drawn from the mere 
 extent of creation, is a very striking example of this form of fal- 
 lacy. It is self-evident, that the element of real infinity in the 
 cause cannot be logically deduced from the mere element of 
 extent in the effect, when that effect, however vast, is known 
 to be of finite or limited extent. Nothing can endanger the 
 ultimate effect of the theistic argument so much as to base such 
 a conclusion upon such premises. Equally fatal and fallacious 
 is the assumption, that if this element in creation does not afford 
 a basis for such a conclusion, none other does exist. To us it is, 
 d priori, certain, that if God has penciled out the evidence of 
 his own absolute infinity and perfection somewhere upon the 
 works of his hands, and no one will say that he cannot do it, 
 and has not done it, those pencillings are to be found, not in 
 the combinations of matter, but in the laws, principles, and sus- 
 ceptibilities of that which is created in the Divine image ; and 
 here, Ave affirm, those pencillings are found. This, however, is 
 not the place to present the proof of this statement. 
 
 3. Fallacy of accidents Fallacia accidentia. The fallacy 
 which next claims our attention as connected with the middle 
 term, is denominated " the fallacy of accidents," and consists in 
 employing the middle term in one premise to represent some- 
 thing considered in itself as to its real essence exclusively, and 
 in the other to represent this in connection with its accidents of 
 time, place, or changes, &c. The well-known example, " What ' 
 is bought in the market is eaten ; raw meat is bought in the 
 market ; therefore, raw meat is eaten," is commonly given in 
 illustration of this fallacy, and well illustrates it. 
 
 4. Akin to the above is the " fallacy of quid," which consists 
 in employing the middle term in its widest acceptation in one 
 
DOCTRINE OF FALLACIES. 247 
 
 premise, and in reference to its special applications in the other. 
 Thus the term " innocent" may be employed to signify univer- 
 sal freedom from moral faults of any kind, or freedom from 
 some particular fault with which an individual stands charged 
 at some particular time. Suppose that in the two premises of a 
 given syllogism, this term is employed in these two distinct and 
 opposite senses. We should then have an example of the fal- 
 lacy of very frequent occurrence. 
 
 CONDITIONAL SYLLOGISMS WHOSE CONDITIONAL PREMISES ARE 
 VOID OF LOGICAL CONSEQUENCE. 
 
 One of the most common forms of fallacy falling under the 
 class we are now considering is, the employment of that form 
 of the conditional syllogism in which the conditional premise is 
 void of all logical consequence. The validity of the conditional 
 syllogism is conditioned wholly upon the relation of necessary 
 consequence between the antecedent and consequent in the ma- 
 jor premise. Where this relation does not obtain, this premise 
 is wholly void of all logical consequence, and the conclusion 
 resting upon it is without any valid foundation. Take as an 
 illustration the common example : " If Cromwell was an Eng- 
 lishman he was a usurper ; he was an Englishman ; therefore, 
 he was a usurper." When we examine the hypothetical 
 premise in this case, we find that there is no relation what- 
 ever of logical consequence between the antecedent and con- 
 sequent. The premises, therefore, prove nothing. In such a 
 palpable case no one would be deceived by the argument pre- 
 sented. Cases, however, often occur in which the error is less 
 likely to be detected, than in almost any other instances of fal- 
 lacious reasoning. Suppose that an individual has a bad cause 
 to advocate. He commences by saying that " if he succeeds 
 in establishing such and such propositions, every one will grant 
 that he has proven the conclusion which he was called upon to 
 establish." In such circumstances, the attention of the listener 
 is very likely to be turned from a consideration of the relation 
 of consequence between the antecedent and consequent, to 
 
that of fact ; that is, whether the individual does, or does not, 
 prove the propositions referred to. If, in addition to this, he 
 can induce his opponent to join issue with him, not in reference 
 to the relation referred to, hut in respect simply to the question 
 of fact, then the fallacy is almost certain not to he detected. 
 
 How often do individuals, in replying to a sophistical argu- 
 ment, err here. They do not turn attention to the want of 
 logical consequence under consideration, hut join issue relative- 
 ly to the question of fact, the very point prohably where the 
 sophist is the strongest, and where, if the position he claims 
 should be granted, it is perfectly impossible to show that the 
 conclusion he deduces is not reached. 
 
 DISJUNCTIVE SYLLOGISMS WHOSE DISJUNCTIVE PREMISES ARE 
 VOID OF LOGICAL CONSEQUENCE. 
 
 Similar fallacies are often connected with the disjunctive syl- 
 logism. The disjunctive premise, to be valid, must, as we have 
 seen, embrace all conceivable or possible hypotheses falling, 
 within the sphere of the disjunction ; else it is void of conse- 
 quence. Suppose, for example, we have the following disjunc- 
 tive syllogism : 
 
 A is in B, C, D, or E ; 
 It is not in B, C, or D ; 
 .-. It is in E. 
 
 All that is requisite to annihilate totally the validity of this ar- 
 gument, is to show that A may be in F instead of E. In that 
 case, when we grant the truth of the minor premise, we do not 
 grant that of the conclusion. 
 
 We will give an example of the fallacy of which we are 
 speaking. It is found in the celebrated statement of Kant rela- 
 tively to the possible proofs of the being of God. We will give 
 the statement in the words of the author himself : 
 
 " There cannot be but three sorts of proof of the existence of 
 God from speculative reason : The physico-theological, in which 
 we begin with the determinate experience, and the thereby 
 known peculiar quality of our sensible world, and mount from 
 
DOCTRINE OF FALLACIES. 249 
 
 it, according to laws of causation, to the very Supreme Cause 
 out of the world ; the cosmological, in which we lay indetermi- 
 nate experience only, that is, any one existence empirically as a 
 ground ; and the ontological, in which we abstract from all ex- 
 perience, and from mere conceptions infer the existence of a 
 Supreme Cause quite d priori." 
 
 "The cosmological proof," in the language of the author 
 himself, " runs thus : If something exists, an absolutely neces- 
 sary being must exist ; now I, at least, exist myself; therefore, 
 an absolutely necessary being exists." In reply to this argu- 
 ment it is enough to say, that it determines nothing specific in 
 regard to the character of this necessary being, and is thus void 
 of logical validity when adduced as proof of the existence of 
 God, that is, of a necessary being of absolute infinity and per- 
 fection. 
 
 The ontological argument concludes from the fact, that there 
 is in the human mind the conception of such a being, that such 
 a being exists. This argument fails for this reason that it is 
 really based upon the assumption, that the existence in the in- 
 telligence of a conception is proof of the existence of a corre- 
 sponding object, which is by no means true. The argument, 
 therefore, is invalid. 
 
 " The main points of the physico-theological proof," in the 
 language of our author, "are as follows : 1. Everywhere in the 
 w r orld there are distinct marks of an arrangement according to 
 a determinate design executed with great wisdom, and in a 
 whole of indescribable variety, as well as of unbounded great- 
 ness of sphere. 2. This arrangement, so answerable to the end, 
 is quite foreign to the things of the world, and adheres to them 
 fortuitously only ; that is, the nature of the different things 
 could not agree of its own accord in determinate designs by so 
 various uniting means, were it not chosen and disposed for that 
 purpose entirely by a rational Principle ordering it according 
 to ideas laid as a foundation. 3. Therefore there exists a sub- 
 lime and a wise Cause (or more of them), which must be that 
 of the world, not only as blind, working all-powerful nature by 
 fertility, but as an Intelligence, by liberty. 4. This Cause's 
 
250 LOGIC. 
 
 unity may be inferred, from the unity of the reciprocal reference 
 of the parts of the world, as members of an artificial structure, 
 in that to which our observation reaches, Avith certainty, but 
 further, on all the principles of analogy, with probability." 
 
 To this argument Kant replies, that admitting its validity, as 
 far as it goes, there is an infinite chasm between the inference 
 which it does yield and the conclusion demanded by theism, to 
 wit, that the Cause under consideration is a being of absolute 
 infinity and perfection. The universe being finite in extent, 
 cannot, by its extent, give proof of the actual infinity of its 
 author. An argument Avhich falls short of proving the being 
 of God as infinite and perfect, fails wholly to prove the being of 
 God. Thus it is that each of the only possible arguments for 
 the being of God fails of its end, and we are left without such 
 proof. The real syllogism of Kant may be thus presented : 
 
 The proof of the being and perfections of God is found in one 
 of the three forms of argument above named, or we have no 
 such proof. That proof is not contained in these arguments. 
 Therefore, we have no logically valid proof of the Divine exist- 
 ence. In reply, we remark, that the above argument, even 
 as presented by Kant himself, does afford the following valid 
 conclusions: 1. The actual existence of a necessary being of 
 some character. 2. This being is a free, intelligent, self-con- 
 scious personality, endowed with attributes inconceivably great, 
 sublime, and incomprehensible. 3. There is the total absence 
 of all evidence, that this being is not infinite and perfect. The 
 error of Kant consists in the assumption, that no form of evi- 
 dence exists of the infinity and perfection of this Being, whose 
 existence is thus demonstrated, but what is yielded by the mere 
 extent of creation. We say that it is not, d priori, certain that 
 God cannot, and has not, in a creation of finite extent, pencilled - 
 out absolute indications of his own infinity and perfection. 
 There may be other elements of proof bearing upon this sub- 
 ject than that of mere extent in creation. The laws of mind 
 may yield absolute proof of the absolute infinity and perfection 
 of this Being. No one can affirm, d priori, that this is not the 
 case. Kant decides wholly, d prioi'i, that all the proof bear- 
 
DOCTRINE OF FALLACIES. 251 
 
 ing upon this question is found in the three forms of argument 
 which he has presented. We reply, that there may he another 
 source of proof of equal validity, which this author has wholly 
 omitted. His syllogism, therefore, is utterly void of logical va- 
 lidity. 
 
 FALLACIES ARISING FEOM THE USE OF INVALID DILEMMAS. 
 
 The nature, appropriate sphere, and use of the dilemma have 
 been fully set forth in the Analytic. We would simply allude, 
 in this connection, to certain quite common fallacies which arise 
 from the use of invalid syllogisms of this character. 
 
 One of the most common forms is this : An individual, wish- 
 ing to embarrass an opponent, puts a question and demands a 
 direct categorical answer to it in this form yes or no. The 
 question answered in this form, may appear, at least, whichever 
 answer is returned, to involve the respondent in palpable con- 
 tradiction. At the same time, if the question is answered with 
 needful explanations, this difficulty will wholly disappear. The 
 questioner denies the right of explanation, and insists upon the 
 specific form of answer referred to. Now, in such cases, a di- 
 lemma with no real horns is presented, while the presentation 
 of it reveals the dishonesty of the questioner and nothing else. 
 The question put to our Saviour, " Is it lawful to give tribute 
 to Csesar, or not ? shall we give, or shall we not give ?" is of 
 this character. Answered with appropriate explanations, the 
 difficulty wholly disappeared. 
 
 Another form of this fallacy consists in presenting a case as 
 admitting of but one of two answers, when, in fact, other hy- 
 potheses are equally supposable. Thus the question of the Sad- 
 ducees to our Saviour, pertaining to the resurrection, assumed 
 that the doctrine of the resurrection is not true, or individuals 
 are, in that state, " married and given in marriage," and that 
 those who have been married here must continue in that rela- 
 tion there. The case was relieved at once of all difficulty by 
 the revelation of the false assumption named, in respect to the 
 state to which the spirit is raised in the resurrection. 
 
252 logic. 
 
 A dilemma, to be valid, must have these characteristics : 
 1. The case presented must have a necessary connection with 
 the circumstances to which it is referred. 2. It must present 
 the only possible hypotheses permitted by the circumstances. 
 3. The individual pushed by the presentation must be necessi- 
 tated to adopt one or the other of the hypotheses presented 
 as true. 4. Each alike must be fatal to his cause. Of this 
 character is the dilemma presented by Demosthenes, so often 
 cited. Any case not possessed of all these characteristics, is 
 a dilemma without horns, that is, an argument which proves 
 nothing at all. 
 
 CONCLUSIONS BASED UPON FALSE ANALOGIES. 
 
 We have already given the principles in conformity to 
 which alone the argument from analogy has force. Conclusions 
 based upon resemblances void of these characteristics, rest 
 upon premises Avhich of course prove nothing. Now this is 
 one of the most common forms of fallacy to be met with the 
 assumption that cases are analogous when they are not. We 
 give the following example and refutation of a false analogy, 
 from Bishop Butler : 
 
 " There is little presumption that death is the destruction of 
 human creatures. However there is the shadow of an analogy, 
 which may lead us to imagine it is the supposed likeness which 
 is observed between the decay of vegetables and of living crea- 
 tures. And this likeness is, indeed, sufficient to afford the poets 
 very apt allusions to the flowers of the field, in their pictures of 
 the frailty of our present life. But, in reason, the analogy is so 
 far from holding, that there appears no ground even for the 
 comparison as to the present question, because one of the two 
 subjects compared is wholly void of that which is the principal 
 and chief thing in the other, the power of perception and of ac- 
 tion ; and which is the only thing we are inquiring about the 
 continuance of. So that the destruction of a vegetable is an 
 event not similar or analogous to the destruction of a living 
 agent." 
 
DOCTRINE OF FALLACIES. 253 
 
 " This may be resolved," says Mr. Thomson, " into two syl- 
 logisms : 
 
 I. Analogy in AUA, Fig. III. 
 The decay of vegetables is total destruction ; 
 
 The decay of vegetables = (for present purposes) the decay of living crea- 
 tures ; 
 Therefore, the decay of living creatures is total destruction. 
 
 II. Refutation. 
 The decay of animals is that of living, acting creatures ; 
 The decay of vegetables is not that of living, acting creatures ; 
 Therefore, the decay of vegetables is not the same as that of animals. 
 
 The conclusion E of the latter syllogism, is opposed as a contra- 
 ry to the premise U of the former." 
 
 The reader will notice, on reflecting upon the previous exam- 
 ples and illustrations, that there are two kinds of premises 
 which lead to no valid conclusions whatever : those which, if 
 admitted, authorize no conclusions of any kind, such as two 
 negative or particular premises, and where there is an undis- 
 tributed middle, &c. ; and those in which one or both of the 
 premises are themselves unduly assumed. Both classes of 
 premises, though for somewhat different reasons, are equally 
 void of all consequence as far as valid conclusions are con- 
 cerned. 
 
 Section II. Conclusions deduced from Premises which 
 
 COME SHORT OF PROVING SAID CONCLUSIONS. 
 
 All are aware that conclusions are often deduced from prem- 
 ises which have some bearing upon said conclusions, but which 
 fail utterly to prove them in full. This class of fallacies next 
 claims our attention, among which we notice the following : 
 
 Drawing a universal conclusion, where only a particular is 
 allowable. 
 One of the most common fallacies of this class is the assump- 
 tion of a universal conclusion, when only a particular one is 
 
allowed by the premises. Suppose that it becomes known, or 
 has been proven, that certain individuals of a certain class have 
 some particular characteristic. Almost nothing is more com- 
 mon than to draw from hence the conclusion, that the same 
 characteristic pertains to the entire class. Individuals are most 
 likely to be deceived by such a course of reasoning when the 
 cases cited are quite numerous. What is shown to be general- 
 ly true, is very readily assumed to be universally so. In such 
 circumstances we should be, in a very special manner, on our 
 guard. 
 
 Proving a part of a conclusion and then assuming the whole 
 as established. 
 
 When the proposition to be proved is made up of several 
 parts, and some of these have been proved or disproved, a skil- 
 ful sophist, by greatly enlarging upon these, will assume, and 
 often induce others to do the same, that all the parts have been 
 proved or disproved, when the main issue has not been touched 
 at all. 
 
 " This," says Dr. Whately, " is the great art of the answerer 
 of a book ; suppose the main positions in any work to be irre- 
 fragable, it will be strange if some illustration of them, or some 
 subordinate part, in short, will not admit of a plausible objec- 
 tion ; the opponent then joins issue on one of these incidental 
 questions, and comes forward with ' a reply' to such and such a 
 work. 
 
 " Hence the danger of ever advancing more than can be well 
 maintained, since the refutation of that will often quash the 
 whole ; a guilty person may often escape by having too much 
 laid to his charge ; so he may also by having too much evi- 
 dence against him, i. e. some that is not in itself satisfactory ; 
 thus, a prisoner may sometimes obtain acquittal by showing 
 that one of the witnesses against him is an informer and spy ; 
 though perhaps if that part of the evidence had been omitted, 
 the rest would have been sufficient for conviction.'' 
 
l yv 
 
 DOCTEIKE OF FALLACIES. 255 
 
 Fallacy of Objections. 
 
 Fallacy of objections, which next claims our attention, con- 
 sists, in the language of Dr. Whately, in " showing that there 
 are objections against some plan, theory, or system, and thence 
 inferring that it should be rejected ; when that which ought to 
 have been proved is, that there are more or stronger objections 
 against the receiving than the rejecting it. This is the main 
 and almost universal fallacy of infidels, and is that of which 
 men should be first and principally warned. This is also the 
 stronghold of bigoted anti-innovators, who oppose all reforms 
 and alterations indiscriminately ; for there never was, nor will 
 be, any plan executed or proposed against which strong and 
 even unanswerable objections may not be urged ; so that, un- 
 less the opposite objections be set in the balance on the other 
 side, we can never advance a step. ' There are objections,' 
 said Dr. Johnson, ' against a plenum, and objections against a 
 vacuum / but one of them must be true.' 
 
 " The very same fallacy, indeed, is employed on the other 
 side, by those who are for overthrowing whatever is established 
 as soon as they can prove an objection against it, without con- 
 sidering whether more and weightier objections may not lie 
 against their own schemes ; but their opponents have this de- 
 cided advantage over thejn, that they can urge with great plau- 
 sibility, ' we do not call upon you to reject at once whatever is 
 objected to, but merely to suspend your judgment, and not 
 come to a decision as long as there are reasons on both sides ;' 
 now, since there always will be reasons on both sides, this non- 
 decision is practically the very same thing as a decision in fa- 
 vor of the existing state of things ; the delay of trial becomes 
 equivalent to an acquittals 
 
 The object sought to be established in processes of reasoning 
 is, in some instances, not the positive but probable. When the 
 latter is the character of the conclusion sought, a fallacy of this 
 
256 LOGIC. 
 
 kind often appears, to wit : when one degree and form of proba- 
 bilities is proven, another is assumed as established. To under- 
 stand this subject we would remark, that probabilities are of 
 two kinds ; one is, where a number of propositions sustain such 
 relations to a given one, that if any of them is true, the one 
 referred to either is or is not probably true, while each of these 
 propositions has a certain independent degree of probability of 
 being true, as one to two, for example. Suppose that the num- 
 ber of such propositions is six ; then, supposing the connection 
 above-named to be certain, the probability of the common con- 
 sequent of said proposition being true is as six to one. If the 
 connection is only a probable one, say as one to two, then the 
 probability under consideration is as three to one. Probabili- 
 ties of this character may be so multiplied as to exclude all rea- 
 sonable doubt. 
 
 The second form of probability arises, when each probability 
 depends upon another, and so on to the last, somewhat in the 
 form of a sorites ; as, A is probably B, B is probably C, &c. ; 
 therefore, A is probably C. Let us suppose that the ratio of 
 probability in each is as above, as one to two. In this case the 
 probability that A is C is only as one to sixteen. In this case, 
 too, when the series of probabilities is very long, all reasonable 
 expectation that the proposition referred to can be true is ex- 
 cluded. 
 
 Now the fallacy to which we refer consists in confounding 
 these two kinds of probability, and assuming one as proven, 
 when the other only has been. Suppose, for example, there is 
 an attempt to prove a proposition sustained by probabilities of 
 the first class. An opponent, in replying, may dilate on the 
 uncertainty of probable evidence, drawing all his examples 
 from the second class, and yet so presenting them, that the 
 characteristics of the two shall be confounded in the hearer's or 
 reader's mind, and thus the force of the evidence destroyed. 
 Suppose, on the other hand, an individual desires to prove a 
 proposition sustained exclusively by probabilities of the second 
 class. He will, of course, dilate upon the safety of resting upon 
 probable evidence, showing how all the transactions of life have 
 
DOCTRINE OP FALLACIES. 257 
 
 no other foundation, taking his examples and illustrations from 
 the first class, keeping out of view, as far as possible, the nature 
 of the probabilities with which he has to do. Nothing is more 
 important in judging of such arguments, than to keep distinct- 
 ly in mind the diverse and opposite character of these two kinds 
 of probability, and to mark clearly the special kind which en- 
 ters into the process which is the subject of investigation. 
 
 Section III. Conclusions deduced from Premises which 
 
 PROVE NOT THOSE REALTY SOUGHT TO BE PROVED, BUT CER- 
 TAIN OTHER AND IRRELEVANT ONES. 
 
 The only remaining topic of remark is that class of fallacies 
 in which false inferences are deduced from premises which 
 prove, not the conclusion really sought, but something else 
 which is irrelevant. Under this head we have two classes of 
 irrelevant conclusions, those in which the conclusion sought is 
 inferred from premises which prove, not said conclusions, but 
 something else ; and those in which something assumed as the 
 real conclusion sought, but which is not, is proved or attempted 
 to be. 
 
 Ignoratio elenchi, or Irrelevant Conclusion. 
 
 Fallacies of the second class named constitute especially what 
 is commonly called the ignoratio elenchi, or irrelevant conclu- 
 sion, a fallacy which consists in a proof, or an attempted one, 
 of a certain proposition assumed to be the real one, when it is 
 not. The example commonly adduced in illustration of this 
 kind of fallacy is given by Dr. Whately in the following lan- 
 guage : " A good instance of the* employment and exposure of 
 this fallacy occurs in Thucydides, in the speeches of Cleon and 
 Diodotus concerning the Mitylenoeans ; the former (over and 
 above his appeal to the angry passions of his audience) urges 
 the justice of putting the revolters to death ; which, as the lat- 
 ter remarked, was nothing to the purpose, since the Athenians 
 
w 
 
 
 G aM^ 
 
 258 logic. 
 
 were not sitting in judgment, but in deliberation, of which the 
 proper end is expediency." 
 
 When we were studying theology, a very distinguished and 
 celebrated professor of that science delivered to us a course of 
 lectures first, on the doctrine of necessity and the Divine sov- 
 ereignty ; and then, on the question of man's freedom and ac- 
 countability for his actions and mental states. These two ques- 
 tions were" discussed separately, and professedly settled by en- 
 tirely independent trains of argumentation. Finally, the ques- 
 tion, How can these doctrines be reconciled ? was propounded 
 for discussion, and was actually disposed of thus : " We have 
 proved," said the learned professor, " that these two great doc- 
 trines are each true, that is, they do both exist, as a matter of 
 fact ; that is, they exist together ; that is, they coexist ; that is, 
 they cosist ; that is, they consist or are consistent." 
 
 This was overwhelmingly convincing to a majority of the au- 
 dience. Who does not perceive, however, 1. That in this de- 
 partment of investigation, the question of consistency in the 
 sense of real compatibility, and not consistency, in the sense 
 of coexistence, was the question to be settled ; and, 2. That, 
 as two incompatible propositions can, by no force of argumen- 
 tation, be both proved to be true, any more than we can prove 
 that the same thing can at the same time exist and not exist, 
 when the question of compatibility is raised, all arguments to 
 prove both true must be held as invalid, till this one is settled. 
 Here, then, was a very striking example of the ignoratio elenchi. 
 
 As this is a very important department of inquiry, we will 
 venture to give another example from a very important and 
 valuable work oh "Systematic Theology," a work originally 
 put forth in this country, and then, with many corrections and 
 enlargements, republished in England, by my former most 
 highly esteemed and beloved associate, President C. G. Finney. 
 In each edition of this work, the question as to the foundation 
 of obligation is discussed at great length. In the first, frequent 
 quotations are made from lectures of mine which were printed 
 for the accommodation of students, but not published quota- 
 tions, without giving names or references. As the source, how- 
 
DOCTRINE OF FALLACIES. 259 
 
 ever, was known, my views were being presented in a form in 
 which I clearly saw they would be, and were being, misunder- 
 stood. This occasioned, when my work on moral philosophy 
 was published, a full examination of the question in respect to 
 which President Finney's and my own investigations had led 
 us to adopt different and opposite views upon the subject. To 
 accomplish this object I first gave a distinct statement of the 
 . two theories, his and my own, with their points 01 agreement 
 and disagreement. I will give the statement of the two theo- 
 ries as found in this chapter : I do it for two reasons the turn- 
 ing of thought to an important question in morals, and as an 
 example of the manner in which, when conflicting views are to 
 be discussed, the questions at issue should be presented. 
 
 " President Finney'' s Statement. 
 
 To attain the object in view, the first thing to be done is to 
 ascertain clearly what this theory is, as distinguished from that 
 maintained in this treatise. Professor Finney fully agrees with 
 myself in rejecting the doctrine of utility. ' The teachings of 
 a consistent utilitarian,' he says, 'must of necessity abound 
 ' with pernicious error.' Again : ' Consistent utilitarianism in- 
 culcates fundamentally false ideas of the nature of virtue.' Of 
 course, he will agree with me in the statement made in the last 
 chapter, that any theory (his own not excepted) that, in its 
 logical consequences, necessarily lands us hi this doctrine, must 
 be false. What then is this theory ? 
 
 1. He maintains that the only ultimate reason in view of 
 which obligation is ever affirmed, is happiness as a good in itself. 
 * It is, then, the intrinsic and infinite value,' he says, ' of the 
 highest good of God and of the universe, that constitutes the 
 true foundation of moral obligation.' 
 
 2. He maintains that obligation in no form or degree is ever 
 affirmed in view of what is perceived to be intrinsic in moral 
 character, holiness or sin, virtue or vice, merit or demerit. 
 None of these contain any ultimate reason for any acts of will 
 whatever. ' The highest well-being of God and of the universe 
 
260 LOGIC. 
 
 of sentient creatures is the end on which preference, choice, in- 
 tention, ought to terminate.' 
 
 3. Holiness or sin, moral character, &c, are esteemed by the 
 mind for no other reason than as a condition or a means of 
 happiness. 
 
 ' Obedience must be a means or condition, and that which 
 law and obedience are intended to secure is, and must be, 
 the ultimate end of obedience. The law or the lawgiver aims 
 to promote the highest good or blessedness of the universe. 
 This must be the end of moral law and moral government. 
 Law and obedience must be the means or conditions of this 
 end. It is absurd to deny this.' 
 
 Again, speaking of virtue, moral worth, &c, he says : 
 
 1 Were it not for the fact, that it meets a demand of the in- 
 telligence and thus produces satisfaction, it could not so much 
 as be thought of as a good in itself, any more than any thing 
 else that is a pure conception of the reason, such, for instance, 
 as a mathematical line.' Further on, he adds : 
 
 ' The willing and the worthiness of willing are valuable 
 only as the end willed is valuable. Were it not that the end is 
 intrinsically valuable, the willing would not be so much as 
 relatively valuable. It would have no value whatever.' 
 
 4. The intelligence does not require ultimate intentions, in 
 other words, does not affirm obligation in respect to them, as a 
 condition or a means of happiness is a good in itself. This sen- 
 timent is often repeated in the work before us. A single quota- 
 tion, however, is all that is necessary to show that I have right- 
 ly expounded the view therein set forth on this point : 
 
 ' Ultimate intention is right or wrong in itself, and no ques- 
 tions of utility, expediency, or tendency have any thing to do 
 with the obligation to put forth ultimate intention, there being 
 only one reason for this, namely, the intrinsic value of the end 
 to be intended. It is true that whatever is expedient is right, 
 not for that reason, but only upon that condition. The inquiry, 
 then, Is it expedient ? in respect to outward action is always 
 proper ; for upon this condition does obligation to outward ac- 
 tion turn. But in respect to ultimate intention or the choice of 
 
DOCTRINE OF FALLACIES. 261 
 
 an ultimate end, an inquiry into the expediency of this choice 
 or intention is never proper, the obligation being founded alone 
 upon the perceived and intrinsic value of the end, and the obli- 
 gation being without any condition whatever, except the pos- 
 session of the powers of moral agency with the perception of 
 the end upon which intention ought to terminate, namely, the 
 good of universal being.' 
 
 5. While obligation to put forth ultimate intentions is in no 
 sense conditioned upon their perceived tendency to promote 
 happiness, the necessary condition of obligation to put forth 
 executive volitions and outward actions is their perceived ten- 
 dency to promote happiness. ' I said, in a former lecture, that 
 the obligation to put forth volitions or outward actions to se- 
 cure an end must be conditioned upon the perceived tendency 
 of such volitions and actions to secure that end ; but while this 
 tendency is the condition of the obligation to executive volition 
 or outward action, the obligation is founded upon the intrinsic 
 value of the end, to secure which such volitions tend.' 
 
 The Opposite Theory stated. 
 
 Such is the doctrine set forth in the treatise on Systematic 
 Theology. Let us now attend to a statement of the opposite 
 theory : 
 
 1. The advocates of this theory agree with Professor Finney 
 in the doctrine, that the good of being is an ultimate reason for 
 ultimate intentions of a certain class, to wit, all intentions in- 
 cluded in the words willing the good of being. 
 
 2. On the other hand, they affirm, that there are other ob- 
 jects, such as virtue and sin, moral character, moral desert, fcc., 
 which contain ultimate reasons for certain acts of will or ulti- 
 mate intentions, besides happiness as a good in itself. Here, 
 and here only, is there a difference of opinion. The doctrine 
 maintained by this class of philosophers may be thus stated : 
 Whenever an object is present to the mind, which, on account 
 of what is intrinsic in the object itself, necessitates the will to 
 act, two or more distinct and opposite acts are always possible 
 
262 logic. 
 
 relatively to such object. The intelligence can never be indif- 
 ferent in respect to the acts or intentions put forth under such 
 circumstances. In its judgment that act, and that act only, can 
 be right which corresponds with the apprehended intrinsic char- 
 acter of the object. All other acts must be wrong. The sphere 
 of moral obligation must be as extensive as the objects the ap- 
 prehension of which intrinsically necessitate acts of will of some 
 kind, and relatively to which distinct and opposite acts are pos- 
 sible. According to Professor Finney, there is but one object 
 in existence the apprehension of which intrinsically necessitates 
 acts of will, to wit, the good of being. According to this class 
 of philosophers, there are other objects aside from this, the ap- 
 prehension of which also necessitates acts of will, and relatively 
 to which, therefore, obligation does and must pertain. We are 
 now prepared for a distinct statement of the arguments which 
 he against the theory of Professor Finney, and in favor of the 
 opposite theory," 
 
 I then, in ten distinct arguments and nine general state- 
 ments, argue the single issue here presented. In the English 
 edition of his great work, President Finney gives a professed 
 reply to this presentation. "What is that reply ? No correc- 
 tions are offered of my statements of the two theories, and the 
 issue presented. All here is thus admitted to be correct. I am 
 equally safe in saying, that not one of my arguments has been 
 met, and to but very few of them is there even a remote allu- 
 sion. On the other hand, I am held before the people of Eng- 
 land as asserting, in different parts of my works, some half a 
 dozen or more distinct and opposite theories pertaining to the 
 foundation of obligation. In no instance is my language cited. 
 On the other hand, a bear reference is made to the work. Had 
 he given quotations in full, the people of England would have 
 seen, not that I have asserted these contradictory theories: for 
 I have done no such thing but that my deeply-respected asso- 
 ciate has most honestly, without a shadow of a doubt, himself 
 misunderstood me.* But what has this to do with the ques- 
 
 * I will give an example or two in illustration. On pages 85-86 I give two formulas for 
 the announcement of the true doctrine of the foundation of obligation, the first as incom- 
 
 r 
 
DOCTRINE OF FALLACIES. 263 
 
 tion at issue ? Absolutely nothing. If I have asserted such 
 theories in another part of the hook, I have done no such thing 
 in this one department of it. Here but two theories stand re- 
 vealed, and but a single issue is presented, and every thing 
 bears directly and exclusively upon that issue. What an exam- 
 ple of the real ignoratio elenchi is it, to divert attention from 
 this single issue to another and different one, to wit, whether 
 in other parts of my work self-consistency is maintained. Yet 
 this is a form of fallacy most common in community. 
 
 Suppressing the Conclusion. 
 
 One of the most effectual modes of accomplishing this result 
 is suppressing the real question, and with logical precision argu- 
 ing some analogous or similar, yet in reality distinct question, 
 as if it was the real one. 
 
 Suppose that the real question in a given case is, whether an 
 individual on a given occasion committed some specific crime. 
 His accuser, wholly unable to prove that single point, makes a 
 violent assault upon his general character, and dilates with in- 
 tense earnestness upon this, omitting to inform his auditory, 
 that not general character, but a specific act at a specific time, 
 is the exclusive subject of inquiry. On the other hand, suppose 
 that not specific acts, but general character, is the subject of dis- 
 cussion. Suppose that here, if the real issue is exclusively pre- 
 
 plete and imperfect and so far wrong; and the second, as announcing the doctrine with 
 " philosophic precision." All this is fully and distinctly stated. After saying this, I state 
 that the first formula is not, and the second is, the true one. Yet, in the " Systematic The- 
 ology," these two formulas are given, and I am represented as having announced each alike 
 as unqualifiedly correct, and thus palpably contradicted myself. 
 
 Again, on page 36, I am represented as teaching the doctrine that "the idea of right is the 
 foundation of obligation." In that place I am speaking of the relative order of the ideas 
 of right and wrong, of obligation, moral desert, and retribution. I then, in accordance with 
 the teachings of all philosophers that I am acquainted with, speak of these ideas as resting 
 immediately one upon the other, in the order above stated. This is the exclusive sense in 
 which I am there speaking upon this subject. When, in another place, I come to discuss 
 the true and proper question of the foundation of obligation, I there state it in form to be 
 synonymous with the question, What is the foundation of the idea of right? There I say 
 that that " which renders in the judgment of the intelligence one action necessarily right, 
 and all others (of an opposite nature) wrong," is " the foundation of obligation." In thia 
 form exclusively have I discussed the subject in my Intellectual and Moral Philosophy 
 both. The examples speak for themselves and here I leave the subject 
 
264 logic. 
 
 sented, the virtue of the accused will appear unblemished. An 
 opponent may attempt to gain his end by pushing forward 
 some specific acts of a questionable character, and by enlarging 
 upon them aim to secure a verdict against the character of the 
 accused. Sometimes the person accused gives strength to this 
 form of attack, by attempting to defend himself on every point, 
 as if this, and not the question of general character, is the ex- 
 clusive issue. In all such cases general character is best de- 
 fended by admitting and confessing all individual aberrations. 
 The very confession is a vindication of general character. 
 
 ARGUMENTUM AD HOMIKEM. 
 
