gjSMIp aBi iS - tffggggfiii HP ISll ngenium usu Splendcscit. DUKE UNIVERSITY LIBRARY DURHAM, N. C. Rec d https://archive.org/details/elementarytreati01wils LOLi. O AN ELEMENTARY TREATISE LOGIC; INCLUDING PAST I. ANALYSIS OF FORMULA-PART II. METHOD. WITH AN APPENDIX OP EXAMPLES DESIGNED FOR THE USE OF SCHOOLS AND COLLEGES AS WELL AS FOR PRIVATE STUDY AND USE. BY W. D. WILSON, D. D., TRINITY PROFESSOR OF CHRISTIAN ETHICS, AND PROFESSOR OF LOGIC, OF INTELLECTUAI PHILOSOPHY, AND OF HISTORY IN HOBAET FREE COLLEGE, AT GENEVA, WESTERN NEW YORK. Logic — the Mathematics of Thought.” — Cousin. NEW YORK : D. APPLETON AND COMPANY, 346 & 34S BBO AD WAT. LONDON: 16 LITTLE BRITAIN. M.DCCC.LVI. Entered according to Act of Congress, in the year 1856, By D. APPLETON & COMPANY, In the Clerk’s Office of the District Court of the United States for the Southern District of New York. The following work has grown out of my necessities and my experience as a teacher. When, several years ago, I accepted a professorship, the duties of which required me to teach Log-ic, I could nowhere find a text-hook that seemed to me to satisfy the demands of the science. Nor was this feeling peculiar to myself. Mr. Thompson, in his excellent work on “ The Necessary Laws of Thought ,” begins his preface with saying : “ The system of pure Logic, or analytic that has been universally accepted for centuries past, is very defective as an instrument for the analysis of natural reasoning. Arguments that commend themselves to any un- taught mind as valid and practically important, have no place in a system that professedly includes all reasoning whatever ; and an attempt to reduce to its technical forms the first few pages of any scientific work, has generally ended in failure and disgust.” It would not be difficult to produce almost any amount of testimony to the prevalence of a similar feeling with regard to the present state of literature in this department of science and instruction. Of all the efforts which have recently been made to remedy this deficiency, two can be considered as requiring notice in this place : that of Prof. De Morgan, and that of Sir Wil- 250436 IV PREFACE. liam Hamilton. The work of Mr. Thompson just referred to, is, in its essential features, little, if any thing, more than an exposition of Sir William’s theory. Prof. De Morgan has earned a name in his own depart- ment (mathematics), which scholars hereafter will he pleased to remember and contemplate. But philosophy, in any of its departments, is not his calling. His theory is essentially nu- merical. He measures every thing by numerical quantity rather than logical. For the purposes of calculation, 2X, X, and X 2 are truly different terms, and can no more be substi- tuted for each other than X, Y and Z. In this case, X, Y and Z, 2 X and X 2 , are assumed as representing simply num- ber ; that is, a number of units. Now, units have no indi- vidual properties — nothing to distinguish one from another. Much less have they any separable accidents ; and the only difference, therefore, between the sums for which X, Y, Z, &c., stand, is in the number of units comprehended in each sum, and, consequently, 2 X and X — the one being twice as much as the other — are no more the same than X and Y, when they represent those different quantities. But the words or symbols used in Logic represent the conceptions that we form of objects of thought, which are not units merely, but individuals also, having each of them insep- arable and peculiar properties of their own, upon which not only their adequate conception, but any use which we can make of that conception in the Formula, whether of mediate or of immediate deduction, depends. This fact has been over- looked in Prof. De Morgan’s Formal Logic, to an extent which deprives it of any great value as a system. Perhaps the best test of any theory, is a comparison of its deductions with the obvious facts and first principles of know- ledge. De Morgan refers to an anecdote told of Zerah Col- burn, which relates, that having been asked how many black beans would make ten white ones, he replied — “ ten if you PREFACE. V skin 'em l” “But,” adds De Morgan, “the ten skinned beans would not he the same beans as before — except, indeed, to those to whom black is white.” — (p. 54 Formal Logic.] In the common sense of mankind, the beans are the same after being skinned. Philosophy may undertake to correct the common sense notions of mankind, but Logic cannot. And with how much success philosophy can pursue such an attempt we will not now undertake to decide. But in this case it can- not succeed. The conclusion, if established, would be gener- alized at once — as in fact it ought to be — and we should have the doctrine that identity depends upon the separable accidents ; and then all science, all knowledge, ethics, and religion, too, will be afloat and dissolved into fragments. A man’s separable acci- dents change from day to day ; consequently his identity changes. He is not the same man to-day that he was yesterday — is not bound to fulfil the contracts of yesterday, or to suffer the penalty due to its transgression. A theory that not only gives such results, but openly avows them, may be safely considered ab absurdo. I cannot but regard Sir William Hamilton’s theory as equally unfounded. Sir William’s name is one of the greatest of the present century of great names in philosophy. His rank will undoubt- edly be in the first class — with Aristotle, Plato, Descartes, Locke, and Cousin — the few great names that stud the galaxy of history. For an acquaintance with the learning and works of others in the department of speculative philosophy, he stands unrivalled, and probably will never be surpassed. But I have not been able to form any such high estimate of his attempts at originality. He assumes that there may be affirmative judgments with distributed predicates. This is so. But, as I have showr (Part I, chap. II, sec. 3. — See also p. 05, § 244), this is nevei done by the mere force of the affirmative copula. The fact, if VI PREFACE. fact it be, in any case, must always be indicated by something not essential to the judgment, and I have provided for all such cases — (p. 124, §498 — see 456). But, again, he assumes that there may be negative judg- ments with undistributed predicates. To this I have given what I think will be found a sufficient answer in p. 67 § 254 and the note. A subject is excluded from a Predicate only because it has not the Essentia of the class-conception denoted by that predicate. But the Essentia of one part of the individ- uals contained in it, can never be different from that of another. Hence, whatever would exclude a subject from a part of the predicate — that is, the predicate as an undistributed term — would exclude it for the whole of the predicate as a distributed term. If Sir William’s theories were correct on these points, doubtless we should be obliged to abandon the old nomencla- ture altogether and begin anew; as, indeed, Sir William pro- poses to do. But believing as I do, and for the reasons given, that his theory of quantification is fundamentally wrong, I have adhered to the old doctrine, so modifying the statement and exposition of it as to provide for the cases which he had regarded as demanding the new theory. It will also be observed, that in the following treatise I have made more account of Method than recent writers have been generally inclined to do. Many of them, in fact, have omitted it entirely. Perhaps the manner in which it had been treated by the scholastic writers, may serve, in some measure, as a justification for the estimate in which the modern authors have held that part of Logical Science. But not only is it of the utmost importance in itself ; there is, moreover, as I conceive, no way of obviating the objection to devoting so much time as is requisite to the mastery of what Whately and others with him who omit method altogether, have included in their treatises, without revising that part of Logic which is properly denoted by the word Method, and in thus giving practical direction and applicability to the whole study. This is what I have attempted to do in the part on Method, and I hope that scholars and teachers will agree with me in the esti mate I have placed upon the subject. If Logic is as Cousin has remarked, “ the Mathematics of thought,” it must comprehend not only an analysis of the For- mula which we use in thinking, hut also the methods of the successful application of these Formulae, and the discussion of Methods will require some consideration of the Matter to which they are to he applied, and the faculties by which we apply them. As the Analytic of Formulae may be compared to Geometry, so Method may with equal propriety be compared to Arith- metic, Algebra, and the Calculus in pure Mathematics — the former treats of Form in Space, considered simply as continu- ous quantity; the latter of methods of finding results in dis- crete quantity. Such Methods are not only Addition, Sub- traction, Multiplication and Division, Involution and Evolu- tion, but also the Binomial Theorem, the system of Indetermi- nate Coefficients, and all the Methods, in short, of Differentia- tion and Integration. Every mathematician knows that the truth of the result depends upon two conditions, (1.) that the Method be applied to proper matter ; and (2.) that the Methods themselves are legitimate. I have also provided in the Appendix a liberal supply of examples for Praxis. These examples may not be sufficient to illustrate every principle and formula, as, from the necessities of the case, they are for the most part ultimate parts in them- selves, and do not admit of the application of some of those prin- ciples which relate to the construction of more comprehensive wholes. Our limits will not allow of the insertion of examples illustrative of some of the principles of Method which we have described. Such examples can be found only in the books and vni PREFACE. treatises which are altogether too long to he reprinted here Nor can they be represented in any brief or abstract, in such a way as to test the principle or be of use in criticising the examples themselves. I have also divided these examples into classes, so that, if thought best, they may be used as the student progresses in the Analysis of Formulae — the first four sections being arranged with a view to corresponding divisions of Part I. of this work. Among the many analogies between Logic and Grammar, no one is more important and striking than that property in common from which it results ; that as iu the one case, so in the other, there is scarcely the possibility of getting a thorough kuowledge of principles and formula without much experience in what in Grammar we call parsing. This practice in Logic has come to be called Praxis. It consists in a careful analysis of all argumentative sentences with reference to the logical connection and sequence of the judgments which they express, the methods of argumentation, and the adaptation of the Methods to the matter. But the very process by which we thus perfect our know- ledge of the Principles and Formulas into familiarity with their use, is precisely that which we are obliged to practise in all cases where we apply our Logic at all in the purposes and uses of life. Praxis only makes perfect in the art of using our faculties and our knowledge in the wider' and more important spheres for which our studies are designed to fit us. It is, I believe, owing to the neglect of Praxis, together with the practical difficulty (which nothing but much practice can remove) of putting propositions into a Formal shape, that the impression that a large part of the arguments in every book to which the mind assents, cannot, nevertheless, be put into any one of the known and recognized Formulae, has become so general. Language seldom expresses all that is in the thoughts, and PREFACE. IX still more seldom all that is implied in what is actually said. Rules of rhetoric and taste would forbid such prolixity, even if it were possible. But Logic supposes nothing. It demands that all that is in the thought should be fully and explicitly stated. And one who has given a thorough logical analysis to any production, must of necessity understand it as well as he who wrote it, and probably, in nine cases out of ten at least, he would really understand it much better. He must understand it thoroughly , which is certainly more than can in all cases with propriety be said of the author himself. How many Enthy- memes are uttered, the suppressed premises of which are wholly unknown and unsuspected to him who expresses the Enthy- meme ? How many conditionals, the sequences of which are un- known to the writer or speaker himself? But all the latent elements of these imperfect arguments must have been brought out, stated, and examined by him who has gone through with a thorough logical criticism of the production. The student and the teacher likewise will probably find the chapter on Methods of instruction the least full and satisfac- tory of any. The reason for this is assigned in the chapter itself. I could not make it full and satisfactory without going further than unity of plan would permit into the department of Rhetoric, nor (waiving that objection), could I go into the subject so fully as such a modification of my general subject would require, without expanding the volume beyond all reason- able bounds. And, after much deliberation, I have decided to send it out as it is, regarding it as the best that I can make of the matter now and under the present circumstances. Such as it is, however, I trust that it will not be found unworthy of attention and diligent study. In conclusion, I wish to express my decided conviction not only of the usefulness of Logic as an instrument, but also that it needs more attention and more time than any work on the subject hitherto given to the public, has seemed to me to X PREFACE. deserve. It is to all the speculative sciences, every branch of knowledge except mathematics, what arithmetic and algebra are to the Mathematics themselves — as an instrument in con- structing those sciences — and it is as necessary as grammar it- self to rhetoric, and all the departments of literary criticism, dialectics, and oratory. In speaking thus of the importance of the science, and of a thorough education in it, I am not of course advocating the introduction of its technicalities and Formulae into public speak- ing and writing ; the analogy of grammar and rhetoric holds here also. No one, in speaking or writing, stops to parse his words, or to name every figure of speech which he uses, or every rule of rhetoric which he may have had in mind when he wrote or spoke. No more is it expected that the same thing should be done in regard to Logic. Here, as elsewhere, it may be said, the greatest art is to conceal art — to write with a perfect knowledge of all the terms and principles of the science of writing, and yet never thrust them forward in such a way as to be offensive to good taste, or vexatious to the reader. To reason logically is not the same as to reason formally. All good reasoning is of necessity logical, just as all good writ- ing must fulfil the rules and requirements of grammar and rhetoric. But it is not expected that the arguments will always be stated in the precise forms that are given in this book; nor that all that is requisite to their completion shall be expressly given. Logic supposes nothing. It allows of no omissions — no ellipses. On the contrary, rhetoric, good taste, brevity, and more than all, the scantiness of thought in the mind of the speaker, make this necessary. Logic teaches what these omissions are, how they are to be restored or produced to fill up the vacancies. And thus the reasoning fulfils the For- mula — becomes formal — or, as it is commonly but very impro- perly called, logical. But nothing can be more idle than the objection to the study of Logic, based upon the fact that its PREFACE. XI Formulas and technicalities do not appear, and are not expected to appear, in the written or published discourse of ordinary life. One might with as much propriety object to the study of the Binomial Theorem, on the ground that in equations of the second degree, we seldom or never find the square of the Binomial complete. Without these Formulae and technicalities, what is written and said can never be comprehended or intel- ligibly discussed. But, after all, it must be distinctly considered that Logic, like the pure Mathematics, is only a means and not an end. The pursuit of the study may be valuable as a discipline. Its results will be of great service to any one who has thoroughly comprehended them. But if one looks to its Formulae as a substitute for common sense in the common affairs of life, or of investigation in the higher pursuits of literature and science, or of patient and laborious thought anywhere, he will be sadly disappointed. W. D. WILSON. Geneva, Dec., 1855. CONTENTS. PAGE Introduction. — Logic Defined ; its Origin, Necessity, and Uses ; its Sphere Pointed out, and the Starting Point Ascer- tained, 1 PART I. ANALYSIS OF FORMULAE. CHAPTER I. OF TERMS. Section I. — Of Conceptions — their Formation, their Object and Rela- tions, 9 II. — Of Substance and Properties • — Sphere and Matter of Con- ceptions, Essentia, Genus, General and Collective Terms, Differentia and Species, Individual and Acci- dents, 13 III. — Of the whole and its Parts , 21 I. — Of Quantity, there kinds, 22 II. — Of Division, three kinds, 24 XIV CONTENTS. Sec. IV . — The Relation of Cause and Effect, 29 V - — Of Difference, Identity, Resemblance, and Analogy, 32 VI. — Of Definition and Description 33 ^ II- Of the Quality of Terms — General, Specific, Synonymous, Analogous, Incompatible, Positive, Negative, and Priva- te, 34 VIII. — Of the Quantity of fTerms — Numerals, Ordinals, Positive and Negative, Infinite, Comparatives and Superlatives, Distributed and Undistributed, 38 IV. — Of the Opposition of Terms — Relative, Contrary, Sub- contrary, Contradictory, 40 CHAPTER H. OF PROPOSITIONS. Section I. — Of Judgments — Scope, Kinds, Categorical, Conditional, Disjunctive, Hypothetical, Relative or Comparative, and Probable, 43 II. - — Of the Terms in a Proposition — how Placed, Propositions Resolvable into Terms, 46 III. — Of the Copula — its Force, Forms, Effects, and Classifi- cation, 48 IV. — Of the Adequacy of Propositions, 55 V. — Of the Quantity of Judgments — Individual, Particular, and Universal Judgments, 59 VI. — Of the Quality of Judgments, 61 VII. — Of the Modality of Judgments, 61 VIII. — Of the Pour Cardinal Propositions — Universal Affirma- tive, Universal Negative, Particular Affirmative, and Particular Negative, 62 IX. — Of the Distribution of Terms in Judgments, 64 X . — Of Immediate Inference, 69 I. — By tiie Opposition of Judgments, 70 II. — By Permutation or Contra- Position, 71 III. By Conversion, 74 IV. — By Substitution of Teems, 76 CONTENTS. XV PAGE Sec. XI . — Of Complex Propositions — Modals, Explicative, Differ- ential, Exceptional, Exclusive, Conditional, and Pro- trusive, 77 XII. — Of Compound Propositions - — Express and Implied, Copu- lative Causal, Discretive, Conditional, and Disjunctive, Exceptives, and Exclusives, 80 XIII. — Of Comparative Judgments 84 XIV. — Of Probable Judgments — The Calculation of Chances, Antecedent and Special Probabilities, 87 XV. — Of Conditional Judgments — The Sequence, Complex Se- quences, Compound and Continuous Conditionals, 91 XVT. — Of Disjunctive Judgments and Excluded Middle, 97 XVII . — Of the Grounds of Affirmation — Identity and Contradic- tion, Sufficient Cause, and Excluded Middle 102 CHAPTER IIL OF SYLLOGISMS. Section I —Classification of Syllogisms — Names of the Terms, and Parts in Pure Categorical Syllogisms, 106 n. — Of Pure Categorical Syllogisms, 110 X. — Of the Figure of Syllogisms, 110 II. — Of tiie Moon of Syllogisms, 115 III. — Application of Moons to tiie Figures, 118 III. — Of Indirect Conclusions , 123 IV. — Of the Conversion of Syllogisms — Ostensive Reduction, and Reductio ad impossibile, 121 V. — Of Complex Syllogisms — Change of Modals and Proten- sive Quantity, 131 VI . — Of Compound Syllogisms, or Sorites, the Reduction of Sorites to Simple Categoricals, 138 VII . — Of the Incomplete Formulas, or Enthymemes, Inductive and Cumulative Formula, 142 Vni . — Of Epichirema, Pro-syllogisms, and Epi-syllogisms, 148 IX . — Of Compound Judgments in Syllogisms , 149 XVI CONTENTS. PAGE Sec. X. — Of Comparative Syllogisms — I. — Simple Comparatives, 152 II. — Comparatives in irmcn tiie Difference of Intensity is Regarded as a Cause, 155 III. — Comparatives, Manner, &c., 156 XI. — Of Probable Syllogisms, the Effect of Discrete Quantity- on Logical, and the Combination of Independent Pro- babilities, 157 XII. — Of Conditional Syllogisms — their Completion, 170 XIII. — Of Disjunctive Syllogisms — Comprehensive and Divisive 175 XIV. — Of the Dilemma 179 CHAPTER IV. OF FALLACIES. Section I. — Of the Ig noratio Elenchi, 185 II. — Of the Petitio Principii, 186 in. — Of the Ambiguous Middle, 189 IV. — Of Division and Composition, 190 V. — Of Accidents and Quid, 191 PAKT II. LOGICAL METHODS. CHAPTER I. of the elements of method. Section I. — Of Method in General 194 II. — Of Order as an Element of Method, 196 III. — Of the Ideas which Determine Methods , 198 CONTENTS. XVII PAGE Sec. IV. — Of the Matter of Logical Methods — Analytical and Syn- thetic Judgments, Necessary and Contingent Matter, Class-Conceptions, Judgments d priori and d posteriori. Material and Implied Properties, Formal and Modal Properties, Absolute, Physical, and Moral Certainty, Analysis, Synthesis, Truth, Opinion, Hypothesis, Theory, and Conjecture, 202 CHAPTER n. METHODS OF INVESTIGATION. Section I. — Of Investigation — The finding of Predicates, 219 II. — Of Observation and Testimony — the External Senses, Consciousness, Experiment, the use of Hypotheses, and of Testimony, ni. — Of Measurement and Calculation — Methods of Obtain- ing Wholes from Parts and Parts from Wholes, 232 IV. — Of Average and Exclusion, or the Abscissio Infniti, 237 V. — Of Analysis — The Analysis of Conceptions and of Ob- jects, 243 VI. — Of Induction and Analogy — Several forms of Induction, 249 VII. — Of Elimination, Causes and Antecedents — Causality Im- plies Substance, Methods of Elimination, 259 CHAPTER III. METHODS OF PROOF AND REFUTATON. Section I. — Of Proof — Direct and Indirect Methods,.- 275 II. — Of Demonstration, 281 III. — Of Deduction, 290 TV. — Of the Argument from Authority — Principles of Inter- pretation, 293 V. — Of the Appeal to Facts, by way of Induction, the Uni- formity of Nature, Final Causes, Example, Analogy, and Circumstantial Facts, 303 XV111 CONTENTS. PAGE Sec. VI. — Of Progressive Approach, 324 VII. — Of the Argumentum ad Ignorantiam, 326 VIII. — Of Refutation, three Methods 328 IX. — Of Direct Refutation, 329 X. — Of Indirect Refutation, 333 XI. — Of Personal Refutations, ad hominem , ad verecundiam, ad invidiam, 336 CHAPTER IV. METHODS OF INSTRUCTION AND CRITICISM. Section I. — Classification of the Sciences — Plato’s Classification, Aristotle’s Scholastic, Bacon’s, Locke’s, Ampere’s and Compte’s — a new one proposed, 338 H . — Of the Conveyance of Ideas from one Mind to Another — as Determining Methods of Instruction, Ideas Con- veyed only by Definition and Reconstruction, 347 III. — Of Definition and Description — Real and Verbal Defini- tions, Definition of “ Simple Ideas,” Ultimate Concep- tions, Description Furnishes no Matter for a Concep- tion, 349 IV. — Of Natural and Artificial Classifications — Natural Classifications made in Cognition, Necessity for Scien- tific Classifications, Recurring Species, 356 V. — Of the Division of the General Subject — Divisions in Pro- tensive Extension, in Comprehensive, 360 VI. — Of the Order in the Treatment — Matter Divided into Classes with Reference to the Order of Statements, Or- der Stated, Rules for Omission of Matter as Irrelevant to the End in View, Necessity for an End or Special Aim, 361 VII. — Methods of Criticism — The Critic’s Point of View, the Relation of Whole and Parts, Argument and Impres- sion, Logical Matter and mere Assertion, Arguments and Artifices, Criticism of Terms, Contradictio in Ad- jectis,...., 369 CONTENTS.. xix APPENDIX OF EXAMPLES FOR CRITICISM. § 1. Of the Order in Criticising Arguments , 377 § 2. Examples in Categorical Syllogisms, 379 § 3. Examples in Hypothetical Syllogisms, 382 § 4. Examples in Complete and Compound Formulce, 386 § 5. Miscellaneous Examples of Formulce and Fallacies, 389 § 6. Examples Involving Questions of Method, 396 § 7. Leslie's Short and Easy Method, 401 § 8. Webster's Argument in the Girard Will Case, 404 § 9. Dana's Argument in the Ellsworth School Case, 407 Index, 411 LOGIC. INTRODUCTION. 1. The word Logic has been used in many different senses, and most treatises on the subject have LoeiP . variou3 . included matter belonging to widely differ- ly defined - ent spheres of thought and inquiry. It sometimes de- notes the science which explains the laws of thought merely. It is sometimes used to denote the art of con- vincing and persuading. It has been thought to imply the consideration of the means of discovering truth, and also the general principles of Method. 2. Philosophy was in existence and cultivated some time before Logic appeared as a distinct philosophy be- Science or Art. The reason is obvious. Men fore Logic - do not seek a Canon of Truth until they feel the danger of error, and have reaped the hitter fruits of its expe- rience. The earliest schools of Greek Philosophy (and of the Hindoo Philosophy we cannot now speak, for want of chronological data)— the Ionian and the Pytha- gorean — argued and dogmatized without fear or expec- tation of contradiction ; they were too sanguine and confident to feel the need of Logic. 1 2 INTRODUCTION. 3. But as soon as the doctrines of these two schools came into conflict, some Canon, or test, of truth was found The origin of to he necessary. Not only terms in which LoBic - to discuss the points at issue, hut an in- spection of first principles, and of the processes of deduction from them, came to he regarded as indis- pensable to the discovery of truth, and the proper testing of the means by which it may be proved to be true. 4. No system of Logic, however, was formally de- veloped and digested until Aristotle. Aris- Author 0 of the totle * himself, however, says Zeno the Elea- rst^tem. tic, was the inventor of Logic, or rather Dialectics, /haXe/cTiicr']. 5. As soon, however, as Philosophy had sufficiently explored the field which it had to occupy, to form any definite idea of what is contained in it, we find Plato dividing it into three coordinate branches : — Physic, Threefold i Ethic, and Logic ; f — the former including vision^ Vhiio- all of the Natural Sciences ; the second, all that concern the relations and duties of man ; and the latter, Logic, the science of mind, and the rules by which its activity is to be guided to the proper results. 6. .Logic is derived from the Greek Aoyos, and in Logic, how the sense used by Plato, it means whatever used by piato. p er tains to the Mind, the Reason, the imma- terial power or faculty which is manifested in the words and speech of men. Logic was used to denote the whole of what, in modern times, has been called Intellectual Philosophy, or Metaphysics. 7. But Intellectual Philosophy or Metaphysics, in this broad extent of meaning, includes at least three distinct departments of science. (1.) Psychology , as it is called, describing the facts of the mind, of which we are immediately conscious ; * Sext. Empir. adv. Math. B. vii. c. 1. f Diog. Laert., Procem. seg. 18. INTRODUCTION. 3 such as Sensation, Perception, Abstraction, psychology. Conception, Association, Imagination, Memory, Intui- tion, Judgment, Inference, &c. (2.) Metaphysics proper, which investigates the necessary a priori conditions and laws of Metaphysics, thought, and the ideas which determine cognition and judgment, and those necessary axioms, or first principles, which are assumed in all sciences, and underlie them, as the ground of their possibility and reality. And (3.) Logic ; which treats of the relations of conceptions to one another ; the deduction Logic in thi3 of secondary from primary and intuitive narrowersen9e - judgments, and the laws of Synthesis, by which truths are constructed into systems. 8. The last element of this definition is what has usually been called Method ; and latterly Me thodnotm- there has been a tendency to regard it as a cluded latterly - science by itself. Excluding Method, therefore, from our definition, Logic may he defined as the Science of Deductive Thinking. 9. As there may be true and legitimate deductions as well as such as are false and delusive, Logic a Sci . there must be a Science of deduction, by ence - which the true may be distinguished from the false ; and the laws and formulas of deduction itself so ex- plained and developed, as to enable one to select and pursue those methods which lead to right conclusions, and avoid those that are fallacious. 10. But it is necessary for the practical benefits of the science, to take some note of language, Its reIation to or the words and signs by which thinking iecti4A? f Rht- is expressed ; of the matter of which we torie - think and reason ; and especially of the various ways in which the Formulae may be used in the construction of what, in popular language, are called Arguments ; these form the transition from Logic, as a Science, to T * ' m Art, is more properly It is, of course, with 4 INTRODUCTION. Logic as a Science, tliat we have chiefly to do in this volume. 11. The purpose which we have now before us does not lead us to regard Logic as a means of discovery, or of so constructing such methods of argu- good V e 4s'omn 18 men tation, as are used in speeches and books, eoo reasoning. ag £ 0 p e mos t successful in a dialectic point of view ; not, in short, to teach directly liow to reason well , but rather what is good reasoning, and why it is so. 12. In this view, Logic sustains about the same relation to public writing and speaking that Grammar Logic annio- does, or that Moral Science sustains to good mT ic.^Ta morals ; the Science of Music to good sing- science. ing • or anatomy and physiology to the prin- ciples of health and the practice of Medicine and Surgery.* 13. As in Grammar, for example, we need some terms and names, by which to represent the parts of speech, and the rules determining the inflec- instrument o" tion and relation of each part to others, and to the whole sentence ; so in Logic we need names for each part of a process of thought, and rules and laws determining their relation, both for the purpose of discussing and analyzing the thoughts of others, and to assist in the due expression of our own. Without such aids it is impossible to study Rhetoric and Oratory, or Psychology and Metaphy- sics with much success ; and they are of the greatest importance in all departments of study and instruc- tion, 14. There is obviously a distinction between a pro- cess of thought and the matter about which the thoughts Form and Mat- are occupied; the order, arrangement, and ter of thinking, dependence of the thoughts upon one another * Of course one may speak without knowing Grammar, or sing without a knowledge of the scientific principles of harmony and mel- ody. But he could speak and sing much better with such knowledge, and he could hardly teach or compose without it. INTRODUCTION. 5 may remain the same, and the matter be different ; and vice versa, the matter may remain the same, and the order and sequence of the thoughts he different. Hence the distinction between the Form of an argument, or processes of thought, and the Matter / the Form denotes merely the order, dependence, and arrange- ment of the thoughts. Thus, if I say, “ men are mortal, and therefore they should prepare for death ; ” and “ men should prepare for death because they are mortal ; ” the Matter would be the same in each case, but the form would be different. But if I should say, “ men are mortal, therefore they should prepare for death ; ” and “ spring is coming, therefore we should prepare for summer;” the Form would be the same in both instances, but they would differ in matter. 15. But again, in any continuous process of argu- mentation, as in a Speech, an Essay, or a Method. Book, these Forms or Formulae may be combined and used in different relations, and follow each other in different order. Hence, besides the Matter and Form of an argument, we have to consider also the Method ; that is, the way in which the Forms are used. Thus, if I wish to prove that four times twenty-five is one hundred, I may do it by writing twenty-five four times, each directly under the other, and then add them up ; or, by writing it once with a four under it, and then multiply, the result will be the same in each case, but the Method will be different ; the former is the Method of Addition, the latter of Multi- plication. 16. Logic is called Formal, and sometimes Ana- lytic, when it investigates the varieties and Formal Logic, laws of the Formulae. When it goes farther and in- quires into the grounds of the validity of these Formulae, it is called Rational / and when it goes one Rational, step farther, and takes into consideration the diversities of the various kinds of matter, and the peculiarities in the forms of expression by which that matter is repre- 6 INTRODUCTION. sented, and the application of Formulae as modified Applied. by the matter, it becomes what we call Ap- plied Logic. 17. Logic always presupposes, or takes for granted, Logic pre- certain premises or starting-points ; the truths? 63 some truth or falsehood of which it belongs to other branches of science to determine. It is concerned how far con- with the truth of Propositi ons, only so far as oMtopo* they are given as resulting from certain sitions. others. But the first elements of reasoning, the primary facts, it takes from other branches of know- ledge, as they have been ascertained and established in those branches representing them. It does not un- dertake to prove the self-evident axioms or the primary facts of science in any department ; but with those axioms and facts, given in philosophy and experience, it directs and guides the mind at every step, to its most remote results, to the highest generalizations, and to the most comprehensive truths ; as well as in every application of those truths to the practical purposes of life. Logic therefore does not supersede, but rather pre- supposes, a knowledge (derived from other sources) of the subject matter with which our minds laws and pro- may be occupied. It simply explains the laws by which the mind is guided in arrang- ing and combining that matter into scientific systems, and in its application to the various purposes and uses of life. 18. ISTor, again, does Logic propose a new way for doing what we have been accustomed to do in an- other. From the earliest development of new way of rea^ intellect, and the very commencement of intellectual activity, the mind has been ac- customed to think and to draw inferences, or think deductively ; so that we have all been long in the practice of Logic, before we begin the study of its science. 19. Those forms and processes in which we proceed INTRODUCTION. 7 from one thought to another, which depends upon the preceding, are called in the popular language Argu ments. How long soever or how complicated soevei they may he, Formula; and Method are thus undistin- guished from each other. The Formulae, or syllogisms separate processes, each of which has one subject and but one, are called in Logical language, Syllogisms ; the word is of Greek origin, and signifies a putting together for the sake of a Conclusion. 20. A Syllogism, therefore, first presents itself to our reflective thought as a completed thing ; The parts of having already all of its parts, and most of aSrUogism - them in their legitimate places, and connected with the other parts. Each argument consists of several Pro- positions ; one of which we call a Conclu- The parts of sion, and the others the Premises ; these a Pr °p° sition - Propositions consist most of them of two terms and a • Copula. One term, called the Subject , de- S ubject-pre- notes that about which we are speaking ; dicate - the other, called the Predicate , denotes what we say of it ; and the Copula is the verb affirming or deny- ing the agreement between the Subject and Predicate : as A is B, or A is not B. Here “ A ” is the Subject, “ P ” is the Predicate, and “ is ” fimS' and and “ is not ” the Copula ; the former of Negatlve - which is called the Affirmative and the latter the Nega- tive Copula. 21. That act of the mind by which the Copula is affirmed or denied, is called a Judgment , A Jud{rment . or when expressed in words, a Proposition, ^fonsorcog- “ A ” and “ B ” are called Terms, and that nitions - in the mind which they represent, is called a Cognition , or a Conception. We come therefore to Conceptions or Cognitions , as the simplest element with which Logic, in our use of the word is concerned, and the the starting- point of departure with which we must polnt ' commence in the methodical construction of the Science. 8 INTRODUCTION. 22. Logic, however, presupposes some knowledge of Psychology, and we must look to that for the expla- nation of some of the tacts and terms which posef" ^syciio- it assumes as already known. These, how- ever, for the sake of completeness, we will run over in a very cursory manner. PART I. ANALYSIS OF FORMULA. CHAPTER I. OF TEEMS. 23. Teems are the words or signs by which any conception or cognition is expressed, for the Terms defined, purpose of conveying it from one mind to another. SECTION I. Of Conceptions. 24. When we look at any object an act of the mind ensues, which in psychology is called per- perceptions. ceiving — and the result of that act is called a Peecep- tion. But the mind retains the result of that act after the object has been removed from any phy- sical connection with us, and the mind can recall it at pleasure. In this view of it, that result is called a CONCEPTION 01’ a COGNITION. 25. Perception is an instantaneous act, and on each occasion, when the same object is pre- An instanta . sented anew to the senses, we perceive it neous act anew, and form anew, or again, a cognition of it. We have thus at the second time a new or second per- 1 * 10 LOGIC. PART I. [CHAP. ception, which the mind compares with the first, and gives the judgment of identity in regard to the object which occasioned them. 26. But if the perceptions differ so much or in such ways as to imply a difference in any of the insepa- , rable properties of the object perceived. Identity and , • i 1 • ,1 -i • , r t ’ diversity of ob- the mind conceives the obiects as diverse jects perceived. « i i ° from each other. 27. In Logic we regard the different cognitions of the same object as one and the same cognition, ex- Different co» ce Pt w ^ ien we wish t° take into considera- nitiinf c of The tion the changes which the object itself same object. t 1 0 i n , t ° may undergo, by a change 01 those separable accidents and modes of existence, which may be changed without changing the identity of the object itself. 28. A distinction is sometimes made in the use of the words “ cognition ” and “ conception ,” by which Distinction be- the former is used to denote the idea of tion en and co c g on- one individual object only: as “ a man,” ception. u a • anc i conception, the idea of a class : as “ mankind ,” “ villages ,” “ pens” &c. I shall not take pains to adhere to this distinction very closely ; although I shall never employ the word “ cognition ” to denote the idea of a class. I shall, however, very often use the word “ conception ” when I mean to refer to the idea or cognition of an individual thing only. 29. A conception or a cognition may be adequate or inadequate. It is adequate only when it includes, so that we may be said to know, all the pro- adeq 2 ?t c e epll and perties, uses, purposes, and the history of the inadequate. 0 pj ec t ; otherwise it is, strictly speaking, in- adequate. 30. No one of the senses by itself and alone can ever enable us to form an adequate conception of any Diverse sen- object. We see its color; we smell its odor ; fifte°to an re a q d D i- we taste its flavor ; we feel its density and quale concep- smoothness, &c. Nor can we ever know, OF TERMS. SECT. I. 11 I-] or form an adequate conception, of any considerable proportion of the objects with which human knowledge is occupied, by any contact of those objects with our own senses. Hence we have to rely upon the testimony of others, historians, travellers, and observers in every department of science, for by far the largest part of what we know. 31. Moreover, there are many objects of thought of which we have conceptions, which how- conceptions ever never have and never can have any of ldeaa - connection with the external senses, as means of cog- nition ; such as truth, justice, virtue, eternity, &c. These objects of thought are sometimes called Ideas, and are said to be furnished by the Reason itself. 32. It would appear that man can have but very few, if any, conceptions or cognitions that are strictly and absolutely adequate ; and tions absolutely hence we are accustomed to call those “ in- a e But a worc [ that expresses the property considered by itself as an object of thought, Abstract terms, is called an abstract term; as “ whiteness” “ length” &c. 44. But such terms as “ white,” “ long,” &c., while they denote the abstract property, also imply some- thing that is “white,” “lonq,” &c. Hence Denotatives -1°. t and connota- sucli terms are called (Jonnotatiyes, and are said to denote the property of “ length” for instance, and to connote the body or substance that is long. 45. Every conception is considered as having two sphere and elements, a Sphere and Matter ; or, as it ception. is sometimes designated, a Comprehension and an Intension. 46. The Sphere or Comprehension is the number of sphere, individuals included in the conception for which a word stands. Thus, take the word “ hard,” or “ hard- ness,” the sphere of the conception includes every ob- ject of which we can say “it it is hard.” 47. The Matter or Intension of a conception is the Matter, number of properties which may be ascribed to the subject or substance of which we have a concep- tion. Thus with the subject “Iron,” the matter of the conception is “ hardness” “ ductility” “ malleability” &c., including whatever may be predicated of iron. 48. Or to take the conception “man,” the sphere includes Csesar, Cicero, Washington, &c.,&c., every indi- vidual of whom we can say that “he is [or was] a man ; ” the matter of the conception is “ bimanous” “ biped” “ rational” “ religious” “ accountable” &c., including every thing that can be predicated of man, whether as a physical, or an intellectual, or a moral being. I-] OF TEEMS. SECT. II. 15 49. A distinction is sometimes made in speaking ol conceptions between being contained in a contained in conception and being contained under it. “ d der co J ta con d The Matter is said to be contained in the con- ception - ception ; thus rational is contained in the conception “man.” But Caesar, Washington, Bonaparte, Frank- lin, &c., are said to be contained under the conception “ man.” 50. The Matter of a conception limits and deter- mines the sphere ; thus we include in the The Matter n- conception or class “man,” every individual mits ‘he sphere, who has the properties of a mat. 51. Conceptions of the same object formed from dif- ferent points of view, are called Alternate Alternate c on - Conceptions. Hence Alternate Conceptions ceptions - each denote the same sphere by different matter, and constitute different names for the same object. Thus “ height ” and “ depth ” are Alternate Conceptions of distance, perpendicular to the horizon, viewed from different points. Almost every object in Nature has several names, according as it is viewed in one or an- other of the relations which it sustains. Thus a Natu- ralist would speak of certain animals as “ sheep ” simply ; the Farmer, with reference to his farm, would call them “ stock /” and the Commissary, with refer- T ence to their use as a supply for the army, would call them “ provisions .” 52. The cognition of the sphere and the matter of a conception are not usually simultaneous acts. In the first perception of a single obiect, we acquired before get the sphere of its conception, by means of some of its most obvious properties ; we acquire the others, one after another. In the question, “ what is that f ” “ that ” refers to the sphere of the conception which we already have in our minds ; and “ what ” to the matter which we have not and wish to acquire. The same thing occurs in efforts at recollection. We remember that something happened, was said or done, without remembering what it was ; we have the sphere LOGIC. — PART I. 16 [chap. of its conception in our memory, but tlie matter has for the most part escaped us. 53. The questions “ who ” and “ what,” are an- swered by the matter of a conception, which enables Questions who? us to determine the sphere. But the ques- what? and which? ti 0 n “which,” is answered by the sphere of the conception, — which enables us to study out the matter for ourselves. 54:. But in regard to the conception of a class, we get the matter of the conception before the sphere, since it is the matter which determines and limits the sphere. 55. Among the properties or attributes of an object of thought, we distinguish some that are inseparable from it, as extension and divisibility from matter ; and in a man his complexion, his features, his stature, &c. ; and other properties which are separable or different, at different times and in different places, as sickness and health ; his posture, as sitting, standing, or walk- ing, &c. Properties of the former kind are said to con- Essence and stitute the Essence * of an object of thought ; Modes. the latter its modes of existence ; thus the name of any object always implies all the essence of its reality. But if we wish to express its modes we must add something to the name, expressive of that mode; thus “George Washington” denotes the man, * but does not imply any thing of his modes, as sick- ness or health, eating or sleeping, commanding an army, presiding in his cabinet, or delivering his fare- well address. 56. Most terms, however, denote a substance as existing in some particular mode ; and substance and * We use the word “ Essence ” in its Logical sense and not its Onto- logical, as denoting that which it is in itself, aside from all the changes it may undergo, without becoming a different object; and not that which is necessary to its existence as an object in reality. Without its Essence, in its ontological sense, an object could not exist at all ; but in the Logical sense it might exist as an individual in another genus. I.] OF TEEMS. SECT. H. 17 mode, in Logic, is somewhat an arbitrary i n J|™bfu5ice distinction. Strictly speaking, in the onto- ,namode - logical sense there are bnt two substances, matter and spirit ; and most other words denote one or the other of these substances existing in some particular mode ; thus take the word “ air” it denotes matter existing in a certain mode. Again, considering “ air ” to be a substance, and “ wind ” is a modal term, denoting the existence of “ air ” in a particular state ; or if we take “ wind ” for one substantive word, then “ gale ” will be a modal denoting the existence of wind in some one of its modes. 57. When any property, or a number of them, are considered as constituting several objects of thought, to which they belong, a class, these properties are called Essentia ; thus “ man ” denotes a Essentia, class ; and those properties, without which one would not be called a man, are the Essentia of the class ; and the class, with reference to these Essentia, Genus, is called a Genus. Essentia is the matter of the con- ception, and the Genus is its sphere.* 58. A word denoting a Genus is called a General term. But if the word denote a number of G e neral and coi- individuals, not by essential marks belong- lective Terms - ing to each of the individuals separately, but rather by some mark which belongs to them only as a whole, or a body, the word is called a Collective term ; as “ congress,” “ church,” “ army.” 59. From the nature of a general term, whatever may be predicated of the term, may be pre- Difference in dicated of any individual object included cates. predl " under it ; thus if we say, “ man is a two-footed being,” * I do not think so much has been made of the distinction between the terms which denote the matter, and those which denote the spheres of conceptions, as might with profit, in explaining what has been called the Predicables. Of these, Porphyry, and after him the Scholastics gener- ally, have reckoned five: Genus, Species, Differentia, Property and Accident ; the two first, Genus and Species, denote spheres, and the other three matter of conceptions. 18 LOGIC. — PART I. [CHAP. we may say of eacli man, “ lie lias two feet.” But this is not true of the collective term ; thus we can say of the church, “it is a divine institution,” but we cannot say of its members, “ they are a divine in- stitution.” 60. Some words are used only as collective terms, as those just mentioned ; while others are sometimes used some words as co ^ ec tive, and at other times as general, used in "bom Thus if we say, “ the Romans conquered Carthage,” we cannot say that “ Cicero con- quered Carthage,” although he was a Roman. “ Ro- mans ” is here used as a collective term. But if we say, the Romans spoke the Latin language, we may say of Cicero, he spoke the Latin, for we then use “ Romans ” as a general term. 61. When we consider any o'f the properties of an object as distinguishing it from a class to which it Differentia. does not belong, those properties are called Differentia, or distinguishing marks. And all the individuals which have these marks or properties, species. are called a Species. Thus woolly hair, black skin, &c., if considered as distinguishing those who have them from other men, are the Differentia ; and “ ISTegro ” is the term denoting the species thus distinguished. 62. Hence the same property may be either Essentia or Differentia, just according to the point of view from Essentia and which it is regarded. If we regard black SMli, to skin, woolly hair, &c., as constituting a class, each other. then ]^ e g ro j s ^ Genus, and these properties are Essentia. But if we have in mind at the same time “ man,” as a higher and more comprehensive class, including those who have black skins, woolly hair, &c., as well as others which have them not, “ man ” is the genus, and “ ISTegro ” is the species. 63. Hence those properties which are the Differen- tia of a class, considered as a species, become Essentia when the same class is regarded as a genus, including species under it, and vice versa. I-] OF TEEMS. SECT. H. 19 61. Properties, when regarded as Essentia or Dif- ferentia, are considered Essential ; but when Pl . 0 pe rt ies e ? - not so regarded, are usually spoken of as j e e n n t'u. or Acci ' Accidental .* 65. When any property is considered as distin- guishing one individual from another, it has inseparable been called Inseparable Accident, Indivi- Accident - dual Mark or Peculiarity ; and the object thus de- noted, is called an Individual, f individual. 66. Hence Individuals are included under Species, SDecies under Genera, and so on : Genus individuals, hending sphere, and Species and Individuals, each in order, lower and comprehended spheres. 67. Spheres are said to coincide or be coincident , when they contain some individuals common spheres coin- to both ; as for instance, “ Christian ” and poslte. dnd 0p “ man ; ” since all who are included in the sphere * Properties that belong to an individual, or to the individuals of a class only, are said to be peculiar to that individual or class. If a pro- perty belongs to all the individuals of the class, it is general in respect to the class, or universal. If it belongs to several classes, it is said to he common ; a common property. Properties, when considered in reference to some end or object, for which the thing to which they belong is designed or desired, are also called Qualities, or that which qualifies a thing for its use or end. f It will appear from the above, that of the five Predicables of Por- phyry, two, Genus and Species, must be nouns, as denoting classes ; and the other three, Differentia, Property, and Accident, will be adjec- tives ; thus, of John Smith, we predicate, as they say, Genus , “ man Species, “Caucasian;” Differentia, “white;” Property, “civilized;” Accident, “ very short,” or “ sitting in a chair.” Genus and Species are said to predicate “in Quid;” Differentia, “in Qualequid Property and Accident, “in Quale.” “Genus,” says Aldrich, “is that which is predicated of many, as their material or common part, as “ animal.” — Differentia, that which is their formal part, as “rational.” — Property, that which is joined with the essence, as “ risible ; ” — and Accident, that which is con- tingently joined to the essence, as “white,” “black,” “to sit.” But in this account of terms, he regards Essentia and Differentia as one, or the Differentia as the Essentia (see Aldrich, Oxford ed. 1849, p. 20, and the notes). 20 LOGIC. — PART I. [CHAP. denoted by “ Christian,” are in the sphere “ man ” also ; since “ Christians are men.” 68. But if two spheres have no individual com- mon to both, they are called contrary or opposite spheres ; as “ dog ” and “ man,” “ Christian ” and “ Mahometan.” Contrary or opposite spheres, however, although they may have no individual contained under them com- mon to both, may, nevertheless, have matter contained Analogous i 11 them in common. Thus any two species spheres. comprehended under the same genus, must be contrary spheres ; as black or white, as properties of men, so that no object can be in both at the same time ; yet black and white may be both species of men, in which the essentia of humanity is common to all the individuals in both species. Such spheres are called Analogous. 69. That genus which can never be comprehended under a higher genus, is called the summum or maximum genus. That species which can never comprehend one below it, is called the infima s P e- infana species. All others are called sub- cies - alternate species and genera. The genus, however, which is next above any two or more co- ordinate species is called, in reference to Summum Genus. those species, the proximate genus y as Proximate Genus. “man” is the proximate genus to “Negro” and “ Mongol.” 70. Those properties which indicate only the dif- separabie ferent modes of the same individual, are Accidents. called Sepaeable Accidents ; as sickness or health in man, sharp or dull in a knife. 71. When attributes are common to all the indivi- duals of two or more species, they are called Indif- indifferentia. ferentia, or points of indifference y or even sometimes “ common properties,” as to have hoofs is common to the horse, the ox, the goat, the sheep, &c. Hence the having hoofs is the point of indifference to those several species, and may become the Essentia of a I.] OF TEEMS. SECT. m. 21 proximate genus, under which all hoofed animals shall be comprehended. 72. Hence the Differentia is essential to the species, and the peculiarities or inseparable accidents are essen- tial to the individual. 73. The matter of a term, used as a general term, is the Essentia of the Genus ; the matter The Matter of of a term, used as a specific term, or to General Terms - denote a species, is the Essentia of the Proximate Ge- nus (and of course, therefore, of all higher of Specifio and comprehending genera), plus the Differ- Terms - entia of that species. And the matter of an individual term is the Essentia, plus the Differentia, of individual plus the Inseparable Accidents or individual Terms - properties. 71. Besides this matter, however, every class must have some properties which are not considered as either Essentia or Differentia, and each individual must have some separable accidents, which Matter of are not necessarily included in the concep- erms tion of the individual. Thus, in forming a conception of a man, it is not necessary that we should include in the conception any particular posture, style of dress, state of health, &c., although he cannot exist except in some posture, state of health, &c. SECTION III , Of the Whole and its Parts. 75. The sphere of any conception is regarded as a whole. But there are three ways of consid- Wh oies, of ering wholes ; that is, there may be three threekinds - alternate conceptions of the same whole, which we call logical , Continuous , and Collective wholes. The esti- mate of a whole is called Quantity ; the process of resolving the whole into parts, is called Division. 22 LOGIC. — PART I. [CHAP. 1. Of Quantity. 76. As there are three alternate conceptions of any whole, so there ai’e three ways of estimating the amount Quantity, of of that whole, or three kinds of Quantity ; three kinds. Logical, Continuous , and Discrete. 77. Logical Quantity is that which estimates the comparative size of the sphere of conceptions, as mea- Logicai Quan- sured by the individuals included under ti,y - them ; thus a species is always less than its proximate genus, and so on. 78. In Continuous Quantity the object of thought is always considered simply as a reality ; thus a point, continuous a line, a surface, a triangle, a circle, &c., are Quantity. considered as continuous quantity. Theo- rems which are demonstrated concerning them in Geo- metry and Trigonometry, have no connection with the length of the lines, or the amount of the area that may be inclosed by them. 79. So also the properties which may be predicated of substances in different degrees of intensity, are con- sidered as continuous quantity. 80. Discrete Quantity contemplates a whole as a union or accumulation of parts. These parts may be Discrete Quan- unequal, and each have a differentia of its tity - own. Or they may be equal and have no distinguishing marks. In that case they are merely units, and quantity is mere number ; — the science of this kind of quantity is Arithmetic. 81. In Continuous Quantity, the whole is not con- Continuous ceived as made up of parts, or divisible into wholes not made , ,1 -i x •, ■% j up of pans. parts ; though ot course it may be so made up, and consequently divisible. 82. In Discrete Quantity we have such terms as the cardinal numbers, fractional expressions. Nothing, or Terms and zero, denotes not any quantity, but the ab- crete hiantity! sence of quantity or quantification ; and the last expression, in discrete quantity, is the indefinite ; I.] OF TEEMS. SECT. III. 23 a sum so large that it cannot he expressed, the limit cannot he pointed out, but not so large that it may not be increased by addition and diminished by sub- traction. 83. In Continuous Quantity we have such terms as denote indivisible objects of thought ; any i « . • n . J -i ° i • J Limits m Con- ODjeCt in fact whose conception does not lm- tinuous Quan- ply a union of parts. And besides names iy ‘ denoting such objects of thought, we have also the positive, the comparative, and the superlative forms of adjectives denoting degrees of intensity; and the last expression of continuous quantity is “ infinite ,” and it implies that of which extension cannot be predicated.* 84:. Logical Quantity begins with the individual, and takes note of the higher classifications, Limits in Lo- up to its last term, the Absolute , — that which gical Quantity - includes all being, which is genus without ever being species, the summum genus. 85. Discrete Quantity is applied to the objects which are included in the terms of the other A ppi icat j 0 n 0 f kinds of quantity ; thus a line, or angle, are Jjiy cr t e o te Lo g u icai continuous quantities. But when we say the and continuous, line has so many feet, or the angle is of so many de- grees, we apply discrete quantity to the measurement * Even space and time form no exceptions to this remark : for nei- ther time nor space, strictly speaking, are extended. We have simply a conception of extension, as applied to something in space or in time, but not to space and time themselves. Among the many classifications of properties, we have one that is useful for many purposes — into primary and secondary ; of which the primary can be predicated of substances only, — the secondary not of substances at all, but only of their primary properties ; thus, extension is a primary property of matter, length is a secondary property — a property of the extension of a body. When we say a body is so long, we mean that its extension or extent is so long. “ Thinking ” is a pri- mary property of mind; “intense,” “close,” &c., are properties of “ thinking.” Now, “ infinite ” and “ extension,” are incompatible properties ; both primary ; and can neither of them be predicated of the other, nor in fact of the same substances. We say space is infinite, and we have extension in space. We say GOD is infinite, but we never speak of His extension. 24 LOGIC. — PART I. [chap. of objects of continuous quantity. In like manner, when we attempt to number the individuals comprehended in the sphere of any logical whole, whether species or genus, it must be done in terms of discrete quantity ; thus the discrete quantity of the sphere “ man ” is 800,000,000 ; that is the whole number of men on the earth. 86. But by far the greatest part of the properties of substances, considered as continuous quantity, can- Not aii objects not he measured by discrete quantity ; thus Quantity carfbe we cannot measure in any such way the in- so measured, tensity of color, of taste, of smell, of density, &c., among the properties of material substances ; nor that of virtue, wisdom, courage, &c., among the pro- perties or attributes of mind. We may be able to distinguish a greater or a less intensity — that is, a more and a less — but how much greater or less is what we have no means of measuring or express- ing. 2. Of Division. 87. That process by which a Whole is resolved into its Parts is called Division ; and, as there are three Division of kinds of Quantity, so there are three kinds three kinds. 0 f Division : Physical , Mathematical or Nu- merical, and Logical. 88. Physical Division divides continuous quantity ; thus we divide a loaf of bread into pieces. Now these physical. parts are bread — that is, have the essentia of the whole, but they have no proper differentia of their own constituting them different species of bread — as “ wlieaten bread,” “ barley bread,” &c., but they are considered still as parts, and are conceived of in rela- tion to the whole. 89. Numerical Division divides a discrete quantity or number into parts, each of which is considered as Numerical. a unit or factor in reference to that whole. Thus we divide a foot into twelve inches, a yard into I.] OF TERMS. SECT. HI. 25 three feet, &c., and the collective whole with Dividend, reference to Mathematical Division is called Dividend. 90. Logical Division divides the sphere of the Genus or Logical Whole into species, each Logical, having the Essentia of the whole and a Differentia of its own, belonging to each individual contained under it ; and into individuals, each having individual marks or inseparable accidents of its own. Logical Division is called Classification. classification. 91. Thus physically we should divide a man into ^ head, trunk, and extremities — or into hones, illustration of muscles, tendons, membranes, fluids, &c. Division - Mathematically we should divide the race into com- panies of tens, or fifties, or thousands, as the case might be. Logically we should divide them into Mongol, Caucasian, and Negroes ; or into Pagans, Mahometans, Jews, and Christians ; or into civilized, barbarous, and savage, &c. 92. The number of individuals included in any con- ception or logical whole may be divided in several different ways. Thus the inhabit- sions of the ants of the Earth may be divided ethically same kmd ' into Caucasians, Mongols, Negroes ; or politically into English, French, Spanish, Russians, Chinese, &c. ; or in reference to their religion into Christians, Jews, Mahometans, Buddhists, &c. 93. That which determines us to any one of these several divisions of which any logical whole Divieive Prin . is susceptible, is called the Divisive Prin- ciple - ciple or the Principle of Division. As in the example just given, Race, Polity, and Religion are the Divisive Principles by means of which the divisions are effected. In mathematical division the divisive principle is called the Divisor. 91. The divisions of the same whole effected by the different Principles are called the Co- coordinate Di- ta* • • A visions. ORDINATE Divisions. 95. The several parts into which any whole may be' divided by means o£tlie same Principle of division 2 26 LOGIC. — PAKT I. [chap. are called Coordinate parts, and tlie terms denoting coordinate them are Coordinate terms, as Christians, pans. Jews, and Mahometans, &c. 96. The Coordinate parts of a numerical Division Factors, species, are called Factors — with reference to the divided whole, or Dividend. In Logical Division, the Whole is called a Genus, and the Coordinate parts are Species. 97. But the parts of two coordinate divisions of the Disparate parts, same whole are called Disparate parts ; and the terms denoting them Disparate terms in reference to each other — as Caucasians, Russians, and Maho- metans. 98. Any one of these parts however may be as- sumed as a whole, and divided as though it were not parts assumed included in a higher and more comprelien- as wholes. give w } 10 i Cj and so on, until the sphere of the conception comes to be an individual. 99. But when any whole is divided into coordinate parts, and these coordinate parts are again subdivided, subordinate these divisions with reference to the first Divisions. division are called Subordinate, and the parts of these subordinate divisions are called Subor- dinate parts. Thus let X be divided by coordinate divisions, and illustrations, on different principles of division, as follows : 1st. 2d. 3d. X into X into X into A, B and C, D, E and F, G, H and I, X i et X 2d - X 3d - are coordinate divisions. A, B and C are coordinate parts in relation to each other, so also are D, E and F, and likewise G, H and I. But A, D and G, or B and F, or E and G, &c., are disparate to each other. Let now A, B and C be subdivided, A into B into and C into a , 1), and c, d, e,f , g , h, i. These are subordinate divisions. I.] OF TEEMS. SECT. m. 27 a, b, c, d, e,f, g, h and i are all subordinate parts to X 18t - But a , b and c, &c., are coordinate to each other, and d , g , &c., are disparate to each other, as in the first division the parts occupying similar places were disparate. 100. Any conception including in its sphere more than one individual, though it may denote but a coordinate or a subordinate part in uo^mayTea reference to another and more comprehen- " )U e ' sive whole, may become nevertheless a logical whole or unity itself with coordinates and subordinates under it. And each term or conception, whether whole, co- ordinate or subordinate, and in whatever degree of subordination, until we come to a term that denotes but one individual, will have a sphere and a matter of its own, and so be capable of a logical division. 101. As we have said, the parts in any Logical Division are called Species. And besides the Alternate parte Coordinate, Disparate, and Subordinate Spe- orS P ecies - cies just described, we have in Logical Division Alter- nate Species also. These are species the Differentia of which is a part of the matter of Alternate concep- tions of the same object. Thus statesman and philoso- pher may be Alternate conceptions of the same indivi- duals, so that the same men may be both statesmen and philosophers, though of course an individual may be one without being the other. In this view of the mat- ter statesmen and philosophers are said to be Alternate Species. 102. The last element of a Logical Division is called individual. But the individual may be either Absolute m- Absolute or Relative. It is absolute when it dividuals - can be divided no farther. Thus the mind is an abso- lute individual ; the chemical simples such as iron, sulphur, sodium, &c., are also absohite individuals, because they cannot be resolved or analyzed into any component elements. 103. On the other hand, most of the objects of 28 LOGIC. PART I. [chap. thought are merely relative or assumed individuals ; Relative in- that is, they are individual only in reference dividuais. to the purposes for which they are at the time before the mind. In this view “ man ” is an individual, in reference to any classification of the animal kingdom. But in reference to a classification of substances as spiritual and material, man is not an individual — his mind belongs to one class and his body to another. So with reference to a Treatise on Materia Medica, carbonate of soda, for instance, is an indi- vidual ; but in reference to chemical analysis it is a compound, resolvable into carbonic acid and sodium. 104:. The following are regarded as the fundamental vf 8 r ns of Di ‘ Canons of Division. (1.) The coordinate parts must contain all that was contained in the whole, and nothing that was not con- tained in it. (2.) Each coordinate part must have a narrower sphere or be smaller than the divided whole. (3.) ISTo unit or individual can be contained in more than one coordinate part. Thus if one should divide his library into the co- Exampies. ordinate division, folios, quartos, octavos, &c., and Greek, Latin, English, French, German, &c., and into philosophy, history, physics, mathematics, poetry, &c., each division would be good. But if he should divide into folios, octavos, Greek, history, philosophy, &c., the division would be faulty. It would not be made on any one principle of division, and the same book might be included in several of the parts. 105. The division of a Logical Whole into Alternate Species is only an imperfect division, and does not fulfil the conditions as above specified. It des ernat vioi£te results from the very nature of Alternate tiiL-se canons. conce pti ong> that they may be all of them predicated of the same object ; since they are but Alternate conceptions or different views of that object. Hence if they are taken as the Differentia of Species, the same individual may be in more than one of them I.] OF TEEMS. SECT. IV. 29 at once ; thus a man may he a Christian, a gentleman, and a scholar, all at the same time. Still, ^ contain however, the Alternate Species must include Aye Xvidl all the individuals comprehended under the Logical Whole or Proximate Genus. If we divide the writers of a nation, for instance, into poets and prose writers, the same writer may belong to both species ; but there must he no one who does not belong to one or the other of them. SECTION IY. The relation of Cause and Effect. 106. When any object of thought is considered in relation to that which brought it into exist- Cause and ence, or as having had a beginning, it is Effect - conceived of as an Effect ; and when an object is con- ceived in reference to what it may bring into existence, it is conceived of as a Cause. 107. Nearly every object of thought is conceived as both Cause and Effect ; — Effect in refer- Every object ence to something which has preceded it as a the“as ed cause condition of its existence ; and as Cause in or Effect - reference to something which follows it or whose exist- ence is either occasioned or conditioned by it. 108. Thus starting from any object of thought con- ceived as effect, we may direct our thoughts Cauge Abso . to its cause, and from that cause conceived ‘ ute - as effect, to its cause, and so on until we come to the First Cause or Cause Absolute. So it is that whatever we know by its own properties directly we always know and conceive of as effect ; and the mind of neces- sity refers to something else as the ground and cause of its being. But when we come at last to that Being whom no man hath seen or can see, and whom we know only through the manifestation of His wisdom, and power, and goodness — through the effects of these transcendent attributes, Him we know only as Cause. He is not only the Cause and Creator of all things 30 LOGIC. PART I. [CHAP. visible and invisible, but He is also the Cause as Au- thor of the Revelation which He has made. Hence we know Him only through His works and His Word, and the mind refuses to conceive of Him as an Etfect. 109. But with this only Exception, cause and etfect cause and Ef. are but alternate conceptions of the same ob- Conceptions. ate ject of thought. Each object of thought is susceptible of both conceptions, and each in turn de- mands both. In this view all objects of thought, con- sidered as causes, are distinguished into Absolute, and Relative — the One only being Absolute, all others being relative. 110. Again we conceive of Mind as a cause in a different sense from what matter can be. Motion, in cause primary matter, always refers the mind to something and secondary. 0U £ 0 f tdig moving mass, as its cause — this cause we call a Force. But if we see a being possess- ing mind, in motion, we are content to consider him- self as the cause of his own motion ; and reason is satisfied when we refer to his will as the cause of the movement.. Hence we distinguish between Primary and Second causes, and call those Primary which are sufficient causes — and those Secondary which only refer us to something else as the cause of its acting, as cause ; and so on until we come to intelligent moral Agency, as the only Primary Causes. 111. Besides the above distinctions there are seve- ral other senses'in which the word Cause is used, or in which the object of one conception may be regarded as the cause of the object of another. (1.) The Efficient Cause is that from which emanates Efficient cause, the force that produces the Effect. (2.) The Occasional or Exciting Cause is that which occasional. puts the Efficient Cause in operation, as the spark in the explosion of gunpowder. (3.) The Material Cause is the matter or Essentia Material. of which any thing consists.* * As the Essentia of any class considered as a Genus is the Material of that Genus, the Essentia may be called with reference to this fact the Material Properties. OF TERMS. — SECT. IV. 31 <1 (4.) The Formal Cause is that which determines the specific mode of the existence.* Formal. (5.) The Final Cause is that for which any thing exists or is done ; and, Final. (6.) We have also what are called Negative Causes, as when we say “ the want of rain caused Negative, a severe drought,” — “ the absence of heat,” or which is the same thing, “ cold congeals the river.” 112. Of the six kinds of Cause just enumerated, the 1st and 2d, the Efficient and Occasional, common Name? are usually spoken of as Causes ; and much ofthem - confusion often arises from not distinguishing between them. The Material Cause is usually spoken of not as a cause but as “ the nature of the thing ; ” the Formal Cause as its “ characteristic ; ” and the Final Cause as its “design” or “object.” 113. Thus if we take an act of virtue, the person who performed it is the Efficient Cause ; illustrations, the motion which induced him to do it is the Occa- sional Cause ; the fact of its being a free act and not one of necessity, or even instinct, is the Material Cause ; the nature of the act, its conformity to right rules of action is its Formal Cause or characteristic, and makes it a virtue and not a vice ; and the object for which it was done is its Final Cause. 114. Causes are sometimes considered as Transient , Permanent , or Immanent. A Transient Cause is one which passes away after its efficiency has been exerted. Thus occa- Transient cause, sional causes are for the most part transient, as the spark that ignites the powder. A Perma- Permanent cause, nent Cause is one that remains, and from which the effect is continually flowing — as the sun and the lamp are permanent causes of light. An Imma- immanent cause, nent Cause is one that remains in its effect ; the Mate- rial and Formal Causes are always Immanent. * As the Differentia of Species are the Formal Cause of the Species, ■with reference to this fact they may he called for the sake of con- venience the Formal Properties. 32 LOGIC. PAKT I. [CHAP. 115. Causes with reference to the fact that they ^called a n to j always exist before the Effect, are sometimes consequents! 11 called Antecedents merely. So also Effects for the same reason are sometimes called Consequents or Consequences merely. 116. Effects are either Immediate or Remote. The ^immediate Ef- Immediate effect is that which follows at Remote. once ; the Remote effects or consequences are those which appear afterwards, but not until after an interval in which they are not seen. 117. Again, Effects or Consequences are Direct and Accidental. Direct when necessarily following Direct. Acci- fi'om the activity of the Cause, and always dental implied in the conception of its agency. But those effects which are not invariable attendants upon the activity of the Cause, and are not considered as necessarily implied in it, or as necessary to its ade- quate conception as a cause, are called Accidental ; undesigned, and in reference to an intelligent cause they are called Undesigned. SECTION V. Of Difference , Identity , Resemblance and Analogy. Difference is of two kinds — (1) in kind, and (2) in Difference of rlcwvroo two kinds. 118. Although any common name may he used as genus, yet there are certain obvious and natural pro- Difference in perties of all objects of cognition, by which kind - they are referred to natural classes. In this classification these more obvious properties are assumed as the basis of the classification. When therefore two objects do not agree in possessing each the same pro- perty in this natural classification, they are said to differ in kind. 119. But when two objects of cognition are con- ceived as belonging to the same natural genus, and are m Degree. compared only with reference to some one property or class of properties which they . have in !•] OF TERMS. SECT. VI. 33 common, they are said to differ in degree only. In this case the objects possess — the one more and the other less of — the property or properties which are made the basis of the comparison. They differ only in the degree or intensity in which they possess the property com- mon to both, and in reference to which they are com pared. 120. When the difference is only in separable acci- dents then it is said to be “ identity .” It is identity, the same individual under different circumstances or at different times ; thus “ sick ” or “ well,” “ sitting ” or “ walking,” “ sleeping ” or “ waking, ” with re- gard to a man ; “ hot ” or “ cold,” “ round ” or “ irre- gular,” “ bright ” or “ rusty,” &c., of a piece of metal, are mere separable accidents denoting different states or modes of the same individual substance. 121. The properties common to any two or more individuals conceived as belonging to the same species, constitute what is called Similarity or lie- similarity and semblance. And the properties which are Contranety - different in any two or more individuals conceived as belonging to the same species, constitute Contrariety. 122. Hence similarity and contrariety are between individuals conceived as belonging to the same species. Or these terms may be applied in the same way to species conceived as comprehended within the same proximate genus. 123. The properties in common between individuals conceived as belonging to opposite or differ- Analogy, ent species constitute what is called Analogy. SECTION VI. Of Definition and Description. Before proceeding to explain more fully the terms which will be of frequent use throughout this Treatise, it may be well to say what we mean by a Definition, and what by a Description ; reserving the fuller dis- cussion of the subject to the chapter on Method. 34r LOGIC. PAKT I. [CHAP. 124. A Definition is any Proposition in which the Definition. word or thing defined is the subject, and the predicate gives us the matter of its conception. 125. A Description is any Proposition which indi- Description. cates the sphere of a conception, either by enumerating its parts or pointing to the place in which or the time where it may be found. SECTION VII. Of the Quality of Terms. 126. The Quality of a Term indicates the manner Quality of Terms, in which it represents the conception or cognition for which it stands.* • * Aristotle divided the categories into ten : Substance, Quantity, Quality, Relation, Place, Time, Position, Possession, Action, Passion, (Organ, c. iv.) And he adds (Top. I. c. ix.), “for accident, and genus, and property, and definition, [I am not responsible for his divi- sion,] will always be in one of these categories, since all propositions through them signify either what a thing is, or its quality, or quantity, or some other category.” Aristotle’s illustration is, Substance “ man,” Quantity "one," Quality “white,” Relation “greater,” where “ in the Forum," when. “ yesterday ,” Position “ sitting,” Action “ whatever he may be doing," Passion “ whatever may be being done to him" Now it is very possible that every thing that can be said of any sub- ject may be included in one or another of these categories. The list seems to be very complete. But I have been unable to see its utility, and therefore I have omitted it. And in that respect it is like much else in the writings of this Father of Logical Science. At a later period Kant gave another list of the categories. Aristotle had classified them from the outward properties of things. Kant classified them from the ideas determining their cognition — into four, each of which contains under it three varieties or dimensions. ( One. I Real. I. Quantity •< Some. II. Quality ■< Limited. ( All. ( Non-Real. f Substance, or Property. III. Relation ■< Cause, or Effect. ( Action, or Reaction. ( Possible, or Impossible. IV. Modality ■< Existence, or Non-Existence. ( Necessary, or Contingent. This list of categories is important rather to Metaphysics than to Logic, as determining the conditions and possibility of knowledge rather I.] OF TEEMS. SECT. VII. 35 127. We have already had occasion to ^concrete ana explain what we mean by concrete and ah- De °^ t j ve and stract terms (see 43), by denotative and con- connotative™ notative (see 44), by substantive and modal M U 0 b d s jf ntiveand (see 55) terms. 128. A term denoting a class is called general with reference to its including more than one in- General Terms, dividual, and specific with reference to its specificTerms. distinguishing them from all others. We will now proceed to notice a few more of the differences in the Quality of a Term. 129. Terms denoting the same conception are called SynOnymOUS. Synonymous. 130. Terms denoting Analogous Spheres are called Analogous Terms. 131. Terms having the same logical force, though not analogous or synonymous, are called Equipollent. Equipollent. 132. Terms which denote sometimes one conception and sometimes another are called Ambiguous. Ambisuous. 133. Terms which cannot be predicated of the same subject at the same time and in the same respect, are called Incompatible. Thus “ sitting ” and incompatible. “ standing ” cannot be predicated of the same man at the same time. “ Master ” and u servant” can be pre- dicated of the same subject at the same time, but not in the same respect. Thus one may be the servant of his superior and master of his dog ; but he is not master and servant in respect to the same thing or in the same respect. 134. A Positive Term is one which implies the reality of that which it denotes. All terms positive, therefore denoting genus, species, or individuals, or the properties of them, are Positive. than the deduction of one thought from another, and the systematic construction of those thoughts into knowledge and science. In the following Sections, therefore, I have confined myself to such classifications of terms as seemed to be useful for the purposes of deduc- tion, and omitted all others on the ground that the inclusion of \yhat- ever is not useful is a hinderanee. 36 LOGIC. PART I. [CHAP. 135. But the sphere of a positive term is a limited p Th* sphere of sphere,* and excludes all that has not the limited? Lrm8 Essentia of the conception denoted by the Positive ; thus the conception circle excludes from its sphere all figures that are not circles. 136. A Positive sphere therefore necessarily im- plies another, in which are included all objects that implies a Ne- do not possess the attributes contained in gative sphere. (] ie matter of that conception. The term that denotes this sphere is called a Negative Term. 137. The sphere of the Negative Term is the com- Neeative a plement of that of its Positive in the sum- the positive, mum genus, or absolute totality ot tilings. 138. A Privative Term is one which denotes an privative. object or class of objects in which there is an absence of some property, usually considered as belonging to the conception of its proximate genus or species. 139. When we speak of the Essentia as that with- out which an individual cannot belong to a genus in illustrations, natural classification, we refer rather to the conception than to the actuality of the individual. Thus one would say that reason is of the Essentia of man, and yet we would not say that an idiot was not a man. We recognize the idiot as one who is accident- ally deprived of that which belongs to the idea or con- ception of his species. He is no less a monster, a lusus natures, than a horse with reason or a dog that could talk. * This is so, or Pantheism is inevitable. Infinite is not so much without limits as out of limits ; as red is not so much a long color as a color out of length ; that is, not included in any Genus of which any of tile terms denoting extension can be predicated. But if the term Goo does not denote a limited sphere, then of course there is nothing which is not God — God is all — or Pantheism. But it is one thing to say, the term “God” denotes a limited sphere; and to say, that God is limited, or not infinite. “Limited” and “infinite” are not antithetic or opposites in the same kind, like “ long" and “ short "red" and "yellow," but disparates rather, like “long" and “red," or “ short ” and “ yellow." OF TEEMS. SECT. VTI. 37 i.] 140. Thus “ idiotic ” when predicated of man, or “ blind ” when predicated of an animal, are Privative terms. We do not speak of “ dumb ” as predicable of a triangle, although it implies the presence of no property, but only the absence of one which never belongs to a triangle. So with “ idiotic ” in reference to a mountain or a brute even ; Privative though it be, it denotes the absence of a Differentia or Property which can never be predicated upon the Essentia of “ angles,” of “ mountains,” or of “ brutes.” 14:1. The Negative, as we have said, is the comple- ment of the Positive in the Summum Genus Privativescom or absolute totality of things. But the Priva- piem?nVofthe tive is the complement of the Positive in prokmate ce e the Proximate Genus only ; as “ wise ” and “idiotic” in reference to men — “blind” and “see- ing” in reference to “animals,” which thus become joro hac vice a proximate genus. 142. Hence it is obvious that Privative terms are vastly more frequent than Negatives. In But few Ne fact there are hut few really Negative terms satlve Terms - in use. Which they are can be determined only by the usus loquendi of each language, and the peculiarities of localities and of the authors who use them ; thus A and non- A are a Positive and its Negative. 143. The distinction between them however is less necessary to be made on account of the fol- lowing facts with regard to their use. If the th™ p d7st1nction term occurs as a subject, it is of no import- tives and pnva- ance whether it be Negative or Privative ; tue6I .‘ otsreat - though not the same they are equipollent in that posi- tion. But if the term occur as a Predicate it is of no importance for the most part, since the subject itself is the sphere of the Proximate Genus, and thus limits the individuals which are taken into the scope of the judgment, and all individuals comprehended in the sphere of the subject and not included in any position used as a Predicate, must be included in its Privative as well as its Negative. Thus let “ wise” be a positive 3S LOGIC. PART I. [chap. Predicate, and we say “ some men are wise, and some men are foolish.” It is of no importance whe- ther foolish is a Negative or a Privative term, since in either case and alike, it includes all men who are not “ wise ; ” since some men are “ wise ” and the rest are “ otherwise.” SECTION Yin. Of the Quantity of Terms. 144. Terms expressive of Discrete Quantity are either Numerals or Ordinals. The Numerals denote Numerals and the number of units, as “ three fi “four” ordmais. “five ; ” and the Ordinals the order in which any particular unit stands with reference to the other units in any given series, as “ third f “ fourth , “sixth.” 145. Terms expressive of Discrete Quantity are also divided into such as express units merely, as “ one,” units, Tens, “ two,” “ three,” &c. ; such as express tens of and Hundreds. xin its, as “ten,” “ twenty “ thirty” &c . ; and such as express hundreds, as “ one hundred ',” “ two hundred ,” &c. This classification of the terms in Discrete Quantity is of great service in discussing the elementary Methods of the science of Numbers. 146. We have also other classifications, as “odd” and “ even,” “ roots,” “ squares,” “ cubes,” “ surds,” “ rationals,” &c. But as we shall not go Roots.' Powers! into the discussion of the Logic of Discrete Quantity — far enough to require the use of these'terms — it will be unnecessary to discuss them at length. 147. Then we have such terms as “ Positive ” and “ Negative fi which have been already considered in positive and the preceding sections. As expressions of D?screte 6 Guam Discrete Quantity they have relation to tity - “ zero ” or “ nothing” They indicate the distance above and below that starting point — the one showing the number of units above or more than nothing, and the other the number below or less. I.] OF TEEMS. SECT. Tin. 39 148. The word “ infinite ” when used in discussions of Discrete Quantity, indicates either the absence of Quantity altogether, or that the object of thought is out of the sphere of Discrete Discrete than 0 Quantity altogether. That which is infi- t,ty ' nitely small is Nothing ; and that which is infinitely large is something with which the terms of Discrete Quantity are incompatible. Thus if we divide nothing by two |, the answer or quotient is said to be infinitely small ; that is, there is none. If we divide two by nothing f , the quotient is said to be infinitely large or infinite. But there is no quotient at all. There is no division in either of the above cases, for the obvious reason that we cannot divide without both a divisor and something to be divided. In each case therefore we perform no operation and get no results in Discrete Quantity. “ Small ” and “ large ” imply Continuous Quantity ; but when they become infinite, they are beyond the reach of Discrete Quantity. This is shown also by the fact that they never occur in the process of a calculation, but only are results at the close of the process. 149. In Continuous Quantity “ Positive ” is a term which denotes the reality of Quantity, Positive and and “ Negative ” is a term which denotes continuous its absence ; the same in relation to Con- Quantity, tinuous Quantity, as “ Infinite ” does in relation to Discrete Quantity. 150. Then we have “ Compa/ratives ” and “ Super- latives , and these too in opposite directions from the Positive ; thus let us take “ wise ” parities,’ and ... . j -l ,, Superlatives. as a positive term, and we have “ m,ore wise,” and “ less wise,” as Comparatives of opposite m- opposite intensity ; and “ most wise,” and tensity - “ least wise,” as Superlatives of opposite intensi- ties. 151. In Logical Quantity we have but two varieties of terms to be noticed. 152. Any term denoting a Logical Whole, whether 40 LOGIC. — PART I. [chap. Individual, Species, or Genus, is called a Distributed Distributed ami term. And any term denoting any unde- undistributed. tei'mined part of such a whole is called an Undistributed term. 153. All individual terms are therefore always and necessarily Distributed. Any term denoting genus or species, standing alone and singly, or used out a sign are as the subject of a Proposition, is always taken as Distributed, or in its broadest sense, unless the contrary is indicated by some word or words limiting its comprehension, as “ some men,” “ many books,” “ few wise men.” 154. we are to notice, however, that any words which give the Differentia of an included species, specific terms constitute thereby a specific and not an un- are distributed, distributed term. As in the cases just given, “ some men” does not indicate what part or how many of the race of men we intend to speak of. “ Many ” im- plies a larger part than “ few ” ordinarily, but neither of them enable us to distinguish the individuals in- tended, from the others included in the same general term. But if we say “ wise men,” “ religious books,” the adjectives “ wise” and “ religious ” give differ- entia of species, comprehended under the genera “ man ” and “ books ; ” and the specific term “ wise men ” is as completely a distributed term as the generic “ men ” itself — some Avise men ” would be undis- tributed of the specific term. SECTION IX. Of the Opposition of Terms. 155. Among the properties of substances we per- ceive some Avhicli always imply others. Thus length as opposition of a property of matter always implies breadth, Terms. g0 that whatever has the one must have the other. (A line can hardly be said to have length ; it rather is length.) A beginning always implies an end, extension always implies divisibility, &c. OF TEEMS. SECT. IX. 41 I-] 156. The relation of such, properties is called a Relative Opposition, and may be of two Relative op- kinds. positio "- (1.) Where the correlative properties inhere in the same substance, as “ length ” and “ breadth,” In the same “ beginning ” i«nd “ end,” “ extension ” and substance - “ divisibility,” &c. (2.) Where they necessarily imply different sub- stances, as “ parent ” and “ child,” “ sub- rn different ject” and “ruler;” and the two terms substances - taken together are called Correlates. 157. Again there are certain properties which im ply the absence of certain others ; this relation consti- tutes Contrary Opposition, as “ vice ” and Contrary Terms. “ virtue,” “ white ” and “ black,” “ hot ” and “ cold.” In fact the differentia of coordinate spe cies are always contraries to each other. Contrary terms are called Antithetic in relation to Antithetic each other. 158. There are properties also which may coexist in the same substance, yet in such a way that the more of the one the less of the other — these are called Sub-contraries. Thus “ bitter ” and “ sweet ” sub -contraries, are words which denote two sub-contrary spheres, since whatever object is the one is capable of being the other. The same object may be both at the same time, that is “ bitter-sweet,” and the more of the one the less of the other. Beauty and Utility are two more such sub-contrary spheres, since the same object may be both beautiful and useful, and for the most part that which is the most of the one is the least of the other. 159. In the case of both Correlative and Antithetic terms the one always implies the other, though in dif- ferent ways, and in both cases also one of the pair can never be fully understood without the other. 160. When terms are opposite, both in Quality and Quantity, they are said to be in a Conteadic- contradictory toey Opposition. Thus anv Positive term Terms - 42 LOGIC. — PART I. [chap. and its undistributed Negative have a Contradictory Opposition, as “ men,” and “ some not-men ; ” or “ some men,” and “ all not-men.” 161. From the foregoing discussions the following inferences may be drawn, which it will be useful to remember. • (1.) Of any term as subject the specific term next above it, as animal to man, or its matter, may be predi- cated, and so on through the subaltern genera and species up to. the summum genus. (2.) Of correlative terms : (a) If they are correlated in the same subject, if one is predicated of a subject the other must be also. (b) If they are correlatives in opposition subjects, the other cannot be. (3.) Of sub-contraries , both may be predicated of the same subject. (4.) Of contraries , both cannot be predicated of the same subject. (5.) Of contradictories , if one is not predicable of a subject the other must be. nj OF PKOPPSITIONS. — SECT. I. 43 CHAPTER H. OF PEOPOSITIONS. SECTION I. Of Judgments. 