HBB BBB 111 s:^i/:oei. Stom f0e £i6rar£ of Q$equeaf#eb 6p 0im to f 0e £i6rar£ of (prtncefon tfteofogtcdf ^eminarg 0C7/ ;A89 Digitized by the Internet Archive in 2010 with funding from Princeton Theological Seminary Library http://www.archive.org/details/manualofelementaOOatwa MANUAL OF Elementaky Logic. DESIGNED ESPECIALLY FOR THE USE OF TEACHERS AND LEARNERS. BY / LYMAN H. ATWATER, PROFESSOR OP MENTAL AND MORAL PHILOSOPHY IN THE COLLEGE OP NEW JERSEY. -*»*- PHILADELPHIA J. B. LIPPINCOTT & CO 1807. Entered according to the Act of Congress, in the year 1867, by J. B. LIPPINCOTT & CO., In the Clerk's Office of the District Court for the Eastern District of Pennsylvania. CONTENTS. PAGE Preface 9 CHAPTER I. THE SPHERE AND OBJECTS OF LOGIC. Section I. Logic the Science of the Laws of Thought 13 II. The General Nature of Logical Judgments 22 III. Reasoning as including Conceptions and Judg- ments 25 IV. Pure and Applied Logic 2S V. Applied Logic further explained 34 VI. Utility of Logical Study 36 VII. Fundamental Axioms of Logic 40 CHAPTER II. CONCEPTIONS. Section I. Conceptions, their Nature and Formation 43 II. Higher and Lower Conceptions 47 III. Genus, Species, Essence, Differentia, etc 49 1* 5 6 CONTENTS. PAGE Sect. IV. Other Distinctions in Genus and Species 51 V. The Three Powers of Conceptions 53 VI. Inverse Ratio of Extension and Intension 55 VII. Denomination of Conceptions 56 VIII. Various kinds of Terms 58 IX. Quality of Conceptions 64 X. Notative and Symbolical Conceptions 67 XI. Logical Division 69 XII. Definition 73 CHAPTER III. JUDGMENT. Section I. The Constituent Parts of a Judgment 82 II. Quantity, Quality, Relation, and Modality of Judgments 87 III. Quantity of Judgments 87 IV. Quality of Judgments 89 V. Distribution of Terms in Judgments 91 VI. Relation of Judgments..... 91 VII. Substitutive Judgments 95 VIII. Analytic and Synthetic Judgments 100 IX. Modality of Judgments 101 X. Plurative Judgments 102 XL Conversion of Hypothetical into Categoricals 102 CONTENTS. 7 CHAPTER IV. REASONING IMMEDIATE INFERENCE. TAGE Section I. Mediate and Immediate Inference Defined 100 II. Immediate Inference by Opposition 107 III. Immediate Inference by Conversion 113 IV. Otber Modes of Immediate Inference 117 CHAPTER V. REASONING — MEDIATE INFERENCE. Section I. Introductory Observations 123 II. Moods of the Syllogism * 132 III. Its Four Figures 133 IV. Aristotle's Dictum and other Maxims 138 V. Unfigured Syllogisms 1-12 VI. Hypothetical Syllogisms 144 VII. Conditional Syllogisms 145 VIII. Disjunctive Syllogisms 146 IX. The Dilemma 148 X. Incomplete Syllogisms 152 XI. Complex Syllogisms 153 CHAPTER VI. APPLIED LOGIC — FALLACIES. Section I. Fallacies, Formal and Material 158 II. Fallacies, partly Formal and partly Material 166 III. Logical Puzzles 179 S CONTENTS. CHAPTER VII. APPLIED LOGIC — METHOD. PAGE Section I. Original and Derivative Sources of Knowledge.... 186 II. Problematic, Assertory, and Apodictic Judgments, 193 III. Deductive Reasoning 196 IV. Inductive Reasoning 197 V. Hypothesis 207 VI. Analogy 211 VII. Categories 213 VIII. Harmony and Co-ordination of the Sciences 217 APPENDIX. APPENDIX A. examples for logical praxis. 223 APPENDIX B. SYSTEMS OF SYLLOGISTIC NOTATION. Notation by Circles 232 Notation by Straight Lines 234 The Hamiltonian Notation 236 PREFACE. The object of this volume is to furnish a text-book of in- struction for the use of teachers and students of Elementary Logic. This object has determined its contents and form. It does not claim to offer any new contribution to the science of Logic, as such, although it is quite possible that, in some instances, the author's way of illustrating known truths may have shed some new light upon them. Still less is it designed to present an exhaustive treatise contain- ing all the truths pertaining to Logic which have been reached by the great masters and expounders of the science. But, as before stated, the object is to present the great elements of the science in a form suited to the wants of teacher and learner. Books for this purpose of decided merit are indeed now in use. Many of them, however, are not constructed in conformity to the now recognized con- ception of Logic, as the Science of the Laws of Thought. Others are too extended, cumbrous, or abstruse, for ele- mentary instruction, especially within any time that can possibly be allotted to this study in our Colleges and High- schools. Some of them need much previous drill in more elementary treatises as a propaedeutic. 10 PREFACE. At all events, the author in this brief manual has at- tempted to meet a want which has become urgent in his own personal experience as a teacher. How far it meets the wants of others remains to be seen. He can only be- speak for it a candid judgment and fair trial. It is only just to add that he has freely used whatever best served his purpose in the works of other authors, some- times without explicit mention of the sources from which he has drawn. It is proper, however, to say that he is in greater or less degrees indebted to the works of Whateley, Kant, Hamilton, Mansel, Bayne, De Morgan, Wilson, Bowen — and most of all to Thomson's Laws of Thought. He trusts this general acknowledgment will suffice for all cases in which none more specific is made. Perhaps no better place will occur for stating, that occa- sional paragraphs will occur of such a description that, though important, they may be postponed for review, or omitted entirely, if pressure for time requires. It is of course always the teacher's province to judge how far any portions of the several chapters may be wisely postponed until the time of review. The author will, however, sug- gest that Sections IY. and V., of Chapter I., may advan- tageously be deferred until the student reaches Chapter VI. , when it will form a suitable introduction to the study of applied Logic. The beginner can better understand and appreciate it at this point, than in that natural order in which it is treated in defining the sphere and objects of logical science. The same view applies in a less degree to Section VII. of the same chapter, on the Uses of Logic. PREFACE. 11 Portions of this will of course be better understood after the student has learned somewhat of the principles involved. On the other hand, it is a strong reason for giving early attention to it, that some idea of the advantages of the study is a strong stimulus to the student to make the effort necessary for its successful prosecution. ELEMENTARY LOGIC. CHAPTER I. THE SPHERE AND OBJECTS OF LOGIC. SECTION I. 1. Logic is the science of the laws of _ , _ _ Logic defined. THOUGHT OR THINKING. 2. Of these two words, thought and thinking, we shall hereafter use the former to denote the object matter of Logic. Thought may Thinking or denote either the process or the product ^ 'JJjj ob _ of thinking, i. e., it may be taken either jective. in a subjective or objective sense. Logic is the science of the laws of thought in both senses; the laws which govern genuine thinking itself, and also the relations of the products of thought to each other, and to all matters to which they are applicable. 3. Object means that about which the mind thinks; Subject, the mind itself. The SnbjectandOb- j. ,• 7 • , • l 7 • #• 1 1 1 ject defined, adjectives subjective and objective, and the 2 13 14 LOGIC. [Chap. T. adverbs subjectively and objectively, have a corre- sponding import ; the former in each case referring to the mind considered as the subject of conscious states of knowing, thinking, feeling, willing; the latter referring to whatever becomes an object of the mind's attention. And since the mind may make itself, its own states and exercises, objects of its attention, it is said, in this case to objectize itself, or become a subject-object. When it is Subject-object. ,„ , ,. . . ,, , . neediul to discriminate other objects from this subject-object, some writers use the term object-object. The student who under- Object-object. , ', „ . .,, ., , stands the foregoing, will easily under- stand the terms objectively and subjectively, when they come in his way. The sooner these terms are under- stood, the better, as they are of constant occurrence, not only in philosophy, but in general literature. 4. The next step in clearing the subject is to Tbougbt de- determine what thought is. wwking and Thought is subjectively the operation, product of tbe an( [ objectively the product of the Dis- Discursive Fac- ulties, cursive Faculties of the mind. 5. It becomes necessary now, in order to make this definition complete and intelligible, to explain what we mean by the Discursive Faculties. Although Sec. I.] ITS SPHERE AND OBJECTS. 15 this is properly within the province of Psychology, yet it is at one of those points of con- Tlie Discursive Faculties ex- tact between it and Logic, which re- p i a ined. quires to be explained in defining the object-matter of either. 6. For our present purpose then, the faculties of intelligence, (leaving;; out of view me- Twofold divi- s 7 v r & sion of Intellec- mory which retains and reproduces tual Powers. what is given by the other faculties), may be di- vided into two great classes — the Intuitive and the Discursive. 7. The Intuitive Faculties are those which dis- cern objects, phenomena, or presentations immedi- ately, and not indirectly, i. e., not Inttlitiv e Fac- through the medium of any process of cities described. thinking. Thus, the objects perceived by the senses are known intuitively, as whatever we see, hear, touch, taste, or smell. So also our states of consciousness, our feelings, volitions, cognitions, at the moment of their occurrence, are known intui- tively. The mind knows them immediately, intue- tur, by a direct beholding, and without the inter- vention of reasoning or thinking. 8. The Intuitive Faculties furnish us ^ *"* , the material oi the original material of all our know- Thought. 16 LOGIC. [Chap. I. ledge. The Discursive Faculties take the matter The Discursive thus furnished, and proceed from it, elaborate it in- to new forms, discitrrunt, to new results founded upon it. They work it up or elaborate it into new forms; Why called Ela- nence by Hamilton and others, they are horative. called the Elaborative Faculties. 9. It is important to observe, that intuitions intuitions are (aside of exceptions in the region of of individual ob- jects, self-evident supersensual truths), that is to say, intuitions of material things or of states of consciousness, are always of individual objects, never of classes of objects. By the senses we per- ceive individual trees, stones, or animals. But the Further Intel- senses do not apprehend them in classes. lectualpro- Tq clagsif ig to per f orm a pr0C eSS of cesses are dis- J r L cursive. Abstraction and Generalization, i. e. of Thought, and goes beyond intuition. So of states or acts of consciousness. They are first perceived singly, not in classes. Now this pure intuition is Logic concerns not thought strictly so-called, nor in the former. the sense here intended. It furnishes matter for thought, but is not thought. With this logic does not concern itself, unless casually and indirectly. It develops the laws of the think- Sec. I. ] ITS SPHERE AND OBJECTS. yj ing process, and of its products, in their constituent parts, combinations, and relations. 10. The Discursive Faculties are those which take the materials furnished by intui- Discursive tion, and, by a process of thought, in- Facillties P™" ° ' ceed by Ana- volving Analysis and Synthesis, reach ly»s and Syn- , thesis to new- new results. JBirst, they separate or results. analyze the single objects or wholes given in intui- tion into parts. They notice one or more of the parts into which any individual whole is thus analyzed, to the exclusion of the residue. That is, they abstract them from the rest. Thus, suppose that this book be the object beheld. It has exten- sion, figure, solidity, color, is composed Abstraction de _ of printed sheets, enclosed in binding, scribed. and is a treatise on Logic, etc. Now the mind may attend to one or some of these properties, neglecting the rest. This is Abstraction. 11. Again, the mind, observing a number of ob- jects that agree in one or more particulars singled OUt by abstraction, forms a class Or Generalization n. -. . . , . , „, illustrated and genus of objects which so agree. Thus, explained. noting extension, not only in this book, but in every material object, it classifies them as extended ob- ; sets. Observing that, besides extension, they have 2 * B 18 LOGIC. [Chap. I. solidity, it forms them into the genus, bodies or matter. Noting also that many of these agree in being composed of sheets of paper for the purpose of containing written or printed language, it classi- fies them as such, under the name of books. This is the manner in which it forms genera or classes from individual objects. And to do this is to gene- ralize. It is obvious, moreover, that generalization may proceed, not only from individuals to classes, but from lower genera to higher, which comprehend them : as from white-oak, yellow-oak, scrub-oak, live-oak, to oak; and from oak, hickory, ash, etc., to tree ; and from tree, grass, flower, grain, etc., to vegetable ; and so on, till we arrive at the highest possible generalization (summum genus), which is Being. Hence Logic treats first, OF CONCEPTIONS.* 12. The product of this Generalization is con- ception [con capio) the taking of many together in * This is the meaning to which logicians now limit the word conception, viz., that act or product of the mind which is denoted by a general term, and is obtained by generalization. In common speech, it has a much hroader import, and is used almost synony- mously with that loosest of words, idea, i. e. for almost any men- tal act or representation. And by philosophers it has been used Sec. I.] ITS SPHERE AND OBJECTS. 19 one, i. e. in one class, denoted by one name. This conception or the name denoting it, re- n r o 7 Conception ex- presents, not all of any individual ob- P lained - ject, but so much thereof as is common to it with the whole class of which it is one. Thus the concep- tion bright denotes, not all of any one bright object, but so much of it, as it has in common with all bright objects. 13. This conception, or mental representation of what is common to a plurality of ob- Concrete and . . _ Abstract Gon- jects, may be abstract, or viewed by cep tions, itself irrespective of any objects to which it belongs, as brightness; or concrete, i. e. belonging to some object, as bright moon. 14. It may also be considered subjectively and objectively, either with reference to the mental pro- almost as vaguely. Particularly they have used it to denote the mental similitudes of past cognitions or objects of cognition which are raised in the mind by the exercise of memory. As, when I remember a house, I have a mental image, or as these philoso- phers would say, a conception of it. So of the products of Con- structive Imagination — new combinations, which are not mere copies or images of any thing else. These, too, by many authors, of whom Reid is an eminent example, are styled conceptions. The strict scientific use of the term, however, in present philo- sophic nomenclature, is to signify the mental exercise or product of generalization. 20 LOGIC. [Chap. I. cess forming it, or with reference to the product of Subjective and that process, considered as formed, and jective on- ma( j e £j ie bj ec t f our thin kino-. Some ception. Con- J ° cept. writers limit the word " conception" (conceptio) to the former ; and denote the latter by the word " concept" (conceptus). And as logic, in evolving the laws of this product of thought, makes it the object of attention, these writers use the word " concept" exclusively to denote this, which is the primary element within this sphere of this science. Since, however, this word serves no purpose not equally well accomplished by the word "concep- tion," we shall adopt the latter to denote the first object-matter that falls within the sphere of the science of logic, i. e. the products of Abstrac- Generaiization tion and Generalization ; of which, be it involves Ab- straction. observed, in passing, the former may take place without the latter, but not the latter without the former. 15. Conceptions, and, indeed, the whole pro- Conceptions in- cess f generalization, are incomplete, complete with- out names. fugitive, and unavailable, until they are set, and so to speak, encased and preserved in names. Each one may easily test this for himself, by an examination of his own consciousness. He Sec. I.] ITS SPHERE AND OBJECTS. 21 will see that he cannot retain, or employ, to any extent, in judgments and reasonings, the ideas or conceptions denoted by general words, without the words themselves. The attempt to preserve and turn to account our generalizations without naming them, has well been likened to the process of making conquests, and leaving them without fortifications for their security and preservation. 16. Hence, as terms are so implicated with the conceptions for which they stand, we Terms and Con- „ , . ceptions inter- may often use the two interchangeably, changeable. The older logicians were wont more commonly to use the former when treating of this department of their science. Some, of whom Whateley is a promi- nent example, have carried this view to the extreme of maintaining that Logic is wholly conversant about language. This has been pronounced by others, as Hamilton, to be utterly groundless. The truth is, assuredly, that logic is primarily and properly conversant about thought, and about language incidentally as the vehicle of thought. The science of language is Grammar, or Philology, and not Logic, which is the science of the laws of thought. 17. And yet, owing to the inseparable connec- 22 LOGIC. [Chap. I. tion, amounting, for practical purposes, to almost Sense in which ail identification of thought and lan- Whateley's doc- trine is true. g ua g e > there is a sense obviously, in which Whateley's doctrine may be regarded as a half truth — often the worst form of error.* 18. The first part of Logic then has to do with The first part of that product of thought which results Los;ic deals with n i« ,• n j /"i li n b irom generalization, called Conception ; Conceptions or © r > Terms. and with terms or names incidentally, as being the vehicles of conceptions. The next of the Discursive Faculties is Judgment. And it gives as its products the second great object of logical science, to which we now proceed. Sect. II. Logical Judgments. 19. We say Logical Judgments, because there is Logical and a sense in which judgment is a con- Primitive Judg- ,. ment compared, stituent ot every act oi mind or exer- cise of consciousness. If we have a pain we can- not but judge that we have it. Consciousness is the knowledge of our mental operations, and in- separable from them. Of course, the knowledge * This interpenetration of thought and language may go far to reconcile and clear up the dispute between the Nominalists and Conceptualists. Sec. IL] ITS SPHERE AND OBJECTS. 