 There are two forms in which what is called the argumen- 
 tum ad hominem may be properly employed. The first we 
 have already considered, and consists in showing that the argu- 
 ment of the opponent proves too much, and therefore is false. 
 The second, which we are now to consider as properly belong- 
 ing to this division of our subject, consists in showing that from 
 his own acknowledged principles, an opponent is bound in con- 
 sistency to admit the conclusion urged upon him. This is a le- 
 gitimate form of argument when properly used. The fallacy 
 connected with it consists, not in showing that consistency re- 
 quires the individual referred to to admit said conclusion, but 
 in assuming that conclusion as really thereby proved as true in 
 itself. This fallacy has been so well elucidated by Dr. Whate- 
 ly, that we will venture another citation from him, and with it 
 close our remarks upon this subject : 
 
 " There are certain kinds of argument recounted and named 
 by logical writers, which we should by no means universally 
 call fallacies ; but which when unfairly used, and so far as they 
 are fallacious, may very well be referred to the present head ; 
 such as the ' argumentum ad hominemf or personal argument, 
 ' argumentum ad verecundiamf ''argumentum ad populumf 
 &c, all of them regarded as contradistinguished from ''argu- 
 mentum ad rem,' 1 or, according to others (meaning probably 
 the very same thing), ' ad judicium.'' These have all been de- 
 
DOCTRINE OF FALLACIES. 265 
 
 scribed in the lax and popular language before alluded to, but 
 not scientifically : ' the " argumentum ad hominem," ' they say, 
 'is addressed to the peculiar circumstances, character, avowed 
 opinions, or past conduct of the individual, and therefore has a 
 reference to him only, and does not bear directly and absolute- 
 ly on the real question, as the " argumentum ad rem'''' does ;' in 
 like manner, the ' argumentum ad verecundiam) is described as 
 an appeal to our reverence for some respected authority, some 
 venerable institution, &c, and the ' argumentum ad populumj 
 as an appeal to the prejudices, passions, &c, of the multitude ; 
 and so of the rest. Along with these is usually enumerated 
 ' argumentum ad ignorantiam^ which is here omitted, as being 
 evidently nothing more than the employment of some kind of 
 fallacy, in the widest sense of that word, towards such as are 
 likely to be deceived by it. It appears then (to speak rather 
 more technically) that in the> ' argumentum ad hominem? the 
 conclusion which actually is established, is not the absolute and 
 general one in question, but relative and particular ; viz., not 
 that ' such and such is the fact,' but that ' this man is bound to 
 admit it, in conformity to his principles of reasoning, or in con- 
 sistency with his own conduct, situation,' &c * Such a conclu- 
 sion it is often both allowable and necessary to establish in 
 order to silence those who will not yield to fair general argu- 
 ment ; or to convince those whose weakness and prejudices 
 would not allow them to assign to it its due weight ; it is thus 
 
 * "The ' argumentum ad hominenC will often have the effect of shifting the burden of 
 proof, not unjustly, to the .adversary. A common instance is the defence, certainly the 
 readiest and most concise, frequently urged by the Sporstman, when accused of barbarity 
 in sacrificing unoffending hares or trout to his amusement: he replies, as he may safely do, 
 to most of his assailants, ' why do you feed on the flesh of animals ?' and that this answer 
 presses hard, is manifested by its being usually opposed by a palpable felsehood ; viz., lhat 
 the animals which are killed for food are sacrificed to our necessities; though not only 
 men can, but a large proportion (probably a great majority) of the human race actually do, 
 subsist in health and vigor without flesh-diet; and the earth would support a much greater 
 human population were such a practice universal. When shamed out of this argument, they 
 sometimes urge that the brute creation would overrun the earth, if we did not kill them for 
 food; an argument, which, if it were valid at all, would not justify their feeding on fish ; 
 though, if fairly followed up, it would justify Swift's proposal for keeping down the exces- 
 sive population of Ireland. The true reason, viz., that they eat flesh for the gratification of 
 the palate, and have a taste for the pleasures of the table, though not for the sports of the 
 field, is one which they do not like to assign." 
 12 
 
266 LOGIC. 
 
 that our Lord on many occasions silences the cavils of the Jews ; 
 as in the vindication of healing on the Sabbath, which is paral- 
 leled by the authorized practice of drawing out a beast that has 
 fallen into a pit. All this, as we have said, is perfectly fair, pro- 
 vided it be done plainly, and avowedly ; but if you attempt to 
 substitute this partial and relative conclusion for a more general 
 one if you triumph as having established your proposition ab- 
 solutely and universally, from having established it, in reality, 
 only as far as it relates to your opponent, then you are guilty 
 of a fallacy of the kind which we are now treating of; your 
 conclusion is not in reality that which was, by your own ac- 
 count, proposed to be proved ; the fallaciousness depends upon 
 the deceit or attempt to deceive. The same observations will 
 apply to ' argumentum, ad verecicndiam," 1 and the rest. 
 
 " It is very common to employ an ambiguous term for the 
 purpose of introducing the fallacy of irrelevant conclusion ; i. e. 
 when you cannot prove your proposition in the sense in which 
 it was maintained, to prove it in some other sense ; e. g. those 
 who contend against the efficacy of faith, usually employ that 
 word in their arguments in the sense of mere belief, unaccom- 
 panied with any moral or practical result, but considered as a 
 mere intellectual process ; and when they have thus proved 
 their conclusion, they oppose it to one in which the word is 
 used in a widely different sense."* 
 
 * " When the occasion or object in question is not such as calls for, or as is likely to excite 
 in those particular readers or hearers, the emotions required, it is a common rhetorical arti- 
 fice to turn their attention to some object which will call forth these feelings; and when' 
 they are too much excited to be capable of judging calmly, it -will not be difficult to turn 
 their passions, once roused, in the direction required, and to make them view the case be- 
 fore them in a very different light. When the metal is heated, it may easily bo moulded 
 into the desired form. Thus vehement indignation against some crime, may be directed 
 against a person who has not been proved guilty of it; and vague declamations against cor- 
 ruption, oppression, &c, or against the mischiefs of anarchy ; with high-flown panegyrics 
 >n liberty, .rights of man, &c, or on social order, justice, the constitution, law, religion, &c, 
 will gradually lead the hearers to take for granted without proof, that the measure proposed 
 will lead to these evils or these advantages ; and it will in consequence become the object 
 of groundless abhorrence or admiration. For the very utterance of such words as have a 
 multitude of what may be called stimulating ideas associated with them, will operate like 
 a charm on the minds, especially of the ignorant and unthinking, and raise such a tumult of 
 feeling, as will effectually blind their judgment: so that a string of vague abuse or panegyrio 
 will often have the effect of a train of sound argument." liheioric, Part II. Chap, ii 
 
 erate like 
 tumult ol 
 panegyrio 
 ), ii. 6. 
 
PART III. 
 
 THE DOCTKINE OF METHOD. 
 
 TERMS DEFINED. 
 
 All thinking is according to rules of some kind. Thought, 
 too, is always, both in writing and speaking, developed ac- 
 cording to rules. There are perfect and imperfect forms of 
 thought, and it is equally true that there are perfect and im- 
 perfect methods or forms of developing thought. The object 
 of the doctrine of method is to develop those rules and laws of 
 thought, in conformity to which the idea of science in all logi- 
 cal forms of thinking, may he most perfectly realized. In the 
 former departments of the present treatise, we have aimed to 
 develop those laws of thought to which all valid logical think- 
 ing must conform. Our present object is to develop those laws 
 of thought by which logical thinking may assume its most per- 
 fect forms. 
 
 MEANS BY WHICH THE LOGICAL PERFECTION OF THOUGHT MAT 
 BE SECURED. 
 
 The doctrine of method must reveal the means or rules by 
 which the logical perfection of thought may be secured. The 
 essential characteristics of such forms of thinking are distinct- 
 ness, systematic order, and completeness, so that the mind at- 
 tains to full and distinct apprehensions of the whole of the sub- 
 ject treated of. The distinct aim of the doctrine of method is 
 to point out the means by which these elements of perfection 
 in logical thinking may be induced. 
 
CONDITIONS ON WHICH THESE ENDS MAT BE SECURED. 
 
 The conditions on which the elements of perfection above- 
 named may he induced are the following, to wit : proper defi- 
 nition and exposition of the whole, and of the principles and 
 parts, of the subject treated of; a proper logical division of said 
 subject ; and a proper order of presentation of the parts refer- 
 red to. We propose to elucidate the subject before us in the 
 order named, closing our discussion with, the elucidation of cer- 
 tain general topics having an important bearing upon a right 
 understanding of the doctrine of method. 
 
 Section I. Logical Perfection of Thought as promoted 
 by proper Definition and Exposition. 
 
 Design of Definition and Exposition. 
 
 The design of definition and exposition is one and the same, 
 to wit, to convey to the mind a,fidl, distinct, and adequate con- 
 ception or apprehension of the thing defined. Distinctness, 
 completeness, and precision, are the essential elements of every 
 perfect definition. The object defined must be so presented, 
 that it shall stand out before the mind with perfect distinctness 
 as it is in itself, and, at the same time, with equally perfect 
 separateness from all objects with which it is likely to be con- 
 founded. 
 
 Proper objects of Definition and Exposition. 
 
 The immediate and proper aim of definition and exposition 
 is not proof, but a distinct understanding of what is to be 
 proved, and also of the terms and propositions by which this 
 end is to be attained. These, then, are the proper objects of 
 definition and exposition. 
 
 In entering upon the elucidation of any particular subject, 
 whether it be some one entire science, or some single part or 
 
DOCTKIUE OP METHOD. 269 
 
 department of the same, or finally, some special aspect of some 
 one subject of thought, the first thing to be accomplished is a 
 full and distinct definition and exposition of the entire subject, 
 whatever it may be, to be treated of, and also of the end to be 
 accomplished in its elucidation ; so that that subject shall stand 
 out with perfect distinctness before the mind, not only as it is 
 in itself, but separated with equal distinctness from every other 
 subject with which, in whole or in part, it is likely to be con- 
 founded. Every science, for example, has a sphere peculiar to 
 itself, and the purpose to be answered by its elucidation is 
 equally special and peculiar. To appreciate the bearing of 
 what may be presented m the elucidation of said science, its 
 special and peculiar sphere, the extent and limits of the same, 
 together with the purpose to be secured by its elucidation, 
 must be distinctly apprehended. To induce such apprehensions 
 is the appropriate and exclusive object of definition and exposi- 
 tion. 
 
 Apply the same remarks to the various terms peculiar to any 
 particular treatise or discourse, to the principles which lie at 
 the foundation of the same, and to the various propositions em- 
 ployed in the progress of the discussion, and we have a distinct 
 apprehension of the proper objects of definition and exposition, 
 together with their design and aim. Unless these ends are 
 fully accomplished, any real approach towards logical perfec- 
 tion of thought is impossible. 
 
 Characteristics of all Correct Definitions. 
 
 The following, then, may be given as the essential charac- 
 teristics of all correct and proper definitions : 
 
 1. That the definition, considered as a proposition, is true, 
 that is, really and truly represents its object, whether the ob- 
 ject in itself be real or unreal. Suppose that the term " cen- 
 taur" is defined as representing a " fabulous animal half horse 
 and half alligator," instead of " half horse and half man." The 
 definition would be incorrect, not because that each being de- 
 fined is not equally fabulous, but because that the latter defini- 
 
270 LOGIC. 
 
 tion, and that only, represents the real object as thought by 
 the mind. A definition, then, as a proposition, is true when it 
 represents its object as really thought by the mind, whether 
 the object in itself is real or unreal, and this is an essential ele- 
 ment of every correct definition. 
 
 2. Not only must a definition be true in the sense explained, 
 but its truth must be self-evident, so much so, that its correct- 
 ness will not be a matter of dispute. Otherwise, a new subject 
 of debate arises, which confuses the mind and involves in dark- 
 ness the whole subject under discussion. This element of all 
 correct definition is quite too often overlooked, and that when 
 the most important questions are involved. Definition is 
 nothing but the preparatory means for discussion, and totally 
 fails of its end when it itself becomes the subject of debate. 
 
 3. Considered as a conception the definition must be distinct, 
 that is, it must induce in the mind a distinct apprehension of its 
 object as it is. The definition of the centaur above given, for 
 example, has the first two characteristics. It wholly lacks, 
 however, the one under consideration, for the reason that no 
 one, from the definition, can form a distinct image of the thing 
 defined, and no two individuals would obtain from it the same 
 conception. Take, in its place, the following definition of the 
 same object : " A centaur is a fabulous being, half horse and 
 half man," to wit, a being whose body entire is that of the 
 horse, with the exception, that the body of a man from the 
 waist upwards occupies the place of the neck and head of the 
 creature referred to. This definition has not only the first two 
 characteristics of all correct definitions above-named, but that 
 also under consideration, to wit, distinctness. From it every 
 one will form a distinct apprehension of the object defined, and 
 all will obtain the same apprehension. This, then, is an essen- 
 tial characteristic of all correct definitions. The object must 
 be so defined, that all will obtain from the definition a distinct 
 apprehension of the object, and all will obtain the same appre- 
 hension. 
 
 4. As a definite conception, also, the definition must be am- 
 ple or adequate, that is, it must distinctly represent not only a 
 
DOCTRINE OP METHOD. 271 
 
 part, but the whole, of its object. Suppose, for example, that 
 the term "centaur" represents not only the fabulous being 
 above denned, but a being possessed also of other equally fun- 
 damental characteristics not named in that definition. In that 
 case the definition would have the first three characteristics, 
 but would lack another equally requisite to constitute it a per- 
 fect definition, to wit, adequateness. Any definition wanting 
 in this one particular is fundamentally defective. 
 
 5. The last characteristic of every correct definition that w<> 
 mention is determinateness, that is, the thing defined must 
 stand out not only in full and distinct amplitude before the 
 mind, but in a state of equally determinate separateness from 
 all objects with which, hi whole or part, it is likely to be con- 
 founded. Every definition is perfect or imperfect as it possesses 
 or wants, in whole or in part, all of the above characteristics. 
 
 Characteristics of Defective Definitions. 
 
 All definitions are defective which lack any of the characteris- 
 tics above elucidated, and especially those which possess the 
 opposite characteristics, such as positive incorrectness or doubt- 
 ful correctness, indistinctness, want of completeness or ampli- 
 tude and of determinateness. A definition is incorrect when 
 it introduces into the conception or proposition any elements 
 not included in it, or formally excludes from it any which real- 
 ly belong to it. Definitions erroneous in one or the other of 
 these particulars are very common in almost all departments of 
 thought. Still more common is the element of doubtfulness in 
 definitions. A definition which raises a dispute in regard to its 
 own correctness is fundamentally defective. 
 
 One of the most common forms of defective, or rather, per- 
 haps, erroneous definitions, is this defining a term or proposi- 
 tion so as to involve, by direct implication, the very question 
 at issue ; an important form of " begging the question." 
 
ELEMENTS WHICH ENTER INTO, AND ARE EXCLUDED EROM, ATT, 
 PERFECT DEFINITIONS. 
 
 The above, we judge, will be universally admitted as the 
 essential characteristics of all perfect, as distinguished from all 
 forms of imperfect, definition. We now advance to the con- 
 sideration of another very important topic connected with our 
 present inquiries, to wit, the elements which will enter into, 
 and be excluded from, all perfect forms of definition. 
 
 Characteristic, Generical, Specifical, and Individual Concep- 
 tions. 
 
 Definitions of characteristic conceptions must designate all 
 the elements of such conceptions, and no more and no less. 
 An error in either of the particulars named would totally mis- 
 lead in the application of the conception defined. If any ele- 
 ment really belonging to the conception is omitted, or any one 
 not belonging to it is included in it, those using the conception 
 as defined in testing the character of objects, would be led to 
 reject what is genuine on the one hand, and to receive as such 
 what is spurious on the other. 
 
 Similar remarks are equally applicable to definitions of ge- 
 nerical conceptions, definitions of ultimate genera especially. 
 Take any element from, or add any to, a genus, and it becomes 
 another thing. For this reason, every perfect definition of a 
 generical conception will include all the elements of such con- 
 ception, and no more and no less. 
 
 Definitions of specifical conceptions should designate, first, 
 the generical conceptions under which the former rank, and 
 then embrace those elements, and those only, which peculiarize 
 and distinguish the species which they represent from other 
 species which rank with them under the same genera ; genera 
 and differentia being the constituent elements of species. So 
 far as such definitions include more or less than these elements, 
 they are fundamentally defective or erroneous. 
 
 Definitions of individual conceptions should designate the 
 
DOCTRINE OF METHOD. 273 
 
 specifical or generical conceptions under which the former as 
 individuals rank, and then designate those properties and acci- 
 dents, and those only, by which such individuals are distin- 
 guished from other individuals of the same class. 
 
 Definitions of Propositions. 
 
 When a proposition is laid down, it is sometimes necessary to 
 define its meaning. In doing so, it is most commonly necessary 
 to define but one of the terms. When the subject is known, 
 and some attribute is by the predicate affirmed of the subject, 
 then the former must be defined as in the proposition, " John 
 is a murderer." When, on the other hand, some well-known 
 attribute as, "God is, exists" is affirmed of the subject, then 
 the latter term, that is, the subject, will need to be denned. If 
 the meaning of each is likely not to be understood, then both 
 alike will require definition. 
 
 True use of Affirmation and Negation in Definition. 
 
 Terms and conceptions must often not only be affirmatively 
 but negatively defined. By affirmation we designate the posi- 
 tive elements included in the thing defined. By negation we 
 separate this object from others with which it may be supposed 
 to agree or to be identical, but from which it is distinct, and 
 should be separated. In defining the crime of murder, for ex- 
 ample, it may be necessary to a clear and distinct apprehension 
 of it, not only to designate its essential and positive characteris- 
 tics, but to show wherein it differs from manslaughter, &c. 
 The former object is accomplished by affirmation and the latter 
 by negation. Negation should be employed in those cases only 
 where some object, really and essentially different from that to 
 be discussed, is likely to be mistaken for it, and with exclusive 
 reference to such object and the points of difference between 
 such object and that to be defined. It would throw no light, 
 ;for example, upon the crime of murder to say that it is not 
 theft, and to show wherein the two crimes differ. The reason 
 12-s 
 
274 logic. 
 
 is obvious. The two forms of crime are never confounded, as ia 
 the case with murder and manslaughter. When two terms are 
 thus separated, it is most commonly necessary to distinctness of 
 apprehension, not only to state the fact of disagreement, hut 
 carefully to explain and elucidate the points of disagreement 
 and dissimilarity. 
 
 Nominal and Real Definitions. 
 
 In some instances we have occasion merely to define a term, 
 by stating 'the conception which the former represents. This is 
 what is meant by the words nominal definition. In this case 
 all that is requisite is to designate the conception, and then the 
 term by which the former is to be represented. Real defini- 
 tion is the definition, not of the term, but of the conception or 
 thing which the term represents. It is to this last class of defi- 
 nitions that the principles above elucidated apply. 
 
 Subjective and Objective Definitions. 
 
 In some instances, also, the object of a definition is to repre- 
 sent the apprehensions which the individual presenting it has 
 of a given subject. In such cases clearness and distinctness is 
 all that others have a right to require, and they are bound, of 
 course, to accept his own statements as correctly representing 
 his views. This is what is denominated subjective definition. 
 In other cases the object is to represent things as they are, or 
 as they are thought by the general mind. This is objective 
 definition. It is to this kind of definition that the principles 
 we have stated and elucidated apply in all their extent. 
 
 EXAMPLES OF PERFECT AND IMPERFECT DEFINITIONS. 
 
 For the purpose of elucidating still further the important 
 topic under consideration, that of definition, we will now pre- 
 sent a few miscellaneous examples of perfect and imperfect defi- 
 nition. 
 
DOCTRINE OF METHOD. 
 
 The term Judgment defined. 
 
 The following is Kant's definition of a judgment : "A judg- 
 ment is the representation of the unity of the consciousness of 
 various representations, or the representation of their relation, 
 provided that they make up a conception." Kant's Logic, 
 p. 141. 
 
 The manifest objection to this definition is its palpable viola- 
 tion of the author's second characteristic of a perfect definition, 
 that, " as a conception," the definition must be " distinct." The 
 definition before us tends to but one result, to obscure the thing 
 attempted to be defined. 
 
 " A judgment," says President Tappan, " is an affirmation 
 of the mind." The defect in this definition is, that it fails to- 
 tally to elucidate the thing to be defined, the meaning of the 
 predicate being quite as obscure as that of the subject, and as 
 much needing definition. Definitions of this kind are very com- 
 mon, and fundamentally defective. We refer to the practice of 
 defining a term by means of some mere synonymous term or 
 phrase. In every perfect definition the predicate is clearly 
 and definitely explicative of the subject, and not merely its 
 synonym. 
 
 " Judgment," says Dr. Whately, " is the comparing together 
 in the mind two of the notions (or ideas) which are the objects 
 . of apprehension, whether complex or incomplex, and pronoun- 
 cing that they agree or disagree with each other ; (or that one 
 of them belongs or does not belong to the other)'." Judgment, 
 according to this definition, includes two entirely distinct intel- 
 lectual processes the act of comparison, and the " pronouncing" 
 that the things compared " agree or disagree with each other ;" 
 the former process being implied by the latter, but really and 
 truly distinct from it. Now a judgment is the mental affirma- 
 tion which succeeds the act of comparison, and notning else. 
 This definition, therefore, is fundamentally defective, inasmuch 
 as it includes elements not found in the thing 'to be defined. 
 
 A much nearer approach to perfection is made in the defini- 
 tion of Professor Wilson, to wit : "A judgment is an act of the 
 
276 logic. 
 
 mind affirming a certain relation between two objects of thought 
 by means of their conceptions." The phrase, "by means of ' 
 their conceptions," is redundant here, and should constitute, 
 as it appears to us, a part of the exposition of a judgment, and * 
 not of its definition. A perfect definition of the term under 
 consideration, we think, would be this : A judgment is an act 
 of the mind an act in which a certain relation is affirmed or 
 denied of two objects of thought. It may then be shown, by 
 way of exposition, that said affirmation is always, in fact, made 
 by means of conceptions, as it is always in view of what objects 
 are conceived to be, that is, by means of conceptions that we 
 affirm or deny any thing of them. Every element of a perfect 
 definition will be found in this definition as thus expressed and 
 expounded. 
 
 Moral Action defined. 
 
 " A moral action," says Dr. Wayland, " is the voluntary ac- 
 tion of an intelligent agent who is capable of distinguishing be- 
 tween right and wrong, or of distinguishing what ought from 
 what ought not to be done." In reading the above professed 
 definition, the question at once arises, whether every voluntary 
 act of such an agent is, in fact, as is here directly implied and 
 affirmed, a moral act. In regard to this question different and 
 opposite opinions are held. We have, then, in this case, not a 
 proper definition at all, but a problematical proposition to be 
 investigated and discussed after a correct definition has been 
 given. Even philosophers have not generally made a proper 
 distinction between a definition of an object, and a problemati- 
 cal judgment connected with such object when defined. A 
 professed definition, the truth of which is not self-affirmed, is 
 not, it should be borne in mind, a proper definition, but a pro- 
 blematical judgment which requires proof. 
 
 Let us now contemplate the following definition of a moral 
 action, to wit, an action of which the intelligence necessarily 
 affirms that it ought or ought not to be done, and on account 
 of the doing of which, merit or demerit is as necessarily attrib- 
 
 
^UV**r*^ 
 
 DOCTRINE OF METHOD. 211 
 
 uted to the subject. "No one can possibly doubt, that if there 
 is such a thing as a moral action, these are its peculiar and 
 special characteristics characteristics which clearly distinguish 
 'it from all other forms of action, actual or conceivable. This, 
 then, is a perfect definition. 
 
 Moral Law defined. 
 
 Moral law, as defined by Dr. Wayland, is " an order of se- 
 quence established between the moral quality of actions and 
 their results." Here undeniably is a fundamental mistake in re- 
 gard to the nature of the thing defined. Moral law is made to 
 be chronologically subsequent to moral action, whereas the lat- 
 ter presupposes the former. Moral action is conformity or non- 
 conformity to law. The law must exist before the action is 
 possible. 
 
 "Moral law," says President Finney, "is a rule of moral ac- 
 tion with sanctions." The author had just defined law itself 
 and correctly too, as " a rule of action." Moral law, then, must 
 be simply and exclusively a rule of action of a peculiar and 
 special kind. Nothing but the kind of action referred to, aside 
 from the idea of a rule, should be included in the definition. 
 Sanctions attach to acts of obedience or disobedience to law, 
 and have their basis in the merit and demerit which attach to 
 - obedience and disobedience, and consequently can constitute no 
 part of the law or rule itself. Then the phrase, " moral law is a 
 rule of moral action," as a proposition, is really tautological, 
 moral action being that form of action which is conformed or 
 not conformed to moral law. The real meaning of the propo- 
 sition is, moral law is the rule of conformity or non-conformity 
 to moral law. Then the definition is totally faulty on the score 
 of perspicuity, the phrase " moral action," the predicate, need- 
 ing to be defined quite as much as the subject of the proposi- 
 tion, the phrase " moral law." 
 
 What, then, is -a perfect definition of the phrase "moral 
 law ?" We answer it is this : Moral law is that rule of action 
 to which intelligent agents necessarily affirm that they ought 
 
278 LOGIC. 
 
 to conform, and to the idea of obedience or disobedience to 
 which they as necessarily attach the idea of merit or demerit, 
 that is, the desert of good or ill. Let any one apply the testa 
 of a perfect definition given above to the one before us, and 
 he will see that it fully meets them all. No one can fail to ap- 
 prehend the real meaning of the definition, or to distinguish the 
 thing defined from every other rule of action actual or conceiv- 
 able, or to admit that, if there is such a thing as moral law, 
 this is that rule, and these are all the requisites of a perfect 
 definition. 
 
 A Moral Agent defined. 
 
 A perfect definition of the phrase " moral agent" would be 
 this : An agent, of whom we necessarily affirm, that he ought 
 to conform to the moral law, and to whom we necessarily attach 
 the idea of the desert of good or ill, as he does or does not 
 conform to what that law requires of him. What was said of 
 the definition of moral law is so manifestly applicable to the 
 definition before us, that we may safely leave it to speak for 
 itself. 
 
 It is quite common to define a moral agent as one " who is 
 capable of obeying or disobeying the moral law," or as one 
 ' who has the capacity to distinguish what is right from what is 
 wrong," &c. These, however, are not definitions at all, but 
 problematical judgments connected with the idea of moral 
 agency. 
 
 Ultimate Intention defined. 
 
 It is now generally admitted that every thing that has real 
 moral character in the conduct of moral agents is, in fact, found 
 in what is called the ultimate intention. The question which 
 arises here is, How shall this phrase be defined so as to express 
 and represent every act of this character,.that is, so as to ex- 
 press all that, and that only, in human conduct which has moral 
 character ? The importance of this question every one will ad- 
 
 
DOCTRINE OF METHOD. 279 
 
 mit. Let us now contemplate a single example of a fundamen- 
 tally defective definition of an ultimate intention. "An ulti- 
 mate intention," says President Finney, " is the choice of an ulti- 
 mate end." In this definition there are, among others, the fol- 
 lowing fundamental defects: 1. The predicate of the proposi- 
 tion is not, what in all correct definitions it is, really and truly 
 explicative of the subject, the words " choice of an ultimate 
 end" requiring definition just as much as the phrase " an ulti- 
 mate intention." 2. The definition presents us with a pro- 
 blematical judgment a judgment which cannot properly be 
 used at all in reasoning until its truth is proven, it being 
 doubted and denied that 'all ultimate intentions consist in tne 
 choice of ultimate ends. 3. The judgment here presented is 
 not, in fact, true, as it cannot, according to the real meaning of 
 the words, be made to include any moral acts or states relative 
 to God ; for neither his happiness nor moral character can be 
 chosen as an end, that is, as something to be secured and pro- 
 moted in the use of means. 
 
 What then would be a correct definition of an ultimate inten- 
 tion ? The following, in our judgment, would be such a defini- 
 tion : All are aware of the fact, that one act or state of the will 
 may be determined by, and thus subordinated to, another act 
 or state. An ultimate intention or act of will is one to which 
 others are or may be subordinated, and by which they are or 
 may be determined, and which is itself subordinated to, and 
 determined by, none others. On this definition we remark : 
 1. That no problematical element enters into it. 2. It clearly 
 and adequately designates the object defined, as distinguished 
 from all other objects. 3. It undeniably includes and desig- 
 nates every thing in human action which can have a moral char- 
 acter, and thus fully answers its end. We thus have the essen- 
 tial characteristics of all perfect' definitions. 
 
 The term God defined. 
 
 The term God may be contemplated in two points of light 
 as representing the idea of ultimate causation as held by all 
 
280 LOGIC. 
 
 men, whether theists or anti-theists ; and as representing the 
 special theistic hypothesis of such causation. In the first sense, 
 the term God would be defined as the ultimate reason why, or 
 determining cause, whatever it may he, by which the facts of 
 the universe are rendered what they are, and not otherwise. 
 Even an atheist would admit the truth and correctness of this 
 definition, and would as readily admit that, as thus defined, he 
 himself believes in God. 
 
 As representing the special theistic hypothesis, the term God 
 may be thus defined : A self-conscious personality possessed of 
 all the attributes involved in the ideas of absolute infinity and 
 perfection, and sustaining to all conditioned existences the 
 relation of unconditioned cause. As representing this one 
 hypothesis, all will admit the truth and adequacy of this defi- 
 nition. 
 
 We have given the above as simple examples, by way of 
 illustration. Every correct definition, it should be borne in 
 mind, will have, among others, the following characteristics : 
 1. No problematical elements will be introduced into the defi- 
 nition. 2. It will clearly and adequately represent its object as 
 distinguished from all other objects of thought. 3. As a prop- 
 osition, its truth, that is, the fact that it does thus represent its 
 object, must be self-evident, that is, universally admitted. In 
 nothing is even educated mind generally more deficient than in 
 this, the habit of correct definition, and almost no department 
 of thought is of greater importance. 
 
 Section II. Promotion op the Logical Perfection op 
 Thought by means of the Logical Division op Con- 
 ceptions or Subjects. 
 
 Terms defined. 
 
 Every conception pertains to its object as a whole including 
 parts. Thus the conception represented by the term mind, 
 pertains to its object as a substance possessed of the attributes 
 
DOCTRINE OP METHOD. 281 
 
 of thought, feeling, and voluntary determination, or as includ- 
 ing the powers or functions of intellect, sensibility, and will. 
 The conception represented by the term matter pertains to its 
 object, as possessed of certain primary, secundo-primary, and 
 secondary qualities. The proper idea of a logical division of a 
 conception or subject treated of, is a distinct separation of the 
 various parts which constitute the given whole. The whole, 
 whether it be a generical with specifical conceptions, or a spe. 
 cifical with individual conceptions, ranking under it, or an indi- 
 vidual conception constituted of diverse elements, is called rela- 
 tively to its parts, the superior, and its several parts, the infe- 
 rior conceptions. The wliole is called, also, the divided con- 
 ception, and the parts the members of the division. The fol- 
 lowing extract from Kant demands special attention in this 
 connection : 
 
 " Schol. 1. To dissect a conception, and to divide it, are 
 therefore very distinct operations. By the dissection of a con- 
 ception, we see what is contained in it (by analysis) ; by the 
 division, we consider what is contained under it. In this case 
 we divide the sphere of the conception, not the conception 
 itself. The division is, therefore, so far from being a dissection 
 of a conception, that the members of division rather contain 
 more in them than the divided conception. 
 
 " Schol. 2. We ascend from inferior to superior conceptions, 
 and may afterwards descend from these to inferior ones, by 
 division." 
 
 Universal Rules for Logical Division. 
 
 We are now prepared to state definitely the universal rules 
 for the logical division of subjects. They are the following : 
 
 1. The members of the division must mutually exclude each 
 other. In other words, they must differ from each other by 
 way of opposition. Things essentially alike must not be sepa- 
 rated, nor those which are fundamentally unlike confounded. 
 Thus the logical division of the mental powers into intellect, 
 sensibility, will, meets fully the requirements of this rule, be- 
 
282 LOGIC. 
 
 cause each member of the division is fundamentally opposed to 
 each of the others. . 
 
 2. The division must be complete, that is, must embrace all 
 the parts of the subject which are thus separated from each 
 other. The division of the mental powers above stated would 
 meet the requirements of this rule also, because all the mental 
 powers are there given. The division made by certain philoso- 
 phers, as intellect and sensibility, or intellect and affections, 
 
 would meet the requirements of the first, while it would violate 
 this rule, the members of the division actually given being op- 
 posed to each other, while one mental power, the will, which is 
 just as distinct from the intellect and sensibility as either of 
 these last is from the other, is omitted. 
 
 3. Each member of the division must rank under the whole 
 the superior conception as a real member or part of the 
 same. In other wdrds, nothing foreign to the real sphere of 
 the superior conception, that is, nothing which does not really 
 and truly rank under it, must be introduced into the division 
 or any part of it. Violations of this rule, which is of funda- 
 mental importance to the perfection of logical thinking, are 
 perfectly common in almost all departments of research. That 
 which exclusively pertains to the sphere of one science is fre- 
 quently discussed as a part of another and different one. 
 
 4. Taken collectively, the members of the division must fully 
 make up or complete the sphere of the divided conception, so 
 that the latter shall be really and truly given and be conceived 
 of, as a whole complete in all its parts. This rule is really im- 
 plied in Rule 2, and is here given for the sake of distinctness. 
 
 Codivision and Subdivision. 
 
 The primary division of a conception or subject into distinct 
 members is called codivision. A similar division of the several 
 parts is called subdivision. The rules for the former are equal- 
 ly applicable to the latter. Subdivision may be continued tc 
 almost any conceivable extent. 
 
DOCTRINE OF METHOD. 283 
 
 The Fragmentary as opposed to the Meal Logical Division 
 of Subjects. 
 
 In reference to every important department of thought, the 
 science of mind, or theology, for example, certain important 
 and general questions arise, and' become the topics of general 
 discussion. Suppose that two individuals attempt to develop 
 scientific treatises ou one or the other of these subjects. One 
 takes up these several topics as they naturally occuf to his 
 mind, throws all the light he can upon them, and then presents 
 his work as a scientific treatise on the subject. The other indi- 
 vidual, first of all, contemplates his subject as a whole with ref- 
 erence to its appropriate and exclusive sphere. It is then 
 divided and subdivided into its distinct and separate parts ac- 
 cording to the fundamental rules of logical division. The sub- 
 ject is thus given as a whole distinct in all its parts. From the 
 nature of the subject, we perceive that it has just so many parts, 
 and can have no more. The idea of order, completeness, and 
 scientific division and arrangement is completely realized. In 
 the first case, we have what may be called the fragmentary, 
 and in this last, the truly scientific and logical division of sub- 
 jects. The former, when accepted as a scientific treatise, tends 
 only to confuse and darken our conceptions of the subject , 
 treated of. 
 
 Section III. The Promotion of the Logical Perfection 
 of Thought by means of a proper arrangement of the 
 parts of the subject treated of. 
 
 Terms defined Analytic and Synthetic Orders of Thought. 
 
 Next in importance to a systematic logical division of sub- 
 jects is the order in which the members of the division should 
 be elucidated and arranged relatively to each other as parts of 
 the whole or superior conception. A chain of reasoning stated 
 in one order may be without logical force in the mind of the 
 hearer, while, stated in another order, it may have the force of 
 
demonstration. Let us then proceed to a consideration of the 
 rules or canons of order. 
 