162. A judgment is an act of the mind affirming a relation between two objects of thought by judgments, means of their conceptions. Hence in every judgment there must be metaphysically two conceptions and the act affirming the relation. The conceptions are repre- sented physically by the terms Subject and Predicate, and the act affirming the relation by the Copula, and the judgment thus expressed is a Proposition. 163. It will be observed that this definition distin- guishes the judgment from the command, D isilLished the question, and the exclamation ; inasmuch Emam u at s ions n , s ’ as no one of them affirms a relation of agree- &c - ment or disagreement between the terms or concep- tions which are included in them. With these forms of speech Logic has nothing to do, except as we shall see by and by the question is sometimes to Question and be regarded as furnishing the matter upon Jud s ment - which a judgment is sought. Thus we say “ A is B ; ” this is a judgment. But in the question “is A, B?” we furnish the matter A and B, and ask for the copula ; or iii the other form “ what is A? ” we furnish the sub- ject and copula, and ask for the Predicate. 164. The terms of a Proposition are regarded as 44 LOGIC. — PART I. [CHAP. constituting its matter. Hence judgments may be in the same matter though differing in form, lVTnttpr and O O 7 Form or judg- as .A. is B, and B is A ; and A is not B, or B is not A ; are all in the same matter. But A is B, and A is 0, and B is 0, &c., are the same in form though differing in matter. 165. By the scope of a judgment we mean its com- prehensiveness in either continuous or discrete quantity, scope of judg- Thus “ one man is walking,” and “ two men ments. are walking,” differ in scope ; the latter being twice as large as the former. Again, “ men catch at straws,” and “ men catch at straws when they are drowning ,” differ in scope also ; the former being more comprehensive, since the latter limits “ the catch- ing at straws ” to some particular time or condition. 166. Judgments have been divided into three classes species of bi reference to the Belation which they aff judgments. firm to exist between the parts of the Judg- ment — Categoric, Conditional, and Disjunctive. 167. This Division corresponds with the three great fundamental relations of conceptions to one another — namely, the Substance to its Attributes or Properties, the Cause and its Effects, and the Whole and its Parts, which have been discussed in the preceding chajiter. 168. If the judgment simply affirms or denies an categorical. agreement between a Subject and a Predi- cate it is called Categorical , as A is B, or A is not B. 169. If the judgment affirms the reality of a Predi- conditionai. cate on the ground of the reality of the Sub- ject, the judgment is called Conditional , thus, If A is, B is. 170. But if the judgment affirms the reality of one Disjunctive. of two terms, on the ground that the other is not real, the judgment is called ^Disjunctive / thus, Either A or B is. If A is not B is. 171. But in both the Conditional and the Disjunc- c O nditi 0na i and tive the terms instead of being single cogni- ?iy ju more e thTn tions or conceptions are always categorical two terms. judgments. Thus If A is, B is,— is the same n.] OF PROPOSITIONS. SECT. I. 45 as if A is existing or is real , B is existing or real. And so with the Disjunctives, Either A or B is existing or real. 172. Now as the Conditional affirms its Predicate on condition that the subject is real, and the Hypothetical Disjunctive on the condition that it is not i ud s meut3 - real ; the two judgments unite in the point of indiffer- ence that they both affirm under a condition ( sub con- ditioner e’£ virodeaecad). They are sometimes considered as two species of Hypothetical judgments. 173. But as the members of both the Conditional and the Disjunctive jugments are, by them- Presuppose ca- selves considered, Categorical Judgments ; minis'* Juds ’ these judgments are never primary. The judgment itself, that is the subjective act, is as simple as in the Categoric Judgments ; but there must always have been a Categorical Judgment before either form of the Hypothetical. 174. We will therefore postpone the consideration of the Conditional and Disjunctive, until after we have examined the Categorical Judgments. 175. Categorical Judgments are of three categoricals of * . i & ® three kinds. kinds : (1.) In the first place they simply affirm or deny the Predicate of the Subject, as A is B, or A is not B ; or (2.) They compare the Subject with the Predicate, as A is greater than B, or A is equal to B. (3.) They represent the Subject and the Predicate as sustaining some numerical relation to each other, as A is one-half of B, or A is three times as much as B. 176. The first of these are Categoricals in Logical Quantity, which we will call Pure Categori- cals • the second class are Categoricals in Continuous Quantity, and are called Com- comparative. parative or Relative Judgments ; and the third are in Discrete Quantity, and in one of their forms of expres- sion constitute what are called Probable Judgments. 177. We will therefore consider these Judgments Pure Catego- ricals. Probable. 46 LOGIC. PART I. [CHAP. and the Propositions in which they are expressed in * the following order. — (1) Categoricals in Logical Quan- tity : (a) simple, (b) complex, (c) compound. — (2) Com- parative Judgments. — (3) Probable Judgments. — (4) Conditional ; — and (5) Disjunctive Judgments. SECTION II. Of the Terms in a Proposition. 178. Categorical Judgments have been defined as those which affirm or deny simply an agreement be- tween the Subject and Predicate. 179. Since a judgment necessarily implies two cog- two Terms, nitions, two terms must be contained ex- pressly or implicitly in every Proposition. In some cases there is no difficulty in finding them at once, as “ man is mortal .” But in other cases it is not obvious to the inexperienced at first glance what the terms really are. A little consideration however will always bring them to light. Thus if we say “ John loves,” we have for subject obviously “John ; ” we predicate of him “ loving ,” and the proposition is the same as “ John is loving .” “ God exists.” — Here existence is what we predicate of God, and we may say “ God is existing.” It is the same if we say “ there is a God ; ” “ God ” is still the subject though coming after the copula, and “ existence ” the predicate implied in the copula itself. Or again if we say “ it rains,” — “ rain ” is the subject, and that which we predicate of it is that it is falling, “ rain is falling.” 180. In English the subject is placed before the subject placed copula for the most part, yet not always or puia. necessarily. And it is otten necessary to know something of the connection of a proposition with others, or of the circumstances under which it was uttered, in order to decide which is the Subject and which the Predicate. But that is always Subject *of which we are speaking, and that is Predicate which is affirmed of it. n.] OF PROPOSITIONS. SECT. II. 47 181. We use the Subject chiefly with reference to the sphere of its conception, and the Predi- subject used cate with reference to its matter ; that is, in ? p f |h nce the subject we are thinking of the thing r f f e e r ence te toit3 itself in its substance, and in the predicate of maWer - its properties or what may be said of it. 182. The Subject may be either a noun or a verb in the infinitive mood, as “ man is mortal,” what may t J0 “ to err is human.” But for the most part Subject when the subject is a verb in the infinitive mood, it is placed after the copula in English, as “ It is hard to deny oneself.” Here “to deny oneself” is manifestly the subject, and that which is said of it is that “ it is hard.” 183. The Predicate of a Proposition may be either a noun denotative, or an adjective connota- What Predi . tive, or a verb in the infinitive mood ; — as cate - “ man is an animal,” “ man is mortal,” “ to be good is to be great.” 184. In perceiving an object we perceive it as a whole — substance and properties all com- objects P er- bined in one objective reality. But by a “holes, subsecpent process of reflection and analysis we come to separate it in our thoughts into substance and pro- perties, and each of these properties may be predicated of the object. We see the snow, we Analyze it into substance and properties, we think of whiteness and say the snow is white ; because that property is one of those which was contained in our very perception of the snow. 185. Any property which belongs thus to a logical whole, whether it be individual or universal, The formation may be predicated of that whole. of judgments. 186. When a property is ascribed to a subject in any judgment, the subject being taken as a Propositions t • , • -i T 5 i , 7 , 1 • t resolvable into distributed term, the judgment may be re- terms, solved into a cognition, as “ the snow is white,” into “ white snow.” 187. But when the property is ascribed to an un- 48 LOGIC. PAJJT I. [chap. determined part, the subject being undistributed, we into Terms may resolve the judgment into a term, mak- w *th Modais. j n g the Predicate an adjective, as “ some ti’ees are deciduous,” becomes “ deciduous trees.” By this process that which in the judgment was the pro- perty of a genus, becomes now the differentia of the species included in the genus, or next higher and com- prehending conception. Thus by every change in our form of expression, and by every assertion we make, we change our classification. We have all noticed such Examples. expressions as “ horse-chestnut ” and “ chest- nut-horse, ” “ brandy -peach ” and “ peach-brandy, ” “ sand paper ” and “ paper sand.” They illustrate the point under consideration — they invert the order of classification ; the noun, here as in all cases, denoting the genus, and the adjective, when not a mere explica- tive, the differentia of the intended species, which is really the subject of the predication. 188. Logically, therefore, the use of an adjective The Logical before a noun is indicative of a contained tives. species, as in the cases just given, “sand paper” and “paper sand” for instance — the former denoting a kind of paper as distinguished from other kinds, and the latter denoting a kind of sand distin- guished from other kinds of sand. SECTION III. Of the Copula. 189. The Copula is the formal Cause or constitutive copula. of the Judgment. The effect of the Copula in pure categorical judgments in Logical Quantity, is that it includes the subject in the sphere of the Predi- cate ; that is, supposing the Copula to be affirmative — and of affirmative Copulas only will we speak at the present. 190. Some Categoricals affirm an identity between in identical the Subject and the Predicate. These are judgments. called 'Identical Judgments. As “Victoria II.] OF PROPOSITIONS. SECT. H. 49 is the Queen of England,” “ common salt is chloride of sodium,” “ a triangle is a figure with three sides,” &c. 191. But in all other cases the Copula in pure Categoricals includes the Subject within the sphere of the Predicate ; and of course shows tegoricau 6 the a coincidence of sphere to the extent of the coincideucl re of comprehensiveness of the sphere of the Sub- andolAf m"t- ject, and an analogy between the spheres so far at least as the matter of the conception of the Pre- dicate extends— which is of course the Essentia of the Genus denoted by the Predicate. The simplest form of the Copula is— “ is,” or “ are.” As “ A is B.” “ All men are,” &c. &c. co F p° u ™ s of th8 192. But we sometimes have the verb “ to be ” in past or future tenses. “ Alexander was King of CoP ui a jn iq . Macedon,” — “ To-morrow will be Tuesday.” transkive Verb3 - For the most part there is no necessity of being more precise in expressing or analyzing the Copula. But if there is, the thing is easily done. “ Alexander is that which was King of Macedon ,” — “ To-morrow is that which will be Tuesday.” This destroys indeed the rhetorical beauty or structure of the sentence. But Logic takes no note of such things. 193. Again and more frequently still the Copula is merged in a transitive verb. As “Fortune copun in van. favors the brave,” “ Fortune is that which sitive Verbs - favors the brave.” — “ A wise King makes happy sub- jects,” “ A ivise King is that which makes happy subjects.” 191. Mistakes are often made in attempting to de- cide what is Copula and what belongs to the Mistakes to be terms in a Proposition, Thus if we say that avoided - “ heat is the cause of fluidity,” we must not suppose that “ heat ” and “ fluidity ” are the terms, all the rest being copula. The predicate in this case is not “ fluid- ity,” but the cognition expressed by the words “ the cause of fluidity.” Again, “ animal includes man.” Here it has been supposed that the predicate is in- cluded in the sphere of the subject. But the predicate 50 LOGIC. — PAKT I. [chap. is not “ man ” merely, but “ that which includes man ; ” that is, “ animal ” is the genus which includes “ man.” 195. In saying that the effect of the Copula in cate- gorical Propositions in Logical Quantity, is to include The Real and the subject in the sphere of the Predicate, I Bfect D of' s the do not mean to say that such is the intended copula. effect ; or that in forming the judgment the sphere of the Predicate is at all before the mind, or consciously in the thoughts. Thus when I say that “ man is an animal,” I am not thinking of animals / that is, I am not thinking of the class of objects to which I refer man. On the contrary, I use the predi- cate as a general term — with reference to its Essentia and not its sphere ; not the individuals contained in it are the objects of thought, but simply and only the necessary matter of the general conception. 196. blow this necessary matter of the general con- ception, as we have seen, is only the Essentia of the predicate used genus to which the subject is referred. It 8?iua r of e the does no t include the Differentia of any com- Genus. preheuded species, still less of course the individual properties Avhich distinguish one individual from another, and without which no conception of any one of the individuals included in the genus can be formed. 197. In the act of judging the Subject is distinctly and conspicuously before the mind as a sphere, and the The subject sphere of the Predicate is only indirectly ““ s ‘ s jn° n the an d remotely before the mind. Hence it is thoughts. the sphere of the subject and the matter of the predicate between which the mind consciously and intentionally affirms the agreement. The effect, how- ever, is that the subject is of necessity thereby in- cluded in the sphere of the predicate as a proximate genus. 198. Since the copula in pure categorical judgments Pure catego- includes the subject within a higher sphere, classification. “ or refers it to a comprehending class, the n.] OF PROPOSITIONS. — sect. m. 5] principles of classification are necessarily implied in the investigation of categorical Propositions. As we have already defined the principal terms used in Classification, we shall need to resume the sub- ject only for the purpose of stating its general princi- ples, so far as they are implied in or requisite for the purposes of Logic. 199. When there are more than the three grades, Genus, Species, and Individual, the same p rjn( , iple ofcias- principle holds in the subordination of to'mjie'thcSfthree classes. Thus the matter contained in the grades - conception of the Genus = Essentia, “ Species = Ess. + 1st Differentia. 1st Sub-species = Ess. + 1st Diff. + 2d Differentia. 2d Sub-species = Ess. + 1st + 2d + 3d Differentia. “ Individual = Ess. + 1st + 2d + 3d Dif. + Pecu- liarities. 200. But besides this, each class will have proper- ties, and each individual accidents, which Ne cessaryand are not included in the above analysis of the matter of the conceptions ; what is named tions - above is necessarily included in the conception. All else is merely contingent and accidental. 201. It will appear from the above statement of subordinate spheres and their matter, that comprehensive- the more comprehensive of individuals the “teES les comprehensive of matter any conception ofMatter - will be ; and vice versa , the more comprehensive of matter the less comprehensive of individuals. 202. As the principles of classification are founded in the nature and truth of things, the Differ- entia of a species must therefore always sus- Differentia to tain a certain relation to the Essentia of any s “ entld ' genus under which it can be included. Thus the Dif- ferentia of “ wise ” and “ foolish,” of “ pious,” of “ humane,” &c., can be predicated only upon the Es- sentia of “ man,” as a genus. We can predicate “right” and “wrong” in a moral sense only of the acts that proceed from freedom of choice, and having 52 LOGIC. PART I. [chap. this [freedom] as an essentia. We can predicate “hard,” “soft,” “heavy,” “light,” &c., &c., only of material things. 203. When a word is used to denote a class, we use it without the article in English, as “ man,” &c. We words denot- do not say that “ an animal ” denotes merely wftho U ^the s ar d - ^ Ie essentia — that which is essential to all tide. animals. For when the word is thus used with the article it denotes some existing animal with- out denoting precisely which perhaps, and consequently implies the differentia and accidents of an individual also. But the word “ animal ” when used simply and without the article, whether definite or indefinite, im- plies merely that which is essential to the animal nature, and by no means all that is found in any exist- ing animal. We can form no image in our minds representing merely “ animal ; ” the image must be of an animal — some animal already existing, or which might possibly exist — and consequently the image must contain in it more than is represented by the generic term. 204. The words “ the animal ” always refer to some individual animal before the mind, and consequently t imply the individual properties necessary to articles “ the ” the conception of the individual referred to. used with the ^ An animal ,” used as a subject, as also subject. « animals ” in the plural, always implies something more than the mere essentia of the genus “animal,” since all animals and each animal must have some system of nutrition for instance ; and the essentia of such a system is always implied when we speak of “ an animal,” or of “ all animals.” But yet as all animals have not the same systems, no one individual system can be included in the conception. But when we use with the pre- the word “an animal ” as a Predicate, the dicate. matter of the conception is precisely the same as if we had used “ animal ” without the article, as “ man is an animal ” is merely ascribing to man the essentia of animal nature, just as when we say “ man is animal.” n.] OF PROPOSITIONS. SECT. IV. 53 205. We have thus far been speaking of the classi- fications that are based upon those insepara- , • j?i-i X i'i ,i , Conspicuous Die properties ot o meets which are the most properties not A “ i , • , the only basis conspicuous, hint such properties are not of ciassifica- always or the only ground of classifications. In classifications, for the purposes of the Natural Sciences, a very different principle is often found the most conducive to the end in view. 206. The classifications of the Natural Sciences or Natural Genera or Species, are for the most ^ part based on properties which are not only turafciassifid- inseparable, hut also incapable of different degrees of intensity — of a more and a less — thus “ man is biped.” We have no such expressions as “more biped,” “ less biped,” &c. So it is also with such words as “ quadruped,” “ winged,” “ dogtoothed,” “ hoofed, ” — and the words “ mental,” “ material,” “ eternal,” “ infinite,” &c. They have no comparatives. It is the same with the mathematical differentia, “ tri- angular,” “ quadrilateral,” “ circular,” “ elliptical,” “ conical,” &c. 207. But besides this it is obvious that any mode or separable accident whatever, may be the L0 gicai ciassi- ground or principle of a mere transient fication3 - classification. Thus we may classify the inhabitants of a city into sick and well — those in a room as those that are sitting, and those that are standing, &c. The mode or accident which serves as differentia to these transient classifications must, however, be such that the terms denoting its presence and absence cannot be both predicated of any one individual at the same mo- ment of time and in the same respect. 208. It will follow from what has been said, that if any individual contains the Differentia of individuals any species, it must be included in that spe- ci e udeTm y sp2- cies ; and if either individual or species con- cies - tains the Essentia of any genus, it must be contained in that genus. The Differentia are essential to the species, and the Peculiarities to the individual. The LOGIC. — PAKT I. 54 [chap. peculiarities also are tlie differentia of the indivi- dual. 209. Hence every assertion we make by the neces- sary laws of thought or of affirmation, makes a classifi- cation. It refers the subject to a class whose classify their essentia or dinerentia, as we may regard the •class, a genus, or a species, is denoted by the predicate. We say that “this man is a farmer;” we refer him to the class of farmers. We say “the snow is falling we refer it to a class of things whose dif- ferentia or essentia is denoted by the state expressed by the predicate “ falling.” We say “ God is good ;” we refer Him to the class of objects which are charac- terized by the attribute or property of goodness. We say “ the wicked will be punished ; ” we refer them to a class, whose only point or property in common it may be, is the doom that is declared by the predi- cate to await them ; and yet this point or property is made, pro hac vice , the ground or basis of a classifi- cation. 210. But by the very nature of the case we cannot make an assertion without referring the subject of which we speak to a class ; and every time we menf Classifies speak of it in a different connection, to a new class — the differentia of which is ex- pressed by the predicate we use. If we call a man, brave or a coward, honest or a knave, wise or ignorant, good or bad, polite or rude ; — if we say of him, he is standing or walking, sitting or sleeping, all these classes are called up before the mind, and every new assertion concerning any subject of which we are speaking, like a fresh turn of the kaleidescope, groups and classifies all things anew. And upon this classification depends alike the cogency of an argument, the merriment of humor, and the keen relish of wit. Even a dicrous cTaAfi- jest is but a ludicrous classification. A sar- casm does no more than to class one with per- sons and things that are contemptible, and a bad name, a disgraceful epithet, a conviction of wrong, brings n.] OF PROPOSITIONS. SECT. IV. 55 upon one only the differentia of the species to which he is thus referred. SECTION IV. Of the Adequacy of Propositions. 211. Let us now consider some of the principles and laws of predication with reference to the adequacy of Propositions, as expressions of the judgments which they represent. 212. A Proposition for the purposes of Logic should be like the testimony given under the Com- Adequacy of mon Law oath in civil suits, “ the truth , the Pr °p° sitions - lohole truth , and nothing hut the truth A (l.j Of any object or class of objects, its Name and De- uame and its definition may ot course be cated. predicated. (2.) Synonymous terms may also always be predi- cated of each other. But any two or more synonymous names, which are not mere individual names, Terms - and which may be predicated of the same object of thought, must denote Alternate Conceptions of that object, and are not likely to be predicable of each other. (3.) Of any general term, that is, a term denoting a genus, we may predicate any term denoting of a Genus, the essentia of the genus, or any one of the essentia in an abstract term, or by a connotative adjective. (1.) Of the Species we may in the same way predi- cate not only the Essentia of any higher and Essen tia of comprehending genus, but also its own Dif- Species - ferentia. (5.) Of any individual we may also in the like way predicate the Essentia of any genus in«which of the Indi it is included, the differentia of the species vidual - to which it belongs, and the peculiarities of the indi- vidual (inseparable accidents). (6.) Whatever may be predicated of each individual 56 LOGIC. PAHT I. [chap of individuals in a class, may be predicated of the class as a whole. Thus if each individual man has two feet, then “ man is a two-footed order of beings.” 213. Besides the above there are always properties Accidental pro- which are not regarded as either Essentia or labilT pre 1 Differentia, as well as separable accidents which constitute the various modes or conditions of being, that may be predicated of any subject when- ever we have any sufficient reason to affirm them of it. 211. If the subject denotes any real or possible predicatea of tiling, then the Predicate may be a positive bie subjects. term and denotes some property that is pre- dicated of it. For if it be a possible or a real thing, we can say “ it is possible,” “ it is real.” But if it be an impossible thing its predicate must be a negative term, since no property or mode can exist without its sub- stance ; thus if the conception denoted by the subject A be an impossibility, we can say that “ it is impossi- sible.” 215. Whenever a given predicate is to be used Alternate con- that Alternate Conception of the subject ject3°' ls dS sub should be used, which represents it by the matter on account of which it is contained in the genus denoted by the Predicate. 216. Alternate Conceptions represent the same ob- ject by different matter. But the subject is included in the sphere of the Predicate, only because it has the properties which constitute the Essentia of the genus Examples. denoted by the Predicate. Thus, Washing- ton as General commanded the American Army ; gave Commissions to the Officers in the Army and Navy, &c. But as President he presided over his Cabinet, nomi- nated Civil Officers, sent Messages to Congress, pos- sessed the Veto" Power. But it would be logically faulty to say, “ the American Commander ate his breakfast,” for instance ; for as Commander he did not eat, but it was simply as George Washington that he ate. So it should not be said of an act in his military n.] OF PROPOSITIONS. SECT. IV. 57 command, — the President did it ; for as President he did not do it, but only as Commander did he do it. Nor should we say George Washington vetoed this bill, for not as George Washington but as President Washington did he possess the veto power, or exer- cise it. 217. Words denoting titles and ranks are however but Alternate Conceptions of the individuals Titles, to Avhom they are given, and custom has so far not only sanctioned, but required the use of a man’s title even when we are speaking of his personal acts and proper- ties, that a disregard of the usage would be regarded as discourteous if not as intended for an insult. 218. The subject of any proposition should always be so comprehensive as to include all the comprehen individuals to which the predicate used m subject. the proposition is applicable. 219. This condition is often violated for rhetorical purposes ; nor does its violation necessarily Rhetorical involve an error in the conclusion, though it violations, renders us liable to fall into one. Thus we say “ the Papists hold to the supremacy of the Pope,” which is correct. But if we say “ the Papists believe in the Divinity of Christ,” we say what is indeed true ; but as other Christians believe in that dogma also, our sub- ject is of too narrow a comprehension, and suggests the inference that a belief in the Divinity of Christ is one of the differentia of the Papists. Although there- fore there may be cases in which the violation of this rule does no harm, yet unless there is something in the context or iii the circumstances under which the rule is violated to guard against the error, the rule must be strictly adhered to, or our proposition does not state “ the whole truth.” * * I have before me a case in point. In an infidel author, whom I need not name, there is an accumulation of statements designed to show that the Scriptures, as we now have them , cannot be relied upon as inspired. He says of the Scriptures (his subject), “ the oldest manuscript does not reach back to within centuries of the origin which the Scriptures claim for themselves. 3 * 58 LOGIC. PART I. [CHAP. 220. When the Predicate is a general term and not a mere connotative of some accident of the subject, the pm erties of accidents of the subject are not included bj the subject in- means of the proposition in the matter of the Predicate. Thus when we say, “ the rich are anxious,” we take no notice of the color, size, or any other accident of the persons included in the word “ rich.” If we say “ John is sick,” this im- separai i 5 Ac P^es n °thi n g concerning his accidents, and cident a a ra 0 r the no connection of the Predicate with them ; eluded f n ° the the Predicate is affirmed of what is essential to the subject as such and not of any of its accidents — that is, what is essential to it as a subject, and not what is necessary to its reality.* 221. But whatever term is predicable at all of either individual species or genus, must be predicable of the individual or individuals (if the subject be must include either a specific or generic term), as contam- matter of the mg in this conception whatever is necessary to their existence as individuals, species, or genus as the case may be. 222. Thus if we say “ This mountain has existed since the creation of the world,” we are understood to say not merely that the matter of which it is composed has existed so long, but that that matter has existed not It is written in a letter entirely different, now divided into words, surrounded by points indicative of the meaning and punctuation of words, divided up into chapters and verses, and the manuscripts abounding in various readings, interpretations, omissions, and corruptions.” But the author does not state, and the unlearned reader does not know, that precisely the same thing could he predicated of the text of Herodotus, Thucydides, Livy, Tacitus, and in fact of every ancient author, and yet no one ever doubted the genuineness of the works which are received under those names on that account. If he had made his subject as comprehensive as the Predicate would allow, and included these works with the Scriptures in his Proposi- tion, it would have destroyed the effect which he designed to produce. * The scholastic writers expressed this distinction by the use of the abla- tive pronoun qua. The subject qua subject — this expression is also used to distinguish between the different predicates which any object of thought may have when represented by its Alternate conceptions. Thus Washington qua President possessed the Veto Power, qua Commander-in-Chief gave Commissions to the Officers of the Army and Navy. n.] OF PROPOSITIONS. SECT. Y. 59 only as mountain [the species], but also as this indi- vidual mountain with its inseparable accidents. So when we say “ men are immortal,” we mean not only that what is essential to humanity, but also whatever is distinctive of each individual as an inseparable acci- dent is included in the immortality ; so that men will exist there individually, distinct and distinguished by the same inseparable accidents of personality as here. 223. For rhetorical purposes this rule also is often violated. In all those figures of speech called Rhetorical „ i0 . Metaphor, Trope, &c., these rules of Logic lat ‘ 0QS - are departed from for rhetorical purposes. It becomes necessary therefore to consider in all cases whether the word used is the real subject, or merely some figure of speech used in its stead. SECTION V. Of the Quantity of Propositions. 221. The scope of the judgment is not important to its deductive force or position in a syllogism, since whether it includes much or little in a numerical esti- mate it goes in for what it is. 225. But the Logical Quantity is of the utmost importance, *since that indicates its relative importance of amount and determines the laws of predica - Terms, tion and deduction. 226. Logical Quantity in its broadest sense is of three varieties, — (1) comprehensive ; (2) in- Three Dimen- tensive ; and (3) protensive. Quantity. (1.) Comprehensive, or Extensive Quantity, is the comprehensiveness of the sphere of the con- comprehen- ception. (2.) Intensive Quantity is measured by the amount of matter in the conception. intensive. (3.) But we have also a Protensive Quantity brought in by the consideration that the facts included protensive. 60 LOGIC. PAKT I. [chap. in the sphere of any conception are not always actual facts at the same moment of time. If we say “ all men are mortal,” we mean to include in our category not only all men now living, hut all who have lived in time past or will live in time to come — all beings that are men. But a predicate may be ascribed to a subject at one time, or as true of it at some times, which could not be ascribed to it with truth at others. After having thus named this variety of Quantity, we shall leave it out of consideration for the present, and proceed to consider Comprehensive or Extensive Quantity in reference to judgments. 227. In reference to the object now before us Inten- intens.ve Quan sive quantity is unimportant in itself, and is tity determined ^ i hensive^ ompre a * wa y s determined by tlie Comprehensive quantity being always in the inverse ratio sumedasabso^ 1° ib The Protensive quantity is assumed lute - to be absolute ; that is, to include all time — and the same as if it were expressed by the word “ always ,” as “ All A is always B ; ” “ Men are always mortal.” 228. There are three dimensions of Comprehensive Three pimen- Quantity, according as the subject of a judg- prehensive om " ment may be ; — (1) an individual ; (2) several individuals considered as a part of a class, not denoted by any term which constitutes them a species within that class ; or (3) several individuals con- sidered as constituting a class, species, or genus. 229. The first class are called Individual judg- ments ; the second Particular j udgments ; and the third are called Universal. 230. It is obvious that on these principles of divi- sion, and in reference to Quantity, there can be but three Species ; for a judgment must be either of one , of some, or of all. If we say that, “ some ” may in- clude many or only a few ; nearly all or only two ; we do not thereby constitute a Logical whole. n.] OF PROPOSITIONS. — SECT. VD. . 61 SECTION VI. Of the Quality of Judgments. 231. The Copula of a Judgment may be either (1) affirmative, or (2) negative; that is, we .Three Qunii. may say A (is) B, or A (is not ) B. The first t!on S of FropOM ' A is B, includes A in the sphere of B, and is an Affirma- tive judgment ; the second A is not B, excludes A from the sphere of B, and is a Negative judgment. But B and not-B are antithetic terms. They denote spheres which are the complements of each other. Hence if A is not in the sphere of B, it is in the sphere of non-B ; and we may say that A is non-B. This is called (3) an Indefinite judgment. Hence three varieties in refer- ence to Quality — 1st, includes the subject in the sphere of the Predicate ; 2d, excludes the subject from the sphere of the Predicate ; the 3d, includes the subject in the Negative sphere connoted by the Predicate of the Affirmative. It is obvious that in reference to Quality there can be no other species of judgments than these three. SECTION VII. Of the Modality of Judgments. 232. In reference to the certainty of the Judgment, we may have three kinds of judgments Three Modes Problematical , Assertive , and Necessary , or ofPro SS^ lons - Ajpodictical. This is called the Modality of Judg- ments. (1.) The Differentia of the Problematical is that they merely affirm that the subject may be Problematical, in the category of the Predicate, or the possibility of the Proposition being true. (2.) The second is called Assertive ; — they affirm the truth of the judgment as a matter of fact and reality. Assertive. 62 LOGIC. PART I. [CRAP. (3.) The third are called Necessary or Apodictical ; Necessary. they affirm that the truth could not be other- wise — as when we say “ two and two make four.” SECTION VIII. Of the Four Cardinal Propositions. 233. Combining Quantity, Quality, and Modality, Twenty-seven we have the following table of Categoric 'ntnrmripfl 1 _ ^ O Categorical Judgments. Judgments. Individual Categoric Particular Universal Affirmative - Negative Indefinite Affirmative - Negative Indefinite Affirmative - Negative Indefinite Problematic. Assertive. Apodictic. Problematic. Assertive. Apodictic. Problematic. Assertive. Apodictic. Problematic. Assertive. Apodictic. Problematic. Assertive. Apodictic. Problematic Assertive. Apodictic. Problematic. Assertive. Apodictic. Problematic. Assertive. Apodictic. Problematic. Assertive. Apodictic. II.] OF PROPOSITIONS. SECT. VIII. 63 234. But as Problematical judgments never enter as Premises into any Argument merely as Problema- tical, we may omit them from any further consideration at present. 235. Again the difference between the Assertive and the Apodictic or Necessary has no effect upon the general principles ot deduction, dais reduced to If a Proposition be true, that is all that is required, the modality of its truth being wholly unim- portant. We may take the Assertive therefore for all our purposes, neglecting the difference between that and the Necessary. 236. But again, the Negative and the Indefinite sub-species are the same so far as all the laws ancl purposes oi deduction are con- nties reduced to cerned. For since the Positive and the Negative Spheres are complements of each other, to exclude from the Positive (which is the differentia of the Negative) is the same as the inclusion in the Negative sphere (which is the differentia of the Inde- finite). 237. Again in respect to Quantity the Individual and the Universal are alike, in that the sub- ject (in which alone is found, the differentia Quantities 7e- of Quantity) is in both of them a logical duct ' d t0 t "°- whole. Whether an individual or a class, it is imma- terial for all the purposes of deduction, so long as it is a logical whole. Hence we consider Individual judg- ments the same as Universal for all the purposes of deduction. 238. But a Universal Judgment may be either Negative or Affirmative, and so likewise may a Particular judgment. We have only Q?arny tlty com. four cardinal judgments which we need con- ine ' sider. These are Universal Affirmative, Universal Negative, Particular Affirmative, and Particular Negative. These may be considered the four cardinal Propositions in Logical Quantity. 239. As these occur so often, writers on Logic have LOGIC. — PART I. 64 [chap. generally designated them by the first four vowels of the Alphabet. Thus U. A. All A is B, is represented by A U. IST. No A is B “ “ “ E P. A. Some A is B is “ “ I P. N. Some A is not Bis “ “ O These are all Categorical, all Assertive, and differ only in Quantity and Quality. SECTION IX. Of the Distribution of Terms. 240. When a term is taken into the scope of a judgment as a logical whole, it is said to be distributed in the judgment ; hut if it does not enter in as" a logical whole, it is said to be undistributed in the judgment. 241. It is immaterial whether the part of the whole undistributed be a large or small part, “ many ” or u few ; ” and these words therefore indicate an undis- tributed term as well as “ some.” 242. So also we may say “ some,” when we mean “ some at least and possibly all ; ” or when we mean “ some hut not the whole.” But the undistributed term as such indicates nothing of the kind, and if any such modification of the term is intended, the Proposi- tion expressing it becomes a compound one [either copulative or discretive], expressing two judgments in fact and not one merely. 243. The conception represented by an undis- tributed term is not a logical whole, and the term itself Not Logical must necessarily be a general one. But if wholes. the term denotes a part of the whole, con- ceived as a species , it is no longer undistributed ; for the part conceived as a species becomes by the very fact of its being so conceived a logical whole. 244. Hence the word “ some” though generally n.] OF PROPOSITIONS. SECT. IX. 65 used to denote an undistributed term in the subject, is not an infallible indication that the term is undis- tributed. Thus in the illustration given b j Mistake G f the Sir William Hamilton, “ some stars are all f orceof “ some ” planets ” (all the planets are stars). But one must have a conception of those stars as a class, which are planets, and as distinguished by the differentia of planets, or he could not say that they were all the planets that there are among the stars. If therefore there ever was, or ever should be such a Proposition, except when got up for the purpose of seeing what one can do, the subject must be regarded as distributed, notwithstanding the usual signs of an undistributed term. 215. There are three ways of ascertaining whether a term is distributed or used distributively Three ways . ... . \ -r-v . i d of distribution m any proposition or not. — (1) By the nature of terms, of the term ; (2) by a modal sign ; and (3) by its position. 446. A term is distributed by its nature when it is used to denote any individual object, such By the nature ,r l J c 7 of the term. as j^roper names oi persons, places, &c. Terms are distributed by signs in three By signs, ways. 24:7. (1.) The particles “ the,” “ this” “ that” by pointing out a particular individual in a class, .. xhe> „ “ t h,v of which the predicate is affirmed, make the and “ that -” term distributed ; since the force of these particles is to include only the one of the individuals comprehended within the genus thus pointed out in the scope of the j udgment. 248. (2.) Such words as “ all,” “ every” &c., dis- tribute the terms ; in fact they are the most <. A1I „ .. eve , usual signs of a distributed term used in the ry ” &c - subject of a Proposition. 249. “ All ” of course clearly and expressly includes all of the individuals included in any genus within the scope of the judgment. 250. As “ all,” so also “ every ” indicates a dis- tributed term, since it necessarily includes all the indi- 66 LOGIC. PAJRT I. [CHAP. viduals of the logical whole within the scope of the Difference -be J udgment. All is indeed sometimes a col- and^Every 1 ”” ^ ec ^ tve ra ^ ier than a distributive sign. Thus ' Lry if we say “ all these trees make a fine shade,” it is most likely that we mean to take “ trees ” as a collective term rather than as a general term ; that we have predicated of them taken together as a collective whole, what could not be predicated of each of them individually. This difference is unimportant to the purposes now before us, but it will be seen by and by that it lies at the bottom of a most serious fallacy. 251. (3.) Two pronouns, as “ he who,” and “ they two pronouns that,” are clearly indicative of a distributed distribute the , ,, 7 u 7 . . subject. subject, as “ he who transgresses the law commits a sin,” — “ who so transgresses the law com- mits sin ; ” these forms of Propositions clearly include the whole class denoted by the specific term, whose differentia is given in the words “ transgresses the law,” in the scope of the judgment. 252. (4.) Again, we have another class of signs, which, although they do not cause the general term to be included as a whole in the scope of the judgment, constitute it what is called a distributed term. These “ Each” and terms are such as “ each” “ any • ” for while “Any.” py t] ie ; r force they apply the predicate of the proposition to one individual of a class only, and sometimes in such a way as that it can be applied to one only at the same time, yet they imply that before any actual predication it is applicable to them all and every one of them taken individually, although it may cease to be so the moment it has been predicated of one. Thus if we say of a young lady, “ any man would marry her ; ” — <£ man ” must be taken as a dis- tributed term, though it is not supposed that more than one man will actually marry her. 253. (5.) The indefinite article “ a” also sometimes The indefinite distributes the subject in the same way, thus "a.” u a poison destroys life ; ” that is, “ any poi- son,” or “ all poisons destroy life.” II.] OF PROPOSITIONS. SECT. IX. 67 254. In all Negative Propositions the Predicate is taken as a Whole.* The differentia [charac- By position the teristic] of Negatives is that they exclude Negate judg- the subject from the sphere of the Predicate. ments - They do not merely partly exclude it, they may exclude merely a part of the subject, but they must exclude the subject whether §s a whole or as a part from the whole of the Predicate, “ No vice is commendable.” If now among all the things that are commendable one vice can be found, the Proposition is not true. Hence it distributes the Predicate or speaks of it as a whole. Or if we say “ some men are not brave,” which is a Proposition in O, the same is found to be the case with the Predicate. We here mean that among all the things that are “ brave,” the “ some men,” are not included. 255. But the Affirmatives do not necessarily dis- tribute the Predicate. If I say that A is B, all that is affirmed thereby is that A is in B, not rm dktlfbute or A is some part of JB. A is included, m the sphere of B. But B may include much besides A. “ Men are mortal ; ” but men are not the only things that are mortal. The sphere of “ mortal ” is not coin- cident and identical with that of “ man,”- — it is much more comprehensive. Hence in A we do not speak * Sir William Hamilton in his new method of Notation, insists that there may be Negative Judgments with undistributed Predicates. But besides the proof given in the text of the position there taken, we may say further that his doctrine directly contradicts the old axiom, “ it is impossible for a thing to be and not to be at the same time.” For suppose S is not P and P not taken as a whole, the sphere of P as of any term is determined by its matter ; and the subject S is included in it if it possesses the matter of P and excluded from it if it does not. Now suppose that S has not the matter of that part of P which we take into the scope of our judgment, when we say S is not P, and the judgment S is not P is true. But suppose it has the matter of the part of P, not taken into the scope of the Negative judgment, and then we have S is P ; — that is, S is not P, S is P, and P is P, and P_is not P. 68 LOGIC. — PART I. [CHAP. of the predicate as a whole. The predicate is undis- tributed. 256. For the same reason we do not speak of the Predicate as a whole in I. “ Some men are black ; ” we do not speak of “ black things ” as an entire class, comprehending no more than the “ some men ” of whom we were speaking. # 257. Hence the following Rules for the Distribution Rules. of Terms by position. 1. All universal Propositions distribute the Subject. 2. All negative Propositions distribute the Predi- cate. Or more definitely : A distributes the subject. E “ both the subject and predicate. I “ neither. O “ the predicate only. 258. Various devices have been resorted to, to repre- iiiustrations. sent by some diagram these various Judg- ments or Propositions. Many of them are ingenious and useful, but all are liable to misapprehension, aris- ing from the nature of the case and the difficulty of representing any mere conception by actual forms. The following is perhaps as good as any that can be given. It is substantially Euler’s : — A. — All S is P, in which case one circle S is included wholly in the other as P, but does not oc- cupy the whole of its sphere. E. — Ho S is P, in which case one circle S is wholly excluded from the whole of the other P. I.— Some S is P, in which case we have two incomplete circles S and P, cutting each other so as to have a part x common to both. II.] OF PROPOSITIONS. SECT. X. 69 O. — Some S is not P, in which we have an incomplete circle, S not included in any part of the complete circle P. 259. One difficulty attending the above diagrams is, that they represent in A and I the sub- Dan „ er of ject as constituting a definite part of the using them - Predicate, or occupying an ascertained portion of its sphere, whereas the judgment does not so represent the spheres. 260. It will be noticed that in A when the sphere of S becomes so large as to fill up and occupy . The predicate the whole of P, the Predicate has become d?stfi*™d Uve9 distributed and is taken as a whole. The spheres are then coincident and identical. SECTION X. Of Immediate Inference. The form Judgments expressed by the Proposi- tions A, E, I and O, which we have just examined, have certain relations to each other which it is impor- tant to examine. 261. Such is the relation of judgments to each other, that no judgment can be true without Every Judg . implying the truth of some other judgment, “ n e o n ther. implie3 either in the same or in the opposite Quality. 262. These judgments which are thus inferred from others, as from All A is B, we infer that Irnme <]iate in- some A is B, and that “ some A is not B ” ference - is not true, are called by Ivant “ Syllogisms of the Un- derstanding.” I shall prefer, however, to adopt the more English name of Immediate Inference. 263. I call it “ immediate ” because the inference or conclusion is drawn without the interven- why so called, tion of that medium or middle term, which is always necessary in the complete Syllogism, as will be seen hereafter, 70 LOGIC. PAKT I. [chap. 264. By Immediate Inferences then I mean all those inferences or conclusions that can he drawn from any Proposition without the intervention of any other matter or term than was given in the Proposition itself. And as it will be the most convenient to point out these Inferences as we examine the Opposition, Permutation, and Conversion of Propositions (since it is by these means that the Inference is made), I will keep them in mind as a subordinate object while discussing these topics. I. Of the Opposition of Judgments. 265. (1.) A and E being Universals, I and O are subalterns. called in reference to A and E their Subal- terns. I being subaltern to A and O to E. (2.) A and E in relation to each other are Con- Contraries. tVCLVicS. sub-contraries. (3.) I and O are Sub-contraries. 266. (4.) E and I as likewise A and O are Contra- contradictories. clictories to each other. 267. If now a Universal be true its Subaltern must be true also. If All A is B, Some A is B, is true as an inference from Immediate Inference, and if the Subaltern subalterns. be true the Universal as a Problematical Judgment is true also, as an Immediate Inference ; that is, If Some A is B, all A may be B. 268. Of the Contrmdes only one can be true in the From contraries, same matter, though both may be false. Hence If A is true E is false as an Immediate Infer- ence, and vice versa; that is, Ho A is B, then All A is B is untrue, although of course Some A may be B. 269. Of Contradictories both cannot be true or false From contra- in the same matter. Hence If E is false I must be true, and vice versa. If A be false O must be true, and if I be false E must be true, and if O be false A must be true as Immediate Infer- ence. II.] OF PROPOSITIONS. SECT. X. 71 270. The Sub-contraries may both be true in the same matter. If some A is B, some A is Sub-contraries cannot both be false. A contraries E co C '// A> m P, HO- VI, -V° H C“ S p, S s> •o ~ E? n 2 o, 3 2 3 c° % t= 3 I sub-contraries 0 not B, may also be true. 271. But the Sub-contraries cannot both be false in the same matter. 272. We may represent the rela- tion of these four Judgments by the following diagram, in which it will appear that the sub-contrary of any subaltern is the contradictory of its Universal ; and if therefore two con- tradictories cannot be false at the same time, then a fortiori the two sub-contraries cannot. 273. The subject in each of the sub-contraries is undistributed, and the more nearly it ap- Rat ioofQua. proaches to the Universal in one quality in llty - any case, so much the more nearly does it approach it in the other. Thus the more nearly Some A is B is to All A is B, so the more nearly is Some A is not B to No A is B. II. Of Contra-Position or Permutation of Quality. 274. The same judgment may be stated in either quality, Affirmative or Negative as we choose, by means of Negative terms and copulas. 275. In reference to this fact we will call the first form in which a judgment is stated, or rather that form which states the judgment in the Proposition of the same quality as the judgment itself, the JEx- posita / and that form of the Proposition contra‘pos!ta which states it in the other quality, the Con- 1 ermutatIon - tra-posita ; and the change itself we call Contraposi- tion or Permutation. 276. Thus let us suppose in the first place that we have the Negative Proposition “ A is not B,” illustration, or “ No A is B.” In this case we have simply ex- cluded A from the sphere of B, and thus denied of it the matter of the conception B. But since the Negative 72 LOGIC. — PAKT I. [chap. of B or non-B is the complementary sphere of B, what- ever is not in B is in non-B, and consequently whatever has not the Essentia of B must have that (if there is any) of non-B. Hence “ A is not B ” is equivalent to “ A is non-B,” — “ non-B ” being a Negative term ; and But A is non-B is an Affirmative Proposition with a Negative Predicate. 277. Hence from a Negative Exposita with an Affirmative Predicate we may always permute into Contra-posita, by substituting for the Positive Predi- cate its Privative or Negative, and dropping the Nega- tive from the Copula. Thus “ if man is not wise,” he is “ -imwise ; ” if he is “ not free ” he is a u slave.” 278. But if the Predicate is a Negative or a Priva- Negative or tive term in the Exposita, we have to substi- dicate' ve rL tute for it its Affirmative, and drop the Negative from the Copula also. Thus we may say that “ Centaurs are not impossible,” then “ Centaurs are possible.” 279. The same holds true of the subject when the Predicate denotes a reality and not a possible only. when true of We may substitute for the subject its anti- the subject. tlietic in the opposite Quality by dropping the negative from the copula, always remembering that the term substituted is an undistributed term. 280. But since no property or mode can exist or be real without its substance, the Predicate may denote a property which has no existence. In that case there can be no Contra-posita by means of the negative sub- ject ; thus if one should say “ horses are not Centaurs,” we could not therefore say “ some not-liorses are Cen- taurs,” for this would imply the reality of “ Centaurs.” 281. But if the Predicate be a reality at all we may always say, if A is not B some non-A is B. Let “ holy ” be the Predicate and “ man ” the Sub- uiustration. ject, “ no man is holy,” or in the other form “ all men are not holy.” If now we connect the negative with the subject “ no-man,” this is no longer the same term taken in a n.] OF PROPOSITIONS. SECT. X. 73 different sense, but it is a totally distinct term. It in- cludes nothing that was included in the first term “ man” and precisely all that was not included in it. It includes whatever is not “ man.” Of these things manifestly not all are holy, although if there be such a thing as holiness, and if it do not belong to man, it must belong to something that is not man. Hence we may say “ some not-man is holy.” 282. If, however, we connect the negative with “ holy,” and say “ All men are not-holy or unholy” the term represents an entirely different cognition from the term “ holy.” But the new term must be regarded as undistributed, for we do not mean to say that man is all that is “ not holy,” or that whatever is “ not holy ” is “ man.” And yet if our first Proposition is true “ some thing not holy ” is “ man.” 283. In the use of intelligible signs we may use the Privative instead of the Negative in the Pr ivatLve used Predicate, since the nature of the subject t f °™ S e th e N pre- limits the range of the thought or judg- dicate - ment to the proximate genus. Thus for “ man is not holy,” we may substitute the privative Predicate, and say “man is unholy ; ” the subject “man” limiting the scope of the judgment to the proximate genus to which the capacity for holiness is an essentia, and also a differentia in the next higher subaltern genus. 281. But when we change the Quality by changing the subject we may not use the Privative, B utnoUnthe since there can be no a priori necessity that Subject - # the Predicate should be predicable of some one indi- vidual in the proximate genus to the subject, or in any genus below the summum or absolute whole of realities. 285. If the Exposita be Affirmative we change the quality by means of two negatives — two Perrnu tation negatives in English making an affirmative. ° f Affirmatives. 286. This change of the quality of Affirmatives by means of two negatives may be effected in three ways. . 4 74 LOGIC. — PART I. [CHAP. (1.) With two negative copulas, as “ there is no A ist case. that is not B,” consequently All A is B. Thus “ there is no man without [that has not\ sin,” or “ all men are sinners.” (2.) The second form is w T ith a negative copula and 2 ti case. a negative Predicate. “ All A is not non-B,” or “ ISTo A is non-B ; ” as “ No earthly creature is im- mortal.” 287. In this case the whole of the subject is ex- cluded from the Negative sphere, and must therefore privative for be included in the Positive which connotes Negative sphere. q ie Negative. A Privative term will answer just as well as the Negative, since the subject always confines the judgment to objects included within its own sphere, which becomes for this purpose a proxi- mate genus, of which the Positive Predicate and its Privative are the coordinate parts. (3.) By a negative copula and a negative subject 3d case. used distributively, we have I by contra- position. As “ No one who has not enough is rich.” Here “ one who has not enough,” or “ all who have not enough,” is a negative term, and the judgment is the same as “ some [perhaps all] who have enough are rich ” (see 277). 288. This form however states something more than I, since it would never appear from the fact that “ some who have enough are rich,” that “ no one who has not enough is rich.” •289. The course of this investigation shows that we may always have from any Exposita its contra-posita by Immediate Inference. III. Of the Conversion of Propositions. 290. By the Conversion of Propositions we change conversion. the relative place of Subject and Predicate, as from A is B to B is A. 291. In the Conversion of Propositions, the first form Exposita and we call Exposita , and the second the Con- Converse. -*■ verse. n.] OF PROPOSITIONS. SECT. X. 75 292. The fundamental canon which governs the Conversion of Propositions is this : Fundamental canon. No term may be distributed in the Converse which was not distributed in the Exposita. 293. As E and I are alike in reference to the distri- bution of their terms, one distributing both conversion of and the other distributing neither — their EandI - conversion takes place in the same way ; that is, sim- ply, No A is B, therefore No B is A. Some A is B, therefore Some B is A. Exposita , No quadrupeds have wings, therefore Converse, No winged animals are quadrupeds. Exposita , Some Poets are Americans, therefore Converse, Some Americans are Poets. 294. This is called Simple Conversion , and hence the Buie, when both Subject and Predicate si;n pie con- are distributed, and when neither are dis- version - tributed the Proposition may be converted simply. 295. But in A the Subject and not the Predicate is distributed. Hence we cannot convert sim- conversion by ply if we say, “ all American citizens are nmitation - free,” we cannot say that therefore “ all freemen are American citizens.” We must limit the subject and say, therefore “ some freemen are American citi- zens.” 296. This is called conversion by limitation or per accidens. 297. A, however, when stated by contra-position, may he converted simply. Thus All A is B, A by contra . No A is non-B, therefore No non-B is A. ge sitio c n onve“ed If the whole of A is in the sphere of B, simply - nothing which is not in B can a fortiori be in the sphere of A. 298. O, cannot be converted except by first chang- ing its quality. This we may do by connect- conversion of ing the Negative with the Predicate by °- which we permute it into I. And then of course it may be converted simply. Thus “ Some A is not B, therefore Some Not-B is A.” 76 LOGIC. PART I. [CHAP. Exposita , Some brave men are not soldiers, Converse , Some not-soldiers are brave men. 299. Hence we may convert E and I simply. A by limitation, or per accidens, or particularly , and O by permutation into I and then simply. 300. In consequence of the laws of Conversion we immediate in- have from any Exposita, its converse as an ference by Con- T -i . . T X 1 version. Immediate Interence. IY. Of the Substitution of Terms. 301. In every categorical Affirmative Proposition we substitution of may always substitute for the Predicate any Predicates in .* 7 i J Affirmatives, term which denotes a wider and compre- hending sphere and the Proposition will remain true, but it will cease to be the whole truth. In the same substitution of way we may substitute for the subject any the subject. term which denotes a narrower and compre- hended sphere, and with the same effect upon the Propo- sition it will still be true, but not the whole truth that was contained in the Proposition before the change was made. Thus, if A B is “ a negro,” he is “ a man,” “ an animal,” “ a created being,” &c. Or if we say, “ men are mortal,” we may say “ Caucasians are mor- tal,” “ Americans are mortal,” “ Yankees are mortal,” “ Bostonians are mortal,” &c. 302. By such change Propositions are said to be- come more general or more indefinite ; they are true but not the whole truth. 303. In Negative Propositions, in consequence of substitution of the fact that the Predicate is distributed, we Negatives.- in may substitute in the Predicate terms in the inverse order ; that is, for any comprehensive term we may substitute any one of its included spheres. Thus A B is not a man, therefore he is not a Negro. If Victoria is not a sovereign she is not Queen of Eng- land. 304. But we may not substitute Predicates in the n.] OF PROPOSITIONS. SECT. XI. 77 inverse order in either case ; that is, not a narrower for a more comprehensive in Affirmatives, . no substitutes x t . n ln *he inverse nor a more comprehensive tor a narrower order, in Negatives. This would be in either case asserting something more than the truth.* 305. By these substitutions new Propositions are made, the truth of which depends upon that immediate in- ot the Propositions tor whose terms the new stitution. ones are introduced. Hence the new Propositions must he true (though inadequate), by Immediate In- ference. SECTION XI. Of Complex Propositions. 306. A Categorical Proposition is called simple when its two terms are expressed by single simple and -r-. , , Complex Pro- WOrdS. But when several words are re- positions, quired to express the cognition the term is called Complex. 307. It is evident that any substantive, or other word which is the name of a thing, a pro- Necessity for perty, an action, or a series of actions, may Complex terms - be a term, as “ man,” “ whiteness,” a “ step,” “ walk- ing,” “ to err.” And if any language were copious enough to afford a name for every possible conception which we might ever wish to express, as either the subject or the predicate in our judgments, we should * It may be well to give a diagram illustrating the preceding para- graph. Thus let S and P he any two circles or spheres. S included SfCSP in P — this represents the affirmative Proposition S is P. It is ( ( S ) ) manifest that any sphere comprehending P must comprehend — */ S also. Let S he Negro, P he Man, and we have “ Negroes are Men.” But let a circle drawn around P denote “ animal,” so that all men are animals, then will it include S also, and we shall have “ Negroes are animals.” But in case of the Negative Proposition the Subject is , — v not included in the Predicate, and we have two circles S and ( S ) ( P ) P, having no point in common. S is not P, consequently S ^ ^ ^ ^ cannot he in any narroxver sphere which is included in P, or any part of it. 78 LOGIC. PAHT i. [CHAP. never need to nse any other words to express our meaning than these simple terms. But such is not the case and never can be the case with any human lan- guage. 308. In most cases also when the predicate denotes a property which is not one of the differentia of a spe- cies, we wish to use in the subject not merely the specific term but also the term denoting the genus under which the species is included. Thus if we say, “ Men who walk by faith place a light estimate upon the mere vanities of worldly splendor,” we give first in the subject the genus “ men,” and then the species “ who walk by faith.” It is obvious that we do not intend to affirm the predicate 0 f the whole genus denoted by the term “ man,” hut only of one species of men, whose differentia is that they “ walk by faith.” 309. A simple term, as “ man,” thus limited be- Moduis. comes a complex term ; and the words limit- ing or qualifying its meaning or its sphere, are called Modals. 310. Modals are either Explicative , Differential , Exceptional , Exclusive , Conditional or Protensive. 311. Explicative Modals are merely rhetorical. Explicative^. They amplify the meaning of the term itself, as when we say “ mortal man.” Since all men are mortal the adjective adds nothing either to the matter or the sphere of the conception for which the term “ man ” stands, however much it may add to the rhetorical effect of its utterance. 312. Differential Modals limit the sphere of the Differential. conception denoted by the absolute or sim- ple term. In that case the term is really the species, as the Differential Modal furnishes the Differentia of the contained species. Thus “ white men, ” — here “ men ” is the simple term, “ white ” the modal ; and “ white men,” the complex term, is but a species of the genus a man ” denoted by the differential “ white.” 313. While Differential Modals indicate the part of the Proximate Genus, which is included in the scope n.] OF PROPOSITIONS. SECT. XI. 79 of the judgment, we have another class of modals called Exceptionals , which indicate the part Exceptional, which is not included in the scope of the judgment. As “ all except the Apostles were scattered abroad.” Instead of giving the differentia of that portion of the Proximate genus which is included in the Predicate, it gives the differentia of the part which is not in- cluded. Hence the Differential and the Exceptional modals are in a sense counterparts and complements of each other. 311. The Exclusive Modals are those which show that the predicate can have no other subject Exclusive, than that of which it is predicated in the judgment. As “ Virtue is the only thing worth living for.” Here virtue is declared to be worth living for. But by the modal every thing except virtue is excluded from the sphere of the conception denoted by the matter “ worth living for.” Hence of necessity Exclusive modals dis- tribute the Predicate. 315. Conditional Modals express some separable mode or condition of the object represented conditional, by the term, so that the object is included in the scope of the judgment only while it is subject to that condi- tion. Thus “ drowning men catch at straws ; ” that is, “ men in the condition of drowning.” It does not ap- ply the predicate to any species of men at all times and under all conditions as the Differential modal does, but it makes it applicable to all men when they are in the specified condition. 316. Protensive Modals limit the inclusion of the term within the scope of the judgment in Protensive. reference to time. Thus “the weather is excessively cold in winter ,” — “ our plans will sometimes fail,” — “ testimony sometimes deceives us.” 117. The Protensive Modal neither makes nor im- plies any change in the properties of the term, bilt only refers to the time when the object denoted by the term is included in the scope of the judgment. This it may do definitely , as “ in winter ; ” or indefinitely , as “ some- LOGIC.— PAKT I. 80 [chap. times ; ” instantly, as “ now ; ” or absolutely , as “ al- ways.” 318. There is another kind of adjective phrase that has sometimes been regarded as a modal, which how- ever I have preferred to regard as constituting a com- pound Copulative Categoric Proposition (see 322), — as “ Hamilton , the greatest statesman of his agef or “ who was the greatest statesman ,” &c., “ was a Federalist .” But the Avords marked in italics do not constitute a modal of “ Hamilton,” they are the Predicate of a judgment to which “Hamilton” is subject, and the Proposition expresses the tAvo entirely distinct and in- dependent judgments, that “Hamilton was the greatest statesman,” &c., and that “ he was a Federalist.” SECTION XII. Of Compound Propositions. 319. Any Proposition which has more than two distinct terms is called a Compound Proposition, and compound contains either expressly or impliedly more propositions, than one judgment. If it has but tAvo terms, whether simple or complex, the Proposition is simple. 320. Compound Propositions are usually divided into Express and Implied. They are called Express Express and when tAvo or more judgments are expressed implied. j n th e same Proposition, and Implied when one only is expressed and the other is implied. The Compound Express Propositions are either Copulative , Causal , Discretive, Conditional , or Dis- junctive. 321. In the Copulative Propositions either the Sub- copuiative. ject or the Predicate, or both, consist of two or more terms connected by a conjunction. Thus A and B are C ; A is B and C ; A and B are C and D. “ Life *and Death are both before us;” — “Bacon was both a philosopher and a statesman.” 322. Sometimes the conjunction is omitted entirely, as “ Hamilton the greatest statesman of his age was a n.] OF PROPOSITIONS. — SECT. IE. 81 Federalist.” And again its place is supplied bj the relative pronoun and the verb, as “ Hamilton who was the greatest statesman, &c., was a Federalist.” 323. Copulative Propositions can be resolved into simple ones according to the number of sim- Resolved in pie judgments contained in them. Thus in «™s! e Prop ° 31 ' the example, “ Bacon was a philosopher and states- man,” we have — Bacon was a philosopher, “ “ a statesman ; or in the other example given, we have the following : Life is before us, 321. Or the connective may be a disjunctive con- junction, as “ Neither wealth nor friends Disjunctively can free the body from its pains, nor the connected - mind from its fears ; ” — and we have, 325. It is of course quite possible that one of the judgments in a compound copulative will be true, and the other or others be untrue. And advan- tage is often taken of this fact for the pur- judgments c»m C pose of introducing and gaining assent to a ine ' judgment which is untrue, by ascribing to a subject two predicates, one true and the other false. 326. Compound Propositions are called Causal wdien one of the judgments assigns the cause or causal, sign of the truth of the other. “ Christians are happy because they have obtained the favor of God ; — “ The evil are exalted that they may fall j ” — ■“ Christ came to save the world / ” that is, “ Christ came [first judg- ment] that he might save the world,” [the final cause or object for which He came into the world.] 327. Compound Propositions are called Discretives when they contain two judgments in oppo- Discretives. site qualities. Thus “ A is B, but it is not D. “ A and not B is C.” “ A is B but C is not D.” “ Fortune Death “ “ “ Friends cannot Wealth cannot 82 LOGIC. — PART I. [CHAP. may take from ns our friends but it cannot take our honor.” “ But few men succeed in enrolling their names on the list of those who are never to be forgot- ten ; ” that is, “ some men do and some do not suc- ceed,” &c. 328. We have already seen that Conditional and Disjunctive Propositions are compounded, implying first categorical judgments and then a hypothetical relation between those judgments. Hence in one point of view they are to be regarded as compounds of cate- gorical judgments. 329. In the compound of the categorical with the conditional. conditional, the conditional clause is to be regarded as a modal. Thus if A is B, C is D ; that is, C is D ( sub modo ) A is B. “ If the Scriptures come from God they are entitled to the highest respect.”— “ The Scriptures are entitled to the highest respect on con- dition [conditional modal] that they come from God.” 330. So with the Disjunctive, A is either B or C. Disjunctive. A is B on condition that it is not C, or either A or B is C ; that is, A is C on condition that B is not. “ The author of this statement is either a fool or a knave.” He is a knave on condition he is not fool enough not to know better. 331. The more usual form, however, of the com- pound categorical with one disjunctive term, is that in which one term denotes a logical whole, and the other the parts ; as “ All men are either Caucasian, Mongol, or Negro.” We shall of course reserve the consideration of the judgments which connect the Conditional and Disjunc- tive members of these compounds until a subsequent place in our treatise. 832. Of the Compound Implied Propositions two only need to be mentioned, the Executives and the Exclusives. They each imply a judgment different in quality from the one expressed — this is done by a modal. II.] OF PROPOSITIONS. SECT. XII. 83 333. Thus Exceptives while including the expressed subject in the sphere of the predicate, make an excep- tion of some of the individuals included in Exceptives. the implied subject, which consequently are excluded from it. Thus “ All but the Apostles fled” implies that there were some who were not Apostles that did flee. 334. In this case the expressed judgment is affirma- tive and the implied is negative. But if we say, “ None but the Apostles remained ,” we have the nega- tive judgment expressed, “None ; ” that is, “ no Chris- tians remained,” — and the implied affirmative judg- ment, “ the Apostles did remain.” 335. The Exclusive Propositions, while including a subject in any predicate, exclude by an im- Exdusivos. plied negative judgment all other subjects from that predicate, as “ Virtue is the only thing worth living for.” This is precisely the same as the Exceptive in which the negative judgment is expressed, as “Nothing but virtue is worth living for.” 336. The article “the” before the Predicate of an Affirmative judgment constitutes it an Exclusive, by making the Predicate a definite and distributed term. Thus “ Christ is the Saviour of the world ; ” this im- plies that He is the only Saviour. 337. In the conversion of complex and compound Propositions they must, as a general thing, be first re- solved into simple incomplex propositions, and per- muted and converted according to the rules already laid down. In one or two cases, however, there are facts in regard to their conversion worth noticing. 338. Exceptionals and Exclusives are easily con- verted into each other. “ All but the Apostles fled ; ” becomes by substituting the exclusive instead Exreptionals of the exceptional modal, and changing the and 'Exclusives quality of the Proposition, “ The Apostles convertlble - alone did not flee.” The same thing would be accom- plished with the antithetic Predicate without changing the qualify of the copula, as the Apostles alone re^ 84 LOGIC. PART I. [CHAP. mained, i. e., did not flee. “ Virtue is the only thing worth living for,” is converted into an exceptional by substituting for the subject “nothing,” and the ex- ceptional modal before the subject, as “ Nothing except virtue is worth living for.” 339. Any Compound Proposition, whether Express or Implied, may always be regarded for the purposes compound of Deduction as a simple Complex Proposi- ducFble tocom! tioii . Thus the Copulative “ A and B are C.” plex - A (sub modo, that is, on condition it is joined to B) is C. For the Causal take “ A is B because it is C.” A ( sub modo , that is, because it is C) is B. For the Discretive “ A is B but not C.” A (sub modo , that is, on condition it is not C) is B. The same is obvious, too, with regard to the Exclusives and Exceptional ; the exclusive and exceptional phrases may be made or regarded as merely a modal of one of the terms. 340. But we may carry this matter one step further, and regard the Complex as a Simple Categorical so far complex to as the purposes of deduction are concerned, simple. ]y depends very much upon the fulness of a language, whether a conception shall be expressed by a single term or not. If we have no single term for it, we must use several, and give either its description or its definition instead of the term itself. And all the words which Logic requires in the expression of judg- ments, are either the copula or the terms ; or instead of terms, their definitions or descriptions. Hence what- ever words are necessary to express any cognition, become but a complex term for that cognition, and it is merely accidental for all logical purposes, whether a term be expressed by one word or by many. SECTION XIII. Of Comparative Judgments. 341. Comparative Judgments do not include the subject in the sphere of the Predicate. n.] OF PROPOSITIONS. SECT. XIII. 85 342. In Comparisons tliere are three terms and two implied categorical judgments : as “ A is Three Terms . x , t? TT ^ ° in Comparative wiser than ±5. Here we mamiestly have Judgments, the two judgments, A is wise and B is wiser. And we have three terms, A the Subject, B the Predicate, and the Comparative term, which in this case is “ wise.” The Predicate is assumed as the Standard ^The^posUive or Positive term, and the Subject is com- pared Terms' 11 pared with it and is the Compared term. 343. Of Comparative Judgments there may be reckoned seven kinds: 1. Comparatives of Different kinds simple Intensity. 2. Comparatives of Inten- °f comparatives sity considered as a Cause. 3. Comparatives of Time. 4. Of Place. 5. Of Manner. 6. Of Means or Method. 1. Of Ratio or Relation. 344. We may have comparisons in Intensity of three varieties : (1) of Equality ; (2) the Indefinite ; (3) Comparisons of Inequality. (1.) In Comparisons of Equality the Positive and Compared terms are affirmed to be equal in comparisons the intensity of the term of Comparison ; of& i ualit y- as A is equal to B, in which it is also implied that B is equal to A, or that A and B are equal in the intensity of that in respect to which they are com- pared. (2.) In the Indefinite we have the Compared term declared to he of as great an intensity as the indefinite. Positive ; as “A is as great as B,” or “ A is as wise as B.” In these judgments it does not appear that B is not wiser than A, &c. (3.) In Comparatives of Inequality the term of com- parison is used in the comparative degree, inequality, and a difference in degree of intensity is declared to exist between the Positive and the Compared terms ; thus A is greater than B, or A is less than B. 345. Comparatives of Inequality differ in their in- tensity, by being on the different sides of the Difference of positive degree, and are accordingly called Intensity - comparisons of greater or of less intensity. 86 LOGIC. PAKT I. [CHAP. sity 346. Comparisons are said to be of greater intensity Greater mten- when the Term of Comparison is affirmed to belong to the Compared in greater intensity than to the Positive, and Comparisons of less inten- Less intensity, sity when the Term of Comparison is affirmed of the Compared in a less intensity. Thus A is greater than B, is a comparison of greater intensity — A is less than B, is one of less intensity. 347. We may have Comparatives in which the in- intensity as a tensity of the comparative term is considered Cause - as a Cause. Thus, “ The weather is so cold that the water freezes.” 348. For a comparison of Time we say that “ A of -rime. occurs when B occurs;” as “It lightens when it thunders.” 349. For a comparison in Place we say, “A is where of piace. B is.” — “ Where two or three are together in My name, there am I in their midst.” 350. For a comparison of Manner we say, “ A is of Manner. like B.” — “ The Boy walks like his Father.” 351. We have also a comparative of Method or of Method and Means, as “He came as he went ; ” in which case the “ as ” comparative may refer to either the means used or to the way by which the act was performed. 352. Then we have Ratios, or comparisons of value, of Ratio. in which one term varies as the other. Thus “ A is to B as C is to D. — “ The Mercury in the Ther- mometer rises and falls as the weather grows warmer or colder.” 353. In comjiarisons of Inequality conversion may Conversion of be effected by change of the intensity to its comparatives. 0 pp 0g jf- e . Thus “ A is greater than B,” — “ B is less than A.” 354. But in the Indefinite no conversion can be as great as B.” gathered Indefinites can- not be convert- ed. effected ; we say, “A is But the judgment leaves it possible for A to be greater than B, and the mind is uncertain whether it is or not. Hence B may be either equal to A, or less II.] OF PROPOSITIONS. SECT. XIV. 87 than A ; and the judgment does not furnish the means for determining which it is. 355. Comparatives in which the Intensity is re- g arded as a Cause, are converted into Causal comparatives htegoric Propositions. “ It is so cold that caS! Ld ‘" t " the water freezes,” becomes “ the water freezes because it [the weather] is so cold.” 356. All the other forms may be regarded as Com- paratives of Equality so far as conversion is concerned, and as such may be converted simply, A is equal to B, therefore B is equal to A. SECTION XIV. Of Probable Judgments. 357. A Problematical Judgment is one in which it is affirmed that the Copula may be affirmative. Probable Judg _ But a Probable Judgment is one in .which ments - there is given an estimate of the reasons for affirming the Copula. 358. The value of the Probability is always esti- mated (if at all) in a fraction of unity or in a Their value, ratio ; unity being assumed as the same as a cer- tainty. 359. The value is ascertained by a calculation of chances. One reason for believing any Pro- How ascer . position which comes into the present class tained - to be true, is because we have known it, or some- thing like it to hold true. Thus of any given side of a die there is a probability that it will fall uppermost at any given throw. If a man commits a crime there is a probability that he will be detected, based indeed upon the means used for his detection ; but estimated by the proportion which the times in which similar means have been successful in similar cases bear to the times in which they have failed. 360. All the known cases are considered as so many Chances , which are divided into two chances favor, classes — the favorable and the unfavorable ; onibie nd u " fav " 88 LOGIC. PART I. [CHAP. and the probability of any affirmative judgment hav- ing an individual case for its subject, and the term in- cluding the favorable cases for its Predicate being true, is determined by the proportion which the favorable chances bear to the unfavorable. Thus a die has six sides — at one throw therefore one of the six sides must come up : call that the favorable chance, and as there are five other sides, no one of which will be up when that specific one is uppermost, we may call the unfa- vorable chances five. The probability, therefore, of any particular side, say the ace , being up, is one to five, or one-sixth of the whole number. 361. In order to estimate the probability of any judgment therefore, we must have a totality of cases. This may be the absolute totality including all actual and all possible cases of the same kind, or it may be any part of that totality which has fallen under assumed total- our observation, assumed as the representa- tive of the whole. For the estimation of the probability, it makes no difference which is assumed, provided the part taken be an exact representative of the whole. Thus suppose the whole to be one thou- sand, out of which one hundred have been favorable and nine hundred unfavorable, the chances are one to nine. How if we take any part of this totality, say one hundred, if it be an exact representative of the totality, the chances will be ten to ninety — that is, one to nine ; or if we take ten, they will be one to nine still as before. 362. The improbability, which is the probability improbability, that the individual will be included among the unfavorable chances, is of course the complement of the probability in the unity of the whole, whether absolute or assumed. Thus if the Probability is three- fourths, the Improbability is one-fourth. 363. The balance of Probabilities is the difference Balance of pro- between the two fractions, and is in favor buiities. 0 f the probability or the improbability, as the one or the other happens to be the largest. n.] OF PROPOSITIONS. — SECT. XIV. 89 364. The Improbability is not however the same as the Probability of the opposite. Thus, in lmprobability throwing a penny, the probability of the not the same as head side falling up is I, the probability of the opposite re- its falling up in two throws is, say f, conse- quently the improbability is f . But the probability that the head will fall down, or the tail fall up, one in two, is also f instead of p 365. Both the Probability and the Improbability are sometimes called Antecedent Probability Antecedent and Antecedent Improbability, with reference Probability, to the fact that they are estimated before or antecedent to the special reasons for affirming the judgment in any given case. Thus the antecedent improbability of a miracle is based upon the uniformity of nature ; that is, the numberless instances in which no mira- Effectof differ- cle has been wrought. On the other hand, ent totam “^ it has been claimed that when we consider the special occasion on which it is claimed that miracles have been wrought, there is an antecedent probability in their favor ; the difference in the estimates arises from the assumption of different totalities of cases or chances. In the one case, forgetting the special occasion or pur- pose,* the absolute totality of histoi’ic events and of occurrences in nature is assumed. In the other it is assumed that the object for which the miracle is al- leged to have been wrought, is to constitute the basis of an entirely different totality, is the Differentia of a much narrower sphere, within which the chances are not only much fewer, but are such as to turn the balance of the probabilities on to the other side. 366. In many cases this value can be expressed with as much certainty as any categorical judgment what- ever. But there are also some objects both Exac t estimate in logical and in comparative quantity, ofvalue - whose quantity cannot be expressed in terms of dis- crete quantity at all. * Nodus deo dignus. 90 LOGIC. — PART I. [chap. 367. In most cases, however, our estimate of the value of a probability cau be only approximate. "We judge Approximate as nearly as we can from what lias fallen estimate. under our experience, assumed as a repre- sentative of the whole, the proportion of the favorable cases to the unfavorable in the absolute whole. 368. The probability against any judgment or Pro- !m’ b rot)' 1 hTt and P os iti° n is called its improbability ; and the mail™ unity . y probability and the improbability together make up a unit or certainty. 369. Hence if we have either the Probability or the Improbability given in a fraction or a ratio, we can find the other by subtracting the fraction from unity, or by converting the ratio. 370. But while the improbability can never be ma mpr be abl iess more ^ ian the complement of the probability than the com- in the unity of the logical whole, it may often plement of the J ° J Probability. be leSS. 371. It will happen in many cases that we know illustration. of many reasons for believing a proposition, and none for disbelieving ; that is, we may know many favorable chances and be entirely ignorant whether there are really any unfavorable ones or not. Thus in the moral government of God, it is perfectly certain that in many cases sins are punished in this world, and perhaps it is not certain that there is any case in which they are not punished in this world. Hence there is on the supposition a strong probability in favor of the opinion, that any particular sin will be punished in this world and none whatever against it. 372. Improbability, therefore, is not the mere want improbability or absence of probability or grounds for be- of Probability, lieviug. But it is something positive. It is based upon and therefore implies positive ground for (Zwbelieving, or believing the contradictory of a pro- position. 373. There may also be an improbability against a proposition, when there is no probability or nothing in its favor ; and for the same reasons as we have just n.] OF PROPOSITIONS. SECT. XV. 91 given for there being in some cases a probability with- out any counter improbability. 371. There may be many cases in which the general probability of which we have just been speak- Generaj^and ing, may be increased or diminished by spe- bmties. cial grounds. Thus, in a community where one in ten die of any special disease, the probability that any particular individual would die with that disease is increased or diminished by the peculiarities of his constitution, mode of life, &c. The rates of life insur- ance are lived upon the general probability of the duration of life. But this probability becomes so much diminished by one’s being sick or constitutionally dis- eased, that Life Insurance Societies refuse insurance in such cases. In Marine and Fire Insurances also, the rate of insurance is increased above the general rates by considerations affecting the probability of loss, aris- ing from the special circumstances of the property insured. SECTION XY. Of Conditional Judgments. 375. Conditional Judgments affirm the reality of the Predicate, on the ground of the reality of conditional the Subject. But as the Subject and Predi- Jud s mf =nts. cate are not cognitions merely but rather judgments, of which the copula of the second is affirmed on the ground of the copula of the first, the first judgment is called the Antecedent , and the second Antecedent and the Consequent / thus “If A is B, C is D.” Conse< i uent - Here “ A is B ” is Antecedent — “ C is D ” is Consequent. 376. The Antecedent and Consequent taken toge- ther are called the Members of the Condi- Members o. tional ; they are also its Matter. concution«i. the 377. In all Conditional Judgments there must be at least three terms and two copulas, as in Three Termg the case just given. There may also be four atleast - terms, as “If A is B, C is D.” “If each man may 92 LOGIC. PART I. [chap. hold what opinion he chooses without blame, atheism itself will he innocent.” Here we have the four dis- tinct terms, “ each man,” “ hold what opinion he chooses,” “ atheism,” and “ innocent.” 378. The ground of affirmation in Conditional Judg- sequence. meuts is called the Sequence. Thus if we have, “ If A is B, C is D,” we may ask why ? On what grounds can we affirm the judgment, “ C is D,” as a consequent of the judgment that “ A is B ? ”- — the answer to this question is what is called the Sequence. 379. For the most part the sequence or ground of affirmation is self-evident ; and for this reason it has Not always seldom received much attention. But we self-evident. may have a conditional judgment when there is really no sequence ; thus the gardener says, that “ If he plants any onions in the new of the moon, they will fail to have large bottoms ;” the judgment is in form a conditional. But still one may fail to see any connection between its members. 380. It becomes necessary, therefore, to consider sequence can the grounds of affirmation in the Sequence. ed as a cate- Ibis can oi course always be stated, as a ment al Jude ' Categorical Proposition. If one says, “ John has a fever he is sick,” and we ask why ?- “ Because all who have fevers If -the appropriate answer is, are sick.£. 381. Any Proposition may be an Antecedent upon which any Immediate Inference — whether by (1) Op- immediate in- position of Judgments, or (2) by Contra- ference. position, or (3) Conversion, or (4) Substitu- tion — may be affirmed as a Consequent, in accordance with laws and principles of Immediate Inference al- ready explained. 382. If the unlike terms are mere synonymes or even equipollent, there can hardly be said to be any identity of An- sequence, and yet the Conditional is good, tecedents. Thus “ If common salt is good for seasoning food, chloride of sodium is good for seasoning food ; ” the sequence in this case is identity of Antecedents. n.] OF PKOPOSITIONS. SECT. XV. 93 383. If tlie Subject is the same in both Members, the Predicate of the Consequent may be a superior sphere, comprehending the Jrredi- the consequent cate of the Antecedent ; and for the same KfcAn- reason, if the Predicate is the same in both Members, the Subject of the Consequent may be any inferior sphere comprehended in the sphere of the Sub- ject of Antecedent. Thus as an example of the first case, “ If the English are Anglo- s coifse t que t n h t e Saxons, they are Caucasians.” Here “ An- m'XaPo'n'ho glo-feaxons are assumed as but a species of “ Caucasians.” As an example of the second take the following : “ If virtue is expedient, temperance is expedient ; ” — “ temperance ” being one species of “ virtue,” or one of the virtues. But in the first case, if the Antecedent is negative, the Predicate of the Consequent may be any narrower sphere predicated negatively ; — ■“ If the English are not Caucasians they are not Anglo-Saxons.” 38-1. If the Predicate of the Antecedent be one of two or more Correlatives inhering in the >Vhen the p,e- same subject, the Predicate of the Conse- riStw s es ar fn C the quent may be any other of these Correia- saioe object tives. Thus, “ If an ultimate particle of matter has extension, it has divisibility.” But if the Correlatives do not inhere in the same object, they must correlatives in be predicated negatively in one of the mem- S si bl°piedr bers ; thus “ If the man is the master he is f y at ^ d onl g Memi not the servant.” Or in general, if one of ber - any two Antithetic terms be predicated of any subject in the Antecedent, the other may be predicated of it negatively in the Consequent, and vice verm. 385. The Cause of any thing is always in some sense the ground of its reality. Under this general principle we may have the following classes of Condi- tional Judgments with Antecedents expressive of the Cause of the Consequent. 386. Hence if of several contrary terms, having- analogous spheres, some property be predicated in the 94 LOGIC.— PART I. [chap. Of opposite Subjects the Material Cause may be predi- cated in both Members. U Antecedent, which is of the essence of the proximate genus — that is, the Material Cause — the same term may be predicated of any contrary term in the Consequent, whether that term be a co- ordinate or the subordinate of any coordi- nate to the subject of the Antecedent. Thus, If vice is voluntary , virtue is voluntary ; ” — here voluntariness of action is assumed as the Essentia or Material Cause of Moral actions, and vice and virtue are two coordinate species of Moral actions, each hav- ing a Differentia or Formal Cause of its own. And we may also have, “ If vice is voluntary, temperance [one of the virtues] is voluntary.” 387. If the Antecedent affirms the conjunction of the Efficient and Occasional Causes, the reality of the Effect may be affirmed in the Conse- quent ; thus, “ If the spark falls upon the powder it will explode, or an explosion will ensue.”