23 that we have them, is in some sense, a judgment that we have them. For distinction's sake this, which enters into all the intuitions of the mind, may be called Primitive Judgment. It Primitive Judg- furnishes the materials out of which ^^^ conceptions and logical judgments are ence. ultimately framed. The only predicate which it gives is that of existence. It simply affirms that a given phenomenon external or internal is. 20. Logical Judgment, on the other hand, in- cludes a conception as one, or concep- Logical j n( i g _ tions as both, of its elements. It com- ^ent defined. pares two conceptions, or a conception and an in- tuition, and affirms that they agree or Compares Con- disagree. Thus it affirms of the con- ^^2d£ ception "man" and the conception "ra- tuitions. tional," that they agree, i. e. that " man is rational." So likewise of horse and quadruped, tree and plant, etc., etc. Or if we take an individual object of in- tuition named Pompey, and the conception man, or horse, as the case may be, we may affirm that " Pompey is a man f " Pompey is a horse." And negatively, we may affirm that the conceptions man and quadruped do not agree ; " man is not a quad- ruped;" that the particular object called Pompey 24 LOGIC. [Chap. I. and the conception, philosopher, do not agree. Pompey is not a philosopher. Similar examples of all these forms of judgments the reader can easily multiply at his pleasure. 21. Remarking here provisionally, that a judg- Terms, Subject me nt consists of two parts or terms and Predicate defined, (termini, extremes) the Subject, or that which is spoken of, and the Predicate or that which is said of the subject, it follows from this defini- The Predicate tion, that while the subject may be always a con- ception, either an intuition or conception, the predicate must always be a conception or common term, the name of a class. If we have Peter for the subject, unless we have a common term as predicate, we can get only the senseless tautological judgment, Peter is Peter. Of judgments it is unnecessary now to say more, in marking out the sphere of Logic, than that they constitute the second great product of thought, and object of Logic as the science of the laws of thought. 22. From Judgments the mind proceeds to de- The mind pro- rive other judgments founded upon ceedsfromjndg- rpi • • -o • • £ ments to new them, ihis is .Reasoning, or inference judgments from premises to conclusion. Thus to founded upon them. conclude from premises is in fact to Sec. III.] ITS SPHERE AND OBJECTS. 25 judge. So all modes of thought, from conceptions to reasonings are in reality forms of - 6 - 11 thought ia . t rru . n reality a form judgment. The third and last great f judgment. province of Logic, therefore, is the laws of rea- soning. Sect. III. Reasoning. 23. This runs into various branches or modes, Mediate and Immediate, Categorical The third pro- and Hypothetical, which need not be Seasoning. further denned nor explained till we come to treat of it in form and in length. Until a recent period, it was largely the custom of logicians to treat Reasoning as constituting the whole primary object-matter of their Former place of science, and to bring Judgments and f^H* ' & & Logical Trea- Conceptions, under the name of Propo- tises. sitions and Terms, into the sphere of Logic, only on the ground of their being elements of the Syl- logism and other forms of reasoning. But they in- variably treated of these terras and judgments in many aspects of the first importance, which are not immediately essential to the Syllogism, or other forms of Reasoning. Thus Whateley has a short introductory chapter in explanation of terms (con- ceptions), so far as their relation to forms of reason- 26 LOGIC. [Chap. I. ing is concerned, while he postpones the considera- Conceptions and tion ° f them in chief > tiU he has finished Judgments tne analysis of the various forms of the have a place in Logic in their Syllogism. This shows that these con- ceptions and judgments have a separate and independent place in Logic on their own account, and in their own right, irrespective of their place in the Syllogism. This will be more evident when the student reaches these subjects. Indeed, it is only necessary to think of Genus, Species, Differentia, Essence, Accident, Absolute, Relative, Correlative, etc., as applicable to Conceptions, to see that these have in their own right, a leading place in the science of Logic. The definition of Logic, till re- cently in vogue, as being the science of Recapitulation. Reasoning, is therefore too narrow. It is, as we have defined it, and as the present masters of the science generally define it, Definition of I- THE SCIENCE OF THE LAWS OF Logic. Thought. II. Thought is the operation, or product OF THE OPERATION, OF THE DlSCUR- Of Thought. sive Faculties, as distinguished from the Intuitive. See. III.] ITS SPHERE AND OBJECTS. 27 III. The Discursive Faculties are, a. Abstraction and Generalization ; the product of Avhich is Conception. Enumeration of b. Judgment, which out of Concep- Discursive Fac- Til TIP^I tions forms Logical Judgments. c. Reasoning which from judgments given evolves other judgments founded upon them. The thinking and products of think- Lo S ic deals with Concep - ing, whose laws Logic unfolds, therefore, tions, Logical ^ x T Judgments, and are, Conceptions, Logical Judg- Rea ° onings '. ments, Reasonings.* * I also rank Constructive Imagination among the Discursive Faculties. Its operations and products, therefore, are of the na- ture of thought. As we unfold the laws of thought, it will ap- pear that they cannot be violated, even in the creative works of this faculty. They may be violated in the apparent form, sound, and sense of the language employed, and the imagery constructed; but not in its real interior significance. All appearance of thought which violates these laws, is not genuine thought, but a counter- feit or simulation of it. The creations of imagination cannot abolish the laws of Conception, Judgment, Reasoning. They can- not legitimate contradictions, render a round-square possible or conceivable, or make arguing in a circle valid. If it tells us that rain-drops are the tears of the sky, it means such resemblance between the tears and rain-drops as actually exists. The laws of Logic, therefore, so far as applicable to Constructive Imagina- tion, are developed in treating of Conceptions, Judgments, and Reasonings. 28 LOGIC. [Chap. I. Sect. IV. — Pure and Applied Logic* 24. Having defined the sphere of Logic, and pointed out the matters with which it deals, it re- mains that we further elucidate it, by showing what it is in itself considered as pure science, in distinc- tion from the application of its principles to the investigation of truth and the ascertainment of facts — Pure and Applied Logic. Pure Logic treats of the Laws of Thought Pure Logic as they are in themselves, whatever be deals with the . laws of Thought the object-matter to which they are ap- lrrespective of pjj e( j an( j irrespective of their applica- their Applica- l ' l ri tions. tion to any case of actual being. Its principles and laws, like those of Pure Mathema- tics, are true in themselves, irrespective of their application to cases of actual being, nay, whether there be any actual being to which they are appli- cable or not. The laws of the Syllogism, the con- ditions of valid reasoning, the principles which determine genus, species, differentia, essence, logical division and definition, are the same, whatever be * This and the following chapter may he passed with advan- tage for the present, to be taken up as an introduction to Chapter VI. on Applied Logic. Sec. IV.] ITS SPHERE AND OBJECTS. 29 the objects to which they are applied, whether angels, men, animals, plants, or grains of sand; and aside of such applications. In this Logic classes with Mathematics, and with strict Metaphysics. The rules of Arith- it classes with metic, and the propositions of Geometry ^ uxe , a ,^ a " 7 r r J tics and Meta- are true, irrespective of their applica- physics. tions to actual being, and in respect to whatever kinds of actual being furnish the conditions to which they are applicable. The Multiplication table is true in itself, irrespective of any actual being, and in regard to all actual being to which it is appli- cable. 12X12 = 144. This of itself, however, does not prove any truth of actual being. It does not prove that there are twelve persons, each twelve years old. But it does prove, that if there are twelve such persons, their aggregate age is 144 years. Logic, as such, does not concern ..,/> .,i,i .., n. Does not in it- ltseli with the original sources ot our self • e ori . knowledge of actual being, or of the nal knowledge of actual being, conditions to which it applies. These may be supplied by intuition, or testimony, or legit- imate logical deduction from them. They may, in various aspects, come within the province of Psy- chology, Metaphysics, Ontology, or the different 3* 30 LOGIC. [Chap. I. departments of physical science. But from what- ever sources the requisite conditions of actual being are furnished, to which any of the principles of Logic apply, the corresponding consequence neces- sarily follows. Logic does not prove that gold is fusible, or that gold is a metal ; but given these truths from whatever source, and it follows that some metal is fusible, on principles of Logic. 25. Hence, pure Logic, like pure Mathematics, is a science of necessary principles or It is a science , ,1 -r» n , of necessary truths. By necessary we mean that, truths. " Neces- the opposite of which, the mind cannot sary" defined. conceive to be true without intellectual suicide. Such are the following, " that the whole is greater than a part," that " all qualities must belong to some substance," that " no two straight lines can enclose a space." So, as in the proper place the student will more fully see, that there can be no valid conclusions in a syllogism vitiated by negative premises, illicit process, or undistributed middle ; that every relative supposes a correlative, that we may predicate of a species its genus and dif- ferentia; these, with all other laws of pure Logic, are necessary truths. They are not only true in parti- cular cases, but, when understood, it is seen that Sec. IV.] ITS SPHERE AND OBJECTS. ^1 they must be true, as the rules of Arithmetic and the propositions of Euclid must be true in all TT t • • , i Logic the sci- cases. Hence pure Logic is not only, as ence of the ne _ before shown, the science of the laws, cessar y laws ° f Thought. BUT OF THE NECESSARY LAWS OF THOUGHT. 26. This characteristic classes Pure Logic with the a priori, as distinguished from the a p ure Logic an a posteriori sciences. By a priori know- P riori science - ledge is meant that which is known from conditions given, without needing verification from Definition of a experience. A posteriori knowledge priori and a pos- depends upon experience for proof. terior1. The axioms and propositions of Geometry are a priori, because they are known and proved inde- pendently of experience. The physical and induc- tive sciences, on the other hand, are a posteriori, because they are dependent on experience for proof. Hence, all sciences of necessary truth, including Logic, are a priori, for they not only show what ex- perience has proved true ; but what ever must be true in all possible experience, and must condition that experience. We know a priori, that no two straight lines can enclose a space, and that every equiangular triangle must be equilateral. So we 32 LOGIC. [Chap. I. know, as the student in the proper place will see, that, as the Extension of a conception increases, its Intension must diminish, and vice versa : and that there can be no conclusion from negative premises. 27. It is putting the same thing in another light, to say that the laws developed by Logic, are those which are necessary to the very form of Logic deals J J ^ with the Forms thinking, whatever be the subject-mat- mg ' ter about which we think, and indepen- dently of such subject-matter. The forms of think- ing in Conceptions, Judgments, and Reasonings, are the same, whether applied to planets or to worms ; just as the forms of Arithmetical Addition, Subtraction, &c, are the same, to whatever they may be applied : and the opposite sides of a paral- lelogram are equal whether it be on wood, slate, iron, or between lines imagined in pure space. This truth is set forth by saying that Logic is the science of the forms of thought ; or of the formal laws of thought — either phrase will serve our pur- pose sufficiently well. And so combining all the elements thus far shown to be comprised in the essence of Logic, we reach this definition : Puke Completed defi- LOGIC IS THE SCIENCE OF THE NECES- nition of Logic. SARY AN J) FORMA I, LAWS OF THOUGHT. Sec. IV.] ITS SPHERE AND OBJECTS. 33 Those sciences, the Mathematics, Logic, and, with- in certain limits, Metaphysics, which other Formal deal with truths, not within themselves Sciences - originally implying actual being, but which are forms regulative of such actual being as presents the conditions to which they apply, are called Formal Sciences. Those on the other hand which have what, in these relations, is called Fom) 0ontent> Content, or matter of actual being:, Matter - whether in the realms of body or spirit, are called Material Sciences. The contrast here Material gcien . is not between Material and Spiritual, ces - but between Material and Formal. The opposite of Spiritual is Physical Science. Mat- ter and Material in these connections £££?£ refer to substances and phenomena of t0 Physical Sci- actual being, whether bodies or spirits. Accordingly, pure Logic is one of the Formal Sciences. 28. These are also sometimes named Hypotheti- cal Sciences ; because they prove truths # Hypothetical of actual being only on the hypothesis. Sciences ex- that the conditions of actual being are p ame ' given to which they are applicable. Thus, that the angle in a semi-circle is a right-angle proves no c 34 LOGIC. [Chap. I. fact of actual being, until we have some substances in the form of a semi-circle, with an angle inscribed in it. Such an angle we know must be a right angle. Sect. V. — Applied Logic. 29. In the actual investigation of truth, we must go beyond Pure Logic, which, of itself, like Mathe- matics, deals only with forms of thought, and has Pure Logic a n0 con tent of actual being. Yet, like calculus. Mathematics, it is of the utmost value as an instrument or calculus in the investigation of truth. The primary facts, which lie at the basis of astronomical science, were not obtained by mathe- matics but by telescopic observation. Mathematics is an instrument for determining what is fairly in- volved in, or results from these facts so observed. . lication of -^ ^ s use ^ ne f° rmer science has made Formal Scien- the immense strides which have ad- ces to facts a . meaus of dis- vanced it to its present perfection. So coveriug truths. Geometry and Trigonometry will not of themselves make a science or art of Navigation, Surveying, or Engineering. They cannot furnish the facts which underlie these sciences. But the application of these Mathematics to facts otherwise Sec. V.] ITS SPHERE AND OBJECTS. 35 discovered, is indispensable in these sciences, and alone makes them possible. 30. So is it with the laws of Thought unfolded by Logic. They do not, of themselves, prove any original fact of existence ; but, given such data, as are furnished by other means, it is an instrument for showing what is and what is not fairly contained in them : for unfolding explicitly what is involved implicitly : for guarding us against unwarranted conclusions from given facts or truths ; n . -1 . , ., .-, (*(*>, Uses of Logici lor guiding us to the avoidance 01 fruit- less, and the adoption of fruitful methods of inquiry in the realms of actual being. Such use of the prin- ciples of Logic in assisting us to right, and pre- serving us from wrong processes of thought in our search after truth, is what is meant A lied Lo ic by Applied Logic. This has two de- defined. partments. 31. a. The doctrine of Fallacies. Showing the various ways in which men consciously or unconsciously employ, a mimicry of .i i, . -,-, r, . p,i Its two depart- thought, especially of reasoning, for the ment3i / alla . things themselves, thus sometimes im- cies and Me " thod. posing upon themselves, or essaying to impose on others. 36 LOGIC. [Chap. I. b. The doctrine of Method, or the right way to ascertain the truth, by modes of investigation, not contrary to, but harmonious with the laws of Thought. 32. Pure Logic then treats of the formal and necessary laws of Thought in Conceptions, Judg- ments, and Reasonings. Applied Logic deals with the application of these laws to the de- Summation. tection of Fallacies, and the develop- ment of a proper Method for the investigation of Truth. Before proceeding, however, to the formal consideration of each of these topics, we will make a few preliminary observations, first on the utility of the study of Logic, and secondly on the funda- mental principles or axioms of the science. Sect. VI. — Utility of Logical Study. 33. The study of Logic is useful as means of disciplining and invigorating the mind. Uses of Logic. intellectual Few studies more effectually promote wcip me. habits of attention, discrimination, and continuous application. 34. The knowledge thus acquired is of high Imparts valu- vame on ^ s own account. All know- able knowledge, ledge is precious and elevating ; but es- Sec. VI.] ITS SPHERE AND OBJECTS. 37 pecially that which sheds light on the laws of our thinking, our intelligent and rational nature. 35. It is invaluable as furnishing the nomencla- ture, the Technical Terms, which define Furnishes apt the products and relations of true Technical Thought, and the nature of the fallacies ems ' which counterfeit it. The possession of these names in a multitude of cases will instantly suggest to the mind the clew to difficulties which would otherwise perplex it. The very terms, genus, differentia, peti- tio principii, ignoratio elenchi, arguing in a circle, will of themselves often suggest an analysis or ex- planation of perplexities which otherwise might long be insoluble. 36. Generally, as a guide to right, and a pre- ventive and corrective of spurious G ., thinking, i. e. of the aimless, erratic, and Thinking. abortive exercise of our faculties. So it is a pro- paedeutic to all other sciences. It furnishes a needful training for every department of study. So it has been crowned by some, as scientia scientiarum, by others, as ars artium. 37. The question has been much discussed whether Logic is a Science or an Art. But as Logic a Science, the end of Science is to know, and of Art, 4 38 LOGIC. [Chap. I. Art to do, or rather to make a product which sur- vives the making, so there can be no doubt that pure Logic is, like pure Mathematics, properly a Science; while Applied Logic, like Applied Mathe- matics, may afford great light in the learning and executing of the arts to which it is applicable, as the art of Reasoning, Rhetoric, and Oratory. Al- though not useful as in itself an art, it is useful as furnishing light and guidance in the noblest arts. 38. The study of Logic as the science of the Laws of Thought, gives, in fact, if not in form, choiogTof Dis- the knowledge of Psychology, so far as cursive Pacul- ^} ie faculties of Thought are concerned. ties, ° Although the necessary and formal laws which all true Thought must obey, are not of them- selves psychological phenomena, yet it is impossible to master them, in their application to the pheno- mena of the Discursive Faculties, without so far forth understanding the psychology of those faculties. So far as Abstraction, Generalization, Conception, Judgment, Reasoning, are concerned, little remains to be learned, which is not acquired in a thorough course in Logic, in the present acknowledged scope of that science. It is easy for the teacher, with little addition of labor, to compass this portion of psycho- Sec. VI.] ITS SPHERE AND OBJECTS. 