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 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," 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 AM; Z=M; M=Z ; Z=M ; Z=X. .-. Z=X .-. Z is lees than X. (4.) (5.) (6.) M] 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 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," 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. . . ,k, last date stamps (N8837sl0)476 A-3-