- — If the boy takes cold he will be Of the conjunc- tion of the Effi- cient and Occa- sional Causes in the Antecedent, the Effect may be affirmed in the Consequent. sick.” 388 ofthe Material cedent, the substance or tecedent the E?" affirmed in the Consequent. feet or quent may affirmed. If the Material Cause is affirmed in the Ante- 3iiu s may be Thus, “ If ex- ■“ If the mode- rate indulgence of pleasures is right, the temperate use of alcoholic drinks is right.” 389. If a Formal Cause be affirmed in the Antece- or the Formal dent the Consequent may affirm the species. Antecedent, the Thus, “ If the temperate use of alcoholic affirmed "inhhe stimulants be in accordance with the law of consequent temperance and self-denial, it is right.” 390. In cases where the Conditional has four dis- compiex se- tinct terms, the sequence becomes complex or double. In this case we may have several grounds of affirming the Consequent. 391. When the Subject of the Antecedent is re- substance and garded as the Cause of the Subject of the Cons b e e tension exists matter exists. 1 indulgence Mode in the An tec of ani Consequent fecedemcauses Consequent, and the Predicate of the Ante- and Mode in the ce dent affirms of its Subject some mode which n.] OF PROPOSITIONS. SECT. XY. 95 is regarded as the Cause of the mode of the Subject of the Consequent, it may be predicated of that Subject in the Consequent. Thus, “ If the Moon is full the tides will be high.” Here the Moon is regarded as the cause of the tides, and the “ fulness ” of the Moon as the cause of the “ highness ” of the tides. 392. Again the Subject of the Antecedent may in- clude the Subject of the Consequent, and the subject of An- Predicate of th'e Consequent include that of the Antecedent. Thus, “ If the English °Lm e a£d on t s he belong to the Teutonic branch of the human conieq‘nt°com e - family, the Puritans must be Caucasians.” SF^™A n ntece- Here “Puritans,” Subject of the Conse- dent - quent, are regarded as part of “ the English,” the Sub- ject of the Antecedent — and “Teutons,” the Predicate of the Antecedent is included in Caucasians, the Pre- dicate of the Consequent. 393. Or again we may have the Subjects of both Members contraries to each other regarded subjects in both as Formal Causes, and in that case the Pre- j°"; dicates will be contraries to each other also ; malCauses - “ If vice produces misery, virtue may be expected to produce happiness.” 394. Or we may invert the order and say, “ If hap- piness results from virtue, misery will result And the re . from vice.” verse - 395. But besides this the Effect though in no sense the ground of the reality of the Cause, is of- 0f the Effect ten the sign or ground of our knowledge of “ n t a the A r n eaiity the reality of the Cause, and for that reason con h se<£m mw becomes an Antecedent, upon which we may be affirmed - always affirm the reality of the Cause. If the Cause be Immanent or Permanent the Antecedent i mma nentand may be affirmed in the present tense or with- out regard to protension. But if it be only ^nt Ten»e. Pre ' a Transient Cause, as most occasional causes Transie nt only are, its reality can be affirmed in the Conse- inthe P ast - quent only in the past tense. Thus, “ If there is day- light we may say that the sun shines ; ” — but “ If there 96 LOGIC. PART I. [chap. is an explosion, we may say that there has been powder and fire.”— “ If there is small pox, we may say that the infecting virus has been communicated to the sys- tem.” 396. I have said nothing thus far of the Quantity of Quantity anti the Members of the Conditional. But as the Members. ° Antecedent is the ground on which we affirm the Consequent, it is evident that no term which has not been used as a distributed term in the Antecedent, may be used as a distributed term in the Consequent. But for the most part terms are regarded as Continuous Wholes in Conditional Judgments. 397. W e have also spoken only of simple Catego- compiex and ricals as Members of the Conditional. -But Membe p r° un in these Members may be either Complex or Conditionals. t/^j • i i Compound Uategoricals ; and as we nave before seen the Compound may be regarded as Com- plex, and the Complex as simple Categoricals — only taking care not to separate or omit any of the parts of the Complex term. Besides the above modes of compounding the Conditional, there are two others which deserve a mention. 398. If we have two or more Antecedents, the Co- pulas of which are each independent of the Copulas of compound the others respectively, and one Consequent, conditionals. pq e (] 0 p U i a 0 f which is affirmed on condition of the truth of all the Antecedents, we shall have what may be called a Compound Conditional ; thus, If A is B ) A - -n. and If A is C j 1S ’ “ If the Departed are cognizant of what takes place on earth, and if they retain the same feelings towards us as they had while they were here, they must sometimes be intensely pained by what they see in the course of life which we are now pursuing.” 399. Again we may have what is called a Con- continuous tinuous Conditional in which the Consequent conditionals. 0 f t } ie q rs t becomes the Antecedent to the XI.] OF PROPOSITIONS. SECT. XVI. 97 second, and so on. Thus, “ If A is B, A is C. If A is 0, A is D,” &c. — “ If God is just He will punish the wicked. And if He punishes the wicked, surely they that blaspheme His Name will be signally con- founded.” SECTION XVI. Of the Disjunctive Judgments. Disjunctive Judgments have been defined to be those in which one of two Categorical Judg- Disjunctive ments is affirmed to be true, on the ground Judgments, that the other is not true. 400. This is called the Principle of Excluded Mid- dle. It supposes two judgments so related Exduded Mid . as that there is no other judgment in the dle - same matter, differing only in quantity and quality, or both, and being in a sense between them. 401. Thus if we take A and E, we have the subal- terns between them ; thus, All A is B, Ho A is B ; How “ Some A is B,” is less than “ All A is B ” (in affirmative quantity), and more than “Ho A is B;” since the latter has no affirmative quantity. In the same way “ Some A is not B ” stands between “ Ho A is B,” and « All A is B.” 402. Hence either of these Subalterns may be true while both the Universals in the same quantity are false. 403. But if we take the Contradictories there such Middle Proposition ; — “ Either All A is None between Contraries. is no B, or Some Between Con- tradictories. A is not B,” — and “ Either Ho A is B,” or “ Some A is B.” There is no Middle Proposition — no other Proposition in the same matter which can be true and both of these be false. 404. The same will hold true of the Sub-contraries also. “ Some A is B, and Some A is not B.” How both may be true — but there is no 5 Between Sub- contraries. LOGIC. — PAJKT I. 98 [chap. Middle Proposition between them ; so that if one be false, the other must be true. 405. Hence in the first place if we have two Pro- in fere nee from positions in the same matter, being either t re oregomg. Q on tradictories or Sub-contraries, we may affirm that one or the other of them is true, and consequently we may affirm one of them to be true on condition the other is not. 406. But we may have Disjunctives in matter either partly or wholly different ; they all come back, however, as we shall see, to the case just stated, of either Contradictories or Sub-contraries. It will be necessary to investigate this relation a little further. 407. Since in nearly all cases of Disjunctive Judg- ments there is one term common to the members, we coordinate may call those terms, which are different in Terms. each, for the sake of convenience, Coordinate the P Proximate vidual contained in that genus. Genus give an hn-n-p U A ?? o-nrl u Excluded Mid- an(1 die. Terms. 408. Any term and its privative being complements of each other in the proximate genus, must be contradic- positive and tories to each other in reference to any indi- If then we non-A,” — as the two coor- dinate parts of a whole, — as S, and Z as an individual contained in that whole ; then “ Z must be either A or non-A ; ” that is, it must be included in one of the parts. But of course the part “ non-A ” may be denoted by a positive term representing a coordinate species of X, just as well as by the privative “ non-A.” Hence making this substitution, we may have “ Z is either A or B.” 409. But again, if instead of Z denoting an indi- vidual, we have any term denoting a class compre- ifthe common h ended also under X, then in one of the general term it members of the Disjunctive it must be used “huted 6 in’one as an undistributed term. Thus let “ man” member. p e a w i 10 l e , and “ free ” and “ slave ” the coordinate species ; — let “Negro” be also a class com- prehended in “ man,” and we may say either “ all n.] OF PROPOSITIONS. SECT. XVI. 99 Negroes are free,” or “some Negroes are slaves;” or either “ some Negroes are free ; ” or “ all Negroes are slaves.” 410. In the second case we may have a logical whole, with a property common to some of The two Mem- the parts or individuals contained in that ornate “'sub- whole. This property we may constitute ject3 - the Differentia of a species, and then divide the whole into parts in such a way that this property will be pre- dicable of some one part or of some thing contained in the whole which is not that part. Thus let “ vege- tables ” be such a whole, and “ poisonous ” such a property, and “ cereals ” a class of vegetables, then we may say, “ Either cereals are poisonous, or some [vegetables] not cereals are poisonous.” Or again, let “ substance ” be any logical whole, and “ matter ” one kind of substance, and we may say “ either mat- ter, or something which is not matter, is eternal.” Now suppose that substance which is not matter is “ spirit,” and we may say, “ either matter or spirit is eternal.” 411. In this case, as in the preceding, One of the co- /» , -l • • j • i i j* i t - ordinate terms one oi the coordinate terms must be undis- must be .undis- tributed in case they do not stand for indi- ire buted gMen3 • 1 -i ° terms. viduals. 412. If there are more than two coordinate terms, they must be positive terms, and each denote More, than two* its part by differentia of its own. These co5rdinates - parts, how many of them soever there may be, may always be reduced to two, by taking any one as posi- tive, merging the Differentia of the others, and includ- ing them in the privative of the one assumed as positive. Thus the coordinate parts, A, B and 0, may be reduced to two, as “A” and “non-A,” — or “B” and “non-B,” in which case “ non-A ” includes “ B and C,” — and “ non-B,” “ A ” and “ C.” 413. The Divided Whole may be regarded as a logical, or a continuous, or a collective whole, The Divided and it may be the absolute whole, or only Whole - 100 LOGIC. PART I. [CHAP. some assumed relative whole. When, however, it is hut a relative whole, some means must he given in the Proposition stating the Disjunctive, to fix the mind upon the limits of the sphere of the assumed whole. Thus, “ A wise lawgiver must either recognize the re- wards and punishments of a future state, or appeal to a Providence administering them in this.” Here the assumed whole is “ wise lawgivers ,” and it is divided into two classes, — (1) those who appeal to rewards, &c., in the future life ; and (2) those who refer to a Provi- dence administering such rewards and punishments in this state of being. 411. Instead of coordinate terms we may have one coordinate and the subordinates of the other, as in the coordinate and following case : “The earth is either eternal, its coordinate, the work oi chance, or the work ot an intel- ligent Author.” Here “ the origin of things ” is the logical whole. The first division, all things either had an origin or had none, i. e., “ are eternal.' 1 '’ But things that had an origin (the positive part, with reference to the whole) are divisible into two classes ; — (1) those that came by chance, and (2) those that had an intelligent Author. Hence the Formula above given: “ The earth is either eternal (had no beginning), or (its beginning) is from chance, or from an intelligent Author.” 415. But it is not necessary that the coordinate terms should denote coordinate parts of any division. The coordinate They cannot indeed be disparate parts, since be ri DispSmte n i > n there is no necessity that any number of the same whole, disparate parts should include all that was comprehended in the Divided whole. Privatives, as well as Negatives, are always and only coordinates of their Positive. But while disparate parts do not Alternate spe- necessarily include all the individuals of a lire coordinate Divided whole, Alternate Species do include Tunctfve" judg- them all ; and more than that, they include ment. some of them twice at least. Every indi- vidual must be contained in one of a set of coordinate n.] OF PROPOSITIONS. SECT. XVI. 101 species, and can be contained in no more than one. In Disparate Species or Parts the same individual may be contained indeed in several, but many may not be contained in any enumeration of Disparate Parts. But in Alternate Species, while no one may be omitted, many may be contained in several of the species. 416. But although the sphere of two Alternate Conceptions is the same, the matter is not. The Matter of Hence the Differentia of several Alternate £es ern not s t p h e e Species is likely to have many points in same - common, and must have some that are not so. How suppose an individual to have a property which we know to be a part of the Differentia of one or two Al- ternate Species, we can predicate these species of that individual disjunctively. Suppose we have a collection, consisting of portraits of poets and philosophers alone, this collection being one whole — poets and philoso- phers would be the Alternate Species, including all the individuals in that whole. But they are not Coor- dinate Species, since the same man may be both a poet and a philosopher, conceived of from different points of view. Hence of any one whose portrait we know to be in that collection, suppose it to be Cole- ridge, we may say, “ Coleridge was either a poet or a philosopher.” 417. But finally there may be Disjunctives with no term common to the members, as, “ Either A is B, or C is D, or E is F,” &c. It is hardly possible p is j Unct j ves to enumerate the particular forms and rela- "' ith '“"terms, tions which the terms may assume ; since these judg- ments, as in all preceding cases, must be parts of a whole, and reducible to an Excluded Middle. We must be able to show that there is no judgment except one of those enumerated, that will contain the truth which the Disjunctive is designed to affirm. 418. Thus if I wish to account for the diversities in the human race, I may say, “ Either they sprang from different origins,” or “ the diversities have been pro- duced by the influence of climate, mode of life,” &c., — 102 LOGIC. PAKT I. [CHAP. or “ God must have interposed to produce the variety miraculously.” Here the divided whole is “ the origin of the diversities in the human family ; ” and if the members of the disjunctive enumerate all the parts and species to which it can be referred, whether Coordinate or Alternate, one of them must be true. If not, there must be some other and Middle Judgment which may be true. 419. The Conditionals and the Disjunctives are compounded in two ways : (1.) A Conditional Antecedent with a Disjunctive compound of Consequent, as, “ If A is B, A is either C or D?sjunctires. & D .” — “ If the world had a beginning, it is either the work of an intelligent Author or the product of chance.” (2.) We may have a Disjunctive Antecedent, thus, “ If either A is B, or A is C, A is D.” This constitutes nnemma. what is called the Dilemma — “ If the patient either eats or abstains from food, he will die” (in the one case from the effects of the food, in the other from want of food). 420. In stating Dilemmas it is not uncommon to omit the Consequent to the Disjunctive Antecedent, as being too obvious to need explicit mention. 421. Since Disjunctive Judgments always affirm Disjunctive one of the Members to be true, on condition verted into con- that no one oi the others is talse, we may always convert the Disjunctive into a Con- ditional by contra-position of one Member for an Ante- cedent, and using the other or others, if there be more than one, as Consequent ; thus, “ Either A or B is C,” therefore “ If A is not C, B is C.” section xvn. Of the Grounds of Affirmation. 422. The grounds upon which judgments are af- firaTuo d n. ofAf ' finned are reducible to three : — (1) thePrin- XT.] OF PROPOSITIONS. SECT. XVII. 103 ciple of Identity and Contradiction ; (2) Sufficient Reason, and (3) Excluded Middle. (1.) The first Principle is sometimes spoken of as two, as in fact it is. (a) Where the terms are synonymous, or the judg- ment affirms the identity of the Subject and Pril?ciple 0 f the Predicate. Such is the case in all Defini- Identlty -- tions ; thus, a triangle is “ a figure with three angles,” — “ a quadruped is an animal with four feet.” ( b ) But there are some terms the relation between which is so founded in the nature of the oh- Princi p )e 0 f jects for which they stand, that the relation Contradlction - cannot be denied without destroying the conception of one or the other of these objects. Thus if we say, “ every effect must have a cause ; ” this is not a judg- ment of identity, for “ effect ” and “ cause ” are not the same. But the affirmation depends upon the prin- ciple of contradiction ; that is, if we say “ here is an effect without a cause,” we at the same time deny that it is an effect. If we say that “ this triangle has but two sides,” we deny that it is “ a triangle.” 423. The force of this ground of affirmation is well exhibited and tested by resolving the judg- illustration, ment into a cognition with its modal. Thus in the Principle of Identity, we have “ Vic- toria is Queen of England,” resolved into a cognition or term, it is “ Victoria Queen of England.” Again, a “ triangle has three sides,” — a “ three-sided tri- angle.” 424. Or to try the principle of contradiction, “ this effect has no cause,” becomes “ a causeless effect ; ” — “ this triangle has two sides only,” becomes “ a two- sided triangle.” In each of these cases the term and its modal are incompatible, and taken together consti- tute an impossibility. 425. (2.) The second ground of affirmation is called sufficient cause or sufficient reason. sufficient reason. {a) This ground assumes that there is no sufficient ground or reason in the nature of the matter itself. 104 LOGIC. — PART I. [CHAP If we say, “ the Earth exists,” the will of the Creatoi Reason of is considered as the ground of the reality of bemg. its being, if we gay^ « all bodies gravitate,” the will of the Creator is again considered the ground of the reality of the truth which we affirm. Or if we speak of the acts of man, whether past, present, or future, his will is considered the sufficient ground of the reality of these acts, the ratio essendi. (b) The means by which we know the reality, the ratio cognoscendi , may and generally are in fact quite Reason of different from the ground of the reality itself, knowing. Take the reality of gravitation, for instance, the ground of the reality is the will of God ; but our means of knowing the reality are experience and ob- servation. The reality of the Positive Institutions of Christianity depends upon the will of God for its ground, but one means of knowing that reality is Reve- lation. 426. (3.) The third ground of Affirmation is called Excluded Middle, the Excluded Middle. Between any Judgment and its Contradictory there is no Middle or Third Judgment. TIence in any case if we prove the falsity of one judgment, this becomes the ground for affirming its contradictory. 427. But there is especially one class of Judgments which can be affirmed on no other ground than that of Excluded Middle. 428. Such is the case with all affirmative Proposi- Affiimatives tions with negative Predicates, and all in Predicates. 11 ' 6 Avhich the Predicate denotes infinity. 429. In proving a Proposition with an affirmative Copula, we include the Subject in the sphere of the proof of Nega- Predicate, and this Ave do by showing that fives. the Subject has the Essentia denoted by the Predicate. But if the Predicate be negative, it is de- noted by no matter of its own ; and Ave can include the Subject in the sphere of a negative Predicate only, by showing that it does not contain the Essentia of its n.] OF PROPOSITIONS. SECT. XVII. 105 Positive. That is, we disprove the Proposition with the positive Predicate (A is B), and infer by Excluded Middle its contradictory that “ A is non-B,” which is at once resolved into “ A is not B.” 430. So also if the Predicate is infinite, as “ space is infinite ; ” we can affirm or prove our own Proof of Infi . judgment only on the ground of the falsity nites - of the contradictory, and by the principle of Excluded Middle.* God, Eternity, and Space can have no bounds, therefore they are infinite. * I do not propose here to touch the question between Sir William Hamilton and Scheliing and Cousin, with regard to our direct cognition of the infini te and unconditioned. I am not speaking of cognition but of proof ; the former in their phrase is the function of the Reason, the latter of the Un- derstanding. 5 * 106 LOGIC. — PART I. [CHAP CHAPTER III. OF SYLLOGISMS. SECTION I. Classification of Syllogisms. 431. A Judgment is called Intuitive wlien the mind intuitive judg- perceives and affirms the relation between ments. two cognitions when they are brought toge- ther in consciousness, without the intervention or aid of any other cognition. 432. But it is not always the case that when two cognitions are thus brought together in the conscious- ly^ to in- ness, the mind affirms or denies any kind of tuition. agreement- intuitively. It may be at a loss or in doubt. This doubt or inability to see the relation must he the result of the limited nature of our faculties. Ho such doubt or hesitation can he felt by an omni- scient mind. 433. If now we have two cognitions, A and B, and cannot see the relation between them, so as to consti- Deduotive tute them into a judgment intuitively, we judgments. ma y se e the relation between each one of them, and a third term, as C for instance. We may see that “ A ” is C, and that C is “ B,” and from these two intuitive judgments we may have the judgment A is B, which in that case is called a Deductvoe Judg- ment. HI.] OF SYLLOGISMS. SECT. I. 107 434. Thus all deductive judgments, which in fact make up the great mass of human knowledge Deductiv# and science, are based upon intuitive judg- e d d u“on n 1n b td- ments as their premises, and may be resolved tlve - hack into such intuitive judgments. 435. The term which is thus brought in as the means of forming the two judgments is called the Middle Tekm. And when there is but one Middle Terms. Middle term, the conclusion A is B is a Deductive judg- ment of the first degree, or but one step removed from the Intuitive. If, however, two such Deductive judg- ments become Premises to a Conclusion still further removed, there will have been more than one Middle term and more than two Intuitive judgments. The Deductive judgments, however, differ from each other only in the degree of remoteness from the primary In- tuitive judgments, which constituted the first elements in their deduction. 436. The Deductive Judgment or Conclusion is never contained in or derived from one of the Me diate infer- Premises alone by any process of Imme- ence - diate Inference. But it is deduced from the two Pre- mises by means of the Middle term, and is therefore a Mediate Inference. 437. By Syllogism we mean any combination of two judgments as Premises in such a way as syllogism de- that a third, different in matter from either fined - of them taken separately, results. The judgment so re- sulting is called the Conclusion. 438. Syllogisms are of three kinds ; Categorical, Conditional, and Disjunctive. They are syllogisms c/ eluded in P. m.] OF SYLLOGISMS. SECT. II. 117 Then we have Some P is not M, S is M, and S may or may not he P ; Or suppose some in P only is in M and the rest not, and then we may have — Some P is M, S is not M, in this case too, S may be or may not be P. 477. From what has been said, it will appear, 1. That if both Premises are negative, Five Canon3 of we can have no Conclusion. validity. 2. If one Premise is negative the Conclusion must be negative. 3. If both Premises are affirmative the Conclusion must be affirmative. 4. The Middle Term must be distributed in one of the Premises ; and 5. Ho Term may be distributed in the Conclusion, which was not distributed in the Premises.* 478. By the First of these Rules the sixteen Moods with negative Premises are excluded from T he First ex- being valid in any Figure. By the Second, sixteen the sixteen with one negative Premise and Second , six . affirmative Conclusions; and by the Third, teenmore - the eight with affirmative Premises and a m ™ rd ’ eisht negative Conclusion. 479. By the Fourth and Fifth combined, all those Moods in which both Premises are particu- FoU rth & Fifth, lar, are excluded ; since if both are particular six - (and one must be affirmative), there can be but one term distributed in the Premises — and if both Pre- mises are affirmative, there will be none. In this case there will be undistributed Middle. But if one Premise is negative the Conclusion must be so too, * The following hexameters have been found to assist the memory in retaining these fundamental requirements of simple Categorical Syllo- gisms : Distribuas Medium : nec quartus terminus adsit Utraque nec praemissa negans, nec particularis : Sectetur partem Conclusio deteriorem : Et non distribuat, nisi cum Praemissa, negetve. 118 LOGIC. PART I. [CHAP. and then we shall have either Illicit Process of the Major or Undistributed Middle. 480. By the operation of the same rules, Fourth and six more. Fifth, it will be found that if one Premise be particular there can be no universal Conclusion. (1st) Suppose the conclusion to be A ; in order to that, the Premises must be both affirmative — and with one of them, Particular Affirmative — there will be but one term distributed in the Premises, if that be the Minor, we shall have undistributed Middle, and if the Middle we shall have illicit of the Minor. (3d) Suppose the conclusion to be E, one Premise must be negative, and all three terms distributed in the Premises. But there are no Premises that fulfil this condition, except A and E, and O and E. But O and E are both negative, and can have no conclusion ; A and E are universal, and therefore do not come under this rule. 481. By the same reasoning it will be found that ieo. IEO will involve an Illicit Process of the Major in all the Figures.* I 482. The eleven valid Moods are— AAA, AAI, Eleven valid. AEE, AEO, All, AOO, E A^, EAO, EIO, IAI and OAO. 483. Hot all of these, however, are valid in each of the Four Figures which we have just described. III. The Application of Moods to the Figures. 484. In the First Figures (1) if the Major Premise Application of be particular we can have no Conclusion — First Figure. for (a) if the Minor be Affirmative we should * The Moods excluded by these Rules are : By the First — EEA, EEE, EEI, EEO, EOA, EOE, EOI, EOO, OEA, OEE, OEI, OEO, 00 A, OOE, 001, and 000— (16). By the Second — EAA, EAI, AEA, AEI, EIA, Eli, IEA, IEI, OAA, OAI, AOA, AOI, OIA, Oil, IOA, IOI— (16). By the Third— AAE, AAO, AIE, AIO, IAE, IAO, HE, 100— (8). By the Fourth and Fifth— (1) OIE, 010, IOE, IIA, III, IIO— (6). “ “ (2) AOE, OAE, IAA, IEE, ALA, EIE— (6). “ “ (3) IEO— (1). In all 16 + 16 + 8 + 6 + 6 + 1 = 63. OF SYLLOGISMS.— SECT. II. 119 m.] have an undistributed Middle ; and (b) if Negative, the Conclusion must be Negative also, and that would in- volve an Illicit Process of the Major. (2.) If the Minor be Negative there can be no Con- clusion ; for the Major Premise would have to be Affirmative, and that would involve an Illicit Process of the Major. Hence in the First Figure the Major Premise must be A or E, and the Minor A or I, and we S ix valid-four may have AAA, AAI, EAE, EAO, All, usefuh EIO. But as AAI and EAO have particular conclusions, when we might have from the same Premises an uni- versal one, they are useless and so dismissed from fur- ther consideration. 485. These Four Syllogisms are called Barbara , Celarent , Darii , and Ferio* Names. 486. In the Second Figure. If both Premises are Affirmative we can have no Conclusion ; second Figure, since the Middle term, being Predicate in both, would be undistributed. * As examples we may have the following : Barbara. “ Those who derive benefit from every exertion of their indus- try, are more likely to be industrious than laborers employed by the day. Journeymen who work by the piece derive benefit from every exertion of their industry ; therefore journeymen who work by the piece are more likely to he industrious than laborers employed by the day.” Celarent. “ No real hardship upon individuals should be authorized by legislative enactment. The impress of sailors is a real hardship upon indi- viduals, therefore the impress of sailors should not he authorized by legis- lative enactment.” Darii. “ Every thing which obstructs the free course of justice deserves the reprobation of the virtuous. There are modes of enforcing the strict letter of the law which obstruct the free course of justice ; therefore there are some modes of enforcing the strict letter of the law which deserve the reprobation of the virtuous.” Ferio. “ Those who endure dangers and face death merely for the sake of acquiring glory to themselves, without being influenced by any desire to benefit their country, are not possessed of true fortitude. But it cannot be denied that some of the heroes of antiquity endured dangers and faced death, merely for the sake of acquiring glory to themselves, without being influenced by any desire to benefit their country. Consequently several of the heroes of antiquity were not possessed of true fortitude.” 120 LOGIC. PAET I. [CHAP. And if the Major Premise be Particular there can be no Conclusion, since that would involve an Illicit Process of the Major. Hence we have in the Second Figure — AEE, AEO, six valid— four EAE, EAO, EIO, and AOO. But AEO and EAO have particular Conclusions when we might have universal, and hence they are dismissed as useless. 487. It will be observed, that all the Conclusions c N o°ncS ive in this Figure are Negative. 488. The four valid and useful Syllogisms in the Examples. Figure are called Cesar e, Camestires , Festino , and Baroko .* 489. In the Third Figure there can be no Universal Third Figure. Conclusion — for in order to such a Conclu- sion both Premises must be Universal ; but if both are no universal Affirmative, the Minor term will be undis- condusions. tributed, and hence a Universal Affirmative would be Illicit of the Minor ; and if the Minor be Negative the Major Premise must be Affirmative, and that would give an Illicit Process of the Major in a Negative Conclusion. And for the same reason there can be no conclusion if the Minor Premise be a Nega- tive. 490. Hence in the Third Figure we can have only six valid names. A AI, All, EAO, EIO, IAI and OAO. * For examples take the following : Cesare. “ No conscientious person wilfully violates a solemn engagement. Every careless clergyman wilfully violates a solemn engagement ; therefore no careless clergyman is a conscientious person.” Camestres. “ All those who are qualified for sea-service must possess some knowledge of the arts of navigation. Mere inland watermen do not possess any knowledge of the arts of navigation ; therefore mere inland watermen are not qualified for sea-service.” Festino. “ No man of sound sense can despise the study of the classics. Some modern pretenders to literature do, however, despise the study of the classics ; therefore some of the modern pretenders to literature are not men of sound sense.” Barolco. “ All the fixed stars emit light from themselves. Yet there are some of the heavenly bodies which do not emit light from themselves ; therefore some of the heavenly bodies are not fixed stars.” III.] OF SYLLOGISMS. SECT. II. 121 The six Syllogisms of the Third Figure are Darapti , Disarms, Datisi , Felapton , Bokardo , and Feriso .* 491. In the Fourth Figure, with A for Major, we must provide for the distribution of the Mid- Fourth Figure, die term in the Minor Premise by making that Premise Universal. If then the Minor Premise be A, we may have I for Conclusion (A would be illicit of the Major). If the Minor Premise be E, we may have E and O for Conclusions. But O is useless. Hence AAI and AEE. With E for Major Premise the Minor must be affirmative. If A, we have O for Conclusion (E would be illicit of the Minor). If it be I, we have O also for Conclusion. Hence EAO and EIO. With I for Major we must have A for Minor to dis- tribute the Middle, and hence I is the only Conclusion. Hence IAI. With O for Major we must have a negative Con- * Examples : Darapti. “ To be ashamed of one’s birth, profession, or rank in life, has been represented as the fault of modesty — whereas in reality it is a symp- tom of pride ; so that even that which is a symptom of pride has been repre- sented as the result of modesty.” Disamis. “ Some practices which the divine law allows are under parti- cular circumstances inexpedient. All practices which the divine law allows however are in themselves consistent with holiness ; therefore some things which are in themselves consistent with holiness are under particular cir- cumstances inexpedient.” Datisi. “ Every kind of pride is wholly inconsistent with the spirit of religion. Yet there are several kinds of pride which are highly commended by the world, therefore there are feelings highly commended by the world which are wholly inconsistent with the spirit of true religion.” Felapton. “ No conspiracies against the liberty of the country lay any just obligation on the conscience. All such conspiracies, however, have the nature of contracts ; hence some contracts do not lay any just obligation upon the conscience.” Bokardo. “ Some compositions of an imitative nature, calculated by sub- limity of idea and beauty of diction to expand and delight the mind and to excite every noble passion, are not written in verse. All such compositions, however, are called poems ; therefore some works justly called poems, are not written in verse.” Feriso. “ No prejudices are compatible with a state of perfection — but some prejudices are innocent ; therefore some innocent things are not com- patible with a state of perfection.” 6 122 LOGIC. PART I. [CHAP. elusion, which would involve an Illicit Process of the Major. Hence in the Fourth Figure we have AAI, AEE, Five valid Forms. E AO, EIO, and IAI. 492. The five valid and useful Syllogisms in the Fourth Figure are, Bramantvp , Camenes , Bimaris, Fesapo , and Fresison .* 493. Of the Eleven valid Moods, we have AAA Recapitulation, valid only in the First Figure ; AAI in the First, Third, and Fourth, but useless in the First ; AEE valid in the Second and Fourth ; AEO in the Second and Fourth, hut useless in both ; All valid in the First and Third ; AOO in the Second ; EAE in the First and Second ; EAO in all, but useless in the First and Second ; EIO valid in all Figures ; IAI in the Third and Fourth ; OAO in the Third. 494. In the whole, then, we have Nineteen valid Nineteen valid and useful elementary Forms in Pure Cate- Syiiogisms. g 0 ri c al Syllogisms ; — their names have al- ready been given. But for the convenience of remem- bering, especially for those who understand Latin Prosody, they have been arranged into the following lines : BArbArA, CElArEnt, DArll, FErlOque, prioris • CEsArE, CAmEstrEs, FEstlnO, BArOkO, secun- dae ; Terlia, DArAptI, DIsAmls, DAtlsI, FElAptON ; ' BOkArdO, FErlsOn habet : Quarta insuper addit BrAmAntlp, CAmEnEs, DlmArls, FEsApO, FrE- slsOn. * Examples : Bramanlip. “All diamonds consist of carbon — but all carbon is com- bustible ; therefore some combustible substances are diamonds.” Camenes. “ All the planets are opaque bodies. No opaque bodies are capable of transmitting light in any other way than by reflection ; therefore bodies capable of transmitting light in other ways than by reflection are not planets.” Dimaris. “ Some of the inhabitants of the sea have antennae and horny pointed legs — hut all animals of this description are insects ; therefore some msects are inhabitants of the sea.” m.] OF SYLLOGISMS. SECT. III. 123 The vowels printed in capitals will be recognized as indicating the Mood of the Syllogism, and the con- sonants besides making out the words serve another purpose, to he explained by and by. SECTION III. Of Indirect Conclusions. 495. There has sometimes been reckoned a class of Indirect Moods, hut this is unnecessary ; indirect Moods, since all that are reckoned as Indirect Moods are merely some one of the Direct Moods with the Premises trans- posed. Thus for example, All B is A, Ho C is B, .■. Some A is not 0. This is simply Fesapo with the Premises transposed, and the Indirect Conclusion. 496. An Indirect Conclusion is one in which the order of the terms of the Direct Conclusion Indirec t con- is inverted, so as that the Subject becomes vereeSfthe'w: Predicate, and vice versa ; and an Indirect rect - Conclusion is valid when (1) it does not change the quality of the Direct Conclusion ; nor (2) distribute any term in the Indirect Conclusion which was not distributed in the Premises. 497. It is worth while to notice, however, that in most cases we may have an Indirect Conclusion as well as the Direct.* Thus — Barbara : Fesapo. “No vice is to be admitted as a species of relaxation suited to a Christian. Every species of relaxation suited to a Christian consists of a cessation from ordinary occupations. Wherefore there are cessations from ordinary occupations which are not vice.” Fresison. “ No fallacious argument is a legitimate mode of persuasion. And some legitimate modes of persuasion fail of securing acquiescence ; therefore some arguments which fail of securing acquiescence are not fal- lacious.” * In fact it will be seen that all the Conclusions in the Fourth Figure are but the Indirect Conclusion from the same Premises, regarded (by con- sidering' the Major term as Minor, and vice versa ) as in the First Figure.” 124 LOGIC. — PART I. [CHAP. Indirect Con- All T IS X, elusions in all All 7 , i a "V Syllogisms. -tt.il Li lb X , .•. All Z is X — or indirectly, Some X is Z. Bramantip gives a more important Indirect Con- clusion still : All X is Y, All Y is Z, .*. Some Z is X — or indirectly, All X is Z. In the Direct Conclusion the Major term appears as undistributed in the Conclusion, whereas it was dis- tributed in the Major Premise. 498. Besides the above-named nineteen Syllogisms, any other of the valid Moods may have an incidental incidental va- validity, if its terms are so distributed either ndity. by s ig ns or the nature of the terms, or of the matter of the judgment as to secure us against Undis- tributed Middle and Illicit Process. 499. Again, if we have two affirmative Premises in Analogy prov- the Second Figure, both extremes are in the Figure. bccu " d same category — the Middle term ; and then they must each of them have the Essentia of the concep- tion which the term denotes. They have therefore so much matter in common — that is, so many points of identity, and consequently there is an analogy between the Extremes. SECTION IV. Of the Conversion of Syllogisms. 500. It has been thought that all Mediate Inference could be reduced to the celebrated Dictum of Aris- Aristotie’s totle, called the Dictum* de Omni et Nullo ; D'dum. that a Whatever may be predicated of a * Aristotle appears to have thought that all Mediate Inference could be reduced to this one Canon. And so by Conversion it can. But later writ- ers have given us dicta for each of the other Figures (Lambert, Neues Organon, Part I. ch. 4, § 232). That for the Second Figure is called the Dictum da Diverso : “ If a cer- tain attribute can be predicated (affirmatively or negatively) of every III.] OF SYLLOGISMS. SECT. IV. 125 class [the Middle term], may he predicated as Major term of whatever is comprehended in that class, as a Minor term ; and conversely whatever may he denied of that class may be denied of whatever is compre- hended under it.” 501. This is substantially the same as the first Axiom of Mediate Inference which we have given (461) ; and to prove that all cases of Mediate Inference can be reduced to it, various expedients have been de- vised for reducing the Syllogisms of the Second, Third, and Fourth Figures to Syllogisms in the same matter in the First Figure. 502. If this were the only object to be gained in the Reduction of Syllogisms, as it is called, it objpct3 of Re . would hardly be worth the time and pains duction - which it costs, since the other axioms given above are as primary and as satisfactory as the Dictum of Aristotle itself. But there is a further practical importance in the Reduction of Syllogisms which makes it worth our while to examine the laws and processes by which it can be done. Such is the nature and imper- fections of language that we cannot always express our judgments exactly as we would, and many an expres- sion which suits all the requirements of Logic, fail to meet the demands of Rhetoric. 503. In order to effect this Reduction or Conver- sion, we need to resort to Conversion, Per- Me an 9 ofcon- mutation, and Transposition of Premises, one version - or the other of them, and sometimes more. member of a class — any subject of which it cannot be so predicated does not belong to that class.” The Third Figure (1) Dictum, de Exemplo : “ If a certain attribute can be affirmed of any portion of the members of a class, it is not incompatible with the distinctive attributes of that class ; ” — and (2) the Dictum de Excepto : “ If a certain attribute can be denied of any portion of the members of a class, it is not inseparable from the distinctive attributes of that class.” He also gives what he calls a Dictum for the Fourth Figure, which he calls the Dictum de Reciproco. But it is hardly worth quoting. The Fourth Figure is at best but an inverse of the First, and depends upon the same Principle inverted. For the above quotations I am indebted to the Oxford edition of Aldrich, 1819, pp. 72 and 80. 126 LOGIC. — PART I. [CHAP. Conversion and Permutation of Propositions have already been sufficiently explained. 504. Transposition consists merely in changing the Transposition relative position of the Premises ; thus, for of Premises. 7 7 This it will be observed is not changing the Syllo- gism from one Figure into another. It is merely writ- ing the Minor Premise first instead of the Major. Sir William Hamilton says that this was generally done for several centuries after Aristotle. And we shall see by and by that in practice, where we are guided by instinct and common sense, with no regard to Logical Formulae, we usually state the Major Premise first in the Deductive Methods, and the Minor first in the Inductive Methods. 505. But as the transposition changes neither the quantity nor the quality of the Premises, nor yet the relative position of any of the terms in regard to the laws of the distribution of terms by Position, it can have no effect upon the concluding force of the Pre- mises. 506. In these cases we obtain the result in three Different forms different forms — we may get (1) the same oto um com iu- Q on( q us j on j n tp e Converse as in the Exposita ; or we may get (2) one from which that is derived as an Immediate Inference ; and we may get (3) a Con- clusion contradictory to that of the Exposita, but false ; from which of course the truth of that in the Exposita is inferred immediately. 507. It is with reference to this process of Conver- sion of Syllogisms, that the Consonants used in the signification of names that have been given to them are §ie ns Name8 !>" selected; the Vowels are used to indicate syllogisms. the Mood. But the Consonants indicate the processes and means of converting them into Syllo- gisms in the First Figure. M is P, S is M, '. S is P, w r e shall have S is P. m.] OF SYLLOGISMS. SECT. IV. 127 All beginning with B, can be proved in Barbara. “ “ “ C, “ “ “ u Celarent. “ “ “ D, “ “ “ “ Darii. 44 44 44 ^ 44 44 44 44 The steps to be taken are indicated as follows : “ m ” denotes that the Premises are to “ m " transposes -j . -• Premises. be transposed. “ s ” denotes that in order to reduce a Syllogism to the First Figure, the Proposition signified converta by the vowel before the s is to be converted simpIy - simply. Thus the Minor Premise in Camestres — Flo Y is Z, is to be converted into Flo Z is Y. “p ” denotes that the Proposition indicated by the vowel before it, is to be converted by limita- tion, or per accidens. “ h ” occurs in Baroko and Bokardo only. These are reduced to Barbara by what is called reductio ad impossibile. The reduction is effected by “ gives a substituting the contradictory of the Conclu- concfus'wnF sion for the Premise, indicated by the vowel imme- diately before the “ k,” and proceeding as before.* In this way we get a Conclusion contradictory to the Pre- mise for which we have substituted the contradictory of the old Conclusion. If now the new Conclusion is false, or absurd, or impossible, the old one must have been true. We are in fact proving that the Conclusion is O, by the indirect method of proving that it cannot be A. 508. In the course of these reductions, it will be observed that the terms undergo several rela- tive changes, so that Major becomes Minor, &c., and vice versa. In that case the name of the Syl- logism ends in “s” or — -as “ Camenes,” “ Bra- mantip.” The Middle term also in Baroko and Bokardo becomes one of the Extremes. “ p converts • per accidens. Change of Terms. These rules have been expressed in the following lines : $ vult simpliciter verti ; P vero per acci- M vult transponi ; K per impossibile duci. 128 LOGIC. — PAKT I. [CHAP. 509. When in the course of the Conversion or Re- duction of Syllogisms we get a Conclusion in the same quality as that in the Exposita Syllogism, the process has been called Ostensive Reduc- tion. But if the Conclusion be in the opposite quality, Reciuctioad the Reduction is called Reductio ad hnpos- Absurdum. sibile, or Reductio ad Absurdum. 510. As examples in Ostensive Reduction, I will Examples. give only a few, as follows : Ostensive Reduction. Cesare to Celarent. No X is Y, s. No Y is X, cesare. All Z is Y, the Minor stands. , All Z is Y, .-. No Z is X, .• . No Z is X. Darapti to Darii. All Y is X, the Major stands , All Y is X, Darapti. All Y is Z, p- Some Z is Y, .•. Some Z is X, '. Some Z is X. Bramantip to Barbara. All X is Y, ) 1 i All Y is Z, Brama"- Y is Z, j m. ■ -i l Ail X is Y, Some Z is X, .\ Some X is Z, p Some Z is Felapton to Ferio. No Y is X, No Y is X, Felapton. All \ is Z, p- Some Z is Y, /. Some Z is not X, . Some Z is not Fresison to Ferio. No X is Y, s. NoYisX, Fusison. Some Y is Z, s. Some Z is Y, .•. Some Z is not X, .\ Some Z is not X. 511. Reductio ad Impossibile is effected by means of Contra-position and Excluded Middle. Baroko. Thus if we have in Baroko : Every star is fixed. Some luminous bodies are not fixed. .-. Some luminous bodies are not stars (such for in- stance as planets, meteors, &c.) in.] OF SYLLOGISMS. SECT. IV. 129 Let ns substitute for this Minor Premise the contra- dictory of the Conclusion and we shall have : Every star is fixed. All luminous bodies are stars. .•. All luminous bodies are fixed. But this Conclusion is false, consequently the Mi- nor Premise of the first Syllogism, Baroko, its contra- dictory, is true. And if that Premise is true (the Major Premise also), the Conclusion is irrefragable. In the same way we may test Bokardo. 512. Or again, we may reduce Bokardo by contra- position of the Major to Ferio ; thus, Baroko t0 All X is Y, Fer ‘°- Some Z is not Y, .*. Some Z is not X. All X is Y, we may state by contra-position and conversion in E. — Xo non-Y is X, then we have as before, Some Z is not Y or non-Y, .•. Some Z is not X, which gives us the same conclusion in Eerio as we had in Baroko. 513. Again, we may reduce Bokardo to Darii, by permuting, and converting, and transposi- Bokardo to tion, as follows : Daril - Some slaves are not discontented. But All slaves are wronged. .•. Some who are wronged are not discontented. We may have : All slaves are wronged. Some not-discontented persons are slaves. .•. Some not-discontented are wronged. 514. This process of Reductio ad Impossibile may be applied to all Syllogisms, as well as to Procesg appli . Baroko and Bokardo, on the ground that if cable to aU - we substitute for any given Premise the contradictory of the Conclusion, we shall obtain for a new Conclusion the contradictory of the Premise ; or its contrary, in which, of course, the contradictory is included. 6 * 130 LOGIC. — PART I. [chap. Thus Barbara to Bokardo. All Y is X, ) by contra-posi- ( Some Z is not X, Bokardo' 0 'All Z is Y, > ti on of tlie Con- 7 All Z is Y, .•. All Z is X, ) elusion becomes ( .’. Some Y is not X. Thus from Celarent we may have Disamis in the Third Figure, and Festino of the Second. ceWent Xo Y is X, Some Z is X, or, Xo Y is X, and Fe”i s All Z is Y, All Z is Y, Some Z is X, no - .’. Xo Z is X, .’. Some Y is X, .’. Some Z is not Y. 515. It is often very important in general discus- sions to disembarrass ourselves of the details of Mood and Figure, and speak of Terms and Premises in the most general way ; even where the Differentia of the Figures would require, if they were recognized at all, a very important modification of our statement. 516. For this purpose we always consider an argu- omission of ment, unless otherwise expressly stated, as Figu!'e arities oi made in the First Figure, and when we speak of the Major Premise we mean that which either is the Major in the First Figure, or that which would become the Major if the Syllogism were converted into that Figure. And for the same purpose we consider all Xegative Propositions as Affirmative with Xega- tive Predicates, as we have a right to do. And hence we may always speak of that term which either is or would become on conversion of the Syllogism into the First Figure the Predicate of the Conclusion, as the Major term. If the Conclusion be affirmative that is the Major term, and if not we substitute for the Predicate of the Xegative Conclusion its connoted negative or privative, which of course becomes a Major to the others. 517. This may, perhaps, be thought to indicate a indicates no looseness and uncertainty with regard to the boutYerms. a whole nomenclature of Mood and Figure, which does not exist. But Ave have to take an argu- ment for the most part as Ave find it. And as it thus stands, it is no matter of choice or uncertainty which HI.] OF SYLLOGISMS. SECT. V. 131 are the Major and Minor terms by position. But to avoid the perplexity and the prolixity of continued repetition or detail, we may avail ourselves of the fact that all the Syllogisms may he reduced to the First Figure ; that is, the fact that with the same matter as that given in the Premises, we may prove the same Conclusion in the First Figure, and thus adopt the simplicity and brevity of discussion which there would be if there were only the one Figure. SECTION Y. Of Complex Syllogisms. 518. We have thus far in the investigation of the laws and formula of Syllogisms spoken only of the Simple Categoric Syllogisms. Although this is the simplest and primary formula, we but sel- aelJom meet dom meet with them in practice. In nearly Pure and sim- /» . i , • pie Formulas. every case one or more ot the terms is com- plex. Hence a Syllogism in which one or more terms has a modal, is called a Complex Syllogism. 519. Strictly speaking the simple term can be nothing more than a single word ; * which is simple Terms, either a noun, an adjective, or a verb in the Infinitive Mood. In adjectives I include participles used ad- jectively. 520. But it often happens that several words are used as the definition of a term instead of Definition for the term itself. Thus we have the term a Term - Negro — but instead of it we may use its definition in any case — as “ men with dark skins and woolly hairf &c. Now suppose that we had not the word “ Negro ” at all. In that case we should be obliged to use its * This must depend, however, somewhat upon the genius of a language. Perhaps the only exception, the only one that I have noticed in the English, is in those words which answer to the Aristotelian category “ where." We say a man is “in the house,” — “on the ground,” &c., &c. We have not in this respect any thing corresponding to the Greek termination 01 as in aypodi, oiicoBi, &C. 132 LOGIC. PART I. [CHAP. definition whenever we wish to nse the conception as a term at all. 521. This is precisely the case with regard to a Necessity for a. large part, by far the largest part of the conceptions which enter into our reasonings. There is no precise term for them ; and therefore we are obliged to use, instead of the term, what is really its definition. The Definition gives first the Genus and then the Dif- ferentia one after another. Thus for “ Negro ” we have [genus] men, — [1st differentia] with dark skins, — and [2d differentia] woolly hair. Suppose we wish to speak of those Christians who adhere strictly to their faith and live pious and devoted lives, as a class distin- tinguished from the rest, we have no one word by which to denote the class. Consequently when we want to express the conception, we are obliged to use the definition for want of a word to denote it. 522. In all such cases Ave may, if Ave please, regard Definition a the Definition as the Term and its Logical Mo™h and IU Modals, or as a simple term for all the ordi- nary purposes of deduction. 523. All Modals which have any logical force at Modais limit all, as has been shoAvn, either limit the com- siveness of the i;>rehensi veness oi the subject m reierence to quantity, or point out some condition, or time necessary to limit the scope of the judgment in order that it may he true. Hence the Modal will often make the whole of the difference between a Propo- sition that is true and one that is false. But as Bhetoric often requires some variety in ex- pression, the phraseology of Modals must often he changed, and in these changes Fallacies often occur. 524. The Modal of a subject limits the scope of the Modais of the judgment, by limiting the sphere of the fhe'tcope of 1 the subject itself. Now from the fundamental axiom, that the narrower the sphere the greater the amount of the matter of any conception, it follows that more may be predicated of a subject which is limited by a modal than can be predicated of the nr.] OF SYLLOGISMS. SECT. V. 133 same term without the Modal. Hence the dropping of the Modal would in some cases render the Proposition untrue. 525. Suppose now that the Middle term is first used with a Modal, and is used in the next Pre- Middle Term mise without one, we have in fact a different wlth a Modal - term ; and it will affect the formula differently accord- ing to its position. Let us then refer to the First Figure in which the Middle term is Subject of the Major Premise ln the First and Predicate of the Minor. If we drop the Figure - Modal in the Minor term we enlarge the sphere denoted by it, and by consequence it may become so large that the Major term could not be predicated of it. Thus, All true Christians enjoy the favor of God. Hypocrites are Christians. Hypocrites — But here it becomes obvious that the matter of the Predicate in the Major Premise could not be predicated of so comprehensive a sphere as “ Christians ; ” that is, “ all Christians,” — nor the Differentia of true Christians of the subject of the'Minor Premise. 526. How let us take an example of the opposite course : All Christians believe in Christ. The Waldenses were true Christians. .•. The Waldenses, &c. Here the conclusion is good. We include the Minor term by means of the Modal in a narrower and com- prehended sphere than that which, as Middle term, we had included in the Major term in the Major Pre- mise. 527. We have already seen that the Middle term must be once distributed in the Premises of a Syllo- gism, and in fact it is distributed in both Premises in two of them, Darapti and Felapton. But wherever it occurs as an undistributed term, it stands of course for a narrower though an undetermined sphere than if it 134 LOGIC. — PART I. [CHAP. were distributed. We have the following Rules for Three Rules, the dropping or assumption of Modals iii the same Syllogism. (1.) In all cases where the Middle term is undis- First Rule. ti’ibuted, as always in the Minor Premise in the First Figure for instance, we may always make the indeterminate undistributed term a determinate dis- tributed term, with a narrower sphere than the abso- lute or simple term, by joining to it its appropriate Modal. And when the Middle is twice distributed as in Darapti, and Felapton, and Fesapo, we may limit it in either Premise at discretion, but not in both unless it be with the same Modal. (2.) And conversely a Modal that was introduced second Rule, and used with the Middle term when used distributively, may not be omitted where it occurs in the other Premises as an undistributed term. This remark, for a reason similar to the one given in case of the last rule, does not apply to Darapti, Felapton, and Fesapo, in which the Middle term is distributed in both Premises. (3.) And finally, if the undistributed Middle occurs Third Rule. in the Maj or Premise, as in the Fourth Fi- gure with a Modal, that Modal may be dropped when the Middle term comes to be used as a distributed term in the Minor Premise. (4.) If in the Major Premise a Modal is used, extending the comprehensiveness of the judgment to Expansive all possible cases, then either in the Minor Modais. Premise or in the Conclusion we may have one pointing to any special case or class of cases, included within the comprehensiveness to which the Modal of the Major Premise extended it. Thus : “ Ho man is justified on any pretence in taking the life of one with whom he is living on terms of con- fidence/’ “ But Brutus was living on terms of confidence with Caesar.” “ Therefore Brutus was not justifiable in taking in.] OF SYLLOGISMS.— SECT. V. 135 Caesar’s life on the pretence which he pleaded — of a higher obligation to his country .” (5.) In regard to the Minor term, if it was used without a Modal in the Minor Premise it M odaisofthe was used in its most comprehensive sense ; MinorTerms - hence if we annex a Modal in the Conclusion we sim- ply narrow the sphere of the subject, which as we have before seen does not render the Proposition untrue. But if the Minor term had a Modal in the Minor Pre- mise, it may not be omitted in the Conclusion, since that would enlarge its sphere and possibly include thereby individuals of whom the predicate may not be affirmed. (6.) And in regard to the Major term the converse holds. If there was a Modal in the Major M 0da i gofthe Premise it may be omitted in the Conclu- Major Term - sion, as by so doing we enlarge its sphere and con- sequently include less matter. If therefore it was pre- dicable of the subject before the enlarge- Generei Rule ment of its sphere, then a fortiori it is after- wards. But if the Major term was in the dal - Premise without the Middle, no Modal can be intro- duced into the Conclusion, except that which was spoken of above as changing the indeterminate undis- tributed into a determined distributed, denoting the individuals included in the scope of the subject as a species. 528. We may then lay down the general proposi- tion that a Modal may at any time, and in General Pro . any position be attached to an undistributed aslimpuSn of a term, provided the Modal expresses the dif- Modah ferentia or peculiar property of that part of the sphere of the term which is taken into the scope of the judg- ment by its undistributed use. We thus convert the indeterminate undistributed term into a determinate distributed one with a narrower and comprehended sphere. 529. It is sometimes a matter of doubt whether a Modal shall be considered as belonging to the Subject or the Predicate of a Proposition. 136 LOGIC. PAKT I. [CHAP Change of the Modal from Subject to Pre- dicate, and vice versa. Protensive Models. It is not of so much importance to which it is con- sidered as belonging as might at first sight appear, as the Modal can easily be transferred from one term to the other. Thus, “ Drowning men catch at straws ; ” — “ Drowning ” is here a Modal of the Subject. But if we say, “Men catch at straws when they are drowning ,” the Modal is transferred to the Predicate, and the Proposition remains the same for all Logical purposes ; although that which was the differentia of a species in the sub- ject becomes the conditional of the genus in the Pre- dicate, and vice versa. 530. We have yet another important class of Mo- dals whose influence upon the deductive force of the Formulae we must consider. I mean those which indicate Protensive comprehension. 531. Such Modals seem rather to limit the Copula than the terms of a judgment. 532. It is obvious that when the Copulas in both the Premises are taken with unlimited Protension — Absolute pro- that is, with the adverb “ always ” or “ uni- tension. versally ” expressed or implied, we may have a Copula in the Conclusion with the same pro- tension. Let ns then consider those adverbial Modals which limit the Protension without giving a definite limit to it, such as “ sometimes,” “ generally,” “ rarely,” &c. 533. It is manifest that such Modals always limit the Subject, so that a Proposition in which one of them occurs cannot be regarded as universal. Nor is this all — they indicate that there is no one part of the Subject of which as a species the Predicate may be affirmed with unlimited Protension. It may be affirmed of any or all the individuals included in the Subject at some time, and at others perhaps it can be affirmed of none of them. 534:. Now if there is such a Modal in both Pre- mises, it is manifest that we can have no Conclusion. For example : Limited tension. In both Pre mises. m.J OF SYLLOGISMS. SECT. VI. 137 M is sometimes P. S is sometimes M. For it does not appear but that M may be included in P precisely then when S is not included in M, and vice versa. The Minor term may be included in the Middle when, and only when the Middle is not in- cluded in the Major term. 535. But if the Modal is in either Premise alone it must be in the Conclusion also. For if either !n one Pre . Subject is in its Predicate only sometimes, mise - then the Conclusion can affirm the Minor term to be in the Major only “ sometimes .” And at any particular time it can predicate the Major of the Minor only in a Problematic or Probable Judgment. The Conclusion with such a Modal in either Premise, therefore, may assume either of the two following forms : S is sometimes P ; or S may be P ; that is, it may be so without contradiction or logical absurdity. 536. We sometimes have a Protensive Modal, how- ever, when we ought to have a differential Protensive for 01' conditional, lhus : dai. “ Testimony sometimes leads us into error. The belief in miracles rests upon testimony. Hence the belief in miracles may be only an error.” Here for “ testimony sometimes ” we manifestly ought to have “ some testimony ; ” that is, “ some kinds of testimony misleads us.” But when we substitute “ some kinds of testimony,” for “ testimony sometimes,” we have not got the full force of the Modal or the exact meaning of the Propo- sition. It does not mean to affirm that there are any kinds of testimony that always mislead. The Modal of the Copula must therefore be still retained in some other form. We may say, “ some kinds of testimony occasionally mislead.” 138 logic. — part i. [chap. SECTION VI. Of Compound Syllogisms or Sorites. 537. The Syllogism gives us a Conclusion but one step further removed from the intuitive judgments than the Premises themselves, having but one Middle term. 538. We may however have in the same Formula sorites. any number of Middle terms with a deduction for a conclusion, of a corresponding degree of remote- ness from the Premises. Thus, A is B, Bis C, Cis D, .*. A is D. This is called a Sorites or Chain Syllogism. 539. In the usual form the Predicate o.f each Prc- prderof Terms mise becomes the subject of the next in a Form'.’ 6 Usual Universal Affirmative Proposition, until in the Conclusion we have the subject of the first Premise for subject as Minor term, and the Predicate of the last for Predicate as Major term.* 540. In this Formula each successive term begin- ning with the Minor, has a wider and comprehending sphere until we come to the last. Consequently what- ever may be predicated of the last or Major term, may be predicated of the first or Minor term just the same as if there had been but one Middle term. 541. It is manifest that as there can be but one One Minor Conclusion, so there can be but one Major Term? 6 aiJJor and but one Minor Premise. But there may * A Sorites, called the Goclenian, has been noticed also — consisting of Propositions in which the terms are arranged in the inverse order ; Thus B is A, Cis B, D is C, E is D, A is E. And this form with the usual form given above, are all that have hitherto been recognized so far as I know. IIX.J OF SYLLOGISMS. — SECT. VI. 139 be any number of Intermediate Premises introduced between the Minor and the Major instead of intermediate one — each Premise introducing a new Mid- Premises - die term, until the last becomes with the Major term either the Subject or Predicate in the same Proposi- tion. Thus : All Z is A, All A is B, All B is C, All C is “ All “ is X, All Is is X, .-. All Z is X. 542. But there is no necessity for confining the Sorites within such narrow limits as have Mor e than one usually been assigned to it. In fact we can- formof Sorite3 - not keep it within these limits. Other forms and varie- ties are constantly occurring, and the business of Logic is rather to account for what is, than to determine what ought to be. 513. It is obvious, that if we can introduce one Universal Affirmative between the Minor and Major Premise of any Syllogism, we can introduce any num- ber so long as the Subject of the one becomes the Pre- dicate of the next, or vice versa / in which case each new Middle term will be once distributed. 541. Hence in any Syllogism, if after transposing the Premises, we can pass from the Minor Any syllogism Premise to an Universal Affirmative and “anded. e from that again to the Major Premise, we may conti- nue on with any number of Universal Affirmative In- termediate Premises, without changing the essential character of the Sorites. 545. In this way we find that each of the nineteen Syllogisms may be expanded into Sorites. 546. In the expansion of the Syllogisms by this means we are to regard only the two Falla- Cautions t0 ba cies of Figure — Undistributed Middle and resarded - Illicit Process. Each Middle term must be distributed 140 LOGIC. — PART I. [CHAP. once, and no term distributed in the Conclusion which was not distributed in the Major or Minor Premise. 547. It is sometimes the case that in the expansion of the Syllogism, we are obliged to resort to the inverse The Gocienian of the usual method, or to what is called the pansion. Gocienian method. Thus in the expansion of Camestres : JSTo Z is A, All B is A, All C is B, All X is C, .-. NoZisX; in which case the Subject of each Intermediate Pre- mise becomes the Predicate of the next, and the inverse method would give an illicit of the Major. 548. The introduction of a Negative Intermediate Premise between two Affirmatives, or of a Particular a Negative between two Universals, will have its usual intermediate, effects upon the quantity and quality of the Conclusion. Thus Darapti expanded by a Negative Intermediate Premise becomes : All Y is Z, No Y is B, All B is X, Some Z is not X. 549. The Sorites may be resolved into as many int S o°sy1iog < ilms ed Syllogisms as it has Premises less one. 550. The hrst Premise containing the Minor term of the Sorites is the Minor Premise of the first Syllo- gism, and the second Premise is the Major. The Con- clusion of the first Syllogism becomes the Minor Pre- mise, and the third Premise of the Sorites becomes the Major Premise of the second Syllogism, and so on, each Conclusion becoming Minor Premise for the next Syllogism. 551. In this way each Middle term after the first serves as a Major term to establish the Minor Pre- mise of the Syllogism in which it is to serve as a Middle. OF SYLLOGISMS. — SECT. VI. 141 m.J Thus the most ordinary form of the Sorites is : All A is B, First Example. All B is C, All C is D, All D is E, .-. All A is E ; which is resolved into Syllogisms as follows : 1st. 2d. 3d. All B is C, All C is D, All D is E, All A is B, All A is C, All A is D, .-. All A is C, All A is D, .-. All A is E. In this case each of the Syllogisms is in Barbara. 552. For another example take the following : All C is A, C is not D, All B is D, .*. Some A is not B ; which is resolved as Second Exam- ple. follows : 1st. 2d. C is not D, All B is D, All C is A, Some A is not D, .\ Some A is not D. .*. Some A is not B. The first of these Syllogisms will at once be seen to be Felapton (3d Fig.), and the second is Baroko of the 2d Fig. 553. In most cases where Bramantip occurs in the course of resolving the Sorites into Syllo- The peculiarity gisms, it is necessary to use the indirect ° fBramant ‘p- Conclusion for the Minor Premise to the next Syllo- gism. Thus : All A is Z, All B is A, All FT is B, All X is X, .•. Some Z is X. (1) All B is A, (2) All X is B, (3) All X is X, All A is Z (ind. Con.) All B is Z, Some Z is X, .•. Some Z is B, .*. Some Z is X, .\ Some Z is X. The same thing occurs in Disamis, Bokardo, Braman- tip, Dimaris, &c. &c. 142 LOGIC. PART I. [chap. 554. In the statement of the Sorites, as in fact in the statement of the Syllogism, there is sometimes a combination rhetorical complication of terms, by means BtaLm'ent'" 'of of which the Subject is kept more constantly sorites. before the mind than it could otherwise be. This is effected by converting each Proposition into a single cognition as we pass along according to the principle laid down [187]. Thus, “ All men are mortal. All mortal men are sinners. Christ died for all sinful men. But the sinners for whom Christ died must exercise faith and repentance towards God in order to obtain the benefits of Ilis death ; therefore those who do not believe in Him and live a life of faith and repentance, will be left to the full consequences of their sins.” 555. The only additional point to be secured in caution against analyzing such arguments, is that no new matter.' 11011 * term be surreptitiously introduced by this process of accumulation. SECTION VII. Of the Incomplete Formula. 556. For the most part in ordinary reasoning one Premise and sometimes two are suppressed ; that is, premises often they are not stated in the course of the argu- suppressed. m ent. The reason is often a rhetorical one. It would be tedious to be constantly repeating what is so obvious as to be known and admitted by all. Logic however never supposes any thing ; it requires all the Premises to be stated, and hence we must examine these abridged forms of argument. 557. They are called Enthymemes , and may be of Four kinds. foul’ kinds (1.) When one Premise of a Syllogism is omitted. First. In this case we have the Conclusion and one Premise, but the Conclusion and the Premise contain III.] OF SYLLOGISMS. SECT. VII. 143 only three distinct terms ; as, All Y is X, therefore All Z is X. (2.) We may have the Conclusion and one Premise with four distinct terms ; as, All A is B, second, therefore All Z is X. In this case the Enthymeme is an abridgment of the Sorites, and the given Premise is the Middle Premise. (3.) Or there may be a Conclusion given with more than one Premise, and yet not a complete Third. Sorites. (4.) In the fourth case we may have several Pre- mises in which there is one term common to Fourth, them all. 558. Enthymemes with three terms are easily com- pleted into Syllogisms. The Conclusion lie- completion of cessarily contains the Major and the Minor of nt tt“ em &st terms. The given Premise contains the Mid- kind - die term and either the Minor or the Major term, and determines the position of the Middle term as Subject or Predicate of the given Premise. From this we learn the Figure, the quality and quantity of the Premise to be supplied. Thus, if the Conclusion he A, the Premises must he AA. If the Conclusion be E, the Premises must be either EA or AE. If the Conclusion be I, the Premises must be either AI or IA. — (AA of course -would he valid but not necessary.) If the Conclusion he O, the Premises must be either El, OA or AO. 559. Ve must always remember that we have no right to supply a Universal Premise in the No Uniyersal completion of an Enthymeme when a Parti- dS' ™iiss r u cular one would answer. This would be 13 nectssary ' attributing to him who made the Enthymeme what he never said and what his argument does not necessarily imply. For this reason no Enthymeme can require to be completed in Darapti, as Disamis and Datisi are in 144 LOGIC. — PART I. [chap. the same Figure, in one or the other of which any En- thymeme with a Conclusion in I in the 3d Figure can he completed. 560. If it is found impossible to complete the Syl- logism — that is, to find a Premise that will connect the given Premise legitimately with the Conclusion, the Enthymeme includes or implies a fallacy which ren- ders its conclusion worthless or worse. 561. Of Entliymemes with four terms there can be Enthymemes only the one variety given, except as the dif- Terms. lerence m quantity and quality may vary it : All A is B, .-. C is D. Any variation of the relative position of these terms would produce no variety in the Formulae. It could only change the term which a given letter represents. 562. If an Enthymeme has four distinct terms, two of them must of course be Middle terms, and it can be completed into completed into a Sorites with three Pre- a sorites. mises ; thus, A is B, therefore C is D. — “The state punishes no man for his religious opinions, there- fore heresy is no crime.” 563. Here we have four distinct terms — “ state,” “ religious opinions,” “ heresy,” and “ crime ; ” and the latter of the two Propositions is given as a Conclu- sion from the former. Let us then put A for state, B for religious opinions, C for heresy, and D for crime, and we shall have : All C is B, No A is B, All D is A, No C is D, or C is not D. 564. From which it appears that the Enthymeme implied the two following Propositions : 1st, the Minor Premise that all “ heresy ” is “ religious opinion ” of some kind or another. — 2d, for the Major Premise whatever is a “ crime ” is “ punished by the stated Or as for rhetorical purposes one would be most likely to m.] OF SYLLOGISMS. SECT. YU. 145 express the same thing by contra-position — “ whatever is not punished by the state is no crime.” 565. But in the third case we may have the Con- clusion of a Sorites with two or more of the Enthymemes -r-> lii j with more than Premises given and others suppressed. four terms. 566. A fundamental maxim in the completion of these Enthymematic Formulae, is that in No new tcrma completing them no term may be used that introduced - was not contained in the Elements of the Formulae that were actually given. If now we have — A is B, B is C, C is D, D is E, E is F, .•. A is F ; it is obvious that if the 1st, 3d, and 5th Premises were omitted, we should have all the terms given, A, B, C, D, E and F. Thus, B is C, D is E, .-. A is F, and we could easily restore the wanting Premises by principles with which we are already familiar. 567. But if one Premise were stricken out or omit- ted, the full form could not he completed. We should have All B is C, j ) All D is E, A is F. \ 01 j All A is F ; which would be completed thus : All A is B, or, All A is D, All B is C, All D is E, AH C is F, All E is F, All A is F, All A is F. 568. As the Middle term is usually a general term, that is a term denoting a class, it is obvious Enth ymemes that the result will be the same if in a sue- stated cession of Propositions we compare either of dlvldually - the Extremes with the individuals of which the Middle term is composed, as if we should compare that Ex- 7 146 LOGIC. — PAET I. [chap. treme with the Middle term, as a Whole in a single ciussificatory Proposition, this gives a Classificatory For- Formula. muld. 569. Thus let M he a genus consisting of the indivi- duals a , b, c, d and e, we may thus predicate P of each of these ; as, a is P, b is P, g is P, d is P, e is P ; and then as whatever may be predicated of all the individuals of a class, whether genus or species, may be predicated of the class, we may have for these seve- ral Propositions, M is P ; since by the supposition M is the general term whose comprehended individuals are a , b, c, d and e. With “ M is P ” we may have the Conclusion S is P — the two constituting an Enthy- meme. 570. This it will be seen by and by is the Form in The Formulas which Induction is usually stated ; thus, of induction, the wolf, the fox, the cat are individuals which make up, or at least represent the class of ani- mals called Oanidce , or animals with canine teeth, blow we may say : The wolf is carniverous, The fox is carniverous, The cat is carniverous, .•. the Canidae, or animals with canine teeth, are car- niverous. 571. It will follow of course on the same principle, cumulative that if we predicate the several individuals Formula. 0 f which the Middle is composed of the Mi- nor term individually, we may predicate the Middle itself of that Minor, thus : S is a , S is b, S is c, S is d, Therefore S is M. m.] OF SYLLOGISMS. — sect. vn. 147 572. This is the Formula of what is called the Cumulative Argument. 573. The Cumulative Formula differs from the In- ductive in that the Cumulative Formula is an Enthy- meme with the Major Premise suppressed. Thus in Mr. Webster’s argument in the case of the White murderers, we have : “ The prisoner was at the place at the time of the murder. “ He participated in the motives which led to the commission of the murder. “ He owned and usually carried with him the weapon with which the murder was committed. “ He shared in the means which were afterwards taken to divert attention from those who were actually engaged in committing the murder. .*. the prisoner is guilty.” 574. It will often happen, as in this case, that there is no one term in the language that will de- sometimes note the genus, which these several terms ^'fterm "brlhe predicated of the Subject taken as a Logical Middle - Whole, would constitute. But whether there is such a term or not they must be considered as making such a Whole, and one too which may be predicated of the Minor in the Inductive Formula, and of which the Major term may be predicated in the Cumulative For- mula. In the case alluded to, Mr. Webster argued his Major Premise at some length ; thus, “ Whoever was present when the murder was committed had a motive and the means for committing it, and subsequent to its commission, endeavored to foil all attempts at dis- covering the murderer, must be held guilty.” Here plainly for want of a single term of which to predicate “ guilty,” he enumerates the individuals of which it is composed — in short describes its sphere. 575. In both of the above-named Formulae it is necessary that the Premise which is thus Must mum- individually stated, should enumerate all ordinate pans 0 ' the coordinate parts of the Middle term as a Logical 14:8 LOGIC. — PART I. [chap. Whole, otherwise it is manifest that we may have an Undistributed Middle. SECTION VIII. Of Epichirema. 576. Besides the Sorites we have sometimes For- mulae in which there is a Proposition, which is redun- dant so far as the purposes of that Formula are con- cerned. These Formulae have been called Epichirema. The Propositions serve an important purpose, and are called either Pro-Syllogisms or Epi-Syllogisms. 577. The Pro-Syllogism is a Proposition thrown in pro syiiogism. either before or after one of the Premises as a Premise to that Premise ; and of course, therefore, is a Premise which with the given Premise for a Conclu- sion constitutes an Enthymeme. For example : “ Con- fidence in promises is essential to the intercourse of human life (because without it the greatest part of our conduct would proceed upon chance). But there could be no confidence in promises if men were not obliged to perform them ; therefore the obligation to perform promises is as essential as the intercourse of human life.” — ( Paley .) 578. Flere the Pro-Syllogism, which is thrown in to confirm the Major Proposition, is enclosed in the paren- thesis. Again, we sometimes have a Conclusion stated im- Epi-syiiogism. mediately after the Conclusion of a Formula, and to which the Conclusion of the Formula is designed to serve as a Premise. This is called an Epi- Syllogism. As, Y is X, Z is Y, .-. Z is X, .-. Z is W, or .-. M is X. 579. Here the Conclusion serves as a Premise to the Epi-Syllogism, and the two together are an Enthy- meme. m.] OF SYLLOGISMS. — SECT. IX. 14:9 SECTION IX. Of Compound Judgments in Syllogisms. 580. We have seen in a previous Section how any compound Proposition may, for all the purposes of the Syllogistic Conclusion, be regarded as a simple Propo- sition with a Modal. 581. Such a process of course implies that the Judg- ments into which the Compound Proposition may be resolved, are either all false or all true toge- AI1 the sim . ther. When they are thus regarded how- Slus t J be!^l n or ever as simple Propositions with Modals, false together ' we proceed with them as though they neither contained or implied more than the one Judgment, and the law concerning Modals already stated must be observed. 5S2. When either of the Premises is a Compound Proposition thus regarded as a simple one, ,i i n n May have a the Conclusion may ot course be a Com- compound con- pound of the same kind; only that it will appear as a Modal Proposition containing one modified judgment. This Proposition may be again resolved back into its component simple judgments by the same process, though in the inverse order — as it has been resolved from a Compound into a simple Modal Propo- position. Thus, M is (X and P), S is M, .-. S is (X and P). But the Major Premises may be resolved into “ M is X,” and “ M is P.” So also the Conclusion into “ S is X,” and “ S is P.” 583. But it is sometimes the case that the Conclu- sion depends upon only one of the simple 0uIy OIie of judgments contained or implied in the Com- us|d Ju iu”“ome pound Proposition. In that case whether the cases - Compound be either copulative or discretive, we must treat the judgment which is not taken into the scope of the Syllogism in the Premises, as in no other way be- longing to it or affecting it. It is a mere rhetorical sumlusage. 150 LOGIC. — PART I. [chap. 584-. Causal Propositions are properly Entliymemes, causal propo- containing a Conclusion and one Premise. The Causal Judgment may be regarded as merely a Pro-Syllogism. We may also regard it as a mere Modal ; thus, “Christians are happy because they have faith ; The early martyrs were Christians : the early martyrs were happy because they had faithS 585. When the Major Premise is a Causal, if the Minor affirms the cause of any new Minor term, the Conclusion may affirm the Predicate of the Major Pre- mise of the new Minor term. Thus we may say : “ Christians are content with their lot, because they have faith j The Early Martyrs had faith : .*. the Early Martyrs were content with their lot.” 586. Now if this Conclusion he not true, it must be either because the Minor Premise is a non vera (un- true), or because the main Proposition in the Major Premise, “ Christians are content with their lot,” is untrue ; or finally, because the cause assigned— “ be- cause they have faith,” is not the cause, is a non causa PRO CAUSA. 587. The Discretive , Exceptional , and the Exclusive Discretives, Ex- Propositions, as has been seen, agree in con- Exclusives. taming or implying judgment ot one qua- lity while they express a judgment of another. These judgments have one term common to them both. The Exceptional affirm the Predicate of the subject and deny it of all other subjects. The Exclusives include the subject in the Predicate and exclude all other sub- jects from it. The Discretives affirm one Predicate and deny another of the same subject. 588. Hence these classes of Propositions may be regarded as negatives or affirmatives, according as we involve in our Syllogism the one or the other of the judgments contained in them. Thus for a Discretive : TTT- ] OF SYLLOGISMS. — SECT. X. 151 A is B, but A is not C, S is A, S is A, .-. S is B, .•. S is not C. For an Exceptive take the following : “ All races of men except the Anglo-Saxons have failed to sustain free Institutions ; Examples. The Canadians are Anglo-Saxons : .*. the Canadians have not failed, &c.” — or with a Negative Minor Premise : “ The Mexicans are not Anglo-Saxons ; .*. the Mexicans have failed, &c.” In the first case the Affirmative Judgment is used as Major Premise, and in the second the Negative. 589. Again, in the case of an Exclusive, we have the same phenomenon : “ Water is the only thing in the sea ; Fish live in the sea : .•. Fish live in the water.” “ Water is the only thing in the sea ; Hot-blooded animals do not live in water : Hot-blooded animals do not live in the sea.” In the above examples we have an Affir mative Conclusion in the 2d Figure, and a Negative Conclusion with an Affirmative Major Premise in the 1st Figure. SECTION X. Of Comparative Syllogisms. 590. It has been usual to regard Comparative Judg- ments as but Pure Categoricals with Modals. Force of Mo _ But the Modals of Comparative Judgments *1^“ | y X: exert an influence upon the Formulae essen- gisms - tially different from that of any class of Modals yet considered. Comparative Judgments, as already shown, are Formally different from any other; and constitute a class by themselves with differentia peculiarly their own. 152 LOGIC. — PART I. [CHAP. Thus we may have — M is P, S is greater than M, .•. S is greater than P. Here we have a Modal to the Middle term in the Minor Premise, and none to it in the Major. We have also a Modal to the Major term in the Conclu- sion and none in the Major Premise ; and yet we see at once that the Formula is valid. Again we may have different Modals in each Pre- mise, as : Y is greater than X, Z is equal to Y, .*. Z is greater than X. 591. Comparative Syllogisms are of three kinds : — Three kinds. (1) Simple Comparatives in Continuous Quantity ; (2) Comparatives in which the difference of intensity is regarded as cause ; (3) Comparatives of time, place, manner, &c. I. Simple Comparatives. 592. In Continuous Quantity the reasoning depends upon the following Axioms : (1.) Axiom of Equality. If any two things are First Axiom, each equal to one and the same third thing, they are equal to each other. Thus, If A and B are each equal to C, A and B are equal to each other. (2.) Axiom of Difference. If of any two things one second Axiom, is greater and the other less than or equal to a common third, then the one is greater than the other. Thus, If A is greater than C, and B is equal with C, A is greater than B ; or if A is less than C, and B is equal with it, A is less than B. (3d.) If two terms are both either greater or less Third Axiom, than a common third term, no conclusion can be drawn concerning them by means of a compari- son with that third term. 593. If, however, in cases coming under the last Application of Axiom we introduce Discrete Quantity also, uty. so as to express how much greater or less in.] OF SYLLOGISMS. — SECT. X. 153 each of the terms compared are, than that with which they are compared, a conclusion can he drawn — thus, three is two less than five, and six is one more. Hence six is three more than three. The two terms of which we speak in these Axioms are the Extremes, Minor and Major, and the common third term is the Middle term. 591. We shall greatly facilitate our examination of the Formulae of Continuous Quantity by introducing a method of notation somewhat similar to Explanation of Sir William Hamilton’s, — in which we will sign3 - denote comparisons which imply the equality of the two Extremes of a Comparative Judgment, by parallel lines drawn between the Subject and the Predicate, as S = P, “ S is equal to P.” Comparisons of Inequality will be denoted by the Convergent when the Subject is larger than the Predicate, and by the Divergent when it is the reverse. Thus, S fc=- P, “ S is larger than P ; ” and S < P, “ S is smaller than P.” 595. The fact that Comparatives of Inequality are converted by transposition of terms and convergent* changing of the Comparative Modal for that convirfe ‘of which is in the same degree of comparison eachottier - as the other side of the Positive, is indicated by the fact that the Convergent and the Divergent are but the converse the one of the other. 596. But the Indefinite Comparisons, as we have seen, affirm only that the Subject is as great Nota tionofthe as the Predicate. We might therefore al- Indefillite - ways represent these Comparisons by the sign of equality — only remembering, however, that such Pro- positions cannot be converted. 597. But as such a mode of notation may lead to confusion in some cases, it will be well to denote the Indefinite Comparisons by two straight lines crossing each other, thus -I — . 598. How since in Comparisons of Equality the compared and the standard of the compari- comparisons son are equal to each other, it will follow of Equality. 7* 154 LOGIC. PART I. [chap. that if both, or all the Premises are Comparisons of this kind, all Moods and all Figures must be valid. 1st, A = B, 2d, A = B, 3d, B = A, 4th, B = A, B = C, C = B, B = C, C = B, .-. A = C, .-. A = C, .*. A = C, .-. A = C. 599. But if both are Comparisons of Inequality, of inequality unless they can be so converted or read as to e” of* the re same come into the 1st or 4th Figure, and of the same intensity, there can be no Conclusion except by means of Discrete Quantity. Thus : 2d, A > B, 3d, B < A, C > B, B < C. In both these cases the Premises offend against the Third Axiom. 600. But if the intensity be unlike in the 2d or 3d of opposite Figures we may have a Conclusion. In that case the Premise may be read either in 1st or 4th Figures, and so brought under the 2d Axiom — the Axiom of Inequality ; thus, A=~B, CP, 4th, P <1, S >M, M< S, .-. S >P, S=>P. 602. If the Premises are Comparisons of Inequality, comparisons of and of opposite intensity, they must be read inequality. pq e gq or 3 d Figure ; thus, 1st, M>P, and 4th, P :>M, S cM, _ M P, and 3d, P > M, MP, .-. S P, S -f — M, .•. S :>P is valid. But MM. S +- M, or P S = M, M but that would not improve the matter at all so far as their conclusive force is concerned, for we could not determine the comparison between S and P. 604. When but one Premise is a Comparative Judg- ment the Comparative may be regarded as a Modal, and we may proceed as in pure cate- goricals ; thus, A is greater than B, C is A, C is greater than B. One Premise only Compara- tive. H. Comparative Syllogisms in which the intensity as a difference of intensity is regarded as a cause. a " 3e ’ 605. As an instance take the following from Kos- suth’s late speech in England on the War in the East : “ Kapoleon failed to conquer Russia ; But Hapoleon was superior to the Allied Powers : Therefore the Allied Powers will fail to conquer Russia ” (that is, if they pursue their present policy). In this case we have a Comparative Judgment for 156 LOGIC. PAKT I. [chap the Minor Premise, in which the Minor and the Mid- dle terms are compared with reference to the intensity of some property which they have in common. In this case it is “ military force” But the Major term here conclusion af- is predicated of the Minor in the Conclusion, ground of sufif- not on the ground of any of the Dicta of the oient cause. Figures, hut because the property common to both of the terms of the Comparative Judgment is conceived to be the cause or reason why the Major term is predicated of the Middle in the Major Premise, and therefore the reason why it may he predicated of the Minor in the Conclusion. But this implies the ex- istence of that which is the cause of the Major term in the Minor also, and moreoA r er that it exists in as great intensity at the least in the Minor term as in the Mid- dle. And this is affirmed by the Comparative Judg- ment which is the Minor Premise. 606. In Syllogisms of this class the difference in intensity must be a real Cause, and one which neces- sarily implies the reality of the effect. ma”?e a r riso umef HI. The Comparatives of manner , time , place, &c. place, ratio, dec. 607. These are all very simple, and are completed by expanding or explaining the Comparative Modal for the Minor Premise ; thus, The Boys are with their Father ; Their Father is in the city : The Boys are in the city. A is to B as C is to D, But A is one half of B, .•. C is one half of D ; or, A is to B as C is to D, But A is the Father of B, .•. C is the Father of D. 608. It will he observed, that in all these cases the the* Major Premie! Comparative is the Major Premise. in.] OF SYLLOGISMS. SECT. XI. 157 609. We may also have an Indirect Conclusion; thllS, Indirect Con- The Boys are with their Bather ; §a^«?§ in sy°“- The Boys are in the city : g,sm3 - The Father is in the city. SECTION XI. Of Probable Syllogisms. 610. By the application of Discrete Quantity to the measure of Wholes in Continuous and Logical Quan- tity, we have a further modification of Formulae and some new principles and rules to consider. 611. Arithmetic, Algebra, and the Calculus are hut methods of calculation in Discrete Quantity. CaIcu]ation9 in It will not of course be expected that we Discrete 'S™ shall go into a discussion of the Rules and 1 y ' Formulae belonging to these Methods in this place. 612. There are but two fundamental Axioms in Discrete Quantity. (1.) The sum of the parts of any whole is that whole itself.* First Axiom. The usual statement that the sum of the “ parts is equal to the whole,” though true, belongs to Continu- ous rather than to Discrete Quantity. (2.) If from any whole a part he taken, the remain- der is such a part as that together with that second Axiom, which was taken from the whole, it will make the whole itself. * We do not say, “ equal to that whole,” for that would imply a want of identity in the terms or objects of the conceptions. We say that “ a whole is equal to the sum of its parts” in Continuous Quantity, Geometry, &c. But in Arithmetic we say, “ 3 times 4 is twelve,” not . “ is equal to twelve.” Units, as such, have no differentia — -and sums or wholes differ only in the number of units which they contain. When, however, in Algebra and the Calculus, we use the sign of equality, and read our statements or Logical Propositions, “ X is equal to A,” it is because “ X ” and “ A ” stand for quantities which while they are equal to each other as quantities have other relations, which must he kept distinctly before the mind. 158 LOGIC. PAST I. [CHAP. The first is the Axiom of Addition , and the last that of Subtraction. 613. Where several equal parts are to be added together to make one whole, the shorter method of Multiplication is adopted, and when several equal parts are to be taken from any whole the method used is called Division. 614. The Involution and Evolution of Roots, the Methods in Binomial Theorem, Fractions, Indeterminate calculation. Quantities, Logarithms, are all but short and convenient ways of finding values. But it is important for us to investigate in this place the effect of the application of Discrete Quantity to Logical and Continuous Quantity. 615. By introducing Discrete Quantity a Compara- Discrete Quan- tive Syllogism which offends against the Continuous. Third Axiom, by having the two extremes either both greater or both less than the Middle term, and which consequently can have no conclusion by a comparison of Continuous Quantity alone, comes to have a valid conclusion ; thus, Three is two less than five, Two is three less than five, .*. Two is one less than three. 616. Again, we may have an application of Dis- crete Quantity to Propositions which are protensively ToProtensive quantified, so as to give a valid conclusion Quantity. one that oan p ave none without it ; thus, 0 The cars stop at W aterloo one half of the time ; The cars carry the mail three fourths of the time : Some mail trains stop at Waterloo. 