39 logy, in connection with his regular course in Logic — a matter of some moment, in view of the scanty time generally allowed to those subjects. 39. It has indeed been said that men reason, whether they know Logic or not. They are not dependent on Logic to confer on them the Objections of power of reasoning. Even Locke is Locke and guilty of such poor burlesque on this others refuted ' high subject, as the following. " God has not been so sparing to men to make them barely two-legged creatures, and left to Aristotle to make them ra- tional. . . . God has been more bountiful than so ; He has given them a mind that can reason without being instructed in methods of syllogizing," etc.* This is quite as relevant, as if one should say, "God has not been so sparing of gifts to men, r fe fe ' Analogy of as to leave it merely to the gramma- Grammar and x f ±i~ jft n 1 1 Rhetoric^ nans to confer the gilt 01 speech, or to the rhetoricians to confer the gift of composition and oratory." The science of Grammar, of course, does not confer the gift of speech. It presupposes that gift. But that it helps to the correct use of language, who will dispute ? Rhetoric does not first * Quoted by Whateley — Logic. Harper's Edition, y>. 37. 40 LOGIC. [Chap. I. make men eloquent; but who can doubt that, rightly used, it will greatly augment this gift of elo- quence in those naturally endowed with it ? Logic does not impart the power of reasoning or thinking. But who will question that it greatly assists in de- tecting and avoiding the spurious counterfeits of them ; and that it is every w T ay a great intellectual tonic? Locke is not alone, even among men of mark in philosophy and literature, in this vulgar and Vandal disparagement of Logic, which, if admissible against this, is valid against all liberal study, discipline, and culture. No less a man than Macaulay has allowed himself to indulge in reflections and implications of like force and effect in regard to Grammar and Rhetoric as well as Logic. 5 * Sect. VII. Fundamental Principles or Axioms op Logic, from which all its Particular Laws Flow, or by which they may be tested. 40. These are commonly reduced to the four following — Identity, Contradic- ts Four Fun- & damental Frin- TION, EXCLUDED MlDDLE, AND SUF- * ' ficient Reason. * See Essay on Lord Bacon. Sec. VII.] ITS SPHERE AND OBJECTS. 41 I. The principle of Identity, which amounts simply to this : that we may affirm of Identity. objects that they are what they are. This lies at the foundation of all Positive Concep- tions, and Affirmative Judgments, and Reasonings. Thus if the Conception rational be a part of the Conception man, we may affirm that " man is ra- tional." On the same ground, we may have the Conception "rational animal," because these may concur in the same being. II. Contradiction. That is we may not affirm the co-existence of Conceptions .. , ,. Contradiction. or attributes that are mutually contra- dictory, as "round-square," "triangular parallelo- gram," " good wickedness." III. Of two contradictions one must -n , , , ,,., Excluded Mid- be true, and the other false. There can die. be no medium between these. This is the Law of Excluded Middle. IV. For every conclusion, affirmation, or nega- tive, there must be a Sufficient Rea- gufficient Eea . son or Ground. It must be evinced son - by self-evidence, or other sufficient evidence. 4* 42 LOGIC. [Chap. I. 41. These principles may seem too obvious and Importance of familiar to be the foundation of any these principles, important science. But we must bear in mind, that the highest sciences are but develop- ments from a few simple elements or axioms. The science of Mathematics is but a development or evolution of a few axioms as simple as the fore- going. Herein, very largely, lies its adamantine strength. What are the laws which keep the myriads of orbs harmoniously circling in the depths of space, but developments and applications of the simple but great law of gravitation? And does not the highest of authorities teach us that, on the simple obligation to love God with all the heart, mind, soul, and strength, and our neighbor as ourselves, " hang all the law and the prophets ?" That is, that all the details of religion and morals, are but the logical unfoldings of this simple principle ? CHAPTER II. Section I. — Conceptions. 1. In unfolding the nature of Conceptions, as also, of Judgment and Reasoning, it will be ne- cessary occasionally to repeat a few things, which were unavoidably introduced by way of anticipation in our brief preliminary exposition. 2. Conceptions stand contrasted with Intuitions, which cognize single presentations, „ ° o x / Conception and whether external or internal, whether intuition com- bodies or states or consciousness, im- mediately and intuitively. Conceptions, on the other hand, grasp (con-capio) a plu- rality in one, through the medium of grasps a plural- i i i ity in one. a common sign or mark, whereby they are, so far forth, represented. This plu- rality may be of objects thus brought to This plurality • , i may be either unity in a common genus, by a common „ , . . J o 7 J of objects or mark or resembling quality, as the marks, included under a common whole class of red things are brought name. 43 44 LOGIC. [Chap. 11. to unity, or classified by the common mark of red- ness. Or it may be a plurality of marks or attributes under one name. As hexagon includes the two _ , , marks, rectilineal figure and six sides. Expressed by a 7 & General Word. Another aspect of the same truth is, Conception is that act or product of the mind which is expressed by a General Word. And hence, 3. Conception is that product of the mind which results from Generalization, whereby many Formal Defini- / . . tion of Concep- individuals are combined in one class, through one or more similar qualities, and are indicated by a common term. Thus, certain pieces of iron-ore are observed to have the property of attracting iron, and are generalized into one class x . ., under the name Magnets. It is obvious Involves Ab- ° straction. that, in attending to this quality of at- tracting iron, exclusively of others, there is a with- drawing or abstracting it from them. Here is Abstraction. There is Comparison, in ximparis orc | er to detect the resemblance of these qualities in the several magnets. Then there is the Classification or Generalization by vir- Generalization. p ,i • n -rv n tue of this resemblance, finally, in order to complete and guard the product of this process, the name " Magnet" is applied to this class. Sec. I.] CONCEPTIONS. 45 This is Denomination. Thus we have a conception formed as the result of Abstraction, Corn- Denomination. parison, Generalization, Denomination. 4. Notion is a term of wider import than Con- ception. It is used almost as loosely if ti n. as Idea. It includes representations I(iea, not only of Conception, but of mental similitudes of objects remembered by simple Imagination. 5. Conceptions and the corresponding terms which express them, may be viewed either as, Abstract, i. e. as expressing a quality irrespective of any object in which it inheres, as Magnetism, Heat, Atstract Con Wisdom, Virtue. Or they may be viewed ceptiona. as, Concrete, L e. as inhering in some object, as magnet, hot-blood, wise man, virtuous person. These dis- Concrete. tinctions will also apply to the inherence of higher in lower conceptions, as will be seen when we come to define this distinction. They also pre- pare us to understand the distinction between Deno- tative, Connotative, and Xon-Connotative terms. 46 LOGIC. [Chap. II. 6. A Term is Denotative in so far as it denotes an object or objects. All names of single objects, . i. e. Singular Terms, have this capacity, Terms. Singu- whether they be proper names, or com- mon terms with an individualizing par- ticle; as "John," "this man." All strictly concrete terms, as fools, stones, trees, have this capacity, besides their power to connote. Abstract concep- tions have not this capacity. They include quali- ties but not objects, as virtue, color, wisdom. 7. Connotative (which are also Attributive), terms Connotative or conceptions denote objects, and con- Attnbutive. n0 ^ e qualities along with them, as men, roses, animals. Such are all Adjectives, inasmuch as they express qualities belonging to the objects indicated by the names to which they belong. The Adjectives foolish, organized, etc., can only be used in reference to their appropriate objects. When, however, adjectives are used to qualify abstract nouns, they denote not so much objects, as the quality which they still further determine. Thus, "great virtue," " scrupulous veracity." Of course, all concrete common nouns, as horses, quadrupeds, etc., are connotative. They denote objects and con- note qualities. See. II.] CONCEPTIONS. 47 8. Non-connotative words are proper nouns which denote objects simply; also ab- Noa _ 0omiota _ stract common terms, which denote qua- tative. lities (and in this sense have denotative power), but connote no objects; as blackness, harmony, etc. Proper names ordinarily denote intuitions or single objects, not conceptions. 9. Proper Names sometimes acquire the attributes of common terms, when the individuals „ >T 7 Proper Names they denote become types of a class, become com- As when we speak of a Webster, a Wash- ington, a Napoleon, or of the Caesars and Nimrods of our race ; i. e. the class of men who have the qualities of Caesar or Nimrod. In such cases, these names are connotative. Adjectives formed from them are like other adjectives in this respect, as British subjects, a Websterian or Johnsonian style, i. e. a style having the qualities of the style of these authors. Sect. II. — Higher and Lower Conceptions. 10. It is evident that the same process of gene- ralization may be applied to classes as Generalization to individuals. Thus triangles, squares, ° c asses ind ^ parallelograms, polygons, etc., may all viduals. 48 LOGIC. [Chap. II. be generalized into the one class of rectilinear figures. Circles, ellipses, parabolas, etc., may be reduced to the one class, curvilinear figures. Recti- linear and curvilinear again may be united as one in the higher genus, plane figure. Dogs, lions, horses, etc., may be generalized into the higher class of quadrupeds. And so of numberless examples which will readily occur to the student. Now in such cases, the broader conception which includes the Higher and low- ° therS > is Called the Hi g her - The liar " er Conceptions. r0 wer ones which are included, are the Lower. Quadruped is a higher conception than dog or fox. As the process of combining lower conceptions into a higher, by laying aside their dif- ferences, is Generalization ; so that of resolving the higher into the lower, by adding on these differences, n . . .. is called Determination. The Concep- Determmation r of Conceptions, tion triangle undergoes this process when it is resolved or determined into equilateral, isosceles, and scalene. 11. In the scale of higher and lower Conceptions we have another application of the Concrete and Abstract ap- distinction of the Concrete and the Ab- plied to Classes. , at^'i n j.* i* i. • stract. A higher Conception which is Abstract when taken by itself alone, becomes Con- Sec. III.] CONCEPTIONS. 49 crete when incorporated with another in a lower Conception. Thus the Conception rationality is Abstract, when taken by itself alone, but when united with animality it becomes Concrete in the lower Conception manhood. Sect. III. — Genus, Species, Individual, Differentia, Essence, Accident, Property. 12. In any series of higher and lower Concep- tions, each higher is a Genus to those Genus. next below it, out of which it is formed by generalization. Those next below it are its Species. Thus birds, fishes, beasts, rep- Species. tiles, men, are species to the Genus animal. Differentia, or Specific Difference, is the mark or quality which distinguishes 1 J & Differentia or one species from others under the same Specific Differ- Genus. Individual or Intuition is that ence ' which is logically indivisible, although it may be capable of physical division. It can- . . Individual. not, therefore, be a species, although it may be one of the constituents of a species. An ox cannot be divided logically, but may be physi- cally into hide, horns, quarters, etc. But then it is no longer an ox. Of course then an individual can 5 d 50 LOGIC. [Chap. II. never be a Species or Genus, which is always com- . „ posed of a plurality of individuals. Es- Essence is Gen- x x ' us and Differ- sence refers to Species, and its essential constituents, i. e. its Genus and Differ- entia. These are called Essence, because when present the Species is present ; if either be absent Lo°ical Defini- that ^ s wanting. These which consti- tion * tute the Essence of a Species, also con- stitute Logical or Essential Definition. As rose (Genus), red (Differentia), constitute the Essence or Definition of red-rose. Accident, or Accidental Conception belongs to a part, and not Accidentt to the whole of a class, as sickness or health to man. Property belongs to the whole of a Species, but is not a part of its Essence: as liability to laugh, or grow gray, in man whose Essence is (Genus) animal, (Differentia) rational. Where these are, whatever else is wanting, there is manhood. Where they, or either of them, are not, there man- hood is not. Sect. IV. — Subaltern and Proximate Genera and Species. Summum Genus and Infima Species. 13. In a series of higher and lower Conceptions, it has been shown that the same one may be a Genus to those next below, and Species to that next above. Sec. IV.] CONCEPTIONS. 51 Those Species to which any given Species becomes a genus, are relatively to it Subaltern Subalter]1 Gen . Species. Those Genera which are Species ns and Species. of a higher Genus are called Subaltern Genera. Thus White-oak, Yellow-oak, Live-oak, etc., are Subaltern Species to oak, which is a Species of the genus tree ; and is therefore a Subaltern Genus to it. Summum Genus is that highest class a n & Summum Genus. which is never a species. Infima Species ^fi^a Species. is that lowest class which is never a Genus. 14. Proximate Genera and Species are those which are next to each other in order of Pr xim t G ascent or descent. Thus triangle is the era and Species. Genus proximate to equilateral, isosceles and scalene triangle. They are proximate Species of triangle. 15. It should be noted that Summum Genus may be Absolute, with reference to the Uni- Absolute Sum- Verse, in which case it is Thing or mum Genus. t> • i • , l -r> i j. • Relative also, hemg simply ; or it may be Kelative to a particular department — as animal is Summum Genus of corporeal beings having life and conscious- ness : plane superficial figure with re- ference to triangle, Square, etc. And Summum Genus fe ' ^ ' and Infima Spo- it is sometimes fixed arbitrarily with cies often arta- o . ,i p . . trarily fixed. reference to the purposes ot some parti- 52 LOGIC. [Chap. II. cular discussion. Infima Species is also often diffi- cult to be fixed, for it is often hard to find classes that have no sub-classes. It might be supposed that isosceles triangle was Infima Species among plane superficial figures. Yet it may be divided into those of different magnitudes : and each of these again into those drawn on slates, boards, paper, etc. This therefore is seldom reached absolutely. It is rather fixed somewhat arbitrarily with reference to the exigencies of the inquiry in hand. 16. It is important to note the difference between t . , j >t Species in Logic and in Natural History. Logical and Na- r ° J turai Species In Logic, as has been shown, it means distinguished. „ . , , , . . one oi the proximate lower classes into which any higher class or genus may be divided. The same class may thus be Genus to a lower, and Species to a higher. In Natural History, however, Species means only such a class of animals as has, or might have de- scended from a single pair, and the varieties of which may permanently inter-propagate among themselves. These sub-species are by the Naturalists rigidly named Varieties. Bull-dog, terrier, grey-hound, etc., are Varieties of the Species, dog. Sec. V.] CONCEPTIONS. 53 In a Logical sense, quadrupeds, reptiles, birds, fishes, are species of the genus animal. In the Naturalistic sense, though they include Species, they are not themselves Species at all, as they want the marks already noted, of actual or possible descent from a single pair, and of inter-propagation. We are aware that some naturalists adopt other criteria of natural species. This, however, is not the place for extended discussion of that question. Sect. V. — The Three Powers of Conception. Exten- sion, Intension, and Denomination. 17. From the analysis already given of the forma- tion of Conceptions, it appears that they Extension of include a plurality of objects through Conceptions. their resembling qualities indicated by a common name, and that the number of objects so included, increases with the height of the Conception. Thus man includes more objects than poet, orator, philo- sopher ; and animal more than man. This power to denote objects constitutes the Extension of Con- ceptions. It is equally plain that every conception in- cludes or connotes qualities or marks, j^tcnaifln or The ground of classification is resem- Comprehension. 5 * 54 LOGIC. [Chap. II. bling qualities. Therefore the conception of any class involves these similar qualities or marks which constitute it. Thus the conception square involves the following marks : 1. Rectilineal figure : 2. Having four sides : 3. And those sides equal : 4. And its angles right angles. The conception man involves the marks, 1. Animal, 2. Rational. This power of conceptions constitutes their Intension, formerly called their Comprehension, which by Whateley has been identified with Extension.* It is not less clear that conceptions have the capacity to receive names, and must re- Denomination, . ,, . -1,1 in ceive them in order to be preserved and used. A conception without a name, is like an un- fenced crop, or a volatile odor. This is the power of Denomination. To these three powers of Conception, three im- portant processes respectively correspond, viz. : Divi- sion to Extension ; Definition to Intension ; and Explanation to Naming or Denomination. * See Logic, Harper's Edition, p. 152. Sec. VI.] CONCEPTIONS. 55 Sect. VI. — Inverse Eatio of Extension and Intension, or Comprehension. 