 Every one is aware that in every department or subject & 
 thought there are two extremes certain first principles which 
 presuppose nothing as having preceded them, and upon which 
 all that follow depend ; and certain final facts or deductions 
 which presuppose and depend upon all that have gone before, 
 and which themselves imply nothing as following them ; and 
 that between these extremes, there are certain intermediate 
 steps depending, the first upon the first truths referred to, the 
 next upon this first step, and so on to the last. 
 
 Every one, also, is equally aware of the fact, that there are 
 two distinct and opposite, and equally valid methods of treating 
 subjects the synthetic and the analytic. The former begins 
 with what is first in the logical order, that is, with that upon 
 which all the rest primarily depend, and then, by successive 
 steps, ascends to the last as above described. The latter method 
 begins with what is last, that is, depends logically upon what has 
 gone before, and, by regular steps, descends to what is first in 
 the logical order. Of the synthetic method the following are 
 the universal canons of order : 
 
 Canons of Order. 
 
 1. Place that first upon which all the rest depend, and which 
 presupposes nothing as having preceded it. 
 
 2. Place each intermediate step next in order after that 
 which it presupposes, and before all others which depend 
 upon it. * 
 
 3. Place that last which presupposes all the rest, and which 
 implies none others as depending upon it. 
 
 4. Where there are two or more intermediate steps which 
 have a common dependence upon something which precedes 
 them, and which do not depend upon one another (cases 
 which often occur), these may be arranged indifferently, as 
 convenience or taste may require. 
 
 The canons of order for the analytic method are, in all re- 
 
DOCTRINE OF METHOD. 
 
 spects, the reverse of those above given. Any departures from 
 these canons tends to confuse and obscure all forms of logical 
 thinking. 
 
 Section IV. Miscellaneous Topics bearing upon our 
 present Inquiries the Doctrine of Method. 
 
 We now advance to a consideration of certain miscellaneous 
 topics which have an important bearing upon our present inqui- 
 ries the doctrine of method. Among the topics which might 
 be considered, we would invite very special attention to the fol- 
 lowing : 
 
 I 
 
 characteristics of evert well-conducted argument. 
 
 We will consider, in the first place, the essential characteris- 
 tics of every well-conducted argument. In all such processes, 
 the following leading features will be, in a very special sense, 
 noticeable : 
 
 1. A clear, distinct, and full presentation of the real question 
 to be argued, such a presentation not only of the subject-matter 
 of the question itself, but an equally distinct one of the points of 
 distinction between it and any one or more questions with 
 which it is likely to be confounded in the hearer or reader's 
 mind. A presentation which leaves any of these points obscure 
 is fundamentally defective. 
 
 2. A presentation equally clear and adequate of the general 
 principle under which this specific case ranks. Here, also, 
 there will be a clear and distinct statement, not only of the na- 
 ture of the principle as it is in itself, but as it stands distin- 
 guished from every other principle with which it may be likely 
 to be confounded. 
 
 3. A corresponding exhibition of the evidence in favor of the 
 reality of the facts (if these are not admitted) bearing upon the 
 case at issue. 
 
 4. A similar presentation of the real bearing of these facts 
 
286 logic. 
 
 upon this one question, and in opposition to every other contra- 
 dictory or opposite hypothesis. 
 
 5. An exhibition of the same character, of the nature and real 
 bearing of any objections which may be urged against this hy- 
 pothesis, and of any arguments adduced in favor of any contra- 
 dictory or opposite hypothesis. Not to give an objection as it 
 is, and not to meet it in all its force, is, in fact, an admission of 
 its validity, and of the corresponding weakness of the hypothe- 
 sis against which said objection is adduced. 
 
 Note 1. In reasoning, strictly and absolutely demonstrative, 
 there is seldom, if ever, any occasion to answer objections, or 
 to consider the bearing of evidence against any hypothesis con- 
 tradictory or opposite to that actually established, inasmuch as 
 no valid objections can possibly he against a conclusion thus es- 
 tablished, and all opposite and contradictory propositions must 
 of course be false. 
 
 Note 2. The order in which the different departments of 
 any subject shall be presented depends upon circumstances. 
 The design of the above statements is to give the characteris- 
 tics of aU well-conducted processes of reasoning, without giving 
 the order in which those characteristics shall appear. 
 
 Methods of Proof the Direct and Indirect, and the two 
 united in the same * 
 
 The subject which next claims our attention is the different 
 methods of proving a proposition. Of these there can be but 
 three the direct, in which the weight of evidence is brought 
 to bear immediately and directly in favor of the fact, that the 
 conclusion is or must be true ; the indirect, in which it is shown 
 that the contrary or contradictory of the given proposition is or 
 must be false, and from hence the truth of the latter is imme- 
 diately inferred ; and cases in which both methods are brought 
 to bear in favor of the proposition to be proven. 
 
 Some propositions admit of proof in the first form only, some 
 in the second, and some equally by both united. Nothing but 
 good sense and the habit of careful reflection can decide which 
 
DOCTRINE OF METHOD. 287 
 
 form of proof should be used on any given occasion. For 
 example, let us suppose that the proposition to be argued is 
 this, that God is good. The common method of arguing this 
 question is, first to adduce the positive evidence of the Divine 
 goodness, and then to answer objections which may be urged 
 against it. Now the argument would be rendered incompara- 
 bly more forcible and conclusive, if the difficulties and objec- 
 tions in regard to the opposite proposition were also set with 
 full distinctness before the mind. 
 
 CHARACTERISTICS OF, ALL FORMS OF VALID EVIDENCE. 
 
 Valid evidence will always be of a, positive character, that is, 
 it will always positively affirm or deny some given proposition. 
 It may affirm the proposition as certainly or uncertainly, as 
 probably or improbably, as possibly T or impossibly, true or 
 false, &c. Whatever the form of the affirmation may be, this 
 will be its fundamental characteristic. Evidence not positive, 
 which does not positively affirm or deny, that is, evidence equal- 
 ly consistent with two or more contradictory hypotheses, is of 
 no account whatever in the matter of proof. 
 
 In all well-conducted arguments, we would also remark, the 
 hind of proposition to be established, that is, whether it is to be 
 proven as certainly, probably, or possibly true, will always be 
 distinctly stated, together with the specific nature and bearing 
 of the evidence to be presented. 
 
 FORMS OF EVIDENCE CLASSIFIED. 
 
 Evidence adduced to prove the reality of facts (testimony, 
 for example), or the truth of particular propositions, belongs in 
 all its forms to one or the other of the three following classes : 
 1. Evidence which never deceives or misleads. 2. Evidence 
 wholly unreliable or wholly indecisive. 3. Forms of evidence 
 lying between these two classes, and partaking more or less of 
 the characteristics of the two. There are statements, as we all 
 know, which all who are acquainted with the facts of the case 
 
288 LOGIC. 
 
 no more doubt, and can no more doubt, than they do or can 
 any of the conclusions reached in the mathematics ; such state- 
 ments, for example, as these, that there are such cities as London 
 and Paris ; that Bonaparte was defeated at Waterloo, &c. The 
 reason is, that such statements are sustained by a kind of evi- 
 dence which all men know, and can but know, never does, in 
 fact, mislead. There are statements, on the other hand, the 
 truth of which, by the evidence which stands around them, is 
 wholly a matter of doubt. There is still another class of state- 
 ments which command our belief in various degrees. In all 
 reasoning from facts, these characteristics of evidence in its va- 
 rious forms should be kept distinctly in mind, and in each given 
 case the specific nature of the evidence bearing upon it should 
 be the object of distinct apprehension. In "Leslie's Short 
 Method with Deists," the characteristics of historical evidence 
 of the first class are very distinctly stated. 
 
 CHARACTERISTICS OF ALL FORMS OF VALID PROOF. 
 
 The forms of proof are various, according to the nature of 
 the propositions to be proven, and the nature of the evidence 
 by which they are, or are attempted to be, proven. Among 
 these forms we notice particularly the following : 
 
 The Mathematical. 
 
 Mathematical proof, commonly called by way of eminence, 
 the demonstrative, has in all cases the following characteris- 
 tics, to wit: 1. The terms, the two extremes and the middle, 
 will be absolutely definite in their meaning, and that meaning 
 equally intelligible and known. 2. In affirmative conclusions 
 the extremes will be given, both alike,- as absolutely agreeing 
 with the middle term. 3. In negative conclusions one extreme 
 will be given as agreeing, and the other as disagreeing, abso- 
 lutely with the middle term. 4. When the conclusions are 
 universal, such must be the relations of both extremes to the 
 middle term, and in particular conclusions one extreme must 
 
DOCTRINE OF METHOD. 289 
 
 be related universally, and the other not so, to the middle term. 
 This last characteristic belongs properly to a previous depart- 
 ment of our subject, and is repeated here only for the sake of 
 distinctness. 
 
 Reasoning from Facts to General Conclusions, or from one 
 Fact to a?iother. 
 
 When reasoning is not mathematical, as when we reason 
 from effects to causes, from facts to general laws, acts to mo- 
 tives, phenomena or qualities to substances, or from facts (testi- 
 mony, for example) to othef facts, &c, the following will be 
 the characteristics of all valid proof: 1. The facts adduced 
 must not only be real, but pertain really and truly to the sub- 
 ject to which they are referred. 2. They must all consist with, 
 that is, none of them must contradict, the hypothesis, to prove 
 which they are adduced. 3. They must undeniably be irrecon- 
 cilable with any conceivable hypothesis but this one exclusive- 
 ly. 4. This one hypothesis they must as clearly affirm. Some- 
 times a class of facts may be reconcilable with no known, or at 
 present conceivable, hypothesis, but one, and with this they 
 may all harmonize. Yet such may be their nature, that they 
 do not certainly affirm this hypothesis as true. In such cases 
 the facts really stand unexplained, this one hypothesis having 
 
 ; the preference to any other now known. Any of these forms 
 of proof wanting any of these characteristics must be held as in- 
 valid, and all possessing these as valid. In all well-conducted 
 
 : arguments the evidence adduced will be shown in fact, if not in 
 form, to possess the above characteristics. 
 
 THE TRUE AND PROPER METHOD OP DETERMINING THE CHAR- 
 ACTER AND VALIDITY OF ANY GIVEN ARGUMENT. 
 
 The question which next claims our attention is the true and 
 proper method of examining any given argument, for the pur- 
 pose of determining its validity. The following we lay down 
 as the most essential elements of such a process : 
 
290 LOGIC. 
 
 1. First of all, attention should be directed to the terms or 
 conceptions employed in the argument, and these should be 
 carefully examined in the light of such questions as the follow- 
 ing : (l.) What is the real meaning of said terms, and what 
 is implied in them ? (2.) Are the conceptions represented by 
 said terms valid, that is, do they correctly represent their ob- 
 jects ? or, is the whole argument based upon a misconception 
 of said objects ? (3.) Are these terms employed throughout 
 in the same sense ? or do they, in different parts of the pro- 
 cess, represent different conceptions ? A failure in either of 
 these fundamental particulars would vitiate the whole argu- 
 ment. 
 
 2. The next object of attention is the major premise, provid- 
 ed it is a general principle assumed as self-evidently true. This 
 principle should always be examined in the light of such ques- 
 tions as the following: (l.) What is the real meaning of this 
 principle, and what is implied in it ? (2.) What is its real char- 
 acter, that is, is it in fact a first truth, or a mere problematical 
 judgment requiring proof? (3.) Is the proposition true in the 
 form in which it is here given ? It is not unfrequently the 
 fact that a principle which is true in one form, is given in 
 another and different form, a form in which it is not true. 
 
 8. The inquiry next in order pertains to the character and 
 bearings of the facts which are arranged under a general prin- 
 ciple, an inquiry which should always take the following di- 
 rection : (1.) Are these facts real, that is, are they affirmed as 
 such by valid evidence ? (2.) Do they really belong to the \ 
 class to which they are referred ? Facts referred to the crime 
 of murder, for example, may have the exclusive characteristics 
 of some other class of acts, such as manslaughter, or justifiable 
 homicide ; or they may have the common characteristics of the 
 three, that is, be equally consistent with each and all alike, and 
 hence affirm neither in distinction from the other. Facts can- 
 not logically be referred to any given class, unless they bear the 
 exclusive characteristics of said class ; that is, they do not prove 
 any one hypothesis, unless they contradict every contradictory 
 and opposite hypothesis. 
 
DOCTRINE OF METHOD. 291 
 
 4. The last object of special attention will be the relations 
 between the premises and conclusion, as to whether the latter, 
 both in respect to its matter and form, does or does not result 
 from the former. 
 
 Example in illustration. 
 
 In illustration of the manner of applying the above principles 
 we will take a single example, the theistic syllogism as stated 
 by Professor Tulloch in his "prize essay" entitled "Theism." 
 " The theistic argument," he says, " may be syllogistically ex- 
 pressed as follows, in a form which appears to us at once sim- 
 ple and free from ambiguity, viz. : 
 First or major premise, 
 
 Order universally proves mind ; 
 Second or minor premise, 
 
 The works of nature discover order ; 
 Conclusion, 
 
 The works of nature prove mind." 
 
 In examining the above argument it will be perceived at 
 once, that as far as the terms employed are concerned, to wit, 
 " order," " mind," and " the works of nature," every condition 
 required is fulfilled. No doubt does or can exist in respect to 
 their meaning or validity. 
 
 Let us then turn our attention to the major premise, " Order 
 universally proves mind." The meaning of this proposition 
 is undeniably this Order, whatever its nature or character, 
 whether it is mental or physical, proves mind as its originating 
 cause. In other words, order, whenever and in whatever form 
 it appears, exists exclusively as an effect, and owes its existence 
 to mind as its originating cause. Such, undeniably, is the real 
 meaning of this proposition. What is its character ? Is it a 
 first truth, that is, is its truth self-evident ? Or is it a pro- 
 blematical proposition which, if true, needs proof? That its 
 truth is not self-evident our author himself admits, and all must 
 
5292 LOGIC. 
 
 admit, from the fact, also, that its validity is denied hy all who 
 deny the claims of theism. 
 
 Then is this proposition true in fact ? To prove that it is not, 
 we have only to adduce a single example of order, which is not 
 an effect of any cause whatever, and which, consequently, does 
 not owe its existence to mind as its originating cause. Such an 
 example we do have in the Divine mind. Here is order in ab- 
 solute perfection, order which is not an effect of any cause 
 whatever, and therefore does not prove mind as its originating 
 cause. Whether we affirm or deny the Divine existence, also, 
 one thing is undeniable, to wit, that the principle of order in 
 the universe, whatever its nature may be a principle which is 
 itself the highest example of order is not an effect of any 
 cause, and consequently does not prove mind in the sense in 
 which order is affirmed to prove it in the proposition before us. 
 The proposition, then, in the form in which it is here stated, is 
 not true, and we have a fundamentally erroneous statement of 
 the theistic argument. This argument syllogistically stated in 
 its true form would stand thus : 
 
 Order, which once did not exist and began to be, that is, order which is an 
 
 effect originated in time, proves mind ; 
 The order discovered by the works of nature is of this exclusive character ; 
 The works of nature, therefore, prove mind. 
 
 No one who rightly apprehends the meaning of the major 
 premise in this syllogism will doubt its validity. The only dif- 
 fer-ence of opinion which can arise will pertain to the validity of 
 the minor premise ; and this must be the character of every 
 scientific argument whose major premise is a general principle. 
 Said premise must be an admitted truth, and the only question 
 on which issue shall be joined, as far as the premises are con- 
 cerned, must be the validity of the minor premise. We shall 
 have occasion to allude to this subject again in another con- 
 nection. We allude to it now for the exclusive purpose of 
 elucidating the -proper method of examining any given argu- 
 ment. 
 
 In regard to the minor premise and conclusion of Professor 
 
DOClfilNE OP METHOD. 293 
 
 Tulloch's syllogism, every condition required is perfectly ful- 
 filled. This fact is too evident to require any further eluci- 
 dation. 
 
 METHOD OR FORMS OF PROVING ANY GIVEN PROPOSITION FALSE. 
 
 The inquiry to which we next advance is, the method or 
 forms in which any given proposition which is false may be 
 proved to be such. They are the following : 
 
 1. In case it is a universal proposition, proving its contrary to 
 be true. The proposition is then proved to be false in all its 
 extent. 
 
 2. Proving its contradictory to be true. In this case, if the 
 proposition is a particular one, it is proven false in all its ex- 
 tent ; if it is a universal proposition, it is proven false in that 
 form. 
 
 3. By showing it to be self -contradictory . No such proposi- 
 tion can, by any possibility, be true. 
 
 4. By proving that its truth is incompatible with some other 
 proposition known to be true. Thus in law, an alibi undeniably 
 established, absolutely disproves any crime charged upon an in- 
 dividual, the fact of his being in one place at the time, being 
 incompatible with the truth of the charge referred to. 
 
 Some propositions may be proven false in one form and some 
 in another, and success in such efforts often depends wholly 
 upon a clear discernment of the form demanded in the particu- 
 lar case under discussion, and the direction of the entire argu- 
 ment upon that one point. How often, for example, is utterly 
 useless and hopeless labor expended in an attempt to prove the 
 opposite of a universal proposition, when nothing is required 
 in the circumstances but the proof of its contradictory, the lat- 
 ter being of very easy accomplishment, and the former equally 
 difficult if not impossible. 
 I 
 
METHOD OR FORMS OF REFUTING ANY GIVEN ARGUMENT. 
 
 Term defined. 
 
 Refutation and disproof are totally different things. In the 
 latter process the object is to prove a proposition untrue. In the 
 former the object is to show, that a proposition is not, in fact, 
 proven by the arguments adduced to prove it. Refutation may 
 be complete and perfect, and the proposition referred to be true 
 notwithstanding. Different arguments admit of refutation in 
 one or the other of the following forms, and any given argu- 
 ment having any of these defects is void of logical consequence : 
 
 1. Some processes of argumentation are based upon essential 
 misconceptions of the subject-matter under discussion. This 
 fact being shown, the logical inconclusiveness of the whole pro- 
 cess is undeniably established, and nothing further in the form 
 of refutation is demanded. 
 
 2. Other processes are defective in respect to the general 
 principle on which they rest, and may be refuted by disclosing 
 this defect. For example, (l.) Such principle may be false in 
 fact. (2.) It may be false in the form in which it is presented 
 in the argument, as in the case which we considered as illus- 
 trative of the proper method of examining arguments. (3.) It 
 may be irrelevant to the subject, and hence, though true in 
 itself, may not involve the conclusion deduced from it. 
 
 3. Other processes are defective in respect to the matters of 
 fact which are adduced as coming under the principle referred 
 to, and the argument based upon this principle may be refuted 
 by showing this defect, (l.) The statement of facts may be 
 untrue. (2.) Those statements may not be sustained by valid 
 evidence. (3.) They may not belong to the principle or class 
 to which they are referred, or may have the essential charac- 
 teiistics of another and different class. (4.) They may not be 
 decisive at all, that is, they may be equally consistent w T ith dif- 
 ferent and opposite hypotheses. No specific crime, for exam- 
 ple, can be proven by facts which may be performed by per- 
 sons perfectly innocent. An argument having any of these de- 
 
DOCTRINE OF METHOD. 295 
 
 fects is void of logical consequence, and is perfectly refuted 
 when any one of them is shown to be involved in it. 
 
 4. Other processes, we remark finally, are defective for the 
 want of logical connection between the premises and conclusion. 
 When such want is shown -in any given case, the refutation is 
 complete. 
 
 In all cases of refutation the first step is a distinct determina- 
 tion of the precise form of the defect in the specific case under 
 consideration. Effort should then be concentrated upon that 
 particular point. Some processes are faulty in one particular 
 and some in another, and some in most if not all respects. Ar- 
 guments perfectly void of logical consequence not unfrequently 
 appear impregnable, because their impregnable instead of their 
 really weak points are assailed. 
 
 OBJECTIONS TO A GIVEN HYPOTHESIS WHEN VALID. 
 
 Against almost every hypothesis on almost any subject not 
 falling within the sphere of absolute demonstration, very plausi- 
 ble objections may be urged. Hence a very important inquiry 
 arises, to wit, when shall an objection to any given hypothesis 
 be considered as valid, that is, as conclusive against the truth 
 of said hypothesis ? All such objections will have the following 
 characteristics : 
 
 1. The facts implied in the objection must be real, that is, 
 must be affirmed as such by really valid evidence. 
 
 2. The reality of said facts must be incompatible, and unde- 
 niably so, with the truth of said hypothesis. It must not pre- 
 sent a mere difficulty, one which we may not now know how to 
 explain consistently with said hypothesis, but one which unde- 
 niably cannot be thus explained. A difficulty, it should be 
 borne in mind, is one thing ; real incompatibility is quite another. 
 Facts difficult or unsusceptible of explanation in our present 
 state of knowledge may be urged against hypotheses undenia- 
 bly true. An objection to be valid must present a difficulty of 
 this kind, that the fact which it asserts must be unreal, or the 
 hypothesis against which it is urged must be false. Against the 
 
296 logic. 
 
 hypothesis of the identity of the nervous fluid and electricity, 
 for example, this objection is urged, to wit, that the latter will, 
 and the former will not, in fact, pass along the nerve when it is 
 tightly hound with a cord. Here is a fact affirmed which is not 
 merely difficult of explanation in consistency with said hypothe- 
 sis, but strictly and undeniably incompatible with it. Either 
 the fact asserted is unreal, or the hypothesis must be false. 
 This is the exclusive character of all valid objections against 
 any hypothesis. 
 
 Note 1. Every one who urges any particular objection 
 against any hypothesis should be required, before an answer is 
 attempted, to prove that the fact he asserts is real, and then, 
 that if it is true, the hypothesis against which it is urged must 
 be false. That is the burden of proof resting upon the ob- 
 jector. 
 
 Note 2. Individuals in treating objections frequently err in 
 two important particulars not distinguishing in the first place 
 between a fact difficult of explanation, and one incompatible 
 with the hypothesis against which it is urged ; and in the next, 
 instead of requiring the objector to prove his facts, and show 
 that they possess the element of real incompatibility, they as- 
 sume the burden of explaining all difficulties, thus practically 
 admitting that unless their hypothesis is totally free from diffi- 
 culties it cannot be true. 
 
 METHOD OP REFUTING OBJECTIONS, OK THE FORMS IN WHICH 
 THEY MAY BE REFUTED. 
 
 One more topic demands our special attention, to wit, the 
 proper method or forms of refuting objections. An invalid ob- 
 jection may be shown to be such in one or the other of the fol- 
 lowing forms, or by more or less of them combined : 
 
 1. It may be shown that the objection is based upon a funda- 
 mental misconception of the subject against which it is urged. 
 
 2. It may be shown that the fact presented in the objection 
 is unreal, or wants valid evidence of being real. 
 
DOCTRINE OF METHOD. 297 
 
 3. That the fact, if admitted, presents a mere difficulty, and 
 wholly lacks the element of incompatibility. 
 
 4. That precisely the same or similar objections lie against 
 the opposite hypothesis, when one of the two must be true. 
 That objection cannot be valid which would, as in such a case, 
 exist in all its force, if the hypothesis against which it is urged 
 were true. 
 
 5. That the same or precisely similar objections he against 
 hypotheses known and admitted to be true. Such objections 
 must be void of validity, of course. " Butler's Analogy" may 
 be referred to as an example of this form of refuting objec- 
 tions. 
 
 13 
 
PART IV. 
 
 APPLIED L OGIC. 
 
 Our object in this, the last department of our present inves- 
 tigations, is an illustration of the principles which we have al- 
 ready presented by applying said principles to a number of spe- 
 cific cases in the various departments of thought and inquiry. 
 As our exclusive object, as far as the science of logic is con- 
 cerned, is illustration, the examples selected will be wholly of a 
 miscellaneous character, with no special reference to scientific 
 arrangement. 
 
 The Anglo-Saxon and German Methods of developing 
 Thought. 
 
 We have already distinguished between the fragmentary and 
 scientific methods of developing thought, the former consisting 
 in a mere aggregation of topics generally contemplated and 
 discussed in connection with some one department of thought 
 and investigation, and the latter in a systematic development 
 of said department itself in accordance with the immutable laws 
 and principles of scientific definition, and logical division and 
 arrangement of topics. As far as method, in the development 
 of thought, is concerned, the productions of the German mind 
 pre-eminently bear the characteristics of scientific development, 
 while those of the Anglo-Saxon partake, to a very great extent, 
 of the fragmentary. Each department of thought is developed 
 by the German mind from a certain " stand-point," and is so 
 
APPLIED LOGIC. 299 
 
 developed that every particular topic is distinctly presented as 
 a necessary part of an all-comprehending whole, thus distinctly 
 realizing the idea of system. In treatises proceeding from the 
 Anglo-Saxon mind, on the other hand, we too often meet with 
 little more than an aggregation of topics falling within the 
 sphere of the department of thought to he developed, while 
 each topic is developed with little reference to the idea of a 
 whole including its parts. 
 
 Reasons for this difference. 
 
 The reasons for this diversity* are obvious. In the German 
 mind, under the influence of the philosophy of Kant, the d 
 priori element of thought is very distinctly, while in the An- 
 glo-Saxon mind, in consequence of that of Locke, it is very in- 
 distinctly, developed. Methods of thinking which distinctly 
 repudiate, as the philosophy of Locke does, all elements of 
 thought hut those immediately derived from experience those 
 immediately given by external and internal perception (sense 
 and consciousness) can have little else than a fragmentary 
 character, while those which not only recognize the facts of ex- 
 perience but also their logical antecedents the d priori ele- 
 ments of thoughts and are developed with distinct reference to 
 the latter, the ideas of substance, cause, and of a whole includ- 
 ing parts, &c, must almost of necessity assume the form of sys- 
 tematic and scientific logical development. The above state- 
 ments present a distinct view of what the philosophy of Locke 
 has done for the Anglo-Saxon, on the one hand, and what that 
 of Kant has done for the German mind, on the other. 
 
 Illustration 1. Systems of Natural Theology developed ac- 
 cording to these two Methods. 
 
 We will elucidate the principles above stated by two exam- 
 ples. The first is a view of systems of natural theology de- 
 veloped according to these two opposite methods. 
 
 According to the fragmentary method, writers, for the most 
 
300 LOGIC. 
 
 part, commence with an attempted demonstration of the propo- 
 sition, " God exists," and this without any specific definition of 
 the term God. Then, hy an independent process of deduction, 
 there is an attempted proof of the fact, that God possesses cer- 
 tain attributes, such as spirituality, omnipotence, omniscience, 
 omnipresence, goodness, &c. In all such cases as these, it will 
 be perceived at once, that we have a mere aggregation of topics 
 generally considered as connected with the subject before us, 
 while there is the total absence of system scientifically consid- 
 ered. The parts have no principles of necessary connection, 
 and hence do not appear as necessary parts of a given whole, 
 parts separated and united according to the necessary laws of 
 logical division and arrangement. 
 
 According to the scientific method, first of all, the term God 
 would be defined as representing a self-conscious personality 
 endowed with all the attributes involved in the ideas of abso- 
 lute infinity and perfection, and sustaining to all conditional ex- 
 istences the relation of unconditioned cause. Then the proposi- 
 tion, " God exists," God, as representing such an idea, would be 
 demonstrated. The next inquiry would be, what attributes are 
 necessarily supposed by such an idea of God, and in what form 
 shall such attributes be affirmed of him ? The number of attri- 
 butes and the form of each would be determined by this one 
 idea, and elucidated in the light of the same. Here we have 
 realized the idea of system, and no treatise developed upon op- 
 posite principles deserves the name of system. Hitherto the 
 fragmentary method has almost exclusively obtained in the 
 science of theology. 
 
 Illustration 2. Systems of Intellectual Philosophy devel- 
 oped according to these two Methods. 
 
 We will, in the next place, contemplate systems of intellectual 
 philosophy developed according to these two distinct and oppo- 
 site methods. In developing a system in accordance with the 
 truly systematic or scientific idea, the first aim would be to de- 
 termine definitely the sphere of the science referred to. In ac- 
 
APPLIED LOGIC. 30] 
 
 complishing this object the threefold distinction will be made 
 between the mental faculties, as consisting of the intellect, to 
 which all the phenomena of thought are referred ; the sensibili- 
 ty, to which are referred all sensitive states or feelings, such as 
 sensations, emotions, desires, &c. ; and the will, to which per- 
 tains all mental determinations. The object or sphere of the 
 science of intellectual philosophy will then be defined as consist- 
 ing in this a development of the functions and laws of the 
 human intelligence or intellect. In entering upon this depart- 
 ment of inquiry, all intellectual operations will be divided into 
 two classes, the primary and secondary the former furnishing 
 us with all the original elements of thought, and the latter con- 
 sisting of the various intellectual operations performed upon 
 such elements. 
 
 The primary functions of the intelligence will be classed, as 
 demanded by undeniable facts, under a threefold division, to 
 wit : sense, the faculty which gives us the qualities of external 
 material substances ; consciousness, the faculty which perceives 
 and apprehends the phenomena of the mind itself, or internal 
 phenomena ; and reason, the faculty or function of the intelli- 
 gence which gives the logical antecedents of the phenomena 
 given by sense and consciousness, that is, the ideas of space, 
 time, substance, cause, the finite and the infinite, of a whole in- 
 cluding parts, of right and wrong, law, &c. The elements of 
 all our knowledge will be shown to be given by these three 
 functions of the intelligence. Having determined the character 
 of these classes of phenomena their mutual relationships and 
 dependencies, and consequently the relations of these faculties 
 to one another the next department of inquiry will be the 
 secondary faculties or functions of the intelligence. Here, first 
 of all, those intellectual operations by which the elements of 
 thought given by the primary faculties are combined into con- 
 ceptions or notions particular and general, will claim special 
 attention the faculty by which such operations are performed 
 being denominated the understanding, the conceptive or notion- 
 forming power. 
 
 The faculty next considered will be that in which the various 
 
 
relations, intuitive and deductive, existing between conceptions 
 or notions, are affirmed, that is, the faculty of judgment. 
 
 Then the associative principle, including memory and recol- 
 lection the principle by which former intellectual states are re- 
 vived by means of present mental states will be elucidated. 
 
 The last object of inquiry will be the imagination, that facul- 
 ty or function of the intelligence by which the elements of 
 thought given by the other faculties are blended into concep- 
 tions corresponding, not like conceptions of the understanding 
 with realities as they are, but with fundamental ideas in the 
 mind itself, ideas of the beautiful, the grand, the sublime, &c. 
 
 A system of intellectual philosophy thus developed undenia- 
 bly realizes the true idea of science in accordance with the 
 necessary laws of scientific definition, logical division and ar- 
 rangement of topics. It will readily be seen that each function 
 of the intelligence referred to really exists, and is as really dis- 
 tinct from every other, and at the same time that these different 
 faculties include all conceivable intellectual operations. Every 
 intellectual operation must be an intuition of one or the other 
 of the primary faculties a notion or conception, that is, an 
 operation of the understanding a judgment intuitive or deduc- 
 tive, or a phenomenon of the faculty of judgment an act of 
 memory or recollection or a creation of the imagination. 
 There are just this number of intellectual faculties or functions, 
 and there can be no more. Such would be the general charac- 
 ter of a system of intellectual philosophy developed according 
 to the German, or what we regard as the only scientific method. 
 
 Let us now contemplate an example of a system developed in 
 conformity to the fragmentary method, to which most systems 
 in this department of science developed by the Anglo-Saxon 
 mind conform. The following is the fist and order of topics in- 
 vestigated by an author of great merit, whose work appeared a 
 few yeai*s since. After certain preliminary observations, the 
 author proposes to investigate the following subjects : I. Per- 
 ception ; in one section under this division the subject of concep- 
 tions or notions is considered. II. Consciousness. III. Origi- 
 
APPLIED LOGIC. 303 
 
 nal suggestion or apprehension. IV. Abstraction. V. Memo- 
 ry. VI. Reasoning. VII. Imagination. VIII. Taste. 
 
 This division and arrangement of topics in general accords, 
 and in no essential particular differs, from most of the popular 
 treatises on this science now before the English and American 
 public. In regard to such a method of elucidating this science, 
 we would invite special attention to the following suggestions : 
 1. There is here no proper recognition of the fundamental dis- 
 tinction between the primary and secondary functions of the 
 intelligence, and no elucidation of their mutual relationships 
 and dependencies upon one another. 2. This distinction is 
 confounded, conceptions or notions being treated of prior to 
 two of the primary faculties, consciousness and oi-iginal sug- 
 gestion. 3. From the form and connection in which concep- 
 tions are treated of, it is implied that they pertain only to ex- 
 ternal objects, while we have, in fact, conceptions respecting 
 mind as well as matter. 4. More than all, abstraction, rea- 
 soning, and taste, are presented as distinct functions of the gen- 
 eral intelligence, whereas they are all only different functions 
 of a single faculty of that intelligence, to wit, the judgment. 
 To judge that different elements of a given conception are un- 
 like to each other, and thus to separate them the one from the 
 other that is, to make abstraction of a given conception, to 
 judge in view of the relations of given conceptions to some 
 common one, that they agree or disagree with one another 
 that is, to reason, and to affirm of certain objects or acts, that 
 one is beautiful, grand, sublime, or the opposite that is, those 
 intellectual operations denominated taste, do not present the 
 operations of different functions of the general intelligence, but 
 diverse operations of one and the same faculty of that intelli- 
 gence the judgment. 5. We have in all such cases, in short, 
 a mere aggregation of topics connected with this science in the 
 almost total absence of all conformity to the laws and principles 
 -of logical division of subjects and scientific arrangement of 
 topics. It is needless to add, that by means of such a method 
 it is impossible to attain to the real science of the human intel- 
 
We have given the above examples for the express purpose 
 of impressing upon all the fundamental importance of scientific 
 method in the treatment of all subjects of thought. 
 
 The character of any System of Intellectual Philosophy which 
 shall meet the fundamental wants of this age. 
 
 Before dismissing the subject of intellectual philosophy we 
 would direct special attention to one inquiry pertaining to this 
 subject, to wit, the character of any system in this department 
 of thought and investigation which shall meet the fundamental 
 wants of this age. Among these characteristics we simply no- 
 tice the two following : 
 
 1. The system itself will be developed in strict accordance 
 with the principles of scientific method above elucidated. Any 
 system developed according to the fragmentary method will 
 leave the great want under consideration unmet. 
 
 2. The system must be so developed that the principles eluci- 
 dated shall underlie and lead to the distinct solution of those 
 great questions which lie wholly within the sphere of intellectual 
 science, and which are now pressing everywhere upon the phi- 
 losophic mind questions pertaining to the distinct and oppo- 
 site systems of realism, materialism, and idealism in its various 
 forms. One of these systems, to the exclusion of all the others, 
 must be true, and it belongs exclusively to this one science to 
 furnish the principles by which the question pertaining to the 
 validity of each may be solved. Any systems that fail to furnish 
 and elucidate such principles fail utterly to meet one of the most 
 fundamental wants of the age, a want which science is bound 
 to meet. Each of the systems of materialism and idealism is 
 either true or false, and science is bound to show which. The 
 influence of these systems upon the public mind can be de- 
 stroyed, not by ignoring the subject, nor by railing against the 
 consequences to which any such system leads, but by a demon- 
 stration of the invalidity of its claims. Here, as it appears to 
 us, lies the grand defect in our systems of intellectual philoso- 
 phy as commonly taught in the progress of a liberal education. 
 