617. The principle involved here is the same as to Logical that which controls the influence of Discrete Quantity m ge- Q uan tity w } ien applied to Logical Quantity in general. For example take the following: — At a certain extensive conflagration it is ascertained that, Three fourths of the buildings in a city were of brick ; One half of the buildings were destroyed : .•. Some brick buildings were destroyed. m.] OF SYLLOGISMS. SECT. XI. 159 618. When one of the Extremes is expressed in integral Discrete Quantity, it does not at all Extremeg in modify the Formula, as in the following ex- auan " amples : All that were in the Ark with Noah were saved ; Eight human beings were in the Ark with Noah : .•. Eight human beings were saved. All terms in which Discrete Quantity is expressed by the numerals, indicating simply how many are in- cluded in the terms are undistributed. Abso- lute Whole belongs to Logical Quantity, and disSbutld" 01 it is a Whole which is not included as an alter- nate genus in any more comprehensive Whole or Sphere. Infinite belongs to Continuous Quantity, such as GOD, Space, Eternity, &c. But in Discrete Quantity we know of no number so large that it may not be a part of a larger and more comprehensive Whole, therefore none which is absolute ; and of none so large that it may not be made larger by addition, and therefore none which is infinite. The Units have no properties by which they are distinguished as Individuals, or divided into Genera and Species. It is true that “ one man ” has such properties, but not as “ one? It is only as “ man ” that he has differentia and peculiarities. Hence in Discrete Quantity there are no Logical Wholes. 619, Since a term expressive of Discrete Quantity alone, as “ six,” “ ten,” “ fifteen,” &c., can never be a distributed term, such a Middle term can i n , 5 i -yt , If the Middle never help us to any conclusion. JN or yet be merely Dis- can any term measured by Discrete Quan- there can be no tity serve as a Middle term, unless it ex- Conclusion - presses the ratio of the number expressed to the Dis- crete Quantity of the Logical Whole denoted by the term. For example : Three men got on the cars at the station ; Three men were killed in the cars : .-. The men killed in the cars were the men who got on at the station. 160 LOGIC. — PABT I. [CHAP. 620. The fallacy is obvious. — Nor from this state- ment can we infer any thing of the amount of the pro- bability that any one of those who thus got on were among the killed. Nor should we gain any thing by using a much larger number for the Middle term. 621. It is only, therefore, when the Discrete Quan- tity expresses the ratio of those included within the The Middle scope of the judgment to the number of either aRatio or individuals included in the Logical Whole a Fraction. denoted by the term which this Discrete Quantity qualifies, that it can be available for the pur- poses of deduction. 622. We shall greatly facilitate our understanding of the principles upon which the conclusiveness of these Method of Syllogisms depends, by resorting to Plouc- Notation. quet’s Method of Notation, or at least a modification of it. Let a line be drawn, which by its length will indicate the unit of which the Middle term is a fraction, and another directly under it, in each case denoting the amount of the fraction. 623. Thus to take the example just given, let us denote the whole number of houses by a line, and then how many at directly under it two lines more — the one least - one half and the other three fourths as long. And since we wish to know whether any, and if so, the least part of the Minor term that is necessarily con- tained in the Major, we will place one of the fractional lines even with the unit line at one end, and the other at the other ; thus, i i i i I whole number ; i i i | number of brick houses ; i i i number of houses burnt. 624. The reason for placing the lines as above, will be obvious from the fact that for aught that appears to the contrary in our statement, all of the not-brick houses were burnt, and only so many of the brick houses burnt as are necessary to make up the one half ; that is, that the two spheres “ burnt and “ brick” OF SYLLOGISMS. SECT. XI. 161 HI.] are as far as possible opposite. Hence tbe distance by which the lower line overlaps the one above it, will he the least part of the Minor term “ burnt ,” which can possibly be included in the Major term “brick.” But the overlapping portion of the two lines is one third of the one and one half of the other. 625. Assuming then the term “ brick houses ” for the Minor term, we have for conclusion : “ One third \ at least, of the brick houses were burnt.” Or taking “ burnt ” for the Minor term, we have : “ One half, at least, of the burnt houses were brick.” 626. But if the two lines when thus placed did not overlap each other at all, there would be no assertive conclusion ; that is, we could not say positively that any of the burnt houses were brick, or that any of the brick houses were burnt. 627. From the foregoing it is certain that unless the sum of the two fractional values used as Surp of the Middle term is more than a unit, we have hfmore t“na no conclusion. Unit - 628. The Conclusion in these cases may he mea- sured in Discrete Quantity, giving the pre- conclusion dis- cise number, which is the least that can fied ey quant1 ' have been included in the Predicate of the Conclusion as above, or we may have the undistributed Subject in Logical Quantity, “ Some brick houses were burnt.” 629. Or if we place the lines differently, we shall see how many at most could have been Howm anyat burnt. most - i i i i i whole number ; 1 i i i brick ; 1 i > burnt. 630. We place the lines thus because it is possible that the two spheres, “ burnt ” and “ brick,” are co- incident to the extent of the comprehensiveness of the narrowest. 631. From this it appears that if the Minor term LOGIC. — PART I. 162 [chap. lias a sphere less comprehensive than the Major it may be wholly included in it. 632. Let us now pass on to consider the application of Discrete Quantity to the calculation of probabilities in Syllogisms. 633. There are three distinct classes of cases in the Calculation of Probabilities, which we will consider as involving all the Logical Principles which belong to that interesting but intricate and complicated sub- ject. 634. (1.) We will first consider the effect of Dis- crete Quantification, expressed in a ratio or a fraction one probable of the units of the Middle term, when one premise. premise only is a fraction and the other is unity ; thus, All the houses in the city were brick ; One half the houses were burnt : .•. All the burnt houses were brick; — or con- versely, One half the brick houses were burnt. And the quantity of the Conclusion will be the same Quantification as that of the Major Premise, as in the above ofthc conciu exam p| eg _ Th e £ W0 Conclusions from the first of these, as will be seen, results from our regard- ing the one Premise as Major in the one case, and the other in the other. 635. (2.) The next class of cases are those in which Dependent the Premises are all probable, and several probabilities, probabilities are dependent upon each other. 636. Of these we have two kinds — ( a ) that in which we have several Premises, and the value of each is expressed in fractions of the common Middle term, as in the case j ust given : Three fourths of the houses were brick, One half of the houses were burnt ; and (b) that kind in which the value of each Premise (after the first) is expressed in fractions of the value of the preceding Premise. 637. (a) The probability that any particular house is brick, when three fourths of the whole are brick, is of OF SYLLOGISMS. SECT. XI. 163 ni.] course three fourths. And the probability that any par- ticular house is burnt, when one half of the whole are burnt, is ot course one halt or the |fJ n on i." Frac - whole. As the number of houses that are S" Middle of brick, and the number that are burnt are each of them separately less than the whole, the pro- bability that a brick house is burnt, or that a burnt house is brick, is of course less than the probability that any particular house is either brick — or burnt ; that is, the probability that any particular house is both brick and burnt, is less than that it is either separately. 638. "We have seen that the probability that any particular house was burnt, when one half were burnt, is one half of the whole. Now of course the probabi- lity that any burnt house was brick, is one half of the whole number of the brick houses. But the whole number of brick houses is three fourths of the whole, the probability therefore that a brick house was burnt is one half of three fourths, which is three eighths of the whole number of houses. 639. The probability that any particular The probabi- 1 • i i -I , • r* ji lity of any one brick nouse was burnt, is ot course the same chance the same as the number ot brick houses that were number of fa- -i i , vorable chan* probably burnt. ces. This results from the principles laid down concern- ing the effect of classification upon predication ; for each brick house is an individual, of which the brick houses burnt is the species. Hence Avhatever we may predicate of the individuals distributively, we may predicate of the species generally, and vice versa what- ever we may predicate of the species we may predicate of each individual. Or the point may be proved in another way, as follows : 640. The probability that any one house was burnt, is the same as the probability that any other house was burnt ; so likewise the improbability. p d mathe . The probability that any house was brick, matically - is as we have seen 3 : 1, three to one : again the pro- 164 LOGIC. — PART I. [CHAP. bability that any one house was burnt is 1 : 1, one to one against it — that is, one half. Now that fraction which sustains the same ratio to the number of brick buildings in the city that the number of the burnt does to the whole is f ; thus | : 1 : : f : £■ — three eighths of the whole therefore must be the number of brick build- ings that were probably burnt. And if more than three eighths of the whole number were burnt from among the brick buildings, then it would follow that since a larger proportion of brick than of the non-brick were burnt, the probability of any particular brick houses having been burnt is greater than the probabi- lity that a non-prick house was burnt. 641. ( b ) In the second class of cases we have suc- cessive Premises, in which the value of each is ex- pressed in fractional values of the preceding Premise, as a whole or unity. This Process implies the form of the Sorites already explained (554), in which each successive judgment expressed as a single cognition, becomes the subject to the one which follows. 642. Thus, suppose that a battle has been fought, concerning which we have the following particulars : Ratio of cai- “ Three fourths of the men in the army were One tenth of the men miss- fhi at rat n ioYs h m hi the engagement. preceding 0 rre^ that were engaged in the battle were mi se . i llg . f-] ie nex (. morning 1 , and one third of the _ 'to? missing were killed.” What is the probability that any particular man was killed ? 643. It is obvious that | of T V of those engaged were slain. But “those engaged” were only three fourths of the rvliole. Hence £ of | of T V that T §„ = — were slain. 644. And from the reasoning already given, the probability that any particular man was slain on the mere general ground of probability, is or 1 : 39. 645. If, however, we have any particular class of special grounds men among whom the individual concerning of Probability. ° . -i -i , • • • ° whom we are making our calculation is in- ni.J OF SYLLOGISMS. SECT. XI. 165 eluded, and they are known to have been especially exposed, the probability of his being among the killed is rendered greater by the consideration of that parti- cular ground affecting the amount of the probability. • 646. (3.) We will next consider the several cases of independent probabilities : {a) We have a class of cases in which we have a probability in one Premise, and an improba- Probability and bility in another. In that case we have only cSmb?ned.“ 7 to subtract the one from the other, and the remainder will be of the same kind as the largest Premise. 647. But when we have a special improbability against an event to be combined with several proba- bilities in its favor, this special improbability must be computed by using its complement as a new proba- bility, to be multiplied in according to the principle in the last named class of cases. 648. Suppose an individual to have belonged to a department of the army which is but slightly General Proba . exposed, call this an improbability of f, then ciai ty tmprobl p bT- the probability that one in that department lity - will be among the killed, will be of course but just of the probability resulting from the other probabili- ties X o' X j ■ j jo ■ ( b ) We will next consider the class of cases in which the question is of one of several One of several 7 • /7 , ° chances in the chances in the same event . same event. 649. Thus, the die has six sides, and therefore six chances for each throw, and each throw is an event in which there are chances. 650. How what is the probability that either of two, say the ace and the deuce , will turn up in any Ratio of the single throw or event ? It is of course dou- Calculation - ble the probability of any one side or chance } + £ =|. 651. This is easily proved by supposing the question to be, what is the probability that some one Proved of the six sides will fall up. By the rule + •§- + £+ | = | = 1 or certainty. 652. But we know previous to any computation, that one of the six sides will fall uppermost at each throw. 166 LOGIC. — PAJ3T I. [chap. 653. Hence in all cases where we have to inquire what is the probability of some one of several chances in the same event, we may add the sum of probabili- ties of the several chances. 654. These “ several ” must, however, be a part several must of some one whole, or totality of chances, as same whole, occurring in one event, otherwise their sum may amount to more than unity ; which is impossible. Thus, suppose we have three probabilities, not included in any such unity, they may be |, i, i, then l+y + |=r| which is absurd. 655. ( d ) This brings us to the last class of cases One chance in which we will consider — namely, that in several events. i • i ,• • l which the question is concerning one chance in several events. 656. Of these there are two kinds — ( d 1st) where the two kinds. events are in the same totality of chances ; and ( d 2d) where they are in ditferent totalities. 657. ( d 1st) For the simplest case in this kind, sup- Differentia ot P ose we have the question, “ What is the pro- the erst. bability of throwing any particular number on a die in two different throws ? ” 658. The probability of its being up in the first throw or event is } , and the independent probability of its being up in the second throw or event is also } . 659. Here the totality — the six sides of the die — is the same in both cases, the two throws are different events. 660. ( d 2d) But for a case of the second kind take the following : Two thirds of the pious are grave persons. Three fourths of the studious are grave persons. Here the different totalities are “ the pious ” and Differentia of “ the studious,” and the question is what is the second. the probability that one who is both- “ pious ” and “ studious ” will be “ grave.” 661. The principle or rule of calculation is the same in both of these varieties of this class of cases. 662. And we have two distinct questions to con- OF SYLLOGISMS. — SECT. XI. 167 in.] sider — (1) What will be the average of the probability of one chance in any given number of events ? The two Ques . and (2) What is that probability in any par- tions - ticular case ? 663. These questions are by no means the same. In any indefinitely large number of events, By no mean3 it is evident that each side would he upper- the same - most — that is, each chance would happen just as often as any other one chance. Each side of the die there- fore would come up just one sixth of the whole num- ber of events. If now we divide this totality of events into pairs, then of course a given side would come uppermost just as often as before ; that is, 1 : 5 in the whole. But the probability of any given side coming up once m every pair ot events, iatin g the aver- ox . i ii age probability. on an average is one tiiircL as great as the probabilitjr of its coming up once in three times as many chances, or twice as great as that of its coming up in each chance ; that is, So if we divide the events into triplets, the probability of any given side on the average of an immense number of events is three times as great as in the single event, that is, L 4-1-4-- = — 6 * 6*6 2 * 661. How in this way the fraction can amount to more than unity, for as there are but six sides -i • r» it..,! -i The result may or chances, so 11 we ask what is the proba- be more than bility of ace, for instance, in sets of ten ums ' events, we have j taken ten times orl; that is, ace will come up on an average more than once in every ten throws. Otherwise ace will not come up so often as some of the other sides. But if it does not then there is some special reason or ground of proba- bility, which is contrary to the supposition on which we started. Let us now consider the other question — what is the probability of any particular chance in a definite number of events. 665. It certainly can make, no difference whether the events are in the same totality of chances or not, 168 LOGIC. — PART I. [CHAP. since in the throw of the die, for instance, the probabi- immateriai an J Particular side in each throw is whether the certainly iust as independent of each and events be in f. . ~ ityornot 6 total ' evei T other throw, as it is ot the probability of the head side of a cent’s coming up in any throw of the cent. 666. We may therefore consider the two kinds of cases in the class which we have named above {d), as depending upon the same principle and requiring to be calculated by the same rule. Now we have two conditions to fulfil : 667. (1.) The probability of any chance in two events Twocondiuons must be greater than it is in either one of ist condition, them alone ; thus the probability of the ace in two throws is greater than it is in one. 668. And not only so, but the probability in any number of combined throws must be greater than that of the sum of all the throws excepting any one of them ; that is, two must be greater than any one in the two, three than any two in the three, four must be greater than any three in the four, and so on. 669. (2.) The sum of the combined probability can 2d condition, never amount to any more than unity — for by the very mode of reckoning probabilities they are but the fractions of unity. When therefore they amount to unity, they are no longer probabilities but a certainty, and there can be nothing beyond. 670. Now in the case of the die, for instance, as there are six sides the probability of throwing any we cannot add particular side, say the ace, at the first throw the fractions. would be 1 1 5. or }. And in six throws it would be |+j+i + H-j+£ or £x6=l unity. And yet it is possible that the given side might not be thrown once in six times, or even in any greater number. There is a bare possibility that that side might not fall upper- most in a thousand times. Still, however, when the And yet cannot event is far from the sum of the probabilities nlehum ofThe (provided they keep within unity) in either probabilities, direction — that is, greater or less ; it creates in.] OF SYLLOGISMS. — SECT. XI. 169 a presumption and finally the unhesitating belief that there is some special cause influencing the chances, as that a die is loaded. 671. It appears therefore that we cannot calculate the probability by adding the value of each fraction, since that method would soon produce unity, and ex- ceed it even. 672. Nor can we calculate it by multiplying the fractions. The value in each successive Pre- we ] cannot mise is not a fraction of that of the preced- Fractions. e ing or of any other fraction. Each one is the fraction of a unity, and of a different unity, as the 1st and 2d throws in the first example, and “ the pious,” and “ the studious ” in the second. And besides the multipli- cation of the fractions would give us a constantly de- creasing probability, when obviously we ought to have an increasing one. 673. If now instead of the probability in each Pre- mise we take its complement improbability, By means of and multiply them together as fractions, and my. lmprobd 1 then take the complement of that product for the pro- bability of the conclusion, we shall have a method answering exactly the demands of the case. 671. Thus in the first case the probability of an ace in two throws is £ and £, the complement is £ and £, multiplying we have ff , and taking the complement we have ££. In five throws it becomes ££££, in six !£!££, thus approaching but never reaching unity or absolute certainty.* * For the gratification of those who would like to see this in a more purely mathematical form I give the following demonstration. Let the probability of a particular chance in one event be and that b of the same chance in another event f , certainty being unity. The com- bined probabilities can never be greater than unity, nor less than the sum of all minus any one of them. Now multiply the complement of A which is (1 — f) by the complement no LOGIC. — PART I. [chap. 675. In the second case we have f, or t comple- ment in unity, and £ , or f complement. Multiplying, we have = T \- or probability that the man who is both “ studious ” and “ pious ” is “ grave.” * SECTION XII. Of Conditional Syllogisms. 676. We are not to consider all sentences stated in the conditional form as expressing a conditional judg- of — which is (1 ■ a -) and we have a ■( b—a ) (d — c) Vd as the comple- ment of the product, which is the combined probability. For as the nume- rator cannot be greater than bd , the fraction itself can never exceed unity. Again this fraction may he put under the form -4- (I — f a quan- b b d tity which can never be less than a b' Now suppose that both independent probabilities are unity, then they are not probabilities ; they have no complements and so of course they cannot be multiplied. Again, suppose them to be indefinitely near to unity, then applying the doctrine of limits, they may be assumed as unity, and so will have no complements to be multiplied. In either case the fraction becomes — - or unity, that is 1 x 1 = 1. bd But suppose the probability in each case to be as near to unity as the nearest assignable quantity, then by this rule the product of two such pro- babilities would be nearer than any assignable quantity or indefinitely near. We may pursue the demonstration in this way for every assignable value to the fraction. If therefore there is any other rule that will give the same result, it is not another but the same. But if it gives a different result it cannot be true. * I have taken no notice of the effect of concurrence upon the probabili- ties ; this will be considered in the Chapter on Methods of Proof. But it will often happen that the concurrence of two very small probabilities will produce an amount of conviction but very little if any short of certainty. Thus, suppose two men whose veracity was nothing should come in and report to me a certain occurrence, the one after the other, and under such circumstances that I could know that there had been no collusion between them — the strength of the combined testimony might be but very slight — • but the fact of their concurring without collusion would be very convincing, and all the more so, the more strange and unexpected the event whioh they narrate. m.] OF SYLLOGISMS. — SECT. XII. 171 ment. It is often the case that statements are made in the hypothetical form where no logical Not al , Comii . dependence of one member upon the other condkifnauSdy is intended. Thus, “ If on the one hand ments - Greece failed by an excess of the popular element in its constitution, Rome on the other became purely a military despotism, the least favorable of all forms of government to popular liberty.” Here manifestly the judgment concerning Rome is not intended to be made dependent upon the truth of that concerning Greece. We must regard the judgments therefore as being logically two entirely distinct categorical affirma- tions. 677. ISTor is it always the case where a Proposition is a Conditional Judgment that the deductive The Conditi- force depends upon the peculiarities of the a n me?”M^li Conditional Judgment. p f remi?e atesoric As examples take the following : Whatever comes from God is entitled to faith and obedience. If the Scriptures are not an imposture they came from God. .'. If they are not an imposture they are entitled to faith and obedience. Or thus : All Y is X, (If Mis Z, A) is Y, .•. (If M is Z, A) is X. 678. In this case the Conditional is merely the Mo- dal of the Minor Term, and is treated accordingly. The Premise is used as a Complex Categorical rather than as a Conditional. 679. But when the Conditional Judgment conditional is used as such, it is the Major Premise, and jor Premise in there are two ways of completing the For- syllogisms, mula. From the nature of Conditional Judgments it fol- lows that : (1.) If we affirm the Antecedent the Consequent cannot be denied. 172 LOGIC. — PAST I. [chap. (2.) If Ave deny the Consequent the Antecedent must be false ; that is, the contradictory of the Ante- cedent must be true. 680. Hence we may complete in what is called the constructive Constructive Method, or modus ponens, by ml""/. rL affirming the Antecedent for a Minor Pre- mise, and have the Consequent for a Conclusion ; thus, If A is B, A is C, But A is B, .-. A is C. 681. Or secondly, we may complete the Formula Destructive in the Destructive Method , or modus toilens ,* mise° r re by using the contradictory of the Consequent for Minor Premise, and then we shall have the contra- dictory of the Antecedent for Conclusion ; thus, If A is B, C is D, But some C is not D, .•. Some A is not B. 682. But by denying the Antecedent in simple conditionals we do not disprove the Consequent, nor by proving the Consequent do we prove the Ante- cedent. 683. But the Conditional Proposition is sometimes Fxninw m n made an Exclusive Conditional by the inser- " tion of “ only,” “ alone,” &c. 684. The effect of this exclusive is to show that the Consequent can have no other Antecedent, and could not exist without the one given in the Conditional. Thus, “ If the Trojans came into Italy contrary to the will of the gods, they would then alone have deserved punishment. But they did not come contrary to the will of the gods. /. They do not deserve punishment.” — Virg. MJn. X. 31. * The words “ posit ” and “ amote ” have sometimes been used to ex- press these processes. Thus if we posit the Antecedent the Consequent must follow, and if we amote the Consequent the Antecedent must be false. m.] OF SYLLOGISMS. — SECT. XII. 173 685. In this case by denying the Antecedent we disprove the Consequent. And if we affirm the Consequent we establish the Antecedent. They deserved punishment ; .•. They came into Italy contrary to the will of the gods. 686. But without the Exclusive Modal we prove nothing concerning the Consequent by dis- no conclusion provmg tne Antecedent. site Methods. 687. This will be obvious by the following illustra- tion “ If John has a fever he is sick.” ITence if we prove the Antecedent, viz., that “John has a fever,” the Consequent that “ he is sick ” will not be denied. But if we disprove the Antecedent and show that “ he has not a fever,” we have not proved that “ he is not sick.” He may be sick from some other disease. 688. For the same reason, though operating in the inverse order, if we prove the Consequent we do not thereby prove the Antecedent ; that is, if we prove that “John is sick,” we have not proved that “he has a fever ; ” his ailment may be something else for aught that would need to appear in our argument. 689. The whole force of Hypothetical reasoning in either method must depend upon the Se- T he validity of quence. There must be some such connection depends ncl upon between the Consequent and the Antecedent the Sequence - in the nature of things and independent of our volition, that the truth of the one follows from that of the other. 690. But as we have already considered the Se- quence or ground of affirmation in Conditionals, we need not add any thing more concerning it Any Enthy . here except to make the remark that the “^“ c ss “ ay co b n c Premise of any Enthymeme may be made ditionally - an Antecedent, and the Conclusion a Consequent in a Conditional Judgment, and then the other Premise will be the sequence ; thus, If M is P, S is P. Completing as before we have : 174 LOGIC. — PART I. [CHAP. If M is P, S is P, But M is P, S is P. 691. But regarding it as an Entliymeme, we have : M is P, S is M , .-. S is P. 692. In the same way, any Conditional by means sequence of its Sequence is converted into a Catego- ric“s me Cate80 ‘ rical Syllogism. 693. It is sometimes the case that the Conclusion depends rather upon some modal of the general Se- Modified se- quence than upon the general sequence itself, quence. Thus if I say, “ If John has a fever he will die,” the general sequence is “ all that have fevers die,” which is non verapro vera ; the Sequence, there- fore, if there be one, must be found in some peculiarity of “ John,” to be expressed by a modal. The Sequence then would be, “ All ( sub modo ) who have fevers die ; ” the sub modo denoting the differentia of the class to which the subject of the Antecedent belongs. This modal, however, should always be stated either in the Antecedent, or by giving the Sequence stated in such a form as to clearly point it out. 694. If the Conditional has four distinct terms, of conditionals course the Sequence becomes double, and tel™. our the Conditional as an Entliymeme is com- pleted into a Sorites. Thus, If A is B, C is D. And we complete thus, C is A, A is B, B is D, .-. C is D. 695. In what is called the Compound Conditional, it is necessary to prove all the Antecedents in order to compound establish the Consequent. If, however, we conditionals, disprove the Consequent, we show that some one or more of the Antecedents is untrue, without de- termining by the Formula which it is. in.] OF SYLLOGISMS. SECT. XHI. 175 696. This makes the Minor Premise a compound compulative categoric Proposition. Thus, 697. In continuous Conditionals if we prove the first Antecedent all the rest will follow. continuous Thus, If A is B, C is D ; — If C is D, E is F ; — conditional,-. If E is F, F is H, and so on ; since each Antecedent after the first is the Consequent of the preceding Con- ditional, it is established by that first Antecedent. And conversely, if we disprove the last Consequent we have disproved all the Antecedents. 698. We may also have Conditionals with Disjunc- tive Consequents. Thus, “ If grain is cheap conditionals it must be either because the crops are large, ^ l e h the consumers are comparatively few, or the quenta - importations are extensive.” 699. Completing this Formula and we have a Dis- junctive Conclusion. Thus, If A is B, either C is D, or E is F, But A is B, .*. Either C is D, or E is F. 700. But if we complete in the Destructive Method, we must deny all the members of the Disjunctive Con- sequent. Thus, If A is B, either C is D, or E is F, But neither is C, D, nor E, F, .*. Some A is not B. 701. It has sometimes been held that there are two classes of Disjunctive Judgments — the Divi- comprehensive sive and Comprehensive. Those which we Disjunctive 1 "™ have already considered are the Comprehensive Dis- junctive Judgments. But A is B, and C is D, .*. E is F. SECTION XIII. Of Disjunctive Syllogisms. 176 LOGIC. — PAET I. [CHAP. 702. The Divisives are rather categorical judg- are h ratherr‘o ves men t s > i n which the divided whole is one pound catego- term and the coordinate terms are the other. Thus, “ All food is either vegetable or ani- mal.” But we will postpone the consideration of the com- pletion of the Formula of this class until we have at- tended to the other, or the Comprehensive Disjunctives. 703. AYe have already examined the Disjunctive Judgments. They affirm that one of two or more judgments contained in the Disjunctive Proposition must be true without at all indicating which that one is. 701. But it is not always the case that the deduc- Deduction does tion depends upon this opposition of the not always de- I T .> . -r-* x pend upon the parts, when a Distinctive Proposition occurs Excluded Mid- 1 7 xi J • mi 1 die. as one ot the Premises, lhus, Every conqueror is (either a hero or a villain) ; Csesar was a conqueror : .•. Csesar was (either a hero or a villain). All Y is (either X or AY), All Z is Y, .•. All Z is (either X or AY). Or the Disjunctive may be the Minor : All Y is X, Either (Z or AY) is Y, .•. Either (Z or AY) is X. Or finally, the Middle Term may be Disjunctive in one of the Premises. Thus, Gold, silver, and platina are malleable ; All precious metals, are either gold, silver, or pla- tina : .•. All precious metals are malleable. 705. But in this case the Disjunctive Middle must enumerate all the coordinate parts, and in one Premise at least, as above, it must not appear as a Disjunctive. For if we say — Either gold, or silver, or platina Not Disjunctive is malleable — as Major, and then write misei u 1 rc ‘ the Minor as above, we should manifestly m.] OF SYLLOGISMS. — SECT. XIII. 177 have an undistributed Middle ; and we might have the following as all the truth there would be necessary in the Formula : Either gold, or silver, or platina is malleable ; (suppose it to be gold only that is malleable) : All precious mettils are either gold, silver, or platina ; (suppose it to be silver and platina only that are pre- cious metals), and then manifestly we should have no Conclusion, for the Major term was compared with gold and the Minor with silver and platina. This is in fact what is always done in the fallacy of undistributed Middle. 706. In all the above examples the judgment is not Disjunctive. It is merely a compound categorical judgment with a Disjunctive for either subject or pre- dicate as the case may be. 707. We have seen that the ground of a Disjunc- tive Judgment properly so called, that is, a Compre- hensive Disjunctive, is the Excluded Middle. It will follow, therefore, that if we deny one of the members the other must be true. 708. Hence in all Disjunctive Syllogisms the Dis- junctive Judgment is the Major Premise. Disjunctive For the Minor we have the Contradictory of Mafo? e plemte one of the Members, and for the Conclusion syii<^lsms. ctive the other Member. Thus, Either A is B, or A is C, But A is not B, .\ A is C. Or, Either A is B, or A is C, But A is not C, .•. A is B. 709. This is called by the Scholastic writers the modus tollente ponens. “ tolleDte 710. But if the coordinate terms are also coordinate parts of the divided whole, and not merely Modus ponente Alternate Species, we may also complete in tollens - the modus ponente tollens. 8* 178 LOGIC. PART I. [CHAP. Thus Either A is B, or A is C, But A is B, .•. A is not 0. This is either gold or platinum ; It is platinum : It is not gold. The validity of this Conclusion depends not upon The mode de- the simple Excluded Middle but upon the vision. Jaw ot .Division, that no individual can be m more than one of the coordinate parts of any divided whole at the same time and in the same respect. 711. When there are more than two members we More than two obtain only a compound categorical Propo- sition for the first answer. Thus, Either A is C, or A is B, or A is D, But A is not C, .-. Either A is B, or A is D. We may thus proceed with this as before, and then we shall get a simple categorical Conclusion. Thus, Either A is B, or C But A is not B, .-. C is D. 712. From the foregoing it will be seen that what Divisive Dis- are called the Divisive Disjunctives, can be pie* :ed 'on i y^by completed by a Discretive Categorical alone. Thus, Discretives. All A is either B or C, S is A but it is not B, .-. S is C ; that is, we must include the Subject of the Conclu- sion in the Subject of the Major Premise, which is the divided whole, and at the same time exclude it from all the parts except one, which one is predicated of the Subject of the Conclusion. 713. ISTor is the Method materially different when the divided whole is the Predicate instead of the Sub- ject in the Disjunctive. As, m.] OF SYLLOGISMS. SECT. XIV. 179 a b and c constitute M, S is M but not a, .*. S is either b or c. SECTION XIV. Of the Dilemma. 711. The Dilemma seldom needs or requires any completion. It differs from the Compound Dilemma. Conditional in that its Antecedents hear such a relation to each other as to constitute an Excluded Middle, and therefore some one of them must be true. And as the Consequent may be predicated on either one of them alone, it is immaterial which of the Antecedents is denied, as its denial affirms the other. 715. These Antecedents are sometimes called the horns of the Dilemma. D ilemma of the 716. The Dilemma is often Complex by having several Antecedents one after another. Thus Demosthenes says : “ If iEschines partook in the public rejoicing he is inconsistent. If he did not he is unpatriotic.” 717. But in all such cases there is a real Conse- quent in which all the Antecedents or series of Antecedents unite. The obvious Conse- to the Complex quent in the above case is that therefore iemma ' “.kEschines is unworthy of public favor and confidence.” The Formula may be thus expressed : If A is B, A is C, But If A is C, ) A • Or, If A is B, A is D, And If A is D, j ^ 1S 718. Hence we may say, “ Whoever committed this fault is either too ignorant to be our guide or too dis- honest to be trusted — in either case he is unworthy of our confidence.” Which we may represent thus : If A is B, A is not C, And If A is not C, ) A is not 180 LOGIC. PART I. [CHAP. 719. The Dilemma is not unfrequently stated in an wiemma stat- inverted form. Thus, If A is B, either A is ed form. invert D, or A is F. “If lie fails, it is because he is ignorant of his profession or inattentive to his duties.” 720. This may be regarded as an Enthymeme stated conditionally with a Disjunctive Conclusion, or a Major Term with a Disjunctive Modal similar to the instance already given, &c. Thus, All B is either D or F, A is B, .’. A is either D or F ; or in the other form, Either A is D, or A is F. 721. It is not unfrequently the case that in stating the Dilemma, the Antecedents are alone stated in dis- junctive opposition to each other, and the Formula is The con e °* course nothing more than a Disjunctive quent some- Judgment. But as the Consequent of the truth ot either member is so obvious, and is in fact suggested by the circumstances and the occa- sion, the statement is considered a Dilemma never- theless. Tims, “ The Dilemma then presents itself to us anew : Either we must accept the doctrine of the transmutation of species and suppose that the organized species of one geological epoch were transmuted into those of another by some long-continued agency of natural causes ; or else we must believe in many suc- cessive acts of creation and extinction of species out of the common course of nature ; acts which therefore we may properly call marvellous .” — ( WhewelVs Indica- tions of the Creator , p. 39.) Here we have the two members of a Disjunctive stated as a Dilemma, and so called ; the first member is considered absurd and the second therefore as true. 722. Another form of the Dilemma is sometimes Antecedents used ; namely, one in which two Antece- dictory < conse" dents are affirmed with contradictory Conse- quents, from which it follows of course that in.] OF SYLLOGISMS. SECT. XIV. 181 one of the Antecedents must be false. Thus, “ Lord Bacon opposed the English system of colonization ; ” therefore, “ If Lord Bacon was right, the English sys- tem of colonization is wrong.” But if the English are right, their system of coloni- zation is not wrong ; therefore, If the English are right, Lord Bacon was not right. Or if Lord Bacon was right, the English are wrong. 182 LOGIC. PAKT I. [CHAP. CHAPTER IV. OF FALLACIES. 723. We have already noticed the difference be- tween the Form and the Matter* of an Argument, and Errors hcs des a ^hough the Analysis of Formula takes no thoae’™in Bl the account of the Matter, and supposes that the Formulas are valid whatever may be the Matter, there are certain sources of error which a mere inspection of the Formulae will never reveal to us. These have been called Fallacies. It is not easy to collect and classify them all, and yet something of the kind is indispensable. 724. A Fallacy may be defined in its broadest and general sense to be any fault or error in an argument, Fallacies de- by means of which it (1) fails to prove any fined - thing ; or (2) the Conclusion which has been assigned to it ; or (3) the Conclusion which was de- manded by the occasion or end in view. 725. It has been customary to divide Fallacies into four classes. — (1) Fallacies in Form ; (2) Fallacies in Divided into Diction; (3) Fallacies in Matter; and (4) four classes. Extra-Logical Fallacies. The differentia of these classes is not very distinctly given anywhere, nor are the specific names used with any great uni- formity or clearness. We may perhaps define each species as follows : * See Introduction, 14. IV.] OF FALLACIES. 183 726. Fallacies are in Form when the Formula of- fends against any of the rules of the mere Fallacies in Form, and is perceptible without any con- Form - sideratiop. of the Matter of the Argument. Hence Fallacies imForm should rather be called Faults than Fallacies, and we shall so designate them hereafter; and then a Fallacy will be that which has the appear- ance of a valid Form, and deceives by its appearance of being FaultZe&s. It does not fail to fulfil called Faults. the formal conditions of a proof, but fails in the essen- tial conditions which lie beneath the Form. 727. The fallacy may he said to be in Diction , when the words in which it is stated are so Fallacies in used as to leave us in doubt as to the mean- Diction - ing, and in fact so as to have several meanings in the same Formula. 728. The Fallacy may be considered as in the Matter, when one Premise or both of them Fallacies in are taken in a sense not intended, or when Matter - they fail to express the judgment adequately. 729. And the Fallacy is extra Logical when it lies beyond the Province of Logic ; * as when it Extra Logicai states as a Premise a Proposition which is Faiiacie3 - not true ; or proves a Conclusion, which though true enough, is not to the purpose. 730. It is quite possible that an Argument should offend in more than one of these points at More than one the same time. "We must however remem- J a a jJ aoy ij ^ e her that a Fallacy is simply a failure to ment - prove. It does not necessarily follow that because the Formula contains a Fallacy therefore the Conclusion is false ; the Conclusion may be true after all, and all that can be inferred or predicated on the T he effect of a ground of the Fallacy is simply that the Con- FaUacy - elusion is not proved. But it is not ^proved ; for disproof implies a concluding force in the Formula of which the Fallacy has deprived it. See Introduction, 17. 184 LOGIC. — PART I. [CHAP. Including the Extra Logical we have seven distinct Enumeration Fallacies, excluding Faults in Form from of Fallacies. 0 ur number ; Ignoratio Elenchi , Petitio Princvpii , and the five in the use of the Middle Term.* • d * .Aristotle [Soph. Eleuch.], and after him most other writers, reckons six Fallacies in Dictione , and seven extra Dictionem. The six in Diction are : (1) Equivocation, as “ the dog is an animal, Si- rius [the star] is a dog, therefore Sirins is an animal ; ” (2) Amphibolies, as ap ’ '6 opq t is, t ovro bpS, or as Aldrich gives it, Quod tangitur a Socrate illud senXit ; Columna tangitur a Socrate : Ergo Columna sentit , — the amphibology is in touto, as being either accusative or nominative, and in the Latin exam- ple it is in the uncertainty as to the subject of sentit ; (3) Composition ; and (4) Division, as explained below ; (5) Accent, as when putting the accent on the wrong word, or the wrong syllable in a word, we give it a meaning different from that which was intended ; and (0) Figure of Speech, where on account of similarity of words one draws a false inference from one to the other, as because Musa is of the feminine gender therefore so is Poeta. The seven Fallacies extra Dictionem are: (1) Fallacy of Accidents ; and (2) a Dido secundum quid ad dictum simpliciter, as explained below ; (3) Igno- ratio Elenchi ; (4) A non causa pro causa, whether it be a rum vera pro vera, or a non tali pro tali. As an example of the first, Aldrich gives, “ A comet shines — therefore there will be war.” This is a non causa, the comet being entirely innocent of causing wars. Of the second he gives, “ Whatever will intoxicate is forbidden ; wine intoxicates, therefore wine is forbidden.” “ Not at all,” he adds, “ but only the abuse of wine.” Here wine is ad- mitted to be a cause of intoxication, but it is prohibited only when it is such, that is, in sufficient quantity as to cause intoxication ; (5) Fallacy of Consequences, as when a Conclusion is given which does not follow from the Premises — this in fact includes all Fallacies in Form ; (6) Petitio Principii, when that is assumed as given which ought to have been proved ; and (7) the Fallacy of Plurium Interrogalionum, when several questions are pro- posed as if they were one, which are yet so related to each other as to require different answers. As, “ .Are honey and poison sweet ? Have you left off your bad habits ? ” These thirteen Fallacies have been arranged into mnemonic lines ; thus, -ZEQUTVOCAT. AMPHI. COMPONIT, DIVIDIT, ACC. FI. ACCI. QUID. IGNORANS, NON CAUSA, CON. PETIT. INTERR. But I have preferred the classification given above in the text, for rea- sons I will not enumerate here ; the 1st, 2d, and 6th are included under Ambiguous Middle ; the 5th, Accent, does not belong to Logic at all — at least it is a mere trick ; the same may be said of the 13th, Plurium Interro- gationum ; the 11th I have reckoned under the head of Faults in Form; the 3d and 4th I have recognized by name, as also the 7th, 8th, and 9th ; the 10th, Non Causa , I have included under the more general head of the Petitio Principii. OF FALLACIES. — SECT. I. 185 rv.] SECTION I. Of the Ignoratio Elenchi , or Mistaking the Issue. A % A The words Ignoratio Elenchi mean “ Ignorance of the Proof” which ought to be given, and ignoratio Eien- are applied equally to cases in which one is i^Lratherthin really and innocently ignorant, and to those aFallacy - in which one chooses to ignore the real issue to be met and the Proof necessary to meet it. In this view of it, therefore, it is not a Fallacy in Logic at all, but simply a fault in sagacity or honesty, or both. It is no fault in Form nor a fallacy in the use of Forms. It is no fault in Method, for the Formula and Method may both be faultless. It is therefore merely a failure to pursue the right End — a failure in Aim or End ; as disastrous of course to the success of an Argument as any fallacy can be, but differing in kind both from Fallacies in the uses of Formula and Faults in Me- thod. 731. Nothing can he more important in the con- struction of an argument than a clear and [mp „tar,ceof adequate conception of the precise point to therightEnd - he proved. Without this we may deceive ourselves or be imposed upon by others. 732. The Ignoratio Elenchi , or mistake of the Ques- tion, is more pernicious when it occurs in a where ignora- p x i . . tio is likely to course ot reasoning where an argument is occur, introduced merely as subservient to some more general purpose or conclusion than elsewhere. In this case the deception is less likely to be detected, and the tempta- tion to it is much stronger than any where else. 733. We have an illustration of this fallacy pointed out in the speech of Diodatus, given in- Thucydides, in answer to Cleon, who had argued that it illustration from would be just to put the Mitylenians to ThucJ ’ dldes - death. Diodatus reminds him that that was not the question ; the question really before them was whe- 186 LOGIC. — PAJBT I. [chap. tlier it would be expedient for the Athenians in their present circumstances to undertake it.* 734. Mistakes of this kind will be found on a careful thf/'kmd 3 fre f scrut i n .y of far more frequent occurrence quent. r than one would at first exppcl^? and nothing but the most careful scrutiny and the most sagacious discrimination of things similar in appearance, but dif- ferent in reality, can secure immunity from this kind of imposture. SECTION II. Of the Petitio Principii. Under this head I shall include all forms of assum- ing for Premises what ought not to be assumed, or used as such without being first proved to be true in the sense and to the extent used. 735. Strictly speaking, the Petitio Principii is the petiuoPrinci - fault in Method which consists in stating as Sin Method a Premise a Proposition which contains the Conclusion, in such a way as that it can be evolved from the Premise by some of the processes of Imme- diate Inference. 736. In the popular sense it means simply the The popular assuming as true that which we are expect- word. mg or wishing to have proved. It is seldom the case that both Premises of an Argument are dis- puted or questioned,! and ivhen the one that is thus * Thucydides, Book III, Year 5. f For this reason some writers, and writers on “Logic,” even, have maintained that every Syllogism is a Petitio Principii. They cite such exam- ples as the following : All men are mortal ; John Smith is a man : .-. John Smith is mortal. But, say they, the Major cannot be affirmed as true unless John Smith be mortal. They forget that they beg the question themselves — the ques- tion, to wit, whether John Smith is a man or not. Let us take a case in which both Premises admit of doubt, or are at least denied : IV.] OF FALLACIES. — SECT. II. 187 questioned is assumed, the assumption is regarded as a begging of the principle or main Premise on which the Conclusion depends. 737. We have several forms of Premises unduly assumed, or untrue. We must, however, distinguish between a fallacy and a falsehood, or mere of pre false statement. It is no part of Logic to mises not a Fal- ascertain whether Propositions introduced aoy ' as Premises are true or false ; thus, If a man affirms that A is B, when it is not so, the false statement is not a Fallacy for Logic to correct; but it is a misstate- ment to be corrected by investigation into the subject matter of the Proposition.* The truth is to be sought in No murderer hath eternal life ; All warriors are murderers : Therefore No warrior hath eternal life. Here we have a Major Premise which some professing Christians deny, and others would of course deny the Minor. Hence in the estimation of some persons one Premise might be affirmed without involving the truth of the Conclusion, and in the estimation of another class the other Premise might be affirmed without involving its truth. In this case, therefore, neither Pre- mise can be regarded as a Petitio Principii. But this differs from others so far as this point is concerned, only in the purely accidental fact, that either one of its Premises are such as to he denied or doubted by any body. * It certainly diminishes our reverence for Akistotle immensely, to find that in his Prior Analytics, Book II, he has devoted three chapters, II, HI, and IV, to the consideration of the cases and conditions in which we may have a true Conclusion from False Premises ! If one could, he would disbelieve that these chapters ever came from the Stagyrite. But there is no help for it that I can see ; I find no intimation of their spuriousness. That there may be no mistake about the matter, and that the reader may see what cases the Father of Logic is discussing, I will give an exam- ple : “ As animal is with no stone, nor stone present with any man, yet if animal is predicated of stone, and stone of man, we shall yet have the Con- clusion, man is an animal.” Thus, “ Every stone is an animal ; Every man is a stone : .". Every man is an animal.” The Conclusion is undoubtedly true ; and it i sfrom, and a good 'wa.ys.from, the Premises too. We might just all well substitute “ jack-knife ” for Minor term, and prove by the same formula that a “jack-knife” is a man. It is no wonder that Logic has fallen into disrepute when we find the Father of the Science indulging in such ridiculous nonsense. Had this acutest of men got bewildered with the intricacy of his own system, aban- 188 LOGIC. — PAKT I. [chap. History, in Science, in Observation, &c. &c. The whole realm of knowledge is to be put in requisition to deter- mine the truth or falsehood of Propositions when used as Premises. Logic is responsible only for the truth of the Conclusion on condition that the Premises are true. The assumptions under this head are reckoned by sumption? Aa the °ld writers as two : 738. (1.) A non vera causa pro verd causd. As when we say, “ There is a comet, therefore there will be a pestilence.” The completion of this Enthymeme Non vem pro would imply the assertion, that “comets vera - cause pestilence,” or “ whenever there is a comet there is a pestilence ; ” the latter of which statements is simply untrue, the former assigning for a cause that which is not a cause of the effect. Hence a non vera pro vera , as it is usually written (omitting the word causa), is stating as a Premise that which is untrue. 739. (2.) A non tali [causd) pro tali [causa.) As, “ Whatever is poisonous should never be taken. But Non tan pro opium is poisonous.” In this case it is ad- tali - mitted that opium is poisonous — that it is a cause of death, but a cause of death only when taken in certain quantities or in certain ways. To these we may add one or two others : 740. (1) When in categorical Premises the two relate to different points of time, as, “ He who is most hungry eats most. But he that eats most is of 0t Faise Fo Ta s least hungry, therefore he that is most hun- gry is least hungry.” These Premises refer to different points of time in relation to the act of eating ; (2) then we may have want of sequence in Conditionals ; (3) non-exclusion of Middle in Disjunc- tives ; (4) want of sameness in kind in things compared in Comparatives. doned his a priori light, and set himself to justify by hook or by crook, as best he could, every possible Formula to which a Conclusion which is true as an independent Proposition, though not as a Conclusion, might be attached ? It would seem so. JV.] OF FALLACIES. — SECT. ILL 189 SECTION m. Of Ambiguous Middle. 741. Hot only must the Middle Term be once taken as a Whole, but it must be used in both Pre- Ambiguous mises in the same sense ; otherwise we have Middle - the Fallacy in Diction of Ambiguous Middle. 742. A word may be equivocal in itself, or intrin- sically, as in fact many words are, so that -words intrinsic- we really do not know precisely wliat one ally amb '" uous - intends by bis Proposition, until we have beard him discourse long enough to render bis terms perspicuous. Thus if one were speaking of “ beat ” in a scientific treatise, we should be in doubt whether by the word be meant that specific beat which is perceptible to the senses, or that latent heat which exists in all bodies to a greater or less extent and yet produces no effects upon the thermometer. And yet a Proposition might be true or false as the term was used in one or another of these senses. 743. But if the Middle Term is taken in a different sense in each Premise, it is the same so far The Middle as all purposes of deduction are concerned, S|uou“yl a the as if these were two entirely unlike and dif- Sj le $? en j£“ ferent terms. 744. “It is worthobserving,” says Whately,* “that the words whose ambiguity is the most fre- Word3 whose quently overlooked, and is productive of the m“stTreq y uentiy greatest amount of confusion of thought and ovcrlooked - 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 cir- cumstances that the danger arises ; words in very common use are both the most liable from the loose- ness of ordinary discourse, to slide from one sense into Appendix, No. I. 190 LOGIC. — PART I. [CHAP. another, and also the least likely to have that ambi- guity suspected.” 745. The Archbishop has collected some forty or Habitual cau- fifty words illustrative of the foregoing re- Bafesuard. °" 5 maim But its truth and force can be appre- ciated only after a long-continued habit of carefully noticing the meaning of words as they are used in ordinary conversation and in the printed works, espe- cially those of a controversial character. A large part of all the controversy that has ever existed in the world has risen from persons calling the same thing by dif- ferent names, or by their meaning very different things when they use the same name or term. 746. The Fallacy of Ambiguous Middle is spoken several varie- of in several different ways, but it is in all ties o ambit, ur (Fese classes (if we are to regard these dif- ferent names as indicating different classes) essentially the same. Thus we have the Fallacy of Equivocation when the same word is used in different senses. The Fallacy of Amphibology when the word is used so as to admit of different senses in each Premise. The Fallacy of Figure of Speech when the Middle Term is used metaphorically in one Premise ; and the Fallacy of Paronomasia &c. SECTION IV. Of the Fallacy of Division and Composition. 747. This Fallacy consists in using the Middle Term in one Premise as a General Term, and in the other as a Collective Term. If now we use the Middle Term as a Collective Fallacy of Divi- Term in the Major, and as a General Term Bion - in the Minor Premise, we have the Fallacy of Division ; thus, The Romans [collectively] destroyed Carthage ; Brutus was a Roman [that is, belonged to the Ge- nus Roman] : .-.Brutus destroyed Carthage. IV.] OF FALLACIES. SECT. V. 191 748. But if the Middle Term is used generally, or as a General Term in the Major Premise, and Fa iia C yofcom- collectively, or as a Collective Term in the position - Minor, we have what is called the Fallacy of Compo- sition ’ thus, Three and two are two numbers ; Five is two and three [collectively] : .\ Five is two numbers. 749. “ This is a Fallacy with which men are ex- ceedingly apt to deceive themselves,” says Wliately ; “ for when a multitude of particulars are presented to the mind, many are too weak or too indolent to take a comprehensive view, but confine their atten- The spend tion to each single point by turns and thus thrirt ’ s Fallacy - decide, infer, and act accordingly. For example, the imprudent spendthrift finding that he cannot afford a certain great expenditure as a whole, resolves upon each of its parts separately, forgetting that all of them together will ruin him.” SECTION V. Fallacy of Accidents and of Quid. 750. The first, Fallacia Accidentis , occurs when- ever in the course of the syllogism a term Fa , lacy of has been predicated of another, in reference Accidents - to its essential and inseparable properties, and taken as predicated of its separable accidents A What we buy in the market we eat ; W e buy raw meat in the market : .•. Raw meat is what we eat ; or, “ we eat raw meat.” Here the Middle Term is predicated of the Minor essentially, and thus by means of the Middle Term the Major is predicated of the Minor, as if the Middle had been predicated of the Accidents rather than the Es- sentia of the Minor. * See Chap. II., 220. 192 LOGIC. — PAKT I. [chap. 751. The Fallacy, a dicto secundum quid ad dictum simpliciter, called for the sake of brevity the Fallacy Fallacy of °1' Quid, is that in which the Middle Term Quid - is taken in one Premise as used in its broad- est signification, and in the other as used only with reference to some special subject or application. As for example, when it is inferred from the decla- rations concerning the Virgin Mary, that she was pure and immaculate [as a virgin], that therefore she was sinless [as an accountable being], and so must have been born without any taint of human depravity. But the pureness and immaculateness as to virginity is one thing and absolute purity is quite another, and cannot be inferred from it. The fallacy is precisely the same as that made by the passenger in a railroad car when on seeing the notice, “ No smoking allowed here,” he inferred that the stove would not smoke. As another illustration take the following : Nebuchadnezzar ate grass like the oxen ; But the oxen eat grass standing on hoofs and chewing the cud : .•. Nebuchadnezzar had hoofs and chewed the cud. 752. This Fallacy it will be seen arises from a dis- Mo ? t assertions regard of the scope and design of a writer, scope d in tlie ‘ r In fact it is but seldom that any proposition is affirmed except when there is some special end in view, or some special object before the mind in reference to which it is true ; while in an application to objects of another class it might be entirely false. 753. Besides the foregoing Fallacies, Whately has enumerated several others which are merely Tricks of the Rhetorician’s Art, and the consideration of which does not belong to a Treatise on Logic. We have defined Faults as failures to fulfil the Formal conditions of an Argument, and Fallacies Tricks as dif- as failures to fulfil the Essential conditions FaX or me” lying beneath the mere form. But a Trick Fallacies. j s something which fails to be a Fault even. IV.] OF FALLACIES. SECT. V. 193 A Fault can always be reduced to some Formula, one of the sixty-four Moods, though an invalid one. But a mere Trick has not the elements to complete any Formula. It cannot be put into the form or shape of an Argument, however successful it may sometimes prove in carrying a point and producing the legitimate results of sound reasoning. PART II. OF LOGICAL METHODS. CHAPTER I. OF THE ELEMENTS OF METHOD. SECTION I. Of Method in General. 754. Method is the way in which the means to any Method defined, end ave used for its accomplishment. Con- sequently Method always supposes an End or object in view, Matter in which it is to he accomplished, supposes an Means to be used in its accomplishment. End, Matter, A . . , n t 1 . 7 and Means. and an Agent to use them ; — the word is from the Greek fied' ohov. Thus if I wish to be in a neighboring village, the road by which I go thither is my Method, while the carriage in which I ride, or my feet if I walk, are the Means which I use by the way. 755. Method itself, however, may he resolved into several elements; as, (1) Method,. properly so called, Elements of that is, the way by which one shall go, as Method. j n going from one place to another ; (2) the Order in which the several steps shall be taken, as which first, and which next, and so on ; and (3) the Manner in which each step shall be taken. In going CHAP. I.] OF THE ELEMENTS OE METHOD. SECT. I. 195 to a neighboring village there is no room for choice, as to which step shall be taken first in order, hut one might take it into his head to walk sideways or back- wards. In this case his Method and Order might be perfectly good, hut his Manner would be very awk- ward. In a general sense, however, all three of these elements are included in Method ; and Order and Man- ner themselves become but the Method of the subordi- nate parts of any whole with reference to which the word Method is used. 756. Method gives unity of plan and efficiency in the use of means towards the attainment of Method gives -i t, • i -i * . -1 i , unity and effi- any end. It is not always the strongest man ciency. that can accomplish the most work in a given time, nor the fleetest of foot that can make the quickest race. Inferior force is often rendered the most efficient by the superiority of Method. Method has to do with every thing. Method is the result of mental power and application. It indicates capacity and attention, as its absence indicates the want of them. 757. Hence Method must form an essential part of any trade or art that is to be learned. It Method is the is in fact the conversion of Science into Art, Knowledge “o the passing from knowledge to practice. practice. 758. The beauty of any operation depends upon the Order and Method pursued in it, and the Beauty of ope- t .1 . • j i i i ration depends pleasure or the pam with which any accom- upon Method, plislied performer in any department of human activity watches the acts of another depends upon the presence or absence of Method in the operator. And a quick insight into the Method of any act or series of actions is called genius for that kind of actions. 759. In writing or speaking, not only the order in which the sentences follow one another, but Force of writ- also that in which the words are placed merits depend 1 , • i , i h upon their Me- relatively to each other in each sentence, thod. depends upon Method ; and upon this arrangement depends the beauty and force of what is said or writ- ten. In a mathematical demonstration there is a cer- 196 LOGIC. PAKT II. [ci-IAP. tain method or order in which the steps should he taken — and we should hardly call that a demonstra- tion, which although it had included all that was necessary, had thrown the parts together in entire disregard of the order in which they ought to follow each other. Such a demonstration, if demonstration it could be called, would demonstrate the want of capa- city in the demonstrator rather than the truth of the Proposition to be proved. SECTION II. Of Order as an Element of Method. 760. Method always implies an End, and yet it is not concerned in the selection of that End. It is con- Ends deter- cerned merely with its attainment. The ”i n s |ty laid N i>y Eiid may be determined for us, or we may choice. be igp- f- 0 c ] 100se it for ourselves. Ethics determine Ends for us when it specifies certain acts as being of moral obligation, and which therefore we are not at liberty to do otherwise than pursue. Theology determines Ends for us by showing acts which by the Will and Command of God are obligatory upon us. Polity determines Ends for us, as when the State commands certain acts by its positive enactments. Necessity determines Ends for us when by a fixed law of our nature it is ordained that we must eat to live, and must work in order to have something to eat. But in regard to many of our acts we are left to select our Ends for ourselves, as Pleasure, or Interest, or Benevolence may incline us. 761. Order, however, is an important element in order neces- Method, and there can be no Method with- thod. lo ML " out Order. The Principles of Order how- ever are very few and simple, and the same in all departments of human activity. Always there is a place to begin, a place to end, and intermediate steps to be arranged. That step or act which presupposes X.] OF THE ELEMENTS OF METHOD. SECT. II. 197 others cannot well be taken first, and that which is necessary to the succeeding cannot well he order to some postponed to the last. The mason cannot byp- lay the wall until the stone, and lime, and cessity - sand have been drawn and the mortar made. The carpenter cannot dress the timber and fit each piece to its place, until the trees have been felled and the hoards hauled to the place where they are to be used. So in studies — the alphabet must be learned first, geometry must be learned before trigonometry, and grammar before rhetoric ; and he that should under- take the calculus before algebra, or history before he knew any thing of geography, would find that he had made a mistake in Method, which would render all his studies and his efforts unavailing. 762. That fault in Method which consists in invert- ing the true order of the steps, or successive The FauIt of acts in any series of actions, has been called later ^ rs! - by the Greek writers a varepov irpoorov, that is, a later- jvrst. 763. In every process there are some of the steps or elements whose position is fixed by the very nature and necessities of the case. Thus in the , . n i , • i The Order of erection oi a house the materials must be many steps left hauled to the spot before the walls can he t0ch0ice - put up. But in every process also there is a large number of elements or steps, the position of which is not so determined by the nature and necessities of the case as that there may not be varieties in the order ; and their disposal furnishes a sphere for the exercise of tact and genius. 7 61. The five great Canons of Order are : of F 6'rder Canons (1.) Place that’ first which presupposes nothing as having preceded it. (2.) Put that last which presupposes all the rest, and neither conduces to nor implies any thing to fol- low it. (3.) Put each intermediate step after that which it presupposes, and before all those which depend upon it. 198 LOGIC. — PART II. [CHAP. (4.) Omit as extraneous matter whatever is not conducive to the End in view. (5.) If there are intermediate steps requiring to occupy the same place, they may he arranged with regard to convenience or taste merely. 765. Method can never be discussed and treated in any full and satisfactory way, except in connection The discussion with a discussion of the Means and the Mat- ter, or at least by presuming that they are Matter and the already known. To teach the Method of Means. any trade or art would he to teach the trade or art itself. We could not teach the Method of ship- building, for instance, without teaching the whole trade of building ships. For the order in which each act should come, each material he used, and the way in which these details should be disposed of, must depend upon the character of the details themselves to such an extent as to involve Method and Means most inextri- cably in the same discussion. 766. For this reason it will he necessary to limit Means of limit- ourselves in the discussion to some special ject. the feulJ - and definite sphere. This we shall best ac- complish by considering those influences which are external to Method itself properly considered, but, which do nevertheless determine it, and constitute species and varieties in Method. SECTION III. Of the Ideas which determine Method. 767. I have said that Method is the result of mind in its application to the attainment of any End. 768. But there may be several W ays or Methods to several Me- the same End. If 1 wish to go to the neigh- same 3 E^d. the boring village, for instance, I may wish to go as quickly as possible ; in that case I should select my means and my method or way with reference to quickness of time. If the time is no object, the ease I.] OF THE ELEMENTS OF METHOD. SECT. III. 199 with which the journey may be accomplished may determine me to select other means and another route. Or again, if pleasure be the leading object, I may select still different means and still a different route from what I should if speed or ease alone were to be con- sulted. 769. There are Five Ideas which determine the mind in its choice of a Method — two of them Five ideas that are relative — Ideas of the Understanding, as thods mine We ' the Germans would call them ; and three are abso- lute — Ideas of the Reason. The two former are Plea- sure and UriLrrY ; the three latter are the Good, the Beautiful, and the True.* 770. The two former, Pleasure and Utility, I have called relative Ideas, because they always pleasure, why relate to the person by whom the Method is relative - determined. What is pleasant is pleasant not abso- lutely and in itself, hut only because it is found to afford pleasure to him who experiences it ; the same thing, as we often see, may be pleasant to one and un- pleasant to another. 771. So of Utility. Nothing is useful in itself or absolutely. It is useful only to some end; utility ahore- and the end by comparison with which we Iative - judge a thing to be useful is also personal and of time. If we ask why a thing is useful, w T e always come round at last as the final answer to the fact, that it conduces to some worldly object which we wush to have accom- plished. 772. But the Good, the Beautiful, and the True are absolute. To say that a thing is Beautiful The Good the because it pleases, is merely to give our f h e e True,’ a 'bTo d means of knowing a thing for the reality of Iute - * There may be good reasons for reckoning tbe Plausible as sustaining the same relation to the True that the Pleasant does to the Beautiful, and the Useful to the Good. But I have chosen not to do so ; hut rather to look upon the Plausible as merely one subordinate species of the Useful ; namely, that which is useful for conviction and persuasion, irrespective of the truth of that which those whom we address are to be persuaded or oonvinced to do. 200 LOGIC. — PART II. [chap. the tiling itself. To say that an act is good because it is useful is to change the standard altogether. The absurdity of the change is seen, when instead of speak- ing of moral excellence or the character of God, we say that it is Useful instead of it is Good. 773. The life of man is for the most part controlled and directed by the relative Ideas of Utility and Plea- The r eiative sure - Devotion to the absolute Ideas im- ideas e most a ilr'o e plies something of self-forgetfulness and ordinary nie of self-immolation that rises into heroism and religion. It implies an elevation and dignity of character which is by no means every where to be met with. 774. These several Ideas when developed into prac- These ideas tical precepts, give rise to systems or codes 1 rules of action. 0 of action. Thus the Idea of Pleasure be- comes the Epicurean theory of Ethics. Pleasure is the Highest Good, and Virtue is only the wise and pru- dent pursuit of Pleasure. The Idea of Utility gives rise to the system of expediency, the Happiness of Man ; and each one’s happiness is for himself the High- est Good -which he can propose to himself to accom- plish. Hence whatever is useful towards the accom- plishment of this end is right, and the pursuit of it is virtue. 775. The Idea of the Beautiful is developed into Development what lias come to be called ^Esthetics ; and ideas. A sullUe the Idea of the Good determines Ethics, or the law of right action. And Logic in its comprehen- sive sense is determined by the Idea of Truth. Aes- thetics says this must be so because it is beautiful. Ethics says this must be so because it is right , and Logic says this must be so because so it is conformed to Truth. 776. These Ideas sustain towards each other a sort Relation of of sub-contram/ opposition, in consequence each other. oi which. one may prevail and control the Method without influence from the others, and yet no Method can be formed in which all of the Ideas can I.] OF THE ELEMENTS OF METHOD. SECT. m. 201 be combined, each in its perfection. At least, man in his present state has never been able thus to combine these ideas, and we are satisfied with any object when in determining its method that idea has had the ascend- ency which in the common estimation ought to have the controlling influence in such cases. Thus in an act, the moral character of which is strongly marked and of an unalterable character, as parental affection, filial duty, gratitude to benefactors, fidelity to an engage- ment, Ac., we are shocked and indignant if considera- tions of ./Esthetics, or of expediency, are allowed to take precedence of that controlling influence which Right and Good ought to have in such cases. In the fine arts, on the other hand, the artist entirely fails of his object unless he subordinates all other considera- tions to that of the Beautiful. The same holds true in regard to objects whose final cause is Utility. Any attempt or pretence of motives of conscience in matters which are indifferent in themselves, as in the cut of a coat, the color of a hat, the shape of a house, &c., &c., is but ridiculous fanaticism ; just as any attempt at the display of ornament in cases where utility alone is sought for is an offence against good taste, which im- plies either a want of culture or a want of sensibility. The man who should attempt the ornaments and plea- santries of poetry in a mathematical demonstration, would be considered hopelessly bad in respect both to taste and good sense. 777. Still however the Ideas of the Beautiful and the Useful are so related, that we seldom The Beautiful pursue the one without some regard to the ;\", d h U e Sm- other. Seldom do we so far abandon our- bined - selves to the luxurious emotions of delight, awakened by the Beautiful either in nature or in art, but that considerations of economy and utility come in for some share in the control of our actions. Nor is it often that the iron rule of necessity so far breaks down the spirit or paralyzes the wings of the fancy, that we are content with fulfilling the conditions and recpiirements 202 LOGIC.— PART II. [CHAP. of utility alone. The commonest tool of the mechanic, the utensils of the housekeeper, and even the imple- ments of the hoy who cleans the stables, are all fash- ioned and finished with some regard to beauty of shape — some regard to good looks — some considera- tions of taste. 778. In most of the transactions of life the desire The desire of to combine as much of usefulness and of of Beauty and beauty as practicable, is a leading; and con- utility combm- p. 0 pq n g mo tiy e . In building a dwelling- house, or a church, for instance, utility is the first object. But we often sacrifice something, and some- times much of utility, for the sake of realizing some conception of beauty which has entered into our plans. And always do we superadd much to what utility alone would require, for the sake of making our struc- ture pleasing to the taste. The same remark holds equally true in regard to articles of dress, of furniture, equipage, and whatever circumstances we may choose to surround ourselves with. And rarely do we become so hurried with business, so engrossed with care, so jaded with over exertion, or broken with affliction and disappointment, that we become entirely indifferent to the appearance of things about us. SECTION IV. Of the Matter of Logical Methods. 779. The second element to be considered as that Matter as de- which determines Method, is the Matter on termimng Me- e fj? 01 q or labor is to be bestowed. This must precede a consideration of the Means, be- cause different matter will require different means. The “ tools” (which are but the Means of the artisan) of a shoemaker, a hatter, and a stonemason, for in- stance, are as unlike as the material upon which they are to work, and the Means themselves must be deter- mined by the Matter. I.] OF THE ELEMENTS OF METHOD. SECT. IV. 203 780. For this reason we will hereafter confine ourselves to the consideration of those Methods which concern the discovery, proof, and communi- Limitalion of cation of knowledge. the Subjeot - 781. We have already reviewed the Matter of Logic so far as the investigation of the Formulae can com- mand.* But its relation to Method requires a recon- sideration of it from another point of view, and with reference to another end to be accomplished. 782. When a Judgment affirms of its Subject only a property which was necessarily implied in the con ception of the Subject itself, the Judgment ^ f ^ is called an Analytical Judgment. But if synthetiijudg- it adds to or affirms of the Subject a pro- men perty which was not necessarily implied in the con- ception of the Subject, the Judgment is called Synthe- tical. Thus, “ Every triangle has three sides,” is an Analytic Judgment, we cannot conceive of a triangle without three sides. Nor can we form a conception of a triangle at all without thinking of its three-sided- ness. Hence Analytical Judgments, while Analytical they serve to amplify our knowledge and put ™t sm 7ncreate our conceptions into Judgments for deduc- K, ‘ mvIcdsc - tive purposes, do not increase our knowledge at all. But the Proposition, “ The angles of a triangle are equal to two right angles,” is a Synthetic Judgment. For although this is a necessary truth, yet the property affirmed in the Predicate is not a part of the matter of the conception of a triangle, as is obvious from the fact that we may know what a triangle is without knowing this property of triangles. Hence a Synthetic Judgment always adds to the stock of our knowledge. 783. An Analytic Judgment affirms of a Subject only what was necessarily implied in the conception of the Subject. But it is one thing to be Matter of the implied in the conception of a Subject, and M°a n t“r pt ‘o°f n the another to be implied in the existence or of ob ' Chap. I. of Part. I. 204 LOGIC. PART II. [chap. reality of the Subject ; thus, to take the example just given, “ three-sidedness ,” is necessarily implied in the conception of a triangle. But “ the equality of its angles to two right angles ,” though necessarily implied in the nature and reality of the triangle, is not, as we have seen, necessarily implied in the conception of it. A triangle however could no more he a reality, that is a triangle, without the equality of its angles to two right angles, than without its three-sidedness. 784. Now the Matter of all Judgments, whether Synthetic or Analytic, which affirm of any Subject Necessary only what is necessary to its reality as an Matter. individual in any particular genus, is called Necessary Matter. Or in other words, all Judgments based upon the principle of contradiction are in Neees- Efiect of con . sary Matter. Hence, if we deny the Predi- tradiction. cate we necessarily exclude the Subject, not from reality, but from the genus which the Subject denotes. Thus if I predicate of a circle that its radii are not all equal to each other, it may be a figure and a curve, but it is not a circle.* * There is no simple term that may not he affirmed as a Predicate of something either real, possible, or impossible in the abstract ; though not always in the concrete (P a rt- 1. 279, 280). Thus we may not always be able to predicate “ walldng ” in the concrete of any individual, hut in the abstract we may always predicate it not only of man but also of other beings, as a property which we conceive as belonging to them in posse if not in esse — Iv eV TeAe'xem if not iv ivtpyaa. Hence when the Predicate is a simple term, the Principle of contradiction can only exclude the subject spoken of from the genus denoted by the name given to it, and used as a subject in the Proposition. As when we say, “ this circle has unequal radii,” the Prin- ciple of contradiction, if applied, would exclude the figure spoken of from the genus “ circle,” though it might leave it in some other genus of reali- ties — as the ellipse for instance. But we sometimes have a complex Predicate, which, by the Principle of contradiction, would exclude the- Subject not only from reality but from possibility also. Thus if one should say, “ this figure is a two-sided tri- angle,” — “two-sidedness” and “triangularity” cannot he combined as predicates of the same subject. Hence their combination produces a com- plex term, which can he affirmed of nothing, whether real or possible, and the Proposition affirms no judgment. It is mere non-sense. It will ho found that the number of such that one meets with in his intercourse with human minds, whether orally or in hooks, is vastly greater than he would at first expect. OF THE ELEMENTS OF METHOD. — SECT. IY. 205 *•] 785. It is manifest, however, that Judgments in Necessary Matter may affirm of a Subject something more than the Essentia of its conception, judgments in Most of the properties of the figures with m? ce may y affi?m which Geometry is concerned, are proper- S e the n l“lm e - ties conjoined in some such way with the t,a - Essentia of their several genera, and yet they are not Essentia, for they are not known as soon as the con- ception of the class is formed. One knows what a circle or an ellipse is, for instance (so that he could never be mistaken in deciding with regard to any figure, whe- ther it is a circle, or an ellipse, or not), long before he knows all the properties which are implied in the very nature of those curves. 786. But if we pass from the consideration of such matter to the consideration of the realities a][ b . ectg of being, we find there that any object of have properties -l ,° i . . i not contained thought has properties winch not only are in this ciass- not contained in its class-conception (as the concei ’ llon - Essentia of the proximate genus has with propriety been called), but which do not appear to us to be in any way necessarily connected with the matter of that conception. Such in fact are most of the properties of the objects of the natural world ; they con- contingent stitute what is called Contingent Matter — for Matter - it seems to be contingent or dependent upon the will of the Creator, whether they should have such proper- ties or not.* * Necessary Matter is that which is affirmed or denied on the Principle of Identity or Contradiction. But there is a class of philosophers who either ignore or deny the dif- ference between Necessary and Contingent Matter. Among those is Mill, in his Logic. Prof. Whewell has affirmed the distinction on two grounds : (1.) That Necessary Judgments affirm what has never been a matter of experience, as when we say, “ Two straight fines can never inclose a space.” To this Mr. Mill replies, that what we can construct in the imagination is as much a matter of experience as that which we may have seen in the reality of being. We can imagine two straight fines infinitely extended, and yet not inclosing a space. (2.) Prof. Whewell said also that the Judgments which we call Neces- 206 LOGIC. — PART II. [chap 787. Now all Judgments, whether analytical or judements in synthetic, in Necessary Matter are called ter a priori. Judgments a prion ; that is, Judgments which are affirmed from a consideration of what was contained or necessarily implied in the very conception judgments in of the object. But all Judgments in Con- conungentfliat. tingent Matter are called Judgments a pos- 0Ti - teriori • that is, Judgments which are and can be known to be true only posterior to and after an acquaintance with the Subject as existing among the realities of being. 788. Necessary Matter, therefore, consists of the conceptions of realities of truth ; and Contingent Mat- Nenessaryand ter, in what is added thereto to constitute to n in" the ‘same them realities of being. Thus, suppose I conception. form a conception of a point in space — as a point it has no extension. It is a reality of truth hut not of being. I conceive that point to move directly towards another point in space — the path which the point is thus conceived to describe, I call a straight sary, differ from the Contingent in that we cannot even imagine or con- ceive of an exception to the Necessary, whereas all Contingent Propositions actually have exceptions. But Mr. Mill replies, that this rather proves the limited capacity of our powers than any thing else. Many things have now become true which not long ago were not and could not have been conceived as true or pos- sible. Without deciding upon the merits of this controversy thus waged, I will add for the consideration of those who think with Mr. Mill, that all men perceive a difference in the kind of certainty which they feel in the truth, that “ every triangle has three sides ; ” and those Contingent Propositions which we are continually offering. Thus I say, “ The rose is red — the apple is unripe — the horse is gray — that man has ten fingers,” — every body sees that the one may have ten fingers and yet be a man, that a horse may cease to be gray without ceasing to be a horse, that an apple may be un- ripe, or a rose yellow. But if the (so called) triangle has not three sides, it is miscalled, it is no triangle, and the Proposition cannot be true. Change the quality of the Copula and you destroy the Logical Essentia of the Sub- ject. But in the other examples given, this change in the quality of the Copula may be made without changing the Essentia of the Subject at all, and thus causing it to cease to be of the species to which by its name we had referred it. No one, I suppose, will deny the difference thus pointed out between those two classes of Judgments — we make it a Differentia of the Species, the one Nocessary and the other Contingent Judgments. I.] OF THE ELEMENTS OF METHOD. SECT. IV. 207 line — the line also is only a reality of truth. I suppose the point to move again towards another point not in that straight line. It generates another straight line. I conceive it to move again directly to the point from which it started. It has now generated a third line in such a relation to the other two as that it joins them, and they then make a triangle. The triangle is a reality of truth ; and I conceive of it, that is, have a conception of it, as a figure with three straight sides, including three angles. These two properties are the matter of my class-conception. From this I deduce A priori de . a priori the further property, that the sum of its angles are just half as much as the ception - sum of all the angles that can be formed around any one point in space ; and that if I know the size of any one of its angles and the two adjacent sides, or if I know the length of one side and the size of the two adj acent angles, I can determine the size of the other angles and the length of the other sides. In the same way, I may construct in my mind a rectangle, a circle, an ellipse, &c., and of each I can ascertain a priori, many properties which did not enter into the class-conception of those figures. 789. But if I take up my crayon, before a black- board, and make a dot, calling that a point, and make a mark as straight as I can, call- tion drau°nm p a ing that a line, &c., these figures on the D,asrdm ’ board are not the realities of being of which I had formed the conception, and of which I had demon- strated, or of which I could demonstrate those propo- sitions. These marks may represent , but they are not the point, the line, the triangle, &c. I can predicate much of those marks that could predated" or not be predicated of the realities of being than 0 ftheco“ which they represent. Thus the mark has ception ' breadth, the line none — the mark has color, and is upon a ground of a different color — a white mark on a blackboard, for instance ; the line has no such pro- perties. These realities of truth, the point, the line, &c., 208 LOGIC. — PAJBT II. [CHAP. have been done or made into facts — realities of being in the outer world. They have been clothed upon with visible forms, having properties of their own in addition to those contained in their class-conception. Now all , . these properties are Contingent Matter. It in contingent depends upon my will whether I will give to my conception of a triangle an outward expression on the blackboard or not ; and whether that expression shall be with a white mark or a mark of another col Or ; whether the mark shall be small and smooth, or broad, rough, and irregular, &c. 790. Let us pass to another class of objects. Sup- creation. pose the Divine Mind to have constructed a conception or an idea of the various classes of beings included in the Creation. As existent substantial reali ties each individual must consist of Matter, extended so as to fill limits in space and to be impenetrable ; be composed of particles, every one of which should have an attraction for every other particle, and this sub- stantial matter must be without life or capacity of originating motion or of acting, except as it was acted upon by a spirit either within or from without each i lividual object. 791. Now, here we have the class-conception of the objects which have a material existence. From this we a priori infer- can deduce a priori many of the funda- conceptio” ‘of mental principles of the Natural Sciences. Matter. From extension must follow the divisibility'' of all material objects ; from attraction must follow density and the phenomena of gravitation ; from in- ertia the three laws of motion may be deduced, and so on. We should, however, know nothing of the phenomena of light, of color, of electricity, of sound, of chemical combination, &c., from these mere class- conceptions. 792. But let this Divine Conception pass into contingent reality of existence — be done into a fact, saniy r impifed and each piece of matter necessarily takes of be!ng. real,ty upon itself, or rather its Creator puts upon I.] OF THE ELEMENTS OF METHOD.. — SECT. IV. 209 it properties and relations not implied in the class- conception or resulting therefrom ; but which are, however, necessary to the reality of each individual object among the facts of existence. The specific color and shape of each piece of matter, for instance, though it must have some color and shape, were to be deter- mined by the will of the Creator, and not necessarily implied in the conception or the resolution to give it reality of being. Those properties of the outward form of the conception — its material body — are contingent Mat- like the diagrams by which we represent ter how known, our conceptions of a triangle, a pyramid, &c., matters of choice and chosen by ourselves, and can never be known by any other mind until he has learned them either by revelation — that is, verbal communication from ourselves, or by an inspection and study of the diagram which we have drawn. 793. From the foregoing considerations of the Mat- ter of Judgments, we may divide the Pro- a new classic- a % . , . d n f? . cation of Pro- perties ot Objects again with reference to penies. Method on another principle and into other classes. 794. Thus all of those Properties which are in- cluded in the class-conception may be called Mater i a i Pro . Material Properties y as three-angledness and perties - three-sidedness of a triangle, extension and inertia in matter, &c. Then all of those Properties which are necessarily implied in, and deducible a priori from these Material Properties may be called the Implied Properties, as the equality of the angles of a Implied Pro . triangle to two right angles, divisibility from perties - the extension of matter, and the laws of motion from its inertia. 795. Those properties of bodies which serve to make the species of objects in the reality of Pr0P e r t ies 0 f being, such as two-footedness of man, canine h‘k g re may be teeth or the carnivora, web-footedness of matcria1 ' aquatic birds, unsupportedness of falling bodies, &c., may indeed be assumed as Material Properties in our conception of the class, and as such we may reason 210 LOGIC. — PART n. [chap. from them a priori to other implied properties, just as from the three-angledness of a triangle in Mathe- matics. 796. But for the most part, and always for all the purposes of science, these properties are learned a pos- . . teriori , from actual observation of the indi- dicaTiv" "of "a viduals existing in the reality of being. Final Cause. 7r , , , , ° , . , J & Jiacli ot these properties, however, is con- nected with and is suggestive of a Final Cause, for which it was bestowed upon individuals of that class ; the two-footedness of man was designed as a means to the upright position in which he walks ; and so through- out the material world we connect those properties which are differentia of species with something in the habits or modes of the individuals of the species, as two-footedness with erectness of stature — canine teeth with carnivorQusness, &c. 797. Flow in reference to this fact we may call the can Formal former Properties which are indicative of properties. tli e Final Cause the Formal Properties ; and those which are thus connected with them and Modal pro- implied in their reality, we may call the perties. Modal Properties. And all those Proper- ties which are susceptible of more and less, as size , variable pro- temperature , density , might , &c., we may perties. C all variable Properties. 798. It will be observed that Material and Formal Material and are ii ot coordinate terms, but only terms ordmat e "te rms* denoting alternate conceptions. Material and Implied are the coordinates in a priori Matter. Formal and Modal are the coordinates in a posteriori Accidental and Matter. Then besides these we have the pe«ies maybe- Accidental and Variable Properties. These, Material "'“of however, m ay become either Material or Formal. Formal. But when they do become so they cease so far forth as they are Material or Formal to be accidental to the individuals into wdiose class-concep- tion they have thus entered. Thus, the “ unsupport- edness ” of bodies which fall is but an accidental I.J OF THE ELEMENTS OF METHOD. SECT. IV. 211 property of those bodies as masses of matter. But we assume it as a Formal Property with reference to the Modal Property denoted by the word “falling when we say that “ all bodies which are unsupported, fall to the ground.” So too “ right-angledness ” is but accidental to “ triangle ; ” but when we take it into our class-conception we have “ right-angled triangles,” and then it becomes Material. 