18. As the Extension of Conceptions increases, their Intension diminishes. It is by . „ . . J As Extension laying aside the distinctive marks of increases, In- -, ,. ,, , . , . , tension dimin- lower conceptions, that we rise to higher, ^ Q3t that is, more extensive conceptions. Thus by laying aside the distinctive marks, Equi- lateral, Isosceles, and Scalene, we arrive at the higher conception, Triangle, which has greater exten- sion, and less intension than isosceles, or scalene triangle. So poet, orator, statesman, , , . -, . . . . ExampleSi have less extension and greater intension than man. The ratio of these to each other, there- fore, is inverse. Conceptions then may be regarded as embracing or constituting the respective wholes of Extension and Intension, each of which decreases as the other increases. Of course in Summum Genus Extension reaches its maximum, and Intension its minimum ; and conversely in Infima Species. These wholes have sometimes been called re- Logical and Me- spectively, the former Logical, the latter taphysical Metaphysical. We agree, however, with ° e " Hamilton, that this distinction is without any sum- 56 LOGIC. [Chap. II. cient ground, each alike being, in one aspect Logical, and in another Metaphysical.* Sect. VII. — Denomination. 19. The process of Denomination keeps pace alike with the Extension and Intension of Names keep Conceptions. Thus, as the extension is pace with the Extension and increased, names are employed to denote Intension of i i ji -mi i. j_l. „ .. each enlarged class, till we reach the Conceptions! ° J highest, which is Being or Thing. And vice versa; as we add on successive marks to Being, names are applied to include or connote them, till the term man includes being, with life, sensation, and reason. All this is well illustrated in the fol- lowing tabular examples from Thomson's Laws of Thought, which we copy, because it is hard to find or invent any other, in all respects so much to the purpose. * Various other modes of expressing this double capacity of a Conception are in vogue. Thus a Conception viewed as an Extensive Whole, Intensive Whole. has has Extension, Intension or Comprehension, Breadth, Depth, Sphere, Matter, Objects, Marks, Power to Denote, Power to Connote. Sec. VII.] CONCEPTIONS. 57 C S3 P - P a R S3 • o Hi H < M a o w A JO '5 a © -pa X w d o O CJ ,p .p ts 5 ffi (h a 00 P as -p» 00 p _o Vn P< o « PH o ■ pH OS 13 ph o p : 5 pj o o p" JO a ! £ ; «2 «2 to _© 2 ■ * ^ •1- •FH fc "oo * CO o .1— 1 -+3 » r— F— r— ' K P CO «o p ' r- r* H -p* f3 •g o o c3 in • r- -4-J H M e CO -1-3 02 : * ^ : It w ffl pp -pi <1 > % > •>>>>% ^ HH» C9 00 o t: c > c 1 c 1 O CO « p. PC PC PC PQ <» . p-^» •e* o p< g <» 5 "} to » . "f "« d C ■sa CB •ph PC to s -p3 l-^L x: 03 c ■> t to < PI 1 -1 c ft J o « M B o £ a % 3 p o O p S3 a CD HV? -u c; ^ "tf 'i a ^ -Q ^2 y3 1 «*H s xn 3 CO 3 CO s 1— 1 2Q O v_ r to TO CD CO 05 --* O s •v4 O in S3 O CQ 4 1 02 S3 03 O -!-> O M 03 W 1—1 03 S3" -4J O CO S3 0) S -M 0) S3 >- M 1= «*h O O £« S3 *% o> M >-, CD ^ O r— ( -pv» 03 02 p— 1 03 43 "ei O 02 1— c a S3 O PH • i-H CD O r3 CD S3 03 ^ O a CD ■-, -Jp3 «*1 • p^ 3 O P*H a S3 Is O QQ a> • fH -*-J r-> -H» CJ • >H +-> 02 O pS* 50 Ol S3 « '•*-! — 03 CD O rH O S3 /-* 02 p— 1 O r^ -M • pH ^ H-> ^ O 03 ■H -*J CD q3 • pH 02 02 02 03 S3 r-> 03 r— ^ S3 Sh 'o O O O O -h> O sa O S3 03 • pH S3 ^ B CD O 03 O -pi 03 S3 CD 02 02 03 0) 5 a p3 03 S3 CD -3 03 03 T3 tuo 02 S3 C3 S3 •pH rv H3 H S3 O • — 5§ 02 e! 58 LOGIC. [Chap. II. Sect. VIII. — Varieties and Characteristics of Concep- tions USUALLY EXHIBITED WITH RESPECT TO THEIR DE- NOMINATION, or the Names which Complete and Indi- cate them. 20. As Conceptions are incomplete till they are , , - named, and these names are called Various kinds of Terms mark- Terms, or Nouns, so certain features of ing feltures n f Conceptions are usually set forth as Conceptions. belonging to these terms or nouns. But as these terms stand for Conceptions, so the different kinds of Terms are but different kinds of Conceptions, save in those exceptional cases of proper names, in which they denote only intuitions or individuals. 21. The first division of nouns is into Proper, Proper Com- Common, and Singular. Proper names rnon, Singular, denote individuals merely, without con- noting any marks or qualities. Common names denote conceptions, and the objects included in them, together with their common marks, i. e. their exten- sion and intension. Singular terms denote single objects by means of a common noun, having its sig- nification limited by an individualizing particle, as this man, a house, some animal. Sec. VIII.] CONCEPTIONS. 59 22. The second principal division of nouns is into Attributive and Substantive. Attribu- Attributive. tives are the adjectives of Grammar. They express qualities not in the Abstract, but in the Concrete, as belonging to some substance. They express the attributes of Nouns, and are therefore used only in connection with the Nouns of which thev are ad j uncts. Substantive Nouns de- J ° ( Substantive. note objects or abstract qualities, to which Attributives may be applied. Thus tree and hard- ness are Nouns Substantive. High and great are at- tributives which may be respectively ascribed to them. 23. Another distinction is that between Distri- butive and Collective Nouns. A Noun Distributive, is Distributive or used distributively, when it is applicable to each and every individual included under it. It is Collective, or Collective. used collectively, when it is applicable to the whole, or a plurality only, but not to each and singular of the objects included under it. Thus man is a Distributive, and crowd a Collective Noun. Soldier is a Distributive, army a Collective Noun. The same noun may, however, be used both collec- tively and distributively. When we say, " these trees are oaks," trees are used distributively. When we 60 LOGIC. [Chap. II. say, "these trees amply shade this park/' they are used Di t ib ti f c °H ec tively. Hence a Term is said to Terms. be Distributed, when it is so used as to include all the objects signified by it distributively ; that is, all and singular of them, not merely a part of them, nor the whole of them collectively. When we say, "all men are mortal/' men is Distributed. If we say, "some men are poets," men is not Distributed; and if we say "all men number 1,300,000,000/' men is not Distributed : for although all men are spoken of, it is not all and singular, but all taken collectively, that are meant. Terms or Conceptions are Absolute and Rela- Absolute and ^ ve * Absolute are irrespective of any Eelative. other, as stone, tree. Relative are those which imply others. As son implies a parent, and king a subject. A pair of relatives like Correlatives. p ,, , n i ^ i ,• father and son are called Correlatives. In all Relative Conceptions there is a ground of Ground of Eela- * ne relation (fitndamentum rdationis). tlon ' In the case of king and subject, it is government. In that of father and son, brother, sister, etc., it is the family. Some relatives imply . not merely one, but two, or even several Cases of several ' ' ' Correlatives. Correlatives. Thus, cousin implies not Sec. VIII.] CONCEPTIONS. 61 only another cousin, but parents, one of whom is brother or sister of one of the parents of the other cousin. 24. Contrary and Contradictory Terms or Con- ceptions. Contraries are the most op- posed that can possibly belong to the same subject, as wise and foolish, soft and hard. Contradictories are simple Negatives of , ,, -. . ;1 .it Contradictories. each other, and between them include all being actual and possible. Thus, man and not man, Ego and non-Ego, are pairs, each of which comprises the universe, not only of actual, but of possible being. And of such a pair of Conceptions one only marks out any definite class of Definite and In- objects. They are for this reason called defimte> Definite and Indefinite Conceptions. Of the two Con- ceptions, man and not-man, the former alone contains any thing definite or positive either as respects ob- jects or qualities. The latter is not only indefinite, but essentially infinite. It embraces all the possi- bles but man, the subtraction of which does not make their number less than infinite, ingnitated Con- Hence such purely Negative Concep- ce P tioils ' tions are sometimes classed by logicians as Infini- tated Conceptions. 6 62 LOGIC. [Chap. II. 25. It is not, however, true of most Negative Most Negatives Conceptions, that in their real and d°fi Lta J In" customai T signficance, they have this finites. infinity. Especially is this not true of Attributives. Thus, if we speak of unkindness, we do not mean every thing that is not kind, but we mean the absence of this quality in intelligent and moral beings who ought to be kind, and in whom to be unkind is to be harsh or severe. Now a conception or term which implies the presence of any mark is called Positive, as virtue, wisdom, benevolent. A term which im- plies the absence of what might belong to a given Privative. subject, is Privative, as an unkind or Negative. unholy man. Negative terms on the other hand, deny not only what does not, but what cannot belong to some given object, as lifeless stone, speechless block. These do not belong to the class of Infinitated Conceptions. 26. These distinctions are not without practical importance. In the first place they add Importance of these Distinc- to our variety of forms of thought and expression, and so to the means of pre- cision of style. The words unkind, unholy, un- learned, give us shades of thought not expressed by Sec. IX.] CONCEPTIONS. 03 the words harsh, wicked, ignorant. Again, the distinction of Privative and Positive is of moment, in reference to the origin of evil as related to God. He is in no sense the cause of sin, except privatively or negatively. It may arise from the absence, not the presence, of his agency, as darkness arises not from the presence but the absence of the sun. 27. Two terms which may be applied to the same object at the same time, are called Com- n , ., , , J 7 Compatible and patible or Consistent, as red and round Consistent. to a table; diligent and healthy to man. They are Opposite or Inconsistent when they can- n rr J Opposite and not be applied simultaneously to the Inconsistent. same object, as "round square figure," "lifeless breathing man." 28. The important distinctions of Abstract and Concrete, Connotative and Non-connotative terms, were sufficiently explained when treating of the cor- responding conceptions. To these the student can recur, chap. II., sect. I. 5, and II. 11. Sect. IX. — Quality of Conceptions. 29. By the Quality of Conceptions is meant the degree of perfection with which they represent to the mind the objects and ceptions defined. (J4 LOGIC. [Chap. II. the marks included in them. In this regard, Con- ceptions, like all cognitions, are perfect in proportion Tm . ' as they have the several virtues of Clear- Wnen they are •> Perfect. ness, Distinctness, and Adequacy. In proportion as they have the opposite vices, they are respectively Obscure, Confused, and Inadequate. The nature of these respective virtues and faults we will now proceed to explain. 30. A conception or other cognition is Clear, ci a Ob wnen ft i s simply distinguishable from scare. others, and Obscure when it is not. Thus in twilight we often see objects, but are unable to distinguish them from each other. Our cogni- tions of them are obscure. As the light gradually comes upon them, our view becomes so clear that we can distinguish them apart. The uninstructed cannot distinguish Logic from Psychology and Me- taphysics, or a Court of Chancery from a Court of Law. These are Obscure conceptions to those un- versed in such matters. All persons are afflicted with more or less of this obscurity of knowledge in departments to which they have not given special attention. 31. But we may know objects or conceptions, so as to distinguish them from each other, without Sec. IX.] CONCEPTIONS. 65 being able to point out the marks by which they are so distinguished. Such knowledge . . Distinct and may be sure as far as it goes. But it is confused Cog- confused with respect to the marks or mtlons ex_ plained. differential features of the object. This is among the most common phenomena of our intelli- gence. How common to know persons of our acquain- tance from each other, without being able to specify the peculiarities of form or feature which distin- guish them severally. How common to , ,,ii i • j • c t r-n Illustrations. be sure as to the hand-writing oi diner- ent persons, without being able accurately to define the peculiarities of each. How often do lawyers in court perplex witnesses, and torture out of them absurd answers, by asking them the marks by which they identify the persons or the hand-writing in regard to which they testify. Yet what tribunal ever discredited a witness on account of any puzzle or inconsistency into which he was thus drawn? Those, however, who have made such subjects a study, are able to give the marks of difference. Their knowledge is distinct, while the other is con- fused. The same distinction holds in regard to our understanding of conceptions. If we take the con- ceptions mineral, plant, animal, man, how few who 6* B 66 LOGIC. [Chap. II. do not surely know the one from the other ? But how few can accurately give the marks which dis- tinguish them respectively from each other? A Clear cognition or conception then knows its objects __ . , _ from other objects. An Obscure one Distinction of u Distinct and does not. A Distinct cognition or con- ception not only knows its objects, but the marks of those objects. A Confused one knows its objects without knowing their marks. 32. This Distinctness of our conceptions may be Ad ate d both Adequate and Inadequate. It is Inadeqnate. Adequate when it not only apprehends their marks, but the marks of these marks. And when it fails of this, it is Inadequate. Thus we have a Clear knowledge of the conception man, when we discriminate it from animal, plant, etc. We have a Distinct knowledge of it, when we know its marks to be animality and rationality. This knowledge is Adequate when we can give not only these marks of manhood, but can also give the marks or defini- tions of animality and rationality, those of the former being life and sensation, of the latter the intuition of supersensual truths and the power of thinking in the light of these truths. This process of giving the marks of marks is in itself capable of indefinite Sec. X.] CONCEPTIONS. 67 extension. That measure of it which is adequate, cannot be decided by any unvarying: « tt ' J J ° No Unvarying rule. It varies with the exigencies and Bales of Ade- requirenients of each particular discus- quacy " sion, and must often be determined somewhat arbi- trarily. Sect. X— Notative and Symbolical Conceptions. 33. This is a pregnant distinction. A Nota- tive Conception is such that when pre- Notative Coi] sented to the mind, it suggests its own ception. marks (notce) by its very name, so that they are at once and indubitably evident, e. g. quadruped, tri- angle, octagon, oligarchy. A Symbol- SymMical ical Conception is one which serves as a Conception. symbol of a number of marks or characteristics which it does not, of itself, bring before the mind using it. It is used as a substitute for, or represen- tative of, the marks which the mind does not stop to bring in detail before itself, and, indeed, which, in many cases, it could not, if it would. Such are the conceptions or terms, church, family, senate, philosophy, etc. Few bring before their minds all the marks involved in these conceptions. Most persons could not do it, who, nevertheless always 68 LOGIC. [Chap. II. use them with substantial accuracy. All concep- tions which are used without an apprehension of their marks or definition, are used Symbolically. 34. All Thorough Knowledge is obtained by re- moving: from our conceptions the several Thorough & r Knowledge how imperfections of Obscurity, Confusion obtained. , T -, , -, , , and Inadequacy, and developing these into Clearness, Distinctness, Adequacy and Particu- larity ; as also by unfolding the marks of Symbolical Conceptions till they have something of the distinct- ness of Notative Conceptions. This is no less essen- tial to invention and style in Rhetoric, than to logical thinking. It is accomplished by two great processes, each of which must be pursued in proportion as we would make our conceptions clear, distinct, and adequate. The first of these is Logical Division, which un- folds the Extension of Conceptions. The second is Definition, which unfolds their In- tension. These processes are now to be considered. Sec. XI.] CONCEPTIONS. 69 Sect. XI. — Logical Division. 35. Logical Division divides a Genus according to its extension, i.e. into its constituent T . , -,>. . 7 Logical Divis- and proximate Species. It may then ion Defined. take any of these proximate Species for a Genus, and divide that into sub-Species. In like manner it may divide any of these again, and so on, until we pass through Infima Species to individuals. 36. The Genus divided as being the higher, is sometimes called the Super-ordinate. ,. 1 Super-ordinate The proximate species into which it is Genus. divided, are called Co-ordinates. If Co-ordinate either of these be divided into parts or pecies ' Species, with reference to its superior Genus, it is called Subordinate Genus. Any one of subordinate given Co-ordinate Species, is called, in Genus. relation to any one part of a higher or lower Co- ordinate Division under the Summum Di spa rate Genus, Disparate. Thus, quadruped is Species. super-ordinate to lions, leopards, horses, E xamp i eSi cats, etc. They are co-ordinate with each other. They are subordinate to quadruped and animal, while lion, as compared to fish, Shet- land pony, or bull-dog, is Disparate. 7Q LOGIC. [Chap. II. 37. The rules for correct Logical Division are : a. It must proceed from Proximate Genera to Proximate Species, and not per saltum, Proximate Ge- or arbitrarily. To Divide animals at nera to Proxi- ouce i n t whales, sturgeon, etc., without mate Species, . . previously dividing them into birds, fishes, ^Ui., would be a violation of this rule. b. There must be but one principle of Division, B ne princi- fandamentum divisionis. In dividing a pie of Division, library, for example, it will not do to divide the books according to price and according to binding, at the same time. To do this is to vio- late the c. Third Eule, which is, that the Divisions must Divisions Hutu- be mutually exclusive. They must not ally Exclusive. run j n ^ eacn other by cross-divisions. This will result from adopting more than one prin- ciple of Division. Thus if we divide the books of a library according to their subject-matter, and ac- cording to the language in which they are written, some books of poetry, history, and oratory, will be in Latin, French, English, etc. One fruitful source of perplexity and confusion in the discussion of subjects is unobserved cross-divisions, which ought rigorously to be avoided. Sec. XL] CONCEPTIONS. 71 d. All the parts should be exactly equal to the genus divided ; any one part, and the gmn of partB sum of any number of parts less than e 1 uals Drrisum. all, should be less than the Divisum or genus divided. To divide mankind into rational ani- mals and all others, or into Europeans, Asiatics, Americans, and Greenlanders, would be a violation of this, as well as of other rules. e. It must not be a priori, or by Infinitation. For this, although in form regular and Not a priori. exhaustive, is in fact useless. It adds nothing to our knowledge. To divide animals into partridges and all others, or partridges and not- partridges, is indeed a formally complete, but a completely useless Division. Such a Division into two members, which inevitably are contradictories, is called a Dichotomy. A division in three mem- bers is called a Trichotomy : into many members, a Polytomy. 