APPLIED LOGIC. 305 
 
 The method pursued in such systems is for the most part, to 
 say the least, of the fragmentary instead of the truly scientific 
 character. Then, when the student leaves his alma mater, 
 with the impression that he understands this science, he finds 
 himself confronted with systems of intellectual science utterly 
 subversive of all his ideas of God, immortality, and retribution 
 systems apparently possessing the highest perfection of scien- 
 tific development, and commended to his regard by the highest 
 forms of apparent philosophic deduction. These systems pre- 
 sent great problems which undeniably fall within the appro- 
 priate and exclusive sphere of the science in which he has sup- 
 posed himself to have been fully taught, and yet he finds him- 
 self furnished with no principles by which he can discern the 
 invalidity of the systems themselves, or give any other solutions 
 to these problems than those furnished by said systems. Un- 
 der such circumstances, the philosophic mind is impressed with 
 the consciousness that it must either ignore philosophy itself 
 what few such minds will do or embrace some one of the sys- 
 tems referred to, or else hang in' painful suspense in regard to 
 the question, What is truth ? Systems which leave the great 
 problems of philosophy in such a state, must be fundamentally 
 unadapted to meet the pressing wants of the age. 
 
 EEBOE OF ME. MILL IN REGAED TO THE SYLLOGISM. 
 
 " It must be granted," says Mr. Mill, " that in every syllo- 
 gism, considered as an argument to prove the conclusion, there 
 is a petitio principii. When we say, 
 
 All men are mortal ; 
 Socrates is a man ; 
 Therefore, Socrates is mortal ; 
 
 it is unanswerably urged by the adversaries of the syllogistic 
 theory that the proposition, ' Socrates is mortal,' is presupposed 
 in the more general- assumption, 'All men are mortal;' that we 
 cannot be assured of the mortality of all men, unless we are 
 previously certain of the mortality of every individual man ; 
 
that if it be still doubtful whether Socrates, or any other indi- 
 vidual you choose to name, be mortal or not, the same degree 
 of uncertainty must hang over the assertion, ' All men are mor- 
 tal ;' that the general principle, instead of being given as evi- 
 dence of the particular case, cannot itself be taken for true with- 
 out exception, until every shadow of doubt which could effect 
 any case comprised with it, is dispelled by evidence aliunde / 
 and then what remains for the syllogism to prove ? that, in 
 short, no reasoning from generals to particulars can, as such, 
 prove any thing ; since from a general principle you cannot in- 
 fer any particulars, but those which the principle itself assumes 
 as foreknown." 
 
 In reply, we remark in the first place, that what Mi\ Mill 
 has here affirmed to be true of the syllogism universally, has no 
 application whatever to any but syllogisms of a certain class, 
 and even in respect to these his assertions do not hold. In all 
 cases where the major proposition represents a strictly necessa- 
 ry and universal truth or principle, and the minor presents a 
 fact coming under said principle, there is not even the appear- 
 ance of the petitio principii. For example : 
 
 Things equal to the same things are equal to one another ; 
 
 A and B are each equal to C ; 
 
 Therefore, A and B are equal to one another. 
 
 Where is even the appearance of the fallacy under considera- 
 tion in this case ? and the syllogism of most of the sciences is 
 exclusively of this character. 
 
 In cases where the major premise, as in the proposition, "All 
 men are mortal," is a general principle or truth of induction, 
 which Mr. Mill falsely assumes to hold of all scientific princi- 
 ples, he would have us suppose that the truth of said principle is 
 y*- . * assumed, that is, begged without proof. We observe a certain 
 
 number of cases of a certain class, and find a certain fact to be 
 true of them. From such mere coincidences we assume that 
 the same fact is connected with all the individuals of the class 
 referred to, and then from this mere assumption we reason back 
 to each individual of said class. Now it is not true in fact that 
 general truths of this character even are affirmed for the reason 
 
 
APPLIED LOGIC. 307 
 
 here assigned. Such deductions, on the other hand, rest upon 
 the principle stated by Kant, to wit : that where a great multi- 
 tude of facts of a given species universally agree in some one 
 particular, there is, in the nature of the facts themselves, " some 
 common ground" for such agreement a ground which, of 
 course, must hold true of all facts of the same species subse- 
 quently met with. It is in view of this principle, that all gen- 
 eral principles of the character under consideration are affirmed. 
 The validity of the general principle is not begged, as Mr. Mill 
 affirms, but affirmed in view of a valid reason. It is not neces- 
 sary for us to observe every solitary fact of a given class, to 
 know the law of their existence and occurrence. When a suf- 
 ficient number' has been observed to discover said law, we then 
 rank all particular facts of this class under that law. We have 
 not seen each individual of the race die. We have seen a suffi- 
 cient number, however, to perceive that mortality is not an acci- 
 dent, but the law of human existence in its present state. This 
 law is expressed in the proposition, "All men are mortal." In 
 no particular, therefore, does the principle of Mr. Mill hold 
 true of the syllogism. 
 
 ERROR OF ME. MILL IN REGARD TO THE NATURE OP ALL 
 PORMS OF INFERENCE. 
 
 As the syllogism in all its forms contains, according to Mr. 
 Mill, a petitio principii, he from hence concludes that in no 
 instance do we really reason or draw inferences from general 
 principles, but in all instances that we reason "from particulars 
 to particulars." " All inference," he says, " is from particulars 
 to particulars ; general propositions are merely registers of such 
 inferences already made, and short formula for making more. 
 The major premise of a syllogism consequently is a formula of 
 this description ; and the conclusion is not an inference drawn 
 from the formula, but an inference drawn according to the 
 formula ; the real logical antecedent or premises being the par- 
 ticular facts from which the general proposition was collected 
 by induction." 
 
308 LOGIC. 
 
 In the above conclusion, Mr. Mill has undeniably been mis- 
 led by his very limited " particular facts." He found that in 
 a few cases of inductions of a particular kind, there was an ap- 
 pearance of inference " from particulars to particulars." This 
 mere appearance of inference, in accordance with his principle, 
 he " made into a short formula for making more," that is, into 
 a universal formula for the explanation of all inferences of 
 every kind. The major premise or "real logical antecedent," 
 in all the leading sciences, instead of being " a formula of this 
 description," is an exclusively analytical judgment, a universal 
 and necessary truth whose invalidity is both inconceivable and 
 impossible ; and it is not merely according to, but from, these 
 universal and necessary truths that all the inferences in such 
 sciences are deduced. Do we, for example, believe the propo- 
 sition, " Things equal to the same things are equal to one 
 another," because we have tried the experiment and found the 
 principle to hold in certain particular cases, and because we 
 have from hence made these individual deductions into short 
 formulas for making more ? By no means. This judgment is 
 exclusively analytic, as we have formerly shown, and therefore 
 absolutely universal and necessary. We have not come to the 
 knowledge of it, as such, by experiment in particular cases, but 
 by direct and immediate intuition. The major premise, we re- 
 peat, in all the leading sciences is precisely such a truth, and 
 all inferences in such sciences is from, and not according to, 
 such truths. Even in those cases also which apparently favor 
 Mr. Mill's theory, we do not reason from individual facts to in- 
 dividual facts, but from certain facts of a given class to the law 
 which governs said facts, and then from this law to all the facts 
 of said class. There never was an inference more wide from 
 the truth, and less authorized by the facts from which it is de- 
 duced, than that of Mr. Mill in regard to the syllogism, on the 
 one hand, and all forms of inference, on the other. 
 
APPLIED LOGIC. 309 
 
 ME. MILL'S POSITION THAT "THE SYLLOGISM IS NOT THE TYPE 
 OF REASONING, BUT A TEST OF IT." 
 
 Mr. Mill, in accordance with the principles of his theory, 
 affirms that " the syllogism is not a correct analysis of reason- 
 ing or inference." Yet he goes on to show, that if we wish to 
 test the validity of a reasoning process we must make use of the 
 syllogism to do it. " It is not the form," he tells us, " in which 
 we must reason, but it is a form in which we may reason, and 
 into which it is indispensable to throw our reasoning when there 
 is any doubt of its validity." The syllogism, he asserts, always 
 involves a logical error, a petitio principii, and " is not a cor- 
 rect analysis "of reasoning or inference," and that it is only when 
 " there is no suspicion of error that we are permitted to use the 
 true process," that is, reason -from particulars to particulars, 
 "from the known particular cases to unknown ones." Now 
 here are a greater number of palpable contradictions than we 
 have space to notice. We will, therefore, specify only two or 
 three of them. The petitio principii begging the question 
 is, according to all the rules of logic, one of the most vicious 
 forms of reasoning, a form, therefore, never to be employed ; 
 and the syllogism, according to Mr. Mill, in all its forms, in- 
 volves this very fallacy. Yet, according to him the following 
 facts are true of the syllogism : 1. In no case is it "a form in 
 which we must reason ;" but it is only " when the case is familiar 
 and little complicated, and there is no suspicion of error," that 
 we may use that form which he affirms to be the only correct 
 " analysis of the reasoning process," the form in which in reali- 
 ty we always do reason, that is, " reason at once" from particu- 
 lars to particulars, " from known particular cases to unknown 
 ones." Now if in all cases but the one here specified, we may 
 not reason according to Mr. Mill's formula, that is, from par- 
 ticulars to particulars, and in no case are we obliged to use the 
 syllogistic form, there must remain a third form which is valid 
 universally, or Mr. Mill has most palpably contradicted him- 
 self. But no third form exists, and Mr. Mill has contradicted 
 himself. 2. According to Mr. Mill's express teachings, a form 
 
 
 y ^m^ 
 
of reasoning always vicious, and according to the immutable 
 laws of reasoning never to be employed, always may be em- 
 ployed. 3. Into this most vicious and never to be used form, 
 " it is indispensable to throw our reasoning when there is any 
 doubt of its validity." 4. The syllogism which presents a false 
 analysis of the reasoning process, and in all its forms involves 
 one of the most vicious forms of fallacy, is, after all, the only 
 proper test of the validity of any reasoning process whatever. 
 This is sufficient to demonstrate one fact, to wit, that Mr. Mill 
 must have fundamentally misapprehended the nature of the 
 reasoning process in all its forms. 
 
 Exclusive condition on which we can legitimately reason from 
 particulars to particulars. 
 
 Before dismissing this subject, attention should be directed to 
 one important inquiry the exclusive conditions on which we 
 can in any form legitimately reason from particulars to particu- 
 lars, that is, from one individual to another. Two individuals 
 are before us A and B. We have immediate knowledge of 
 the fact, that a certain element C exists in A, and have no such 
 knowledge relatively to B. On what condition can we infer 
 that because A has C, B has it also ? On this condition only, 
 that A and B have in common another element M, and that M 
 and C are necessarily connected, so that where M is, C is also. 
 Then, and then only, can we affirm positively that because A 
 has C, B has it also. If the connection between M and C is 
 merely accidental, we cannot reason at all from A to B. If we 
 do not know whether this connection is necessary or accidental, 
 then our reasoning is, as Mr. Mill himself has shown, analogi- 
 cal and not inductive. We never, then, in accordance with the 
 formula of Mr. Mill, reason from particulars to particulars, and 
 this Mr. Mill himself has fully shown in other parts of his work. 
 On the other hand, our reasoning from individuals to indi- 
 viduals is always in view of some element common to the two, 
 together with the known relations of this common element to 
 another known to exist in one individual, and not otherwise 
 
APPLIED LOGIC. 311 
 
 than inferentially known to exist in the other. In such cases 
 our reasoning is always from a general truth, to wit, Every in- 
 
 lividual which has the common element M has the implied 
 
 >ne C. 
 
 RELATIONS OF THE SYLLOGISM TO THE DISCOVERY OF TRUTH. 
 
 It is a doctrine of Mr. Mill and other logicians, that in no 
 case do we, hy means of the syllogism, discover truth, its only 
 use being the proof of truth when discovered. By investiga- 
 tion we discover, and by the syllogism we prove what has been 
 discovered. To this dogma we by no means yield our assent. 
 On the other hand, we believe that all inferred truth is origi- 
 nally discovered, as well as subsequently proved, by means of 
 the syllogism, and can be discovered by no other means. An 
 individual, for example, may know perfectly the relations of 
 two objects A and B to a common third C. Yet he may never 
 have perceived the inference involved in these relations. The 
 individual who points out that inference as really conveys a new 
 truth to that person, as the one who conveyed to him a know- 
 ledge of the relations referred to. Yet this new truth is re- 
 vealed wholly by means of the syllogism. A jury may have 
 before them all the facts bearing upon a given case, and yet not 
 perceive at all the real bearing of these facts upon that case. 
 The advocate or judge who reveals to them the conclusions in- 
 volved in said facts, as really makes a discovery to them as the 
 witnesses who revealed to them the facts. Yet those conclu- 
 sions were wholly revealed by means of the syllogism. Every 
 inference when first obtained is a newly discovered truth, a 
 truth discovered by means of the same premises by which it is 
 subsequently proven. These remarks apply to inferred truth 
 in all its forms. This is first discovered and then subsequently 
 proven by the same means, the syllogism. Investigation conse- 
 quently has two directions facts for the purpose of discovering 
 premises, and premises for the purpose of discovering the de- 
 ductions or inferences which they yield. The inference, as 
 originally given, is as much a discovery as the facts, and the 
 
312 LOGIC. 
 
 inference, we repeat, is always obtained by means of the syllo- 
 gism. 
 
 \/ THE GREAT PROBLEM IN PHILOSOPHY ACCORDING TO KANT. 
 
 In his " Critick of Pure Reason," Kant has rendered demon- 
 strably evident the actual existence in the human intelligence of 
 " cognitions d priori'''' that is, of ideas and principles having the 
 characteristics of absolute universality and necessity ; such, for 
 example, as the principle, " Body supposes space," " Succession, 
 time," " An event a cause," &c. In demonstrating the reality 
 of such principles he has rendered equally evident the fact, that 
 the fundamental principle of the philosophy of Locke, that all 
 our knowledge is derived from experience, is and must be false. 
 No man can, by any possibility, read and understand the first 
 five or six pages of the " Critick," and remain a disciple of the 
 empirical philosophy. By experience we only learn, and can 
 only learn, what is true in a certain number of particular cases, 
 but never what is and must be true in all cases universally. 
 As a matter of fact, we have cognitions of which we know ab- 
 solutely, that they not only are true in certain cases, but that 
 they are and must be true in all cases. Such cognitions, there- 
 fore, never could have been derived from experience. All such 
 cognitions Kant denominates " synthetic cognitions d priorV 
 Having demonstrated the existence of such cognitions, he pro- 
 poses this one question as the then great problem in philosophy, 
 to wit : " How are synthetic cognitions d priori possible ?" 
 " All metaphysicians consequently," he says, " are solemnly and 
 legally suspended from their occupations, till they shall have 
 answered in a satisfactory manner the question, How are syn- 
 thetic judgments, d priori, possible?" In this statement Kant 
 was unquestionably right, and philosophy can never be placed 
 permanently on the track of truth, till this question is correctly 
 / answered. 
 
APPLIED LOGIC. 313 
 
 KanVs solution of this Problem. 
 
 The following is Kant's solution of this problem. Through 
 the action of some unknown and unknowable cause, a certain 
 feeling sensation is produced in the mind. On occasion of 
 such feeling being excited, the ideas of time and space, by the 
 spontaneous action of the intelligence, are awakened in the 
 mind. Through these ideas the sensation which is purely and 
 exclusively a subjective state, appears to the mind as an object 
 external to the mind, an object having extension, form, color, 
 &c. We do not first perceive an external object, and then, as 
 the ideas of time and space are thus awakened in the mind, 
 conceive of it as existing in time and space. On the other 
 hand, these ideas are originated independently of perception 
 and prior to it, and when awakened cause the sensation to ap- 
 pear as an object external to the mind. The sensation, he af- 
 firms, is the content of the perception, the only thing really per- 
 ceived, while the ideas under consideration give "the form 
 thereof," that is, make the sensation appear as an external ob- 
 ject having extension and form. Under the influence of other 
 d priori ideas subsequently awakened in a similar manner to 
 the former ones, the object thus perceived is conceived of as a 
 substance having qualities, as acting upon other substances, and 
 being acted upon by them, as existing in time and space, &c. 
 Thus it is that the universe, with God as its author, rises before 
 the mind. The universe which we seem to see, and conceive of 
 as a great reality really and truly external to the mind, has no 
 real existence out of the mind itself. The universe which we 
 actually perceive is nothing but sensation made to appear 
 through d priori ideas, as a universe external to the mind ; 
 and God is nothing but an ideal cause of an ideal creation. 
 On no other supposition, he affirms, can we account for the ex- 
 istence of d priori cognitions, and sciences such as the pure 
 mathematics, in the mind. A priori ideas, he assumes, must 
 be derived from experience, that is, be directly and immediate- 
 ly given by perception external and internal, or they must exist 
 in the mind prior to perception and independent of it, and them- 
 
selves determine the perception and all subsequent mental oper- 
 ations. The first hypothesis is not, and cannot he, true. The 
 second, therefore, must be true. The universe, then, which we 
 perceive, is not an object external to the mind, an object which 
 the intelligence as a power of knowledge perceives as it is, but a 
 mere succession of sensations which, through these d priori 
 ideas, are made to appear as such a universe. The universe is 
 not to the mind an object, and the mind to it a faculty of know- 
 ledge ; and knowledge does not exist in consequence of this cor- 
 relation between the two. The external universe, on the other 
 hand, is nothing, we repeat, but sensation itself, made to appear 
 as such by means of d priori ideas awakened in the mind on 
 occasion of sensation by the spontaneous activity of the intelli- 
 gence itself. If these ideas are awakened prior to all other 
 intellectual operations, prior to all perception external or in- 
 ternal, if they give form and direction to perception and all 
 other intellectual operations, then we can see clearly how we 
 can have from these ideas pure d priori sciences, such as the 
 pure mathematics sciences, all of whose principles and deduc- 
 tions shall have the same characteristics of universality and ne- 
 cessity which their original principles have. We can see, too, 
 how it is that all the facts of the universe shall accord with 
 these d priori ideas and principles. Inasmuch as the latter de- 
 termine the former universally, there must be this accordance 
 between them. On no other supposition, Kant affirms, can the 
 existence of the pure sciences be accounted for, together with 
 the perfect and universal accordance of all the facts of the uni- 
 verse with the principles and deductions of these sciences. 
 Such is Kant's solution of the great problem in philosophy 
 which he has himself propounded. Let us now contemplate 
 the fundamental mistakes into which he has fallen in the solu- 
 tion of that problem. Among these we notice the following : 
 
 Errors of Kant in the solution of this Problem. 
 
 1. The first error that we notice is found in the assumption 
 which lies at the basis of this solution. The assumption is this : 
 
APPLIED LOGIC. 315 
 
 Either d priori ideas and principles are given directly and im- 
 mediately by experience (perception external and internal), ac- 
 cordig to the theory of Locke, or they must arise in the mind 
 by the spontaneous action of the intelligence, and that inde- 
 pendent of and prior to all acts of perception, external or inter- 
 nal, according to the theory of Kant. One of these theories, 
 he assumed, must be true, because none other is conceivable or 
 possible. The former cannot be true. The latter, consequent- 
 ly, must be true. 
 
 The error of Kant in the above assumption is obvious and 
 undeniable. He assumes that one or the other of these theo- 
 ries must be true, because none other is conceivable or possible. 
 Now there is a third theory differing alike from that of Locke, 
 on the one hand, and that of Kant, on the other a theory which, 
 in common with the latter, recognizes the reality of all d priori 
 cognitions, and as fully and perfectly as. that accounts for the 
 same, together with all other forms of knowledge. Let us sup- 
 pose that the universe exists as relatively to mind an object, 
 and mind to exist as relatively to the universe a power or 
 faculty of knowledge. Let us suppose further, that while there 
 is in the intelligence a power to perceive existing substances as 
 they are, there is also in the same intelligence the power to ap- 
 prehend other realities necessarily supposed by those which are 
 the objects of perception. In other words, let us suppose that 
 the intelligence not only has the power to perceive body, for 
 example, but on occasion of such perception, to apprehend the 
 reality of space, which must exist or body cannot exist. In 
 this case, we should have the idea of space just as it is given in 
 the theory of Kant. The same power which, on the perception 
 of extension, gives the idea of space, would, on the perception 
 of succession, phenomena, and events, give us the ideas of time, 
 substance, and cause. In a similar manner the existence of all 
 d priori ideas of every kind may be accounted for : 
 
 With equal readiness can we account, in consistency with 
 the principles of this theory, for all d priori judgments the d 
 priori synthetical cognitions of Kant with all their character- 
 istics. When we reflect upon the relations of what we perceive 
 
31 6 LOGIC. 
 
 to that which we apprehend as necessarily supposed as ante- 
 cedently true that is, supposed by what we perceive we see 
 at once, that those relations are absolutely universal and neces- 
 sary. These necessary and universal relations are expressed in 
 the principles, " Body supposes space," " Succession, time," 
 " Phenomena, substance," " Events a cause," &c. When the 
 necessary or d priori elements of thought are separated from 
 the empirical, and the principles and logical consequences of the 
 same are developed, we have the pure sciences- 1 such as the 
 mathematics. When the two forms of thought are developed 
 together, then we have the various mixed sciences. Thus wc 
 have a theory of knowledge which gives us all forms of know- 
 ledge as they are, and accounts for such knowledge as fully and 
 perfectly as the theory of Kant. The argument of Kant, then, 
 for the truth of his theory involves a fundamental fallacy a fal- 
 lacy in the employment of the disjunctive syllogism. This syl- 
 logism is this : Either the theory of Locke or my own must be 
 true. The former is not, and the latter consequently must be 
 true. The true syllogism applicable to the case as thus far pre- 
 sented is this : Either the theory of Locke, or one or the other 
 of the two under consideration, must be true. That of Locke is 
 not, and therefore one of these and so far it does not appear 
 which must be true. This last syllogism is and must be valid, 
 for the reason that there are no other conceivable theories for 
 accounting for the existence of d priori cognitions in the intelli- 
 gence but these three. The whole transcendental philosophy, 
 therefore for all its forms rest upon this one common founda- 
 tion rests exclusively upon an illogical basis. 
 
 2. But we remark, in the next place, that the theory of Kant 
 is not, while the opposite theory is, in fact, true. According 
 to the former theory, d priori ideas those of space and time, 
 for example arise in the mind prior to all forms of perception, 
 and, as laws of thought, give form to perception and all subse- 
 quent intellectual operations. Now we have no consciousness 
 whatever of any such relation as this between these ideas and 
 the act of perception. Who, by a reference to consciousness, 
 could perceive the truth of the statement of Kant, that " space 
 
APPLIED LOGIC. 317 
 
 and time are the pure forms of them" (perceptions), that is, 
 make the object perceived appear to the mind as possessed of 
 such qualities as extension and shape, " sensation the matter" 
 that is, that the thing really perceived is not an object really 
 external to the mind, but a sensation made through the means 
 of the ideas of time and space to appear as such object ? If 
 these ideas do thus cause a purely and exclusively mental state 
 (sensation) a state having no extension or form to appear to 
 the mind as an external object having extension and form, we 
 certainly have and can have no consciousness of the fact. On 
 the other hand, the testimony of consciousness is very distinct and 
 explicit against the theory of Kant, and in favor of the one which 
 we maintain. We are conscious of a direct and immediate per- 
 ception of an object external to the mind, and then subsequent- 
 ly of conceiving of that object as existing in time and space. 
 According to the distinct and explicit testimony of conscious- 
 ness, therefore, the ideas of time and space do not arise in the 
 mind prior to perception and as determining laws of the same, 
 but subsequently to perception and as laws of the secondary 
 operations of the intelligence to wit, conceptions or notions. 
 The theory of Kant is undeniably based upon a manifest psy- 
 chological error. Ideas which exist in the mind subsequent to 
 perception and exclusively as laws of the secondary operations 
 of the intelligence, are given as existing prior to perception and 
 as laws of perception itself that is, of the primary operations of 
 the intelligence. A greater psychological error can hardly be 
 conceived of than this. There is another consideration of the 
 greatest weight which renders demonstrably evident the fact, 
 that Kant's theory of the origin of d priori ideas and principles 
 is not, and that that of the opposite theory is, the true one. If 
 d priori ideas, those of space and time, for example, do arise in 
 the mind prior to perception, and consequently independently 
 of it, then the objects of these ideas, time and space themselves, 
 may be conceived of and defined by themselves, and without 
 any reference to any of the objects of perception. So of all 
 other d priori ideas. If this were so, we should also be equally 
 unable to conceive of or define objects of perception without 
 
318 LOGIC. 
 
 reference to the objects of d priori ideas. Now the reverse of 
 all this is undeniably true of both classes of ideas under consid- 
 eration. We conceive of and define no d priori idea but by 
 referring to objects of perception, while we can conceive of and 
 define the latter class of objects without referring to the former. 
 We can conceive of and define space and time, for example, 
 only as the places of bodies and events, and a cause only as that 
 which produces events. So of all other d priori ideas of every 
 kind. Their objects can be conceived of and defined but with 
 fixed reference to objects of perception. On the other hand, 
 objects of perception, body, for example, may be conceived of 
 and defined, and commonly are defined, without reference to 
 space, or other objects of d priori ideas. Such facts render it 
 demonstrably evident that d priori ideas do not, as Kant's 
 theory affirms, arise in the mind prior to perception, but that, 
 in accordance with the opposite theory, conceptions of the ob- 
 jects of perception are, in all instances, the chronological ante- 
 cedents of d priori ideas. The position of Cousin in regard to 
 the relation of these two classes of ideas, the latter of which he 
 denominates, and rightly too, necessary, and the former con- 
 tingent ideas, will unquestionably stand the test of time and of 
 the most rigid psychological investigation, to wit : that contin- 
 gent ideas (conceptions of objects of perception external and in- 
 ternal) are the chronological antecedents of necessary ideas, 
 that is, the former arise in the mind prior to the latter ; while 
 necessary ideas are the logical antecedents of contingent ones, 
 that is, we must admit the reality of the objects of the former 
 class of ideas, as the condition of the reality of the objects of the 
 latter class. These undeniable facts are perfectly fatal to the 
 claims of the theory of Kant and of every other form of idealism, 
 and as necessarily and absolutely affirm the truth of the oppo- 
 site theory, the theory which we have expounded. 
 
 3. The theory of Kant, we remark finally, cannot possibly be 
 true, because it involves the greatest conceivable contradictions 
 and absurdities. According to this theory, when we suppose 
 ourselves to perceive an external object, the only thing really 
 perceived by the mind is one of its own states a sensation. 
 
> APPLIED LOGIC. 319 
 
 The thing perceived the sensation has undeniably neithei 
 extension nor form. Yet it appears to have both. It is exclu- 
 sively a mental state. Yet it appears with equal exclusiveness 
 as an object external to the mind, and having an existence in 
 dependent of it. What is it that imparts to such an object such 
 an appearance ? The ideas of time and space, says Kant. Such, 
 also, is the answer of idealism in all its forms. These ideas 
 (those of time and space), it should be bome in mind, pertain 
 to their objects as absolutely infinite. Now here the following 
 important questions arise, and demand distinct and specific an- 
 swers from philosophy: (1.) How can one purely mental state 
 ideas pertaining to their objects as infinite cause another 
 purely and exclusively mental state a sensation to appear to 
 the mind as an object wholly external to the mind, and having 
 an existence as wholly independent of it ? Idealism has never 
 answered this question, and we are quite sure it never will. 
 (2.) How can ideas pertaining to their objects as having infinite 
 extension, give to purely mental states, void wholly of all exten- 
 sion, the appearance of having any kind of extension whatever ? 
 Is there here even a conceivable relation of cause and effect ? 
 (3.) How can ideas which peitain to their objects as having in- 
 finite extension, cause mental states, void in themselves of all 
 extension, to appear as possessed not only of an external exist- 
 ence, but finite extension ? Would not such ideas, if they im- 
 parted to such objects the appearance of any extension at all, 
 impart that of infinite extension ? Is not the opposite supposi- 
 tion a palpable absurdity and contradiction? (4.) How, we 
 ask finally, can ideas pertaining to their objects as exclusively 
 infinite, impart to two sensations, each of which is alike void of 
 all extension and form, and therefore in these respects absolute- 
 ly equal, the appearance even of not only having definite ex- 
 tension and form, but the one as being twice or a million of 
 times as large as the other ? Is not here an undeniable viola- 
 tion of the principle, " If equals be added to equals, the sums 
 are equal ?" He who assigns a cause for a given effect, must 
 assign an intelligibly adequate cause, a cause, too, intelligibly 
 adapted to produce the effect. The cause assigned by idealism 
 
for external perception is not only void utterly of both these 
 characteristics, but involves the greatest conceivable absurdity 
 and self-contradiction. That theory, therefore, cannot be true, 
 and the opposite one must be true. 
 
 The Sensational Theory of External Perception. 
 
 While systems of intellectual philosophy developed by the 
 Anglo-Saxon mind have generally repudiated the claims of 
 idealism in all its forms, they have, with hardly an exception, 
 admitted and affirmed the validity of that assumption upon 
 which every form of that system is based, to wit : that all our 
 knowledge of the external universe is not immediate, but me- 
 diate, and derived exclusively through the medium of sensation. 
 We are now prepared to form a correct estimate of this theory 
 of perception. According to its fundamental assumption, what 
 we really perceive, when we conceive of ourselves as having a 
 , perception of an object external to the mind, is not such object 
 at all, but an exclusively mental state, a sensation. This pure- 
 ly mental state, which is in itself utterly void of all extension 
 and form, is, by means of laws inhering in the intelligence itself, 
 made to appear as an object wholly external and foreign to the 
 mind, an object having extension and form. Against such a 
 theory we urge the following fundamental objections : 
 
 1. The theory rests exclusively upon a mere assumption, an 
 assumption for the validity of which no form or degree of evi- 
 dence whatever can be adduced. No self-evident principle or 
 valid deductions of science can be presented from which the va- 
 lidity of this theory can be deduced. This is undeniable. Let 
 any one attempt to prove the dogma that what we really per- 
 ceive, when we suppose ourselves to be actually perceiving an 
 external object, is no such object, but a mere sensation, an ex- 
 clusively mental state, and he will find that he has attempted 
 an impossibility. 
 
 2. This theory in all its developments is opposed to the direct 
 and absolute testimony of consciousness. In the consciousness 
 of perception two factors are given with equal absoluteness, self 
 
APPLIED LOGIC. 321 
 
 as the subject of the perception, and a not-self as its object. On 
 no subject is the testimony of consciousness more distinct and 
 absolute. In this theory, this distinction between the self and 
 the not-self is utterly confounded, and each is given as identical 
 with the other. " Consciousness, then," in the language of Sir 
 William Hamilton, " is a liar from the beginning," or this theo- 
 ry is and must be false. 
 
 3. This theory necessarily subverts the foundation of all valid 
 knowledge of every kind. If the intelligence, by virtue of its 
 own fundamental and immutable laws, deceives us, as this theo- 
 ry affirms that it does, in a matter so fundamental as percep- 
 tion, then undeniably it is to be trusted nowhere, and know- 
 ledge on any subject is an absolute impossibility. There is no 
 escaping this conclusion. And here permit us to remark, that 
 nothing conceivable is more unreasonable than the complaints 
 of the advocates of theism against the deductions of idealism, 
 while they themselves admit and affirm the foundation-principle 
 from which, by an absolute necessity, such deductions arise. 
 There is not a deduction of idealism which cannot be shown to 
 have a necessaiy logical connection with this one assumption. 
 
 4. This theory, we remark finally, involves the most palpable 
 conceivable absurdities and contradictions. This we have al- 
 ready shown in our remarks upon the Kantian theory of per- 
 ception. No philosopher has yet answered, in consistency with 
 this theory, the questions : How can a purely and exclusively 
 mental state be given in consciousness as an object wholly ex- 
 ternal and foreign to the mind ? How can such a state, which 
 undeniably has neither extension nor form, be given in con- 
 sciousness, not only as an object wholly external to the mind, 
 but also as having both these qualities ? The only answer ever 
 attempted to be given to these questions is the one already no- 
 ticed, to wit : that this is done through the ideas of time and 
 space, a solution, as we have shown, self-contradictory and ab- 
 surd. As no other solution is even conceivable, the theory 
 itself must be held as utterly foundationless and false. Yet 
 this theory, so utterly void of all valid claims and so demon- 
 strably false, has for ages lain at the basis of great systems of 
 
 14 , 
 
theology and philosophy. In this connection, we are surely 
 strongly admonished to examine with great care the principles 
 or first truths which we lay at the foundation of our systems of 
 belief, before we proceed to construct our systems upon such 
 principles. 
 
 THE GREAT PROBLEM IN PHILOSOPHY OP THE PRESENT AGE. 
 
 The progress of thought in every age throws upon the sur- 
 face of the public mind certain great problems in philosophy, 
 problems which demand of philosophy a satisfactory scientific 
 solution. The demonstration of the reality of d priori cogni- 
 tions in the human intelligence, presented for solution the great 
 problem propounded by Kant, to wit, "How are synthetic 
 cognitions d priori possible?" That problem, as we judge, has 
 now received the required solution. 
 
 Were we called upon to express an opinion in regard to the 
 question, What is the great problem in philosophy of the present 
 age ? it would be this : By what formula shall we represent this 
 one fundamental idea, to wit, the extent, limits, and test of 
 valid knowledge ? Every system of belief, whatever its na- 
 ture and character, assumes and affirms the fact that there is : 
 1. Such a thing as truth ; 2. Such a thing as valid knowledge 
 of truth ; and, 3. Such a thing as a valid test of such know- 
 ledge. All systems of philosophy, especially all theories of on- 
 tology, are based upon, and throughout take form from, certain 
 definite assumptions in respect to this one problem. Realism, 
 materialism, and idealism in all its varied forms and develop- 
 ments, commence in fact with the question, What can we 
 know ? and are wholly constructed in accordance with certain 
 definite answers to this one question, answers assumed as true. 
 The same holds true of all the deductions of these systems in 
 respect to God, duty, immortality, and retribution. 
 
 Now, while this is the case, no philosopher, we believe, has 
 ever attempted to give us a formula which shall undeniably and 
 self-evidently represent all forms of valid knowledge, together 
 with the certain test of such knowledge. We propose, then, 
 
APPLIED LOGIC. 323 
 
 the question, What is this formula, as the first and great prob- 
 lem in philosophy in the present age ? Till this problem is 
 solved, it is self-evident that we are not prepared to take up the 
 other great questions professedly answered in these various sys- 
 tems. The language, then, which Kant applied to the problem 
 which he propounded we will now venture to apply to the one 
 before us : " All metaphysicians consequently are solemnly and 
 legally suspended from their occupations, till they shall have 
 answered in a satisfactory manner the question," By what 
 formula shall we represent all forms of valid knowledge, and 
 what is the certain test or criteria of such knowledge ? 
 