799. Now as the Matter of all a priori Judgments is necessary Matter, if the Judgment be af- Contra firmative, its contrary or contradictory is dictory or j"dg- n , . ' 7 7 ., ^ t , • , -i ments in Neces- called an absurdity. It is not merely an sary Matter ab- i/ i/ curd error. Of this kind are all mathematical and all analytic Judgments. If the Judgments be negative, the affirmative would give a nihil pururn — - that is, an impossibility ; as that two and two make five, two straight lines may inclose a space, an effect without a cause. 800. In Necessary Matter if the subaltern is true, its universal must be true also. That is, It I IS true A must be true also. ferences from If O is true E must be true also. Nere“a?^Mat n - And all contraries are virtually contradic- tories, and only one of the sub-contraries I and O can be true. 801. Contingent Matter is also divided into Natural and Moral. Although the order of Nature seems to be per- fectly stable and uniform, we conceive this order as having been established by an Intelligent Knowledge Author as the choice of His will. In many Matter on o in p e injinm, its fully of the Differentia of both classes of Me- Use ' thods that we are in doubt with which of them to place it in our present Treatise. We put it here, however, because we are treating of Methods of Investigation before Methods of Proof. 910. Perhaps the best illustration of the first form of Abscissio for our present purpose, is the niustration of one which we have already made use of in the fim variety, examining the validity of Moods and Figures of Syllo- gisms [478 et seq.~\. Thus we said (or rather used the implied Disjunctive), “ Either those with negative Premises, or some of those that have not both Pre- mises negative, are valid,” we completed by the modus tollente joonens / proving that those with negative Pre- mise could not be valid. "VVe then divided the re- maining coordinate, “ those which have at least one Premise affirmative,” into two coordinate parts, and said or implied again, “ Either those with Particular Premises,” or “ some of those whose Premises are not both Particular are valid ; ” and proceeded as before until we come to the species of which alone “ validity” could be predicated. 911. In this case we knew at the outset that some of the individuals included in the divided whole — that is, some syllogisms, were valid, may be used But if we had not known this we could even bi-jl MA 1 then have proceeded in the same method not ' J until we had found that there was no individual in the 11 24:2 LOGIC. — PART n. [chap. divided whole of which “valid” could he predicated. In that case we should have ascertained that “ valid ” is a Differentia incompatible with the Essentia, which is constitutive of the Logical Whole as a genus ; that is, with the Material Properties of the Logical Moods. 912. But in this case there would have been only the form without the reality of a Disjunctive Judg- ment. The Disjunctive would have been merely sup- posititious, designed or supposed foT the sake of the Method, since a true and valid Disjunctive always im- plies that one member at least shall be true. 913. This Method is often of great use as a Method of Proof in Geometry. Thus in the Theorem, “ A line used in Geo- let fall from any point perpendicular to a metry - straight line, is the shortest distance between the point and the line. For either the perpendicular is the shortest line or some not perpendicular' is the shortest.” But as the perpendicular makes a right angle with the line, any other line would be the hypothenuse of a right-angled triangle, of which the perpendicular is one of the legs. ILence no non- perpendicular line is the shortest. Consequently the perpendicular is the shortest. This Method is of course vastly shorter than that by which we prove of each possible line, not a perpendicular, separately — that it is not the shortest. 911. But let us now take a case of the other kind, illustration of in which we have an individual or several riety. forming a sub-species, anu are desirous ot finding to which of the species it belongs — in short to find what it is. 915. Let us take for an illustration a case of chemical analysis. We there say this is either an acid or an alkali. We test it and find, let ns sup- pose, that it is not an acid. It is therefore an alkali. We must say this is either potassa, or soda, or am- monia, &c., enumerating all of the alkalis. We pro- ceed as before and test it for potassa, for soda, &c., until by proving that it is not one or the other in turn, n.] METHODS OF INVESTIGATION. — SECT. V. 243 we come to the last. But of course it is quite possible that we shall find which species of alkali it belongs to, that is, what kind of an alkali it is, before we have tested it for all. Or again, as in the former case, we may test a metal, for instance, for each of the alkalis in turn, and disprove each member of the supposed disjunctive in turn, and thus find that it is not an alkali at all. Here, as before, the Disjunctive form was merely sup- posititious — made # for the occasion, without knowing before-hand that the individual was included in the Logical Whole at all. SECTION V. Of Analysis. 916. We may have two kinds of Analysis : (1) An- alysis of the Conception, and (2) Analysis of the Object of that Conception. The former conceptions & is Logical Analysis and the latter is Phy- 01 Subject °’ sical Analysis. 917. We have seen that every conception of a reality contains as its matter certain proper- The Matter of ties of that reality. These properties make Conce P tions - up its Essentia and Differentia ; its Essentia as includ- ing it in the nest superior Natural Genus (thus show- ing what it is) ; and its Differentia limiting or deter- mining its reality by showing what it is> not ; — thus giving the boundaries that separate it from other objects. 918. The Analysis of this Conception therefore gives us each of these properties as separate The Analysis predicates, which may be affirmed of the |ivS 0 5fpVe 0 dr conception of the object as a Logical Sub- j e a d e of thecon- ject, and consequently of the object itself, ception - if the conception justly and properly represents it. Thus we may say of a triangle, “ it has three sides ; ” since three-sidedness is necessarily included in the conception of a triangle. 244 LOGIC. — PAKT II. [chap. 919. So too in Contingent Matter. The Matter of any superior and comprehending genus is always con- Anaiysis of tained in the conception of a lower and contms'ntMat' comprehended species, and it may therefore ter - be evolved as a predicate to that conception by Analysis. Thus I may say of a tree, “ it is a vege- table ; ” of an ox, u it is an animal,” &c., since “ tree ” and “ ox ” are but species of the proximate genera “ vegetable ” and “ animal.” Or we may predicate any one of the essential properties of the higher genus, as of animal, the circulation of the blood — of the tree, its growth from a seed, &c. 920. So far as Predication on the ground of Ana- lysis is concerned, it is of but little if any consequence how the conception which we analyze was formed. It may have been that which we formed in- conception may stmctively on our first comparison ot one of thehmicep- object with another, or it may have been that more elaborate and scientific class-con- ception formed by scientific investigation. In either case we may analyze the concejition, consider the ele- ments of which it is constituted separately, and sepa- rately they are Predicates which we may affirm of either the ciass-conception or of any individual com- prehended under it. 921. The only possibility of mistake is in the forma- tion of the conception itself. If the judgment is untrue the conception was ill-formed. Thus, if I ject o? thehon" should say that “ horses have wings,” the cooceptimi "lie iude;ment would show that my conception adequate. n f? l • i , J 1 ot “ horse was inadequate or erroneous. Or in popular language, one would say that I did not know what I was talking about. 922. But in Geometry, the Mathematics of Con- tinuous Quantity,* we speak only of the conception ; * In Mathematics we deal with the conception exclusively. The very names which we use denote the conceptions and not the diagrams. But in what is called contingent matter it is not so. The names denote the indi- viduals as they are in the reality of being or existence. With these the II.] METHODS OF INVESTIGATION. SECT. V. 245 and that conception is one which we have formed in our own minds a priori, and by a conscious pro- In Mathematics cess of construction. Hence in our analysis ™ 'TmSeous of such conceptions we merely evolve what con^ 1 ' 0113 - we had consciously and designedly put into it, and there is no liability to error. Conceptions cannot be communicated from one mind to another. Each mind must form them for itself,* and as the process of form- ing the conception of a triangle, for instance, is the same in all minds, the conception itself of all geometri- cal figures must be the same in all minds. 923. But in forming class-conceptions of the objects in the external world, different properties of the objects themselves will seem most conspicuous and characteristic to different minds. Hence the error in Con- * matters of those class-conceptions will be dif- u “° ent MaMer ' ferent to some extent, and may be different for each mind. Or if we undertake to reconstruct in our own minds the conceptions which others have formed from their description of the objects comprehended under that conception, the description never is and never can be quite adequate. Hor will it be understood by all minds alike. Every one has a conception of “ apple,” for instance, and yet who has analyzed that conception so that he can enumerate and describe precisely every element of its matter? We can all tell an apple from a pear, but who can describe precisely and exactly all the points of difference between them ? Some of the most striking points all persons can give ; but no one, I apprehend, can give them all. 924. The question will always arise, therefore, whe- ther the elements of our analysis he predicable of the individuals comprehended under our class-conception ; thoughts are occupied, and while in the former case we ignore the differ- entia between the diagram and the conception — in the latter the mind is chiefly occupied at first with those Formal Properties, and it is only hy a slow process, and one that is at best liable to error and mistake, that we arrive at the class-conception as it actually existed in the Divine Mind. * See Part II. Chap. IV. Sec. I. 246 LOGIC. — PART II. [CHAP. not, however, in consequence of any fault or fallacy in False conce ^ ie ana ly s i s > but on account of the doubt tions" c source or uncertainty about the formation of the raise state- conception itseit. And many persons are charged with intentional falsehood when the fault is not the moral one of uttering what they know to be false. It is merely the misfortune of having so conceived the subject as that predicates which do not belong to it are included in their conception of it. 925. This analysis of our conceptions is carried on Reason the by the Reason itself ; and the Reason pos- lysis. sesses a faculty ot insight or immediate in- tuition for the facts of consciousness, precisely as the external senses do for the facts of the external world. Thus, if I see that my class-conception of horse includes the property of solid-ungularity [having but one hoof for each foot], I can no more doubt that my mate judge of conception oi horse includes that property, us correctness. j.p an j can f-} u p the horse before me has but one hoof for each foot when my eye is distinctly fixed upon the object itself. 926. But let us pass to the consideration of the ana- lysis of the object itself. We cannot here give any pre- Anai ys is of the cepts or rules for accomplishing such analysis, object itself. Those rules are not and cannot be reduced to any simple system. Success depends to a great extent upon original gift. It is a matter of quickness of in- sight in the Reason, just as the perception of colors and of sounds is matter of difference in the constitu- tional peculiarities of the eye and the ear. No rules Can be given which will enable one to distinguish between the different shades of color, or the different tones of the diatonic scale in music. If one cannot make the discrimination without rules, no rules will enable him to make it. 927. In chemistry, however, analysis forms so large Rules and Me- and so indispensable a part of its Methods, Natural * n scf- that the rules and tests for analysis have ences. been extensively systematized and recorded. n.] METHODS OF INVESTIGATION. — SECT. V. 247 Nearly every science has done something of the kind. But the most that can he reduced to rule and formula, will in all cases be but a comparatively small part of what is to he done. 928. An analysis of this kind is always an experi- ment, and the elements evolved are objects AnaIysig an of observation ; and Ave can of course predi- ex penment. cate them of the object analyzed as having been con- tained in it. Thus common salt is analyzed into chlo- rine and sodium. Hence we may say, “ common salt contains chlorine,” — “ common salt contains sodium.” 929. There is no appeal from the result of an ana- lysis. We may mistake the name of the sub- The certainty ject analyzed, and also that of the element of Analyst, given out. But the things themselves cannot he mis- taken. The greatest danger is in the too hasty infer- ence from the analysis. We may suppose Liability t 0 the example which we analyzed Avas a fair mistakes - specimen of all the individuals of its class, and con- tained nothing which Avas not in them all and an essen- tial constituent, Avhen in fact it was not so. Hence we may predicate of a class as one of its constituent ele- ments that which was only a foreign substance, acci- dentally in the specimen which Ave had subjected to our analysis. 930. It is evident from these considerations that the analysis of any object may give us ele- ments of its constitution of which we were ^element! 1 ™! ignorant before the analysis. Thus the before known -. analysis of water gives us hydrogen and oxygen. And it is especially characteristic of chemical analysis, that the elements evolved are totally unlike the compound that was subjected to the analysis. 931. It will be observed that analysis can give as results nothing except that which was in the AnaIysis can analyzed compound. Thus if we analyze & on p y ro “,: water we get oxygen and hydrogen, and ties - whatever else there may he in the Avater — but nothing more. Otherwise we have no certainty in our results. 248 LOGIC. — PAKT II. [chap. 932. But we often find on analysis wliat we do not and cannot find in analysis. This is especially true of the analysis of our conceptions. By the analysis we it enables us get primarily merely what was contained in piie s d e l p?opef our conception as the material properties. ties - But after the analysis has been completed, we are able to contemplate each element by itself, and also their relations to each other ; and thus we gain an insight of many implied properties, which of course were not contained in the conception. 933. This distinction between what we get in an analysis and what we get on analysis, is very generally overlooked or omitted in speaking: of the often overlook- results, lhis, lor instance, is very constantly done by Cousin, ivlio is certainly one of the most skilful and lucid in his analysis of all the meta- physicians that the world has ever seen. 934. But as the conceptions which we form of The results of objects in the reality of being are liable to conceptions differ somewhat from those which existed in eriTior different the Divine Mind before their creation ; and as the conceptions which one mind forms of objects in the reality of being will differ somewhat from those formed by other minds of the same objects, and as analysis of the conception can give only what is contained in the conception, the results of these analy- ses by different persons will be as various as their con- ceptions ; agreeing necessarily in some of their elements while they differ in others. 935. So, too, that which may be expressly contained Material and in .one man’s conception as a material pro- tie? may ieTb perty in contingent Matter — that is, material ent minds. to his conception, may be only implied in another and vice versa. 936. This results from the fact that our minds are Difference in imperfect and limited, “ Variasse est error is.” Analysis!" 3 ° And there is probably no intellectual endow- ment in respect to which men differ more than in their powers of analysis. A Newton or a Pascal could see IX.] METHODS OF INVESTIGATION. SECT. VI. 249 at a glance into tlie relations and properties of geome- trical figures, what men of ordinary powers can see — for to understand is to see — only after hours of study and a long process of demonstration. And to an infi- nite mind the result of the longest and most compli- cated calculation must be as evident at the first glance, as the first axioms of Geometry are to us. SECTION VI. Of Induction and Analogy. 937. The words Induction, and Analogy, are each of them used to denote Methods of Investi- mduction and gation, and Methods of Proof also. In one ^ods^finve^tl- sense of the word they are regarded as fur- gatlon & Pr00f - nishing Predicates, in the other as proving them to be true. In this latter sense I shall consider them in the next Chapter." 938. Induction f is the Method by which we colli- gate several facts, having identity of Formal induction. Properties as a species, and in consequence of these facts agreeing in some other property not at first con- ceived as Formal, we predicate that fact of all indi- viduals in that species, or of the species as a whole. 939. But when the facts of any two opposite species agree in any of their Formal properties (123), Analogy, and we affirm a predicate of the second, on the ground that we had found it true of the first, we call this the Method of Analogy.]; And the Method is said to be * Part II. Chap. III. Sect. V. t Aristotle Top. Book I. Cap. XII. defines Induction to be r; curb twv k ad' '4 ko.(ttov e-nd to KaOoSov etpoSoi, “ the way of passing from particulars to universals.” J Whately has defined Analogy as being a “ resemblance of ratios ; ” and quoted Aristotle for it \_Ki-yuv o^aoidrij?]. But this definition does not seem to me either correct or sufficiently definite to answer any good pur- pose. We certainly speak of “facts” as analogous, as well as “ratios” or “ relations.” But is the analogy in the relations at all ? Is it not in all cases and necessarily in tho facts ? Thus suppose A and B each entertain a similar 11 * 250 LOGIC. — PAHT II. [chap. that of Contraries when we affirm unlike or contrary contraries. predicates on the ground of contrariety of Formal properties. 040. JSTot only do many of the facts or objects in objects in Na- Nature have such properties in common, but, pnmd“prope£ these properties are taken as Formal at plea- ties - sure, and thus become matter determining a sphere, and the facts are subsumed under that concep- tion. The word “ subsumed” which I have just intro- duced, has been pretty extensively used to denote the inclusion of individuals within the sphere of a con- ception. 941. But no sooner do we find that we have thus other proper- constituted a class of individuals, by their the class be- subsumption under any one of their proper- mai. ties, than we find that there are other pro- perties also which are common to all the individuals of this class. 942. By this fact both science and memory are greatly assisted. One can learn as quick, remember as easily and as long a general statement like this : cias hap n U ^11 res i nous bodies produce negative elec- savestimTand tricity,” as lie could the specific statements predicating the same thing of each kind of resin separately ; or even the individual statements predicating it of each particular piece of resin — the specific statements would be quite numerous, the indi- viduals innumerable. But the general statement occu- pies no more space on the written page, and requires no more time in enunciation and committing to me- mory, and no more effort to retain it, than each of the individual statements taken separately. relation to C, is not the analogy between A and B ? If not, Analogy can answer only for illustration, and never for investigation and proof. We infer the relation of B to C, for instance, from (1) the known relation of A to C, and (2) the known analogy of B to A in that particular point which thus connects A to C. But if the Analogy be in the relations and not in the facts, the relation must he known before the Analogy ; and hence Analogy as a means of investigation or proof is a vaTtpov irpioTov, a “ later-first,” or as some might prefer to call it, a Petitio Principii. H.] METHODS OF INVESTIGATION. SECT. VI. 251 913. Hence it is of the utmost importance to science that such classifications should he made, and ^ w b that in each case the generalization should riedas h.ghlb he as high — that is, the sphere of the subject 1>u “‘ e ' as comprehensive as the matter of the predicate will allow. 914. But we see objects one by one and indivi- dually. Ho where are species and genera No . direct pe r- objects of direct observation and intuition, properties 1 ' ‘of W e can never therefore find any one of the cksses as such - contingent predicates of a class by direct intuition of the class-conception. We must have some other Me- thod of investigating their properties. 915. We have three classes of cases coming under what is commonly called Induction. The Three cases, first is that in which we have the Formal Proper- ties of some class given to find the Modal Proper- ties common to the individuals in that class. Or secondly, we may have the Modal property as our start- ing-point, and reason from it back to the Formal ; and thirdly, we may have some event or phenomenon re- garded as an effect to find the class of objects that will produce that effect. 916. (1) In the first place we fix upon the promi- nent and striking features which certain facts Giving a class have in common. We give them a general name - name, and have made the Properties the Essentia of a Genus. Then we group together other facts in the same way into another Genus, based upon plain and obvious properties as Essentia. 917. But suppose we have a Whole to be embraced in our classification. Take for example the domestic animals of a farm. We then complete the We complete classification already begun by division. ^ by 3SI diu- We refer all having the properties which we sion - had assumed as the Essentia of horses, for instance, to the class “ horses ; ” all having the Essentia of cows to the class “ cows ; ” and so on with all the classes which we had formed. But starting from the idea of a 252 LOGIC. — PAKT II. [CHAP. Whole, all the individuals in that Whole must he in- cluded in some one of the classes which were in the other process regarded as so many genera, but which are now in this process regarded as coordinate species. And if in our process of division we find any indivi- duals not included in any class which we had pre- viously constituted, we either constitute that Change of Pnn- . d . . . . . . dpie of ciassi- at once into a new coordinate species or lication. i »«i <■» -1 • • • -i -j • <-» change our principle ot division, and classify on other differentia than those with which we had commenced. 948. Thus in all the Natural Sciences different () often done in principles of classification have succeeded sciences. 11 ura each other with every important step in ad- vance which the science has taken. New discoveries or a more careful analysis has brought to light new facts and new relations of fact to fact, and suggested a better principle of classification and nomenclature than was possessed before. In Botany, in Zoology, in Crys- talography such changes have frequently occurred. 949. Now in this process of classification the For- mula used is that described above (569), in wljich a Formula of common predicate denoting the Essentia of classification. t] ie Grenus is affirmed of the individuals com- prehended under it individually. When this has been done we give to the individuals a class-name, and then the matter of this class-conception gives the limits to its sphere, by including in it not only the colligated individuals which had been named in the process of the classification, but also all others which have the Essentia of the colligated individuals, and which con- stitutes the matter of the class-conception. 950. We now come to the next step in the Induc- common mo- tioii. We find that several individuals in predicated 11 8 the genus thus formed have a Modal pro- perty common to them all, which however was not so obvious as the property upon which our classification was based, or which at all events was not included in our class-conception. We then predicate this property n.] METHODS OF INVESTIGATION. SECT. VI. 253 of the individuals in the class, one after another as above (571), and then predicate this property of the class as a whole. And this deductive judgment affirms the Modal property of the species as in the example given (570). The wolf is carnivorous ; The fox is carnivorous ; The cat is carnivorous, &c. : .•. The Canidai are carnivorous. 951. And when we have thus affirmed a property of a whole class we speak of it as a law of Nature. General Facts. It is in truth, however, but a general fact, and wants much yet of being what can properly be called a law.* 952. There are three steps in Inductions of this class which it will be well to notice separately; Three steps of not indeed as involving or depending upon Indu( ' tl0n - different principles, but as being different and wider applications of the same principle. 953. (a) For the first let us take the following : We learn of an individual animal a property which was not included in its class-conception, as First step, of the horse, the fact that he sheds his hair every spring. We soon learn of the next horse that we become ac- quainted with, that he also sheds his hair in the same way. After learning this fact of a number of indi- viduals in the species horse, we predicate the fact as a general fact or law with regard to the species, that “ horses shed their hair every spring.” 951. This may be regarded as illustrating the first and primary step in Induction. It is a pro- This p , ocess cess which we all go through with in refer- ence to many of the most common species kn0 " led s e - of facts, long before we reflect upon the process at all, or study its laws. 955. (5) Then for the second step take the case in which we extend or widen our induction by The Second including several species. Thus, step - * See Part II. Chap. III. Sec. V. 254 LOGIC. PART n. [CHAP. The cat has canine teeth ; The dog has canine teeth ; The wolf has canine teeth ; therefore the dog, and the wolf, the cat and all animals which have canine teeth constitute a natural genus, which we will call the Canidce. But the dog is carnivorous ; The cat is carnivorous ; The wolf is carnivorous ; therefore the Canidse, or all animals with canine teeth, are carnivorous. 956. ( lt- but the causality is a matter of inference. selt: 974. Causality , however, is something more than mere antecedence and necessary connec- causality some- tion.* Day and night follow each other, mi?f mo antece n - tlie successive steps of the pedestrian, the dence - * The Fallacy which we sometimes hear spoken of as the Fallacy of post hoc ergo propter hoc , consists in inferring that because one event is after another, therefore it was caused by that other. Bishop Latimer exposes this fallacy in some who attributed the laxity of morals in his time to the Reformation, by narrating the anecdote of a countryman who accounted 260 LOGIC. — PAET II. [CHAP. days of the week, the months of the year, all succeed each other, and yet no one supposes that each is the Effect of that which preceded or the Cause of that which follows. So the antecedence is a fact in the reality of being ; the causality, where there is any, belongs to the reality of truth alone. It seems to direct the thought into the unseen realities of truth ; and the Reason, by an intuition peculiar to itself, sees there what is not expressed in the sensible properties of ex- ternal objects. 975. By means of Induction we may always find the Invariable Antecedent in the phenomena of Nature, invariable An- But the distinction between a mere Antece- dent and a Cause, is what no processes of a duction. posteriori investigation can give. It is some- thing which the Reason superadds to the results of our investigation in certain cases, just as in Induction the Reason superadds that which distinguishes a General Law from a mere General Fact. By the insight which Induction enables us to get into the Class-conceptions and Final Causes of the Creator, we are enabled to affirm the concomitance of certain properties of objects as Laws arising from that physical necessity which is based upon the volitions of the Divine Will. So, too, by Induction we establish certain antecedences and consequences in Nature as general facts, upon which the Reason infers or rather superadds the relation of Cause and Effect. 976. All investigation of Causes must of course end The causes in at last in the Absolute or First Cause (108). cMdaTy 0 "' 1 SIJ But the Method which we are now describ- ing must proceed step by step, and from an}' one fact or event it can give us only that which next preceded it in the order of time and of causality. This becomes for the sands that obstructed the Goodwin Harbor — by the building of Ten- terden Steeple — “There were no sands,” said he, “in the harbor; that is, none that gave trouble, until just after the steeple was built on Tenterden Church.” Hence the good people of Tenterden supposed that the steeplo had caused the sands in their harbor. II.] METHODS OF INVESTIGATION. SECT. VII. 261 in its turn an Effect to be investigated in like manner, until in like manner “ omnia exeunt in Deum ” (all things lead to God). Then and then only do we find an Efficient Cause for the facts and phenomena of Nature. 977. This results from the fact that Matter is always regarded as inert, and incapable of acting And Instru . except as it is acted upon. Even the im- mentaI - ponderable agents, heat, light, electricity, &c., can hardly be regarded as exceptions to this rule. As yet we know not what they are. But the Reason refuses to regard them as any thing more than means, Instru- mental or Second Causes in the hands of an Intelligent or First Cause. 978. Our inquiry into Causes therefore can be only an investigation into the antecedents of any event, along which the mind conceives that dit.ons required the efficiency which brought that event into by lhe Rtason ' the reality of being may have passed. And the only conditions which the Reason imposes are, (1) that that which is to be regarded as a cause be an invariable antecedent ; (2) that it be a true cause ; and (3) that it be a sufficient cause [causa vera and causa suffi- cient 979. Of the first we need say no more than the self- evident proposition, that a cause must pre- First; A ntece- cede its effect in point of chronology. dence in Time. 980. Of the second, we can only say that, a true cause must be a substance acting through second: a suh- some of its properties. A mere state or mode stanGe - of a substance is no cause, although of course it will often be an antecedent. Thus “ day ” is a mere mode of light, and is no cause of the succeeding mode A Mode no which we call “ night.” One of the steps of a proper Ciiuse - pedestrian is merely one condition or stage in his pro- gress, and no cause of the succeeding one. “Day” and “ step ” are not substances in the metaphysical sense of the words at all (Part I. 55 and note), but merely modes or stages of certain substances. Thus 262 LOGIC. — PART II. [chap. the step that crushes the worm cannot be regarded as tlie cause of the crushing. Not the step but the man Mho steps is the cause ; and the word “ step ” denotes substantive* merely the accidental condition or mode in Modal causes. w i 1 i c ] 1 the cause happened to be when it exerted its efficiency. It may be well, therefore, for the sake of having a name, to call the former the Sub- stantial or Substantive Causes, and the latter the Modal Causes. 981. But not only must the antecedent which we are to regard as a cause be a substance, in order to be cause must a vera causa , it must also bear some propor- porfio s n m t e o pr iti ti° n or relation to the effect in order to be a Effect. sufficient cause, or causa sufficiens. Thus, a boil on one’s hand may be a vera causa of a good deal of pain and annoyance, but it would not be re- garded as a sufficient cause of the death of an indi- vidual, if one having such a sore should be found dead. 982. The substantiality* (38) of causes must be af- firmed by an ultimate intuition of the Mind itself. One The substan- can 110 more prove that a “ day ” is no sub- uit!mate es intub stantial cause than that the sun is round, or tlon - a rose is red. If our faculties do not so see these objects, there is no help for us in one case any more than in the other. The fault is an individual in- firmity, and can he regarded as requiring no diminu- tion of the confidence which all persons whose faculties are in their normal condition are entitled to place in the exercise of those faculties. 983. But the sufficiency of causes in Nature is what The sufficiency we can learn only from observation. Of Nature 11 learned Primary Causes, as of the Infinite Mind, and tionand^fndul: °f the human mind, from the very conception tmn. 0 f them we can predicate certain events or phenomena as effects. We know that Infinite Wisdom * When we speak of a cause as being necessarily a substance, we must be understood as speaking not of mere antecedence, but of causality. An antecedent need not be a substance, but a cause must. II.] METHODS OF INVESTIGATION. SECT. VII. 263 will know all things — Infinite Power can do all things, that Mind or Reason can understand, that Will can choose, and determine the formal character of actions. And so in Mature we may predicate a priori, on the class- conception of certain objects something of their conca- tenation in the antecedents and consequences of Mature. But this class-conception is itself obtained a posteriori , and the nature and efficiency of their causality is a part of that which we learn by observation, and through which we are enabled to arrive at this class-conception. It is certainly very possible, and perhaps we had bet- ter say that it is probable, that the causality of all objects was an element in the class-conception which preceded in the Divine Mind the act of their creation. 981. In the sufficiency of causes we have two dis- tinct elements to take note of — the adequacy Sufficiency of in amount and homogeneity in kind. Thus Cause includes . . nr* • . ° n • , • .• two Elements. wine is the sufficient cause of intoxication. But a single wine-glassful would be inadequate in quantity. But if one should attribute a scarlet fever or the small-pox to the use of wine, he would mistake the homogeneity of the cause to the effect which ho ascribes to it. Wine is a cause, a vera causa , and a causa sufficiens of a variety of phenomena, hut not of the diseases just named. 985. As every cause must he a substance, and every substance is known only by its properties, so also it is known only as existing in some certain con- causality often dition or mode ; and this condition or mode ft* mode 0 fth“ is often inseparable from that antecedence Substance - to the effect which renders the substance a cause of it. Thus wine is a cause of intoxication only when taken into the stomach and in a certain quantity. The Air is a cause, but it causes the uprooting of trees, and the other effects of tornadoes only when it exists in the mode of violent motion. 986. Hence we have four classes of words Four classes , i i j j of words used or terms winch are used to denote causes : — to denote cau- (1) Simple words denoting substances, as se8 ' 264: LOGIC. — PAKT II. [chap. “ heat,” “ electricity,” “’light,” &c., substances whose efficiency as causes is always active wherever the sub- stances themselves are found ; then (2) we have such words as denote merely the condition or mode in which the cause exerts its influence, as when we say that “ walking fatigues one,” — “ the succession of day and night causes great changes in the temperature,” &c. Then we have (3) those complex terms which express both the cause and the mode or condition upon which the production of the effect depends, as “ the spake falling upon gunpowder caused the explosion.” Or sometimes (4) we have single words which in them- selves express the substance and its modes, as “ earth- quake,” “ hurricane,” “ lightning,” &c. 987. Words or terms in order to express a cause adequately should always he of this last-named kind. The last kind They should express not only the substance Seadequate 6 which is the cause, but also the mode or ly - condition on which the efficiency as cause is exerted. 988. The immediate Antecedent of any phenomena simple and will sometimes he complex, consisting of cedents. several elements, and at others simple. Thus Heat is a simple antecedent. It admits of no phy- sical analysis. But the sun — a burning lamp — acidi- fying vegetable matter — the mixing of sulphuric and nitric acids — are all complex antecedents, compound- ed of the simple antecedent or cause, heat, among others. 989. We must remember also that in regard to many of the compound facts in Nature, as elsewhere, The Causality the causality is not to be found in any one Spon the ep c e om s of the ingredients or elements alone and by piexity. itself. Thus, it is not the charcoal, nor the nitre, nor the sulphur which causes the explosion when a spark falls upon that combination of these three ele- ments which constitute what is called gunpowder. Neither of those elements are explosive alone and by 265 n.] METHODS OF INVESTIGATION. SECT. VII. itself.* Not any property of either of the substances, therefore, is the cause of the explosion — the combina- tion itself is the cause. 990. When therefore the combination is the cause, and not any one of the simple elements in that combina- tion, the complex antecedent is to be regarded No E , imina . as the cause. But it is often the case 'that wTelfthe™^ 6 some one element in the complex antecedent t he ep co n ml may be the cause, and it will in many cases r ’ exity - be found of the greatest importance to ascertain which of the simple elements in any complex antecedent is the real cause of the phenomena which we are investi- gating. 991. For this purpose several Methods have been resorted to, which have "been called Methods Elimination, of Elimination. They consist in removing entirely or varying in quantity certain of the elements in any complex antecedent or consequent for the purpose of ascertaining its relation to the supposed Consequent or Antecedent. 992. Elimination depends upon the four following axioms : (1.) No two simple causes will produce the same effect and the converse. Hence identity of First Axiom, effect implies identity of cause, and diversity of effect implies diversity of cause. 993. Several complex antecedents may be followed Ixy fhe same’ effect". Thus a wax-taper, an oil-lamp>, a coal-fire, the concentrated .-.rays of the sun, may each be the cause of the melting of sealing-wax. But in these complex antecedents, there is identity in one sim- ple element “ heat,” by which the effect is produced. 99d. And so strong is the belief in this axiom of identity of cause, where there is identity of effect, * This has recently been disputed in regard to Nitre. But I believe that its explosiveness has not been proved. But even if it has it will not affect the propriety of the illustration ; since if it is explosive at all, it is not explosive under any such circumstances as those contemplated in the text. 12 266 LOGIC. — PAKT II. [chap. that scientific men cling to it even when facts seem to influence of he, against them, and the belief in its infalli- llle b mlnds up of bility has often led by means of an analysis men - of the complex antecedent to the discovery of what would otherwise, perhaps, never have been suspected to ejist. And in investigations of the phe- nomena of Electricity, Galvanism, and Magnetism, the identity of effects produced in many cases have led very generally to the belief that these forces are but one and the same thing, acting in different ways and under different circumstances. Nay, so far has this matter gone, that it has been suggested that this one cause “ Electricity,” if that be the name of it, is the cause of heat and light, and the medium through which the mind exerts its control over the body. 995. As we know nothing a posteriori of substances except through their properties, so we know nothing Axiom proved of causes as causes — that is, nothing of the a priori causality of objects in Nature, except by inference from their effects. As we have already said, a cause must be a substance, it must be adequate and homogeneous to its effect. And as the identity of ob- jects in Nature depends upon the identity of their inseparable properties, so the identity of causes as such must depend upon that which constitutes their adequacy and homogeneity to the effect produced. Hence the proposition already laid down, “ the identity of effect implies identity of simple cause.” 996. (2.) The second axiom is, that if the cause is second Axiom, removed the effect will disappear. Other- wise we should have an effect without a cause, which is absurd. 997. (3.) The magnitude of the effect varies with Third Axiom, and is determined by the magnitude or in- tensity of the cause. Otherwise we should have some portion of causation without any effect, or some por- tion of effect without a cause. 998. (4.) And fourthly, that cceteris paribus the same Fourth Axiom, cause will always produce the same effect. n.] METHODS OF INVESTIGATION. — SECT. VII. 267 999. The effect always depends very much upon the substance or matter upon which the cause exerts its force. Thus heat expands iron, and con- p Efficiency de- tracts clay ; and as has been said, u what is subject matter 1 ! one man’s meat is another’s poison.” 1000. This leads us to mention the fact that Con- sequents as well as Antecedents are complex consequents ai- also, and as such the result of more than IL£?e mp ex or one simple cause. Thus, for example, an eclipse of the Moon, considered in its essence as an eclipse, and in its modes as occurring on such a moment and visible only at such a place on the Earth’s surface, is a com- plex result, caused by the various forces of the diverse attractions of the different heavenly bodies. In this case the cause of the eclipse was one thing, the cause of its occurring at precisely that moment rather than another, or so as to be visible on one part of the Earth’s surface rather than another, are each of them different causes, and may be called Formal Causes. In this case, however, we use the name Formal Cause in a sense somewhat different from what we have given to it in reference to logical classifications, and yet not so dif- ferent as to occasion any confusion or error. 1001. Let us now proceed to consider the several Methods of Elimination. Of these we may F ive Methods have five that are specially useful, arising of Eliminatl0n ' out of the axioms already mentioned as applied to the different cases which may arise for investigation. 1002. The first law of Elimination in the order in which I shall name them is the following : (1-) By the Elimination of any one element in the complex antecedent , its appropriate conse- First Method. quent or effect will disappear also. 1003. Thus suppose a physician administers a pre- scription consisting of three ingredients, camphor, and morphine, and ipecac — and finds unpleasant illustration, symptoms ensue that can be ascribed to nothing but the dose which he had prescribed. Suppose now that he administers two of the ingredients without the third, 268 LOGIC. — PART n. [CHAR. or the two combined with some others, and the un- favorable symptoms do not ensue, he would doubtless ascribe those symptoms as an effect to that ingredient in the dose which in the second administration he had omitted. 1004. (2.) When there is a uniform disagreement second Method, in several Antecedents in ail the elements except one, that one must be regarded as the cause of any unvarying element in the Consequents of those di- verse Antecedents. 1005. Thus suppose we have an Antecedent A, illustration. consisting of elements x, y, and s, and a Consequent C. If now we can form or avail ourselves of new combinations as w x and v, or s x and t , having x alone common to them all, and the Consequent C following in each case, Ave should have no doubt that A is the cause of C, by reason of its element x. 1006. Such cases occur not unfrequently in Chem- of use in chem- istry, when we have to deal with agents macy. which we either cannot get in a separate and pure state, or if we could their use would be in- convenient or unsafe. The same thing holds true also in Medical practice. Some of the most indispensable of the medical agents, in fact nearly all of those that are the most efficient can never be used except in combination with others. Hence their effect can be ascertained only by forming them into different com- binations, varying in each experiment every other ingredient. 1007. (3.) By diminishing or increasing the cause, Third Method, a corresponding increase or diminution of the effect will ensue. 1008. This law of Elimination supposes a case in which the element in the compound Antecedent cannot be wholly eliminated. 1009. Thus “ heat ” is an agent of this kind. There illustration. is no absolute of cold or total absence of heat. But we can increase or diminish the intensity of heat to a very great extent. Thus we find that n.] METHODS OF INVESTIGATION. SECT. VII. 269 nearly all bodies expand — become liquid, and finally vapor, and even gas, under intense beat ; and in tbe absence of heat all bodies contract, condense, and be- come solid. lienee heat is assumed to be the cause of fluidity. The same may be said of density. There is no body without some density ; and as the gravitation of bodies, so far as we can ascertain, varies with their density — we assume that density is the cause of the gravitation of bodies, or that all bodies gravitate in proportion to the quantity of matter. 1010. (T) If , from any pair, consisting of a complex Antecedent and a complex Consequent , we Fourth Metnod. separate the elements in the Antecedent , whose effects in the complex Consequent are known, and find an element in the Consequent whose cause is not contained in the Antecedent , it is called a Residual Phenomenon, for which a cause must be sought. 1011. We have many cases in which the several elements of a complex Antecedent have been Resi d ua i phe- so far examined, as that their effects both in nomena - quality and quantity in the Consequent are known, and yet something remains to be accounted for. The return of a Comet may be regarded as such In the retura an effect. Row among the causes which Comets - determine its return we know many — the attraction of the Earth, the attraction of the Sun, and of each of the other heavenly bodies to which it approaches in its path near enough to be influenced by them. These different attractions are the elements in the cause of its return, considered as a complex Consequent, in- cluding its return at a precise day and hour, &c. If now we begin and abstract from the Cause each ele- ment, deducting from the Consequent also its appro- priate effect — appropriate both in character and in amount, in quality and quantity, and after thus ab- stracting each element in the Cause with its element in the effect, we find something remaining in the effect still unaccounted for— we have what Sir John F. W. Herschel called a Pesidual Phenomenon. Thus if we 270 LOGIC. — PART n. [chap. have Antecedent compound of a, b, c, and d ; and Con- sequent consisting of w, x , y , 2 , and s ; and abstracting a from the Antecedent removes w , b removes x ; c, y ; and d, z. We have s remaining as a Residual Pheno- menon, for which a cause is yet to be sought, and to he added to our enumeration of the elements a, b, c, and d in the Antecedent. For the elements in any Cause must be adequate to the Effect, and the whole of it both in Substance and in Form. 1012. The existence of a resisting medium filling all space, and yet so rare as not to exert any perceptible influence upon the motions of the planets of a resisting and satellites of our system, has been sup- as a Residual posed to have been discovered as a Residual 1 henomeno". pp enomenorij effected by means of this Me- thod in accounting for the return of comets at a period somewhat less than that assigned them by the calcula- tions of astronomers. But whether there be such a medium or not, the Residual Phenomenon shows that there is some agency at work of which as yet we pos- sess no satisfactory knowledge, and which will need to be investigated before the science of Astronomy will be complete. 1013. (5.) Again and finally, there may sometimes a doubt arise as to which of the two phenomena are Necessity for a f° he regarded as cause and which as effect. Fifth Method, qq ulSj p j s always observed in cases of snow- storms, that just as the snow begins to fall the mercury in the thermometer rises a little. Row, is the change in the temperature the cause or the effect of its begin- ning to snow ? In thunder-storms, a flash of lightning is sometimes attended by an increase in the quantity of rain that is falling ; which is cause and which is effeef? 1014. In many of these cases we can answer from The doubt set- our knowledge of the nature of the plieno- cases by a pri- mena themselves. And there are many 0? 'i knowledge . -i . i i • ? of causes. cases m which we can make no experiments of Elimination. But when elimination can be made, n.] METHODS OF INVESTIGATION. — SECT. VH. 271 the case comes under the second axiom. Hence we have as the fifth rule of Elimination, 1015. (5.) Remove one of the phenomena, and if the other disappears also , that which was re- Fifth Method. moved is the cause and the other is the effect. Rut if the other does not disappear, that which was removed was the effect and not the cause. 1016. For an illustration of this law it is very com- mon to refer to the case of Dr. Wells’ researches into the phenomena of dew. It was found in the illustration, course of his experiments that those surfaces on which dew collected, were colder than those upon which there was none. But which was the cause and which the effect, the cold or the dew ? By substituting metal surfaces, which do not easily become cold in the posi- tion in which he placed them, for glass, which being a bad conductor does easily become cold, he found that the glass surfaces and not the metal were covered with dew, whence he inferred that the cooling of the surface was the cause of the dew, and not the dew the cause of the cooling of the bedewed surface. 1017. Having in these ways learned the nature of objects considered as causes, we can. often Reasoning from reason or investigate into the future from into the future, causes to their yet undeveloped effects.* Reasoning- in this Method, however, is always attended with some- thing of danger. W e seldom thoroughly comprehend all the properties of a Cause, or the influences which may be exerted upon its efficiency by its combination with other causes. Nor can we ever see far enough into the future to enable us to take into our account all of the contingencies that may arise to modify the course of events. Thus we can predict the fall of an unsup- ported body from our knowledge of the law of gravita- tion. But another law, as magnetism or electricity, &c., * This has also been called “ reasoning a priori ." — Whately’s Rhetoric, Part I. c. II. 32. It is not, however, a priori in the sense in which wo nave thus far used these words. LOGIC. — PART n. 272 [chap. may interpose between the cause and the effect and break the connection. 1018. But yet there are many cases in which this sometimes our is the only Method by which we can pene- torecaTti’ng 16 the trate the future. The astronomer reasons 1 in' Astronomy, upon it in predicting the rise and set of the sun, the changes of the moon, .the recurrence of eclipses, comets, conjunction of the stars, &c., &c. And he feels perfect confidence in bis conclusions. 1019. The chemist reasons in this Method when he In Chemistry. designs an experiment. He knows the ef- fects which certain agents as causes generally produce, lie reasons from this knowledge to the eflect which those agents will produce in the new case, and trusts to this calculation to produce the test or crisis which he wishes to determine by his experiment. 1020. The physician reasons on this principle when m Medicine, lie prescribes his remedies, and looks for the desired change in the condition of the patients as the effect of what he had prescribed. 1021. The legislator has to rely on this. Method in in Legislation, the discharge of his duties, as legislator, to a very great extent. It is often his only guide in devis- ing' laws and institutions for the welfare of those for whom he is called upon to legislate. And the causes whose influence he has to calculate, are moreover often of the subtlest and most evanescent or incomprehensi- ble character. 1022. It will have been observed from the fore- Reasoning from o;oin it remarks — that in speaking of the cause limited. oi any tact or event, we reier to a compound object within which one element alone was causal of the eflect. Hence reasoning from effect to cause, we can reason only to that element, and not to any one of the combinations into which it may enter. Thus heat is the cause of fluidity. If now we start from fluidity, as an eflect, we can argue to the existence of heat as a cause. But as this heat may have been pro- duced by the sun, by a spirit-lamp, by a chemical n.] METHODS OF INVESTIGATION. SECT. VII. 273 decomposition, by friction, &c., &c., we cannot argue to the reality of any one of those combinations of heat from the mere fact of fluidity. Hence we can investi- gate and argue much more specifically from cause to effect than from effect to cause. 1023. In some of the most important inquiries which we can have to make, however, we Limit ed ,- n have no other Method that we can pursue, but that from effect to cause. In Medical Effect 10 cause, diagnosis, for instance, this is for the most part the only means of ascertaining the nature of the disease to be cured. 1021. The -physician is called to see a patient — the prominent symptom is we will suppose a illustration, headache — this is an effect which may proceed from a variety of causes. If it were the first case of headache, and had never been investigated, there would be no other Method that could be pursued with success than those we have already described. But in the present state of the science almost all causes, and varieties of causes, have been investigated. The causes which may produce such results are pretty well known and recorded. 1025. Each cause also, for the most part, produces some other effects also besides the one that is chiefly conspicuous ; and no two causes Antecedent has J i , t • i n o several Effects. ever produce effects which are all of them precisely alike in all respects. Hence the physician is to look for the other effects, or “ symptoms,” as he will call them, until he finds one or more that is pecu- liar to one of the causes of headache. This one becomes, what Bacon proposed to call an experimen- tum crucis, or a test fact. And in the pur- E!£P „imentum suit of such a test, he will often find it neces- crucis - sary to experiment with tests voluntarily applied, as well as to observe the facts that already exist without his procurement. 1026. In our attempt, to reason into the future of 12 * 274 LOGIC. — PART n. [CHAP. human conduct, however, the moral freedom of man Reasoning from and the uncertainty as to the determinations in aU Momi G Ma? °f will, render our conclusions pecu- ter - liarly liable to error. Investigation or rea- soning in this way, however, is much more reliable when applied to masses than when applied to a single individual (800, 801). HI.] METHODS OF PROOF AND REFUTATION. SECT. I. 275 CHAPTER IH. OF METHODS OF PROOF AND REFUTATION. SECTION I. Of Proof. 1027. Methods of Proof presuppose both terms of the Proposition, whereas, as we have s.een, Methods of Investigation presuppose merely the Subject. By Proof, then, we mean the establishment of the proof. Copula, affirming or denying the relation between the given Subject and Predicate. From what has been said (131), it is' evident that no proof is required of Intuitive Judgments. Hence in all our inquiries into Methods of Proof, we are understood to have reference to the Proof of Deductive Judgments only. 1028. In the preceding Part of this Treatise, we have examined the ways in which Cognitions and Judg- ments can be so combined as to serve as Means of Proof. We have here now to con- u^Ahe F ° r . sider the ways in which these Means or For- mula may be used, with an especial reference to the Matter on which they are to he used. 1029. I have already remarked that Methods of Investigation are, to some extent, Methods ot Proof also. In Investigation we expect vesication to to find as the result, that with which we start Methods ex A as a Proposition in Methods of Proof. But Fl00t al>0 ' besides being thus in respect to Methods the converse 276 LOGIC. PAJRT II. [chap. of each other, their Differentia as Alternate Species of Methods is as stated above ; the one gives (Whately would say proves)* the Major Terms, and the other proves the Copula. f 1030. Methods of Proof may he either direct or Direct and in- indirect. Direct Methods prove the Propo- oi r iw! ethods sition to be established ; the Indirect prove its contradictory to be untrue, from which we have the desired Proposition by Immediate Inference. 1031. Direct Proof is effected by whatever Means Direct proof, or in whatever Method, wherever we show that the Subject of the Proposition has or has not the essential matter of the Predicate. Since whatever has * Rhetoric, Part. I. Chap. I. § 1. f We have in popular use the words Induction and Deduction, which are understood to denote Methods of Proof the reverse of each- other. Both, however, may he regarded as Methods of either Investigation or of Proof, since even Deduction may give a new Major Term for a subject (see Part II. Chap. III. Sec. III.) ; and the word Induction is also used to denote a Method of proving the truth of the generalization which it effects. But the contrast between the two Methods in the common estimation just referred to, is between Induction and Deduction as Metlwds of Investigation. No contrast or comparison between the former as a Method of Investiga- tion, and the latter as a Method of Proof, would ever be made with any view to a disparagement of either Method. The contrast for the disparage- ment of “ the Deductive Method,” as it is called, was undoubtedly occa- sioned by the misuse of it as a Method of Investigation, which seems to have had its origin to some extent at least in the “ Organon ” of Aristotle; and was encouraged by the schoolmen and philosophers generally until the time of Bacon, the famous author of the “ Novum Organon.” But there is no occasion for such a contrast. Induction as a Method of Proof is itself deduction from the very necessities of the case, as we shall see in our inquiry into the grounds of its validity as a Method of Proof. But regarded as Methods of Proof, Induction and Deduction differ in one . of their more obvious properties whioh has not yet been mentioned. In Deduction the General Principle or Major Premise is most conspi- cuous and will be made most prominent. In Induction the particular facts or cases — that is, the Minor Premise is made the most conspicuous. So that Deduction and Induction are both of them for the most part made by means of Enthymemes ; the former suppressing the Minor and the latter the Major Premise. In Deduction the inclusion of the Minor Term or Subject of the Syllogism in the Subject of the Major is considered too ob- vious to need express statement. In Induction the general principle of all Induction — the uniformity of Nature is assumed as too obvious and un- disputed to require explicit recognition. HI.] METHODS OF PROOF AND REFUTATION SECT. I. 277 the Essentia of any class, is of necessity included in that class, and vice versa. To render Direct Proof possible, therefore, two conditions are necessary: — itstworequi- (1) that the Proposition to be proved must sites - have a Positive Term for its Predicate ; and (2) that there may be a conception occupying a middle posi- tion in Logical Quantity between its Subject and its Predicate. 1032. Without this last condition the Proposition must be either intuitive (131), or incapable of proof. 1033. Thus for the first case — Every Effect has a Cause. This is something more than a simple Propo- sition in A, as stated ; for it results from the Jud „ ment - nature of the Matter, that whatever has a wit^noMiddie cause is an effect. Hence the Subject “ every Effect,” and the Predicate “ has a Cause,” are coex- tensive spheres, and both distributed. Hence there can be no Middle Term in Logical Quantity between them. The one is not included in any species which is comprehended by the other.* 1031. For the second case, take any Proposition which affirms what is not true, as “ apples are gingerbread. It is seen at once that capable of although these articles may be made coor- dinate species in a comprehending genus, as “food” for instance, yet in no way can one of them be made to be a comprehending sphere to the other, and conse- * We may, however, need to have the terms of an Intuitive Judgment defined or explained before the mind can assent to them. This processs, however, is not to be mistaken for, or confounded with, proof of the Proposi- tion expressing the judgment. Thus in the case above given, one would hesitate at the judgment until he might obtain an adequate conception of what we mean by “ cause,” and what by “ effect.” In that case he would be in want rather of instruction than of proof. And such in fact will be the case universally when one of the terms is but a synonyme of the other, or both are but alternate conceptions of the same subject (460). In this case the Syllogism which we may construct is rather for instruction than proof, designed to explain our terms rather than to prove that the Predicate may be affirmed of the Subject of the Con- clusion. 278 LOGIC. — PART n. [chap. quently there can be no conception coming between them in Logical Quantity. 1035. Without the first condition, namely, that the propositions Proposition to be proved must have a Posi- predicatc! atlve tive Term for its Predicate, there can be no direct proof, since Positive Terms only denote their spheres by their matter (131). Hence if the Predicate be not Positive it has no matter, or rather it gives none, by which we can determine whether the given Subject be included in it or not. 1036. The Indirect Proof depends upon the Prin- indirect proof, ciple of Excluded Middle (100), and is ac- complished by proving the falsity of the contradictory of that which we wish to prove. But as the contra- dictory of an Affirmative is always Negative, the Indi- rect Method is seldom used to prove Affirmatives, except in three classes of Propositions, which do not admit of the direct Method ; namely, (1) Intuitive Judgments ; and (2) those in which the words “ infi- nite ” and “ eternal,” &c., are used as Predicates ; or (3) Affirmative Propositions with Negative Predicates. 1037. It has commonly been held, that Axioms Axioms inca- expressive of Intuitive Judgments a priori , rect proof. are incapable ot proof ibis must be under- stood of Direct Proof only — for of Indirect Proof they all admit. It consists in this case in showing that the May be proved contradictory violates either the Principle indirectly. 0 f Identity (122), and Contradiction (123), or of Sufficient Cause (125). If it violates the first it destroys the Subject (781 and note ) ; if the second, it involves an absolute scepticism or unbelief, by im- peaching the veracity of our means of knowledge. It thus removes the very foundation upon which we can pretend to know any thing ; and so the very ground upon which we would base the assertion by which we seek or expect to accomplish our object. Thus if one denies the proposition, “ the foliage is green,” he asserts a proposition contradictory to the sense of sight, concerning matter in regard to which we have nr.] METHODS OF PROOF AND REFUTATION. — SECT. I. 279 absolutely no means of knowledge but the sense of sight. Hence if that sense cannot be relied upon, his assertion cannot he relied upon, and we know nothing of colors. And so of all other propositions asserting the primary sense-perceptions. 1038. The words “ eternal ” and “ infinite ,” have been sometimes regarded as Negatives. At others they are claimed as Positive. But for infinite" use the that is, a limit in Continuous Quantity. If word bvau ' so, beyond or outside of this limit space is not or it is not space. But even if it is occupied by material sub- stance, it is still space ; and we have space occupied and space unoccupied. Hence the judgment that that which is outside of any limit is not space, is a contra- diction in terms. If it be not space, there is no such £ outside of the limits.” Hence as the Proposition, “ space is finite,” is absurd, a contradiction in terms — its contradictory, “ space is infinite,” must be true. In the same way all Affirmative Propositions with Negative or Privative Predicates must be proved (429). 1039. If, however, the Predicate be a Positive Term, and the Copula Negative, we still have the positive p re - Essentia of the Predicate given, and must in Ju ^|; prove that the Subject has not that Essentia, ments - if so be it has not, by either Observation, Testimony, Analysis, or the Abscissio infiniti ; since none of the 280 LOGIC. — PAUT II. [CHAP. other Methods of Investigation give negative results directly, or in any other way than by Immediate Infer- ence on the ground of the Excluded Middle. We can neither count, nor measure, nor average what is not. Induction, Analogy, Example, and Elimination are all based upon the properties which the objects of inquiry do possess, and not upon those which they do not. 1040. But Testimony comes at last to Observation and Authority. The Abscissio is based upon Observa- proved only tion and Analysis. And Analysis of Objects A y utoo s r!ty, atio Sr ' s based upon Observation ; and Analysis Analysis. 0 f Conceptions upon the Intuitions of the Reason. Hence in the last analysis of our means of proving Negative Propositions with Positive Terms for Predicates, we have Observation, Authority, and An- alysis — Methods which give both the Predicate and the Copula in the one act and at the same time. It is a question which it will often be important to have answered, when are we to regard any Proposition as proved ? 1041. Most Premises will be Conclusions of pre- premises fur vious Syllogisms ; that is, they will be tliem- DeductfveJud^ selves but Deductive Judgments — and so merns. lead us consider the Premises from which they are deduced. 1042. But there can be no infinite retrogression. There must We must come at last to something that p?es. ,rst nnu " cannot be proved (directly), simply because there is no Middle Term that can come between its Subject and Predicate by Avhich it can be proved. Such are Axioms or Intuitive Judgments. When we have got back to these the mind is satisfied, satisfied with The question, Why ? which always implies a belief in an anterior judgment, will and can be no longer asked. The judgment is intuitive, and affirmed by all minds as soon as the cognitions of which it is composed are apprehended by the mind. . 1043. Yet in practice we seldom need to go through ni.] METHODS OF PROOF AND REFUTATION. — SECT. II. 281 this whole process. "We may always assume something as known and admitted — something as hav- Inpract icewe ing been already proved to the satisfaction ”educ«£eJud“ of those whom we address ; and which, con- ments - sequently, like the succeeding theorems in Mathematics, are as certain to those who have been over them tho- roughly, as the ultimate axioms and facts themselves. 1041. But as we have seen already (186), it is un- important whether we come to an ultimate p actg and fact, or to an Intuitive Judgment or Axiom ; ^f e °^ to re |° I c v t ; for the fact can always be transferred into a other - judgment by predicating of its sphere, any one of its properties which we wish to make the Major Term to a Syllogism. SECTION n. Of Demonstration. 1045. The words “ Demonstration ” and “ demon- strate ,” are often used in popular language, popular sense with reference to the absolute certainty of Son. emonb ra the conclusion, rather than to denote the method of argument by which it has been attained. 1046. Demonstration, however, in the proper sense of the word, is that Method of Proof in which J rict se „ se 0 f we establish the truth of a Proposition by the word - means of the matter necessarily contained in the con- ception of its subject. Hence the Predicate must always be either (1) a Material Property, in which case the Proposition expresses an Intuitive Judgment which is analytic a priori j or (2) an Implied Property — and in that case the Proposition represents a Deductive Judg- ment which is synthetic a priori. 1047. In each case the judgment is a priori, and implies an analysis of the conception. In the first case it affirms what is given in the Analysis, "and analysis ; and in the second it affirms what Intuitive Judg- is seen, on analysis, to be implied in the mat- mentb ' ter of the conception. And the judgments at each 282 LOGIC. — PAKT II. [CHAP. step, from the analysis to the conclusion must he intui- tive ; and of course capable of proof, on the Principle of Identity and Contradiction. 1018. In practice, however, we for the most part use of pre- adopt a previously made analysis of the con- tions. s ception ; and instead of taking each of the steps, one by one, we adopt the results of previous demonstrations. Thus in the successive Theorems in Geometry, we adopt the results of the analysis — -that is, the Definition — given in the first two or three pages ; and in each successive theorem, we adopt as our starting-point some proposition proved in a preceding theorem. But beside the Analysis of Conceptions we have also the meaning of words, or force of terms , as it is sometimes called, furnishing us the matter for demon- strations. 1049. The force of terms or names is often very Arguments great in determining our conceptions of or Terms. things, and m contributing to our stock ot knowledge. Most names instead of being an arbitrary sign for the representation of things, have an • etymolo- gical force or meaning from which we can draw some inference as to the idea which they are designed to convey — the conception of the thing itself, which was in the mind of the persons who first gave the name to the thing. This is sometimes called the Argument or Inference, ex vi termini. It is however strictly demon- strative. 1050. Demonstrations, ex vi termini , may be based Based upon the either (1) upon the necessary matter of the etymotogy ot a term ^ or upon its etymology, or (3) the common acceptation of its meaning. 1051. We have already seen (212), that whatever is On the neces- contained necessarily in a term may be pre- the term. dicated of that term. Thus it is ex vi termini that a triangle has three angles — that a quadruped has four feet, &c. 1052. And universally the Essentia of any class, m.] METHODS OF PROOF AND REFUTATION. — SECT. II. 283 considered as a genus, may be predicated of any indi- vidual of that genus. In necessary matter this ground ot predication, moreover, extends tween neces- to all the properties which are common to tmgent matter the class ; as from the nature of the matter m thI ° re “ pect ' there can here be no exceptions to a general rule — all triangles must have three angles and three sides — and the sum of their angles must be equal to two right angles, &c. 1053. But in Contingent Matter this ground of Demonstration must be regarded as most strictly lim- ited to the Essentia of the class. Otherwise it might be applied to an exception from the general rule and result in error. 1054. When this argument is based upon the ety- mology of the word, we must take heed to the changes which words undergo in their signification, by lapse of time or the peculiar circurn- based® on Et y . stances of their use. Thus allegiance is ad mo '°® y unsafe ' legem , to the law. But if one should argue, ex vi ter- mini , that therefore it does not bind him to his king or chief magistrate, he would err about as widely as if he should argue that because Mr. Mason is Speaker of the House of Representatives, he is the man who does all the speaking in the House. 1055. The conclusive force of this argument is of course still less, where it is based upon the mere common acceptation ot the meaning ot on the common terms. Such meanings are otten given or words stm more taken very much at hap-hazard, or varied s0 ' when they have once been given by very insignificant and accidental circumstances. 1056. In order to the absolute certainty which the Demonstration is capable of producing, it is necessary that there be no mistake in regard an absolute cer- to the Material or Essential Properties of the u " u> ’ Conception from which we demonstrate. And in Ma- thematics there is for the most part no difference of opinion in regard to them, and of course no possibility 284 LOGIC. — PAKT II. [CHAP. of mistake ; the essential properties of a triangle, or a circle are the same in the estimation of all men. Every class-conception of necessity has such properties. Reason why it But in the class-conceptions which we form fn " n c o ri tin gent of objects in the reality of being, there is Matter. always also some contingent matter includ- ed ; and hence there will be diversity in the estimates which men will form of the properties included in tlie conception — some regarding those as essential, which others will regard as merely accidental and contingent. In this fact is great liability to error, and the great source in fact from which errors in Demon- stration proceed. 1057. We must also remember that a property which is only accidental to the conception of an object for one purpose, may become essential to its perties become conception tor another. lx ig ht-angledness , for example, is accidental to the conception of triangle, but essential to the conception of the class or species which we call “ right-angled triangles P So “unsupportedness” is purely accidental to the concep- tion of ponderable bodies. But it is an essential pro- perty of the class-conception, formed for the purpose of investigating and proving the fact, and the law of gravitation. 1058. And as a general rule, we may say that any General Rule, property by means or on account of which we may include its substance in any predicate, is an essential property in the conception which we form of that subject with reference to the use of that pre- dicate. 1059. When we enlarge the matter of any class- increasing the conception, and thereby narrow its sphere ter, enlarges the by taking into our class-conception another monstrauon. as a Material property, we are enabled to proceed still farther and demonstrate still other implied properties, which have been brought in by means of the newly admitted Material property. Thus, suppose to the Material properties of triangle, which are two, nr.] METHODS OF PROOF AND REFUTATION. SECT. II. 285 three-sidedness and three-angledness , we add the one more, right-angledness. We now have a narrower sphere, but we are able to demonstrate many properties of right-angled triangles — the species — which we could not demonstrate, and which were not true of triangles — the genus merely. 1060. But besides Mathematics, a large part of As- tronomy, Mechanics, and what are called Demonstration the Mixed Sciences generally, are largely in a11 Sciences - indebted to Demonstration. The same is true in Logic, in Ethics. These are, and of necessity must be to a very great extent, if not wholly a priori and demon- strative sciences. 1061. Logic has especially been called “ the Mathe- matics of Thought.” And in Logic, as in in Logic. Mathematics, we must prove the legitimacy and force of both our Formulae and our Methods a priori, before we are entitled to place any confidence in the Conclu- sions or results to which they may lead us. 1062. We have already remarked that Arithmetic, Algebra, and the Calculus, are but Methods of Inves- tigation in Discrete Quantity (883). But we are obliged to justify the Methods by De- b^fustmelTby monstrations. Take the Rule of Addition, Demonstratlon - of Subtraction, of Multiplication, of Division, of Invo- lution or Evolution, or the Binomial Theorem, or any other, and we see at once that they are but Methods of finding results. But the Methods are all justified a priori , by inferences from the Necessary Matter of the Conception ; that is, from the Material Properties of the Methods themselves. We say, for example, that the square of any Binomial, as a + 5, is the square of the first term plus twice the product of the two, plus the square of the second, or a? + 2 ab + 1> 2 . And this is shown to be true from the nature of the Process or Method itself, as will be seen by a reference to any treatise on Algebra, where the Binomial Theorem is discussed. 1063. So in Ethics. We lay it down as a rule that 286 LOGIC. — PART n. [chap. the communications between man and man should be Demonstration based upon veracity and benevolence. We in Ethics. prove it from the class-conception of society, having proved or assumed that man, as a species, can live only in society. Thus, suppose the contrary, that deception and hate were the conditions or laws of human association. Deception and hate would destroy society, not only by rendering association among men impossible— hut hate would take the life of man, begin- ning with the weakest and most defenceless, until only one, and he the strongest, were left alive. But one does not make “ society .” Hence, on the principle of contradiction (422), we affirm veracity and benevolence to be necessary rules of morality. 1064. The same holds true of all class-conceptions in every department of knowledge. There are certain Demonstration properties not contained but implied in the ments’ofknow- class-conception, which may be predicated ledge. 0 f every individual comprehended under that conception. I have instanced the laws of Motion as predicable on the class-conception of Matter (791). 1065. In Theology, also, we may predicate “ sin ” of the class-conception, man, as a being having the illustration power of choice, finite in capacity, sur- from Theology, rounded py objects of desire, some of which are prohibited. 1066. How in every department of knowledge, just sciences be- in proportion as our class-conceptions be- of insi|ht ^as come distinct, definite, and adequate, mclud- mom peribct” 11 ing all that belongs to the class-conception and nothing that does not, does our knowledge of the objects in that department become a matter of insight, or of a priori intuition and affirmation. And upon this part of what we know of the objects in any science, does the science itself depend for its existence as a science. 1067. It is worthy of note that Demonstration being conciusioiifrom occupied with necessary matter exclusively, m“ses ular Pre ' we may have a universal conclusion when, UI.] METHODS OF PROOF AND REFUTATION. SECT. n. 287 as is usually the case, the Minor Premise is Particular, or rather Individual, including in fact only one instance. Thus in regard to the side of the triangle,* and the position of a straight line,f we have no hesitation in including in our conclusion all sides of all possible triangles and all possible straight lines, although in our demonstration our attention may have been con- fined to a single case alone. This results from the nature of the matter, and is more obvious in general practice than in the statement just made, for then a diagram is usually drawn, and the line, &c., is desig- nated as line AB, or by some other such sign. 1068. It is obvious from this slight examination that Demonstration is not a Formula, but a Demonstration Method in which any Formula may he used whkhTmy fo“ as bests suits the taste or the matter at our may be disposal. 1069. It should he distinctly observed, however, that nothing accidental enters into the De- No contingent monstration — that is, nothing except what into the scope was either contained or necessarily implied in the process in the class-conception of the subjects of the uon Demonstra ' several propositions. Thus when we speak of a tri- angle, all the matter that is contained in the conception is “ a figure made by three straight lines so meeting as to make three angles.” The Differentia right-an- gled, isosceles, equilateral, scalene, Ac., does not enter into the Demonstration, concerning triangles merely. But as triangle is the genus which includes all of these species, when we have proved the proposition of the genus, it must hold true of every included species. 1070. The Demonstration, moreover, holds true only of the reality of truth, represented by the Conception, and not by any means or necessarily of any diagram * “ Any one side of a triangle is less than the sum of the two other sides.” f “ A straight line let fall from any point without a straight line per- pendicular to that line is the shortest line that can be let fall from the point to the straight line.” 288 LOGIC. — PAUT II. [chap. which we may draw, or of any piece of matter which may be brought into the form of a triangle. For not the diagram nor the piece of matter was the subject of our Demonstration ; they serve only to illustrate and represent it at most, and the conclusion holds good of them only in proportion as they conform to the con- ception. 1071. An Hypothesis, as we have seen (827), is a Hypotheses supposition or nuess put into the place of a used. tact or a judgment, m the structure ot an argument or system of any kind. • Of the case in which hj-potheses are unintention- ally mistaken for facts or ascertained truths, or of those cases in which they are 'intentionally but fraudu- lently and surreptitiously introduced instead of fact and truth we have nothing here to say : the first consti- tutes a fallacy in matter, and the latter is a mere trick of sophistry. 1072. But there is a legitimate use of hypotheses in Demonstrations. Thus in Mathematics we have a theorem enunciated — we suppose cases, for the sake of testing it. We may suppose the contradictory of the theorem and disprove it, thus proving the theorem. ah s bin we ma y su PP ose various cases to test the ties rea l i°fn l Ne- comprehensiveness and adaptability of the cessary Matter. . x • j 1 -r "Ii n ** j. i principle enunciated. In the first-named case either the hypothesis or the theorem is impossible and absurd, and the method adopted enables us to determine what is absurd and by consequence which is true. In the last case the only limit to the right to make suppositions is that they be possible. For as in necessary matter there can be no exceptions, so any rule or principle must meet all conceivable cases com- ing under that rule or principle. If, therefore, we can suppose one that is possible, it is just as good for the sake of any argument claiming to be based on a priori grounds, as if instead of being merely supposed, it were actually real. For in necessary matter all conceiv- able things are possible, and so must be included m.J METHODS OF PROOF AND REFUTATION. SECT. II. 289 within, the comprehensiveness of the class-concep- tion.* 1073. But in contingent matter it is far otherwise. Here we are hardly competent to judge of NotS oincon- the possibility of what may become or may tmgent Matter - have become real. And in moral matter the danger of resorting to hypotheses is still greater. 1074. In contingent matter we may use hypotheses or supposed cases for the sake of illustration. Legitimate use But even then we must be careful that they contingent are not only supposable hut also possible. Matter - We never do and never can understand sufficiently the designs of the Creator and the limits to the possibility of the realities of being, to be very confident in our opinions as to the possible and the impossible in con- tingent matter. There are always influences and prin- ciples at work of which we know but very little, and others of whose very existence we know nothing, ex- cept the constant appearance of unaccountable events and facts— events and facts which in our ignorance of these principles we ascribe to chance — to render a resort to hypotheses as elements in the construction of arguments and sj^stems in all cases of contingent mat- ter unsafe. 1075. From the account which we have now given of Demonstration, it will be seen that while in some cases, as in Mathematics, Logic, ii?l“ 0 Method" Ethics, &c., it will constitute the whole of ot Proot the Proof, it will also enter more or less extensively into all the other Methods as subordinate parts. For in all there must he some reliance upon or reference to the force of the terms, some analysis and development of the matter necessarily contained or implied in the conception of the subject of the Argument. It is this part of an argument which gives it much of what it has of clearness and cogency. If it does not give the * In fact it has been held by one class of philosophers that Mathema- tics is based wholly on hypotheses. 13 290 LOGIC. PAKT II. [chap. argument force, it makes tlie force which it has, felt, and often carries conviction where it would not other- wise be produced. I know of no illustration of this remark so good as is to be found every where in Web- ster’s Argumentative Speeches. And no mind, so far as I have known, has ever surpassed his in the capacity to see what was necessarily contained or implied in the conception of any subject, and to develope it with overwhelming force of conviction. 1076. And in all sciences it will he found that before the facts can be constructed into a science at all, some fundamental Principles or Axioms* an sciences a" must be evolved by analysis of the concep- lundamentai tioii of subject-matter, and proved by De- monstration. Methods of Investigation may he necessary to precede this step in order to give us adecpiate conceptions of the subject-matter from which to evolve and demonstrate the fundamental principles. But these principles themselves must be demonstrated a priori before the science can receive any permanent or satisfactory form. SECTION III. Of Deduction. 1077. By Deduction we mean the Method or Pro- peduction. cess of proving a Proposition with a less comprehensive subject, as a Conclusion from one with a more comprehensive subject, by the subsumption of the less under the more comprehensive — the Predicates of both being common. Thus in Barbara : M is P, S is M, .-. S is P. * The difference between an Axiom and a Maxim is, that the latter is a general truth obtained by classification and induction to a maximum genus ; whereas an Axiom is a necessary truth, and may be either intuitive or obtained by demonstration from the necessary matter of the class-con- ception of the subject. HI.] METHODS OF PROOF AND REFUTATION. SECT. m. 291 Here S is- subsumed as a class under M in the Minor Premise, whence it follows that M is the more comprehensive Sphere of the two, and that P is predi- cable of S if it may he predicated of M. 1078. Deduction forms a large part in the develop- ment and completion of any science. A few The Sphere of leading principles are ascertained from oh- Deduction - servation and experience, and from them deduction is made to particular facts with much more ease and certainty even, in most cases than an observation of the fact itself could be made. And in many cases, as in Physiology, the fact is beyond the reach of any ob- servation ; or in others, as in Astronomy for instance, it will not come round in centuries perhaps. Thus the details of any science will be made out to a consider- able extent by deduction from its general principles. 1079. In the practical application of sciences the Method is always deductive. Even those Thg th d books which are written with the most espe - always deduc- cial reterence to application to practice, never plication 0 f sol- do and never can mention and enumerate all ence ' the individual cases. The most they can do is to specify classes of cases, and the more nearly in their enumeration of classes — that is, in their division and classification — they approach to the Infima Species , the more practical do they become in the ordinary sense of the word. 1080. In that case the Infima Species is the Middle Term, the particular individual case to which the ap- plication is to be made is the Minor Term, and the other term, whether Subject or Predicate, which enters into the “ Precept,” as it is called, with the Infima Species as the Middle Term, is the Major Premise. 1081. Thus the physician examining a patient decides the case to be intermittent fever. ni ustra ti 0 n in His science has taught him that quinine is pharmac y- required in intermittent fevers. Accordingly he pre- scribes quinine. His reasoning, stated at length, is as follows : 292 LOGIC. — PART II. [CHAP. Intermittent fevers require quiriine ; This case is an intermittent fever : .•. This case requires quinine. 1082. It will be seen at once that this is precisely the form in which the principles of science are applied to useful purposes. 1083. In the same way established principles and in Astronomy, laws are applied to new cases. For exam- ple, in Astronomy the laws of motion, the relation of distance to time in the periodic revolutions of planets, comets, &c., are so well known that the moment a new one is discerned, the astronomer proceeds by way of demonstration to determine from those elements of its sphere nearly all that can be known about it, without waiting for the much slower and more tedious process of observing these revolutions, as they occur in the course of centuries of our years. 1084. It will have been observed that one leading i A ome Sci mofl °^j e °t i 11 Methods of Investigation is to de- .ieductive ““as temiine definitely and adequately the class- more penect. conceptions which are based upon the nature of things in the reality of being. It has been remarked* that just in proportion as any science progresses from its inception and the first rude accumulation of ele- mentary facts, does it become more and more deductive and even demonstrative in its Methods. Our class- conceptions of its subject-matter by this means become more distinct, definite, and adequate — more conformed to the constitutive Idea of the classes, more compre- hensive of individuals and of phenomena — and our confidence in the results and teachings of that science become proportionally great. * Mill’s Logic , Book II. Chap. IV. § 6. — See also Devey, Book V. Chap. I. §. 5. m.] METHODS OF PROOF AND REFUTATION. SECT. IV. 293 SECTION IV. Of the Argument from Authority. 1085. There are many Propositions, which from their relating to subjects above our compre- Authority of hension, or from their being beyond the Revelatlon - reach of our observation, and differing so far from what we can observe and know in this state of being that Analogy fails to be a safe guide, can be proved only by an appeal to the Authority of God in the Revelation which Tie has been pleased to make. 1086. Then we have also another class of Propo- sitions in which stat pro ratione voluntas, Authority of where the will of some Authority so deter- Governance - mining, is the ground and the only ground on which we are obliged to receive them as true, because they have been so declared by a competent authority. 1087. Of this kind are the laws of a State, whether enactments of the legislature, or decisions of the courts, for all citizens ; the laws, canons, rubrics, &c., of a Church for all its members : the constitu- tions, rules, and by-laws oi any voluntary only limited ob- society or corporation tor economical, social, moral, political, philanthropic or religious purposes, upon the members of those societies or corporations as members and during their membership. 1088. Propositions of the kind now under consider- ation are authority, and therefore to be received as true only in relation to the particular things which come under the jurisdiction of the authority, and for those persons over whom that authority justly extends. Thus Revelation is final to all the creatures of God to whom it is made ; the authority of the state to all citizens and subjects; that of a voluntary society to those only who voluntarily belong to the society. 1089. There are some spheres in which by the very nature of the case this Means of Proof is made neces- 294 LOGIC. — PART II. [CHAP. sary, and is the only one that is proper. In Statute Luav and Theology, for instance, the dicta only 1 e'roui]d°in of the proper Authority must be an end to some cases. . 1 x ° controversy. Any arguments on general grounds, as to what ought to he true , can do nothing more at most than to create a presumption in favor of any doctrine. 1090. Besides the foregoing, the common sense or consent of mankind, as well as the admissions of those against whom we are arguing, become first and “common principles of the nature of authority within certain limits, and to certain persons the argument from the admissions of parties ex . concessis , is scarcely any thing more than an argumentum ad homi- nem , and for that I will refer the reader to Sec. XI. of this Chapter below. 1091. But the common opinion of men is an Au- thority or first principle, on which a large part of our Extent of ciost important deductions are based, espe- mo?! 1 a°a pmi cially in practical matters, and among those dole. whose minds have never been trained to look into the philosophical grounds of their actions. These are commonly called Arguments from Corn- common sense 111011 Sense, sensus communis omnibus , and fues V in ri dmerent their value has been very variously esti- Spheres. ma ted. 1092. In matters of Religion, if man is to he Religion. regarded as a fallen and depraved being, it is to he distrusted and scanned very closely. In fact it can never be used except as confirmatory of the Argument from authority, or as serving the rhetorical purpose of removing a prejudice or supposed antece- dent improbability. But if man is not fallen or de- praved, his common sense must be as infallible an indication of the law and will of God (vox joojnili vox Dei ), as the facts and changes of the physical world are of Iiis laws and will in relation to matter. 1093. In Polity and Ethics the common sense of man is of more value ; for they relate to matters that in.] METHODS OF PROOF AND REFUTATION. SECT. IV. 295 are more comprehensible, and which have of necessity been not only subjects of reflection, hut also In PoUty and and moreover they have been tested by the Ethics - experience of all and in all ages. What has been thus found to he best and true, is most likely to stand the trial to which it can be brought. The latter schools of philosophy have professedly regarded this common sense as of great value as a standard of truth. 1094. In the Natural Sciences it has been found to he an unsafe guide. It always depends upon tn the Natural the appearances of things, while in many Sciences - cases the reality lies much deeper and is often very unlike the appearance. The contrast between the com- mon belief in regard to the motion of the Sun and the Earth is familiar to all, and a case in point. 