38. Physical Division or Partition. — Logical Division must be clearly distinguished from Physi- cal Division or Partition. The latter divides an individual, which is logically logically divisi- indivisible, into its component parts, as a ship into hull, masts, sails, etc. The test of this LL 2 LOGIC. [Chap. II. sort of Division is that the Divisum cannot be predicated of parts. In Logical Division it always may. We cannot predicate ship of sails, masts, etc., but we can predicate it of steamship, sailing- ship, etc. It should be further observed, that we may arbi- trarily make collective wholes logical individuals, when it suits the end in view. Thus Collective Wholes Logical nations, armies, regiments, etc., may be Individuals. , i -r • i • v • i i r\n treated as Logical individuals. Uiten like literal individuals they cannot be so divided that the divisum can be predicated of the parts. Thus army cannot be predicated of regiments, nor regiments of companies, nor nations of towns. 39. The thorough logical division of any subject, Uses of Divis- thus defining the sphere and the objects ion ' it includes, greatly assists the clear, tho- rough, and facile discussion of it. It also aids in- vention. The most sterile mind will find some- thing to say on a subject well mapped out. Indeed so to map it out, is to say something important. Division gives clearness to our Conceptions by pointing out their objects. But to gain distinctness and adequacy, we must resort to Sec. XII.] CONCEPTIONS. 73 Sect. XII. Definition. 40. This gives the marks of Conceptions, and unfolds their Intension. It thus bounds Definition de- them off from all other Conceptions, so scribed, that we not only know that they differ, but in what way they differ. The rules for correct defini- tion are, a. It must be by essential marks. The essential marks of a species are what constitute B essential its essence, i. e. its genus or matter, and Marks - differentia or form. This is normal, logical defini- tion, or definition strictly so-called. All other definition is valid in proportion as it approximates to tins. HHP"* Let not the student forget when ashed what is logical or essential definition, that it is ^^i Defmi- made up of the genus and differentia. tion ' b. It must include the objects covered by the definitum, or species defined, neither ^ ot too Broad more nor less. If it include more, it is nor Harrow, too broad. Thus to define a whale as a fish, is too broad. To define a fish as a whale is too narrow. A definition too broad is detected by simple conver- sion. If it is a good definition of a whale to say that 7 74 LOGIC. [Chap. II. it is a fish, then all fish are whales. A definition too narrow is detected by conversion by How Detectedi . ... ,-m . P .. ■. , contraposition, lnus, it it be a good definition of a fish, that it is a whale, then whatsoever is not a whale is not a fish. For the fuller under- standing of this, the student must recur to it after studying the subject of conversion, in its proper place, under the head of Reasoning. c. It must not be by Negatives, if this can be Not by N avoided. Negatives show what are tives. n0 ^ instead of what are marks, and so add little to our knowledge. To define man, as not an angel, or not a brute, is unsatisfactory. It does not tell what he is. There are, however, Nega- tive words and conceptions, which in "their very nature require a negative definition, as unholy is simply not holy. d. It must not be in vague, ambiguous, or sense- Must be in dear less language. To say that "truth is Language. ^he grand scope of all existence/' or that " beauty is the harmony of being," are exam- ples in point. e. It must not be Tautological, i. e. through the w m , word defined, or any of its derivatives, or Not Tautolo- ' J 9 gical. synonyms from other tongues, or the Sec. XII.] CONCEPTIONS. 75 negative of its opposites. To define life as the vital force, or the state of living, or the opposite of death, is thus to err. This is definition in a circle, cireulus in definiendo, for such definitions return upon them- selves. If light be defined as " that which illumi- nates," per contra, "that which illuminates is light." The circle in definition as in argument, is often un- observed. How easy to define a plank as a thick board, and a board as a thin plank? /. It must be Precise and free from surplus words. These surplus words, though Precise and free true, may convey a false implication, from Surpius- To say that a parallelogram is a rectili- age ' neal four-sided figure, whose opposite sides are parallel and equal, is to state the truth. But the words "and equal," are unnecessary to the definition : and they convey this false implication that there may be such figures whose opposite sides are parallel, but not equal. This vice is of more frequent occur- rence in ordinary thought and speech, than in formal definition. How natural to say, " we ought not to calumniate so good a man," as if it were right to calumniate anybody ? 41. Absolute Summum Genus cannot be logically 76 LOGIC. [Chap. Li defined, because it has no differentia. Thus, being can only be defined by some synonym or de- scription casually substituted for it. It Absolute Sum- , -, P , ,,. . , . , . , mum Genus uot ma 7 be defined as a thing, or that which Logically Defi- h as existence. Summum Genus in any nable. particular sphere, being such only rela- tively, and always a species of a higher genus, is of course capable of strict logical definition. 42. Simple Ideas are incapable of logical defini- Simplo ideas tion > as the y cannot be analyzed into likewise. elements, and therefore are without genus and differentia. They can only be defined like Summum Genus, by synonymous or descrip- tive equivalents. Red is a color. This is genus. But who can give the differentia, that separates it from other colors ? What is color ? What is good- ness or beauty ? What is the respective genus and differentia of each ? But although not definable, do they need defining ? Are they not self-evident and plainer in themselves than any definition could make them? 43. Logical definition, strictly considered, refers only to Species, and therefore does not technically apply to Individuals. Hence other Individuals, how Defined. methods of defining them have been de- Sec. XII.] CONCEPTIONS. 77 vised. They may be defined by the intuition of them, through the senses if they be bodies, or through the light of consciousness, if they be men- tal states. Or they may be defined by some pecu- liar and inseparable Accidents, as a virtual Differ- entia. Thus, Cicero might be defined as "the greatest Roman Orator," and the first Napoleon as " the greatest French General." They are, however, thus defined by all that is essential in a logical defi- nition. They are referred to the Infima Species under which they fall, and discriminated from other individuals under it, by some mark peculiar to them- selves. Thus Washington may be defined as " the first President of the United States." Here the Infima Species, President of the United States, is to the individuals under it, what every proximate genus is to its co-ordinate species. This then may be taken as the genus, and " first" as the dif- ferentia. 44. Indeed, in all definition, whether of indi- viduals or species, the genus and differ- Q enus an a £if. entia may be considered as two com- ferent ^ a reall y J two Commum- municant genera, and the Conception cant Genera. defined that which is included within the sphere of their coincidence. Either raav be considered 78 LOGIC. [Chap. II. genus and the other differentia, and vice versa, at convenience. Thus, if we define a man as a rational animal, this extends over so much of the concep- tions, rational and animal, as overlap each other. Thus : In like manner, so much of the genera, " Presidents of the United States," and " fourth," as overlap each other, are just equal to, and define James Madison, fourth President of the United States. 45. As there are many cases in which a strictly Methods of De- l°gi ca l definition is either impracticable finition. or inconvenient, several other methods of defining are occasionally adopted, which serve more or less effectually to clear the definitum, and to bound it off from all else. Including these, the methods of definition in all amount to six, arranged by logicians as follows : a. Resolution. This resolves the Conception into Resolution, its marks, genus and differentia, and is, Sec. XIL] CONCEPTIONS. 79 as we have seen, the standard, normal, logical, essen- tial definition. Thus, " man is a rational animal." b. Composition. This is the reverse of resolu- tion, and unites the marks into the r* ,. r. , . t ,, , Composition. Conception ot which they are concrete parts. Thus, " a rational animal is man." c. Division: i. e. according to extension, into its constituent parts, whether species or in- dividuals. Thus, "the New England States are Maine, New Hampshire, Vermont, Mas- sachusetts, Connecticut, and Rhode Island." " The animal kingdom consists of Radiates, Mollusks, Ar- ticulates, and Vertebrates." d. By Colligation, the reverse of the last, i. e. uniting the constituent parts acccording to extension together, as James, John, Matthew, Thomas, etc., were the twelve Apostles. The Earth, Mars, Mercury, Venus, etc., are the Planets. This formula furnishes the minor premise for the Inductive Syllogism. e. By the substitution of Symbols or Exchange of names ; as " religion is piety." Symbols. /. By Casual Substitution of narrative or de- scriptive phrases, as, wisdom leads to Casual Substi- virtue and happiness. This last, how- tution. 80 LOGIC. [Chap. II. ever, hardly conies up to the exactness required in real definition. Nor should the fifth method be used when it can be avoided. 46. Most logicians refer to the distinction be- tween Nominal and Heal Definition, and. strangely Nominal and inconsistent accounts have been given real Definition. f [^ These terms are adapted to mis- lead. Nominal Definition is the Definition of a name ; Real, of a thing. But the Definition of a name is none the less a Real Definition. Indeed, all strictly Logical Definitions are of names, and give the marks which these names stand for. That is, they give the marks connoted by these names. This is the proper, normal province of Definition. As to qualities of things not connoted by the name, they are important, and belong to scientific investi- gation and the increase of our knowledge, but do not directly constitute Definition. They may afford the means of correcting or improving the accepted Definition of these names, which is Definition pro- per. In Mathematics and the Ideal and Formal Sciences, the Definition of the Name, is of necessity the Definition of the Thing. The Definition of the names, " Circle," " Conception," " Extension/' " In- Sec. XII.] CONCEPTIONS. 81 tension," etc., is, of course, the Definition of the thing. 47. From this analysis, it appears that Definition, or the distinct explication of the marks i m p 0r t a nce of of conceptions, is of fundamental im- Defillitlon ' portance in thinking, investigating, and discoursing. An accurate Definition, or presentation of the status questio7iis, will often settle controversies otherwise interminable. Without such Definition, all discus- sion and investigation must be futile and unsatis- factory. And it is quite as powerful a stimulus to invention as Logical Division. 48. It is, moreover, quite plain that Definition and Division are mutual helps to each •. , , Definition and other. When we Divide a Genus into Division mntnai ., , • n •» aids. its proximate species, we, oi necessity, are bringing to light the differences between those species. These, with the Genus, make up the Defi- nition. On the other hand, looking for the differ- ences, we, of course, are finding the boundaries of the several species into which Division separates the genus. F CHAPTER III. JUDGMENT. Section I. Its Constituent Parts. 1. Judgment is that act of the mind which, upon Judgment de- comparing two Conceptions, or an in- fined, dividual object of intuition with a Con- ception, affirms that they agree or disagree ; that they do or do not belong to each other. Thus, "Vic- toria is queen." "Angels are not men." A Judg- ment expressed in words is a Proposi- Proposition. , . T -. . -. ^ tion. Judgments and Propositions are always either true or false. No other form of thought or expression has these attributes. 2. Strictly speaking, as has been already ob- served, in the last analysis, every intel- Strictly every 7 J J Mental Act a ligent act is a Judgment. To know is to discriminate, and therefore to judge. Even feeling and sensation, the most rudimental form 82 See. I.] JUDGMENT. 83 of consciousness, involves a knowledge and so a Judgment that it exists. This is Primitive as distinguished from Logical Judgment. Primitive Judg- And yet it is hard to maintain this dis- ment ' tinction without qualification. For the most Primi- tive Judgment affirms that something is p re dicates ex- or is not; i. e. it affirms that the Concep- istence op- tion, Existence, agrees with some individual sub- ject. But beyond the mere predication of Existence, Primitive Judgments do not go. Logi- Logical Judg . cal Judgments are founded on Concep- ments - tions formed by Abstraction and Generalization from these Primitive Judgments. Yet, since Primitive Judgments involve the Conception of Existence, which withal is Summum Genus, the two flow into each other. 3. And it is to be observed, that all the processes of Thought, whether by Conceptions, _ to ' J r ? All Thought Judgments, or Reasonings, in reality resolvahie into , p, -, , • , • t i Judgments. proceed from and terminate in Judg- ments. Conception is the product of the Judgments involved in abstraction and generalization, whereby many objects, through some common mark or point of similitude, are grasped together. Conception fixes and preserves this Judgment, by a common name. 84 LOGIC. [Chap. III. Thus, the conception and the name, bi-ped, is the fruit and confirmatory sign of the Judgment, that animals, which agree in having two feet, may be put in a class denoted by the common name, biped. As Conception is the product of a Judg- Conceptions , ... , . . , , T , formed and ex- ment > so xt 1S explicated by a Judg- piicated by ment. Thus " bi-peds are two-footed Judgments. t # . „ animals." "Animals are conscious. They interpen- J n short, Conception and Judgment in- etrate each other. terpenetrate each other. In one view, Conception is a certain stage of Judg- ment. Judgment in form develops Conception. Reasoning, too, the third great process Seasoning also is by Judg- or form of thought, deals only with Judgments, and their relations to each other, as will be seen, when we come to treat of it. It proceeds from one or more Judgments given to others founded upon them. Thus, in the last analysis, Logic being the Science of Logic the Sci- . ence of Judg- Thought is the Science 01 Judgments, ments * into which all thought is finally resol- vable. Nevertheless it is convenient to treat of pure formal Judgment by itself, after Conception which furnishes the materials of Judgments ; and before Reasoning, which is composed of them, and Sec. L] JUDGMENT. 85 in concluding that one Judgment flows from others, forms the Judgment that it does so. 4. Judgment being thus a mental affirmation of the agreement or disagreement of two notions, one of which at least is a Conception, Terms f a these two notions are called the terms Jud s menti {termini, extremes) of the Judgment. That which is spoken of is the Subject of the Judgment. That which is affirmed or g u w eot| p re( ji- denied of the other is called the Predi- cate ' cate. That which connects the two is M , , Copula is verb the Copula. This is always the verb "to be "in pres- to be, in the Present Tense Indicative, if the Judgment be affirmative : and the same with the negative particle affixed, if the Judgment be negative. Thus : Sub. Cop. Pred. The earth is round. Sub. Cop. Pred. Oaks are not pines. The Copula, in many cases, is not directly ex- pressed by the word is, or is not, but is copula often im- in other phrase, which implies them. P lled< When any other than the Substantive verb is em- ployed as Predicate it includes the Copula. Thus, 86 LOGIC. [Chap. III. Sub. Cop. Prert. " he runs," is equivalent to, he is running. iC No men Sub. are sinless/' is the same as to say of all men that Cop. Pred. they are not] sinless. When Existence simply is expressed, the verb Predicate when to be is both Predicate and Copula ; as, , Sub. Pred. Cop. implied. God ig = ig exigting> 5. When any mood or tense of the verb, except m , , the present indicative in the Copula, is What belongs x x ' to the Predi- significant, this significance belongs to the Predicate and not to the Copula. Thus, if we say, " This farm was fertile, whether it be so now or not," it is the same as to say, this farm Pred. IS one formerly fertile . The weather may be good, Pred. the weather is what may be good|. As either term of a Judgment may be a Conception including differ- ent objects, or having several marks, so several words may be employed to make up a term. Thus, |" The Sub. Cop. Pred. }} dews of the evening are |the tears of the sky. " Birds, fishes, beasts, and reptiles, are animals." 6. Words which alone cannot express conceptions, Categorematic or intuitions, cannot of themselves con- and Syncatego- rematio Words, stitute terms of a Judgment. They can Sec. III.] JUDGMENT. 87 only enter into these terms by combination with verbs and nouns substantive and adjective. Such are articles, prepositions, conjunctions and adverbs. These are Syncategorematic; nouns, adjectives, and verbs, on the other hand, are Categorematic, because they can of themselves be Terms. Sect. II. — Quantity, Quality, Eelation, and Modality of Judgments. 7. Judgments may be viewed, I. Judgments in With reference to the relation of the respect of Quan- predicate to the extension of the sub- tlty " j ect — Quantity. II. With respect to the relation of the predi- cate to the intension of the subject — Quality. *""* III. With respect to the manner of connecting the predicate with the subject — Relation. Relation. IV. With respect to the degree and kind of cer- tainty in the connection of subject and predicate — Modality. Sect. III. — Quantity op Judgments. 8. With respect to Quantity, Judgments are either Universal, Particular, or Singular. ' & Universal Judgments are Universal when the Pre- Judgments. 83 LOGIC. [Chap. III. dicate is affirmed or denied of all the Subject taken distributively, as, " all men are sinners ;" " no men are angels." Judgments are Particular when the Predicate is affirmed or denied of an indefinite part of the sub- ject, as, "some men are orators;" "some Particular, ^ -^ . „ (jrovernments are not Democratic. Judgments are Singular ; a. when the Predicate is affirmed or denied of individuals, as, " Caesar was a Conqueror ;" "this man is not learned." b. When the subject is a plurality of individuals taken collectively. A collective noun is, for Logical purposes, Singular: as, "This crowd is tumultuous," "An army consists of soldiers." 