 PROPOSED SOLUTION OF THIS PROBLEM. 
 
 To the question, What is the origin of knowledge ? many 
 philosophers have propounded many and different answers ; 
 but to the question now before us, none, to our knowledge, 
 have even attempted to give a specific answer. To the follow- 
 ing proposed solution of this problem special attention is now 
 invited. 
 
 Distinction between Presentative and Representative Know- 
 ledge. 
 
 As preparatory to the solutior, we would restate a distinction 
 made in a previous department of this treatise between presen- 
 tative and representative knowledge. We will give the dis- 
 tinction in the language of Sir William Hamilton : 
 
 " 1. A thing is known immediately or proximately when we 
 cognize it in itself; mediately or remotely, when we cognize it 
 in or through something numerically different from itself. Im- 
 mediate cognition thus the knowledge of a thing in itself in- 
 volves the fact of its existence ; mediate cognition t^us the 
 knowledge of a thing in or through something not itself in- 
 volves only the possibility of its existence. 
 
 " 2. An immediate cognition, inasmuch as the thing known is 
 itself presented to observation, may be called a presentative / 
 
324 LOGI'C. 
 
 and inasmuch as the thing presented is, as it were, viewed by 
 the mind face to face, may be called an intuitive cognition. A 
 mediate cognition, inasmuch as the thing known is held up or 
 mirrored to the mind in a vicarious representation, may be 
 called a representative cognition. 
 
 " 3. A thing known is called an object of knowledge. 
 
 " 4. In a presentative or immediate cognition there is one sole 
 object ; the thing (immediately) known and the thing existing 
 being one and the same. In a representative or mediate cog- 
 nition there may be discriminated two objects ; the thing (im- 
 mediately) known and the thing existing being numerically dif 
 ferent." 
 
 That we have these two kinds of knowledge no one does or 
 can doubt. Of some realities, to say the least, we have a direct 
 and immediate knowledge. Of other realities our knowledge 
 is not direct and immediate, but indirect and mediate. All 
 forms of mediate knowledge, as all admit, are originally given 
 through one source, sensation. We shall employ the words 
 presentative knowledge to represent knowledge of the first 
 kind, and representative for that of the second. 
 
 In addition to these two kinds of knowledge, we have two 
 other kinds also, which have the same validity as these, to wit : 
 those truths which are necessarily presupposed by these as their 
 logical antecedents, and those which necessarily result from 
 them as logical consequences. All that is logically presupposed 
 and which logically follows from any form of knowledge, must 
 undeniably have the same validity that the latter does. No 
 one will or can doubt the truth of this principle. 
 
 The formula stated. 
 
 We are now prepared to give a distinct statement of the 
 formula above suggested. It is this. Presentative knowledge, 
 with all its logical antecedents and consequences, must be held 
 as universally and absolutely valid for the reality and charac- 
 ter of the objects to which it pertains. 
 
 Representative knowledge, with its logical antecedents and 
 
APPLIED LOGIC. 325 
 
 consequences, must be held as relatively valid. In the con- 
 sciousness of a sensation, for example, we at once recognize the 
 fact that it had a cause a cause adequate and adapted while 
 we remain constituted as we are, and that cause sustains its 
 present relations to us, to affect us as it now does. So far our 
 knowledge of that cause, with all that is necessarily implied in 
 its existence, must be held as having the same validity that our 
 knowledge of the sensation has. 
 
 . The test, the criteria by which we are to determine whether 
 any given form of knowledge is presentative or representative, 
 is consciousness. If we are conscious of a direct and imme- 
 diate perception- of any object whatever, we must admit the 
 fact that our knowledge of that object is presentative. If we 
 are conscious of knowing the object through the medium of 
 sensation, then our knowledge of said object must be held as 
 representative. 
 
 The question whether any particular cognitions must be held 
 as absolutely valid for the reality and character of its object, 
 will in reality stand thus : 
 
 Presentative knowledge, with its logical antecedents and consequences, is 
 universally and absolutely valid for the real nature and character of its 
 objects ; 
 
 These cognitions are or are not constituted of this one form of knowledge. 
 Proof consciousness ; 
 
 These cognitions consequently are or are not thus valid. 
 
 The syllogism of representative knowledge will stand thus : 
 
 Kepresentative knowledge, with its logical antecedents and consequences, 
 is universally valid for the relative character of its respective objects. 
 
 These cognitions are or are not constituted of this form of knowledge. 
 Proof consciousness. 
 
 Therefore it is or is not thus valid. 
 
 As all cognitions are in fact presentative or representative, 
 these formulas must, of necessity, include all forms of know- 
 ledge. The only question which here arises is this : Are these 
 formulas themselves really valid for the high purpose here as- 
 signed to them ? That they are, we argue from the following 
 considerations : 
 
These Formulas and Test verified. 
 
 1. We must admit their absolute and universal -validity, or 
 deny that of all knowledge of every kind. Presentative is, in 
 fact, the highest form of knowledge of which we can by any 
 possibility form any conception. Its validity can be denied on 
 but one condition, the impeachment of the integrity of the in- 
 telligence itself, as a faculty of knowledge, and pronouncing the 
 idea of valid knowledge on any subject whatever an absolute 
 chimera. 
 
 2. No other formulas and test besides these are even con- 
 ceivable. We must, consequently, admit their validity, or af- 
 firm, that if valid and invalid cognitions do exist, we have no 
 criteria by which we can distinguish one class from the other. 
 Those who deny the validity of these, are bound to furnish 
 some others possessing really valid claims. This, we are quite 
 confident, they will never even attempt to do. 
 
 3. Every form and system of knowledge, as a matter of fact, 
 admits the validity of these formulas and test in certain cases 
 in all cases where they profess to find valid knowledge and 
 all profess to find such as far as their own fundamental princi- 
 ples and deductions are concerned. No one will deny these 
 statements. Now the validity of these formulas and test is to 
 be admitted universally or denied universally. If one form of 
 knowledge given in consciousness as presentative, and for the 
 reason that it is thus given, is to be received as valid for the 
 nature and character of its object and all admit that some 
 forms thus given are thus valid, and none pretend that any 
 form not thus given is thus valid, nor that any form of know- 
 ledge can be valid for any other reason if any form of know- 
 ledge given in consciousness as presentative, is, we say, for the 
 reason that it is thus given, to be regarded as valid, every other 
 form thus given must be regarded as thus valid, or we make a 
 discrimination without a difference, and assume that things 
 equal to the same things may not be equal to each other. 
 With these considerations, the subject is left to the reflection 
 of the thoughtful reader. 
 
APPLIED LOGIC. 327 
 
 Searing of these Formulas upon Systems of Ontology. 
 
 \ 
 In the human intelligence two orders of cognitions appear, 
 
 the subjective and objective those pertaining to mind, on the 
 one hand, and those pertaining to matter or the external uni- 
 verse, on the other. The great problem in philosophy for all 
 ages has pertained to the question of the validity of such cog- 
 nitions. In view of the formulas and test under consideration, 
 but one answer can be given to this question. No one will 
 deny, that if presentative knowledge must be held as universal- 
 ly valid for the reality and character of its object, then the uni- 
 verse of matter, on the one hand, and of mind, on the other, 
 must be held as distinct and separate realities the one having 
 real and absolute extension and form, and the other as a sub- 
 stance possessed of the faculties of thought, feeling, and volun- 
 tary activity. That we have a distinct and absolute conscious- 
 ness of a presentative knowledge of each, as such realities, no 
 one will deny. The validity of our subjective or objective cog- 
 nitions for the reality and character of their respective objects 
 can, by no possibility, be denied, but upon one condition exclu- 
 sively the denial of the validity of the formula, that presenta- 
 tive knowledge, with its logical antecedents and consequences, 
 shall be held as universally valid for the reality and character of 
 its objects. Those who make this denial can maintain their 
 integrity but by a total denial of the fact, that we have or can 
 have valid knowledge in respect to any subject whatever. 
 
 Character and claims of Empiricism, Materialism, Idealism, 
 and Realism, as systems of philosophy . 
 
 Empiricism, which affirms that all our knowledge is derived 
 directly and immediately from experience (external and inter- 
 nal perception) materialism, which affirms matter to be the 
 only substance really existing idealism, which affirms mind or 
 its operations to be the only realities, and consequently denies 
 the reality of an external material universe and realism as 
 above presented realism, which affirms the reality of matter, 
 
328 logic. 
 
 on the one hand, and of mind, on the other, and asserts the 
 reality of the two as distinct, separate, and opposite orders of 
 existences, embrace all conceivable or possible systems of phi- 
 losophy. Of empiricism and realism, one must be true and the 
 other false. That we have empirical cognitions both systems 
 affirm. That the d priori element of thought exists as a matter 
 of fact, the former theory denies and the latter affirms. One 
 of these theories, consequently, must be time and the other 
 false. As far as the question of ontology is concerned, but 
 three systems are conceivable or possible, and one of these to 
 the exclusion of the others must be true to wit, materialism, 
 idealism, or realism which affirms the reality of matter and 
 spirit both. Let us contemplate the character and claims of 
 these systems. 
 
 In regard to empiricism, we would remark, that it admits the 
 validity of presentative knowledge as far as the empirical, but 
 denies its validity as far as the d priori, elements of thought are 
 concerned. Now we are just as conscious of the presence in 
 the intelligence of one of these elements of thought, as we are 
 of the other. In other words, we are just as conscious of the 
 presence in the intelligence of necessary and universal ideas and 
 principles such, for example, as the ideas of space, time, sub- 
 stance, cause, personal identity, &c, and of the principles, 
 "Body supposes space," "Succession, time," "Phenomena, 
 substance," " Events a cause," <fcc, as we are of the ideas of 
 body, succession, events, &c. Empiricism, therefore, affirms 
 the validity of presentative knowledge so far forth as the em- 
 pirical or contingent, and denies its validity so far forth as the 
 d priori or necessary, element of thought is concerned. 
 
 Materialism, in all its forms and developments, rests wholly 
 upon the assumption that presentative knowledge Avith its logi- 
 cal antecedents and consequences is valid for the reality and 
 character of its objects, so far forth as external perception (ob- 
 jective cognitions), and not thus valid, so far as internal per- 
 ception (subjective cognitions) are concerned. No one can 
 deny, that we are just as conscious of knowing ourselves as 
 substances exercising the functions of thought, feeling, and vo- 
 
APPLIED LOGIC. 329 
 
 lition, as we are of knowing matter as a substance having ex- 
 tension and form. Each reality is alike, and with equal abso- 
 luteness, given in consciousness as the object of presentative 
 knowledge. Taking the principle, that phenomenon supposes 
 substance, together with its necessarily implied one, that sub- 
 stances are as their presentative phenomena, and the doctrine, 
 that matter and mind are real existences fundamentally distinct 
 and separate from each other, is just as demonstrably evident 
 as any of the deductions of the mathematics. Materialism rests 
 exclusively upon the assumption, we repeat, that presentative 
 knowledge, with its logical antecedents and consequences, is 
 valid for the reality and character of its objects so far as exter- 
 nal material substances are concerned, and not thus valid in re- 
 gard to mind, and must stand or fall with the claims of that 
 assumption. The materialist must, to maintain his integrity, 
 abandon his theory entirely or give a satisfactory answer to the 
 question, Why is the same identical form of knowledge to be 
 regarded as valid for the reality and character of one class of 
 facts, and not as thus valid for those of another ? 
 
 Idealism, in all its forms, rests upon the assumption, that pre- 
 sentative knowledge, with its logical antecedents and conse- 
 quences, is valid for the reality and character of the facts of in- 
 ternal perception (subjective cognitions), and not thus valid for 
 the reality and character of the facts of external perception 
 (objective cognitions). This theory is throughout nothing but 
 the opposite pole of the same assumption on which materialism 
 rests, and is encumbered in all its principles and deductions, 
 with the same identical difficulties, to wit : that the same iden- 
 tical form of knowledge is valid for the reality and character of 
 one class of cognitions, and not for those of another that is, 
 that things equal to the same things are not universally equal 
 to one another. We are just as undeniably conscious of a pre- 
 sentative knowledge of matter as possessed of extension and 
 form, as we are of .a similar knowledge of mind as exercising 
 the functions of thought, feeling, and voluntary determination, 
 and in respect to each, alike and equally, that knowledge is un- 
 deniably absolute. The idealist, then, in common with the ma- 
 
terialist must, to maintain his integrity, abandon his theory en- 
 tirely or give a satisfactory answer to the question, Why does 
 he assume that the same identical form of knowledge is valid 
 for the reality and character of the objects of one class of cog- 
 nitions, and not valid at all relatively to those of the objects 
 of another class of cognitions ? We affirm that his theory is 
 in fact based upon the assumption, that the principle, "That 
 things equal to the same things are equal to one another," is 
 not universally valid and must be held as false, if this principle 
 must be held as true. 
 
 Let us now turn our attention to a consideration of the sys- 
 tem of realism, as we have above presented it the only con- 
 ceivable system aside from those above noticed. On this sys- 
 tem we remark : 
 
 1. It is based, in all its principles and deductions, upon the 
 principle, that the formulas and test above given are absolutely 
 valid throughout the entire sphere of their applications. What- 
 ever form of knowledge is given in consciousness as presenta- 
 tive or representative, it recognizes as such, and together with 
 all its logical antecedents and consequences, as absolutely or 
 relatively valid for its objects, according as it falls under one or 
 the other of these categories. 
 
 2. In common with empiricism, it recognizes the reality of 
 the empirical or contingent elements of thought. In opposition 
 to the former, however, it recognizes also the d priori or neces- 
 sary element. It recognizes both alike as real, because both 
 alike are given in consciousness as such that is, both alike are 
 given as objects of presentative knowledge. 
 
 3. By recognizing the reality and validity of these two ele- 
 ments of thought, it lays the foundation for all the sciences just 
 as they are, and also for the most satisfactory explanation of 
 their possibility. By abstracting the d priori (necessary and 
 universal) element of thought, and finding its logical conse- 
 quences, we have the pure sciences as they are those of the 
 pure mathematics, for example. Blending the two, and ex- 
 plaining the facts of the universe in the light of d priori or in- 
 
APPLIED LOGIC. 331 
 
 tuitive principles and deductions, we have the mixed sciences, 
 physical and mental, as they are. 
 
 4. In contradiction to materialism and idealism both, this 
 system recognizes the reality of the universe of matter in oppo- 
 sition to mind, on the one hand, and that of mind in opposition 
 to matter, on the other ; and this because that each alike and 
 equally is given in consciousness as the object of presentative 
 knowledge. 
 
 5. Instead, we remark finally, of giving us an exclusively ma- 
 terial universe with no deity to preside over it, or a mere ideal 
 one presided over by an ideal divinity, this system, in its ulti- 
 mate necessary logical deductions, gives us a real universe, ma- 
 terial and mental a universe presided over by a real deity who 
 is nothing less than an infinite, eternal, all-perfect, self-conscious 
 personality. 
 
 General Remarks upo7i these Systems. 
 
 Such are the specific character and claims of these different 
 and opposite systems. We would now invite attention to a 
 few general remarks upon them : y 
 
 1. Realism, as we have expounded the system, is really and 
 truly based upon all the facts of consciousness, while each of 
 the others is undeniably a system of partialism recognizing 
 but a part of these facts, while all alike have absolute and equal 
 claims to validity. All forms of presentative and representative 
 knowledge, with all their logical antecedents and consequences, 
 have their proper place in the system first named, while the va- 
 lidity of a part of said forms of knowledge is admitted, and that 
 of another part denied by each of the other systems ; and all 
 this while no reasons whatever exist for the fundamental dis- 
 tinctions which are made. 
 
 2. Realism has undeniably a truly scientific basis and struc- 
 ture throughout, inasmuch as all its foundation-principles are 
 universally necessary intuitive truths, and all its subsequent de- 
 ductions are exclusively the logical consequences of such princi- <y 
 pies, and the actual facts of consciousness. The formulas and 
 
332 logic. 
 
 test above given which lie at the basis of this system, have the 
 same claims to the place claimed for them as principles of sci- 
 ence, that any other principles that can be named have or can 
 have. From the facts of consciousness elucidated by these prin- 
 ciples, all the deductions of this system possess a demonstrative 
 certainty. On the other hand, the principles on which every 
 one of the other systems rests are nothing but mere assump- 
 tions, whose validity is neither intuitively certain nor capable 
 of being established by a process of scientific deduction. Each 
 of these systems, as we have seen, rests upon the assumption 
 that one class of presentative cognitions is, and another is not, 
 valid for the reality and character of its objects, and cannot 
 itself be true unless that assumption is valid. Is the truth of 
 that assumption intuitively certain ? No one will assert or con- 
 jecture that it is. Can its validity be established by any pro- 
 cess of scientific deduction ? The universal intelligence an- 
 swers, No. Neither of these systems, therefore, have or can 
 have a scientific basis ; nor can any of its deductions have any 
 legitimate claim to a place as truths of science in any of our 
 systems of knowledge. 
 
 3. Realism, we remark in the last place, gives us in its prin- 
 ciples and deductions, systems of real valid knowledge in re- 
 gard to ourselves, to the world and God, while each of the op- 
 posite systems utterly unsettles the foundations of knowledge 
 on all these, and all other subjects alike, if there be any other. 
 In the one case, the foundation of our system of knowledge is 
 the rock of truth, absolute intuitive principles, and the whole 
 superstructure rises before us as throughout constituted of cor- 
 responding materials. In each of the other cases, we commence 
 with a formal impeachment of the validity of the intelligence 
 itself as a faculty of knowledge that is, with a formal displace- 
 ment of the foundations of valid knowledge. What logically 
 follows, consequently, can have no higher claims to validity. 
 With these suggestions these systems are handed over to the 
 careful reflection of inquirers after truth. 
 
APPLIED LOGIC. 333 
 
 DOGMATISM, SKEPTICISM, POSITIVEISM. AND FREE-THINKING. 
 
 Dogmatism and skepticism are terms in frequent use terms 
 which require specific definition, inasmuch as they represent 
 two distinct and opposite systems of belief, systems which are 
 not very clearly apprehended even by educated minds general- 
 ly. The system represented by the former term is based upon 
 the principle, that the facts of the universe, material and men- 
 tal, as given in the intelligence, are of such a nature as to affirm 
 positively a certain definite system of belief, and to deny as 
 positively every opposite system, and hence positively requires 
 us to hold this one form of belief as true, and all opposite ones 
 as false. In opposition to this principle, skepticism affirms that 
 the entire facts under consideration are of such a nature as to 
 admit of an equally consistent explanation in full and perfect 
 harmony with several distinct and opposite systems, such as 
 realism, materialism, and idealism in its various forms. Such 
 facts, consequently, simply indicate each of these various sys- 
 tems alike as possibly true, with the absolute impossibility of a 
 valid determination which, in distinction from the others, is 
 true. Realism, materialism, idealism, theism, atheism, &c, are 
 all dogmatic systems, because each of them holds a certain form 
 of belief as positively affirmed as true, and all opposite ones as 
 false, by the facts of the universe. Skepticism affirms of each 
 system alike, This system may or may not be true, and by 
 no possibility can it be determined whether it is or is not true, 
 and hence condemns the dogmatism of each alike, that is, de- 
 nies the claims of each alike to be held, in distinction from the 
 others, as true. 
 
 Skepticism, it will readily be perceived, is, in fact, as a sys- 
 tem, as really and truly dogmatic as either of the others, but in 
 a different form. To the facts of the universe it gives an ex- 
 planation as positive as they. While they assert that these 
 facts do affirm one system, in distinction from all others, as 
 true, it as positively and dogmatically affirms that said facts 
 simply suggest various systems, and each as possibly true, with 
 the absolute impossibility of determining whether any one sys- 
 
334 logic. 
 
 tern is or is not true. In opposition to the dogmatic teachings 
 of these systems, skepticism as dogmatically affirms, You can- 
 not prove that< there is an external world, nor that such a world 
 does not exist you cannot prove that there is a God, nor that 
 there is not a God, &c. 
 
 Positiveism and free-thinking are terms nearly synonymous 
 in their meaning with those already considered, and may be 
 considered as representing them in their practical principles or 
 developments. The categorical imperative of positiveism is, 
 Thou shalt hold this specific system as true, and all opposite 
 and contradictory ones as false. That of free-thinking is, Thou 
 mayest assume any of these hypotheses you please as true, and 
 explain the facts of the universe accordingly, provided you hold 
 said hypothesis as only possibly true, and do not dogmatically 
 impose it upon others. The imperative of positiveism has place 
 where, and only where, the facts presented positively affirm one 
 hypothesis, and are explicable on no other, that is, positively 
 contradict every other. That of free-thinking has place where, 
 and only where, the facts presented suggest two or more dis- 
 tinct and opposite hypotheses, as each possibly true, and equal- 
 ly so, without indicating or affirming either in distinction from 
 the others as true. 
 
 CONDITIONS OF THE POSSIBILITY OF SCIENCE IN ANY PARTICU- 
 LAR DEPARTMENT OF THOUGHT. 
 
 We are now prepared to state definitely the conditions on 
 which real science, in any particular department of thought is 
 possible. They are the following : 
 
 1. The facts presented in said department must yield certain 
 specific analytical judgments that is, certain universal and 
 necessary intuitive truths under which all such facts may be 
 ranged, and in the light of which, as principles, said facts may 
 be explained. 
 
 2. Said facts must sustain certain fixed, determinate, and de- 
 terminable relations to each other relations the same in kind 
 as those represented in the principles under consideration. If 
 
APPLIED LOGIC. 335 
 
 the relations determined were not the same in kind as those 
 designated by the principles above presented, the former would 
 not be ranged under the latter, and no inferences or deductions 
 would be yielded. 
 
 ' 3. These principles and relations must yield important de- 
 ductions, which, as principles, will yield ethers, and so on till 
 the mass of facts referred to stand before us distinctly eluci- 
 dated. 
 
 In illustration of these statements, we may refer to the sci- 
 ence of geometry. The ideas of quantity which it is the object 
 of this science to elucidate, present, first of all, certain analyti- 
 cal judgments which may be employed as scientific principles 
 the principles, for example, " Things equal to the same things 
 are equal to one another," " If equals be added to equals the 
 sums are equal," &c. Then these quantities, when defined as 
 lines and figures, are found to sustain certain determinable rela- 
 tions to each other relations the same in kind as those desig- 
 nated by the principles referred to as, A and B are each equal 
 to C. These relations, in the light of those principles, yield 
 certain important deductions as, A and B are equal to one 
 another deductions which, as principles, lead to others, and 
 so on till our ideas of quantity stand before us distinctly eluci- 
 dated. All these conditions must be fulfilled in any given de 
 partment of thought, or science there is an impossibility. 
 
 Bearings of the Sensational Theory of Perception. 
 
 As preparatory to discussions hereafter to be introduced, we 
 would now re-direct attention to the necessary deductions and 
 consequences of the sensational theory of external perception. 
 According to the fundamental assumptions of this theory, of an 
 external world, if it exists at all, we have no real perception 
 whatever, the sensation itself, a purely and exclusively mental 
 state, being the only object which we really perceive, when we 
 suppose ourselves perceiving an extended object external to the 
 mind itself. Further, according to the fundamental principles 
 of this theory, if our sensations as they are were induced from 
 
336 LOGIC. 
 
 any cause whatever, we should have, from the nature of the in- 
 telligence itself, the same identical perceptions and subsequent 
 mental operations that we now do have, even supposing that no 
 external world at all exists, or no external cause of the sensa- 
 tion. All that we can know of the actual cause of the sensation 
 is from sensation itself, and nothing else. Now it is undenia- 
 ble, that sensation contains, and can contain, within itself no 
 indication or revelation whatever of what the nature of that 
 cause is or must be. Of a thing utterly void of extension and 
 form, we cannot say that its cause must be an extended sub- 
 stance having any form whatever, much less a definite form. 
 For aught that we know or can thus know, that cause may or 
 may not be an external extended object such as we seem to 
 perceive. Or it may be an unknown and unknowable some- 
 thing according to the theory of Kant. Still further, for aught 
 revealed in and by sensation, its cause may not be any external 
 object whatever, but wholly ab intra, the result of the mind's 
 spontaneous activity, according to the theory of Fichte. For 
 aught that we know or can know from the sensation itself, we 
 remark in the last place, its cause may accord with the assump- 
 tions of pantheism, or exist as a mere idea according to the 
 teachings of pure idealism. When we would reason, then, 
 from sensation to its cause, several distinct and opposite hy- 
 potheses present themselves, each equally consistent with all the 
 facts and all their characteristics, with an absolute impossibility 
 on our part of knowing which, in distinction from the others, 
 is true. Yet these hypotheses involve perfectly distinct and 
 opposite deductions in regard to ourselves, our duty and desti 
 ny, the world and God. All this is undeniable. What then is 
 the necessary logical consequence of this theory ? The system 
 of absolute skepticism, in accordance with our explanation of it, 
 and nothing else. No man can hold this theory of perception, 
 and, without the grossest inconsistency and self-contradiction, 
 be any thing else than a universal skeptic and free-thinker. 
 
APPLIED LOGIC. 33*7 
 
 CONDITIONS ON WHICH THE PROPOSITION, V GOD EXISTS," CAN 
 LEGITIMATELY TAKE ITS PLACE AS AN UNDENIABLE TRUTH 
 OP SCIENCE. 
 
 We would now invite very special attention to the following 
 question, to wit : On what conditions can the theistic proposi- 
 tion, " God exists," legitimately take rank as an undeniable 
 truth of science ? In other words, On what conditions can the 
 validity of that proposition be established on scientific grounds ? 
 They are the following : 
 
 1. An analytical judgment in respect to the facts of the uni- 
 verse must be presented, a judgment having such intuitive, ab- 
 solute, and necessary certainty, that no one, not even the skep- 
 tic or anti-theist, will or can deny it ; a judgment, too, necessa- 
 rily involving the validity of the theistic hypothesis of ultimate 
 causation, on the supposition that the facts of the universe 
 do accord really and truly with that principle. This judg- 
 ment will stand as the major premise of the theistic syllogism. 
 About the question of its validity as a scientific principle there 
 must be no dispute. 
 
 2. As the minor premise, it must be shown undeniably that 
 the facts of the universe bearing upon this question do really 
 and truly accord with this principle, and thus affirm the validity 
 of this hypothesis as a matter of fact. 
 
 3. The necessary deduction from these premises, to wit, 
 " God exists," then legitimately takes its place as a truth of 
 science. On no other conditions is this possible. 
 
 The same conditions hold in regard to all other deductive or 
 inductive truths. Long before the science of geometry or of 
 the mathematics in any form, for example, was developed, all 
 men Avould conclude, from the fact that A and B were each 
 equal to C, that they were equal to one another just as the 
 general intelligence now, from its spontaneous activities, affirms 
 in view of the facts of the universe within and around us, the 
 being and perfections of God. Yet, never till the analytical 
 judgment, "Things equal to the same things are equal to one 
 another," was distinctly developed, and the judgment, "A and 
 
V 
 
 B are equal to C," was specifically arranged under the above- 
 named principle, could even the deduction, " Therefore, A and 
 B are equal to one another," be ranked as a truth of science. 
 So of the great truth of theology under consideration, and of 
 every other inferred truth. 
 
 There are two distinct elements of the theistic proposition, 
 " God exists," to wit, that the ultimate unconditioned cause of 
 the facts of the universe is a power out of and above nature, 
 and one which exercises an absolute control over it and that 
 this cause is a self-conscious personality possessed of all the at- 
 tributes involved in the ideas of absolute infinity and perfection. 
 Two separate formulas may be required to represent these two 
 distinct elements of the above-named proposition. We will 
 simply indicate what, in our judgment, would be formulas 
 which would stand as undeniably valid majors in the different 
 forms in which the theistic syllogism should be presented 
 formulas which must be universally regarded as possessing ab- 
 solute appodictical certainty. 
 
 The Theistical Formulas. 
 
 1. On two conditions would the facts of the universe demon- 
 strably affirm the truth, that the unconditioned cause of said 
 facts is a power not inhering in, but out of and above, nature 
 the supposition that the order, scientific arrangement, and har- 
 mony, mental and physical, everywhere existing in the universe 
 is an event originated in time, that is, a reality which once did 
 not exist but began to be and that the course of events which 
 has been in progress since this order was established has been, 
 from time to time, interrupted in forms which can be accounted 
 for by a reference to no inhering law of nature. This cause 
 must of necessity be a law inhering in nature itself and acting 
 potentially and necessarily in it, or a power out of and above 
 nature. On the former supposition, the order of creation could 
 by no possibility be an event originated in time, but must have 
 existed from eternity. On the same supposition, also, this order 
 could never from eternity to eternity be interrupted in any 
 
APPLIED LOGIC. 339 
 
 form. This is undeniable. The formulas above given, on the 
 supposition that the facts of the universe do accord with them, 
 will of necessity yield the one element of the theistic hypothe- 
 sis under consideration. 
 
 2. The following formula would as necessarily yield the other 
 element of this hypothesis, the infinity, and perfection of this 
 cause, to wit, that universal mind is so constituted as of neces- 
 sity to form the idea of this cause as a self-conscious personality, 
 possessed of all the attributes involved in the ideas of absolute 
 infinity and perfection, and that the assumption of the objective 
 validity of that idea in opposition to all opposite conceptions, is 
 an immutable demand of its moral and spiritual being. The 
 case is then brought under the universal and immutable law, a 
 law whose validity none will dare to deny, to wit, that for 
 every fundamental want of sentient existence there is a cor- 
 related provision, and for every fundamental adaption a corre- 
 sponding reality or sphere of activity. 
 
 It will then remain to show in arguing the minor premise, 
 that the facts of the universe do in reality accord with these 
 two formulas, and with none others. The necessary deduction, 
 "God exists," will then undeniably take rank as a truth of 
 science. 
 
 The Disjunctive Argument for the Theistic Hypothesis. 
 
 The argument for the theistic hypothesis may be presented 
 in another form the disjunctive in which form it will possess 
 the most absolute validity. There are but three conceivable 
 hypotheses of ultimate causation, that of theism, materialism, 
 and idealism in its various forms. One of these hypotheses to 
 the exclusion of the others must be true. Now it can be ren- 
 dered demonstrably evident, that the entire facts of the uni- 
 verse can by no possibility be explained in consistency with 
 either of the two last named a fact which renders equally 
 evident the validity of the first. This form of the theistic argu- 
 ment has never yet, to our knowledge, b^en presented in its 
 
340 LOGIC. 
 
 full force, and has for the most part been entirely overlooked 
 by the advocates of theism. 
 
 The ultimate principles on which the hypotheses of Theism, 
 Skepticism, and Anti-Theism in all its forms, rest. 
 
 In conducting the argument under consideration on right 
 principles, it will ultimately be found that the following are the 
 principles on which theism, on the one hand, and all opposite 
 systems, on the other, finally rest. The theistic principle is 
 this : The entire facts given in consciousness as the real objects 
 of presentative knowledge, are all alike to be held as together 
 constituting a valid basis for absolute deductions in respect to 
 the nature and character of the ultimate unconditioned cause of 
 the facts of the universe. Every hypothesis opposed to that of 
 theism, on the other hand, rests upon the assumption, that a 
 part of the class of facts under consideration that part which, 
 if admitted as constituting the whole of the kind that do exist, 
 would affirm the skeptical or anti-theistic hypothesis and deny 
 that of theism are to be held as valid for deductions on this 
 subject ; while all others of the same identical class, those which, 
 if admitted, would affirm the theistic, and deny every opposite, 
 hypothesis, are to be held as void of all validity as the basis of 
 such deductions. It will be seen that, granting the validity of 
 the principle first named, theism must be true, and that upon 
 no other condition than that of the second, can any opposite 
 hypothesis by any possibility be true. The validity of the 
 theistic hypothesis has never, as a matter of fact, been denied or 
 doubted but upon one condition a denial of the reality of the 
 material, on the one hand, or of the mental world, on the 
 other, or of both together that is, on a denial of the validity 
 of our knowledge in respect to matter, or mind, or of both to- 
 gether. Materialism denies the validity of all knowledge of 
 mind idealism of matter and skepticism of both together, 
 "so far as any valid basis for positive systems of knowledge and 
 belief are concerned. Now of matter, on the one hand, and 
 of miaad, on the other, we are conscious of having a real presen- 
 
APPLIED LOGIC. 341 
 
 tative knowledge. Materialism, then, rests upon the assump- 
 tion, that this form of knowledge is valid so far forth as the 
 class of cognitions pertaining to matter is concerned, and not 
 valid as far as that class which pertains to mind is concerned. 
 Idealism, as the basis of its deductions, affirms the validity of 
 the latter class, and denies that of the former. 
 
 COMMON THEISTIC SYLLOGISM AND ARGUMENT. 
 
 Hitherto, with very few exceptions, what has been called 
 " the design argument" has been almost exclusively employed 
 in all attempted demonstrations of the being of God. The prin- 
 ciple on which the argument has been conducted has always 
 been one and the same. The main difference which has charac- 
 terized the productions of different authors, has been the class 
 of examples of design which has been adduced as the basis of 
 specific deductions. The validity of the procedure itself, that 
 is, of the form which the argument has assumed, has been taken 
 for granted as self-evident. The time, in our judgment, has 
 come when the form itself of the argument should receive a 
 rigid examination ; and this because its validity has always been 
 positively denied by anti-theists is now seriously questioned by 
 some, at least, of the best thinkers among theists has, as far 
 as our knowledge extends, failed altogether as a means of 
 convincing unbelievers, and been nearly, if not quite, equally 
 inefficacious in confirming the faith of believers. We propose, 
 then, to offer a few brief criticisms upon what is denomina- 
 ted the theistic syllogism, and upon the form of argumenta- 
 tion pursued under that syllogism. The syllogism 'may be thus 
 stated : 
 
 Marks of design, that is, where the parts of any given whole 
 are so arranged as to accomplish some intelligible purpose or 
 end the adjustment of the parts of the watch, for example, so 
 that a regulated motion which points out the hours of the day, 
 is produced imply an intelligent designing cause. The works 
 of nature are of this character. They therefore imply a design- 
 ing cause. 
 
342 logic. 
 
 The best formal statement of this syllogism, probably, is that 
 given by Professor Tulloch, and which we will here cite again : 
 " First or major premise, 
 
 Order universally proves mind ; 
 Second or minor premise, 
 
 The works of nature discover order ; 
 Conclusion, 
 
 The works of nature prove mind." 
 
 In regard to this syllogism, we would observe, that the ma- 
 jor premise is the only one which has ever been disputed. No 
 skeptic or anti-theist of any school has ever questioned the truth 
 of the statement, that " The works of nature discover order." 
 The validity of the major, however, to wit, that " Order uni- 
 versally proves mind," has been universally denied by the op- 
 posers of theism, while its right to a place as a first truth or 
 principle of science has, as we have said, been doubted by not 
 a few leading minds among theists themselves. While this has 
 been the case, the minor premise, which has never been denied 
 or doubted even, has been almost exclusively argued and ar- 
 gued, too, as if it was the only one which is doubted or denied. 
 The theistic syllogism and argument, then, as hitherto almost 
 exclusively presented, exhibits the following, we believe, unex- 
 ampled phenomena in the history of science to wit, a syllogism 
 with a disputed major and an admitted minor ; while the former 
 has been assumed as a universally admitted principle, and the 
 latter argued as the only disputed premise. "We would now 
 invite special attention to the following suggestions in respect 
 to the syllogism and argument before us. 
 