1095. But in matters which depend upon a priori conceptions or upon facts, the appeal to com- In the Pure mon opinion is out of place. By authority, Sciences - however, in this connection, I do not mean testimony to the reality of facts. Such testimony we must use and depend upon. But testimony to a fact Distincti0 n be is one thing, and opinion or inference from the fact is quite another. And the differ- mony - ence between them is one of the things which it is most important to notice. Testimony is the means by which we know what are the Principles which have been established by Authority. Thus in Religion, God him- self is the Authority ; and the Scriptures are the Testi- mony which make known to us what has emanated from that Authority. In Law, the State is the Author- ity ; and the statute-books and the decisions of the Courts are the Testimony from which we learn what are the laws established by that Authority. 1096. Hence, although we may use testimony in the Natural Sciences, in History, &c., Au- Legitimate use thority, strictly speaking, we do not use. ot T est ‘ m °“y- We use testimony as a means of ascertaining facts, whether they be the facts which any Authority has made such, as when a State enacts a law, that enact- 296 LOGIC. — PART II. [chap. ment is a fact ; or whether they are the facts evolved in the history of man and the world, or finally the facts of Nature. 1097. Yet even Testimony is often called Author- Testimony of- ity — an authority for believing the Tacts to thority. which it bears witness only. We speak of believing a fact in Roman history on the authority of Livy or of Tacitus, when in strictness of language we in what sense, mean the testimony of those writers. This distinction between Authority and Testimony is indis- pensable to a right apprehension of Methods of Investi- gation and Argument in which they are used. 1098. Testimony can prove facts only, and a law or an opinion only as the facts themselves prove the in what way opinion. Testimony may prove the acts and Jrove m a°n ny opTn n words of our Lord, as recorded in the Holy ion or jaw. Scriptures. But these acts and words, as facts , must prove the Revelation, and that that which is given as a Revelation of the Will of Grod is really His will. Testimony can prove the enactment of a law, or the issuing a command — but the enactment itself, and the giving of the command, as facts must prove, if it is proved at all, that the law enacted and the command given are laws and commands of Authority. 1099. Hence in Mathematics Testimony is never Testimony used as a means of Teaching or of Proof. o'f h beHerf round All must rest on the personal intuition of the learner. In the Natural Sciences we have to depend upon Testimony for a large part of our facts. But the facts speak for themselves. Testimony cannot even prove an opinion , but only the fact that such and such an one held it as an opinion. It does not prove the opinion to he true ; and all that can be gained by the opinion of others in the fields of scientific inquiry, is at most a probable ground of action , when we must act and can have nothing l>ettcr to act upon. 1100. Thus a physician, in a critical case, may act And of Action, upon a mere opinion of a distinguished in.] METHODS OF PROOF AND REFUTATION. SECT. IV. 297 physician, provided there is no prescription for it which experience has satisfactorily proved, and where, if he does not act at all, only the worst of consequences can ensue. 1101. In all appeals to Authority, and to Testimony also, howsoever and wheresoever expressed, Necessity f 0r the true meaning of the words in which it is in n 7hT e use io of expressed is of material importance, and of Authonly - course one of the first things to be obtained. Language itself is but an imperfect instrument for the expression of thought, and often it is used without clearness in the mind of him who uses it, and without any successful effort to make it as adequate to the expression of the thought as its capabilities would allow. 1102. The process by which we evolve a man’s thoughts from his words, is called Interpre- tation or Hermeneutics. Something of inter- or In 5™“ pretation is always necessary when we read. But when such words are used as we are familiar with, and the clear thought is clearly expressed in familiar phrase, the process of interpretation is performed so quickly and so easily, that we are wholly unconscious of it. It is only when it becomes difficult, and takes time, and causes delay and doubt, that we become conscious of the effort, and feel the need of rules and principles to guide us. A few of these leading and most important princi- ples we will now briefly specify. 1103. (1) In the first place, wherever there is one plain and obvious meaning to a passage, that taken ds i™ u theh- is to be adopted. f n b g vious mta "~ Seldom, indeed, will it be expedient or allowable to go behind the text itself to any evidence or indications of what the author may have intended to say, provided his language is clear and appears to have been used by one who knew how to express whatever thought he may have intended to communicate. The choice of words and expressions was with him, and he must be responsible for what he has clearly and plainly said. 13* 298 LOGIC. PART n. [chap. 1104. (2) But secondly, where language is ambi- Ambiguous lan- guous, or the meaning of a passage is doubt- terpretcd 0 " ful, we are to interpret in accordance with truth and right sentiment if possible. This rule is charitable enough, and may sometimes give one more than his due. But it is better to do so than otherwise. Let the error, if there be one, be put down to the account of charity. 1105. (3) Thirdly, we must take heed to the usus quendi. USUS ' 0 ' loquendi / (a) Of the author himself. (b) Of the sect or people to which he belongs. There is scarcely a writer or speaker who has not some peculiarities in style, and in the use of some of the words which will occur in the course of his writings or speeches. The exact meaning of such words, as used by any man, is best obtained from a study of his own writings ; or secondly, in case there are none, in those of the sect or school to which he belongs. Thus the word “ Idea ” means one thing, in Plato’s use of it, another in Mr. Locke’s, and still another in the writ- ings of some modern philosophers, as Kant and Cousin. If, therefore, we should undertake to read the writings of any one of these authors, with the sense which the other attaches to the word whenever it occurs, we not only should fail to find our author very clear and intelli- gible, but we should deduce from his statements conclu- sions which his words, when understood as he intended them , would not justify. It would be easy to accumu- late a long list of words, illustrating this point, but we have not room. 1106. (4) The fourth rule is, that technical terms Technical Terms, must be explained by the science to which their use belongs. Every science has, and of necessity must have some terms to which those who are proficient in that science will attach a meaning, somewhat different from that which it has among those who are unacquainted with its scientific use. The word “ switch,” as used by in.] METHODS OF PROOF AND REFUTATION. SECT. IV. 299 boys at their plays, and by a railroad manager, has two entirely distinct senses. In fact no one can read any treatise on a scientific subject with which he is unacquainted without finding new words, and old words used with new significations. Lexicographers, in pre- paring their Dictionaries, derive their definitions from the sources now indicated, or at least should do so. But in no case can a Dictionary give all the technical words with all their meanings. Let any one, for in- stance, attempt to find in any Dictionary a definition of the terms used by sailors at sea, by printers in the ju’inting-office, to say nothing of the technicalities of Law, Medicine, and Theology, and he will see the necessity and reasonableness of the rule of interpreta- tion now laid down. 1107. (5) All language used in deeds, wills, and other documents, conveying property from one to another, are to be interpreted in favor giving ana con- of the grantor, if there is any of ambiguity. The obvious reason for this, is that the right of property requires that no one should be presumed to have intended to give away any more than he ex- pressed his intention to give. 1108. But to this there are several modifications ; and the first is in conveying away any obj ect, Modifications we convey with it whatever is inseparable totherule - from it, even though it be not mentioned ; and secondly, as a grant is seldom if ever made except for a consider- ation of something in return, the amount of this con- sideration may sometimes be taken into account to determine the true sense of the grant. 1109. (6) Oaths are always to be understood (in sensu iinrponentis ), in the sense of the au- oaths, thority which imposes the oath. Oaths are given to secure the fidelity and truthful- ness of those on whom they are imposed. But if those who receive the oaths may take advantage of any ob- scurity or ambiguity which may exist in the language of the oath itself, or which by ingenuity and prejudice 300 LOGIC. PART n. [CHAP. persons interested can cause to exist, the obligations of an oath and the very purposes for which they are imposed will be at an end. One has a right to know, before taking an oath, what it means and what it is designed to impose upon him. And although he would be justified in some cases in refusing the oath and submitting to the consequences, yet in no case would one be justified in taking the oath and then per- juring himself, under the plea that the oath is suscep- tible of another construction, than that designed by the authority imposing it, or that he chose to put an- other construction upon it. 1110. (7) All laws, edicts, &c., restraining personal Laws, Edicts, liberty and the right of private judgment, restraining lib- , /> J ° , 7 crty. are to be interpreted as lavorabiy as possible to those who are thus restrained. All law and authority is of necessity and essentially a restraint upon the personal liberty of those who are subject to the law or authority. We seldom speak of it in this light, however, except where the restraint becomes greater than there is any good reason for. But as such restraints should be as little as the cause of order and morality will allow, we are to interpret all laws which go beyond those requirements in favor of the subject, and give him the benefit of any ambi- guity that there may be in the language in which the laws are expressed. 1111. (8) Commissions and other documents con- commissions ferring authority or privilege, are to be privilege. regarded, as iLxclusives ( expressio unites, exclusio alterius). This is substantially the same as the fifth rule above, in a different application. No one is presumed to have any authority over another, or special privileges and exemptions. If he has them there must be proof of it, and the mention of one or more in the words that confer the authority or privilege, leaves the others in possession of no more than they would have had if no such document had been issued. The commission of- one man in a company does not m.] METHODS OF PROOF AND REFUTATION. SECT. IV. 301 constitute all the privates captains. Nor does the appointment of one man to be a justice of the peace make the whole neighborhood to he esquires. 1112. (9) When the quantity of a proposition is doubtful we are to take it at its least value, The Quant ity unless the conclusions of the argument, or ° faPr0p0i ‘ tl0n - the truth of the statement require otherwise. Thus in Wayland’s Political Economy occurs the remark, which is universal in its form, “ All men are not merchants .” But truth requires that it be considered as particular negative — that is, “ Some men are not mer- chants.” And again ; from the connection in which it occurs, it appears to have been designed as a contra- dictory of a supposed preceding universal affirmation, “ All men are merchants.” Again, the following oc- curs in a work before me, “ Abstinence from eating flesh had reference to the divine institution of sacri- fice ; ” the author’s argument, as well as the ordinary principles of interpretation, require that the proposition should be regarded as universal. But the truth of the proposition would in that case be a matter of doubt at least, and most likely the proposition would be false if taken universally. But if the proposition had occurred where no use was made of it, requiring it to be regard- ed as a universal proposition, it would have passed without notice as a statement generally true, perhaps, but yet only the expression of a particular judgment, “ Abstinence ” being regarded as not a distributed term ; the abstract term being used for the concrete plural. 1113. (10) Parables and metaphors are to be con- strued with special reference to the design Parab i es and for which they were used. Metaphors. Parables, metaphors, fables, and all of that kind of illustrations, are. based upon analogy and not identity of cases. But in all analogies there are points of diversity, and the case upon which the parable is based is assumed to be identical only in the point to be illus- trated by it. In that point there must be identity, else 302 LOGIC. — PAHT n. [chap. tlie illustration fails ; beyond that point there must be some diversity. These points must not be brought into the illustration, nor may its force and appropriateness be objected to on their account. 1114. In the Parable of the Rich Man and Laza- rus (Luke xvi.), for instance, the main design, undoubt- edly, was to show the impossibility of changing one’s doom by repentance after death. And it would be unsafe and unwise to attempt to infer any thing further frgm it concerning the condition of man in the future state. We can hardly go so far with safety, (I think,) as to infer from it that the two classes of persons repre- sented by Lazarus and the Rich Man, are in a condi- tion to hold conversation with each other, or with those of the other class at all. 1115. (11) Mere obiter dicta are never to be re- obiter dicta, garded as of equal authority with the as- sertions made to the point directly before the mind. In nearly all discourse and reasoning there is a leading object, to which the attention is especially directed. The assertions bearing directly on that point are always to be regarded as the most mature and carefully guarded opinions of the author. But there are almost always expressions dropped by the way, called obiter dicta , on incidental and collateral matters, to which the attention is not directed with so much energy as to the main point, and consequently these obiter dicta are less valuable as expressions of opinion or authority, than those to which the attention is mainly directed. 1116. The science of Interpretation is a compre- speciai Rules hensive one, and cannot be fully treated in departmerftl ery this place. And as in each special depart- ment of inquiry, Avhere we have to depend upon Testi- mony and Authority, some special rules and ' cautions are found necessary, I have aimed above to give only such general rules as seemed necessary to my present purpose, and of the most extensive application. m.] METHODS OF PROOF AND REFUTATION. SECT. Y. 303 SECTION V. Of the Appeal to Facts. 1117. The Appeal to Facts, as a Method of Argu- ment, is in some respects the converse of the AppeaI t0 foregoing Methods. We reason from Facts Facts - to Principles rather than from Principles to Facts. 1118. These Facts may he introduced by way of Induction, Analogy, Example, or as Contra- Facts how in . ries, Exceptions,* Circumstances, Cause or troduced - Effect. But in all cases they require the force of Prin- ciples lying deeper than the facts themselves, in order to render their argumentative force of any value. 1119. I have already in the last Chapter (Section VII.) said concerning reasoning from Cause Cause and Ef . to Effect — that is, concerning the appeal to fect - Facts as Causes or Effects, all that I shall deem it advisable to say in the present Treatise. I will, there- fore, proceed at once to consider the general Principles involved, and the Methods of proceeding in reasoning from Facts in the various other conceptions of them. 1120. An important distinction is made between a law and a general fact. Thus it is a general General Facts fact, proved by Induction, that “ all Canidse and Laws - are carnivorous ; ” — “ all bodies gravitate towards the Earth.” But that which lies under this general fact and determines the manner in which the Cause shall act, is called the law. Hence the law of gravitation is that which accounts for the general facts of gravity. It is the law which produces, or rather guides the cause in producing the general fact of a carnivorous habit of life in animals, constituted by their Creator * For facts introduced by way of Exceptions, see Sec. IX. below. Since they always presuppose that to which they are exceptions, I have chosen to consider them as means of disproof ; that is, disproving the uni- versality of that rule in view of which alone they can be regarded as ex- ceptions. 304 LOGIC. PART II. [chap for that habit of life. Hence the law always implies the fact and the fact the law, and the two are often confounded. 1121. We place but very little confidence, how- ever, in any mere induction of facts, unless we can go induction must a little farther. The Formula of Induction mere^cfassffictu itself, as will be seen (569), is an undistri- tlon - bated Middle, and becomes valid at all only by a sort of transfer of the matter over into the domain of necessary matter. 1122. This we accomplish by means of principles, logically antecedent to all induction, and lying deeper how accom- i n the subj ect-matter than Induction itself piished. can i-eacP. By this means we can extend our predication from what is and has been to what will be. We pass from the general fact to the law.* The first of these Principles which we shall con- sider is the Uniformity of Nature — the second is that of Final Causes. 1123. We use the word “Nature” \_N~atura, from ■Nature "in nascor], as a collective term, including all used. senoe those realities of being in the external world, whose existence is contingent, and which are not the product of human agency as their Efficient Cause. Thus a blow with the hand would not be a fact in Nature, since it proceeds from the will of man as its * We have given above, p. 249 n., Aristotle’s definition of Induction, Top. B. I. Cap. XII. In the Prior Analytics, Book II. Cap. XXII. Aris- totle speaks of Induction as a means of proving one extreme through the other, i. e. to prove the Major Term of the Middle , by means of the Minor. Thus he gives for example : Men, horses, and mules are long lived ; Men, horses, and mules are void of bile. If then, says he, (men, horses, and mules) and (long-livers) may be converted “ without excluding the Middle,”— that is, if (long-lived) is not a more comprehensive sphere than (men, horses, and mules), we may have the conclusion : All animals void of bile are long-lived ; But this is the very difficulty ; the Major Premise can never be con- verted in that way. The Predicate is always comprehensive of more than the inducted particulars, and it is precisely this peculiarity of induction that we wish to account for and justify. III.] METHODS OF PROOF AND REFUTATION. SECT. Y. 305 Efficient Cause. But the growth of a blade of com would he a fact in Nature, although the growth might depend upon the fact that man had planted it, or still keeps the soil in a condition to continue its growth towards maturity. In this case man is not the Efficient hut only the Occasional Cause. 1124. By the Uniformity of Nature we mean what may be stated generally as the fact, that the J 0 . 17 i j i i What is meant same causes acting under the same laws, by y umfomu- and cwieris paribus — (that is, all the modify- tJ ' ing circumstances being the same,) will produce the same effects.* 1125. But let us try to get a little more definite idea of this uniformity, and the grounds upon which it rests. It is, doubtless, first suggested by the facts in the external world. Thus, for instance, a tree ^ o always produces leaves and fruit of the same uniformity how kind. So, too, with the offspring of animals. f ‘ rst ° taa,e ' Each new individual is not the germ of a new class or species. Nor does it even belong to a species different from that from which it derived its origin. In short the objects of nature at once suggest the classifications, by means of Essentia and Differentia, which have al- ready been spoken of as so advantageous to science. * Mr. Mill thinks (besides expressing some doubts about the Uni- formity of Nature) that what we know or believe of it we have learned from experience. In a certain sense this is true. And using words still in the same sense all that we ever know is learned from experience. But then we may easily get to be wiser than our teacher. We learn from ex- perience a great deal more than there is in experience. Experience is con- fined to the past, and generalizations upon its facts can give us only what has been. But by induction from the facts of experience we infer what is to be in the future, and every where in the reality of being constituted like that in which we are placed. From mere uniformity we do not expect its con- tinuance, as Mr. Mill has indirectly shown. From the fact that the first five or six of the Presidents of the United States retired from office at the age of sixty-six, the people of the country formed no expectation whatever that such would continue for ever to be the uniform fact with regard to the age of the retiring Presidents. Hence it is something not given in experience which leads us to expect a continuance of this uniformity in some cases and not in others. This “ something,” call it what you will, is what we are now inquiring after, and it must be a priori. 306 LOGIC. PART H. - - [CHAP. 1126. But if they suggest to our minds these classi- fications, it must be because they proceeded from a implies a creat c ^ ass ' conce pti° n Li a mind like our own, at ing mind essen- least in respect to the faculty of constructing tially like ours. x . . T P u -i t 0 such conceptions. It the words I use sug- gest to the mind of the reader or hearer a thought, it must be because they proceeded from the same thought, and are used, as a means of expressing it in my own mind. 1127. Let us then consider the operations of the An analogy in human mind. Take the case of an artisan. of man. lie iorms the plan ot a piece oi mechanism, a watch for instance — that plan is his class-conception, his object being not to produce one watch only but a number — a supply for the demand of his customers. Hence we have a species of watches agreeing exactly with each other, so far as the properties included in the class-conception are concerned, hut differing in the accidents of having been finished at different times, by different hands perhaps — made in part of different materials, some having gold and others silver cases, &c. ; and differing also in size and ornamental decorations. How, suppose the same artisan to form a different plan or class-conception, one differing therefore in some of the essential parts of a watch, as in the form of the escapement, &c., and we shall have from that model another species of watch. 1128. How before creation, the Creative Mind must The class con- have formed such class-conceptions for each creative wind, species oi created objects; and each nidi- vidual in a species is like all the others in all the pro- perties which were included in that class-conception ; and differing from others only in those which, from their not being included in the original class-concep- tion, are called accidental.* * This illustration of the operation of the Divine Mind might he car- ried much farther. One point more only, however, will I notice in passing. It is not altogether voluntary with man what elements he will include in.] METHODS OF PROOF AND REFUTATION . SECT. V. 307 1129. We may then say that the uniformity of Nature consists in the agreement of all objects Unilorm within the same species in the matter of their in ( of Nature class-conception. And our Induction is but the process by which we make our conceptions of the material species adequate. We get one of its elements. We classify upon that; then find another property common to all the individuals in that species which have fallen under our observation — predicate this latter property of the species by means of the specific name which we have given it, and call the Proposition so made a statement of a law of Nature. It is an indica- tion of the Divine will and conception ; and therefore we expect all individuals in any class to conform to the essentials of that class — -which essentials we are learn- ing one after another by Induction. If there were no such class-conception, there could be no classification ; no Uniformity of Nature ; consequently no Induction. in his class-conceptions. Having fixed upon some which are material to it, there are othei-s that are necessarily implied, and others that are acci- dental — over which, however, he has no control, any further than his own hand may he employed in making the objects in the class. Thus in a watch, if he would have a lever escapement, he must have a hair-spring, whether he would or not, he must have wheels and pinions to graduate the motion ; and he must have the liability to break, to wear, &c., as insepar- able from all the materials that man has at his command to use. And as all the watches of that species are to be made by himself, or under his control, he can control the purely accidental properties of size, ornament, &c. But beyond that he has no control over what is accidental. In Nature, however, there is but one Creator and Producer. All those properties of the objects of nature, therefore, which so far as we can see, are only accidental to the class-conception, are yet under the control of the Will of Him who designed and still produces them ; and in all of them, therefore, He can secure a perfect uniformity, and make them to be for all practical purposes, not accidental but essential. Hence individuals in the natural species, as apples, pears, peaches, dogs, horses, men, &e., &e., do not differ so much from each other, or from their idea or class-conception as the works of man, watches, hats, boots, coats, &c., &c., nor even so much as the diagrams which we draw to represent the mathematical figures, triangle, circle, ellipse, &c., differ from one another, even among those which are designed to represent precisely the same conception. Always do they come short of the conception to some extent, come short of realizing it as an idea ; and go beyond it in present- ing to the mind for its consideration, properties which were not contained in the conception. 308 LOGIC. — PAKT II. [CHAP. 1130. Now whatever is necessary, to the proof of any Proposition is in some way a Premise to that whatever is Proposition. Hence the Uniformity of Na- con e cSn!° is ture being necessary to the belief in the that rem conciu“ result of any Induction, that uniformity sum. must enter in some way as Premise to the Conclusion from the Induction, when announced as a Law' Of Nature. 1131. Using these principles as Premises, we are induction com- able to complete the Induction into a Syllo- pleted into a r. m d syllogism. gism as follows, ror Major Jr remise we have, “All similar instances in Nature are governed by the same law.” For Minor Premise we may say, “ The cat, the dog, the wolf are instances of carnivorous animals, similar in having canine teeth.” .•. All animals with canine teeth, will be instances of the same law, viz., carnivorous animals — that is, “ All animals with canine teeth will be carnivorous.” * 1132. But if the Major Premise were removed or * It lias been pretty extensively held that Induction is a Method of Argumentation totally unlike the Syllogistic, and one which can never be reduced to a Syllogism. Sir William Hamilton was of this opinion. Now there can be no doubt that Induction, as a Method of Investigation, is a Me- thod radically different from Deduction or the Syllogism. But the Induc- tion, as an investigation of the predicates of Natural Species, is a very dif- ferent thing from the verification of that Method, or the use which we make of the Induction as a means of proof. The Binomial theorem is one thing, the use we make of it in practice quite another — and the reasoning and principles by which we verify the theorem is another still — and quite as distinct from the theorem itseif. Now Methods of Investigation cannot be reduced to the Logical For- mula. The Formulae are the Means to be used in the Methods of Proof, and whatever can be proved must be proved by some Formula — one that has been catalogued and examined, or one that yet remains to be entered upon our list. But Methods of Investigation prove nothing. There can be no need of the accumulation of authorities or of argument to show, not that the Induction, but that our confidence in its results — and hence Induction, as a Method of Proof, depends upon the uniformity of Nature. This point is nowhere denied or doubted. If this be so, this Uniformity, stated as a Principle or Premise, must be the Major Premise in all Proof from Induction ; and the basis of the verification of Induction itself as a Method of Investigation. III.] METHODS OF PROOF AND REFUTATION. — SECT. Y. 30& denied, no confidence whatever would be placed in the Conclusion. That is, take away the Uni- ^ Inductjon formity of Nature, and we should place no withouttheMa- confidence in Induction as a means of Proof, Jor or as indicating a law upon which we could base any predictions or expectations for the future. 1133. We have seen that Induction is the Method which most appropriately belongs to the facts in the reality of being, and within the range Inductjon be of what is called Nature — including as it longs' to Physi- does all facts which are not considered as CJ 1 d er ' depending directly upon the will and volitions of a moral agent. But inasmuch as the will of man is subject to no such law of necessity and uniformity, as the course of Nature, and inasmuch as the courses of events in God’s providential government of the world are to such an extent above our knowledge B utr.ottoMo- and comprehension, the facts or events in ralMatter - each of these two Spheres are hardly to be considered as within the province of Induction. W e can indeed in this way learn much of the nature of man, and of the plans and principles of God’s moral government, hut not enough to enable us to speak with the same confidence as we may use in regard to the facts of Nature. That God is just, we know indeed as well as we know any truth of Natural Science, and that He will punish any particular sin we may also know with the same certainty. But the particular time, way, and means we cannot infer from any induction of the past with any thing that approaches a physical certainty. 1134. So, too, from an observation of human nature, we see that men for the most part are gov- erned m their actions by a regard to their destroys uni- own interests. But we cannot therefore say, in any particular case, with any thing like the certainty of an induction, that this man will be -controlled by considerations of self-interest. There are not only too many exceptions to the rule to allow • of such a cer- tainty, but we recognize in all men a capacity to resist 310 LOGIC. PABT n. [chap. all sucli considerations whenever they choose to clo so ; not only for the purpose of following their passions, but also in many cases for the heroic purpose of sacrificing themselves and their own interests for the truth and the good of others. 1135. The next condition, limiting the sphere of Induction, is that the Predicate be not an Accidental induction can- property, hut such as are regarded as inse- dentai° v proper- pcirable properties. Induction does not ex- ties - tend to separable accidents or properties. If they are inseparable it is because there is some law or necessity connecting and binding them to a con- comitance with the more obvious properties which make up the Essentia of the class-conception. But if they are separable their connection with the indivi- duals of the genus is regarded as merely accidental, implying neither necessitv nor law ; and the considered acci- connection remains, tor the present at least, found tcTbe es e an isolated fact. Further discoveries, how- ever, may find relations which indicate law and design, and then a new genus will be formed to which this property will no longer be an accident but an inseparable property. 1136. But until that is done and we gain some in- sight into the will and designs of Providence, farther than the mere Induction of facts can give, we hardly call our investigation an Induction at all. Thus M. Cousin lias observed that great events take trat?onftom his- place in the middle of centuries. He speaks of the Middle of the Fourteenth as remark- able for the discoveries and revival of learning ; the Fifteenth as remarkable for the fall of Constantinople ; the Sixteenth for the Reformation ; the Seventeenth for the English Rebellion, &c. ; and yet no one regards this as an induction establishing a law, that the middle of every century will be accompanied by some great event in history. Again, five of the Presidents of the United States — the first five, went out of office when they were sixty-six years old. No one regards this. HI.] METHODS OF PROOF AND REFUTATION. — SECT. V. 311 however, as an induction that establishes a general fact or law, that all Presidents shall hold office until they are sixty-six years old. 1137. And yet there is undoubtedly an important sense in which the facts of History constitute Facts of His . a field for inductive investigations. jgfo One of the most striking and extraordi- for rnduction - nary illustrations of this that I have ever seen, is Spel- man’s History and Fate of Sacrilege ; in which, after deducing the law of God upon the subject from the Scriptures, he runs over the whole of History, and especially the History of England since the Reforma- tion, to show how the facts of History indicates prin- ciples the same as those educed from the Scriptures. 1138. This use of History assumes that God has a plan and a purpose in History, and governs the moral world by laws as completely as He does the natural world ; and that from This use of History assumes a Moral Govern- ment of the world. the facts evolved, His will can be learned in the one case as certainly as in the other. 1139. Induction, therefore, becomes a ground of Proof, or belief in the result obtained by our induction ap - classification, only as it approaches to the Demonstration, condition in which we could demonstrate the .conclu- sion which we reach by our inductive investigation from the class-conception. In Mathematics we get the class-conception by constructing in our own mind the figures which are comprehended under it. But before the creation of the world, the Creator must have con- structed the same class-conception of all objects to be comprehended under each species of being that He would create. These conceptions are what Plato called Ideas, and Aristotle called Motions {ra vorjTa), or as we render the word, “ conceptions.” • 1139. Induction helps us to these Ideas or Concep- tions, and puts us, so far as it is successful, Induction lim . into the position which the Creative Mind e £ occupied with regard to them before crea- “nlm "i ud S® tion. It puts us into the same relation in “““ptions. 312 LOGIC. PART II. [CHAP. regard to objects in the natural world as we sustain to the Figures of Geometry, which we have constructed in our own imagination, or those conceptions of the various machines and implements of human contriv- ance with which the abodes of civilized man every where .abounds. And from the matter of the Ideas or class-conceptions, as Material Properties, we see that other properties are necessarily implied. And it is a matter of doubt if there is or can be any Induction which deserves to be so called — that undertakes to prove any property of a species in natural objects which is not implied in the Matter of its class-concep- tion, as that conception existed in the Creative Mind.* * Since these pages were put into the Printer’s hand, I have met with a report of the doings of “ the American Association for the Advancement of Science ,” lield at Providence, R. I. In the report of the doings for August 16th [1855], there is an account of Prof. Agassiz’ paper of “ The System in Zoology,” from which I make the extract below. I have long regarded Prof. Agassiz as the most philosophical of all our naturalists ; perhaps more so than any other scholar in that department now living. And it affords me great pleasure to find that after some twenty years study and effort at an attempt to classify, and so proceed with his Induction on some other principle than that to which I had arrived on phi- losophical grounds, he has at last found by his experience that it is impos- sible to do so. And, aside from the pleasure which it affords me as a con- firmation. of my view on the subject, I cannot hut regard his announcement as not only a great triumph of philosophy in general, hut also of Christian Faith in particular. I give his words as I find them in the Report (N. Y. Daily Times, Aug. 18, 1855). Even the Italics are given as I copy them. “ Even as late as the last classification of the animal kingdom by Cuvier — a system which has made his name so famous — that distinguished naturalist depended more upon arbitrary groupings than upon critical ob- servations of natural affinities. To be understood well, the true relations of the system o"f Nature ought to be considered as an analysis of the thought ex- pressed by the Creator. Classification is in reality nothing but the expression of that thought. We may no longer speak of our system. We may only speak of our readings of that thought which constitutes the animal system ; which has gone on developing through countless ages. No longer do naturalists consider the Animal Kingdom without reference to the cause of existence. They are ail driven to one point. They are compelled to ascribe existence of animal forms, either to physical causes or to an intelligent Maker. Be- tween these two there is no medium point, no other alternative. The classes of animals are either the result of the general forces which we ob- serve in Nature, or they are the work of an intelligent Being. Do we see in these classes the evidences of physical force — or thought ! And now, HI.] METHODS OF PROOF AND REFUTATION. — SECT. V. 313 Thus if carnivorousness was an element in the class-con- ception of the Canidse, just as equality of radii is in that of the circle, then canine teeth were as necessarily implied as a property of the Canidse, as the Formulae and Propositions of Trigonometry are in the conception of the Triangle. 1140. We can also accomplish our object of passing from the facts of Nature to a law by means We may als0 of the conception of Final Causes. A Final §f|w f bymeaS Cause, as has been defined, is that for which ofFiaal c l| es - any thing is or is done. 1141. We are conscious of acting from purpose or design. Our actions are conformed to our 0rigin of the designs and reveal them to others. We can I c d a ea se3 of in F ty l also see in the motions, features, and acts of ture - other persons indications of their designs. We can often see in the structure of a piece of machinery or an implement of any kind, the design which its framer intended and expected it should accomplish. 1142. Precisely so in Nature we see, and cannot help but see marks of design — proofs that the Nature indi . Creator had an end in view — that He created cates Design - from regard to Final Causes. If now we find by our induction that animals with canine teeth are carnivo- rous, and can moreover see that that kind of teeth are especially adapted to that kind of food, we have scarcely less doubt that all animals with canine teeth are carni- vorous, than if we had seen them all in the pursuit of that mode of life — or if the Omniscient Creator Him- self had revealed to us the fact. 1143. When then our induction leads us to see any connection between the Essentia of the Ge- Final Causes nus and the Property predicated of it, as is based upon the implied in the doctrine of Final Causes, or creator as the necessary correlates of each other, we feel when we come to consider the Animal Kingdom practically, as a process of Zoological Investigation, it comes first in order to ascertain whether, in the combinations already ascertained, we can read that thought, or whether any other result can there he read.” 14 314 LOGIC. — PAHT II. [chap. confident that we have found a law, which if it he not based upon the necessary nature of the things, is at least based upon the will of the Creator, and will not therefore be changed while the present order of things remains. 1144. But so expressive are the works of Nature every where of purpose and design, that long before Nothing made we come to conscious reflection upon the m vain. subject, we have come to believe that what- ever exists as the work of the Creator, was made for some purpose, or “ Nothing was made in vain.” The Formal properties — that is, those properties in any object which are regarded as constituting it an indi- vidual in the species between itself and the next sub- altern species or genus, which is in our minds at the time, put us on the inquiry to ascertain what are the implied properties which accompany these Differentia or Formal properties; and what are they for; what fact or law in regard to the individuals of their class do they indicate. 1145. Now this way of regarding the Formal pro- perties of objects is not the result of any system of phi- The idea of losophy. It exists before philosophy. One eS before of the first questions that the child learns to philosophy. ask w ith regard to any thing new that at- atracts its attention is, “What is it for?” Thus to take the case already spoken of — we see certain ani- mals with teeth of a peculiar shape ; we see one of them using these teeth to tear the flesh of some animal which it has just caught, and devouring that flesh as food. The adaptation of the teeth to the end for which we see them being used, is such that we have no doubt that such Avas their design or Final Cause. 1146. One case is enough. It seems to let us into one case suffi. the secrets of Nature — the counsels of the the"bei°ief! ssest Creator. We feel as though we knew why He had so made the animal ; and we predicate that mode of life of all animals having the same Formal property, as a general fact. We hold it as a physical m.] METHODS OF PROOF AND REFUTATION. — SECT. V. 315 certainty — but not $s an absolute certainty. For not only may tlie nature or formal properties change in some respects, but influences may exist in some cases which will turn individuals and even whole species from the course of nature. 1147. There are sometimes cases of individual de- formity. Most of the species of domesticated Cases of de . animals have been changed by domestica- fonnity - tion ; and some of them so much that it is now diffi- cult to ascertain precisely what they were in their undomesticated state. Man, we see was made for vera- city, benevolence, and virtue ; but his history shows that there has been a very general departure from what his nature shows that he was intended for. 1148. The Fundamental Principle of this doctrine of Final Causes is, that whatever exists in -i • t* -\t i . . ry -i Fundamental tlie domain oi JN ature exists lor some end or Principles in -i . ■ , , • this doctrine. purpose, and consequently where its consti- tution and use indicates a purpose, we infer that that was the purpose designed, and consequently the law of its being which was imposed upon it by its Creator, 1149. Now taking this Principle for our Major Premise and we have : That for which any thing in Nature was evidently designed it will accomplish. Canine teeth were evidently designed for a carni- vorous habit of life. Therefore , Animals with canine teeth will always be carnivorous. 1150. Hence as Induction always implies that whatever is or occurs, is or occurs for some Induction ai- purpose or design ; so it implies also a ^hntd^ent Wisdom which comprehends all things and Creator - events, and never errs — and a Power which can ac- complish all that that Wisdom can design. 1151. In the domain of Nature it is immaterial, so far as the result is concerned, whether we In Phy9ica , Mat . begin with the constitution of the object as ftom' e Cdai re pfo“ seen in its Formal Properties, or with the £ e a r ^ e e s 10 theFina ‘ 316 LOGIC. — PART II. [chap. Final Cause as seen in its Modal — -the result is in each case and alike the same. But with man it is not so. We see from his constitution that he was designed for But not in Mo- virtue. But we see much in his Modal pro- ral - perties — that is, in his thoughts, feelings, and actions- — that is not in accordance with the Final Cause of his being ; much which therefore we pro- nounce to be wrong, or at least abnormal. 1152. So too in Nature, there are abnormal cases in which we cannot infer from the individual the de- Abnormai cases sign or law °f the m|fde of life which his in Nature. species was intended to pursue. If we should find a man, without legs from his birth, it would not answer to infer from him that all men were designed merely to sit or to crawl, and that walking is a viola- tion of the law of man’s being. Such anomalies occur in nearly all species of being. And FIugh Miller* has suggested that there may be, and that in fact there are reasons for believing that there are, in Nature whole species which have been degraded from their idea or normal condition. Of such he thinks that serpents, venomous insects, and insects with stings, are exam- ples. His remark would include all those which have means of injury to other beings not necessary as either means of defence or of taking their prey. 1153. The Argument from Examples, or a Fact as an Example, is evidently but an induction from a sin- F ac ,3 as Ex . gle inducted fact ; as when we argue from ampies. the fact that Astronomy was opposed by religious bigotry, when it first began to be cultivated by the Christian Philosophers in the Middle Ages, that Geology will be in like manner opposed as sub- versive of the Christian faith. 1151. It is evident that the particulars denoted by the terms “ Astronomy ” and “ Geology ” in this case, There must be must have a resemblance, consisting of iden- J.oinFof'com'i tity in the properties on which the compari- parison. son or argument is based. And in estimat- Old Red Sandstone, final Chapter. HI.] METHODS OF PROOF AND REFUTATION. — SECT. V. 317 ing the force of an Argument of this kind, the first step in each case is to consider whether there really is that resemblance or identity or not. 1155. But we are at present concerned only with the Method and its proper force. The Argument stated in brief is this : Astronomy when first introduced was opposed as adverse to religion. .•. Geology when first introduced will be opposed as adverse to religion. 1156. This is manifestly an Enthymeme, in which the Minor Premise is suppressed. A is P, .-. G is P. We may complete the Formula by affirming A of G. Thus, A is P, G is A, .•. G is P ; that is, by saying that “ Geology is Astronomy.” But that is not true. Astronomy and Geology are not iden- tical ; nor is Astronomy a species within which Geo- logy is included. All we can say, and all that the Argument from Example means to say, is that they are alike. But as this does not affirm either identity of spheres, or include the one in the other, no inference can be drawn by means of such a proposition in a categorical Syllogism. 1157. The Force of the Argument from Facts as Examples, therefore, must be sought in the The In f ere nce point of resemblance, considered as the thatfdentity 1 ! 011 Formal Properties of a Species. Thus Astronomy, when first introduced, was a new science, contradicting some of the prevailing theologi- cal opinions. But Astronomy was opposed by the religious when first introduced, because it contradicted, &c. Therefore all sciences which contradict the preva- lent theological notions, will be opposed when first introduced. 318 LOGIC. — PART H. [CHAP. 1158. With this Conclusion for a Major Premise, we introduce “ Geology is a new science, contra- dicting the prevalent theological notions ; ” and we have the conclusion, therefore “ Geology will be op- posed,” &c. 1159. It will he seen that in form this is but an iJS'n e from I 11 ^ 110 ^ 011 from a single Example as an in- a single Fact. m ducted fact, and as such depends for whatever value it may have either as a Method of Investigation or of Proof, upon the principles and laws of Induction, and the extent to which it fulfils them.* 1160. This Method is seldom, if ever, spoken of in except common use °f language as an Argument inM^aiMatfer from Example, except when it is applied to Moral Matter. In that case the value of the Method is much less, since there is no such uniformity of Causes and Laws in Moral as in Physical Matter. * Whatf.ly, in liis Rhetoric, Part. I. Chap. II. § 6, has given the Ar- gument from Example in a form which is, perhaps, more striking than that in the text, as follows : Astronomy was decried at its first introduction as adverse to religion : I % Ob . Every science is likely to be decried religion. Geology is likely to be decried, &c. : its first introduction as adverse to But this Major Premise is untrue, and can be saved only by the Modal, inserted above : “ Every science which contradicts the prevalent religious opinions — •” In this case the Modal not only limits the subject to an included species, hut is also in fact assigning the Cause, and we might therefore have the Causal Argument. Astronomy was decried because it opposed the prevalent religious opinions. Geology opposes the prevalent religious opinions. .•. Geology will he decried. And in fact the inference of a General Principle- from a single fact as Example, or many, as inducted particulars, must always be limited in one of these two ways — namely, either to instances of the same kind only, or to instances in which the same cause is at work upon matter which is essen- tially the same. m.] METHODS OF PROOF AND REFUTATION. SECT. Y. 319 1161. The Induction of Facts by way of Example, is' but a loose and vague way of reasoning, Argume ntfrom and is seldom satisfactory. For in all con- fom mp latis&£ . tingent matter, that there are exceptions to tory - all rules is proverbial ; and the Argument from Exam- ple often has the appearance, and is in danger of the reality, of being based upon the exceptions rather than upon the individual facts coming under the Rule. Thus if one should attempt to prove from Examples of dreams coming to pass, that dreams are to be regarded as generally prophetic, or signs of what is to take place, he would most manifestly be arguing from the exception to the general rule. Yet Examples of what he is trying to prove can undoubtedly be produced. Nor in fact is there any proposition in Contingent Matter, however absurd, which may not find some Minor Premise, which by way of Example, will connect it in the fulfil- ment of Formula with some indisputable Major Pre- mise, and thus prove it to be true with all the force of which the Argument from Example is capable. 1162. Two affirmative Premises in the 2d Figure constitute an Analogy between their sub- Ana , 0 „ y how ieCtS. AS, constituted. A is B, C is B. A and C must therefore be analogous, or identical in the Matter of the conception B. 1163. But if we take that Matter as a Formal Pro- perty, and then predicate of A or C some other Modal Property in a compound Causal, perty taken as assigning B as its Cause, we may predicate LJll “ e ' that Property also in an Argument from Analogy of the other of those subjects. Thus, A is C, Bis C. But A is X because it is C, .-. B is X. 1161. Thus Bishop Butler argues from the analogy between the death of man and the chrysalis state of 320 LOGIC. — PART II. [chap. This Argument put into Form would stand the worm, that the soul of man is immortal. The* Bishop Butiefs chrysalis and the man have hut few points argument. j n common. Yet some such points or pro- perties they have — and the analogy is in this case somewhat remote ; and in consequence requires much greater scrutiny, and can never in fact produce the same degree of certainty as the closer analogies. 1165 ” ‘ ‘ ‘ thus : Man has a principle of life. The worm has a principle of life. The worm lives through an apparent death, because com e P i1tId ment it has the principle of life. Therefore man will live through the appearance of death at the dissolution of his body. 1166. Or without the Causal we may have the problematic Problematic Conclusion, (which is in all conclusion. cases valid of the Affirmative Premises in the 2d Figure,) Therefore man may live through the apparent ex- tinction of his being at the death of his body. 1167. There is sometimes a presumption, but no- thing more, arising from the fact that two individuals Analogy in which are known to agree in many points as aiways 0, a ts sa?is a common Essentia, will agree in a certain encel'o 'analogy other point in regard to which it is not yet mothers. known whether they agree or not. Put arguments based on such supposed analogies are of hut little value. Thus a man and a horse agree in a vast number of points of the animal economy, but still they may disagree in regard to that property by which a certain plant is food for one and a poison for the other. The probability is against any such proposition on the ground of general analogy, hut still it is only a proba- bility ; and the proposition may he true, as we know that it is true in a vast number of instances. 1168. The reason for the inferiority of the Argument why Analogy from Analogy to an Induction, results as will induction. be seen irom the inadequacy oi the class- ni.] METHODS OF PROOF AND REFUTATION. SECT. V. 321 conceptions which we have in onr own minds — an inadequacy which Induction and Analysis properly used are all the while removing, and the removal of which converts the Induction into Demonstrative Sciences just as fast as it progresses. 1169. There is another use of Analogy which is of great value, and which we ought not to fail Ana iogy as a to notice in this place. It consists in remov- “meet- ing antecedent objections and improbabili- dent objections, ties, in interposing objections to too hasty inductions, or inferences from inductions too broad for the inducted facts. 1170. Any inference which is too broad for the facts — that is, an inference including a Genus m what way. comprehending several species from facts gathered from one species alone, must comprehend the facts of the other species also as being necessarily analogous to the extent of their common Essentia. If, therefore, such analogous facts can be adduced, which are not in accordance with the inference, they are an answer to it. This is the case with Butler’s Analogy. It refutes the Major Premise of the sceptic, by substituting a new Minor Term, “ the Chrysalis ” for “ Man ; ” and with the same Middle and Major Terms, the Bishop deduces a Conclusion which is contradictory to an indisputable fact.* But as the new Minor Premise cannot be dis- puted, the Major Premise is proved thereby to be untrue, and consequently the inference from it to the death of the soul of man, is invalid. * The Infidel had inferred from the appearance, that man’s being ter- minated at the death of the body. His argument was that : Man appears to end his being at death. Therefore his being does end, and the immortality of the soul is but a dream. But the Bishop says, Your principle, Major Premise, proves too much ; for the worm when it goes into the chrysalis state, appears to die, as evi- dently as man, and yet the worm comes out a butterfly. Man may, there- fore, notwithstanding the appearance, come out of the apparent death a purely spiritual being, with powers and faculties which he does not now T possess. 11 * 322 LOGIC. PART II. [chap. 1171. In the same way the antecedent objection to a miraculous revelation of the will of'.God in Cliristian- Removes also i ty , is answered by the fact that there has fe n cu™ d to n Re°e- been an interposition at the creation of man ; latl0n - and if there has been one such interposition, there can be no antecedent presumption against an- other’s being made when there is sufficient occasion for it. 1172. Both Testimony and Circumstances are to be Testimony and regarded by Logic as Facts. The reality and Circumstances V pi*i*t*i n i ji as Facts. value oi which, individually and separately, are to he determined by principles which do not belong to the sphere of Logic. But the force of concurrence in testimony and in circumstances, is a fact which it becomes important to consider in this connection. 1173. By Concurrence we understand such a con- concurrence. nection between two or more circumstances, or pieces of testimony, as that one did not cause the other ; nor does the one serve to explain and account for the reality of the other, except through or by means of the principle which they are adduced to ptrove. 1174. Thus two witnesses testifying in the presence of Testimony of each other, or after an interview between accumujated. them on the subject ot their testimony, could hardly give what would be fairly considered concurrent testimony. It would be accumulated testimony, and worth just as much additional force as the moral char- acter of the second witness, and his opportunity to know could give it. But the testimony of the second might be accounted for on the ground that he knew what was the testimony which the first had given or was about to give. It could be a case of concurrence, and have the force due to a concurrence only on condi- tion, that the two witnesses had had no opportunity of knowing what each other had testified, or were about to testify to. 1175. And so of circumstances ; when one will ac- c C i?c n u c Ztancea f count for the existence of others, there is no III.] METHODS OF PROOF AND REFUTATION. SECT. V. 323 concurrence. It is merely an accumulation of circum- stances, and in fact of but little value. 1176. This is the Method of Argument upon which, for the most part, the conclusions of the The sphere of Historian — that is, the series of statements itsuse - which make up what he calls his history, depend. Such is the infirmity of human testimony — man’s liability to error in perceiving — his susceptibility to the uncon- scious influences of prejudice and passion, m History, and worse than all his perverse inclination to mistake and misrepresent others, that the cautious student of history will seldom believe even the most explicit testimony of a single witness, unless there are other witnesses or material circumstances concurring with his statement. And if the influence of this concur- rence be against any man’s testimony clearly, and with any very great force, we set it aside with the charitable judgment that it was a mistake of his. 1177. In the criminal jurisdiction of our Courts also, concurrence of testimony, or Circum- stantial Evidence, as it is called, is for the crimitia["jun ? 3- most part all that can be had. The criminal ictl °"’ never surrounds his acts with witnesses who can testify to his guilt. On the contrary he seeks to be as far removed as possible from such means of convicting him of the crime. 1178. Moreover, as showing the value of this kind of testimony, there are some crimes of which a man cannot be convicted on the testimony superior to sin- of a single witness, without a strong concur- mony’m 1 some rence ot circumstantial evidence, as perjury CiSes ' for instance ; and in many cases concurrence of cir- cumstances is sufficient to destroy entirely the direct testimony of an individual witness. 324 LOGIC. PART II. [CHAP. SECTION VI. Of Progressive Approach. 1179. There are certain Methods of Argument which, while from their nature they are incapable of occasion for establishing an absolute certainty, do never- g?lssfw ot ap' theless answer a good practical purpose ; proacti. and for certain extraneous reasons are pre- ferred in some cases to Methods which could give a different kind or degree of certainty. There are other cases where absolute certainty is unattainable, though we may make some approach to it. All these Methods we call Methods of Progressive Approach •, of which there are several kinds. 1180. (1) A posteriori efforts to prove an a priori proposition. 1181. Suppose we take for illustration the first law First case. of motion — ■“ A body in motion will continue illustration. to move for ever unless it be stopped by some force external to itself.” This proposition contains terms and elements which can never be justified by any a, posteriori Method. In the first place we can never remove all the proof pos Se- external forces that act upon any body, so as terms of tile to see it in motion uninfluenced by any thing i roposition. external to itself. Always there will be some friction, some resistance of the atmosphere, &c. But in the second place if we could fulfil this condition, an observation or experiment could never extend through the time implied in the Proposition to be proved, “for ever.” We might, if the first condition was fulfilled, see it move a long time — but “for ever” is not only some- what longer than any individual observer will live to test the matter; but, even if that difficulty could be satisfactorily disposed of, the proof of the proposition by this method could not be completed until it would, be too late to be of any practical utility. HI.] METHODS OF PROOF AND REFUTATION. SECT. VI. 325 1182. Our only resource, therefore, is to approach the conditions as nearly as possible. We We can only set a body in motion with a given amount ™' ox p™wnon of friction and retarding forces — it goes a means - certain length of time. We start the same body, or another precisely like it, with less of friction, and it keeps moving much longer ; and the less there is to retard it, the longer it moves — -and we infer that if it had nothing to retard it it would move for ever. 1183. The Proposition can he proved a priori from the property of inertia, which is contained in It may be 0e . the class-conception of Matter as a material monstrated - property. 1184. But a posteriori we can prove only general truths, with the possibility of exceptions to , ,i i . Absolute truths them, while the absolute certainty ot um- proved only by \ . . n -i ,• Demonstration. versa! truths, which admit no exceptions, can be proved only a priori by Demonstration. 1185. (2) A second modification of this Method is afforded in the mathematical doctrine of The D(?ctrine limits. That is, “Whatever is true of any p rog re^ve AP * point indefinitely near to any limit, is true proach - at that limit.” 1186. Thus if we have the question of the quadra- ture of the circle, What is the ratio of the diameter to the circumference ? We can ture of the Ch- answer only by Progressive Approach. We can construct a polygon within the circle, whose sides are near to the circumference of the circles, but not coincident with it. We may then bisect the sides of that polygon, and so on, but the polygon can never become a circle. It can only approach it indefinitely near. So, too, the number that expresses the ratio of the radius to the circumference becomes a decimal 3.141, and extend- ing indefinitely, but it can never become complete. 1187. Arguments from the force of Terms, from Testimony, from Concurrence, from Circum- cumulative stances, in fact Cumulative Arguments, and Probable Arguments of all kinds, are but Ap ' 326 LOGIC. — PAHT II. [CHAP. Progressive Approaches towards the absolute certainty of the truth of the Proposition which they aim to establish. A jury in criminal cases, for instance, is bound not to convict a criminal so long as there is a reasonable doubt left of his guilt. And yet the records of criminal jurisdiction furnish many instances in which persons have been convicted, who were afterwards found to have been entirely innocent. 1188. In speaking of Arguments of this kind as progressive ap- but Progressive Approaches to certainty, we to^than^D 0 " iruist be understood to refer to their Logical monstrative. character rather than to their practical effect, in point of fact the mass of minds are sooner and easier persuaded by a Progressive Approach than by a De- monstration, even in those cases where a Demonstration is possible. It requires a peculiar mental constitution, or at least much practice, to be so familiar with the Method of Demonstration as to be fully under the in- fluence of its power. 1189. And on the other hand, minds which are particularly accustomed to the Methods of Demonstra- te,. of do- tio n j or which are constitutionally peculiarly gress!vi ng ap- susceptible to its force, not unfrequently ac- proach. quire a contempt for what is called moral reasoning, and a distrust of its conclusive force, which iS entirely unjustifiable. And it is, perhaps, one of the most difficult branches of practical Ethics, to deter- mine where the force of a Progressive Approach be- comes a sufficient ground for the responsibility of action. SECTION VII. Of the Argumentum ad Ignorantiam. 1190. This Argument consists in proving that a Argumentum given Proposition is true, because we know tium. lenoran " of no reason why it should not be true, or why the truth should be otherwise. III.] METHODS OF PROOF AND REFUTATION. SECT. VII. 327 1191. An instance of this occurs where we should least of all expect it, in Herschel’s Discourse on the Study of Natural Philosophy. He says that illustration, on the old principle, “ that Nature abhors a vacuum,” as accounting for the rising of the mercury in a Baro- meter, and such like phenomena, “We know of no reason why Nature should not abhor the vacuum as much on a high mountain as in the plain below.” Therefore the Barometer ought to stand as high on a mountain as in the plain below. This of course as- sumes that if there was any reason for its being other- wise, he or we should know it ; or which is the same thing, that we know all the reasons for whatever phe- nomena may come before our minds. 1192. Now there are undoubtedly cases in which one’s ignorance of any fact or phenomena, ^ f is a presumption at least of its non-existence, fact" or princi- Thus an alleged fact in any science of which none of those most familiar with the science no,1 ' reaitJ ' had any knowledge, would be looked upon with great suspicion. And so universally just in proportion to one’s opportunity to know, is his ignorance a ground or principle of proof of the non-reality of the alleged fact. 1193. The Ad Ignorantiam labors not only under the disadvantages of Negative Testimony, and of Posi- tive Testimony to a Negative Proposition (858-863), but also under peculiar disadvantages of its -n i i , t ° . Value increases own. _b or what man adequately conceives with our know- and knows, is an indefinitely small amount e se ' when compared to the infinitum of the knowable ; and the value of the Argumentum ad Ignorantiam increases from nothing up towards certainty, only as our know- ledge advances from total ignorance up towards omnis- cience. 1194. There are some cases, however, in which this element enters pretty largely into our Methods of In- vestigation and Argument. In investigating Use in investi . Causes, for instance, both Final and Efficient, gatins Causes - 328 LOGIC. PART II. [chap. so strong is the belief in their reality, that we often affirm the causality of a particular Antecedent or Mode, not because we can see any connection between the facts, but simply because we can see no other fact of which to affirm it. We can see no connection, for instance, between the resin and the kind of electricity that it excites. But Induction having established the invariable antecedence, we affirm a causality simply because we believe that there is a cause, and we do not know of any thing else that could have produced the observed phenomena, except the resinous sub- stances. 1195. Such reasoning can hardly be said to be based upon any general principle which comprehends want of prin- the facts of the case ; or in more exact terms, ciple - any principle, the statement of which fur- nishes a Middle Term, as a means of proving the Pre- dicate of the Subject in the Conclusion. SECTION VIII. Of Refutation. 1196. Refutation supposes a foregoing proposition already asserted or assented to, which it is desirable to disprove. As this foregoing proposition Refutation sup- poses a conrju- can hardly be an axiom or intuitive uidg- going Argu- merit, it must be regarded as a conclusion to a course of reasoning, or at least as resting on Premises or grounds, which must in some way be removed before we can expect those who have adopted the conclusion to give it up, or justify ourselves in dissenting from it. 1197. In cases where there has been an Ignoratio Elenchi , or the proof of a Proposition which is not gnoratio a Re- to the purpose, we have no occasion to show futation. that the conclusion is untrue, by any method. It is enough to show that it is not to the purpose. This is not in fact so much a refutation of the Argument or m.] METHODS OF PROOF AND REFUTATION. — SECT. IX. 329 Conclusion, as the rescuing our cause from the effects of a false and improper attack. 1198. Setting this case aside, therefore, as not strictly belonging to Methods of Refutation, we may divide all our Methods into three classes : — Three Methods. (1) the Direct ; (2) the Indirect ; (3) Personal Refuta- tions. SECTION IX. Of Direct Refutation. 1199. The first form of Direct Refutation to he con- sidered, is that in which we prove the contra- First Method, dictory of the Proposition , which may have been af- firmed without regard to any Premises or means of Proof which may have been given to prove its truth. 1200. Mo Proposition and its contradictory can be true at the same time. If now we have any universal p ro - Universal Proposition asserted, we can refute ^‘‘by e/mp- it directly if we can find what is called an tions - Exception — that is, a fact included in the sphere of its Subject, with which the Predicate of the Proposition cannot he connected by a Copula in the same quality as in the original Proposition. If that Proposition was affirmative, its Predicate must be denied of the Excep- tion ; or if negative, it must be affirmed of it. Thus if I say that all the men in a given company are sit- ting down, the Proposition would be refuted if one could show-that there was so much as one exception, one individual that was not sitting down. 1201. The mere inability to affirm the Predicate could hardly be regarded as a refutation. a caution. It would be a piece of mere negative testimony (see 860). 1202. In all . such cases the appeal is always to some of the primary means of investigation, Exceptions which, because they are primary, are both how p^'-ed. investigation and proof (1040). 1203. We must remember that Individual judgments always precede Universal or General judgments, and 330 LOGIC. — PABT II. [CHAP. that general judgments are based upon the individual.* And by no principle can the general judg- Individual \ 1 1 . . .V 5 ,-i i judgments first ment be made more certain, than the least and surest. . • p , i •-!••-» ■ certain ot the individual judgments compre- hended in it ; as the chain can never be any stronger than its weakest link. Hence the assertion of an exception to any Universal Proposition is but an ap- peal to the primary judgments ; and of course, there- fore, it must have a greater degree of certainty than the Universal Proposition itself. 1201. An Exception, however, never refutes a Exceptions do mere general Proposition, since in all con- not refute Ge- . . • , • • i • • -> nerai Proposi- tmgent matter it is a recognized principle universal. only that all suck admit of exceptions. “ Excep- tio probat regulam ,” has come to be an axiom. f But an Exception is a refutation to a Universal Proposition. It destroys its Universality, and therefore its Formal character. Of course it is immaterial whether the Proposition was affirmative or negative, so far as the effect of the Exception is concerned. 1205. But if the Proposition to be refuted be Par- Refutation of ticular rather than Universal, then of course proposition. 1 ' 111 " it can be refuted only by the Proof of its contradictory Universal. And this can be proved in one of two ways only : (1) first by an a priori demon- stration in necessary matter ; or (2) by an actual in- spection of all the individuals included in the sphere of the Logical Whole ; a part of which constitutes the subject of the Particular judgment which -we wish to refute. :[ * The Individual judgment is always first in point of time, and if we proceed from that hy Induction we get a General judgment ; but if we evolve the Predicate from the necessary matter of the conception of the subject, our judgment becomes a Necessary one. f Of course it is not the Exception that proves the rale, strictly speak- ing : hut the fact that it has been noticed as an exception , proves that the general Proposition, to which it is contradictory, has been recognized as a rule which is true in general. { In the first case we obtain a judgment, which is Universal, ex neces- sitate rei ; in the second it is only Universal, de facto — as in fact there is no necessity that it should be so or always remain so. m.] METHODS OF PROOF AND REFUTATION. SECT. IX. 331 Second Me- thod of Direct Refutation. 1206. But there may he many cases in which nei- ther of these modes of direct refutation are Refutation of practicable, where we can have no a priori not demonstration — nor yet submit the indivi- slble - duals included within the sphere of the subject to the test of observation arid experiment. 1207. In all such cases we may release ourselves from the obligation to assent to a Conclusion lyy ref uting the Reasoning. This we accom- plish not by disproving the Conclusion, but by showing that it is not proved by the Premises ; we show in fact from the Premises themselves without referring to any matter not contained in them, that the Conclusion is invalid, and ought not to have been drawn from those Premises. It may be true as a Pro- position, but is not proved as a Conclusion. 1208. This may be done in four ways : (1) in the first place we may have a simple Non sequi- Non sequitur. tur , as in all cases of Fault or Fallacy in Form. In this case the Premise may be true and the Conclusion true, and yet no connection between them ; or the Premise may be true and the Conclusion false. Thus if any of the five Canons (177) be violated, we have a simple Non sequitur. 1209. So, also, if in Conditionals we deny the Ante- cedent to destroy the Consequent (682), or Non sequitur from the denial of the Consequent infer the kT u c on d isfu nc - contrary and not the contradictory merely tives - of the Antecedent. Or if in Disjunctives, we apply the Modus ponente tollens (710), where the excluded Middle is produced by the opposition of alternate rather than coordinate species or parts. In short any Fault or Fallacy in Form will give a Non sequitur. Hence it is always a sufficient refutation to point out such a fault. 1210. (2) In the second place we may have a Sequi- tur per Fallaciam — using the word F allacy in seqmter its strictest sense — as indicating some decep- tive use of a Formula, where the Premises, each taken 332 LOGIC. — PART II. [CHAP. by itself is true, and the conditions and require- ments of the Formula are fulfilled. Of these it will be seen (Part I. Chap. IY. Sec. 3,) that there are five : (1) Ambiguous Middle; (2) Division; (3) Composi- tion ; (4) Accidents ; (5) Quid. 1211. Any one of these Fallacies of course destroys the validity of an Argument ; and although the Con- i The n conciu. elusion may still be true, we are no longer true^ notwith- bound to receive it as a Conclusion after Fallacy f e such a Fallacy has been pointed out in the process by which one has arrived at it. 1212. (3) In the third case we may have a Sequitur per non veram , in which case there is neither fault in sequitur P cr F omi nor Fallacy in the use of matter, but non veram. simply the assumption of Premises, one or more of which are not true. 1213. This will be seen occurs in the case of Non causa pro causa , as stated in Part I. (738), together cases of Pen- with the assumption of Sequence where there tto Pnncipii. j s none? non-exclusion .of Middle, &c., &c. In all these cases a Proposition is assumed as true, which is not so. And whether it be expressly stated or inqfiied as the suppressed Premise of an Enthy- meme, the Sequence of a Conditional, &c., it is equally mischievous; and needs to be distinctly evolved if it were not expressly stated. 1214. It thus becomes a Proposition, which we shall The False pre- need to disprove — unless its falsity be ob- disproof. vious witnout any proof. I Ins can be clone of course only by proving the contradictory of the False Pi ■emise. 1215. (4) But finally, we may have a Fault in Me- thod, or a misapplication of Method to Matter ; as if Fault in Me- we should attempt to apply Demonstration thod. to contingent matter, and determine realities in being from our conceptions, stated as definitions. This was the great fault that prevailed among the students of the Natural Sciences from Aristotle down to Bacon. HI.] METHODS OF PROOF ASD REFUTATION. — SECT. X. 333 1216. But in modern times we have a tendency to the opposite error. One writer* has attempted to ap- ply Induction to the religious history of the voiney’s Fault, world, and to prove the falsity of Christianity from the fact, that all religions except that contained in the Scriptures have been delusions. SECTION X. Of Indirect Refutation. 1217. This consists in proving a Proposition untrue, by showing that it contains or comprehends Indirect Retu- that. which is false. tat,on - 1218. In the first place we may show a Proposition to be false by evolving from it, by Immediate By j mme(i iate Inference , an untruth. Thus, one writer says Interence -. that the human souls are propagated by “ decision ; ” and the context shows that by “ decision ” he means the cutting off of a part. But “ decision ” or division implies extension, and extension is a property of mat- ter and not of spirit. 1219. In the second place we may refute one’s reasoning by what is called the Reductio ad Absuraum. in tins process we introduce a Reductio ad other matter, which is either ‘admitted as true, or which admits of proof beyond further cpiestion, and combines this new matter with that part of which was given before, which we wish to show to be false. 1220. This Method is often spoken of as the process of showing that one’s “ Principles ” or “ argu- Po p„iar names ment proves too much.” Thus the infidel’s forlhe Method, argument, that the apparent death of the body implies the death of the soul and the cessation of existence, as Bishop Butler shows in his Analogy, “ proves too much.” It proves that the larvse of the Metabolians die when they go into the chrysalis state ; whereas See Voiney’s Ruins, or Meditations among the Ruins of Empires. 334 LOGIC. — PAKT n. [chap. they do not die but only change their mode of exist- ence. 1221. Now if any general Proposition, that is, a Proposition with a general term for a subject he true, Fundamental its Predicate must he true of every species Fndirect 6 Reiin included in the genus denoted by the sub- tation. ject. If then we can discover a species, of which the subject of that general Proposition can be predicated, while its Predicate cannot, the general Proposition itself must be untrue. 1222. Thus to recur to Bishop Butler’s argument illustration. again. The infidel had asserted that the soul dies with the body — fihe assertion was based on the appearance of death — and hence implied the Major Premise, that “ in all cases of an apparent death of the body, there is a total cessation of the existence of the individual.” — Using this Major Premise, we may com- plete the Formula thus : Whenever the body dies there is a termination of the individual existence. The body dies in what we call the death of man. .•. In what we call the death of man there is a ter- mination of the individual existence. But says Bishop Butler there is a death of the body in the larvae of Metabolian insects. Using this for a Minor Premise to the .Major Premise just given, and we have for Conclusion : .*. There is a termination of the individual existence of each Metabolian when it goes into the chrysalis state. This Conclusion, however, is confessedly untrue, and yet the Major Premise is the same as the infidel had used ; the Minor Premise is indeed different, but then it is a Proposition that no one can dispute. Hence the Major Premise, common to both Conclusions, must be untrue. 1223. By this we do not mean to say that the Pro- The disproved position had no element of truth in it, or ! b0 that this Reductio has shown that the Predi- 1H.] METHODS OF PROOF AND REFUTATION. SECT. X. 335 cate is not true of any individuals included in the sub- ject ; but only that inasmuch as the Proposition is not true of all, we cannot admit it to be true of any, until it is modified by some modal which shall give either the Differentia of an included species of which it may always be affirmed, or expressive of a term or a condi- tion in which it may be affirmed of any one of them generally. And until this has been done by the infidel the refutation is complete, 1221. The Indirect Methods of Disproof as well as the Indirect Method of Proof imply that there Indire ct Me- is more than one way of knowing the truth a a o!Vect of the Proposition which it is sought to dis- “ od C ‘° nc t 1 1 j: prove. Otherwise there would he no means sion - of disproving. Thus, as we have seen, we may dis- prove a Proposition by proving directly its contra- dictory. This gives us two methods to the same Pro-, position, since from any Proposition to its contradictory is an immediate inference. 1225. Or again, we may disprove a Proposition as a Premise by the reductio ad ahsurdum. But this implies that we have some other the Reductio •S T n • , i -l • ad Absurdum. means or method or proving that Conclusion or its contradictory, as the case may be. Otherwise we should not know which of the two Conclusions was right. We cannot pronounce our Proposition to be absurd or false, until we have ascertained that it is contradictory to another which we know to be true. Affirmative judgments are antecedent in point of time to the Negative, and the test of a theory or Method is that it gives results in aocordance with what we know to be true, independent of the Method or theory in all those cases of which we know any thing, except by means of the theory or Method itself. 1226. The value of the Method will of course de- pend upon the certainty of the newly intro- .The Refuta- duced Premise or Matter, and of course is upon the cer- worth nothing unless that Premise be more new Matter, certain than the common Premise which it seeks to redargue. 336 LOGIC. — PAItT II. [chap. 1227. What is called the Argumentmn ab Ahsurdo The Argumen- is merely the inference from the Absurdity do. oi the Conclusion, that one or the other ot the Premises, or both of them must be untrue. This can seldom be of any further use than a mere appeal to prejudice, since one is not likely to announce an absurd opinion without some force of Premises to sup- port it which may need a Refutation. SECTION XI. Of Personal Refutations. 1228. There are certain Methods of Refutation, which, while they have no conclusive force of a general personal Refu- character, are often of great rhetorical effi- tahons. ciency in putting a stop to further contro- versy. These I have called Personal Arguments. 1229. (1) The Argumentum ad Hominem consists Ar?um.entum i n appealing to a man’s acts, or previous de- ai Homirnm. clarations, or avowed principles, as being inconsistent with the position he is at present main- taining. 1230. The ad liominem proves nothing categori- what it proves, cally. The ojiinion of the Respondent is used as a Premise against himself: It may effectually annoy or even answer him ; but it can prove nothing more than that such and such is his opinion, or results from his opinion. The Conclusion can have no more truth than the subjective Premise or personal opinion of the person to whom the Argument is addressed. 1231. (2) The Argumentum ad Verecundiam is an Argumentum appeal to the opinion of an authority which diam. Verecun ' the person against whom the argument is used is bound to respect and follow, on the score of modesty. 1232. This argument also can hardly be said to ita force. prove any thing categorically. It is used and very well serves to embarrass an antagonist. in.] METHODS OF PROOF AND REFUTATION. SECT. XI. 337 Beyond this it has but little force. It gives for a Pre- mise the opinion of the individual or authority cited, and the Conclusion can have no force except what results from the respect due to that authority ; a force which may have far greater moral than logical weight. 1233. The Argumentum ad Invidiam as it is some- times called, is really no argument at all. Ar^umentum It consists in appeals to the passions, preju- ai Invidiam - dices, or feelings of people, for the purpose of exciting emotions unfavorable either to a cause or the person of him who advocates it. However effective this may be in a rhetorical point of view, it accomplishes nothing logically ; and proves, if it proves any thing, only that those who resort to this mode of argument are better skilled in Rhetoric than in reasoning, and know more of the Formulae of Billingsgate than of Logic. 338 LOGIC. — PART II. [chap. CHAPTER IV. METHODS OF INSTRUCTION AND CRITICISM. SECTION I. Classification of Sciences. 1234. It may not be inappropriate to give a Classi- fication of the Branches of Human Knowledge before proceeding with the appropriate topics of this Chapter. 8uch a classification has been already anticipated in some measure, and seems very generally to have been considered as belonging to this part of Philosophy. 1235. We have already referred to the early divi- sion of human knowledge into three branches : Physics, Early ciassi- Ethics, and Logic (5). But a slight advance becomes inade- i" science, however, rendered this classi- quate - fication inadequate and unsatisfactory. It must however be, to some extent, the basis of all divi- sions. The first department, Physics, including all branches of knowledge that have for subject-matter material objects in the concrete ; Logic, including all branches that treat of the intellect, and are based upon the elements furnished by it, the realities of truth, and the a priori conceptions ; and Ethics, including all that relate to man as having a destiny to accomplish, im- plying society, religion, and the state with its institu- tions and vested rights, as of Property, &c., as a means of accomplishing that destiny. XV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. I. 339 1236. It would not be worth the while to follow the history of these classifications minutely if we had time. One or two of the classifications, how- Aristotle’s ever, it may he well to notice. Aristotle classification, divided all knowledge in the first place into two coordi- nate parts, the Immediate , in which we learn every thing in particulars and each by itself (to. hclA e/cacrra), and the Mediate , in which we acquire a knowledge of univer- sal (ra naA oXov). From the Immediate in his theory, we deduce by means of Logic the knowledge of the Mediate. Hence Logic is the instrument or organ of all science, so far as its form is concerned. With another view he divided all knowledge into Philosophy and History. Philosophy he divided into Speculative and Practical. The Speculative becomes Physics or Mathematics , or what is afterwards called Metaphysics, according as it advances in abstraction ; and relatively to its end , it is divided into Physics, Cosmology, Psycho- logy, and Theology. Practical Philosophy includes Ethics, Politics, and Economy. 1237. In the Scholastic Philosophy of the Middle Ages we have the division into the Trivium and the Quadrivium ; the first including Grammar , scholastic Rhetoric , and Logic / and the lattet includ- classification, ing Arithmetic, Music, Geometry, and Astronomy . They were described in these mnemonic lines : “ Gram, loquitur ; Dia. verba docet ; Rhe. verba ministrat ; Mus. canit ; A r. numerat ; Ge. ponderat ; As. colit astra.” 1238. These seven sciences constituted what in the University distribution was called the Faculty of Arts. And besides these were three others : Divi- nit/./, Law, and Medicine. The first is tribution of the ^ 7 7 . it i. Faculties. regarded, as including whatever concerns Religion and its duties ; the second whatever relates to the State and its administration of affairs ; and the third was understood to include the Physical Sciences generally. 1239. Bacon proposed a new classification, dividing 340 LOGIC. — PART II. [chap. all Sciences into three classes, as they refer to either Memory , Imagination , or Reason. But this resulted Bacon's ciassi- i n g reat confusiou, as there is scarcely any fication. branch of knowledge in which all these faculties are not called into use ; and as has been re- marked, “ his classification would put Boswell’s Life of Johnson in the same class with the labors of Cuvier, and the researches of Hunter.” Botany and Zoology were classed with Metaphysics, and Painting and Mu- sic among the “ artes volwptuarias ,” were ranked with Cookery and Cosmetics. 1240. Locke gave a much more sensible classifica- ficaiion! 3 cIassi ’ ti°n? as follows : 1. Physioa { Experimental Rational { Economies, Politics, Ethics. 1 Natural History, Physiology. Theology, Ontology. • ( Logic, 3. Semeiotioa < Rhetoric, ( Grammar. 1241. Dugald Stewart believed a classification of the Sciences impossible, at least in his day. Coleridge stewart and attempted it as a basis for the Encyclopedia coieridge. Metropolitana , which was constructed on his pian. But as a confession of failure, he was obliged to give an “ and so forth ” at the end ; or rather a chapter of “ Miscellanies ,” which could not be in- cluded in any part of his division. This reminds us of the Treatise of Smalgruenius, entitled “ Re Omni- bus Rebus,” with a supplement, “ Re Quibusdam Aliis.” 1242. Ampere, however, elaborated a classification which is perhaps complete enough. But it is too com- Ampfere’a plicated. Coleridge had failed by so classi- ciassiiication. lying, as to make his exceptions too nume- rous. Ampere made his parts too numerous, and had to create names and sciences which were never before heard of. ITis division does not recognize those names m.] METHODS OF INSTRUCTION AND CRITICISM. SECT. I. 34:1 and divisions which are already in 'use. Nor is there the remotest probability that the progressive develop- ment of Science will take the form and divisions that he has pointed out. He makes one hundred and twenty-eight sciences in the last subdivision, or third order, as he calls it — and thirty-two of the first order. He first divides into two kingdoms Cosmological, including (1) Mathematics •; (2) Physics ; (3) Natural Sciences; (4:) Medical Sciences ; — and Noological Sciences, including (1) Philosophies ; (2) Dialegma- tics ; (3) Ethnological Sciences ; (4:) Political Sciences. 1213. Compte has given a classification also in his and then, as preceding and implied in all, he gives Mathematics or the Science of Numbers. 1244. This classification, as will be seen, does not include many of those which have thus far always been regarded as distinct sciences. Nor is the division suffi- ciently minute to be of much service. His Theory of Knowledge and his Philosophy are too hopelessly bad to allow of any useful classification being based upon it. 1245. In the following classification which I shall give, I divide first into three classes with A new one reference to the end in view ; and in the sub- pr0p0ied - divisions I have followed the received divisions and names. Each class naturally divides itself into two departments, differing in the first class both in the starting-point and in the Method. In the second class they differ in the starting-point only ; and in the third class the two departments differ chiefly in the object in view — the one producing objects of Beauty and the other objects of Utility. The Sciences in the depart- ments in the first class are^jiecessary to those in the second class, and those in the second are necessary to the third. Positive Philosophy, as follows : Compte’s clas- sification. II. Organic S Physiology, \ Sociology ; 342 LOGIC. — PART n. [chap. Class I. — Theoretical, including those Sciences the object of which is “ to know” DEPARTMENT I. Exact Sciences * (purely physical), based upon Primary Phenomena f in the Atmosphere . above the Atmosphere { in the structure and Nat. History of the Earth on the surface of the Earth . in the analysis and combination of the simple Elements in the form and Nat. History of Solids on the Earth’s surface . in the structure of living bodies . of the internal functions of Life in the structure and varieties of Vegetable Life in the varieties and habits of Ani- mal Life .... in the varieties and migrations of Men { as exhibited in Con- sciousness in the external acts of man Meteorology. 