9. Singular Judgments, for all Logical purposes, may be accounted as Universals, since mente^'eq^va' in them > the whole Subject is Spoken of, lent to Univer- an( J t } ie y are subject to the laws of sals. Universals. In like manner, when any Definite part of the Subject is taken, it may be considered Also a Definite J . part of the Snb- as a universal. For the whole class jec ' denoted by the subject-name with its limiting adjuncts is spoken of — Thus " these men are natives of Ireland." Sec. IV.] JUDGMENT. £9 It is in place here to add, that Judgments are further distinguished as Simple and Compound. Judgments are Simple when, in fact as well as form, there is but one subject and one Predicate, as, " men are rational animals." A Judgment is „. , ° Simple and Compound when, though simple in form, Compound by a plurality of subjects or predicates, u gmen s ' there is in force and effect a plurality of Judgments. Thus, " Peter, James, and Thomas were Apostles,' ' amounts to three propositions, one affirming of Peter, another of James, and another of John, that he was an Apostle. " Men are rational, accountable and im- mortal," may be divided into three propositions, each having "men" for the subject, but one having the predicate * rational," the other " accountable," etc. Sect. IV. — Quality of Judgments. 10. The differential Quality of a Judgment is that it affirms or denies the agreement of Subject and Predicate. Hence in respect Affirmation or of Quality, Judgments are either Affir- Negati which, they nave been accus- als, tomed to mark by the Symbols, A. E. I. O., as follows : Universal Affirmative, .... A. Universal Negative, E. Particular Affirmative, .... I. Particular Negative, . . . .0.* * The additional Judgments recognized by recent Logicians will be noticed in due time. Sec. VI.] JUDGMENT. 91 Sect. V. — Distribution of Terms in Judgments. 12. Of the foregoing Judgments all Universals and no Particulars distribute the Subject. All Negatives and no Affirmatives tribute the Snb- distribute the Predicate. J ectl Ne g atives the Predicate. The reason of the first rule is obvious, for in Universals the whole subject is spoken of Distributively.* In Particulars only a part of it. No Negative Judgment can hold good unless it cuts off the whole of the Predicate from the subject. Thus, if we say, " some men are not poets," the whole of the class of poets is cut off from these "some men." " No men are perfect," cuts off the whole of the class " perfect " from the class men. Sect. VI.— Eelation of Judgments. 13. The Relation of Judgments has respect to the manner of the connection between the Relation either subject and Predicate. In this respect Categorical or Judgments are either Categorical or ypo Hypothetical. * Collective Nouns are no real Exception, since in a Logical sense, they are individuals and form the subjects of Singular Judgments. 92 LOGIC. [Chap. III. 14. A Categorical Judgment asserts or denies the agreement between the subject and Pre- dicate, simply and unconditionally, as, " Brutus killed Caesar," " a traitor is not a patriot." 15. A Hypothetical Judgment asserts or denies such agreement upon a condition, viz : ypo e of the truth or falsity of some other Judgment. Thus, "if crops are large, food is cheap." " This man is either holy or unholy." '. , „ 16. Hypothetical Judgments are of Three kinds of Jr & Hypothetical three kinds : Conditional, Disjunctive, Judgments. i -rv«i j* and JDilemmatic. 17. The Conditional Judgment affirms such a Conditional region between two others, respec- Jndgments. tively called Antecedent and Conse- Antecedent and that > if the former be trUe > the Consequent, latter is true also, as, "if the sun shines, it will give heat." Conditionals are indi- cated by the particles, "if," or its equivalents, " when," " in case of," etc. 18. The conditional, like all hypothetical, has in it a categorical element, i. e. it asserts Hypothetical have a Categori- categorically a certain relation between the Antecedent and Consequent ; such, that, if the former is true, the latter is true ; and if See. VI.] JUDGMENT. 93 the latter is false the former is false. It often ex- presses the relation of cause and effect. m _ _ , ^ x Causal Relation If the cause operates the effect will fol- often in Condi- low. It is to be observed that a condi- tional does not assert the truth of either of its mem- bers, but of the relation between them. 7 Do not assert It may assert, not only a causal rela- the truth of .. 1 , ,1 ,i r. , • either member. tion, but the truth of a certain argu- ment. Thus, u if drunkards drink what intoxicates, A. B. drinks what intoxicates." This . , . Other relations. is not an assertion either that drunk- ards, or A. B. drink what intoxicates ; nor that the former is the cause of the latter ; but that there is such a relation between the two, that if the former be true the latter is true. A certain fact, however, is by implication asserted as the foundation of this relation, viz., that A. B. is a drunkard. 19. Disjunctive Judgments assert the connection between the predicate and the subject, _. . x . L or Disjunctives as- with an alternative indicated by the sert with an ai- • i .i i m, // .. • ternative. particles, either and or. lhus, "it is either Spring, Summer, Autumn, or Winter." The force of it is that if one member be affirmed, all the others are denied. If one is denied, then some one of the residue is true. This is founded on the law 94 LOGIC. [Chap. III. of Excluded Middle. A judgment or its contra- .p , , -n dictory must be true, and there is no Founded on Ex- J 7 eluded Middle, middle between them. So conditionals are founded on the law of Sufficient Its members mutually exciu- Reason. Of categoricals the affirma- tives are founded on the principle of Identity, and the negatives on the law of Contradic- tion. 20. Hence, in order to any valid conclusion from the affirmation or denial of either member of a dis- junction, these members must be mutually exclusive. Indeed such alone are genuine disjunctives. Dis- Differ from Par- junctives must not be confounded with titives. Partitive Judgments, which, under the form of a disjunctive, simply predicate of a genus its several species ; as, "all Africans are either bond or free." This is but dividing the genus into its component parts or species. It differs from the dis- junctive in this, that the predicates are affirmed concurrently, and not alternatively, of the subject. The affirmation of the one is not, as in a pure dis- junctive, a denial of the other, although the predi- cates are still mutually exclusive with regard to the portions of the subject to which they respectively belong. Sec. VII.] JUDGMENT. 95 21. Dilemmatic Judgments involve a combina- tion of the conditional and disjunctive. Dilemmatic Thus, " if A. B. succeeds, he will either Judgments. rule or ruin." Here the disjunction is in the conse- quent of the conditional. It may also be in the antecedent. " If man is either good or ill deserving, he is a moral agent." Sect. VII. — Substitutive Judgments. 22. Substitutive Judgments are those which being affirmative have a distributed predicate, g^stitntives This distribution of the predicate can- defined. not be known from the mere form of expression. As we have already seen, affirmatives as such, do not distribute the predicate. To say that men are mortals, is merely saying that they are in the class of mortals. They in fact comprise a part but not the whole of mortals. But if we say, " men are rational animals," we mean all rational animals, for there are none but men. This, however, does not appear from the affirmative form of expression, any more than, if we were to say, " men are animals." We know it from other evi- dence. "Rational animals" is the definition of 96 LOGIC. [Chap. Ill, men, and is, therefore, co-extensive with it. In all All Definition cases °f Definition then, and in all the Substitutive. kinds of Definition which have been pointed out, we have Substitutive Judgments. 23. Judgments of this kind are called Substitu- Wh called *^ ve ' because the predicate may be sub- Substitntive. stituted for the subject without limiting the quantity, either of the j udgment, or of the predicate substituted. If we define men to be rational ani- mals, we can sav that "all rational animals are men." If we say that "Maine, New Hampshire, etc., are the New England States," we can, by sim- ple substitution, say that " the New England States are Maine, New Hampshire, etc." 24. Substitutive Judgments are either Particular „ . or Universal. Of these latter we have Eitber Particu- lar or Univer- already given examples. The former are such as, " some stars are planets," i. e. all the planets: "some men are poets," i. e. all poets. 25. Affirmative Judgments, in which the predi- Attributive cate 1S undistributed, are called Attri- Judgments. butive, because they affirm an attribute of the subject, without taking this attribute in its whole extent, or substantively. Thus, " men are rational." Sec. VII.] JUDGMENT. 97 26. The importance of Substitutive Judgments will appear, when we come to treat of the subject of reasoning. They render Substitutive many processes of reasoning valid, Jud s meilts ' which would otherwise be invalid, owing to the non- distribution of affirmative predicates, as will be ex- plained in the proper place. 27. The reason why logicians who have recog- nized this class of judgments, have why this per- treated this subject as belonging to the *** VtT" J & fe lation of Judg- Relation of judgments, or as concerned merits. with a peculiar class of them, in respect to the man- ner of the connection of the subject and predicate, is, that it exhibits the quantity of the predicate as related to the subject. Indeed every affirmative judgment, when fully explicated in language, be- comes an equation of the subject and predicate as to quantity, and so a Substitutive Judgment. This will appear if we explicitly quantify EqnationofSuI) . the predicate, i. e. fully express in words ject and Predi- what we mean in thought. Thus, if we say, " all men are mortals," we mean, " they are (i. e. =) some mortals." " All men are rational animals/' means " all men are (i. e. =) all rational animals." 9 G 98 LOGIC. [Chap. Ill, 28. Substitutive Judgments are indicated respec- tively, the universals by the letter U, and the par- ticulars by the letter Y. Thus, we have The Symbols of Substitutive six different kinds of judgments, desig- Judgments. , ^ ^ ±.\ ' l r. i nated by their several symbols as follows : Universal Attributive, .... A. Particular Attributive, .... I. Universal Negative, . . . . E. Particular Negative, . . . . O. Universal Substitutive, . . . U. Particular Substitutive, . . . Y. 29. [Besides these, Sir William Hamilton has lx . undertaken to develop two others ; viz., Negatives with x 7 7 undistributed Universal and Particular Negative PredicateSi T , . •,-! .• , »i , i *■ Judgments with undistributed predi- cates, which he marks by the respective symbols tj and w. But undistributed negative predicates are so contrary to all normal thought and language, that, at best, they are useless, and need not claim our attention. The Judgments, " No men are some animals," " and some men are not some Insignificant and worthless, animals," are awkward, insignificant, Sec. VIII.] JUDGMENT. 99 and worthless, being nearly, if not quite incapable of real contradiction.*] Sect. VIII. — Analytic and Synthetic Judgments. 30. Analytic Judgments are those in which the predicate is involved in the very Con- Analytic Judg- ception or Definition of the subject. As, ments - " man is rational." " Quadrupeds are four-footed." * They carmot, with slight exception, be opposed by contrary or contradictory propositions, in any normal use of language. The following table in which A stands for a distributed, and I for an undistributed term, and the letters f and n respectively for an affirmative or negative copula, exhibits at a glance the import and force of the Eight Judgments recognized by Hamilton. A. Afi. All are some. All men are mortals. E. Ana. Not any is any. No men are angels. I. Ifi. Some are some. Some trees are beautiful. 0. Ina. Some are not any. Some coins are not silver. U. Afa. All are all. All men are all rational animals. Y. Ifa. Some are all. Some men are all the poets. 77. Ani. Not any are some. No planets are some stars. g>. Ini. Some are not some. Some trees are not some oaks. a is without force because not contradictory to nor inconsistent with any other proposition. >j may indeed have greater force. But this is seldom important in actual thought. Both judgments in- deed are rather conceivable than actual in normal thought, and for practical purposes, without assertory force. 100 LOGIC. [Chap. III. They therefore require no proof. They are evident simply from the analysis of the subject. Hence they are a priori, i. e. known from the conditions given, if not always in the most absolute meaning of a priori, yet from the definition of the subject. 31. Synthetic Judgments are those in which the Synthetic Judg- predicate adds to the conception or defi- meats. nition of the subject. They, therefore, require proof. Thus : " laurel- water is poisonous," "horned animals are ruminant," "the conception of a perfect being involves his existence." Synthetic Judgments are, with a qualification to t, be noted, a posteriori. The Formal Exception in f Mr Formal Sci- Sciences, and those which deal with ences. necessary truth, furnish us a peculiar class of Judgments that are both synthetic and a „ , . priori. All the demonstrated proposi- How they give ± x x Synthetic Judg- tions in Geometry, e. g. are a priori. Yet they are not a part of the definition. They are not immediately suggested or implied by it. They require to be proved by a chain of reason- ing from the definitions, more or less extended. Yet this reasoning is a priori. The same is true of most of the principles of Logic. In this sense we have Synthetic Judgments a priori. They are, in truth Sec. IX.] JUDGMENT. 101 partly analytic, in that they are ultimately evolved from the definitions ; synthetic in that they require proof beyond the mere statement of the definition. The origin of this use of the terms analytic (avaloco, to take asunder), and synthetic (oovridyfii, to put together), is evident from their etymology. The terms Explicative and Ampliative have, for obvious reasons, been employed to de- Ex u .. note the same properties of Judgments Ampliative. as Analytic and Synthetic. Sect. IX.— The Modality of Judgments. 32. The Modality of Judgments respects the pos- sibility, certainty, or necessity of the The Modality of connection of the predicate with the **»* *>; * longs to Applied subject. This, however, really belongs L °s ic - to the meaning of the predicate rather than to the copula, or any part of the logical form of the judg- ment. Strictly, therefore, it pertains to the matter rather than the form of the judgment, to Metaphy- sics instead of Logic. It belongs, accordingly, rather to applied than to pure Logic. To this we shall therefore defer it, although it is sometimes treated at this point. 9* 102 LOGIC. [Chap. III. Sect. X. — Plueative Judgments. 33. Plurative Judgments are those in which Plurative Judg- more tnan ^alf, but not all of the Sub- menu defined. j ec £ [ s taken ; as, " Most men are vain." Of a similar nature are Numerically Definite Judg- ments, i. e. those in which a definite Numerically Definite Judg- number or numerical proportion of the ments. i . • ■> subject is taken. Both of the foregoing have some importance as giving rise to a peculiar kind of valid syllogism which will be explained in its proper place. See chap. V., sect. I. 5. Sect. XI. — Conversion of Hypotheticals into Catego- RICALS. 34. It has already been shown that in every _ . . , Hypothetical Judgment there is a cate- Hypotheticals J L ° have a Cate- gorical element, which affirms or de- gorical element. . , , . , . , . . , , , . , nies the given hypothetical relation be- tween certain categorical judgments. This being so, by a slight change of phrase, they may be made Categorical in form. This can be done, as follows, a. Conditionals may be so converted by substi- Conditionals tilting for the particles " if," " when," how turned into Categoricais. etc., which have a conditional force, Sec. XL] JUDGMENT. 103 such phrases as "the case of," the "circumstances in which/' etc. Thus the conditional, if A is B, X is Y, is the equivalent of, " the case of A be- ing B is the case of X being Y," which is a categorical. The conditional, " if the thermometer is at zero, ice forms rapidly," may be transformed into, " the case of the thermometer being at zero," or "the case," or "the circumstance," or "the time in which the thermometer is at zero, is that in which ice forms rapidly." Certain Abbreviations are practicable when the same terms are found in both antece- ,. Abbreviations dent and consequent. Thus the condi- in the case tional, "if Peter is a drunkard, he of only tbree 7 Terms. (Peter) is degraded," is equivalent to " every drunkard is degraded," otherwise it could not be true. b. Disjunctives may be turned into Categoricals by using all their members for one of , . • ,. ., , Disjunctives. the terms, and the phrase, "possible cases," or the like, for the other, thus forming a judgment by Colligation, which, as we . „ _ . , By Colligation. have seen, is the opposite ot .Logical Division. Thus: "This season is either Spring, 1Q4 LOGIC. [Chap. III. Summer, Autumn, or Winter," is equivalent to either of the categoricals, "the possible cases in regard to this season," or " the only alternatives in regard to it, are Spring, Summer, Autumn, Win- ter." As has been shown before also, Disjunctives may „ „ , . be turned into Conditionals, by taking; By first being ' J & turned into Con- the contradictory of one of their mem- bers for the antecedent, to which the other members become consequents. Thus, in the foregoing example, " if it is not Spring, it is either Summer," etc. When once a conditional, it can be made a categorical, according to the rules already given, e. g. " The case of its not being Spring, is the case," etc. c. Dilemmatic Judgments being compounded of Conditionals and Disjunctives, may be Dilemmatic Judgments to be resolved into these, and each of these Eesolved. , , 1 . . , 1 may be changed into categoricals, ac- cording to the methods just indicated. Thus, the Dilemmatic Judgment, " If iEschines did or did not join in the public rejoicings, he was either in- consistent or unpatriotic," may be analyzed ; " If he joined, etc., he was inconsistent ;" " If he did Sec. XL] JUDGMENT. 105 not join, etc., he was unpatriotic;" "But he did or did not join f " He was either inconsistent or un- patriotic." These may be turned into Categoricals by the methods already prescribed. CHAPTER IV. REASONING IMMEDIATE INFERENCE. Section I. — Introductory Remarks. 1. The next stage of Thought after the forma- Zoning De- tion of Judgments, is that of deriving fined. from judgments given other judgments founded upon them. This is Reasoning. 2. Reasoning is by inference from one Judgment to another derived from it : or from two Media ie and Im- mediate Infer- judgments to a third, which could not be derived from either alone, but flows from both combined. The former is called Reasoning by Immediate Inference, the latter by Mediate In- ference, i. e. from one judgment through the medium of another ; or more strictly, as it will more fully appear, through a middle term, mcdius term huts, common to both the judgments given, by means of a common or opposite relation to which, the two 106 Sec. II.] IMMEDIATE INFERENCE. 