 1. The order of the premises in this case is, in one funda- 
 mental particular, the reverse of what science universally de- 
 mands an order which renders scientific development in the 
 theistic department of thought unattainable. In all the sci- 
 ences, the major is never allowed to be a disputed premise. 
 If either is disputed, it must be the minor, and that only. 
 Yet here we have a disputed major and an admitted minor. 
 
APPLIED LOGIC. 343 
 
 HoV can the idea of science be realized under such circum- 
 stances ? 
 
 2. The major premise, in this case, is not only not what sci- 
 ence universally requires in regard to the major, an analytic 
 judgment that is, a universal and necessary intuitive truth 
 but a problematical proposition requiring proof before it is ad- 
 mitted as a premise at all. This is evident, in the first place, 
 from the fact that its validity is universally denied by the op- 
 posers, and its claims, as a first truth, doubted by many of the 
 advocates, of theism, Professor Tulloch, for example. 
 
 That such is the character of this premise may, we would re- 
 mark in the next place, be rendered undeniably evident, by the 
 statement of a few self-evident truths. It is self-evident that 
 we cannot know d priori what kind of realities or substances 
 do or do not exist. For aught that we can thus know, mat- 
 ter and spirit both may have existed from eternity. On the 
 supposition, that either has existed from eternity, we cannot 
 affirm d priori in what state it may have existed, whether 
 in a state of order or not. In one or the other of them (mat- 
 ter or mind) it is undeniable that order must have existed with- 
 out a cause, and we cannot affirm d priori in which it has, 
 and in which it has not, thus existed. It is equally as conceiva- 
 ble that it might thus have existed in one as in the other. No 
 one can affirm d priori that this is not the case. If, then, we 
 consider nature as having existed from eternity that is, un- 
 caused we cannot affirm d priori that it might not have exist- 
 ed in a state of order, and that order the result of no cause out 
 of and above nature. The proposition, then, " Order univer- 
 sally proves mind," mind as its originating cause is, either 
 not in its absolutely universal form true, in fact, or its truth in 
 this form is not self-evident. That proposition, consequently, 
 has no claim whatever to take the rank assigned to it in the 
 common theistic syllogism, to wit, that of a first truth or princi- 
 ple of science. It is only in the form in which we have stated 
 it, that it has or can have intuitive certainty, to wit, Order 
 which once did not exist and began to be, or which has, from 
 time to time, been interrupted and changed in forms which can 
 
be accounted for by a reference to no inhering law or Ia^s of 
 nature order of this character universally supposes, as its origi- 
 nating cause, a power out of and above nature, that is, mind. 
 This, then, and not that above given, is the proper major in the 
 theistic syllogism. This leads us to remark : 
 
 3. That the objections urged by the opposers of theism 
 against this proposition as having a claim to the rank of a first 
 truth of science, the place assigned it in the syllogism under 
 consideration, have never, to our knowledge, been satisfactori- 
 ly answered, and they are in our judgment, we are free to say, 
 unanswerable. These objections are embodied in the celebrated 
 formula of Mr. Hume, which is in substance as follows : The 
 supposition of an eternally existing order in nature an order 
 which exists without a cause is no more inconceivable or self- 
 contradictory than that of the eternal existence of an infinite 
 mind a mind capable of conceiving of the order existing in 
 nature and actually establishing it, and all this without a cause. 
 No individual has yet shown that this formula is not self-evi- 
 dently true ; nor, in our judgment, can any one do it. In our 
 development of the principles by which the validity of objec- 
 tions against any given hypothesis may be tested, we laid down 
 this as a universal principle, that no objection which- exists in 
 full force against a proposition known to be true, has any validi- 
 ty when arrayed against any other proposition. Leaving out 
 of view the idea that the order existing in nature once did not 
 exist and began to be, every objection against the conception 
 of such order existing without a cause, lies equally against the 
 conception of the being and perfections of God. But one of 
 these must be true. The objection, then, is void of validity 
 against either. The way, and the only way, in which the argu- 
 ment of Mr. Hume can be met, is by showing that the order 
 actually existing in nature does not come under the principle 
 to which he has assigned it, but falls, in fact, under a very dif- 
 ferent principle a principle which necessarily afiirms the theis- 
 tic hypothesis, on the supposition that the order existing in na- 
 ture falls under that principle. 
 
 4. Equally valid, in our judgment, are the objections urged 
 
APPLIED LOGIC. 345 
 
 by Mr. Hume, Mill, and others, against the proof of this prin- 
 ciple, as adduced by theistic writers. " If," says Dr. Chalmers, 
 " we can infer the agency of design in a watchmaker, though 
 we never saw a watch made, we can, on the very same ground, 
 infer the agency of design on the part of a world-maker, though 
 we never saw a world made." The above we regard as strict- 
 ly an analytical judgment. It is impossible even to conceive of 
 the opposite as true. The reason is obvious. There is here a 
 common assumption in regard to the two cases the watch and 
 the world to wit, that both alike were, in fact, made, that is, 
 once did not exist and then were produced. In all such cases, 
 we can, as Dr. Chalmers shows, legitimately reason from the 
 character of the' thing made to that of the maker. But sup- 
 pose we do know that the watch, and do not know that the 
 world, was made ; in other words, suppose that we do know 
 that the order and arrangement existing in the watch once did 
 not exist, and began to be, while we do not know this of the 
 order and arrangement existing in nature. The cases then are 
 not at all parallel, and we cannot, reason from the one to the 
 other. Let us suppose, still further, that the order and arrange- 
 ment existing in the watch are not only known to be an effect 
 originated in time, but to be of such a nature that they could, 
 by no possibility, have been produced by any laws inhering in 
 nature itself, while we do not and cannot know that the order 
 and arrangement existing in nature ever were produced at all, 
 that is, do not and cannot know but that they have, in fact, 
 existed from eternity. The two cases, on that supposition, not 
 only do not fall together under the same inductive syllogism, 
 but do not fall under that of analogy. In other words, they 
 are not even analogous cases. We cannot logically reason from 
 a case which we know must have been produced by one specific 
 cause, to one that we do not know was produced by any cause 
 whatever. The validity of this principle, Dr. Chalmers distinct- 
 ly recognizes in his " Natural Theology," affirming, that before 
 we can reason from the order existing in nature to the charac- 
 ter of God as the cause of that order, we must show that the 
 former is, in fact, an effect, that is, was originated in time. If 
 15* 
 

 
 it existed from eternity, it cannot be affirmed to be an effect at 
 all, and we cannot reason from it to any cause whatever. 
 When we reason from the mere fact of order, therefore, irre- 
 spective of the question of its origin, to the character of God, 
 Ave reason most illogically. 
 
 There are events, however, that we know were produced by 
 a designing cause the watch, for example. On what condition 
 can we conclude that because marks of design or facts of order 
 here imply a designing cause, that marks of design or facts of 
 order in any other case suppose a similar cause ? On this con- 
 dition exclusively, that the facts of order in both cases are the 
 same in kind, that is, belong to the same species. If we have 
 different kinds of order, we cannot, by induction, but exclusive- 
 ly on the principle of analogy, reason from the one to the other, 
 and then we obtain only probable deductions. Now Mr. Mill, 
 Hume, and others, contend that when we reason from the facts 
 of order which appear in the watch to those which appear in 
 nature, we do not reason from one individual of a given species 
 to another of the same species, and that in view of the specifical 
 element common to the two, but from one individual of one 
 species to another of a different and opposite species, and this 
 in view merely of the generical element which they possess in 
 common, and all this under the assumption that the two cases 
 fall under the former instead of the latter relations. The facts 
 of order which appear in the watch have certain fundamental 
 characteristics utterly wanting in those which appear in nature, 
 and which separate the two classes into distinct and opposite 
 species of the general class, facts of order. The fonner, for ex- 
 ample, possess essential characteristics that is, peculiar combi- 
 nations unlike any thing resulting from the action of nature's 
 laws. The time was, for example, when no such thing as a 
 watch, nor any thing of the kind, had an existence. There are, 
 also, artificial combinations of a kind not only unlike any thing 
 produced in nature, but which we know can result from the ac- 
 tion of no inhering power of nature, and therefore, aside from 
 the elements of order, supposing the action of a designing power 
 out of and above nature. These circumstances separate such 
 
APPLIED LOGIC. 347 
 
 facts by fundamental specifical differences from facts of order 
 produced through the action of nature's laws, and to the pro- 
 duction of which, from aught that appears in the mere facts 
 themselves, said laws are adequate. It is only under the prin- 
 ciple of remote analogy, in view, not of their specifical, but ge- 
 nerical elements, that we can reason from one of these classes 
 of facts to the other. Such, in substance, is the reasoning of 
 the individuals referred to, on this subject. In our judgment, 
 that reasoning has absolute validity. Before we can reason in- 
 ductively from the one class to the other, we must show that 
 they belong to the same species, and our reasoning must be 
 based wholly upon the specifical elements common to the two. 
 This is done when (what is not done in the design argument as 
 almost exclusively presented) the order existing in both alike is 
 shown to be an effect originated in time, and to possess other 
 common characteristics which render it undeniably evident that 
 neither any more than the other, could result from the action 
 of laws inhering in nature. 
 
 5. The principle on which the theistic argument under this 
 syllogism has hitherto been conducted now claims our atten- 
 tion. In our judgment, the conduct of this argument, we re- 
 peat, is without a parallel in the history of science. In all cases, 
 where, in a given syllogism, one premise is doubted or denied 
 and the other universally admitted, and where the validity of 
 the latter is too obvious to admit of doubt or denial in any 
 form, science requires universally that the disputed, and not the 
 admitted premise, should be argued. In regard to the theistic 
 syllogism now before us, no form of doubt or denial does exist, 
 or ever has existed, of the validity of but one of its premises 
 the major. Yet in the conduct of the argument, a few simple 
 illustrations aside the watch, for example the admitted, in- 
 stead of the disputed premise, has been exclusively argued. 
 Astronomy, geology, and the sphere of all the sciences have 
 been traversed, to find facts of order to fortify and defend the 
 admitted premise, and all this while mountain ridges of facts of 
 this kind lay piled up, " Pelion upon Parnassus," before the uni- 
 versal mind facts, the reality of which all the world admit, to- 
 
gether with the absolute and undeniable validity of the premise 
 whose validity they affirm. In the conduct of this argument, 
 the hostile forces have, in the presence of all the world, passed 
 each other. Each has assaulted positions which the other has 
 left undefended, and thrown up fortresses around positions which 
 the other has not thought of assailing. The time has now ar- 
 rived when they are called upon to join issue on the real point 
 in dispute, and that the vital one. The time has come espe- 
 cially, for the advocates of theism, to find a major which will not 
 be disputed, or to place the one which they have selected be- 
 yond dispute by demonstrating its validity. This is the exclu- 
 sive burden now resting upon them. 
 
 6. We will now, in the last place, give our own estimate of 
 the real value of the theistic argument as thus far conducted. 
 There are two points of light in which this subject may be con- 
 templated the value of the argument as a means of conviction, 
 and as a source of illustration. As a means of conviction, that 
 is, of confirming the faith of actual believers, or of inducing con- 
 viction in the minds of unbelievers, we regard the argument as 
 it now stands as almost, if not quite, worthless. No facts ranged 
 under a general principle, for the purpose of establishing a cer- 
 tain conclusion, can possibly raise any convictions of the truth 
 of said conclusion of a higher nature than those already existing 
 in respect to the validity of the principle itself. When this ar- 
 gument is addressed to the believer, it finds him already more 
 immovably assured of the truth of the conclusion sought, to wit, 
 " God exists," than he is of the validity of the principle pre- 
 sented as the exclusive basis of the argument, to wit, " Facts 
 of order universally prove mind." The argument, then, can 
 have ho efficacy as a means of confirming existing convictions, 
 and if a doubt of the validity of the principle exists, will tend 
 exclusively to weaken those convictions. On the other hand, 
 if the argument is presented to one who not only doubts the 
 conclusion sought, but also denies the validity of the principle 
 under which our facts of order are arranged, every fact of this 
 character adduced will tend to but one result, that is, to in- 
 crease the pre-existing mental state, and that by continuously 
 
APPLIED LOGIC. 349 
 
 arousing the mind to a more distinct and reflective conscious- 
 ness of the grounds of the doubt and disbelief referred to. 
 Such, in our judgment, is the value of the argument before us 
 as a means of conviction, the great end for which it has been 
 perfected. On the other hand, if we would refer to the various 
 productions embodying this argument as sources of illustration, 
 that is, as furnishing examples of the handiwork of an intelli- 
 gent first cause already known to exist, then such productions 
 as those of Paley are invaluable. As such, these productions 
 will be resorted to long after they have been forever set aside, 
 as sources of valid proof of the being of God. 
 
 INFLUENCE OF THE HYPOTHESIS, THAT THERE ARE DIFFERENT 
 KINDS OF PROOF OF THE BEING OF GOD. 
 
 Nothing, in our judgment, has tended more to obscure and 
 mystify the whole subject under consideration, than the suppo- 
 sition that there are different kinds of proof of the being of 
 God such as the d priori, the d posteriori, the cosmological, 
 and teleological. What, for example, is the proper and exclu- 
 sive sphere of d priori cognitions ? Not the real, as far as sub- 
 stances and causes are concerned, in any department of thought 
 whatever. A priori, we do know, for example, that " Qualities 
 suppose substances," " Events a cause," and " Conditioned ex- 
 istences an unconditioned or ultimate cause." A priori, we do 
 not and cannot know, however, what kind of substances, causes, 
 or unconditioned realities actually exist, any more than we can 
 thus know what particular qualities, events, or conditioned 
 realities actually exist. What would be thought of a natural 
 philosopher who should profess to give d priori demonstrations 
 of the nature and specific character of particular proximate 
 causes existing in the world around us? Such a procedure 
 would be no more absurd than an attempt at a similar proof of 
 the being of God. God is and can be known only as a cause 
 the unconditioned cause. We can no more determine d priori 
 what this cause is, than we can thus determine the nature of 
 the phenomena of " things that are made." We can no more 
 
350 LOGIC. 
 
 determine d priori whether a world-maker exists, than we can 
 thus determine whether a watchmaker exists, and that when 
 we do not know whether a world or a watch exists (*- not. 
 A priori we cognize formulas yielding certain specific deduc- 
 tions in regard to the nature and character of proximate causes 
 in the world around us, and of the unconditioned cause of all, 
 and yielding said deductions, on the supposition that the facts 
 of creation accord with those formulas. A posteriori we deter- 
 mine whether said facts do or do not accord with those formu- 
 las, and thus obtain scientific deductions in regard to the nature 
 of causes proximate and ultimate. This is the exclusive pro- 
 cedure in all the sciences. From the very nature of the idea of 
 God, we have and can have no other forms of valid proof of his 
 being or perfections. The following may be given as the forms 
 of the only real syllogisms yielding the different elements of the 
 theistic deduction, " God exists" : 
 
 First Syllogism. 
 A priori premise, 
 Facts of a certain character affirm that the unconditioned cause of the order 
 existing in nature is a power out of and above nature ; 
 
 A posteriori premise, 
 The facts of the universe are of this character ; 
 
 Conclusion, 
 The unconditioned cause of the order existing in nature is a power out of 
 and above nature. 
 
 Second Syllogism. 
 A priori premise, 
 Facts of a certain character reveal this cause as a self-conscious personality, 
 possessed of the attributes involved in the ideas of infinity and perfection. 
 
 A posteriori premise, 
 Facts of creation of this character do exist ; 
 
 Conclusion, 
 The unconditioned is a self-conscious personality, &o 
 
APPLIED LOGIC. 351 
 
 There is no other possible form in which we can reason scien- 
 tifically from facts to causes of any kind whatever. A priori 
 we determine what deductions must be valid, on the supposition 
 that facts of a certain character do exist. A posteriori we de- 
 termine whether facts of that character do or do not exist. 
 This must hold in the science of theology as well as, and in the 
 same form as, in all other sciences. A priori we determine 
 nothing whatever in regard to the questions, whether real 
 causes do or do not exist, and what are the real character of 
 causes. A posteriori we simply determine what facts do or 
 do not exist. By the union of the two elements of thought be- 
 fore us, we deduce, from principles and facts thus given, valid 
 conclusions in regard to the reality and character of causes 
 proximate and ultimate. To this one form of procedure, sci- 
 ence knows no exceptions whatever. 
 
 THE TWO ABERDEEN PRIZE ESSAYS DENOMINATED "CHRISTIAN 
 THEISM," AND " THEISM." 
 
 As a further elucidation of the principles of logical deduction, 
 we have deemed it expedient to offer a few criticisms on the 
 two works above named. Our special object in criticising these 
 works is the correction of certain false systems of philosophy 
 systems which need correction in order to place philosophy itself 
 on a scientific basis. From the circumstances of their origin, 
 we should naturally conclude that these essays would embody 
 the theistic argument in the strongest forms in which it now 
 exists, the prizes offered having been so great (one of $9,000 
 and the other of |3,000), and the competitors so numerous (up- 
 wards of two hundred). For ourselves we took up these pro- 
 ductions with the highest expectations, and read them with the 
 intensest interest. We laid them down with the deep impres- 
 sion, that if said productions do present the theistic argument 
 in its present and especially in its present and highest forms 
 then natural theology is not only in its infancy, but is yet in the 
 meshes of unsound and erfoneous principles of science. The 
 logic only of these productions will be the subject of criticism. 
 
"We will first direct attention to the essay which took the second 
 prize that of Professor Tulloch. 
 
 Professor Tulloch'' s Treatise {Theism). 
 
 We have already given the syllogism in conformity to which 
 the theistic argument is elaborated by our author, and which is 
 given in the first chapter of the work. Professor Tulloch dis- 
 tinctly admits the fact, that the major is the only disputed 
 premise of the theistic syllogism, as given by himself and 
 others. Hence, when he comes to argue the minor, he very 
 pi'operly argues that under the title, "Illustrative (inductive) 
 evidence." The only real question at issue, he asserts, pertains 
 exclusively to the claims of the major premise. In respect to 
 it to wit, that " Order universally proves mind," he says, 
 "Upon this fundamental position rests the whole burden of the 
 theistic argument." Again, he adds, speaking of the same 
 premise, " There, accordingly, the whole contest of theism cen- 
 tres, and finds its most vital struggle. And of this the opposite 
 school of thinkers are sufficiently aware. They clearly feel that 
 it is here alone that a consistent position of denial can be taken 
 up." We were not mistaken, then, when we asserted that the 
 theistic syllogism, as presented by our author and others, has a 
 disputed major and a universally admitted minor. Nor will it 
 be doubted that previously to the appearance of Professor Tul- 
 loch's work, the admitted instead of the disputed premise had 
 been almost exclusively argued by theistic writers. 
 
 In what position does this representation place the science of 
 theology ? It has within its own proper sphere, if this repre- 
 sentation is true, no ultimate principles or " first truths." It is 
 altogether a secondary science, its highest principle the major 
 premise, in itself a problematical judgment being the conclu- 
 sion of a prosyllogism, whose validity is to be determined exclu- 
 sively within the sphere of another and totally different science. 
 For ourselves, we do not believe that the eternal truth which 
 lies at the foundation of all religion ,' has such a basis. The sci- 
 ence of theology, we believe, rests upon ultimate principles lying 
 
APPLIED LOGIC. 353 
 
 within its own appropriate sphere, and which must and will, 
 when rightly presented, be universally admitted to be strictly 
 analytical judgments that is, universal and necessary intuitive 
 truths. " The whole contest of theism," on the other hand, 
 must, when the science is properly developed, centre and " find 
 its most vital struggle," not in reference to the first principle of 
 the science the major premise but in regard to matters of 
 fact, that is, the minor premise. It is a reversal of all the laws 
 and principles of scientific procedure to suppose the opposite. 
 
 In resting the whole science of theology, therefore, upon a 
 mere problematical judgment, it became the author to place the 
 question of the validity of that judgment beyond dispute, by an 
 unanswerable demonstration of its truth. Otherwise the funda- 
 mental doctrine of all religion is made to rest upon an uncer- 
 tain basis. The question which now arises, the question upon 
 which the entire logical claims of his whole work must rest, 
 is, Has he done this ? Has he demonstrated the truth of his 
 major premise, " Order universally proves mind ?" To a con- 
 sideration of this one question we will now advance. After 
 some explanatory statements and remarks in the first chapter, 
 this question is argued at length in chapter second, and the en- 
 tire superstructure subsequently reared must stand or fall with 
 the validity of the argument in this single chapter ; for here 
 alone he argues what he himself affirms to be the " vital ques- 
 tion" the major premise. Let us, then, examine the argu- 
 ment as here developed. 
 
 Professor TullocJi's professed Demonstration of Ms Major 
 Premise. 
 
 On a careful examination of what appears in this chapter, it 
 will be seen at once that the learned author does not argue this 
 question directly and immediately at all, but another and dif- 
 ferent question ; one, however, which, as he affirms, directly 
 and immediately implies this. The proposition which he at- 
 tempts to establish is not this : " Order universally proves 
 mind," but this : Any event, whatever it may be, proves mind. 
 
354 LOGIC. 
 
 If the latter proposition is established, the former, par emi- 
 nence, he concludes, and rightly too, is established. That we 
 may not, even in appearance, misrepresent our author, we 
 will present the following somewhat lengthy extract from the ' 
 first chapter an extract in which he distinctly defines his own 
 position : 
 
 " In endeavoring to verify the position which forms the argu- 
 mentative basis of our evidence, there are two special lines of 
 proof demanded of us the one relating directly to the position 
 itself, that ' Order universally proves mind,' or, in other words, 
 that ' Design is a principle pervading the universe ;' and the 
 other relating to a doctrine which, as it appears to us, lies every- 
 where involved in the more special theological principle. This 
 principle, in the form announced in our first proposition, un- 
 doubtedly implies a definite doctrine of causation. In asserting 
 the principle of design, we clearly assert at the same time, that 
 mind alone answers to the true, or at least ultimate, idea of 
 cause. We pronounce causation, or at least our highest con- 
 ception of it, to imply efficiency. But does it really do so ? 
 We find ourselves met on this general philosophical ground as 
 to the true nature of causation, as well as on the ground of the 
 special theological application which we make of the general 
 truth. They who dispute the theistic interpretation of nature, 
 no less dispute the doctrine of efficient causation, and in fact 
 base their opposition to the highest principle on this lower and 
 wider ground. 
 
 " In order, therefore, fully to sustain our position, we must 
 make it good on this lower ground. According to our whole 
 view, the one position is untenable apart from the other." 
 
 Here, it will be seen, that our author not only affirms, as the 
 doctrine which he is to establish, that mind is the only existing 
 real or efficient cause, but that to prove the higher proposition, 
 *' Order universally proves mind," he must prove the lower 
 one, Any event proves mind. Further on, this last proposition 
 takes a still different form, to wit, Any event proves a rational . 
 will the doctrine of the essay being this, that will is the only 
 existing real'cause of any event whatever. "A cause," he says, 
 
APPLIED LOGIC. 355 
 
 " we have found to be truly coincident with an agent ; to have 
 its primitive type in the ego, the living root of our being ; and 
 to be especially represented in that which constitutes the highest 
 expression of our being free will. A cause, therefore, implies 
 mind. More definitely, and in its full conception, it implies a 
 rational will." This is the only proposition bearing upon the 
 subject that he even attempts to establish in this chapter. The 
 theistic syllogism as argued by him is really and truly this : 
 First or major premise, 
 
 Any event whatever proves a rational will ; 
 Second or minor premise, 
 
 The works of nature discover events ; 
 Conclusion, 
 
 The works of nature prove a rational will. 
 
 Upon the validity of the major premise of this syllogism, or 
 rather upon our author's professed demonstration of its validity, 
 the claims of the fundamental doctrine of all religion is wholly 
 based in this treatise, and all who accept the treatise as proper- 
 ly and adequately representing the theistic argument, must ac- 
 cept of the doctrine of the being of God as having a foundation 
 no more solid and immovable. Let us now advance to a direct 
 consideration of our author's professed demonstration of the 
 proposition before us. 
 
 Our Author's Indirect and Preliminary Argument. 
 
 In his indirect and preliminary argument, in which he com- 
 bats the doctrine of causation as maintained by Messrs. Hume, 
 Brown, Mill, and others to wit, that cause is nothing but " an- 
 tecedence immediate and invariable," our author is undeniably 
 triumphant. All that we perceive relatively to the facts of the 
 universe^ these authors maintain, is simply succession of events, 
 and nothing else. From this fact, which is undeniable, and 
 equally so in respect to mental and physical facts, they assume 
 that no other relation than that of mere antecedence and conse- 
 quence exists between successive events. There is no correla- 
 
356 LOGIC. 
 
 tion between the antecedent and consequent which makes it 
 necessary that one particular consequent instead of another, or 
 none at all, should be connected with any particular antecedent. 
 Take away all antecedents of every kind, and as far as the na- 
 ture of things is concerned, precisely the same consequents as 
 now appear are just as possible and as likely to arise, as when 
 these antecedents are given. To this view of the doctrine of 
 causation our author replies in the following language : 
 
 " When on the appearance of any change we instinctively 
 pronounce it to have a cause, what do we really mean ? Do 
 we affirm merely that some other thing has gone before the ob- 
 served phenomenon ? Is priority the constitutive element of 
 our intellectual judgment ? Is it not rather something quite 
 different ? Is not our judgment characteristically to this effect 
 that some other thing has not only preceded, but produced 
 the . change we contemplate ? Nay, is it not this idea of pro- 
 duction that we particularly mean to express in the use of the 
 term ' cause ?' Succession is no doubt also involved, but it is 
 not the relation of succession with which the mind in the sup- 
 posed judgment is directly and initially concerned, but rather 
 the relation of power. That when we speak of cause and effect, 
 we express merely the relation of conjunction between phe- 
 nomena of antecedence and consequence in any defined sense, 
 is something of which no ingenuity of sophistry will ever be 
 able to persuade the common mind. It matters not in the least 
 degree that it can be so clearly proved that nothing intervenes 
 between the simple facts observed, that we see in the sequence 
 of the phenomena. This is not in dispute. Only the intel- 
 lectual common sense insists on recognizing a deeper relation 
 among phenomena than mere sequence. It accepts the order 
 of succession, which is the special function of science to trace 
 everywhere to its most general expression ; but it moreover 
 says of this order, that it is throughout produced, or, in other 
 words, that it is only explicable as involving a further element 
 of power. That it is really the import of the intellectual judg- 
 ment which we pronounce in speaking of cause and effect to 
 which the very words themselves testify in an unmistakable 
 
APPLIED LOGIC. 357 
 
 manner is so clear, that it is now admitted by every school of 
 philosophy which does not rest on a basis of materialism, and 
 has even been conceded by writers of this school, however irre- 
 solvable on their principles." 
 
 No individual, we are bold to affirm, can by any possibility 
 refute the above argument, or show that it is not perfectly fatal 
 to the theory of causation to which said argument stands op- 
 posed. The advocates of this theory overlook wholly a fundar 
 mental fact of universal consciousness, the absolute affirmation 
 that there are in the human mind two distinct forms of know- 
 ledge equally valid a knowledge of what we directly and im- 
 mediately perceive to be true, and a knowledge of what is 
 necessarily implied in what we perceive. We know that body 
 exists, because we have a presentative knowledge of it as ac- 
 tually existing. In knowing that body does exist, we know 
 that space must exist, although it is not an object of immediate 
 perception, the reality of space being necessarily implied in that 
 of body. So in cognizing succession and phenomena as reali- 
 ties, we know that time and substances must be realities also. 
 As body necessarily supposes space, succession time, and phe- 
 nomena substance, in knowing by immediate perception the 
 first class of objects as real, we know with equal absoluteness 
 that the latter class must be realities also. The same principles 
 apply to our knowledge of causation. In knowing that any 
 event whatever has occurred, we know absolutely, as necessarily 
 implied in the occurrence of said event, not only that it had an 
 antecedent, but a real efficient determining cause. We know 
 that this must be true, because we cannot even conceive the op- 
 posite as being true. We will now consider, 
 
 Our Author's Direct and Positive Argument. 
 
 In demonstrating the fact that the theory of causation main- 
 tained by Mr. Hume, Mill, and others, is not true, we have de- 
 termined the truth of the doctrine that there are real determin- 
 ing efficient causes causes which are the true and proper ante- 
 cedents of all events. We have by this means, however, deter- 
 
858 LOGIC. 
 
 mined nothing in regard to. the nature or location of said causes, 
 whether, for example, they are exclusively physical or mental, 
 or whether there are in reality both mental and physical causes. 
 According to our author, all real causation is exclusively men- 
 tal. "According to this whole view," he says, "there is no 
 such thing as mere physical causation." Again, "Physical 
 causes, apart from the idea of a will in which they originate 
 and which they manifest, have no meaning." 
 
 How, permit us to ask in the first place, can the truth of such 
 a doctrine supposing it true he established ? Not surely d 
 priori. We cannot thus determine whether matter, on the one 
 hand, or mind, on the other, is or is not the real and proper 
 cause of certain effects. For aught that we can thus determine, 
 there may be real physical causes of physical effects, and also of 
 mental phenomena, as well as mental causes of mental, on the 
 one hand, and of physical effects, on the other. A priori we 
 cannot affirm, that matter as well as mind is not. a real and 
 proper power in regard to certain events. This is undeniable. 
 It is wholly d posteriori, that is, by a knowledge of facts mental 
 and physical, that this doctrine, if true and if its truth is ascer- 
 tainable, can be established. 
 
 It is further evident, and undeniably so, that this doctrine if 
 true cannot be proven by any reference to what is intrinsic in 
 any mental or physical facts contemplated by themselves, or 
 when compared with one another. Take any act of will, for 
 example, we please, and from what is intrinsic in the act itself, 
 or by comparing it with any mental or physical fact, we cannot 
 determine that such act is a cause proper of such fact, much 
 less that acts of will are the only real causes of other mental 
 and of all physical events. It is by no inspection or dissection 
 of mental and physical facts that this doctrine, if susceptible of 
 proof, can be proven. If susceptible of proof at all, it must un- 
 deniably be through some relation of these tacts to one another 
 a relation given in consciousness. 
 
 We are now prepared to take up the question, By what means 
 does our author attempt to prove his own doctrine ? Simply 
 and exclusively, we answer, by an attempted proof of the psy 
 
APPLIED LOGIC. 359 
 
 chological proposition, that it is exclusively through the con- 
 sciousness of our acts of will as causes that we originally ob- 
 tained our idea of causation. From this one source exclusively, 
 he affirms, was our idea of causation originated. On this one 
 assumed fact, the universal assumption is based that a rational 
 will is the only real existing efficient cause. " The question be- 
 fore us, then," he affirms, " really passes into the old one as to 
 the origin of our knowledge." To prove that this idea was not 
 originally given by external material facts, and that it Avas given 
 by the consciousness of mental acts acts of will he makes the 
 following statements : " That this idea" (that of causation) " is 
 not derived from without that it does not come through any 
 phase of sensational experience is already clear in the fact ad- 
 mitted on all hands, that we only perceive succession^-that we 
 are only conversant through the senses with the two terms of a 
 sequence. But if not from without it must be from within ; we 
 must have the idea of power given us in our own mental expe- 
 rience." Again : " With the dawn of mind we apprehend our- 
 selves as distinct from the objective phenomena surrounding us ; 
 the ego emerges, face to face, with the non-ego. And in this 
 springing forth of self, so far back in the mental history as to 
 elude all trace, is primarily given the idea of power. 
 
 " What is commonly called the will, therefore, is, according 
 to this view, the ultimate source or fountain of the notion of 
 power." 
 
 In thus determining, as our author supposes he has done, the 
 source from whence the idea of power or cause was originally 
 derived, he assumes that he has also determined the exclusive 
 source of causation itself, that is, that he has demonstrated that 
 " rational will" is the only real existing cause. In other words, 
 in proving that we originally derived our idea of cause from the 
 consciousness of mental acts, we have demonstrated the fact, 
 that a " rational will" not only is a cause of some facts, but the 
 exclusive cause of all facts whatever that matter, consequently, 
 is not the cause" of any events whatever. Such is the argument 
 of our author. In regard to it we remark : 
 
 1. That granting our author's theory of the origin of our idea 
 
360 LOGIC. 
 
 of causation to be true, the inference that he deduces from it 
 presents one of the most palpable and singular leaps in logic 
 that Ave ever met with. The fact professedly ascertained is 
 this : In the consciousness of mental acts we originally obtained 
 our idea of causation. The conclusion deduced from this as- 
 sumed fact is this : " There is no such thing as mere physical 
 causation." In other words, facts of mind originate the idea of 
 causation in the mind itself. Matter, therefore, is the real cause 
 of no facts whatever. What conceivable connection is there 
 between such a fact, granting it real, and such a conclusion as 
 that ? How do we, how can we know, that that which origi- 
 nates the idea of cause in our minds is itself the only source of 
 real causation ? Matter, for aught we know or can know, may 
 be the real cause of certain facts, and yet we have derived our 
 idea of cause, not from matter but from facts of mind. This is 
 undeniable. 
 
 2. By no possibility can the validity of this theory of the ori- 
 gin of our idea of causation be verified. We have no remem- 
 brance of the source from whence this idea was derived. Nor 
 can we legitimately affirm that because, as far as physical phe- 
 nomena are concerned, we perceive nothing but succession, we 
 did not from hence derive our original idea of causation. In 
 our present consciousness, in cases where we perceive nothing 
 but succession, the idea of any event whatever is, by a necessi- 
 ty of our intellectual constitution, connected with the idea of 
 cause. For aught that we can know, this idea by the same ne- 
 cessity did, in fact, connect itself with the very first event which 
 we did perceive, whether it was mental or physical. We know 
 that it is a fixed law of our intellectual constitution, that when 
 any fact whatever is perceived, with the conception of that fact 
 is originated also its logical antecedent. Thus with the concep- 
 tion of body, which we perceive, is originated the conception of 
 space, which we do not perceive. Thus also the perception of 
 succession originates the idea of time, and the perception of 
 phenomena that of substance. Now the same law which origi- 
 nates the ideas of space, time, and substance, on the perception 
 of body, succession, and phenomena, must originate that of 
 
APPLIED LOGIC. 361 
 
 cause, on the perception of any event whatever, whether men- 
 tal or physical. Unless it can be shown, therefore, and it can- 
 not be that acts of will were, in fact, the first objects of per- 
 ception, it cannot be shown that we did derive from them our 
 idea of cause. In that case, also, that origin would be merely 
 accidental, any other event being equally adequate to the origi- 
 nation of the idea. 
 