0 URANOGRAPHY. . Geology. . Geography. . Chemistry. . Mineralogy. . Anatomy. . Physiology. , Botany. . Zoology. . Ethnology. . Psychology. . History.! * Beginning first with the facts of Observation, we have what are the strictly Inductive Sciences. I have called them the Exact Sciences, in ac- cordance with the popular usage ; not because they are any more exact than others, hut because (if any reason can he given) they depend upon and require the greatest exactness of Observation — they depend upon Observa- tion and Testimony. f History, properly understood, will of course include a knowledge of ancient Geography, the Languages of ancient as well as foreign nations of the present day. It will also imply a knowledge of the systems of religion and modes of worship that have ppvailed, and the progress that man haa made in the Arts and Sciences, in Philosophy and Literature. IV.] METHODS OF INSTRUCTION AND CRITICISM. — SECT. I. 343 DEPARTMENT II. Pure Sciences * (purely metaphysical), based upon Primary Conceptions ' of unity Arithmetic. of forms in Space .... Geometry. ) f Constant represent- j Quantities . Algebra. ing 1 Fluxional 1 Quantities . Calculus. of the meeting of lines and planes in a point ..... Trigonometry. of visible representation of Equa- tions .... Analytic Geometry. of the combination of Conceptions in Syllogisms Analytics. of Matter as modifying processes of Thought Method. of the conditions and forms of Know- „ ledge f Ontology. J * Then in the nest place I start with that other great coordinate in all knowledge, the elements of thought which exist nowhere in the reality of being, but which the Reason itself furnishes ; and where all possible things are assumed as real, or rather the distinction between the possible and the real entirely disappears. Even the varieties of Method are based rather upon the varieties of Matter conceived as possible, than upon the results of experience in matter, although as the two coincide there is no necessity of observing the distinction in discussing Methods. f By Ontology we mean the science of being, and it should include the discussion of the necessary law or forms of thought under which we know and believe whatever is supposed to exist out of the individual mind of the thinker. It will thus be found to furnish the fundamental and axiomatic principles of all the Exact Sciences, and in fact give to them their form or their Formal Cause. f The Sciences in this Department are purely instrumental and valu- able as Means and Helps to the construction of the Materials given in the preceding Department into the Sciences in the next two Departments, and in applying them to use as in the Departments in the third Class. The six first named, Arithmetic , Geometry , Algebra , Calculus, Trigonometry, and Analytic Geometry, constitute the Department of Mathematics ; while of the other three, two, Analytics and Method, constitute Logic ; and the three together,- with one from the first Department, Psychology, constitute what is ordinarily called Metaphysics. LOGIC. — PART II. [CHAP. 344 Class II. — Practical,* including Sciences tlie object of which is “ to do.” DEPARTMENT I. Mixed Sciences f based upon the Conception of Matter and Motion f. v , , i on the Earth in solid bodies j in the Heavens . < at rest - ln 1( ^ U1 S | in motion in gaseous masses in bodies as affecting {j£® . Mechanics. Astkonomy. Hydrostatics. Hydraulics. Pneumatics. . Acoustics. . Optics. DEPARTMENT II. Ethical Sciences ;[ based on the conception of Man and Action f in relation to the Idea of the Good . I as exercising authority in temporal affairs as under Divine Providence , . ( the State . as under An- V he Church _ _ 1011 y (a Revelation from God . . Ethics. Polity. Nat. Religion. Jurisprudence. . Ecol. Polity. . Rev. Religion. * The sciences in the second class are those which develope and state the laws of motion and of action. I have called them Practical because their End is Action ; they all assume more or less of the results of the Theoreti- cal, or sciences included in the first class. They proceed from the results there obtained by demonstration to the evolution of rules or laws. f These sciences I have called Mixed, since although the laws of Mat- ter are determined from the conception of its nature and constitution alone, yet the law itself is in point of fact for the most part first ascertained by observation. But it is soon found to be implied in our conceptions, (1) of Matter (as opposed to Mind) ; (2) of Force (as opposed to Motive) ; and (3) of Motion (as opposed to Thought). % In the second Department we consider the laws which man ought to obey. These are derived from a consideration of man as he is (Psychology and Physiology), and of the destiny, which, by his voluntary activity, lie ought to attain. But as this destiny implies as a means of its accomplish- ment Society or the Family, and the State, that is, a society having sov- ereignty over individual men, and a Providence or Moral Governor of tho IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. I. 345 Class III. — Productive,* including tlie Sciences the object of which is “ to create .” department i. The Fine Arts f or Sciences which guide the expen- diture of labor, directed to the production of ' in the Soil . in the construction of Edifices . in solid representations of Life The Beautiful in perspective representations by Color . in the combination of Sounds . _ in the use of Language . Gardening. Architecture. . Sculpture. . Painting. . . Music. . Poetry. world, to whom man is accountable, and whose final approbation is an essential part of his destiny, we evolve by Analysis and Demonstration from these conceptions Society, State, and Providence — the rules which man ought to obey. Hence Ethics, Polity, and Natural Religion, are based upon Reason alone. And the realization of Religion implies a Church having authority in matters of faith. Hence we have, besides the. authority of God over us, the two others, State and Church, which we find that He has recognized and sanctioned as guides and authority, each within its appro- priate sphere, and we have both Jurisprudence and Ecclesiastical Polity as rules of action within certain limits. * In the third class I have included all those sciences the end of which is to aid man in the accomplishment of results out of himself, and have divided them into two classes, the Beautiful and the Useful. The Subjects included in this Class are more commonly called Arts than Sciences. They are, however, Sciences of the Arts ; that is, branches of knowledge which teach how to produce results, the production of which is called Art. Art is dis- tinguished from mere Instinct by this fact — namely, that it is guided by a scientific comprehension of its principles and processes, whereas Instinct has no such comprehension. t I have not regarded the Methods of ^Esthetics as properly coming within the province of Logic. They are determined rather by the Suscep- tibility than the Reason. Their ultimate Facts are only experimental ; we can only refer to the fact that a beautiful object does excite the Emotions, which we call the emotions of Beauty ; and we judge an object to be beau- tiful because it does excite such emotions. We cannot prove that it ought to do so. We can discover no necessity in the nature of the case for its exciting such emotions. Its judgments in fact are all Relative, while Logic deals with the Absolute alone. 15 * 346 LOGIC. — PART II. [chap. DEPARTMENT II. Useful Arts’* or Sciences which guide the expen- diture of labor, directed to the production of The Useful the products of mind in the Soil Agriculture. in objects beneath the Soil . . Metallurgy. in the manufacture of the raw ma- terial Technology. i . 'i [ written Lan- in nm ip ying | eX p resse( jJ guage . Typography. in 1 works of the [ Fine Arts-. Engraving. in the increase of value by Ex- change Commerce. in the promotion of Health . . Medicine. in the expression of thought by Language Khetorio. in promoting pecuniary prosperity . Polit. Economy. in promoting the National Defence . . War. 1246. Of course all the above-named or described Sciences admit of being greatly subdivided. In fact Each science an } r author has the right to take any part of -fables 6 admit 6 an y one Science and treat it as a Science by for subdivision, itself, if he chooses to do so. This is, in fact, making a subdivision of some part of the division of Science as it previously existed. In this way the names on our Catalogue of Sciences become more numerous, and may in fact extend beyond any known or conceivable limit. I have not thought it worth while, however, to follow the subdivisions already made, any further than they are given in the preced- ing three Tables and the Notes accompanying them. * But in the second part of this Class we have the Useful Arts. They take the results of the General Facts obtained by the Sciences in the First Department of the first Class, and the Laws obtained in the corresponding Department of the second Class, and hy Deduction apply them to the results which minister to man’s physical and temporal wants, as being subservient to the purposes of life ; which purpose again is the attainment of that End or Destiny for which his Creator placed him in this state of existence. TV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. H. 347 SECTION H. Of the Conveyance of Ideas from one Mind to another. 1247. All Methods in so far as they belong to the Sphere of Logic, are determined by the Idea of the True. They aim merely to satisfy the demands of comprehension and conviction. Blit most, if not all, the Methods of Argument and Instruction Method . of come also within the Sphere of Rhetoric, lo g fc and of They aim not only to convince, hut also to ' e ° nc ' please and to persuade ; and in Instruction especially, to save time and labor, and to facilitate the ease with which we remember what we have once learned. But the Methods of Rhetoric are determined by the Idea of the Useful. Its precepts are valuable only because they are useful — useful for pleasing and persuading — useful for the perspicuity of statement — lucidness of illustration or impressing upon the mind a sense of the importance of what is communicated. 1248. It is obvious, therefore, that by far the largest, though by no means the most important, Methods of part of what properly belongs to any ade- struction. quate discussion of the Methods of Instruction, must come within the appropriate sphere of Rhetoric. I shall, therefore, make but a very short Chapter on the Method of Instruction in this place. 1249. By Instruction we mean not merely the communication of the knowledge which we instruction and have obtained. Our attention is much more construction, completely fixed upon the means of Construction , or the putting it into a system, and so arranging the parts . as that they may best fulfil the conditions of a thorough comprehension of the general subject by those who are unacquainted with it. 1250. I regard it as a controlling fact in regard to Methods of Instruction, that a conception conceptions cannot be conveyed or transferred, as a m™i°A b ed C0I £ whole, from one mind to another. Each one Wholes - 348 LOGIC. — PAKT n. [chap. must be formed de novo in each mind. No one can convey bis sensation to another ; we can describe them to those beings, and those only who have had sensa- tions of the same species — the sensation of color, for instance, which I have when I look at the object before me, I cannot communicate to any other person. If he can see, I can describe it to him so that lie can form a conception of it. But if he be blind, he cannot con- ceive of a sensation of color, nor can one be conveyed into his mind. 1251. A judgment may be conveyed from one mind judgments to another, provided both minds have the may - conceptions which constitute the matter of the judgment. Thus if I affirm that “ gold is yellow,” the person hearing me does not need to judge whether it is yellow or not, in order to understand my judg- ment, or the proposition affirming it — the proposition conveys the judgment to his mind, and he may then affirm or deny it as he pleases. 1252. But a conception cannot be conveyed in that way or in any way. It is necessarily constructed by and within every mind in which it can exist may be mean"! at all. Thus suppose I have a conception of known s 'lor an an object, and use some word in an unknown unknown word. . ° . . . . i . tongue to express it, that word is just as good in itself as any other, and j ust as good relatively to all who understand the language to which it belongs. But it has no power of itself to convey or suggest the conception. If the conception is one which has been already formed, and is in the mind of the person to whom I am speaking, all that I need to do is to define my word by giving its synonyme in the lan- guage which he uses. If I had used the word “ calebfi which is Hebrew, I have but to give the English word “ dogfi and I have defined the word and re- called to his attention the conception which the two words are used to represent in their respective voca- bularies. 1253. But suppose the conception be entirely new IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. IH. 349 to tlie person addressed, no mere definition of the word by which I denote it will suffice. I must verbal Defini- give him first the Essentia of the object by c°n4y w eoncep- referring it to the Proximate Genus, and tlons - then the Differentia, which distinguishes it from the coordinate species in that Genus. And then further if it be an individual object, I must give some of the individual marks or inseparable accidents. 1254. The person addressed then takes up together (for that is the meaning of the word 11 conceive'’), all the matter which I have given and puts it The person ad- together in his own mind, as I gave it to ^„e& d the e conf him, and he has the conception which I ception - had. But he has formed it anew in his own mind ; I gave him the material only. I defined my conception by an analysis of its matter, and he constructed his by a synthesis of the same matter. 1255. But each of these elements into which I resolved my conception by analysis, and out of which he constructed his by synthesis, are also conceptions conceptions ; and if they are conceptions ^ui 0 z n ed m ,nto which he has not already formed, he is not |^ e e c ’ 0 e ”®£: prepared to synthesize out of the material tions - which I have given him. My Definition has not been sufficiently elementary, I must go back one step further and define the elements of which he has not yet formed a conception. SECTION HI. Of Definition and Description. 1256. The predicating of any subject its Essentia and Differentia is what is called Definition. Definition. Thus if I say, “ Mahomet was the man who founded the religion called by his name,” I give first the Essen- tia — what he was — “ a man ; ” and secondly, Where the Differentia, which distinguishes him from qua “- all other men “ who founded the religion ,” &c. By these words I have given an adequate definition. 350 LOGIC. — PART II. [CHAP. 1257. But suppose I had omitted the Essentia, and specific Defi- said, “ he was the founder of the religion, ” quate. &c. ? this would be a specific definition ; but the question might still recur as to his Essentia, whe- ther he was “ man,” “ angel,” or “ demon.” In that case the definition would have been inadequate, inas- much as “ founder of the religion,” &c., may be the Differentia of Species in several different Proximate Genera, as “ man,” “ angel,” &c. 1258. Or again, suppose I had merely said, “ Ma- homet was a man of Arabia .” Here the Essentia Definitions of in- “man” would be satisfactory to give me a eiv^thebnTvf distinct conception, but the words “ of Ara- Snai marks. tfi a ,” are no Differentia of an individual man, since there are many “ men of Arabia.” The De- finition would be inadequate. It would not be definite. It would give the Essentia with the Differentia of the species, but no peculiar or distinguishing mark of the individual. 1259. A Definition is either of a name or of the Definition ofa conception which we have of a thing, or of ception° or c °of the thing itself by means of its conception or name. 1260. When we define a name or a word, we ex- Definition of a plain its meaning by other words having name. the same meaning. Thus we define cjnXeco in Greek and arno in Latin, by the word “ love ” in English. We explain the name “ sulphuric acid,” by verbal Defini- saying that it is the “ oil of vitriol.” This tions. is called a Verbal Definition, as merely de- fining words. 1261. A real Definition is one that defines the thing itself of which the conception is formed. But as we Real Defini- know the thing or subj ect-matter only by the lions. conception which we form of it, we can of course define it only by means of that conception. To define any thing, therefore, is to define or give by analysis the conception which we have of it. Our con- ception may be compared by this means with those IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. III. 351 which other persons have of the same object, and cor- rected, if found to be erroneous or inadequate, by means of theirs. This correction, however, implies that their means and opportunities of investigation have been superior to ours. 1262. We may, however, sometimes enable another to form a concejition of the thing itself, with- Descriptions out the intervention of any conception which conve?in“con f we may have formed of it ourselves. This ceptions - we do by a Description pointing to the place in which it is situated, the time when it occurs, or the circum- stances by which it is surrounded. ^In this case we simply refer to the sphere of its conception, and leave others to learn the matter for themselves by their own observations or investigation. 1263. It has been very generally held that there are certain simple Ideas and ultimate elements in all conceptions which cannot be defined. And the reason given for the opinion is, that being simple or ultimate elements they can be divided or analyzed no farther. 1261. But this is evidently a mistake. We do not analyze the object in our definition, but only our conception of it. JNow a conception ex tion that can- • , • • ° • . r* not be defined. m termini can never consist ot a simple ele- ment. It is the taking together of several properties as Essentia and Differentia into a Logical Whole which to the mind represents the object denoted by the term which represents the conception. We get a conception of an object only by its Essentia and Differentia. And here the conception, including these elments, can be analyzed and so defined.* * We must remember that it will often happen that the Differentia of any object, or class of objects, as we form our conceptions of them, will not consist of properties which can be predicated of the objects considered solely and by themselves. They are rather relative properties. Thus we may predi- cate “ hardness” of iron in and by itself ; but “ magnetism” is but a relative property, since we could never know its reality except by the relation which the magnetic body sustains to others which are attracted by it while in that condition. So with “ causality,” and many of the other elements which enter into our conceptions ; they indicate rather the relations which the objects sustain to others, than any properties which are directly perceptible by themselves. 352 LOGIC. PAKT n. [CHAP. 1265. The difficulty however is in us. It is often the case that we have a distinct conception without its Reasons why being definite in our own minds. We never times ar unabTt e o have analyzed it, and perhaps cannot analyze define. it g0 as to name each element of its matter, and say what precisely is its Essentia and what its Differentia. Thus I suppose all persons have a pretty distinct conception of an apple. But I doubt if any one can give the Differentia of it so as precisely to draw the line between it and the pear for instance. 1266. Again there are objects the definition of which is made difficult, and practically impossible in want of gene- some cases, by our having no well known rai terms. Proximate Genus to which to refer them as expressive of their Essentia. Thus Prof. Loomis, in his Geometry, in attempting to define a “ straight line,” says, “ It is the shortest path between two points.” The Differentia, “ shortest between two points,” is fault- less. But the Essentia, “ path,” sounds strangely. A line is not a “path” in any sense in ivliich we are accustomed to that word ; that is, a “geometrical line” does not belong to any genus which we are accustomed to denote by the word “ path.” 1267. This is in fact a difficulty often met with. We may have the Differentia of a conception at our a frequent dif- command, but not its Essentia. In all at- fi cu| ty- tempts to define “ consciousness ,” for exam- ple, the same difficulty is encountered. Shall we call it a “ faculty,” a “ function,” or simply a “ state ” of the mind ? 1268. The usual resort in such cases of our inability to define that of which, however, we have a definite The usual re- but no distinct* conception, is to describe' 80rt - the sphere by means of the Differentia, and leave the Genus or Essentia undetermined. 1269. But an adequate Definition defines its object by referring it to its species and genus. Thus we say * It may be well to remark that the Essentia makes a conception “ distinct" the Differentia makes it “ definite." IV.] METHODS OF INSTRUCTION AND CRITICISM. — SECT. m. 353 that “ Iron is a metal of great malleability , density , and of a darkish gray color.” When we say What consti . it is a “ metal,” we refer it to the genus ‘“‘ a e t s e an De ^: “ metals ; ” and of course we may thereafter tion - predicate of it all the Essentia of metals. By saying “ it is of great malleability, density, and of a darkish gray color,” we refer it to each of the species whose Differentia are respectively “ malleability,” “ density,” and “ gi’ay color.” 1270. We are said to define a conception generally or qenerically. when we refer it to its nenus, u ,, • ° • 755 • /? 77 ^ 7 Generic Defi- as “ man is an animal / specifically, .when nitions sped- we give the Differentia of the species with- out the genus, as “ man is rational ,” or “ a being with reason ; ” accidentally , when we give merely Accidental, some accidental property of the object ; phy- physical. sically , when we enumerate the physical parts, as “ man has two hands, two feet, erect form ; ” and metaphysically , when we refer to the invi- Metaphysical, sible nature, as “ man is a spiritual being, with reason, intellect, memory, conscience,” &c.* 1271. In defining a Genus, as such, the Essentia only can be given. f But in defining a Species, both the Essentia and the Differentia must be • i • ixi* Ti**iiii AVho.t Defini- given ; and m denning an Individual there tions can be must be added to the Essentia and Differ- gnen ' entia the peculiarities which distinguish the Individual defined from others of the same species. 1272. But when a Definition fails to fulfil these conditions, as if in defining a Species, there inadequate De- is an omission of the Differentia ; or in detin- finitioift - ing an Individual an omission of the peculiarities, the definition is inadequate. * What is sometimes called a Negative Definition, or defining negatively, is no definition of the subject at all. It consists merely in naming the Dif- ferentia of the coordinate species, and saying that they are not properties of, and do not belong to the Species which we are defining. f We may of course refer it to the next higher of the subaltern Genera, in which case it becomes a Species to be defined as such by the Essentia of its Proximate Genus and its own Differentia. 354 LOGIC. — PART n. [chap. 1273. Definition, therefore, always implies a classi- Definiiion im- fication of the thing 1 defined, by referring it tion. ' to its Genus and Species. Hence it appears that we can cognize the Individual only through the Species. Each property which we ascribe to it or see that it possesses refers it to a class, whose Differentia is the property thus ascribed to the individual object. 1274. One of the readiest and best illustrations of this principle is afforded in the conjugation of the verb. The conjuga- The verb itself is the Genus, and its Essentia sion ofyerbaTii the meaning of the word in its most general illustration. sense. The Species is the voice, as active, passive, &c., whose Differentia is the mode of the action of the verb in reference to the agent and the object. Mood is the first sub-species, the Differentia of which is the mode of affirmation as declaring (In- dicative), representing it as possible, &c. The second sub-species is Tense, and its Differentia is the relation of the action to the time in which the word is used by the speaker. The next sub-species is “ number,” indi- cating as its Differentia whether the subject of the verb included one or more ; and the infima species is the “ person,” limiting by its Differentia the subject still further, by showing whether the subject is the person speaking, the person spoken to, or some person spoken of. And the word itself, as it stands on the written page, or is heard in oral speech, is the individual. 1275. It is very likely to happen that the terms used in any Definition will also need to be defined. In this case the laws of Definition are the same as to define 1 before ; we define by Essentia and Differentia still. Thus if I should define the palm as “ an endogenous tree,” &c., one might be wholly un- able to construct the conception, because he had not previously the conception for which “ endogenous ” stands. I should then be obliged to define that con- ception by giving its conception, as applied to plants — growth Inj mccesive additions to the inside. But sup- pose my definition were not yet sufficiently elementary, IY.] METHODS OF INSTRUCTION AND CRITICISM. SECT. HI. 355 and that he had no definite conception of “ growth,” I should he obliged to define it as a species of the genus “ increase,” giving the Differentia which distin- guish it from the coordinate species — accretion , agglo- meration , &c. Or suppose the words “ by successive additions to the inside,” represented a conception not previously formed in the mind of the person addressed, I should have to explain or define them in the same way, either showing what an “ addition ” is, or the difference between the kind that is “ to the inside,” and that which is “ to the outside,” its coordinate. 1276. Hence as each Definition may need a defini- tion of its terms, there must be a constant ultimate retrogression until we come to some ultimate conceptions, conception, which is formed at the first sight of the ob- ject ; or to Description, pointing out the sphere of the object of which the conception is to be found. 1277. A Description, therefore, does not furnish the material for the construction of a conception. A Description It merely informs us when, or where, or how M e M^uer Sh ibr we may find it for ourselves. And the pro- a conception, cess of finding it is one of the original Methods of In- vestigation. It brings us back, therefore, to primary or elementary conceptions. 1278. These primary or elemental conceptions of external objects are formed spontaneously, Primary Con . and of necessity are the perception of the tlneiuTandSe- external senses. And of invisible objects, cessary - such as geometrical figures, &c., they are formed by the Reason constructing them in the mind itself. Thus suppose I imagine a point moving from one position in space always at the same distance from another point, until it comes back to the place of its departure, I have formed the conception of a circle by constructing the circle itself. It is for Genus a figure in space, and for Differentia it has a circumference every point of which is equally distant from one and the same point within it. 1279. But this Genus, “ figures in space,” cannot be a nrimary conception for us, since we never have 356 LOGIC. — PART n. [CHAP. the Differentia denoted by the words “ in space,” ex- conceptions of ce pt as a counterpart to objects having shape trath te SJip5y °a and outline in the external world or in place. S'™ of relf- I do not deny that the conception would be ities of being, possible without such observation. That is a question of metaphysics with which we have nothing to do in this place. But as a fact, all mortals here on Earth, do not form conceptions of the invisible realities of truth, until after experience of the visible realities of being in the material world. SECTION IY. Of Natural and Artificial Classifications. 1280. The conception of each individual object — for with the individual we always begin in actual expe- rience — is formed by means of the Essentia first" form e d‘u ff- and Differentia. I see an object before me those mode by winch is yellow and round ; it 1 call it an “ orange,” I refer it to a conception already formed, and consequently this is not a primary one. It is, however, the point at which each of us who live at the present day begin with the formation of our con- ceptions. We learn the names that have already been given to things, and base our classifications and con- ceptions upon those that have been made before us. 1281. The primary classifications are always of necessity very simple and unscientific. They are based on some property immediately obvious to ficadons very the senses, as color, shape, odor, &c., lor their Essentia. The next step is a division of the Genera, using different colors, odors, shapes, &c., as Differentia. This classification is almost instanta- neous if not quite so, at the first instant when the mind is awakened to activity by the presence of material objects to our senses. 1282. From these first and purely accidental prin- cioles of classification, we pass on in our progress of IV.] METHODS OF INSTRUCTION ANT) CRITICISM.— SECT. IV. 357 comprehension, at each step adopting as permanent and useful such as have been found so in S omeofthem times past, and because they have been so b c a ”f in Q f iL h n e found have received those common names suase - which constitute the basis of all languages, as “ com- mon names.” 1283. But no sooner do we begin our scientific investigations than we find in most cases that a new classification becomes requisite, new ciassifica- one requiring for its construction a new lons ' analysis of the objects to be included in the classes. 1281. Hence the distinction between* natural and artificial, or scientific classifications. ISTatu- Distinction be- ral classifications are such as are formed at ind en sdeS once instinctively and of necessity by the Clas5lficat10 " 3 ' mind. They are based upon the more obvious and conspicuous properties of the objects, and denoted by such words as the common names of all languages. The scientific classifications, on the other hand, are such as are based upon less obvious properties, and are devised for the purpose of expediting Science. They are, for the most part, denoted by what are called the technical terms of a language or science. 1285. The problem in all scientific classifications is to group together in one species those facts which have the greatest number of properties in com- mon, and to classify on those properties in scientific i • i i i ^ i <• Classifications. which are regarded as h ormal with reference to those which are Modal. The fewer the classes therefore the better, provided that in reducing the number of classes we do not increase the exceptions to each, so as to make the aggregate of Species and Ex- ceptions greater than in some other classifications. 1286. Thus to take an example from Ethnology. If we divide men into three coordinate classes, red, black, and white, not only are the Modal An illustration properties common to each species in classi- from Ethnology, fication few, but the exceptions to any statement that might be made concerning any one of the speeies are 358 LOGIC. PART II. [CHAP. very numerous. As the result of much investigation, it has been found that if we class them as woolly- headed, bearded, and beardless, the number of state- ments, including both the rules and the exceptions, requisite for a full treatise on the Natural History of Man, is greatly reduced. Of course, therefore, that natural history when thus presented, is much more easily and much more quickly learned, and longer remembered than when presented' to the mind of the learner by means of any other classification. 1287. To take another illustration. In Botany the primary classification of its objects was into Trees, illustration Shrubs, and Plants. CLesalpinus proposed fromuP history the first scientific classification based on “ the number, position, and figure of organs,” as “ the flower, the seed receptacle, and the seeds ; ” for the purpose, as he said, of “ ranging them into bri- grades, regiments, and companies, like a well-ordered army.” Soon after Bauiiin undertook another and simpler classification. Ray proposed another ; and in 1687 Tournefort proposed to classify on “ the regu- larity or irregularity of the flowers in form, and by the situation of the receptacle of the seeds below the calyx or within it.” Then Linnaeus appeared and classified by “ the pistils and stamens of the flowers.” And finally, we have the system of the Jussieus, based on “ the number of the cotyledons and the structure of the seeds, and subordinate to this the insertion of the stamina, as over, about, or under the germen.” 1288. A primary object is undoubtedly to make the number of the species as small as practicable. And ■me limit to the limit to this reduction, as has been said, of e the re number ‘ s the number of exceptions and abnormal species. peculiarities which always increases with the reduction in the number of classes, so long as we ad- here to the same principle of classification. And that principle which will give us the smallest aggregate of species and of exceptions, is said to be the simplest or to simplify the classification the most. IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. IV. 359 1289. Now wherever we begin in our instruction, whether with the most general subject, as in the Syn- thetic Method — or with the individual, as in We must de . the Analytic, we must define our subject, tX and each subject as we pass along, by refer- sdSfic etas'! ring it to the natural and well-known classi- 61fications ' fications. And if we have adopted a scientific classifi- cation, we need always to give the common one also, and explain ours by the difference between them. Thus a chemist would say, “ chloride of sodium is the muriate of soda of the old classifications — the common salt of the common use. It consists of so many parts of sodium, so many of chlorine,” &c., &c. 1290. In the course of our classifications we shall sometimes encounter a phenomenon which similar Differ- we have not yet noticed — namely, the recur- ®nt ia proximate rence of the same Differentia of Species in G6nera - different Proximate Genera — these we may c f e s Curring Spe_ call Recurring Species. 1291. Thus in Mathematics we have “ curved lines ” and “ curved surfaces,” in which the Genera “ lines ” and “ surfaces ” comprehend Species, whose illustrated Differentia is “curved;” as “curved lines,” [™ 3 m Snd th from and “ curved surfaces.” Again in Gram- Grammar - mar, in the conjugation and declension of the Verb, we have three voices, for instance, Active, Passive, and Middle. Now taking these as Proximate Genera, we have in each of them the same Differentia of Mood, Infinitive Mood, &c. ; and the Differentia, that is, the signification and force of Mood is precisely the _ same in one voice as in the other, although modify- ing a different Essentia. -So, also, each Mood has dif- ferent Tenses, as a Present, and Past, and a Future. The force or Differentia of Tense is precisely the same in one Mood as in the other. It is defined as deter- mining “ the time at which the Verb represents the act as taking place ; ” the Present represents it as taking place at the time of speaking, whether in one Mood or mode of representing the action or another, and irre- spective of the Differentia of voice. 360 LOGIC. — PAItT II. [CHAP. SECTION V. Of the Division of the General Subject. 1292. The subjects of which, we treat have exten- sion in two different directions, Comprehension and two kinds of Protension. If we are treating a general sion™ma*Gene- subject, as Chemistry, Mechanics, &c., it has mi subject. Comprehensive Extension, and admits of course of division into subordinate parts. If we are treating of an individual subject, as the history of a nation, the biography of an individual, it has Proten- sive Extension only. 1293. In this latter case there is no logical neces- sity for a division at all. A division is only a conve- Noioicaine nience > an d one that is often of very great visfon y ° oF 1 pm' im P 01 't ailce both to the writer and the reader, tensive Exten- And as it is one that is required and deter- mined rather by the idea of Utility than the idea of Truth, we will leave its discussion to the Rhe- toricians. 1291. But in treating of a general subject a division becomes necessary, in consequence of the fact that d . . jon f a much which it is necessary to say, may be Generalsubject predicated of a part of the included indi- vidual subjects which cannot be predicated of the wdidle ; and much of some parts which cannot be predicated of others. 1295. If the subject will admit of a division into coordinate parts, it is best to divide in that way. And coordinate then the division is to be determined by the pan preferable. } aw already laid down for scientific classifi- cations ; namely, so divide as that the aggregate of the number of the parts and of the exceptions to the predi- cates affirmed of the parts, will be the smallest that the nature of the matter will allow. 1296. The reason for this rule is the same as that given above. The instruction can be given in fewer TV.] METHODS OF INSTRUCTION AND CRITICISM. — SECT. VI. 361 words, consequently in shorter time, is more easily and sooner understood and better remembered, Rea sonforthe than when the mind is encumbered by a Rute - multiplicity either of subdivisions or of exceptions to the statements made for general. Each coordinate and each subordinate part, as well as each exceptional case or individual, becomes a separate and distinct subject of predication, which it takes as long to teach and requires as much, and often more, effort to remember than the most comprehensive statement in the whole science. 1297. But there are cases in which no division into coordinate parts can he made unless it be a very clumsy one. Our present general subject (828), “ Me- Il? some casca thod,” as has been already said is such an |p|ate“?ait 3 one. Again, if one were treating of the im p° ssibIe - Literary Men of a nation, it would be impossible to make a coordinate division that would answer any good purpose. 1298. In such cases we must divide into Alternate Species. As in the case just named, we might divide the Literary Men into Historians, Poets, Essayists, Philosophers, Naturalists, Ac. Alternate 1 s"e This would be a useful division. But the same man might be distinguished in more than one of the classes named, as for instance, the English Southey as a poet and as a historian ; Coleridge, a poet and a phi- losojiher ; Macaulay as a poet, historian, and essayist. 1299. And with regard to the number of Alternate Parts into which the General Subject should The same rule be divided, the same rule holds as above : number of Al- it should be the minimum aggregate of parts cdorAatespL and exceptions. SECTION VI. Of the Order in the treatment. 1300. In the first acquisition of knowledge we are obliged to begin with the individual and concrete, and, 16 362 LOGIC. — PART II. [chap. examining them one by one, we ascend to the general and the abstract. Thus the knowledge of human know^vith the nature is acquired by an acquaintance with individual men one after another, analyzing, abstracting, and omitting what is peculiar to each, and retaining as the matter of the conception to be ex- pressed by one general term “ man,” all that is com- mon to all men. 1301. So, too, in acquiring the knowledge of any we also learn particular or individual object, we may per- by one. ceive its properties, many ot them at a tune. But we have to learn or study them, property after property, one at a time. 1302. Now in teaching others, which is instruction, we may pursue the same method ; beginning with the ■rhe Analytic individual and the concrete, and proceed to Method in the general and abstract. This is called the Analytic Method of teaching. But it is gene- rally found tedious, uninteresting, and unsatisfactory. And it moreover requires an examination of each of the individuals separately and in detail, which is in some cases impossible on account of the number, and in others they are inaccessible. 1303. Still, however, in some branches of science this method is preferable, and perhaps even indispen- sable. In Botany, in Chemistry, in Anatomy, thod on^ Me ‘ ana suca hke sciences, which consist almost entirely of details, and in which there are comparatively but very few general principles as yet established, we must of course confine ourselves to teaching the facts as they are known, and as far as they are known. The Causes and Laws which determine those facts are as yet unknown to us, if not altogether beyond the reach of our faculties. 1304. In the Analytic Method of Teaching, the subject of which we speak is, of course, an individual, Analytic Me- and we P ass from one to another as fast as th“ a individual we have predicated of each what we know subject. 0 f it 5 or at least that portion of what we IV.] METHODS OF INSTRUCTION AND CRITICISM. — SECT. VI. 363 know of it wdiich our purpose requires us to com- municate. 1305. But in the Synthetic Method we begin with the general subject which comprehends the Tlje synthetic individuals. We predicate of it whatever Method - belongs to it as a general subject, then divide it into its coordinate parts, and those parts again into their subordinates, and so on until we come to the indi- viduals included in each part. 1306. As each part is less comprehensive than its whole, and so on until we come to the indi- vidual, each part will have something to be quires special said of it which could not have been predi- predlcall0n - cated of its superior and comprehending part in any previous sections, and which ought to be predicated before we proceed to its subordinates. 1307. These two Methods differ much less in rela- tion to the fulfilment of the Logical condi- tions of Method than would appear at first the’ ff Tn!thods sight. There is but one way of forming a not great conception of a subject, whether that subject be the general subject of our treatise or the special subject of any subordinate chapter, section, or paragraph, even down to the individual. In all cases we form, and must form, our conceptions by means of classification. By classification also, and by that only, can we com- municate our conceptions to others. In the Analytic Method we teach by means of the natural classifications which all make naturally and necessarily ; while in the Synthetic we teach by means of those scientific classifi- cations which are the results of reflection, and some degree at least of advance towards the maturity of Science.* * For an illustration take the following. Suppose a writer treating of Zoology synthetically, he would begin by defining his general subject, “ animals ; ” giving its Essentia as “ living beings,” its Differentia “ with material organizations, and living only on organic matter, either vegetable or animal.” The first clause limiting against spiritual beings, angels, &e., and the second against the vegetable kingdom. He would then divide into 364 LOGIC. — PART II. [chap. 1308. Our conception of an object may be analyzed into its Essentia, Differentia, Accidents, Quantity or Comparison, Cause and Effects. This order ception divided is not in all its successive steps strictly neces- with reference T , . i . i x ° to the order of sary. it is, however, the most convenient, communication. rpj ic conce pj-j ou j s completed by the two first, Essentia and Differentia, in all that is essential to its completeness. The others are necessary to its adequacy. 1309. The Essentia and Differentia give us all the matter which is necessary to enable us to form the conception of any object of thought. They and Differentia are, therefore, all that is necessary to the alone necessary -i * . • n liii for the a priori adequacy ot the conception for ail the pur- poses of a priori Methods of Investigation or Proof, as in the Analysis of a Conception, giving us the Matter of Analytic Judgments and in the Demon- stration of the reality of Implied Properties. 1310. But our conception of an object is never ade- cpiate, nor can our Science be completed until we have ascertained by the Methods of Investigation Quantity, Ac the Accidents — including the separable and necessary to the . i -t j 1 conception lbr inseparable — and the Continuous or Discrete Quantity and its Protensive Relation to its antecedents and consequents. 1311. Comparison is by no means a necessary ele- ment in the formation of our conception of an object. It may serve instead of Quantity. Thus if nrd 0 uhvays S0 "e- the question be asked, flow large are the evssary. Hottentots ? The answer may be definite four “ Departments,” — Vertebrata, Articulata, Mollusca, and Radiata, each department into Classes, classes into Orders, orders into Genera, genera into Species, species into Varieties, and varieties (the infima species) into Individuals, describing each in its order ; and in describing the individual he would refer it to the species, and thereby in effect predicate of it all that had been said of each subaltern species or genera up to the highest. Its specific name would at once classify and describe all that for the most part we care to know of it. But in the Analytic Method he would begin with the first animal he might meet. He would have to begin with saying, “ this dog,” “ this cat,” “ this worm,” &c., as the case might be, in all cases, however, referring to the common and well-known class-names of the indi- vidual he might be examining. rv.] ME'l'HODS OF INSTRUCTION AND CRITICISM. SECT. VI. 365 in Quantity — '•'•four feet and a half • ” (which, how- ever, is after all a comparison with the foot , taken as a unity of measure,) or it may he by comparison , thus, “ much less than the ordinary height of Europeans.” 1312. Or we may have the question of quantity as to the comprehensiveness of the sphere of the concep- tion. Thus in describing a class, we say it Quamity of is a “ large ” or a “ small ” one. Or possi- h h e e nsive^ 0 e“ p o e f bly we give the precise number of indivi- the Sphere - duals included in it, especially if the number be small. Or again, we may give an idea of the quantity by comparison with another class, calling it larger or smaller than some other whose comprehensiveness is known. 1313. There are many objects which we do not conceive of as Cause or as Effect. Thus in speaking of a Geometrical Figure, we should feet not always not be likely to conceive of it as an effect rei|l “ re ' whose cause is important to our knowledge ; nor yet should we think of it as a cause whose effects it could be important to investigate. Still, however, the con- ception of a triangle for example is an effect. It is the creation of mind, and it is a cause ; for it has stirred up all that mental activity which has produced the Sciences of Geometry and Trigonometry. 1314. We come, therefore, to the Essentia and the Differentia as that which is always necessary Essentia an d to a distinct and definite conception of any w a ^ renti necel- subject ; and which, therefore, must be Lo- sa,y - gically first in all Methods of Instruction,* as well as in all constructions of systems and sciences. Without them there can be no conception of the subject, whe- ther general, special, or individual. * It is often advisable, for rhetorical reasons, not only to state the Differentia in such positive terms as connote the subject, but also to in- crease the distinctness of the outline of our conception, by contrasting it ■with its coordinates speaking of their Differentia, thus fixing the attention upon them, and thus affirming that they do not belong to the class of objects of which we are speaking. This is sometimes called defining a subject by negatives, or negatively — that is, distinctly saying what it is not. 366 LOGIC. — PAKT n. [chap. Distinct and Definite Con- ceptions by Es- sentia and Dif ferentia. 1315. By the Essentia we get a distinct concep- tion — the mind is assured of a reality, a substance, since it has its Constitutive or Material Pro- perties. But the conception becomes defi- nite only by means of the Differentia. The Differentia distinguish it from others, conse- quently defines it, or fixes the limits within which it is a reality. We may, therefore, perhaps sum up the principles principles of of Order in the Method of Instruction as Order. follows : 1316. (1) State first the general subject by its Es- First principle, sentia and Differentia ; referring always to the natural classifications, even when we have occa- sion to use a scientific one.* 1317. (2) Divide it into coordinate parts or species, on the simplest principle at your command, and then second prin- subdivide as far as the case may require, cipie. giving to each coordinate and subordinate part its Differentia, as we proceed to treat each of the parts in the order and degree of their subordination. 1318. (3) Whatever subject we teach, whether the Third principle, general or either of the subordinate parts, define it first by Essentia and Differentia, that so the learner may know distinctly and definitely what we are treating of. 1319. (4) The order in which the other topics, as Accidents, Quantity or Comparison, and Cause and Fourth prin- Effect ought to follow, will depend upon the cipie. End we ] ia ve in view. It is possible that Quantity is all that is desired. It other cases it will be wholly unimportant, and therefore deserving to * We are to remember that not all the Peculiar Properties of any class are to he regarded as its Differentia. The Differentia are only those pecu- liar properties which are most obvious and conspicuous. At least this is always so in the Natural Classifications. And much is added to the per- spicuity and vividness with which instruction is communicated, by a suc- cessful tact in characterizing the subjects by those properties which, while they are peculiar and so determinate of species, are also conspicuous to the observation. rv.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VI. 367 be omitted as surplusage. Again, the Cause or the Effect, either or both, may be the only thing demanded, or they may be a matter in which no interest is taken, and must be given or omitted accordingly. And so among the Accidental Properties — those must be selected which the object in view requires, reipember- ing here as every where, that whatever is not condu- cive to the End, is to be rejected (761). This is one of the most fundamental principles of Method. 1320. The mind is always impatient of any matter that is irrelevant to the End in view, and T hemmdim- even of the intrusion of any piece of matter which is relevant, provided it be out of place ter - and comes in before something else that is necessary to its proper progress. Take the following example : — - “ The Coquallin was sent from America, by the name of the Orange-colored Squirrel. It is, however, not a squirrel. It is a beautiful animal, and very remark- able for its color, its belly being of a fine yellow, and its head as well as body varied with white, black, brown, and orange ; it covers its back with its tail, like the squirrel, but has not, like that animal, small brushes of hair at the tips of the ears : it never climbs up any trees, but dwells in the hollows and under the roots of trees, like the garden squirrel.” 1321. Mow here after the assertion, “ it is not a squirrel,” the mind was expecting the Differentia be- tween it and the squirrel, whereas the author gives a series of propositions, which so far from being Differ- entia of natural species, may as well be applicable to the Squirrel as to the Coquallin. 1322. Every body has observed the difference in the degree of ease with which they remember the writ- ings and instructions of different teachers. This is owing in a great measure to the per- mcmkrmg de- fection of the Method of the Teacher. He FhodhTi^ch- lias what is always necessary to successful In? ' teaching, a clear conception in his own mind of the subject and of the snecial end for which the instruction 368 LOGIC. — PART H. [CHAP. is at that time sought, and upon which therefore the interest in the subject itself depends. He, therefore, by the natural laws which govern the operation of his own mind, mentions the subject, referring it to a well known Proximate Genus, and then giving the most marked and distinguishing Differentia of its species. He carefully excludes all matter that is not pertinent and conducive to the end for which he is communicat- ing the instruction,* and finally selects and arranges whatever he is to predicate of his subject with reference to that end. 1323. Rhetorically one of the first things for a teacher to do is to awaken an interest in his subject, Fir t awaken ^7 fixing in the mind some End to be gained an 'interest e in by the instruction. Although this is a vio- tho lation of the principles of Logical Method, it is nevertheless so important to the rhetoric of in- struction, that it may well be placed in the rank of the highest importance. 1321. The End must of course be sufficiently im- portant to awaken an interest in the subject itself, and Nature of the 1° excite that interest to such a degree of End - intensity as to raise the mind to a high state of activity, and do away with the sense of tediousness which attends upon all aimless exertion. 1325. If the mind were sufficiently capacious to comprehend all things — all the properties and bearings of any one subject even — there would be omission of many cases m winch there could be no need of such a principle of selection and omission as we have referred to. But the mind is not of suffi- cient comprehension to receive and retain all that we can learn or may desire to know. This fact is not per- haps very flattering. But it is well to have it distinctly understood and admitted. It may humble oar pride * Quidquid praecipies, esto "brevis : ut cito dicta Percipiant animi dociles, teneantque fideles. Omne supervacuum plcno de pectore manat. Hor. De Ars Poet. 335. IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VII. 369 somewhat, hut it will make us wiser and teach us at an early day the necessity of economizing time and labor, and saving ourselves a vast amount of labor and toil, which would otherwise have been spent in vain. 1326. It is no part of Logic to ascertain the various Ends for which instruction may be sought, and from which we may derive our interest in any subject. The End may be merely and purely the love of truth. It may be some immediate practical application which we wish to make of the knowledge we are seeking. But Avithout such an End in view, hut little will be sought and still less, effectually obtained. SECTION VII. Method of Logical Criticism. 1327. Hitherto in our discussion of Formulas and Methods, we have supposed ourselves occupying a point of time anterior to construction ; and discussing the Formula and Principles by view occupied which to be guided in our work. But in bythecnt,c - experience it is quite as often that we occupy a differ- ent position, and have to perform the part of the judge or the critic of that which has already been produced or constructed, or at least imagined for construction. We wish to criticise our own arguments and investiga- tions, theories and systems, before they go out to the world. And every where in Literature and Necessity for Science we meet with the like productions Criticism - of other minds which need to be thus examined and criticised, as a part of the process by which they can become our own or in any way profitable to us. 1328. It is obvious that the Formula} and Principles must be precisely the same for Criticism as principles of for Construction. And so far as the Method ^ cis “ th tb ® of Criticism is determined by the Idea of the ° f construction. True, nothing further need be said than is contained in the preceding pages. It is immaterial in what way or 16* 370 LOGIC. — PART II. [CHAP. order we apply these principles, if so be that we apply them and find the conformity or want of conformity to them in what comes under our notice. What we shall its Methods, have to say further of the Method of Criti- cisms, therefore, will be determined by the Idea of the Useful, as giving the readiest and quickest way of ac- complishing the result. 1329. In order to a successful and scientific Criti- cism, the first and indispensable step is to get an ade- idea of the T uate idea 01 ’ conception of the work to be whole the start 6 - criticised, as a whole, its structure and its aim. For in most cases we cannot get at the parts to form any conception of them, and criticise them without first analyzing the whole, that we may thereby discover what are its parts. But more than this an adequate conception of a part can never be formed without considering its relation to the whole The necessity as a constituent part of it. Considered as a font. whole and absolutely, many a subject of our criticisms may be faultless, while yet it has no value or adaptation if considered relatively to its whole ; and vice versa, parts that are faultless in reference to their comprehending wholes, are without comeliness and meaning, considered by themselves. 1330. Wholes are never a mere accumulation or generalization of the parts. They are rather collective The whole not g enera T Many things may be predi- a mbe general cated of them which cannot be predicated Conception. , -i j • l x iii ox any one oi the contained or comprehended parts. Much, for example, can be said of man as a living whole, which could not be predicated of any of the parts into which Anatomy, Chemistry, or even Metaphysical Analysis can resolve him. It is so of all wholes, and hence the necessity of examining and cri- ticising them as wholes over and above any examina- tion or criticism which we may give to their component parts. 1331. This fault of judging of parts as wholes and not as parts merely, or in their relation to the whole, IH.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VII. 371 Whately has referred to the Fallacy of Division and Composition. It is, however, no Fallacy in Form. It is a Fault of Method originating in a want of com- prehensiveness of views. I have already quoted Wliately’s language in regard to it (749). To take his example : “ The spendthrift compares his in- T1?e gpend . come with each particular item as a whole, thrilt s Fault ' and finds it small compared with what he has to ex- pend — five dollars for an evening’s amusement out of an income of a thousand ! It is certainly inconsider- able. Such a sum cannot ruin any body. It is mere niggardliness not to afford it.” But considered as a part of the annual expenditure it may, after all, be found to be just the sum and the item which will leave one in arrears at the end of his financial year. The same fault is often committed by persons in mak- ing their estimate of their own character and abilities. Hot considering that one or two acts are sufficient in some cases to determine the character, they form quite a different estimate of themselves from that which their neighbors have formed. One or two acts of fraud, of intemperance, of intentional deception, destroy entirely one’s character for honesty, temperance, and veracity. So, too, although it be true that “ the best fail some- times,” yet frequent failures to meet our engagements, or to perform the duties required or expected of us from our position, is ruinous to one’s character for capacity or competency to the duties and responsibili- ties of his position.* * It is often a successful trick of Sophistry to criticise what are called “ the Points ” of an Argument, as if they were wholes ; that is, Arguments each complete in itself, obstinately and artfully keeping out of view and out of consideration the fact that they are hut parts of a cumulative whole. In this way the force of any Argument from circumstantial testimony or cumt lative Argument of any kind, may be shown to have little or no force. The Method is no less absurd than would be the attempt to estimate the strength of an arch by ascertaining how much each stone taken separately would sustain, and then taking the aggregate as indicative of the strength of the whole arch ; when in fact more than one-half of the stones, per- haps, not only would not sustain any thing in their position, hut need to be supported by thoso below them to keep them from falling. 372 LOGIC. PAKT II. [ciiap. 1332. What are to be regarded as wholes and what as parts, is determined by the choice of the mind from whole, i which they emanate ; and the same thing what dciermiio may be regarded as a part or as a whole, j list as in the use which has been made of it in the case under consideration it was designed for a whole in itself, or to serve as a part to a larger whole and a means to an end not contained in itself. Thus a Treatise on the Evidences of Christianity may be planned and executed as a whole, to be complete in itself; or it may be planned and written with reference to a particular end, to serve, for instance, as an intro- The same thing duction to a Treatise on Christian Ethics, or who e ie'&s S ome a as a part of a system of Theology. A volume times a part. on Algebra may be designed to be complete as a whole, or only to serve as a part of a series on Mathematics ; and it will be modified in its plan and in its execution, according as it is to be a whole or a part, and will of course require to be criticised and judged by different rules, as it is to be regarded from the one or the other of these points of view. 1333. Wholes are to be criticised chiefly with a view to the Principles of Method, the Methods by pans to be which they are constructed. We may, t°e sid c$leism °f course, have them as Investigations or or wholes. Inquiries as they are sometimes called, as Arguments, or as Scientific Systems. And in con sidering the Methods the points to which our attention is to be chiefly directed, are (1) the End or Aim to be accomplished ; (2) the compatibility of the End with the Matter in which it is to be accomplished ; and (3) the adaptation of the Method to the Matter and the End. For example, we cannot produce the absolute certainty of demonstration in Moral Matter, or by means of Testimony. Nor would it be in accordance with the Principles of Method to prove a proposition in Geometry by an induction of facts, or a doctrine of Revelation by means of the opinions of uninspired men. IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VH. 373 1334. We are not to suppose that the whole of any hook or treatise designed to convince or persuade, can he reduced to any Logical Formula, or will No t aii of books fulfil the conditions of any Method of Proof SSofLo 8 or Refutation. Much is often thrown in for g,cal CritJCI3m ' embellishment addressed to the Fancy, and much is designed merely to make an impression upon the sen- sibilities and feelings either in favor of or against the main conclusion ; and some whole hooks have no other object than to please or amuse, or to make an impression upon the feelings without convincing the reason. Even books designed to convey instruction do not necessarily contain much or even any argument. They may be oc cupied with stating facts alone, from which no conclu- sion is designed to be drawn. 1335. An impression made by a description, a nar- rative, a sarcasm, or a jeer, may often be a more efficient motive of action than a conviction of the understanding produced by facts and upon the sensi- . t> , x ^ -i bilities more reasoning. Rut these impressions, unless effective than under the control of the Conscience and Arguments - Reason, are always in danger of misleading us. They are not, however, Fallacies. We cannot reduce them to Logical Formulae. We can meet them for the most part by arguments addressed to the Reason, designed to show that the course to which the impression would lead us is wrong. Yet it is probable that the largest part of' mankind are governed and guided more by their impressions than by their convictions. Convic- tions alone, however, belong to the sphere of Logic and of Reasoning — Impressions and Persuasion to Rhetoric. 1336. It is the right and privilege of the framer of an argument to introduce whatever terms, and to put them in whatever relation to each other he No new mat . may choose. W e may introduce no new ^odS be ? n ones in completing the Formula, and if he Praxis - has not given us material enough to complete the For- mula, the responsibility of the failure must be his. LOGIC. — PART n. 374 [chap. His language must be regarded as mere declamation, unfounded assertion, vox et prceterea nihil. 1337. And here, I take it, is the distinction between argument and mere assertion. The former contains Distinction be- that is necessary to complete the Formula me e nt n an/ls- under the rules already given, so as to satisfy sertion. the mind completely what are the grounds upon which the speaker or writer would rest his con- clusions. But from mere assertion no form of a com- plete argument can be made out without introducing new matter ; and this would throw the responsibility for the Argument upon the critic who completes it, rather than upon the author who should have given it already completed. 1338. But besides all that is addressed merely to the fancy and the feelings, all that is intended as mere instruction to be received on authority of the gumects 6 " and teacher, and all that is mere declamation, mere Artifices. i j • i j i there are also the artifices or tricks to be separated from what properly comes within the sphere of Logic. These tricks have already been defined (753), and discriminated from Faults or Fallacies. They have not been enumerated ; for no diligence could collect, classify, and describe all the artifices of this kind which carelessness may let fall or cunning devise.* Sagacity and constant watchfulness alone can guard one against falling into them himself, or being entrapped by them when dealing with the unscrupulous and designing. 1339. The first step, therefore, towards a Logical Analysis of any work is to discriminate the Thought from the Rhetoric, to select all that belongs to the pro- vince of reasoning and intelligence, from that which is mere Trick or Artifice — gaseous declamation, or mere didactic development of Premises. 1340. In criticising the Terms it will be necessary to consider whether they are properly used or not, and * “ Quas aut incuria fudit Aut humana parum cavit natura.”— Hok. IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VII. 375 whether a word may not be improperly used to express a cognition, which is after all just the one criticism of which is required. And if the Term be com- Terms - plex we are to consider whether the Modals and the Term are not incompatible ; as for example, “ trian- gular ellipse.” Or to give some illustrations from a book that is before me, the author speaks of “ the sub- stantiality of motion,” “ absolute relativity,” “ ab- stractly extended subsistence.” It is impos- contmdictio sible to form any conception of what is inad J ecti » meant (if any thing is really meant) by such terms. This Fault of Terms has been called a Contmdictio in adjectis. 1341. In the criticism of Arguments, it will be necessary to identify in the first place the Conclusion aimed at, since this determines the whole with reference to which all the parts, as whiles of Ar d Terms, Premises, &c., are to be criticised, mined by the and in the next place to identify the subject tonclusion - of the Conclusion as that which determines the unity of the Formula. By means of the Subject and Predi- cate of the Conclusion as Minor and Major Terms, we are to identify the other parts of the Formula. In doing this we shall, of course, find all of the principles and statements of the preceding work called into requi- sition. And I trust that it will be found that nothing is required which is not contained more or less expli- citly and fully in these pages. If any thing more is required, the fact will serve to show how far this Trea- tise is from being complete. 1342. In the Methods of Investigation and of In- struction the unity of the End or Object will determine for us what are to be regarded as Wholes, and -wholes and of course by the same means what are to be ^ 0 n n In and regarded as subordinate Parts. The means d ?Sned on by to any End are always the parts of any Me- theEnduivlew - thod to that End. The End of an Investigation is the attainment of the Predicate which we are investigat- ing. The End of a Construction is to put our thoughts 376 LOGIC. PART n. [chap. rv. into such form and order as to be communicable to others. To this End, division of the Subject, order in arranging, definition and description, and each part of the division — the order, the definitions, descriptions, comparisons, and whatever else we may have occasion to use, are Parts, and should be judged as Parts, sub- ordinate and conducive, according to the rules and principles already discussed ; and whether faultless or faulty in themselves, they are each to be approved or condemned, according as they shall be found conducive to that End or not ; always remembering that whatever does not conduce to the End which is most promi- nently before the mind, and help on towards its attain- ment, is a fault, a hindrance, and an annoyance. APPENDIX. EXAMPLES FOR ANALYSIS AND' CRITICISM. § 1. Of the order in criticising Arguments. In analyzing and criticising the following Examples, which have been selected with a special view to illustrate the Prin- ciples and Formulae of the foregoing Treatise, we shall find the following order useful as expediting the process. In the first place, in each unity or totality of an Argument we must ascertain what is the point to be proved — the Con- clusion of the Argument as a Whole. This is necessary at this stage. For by this only can we identify the Minor and Major Terms — the Subject of the Argument, and what is proved of it. And it is only by this process of identifying the Subject and Predicate of the Argument that we can identify the Premises, and ascertain their character and position. Having identified the Minor, Middle, and Major Terms by means of the Subject and Predicate of the Conclusion, we can next identify the Premises, and arrange the Matter of the Argument into its appropriate Formula, and complete the Formula if it should require completing. And as soon as we have done this, we shall find an advan- tage in disconnecting the Matter from the Form, by substitut- ing in the Formula some one of the Letters of the Alphabet. We derive the same advantage in Logical Analysis as in Algebra, from using the symbolical letters for the sums and quantities which they represent. It facilitates the process, and 378 LOGIC. — APPENDIX. errors are less likely to be made, and are more easily detected if they are. In the next place we are to consider if there is any Fault or Fallacy in the general form or argument. It will always be best to look for them in the following order : (1) An Ignoratio Elenchi. (2) Any Fault in Form or in Method. (3) Any Fallacy in Matter or in Diction. If either of these defects is found, the work, whatever other excellencies and attractions it may have, is worthless as an Argument, or effort to sustain the truth of its Conclusion. The next step, after having selected and arranged the parts of the main Argument, is to separate each of the subordinate parts into logical wholes or unities ; remembering always that the unity of the Argument or Formula consists in the unity of its Subject. Having thus divided the work up into its smallest parts that can be regarded as wholes at all, we are to proceed to reduce them to the Formulae.* The first thing here is to identify the Conclusion, and from the Conclusion the Terms, Minor and Major, which are given in it. We are also to notice whether it be simple, complex, or compound ; and what is the complicity of the judgment of which it is compounded, with reference to its including any thing illicit, by this means. We may here consider whether there be any Ignoratio Elenchi, or Fault in Method in this part of the main argu- ment, or not ; for if there is, we need go no farther in our analysis of this part, since though it should be otherwise fault- less, it is nothing to the purpose. We are next to identify the Premises by means of the Terms which we have found in the Conclusion ; note their Relation, as whether Categorical, Conditional, or Disjunctive. Then put the elements thus given into the Formal position, and complete the Formula if it be not complete. * Most of the Scholastic Writers on Logic whose works I have seen, speak of two kinds of Syllogisms, Formal and Material ; the Material Syl- logisms are those which contain all the Matter of a Syllogism, but not stated in any recognized Formula. A Formal Syllogism is an argument stated in a recognized Formula. The business of Praxis is, therefore, to reduce Material to Formal Syllogisms. EXAMPLES FOR CRITICISM. 379 In the course of this completion, we are not only to find the supposed or assumed Premises in Enthymemes of the various forms, but also the Sequence in Conditionals, the Excluded Middle in Disjunctives, and the identity of kind in things compared.* Having completed the Formula, we are next to consider it in relation to the Faults and Fallacies in the order above given. If we find the part of the main argument which is under examination inconclusive for any reason, we are next to con- sider how important it is as a part of the main argument. And whether a failure or not, we are carefully to estimate its value and its force, if it has any, as a means of establishing the main Conclusion. We shall find the Conclusion either a Pre- mise in the main Argument, or the assertion of a fact which is used by way of Induction, Analogy, Example, or Circum- stance, &c., to prove a Conclusion which is used as such a Premise. In this way we are to analyze each subordinate part of the main Argument, taking as an ultimate part or unity of argu- ment only those which have but one subject, and which there- fore, as arguments , can be resolved no farther. § 2. Examples in Categorical Syllogisms. 1. Every effect must have had an adequate cause — the creation of the world is an effect ; therefore the creation of the world must have had a cause. 2. He that is always in fear cannot be happy. But those that are conscious of guilt are always in fear ; therefore those that are conscious of guilt cannot be happy. 3. Satire is a legitimate mode of exposing the failings of others. But the calling others by ill-names is not satire ; therefore it is no legitimate mode of exposing their failings. * As it is convenient to have a name for this fault, of passing from one species to another improperly (for it is one of frequent occurrence), we may call it Metabasis. This, if I understand him rightly, is what Aristotle means when he speaks of “ passing over into another species : ” MerdPuais (is to &A\o y(vos. 380 LOGIC. APPENDIX. 4. Tyranny is an unnecessary restraint upon human liberty. The English government imposes no unnecessary restraint upon the liberty of its subjects ; therefore the English govern- ment is no tyranny. 5. No one is free who is enslaved by his appetites. The sensualist is enslaved by his appetites ; therefore no sensualist is free. 6. All accountable beings are free agents. Men are ac- countable ; therefore they are free agents. serpetual gratification without sires what can never be attained. 8. That which has no reality of being cannot, as cause, produce or be the ground of existence to any thing. Chance has no reality of being; therefore nothing can be properly ascribed to chance by way of accounting for its origin. 9. Liberality is a means of making others happy. But it is not a means of making one’s self rich ; therefore making one’s self rich does not always make others happy. 10. Murderers never escape punishment. Yet even mur- derers hope to elude the laws of their country ; therefore some who hope to elude the laws of their country do not escape punishment. 11. All amiable men merit the esteem and respect of their fellow men. And certainly all who aim only to do good to their fellow meD, deserve to be esteemed and respected on that account. Hence all who are striving to do good to others are amiable men. 12. Some effectual check to the progress of seditious pub- lications is absolutely essential to the safety of our country. The total abolition of the art of printing would prove such a check ; therefore the art of printing should be totally abol- ished. 13. No one is rich who has not enough. No miser has enough ; therefore no miser is rich. 14. The things that cannot be enumerated do not exist. Innate ideas cannot be be enumerated ; therefore there are no innate ideas. therefore the sensualist de- EXAMPLES FOE CEITICISM. 381 15. Some poisons are vegetable. But no poisons are use- ful drugs ; therefore some useful drugs are not vegetable. 16. Some recreations are necessary to the preservation of health and spirits. All recreations, however, are liable to be carried to excess and be abused ; so that some things liable to abuse are nevertheless necessary for man. 17. No tale-bearer is worthy of confidence. But all tale- bearers are great talkers ; therefore great talkers are never worthy of confidence. 18. That one who has been accustomed to liberty can never be happy in the condition of a slave is indeed true. But the negroes on our Southern plantations have never been accustomed to liberty. Hence they are content and happy in their present condition. 19. “ He that is of Hod heareth my words ; ye therefore hear them not, because ye are not of God.” 20. All the most bitter persecutions have been religious persecutions. Among the most bitter persecutions were those which occurred in France during the French Revolution. Consequently they must have been religious persecutions. 21. That man is independent of the caprices of Fortune who places his chief happiness in moral and intellectual excel- lence. A true philosopher is independent of the caprices of Fortune ; therefore a true philosopher is one who places his chief happiness in moral and intellectual excellence. 22. Of two evils the less is to be preferred ; therefore since occasional turbulence is a less evil than a rigid despotism, it is to be preferred. 23. Some objects of great beauty answer no other percep- tible purpose but to gratify the sight : many flowers have great beauty ; and many of them accordingly answer no other purpose but to gratify the sight. 24. A man who deliberately devotes himself to a life of sensuality is deserving of strong reprobation ; but those do not deliberately devote themselves to a life of sensuality who are hurried into excess by the impulse of the passions : such there- fore as are hurried into excess by the impulse of the passions are not deserving of strong reprobation. 382 LOGIC. APPENDIX. 25. It is a difficult task to restrain all inordinate desires : to conform to the precepts of Scripture implies a restraint of all inordinate desires ; therefore it is a difficult task to conform to the precepts of Scripture. * 26. Any one who is candid will refrain from condemning a book without reading it : some Reviewers do not refrain from this ; therefore some Reviewers are not candid. 27. My hand touches the pen, the pen touches the paper ; therefore my hand touches the paper. 28. Lias lies above red sandstone, red sandstone lies above coal ; therefore lias lies above coal. 29. A true prophecy coincides precisely with all the cir- cumstances of such events as could not be conjectured by natural reason. This is the case with the prophecies concern- ing the Messiah in the Old Testament ; hence these prophecies are true. 30. All that glitters is not gold : tinsel glitters ; therefore it is not gold. 31. No trifling business will enrich those that engage in it. A speculation is no trifling business ; therefore speculation will enrich all who are engaged in it. § 3. Examples in the Hypothetical Formulae. 32. If some fishes have no teeth, some animals without teeth are fishes. 33. If some who are very sentimental are nevertheless not benevolent, then some who are not benevolent are sentimental. 34. If fire may be separated from a flint, a property may be separated from its subject : but fire cannot be separated from the flint ; therefore a property cannot be separated from its subject. 35. If hatred and malice are contrary to the Divine law, they ought to be avoided : that they are so no one can deny ; therefore they should be avoided. 36. If the penal laws against the Papists were enforced, they would be oppressed and wronged. But those laws are EXAMPLES FOR CRITICISM. 383 not enforced, and therefor** they have nothing to complain of in the way of oppression or persecution. 37. If testimony to miracles is to be admitted, the miracles claimed for Mahomet are to be admitted. But as the narrative of those miracles cannot be admitted, no testimony to mira- cles is to be admitted. 38. If the exercise of war in defence of one’s country were sinful, it would have been forbidden in the Scripture, either expressly or by implication. But it is not so forbidden ; therefore we may safely infer that defensive wars are not sinful. 39. If the fourth commandment is obligatory, we are indeed bound to set apart one day in seven. But no one sup- poses now that that commandment is obligatory. Hence there is no obligation to keep one day any more sacred than an- other. 40. Romanism is that form of religion which has the most forms : and if forms are necessary to religion, then that religion which has the most forms is the best, and we ought all to turn Romanists. 41. The adoration of images is forbidden to Christians if the Mosaic law was designed, not for Israelites alone, but for all men. It was, however, designed for Israelites alone ; hence the adoration of images is not forbidden to Christians. 42. A wise lawgiver must either recognize the rewards and punishments of a future state, or he must be able to appeal to a Providence dispensing them in this life. Moses did not do the former, and therefore he must have done the latter. 43. The virtues are either passions, faculties, or habits. But they are not passions : for passions do not depend on pre- vious determination. And they are not faculties : for faculties are possessed by nature. The virtues, therefore, are habits acquired by voluntary exertion and effort. 44. The early assignment of the Epistle to the Hebrews to St. Paul as its author, must have been either from its being really his, or from its professing to be his and containing his name. But it makes no claim to being his. Consequently, nothing but a knowledge of the fact that he wrote it could have led the early Christians to attribute it to him. 384 LOGIC. APPENDIX. 45. If the everlasting favor of God is not bestowed at ran- dom, and on no principle at all, it must be bestowed either with respect to men’s persons, or with respect to their conduct : but “ God is no respecter of persons ; ” therefore his favor must be bestowed with respect to men’s conduct. 46. If every objection that can be urged would justify a change of established laws, no laws could reasonably be main- tained. But some laws can be reasonably maintained; there- fore no objection that can be urged will justify a change in established laws. 47. If any complete theory could be framed to explain the establishment of Christianity by human causes, such a theory would have been propounded before this time. But no such theory has been proposed ; therefore we may conclude that no such theory can be devised. 48. If a man is ignorant he should consult others as a means of making up his deficiency in knowledge. If he is wise, yet two heads for counsel are better than one ; therefore in all important matters one should take counsel with others. 49. If one is superior to others he should be polite and gentle in his manners towards them, as a matter of Christian compassion and magnanimous condescension. If he is among equals he should be civil and courteous, since such a demeanor is as much their right from him and his right from them. And if he is among his superiors, he should show himself courteous and civil, as being due to those having authority over us for the good of the whole. In any case, therefore, we are bound by the most sacred obligations to be civil and considerate of the feelings of others. 50. If the Government provides for these debts by impo- sition, it will become odious to the people and perish. If it does not provide for them, it will be overthrown by the most dangerous of all parties, I mean extensive discontent of the moneyed interest. 51. If I am under the chastening hand of God, and if there is no unrighteousness in Him, it must be that I am punished for my iniquity. 52. If virtue is voluntary, vice is voluntary. But virtue is voluntary ; therefore so is vice. EXAMPLES FOR CRITICISM. 385 53. If expiatory sacrifices were divinely appointed before the Mosaic law, they must have been expiatory not of ceremo- nial sin (for there could be none then), but of moral sin. If so, the Levitical sacrifices must have had no less efficacy. In that case the atonements under the Mosaic law would have ‘ made the comers thereunto perfect, as pertaining to the con- science.’ But this they could not accomplish. Hence we infer that expiatory sacrifices could not have been appointed before the Mosaic law. 54. If transportation is not felt as a severe punishment, it is in itself ill-suited to the prevention of crime : if it is so felt, much of its severity is wasted, from its taking place at too great a distance to affect the feelings, or even come to the knowledge, of most of those whom it is designed to deter ; but one or the other of these must be the case : therefore trans- portation is not calculated to answer the purpose of preventing- crime. 55. Fontenelle on seeing a criminal led to punishment said, “ There is a man who has calculated badly; ” whence it follows that if he could have escaped punishment, his conduct would haye been laudable. 56. If the prophecies of the Old Testament had been writ- ten without knowledge of the events of the time of Christ, they could not correspond with them exactly ; and if they had been forged by Christians, they would not be preserved and acknow- ledged by the Jews : they are preserved and acknowledged by the Jews, and they correspond exactly with the events of the time of Christ ; therefore they were neither written without knowledge of those events, nor were forged by Christians. 57. Now “ if Christ be preached that He rose from the dead, how say some among you that there is no resurrection from the dead ? But if there be no resurrection of the dead then is Christ not risen ; and if Christ is not risen then is our preaching vain, and your faith is also vain. Yea, and we are found false witnesses against God, because we have testified of God that He raised up Christ whom he raised not up, if so be that the dead rise not. For if the dead rise not, then is not Christ raised ; and if Christ be not raised your faith is vain, ye are yet in your sins. Then they also which are fallen alseep in Christ are perished.” 17 386 LOGIC. APPENDIX. 58. If the bishops of England, before the Reformation, when they were nominated by the Pope, were true and valid bishops, then the bishops since the Reformation, when they have been nominated by the Crown, are not true and valid bishops. But if the bishops since the Reformation, which have been nominated by the Crown are true and valid, then these before the Reformation are not so. In either case the claim of Apostolic succession and authority for the English bishops is absurd. § 4. Incomplete and Compound Formulae. 59. The study of Mathematics is essential to a complete education, because it produces a habit of close and constant reasoning. 60. Familiarity is productive of contempt, inasmuch as it occasions a needless exposure of private failings. 61. Man needs the restraints of law, since he is naturally selfish ; and is, moreover, subject to desires and passions which have no limits or power of restraint in themselves. 62. Sin is hateful, because it is opposed to the Divine Will. 63. A good face is a letter of recommendation, for it pre- possesses the beholder in favor of its possessor. 64. A wise man is never surprised because he is never disappointed ; and he is never disappointed, because he forms no expectations that are not placed upon the most certain basis. 65. Discord is a greater vice than intemperance, since discord always implicates more than one person in its guilt. 66. Jupiter was the son of Saturn ; therefore the son of Jupiter was the grandson of Saturn. 67. They who are not conscious of guilt are not subject to fear : hence while conscious hypocrites are always shy and timid, the innocent are unsuspecting and self-possessed. 68. A negro is a man ; whoever, therefore, kills a negro wantonly or maliciously, is guilty of murdering a fellow man. 69. I think ; therefore I am. EXAJMPLES FOR CRITICISM. 387 70. Discord is not so great an evil as intemperance, for that generally arises from the impulse of anger ; while the lat- ter almost invariably proceeds from an uncontrollable appetite, or an inveterate habit. 71. Americans enjoy a greater degree of political liberty than any other civilized people, and therefore they can have no excuse for sedition. 72. Hard substances are elastic ; for ivory is both hard and elastic. 73. Meanness is never useful since it is always base ; and because it is always honorable to be honest, it is always useful. 74. “ Whosoever shall keep the whole law, and yet offend in one point, is guilty of the whole ; for He that said, Do not commit adultery, said also, Do not kill.” 75. The care of the poor ought to be the object of all laws, for the plain reason that the rich can take care of themselves. 76. Wilkes was a favorite with the populace : he who is a favorite with the populace must understand how to manage them : he who understands how to manage them, must be well acquainted with their character : he who is well acquainted with their character, must hold them in contempt : therefore Wilkes must have held the populace in contempt. 77. The child of Themistocles governed his mother : she governed her husband ; he governed Athens ; Athens, Greece ; and Greece, the world : therefore the child of Themistocles governed the world. 78. The Scriptures are the standard of truth : and it is admitted that the Church of England is in accordance with the Scriptures. Hoadley was iu the English Church. But Hoadley denied the divine institution of Episcopacy, and the authority of the Church in matters of Faith. Hence no mem- ber of the English Church can condemn those doctrines as unscriptural or heretical. 79. None but whites are civilized : the Hindoos are not white ; therefore the Hindoos are not civilized. 80. None but whites are civilized : the ancient Germans were whites ; therefore they were civilized. [See 332-339, and 587.] - ry. Tvo C j ; L 'pr) 388 LOGIC. — APP&rfllX. 81. None but civilized people are white; the Gauls were white, therefore they were civilized. [See 587.] 82. Popular commotions, though commencing on a small scale, are so liable to ripen into systematic sedition, that they ought to be speedily and decisively suppressed. 83. Every duty is accompanied with a certain propriety and decorum ; whatever, therefore, is not accompanied with propriety and decorum cannot be a duty. 84. The Earth has been repeatedly circumnavigated ; we need, therefore, no other proof that it is not an interminable plane, as the ancients supposed. 85. Whatever subjects fall under one and the same general definition are of one and the same kind ; consequently those things which do not fall under that definition, must differ in kind from each other and from all that do. 86. Those only who understand other languages are com- petent to teach correctly the principles of their own ; since such a competency requires that philosophic view of language which can be acquired only by the comparison of several with each other. 87. Not a man of all the antediluvians escaped except those that were in the Ark with Noah. Hence after the flood there were none who had not proceeded from him as their progenitor, and been acquainted with what he knew of divine things. 88. Will often combats desire as it often also yields to it : will is not therefore desire. 89. If Paley’s system is to be received, one who has no knowledge of a future state has no means of distinguishing virtue and vice : now one who has no means of distinguishing virtue and vice can commit no sin : therefore, if Paley’s sys- tem is to be received, one who has no knowledge of a future state can commit no sin. 90. When the observance of the first day of the week, as a religious festival in commemoration of Christ’s resurrection, was first introduced, it must have been a novelty : when it was a novelty, it must have attracted notice: when it attracted EXAMPLES FOE CEITICISM. 389 notice, it would lead to inquiry respecting the truth of the resurrection : when it led to this inquiry, it must have exposed the story as an imposture, supposing it not attested by living witnesses : therefore when the observance of the first day of the week, &e. was first introduced, it must have exposed as an imposture the story of the resurrection, supposing it not at- tested by living witnesses. 91. A system of government which extends to those ac- tions that are performed secretly, must be one which refers either to a regular Divine Providence in this life, or to the rewards and punishments of another world : every perfect sys- tem of government must extend to those actions which are performed secretly : no system of government therefore can be perfect, which does not refer either to a regular Divine Provi- dence in this life, or to the rewards and punishments of another world. § 5. Miscellaneous Examples of Formulce and Fallacies. 92. The end of a true soldier’s life is the welfare of his country : but death is the end of a soldier’s life : therefore his death is requisite to the safety and welfare of his country. 93. The fish inclosed in the net were an indiscriminate mixture of all kinds : those that were set aside and saved as valuable, were fish that had been inclosed in the net : therefore fish of all kinds were set aside and saved as valuable. 94. No man can possess the power to perform an impossi- bility. But a miracle is an impossibility ; therefore no man can work a miracle. [See 75.] 95. Few scientific treatises communicate truth in a clear and conspicuous manner, without any admixture of error. Although a treatise which should so convey truth would be exceedingly valuable, yet it must be admitted that there are but few treatises comparatively which are very valuable. 96. All the miracles of Jesus would fill more books than the world could contain ; the things related by the Evangel- ists are the miracles of Jesus : therefore the things related by the Evangelists would fill more books than the world could contain. 390 LOGIC. APPENDIX. 97. If a man say, I love God, and hateth liis brother, he is a liar ; for he that loveth not his brother, whom he hath seen, how can he love God whom he hath not seen ? 98. If the Romish doctrine of Transubstantiation be true, in receiving the Eucharist, the Romanists are guilty of can- nibalism. But if they are not guilty of cannibalism their doctrine is false. [See 221.] 99. The principles of justice are variable ; the appoint- ments of nature are invariable : therefore the principles of justice are no appointment of nature. 100. A story is. not to be believed, the reporters of which give contradictory accounts of it ; the story of the life and exploits of Bonaparte is of this description : therefore it is not to be believed. 101. It is certain that in the moral government of God, virtue will produce happiness and vice will produce misery. We may therefore say, that whatever will produce happiness is virtue, and define virtue to be the pursuit of happiness in accordance with the will of God. 102. It is evident that drunkenness is a sin most odious in the sight of God. It is equally certain that the use of alcohol is destructive to the moral and physical energies of man. I claim, therefore, not only that it is the duty of every man to abstain totally from the use of alcoholic drinks, but as a good citizen and a philanthropist, to exert all his influence to obtain and enforce a law which shall totally prevent the sale of intoxicating drinks of any kind. 103. Nothing which is of less frequent occurrence than the falsity of testimony can be fairly established by testimony ; any extraordinary and unusual fact is a thing of less frequent occurrence than the falsity of testimony (that being very com- mon) : therefore no extraordinary and unusual fact can be fairly established by testimony. 104. Testimony is a kind of evidence which is very likely to be false ; the evidence on which most men believe that there are pyramids in Egypt is testimony : therefore the evi- dence on which most men believe that there are pyramids in Egypt is very likely to be false. EXAMPLES FOE CKITICISH. 391 105. He who cannot possibly act otherwise than he does, has neither merit nor demerit in his action. A liberal and benevolent man in relieving the sufferings of the poor cannot do otherwise than relieve them : therefore there is no merit in his actions. 106. Slavery is an outrage upon the inalienable rights of man. It operates, wherever it exists, as a means of corrup- tion and degeneracy to the social and political condition of mankind. Hence, as citizens, as Christians, and as philanthro- pists, we are called upon to labor for the promotion of its im- mediate abolition. 107. It is generally held that St. Paul wrote the Epistle to the Romans. But th^ Epistle itself expressly declares that Tertius wrote it (xvi. 22). Therefore St. Paul cannot pro- perly be regarded as its author. 108. The publication of a libel is criminal : but the act of putting a libel into the post, is an act of publication (for the moment a man passes the libel from his hand his control over it is gone) ; that act, therefore, must be pronounced criminal. 109. True wisdom cannot be too dearly purchased. Hu- mility always ' accompanies true wisdom : therefore humility cannot be too dearly purchased. 110. No man could bind him, no not with chains; because that he had been often bound with fetters and chains, and the chains had been broken asunder by him, and the fetters broken in pieces. [See 425.] 111. That which is greater than faith and hope must be the highest Christian grace. Charity, therefore, which is but another name for almsgiving, is greater than faith and hope, and must therefore be more important than any degree of accuracy or orthodoxy in the faith. 