107 terms of the conclusion are found to agree or disa- gree with each other. These two kinds of reasoning will be severally treated in their order. 3. Immediate Inference, i. e. infer- Three kinds of n • j i r» xi Immediate In- ence of one judgment irom another, is f of three kinds, termed Opposition, opposition, Con- Conversion, and Equipollence or Infi- ^Jf 011 ' *f" 7 *• x pollence or Inn- nitation. And first of, nitation. Sect. II. — Opposition. 4. Opposition exists between judgments having the same subject and predicate, but dif- opposition de- fering in quantity, or quality, or both. fined< Thus, " all A is B," and "some A is not B," are op- posed. They differ both in quantity and quality. This is the strongest kind of opposition, called con- tradictory. From any judgment whatever, an infer- ence can be made regarding its contra- , . , . , ., . Contradictories. dictory, or which is the same thing, any affirmation or denial regarding either of two con- tradictories, warrants an inference in regard to the other. Thus, if we take the two contradictories, " all men are mortal/' " some men are not mortal/' when either is true the other is false ; when either is false the other is true. 108 LOGIC. [Chap. IV. 5. Besides the Contradictories, we have the Con- traries A and E, and the Sub-Con- Contraries, Sub-Contraries, traries I and O, which respectively dif- fer in quality alone. Also the Subal- terns A and I, E and O, in which the members of each respective pair differ from each other only in quantity. In each pair of these the Universal is Snbaiternans. called the Subalternans, the Particular Snbaltemate. the Subalternate. All these forms of op- position are brought compactly and clearly to view by the following ingenious and simple diagram, which has been devised by logicians. Contraries. E to 'a XJ1 &/ {; CD Sub-contraries. Sec. II.] IMMEDIATE INFERENCE. 109 6. The Laws of Inference in the case of judg- ments in Opposition are, in brief, as fol- Laws of Infer- ence in Opposi- 10WS : tion. a. Of Contradictories one or the other must be true, both cannot be true. And by the Ee-Contradicto- law of Excluded Middle no interme- ries * diate between them can be true. Therefore, from the truth of either of two contradictories, it follows that its opposite is false ; and from the falsity of either, the truth of the opposite may be inferred. b. From the truth of either Subalternans, the truth of its Subalternate follows. From • i i Subalterns. its falsity nothing follows with regard to the Subalternate; from the truth of either Subal- ternate nothing follows in regard to its Subalter- nans. From the falsity of the Subalternate the falsity of the Subalternans results. c. From the truth of a Contrary the falsity of the opposite Contrary follows. But Contraries. from the falsity of one Contrary, nothing follows in regard to the other. d. From the truth of either Sub-Contrary nothing follows in regard to the other Sub-Con- trary. But from the negative of one of them, it follows that the other must be true. Sub-Contraries. 10 110 LOGIC. [Chap. IV. 7. From this it appears that the Opposition be- tween Contradictories is far the most im- Contradictory Opposition most portant and fruitful of inferences. The Important. • i 1 1 i j? • ,1 * most available mode ot proving the truth of many propositions, is to prove their Con- tradictories false. 8. The foregoing view exhausts opposition as between the four fundamental judg- OppositionTrea- ments A E I and O above recognized tedbytheJudg- jj y t ] ie i tion. In the nrst case fe and r agree — are one with each other, — because they each agree with, are the same as, M. Oak and stone do Illnstration, , .., , .-. ■, .-, not agree with each other, because the one is, the other is not, a tree. To say that they are one, would therefore be a contradiction. 3. This process of reasoning from two judgments given, to a third derived from them, through a middle term, is called an Argument, (from Argumentum, proof) and, when stated in regular logical form, so that the connection of the premises with the conclusion is immediately evident : it is called a Syllogism, aollo- yiafxoq^ i. e. collecting the elements given in the premises into a conclusion. 4. The subject of investigation now before us, therefore, is the doctrine of Syllogisms. A Syllogism, like all other reasonings, consists of Parts of the two P ar ts, that which is to be proved, Syllogism. anc j t ] iat j 3 y wn i cn it is to be proved. Sec. I.] MEDIATE INFERENCE. 125 Of these, in whatever order they may stand, the latter are called the Premises. These . __ . . , r , Premises. Premises are Major and Minor. The Major Premise is that in which the Major Term is compared with the Middle, , , i ,i i i • i Major Premise. whatever may be the order in which they stand. The Minor Premise is that in which the Minor Term is compared with the Middle. The Premises, as the word implies, are put before the Conclusion, when the syllo- * J Order of Premi- gism is arranged in regular logical ses and Oouciu- order. Thus : " All conquerors are tyrants. Buonaparte was a conqueror. He was a tyrant." In this case the Conclusion is connected with the Premises by some inferential particle, such as " therefore/' " hence," etc. But it is more common, and quite as natural, to adopt the reverse order in actual reasoning — to put the Conclusion first and the Premises afterward. Thus : " Buonaparte was a tyrant for he was a con- queror, and all conquerors are tyrants." And fre- 11* ^26 LOGIC. [Chap. V. quently, in either case, not more than one premise is expressed, the other being understood and obvious. Thus : " Many voters are tools of demagogues be- cause they are ignorant." " Free government will continue since the people are virtuous." This, re- gularly drawn out would be, " A virtuous people will preserve a free government. This people is virtuous. .*. It will preserve a free government." A Syllogism in which the premises are stated first is called Synthetic, because it puts Synthetic and . . , r Analytic Sylio- together the premises in order to form gisms, ^ e conc l us i on# When the conclusion is stated first, it is called Analytic, because this conclusion is analyzed into the proofs out of which it grows. The Major Term is the predicate of Major Term, ,, ^ , the Conclusion. The Minor Term is the subject of the Minor Term, ~ , Conclusion. Hence every Syllogism must have three, and but HasthreeJndg- three, Judgments. The Major Premise, ments. the Minor Premise, and the Conclusion in which the major and minor terms are compared with each other. Sec. I.] MEDIATE INFERENCE. 127 Every Syllogism must have three, and but three, Terms; the Major, Minor, and Middle. If there be four Terms, either in form or in fact (from the ambiguity of either of them), the two terms of the conclusion will not have been compared with one Middle Term, and no conclu- sion can follow. 5. From the principles of Identity and Contradic- tion, the following Canons for testing Canong of the the validity of all Syllogisms result. Syllogism, a. If the Major and Minor Terms, each being compared with the same third or Mid- „ r Canon of Affir- dle term, both agree with it, they agree mative Conclu- with each other. This underlies all Affirmative Conclusions. b. If of the Major and Minor Terms, both being compared with the same third term, one of Negative agrees and the other disagrees with it, Conclusions. they disagree with each other. This is the founda- tion of Negative Conclusions. Therefore if one premise be negative, the conclusion must be negative. c. If they both disagree with the same third term, no conclusion follows as to whether , T . 7 . Negative Pre- they agree or disagree with each other, mises give no This is the case of Negative Premises, 128 LOGIC. [Chap. V. from which there can be no Conclusion. Thus, from "A bird is not a sheep," "a robin is not a sheep" — nothing can be inferred. d. The Middle Term must be distributed at least once in the premises, otherwise the Middle Term _ . must be Distri- Minor Term may be compared with one part and the Major with another part of it. From, "Some men are poets, Some men are Indians," Nothing follows. Plurative Judgments, however, give rise to a peculiar class of valid Syllogisms with an undis- tributed middle. Thus : " Most men have some kind of religion, Most men are uncivilized, .'. Some uncivilized persons have some kind of religion." The same is true of numerically definite Judg- ments. Thus : "60 out of every 100 are unreflecting, 60 out of every 100 are restless, .*. 20 out of every 100 restless persons are unreflecting." e. No term may be distributed in the conclusion Sec. I.] MEDIATE INFERENCE. 129 which was not distributed in the premises. This, which is Illicit Process, is furtively No Illicit p ro . speaking of more in the conclusion cess " than was contained in the premises. Thus : "All beasts are animals, Birds are not beasts, They are not animals." /. From Particular Premises, of which Y is not one,* nothing can be inferred. With Particular pre- none but the particular judgments I mises give us no 3 /-v a , 1 ill • • • x l Conclusion. and O oi the old logicians in the pre- mises, no conclusion can follow, because, if both were I, no term would be distributed, whence would result an undistributed middle. From "some men are heroes," and "some men are poets/' nothing can be inferred. If both premises be O, they are both negative, and no conclusion can follow. If one be O and the other I, the middle term must be the predicate of O in order to be distributed, and in that case all the other terms will remain undistri- * The following is a valid conclusion from the particular judg- ments Y and I. Y. Some trees are all the oaks. I. Some oaks are white oaks. ..*. Some white oaks are trees. I 130 LOGIC. [Chap. V. buted. But, one premise being negative, the con- clusion must be so likewise. This would distribute the major term in the conclusion, which by suppo- sition was undistributed in the premises. Illicit pro- cess results. Thus: "Some men are not cultivated, Some poets are cultivated, Some poets are not men." g. If either Premise be particular, the Conclu- Conclusion par- s i° n m ust be Particular. In other ticuiar when W ords, a universal conclusion requires either premise is so. both premises to be universal. If the universal conclusion be A, then the sub- ject of it must be distributed in the premises, and must therefore be the subject of one of them, since being both affirmative, neither can distribute the predicate. For the same reason the middle term will be undistributed in that premise, being then the predicate of an affirmative. Therefore the middle term must be the subject of the other pre- mise, which must also be universal, in order that it may be distributed. Thus a universal affirmative conclusion requires both premises to be distributed. If the universal conclusion be E, then both its terms must be distributed in addition to the middle Sec. I.] MEDIATE INFERENCE. 131 term the premises. This requires both premises to be universal and one of them negative, or both nega- tive and one universal. The latter is impossible as no conclusion can come from two negative premises. Therefore the premises must be both universal. The principle that one negative or one particular premise renders the conclusion respectively nega- tive or particular, logicians have expressed by saying that the conclusion follows the weaker part. The whole of these canons have been condensed into the following Latin lines : " Distribuas medium nee quartus terminus adsit, Utraque nee prsemissa negans, nee particularis : Sectetur partem conclusio deteriorem, Et non distribuat nisi cum prsemissa, negetve." This reasoning, however, applies only to syllo- gisms in the old Logical Judgments, A E I and O. Syllogisms with U or Y in the premises, may have universal conclusions with one premise particular. Thus: U. " All men are rational animals, Y. Some men are all the poets, All the poets are rational animals." A. " All men are rational, Y. Some men are all the Polynesians, All the Polynesians are rational." 132 LOGIC. [Chap. V. U. " Animals are all bodies having sensation, Y. Some animals are all oysters, .*. All oysters have sensation." Sect. II. — Moods. {For Moods as affected by Substitutive Judgments, see Appendix B.) 6. The Mood of a Syllogism is the relation of its several judgments to each other, with Mood Defined. „ . . reference to their respective quantity and quality, these being designated by the symbolic letters A E I O. The Mood of a syllogism, whose premises and conclusions are universal affirmatives thus becomes AAA. If the major premise were universal affirmative, the minor universal negative, and the conclusion universal negative, it would be A E E, etc., etc. The possible combinations of these four kinds of Number of propositions are of course 4X4X4 = Moods. 6^ j> u £ mos t of these are invalid as involving violations of some of the preceding canons. Thus E E E, E O O, and others, are bad on account of negative premises. I O O and others, for parti- cular premises. I E O, for illicit process. Sifting Only eleven ou ^ a ^ mo °ds that are thus invalid, only valid Moods, eleven valid ones remain. And of these only a part are valid in any one figure. Sec. III.] MEDIATE INFERENCE. 133 Sect. III. — Figure. 7. The Figure of a Syllogism depends upon the situation of the Middle Term in the premises. The Figures as fixed by Aristotle were three. The first and normal figure is when the Figures of Aris- middle term is the subject of the major totle ' and predicate of the minor. In the second, the middle term is the predicate of both, and in the third the subject of both. The fourth, which is reputed to have been introduced by Galen, and is largely dropped by logicians as an awkward and useless in- version of the first, occurs when the middle term is made the predicate of the major, and subject of the minor premise. Taking S, M, and P, respectively, for minor, middle, and major terms, the figures would be represented thus : 1st Fig. M P. 2d. P M. 3d. M P. 4th P M. S M. S M. M S. M S. S P. S P. S P. S P. Sub. Pr£e.; Turn Prae. Prfe. ; Turn Sub. Sub.; Turn Prse. Sub. 8. Of the eleven valid Moods, some are Invalid in one figure which are valid in another. y alid and - Thus A E E would be valid in the valid Moods - second figure, as, 12 134 LOGIC. [Chap. V. " All men are mortal, No angels are mortal, V No angels are men." But in the first figure, it would involve illicit process of the major term. Thus : " All birds are animals, No reptiles are birds, .*. No reptiles are animals." The only valid moods in the first figure are A A A, E A E, A 1 1, E I O. As this is the mood into which the normal syllogism falls, logicians have usually unfolded the principles which govern the syllogism primarily with reference to that, and have devised ways of converting syllogisms in the other figures into it, and subjecting them to its tests. The canons which have been presented, however, apply immediately to the syllogisms in all the figures. 9. As is their wont, logicians have wrought out mnemonic lines in Latin to designate the valid moods and syllogisms in the several figures, with the modes of reducing the subordinate figures to the first. j-bArbArA, cElArEnt, dArll, fErlOque prio- ns. Figure 1. \ „ rcEsArE, cAmEstrEs, fEstlnO, bArOkO (or Figure 2.< l fAkOrO), secundse. Sec. III.]. MEDIATE INFEREXCn. lgg 'tertia, dArAptl, dlsAmls, dAtlnl, fElAptOn, Figure 3. -I bOkArdO (or, dOkAmO), f ErlsO, habet, quarta, insuper addit, rbrAmAntip, cAmEnEs, dlmAarln, fEsApo FigUrc4J l frEsIsOn. In the foregoing lines the vowels signify the moods of the syllogisms respectively al- Erplanation of lowablein each figure. The initial letters Mnemonic b, c, d, f, denote that the syllogisms having them in the lower figures are to be reduced to the corresponding ones in the first, m indicates that in doing this, the premises are to be transposed, s and p that the proposition denoted by the vowel immediately preceding, is to be converted, s, simply p, per aeddensy i. e. by limitation of quantity from universal to particular. 10. A slight examination of the three first figures —and for practical purposes the fourth Limitationg may at present be passed by — will show npon the several that, in the First Figure, the minor pre- mise must be affirmative in order to Upon the 1st. escape illicit process of the major term or negative premises, and that consequently the major premise must be universal in order to distri- bute the middle term. The Second Upon the 2d. 136 LOGIC. [Chap. V. Figure can prove only negatives, because the mid- dle term, being a predicate in both premises, re-« quires at least one negative premise to distribute it. The Third Figure yields only particulars, because the major and minor terms, being both predicates, can only be distributed by having their respective premises negative. But only one of these can be negative, and if either be so it must be the major, for if it be the minor, it will make the conclusion negative, and thus distribute the major term, which, in this case, would be un- distributed in the premises — thus bringing in illicit process of the major. 11. It must, however, be remarked, that these Exceptions to properties of the several figures will be t e oregomg in ~ rea £}y modified in the case of the iudff- tne case of pre- ° J J ° mises u and Y. ments in U and Y, which afford dis- tributed affirmative predicates, and therefore cure all faults of the syllogism arising from the non- distribution of affirmative predicates. Inasmuch as it does not appear from the mere form of ex- pression that any affirmatives distribute their predicates, it is always presumed that they do not, unless proved by other evidence. The analysis of the normal syllogism and its properties is therefore Sec. III.] MEDIATE INFERENCE. 137 conducted on this presumption. But if the judg- ments usually classed as A and I, can in any case be shown to be U and Y in the syllogism, then neither of the foregoing limitations in respect to the several figures will hold. Thus, with these substitutive judgments, as premises, the first figure may have a negative minor without either illicit process or negative premises. Take the example, U. " All men are (all) rational animals, (Negative Minor.) E. No angels are men, No angels are rational animals." Again, (Particular Major.) " Some poets have genius, Y. Some men are (all the) poets, Some men have genius." Again in the second figure, U. " Rational animals are men, A. Poets are men, (Affir. Conclusion.) .*. Poets are rational animals." Also in the third figure, " All men are mortal, U. All men are (all) rational animals, (Universal Con.) A. .*. All rational animals are mortal." This is the proper formula of the Inductive Syl- logism, which naturally falls into the Formula of In- ductive Syllo- third figure, and could not, aside from a gi sm , 12* 138 LOGIC. [Chap. V. substitutive judgment, yield a universal conclu- sion. Thus : "XYZ, are ruminant, X Y Z, are (as good as) all horned animals, .*. All horned animals are ruminant." Sect. IV. — Maxims by which different logicians have APPLIED THE PRINCIPLES OF IDENTITY AND CONTRADIC- TION to the Syllogism. 