 3. By the same argument granting its validity by which 
 our author would prove that we could not have derived our 
 idea of cause from external, we will prove that we could not 
 have derived it from internal, phenomena. We could not have 
 derived it, he argues, from the former, because here we perceive 
 only succession. It is equally and undeniably true that in the 
 consciousness of internal facts, we perceive nothing but succes- 
 sion. We have the consciousness of one mental act or state, 
 and then of another. So also of all mental states and their 
 physical consequents. Nothing but succession of phenomena 
 can, by any possibility, be an object of perception, external or 
 internal. The idea of causation is exclusively an idea of reason 
 an idea given, like those of space, time, and substance, on 
 occasion of perception, but not in perception itself, external or 
 internal. If these external facts, because we find in them only 
 succession, cannot give this idea, for the same reason internal 
 facts cannot give it, for here also perception gives only succes- 
 sion. From the nature of the idea, however, each class of per- 
 ceptions is equally capable of originating the idea ; and which, 
 in fact, does originate it in the experience of any one individual, 
 we have no means of determining. 
 
 4. We have all the evidence that matter is the cause proper 
 of certain physical facts and mental states, on the one hand, 
 that we have or can have, in our present state of knowledge, 
 that mind is the cause proper of certain mental and physical 
 facts, on the other. As far as we can perceive, certain physical 
 causes are as necessarily connected, and that in the relation of 
 real causation, with certain physical facts, as mind is with any 
 mental facts. Let us now contemplate the proposition, that we 
 have the same evidence that material substances are the causes 
 
362 LOGIC. 
 
 proper of mental states, that we have that mind or will is the 
 cause proper of physical facts. When " for the" first time the 
 ego emerges, face to face, with the non-ego? what relation 
 does the former then recognize itself as sustaining to the lat- 
 ter ? Is it this, that the former as " a rational will," is the ex- 
 clusive cause of all effects, and that the latter is, in no proper 
 sense, a real power, in no real sense the cause proper of any 
 effects whatever effects mental or physical ? By no means. 
 Prior to all acts of will of any kind, mind finds itself to have 
 been the subject of the action of causes whose action produced 
 fundamental mental states, and that antecedent to and wholly 
 independent of all forms of voluntary activity on its part. Sen- 
 sation, perception, and the consequent consciousness of the same, 
 precede all acts of will, and as antecedents lead to the same. 
 In the consciousness of sensation particularly, mind the ego 
 is not revealed to itself as a cause at all, but exclusively as the 
 subject of the action of causes wholly ab extra. Now it is un- 
 deniable, that the mind has and can have no higher evidence 
 that it is the cause proper of any physical facts whatever, than 
 it has that the non-ego which it thus beholds " face to face," is 
 the cause proper of sensation. We have all the evidence that 
 the non-ego, as a real cause, induces primal mental states, that 
 we have or can have that mind, in its subsequent voluntary ac- 
 tivity, is the real cause of any. changes whatever in external na- 
 ture. There is just as much evidence of the truth of the dogma, 
 that matter is the exclusive efficient cause of all effects, and that 
 there is no such thing as mental causation, as there is that mind 
 or will is the only real cause, and that there is no such thing as 
 mere physical causation ; and there is and can be absolutely no 
 evidence whatever, in our present state of knowledge, of the 
 truth of either dogma. The evidence that matter, on the one 
 hand, and mind, on the other,^re each alike causes proper, is, 
 in our conscious experience, perfectly balanced. We have pre- 
 cisely, we repeat, the same evidence that the non-ego really 
 produces changes in and limits the activity of the ego, that we 
 have or can have that the latter produces any changes in the 
 former. The most that can in any case be said of the theory of 
 
APPLIED LOGIC. 363 
 
 our author is, that it possibly may be true in fact. Of its truth, 
 however, if true, we have and can have without a revelation 
 from God no positive evidence in any form whatever. 
 
 5. That will, we remark finally, is not the only efficient cause, 
 we have well-nigh, if not quite, demonstrative proof. In the 
 order of nature in the infinite and eternal mind, the action of 
 intelligence precedes that of the will. This is undeniable. In 
 the finite mind, too, states of the sensibility and intelligence 
 were originally induced by causes wholly db extra, prior to 
 all foi ms of voluntary activity, and we have now in conscious- 
 ness continuous experiences of precisely similar results. What 
 higher evidence can we have of any fact than we have here of 
 the truth of the doctrine, that the will is not the only form and 
 source of efficient causation ? We have, then, not only no evi- 
 dence whatever of the truth of our author's theory of causation, 
 but nearly, if not quite, demonstrative proof that it is not and 
 cannot be true. 
 
 What then is the bearing of such a conclusion upon the 
 merits of the work before us, upon its merits in a logical point 
 of view ? Nothing but this : As an argument for the being of 
 God the work is a total failure. The author has himself formal- 
 ly committed the logical claims of the whole argument through- 
 out to the validity of one principle his theory of causation. 
 That theory failing of valid evidence, as it undeniably does, 
 the whole argument as developed in the work visibly appears 
 resting upon nothing but a bank of sand. 
 
 But this work is not only logically inconclusive, but equally 
 self-contradictory. After spending upwards of three hundred 
 pages in elaborating the theistic syllogism, as presented in chap- 
 ter first and already considered by us in Sect. 3, Chapter. IV., 
 he formally abandons his previous argument as inconclusive, 
 and affirms that the real proof* of the divine existence is intui- 
 tive or a priori. In treating of the divine infinity in this chap- 
 ter, he falls back from " the theistic syllogism" altogether, and 
 rests the whole" question of the divine existence itself exclusive- 
 ly upon intuition. By one form of intuition (the lower) we 
 attain to a direct and immediate knowledge of the finite as real. 
 
364 LOGIC. 
 
 By another and higher form of intuition we similarly attain to 
 a similar knowledge of the infinite. " The infinite," he says, 
 " is the peculiar object of this higher intuition. It" (the infi- 
 nite) " is the revelation of reason, as the finite is the revelation 
 of sense." " The infinite," he says again, " is apprehended by 
 us in the strongest manner, but then the evidence of this reali- 
 ty is directly found in the intuitive apprehension of the ego?'' 
 If " the evidence" of the divine existence is found here and 
 our author now affirms that it is it is not, of course, to be 
 found in any of his previous presentations. According to the 
 express teaching of inspiration, however, " the eternal power 
 and Godhead" of deity, are, in fact, " clearly seen, being under- 
 stood," not by immediate intuition, but " by the things that 
 are made." We have, also, as we judge, already sufficiently 
 proven the fact, that there is no such d priori proof or know- 
 ledge of God, or of any other power or cause in existence. For 
 this one form of proof, however, our author formally abandons 
 all others. " The infinite," he says, " no longer regarded as a 
 mere subjective reflection in the understanding a mere logical 
 necessity but as intuitively given in reason, needs and admits 
 of no other proof of reality than its being thus given." Again : 
 " And in thus abandoning all claim to demonstration, the evi- 
 dence of the being of God, so far from being weakened, is in- 
 deed strengthened. For in all our knowledge there is and can 
 be no higher warrant for reality than the grasp of intuition." 
 
 Has this learned author spent three hundred pages in elabo- 
 rating what he calls " the thelstic syllogism," for the purpose of 
 thus exposing its utter invalidity, and of showing that the case 
 "needs and admits" of no such form of proof ? This must 
 have been the case if he understood himself. 
 
 * 
 
 MR. THOMSON'S TREATISE (CHRISTIAN THEISM). 
 
 The theistic argument, as developed by Mr. Thomson, rests 
 upon the same principle, and is elaborated, as far as the ques- 
 tion relative to the being of God is argued at all in his treatise, 
 in conformity to the 6ame syllogism as that of Professor Tnl- 
 
APPLIED LOGIC. 365 
 
 loch, to wit, the argument from design. " It is the argument 
 of natural theology," says Mr. Thomson, "that design must im- 
 ply a designer, and that which designs is mind." Again, in an- 
 swer to the question, "Is the First Cause a living God ?" he 
 says, " The answer to this question depends chiefly on the argu- 
 ment from design. The cosmological argument gives us a First 
 Cause of all things, an origin of all the latent causes of living 
 mind, but it cannot assure us that he is himself mind or spirit, 
 till we have observed what are the particular powers and prop- 
 erties of this living mind, and what are the particular forms and 
 adaptations of exteraal nature." But while the syllogisms of 
 the two treatises, though perhaps somewhat different in form, 
 are really and truly identical in substance, there are, among 
 others, the following fundamental differences between them as 
 far as the conduct of the argument is concerned : 
 
 1. While Professor Tulloch, in the commencement of his 
 work, lays out his whole strength in an attempted demonstra- 
 tion of the validity of his major premise, Mr. Thomson spends 
 nearly, if not quite, the first third of his treatise in the work of 
 invalidating the minor premise in his syllogism, and that while 
 he substitutes no other premise in its place. 
 
 2. The entire production of the former proceeds upon the 
 assumption, that our knowledge of the facts from which he rea- 
 sons is valid objectively so and hence that the deductions 
 which they yield have a corresponding validity. That of the 
 latter proceeds upon the assumption, that all our assumed 
 knowledge, external and internal, is only phenomenal, and has 
 no objective, but merely a subjective validity ; and that when 
 we reason from the objects of said knowledge to God, we rea- 
 son only from the really unknown to the still more profoundly 
 unknown. 
 
 3. The principles and deductions of the former are through- 
 out evangelical. The fundamental principles, together with 
 their entire logical consequences of the latter, are in a corre- 
 sponding degree skeptical, and tend exclusively to confirm the 
 doubts or disbelief of the skeptic, and utterly to unsettle the 
 faith of the theist. We speak only of the principles of the 
 
work, and of the logical consequences of the same, and not at 
 all of the intentions of the author. We will now proceed to 
 verify all these statements in respect to the work before us. 
 
 On what condition can any deductions from the facts of na- 
 ture, mental and physical, as given in our intelligence, have 
 logical validity in regard to God as the first cause of said facts ? 
 On one condition exclusively, that our knowledge of said facts 
 has objective as well as subjective validity ; in other words, that 
 our knowledge pertains to realities as they are. Otherwise we 
 do not and cannot know, that we are in the presence of any 
 real indications of design or not. Suppose that we have had 
 dreams, and know them to be such dreams yielding visions 
 corresponding throughout to all forms of our present know- 
 ledge of the universe. Would not the world justly affirm that 
 we were logically dreaming, if we should under the principle, 
 that " design supposes a designer," reason from those objects as 
 real external and internal objects to God as their creator? 
 Suppose, further, that we have precisely similar visions, and do 
 not and cannot know whether they are, in fact, mere dream- 
 visions or valid perceptions of real objects. Should we not still 
 be guilty as before of logically dreaming, if, in a state of ac- 
 knowledged ignorance of the fact whether what appears as ob- 
 jects external to the ego are real external objects or mere crea- 
 tions of the ego itself, we reason from said visions as valid for 
 the reality and character of their objects as objects external 
 to the mind to the being and character of God as the creator 
 of such objects? and all this under the principle, "Design sup- 
 poses a designer ?" Whenever we reason from facts of the ex- 
 ternal universe to God, as the author and arranger of said uni- 
 verse and that under the principle, "Design supposes a de- 
 signer," We assume, as the exclusive basis of our deductions, 
 the reality of said universe, and the objective validity of our 
 knowledge of the same. Take away this one assumption, and 
 nothing is left for us to reason about; nothing whatever is 
 given as actually created, and then arranged according to the 
 principle under consideration. If, in this state of ignorance, we 
 proceed to reason from nature to nature's God, we employ a 
 
APPLIED LOGIC. 367 
 
 syllogism not merely having a disputed major, but no valid mi- 
 nor at all. To admit and affirm, then, that such is the exclusive 
 character of our knowledge of nature, is to invalidate utterly 
 the theistic syllogism as employed in the design argument. 
 
 What has our author done in respect to this subject ? On 
 this subject we will permit him to speak for himself. After af- 
 firming that many, to say the least, of the elements of our im- 
 pressions in regard to external nature have exclusively a sub- 
 jective or mental, and no external origin, he presents the fol- 
 lowing questions with his own answers to them annexed : 
 
 " But may not the perceiving mind be the creator of its 
 whole world of perception ? It gives light and coloring to na- 
 ture's picture, may it not be the author also of the outline or 
 shape, and of the invisible network which receives the color- 
 ing ? Mind, it is true, is distinguished from matter, so far as 
 we can see, by the facts of the will. Yet of that which is 
 known as matter, something, we see, comes of the mind's sensi- 
 bility. May not this faculty be the origin of the whole ? May 
 not all the laws and appearances of nature be evolved from a 
 spontaneous action of the soul according to the laws of its be- 
 ing ? May not life be a self-consistent dream ? It is a suppos- 
 able theory of existence, and one not to be refuted by argu- 
 ments, nor quite evaded on any theory of perception. We 
 have an immediate knowledge of the self and the world ; but 
 so long as it is only relative till we can descend beneath phe- 
 nomena to realities we are open to the question, May not the 
 non-ego be presented by the mind to its self, and the act of per- 
 ception a relation between one faculty and another ?" 
 
 In another place, when speaking of the theory of Berkley 
 which denies absolutely the existence of an external world, of 
 all existences external to finite mind but God himself our au- 
 thor says, "No reasoning can refute it, nor prove it to be im- 
 possible in the nature of things. It is quite conceivable that 
 our life may be not a reality but a dream, of which the figures 
 and visions are represented according to certain rules and un- 
 changing laws by the agency of a superior being." Again : 
 " No appeal to the truth of God or the common sense of man- 
 
368 LOGIC. 
 
 kind can wholly set aside the pretensions of the idealist," &c. 
 It is also a fundamental doctrine of this author, that we have 
 no valid knowledge of matter or spirit either ; that we do not 
 and cannot know but that in their ultimate essence they may 
 he one and the same substances. " All our immediate know- 
 ledge, it will be seen," he says, " is relative and of phenomena, 
 not of real being." Again : " We cannot know that any di- 
 vision of conceptions will correspond to the reality of things." 
 Of matter and spirit, he says, that they are " two things which 
 are wholly unknown in themselves." "It is only to ws-that 
 matter is massive, heavy, and inert. In itself, and without ref- 
 erence to the senses, it may be conceived to be as spiritual as 
 even spirit." These are the principles and dogmas which per- 
 meate and characterize this whole production principles and 
 dogmas which affirm the following propositions as true : 
 
 1. We have and can have no valid evidence even of the ex- 
 istence of any finite realities external to the mind itself, it being 
 absolutely impossible to disprove the theory of idealism. 2. Of 
 such realities, if they do exist, we have and can have no form of 
 valid knowledge any knowledge by which we can even deter- 
 mine whether such objects are material or spiritual in their na- 
 ture. 3. The mind itself is and must be equally unknown to 
 itself. What are the necessary logical consequences of such 
 principles ? They are the following, among others : (l.) We 
 are undeniably doing nothing else than logically dreaming 
 and that with our own eyes wide open, and the absurdity of 
 the whole procedure visible to all the world when we reason 
 from a imiverse that we admit we do not and cannot know to 
 exist at all, to a really existing creator and governor of said 
 universe. If we cannot prove idealism false, we cannot prove 
 theism true. Without logical inconsistency we cannot assume 
 any other ground than that of skepticism, and moral integrity 
 requires us to admit the fact. (2.) Equally absurd is it to 
 present cognitions which we " cannot know to correspond with 
 the reality of things" and whose utter want of objective va- 
 lidity Ave admit as the basis of deductions in regard to the re- 
 lations of such things to any other reality or realities whatever, 
 
APPLIED LOGIC. 369 
 
 and above all as the only basis of a proof of the being and per- 
 fections of God. A court of justice would cover itself with uni- 
 versal reprobation, which should upon such evidence impose 
 upon any man a fine of six cents. Yet such cognitions, our au- 
 thor affirms, present all the evidence we have of the validity of 
 the fundamental doctrine of all religion. (3.) All the deity 
 such cognitions can in any case give us, is an unknown and 
 unknowable something sustaining unknown and unknowable 
 relations to unknown and unknowable somethings, called, for 
 convenience, matter and spirit. Any skeptic whatever may 
 readily admit all the valid logical deductions of our author's 
 system as expounded by himself, and not abandon any one arti- 
 cle of his faith. (4.) In using the design argument in proof of 
 the being and perfections of God, our author, we remark in the 
 next place, einploys a syllogism with a disputed major, and a 
 minor which he himself has' proven if we admit the truth of 
 his previous deductions to be utterly void of validity. In 
 other words, he has first laid down a principle " Design sup- 
 poses a designer" which every skeptic disputes, and then 
 ranged under that principle cognitions which he himself affirms 
 to be utterly void of objective validity, and all this as the basis 
 of the proof of being of God. (5.) In the conduct of his argu- 
 ment under this syllogism, our author assumes that these cogni- 
 tions previously affirmed to be invalid objectively have ob- 
 jective as well as subjective validity, and the whole procedure 
 presents naught but the aspect of absurdity when we drop that 
 assumption. What conceivable bearing have the extent of 
 creation, the asteroids, and other heavenly bodies ; what have 
 the harmony, diversity, and beauty of nature to do in regard 
 to this subject, but upon the assumption that these are known 
 realities ? Admit that this vast universe, for aught that we do 
 or can know, is naught but " the baseless fabric of a vision," 
 and this is precisely what our author would have us affirm of 
 it and what valid evidence does it then afford of the existence 
 of any power out of and above the unknown and unknowable 
 something called mind, which, for aught that we do or can 
 know, is the exclusive creator of the whole fabric before us ? 
 16* 
 
370 LOGIC. 
 
 (6.) Our author, we remark finally in this connection, was logi- 
 cally bound by his own fundamental principles and assumptions 
 to deny absolutely the possibility of valid knowledge on any 
 subject whatever, and thus to ignore the whole subject of his 
 treatise as far as the use of the logical faculty is concerned. 
 When we make use of cognitions as the basis of deductions, the 
 former become themselves the objects of cognition. Our cog- 
 nitive faculty, our author affirms, does not, as far as we do or 
 can know, cognize any reality as it is. What validity, then, 
 has its procedures when its own operations are made the ob- 
 jects of cognition, and the cognitions thus obtained are made 
 the basis of scientific deductions? In all such cases, all our 
 procedures have, and must have, more and more palpable char- 
 acteristics of absolute invalidity. We begin with that which 
 has mere subjective validity, and end with what is not likely to 
 have any form of validity, objective or subjective. 
 
 All the above conclusions are further confirmed by Mr. Thom- 
 son's own statements of the consequences of his own principles, 
 and of the nature of the theistic problem as understood by him- 
 self. " Let it be granted," he says, " that nature, as manifested 
 in .the soul and in the world, is the province of reason. Yet in 
 itself it is unknown. Reason is obliged to regard it as the 
 manifestation of occult causes, and is compelled, as we have 
 seen, to make its choice between one and many incomprehensi- 
 bles. It demands an unknown substratum of the visible, and 
 an unknown essence of the intelligent ; and may thus be led 
 to an unknown cause of both, wherein to find the cause and ex- 
 planation of their marvellous relationship." 
 
 We venture the affirmation, that no skeptic can make, or 
 would desire to make, a more distinct and explicit statement ot 
 his own principles and deductions, than Mr. Thomson has here 
 made for him. When, from the sphere of our own conscious 
 mental operations, we advance into that of realities subjective 
 or objective, we are exclusively, says the skeptic, in the regions 
 of the wholly unknown. So says Mr. Thomson. As many 
 hypotheses of immediate and ultimate causation here present 
 themselves, each and all equally consistent with all. the facts, 
 
APPLIED LOGIC. 371 
 
 each alike must be held as only possibly true ; and if we would 
 assume either as true, we must, says the skeptic, act without 
 valid reason " choosing one among many incomprehensible^." 
 So says Mr. Thomson. The real cause of the ego and of the 
 non-ego, says the skeptic, is and must be unknown. So says 
 Mr. Thomson. As this cause is and must be wholly unknown, 
 no one hypothesis relative to its character can have any logical 
 preference over any of the others referred to. So says Mr. 
 Thomson. " We are compelled to make choice between one 
 and many incomprehensibles." 
 
 The nature of the deductions which Mr. Thomson professed- 
 ly reaches in respect to the being and character of God, are in 
 full accordance w T ith his principles. As the cognitions from 
 which he reasons have, as he professes, only subjective validity, 
 the same must be equally true of their consequences. Such ex- 
 clusively is the character of his theistic deductions as given by 
 himself. " We speak," he says, " of a certain relation to our- 
 selves when we say of matter that it is hard. We do the same 
 thing when we say of God that he is good. When he is said 
 to be powerful, it is meant that he reveals himself to us in 
 works, which, in human thought, are works of power," &c. 
 Mr. Thomson, we should remember, does not profess and his 
 principles do not allow him to profess to find a real God of 
 ascertained attributes of any kind. The skeptic may accept of 
 every one of his deductions, as explained by Mr. Thomson him- 
 self, and not change, in the least, one of his own principles and 
 deductions ; and the true believer can say to Mr. Thomson in 
 truth, You have taken from my heart and my intelligence both 
 my God, and placed him where he can never be found, or 
 known if he was found. 
 
 Mr. Thomson has also himself shown the skeptic how he may, 
 upon purely scientific grounds grounds which Mr. Thomson 
 admits to be valid from his own principles escape all theistic 
 deductions of every kind : 
 
 " From a theology founded on the foregoing principles, the 
 atheist," he says, " may find an outlet in total skepticism. If 
 it be demonstrated that our knowledge of the Supreme Being 
 
372 LOGIC. 
 
 is as valid, and not less inadequate than that of an external 
 "world, he may then have the hardihood to affirm that both 
 knowledges are illusive, and all philosophy impossible. He 
 may deny that we have as yet attained any strict cognition 
 either of the soul or of the world, as dependent or inde- 
 pendent in existence. "We see, indeed this is indisputable 
 that the world is not dependent in existence upon that con- 
 scious energy of the soul which we call will. But may it not 
 be evolved by a spontaneous energy of our nature, lying be- 
 yond the reach of consciousness and independent of the will ? 
 The s]3ringing up of our own existence, it may be alleged, is 
 beyond the consciousness and out of the sphere of the volition. 
 Or again, the materialist may assign real existence to matter, 
 and make mind to be but a certain evolution from it, or a hap- 
 py result of organization. Or, he may affirm that many con- 
 ceivable theories have not been confuted. 
 
 " Granted. We profess to find in the foregoing observations 
 a basis for the demonstration that our knowledge of the Infinite 
 Being is as valid as that of the finite. If the question is to be 
 pressed further, it must be admitted assuredly that the depths 
 of being are unfathomable. Whether, in the absolute nature 
 of things, the mind is wholly distinct from the world or in any 
 way related to it, is beyond the province of man's intelligence. 
 It cannot be seen how things which do appear, flow forth from 
 the fountain of existence." 
 
 The skeptic can ask no more, and does ask no more, than is 
 here granted him, and that upon professedly scientific grounds. 
 ISTow, if the skeptic may upon scientific grounds affirm all this, 
 then theism undeniably can be held as true upon no scientific 
 grounds. 
 
 Mr. Thomson, we remark again, refutes the claims of mate- 
 rialism upon the exclusive assumption of the validity of the 
 skeptical hypothesis, and upon grounds, too, utterly subversive 
 of the claims of theism. As matter and spirit are wholly un- 
 known to us as substances, we cannot- affirm such is his ar- 
 gument as materialism does, that one is the other. " Two 
 things," he says, "which are wholly unknown in themselves 
 
APPLIED LOGIC. 373 
 
 cannot be known to exist in the same way, or with any com- 
 munity of properties or attributes." Very true, replies the 
 skeptic, and for the reason here stated materialism may be 
 true. Of two things wholly unknown, you cannot say that 
 they do not exist in the same way, and with an absolute com- 
 munity of properties and attributes. Further, of two such 
 things, you caimot know that they sustain any relations to any 
 third reality whose existence even can be revealed only through 
 these. Of such things, you cannot know that they are or are 
 not created and controlled substances at all, and, consequently, 
 that any such creator or governor exists. Mr. Thomson must 
 renounce his first- principles the validity of the sensational 
 theory of external perception or accept of these deductions in 
 their fullest extent. 
 
 The nature and kind of validity which in his own estima- 
 tion does attach to Mr. Thomson's demonstration of the exist- 
 ence and character of God, should not be overlooked in tins 
 connection. Our knowledge of God, he teaches, has the- same 
 and no other validity than that winch attaches to our know- 
 ledge of nature. This is directly expressed in the extracts 
 above given, and often affirmed and reiterated in the treatise 
 before us. What then is the theistic, and what is the skeptical 
 syllogism on this subject ? and in which do we find our author ? 
 The theistic syllogism is this : 
 
 If we have valid knowledge of the existence and character of the finite, we 
 
 have a similar knowledge of the Infinite : 
 "We have such knowledge of the finite ; 
 We have, therefore, a similar knowledge of the Infinite. 
 
 The skeptical syllogism is this : 
 
 If we have no valid knowledge of the existence and character of the finite, 
 
 we have and can have no such knowledge of the Infinite ; 
 We have no such knowledge of the finite ; 
 We have and can have, therefore, no such knowledge of the Infinite. 
 
 Mr. Thomson's principles and deductions in respect to the 
 finite, place him undeniably within the exclusive sphere of the 
 latter syllogism, and it is only by a renunciation of the funda- 
 
374 LOGIC. 
 
 mental principle of his philosophy of nature, that he can possi- 
 bly get into the former. 
 
 Let us now contemplate Mr. Thomson's own estimate of the 
 real character of the evidence which exists, and which he has 
 to offer, in proof of this great fundamental truth of all religion. 
 After professedly showing us that we have no valid evidence 
 that there is any created universe matter and spirit as they 
 are, being both alike absolutely unknown to us after saying 
 that " to a mind which has not been initiated in the difficulties 
 of skepticism, all nature declares with the unanimous voice of 
 ten thousand tongues, There is one God, the Father of all ;" 
 after saying that " in examining the evidences of this truth, and 
 inquiring whether this voice be credible, we become aware of 
 the wide difference which exists between truth as it is in itself, 
 and truth as it becomes known to the mind of man," he says, 
 " The method of theism is therefore humble, and such as be- 
 comes man on such a subject." The real meaning of the term 
 "humble" can, in the present connection, hardly be deemed 
 doubtful. It can mean nothing else, as it appears to us, than 
 this inconclusive on scientific grounds. Religion or theism 
 addresses us in tones of authority the most absolute conceiva- 
 ble, " Thou shalt have no other gods before me," " Thou shalt 
 worship the Lord thy God, and him only shalt thou serve," 
 You know God, and shall worship him as God, &c. When 
 humbly asked for the evidence of the validity of these high 
 claims, her tone, as interpreted by Mr. Thomson, is suddenly 
 changed. Her voice is now very humble. Theism appears 
 now only as " one among many incomprehensibles," each of 
 which has upon scientific grounds equal claims, and each in dis- 
 tinction from the other having no claims at all. Now we en- 
 ter our solemn protest against such a presentation of the claims 
 of our holy religion. We boldly affirm that religion is as able 
 to meet fully the logical demands of our nature as any other, 
 and is able to meet them all perfectly. On account of such 
 presentations as the above, we are free to say, that we regard 
 the production before us as one of the most dangerous books of 
 modern times, especially when we consider the circumstances 
 
APPLIED LOGIC. 375 
 
 in which it comes before the world. We solemnly believe, 
 that no anti-theist has produced a work so adapted to confirm 
 immovably the doubts of the skeptic, and to unsettle the faith 
 of the believer, as this. 
 
 The character of Mr. Thomson's treatise, we remark in the 
 last place, is the necessary logical consequence of the theory of 
 external perception which he has laid at the foundation of all 
 his deductions the sensational theory. If all our knowledge 
 of external nature is indirect and mediate, and exclusively de- 
 rived through one medium sensation ; if we have and can 
 have no real or presentative knowledge of the self or of the 
 not-self, then, indeed, as we have before shown, mind, matter, 
 and God must be alike unknown and unknowable realities to 
 us, and skepticism is the only true philosophy of the finite and 
 of the Infinite. If we attempt to reason about either, we shall 
 find ourselves eternally tempest-tossed upon a boundless chaos 
 of conflicting hypotheses, each pressing questions upon us which 
 neither it, nor either of the others, can ever resolve ; every de- 
 duction apparently reached will be found at last to have been 
 settled upon grounds more debatable than the original issues, 
 and we shall retire from the conflict with but one impression 
 resting upon our minds, to wit, that nature itself is a lie, and 
 that he that thinks the least is, of all men, the wisest, and at 
 the furtherest remove from error. 
 
 Of the two treatises which, for the sake of science and reli- 
 gion, we have thus freely criticised, we should say that the 
 former, in its relation to the doctrine of method, in the articles 
 of definition, logical division and arrangement of topics, and 
 distinctness and force in the statement of thought, as nearly 
 realizes the idea of science as almost any treatise that we have 
 met with on any subject; while the latter is one of the most 
 fragmentary productions, and the least systematic even in the 
 arrangement of the fragments, that we ever read. Both au- 
 thors have, in the development of the theistic argument, erred 
 fundamentally in basing said argument upon the deductions 
 of certain disputed theories in respect to the origin of know- 
 ledge. 
 
THE DOGMA THAT OUR IDEA OF GOD IS PURELY NEGATIVE. 
 
 Among a large class of thinkers, it has now come to be re- 
 garded as a first truth in science, that our idea of God is purely 
 negative, the elements constituting it being mere negations of 
 the finite. In regard to this dogma we would simply drop the 
 following suggestions, and leave them for the reflection of the 
 reader : 
 
 1. This dogma is based upon an undeniable psychological 
 error, a false analysis of the idea itself as given in consciousness. 
 No individual, from a careful analysis of the idea as thus given, 
 would ever come to any such conclusion in respect to it. What 
 are the elements which do, as a matter of fact, enter into it ? 
 In the first place, we conceive of God as a being actually exist- 
 ing. So far our conception of him is, undeniably, as positive 
 as any other which we can have of any object whatever. In 
 the next place, we conceive of him as a real cause the actual 
 ultimate cause of all that exists conditionally. Now no ideas 
 are more positive than those of causation, and our ideas of ulti- 
 mate are just as positive as are our ideas of proximate causa- 
 tion. Again, we conceive of God as a self-conscious personali- 
 ty, having an absolute knowledge of himself and all other reali- 
 ties. No element more positive does or can enter into any con- 
 ception whatever. Now when we attach the idea of infinity 
 and perfection to each of the divine attributes, we do not there- 
 by annihilate the positive elements in the general idea itself, 
 and change the character of the whole from the positive to the 
 negative form. The positive does not, by mere enlargement, 
 like, circles in the water, " vanish into naught." 
 
 2. This dogma is based upon a total misconception of the na- 
 ture and sphere of negation. Negation is always, and from the 
 nature of the case must be, subsequent to affirmation. The 
 former has its exclusive basis in the latter. To deny a given 
 attribute of any object as A of B, for example implies that 
 the two are known to the mind, and that the known attributes 
 of A are perceived to be incompatible with the existence of 
 B in the same subject. To deny limitation of God implies 
 
APPLIED LOGIC. 377 
 
 (1.) that we know him as existing; and (2.) as possessed of 
 attributes incompatible with the idea of limitation. The dog- 
 ma of a negative concept of any reality whatever is a pure 
 absurdity. 
 
 3. This dogma, we remark once more, is utterly subversive 
 of all religion. " Ex, nihil, nihil Jit." The commands, prohi- 
 bitions, and teachings of religion are all positive, absolute, and 
 the idea of God lies at the basis of them all. From mere ne- 
 gation if it could exist as a concept nothing positive can pro- 
 ceed. A god represented by " a bundle of negations," the 
 expression used by a distinguished author to express our idea 
 of God can no more, nor so much, be an object of fear, love, 
 reverence, &c, than infinite space. With a mere negative idea 
 of God, if we could have such a concept of him, religion with 
 its absolute teachings would be an absurdity, and nothing else. 
 
 THE REAL BASIS OF ALL VALID SCIENTIFIC PROCEDURES. 
 
 With certain individuals who assume to themselves the pos- 
 session of the highest forms of wisdom, it is not uncommon to 
 decry science and to deny the possibility of philosopliy. 
 
 " Science," says Professor Lewis, " has indeed enlarged our 
 field of thought, and for this we will be thankful to God and to 
 scientific men. But what is it after all that she has given us, or 
 can give us, but a knowledge of phenomena appearances ? 
 What are her boasted laws, but generalizations of such phe- 
 nomena ever resolving themselves into some one great fact 
 that seems to be an original energy, whilst evermore the appli- 
 cation of a stronger lens to our analytical telescope revolves 
 such seeming primal force into an appearance or manifestation 
 of something still more remote, which in this way, and in this 
 way alone, reveals its presence to our senses. Thus the course 
 of human science has ever been the substitution of one set of 
 conceptions for another. Firmaments have given place to con- 
 centric spheres, spheres to empyreans, empyreans to cycles and 
 epicycles, epicycles to vortices, vortices to gravities and fluids, 
 ever demanding for the theoretic imagination other fluids as 
 
378 LOGIC. 
 
 the only conditions on which their action could be made con- 
 ceivable." 
 
 Why does this author give us such a view of the scientifip 
 procedure ? Simply on account of his theory of external per- 
 ception the sensational theory which gives us nothing but 
 shadows of we know and. can know not what. When we 
 attempt to cognize scientifically these shadows, new shadows 
 present themselves which convert original cognitions into mere 
 appearances ; and so on forever without any nearer approach 
 to truth being made. Science may change our modes of think- 
 ing, but can never add to our stock of real knowledge. This 
 is science according to the sensational theory. 
 
 Let us now suppose that we originally obtain, not shadows of 
 things unknown, but real valid presentative and representative 
 intuitions, together with the logical antecedents of the same 
 of internal and external realities themselves. What we have 
 gained is then an eternally enduring acquisition. Subsequent 
 investigations may add new elements to these cognitions ; sepa- 
 rate erroneous ones, which, by assumption, may be introduced 
 into them, may abstract the elements which constitute said cog- 
 nitions, and classify and arrange them accordingly, &c. The 
 progress of science is not the substitution of one shadow for 
 another, but a perpetual accumulation of imperishable treasures. 
 The thinker who sneers at science and denies the possibility of 
 philosophy, has himself been deluded by a false philosophy into 
 the belief that he is looking only at shadows, when, in fact, he 
 is beholding with open face realities as they are. The sciences 
 have not a phenomenal, but a real basis, and are, when rightly 
 conducted, the valid interpreters, not of appearances, in which 
 nothing appears, but of truth itself. 
 
 THE DOGMA THAT OUR KNOWLEDGE OF NATURE IS CONFINED 
 TO PHENOMENA, AND DOES NOT PERTAIN TO SUBSTANCES 
 THEMSELVES. 
 