112. It is sufficient to show the fallacy of the Protestant dogma, ‘‘ the Bible, and the Bible alone is the religion of the Protestants,” to state the fact, that many parts of the Bible are wanting, as for example, the Book of the Wars of the Lord, the Book of Jasher, and of the New Testament, the Epistle to the Laodiceans, to mention no more. If, therefore, the whole Bible would be a sufficient rule of faith to the 392 LOGIC. APPENDIX. Protestant if lie possessed it, yet since lie has not the 'whole, what he has can be no sufficient rule. 113. The New Testament as a distinct book, was nevei heard of until the Council of Laodicea, which at the earliest was 314 years after the commencement of the Christian era. It is, threfore, absurd to pretend that it was written by the Apos- tles, who were all dead more than a century before this date. 114. A collection of rules, designed to enable us to under- stand the principles of any subject, is a science ; but if those rules are designed to assist us in the application of these prin- ciples to a specific end, they constitm/e an art. Now Logie collects and states the rules with a view to the comprehension of the rules themselves ; but Rhetoric*with a view to their ap- plication to the specific end of conviction and persuasion : therefore Logic is a science, and Rhetoric is an art. 115. Russia knows full well that she is engaged in a con- test with two nations that were never yet overcome by valor of arms, nor circumvented by fraud or cunning in diplomacy. Rut Russia is contending against France and England : there- fore neither France nor England was ever overcome by valor, or circumvented by cunning or fraud. 116. If the forgiveness of sins was imparted at one’s con- version, Ananias could not have said to St. Paul three days after his conversion, “ Arise, be baptised, and wash away thy sins.” But such was precisely the message which he was commissioned by the Holy Ghost to deliver to him ; therefore remission of sins takes place in Baptism. 117. An unholy minister is the greatest of all sinners; for either he is a person of more than ordinary knowledge or he is not. If he is not, he sinned greatly in undertaking that office, for which so great knowledge is required. If he be, his knowledge will doubtless increase his guilt. 118. - The works of creation imply far more of design and of wisdom than the Iliad of Homer or the Geometry of Euclid. But no one ever supposed that the Iliad, or the Geometry of Euclid were composed without an intelligent author ; there- fore the works of creation must have had an Intelligent Creator. 119. The Jesuit cites Ruffinus in proof of the infallibility EXAMPLES FOK CRITICISM. 393 of his church. But if Ruffinus is right the church is not in- fallible, since it does not agree with Ruffinus. If, however, Ruffinus is wrong, his testimony is worthless. 120. The doctrine which holds to an omnipresent divine power and agency in the operations of Nature, is as contrary to the Scriptures as it is to sound philosophy ; for the Scrip- tures say expressly, “ the earth bringeth forth fruit of herself ” (St. Mark iv 28). 121. Nature is either the author of Nature, or it is the order of things established by a Supreme Intelligence. But nothing can be the author of itself; therefore, Nature can be only the order of things established by a Supreme Intelli- gence. •122. The cause of evil is itself an evil. But that Chris- tianity has caused much evil in the shape of wars, oppression, imposture, fanaticism, and persecution, cannot be denied. 123. Our Lord said, “ If a man keep my saying he shall never taste of death. Then said the Jews unto Him, Now we know that thou hast a devil. Abraham is dead, and the Pro- phets. Art thou greater than our father Abraham ? whom makest thou thyself ? ” 124. “ The argument of the atheist assumes that it is pos- sible to create an intelligent moral agent, and place it beyond all liability to sin. But this is a mistake. Almighty Power itself cannot create such a being, and place it beyond the pos- sibility of sinning, as we shall prove,” &c. 125. He who has a confirmed habit of any kind of action, exercises no self-denial in the practice of that action ; a good man has a confirmed habit of virtue ; therefore he who exer- cises self-denial in the practice of virtue is not a good man. 126. He is the greatest lover of any one who seeks that person’s greatest good ; a virtuous man seeks the greatest good for himself ; therefore a virtuous man is the greatest lover of himself. 127. Whatever is real is limited [by that which it is not]. But whatever is limited is not infinite ; therefore if God is real, and not a mere fiction of the imagination, He is not an infinite being. 17 * 391 LOGIC. — APPENDIX. 128. Theft is a crime : theft was encouraged by the laws of Sparta ; therefore the laws of Sparta encouraged crime. 129. Every hen comes from an egg : every egg comes from a hen : therefore every egg comes from an egg. 130. Nothing is heavier than platina : feathers are heavier than nothing : therefore feathers are heavier than platina. 131. Meat and drink are necessaries of life : the revenues of Yitellius were spent on meat and drink ; therefore the revenues of Yitellius were spent on the necessaries of life. 132. No evil should be allowed that good may come of it. But all punishment is an evil ; therefore no punishment should be allowed. 133. Repentance is a good thing. But no persons have so much repentance as the wicked ; therefore none have so much good as the wicked. 134. He who bears arms at the command of the magis- trate does what is lawful for a Christian. The Swiss in the French service, and the British in the American service bore arms at the command of the magistrate ; therefore they were doing only what was lawful for a Christian to do. 135. He who calls you a man speaks the truth ; but he that calls you a knave calls you a man ; therefore he who calls you a knave speaks the truth. [This Minor Premise may be pronounced a non vera. But I should prefer to refer the Formula to the Fallacy of Accidents (750, 1057-8). In this view we must regard as accidental, that which is not in the Con- ception when used as a Predicate (195), however essential it may be to the existence of any individual in that genus among the realities of being.] 136. A monopoly of the sugar-refining business is bene- ficial to sugar-refiners ; and of the corn-trade to corn-growers ; and of the silk-manufacture to silk-weavers, &c., &c. ; and thus each class of men are benefited by some restrictions. Now all these classes of men make up the whole community ; therefore a system of restrictions is beneficial to the community. [See 58-60, 748.] 137. “We have seen in a preceding chapter, that naturally no man has any authority over another — his pursuits, his posses- sions, his life or his liberty, except what arises from the pri- EXAMPLES FOE CRITICISM. 395 mary law of nature, self-defence. Now as a State is made up of men, the State can have no authority which each man in the State did not possess before he entered into the body politic. And from this it follows, not only that capital punishment, banishment, and such like punishments are unauthorized and wrong, but that all attempts on the part of the State to pro- mote education, impose oaths, or to encourage religion in any form, or to regulate the institution of marriage in any way, is a tyrannical assumption of rights over man, which power may indeed enable it to enforce,” &c., but nothing can jus- tify. [58.] 138. If the diiference in the various races of men has not been produced by climatic causes, they must each of them have had a separate proto-plastic pair for their progenitors. But these differences cannot have been produced by climatic causes ; therefore the races cannot have sprung from the same parents originally. [See 400 and 412.] 139. Opium is a poison ; but physicians advise some of their patients to take Opium ; therefore physicians advise some of their patients to take poison. 140. Animal food may be entirely dispensed with (as is shown by the practice of the Brahmins and of some monks) : and vegetable food may be entirely dispensed with (as is plain from the example of the Esquimaux and others) : but all food consists of animal food and vegetable- food ; therefore all food may be dispensed with. 141. I have shown, gentlemen, that it is the natural right of all God’s creatures to be free. I have shown that a people having the same tongue, historic recollections and associations, conveniently situated, and existing in sufficient numbers for the purpose, are entitled to a distinct national existence ; and I claim, therefore, not only the sympathy of Americans for my poor and oppressed Hungary, which I know that I shall have, but also their intervention as a nation, and their generous liberality in furnishing the material aid neces- sary to enable us to carry on our struggle, and secure our independence of Austrian rule and despotism. 142. Whilst all other sorts and orders of men conversed with our Lord, never do we hear of any interview between Him and the Essenes. Suppose one Evangelist to have 396- LOGIC. APPENDIX. overlooked such a scene, another would not. One Evangelist was impressed with one scene and a second by another. And thus it must have happened that, amongst the four, at least one would have noticed the Essenes. But no one of the four Gospels alludes to them. The Acts of the Apostles is a fifth body of recollections, but this does not notice them. The Apo- calypse of St. John says not one word about them. St. Peter and St. James in their Epistles entirely overlook them. St. Paul gives no sign that he had ever heard of them. Where- fore we must conclude that there was no sect known by that name, except iu the delusions conjured up by his own igno- rant heart (Josephus). § 6. Examples presenting Questions of Method. 143. All the facts of man’s mental activity may be referred to two classes, Spontaneity and Beflection. But of the two classes, the spontaneous must be first in point of time. For reflection implies volition, and volition implies that the thing chosen is already in the mind, as an object of conscious thought before the choice. Hence it could not have been given in reflection, and must therefore have been given in spon- taneity. 144. “ With God nothing is impossible.” But God can- not make the three angles of a triangle more than two right angles ; therefore some things are impossible with God. [See 4:23, 424.] 145. The religion of the ancient Greeks and Romans was a tissue of extravagant fables and groundless superstitions, credited by the vulgar and the weak, and maintained by the more enlightened, from selfish or political views : the same was clearly the case with the religion of the Egyptians : the same may be said of the Brahminical worship of India, and the religion of Fo professed by the Chinese : the same of the romantic mythological system of the Peruvians, of the stern and bloody rites of the Mexicans, and those of the Britons and of the Saxons : hence we may conclude that all systems of religion, however varied iu circumstances, agree in being super- stitions kept up among the vulgar, from interested or political views in the more enlightened classes. EXAMPLES FOE CEITICISM. 39T 146. A feeble Executive implies a feeble execution of the Government. A feeble execution is but another name for a bad execution ; and a government ill executed, whatever it may be in theory must be in practice a bad government. Hence with a feeble or inefficient executive, a government will always be bad, whatever may be its form or its theory. 147. In the Scriptures it is written concerning the Church, and we see that the Church exists. There it is written con- cerning idols that they shall cease, and we see that they are not. There it is written that the Jews were to lose the king- dom, and we see that the fact is so. There it is written con- cerning heretics that they should exist, and we see that it is so. There it is written also concerning the Day of Judgment. There it is written concerning the rewards of the good and the punish- ment of the wicked. In all things we have found God faith- ful. Will He fail and deceive us in the last ? 148. I maintain that the Fugitive Slave Law is uncon- stitutional, or at least a law not required by the Constitution. “ Slaves ” are not mentioned in the clause requiring the ren- dition of persons held to service in one State escaping into another. The gentlemen [of the South] say indeed that slaves are included in the scope and intent of the law. But I answer so are undoubtedly the Negroes, who have been admitted to citizenship in the Northern States, included in that clause of the Constitution which declares that the “ citizens of each State are entitled to the privileges and immunities of citizens in any of the other States into which they may go to reside.” And they exclude Negro citizens of the Northern States from citizenship in their States, if they choose to go into their borders. 149. St. Paul says, “ Whom God did foreknow He also did predestinate to be conformed to the image of his Son. More- over whom He did predestinate them He also called, and whom He called them He also justified, and whom he justified He also glorified.” But Christians, so long as they are living in the body are not glorified ; therefore they are not among those of whom St. Paul was speaking as predestinated by God to be conformed to the image of His Son. 150. If these acts are valid, the old corporation is abol- ished and a new one created. The first act does, in fact, if it 398 LOGIC. APPENDIX. can have any effect, create a new corporation , and transfer to it all the property and franchises of the old. The two corpora- tions are not the same in any thing which essentially belongs to the existence of a corporation. They have different names and different powers, rights and duties. Their organization is wholly different. The powers of the corporation are not vested in the same or similar hands ; and the act itself provides for the first meeting and organization of the new corporation. It expressly provides that the new corporation shall have and hold all the property of the old ; a provision which would be cjuite unnecessary upon any other ground than that the old corporation was dissolved. 151. It has been noticed that when we see a good act per- formed, we approve the act and feel a sympathy with the agent. It has hence been laid down as a fundamental principle in Ethics, that those actions are good which thus elicit our sym- pathy and approbation. But this is a false criterion. It implies a judgfnenit concerning the act, “ it is good,” and a feeling or emotion, and holds that the judgment is based upon the emo- tion. But the judgment precedes and is the cause of the emotion, for the emotion will always remain the same so long as our estimate of the act remains unchanged. But let us hear something concerning the act which changes our estimate of its character, and the emotion or feeling towards the person who performed it changes also. 152. If a paste be made of wheat flour, boiled in water, and allowed to stand for a few days, there will be in it not only small plants or vegetables, but also small animalculse. Now the boiling would of itself have destroyed all the seeds of vegetables, as well as the ova of any animal existence, so that we are led inevitably to the conclusion that inorganic matter will produce both vegetable and animal life, without the seeds or ova ofi^ preceding plants or animals of the same species ; and if so, the theory of creation, and a personal Creator, is shown to be unnecessary to philosophy, and even unphilosophical. 153. It is said that at death all appearance of life becomes extinct, and every indication of a total cessation of existence is presented. But in the first place we see that parts of the body, as EXAMPLES FOE CRITICISM. 399 hands, feet, &c., may die and decay, and the soul remain en- tirely unimpaired. Again, it is a principle which prevails every where in Nature, that nothing once in existence can be lost. The wood that is consumed in the fire is resolved thereby into its ele- ments, but every particle of it exists somewhere. So with the body at death. But the soul being immaterial is not capable of dissolution, or resolution into constituent elements. Again, we have frequent cases of change of the form of existence, without a cessation of the existence of that whose form is changed. Such changes we have in the foetus in passing from its state before birth to its mode of life after ; in the chick emerging from the shell, and especially in the case of all the metabolians which appear as worms : these go into a state of apparent death, and after a while emerge as insects with wings. In all these cases that which is once in being, continues to exist notwithstanding the changes in its form or state of existence. Hence we may conclude that the human soul will do so likewise at death. 154. Some years since there appeared in the West a dis- ease, which was called the milk- sickness. The following hypo- theses were suggested as accounting for it; namely, that (1) it proceeded from some miasma in the air ; (2) from some pecu- liarity in the ivaier ; (3) from arsenic, cobalt, and other mine- rals in the soil; and finally, (4) that it was owing to some disease in the vegetable productions. As facts it was found : (1) that its appearance was con- fined within narrow limits ; (2) that when it makes its appear- ance among men, there has heen preceding it a disease among the animals, ealled the Slows or Trembles. It is also ascer- tained (3) that the flesh, the milk, the butter, and the cheese made from animals having the Slows, causes the milk-sickness in men [hence its name] ; (4) the disease appears in pastures where there is no water ; and (5) the flesh of animals diseased imparts none of its poisonous properties to the water in which it is boiled ; (6) the disease affects those animals which graze at night, and especially in the woods ; (7) carnivorous animals never have the disease until they have taken it by eating ani- mals already affected ; and (8) females during lactation, cows, sluts, &c., often escape the disease themselves after having 400 LOGIC. APPENDIX. eaten the poison, but communicate it to their offspring. And (9) in those cases in which the flesh of diseased animals had been swallowed aud vomited up soon afterwards, there was either no disease or only very little following. [To be treated as a case of Elimination.] 155. The various systems of pagan idolatry correspond so closely, that they cannot have been struck out independently in the several countries where they have been established, and must therefore have originated from a common source. But if they had a common source, then either one nation must have communicated its peculiar theology to every other people in the way of peaceful and voluntary imitation, or through the medium of conquest and violence ; or all nations must have been assembled together in a single community, and then agreed to adopt the theology in question as a new and recent inven- tion ; or, having received it from the past, and believing it on whatever grounds to be true, they must have carried it with them as from that common centre to all parts of the globe. The first and second are impossible in the nature of things ; therefore all these various systems must have had a common origin. But the third position is nearly as incredible as either the first or the second ; namely, that they should have all agreed in one stupendous system of imposture, professing to believe as divine that which they knew that they had of themselves but recently invented. Idolatry, therefore, must have arisen before the dispersion of mankind, and be a corruption of a tradition that was be- lieved true at au age St) near to the origin of the race (or its restoration after the flood), that its foundation must have been in the truths which were either observed by man, or super- naturally communicated to him at the time of his creation. 156. The fundamental doctrines and institutions of Chris- tianity are not to be held as mere opinions, with regard to which men may innocently differ, and be entitled in their diver- sities to that consideration and respect to which they are enti- tled in matters of mere indifference or uncertainty. For other- wise no persons could be allowed to affirm the truth with that confidence and certainty which its proper influence requires. It follows, moreover, from the wisdom and justice of God, that the evidence of the truth of those doctrines and institutions is EXAMPLES FOR CRITICISM. 401 such that they cannot he innocently rejected. If God is infi- nitely wise he knew what was sufficient evidence, and if He is just He would never require belief and obedience without giv- ing such evidence as would throw the guilt of unbelief upon the unbeliever. And in all other cases, in all departments of thought, we hold to certain fundamental principles with regard to which we allow of no differences of opinion, which we ac- knowledge to be entitled to respect. In Geometry, in Astro- nomy, in Mechanics, every where in fact, we expect the assent of all intelligent and well-disposed men to certain fundamental principles. We do not treat the man who pretends to science, and yet denies that the earth revolves on its axis around the sun, instead of the sun’s moving around the earth as entitled to argument. We regard him as either a fool or a madman. In like manner the Articles of Faith contained in the Apos- tles’ Creed, the Ministry, the Worship, and the Sacraments of the Church, have been held in all ages of the Church as too fundamental in their character, and too fully and obviously revealed in the Scriptures, to be properly regarded as mere subjects of opinion and preference, in regard to which unbelief could be innocent or properlv entitled to favor. § 7. Abstract of Leslie’s Short and Easy Method. “ What you ask and I undertake to accomplish, is to furnish some one topic of reason which shall demonstrate the truth of the Christian Religion, and at the same time distinguish it from the impostures of Mahomet and whole pagan world.” “ If the matters of fact which are recorded in the Gospels be true, the truth of doctrine of Christ will be sufficiently evinced ; for if His miracles be true they do vouch the truth of what He delivered.” “ The same is to be said as to Moses and the Old Testa- ment.” I shall then first lay down such rules as to the truth of matters of fact in general, that where they all meet, such mat- ters of fact cannot be false. And then, secondly , I shall show that all these rules do meet in the matters of fact of Moses and of Christ ; and that they do not meet in the matters of fact of Mahomet and the Heathen deities, nor can possibly meet in any imposture whatever. 402 LOGIC. APPENDIX. I. The Rules are : 1st. That the matters of fact be such as that men’s out- ward senses, their eyes and ears may be judges of it. 2d. That it be done publicly in the face of the world. 3d. That not only public monuments be kept up in memory of it, but some outward actions to be performed. 4th. That such monuments, and such actions or observ- ances be instituted, and do commence from the time that the matter of fact was done. The two first rules make it impossible for any such matter of fact to be imposed upon men at the time when such matter of fact was said to be done. The only alternative, therefore, is that such matter of fact might be invented some time after. But against this the two last rules (3d and 4th) secure us, as much as the two first rules in the former case. II. The matters of fact of Moses and of Christ have all these rules or marks before mentioned, and that neither the matters of fact of Mahomet, nor what is reported of the Hea- then deities have the like, and that no imposture can have them all. As to Moses. He persuaded the Israelites that he had brought 600,000 of them from Egypt and through the Red Sea, that he fed them forty years without bread by a miracu- lous manna. But he could not have persuaded them of these facts if they had not been true, since every man’s senses that were then alive must have contradicted it. So that here are th q first and second of the above-mentioned four marks. For the same reason it would have been impossible for him to persuade them to receive his five Books (the Penta- teuch) as truth, unless they were so ; since in those books he constantly appeals to them as eye and ear witnesses of those things. The utmost that we can suppose then is, that these Books were written in some age after Moses and put out in his name. But in that case it is impossible that the Books should have been received, for they speak of themselves as delivered by Moses, and kept in the Ark from his time, and likewise a copy with the King. Now in whatever age we may suppose the imposture to have been attempted, it was impossible that it should be EXAMPLES FOE CEITICISM. 403 received as truth, since no such copy would have been in ex- istence in the Ark or in the King’s possession, as the Book itself claims. But besides this the Book speaks of laws and ordinances, and of the time and circumstances of their origin, and claims that they had been observed from the time of their origin, as of the Passover, the institution of the Levites, the budding of Aaron’s rod, which was still kept in the Ark, the pot of manna, the brazen serpent, and the Feast of Pentecost. Then there was also the Sabbath, the daily sacrifices, the yearly expiation, the new moons, and other monthly, weekly, and daily remem- brances and recognitions of these things. Here then the third and fourth marks mentioned above are found. But suppose that these things had been practised before the Books of Moses were forged ; that these Books imposed upon the people only in making them believe that they had kept these observances in memory of what had never occurred. Now this supposes that the Jews kept these observances either in memory of nothing, or without knowing what they commemorated. But the observances themselves express the ground and reason of their being kept. Again, suppose the Jews did not know any reason why they kept these observances, and that they were persuaded that they had been keeping them as observances of that of which they had never heard before. Does any Deist think it possible that such a cheat could pass ? Secondly, all these four marks do meet in the matters of fact which are recorded in the Gospel, of our Saviour. For the two first : the miracle of feeding three thousand at one time ; five thousand were converted at one time by what they had seen — miracles that were done publicly and before their own eyes. Then for the two last : Baptism, the Lord’s Supper, were instituted as memorials of what was then done ; and the institution of the Ministry, which has continued by a regular succession to this day, in all which respects the matters of fact of the Gospel narrative as completely fulfil the four rules as those that are related of Moses. III. The matters of fact of Mahomet and the fabled dei- ties, do all want these four marks. First, Mahomet did not claim in his day to have performed any miracles. 404 LOGIC. — APPENDIX. Secondly, those that are told of him want the first two rules ; they were not performed in the presence of any one, and we have only his word for them. The same is to be said of the fables of the Heathen gods. It is true that the Heathen deities had their priests. They had also feasts and games, and other institutions in memory of them. But all these want the fourth mark, they were not instituted at the time of the occurrence of the events which they claim to commemorate ; and their priests were not ap- pointed by the gods, but only by others in honor of them. And therefore these orders of priests are no evidence to the truth of the matters of fact which are reported of their gods. IV. Now to apply what has been said. You may challenge all the Deists in the world to show any action that is fabulous, which has all the four rules or marks before mentioned. No, it is impossible. And (to resume a little what has been spoken of before) the histories of Exodus, and the Gospel, never could have been received, if they had not been true ; because the institution of the Priesthood of Levi, and of Christ ; of the Sabbath, of the Passover, and of Circumcision ; of Baptism, and of the Lord’s Supper, &c., are there related as descend- ing all the way down from those times, without interruption. And it is full as impossible to persuade men that they had been circumcised or baptized — had circumcised or baptized their children — had celebrated passovers, sabbaths, sacra- ments, &c., under the government and administration of a cer- tain order of priests, if they had done none of these things, as to make them believe that they had gone through seas upon dry land, seen the dead raised, &c. And without believing these, it was impossible that either the Law or the Gospel could have been received. § 8. Mr. Webster’s Argument in the Girard Will Case. This Will devises a certain sum of money to be appro- priated to the erection and support of a College (10).* The first question is whether this devise can be sustained * These numbers in parentheses refer to the page in the printed speech, from which the statements preceding them are taken. EXAMPLES FOR CRITICISM. 405 otherwise than as a charity. If the devise he a good limita- tion at law, if it require no exercise of the favor which is bestowed upon privileged testaments, there is already an end to the question — this point is conceded. The devise is void according to the general rules of law, on account of its not mentioning the persons to whom the be- quest is made. The bequest must stand then, if it stand at all, on the pecu- liar rules which equitable jurisprudence applies to charities. But I maintain that neither by judicial decisions, nor by correct reasoning on general principles, can this devise or be- quest be regarded as a charity; (11) because, It is derogatory to the Christian Religion. It tends to weaken men’s reverence for that Religion, and their conviction of its authority and importance ; and, there- fore, it tends in its general character to mischievous and not to useful ends. The College is founded to promote infidelity, and a gift or devise for such objects is not a charity (12). The object of this bequest is against the public policy of the State ; therefore the devise ought not to be allowed to take effect. These are the two propositions which it is my purpose to maintain on this part of the case (12). The Will excludes all Ministers of the Gospel from the College (13). There is no Christian charity that excludes the Minis- try (16). It has so been understood from the time of Constantine down to our own (16). The opening counsel admitted that there is no charity without Christianity (19), and I maintain that wherever the authority of God is disowned, the duties of Chris- tianity derided, and its Ministers shut out, there can be no charity (19, 20). He who rejects the ordinary means of accomplishing an end means to defeat that end itself, or else he has no meaning ; this is true even if the means be but of human appointment, althpugh the end rested on divine authority. But if the means be of divine authority also, then the rejection of them is direct rejection of that authority (30). 406 LOGIC. — APPENDIX. But nothing is more certain in Christianity, than that the Author of the Christian Religion Himself did appoint a Chris- tian Ministry. He who does not believe this cannot believe the rest (31). This Ministry have continued to our day, and gone over the whole world performing their work. Nowhere has any part of the globe been Christianized without the Ministry. It is therefore idle mockery to pretend that that man has any respect for the Christian Religion who derides and rejects its Ministers (32). In the next place this scheme of education is derogatory to Christianity, because it proceeds upon the presumption that Christianity is not the only true foundation, or any necessary foundation of morals. So the world has not thought. The Word of God declares otherwise in the Decalogue (34). Christ taught otherwise (35). Reason and human nature teach otherwise (35, 36). Again, the Will excludes the observance of the Christian Sabbath. But the Christian Sabbath is a part of Christianity. This is admitted by all Christians (37), and the Will excludes the means for observing the Sabbath (37, 38). And where the Christian Sabbath is not observed, there is no public worship of God. But the reasons assigned for the exclusion of Christianity from the College, are still more derogatory to Christianity. They are that the evils resulting from the diversity of opinions and sects, is greater than the good which Christianity itself produces ; whence he infers that we should cut up Chris- tianity by the roots (42). But this mode of reasoning, if it were allowed, would destroy men’s social relations and all human institutions (46, 47). But there is a settled policy of the State of Pennsylvania ; this is not denied ; and Christianity is a part of that policy. Any school or system of education which is contrary to that policy, cannot be sustained by the State (65). The Courts of Pennsylvania have declared that a charitable EXAMPLES FOE CRITICISM. 407 bequest which counteracts the public policy of the State can- not be sustained (67). [The case of Methodist Church vs. Remington and the 8th of Johnson, p. 291.] § 9. Mr. Dana’s Argument in the Ellsworth School Case. This was a suit brought by Laurence and Bridget Donahoe against Richards and others, Superintending Committee of Schools, claiming damages of the Committee for having ex- cluded the Plaintiffs from the benefit of the common schools, by making the reading of the Bible, in the common English Version, obligatory upon all the pupils. The Plaintiffs being Roman Catholics could not comply, on grounds of conscien- tious scruples. This is a novel suit ; there is no one like it in the Reports. The general principle of law is, “ that a public officer exer- cising a discretion, judicial in its character, cast upon him by the law, is not liable to private actions for damages, unless he acts in bad faith or from malice.” But in this case it is not pretended that there was malice or bad faith (6). By the constitution and laws of Maine it is the duty of the Committee, “ to direct the general course of instruction, and what books shall be used in the respective schools.” In the exercise of this authority, the Committee continued the use of the Bible in the common English Version (7). By authority of the State also they have power to expel from any school, any pupils who shall not comply with the regulations which they have made (7). Now the point whether the Defendants in this suit are lia- ble has never been decided. But in the case of Wheeler vs. Patterson, 1 N. H. 88, it was decided that Selectmen of a town, were not liable for refusing a man his privilege of voting, even though they were wrong in their act, “ so long as their motives are pure and untainted with fraud and malice.” In the case of Griffin vs. Rising, 11 Met. 339, it was held that Assessors were not liable for refusing to tax a man, al- though he lost his vote thereby, on the ground that they “ are 408 LOGIC.— APPENDIX. exempted from liability for damages when acting with in- tegrity.” In Allen vs. Blunt, 3 Story 141, it was held that, “ where a particular duty is confided to a public officer, to be exercised by him at his discretion, upon an examination of facts, of which he is made the appropriate judge, his decision is con- clusive.” In 7 Howard 89, and 12 Howard 390, it was held that the commander of a ship was not responsible for the punishment of a marine, though he were innocent, so long as he did it not from malice, and that he was not responsible for error of law, or in his judgment of facts if he acted in good faith. All these cases are analogous to the one before the Court. The only exception is the case of Lincoln vs. Hapgood. This decision, however, has been overruled. But not only are the defendants not liable for damages in this suit. The continuance of the use of the Bible is a rea- sonable exercise of their discretionary power. It has always been used in the schools of Maine. The Defendants are obliged by law to see that the princi- ples of morality and all the virtues shall be taught in the schools. But how can principles of morality be taught except on the basis of religion ? A system of morality not founded on religion is not morality, but only a system of self-interest. The objection however is not, they say, to the Bible, but to our English Version of it. But “ great portions of the translation were made by men in the bosom of the General Church before the Reformation.” Testimony to its accuracy has been borne by learned men of the Roman Church. As a fountain of pure idiomatic English it has no equal in the world. From it we derive our household words. Hence as a preparation for life, an acquaintance with the common English Bible is indispensable, while the Romish Version is un-English. But the effect of this objection is to exclude the Bible altogether. Each denomination has a translation, or at least prejudices and peculiar views of its own. If one is to insist on his version, others will ; and all will be excluded. The question, therefore, is whether the Bible shall be read at all or not. EXAMPLES FOE CRITICISM. 409 It only remains to consider the constitutional objections against the law under which the Committee acted. The power to regulate schools and determine what studies shall be pursued, and what books read, must be lodged some- where. The Constitution of Maine gives the Legislature power “ to make and establish all reasonable laws and regula- tions for the defence and benefit of the people, not repugnant to the Constitution of Maine, or to that of the United States.” And if this power to select books, and suspend or refuse chil- dren for disobedience, were not expressly given in the Consti- tution, it would be implied in the necessity of the case (Sher- man vs. Charlestown, 8 Cush. 161 ; and Spear vs. Cummings, 22 Pick. 223). It is said that the schools are public, and that all resident tax-payers have a vested right in them. But this right must be enjoyed subject to restrictions and limitations, necessary for the good and rights of others. This does not subject one denomination to another, but the choice of a few to the good of the many. The only constitutional question worthy of attention, is that which arises from the clause which declares that “ no one shall be hurt, molested, or restrained in his person, liberty, or estate for his religious opinions.” This clause was intended to guard against persecution, directed against person or property. But there is no such persecution in this case ; whatever inconvenience may have been suffered, is the incidental and indirect consequence of the opinions which the Plaintiffs choose to hold. But if they were “ hurt or molested,” in the sense of the Constitution, still the act of the Committee is not unconstitu- tional. It is a constitutional provision, for instance, that no man’s property shall be taken for public uses without compensation. And yet the Legislature has full power to regulate the manner in which men shall use and enjoy their property, so as to pre- serve the rights of the public. In this exercise of legislative power, a man’s property may sometimes be much diminished, or even destroyed, and he have no remedy. In the Warren Bridge case it was established that the State may impair or destroy the value of an existing franchise for the public good, and that no compensation need be made, 18 410 LOGIC. APPENDIX. if it be not confiscated or abolished. The daily making of highways, railroads, and canals for the public good, is con- stantly impairing the value of some private property, and in some cases totally destroying it, and yet no compensation is made. In the case of Tewksbury it was held (11 Met. 55) that the State might prohibit Mr. T. from taking sand from his own beach. So in Alger’s case (7 Cush. 53), burials in cities may be prohibited without compensating the owners of vaults for their loss, however costly or valuable they may have become. The Sunday laws also are held to be constitutional, although the Jews, by reason of their religious profession, lose one sixth of their working life, and are “ hurt and restrained in their liberty and estate,” and put to an inequality with Christians. The Constitution prohibits religious tests as qualifications to office. Y et all judicial officers are required to administer oaths, although the Quakers regard the taking of oaths as un- lawful. Hence we must conclude that the power of the Committee is not rendered unconstitutional, by the mere fact that it inci- dentally operates to the disadvantage of an individual who, by his opinions or preferences, has put himself in opposition to the laws of the land and the acts of its legitimate authorities. INDEX OF SUBJECTS AND OF THE TECHNICAL TERMS OCCURRING IN THE WORK. Abscissio Infiniti 241, its uses 241, 242. Absolute truth, proved only by Demonstration 325. Abstract, knowledge of the, subse- quent to that of the concrete 361. Abstract Terms explained 14. Abstraction what 215. Acategorematic Terms 13. Accidents separable and insepara- ble 19, predicated of all subjects 56, Fallacy of 191. Accidental Properties may be- come Formal 222, may become Material 284, may become Essen- tial 310. Achilles and the Tortoise, sophisms of 235 n. Acquisition of knowledge begins with the individual and concrete 361. Addition, the Principle of 234. Adequacy of Propositions 55. Adjectives, their logical force 48. Affirmation, grounds of 102. Affirmative Judgments classify their subject 54, how related to Negative 61, do not distribute the Predicate 67, substitution of terms in 76. Agassiz Prof, view of Classification and Induction 312 n. Aldrich’s account of the Predica- bles 19 n. Algebra, a series of Methods of In- vestigation in Discrete Quantity 234. Alternate Conceptions 15. Alternate Species 27, used as subjects 56, constitute coordinate terms in Disjunctive Judgments 100 . Amotion of a Proposition, what 172 n. Ambiguous Middle what 189, vari- ous forms of 190. Ampere’s Classification of the Sci- ences criticised 340. Analogous Spheres 20. Analogy 33 and 249 n., proved by Affirmative Premises in the 2d Figure 124, as a Method of In- vestigation 249, Aristotle’s and Whately’s definition of 249 n., stops short of an Induction 257, its use 257-259, argument from 319, its value 320, as a means of removing antecedent objec- tions 321. Analysis, what 215, different kinds of 215, proximate and ultimate or last 216, must precede synthe- sis 218, as a Method of Investi- gation 243, of conceptions and of 412 INDEX. things, logical and physical 243, certainty of its results 244 et seq„ enables us to see Implied proper- ties 248. Analytic Method of Teaching 362, based upon the Natural Classifi- cation 363. Analytic Judgments 203, do not add to our knowledge 203, a priori 206. Antecedence not Causality, though implied in it 259, proved by In- duction 260. Antecedent in a Conditional Judg- ment 91, ground of the truth of the Consequent 171. Antecedents in Nature, simple and complex 264. Antecedent Probability and im- probability with reference to dif- ferent totalities 89. Antithetic Terms 41. Apodictic or Necessary Judgments 60, their relation to the. Assertives as used in Formula 63. Appeal to facts 303. Approach progressive 324. Argument analyzed 7, from Con- ceptions 281, from Principles 290, from Authority 293, from Facts 303, by Induction 304, by Exam- ple 316, by Analogy 319, by con- currence of Circumstances and Testimony 322, by Progressive Approach 324, Argumentnm ad Ig- narantiam 326, from Exceptions 330, ad Hominem. 336, ad Veream- diam 336, ad Invidiam 337, distin- guished from Assertion 374, and Artifices 374. Aristotle the founder of Logic 1, attributes its origin to Zeno 2, his Categories 34 n., his Dictum 124 n., his list of Sophisms or Fallacies 184 n., his true Conclusion from false Premises 187 n., his defini- tion of Induction 249 n. and 304 n., his Notions 311, Classifi- cation of the Sciences 339, Meta- basis 379 n. Arithmetic a series of Methods of Investigation in Discrete Quan- tity 234. Article not used before words de- noting Genera 52. Artifices to be distinguished from Formula and from Fallacies 192, from Arguments 374. Arts, the Faculty of 339. Assertion to be distinguished from Argument 374. Assertive Judgments 61, their re- lation to the Formula 63. Authority proved by Testimony 231, Arguments from 293, our only ground of proof in some cases 294. Average, a Method of Investigation 237, its various uses 238, 239, 240. Axioms 290 note , how proved 278. Bacon’s Experimentum Crucis 273, Classification of the Sciences 340. Barbara, Syllogism in 119, all Syl- logisms whose names begin with B may be reduced to 127. Baroko 120, reducible to Barbara 127, 128, to Ferio 129. Beautiful, the Idea of the, as de- termining Methods 199, its rela- tion to the Useful 201. Begging the Question, Fallacy of 186. Boicardo 121, may be reduced to Barbara 127, 129, to Darii 129. Botany cited as an illustration of the Progress of Scientific Classification 358. Bramantip 122, may be reduced to Barbara 127, 128, peculiarity of in the resolution of Sorites 141. Butler Bishop, Method of in the Analogy 321, 334. Calculation, Methods of in Dis- crete Quantity 233. Calculus, a series of Investigations in Discrete Quantity 234. Camenes 122, may be reduced to Celarent 127. INDEX. 413 Camestres 120, may be reduced to Celarent 127. Categorematic, terms when said to be 13. Categorics 13, of Aristotle 34 n., of Kant 34 n. Categoric Judgments 44, Pure, Comparative, and Probable 45, make a Classification 50, simple and complex .77, Compound, Co pulative 80, Causal 81, Discretive 81, Conditional 82, Disjunctive 82, Exceptive and Exclusive 83, Com- parative 84. Categorical Syllogisms include three Propositions and three Terms 108, names of Terms and Premises in 108, 109, number and names of 122, indirect conclusions of 123, conversion of 124, Modals in 131, Compound or Sorites 138, Compound Propositions in 149. Causal Propositions 81, are pro- perly Enthymemes 150, how com- pleted 150. Causality something more than Antecedence 259, not proved hy Induction 260, three conditions required 261, often depends upon the Mode of the Substance 263, often depends upon the complex- ity of the Antecedent 264. Cause absolute 29, and effect alter- nate conceptions 30, relative 30, primary and secondary 30, effi- cient, occasional, material, formal, final, and negative 30, transient, permanent, and immanent 32, in Nature only secondary 260, called also Instrumental 261, Substan- tial and Modal 259, must be a substance 261, causa vera and causa sufficiens 262, adequate and homogeneous 263, four kinds of words denoting Causes 264, when to be given in Instruction 365. Celarent 119, all Syllogisms begin- ning with C may be reduced to 1 27. Certainty absolute 211, physical 212, moral 213, in regard to masses of men 213. Cesare 120, reduced to Celarent 128. Chain Syllogism or Sorites 138. Chances favorable and unfavorable 87, in the same and in different Events 165. Circumstances, facts regarded as 215, argument from 322, its pro- per sphere 323. Class-conceptions what 205, of the Creative Mind the basis of Induction 306. Classification implied in all Cate- goric Judgments 50, Principle of extends to more than three grades 51, based upon accidental proper- ties 53, become jests 54, Formula of 146, made at the second ob- servation 221, and a new one at the next 221, the basis of Induc- tion 250, the principle of changes in the progress of science 252, 357, a new one required when the exceptions become numerous 256, not properly based upon variable properties 256, of the Sciences 338, Plato’s, Aristotle’s, and the Scho- lastic 339, Bacon’s, Locke’s, Cole- ridge’s, and Ampere’s 340, Comp- te’s 341, a new one 342 et seq., character of the Primary 356, necessity for the transition from Natural to Scientific 357, test of the perfection of 357, 358, illus- trated from Botany 358. Cognition 7, 9, distinguished from Conception 10. Collective Terms distinguished from General 17, may not be pre- dicated of the individuals 18. Commissions conveying authority how to he interpreted 300. Common Sense, a ground of belief 294. Comparative Judgments 45, do not include the Subject in the Sphere of the Predicate 84, con- tain three terms 85, of seven va- rieties 84-87, conversion of 86, in Syllogisms 151. Comparative Syllogisms, not the 414 INDEX. same as pure Categoricals 151, simple comparatives 152, the con- ditions of their validity 154, in which intensity is regarded as cause 155, of manner, time, place, &c. 156. Comparisons, imply three terms 85, of equality and inequality, and of greater and of less intensity 85, of time, place, &c. 86. Composition, Fallacy of 190. Complex Propositions reducible to simple incomplex 84. Compound Categorical Proposi- tions reducible to simple complex 84. Compound Conditionals 96, 174. Comprehended Sphere always the Subject 111. Comprehending Sphere always the Predicate 111. Comprehension of Terms 14. Comprehensive Quantity deter- mines the intensive 60, of three degrees 60. Comprehensiveness of terms ex- clusiveness of matter 51. Compte’s Classification of the Sci- ences 34 1 . Conception 7, 9, adequate and in- adequate 10, of Ideas, how made adequate 11, of the Impossible 12, the relations of 13, the sphere and matter of 14, matter determines the sphere 15, Alternate 15, dis- tinguished from facts 214. manner of passing from one mind to an- other 216, 347, Analysis of 244, cannot be conveyed from mind to mind as wholes 348, reconstructed by the person receiving it 349, none that cannot be defined 351, Ultimate and Primary 355, imply previous perceptions 356, made distinct by the Essentia, definite by the Differentia 366. Concessions a ground of proof 294. Conclusion, what 7, 107, no af- firmative in the 2d Figure 113, no universal in the 3d 114, quantity and quality of determined by the Premises 115, indirect 123, direct 123, compound 149, true from false Premises, Aristotle’s account of 187 n., when proved 280, as determining wholes in argumenta- tion 375. Concrete, knowledge begins with objects in the 361. Concrete Terms 14. Concurrence of fjacts or of testi- mony, what 322, its value 323. Conditional Judgments 44, imply categoric 45, three terms and two copulas 91, members of 91, depend upon the Sequence 92, compound- ed with Disjunctives 102. Conditional Modals 79, may be- come Differential 136. Conditional Propositions 82, 91, compound 96, continuous 96. Conditional Syllogisms, not all that contain conditional judg- ments are so 171, methods of completing 172, method for find- ing the Sequence 173, may be completed into a categorical 174, with four terms 174, compound 174, continuous 175, with com- pound consequents or antecedents 175. Conjecture, what 218. Conjugation of the Verb as an illus- tration of Definition 354. Connotative Terms 14, how predi- cable 42. Consciousness, a means of Investi- gation 224. Consequent in conditional judg- ments 91, the denial of destroys the Antecedent 172. Construction, object and method of 347. Constructive Method with Condi- tionals 172. Contingent Matter 205, judg- ments in a posteriori 206, in all realities of being 209, how known 210, Analysis as a means of In- vestigation in 244. Continuous Conditionals 96. Continuous Quantity 22, limits INDEX. 415 and terms in 23, 39, axioms of 152. Contradictio in adjectis 3T5. Contradiction, principle of, a ground of affirmation 103. Contradictory Terms 41, how pre- dicable 42. Contradictory Judgments cannot both be false in the same matter 70. Contraries, a means of Investiga- tion 250. Contrariety 33. Contra-position of Judgments 71, by means of Negatives 73. Contrary Judgments cannot both be true in the same matter 70. Contrary Terms 40, how predica- ble 42. Conversion of Propositions 74, sim- ply and by limitation 75, of O 75, of Comparatives 86, of Syllo- gisms 124. Conveying words of, bow to be in- terpreted 299. Coordinate Divisions 25, parts 26. Copula, affirmative and negative 7, its force 48, its effect in pure cate- goricals 49, its form 49, real and designed effect of 50. Copulative Propositions 80, may be resolved into simple Propositions 80, danger of them including er- ror 81. Counting, a method of Investiga- tion 234. Critic the, position occupied by 369. Criticism, principles of, the same as those of Construction 369, starting point of 370. Damascene, St. John, on Analysis 215 n. Darii 119. Datisi 121, mav be reduced to Da- rii 127. Deduction, compared with Induc- tion 276 »., as a method of Proof 290, the method of application of Sciences 291, and of completing Sciences 292, Deductive Judgments, how differ- ent from Intuitive 106. Definition 33, may be predicated of any object 55, used instead of the term 131, analyzes conceptions 349, when adequate 349, 353, verbal and real 350, may be given to all conceptions 351, some difficulties noted 352, Ac- cidental, Physical, and Meta- physical 353, negative, what 353 n., the conjugation of verbs a definition 354, may need to be defined 355, must always refer to the natural classification 359, use of negative in instruction 365 n. Demonstration, popular and strict senses of the word 281, from the force of terms 282, based on ety- mology 283, not used in Contingent Matter 284, 287, the basis of all Sciences 285, 290, gives Universal Conclusions from Individual Pre- mises 286, based upon Hypothe- ses 288. Demoniacal Possessions, how prov- able 227 n. Description, what 34, as a means of conveying conceptions 351, does not furnish the matter for the con- ception 355. Destructive Method with Condi- tionals 172. Devey’s Logic cited 292 n. Diagrams in Mathematics as repre- senting conceptions 207. Dictionaries a Testimony to the meaning of words 232, gives ver- bal definitions. Dictum of Aristotle 124 n., of Lam- bert 125 n. Difference in kind and in degree 32. Differently must bear some rela- tion to the Essentia 51, may be merely relative Properties 351 n., the same in different genera con- stitute Kecurring Species 359, always necessary in Instruction 364. 410 INDEX. Differential, Modals 78, may be converted into Conditional 136. Dilemma 102, seldom needs comple- tion 179, its various forms 179- 181. Dimaris 122, may be reduced to Darii 127. Disamis 121, may be reduced to Darii 127. Discrete Quantity 22, terms and limits of 22, applied to Logical and Continuous 23, terms in 38, gives validity to syllogisms other- wise invalid 152, two axioms of 157, applied to continuous in cate- gorical Syllogisms 158, affords no distributed terms 159, its effect when applied to one Premise only 162. Discretive Propositions 81, in Syl- logisms 150. Disjunctive Judgments 44, imply categoric 45, depend upon the Ex- cluded Middle 97, with four terms 101, compounded with condition- als 102, convertible into condi- tionals 102, comprehensive and divisive 175. Disjunctive Propositions 82. Disjunctive Syllogisms 175, com- prehensive and divisive 176, Syl- logisms not always disjunctive when there is a disjunctive Pre- mise 176, the Major Premise dis- junctive 177, how completed mo- dus tottente pawns, and pownte tol- lens 177, with more than two mem- bers 178, divisive, how completed 178. Disparate Parts 26, do not consti- tute an Excluded Middle 100. Distributer Terms 40, in judg- ments 64, by nature, by signs 65, by position 67. Division 21, of three kinds 24, prin- ciple of 25, coordinate and subor- dinate 26, canons of 28, fallacy of 190, numerical 236, of general subject in teaching 360, into coor- dinate parts if possible 361, into alternate species 361. Divisive Judgments 175. Divisive Principle 25. Divinity, the Faculty ofj in the Uni- versities 339. Each, a sign of a distributed subject in a Proposition 66. Edicts restraining liberty, how to be interpreted 300. Effect and Cause alternate concep- tions 30, immediate and remote, direct and accidental, designed and undesigned 32, investigation of 271, 273, when to be given as an element of Instruction 365. Elimination, when practicable 265, depends upon four axioms 266, first Method of Elimination 267, second and third 268, fourth 269, fifth 271. End, Method supposes one, hut does not furnish it 196, determines the selection of matter in Instruc- tion 367, 369, in determining wholes 375. Enthymemes, what 142, of four kinds 143, with three terms may be completed into Syllogisms 143, with four terms, completed into Sorites 144, may be stated as Con- ditionals 173. Epichirema 148. Epi-syllogism 148. Equality, comparisons of 85, mean- ing of in Algebra 157 re. Essence of an object 16, different senses of the word 16 re. Essentia of a Genus 17, always ne- cessary in Instruction 364, makes the conception distinct 366. Ethnology, cited as an illustration of the principle of classification 357. Exact Sciences, what and why so called 342 re. Example, argument from 316, an induction from a single fact 318, YVhately’s view of the reasoning from 318 re., chiefly confined to moral matter 318, its value 319. Exceptions, becoming numerous INDEX. 417 indicate a faulty classification 256, as a means of refutation 329. Exceptional Modals 78. Exceptive Propositions 83, easily converted into Exclusives 83, in Syllogisms 151. Excluded Middle, what 97, be- tween contradictories and subcon- traries 97, a ground of affirma- tion 104. Exclusion, as a Method of Investi- gation 240, two forms 241, its uses 241, 242. Exclusive Modals 79. Exclusive Propositions 83, easily converted into Exceptives 83, in Syllogisms 151. Experiment, as a means of investi- gation 224. Experimentum crucis 273. Explicative Modals 78. Exposita, what 71. Extension, not predicable of time and space 23 n., incompatible with infinite 23 n. Extremes, in a categorical Syllo- gism 108. Event, in the calculation of chances what 165, distinguished from a fact 214. Facts defined 213, distinguished from Events, Conceptions, and Ideas 214, phantasms and fancies 215, as circumstances 215, first known as complex wholes 215, distin- guished from inference 230, how used in Arguments 303, distin- guished from laws 303. Faculties, University distribution of 339. Fallacies, defined and classified 182, in form, in matter, in diction, and extra-logical 183, effect of 183, Aristotle’s list of them 184 »., Ignoralio Elenchi 185, Petitio Prin- cipii 186, Ambiguous Middle 189, Division and Composition 190, of Accidents and of Quid 191, post hoc ergo propter hoc 259 n., Contradic- tio in adjectis 375, Metabasis 379 n. Fancies, distinguished from facts 215. Faults, distinguished from Fallacies 183. Felapton 121, reduced to Ferio 128. Ferio 119, all Syllogisms beginning with F may be reduced to 127. Fesapo 121, may be reduced to Fe- rio 127. P’estino 120, may be reduced to Fe- rio 127. Figure, of Syllogisms what, and the differentia of each 110, the 4th Figure valid, though unnatu- ral and inelegant 111, the 1st and 4th depend upon the same prin- ciple 112, the 2d 113, the 3d 113, the 1st has six valid and four use- ful Syllogisms 119, the 2d has also six valid and four useful 120, the 3d Figure has six 121, the 4th Figure has five 121, the 2d Figure proves Analogy by affirmative Pre- mises 124, the peculiarities of omitted in general discussion 130. Final Causes, what 31, a basis for Induction 313, imply a Creative Intelligence 314. Form, distinct from the matter 5, of judgments 44. Formal Properties 210, imply Mo- dal 222, an accidental may be formal 222, the basis of classifica- tion for the purpose of Induction 249, 250, the basis of Analogy as a Method of Investigation 258. Formula 7, of Classification and In- duction 146, of the cumulative Argument 147. Fresison 122, reduced to Ferio 128. General Subject in instruction, its division 360. General Terms, how distinguished from Collective 17. Genus, a sphere 17, predicable in Quid 19 n., Summum and Proxi- mate 20, what may be predicated of 55. Giving and Conveying words of, how to be interpreted 299. 18 * 41 S INDEX. Goclknian Sorites 140, 138 n. Goon, the Idea of, as determining Methods 199. Hamilton Sir William, his new Me- thod of Notation and Quantifica- tion G7 n., see also Ike Preface, his Unfigured Syllogism 111, his opii ion of Induction 308 n. History, the facts of, in what sense a field for Induction 311. Hypothesis, what 218, use of in investigating modal properties 223, in general 226, used in Demon- stration 288, legitimate use of in contingent matter 289. Hypothetical Judgments, why so called 45. Ideas, furnished by the Reason 11, which determine Methods 198, dis- tinguished from facts 214, how transferred from one mind to an- other 347, of Totality 370 et seq. Identical Judgments 48. Identity of objects perceived 9, explained 33, principle of, a ground of affirmation 103. Ignoratio Elenciii not a mistake in Logic 185, why so called 185, when most likely to occur, and the effect of 185. Illicit Process of the Minor and of the Major 115, 116. Immediate Inference explained 69. Immortality of the Soul, Bp But- ler’s method of reasoning about 321, 334. Impertinent matter always to be rejected 367. Implied Properties 209, learned by Observation 222, by Measure- ment 233, by Analysis 248. Impression often made without ar- gument or Instruction 373. Improbability, what 88, not the same as the probability of the op- posite 89, nor as the mere want of probability 90. Indifferentia, what properties so called 20. Indirect Conclusion in pure cate- gorical Syllogisms 123, must he used instead of the direct in cer- tain cases 141. Individuals, what 19, absolute and relative 27, necessarily included in a Species 53, what may be predi- cated of 55. Individual Judgments 60, formed before Universal 330 n. Indefinite Judgments, what 61, how related to the Negative 63'. Induction, the Formula of 146, as a Method of Investigation 249, Aris- totle’s definition of 249 n., three classes of cases 251, three steps in the first class 253, second class 254, third 255, compared with Deduc- tion 276 »., as a Method of Proof 303, implies the Uniformity of Na- ture 304, and a Creative Mind 306, completed into Syllogism 308, be- longs to physical matter 309, does not extend to accidental proper- ties 310, approaches Demonstra- tion 311, limited to properties im- plied in the original class-concep- tion 3 1 1 , by means of Final Causes 313, implies an Intelligent Creator 315, how far applicable 316. Inequality, comparisons of 85. Inference Immediate, from subal- terns 70, from universals 70, from contradictories 70, from Exposita by permutation 76, by the sub- stitution of terms 77, from judg- ments in Necessary Matter 211. Infima Species 20. Infinite, a term in Logical Quantity 23, incompatible with extension 23 n., meaning of the word 36 n., in Discrete Quantity 39, as a Pre- dicate, how proved 279. Intensity, regarded as a cause 86, in Syllogisms 155. Intensive Quantity, determined by the Comprehensive 60. Interpretation, necessity for 297, Rules of 297. Intuitive Judgments 106. Instruction, Methods of, how far INDEX. 419 belong to Rhetoric 347, determin- ed by the conditions of conveying conceptions 348, two Methods of 362, division of matter in refer- ence to 3G4, order in 366, End as determining the selection and order of the matter 367 et seq. Investigation the method of find- ing Predicates to given subjects 219, of accidental and modal pro- perties 222, of implied 223, Modal by means of hypotheses 223, be- gins with individual objects 225, de novo and following another 226, use of hypotheses in 226, in Dis- crete and Continuous Quantity 232, by Average 237, by Exclusion or Abscissio 240, by Analysis 243, by Induction 249, of Causes by Elimination 259, leads to a first and absolute Cause 260. Jests are hut ludicrous classifica- tions 54. Judgment 7, defined 43, form and matter of 44, scope of 44, of three kinds 44, Categoric, Conditional, and Disjunctive 44, Hypothetical 45, Comparative and Probable 45, formation of 47, resolvable into terms and terms with modals 47, Identical 48, Individual, Parti- cular, and Universal 60, quality of Affirmative, Negative, and In- definite 61, Modality of, Problem- atic, Assertive, and Necessary 61, four cardinal A, E, I, and O 62, Negative with undistributed Pre- dicates 67 n., every judgment im- plies another 69, opposition of 70, Permutation or contra-position of 71, Comparative 84, Probable 87, Conditional 91, Disjunctive 97, Intuitive and Deductive 106, An- alytic and Synthetic 203, in Ne- cessary blatter 205, a priori and a posteriori 206, when incapable of proof 277, Individual before the Universal 330 n., Universal ex ne- cessitate rei and de facto 330 n. Kant, his Categories 34 re., his Syl- logisms of the Understanding 69. Lambert, Iris dicta of the Figures 124 n. Later-first, a fault in Method 197. Latimer Bp., his exposition of the Fallacy of post hoc ergo propter hoc 259 n. Law, the Faculty of 339. Laws restraining liberty, how to he interpreted 300, distinguished from facts 303. Length, a secondary property 23 re. Liberty, laws restraining, how to be interpreted 300. Limits, doctrine of, in Progressive Approach 325. Loci, what 219 re. Locke’s classification of the Sci- ences 340. Logic defined 1, later than Philoso- phy 1, its necessity 2, holds the second place in Philosophy 3, the science of deductive thinking 3, a Science 3, in what sense an Art 3, its relation to Rhetoric and Dia- lectics 4, 347, not to he regarded as a means of discovery 4, Formal or Analytic 5, Rational 5, Applied 6, presupposes a knowledge of the Matter 6, proposes no new way of reasoning, but explains the old 6. Logical Division 25. Logical Quantity 22, limits and terms in 23, 39, of three dimen- sions 59. Major Premise in categorical Syl- logisms, what 108, called the “Principle,” not usually expressed in Induction 275 re. Major Term by nature and by loca- tion 108, change of its Modal 135. Material Properties 209. Mathematics deals with Concep- tions only 244 and note. Matter of Arguments 5, of a Con- ception 14, determines its Sphere 15, of a Genus and of a Species 21, accidental 21, of judgments 44, 420 INDEX. of conditional judgments 91, as determining Methods 202, Neces- sary 204, Contingent 205, Neces- sary and Contingent in the same Conception 200, Moral 212, of a Conception divided with reference to the order of treatment 364, im- pertinent to be rejected 367, new matter not to he introduced by the critic 374. Maxims 210 n., how distinguished from Axioms 290 n. Measurement, as a Method of In- vestigation 232, a means of inves- tigating implied Properties 233. Mediate Inference, always implies a Middle Term 107. Medicine, Faculty of 339. Members of conditional judgments 91. Memory depends upon Method 367. Metabasis, fault of 379 n. Metaphysics, one branch of Philo- sophy 3. Method, included in Logic 1, distin- guished from the Matter and the Form of Arguments 5, Method in general 194, gives unity and im- plies capacity 195, order implied in 196, the Ideas that determine 198, Matter as determining 202, of Investigation 219, Observation and Testimony 223, Measurement 232, Counting and Calculation 234, in Mathematics 234, Average and Exclusion 237, Analysis 243, In- duction and Analogy 249, of find- ing causes (Elimination) 259, of Proof 275, Demonstration 281, Deduction 290, of appeal to Au- thority 293, of appeal to Facts 303, Induction 304, by Example 316, by Analogy 319, by concurrence of circumstances 322, of Progres- sive Approach 324, of Refutation 328, Direct 329, Indirect 333, In- direct Methods always imply Di- rect Methods to the same result 335, Personal 336, of 1 Historic determined by the Idea of the Useful 347, of Instruction for the most part Rhetorical 347, Ana- lytic and Scientific in teaching 359, 362, of Criticism 369, how criticised 372. Middle Term, its office in Syllo- gisms 107, 110, must be once dis- tributed 1 14, the law of changing its Modal 134, may be stated indi- vidually 146, the necessity for so stating it 147, may be a disjunctive judgment in one Premise 176, am- biguity of 189. Mill denies the reality of necessary matter 205 n., opinion on the Uni- formity of Nature 305 n. Minor Premise in Categorical Syl- logisms 108, called “ the case,” “ the example,” or “ instance,” 109. Minor Term, by nature and by po- sition 108, the real subject of the Syllogism 108, change of its Mo- dal 135. Modal Properties 210, investi- gated by observation 222, by means of Formal Properties 223, 225, by Induction 251, 252, In- duction commencing with 254. Modality of Judgments, three va- rieties of 61. Modals 77, Explicative and Differ- ential 78, Exceptional, Exclusive, Conditional, and Protensive 79, when omitted and when inserted in the course of an argument 132- 135, may be transferred from one term to the other 136, protensive Modals in Syllogisms 137. Modus (aliens and ponens 172, tollente ponens and ponenle tollens 177, po- nente Wiens, when valid in disjunc- tive Syllogisms 178. Moods oi Syllogisms 115, not all valid 115, 116. Moral Matter 212, does not admit of Induction 309. Multiplication, a Method of Addi- tion 236. Name of any thing may be predi- cated of that thing 55. INI) MX. ±21 Nature, uniformity of, what 304, how used in Induction 308, ab- normal cases in 316. Necessary or Apodictic Judgments 60 . Necessary' Matter of the subject included in the scope of the Judg- ment 58, in relation to Method 204, Mill and Whe well’s contro- Y’ersy about 205 re., and contin- gent in the same conception 206, Analysis of 245. Necessity, Physical and Moral 212. Negative Definitions, ivliat 353 re., use of in Instruction 365 re. Negative Judgments, what 61, al- Yvays distribute the Predicate 67 and note, substitution of terms in 76. Negative Terms, complements of the Positive 36, hut few 37, dis- tinction between them and Priva- tive unimportant 37, in Discrete Quantity 38, in Continuous Quan- tity 39. Non tali pro tali, Fallacy of 188. Non vera pro vera, Fallacy of 188. Numerals 38. Numerical Division 24. Oaths, how to he interpreted 299. Obiter Dicta, how interpreted 302. Objects of Thought, possible, im- possible, and real 12, perceived as wholes 47, classified as soon as we have more than one 221. Observation, a Method of Investi- gation 220, difference between and Testimony 221,. as a Method of Investigation 223. Omission, as an element of Method 198, not testimony 229, in In- struction 368. Opinion, as distinguished from Truth 217, not provable by Testimony 296. Opposition of Terms, relative, con- trary, subcontrary, and contradic- tory 41. Order, as an element of Method 194, 196, five Canons of 197, of treatment in Instruction 361 et seq. Ordinals 38. Ostensive Reduction of Syllogisms 128. Pantheism, results from denying the limited nature of Positive Spheres 36 re. Pappus’ account of Mathematical Analysis 215 re. Parables, how to be interpreted 301.. Particular Judgments 60. Particular Affirmative Judg- ments distribute none of their terms 68. Particular Negative Judgments distribute their Predicate 68. P arts, Disparate 26, assumed as ivholes 26, subordinate 26, to be criticized only in relation to their Yvholes 372. Perception, an instantaneous act 9. Permutation of Judgments, what 71, by means of Negatives 73. Personal Refutations 336. Petitio Principii, Yvhat 1S6, why so called 186, several forms of 187, 188. Philosophy' before Logic 1, neces- sitated it 1, divided into three branches 2. Physical Division 24. Plato divided Philosophy into three brauches, 2, 338, his use of the Yvord “ Ideas” 311. Plausible, the Idea of, as deter- mining Methods 199 re. Pleasure, the Idea of, as determin- ing Methods 199. Porphyry, his account of the Pre- ■ dicables 17 re., 19 re. Post hoc ergo propter hoc, Fal- lacy of 259 re. Posit to, a Proposition, what 172 re. Positiy'e Terms 35, imply nega- tives 36, in Discrete Quantity 38, in Continuous Quantity 39. 422 INDEX. Predicables 13, as reckoned by Porphyry 17 Aldrich’s account of 19 n. Predicate 7, usually placed after tlie Copula 4G, used with refer- ence to the matter of the Con- ception 47, what words may be so used 47, used for the matter of its Conception 50, must include the necessary matter of the Subject 58, matter expressed in 224, found by the Methods of Investi- gation 219. Premises in Categorical Syllogisms 108, both negative 112, the rela- tion of their quantity and quality to rest of the Conclusion 108-117, affirmative give no negative Con- clusion 117, their order unimport- ant 126, one sometimes suppressed 1 42, a universal may not be sup- plied when a particular will an- swer 143, compound in Syllogisms 149, Premises unduly assumed, various forms of 188, may be con- clusions of preceding premises 280, to a Conclusion, whatever is ne- cessary to it 308. Primary Properties, their relation to the Secondary 23 n. Privative Terms complements of the Positive 36, used instead of Negatives 73. Probability, its nature and the method of estimating it 87, and improbability, complements of each other in unity 88, antece- dent 89, exact value of 89, ap- proximate 90, general and special 91, dependent 162, in the same and different events 165, Alge- braic formula for its computation 170 n. Probable Judgments 45, 87. Probable Syllogisms 157, method of notation in 160, how many at least 160, at most 161, when the probabilities are dependent upon each other 162, when they are independent 165, methods of cal- culating 168, 169. Problematic Judgments 60, not used in the Formulae 63. Progressive Approach, the argu- ment of 324, first class of cases 324, second class 325, often more satisfactory than Demonstration 326. Proof, how different from Investi- gation 275, Direct 276, requires two conditions 277, Indirect 278, of Negative Predicates 278, of Negative Copulas 279, Demon- stration 281, Deduction 290. Properties, what 13, belong to more than one substance 13, Es- sentia 17, Differentia 18, Acci- dental 19, when called Qualities 19 n., separable, inseparable, and individual 19, as primary and secondary 23 «., material and im- plied 209, formal, modal, and va- riable 210, not distinguished into kind at the first observation but at the second 221, Formal first distinguished 222, Formal and Implied not distinguished by In- vestigation 222, Implied learned by measurement 233, by analysis 248, of classes investigated by Induction 251, by Analogy 257. Propositions in an argument 7, contain two terms and a copula 46, permutation of 71, 73, con- version of 74, simple and complex 77, Compound, Express, and Im- plied 80, with Negative Predi- cates, how proved 278. Protensive Modals 79, their effect upon the Formula 136. Protensive Quantity 59. Pro-syllogisms 148. Psychology, a branch of Philoso- phy 2, some knowledge of requi- site in Logic 8. Qua, as indicative of alternate con- ceptions 58 n. Quadrivium the, what 339. Quale, predication in 19 n. Qualequid, predication in 19 n . INDEX. 423 Qualities, properties when so called 19 n. Quality of Terms 34, of Judgments 61, of Propositions changed by means of Negatives. Quantity, what 21, of three kinds, Logical, Continuous, and Discrete 22, of terms 38, of judgments 59, of three dimensions 59, and three degrees 60, in conditional judg- ments 96, when to be given in Instruction 364. Question distinguished from the judgment 43, its relation to the Conclusion 109, mistaking the, fallacy of 185, begging the, fallacy of 186. Quid, predication in 19 n., (dictum secundum quid ad dictum simpli- citer) fallacy of 191. Realities of Being and of Truth, how distinguished 12. Reasoning from Cause to Effect 271, called also reasoning a priori 271 7i., from Elfect to Cause 272. See Arguments. Recurring Species 359. Reductio ad Absurdum, as a Me- thod of Refutation 333. Reductio ad Impossibile 128, may be applied to all Syllogisms 129. Reduction of Syllogisms 127, os- tensive and ad impossibile 128. Refutation 328, three Methods 329, Direct 329, by Exception 329, of a Particular Judgment 330, of the reasoning instead of the Proposi- tion 331, Indirect 333, Personal 336. Relative Judgments 45. Relative Terms of two kinds 40, imply and explain each other 40. Religion, Method of Investigation in 231, proof in Matters of 293. Remembering, ease of, depends upon Method in Instruction 367. Residual Phenomenon 269, how to be disposed of 270. Rhetoric, its Methods determined by the Idea of the Useful 347. Scholastic classification of the Sci- ences 339. Sciences become more deductive as they advance 292, classifications of 338. Scope of Judgments 44, what pro- perties of the Subject included, in 58. Secondary Properties, their relation to Primary 23 n. Senses, the external, as Means of Investigation 224. Separable Accidents 19, not in- cluded in the Scope of a Judg- ment 58. Sequence in Conditional Judgments 92, may be stated as a Categorical Proposition 92, of various kinds 92-94, complex Sequence 94-95. Similarity 33. “ Some” not always indicative of an undistributed Term 64. Sophisms or Fallacies, Aristotle’s list of 184 n., of Achilles and the Tortoise 235 n. Sorites, the usual form of 138, the Goclenian 138 n., may he made from any Syllogism 139, resolv- able into Syllogisms 140, cautions in regard to their formation 139. Species, what 18, predicates in quid 19 n., Infima 20, what may be predicated of 21, 55, parts of a Logical Division 27, Alternate 27, Recurring 359. Specific Terms 35, distributed 40. Spendthrift’s Fallacy 191, rather a fault in criticism 370. Sphere of Conceptions 14, deter- mined by the Matter 15, Coinci- dent and Opposite 19, Analogous 20, of positive, negative, and pri- vative terms 36, 37. Stewart Dugald, his opinion of the classification of the Sciences 340. Subaltern Genera and Species 20, Judgments 70, inferences from 70. 4 : 24 : INDEX. SUBCONTRARY' JUDGMENTS 70, may both be true in the same matter, but not both false 71. Sdbcontkauy Terms 41, how pre- dicable 42. Subject 7, placed before the Copula 46, used in reference to the sphere of the Conception 47, what words may be subject 47, used with re- ference to its sphere 50, classified in all affirmative judgments 54, distributed in universal judgments 68, given by its sphere or by its matter 220, general and individual in Instruction 360. Subordinate Divisions 26, parts 26. Substance, what 13, must have se- veral properties 13. Substitution of Terms in affirmative propositions 76, in negative 77. Subtraction, the principle of 236. Sufficient Reason, a ground of affirmation 103. Syllogism analyzed 7, divided into classes 106, pure categoricals 110, Canons testing the validity of 1 17, number and names of those that arc valid and useful 122, their names indicative of the means of their conversion 126, complex ca- tegorical 131, protensive modals in 136, compound or Sorites 138, any Syllogism may be expanded into a Sorites 1311, of Modals in 131, the effect of protensive quan- tity upon 136, compound proposi- tions in 149, comparative 151, probable 157, conditional 170, disjunctive 175, not a Petitio Prin- cipii 186 and note , material and formal 378 n. Syllogisms of the Understanding 69. Synonymous Terms 35, may be predicated of each other 55. Synthesis, what 216. Synthetic Judgments, what 203, a priori and a posteriori 206. Synthetic Method of Teaching 359, 362, why preferable 362, based on scientific classification 363. System, what 217. Technical Terms, how interpreted 298. Terms 9, predicable 13, acategore- matic 13, concrete 14, abstract 14, denotative and connotative 14, comprehension and intension of 14, essential and modal 17, gene- ral and collective 17, matter of 21, synonymous, equipollent, ambi- guous, incompatible, and positive 35, negative and privative 36, in discrete quantity 38, in continu- ous quantity 39, in logical quan- tity 39, distributed and undistri- buted 40, their opposition 40, re- latives and correlatives 41, anti- thetic 41, contrary and sub-con- trary 41, contradictory 41, in a proposition 46, importance of their quantity 59, distribution of, in judgments 64, distributed by na- ture 65, by signs 65, by position 67, substitution of in affirmative propositions 76, in negative 77, in comparative judgments 85, in conditional 91, in disjunctive judg- ments 98, in a categorical syllo- gism 108, definitions used for 131, the modal of one transferred to another 136, denoting causes 264, force of, as a basis for demonstra- tion 282, criticism of 375. Testimony' distinguished from Ob- servation 221, of two kinds 226, tests of its value 227, 228, 229, must be positive 229, negative, of Yvhat force 230, in necessary, phy- sical, and moral matter 231, to matters resting on* authority 231, resolvable into observation and authority 280, legitimate use of, in Natural Sciences 295, regarded as a fact 322. Theology, Methods of Investiga- tion in 231, of Proof in 293. Theory, what 217, may be several for the same facts 217. Thinking, a primary property of mind 23 n. INDEX. 425 Thompson, his Outline of the Laws of Thought, quoted as of teaching an un figured Syllogism 111. Titles, alternate conceptions of subjects 57. Topics, what 219 re. Totality, absolute and assumed 88, the idea of, an element of Criti- cism 370. Thicks of Rhetoric, defined 192, to be distinguished from Argument in Criticism 374. Trivium the, what 339. True, the Idea of the, as determin- ing Method 199. Truth, when a proposition is so called 217, absolute proved only by Demonstration 325. Undistributed Middle, Fallacy of 114. Undistributed Terms 40, their re- lation to Judgments 64-69. Unfigured Syllogism 111. Uniformity of Nature, what 307, how used in Induction 308. Universal Judgments 60. University distribution of the Sci- ences and Faculties 339. Useful, the Idea of' determining Methods 199, relation to the Beautiful 201, determines the Methods of Rhetoric 347. "T GTepov ivpwTov , a fault in Method 197. Usus Loquendi as a guide in Inter- pretation 298. Validity of Syllogisms, Canons de- termining the 117. Variable Properties 210, may become material or formal 210, not properly the basis of classifi- cation 256. Volney’s “ Ruins,” cited as an ex- ample of fault in Method 333. Wells Dr., his discovery of the cause of Dew 271. Whately Archbp. his account of Analogy 249 re., his account of reasoning a priori 271 re., from Example 318 re., his “ Spend- thrift’s” fallacy 371. Whewell Prof., his controversy with Mill concerning Necessary Matter 205 re. Whole, the Idea of, necessary to Criticism 370, by what deter- mined 371. Wholes of three kinds 21, as Me- thods 372, in Arguments how determined 375, in Investigation and Construction 375. Witnesses, their character and po- sition as affecting the value of their testimony 226. Words denoting Genera used with- out the article 52. Zeno the Eleatic, the inventor of Logic 2. Zoology, cited as an illustration of the two Methods of Teaching 363 re. THE END. ■ D. APPLETON §■ CO., PUBLISHERS. FIRST LESSONS IN ENGLISH COMPOSITION. BY G. P. QIJACKENBOS, A. M. 12mo. Price 45 Cent? These “ First Lessons ” are intended for beginners in Grammar and Composition, and should be placed in their hands at whatever age it may be deemed best for them to commence these branches — say from nine to twelve years. In the first fifty pages, by means of lessons on the inductive system, and copious exercises under each, the pupil is made familiar with the nature and use of the different parts of speech, so as to be able to recognize them at once. He is then led to consider the different kinds of clauses and sentences, and is thus prepared for Punctuation, on which subject he is furnished with well considered rules, arranged on a new and simple plan. Directions for the use of capital letters follow. Next come rules, explanations and examples, for the purpose of enabling the pupil to form and spell correctly such derivative words as having, debarring, ■pinning , and the like, which are not to be found in ordinary dictionaries, and regarding which the pupil is apt to be led astray by the fact that a change is made in the primi- tive word before the addition of the suffix. This done, the scholar is prepared to express thoughts in his own language, and is now re- quired to write sentences of every kind, a word being given to suggest an idea for each ; he is taught to vary them by means of different ar- rangements and modes of expression ; to analyze compound sentences into simple ones, and to combine simple ones into compound. Several lessons are then devoted to Style. The essential properties, purity, propriety, precision, clearness, strength, harmony, and unity, are next treated, examples for correction being presented under each. The different kinds of composition follow ; and, specimens having been first given, the pupil is required to compose successively letters, de- scriptions, narrations, biographical sketches, essays, and argumenta- tive discourses. After this, the principal figures receive attention ; and the work closes with a list of subjects carefully selected, arranged under their proper heads, and in such a way that the increase in dif- ficulty is very gradual. The work has received the universal approval of Teachers and the Press throughout the Union. QUACKENBOS’ ADVANCED LESSONS IN COMPOSITION AND RHETORIC. (nearly ready.) 18 D. APPLETON $ CO ., PUBLISHERS. A DIGEST OF ENGLISH GRAMMAR. BY L. T. COYELL. 12mo. Price 50 Cents. This work, which is just published, is designed as a Text-Book loi the use of Schools and Academies; it is the result of long experience, of an eminently successful Teacher, and will be found to possess many peculiar merits. At a regular meeting of the Board of Education of Rochester, held June 13, 1853, the following resolution was unanimously adopted: u Resolved, That Covell's Digest of English Grammar be substituted for Wells Grammar, as a Text-Book in the public schools of this city, to take effect at the com- mencement of the next school year.” Extract from the Minutes of a Regular Meeting of the Board of Education of Troy, May 31. s?, 1853. “Mr. Jones, from Committee on text-books, and school librarias, moved, that Bul- lion's English Grammar be stricken from the list of text-books, and Covell's be substi- tuted. —Passed.” From forty-four Teachers of Public Schools, Pittsburg, Pa. “The undersigned have examined ‘ Covell's Digest of English Grammar, 1 and are o< opinion that in the justness of its general \ ievvs, the excellence of its style, the brevity, ac- curacy, and perspicuity of its definitions and rules, the numerous examples and illustra- tions, the adaption of its synthetical exercises, the simplicity of its method of analysis, and in the plan of its arrangement, this work surpasses any other grammar now before the public ; and that in all respects it is most admirably adapted to the use of schools and academies.” From all the Teachers of Public Schools of the City of Alleghany, Pa. “We, the undersigned, Teachers of Alleghany city, having carefully examined Mr. Covell's Digest of English Grammar,' and impartially compared it with other gram- mars now in use, are fully satisfied that, while it is in no respect inferior to others, it is in very many respects much superior. While it possesses all that is necessary for the ad- vanced student, and much that is not found in other grammars, it is so simplified as to adapt it to the capacity of the youngest learner. We are confident that much time and labor will be saved, and greater improvement secured to our pupils in the study of this science, by its introduction into our schools; hence we earnestly recommend to the Boards of Directors of this city, its adoption as a uniform text-book upon this science In the schools under their direction.” From John J. Wolcott, A. M., Pr. and Supt. 9th Ward School , Pittsburg, Pa. “ ‘ Covell’s Digest of English Grammar' not only evinces the most unceasing labor, the most extensive research, the most unrclaxing effort, and the most devoted self-sacrificing study of its author, but it is the most complete, the most perfect, and, to me, the most satisfactory exposition of English Grammar that has come to my notice. It appears to me that every youth aspiring to become master of the English language, from the rudi mental principles to the full, round, beautiful, faultless, perfect period, will make this vol ume his ‘ vade mecum. 1 ” U D. APPLETON $■ CO., PUBLISHERS. EXPOSITION OF THE GRAMMATICAL STRUCTURE OF THE ENGLISH LANGUAGE. BY JOHN MULLIGAN, A H. Large 12mo. 574 pages. $1 50 This work is a comprehensive and complete system o English Grammar, embracing not only all that has been developed by the later philologists, but also the results of years of study and research on the part of its author. One great advantage of this book is its admirable arrangement. Instead of proceeding at once to the dry details which are distasteful and discouraging to the pupil, Mr. M. commences by viewing the sentence as a whole, analyzing it into its proper parts, and exhibiting their connection ; and, after having thus parsed the sentence logically, proceeds to consider the individual words that compose it, in all their grammatical relations. This is the natural order; and expe- rience proves that the arrangement here followed not only imparts additional interest to the subject, but gives the pupil a much clearer insight into it, and greatly facilitates his progress. From Dk. James W. Alexander. “ I thank you for the opportunity of perusing your work on the structure of toe English language. It strikes me as being one of the. most valuable contributions to this important branch of literature. The mode of investigation is so unlike what appears in our ordinary compilations, the reasoning is so sound, and the results are so satisfac- tory and so conformable to the genius and great authorities of our mother tongue, that I propose to recur to it again and again.” Extract, from a letter from E. C. Benedict, Esq., President of the Board of Educa- tion of the City of Few York. “ I have often thought our language needed some work in which the principles of grammatical science and of the structure of the language, philosophically considered, were developed and applied to influence and control the usus and consuedo of Horace and Quintilian, which seem to me to have been too often the principal source of sole- cisms, irregularity and corruption. In this point of view, I consider your work a valu. able and appropriate addition to the works on the language.” From Vm. Horace Webster, President of the Free Academy, Few York. “ The exposition of the grammatical structure of the English language by Professor Mulligan, of this city, is a work, in my opinion, of great merit, and well calculated to impart a thorough and critical knowledge of the grammar of the English .anguage. “ No earnest English student can fail to profit by the study of this treatise, yet it Is designed more partieulary for minds somewhat maturer, and for pupils who are capable end have a deBire, to comprehend the principles and learn the philosophy of their owe tongue.” APPLETOI PUBLISHERS DICTIONARY OF THE ENGLISH LANGUAGE BY ALEXANDER REID, A. M. 12mo. 572 pages. Price $1 00. Tliis work, which is designed for schools, contains the Pronunciation and Explanation of all English words authorized by eminent writers. A Vocabulary of the roots of English words. An Accented List of Greek, Latin, and Scripture proper names. An Appendix, showing the pronunciation of nearly 3,000 of the most important Geographical names. It is printed on fine paper, in clear type, strongly bound. And is unquestionably one of the best dictionaries for the school- room extant. From C. S. Henry, Professor of Philsosophy, History, and Belles-Lettres , in the University of the City of New York. “ Reid's Dictionary of the English Language is an admirable hook foi the jse oi schools. Its plan combines a greater number of desirable conditions for such a work, than any with which I am acquainted ; and it seems to me to be executed in general with great judgment, fidelity, and accuracy. - ’ From Henry Reed, Professor of English Literature in the University of Pennsyl- vania. “ Reid’s Dictionary of the English Language appears to have been compiled upon sound principles, and with judgment and accuracy. It has the merit, too, of combining much more than is usually looked for in dictionaries cf small size, and will, I believe, be found excellent as a convenient manual for general reference, and also for various purposes of education.” GRAHAM’S ENGLISH SYNONYMS, CLASSIFIED AND EXPLAINED; WITH PRACTICAL EXERCISES. DESIGNED FOR SCHOOLS AND PRIVATE TUWSION WITH AN INTRODUCTION AND ILLUSTRATIVE AUTHORITIES. BY HENRY REED, LL. D. 1 Vol. 12mo. Price $1 00. This is one of the best books published in the department ol lan guage, and will do much to arrest the evil of making too eommon us« of inappropriate words. The work is well arranged for classes, and can be made a branch of common school study. It is admirably arranged. The Synonyms are treated with reference to their character, as generic and specific ; as active and passive; ns positive and negative; and as miscellaneous synonyms. D. APPLETON $ CO PUBLISHERS . HAND-BOOK OF THE ENGLISH LANGUAGE BY G. R. LATHAM, M. D., F. R. S. 12m-o. 400 pages. Price. $1 25. This work is designed for the use of students in the University dud High Schools. “ His work is rigidly scientific, and lienee possesses a rare value. With the wide- spreading growth of the Anglo-Saxon dialect, the immense present and prospective power of those with whom this is their ‘ mother tongue, 1 such a treatise must be counted alike interesting and useful .” — Watchman and Reflector. “A work of great research, much learning, and to every thinking scholar it will be a oook of study. The Germanic origin of the English language, the affinities of the Eng i&h with other languages, a sketch of the alphabet, a minute investigation of the etymo ogy of the language, &c., of great value to every philologist.” — Observer. HISTORY OF ENGLISH LITERATURE. BY WILLIAM SPALDING, A. M. FBOFESSOR OF LOGIC, RHETORIC, AND METAPIIYSIOS, IN TUB UNIVERSITY OF ST. ANDREWS 12m.o. 413 pages. Price SI 00. The above work, which is just published, is offered as a Text-book for the use of advanced Schools and Academies. It traces the literaiy progress of the nation from its dawn in Anglo-Saxon times, down to the present day. Commencing at this early period, it is so constructed as to introduce the reader gradually and easily to studies of this kind. Comparatively little speculation is presented, and those literary monu- ments of the earlier dates, which were thought most worthy of atten tion, are described with considerable fulness and in an attractive manner. In the subsequent pages, more frequent and sustained efforts are made to arouse reflection, both by occasional remarks on the rela- tions between intellectual culture and the other elements of society, and by hints as to the theoretical laws on which criticism should be founded. The characteristics of the most celebrated modern works are analyzed at considerable length. The manner of the author is remarkably plain and interesting, almost compelling the reader to linger over his pages with unwearied attention. n V. APPLETON §■ CO., PUBLISHERS. CLASS-BOOK OF CHEMISTRY. upenoi ability of perfectly conforming his style to the capacity of youth. This is a merit rarely possessed by the authors of scientific school-books, and will be appreciated by every discriminating teacher. It is espe cially commended by the eminently practical manner in which each subject is presented. Its illustrations are drawn largely from the phe- nomena of daily experience, and the interest of the pupil is speedily awakened by the consideration that Chemistry is not a matter belong- ing exclusively to physicians and professors. From Prof. Wit. H. Bigf.low, Principal of Clinton Street Academy. “ The eminontly practical character of the Class-Book treating of the familiar ap- plications of the science, is in my opinion its chief excellence, and gives it a value fin superior to any other work now before the public.” From David Syme, A. M., formerly Principal of the Mathematical Department , and Lecturer in Natural Philosophy, Chemistry and Physiology, in Columbia Col “ Mb. Youmans : Df.ar Sir, — I have carefully examined your Class-Book on Chem- istry, and, in my opinion, it is better adapted for use in schools and academies than any other work on the subject that has fallen under my observation. “ I hope that the success of your Class-Book will be proportionate to its merits, and that your efforts to ditfuse the knowledge of Chomistry will b« duly appreciated by the friends of education.” “Either for Schools or for general reading, we know of no elementary work on Chomistry which in svory respect pleases us so much as this.” — Com. Advertiser. “Youmans’ Chart of Chemistry” accomplishes for the first time, for chemistry, what maps and charts have for geography, astronomy, geo- logy, and the other natural sciences, by presenting a new and admir- able method of illustrating this highly interesting and beautiful science. Its plan is to represent chemical compositions to the eye by colored diagrams, the areas of which express proportional quantities. CHART OF CHEMISTRY. BY EDWARD L. YOUMANS. ABOVE, IN ATLAS FORM, Nearly Ready. 18 160 W754E Wilson 250436 Elementary Treatise on Lo gic DATE I ISSUED TO i ~ 160 W754E <5o0436