 Ages commonly intervene before the mind fully emancipates 
 itself from the influence of false assumptions, which it has for- a 
 
APPLIED LOGIC. 379 
 
 time employed as first truths. This is emphatically true of the 
 dogma above stated. According to its real import there are, 
 in respect to mind and external nature, three classes of reali- 
 ties the mind which perceives ; external substances never per? 
 ceived or known at all ; and a tertium quid, phenomena, exist- 
 ing between the two realities named and themselves, the exclu- 
 sive objects of perception and knowledge. Now it should be 
 borne in mind that there are but two classes of perceptions, the 
 presentative and the representative. In the latter, nothing 
 whatever external to the mind is perceived, but simply and ex- 
 clusively a mental state, a sensation, or the mind itself in thai 
 state. The external object is the unperceived cause of the sen- 
 sation, and the latter the perceived effect of said cause. In this 
 case, there is no third thing between the percipient and the 
 thing perceived. In presentative perception of an external ob- 
 ject, the thing perceived is the object itself, so far forth as it or 
 any thing relating to it is perceived at all. We never perceive 
 the whole object, but so far as it is presentatively perceived at 
 all, the phenomenon and object, or substance, are one and iden- 
 tical. In reference to presentative perception, therefore, the 
 principle holds universally, that substances are as their phe- 
 nomena. In representative knowledge, external substances are 
 the unknown causes of known sensitive states sensations. In 
 presentative knowledge of such objects, substances substances 
 themaelves are the known objects of known intellectual states, 
 to wit, perceptions. The doctrine of appearances in which 
 realities themselves do not appear, should, by this time, be ex-, 
 eluded from the domain of science. 
 
 THE DOGMA THAT INDIVIDUAL CONCEPTIONS PERTAIN TO OB- 
 JECTS, AND GENERAL ONES ONLY TO THE MIND WHICH 
 FORMS THEM. 
 
 It is now commonly assumed as a principle in science, that 
 while individual conceptions pertain to objects, general ones 
 the specifical and generical pertain exclusively to the mind 
 which forms them for its own convenience. It is deemed im 
 
portant that we should understand distinctly hi what sense this 
 maxim is and is not true. In illustration, let A represent the 
 individual conception of some object, John, B a specifical, C a 
 generical, conception, of the same person. . Whatever is im- 
 plied in A, or in any element of the same, is' true of John. The 
 same holds equally of B and C. The only difference is this : A 
 represents in the concrete what is true of him only ; B repre- 
 sents what is equally true of him, but what is also true of a 
 large number of other individuals ; and C what is true of him in 
 common with a still wider circle. B and C, then, pertain to 
 the individual as really and truly as A does, only in different 
 relations A on the principle of exclusion, and B and C on that 
 of inclusion. Without explanation, therefore, an explanation 
 which renders the thing explained almost, if not quite meaning- 
 less the maxim before us tends only to " darken counsel by 
 words without knowledge." 
 
 THE IDEA OF A " POSITIVE PHILOSOPHY." 
 
 Some of the greatest ideas that ever enter the human mind 
 are not unfrequently first presented to the world in connection 
 with systems of error, and are, for that reason, for a time at 
 least, regarded by the friends of truth as meteors of darkness, 
 and not as being what in reality they are, great central suns in 
 the firmament of science and of truth. Such an idea has been 
 announced to the world in the title of a work embodying 
 naught almost but fundamental error. We refer to the phrase, 
 " The Positive Philosophy." All thinking of every kind is pos- 
 itive. To think is to affirm to affirm the presence or absence 
 of some positive attribute in some positive subject. All denial 
 is positive to affirm incompatibility of two positive things, or 
 to affirm the absence in a known object, of some known attri- 
 bute. Till an object is known, and so far only as it is known, 
 can we deny any thing of it, thus separating the known from 
 the known. The dogma of a purely negative conception of 
 any object is one of the absurdities of " science falsely so called." 
 To have a purely negative idea we must cease to think at all, 
 
APPLIED LOGIC. 381 
 
 that is, have no thought whatever. The " positive philosophy" 
 assumes, that relatively to some realities, at least, mind is a 
 faculty, and they objects of real valid knowledge, and professes 
 to determine the extent, limits, objects, laws, and tests of such 
 knowledge. It may, therefore, be defined the science of the 
 thinkable, its object being to give upon scientific grounds the 
 answer to the question, "What can I know ?" We will ven- 
 ture the expression of a few suggestions in regard to the prin- 
 ciples in conformity to which such a system should and must 
 be developed. On this subject we remark : 
 
 1. In developing such a system the first thing to be done, 
 as we suppose, would be clearly to define and distinguish two 
 conceptions a mystery and absurdity. The former would 
 be shown to imply a fact known to exist, while the cause, 
 or grounds, or both together, of its existence, is unknown and 
 unknowable to us. The latter refers to statements relatively 
 to matters of fact coming under the principle of contradiction 
 statements in which the same things are aflirmed and denied 
 of the same object. ISTo facts of the latter class can occur. 
 Any facts whatever of the former class, for aught that we know 
 or can know, may occur. 
 
 2. Existence in all its forms, actual and conceivable, would 
 be distinctly recognized as a mystery, but no absurdity. A 
 priori we cannot tell what does exist, nor in what state it 
 exists. Whatever then is manifested as existing must be rec- 
 ognized as a reality. The question of its existence is to be con- 
 sidered as forever settled by the fact of its actual manifestation. 
 When any reality is manifested as existing, its existence as a 
 fact is not only to be admitted, but also that of all realities 
 necessarily supposed by such fact. If, for example, we admit 
 the actual existence of body, we must admit the objective reali- 
 ty of space ; for the reason, that the latter not being, the former 
 could not be. So in all other instances. 
 
 3. The condition of the possibility of knowledge is the 
 actual existence of a subject sustaining to actual realities the 
 relation of a power, while they sustain to it that of an object 
 of real knowledge, and these two in such relations to each 
 
382 logic. 
 
 other that actual knowledge arises in consequence of this cor- 
 relation. 
 
 4. The sphere of the conceivably knowable is all realities as 
 they are, with all their properties, laws, and relations ; that of 
 the actually knowable in any given case*, depends upon the 
 question how far this correlation obtains, in fact, in said case. 
 
 5. We can never determine d priori whether such power 
 does exist in any given case, or what is its sphere, any more 
 than we can thus determine what realities do and do not exist. 
 The existence of a power of knowledge can be manifested but 
 by its actual exercise, and the question, What can we know ? 
 can be answered but through these two, to wit, What do we 
 know ? and, What is implied in this knowledge ? 
 
 6. There are but three conceivable forms in which any reali- 
 ty can be known to us, to wit, presentatively, representatively, 
 and impliedly that is, it may be to the knowing faculty an ob- 
 ject of direct and immediate perception, or an unknown cause 
 of a known state of the sensibility, or necessarily presupposed 
 as the condition of the existence of that which is known to be. 
 
 7. In determining our theory of existence that is, of reali- 
 ties as actually existing we are to hold ourselves as bound to 
 admit nothing as real, which is not manifested in one or the 
 other of the above-named forms as actually existing. On the 
 other hand, we are bound by the principles of intellectual and 
 moral integrity, to admit as real all forms of existence thus 
 manifested, and as manifested. Nothing is to be admitted as 
 actual which is not thus known, and all that is thus known 
 must be admitted as actual. The objects of presentative know- 
 ledge with their logical antecedents are to be held as really 
 known, that is, known as they are, and those of representative 
 knowledge with their logical antecedents as relatively known. 
 
 8. In determining what realities do exist from what we know 
 to exist, the following systems present themselves. We may 
 suppose that the knowing faculty has an actual presentative 
 knowledge of mind the subject, on the one hand, and of the 
 external universe or matter, on the other. This gives us the 
 system of realism. We may suppose again, that matter is the 
 
APPLIED LOGIC. 383 
 
 only object of such knowledge, and hence resolve all realities 
 into it the system of materialism. Or we may suppose that 
 there is " a synthesis of being and knowing," that presentative 
 knowledge pertains exclusively to mental states. All known 
 realities are consequently to be resolved into such states, and 
 here we have three theories. If the cause of the mind's activi- 
 ties is supposed to be exterior to the mind, then we suppose 
 two unknown realities mind which cognizes, and the unknown 
 something which first induces sensations. This is the system 
 of ideal dualism of Kant. Or we may suppose the cause of sen- 
 sation to be interior the result of the mind's own spontaneous 
 activities. We then have the system of subjective idealism, 
 that of Fichte. If we suppose the cause of the sensation to be 
 the infinite and absolute, and that all perception pertains to 
 said reality in its efforts of self-development, then we have the 
 doctrine of pantheism as developed by Schilling. If, finally, we 
 assume that there is an absolute identity of being and knowing, 
 that is, assume thought itself to be the exclusive object of pre- 
 sentative knowledge, then, as disciples of Hegel, we are to hold 
 the doctrine of pure idealism. 
 
 Now one or the other of the above-named theories of exist- 
 ence must be true, because none others are conceivable or pos- 
 sible. In determining which of these theories is true, we have 
 but one standard of appeal, to wit, what are we conscious of 
 actually perceiving ? If we are actually conscious of exercising 
 the functions of thought, feeling, and volition, on the one hand, 
 and of an actual presentative perception of matter, as a real ex- 
 ternal existence having extension and form, on the other, then 
 we are to hold matter and mind as known realities, and con- 
 struct our theory accordingly, that is, hold the doctrine of 
 realism. If we are conscious of a similar knowledge of matter 
 only, then materialism must be held as alone true. If, finally, 
 we are conscious of an actual synthesis or identity of being and 
 knowing, that is, of having an actual presentative knowledge of 
 subjective states exclusively, then we are to hold some of the 
 forms of idealism. These are the exclusive conditions of set- 
 tling these questions on scientific grounds. Philosophy and 
 
384 logic. 
 
 philosophers, too, must be brought to the bar of facts, real 
 facts of consciousness, and held to the strictest account there. 
 Every thing must be settled by an appeal to one question, 
 What realities are actually manifested as the actual objects of 
 conscious presentative knowledge ? When this is done, the 
 idea of a synthesis or identity of being and knowing, together 
 with the dogma of materialism, will be forever dissolved and 
 take rank among the vagaries of " science falsely so called ;" 
 while realism will stand before the world as affirmed by science 
 as well as by the intuitive convictions of the race as based 
 upon the immovable rock of truth. We shall then have a posi- 
 tive philosophy of nature. 
 
 9. Let us now suppose that nature, the universe of matter 
 and mind, as given in the universal intelligence, stand before 
 us as scientifically ascertained and known realities, and that we 
 wish to know whether upon similar grounds the being and 
 perfections of God are affirmed by the great facts of creation 
 which he out before us. Here two hypotheses present them- 
 selves as alone conceivably and possibly true. Either these 
 facts are the exclusive result of powers and laws inhering in . 
 nature, or of a power out of and above nature. Then our next 
 step is to determine our formulas, that is, to determine what 
 facts, material and mental, if found, would affirm the truth of 
 the theistic hypothesis, and then determine whether the great 
 facts of the universe do or do not rank under those formulas, 
 and thus upon scientific grounds affirm the being and perfec- 
 tions of God. If we find that they do and we shall, if our in- 
 vestigations are rightly conducted we then, not only as de- 
 manded by the intuitive convictions of the race, but by the im- 
 mutable principles of science, erect our altar to the ''Known 
 God," and " knoicing God, we worship him as God." 
 
 10. The reality of mind, finite and infinite, being admitted as " 
 a truth of science, the question of the soul's eternity or of the 
 truth of the doctrine of immortality arises. How shall this 
 question be answered ? On reflection every one will perceive 
 that science requires us to lay down as the basis of our deduc- 
 tions the principle, that every sentient existence, owing its be- 
 
APPLIED LOGIC. 385 
 
 ing as it does to infinite and infallible wisdom, was created 
 for a certain destiny; that its powers and susceptibilities are 
 in fixed and immutable adaptation to that destiny, and that, 
 consequently, the destiny of each creature is as his manifest 
 powers and adaptations. If on investigation we find in the 
 human mind the elements of endless progression, together 
 with the idea of immortality, and a nature immutably corre- 
 lated to it, then the doctrine of immortality becomes a truth 
 of science. 
 
 11. If we desire to ascertain upon scientific grounds, aside 
 from the teachings of inspiration, whether, as an immortal be- 
 ing, man's immortality is or is not to be a state of retribution, 
 we are then to dismiss entirely all assumptions based upon what 
 we might desire to have true, or upon what we might abstract- 
 ly think it fitting in the Most High to do. "We are, on the 
 other hand, to take our stand amid the great facts of our moral 
 nature, and lay down these as they are, as the exclusive basis 
 of our deductions. Do the ideas of right and wrong, of obliga- 
 tion, of merit and demerit, and of consequent retribution, as a 
 matter of fact, exist in the mind ? and if so, what are their ac- 
 tual characteristics ? Further : what, as a matter of fact, is the 
 tendency of individual progression ? Is it from a state of 
 changeableness to one of fixedness in good or evil ? If so, such 
 is the state towards which we are advancing. 
 
 12. Finally, having determined the objects and the sphere of 
 the thinkable, the great object of " the Positive Philosophy" 
 will then be to fix and define the number, the sphere, and ob- 
 jects of the various sciences, to determine the nature of the 
 great problems to be solved by each, and to give the formulas 
 which lie at the basis of their solution. In what we have said 
 previously, we have anticipated some subjects which belong to 
 the particular subjects just named. 
 
 We leave these thoughts as they are, with the remark, that 
 when science shall proceed exclusively upon such a basis, its 
 teachings throughout will all be positive, and its entire deduc- 
 tions will be the revelations of immutable truth. A " Positive 
 Philosophy" is possible, for the reason that the intelligence as a 
 17 
 
faculty exists in the midst of realities sustaining to it the rela- 
 tions of objects of real knowledge. 
 
 FALSE METHODS IN PHILOSOPHY. 
 
 " As is the method of a philosopher," says Cousin, " so will 
 be his system ; and the adoption of a method decides the des- 
 tiny of a philosophy," a maxim of fundamental importance. 
 We close the present treatise with an example of method in 
 this science, and with a few thoughts upon the same. Krug, 
 the successor of Kant, and one of the great expounders of the 
 transcendental philosophy, thus commences his own treatise on 
 " Fundamental Philosophy :" 
 
 " I put myself, when I begin to philosophize, into the state 
 of not-knowing, since I am to produce in me for the first time 
 a knowledge." " I accordingly," he adds, " regard all my pre- 
 vious knowledge as uncertain, and strive after a higher know- 
 ledge that shall be certain or be made so." 
 
 Here, then, is an end proposed to be attained, and a method 
 also of obtaining that end. The end proposed is to ''''produce 
 a knowledge" which is certain. The method of obtaining it is, 
 to assume that all we now know is uncertain, and then to enter 
 upon the process of production. What will and what must be 
 the result of such a procedure, or the character of the thing 
 produced ? It will and must, of course, be a realization of the 
 author's presupposed conceptions of what that knowledge is, 
 and nothing else. To produce, and to interpret what is, are 
 very different things. In the former process we select our own 
 materials, and impart what form to the building we please. So 
 if Mr. Krug previous to this act of dementation in which, with- 
 out evidence, he arbitrarily assumed that all his previous know- 
 ledge was uncertain was a materialist, the system produced, 
 as having appodictic certainty, would be materialism. If he 
 was an idealist, of course he would lay at the basis of his super- 
 structure the principle of " a synthesis," or " identity of being 
 and knowledge in the I," and thus rear up some of the super- 
 structures of idealism. Nothing in the world is so easy aa 
 
APPLIED LOGIC. 387 
 
 "producing a knowledge" by such a method. Any man of 
 common ingenuity can produce to order, in any form and to 
 any extent required, systems of this kind. But what claims 
 have such productions to be regarded as valid systems of know- 
 ledge ? No more than the wildest vagaries of the maniac have 
 to be thus regarded. Yet it is precisely such a method as this 
 that lies exclusively at the basis of all forms of materialism, on 
 the one hand, and of idealism, on the other. All these systems 
 without exception rest upon mere arbitrary assumptions as- 
 sumptions which will not stand a scientific scrutiny for a single 
 hour. Idealism especially, in all its forms, begins with the prin- 
 ciple, that to philosophize is to "produce a knowledge," and 
 that the exclusive method of production is to assume that what 
 is now known is wholly uncertain, and then to lay down as- 
 sumptions which will yield the deductions which the subject 
 desires to reach, and finally to construct his system according- 
 ly. Transcendentalists are great system-makers ; but not one 
 of them has any claims whatever to be regarded as, in any 
 proper sense, a world-expounder. 
 
 fUHIVBRSiry) 
 
 THE END. 
 
BECOMMENDATIONS OF DAVIES' MATHEMATICS. 
 
 Da vies' Course of Mathematics are the prominent Text-Books in mosl 
 of tlie Colleges of the Untied States, and also in the various Schocls at i 
 Academies throughout the Union. 
 
 Yokk, Pa., Aug. 28, 185S. 
 
 Dames' 1 Series of Mathematics I deem the very best I ever saw. From a number 
 of authors I selected it, after a careful perusal, as a course of study to be. pursued V>y 
 the Teachers attending the sessions of the York Co. Normal School -believing it also 
 to b* well adapted to the wants of the schools throughout our country. Already two 
 hundred schools are supplied with Daviks' valuable Series of Arithmetic* ; and 1 
 tolly believe, that in a very short time the Teachers of our country en masse will b* 
 wigaged in imparting instruction through the medium of this new and easy method 
 f analysis of numbers. A. K. BLAIR, 
 
 Principal of York Co. Normal School. 
 
 Jackson Union School. Michigan, Sept. 25, 1S5S. 
 Mkssrs. A. 8. Barnes & Co. : I take pleasure in adding my testimony in favor ol 
 Davies' Series of Mathematics, as published by you. We have used these works in 
 this school for more than four years; and so well satisfied are we of their superiority 
 over any other Series, that we neither contemplate making, nor desire to make, any 
 change in that direction. Yours truly, E. L. EIPLEY. 
 
 Nbw Britain, June \2lh, 1858. 
 Messrs. A. S. Barnes & Co. : I have examined Davies' Series of Arithmetics 
 with some care. They appear well adapted for the different grades of schools for 
 which they are designed. The language is clear and precise; each principle is 
 thoroughly analyzed, and the whole so arranged as to facilitate the work of instruc- 
 tion. Having observed the satisfaction and success with which the different books 
 have been used by eminent teachers, it gives me pleasure to commend them to others. 
 DAVID N. CAMP, Principal of Conn. State Normal School. 
 
 I have long regarded Paries' Series of Mathematical Text-Books as far superioi 
 to any now before the public. We find them in every way adapted to the wants of 
 the Normal School, and we use no other. A unity of system and method runs through- 
 out the series, and constitutes one of its great excellences. Especially in the Arith- 
 metics the author has earnestly endeavored to supply the wants of our Common and 
 Union Schools: and his success is complete and undeniable. I know of no Arith- 
 metics which exhibit so clearly the philosophy of numbers, and at the same time lead 
 the pupil surely on to readiness and practice. A. S. WELCH. 
 
 From Phof. G. W. Plympton, late of the State Normal School, N. Y. 
 ' Out of a great number of Arithmetics that I have examined during the past year, 1 
 find none that will compare with Davie*' Intellectual and Dories' Analytical and 
 Practical Arithmetics, in clearness of demonstration or philosophical arrangement 
 I shall with pleasure recommend the use of these two excellent works to those who 
 go from our institution to teach. 
 
 From C. May, Jr., School Commissioner, Keene, N. H. 
 I have carefully examined Davies' Series of Arithmetics, and Higher Mathe- 
 nsider them far superior to any with which 
 
 sor of Mathematics, Natural Philosophy, awl 
 i Wabash College, Indiana. 
 
 Wabash College, June 22, 1S58. 
 Mkssrs. A. S. Barnes & Co. : Gentlemen: Every text-book on Science proporly 
 consists of two parts the philosophical and the il/ustratire. A proper combination 
 of abstract reasoning and practical illustration is the chief excellence, in Prof. Davie* 1 
 Mathematical Works. I prefer his Arithmetics, Algebras. Geometry, and Trigonom- 
 etry, to all others now in use. and cordially recommend them to all who desire the 
 advancement of sound learning, Yours, very truly, JOHN L. CAMPBELL. 
 
 "In the distinctness wiih which the various definitions are given, the clear and 
 rtrictly mathematical demonstration of the rules, the convenient form and well-chosen 
 ir.ntter of the tables, as well as in the complete and much-desired application of all to 
 the business of the . juntry, the University Arithmetic of Prof. Davies is si perior to 
 any other work of the kind with which we are acquainted" 
 
RECOMMENDATIONS 
 
 OF 
 
 CLARK'S ENGLISH GRAMMAR. 
 
 not better set forth the merits of this work than by quoting a part of a com- 
 _.. n from Prof. K. S. .Tewkll, of the New York State Normal School, in wbick 
 school this Grammar is now used as the text book on this subject : 
 
 -Clark's Systkm op Grammar is worthy of the marked attention of the friends Oi 
 jducation. Its points of excellence are of the most decided character, and will nei 
 toon be surpassed. Among them are 
 
 1st "The justness of Its ground principle of classification. There is no simple, phil- 
 osophical, and practical classification of the dements of language, other than that buill 
 i.!! their use or office. Our tendencies hitherto to follow the analogies of the classical 
 languages, and classify extensively according to forms, have been mischievous and ab- 
 surd. It lutlnie we corroded them. 
 ' Its thorough and yet 
 
 d power of the language can be attained. 
 
 absence of this analysis has hitherto precipitated the study of Grammar upon a surface 
 of dry details and bare authorities, and useless technicalities. 
 
 3d." "Its happy method otillustrating the relations of elements by diagrams. These, 
 however uncouth they may appear to the novice, are really simple and philosophical. 
 Of their utility there can he no question. It is supported by the usage of other sci- 
 ences and has been demonstrated by experience in this. 
 
 4th. "The tendency of the system, when rightly taught and faithfully carried out, 
 to cultivate habits of nice discrimination and close reasoning, together with skill in 
 Illustrating truth. In this it b not excelled by any, unless it tie the mathematical sci- 
 ences, and even there it has this advantage, that it deals with elements more within 
 t grasp of the intellect. On this point I speak advisedly, 
 'he system is thoroughly progressive and practical, and as such. American in 
 ;er. It does not adhere to old usages, merely because tbey are venerat.y 
 musty; and yet it does not discard things merely because they are old, or are in un- 
 important mi'nutiai not prudishly perfect. It does not overlook details and technicali- 
 ties, nor does it allow them to interfere with plain philosophy or practical utility. 
 
 "Let any ciear-headed. independent- minded teacher master the system, and then 
 give it a fa'ir trial, and there will be. no doubt as to his testimony." 
 
 A Testimonial from the Principals of the Public Schools of Rochester, N. Y. 
 
 We regard Clark's Grammar as the clearest in its analysis, the most natural and 
 
 logical in its arrangement, the most concise and accurate in its definitions, the most 
 
 systematic in design, and the best adapted to the use of schools of any Grammar with 
 
 which we are acquainted. 
 
 C C. MKSERVE, WM. C. FEGLES. 
 
 M IX ROWLEY, OIIN ATWATKR. 
 
 C. R. BIT; HICK. EDWARD WEBSTER, 
 
 J. R. VOSBURG, S. W. STARKWEATHER, 
 
 & R. ARMSTRONG PHILIP CURTISS. 
 
 Lawrence Institute. Brooklyn. .Jan. 15, 1859. 
 Messrs. A. S. Barnf6 & Co: Having used Clark's \ew Grammar since its publica- 
 tion, I do most unhesitatingly recommend It as a work of superior merit. By the use 
 of no other work, and I have used several, have I been enabled to advance my pupilt 
 so rapidly and thoroughly. 
 
 The author has, by "an "Etymological Chart and a system of Diagrams, made Gram 
 mar the study that it ought to be, interesting as well as useful. 
 
 MARGARET S. LAWRENCE, Prinoipai. 
 
 ir 
 
 WELCH'S ENGLISH SENTENCE. 
 
 From Prop. J. R. Boisrc, A. M., Professor of the Latin and Greek Language* and 
 Literature in the University of Michigan. 
 This work belongs to a new era in the grammatical study of our own language. "We 
 hazard nothing, in expressing the opinion, that for severe, searching, and exhaustive 
 analysis, the work of Professor Welch is second to none. His book is not intended fot 
 beginners, but only for advanced students, and by such only it will be understood and 
 pproeiat*d. 
 
RECOMMENDATIONS 
 
 or 
 
 PARKER & WATSON'S READERS 
 
 From Prop. Frederick S. Jewell, of the New York State Normal School 
 It gives me pleasure to find in the National Series of School Readers ample i^^ 
 fcr commendation. From a brief examination of them, I am led to believe tilt' r 
 have none equal to them. I hope they will prove as popular as tboy are excellent 
 
 From Hon. Theodore Frelinghuyskn, President of Rutgers" College, N J. 
 A cursory examination leads me to the conclusion that the syetem contained ta 
 these volumes deserves the patronage t>f our schools, and I have no doubt that it will 
 become extensively used iu the education of children and youth. 
 
 From N. A. Hamilton, President of Teachers" Union, Whitewater, Wis. 
 
 The National Readers and Speller I have examined, and carefully compared with 
 
 others, and must pronounce them decidedly superior, in respect to literary merit, 
 
 tyle, and price. The gradation is more complete, and the series much more desirable 
 
 for use in eur schools than Sanders' or McGuffey's. 
 
 From Prof. T. F. Thickstun, Principal of Academy and Normal School, 
 Meadville, Pa. 
 1 am much pleased with the National Series of Readers after having canvassed 
 their merits pretty thoroughly. The first of the series especially pleases me, because 
 It affords the means of teaching the " word -method" in an appropriate and natural 
 manner. They all are progressive, the rules of elocution are stated with clearness, 
 and the selection of pieces is such as to please at the same time that they instruct 
 
 From J. W. Schermerhorn, A. B., Principal Coll. Institute, Middletown, N. J. 
 I consider them emphatically the Readers of the present day, and I believe thtt 
 their intrinsic merits will insure for them a full measure of popularity. 
 
 From Peter Rouget, Principal Public School No. 10, Brooklyn. 
 It gives me great pleasure to be able to bear my unqualified testimony to the excel 
 lence of the National Series of Readers, by Pakkrr and Watson. The gradation of 
 the books of the series is very fine ; we have reading in its elements and in its highest 
 atyle. The fine taste displayed in the selections and in the collooation of the piecet 
 ieserves much praise. A distinguishing feature of the series is the variety of the 
 ubject-matter and of the style. The practical teacher knows the value of this charac- 
 teristic for the development of the voice. The authors seem to have kept constantly 
 In view the fact that a reading-book is designed for children, and therefore they havo 
 ucceeded in forming a very interesting and improving collection of reading-matter, 
 highly adapted to the wants and purposes of the school-room. In short, I look upon 
 the National Series of Readers as a great success. 
 
 From A. P. Harrington, Principal of Union School, Marathon, N. Y. 
 
 These Readers, in my opinion, are the best I have ever examined. The rhetorical 
 oxercises, in particular, are superior to any thing of the kind I have ever seen. I havo 
 had better success with my reading classes since I commenced training them on these 
 than I ever met with before. The marked vowels in the reading exercises convey to 
 the reader's mind at once the astonishing fact that he has been accustomed to mispro- 
 nonnce more than one-third of the words of the English language. 
 
 From Charles S. Halsey, Principal Collegiate Institute, Newton, N. J. 
 
 In the simplicity and clearness with which the principles are stated, in the appro 
 priatenees of the selections for reading, and in the happy adaptation of the ditfeient 
 parts of the series to each other, these works are superior to any other text-books on 
 oii aubject which I have examined. 
 
 From "William Tratib, Principal of Union School, Flint, Mich. 
 I hive examined the National Series of Readers, and am delighted to find it so far 
 ta advance of most other series now in use, and so well adapted to the wants of the 
 f dbii* Schools. It is unequaled in the skillful arrangement of the material used, 
 beautiful typography, and tl 
 souks. I predict for it a core 
 most enterprising toichers. 
 
IIIONTEITH AND McNALLTTS GEOGRAPHIES: 
 
 THE MOST SUCCESSFUL SERIES EVER ISSUER 
 
 RECOMMENDATIONS. 
 
 A. B. Clark, Principal of one of the largest Public Schools in Brooklyn, s*ys: 
 "I have used over a thousand copies of Monteith's Manual of Geography since tti 
 adoption by the Board of Education, and am prepared to say it is the best work tot 
 Junior and intermediate classes in our schools I have ever seen." 
 
 The Series, in whole or in part, has been adopted in the 
 
 New York State Normal School. 
 New York City Normal School. 
 New Jersey State Normal SchoeL 
 Kentucky State Normal School. 
 Indiana State Normal School. 
 Ohio State Normal School. 
 Michigan State Normal School. 
 York County (Pa.) Normal BchooL 
 Brooklyn Polytechnic Institute. 
 Cleveland Female Seminary. 
 Public Schools of Milwstikio. 
 Public Schools of Pittsburgh. 
 Public Schools of Lancaster, Pa. 
 Public Schools of New Orleans. 
 
 Public Schools of New York. 
 Public Schools of Brooklyn, L. L 
 Public Schools of New Haven. 
 Public Schools of Toledo, Ohio. 
 Public Schools of Norwaik, Conn. 
 Public Schools of Richmond. Va. 
 Public Schools of Madison, Wis. 
 Public Schools of Indianapolis. 
 Public Schools of Springfield, Mass. 
 Public Schools of Columbus. Ohio. 
 Public Schools of Hartford. Conn. 
 Public Schools of Cleveland, Ohio. 
 
 And other places too numerous to 
 mention. 
 
 They have also been recommended by the State Superintendents of Illinoib, 
 Indiana, Wisconsin, Missouri, Noutii Carolina, Alabama, and by numerous 
 Teachers' Associations and Institutes throughout the country, and are in successful 
 use in a multitude of Public and Private Schools throughout the United States. 
 
 From Prof. Wm. F. Phelps, A. M Principal of the New Jersey State 
 Normal Softool. 
 
 Trentok, June 17, 1868. 
 Messrs. A. S. Barnes & Co. : Gentlemen : It gives me much pleasure to state 
 that McNally's Geography has been used in this Institution from its organization In 
 1855, with great acceptance. The author of this work has avoided on one hand the 
 extreme of being too meager, and on the other of going too much into detail, while 
 he has presented, in a clear and concise manner, all those leading fucts of Descriptive 
 Geography which it is important for the young to know. The maps are accurate and 
 welf executed, the type clear, and indeed the entire work is a decided success. I most 
 cheerfully commend it to the profession throughout the country. 
 
 Very 'July yours, WM. F. PHELPS. 
 
 From W. V. Davis, Principal of High School, Lancaster, Pa. 
 
 Lancaster, Pa., June 26, 1858. 
 
 Dear Sirs : I have examined your National Geographical Series with much 
 care, and find them most excellent works of their kind. Tliey have been used in the 
 various Public Schools of this city, ever since their publication, with great success and 
 satisfaction to both pupil and teacher. All the Geographies embraced in your series 
 are well adapted to school purposes, and admirably calculated to impart to the pupil, 
 in a very attractive manner, a complete knowledge of a science, annually becoming 
 more useful and important. Their maps, illustrations, and typography, are unsur- 
 passed. One peculiar feature of McNally's Geography and which will recommend 
 it at once to every practical teacher is the arrangement of its maps and lessons ; 
 each map fronts the particular lesson which it is designed to illustrate thus enabling 
 the scholar to prepare his task without that constant turning over of leaves, or refer- 
 ence to a separate book, as is necessary with most other Geographies. Yours. &c. 
 
 Messrs. A. S. Barnes & Co., New York. V. W. DAVI8. 
 
 From Charles Barnes, late President State Teachers' Association, and Superin- 
 tendent of the Public Schools at New Albany, Indiana. 
 Messrs. A. S. Barnes & Co. : Dear Sirs : I have examined with considerable 
 eare the Series of Geographies published by you, and have no hesitation in saying 
 that it is altogether the best with which I am acquainted. A trial of more than a 
 year in the Public Schools of this eity has demonstrated that Cornell is utterlv unfit 
 for the school-room. Yours, &c a BARNES. 
 
RECOMMENDATIONS 
 FEOK'S GANOT. 
 
 From the New Fnalander. 
 
 As an elementary work, it is concise in style, yet remarkably clear in definitions 
 and explanations, h.gical in arrangement, and beautifully illustrated with numerous 
 engravings. These engravings are so complete and accurate that they are not only 
 well calculated to convey to the mind of the pupil a clear conception of the prin- 
 ciples unfolded, but exhibit so full the structure of apparatus and methods of exper- 
 imenting, as to render the apparatus Itself in many eases unnecessary. Prof. Peck 
 lias done a good thing for American education in producing so attractive and excel- 
 lent a book. 
 
 From the New York Teacher. 
 
 We were particularly pleased witli the beauty of the engravings. They are, by 
 tar, the most satisfactory of any that have appeared in works of this elass'and many 
 of them are gems of art. The'book itself redeems all the promises thai were made 
 for it, prior to its appearance. It is clear and concise in definitions, logical in 
 arrangement, and full and exhaustive in descriptions. The illustrations of prin- 
 ciples and detail of philosophical experiments leave little to be desired except what 
 the reader himselt will be impelled to discover. The science is made attractive, and 
 the clearness of statement where a principle or law is enunciated will be appreci- 
 ated by both teacher and pupil. The practical Illustrations in the work will com- 
 mend it to all who look for tangible results. A too common 'ault in our school 
 philosophies is their abstract character. Mr. Peck has added to the other excel- 
 lences it possesses a felicity of language which will attract the scholar and the tyro 
 alike. We think it will be found a \ alualile contribution to this branch of science. 
 
 PORTER'S CHEMISTRY. 
 
 By Professor Porter, of Yale College: the most Practical and Popular Scientific 
 Work ever published. 
 From the Amer. Journal of Education, Hartford. 
 We have examined it with reference to its qualities as a school-book, its adaptation 
 to the wants of beginners in the study of a science which to many, even of College 
 students, is as obscure in nomenclature and symbols as it is brilliant in demonstra- 
 tions. As a text-book for the higher classes in schools and academies, we regard the 
 work as deserving of high praise. The language is clear and concise, the illustrations 
 are well chosen, and the arrangement of topics is natural and methodic. While the 
 technical terms of chemistry are explained sufficiently to introduce the student to 
 more extended treatises in the science, they are not employed so much as to impede 
 his progress at the outset of his course. 
 
 FIRST BOOK OF SCIENCE. 
 
 By Professors Norton and Porter, of Yale College. 
 
 Office of Superintendent of Schools, Buffalo, Feb. 27, 1559. 
 Messrs. A. 8. Barnes & Co. : Gkntt.emen : I have examined with much interest 
 the "First Book of Science," by Professors Porter and Norton, and I am free to say 
 that it is admirably designed to meet, a want in the Public Schools. Comparatively 
 few of those who attend "our Common Schools remain long enough to gain any valu- 
 able knowledge of Philosophy. Chemistry, and the Allied Sciences; and the text- 
 books on these subjects which hive been in use hitherto are too abstruse and cumber- 
 some for the young scholar. I should regard the introduction of this book f.s the best 
 means of exciting popular interest in the Natural Sciences, and of trivial: pupils who 
 cannot pursue a "course of study much desirable and practical information upon the 
 subjects treated. I am confident it will commend itself to the attention of the friend* 
 of education throughout the country. Respectfullv vonrs. 
 
 JOSEPH WARREN Sup't of Schoolt 
 
 
LOAN DEPT. 
 
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