12. Most of these are founded on the prin- Genus Predica- c ipl e that, in a normal judgment, the ted of Species. Genus is predicated of the Species, and therefore that the extension of the subject is included in that of the predicate. A. First among these maxims is the celebrated Aristotle's Die- Dictum of Aristotle, that whatever can tum ' be predicated affirmatively or negatively of any class or term distributed, can be predicated in like manner of all and singular the classes or in- dividuals contained under it. This is self-evident. Whatever can be affirmed or denied of all men, can be affirmed or denied of whatever is contained un- der the class man. This maxim is Directly appli- cable to First directly applicable to, and illustrated by the First Figure. Thus : Sec. IV.] MEDIATE INFERENCE. 139 " All men are mortal, Poets are men, .'. Poets are mortal." Here mortal, being affirmed of the genus man, is also affirmed of the species poets included under it, " No men are brutes, Poets are men, .*. They are not brutes." Here, what is denied of the higher class, is also denied of the lower class or species included in it. B. An equivalent maxim is that founded on the relation of Whole and Parts, that what wllole and may be affirmed or denied of a whole Parts ' (in extension), may be affirmed of its parts, i. e. what is predicated of a genus may be predicated of the species and individuals, or the parts com- posing it. Pars partis est pars totius. C. To the same effect is the maxim contention contenti est contentum continentis. Men, the content of biped, is also the content of animal, which con- tains biped. D. Kant's formula is, nota notaz est nota rei ipsius. This probably has reference to construing and testing Syllogisms according: to the Intension of T . „ • J fe & Intensive Syllo- the terms. To this some of the fore- gisms, 140 LOGIC. [Chap. V. going maxims apply, but in a reverse order, since the whole of intension increases as the whole of in- tension decreases. Therefore, in the Intensive Syl- logism, the term of least extension, i. e. the minor, becomes the greater whole, and so in effect the major. Thus the Syllogism according to extension, " All conquerors are brave, Caesar was a conqueror, .'. He was brave," according to intension would be construed thus: " Csesar was a conqueror, i. e. had the mark or attribute of one, Conquerors are brave, i. e. have the mark of bravery, .'. He had the mark of bravery (was brave)." Construed either way, the connection of the same Conclusion the conclusion with the same premises, is same construed n , • j o , t, , . equally certain and necessary, bome- by Extension x J J and intension, times the Extension, sometimes the In- tension, is more prominent in the mind of the thinker. 13. The relation of the several terms of the Syl- Iliustration by logism to each other has often been ex- Diagrams, hibited to the eye by Circular Diagrams. Thus the Syllogisms of the several figures may be exhibited. Sec. IV.] MEDIA TE INFERENCE. 141 Barbara. Celarent. 1st Figure. Darii. Ferio. 1st Figure. Cesare. Camestres, etc., etc. 2d Figure. 142 LOGIC. [Chap. V. Darapti. Felapton, etc., etc. 3d Figure. For a fuller view of the different schemes of Syllogistic Notation, see Appendix B. Sect. V. — Unfigured Syllogism. 14. Before leaving this subject, it is proper How Figure dis- ^° ca ^ attention briefly to a mode of appears. analyzing the Syllogism introduced by Hamilton, which dispenses with Figure altogether. After the explicit quantification of both terms of a judgment, the relation between them may be ex- pressed by the sign of equality, and either of them may become indifferently subject or predicate. In this way Figure disappears. If we say " Men are rational, Negroes are men, .'. Negroes are rational." Sec. VI.] MEDIATE INFERENCE. 143 we may more explicitly, though awkwardly, state our meaning thus ; "All men are = some rational. All negroes are = some men. .*. All negroes = some rational." And it is obvious that the terms of either or all of these judgments may be transposed, without impair- ing the sense or reasoning. Thus : "Some rational = all men. Some men = all negroes. .*. Some rational = all negroes." All other figures may be similarly reduced. It is thus apparent that the Unfigured Syllogism ex- presses nakedly the essential principle which under- lies reasoning in all the Figures. Sect. VI. — Hypothetical Syllogisms* 15. These are syllogisms in which the reasoning * The use of the terms "hypothetical" and "conditional," as applied to judgments and syllogisms, varies with different logi- cians. Some use the word hypothetical to denote the genus, of which they make conditional and disjunctive the species. Others make conditional the genus, which includes hypothetical and disjunctive as species. That is, different writers make the words hypothetical and conditional change places. 144 LOGIC. [Chap, V. turns upon the Hypothesis in a hypothetical judg- ment. A syllogism may contain hypo- Turns on the thetical judgments in which the rea- soning does not turn upon the hypothe- Syiiogism is s * s > but simply retains it as one of the Categorical. terms Q f the conc l us i on# Thus : " Every man is either a hero or a coward, A. B. is a man, .*. A. B. is either a hero or a coward." " The books of Scripture are entitled to reverence, if its authors are not impostors, The prophecies are books of Scripture, Therefore the prophecies are entitled to reverence, if their authors are not impostors." Such syllogisms are categorical. 16. But when the Reasoning turns on the Hypo- H th t" l * nes i s ? the Syllogism is Hypothetical, and Syllogism De- becomes either Conditional, Disjunctive, or Dilemmatic, according as the Hypo- thetical Judgment on which it is founded, falls into one or the other of these classes. In these syllo- gisms the hypothetical judgment forms the major premise : one of its members affirmed or denied the minor — and the consequent affirmation or denial of some other member forms the conclusion. Thus : Sec. VII.] MEDIATE INFERENCE. 145 "Major. If rains are plenty, the crops are plenty, Minor. The rains are plenty, The crops are plenty." Sect. VII. — Conditional Syllogisms. Conditional Judgments are founded on the prin- ciple of sufficient reason, otherwise _ x Grounded in called Reason and Consequent. Eeason and 17. The nature of the Conditional ie( i™ n ■ Judgment thus being, that on the ground of Rea- son and Consequent, if the antecedent is true the consequent is true, it follows ; A. That, if the Antecedent be affirmed in the minor premise, the Consequent must be r ^ Laws of Condi- affirmed in the conclusion. tional Syllo- B. If the Consequent be denied, the glsm " Antecedent must be denied, since, if the latter were true, the former would be so likewise. C. If the Antecedent be denied or the Consequent affirmed, no conclusion follows, for the latter may be true or the former false on other grounds. Of these the following are examples : A. If AisBCisD, AisB, .*. C. is D. B. If A is B C is D, C is not D, .'. A is not B. r If A is B C is D, A is not B, .*. no conclusion. C. < (■ If A is B C is D, C is D, .'. no conclusion. 18 146 LOGIC. [Chap. V. The fallacy of any inference in the cases under Fallacies illus- C > wiU a PP ear m0re P lainl y fr0m COn " trated. crete examples. Thus, if we deny the antecedent, the following example will show that nothing follows. " If James is a drunkard he is unfit for office, He is not a drunkard," .*. Nothing can be inferred. So likewise from affirming the consequent nothing follows. Thus : " If the people are virtuous they will establish schools, They will establish schools," .*. No inference is warranted. No fallacy is more common than that of drawing inferences in such cases. Sect. VIII. — Disjunctive Syllogisms. 18. These are founded on the principle of Ex- cluded Middle. Of two Contradictories, Eest on law of Excluded Mid- one must be true and the other false. There is no other alternative, no mid- dle ground. Genuine disjunctives are mutually exclusive. That is, each member excludes the others. Whichever is true, the others are false. If either be false, some one of the others is true. Thus, " it is either Spring, Summer, Autumn, or Winter." Sec. VIII.] MEDIATE INFERENCE. 147 Either of these excludes the others. Whichever is true, the others are false. Whichever is false, some one of the others is true. Hence with a disjunctive major ; First. If either member of it be af- Laws of the Dis- firmed in the minor, the other mem- junctive Byl- bers are false. Thus : ° slsm ' " Men are either angels, brutes, or rational animals, They are rational animals, .*. They are neither angels nor brutes." This is what the logicians call modus ponendo tollens. Second. If, in the minor, either member of the major be denied, then some one of the other mem- bers is true. Thus, in the preceding example, if in the minor we say, " Men are not angels/' it follows that they are either brutes or rational animals. This is 7nodus tollendo ponens. 19. It is proper to repeat that a Disjunctive may be turned into a Conditional by _, Disjunctives taking the contradictory of one of its turned into Con- members for the antecedent. "It is either Spring or Summer," is the same as " if it is not Spring it is Summer." Increasing the members thus : " It is either Spring, Summer, Autumn or 148 LOGIC. [Chap. V. Winter" — we get by conversion, "if it is not Spring, it is either Summer, Autumn, or Winter." Sect. IX. — The Dilemma. 20. The Dilemma is a syllogism having a Dilem- Dii mma De- ma ^ c Judgment for its Major Premise, fined. with a Minor so affirming or denying some member or members of the major, as to lay the foundation for an inference. As this judgment is a combination of the conditional and disjunctive, so the Dilemma partakes of the characters of the con- ditional and disjunctive syllogism. The major pre- mise of the dilemma mav be of various forms, each capable of different minor premises, and so furnishing a ground for different conclusions. A. The Major Premise may consist of one An- Different forms tecedent with a Disjunctive Consequent. of the Dilemma, jf ^ ; s g ? e i tner C is D or E is F. Affirm One Antecedent m and a Disjunct- the Antecedent, A is B, and the Dis- ive Consequent. j unctive Consequent, either C is D or E is F, follows. Deny the Consequent wholly, and the Antecedent must be denied. If neither C is D nor E is F, then A is not B. If, however, the Conse- quent be denied only disjunctively nothing can be inferred, for if either member of the Consequent be Sec. IX.] MEDIATE INFERENCE. 149 true, the Antecedent may or may not be so. As in pure conditionals, from the mere denial of the Ante- cedent or affirmation of the Consequent, nothing can be inferred. B. There may be a Plurality of Antecedents in the major, all having one Common Con- Plurality of An- sequent. If A is B, X is Y, and if C is J? cedentB n and a * 7 7 Common Conse- D, X is Y. qnent. In this case, if the Antecedents be wholly or dis- junctively granted, the one Common Consequent must follow. For if either of the Antecedents be true, the Consequent is true. If the Consequent be denied, all the Antecedents must be denied. But from affirming the Consequent or denying either or all the Antecedents, nothing can be inferred. C. There may be a Plurality of Antecedents in the Major, each with its own Conse- plurality of An- quent. In this case, if the Antecedents tec * dent + s ' each ^ 7 with its own be affirmed wholly, the Consequents Consequent. may be affirmed wholly. If the Antecedents be affirmed disjunctively, the Consequents may be affirmed disjunctively. From the denial of Conse- quents wholly or disjunctively, the Antecedents may, in like manner, be denied wholly or disjunc- tively. But from any denial of the Antecedents or 13* 150 LOGIC. [Chap. V. affirmation of the Consequents, nothing can be in- ferred. " If men are virtuous they are wise, And if they are vicious they are unwise ; But they are either virtuous or vicious, .*. They are either wise or unwise." Or denying the Consequent disjunctively, "But either they are not wise or they are not unwise, .'. Either they are not virtuous or not vicious." That affirming the Antecedents or denying the Consequents wholly, would lead to a correspond- ing affirmation the Consequents or denial of Ante- cedents respectively, appears in the following ex- ample : " If A. B. is diligent he will prosper, And if C. J), is wise he will be diligent, But A. B. is diligent and C. D. is wise, .'. A. B. will prosper and C. D. will be diligent." In like manner the denial of both Consequents involves the denial of both Antecedents. Some Logicians, as Whateley, exhibit that alone as the only true Dilemma which has a Kestriction of the Dilemma by plurality of Antecedents in the Major, some Logiciansi n -i. . ,• -ivr* and a disjunctive Minor. 21. The Dilemma has been named the Syllogis- Sec. IX.] MEDIATE INFERENCE. 151 mus Cornutus, or Horned Syllogism, because it con- fronts an adversary with two assump- Horns f ^ tions or arguments, on which it tosses Dilemma. him as on horns from one to the other, each being equally fatal to him. Hence the common phrase, " Take which horn of the Dilemma you will, it is equally fatal to you." Thus : " If things are what we can help, we ought not to fret about them, and if they are what we cannot help, we ought not to fret about them. But all things are either what we can or cannot help. .'. They are what we ought not to fret about." 22. The names Trilemma, Tetralemma, Poly- lemma have been sometimes given to Trilemma Te- this sort of Syllogism according to the fralemma, etc. number of members or horns, if they exceed two. Thus : " If A is B, X is Y, and if C is D, X is Y, and if E is F, X is Y. But either A is B or C is D or E is F, .*. X is Y," is a Trilemma. 23. The ultimate principles which determine the resolution of the Dilemma are those ultimate prin- which determine the conditionals and ci P les - disjunctives out of which it is formed. 152 LOGIC. [Chap. V. Sect. X. — Incomplete Syllogisms. 24. In ordinary reasoning, it is seldom that the process is fully expressed in a completed Syllogism. One of the premises is often wholly, and the other partially unexpressed. A syllogism with one premise unexpressed is an Enthymeme. Thus : " The Americans are a free people, .'. They are happy.'' Here the unexpressed Major premise, " All free peoples are happy," is obvious. In this : " Bankers are wealthy, .*. A. B. is wealthy," The Minor premise, " A. B. is a banker," is unexpressed. 25. Enthymemes, like Complete Syllogisms, often express the conclusion with " because," Li varied forms. , , -, . . . -, -, . or other equivalent particles, between it and the premise. Thus : " A. B. and C. are unfit to vote because they cannot read." The learner will readily complete such a Syllo- gism in regular form. Indeed the forms of En- Sec. XL] MEDIATE INFERENCE. 153 thymerues, occurring in ordinary speech, are in- numerable. Thus : " These men are good and therefore brave," etc., etc. Sect. XI. — Complex Syllogisms. 26. Several Syllogisms may be combined and abridged, so that the conclusiveness of the reasoning shall be just as evident as if they were all fully ex- pressed. Chief of this kind is the SORITES, Or chain-syllogism, in which a number of syllo- gisms in the First Figure are so'com- u* j xi x xi t p xi y i Sorites defined, Dined, that the predicate 01 the first pre- mise becomes the subject of the next, and so on, until, in the conclusion, the predicate of the last premise is predicated of the subject of the first. Thus : " The Hindoos are Asiatics, The Asiatics are men, Men are rational animals, Rational animals have body and spirit, .'. The Hindoos have body and spirit." The conclusiveness of this may be represented thus: 154 LOGIC. [Chap. V. 27. The following principles control the Sorites. Principles and A. ^he several unexpressed proposi- laws of Sorites, tions are respectively conclusions of each next preceding syllogism. Each of them be- comes in turn the minor premise of the next follow- ing, as will easily appear by completing the several syllogisms. B. All the intermediate expressed premises, therefore, between the first and the conclusion, are major. The first alone is minor. C. Hence no premise except the first can be par- ticular, for the first figure must always have a uni- versal major in order to distribute the middle term. D. Hence, again, no premise can be negative ex- cept the last; for a negative premise would make the conclusion negative, which in turn would become the negative minor premise of the next syllogism. This Sec. XI.] MEDIATE INFERENCE. 155 has been shown, in the first figure, to beget illicit process of the major, and is not allowable.* GOCLENIAN SORITES. 28. This is a form of the Sorites, so named be- cause it was first invented or brought , /~i i • T . . i Inverted Sorites, to view by (jroclenius. It simply in- verts the order of the premises as found in the com- mon Sorites. Thus, if we take the example before given, it can be stated as follows : " Rational animals are composed of body and spirit, Men are rational animals, Asiatics are men, The Hindoos are Asiatics, .•. The Hindoos are composed of body and spirit." In this form of Sorites, each preceding subject becomes the predicate of the next, until, in the con- clusion, the predicate of the first premise is predi- cated of the subject of the last. The last premise alone may be particular, and none but the first can be negative. • These conditions, however, are subject to any exceptions which might arise from substitutive judgments in any of the premises. So also of the Sorites in every form. 156 LOGIC. [Chap. V. HYPOTHETICAL SORITES. H othetical ^9. It is plain that a Sorites may be Sorites. conditional as well as categorical. Thus : If A is B, C is D, If C is D, E is F, If E is F, X is Y, but A is B, .'. X is Y. (Modus ponens), or X is not Y. .-. A is not B. (Modus tollens). In regressive form thus: If E is F, X is Y, If C is D, E is F, If A is B, C is D. But A is B, .*. X is Y. Or X is not Y. .'. A is not B. Direct Form, If A B is virtuous, he is brave, If brave, he is magnanimous, If magnanimous, he will do noble deeds, But he is virtuous, .". he will do noble deeds. PROSYELOGISM, EPISYEEOGISM AND EPICHEIREMA. 30. The different forms of complex Syllogisms comprise the modes in which separate syllogisms are combined into wholes of connected reasoning. In these the Sorites is rare. The Prosyllogism and Episyllogism are of constant occurrence. The Prosyllogism is one whose conclusion fur- Prosyllogism. wishes a premise for the principal argu- Episyliogism. ment. The Episyllogism makes the Sec. XL] MEDIATE INFERENCE. 157 conclusion of the main argument one of its pre- mises. "Useful studies ought to be pursued : Prosyllogisrn. Logic is a useful study (since it helps to think well), Episyllogism. .'. It ought to be studied, and (hence an educational course which omits Logic is deficient)." 31. Epicheirema denotes a Syllogism which has a Prosyllogisrn to establish each of its Epicheirema. premises. Thus : "Man has a spirit, for he is rational, And he has a body, for he fills space, .*. Some thing that has a spirit has body." This name is also applied sometimes in cases where there is a single Prosyllogisrn. Polysyllogism is a combination of several syllo- gisms in one argument. The Sorites is Polysyllogism, one species 01 it. 14 CHAPTER VI. APPLIED LOGIC — FALLACIES. 1. Having brought to view the fundamental Transition to ^ aws °^ P ure thinking, or principles of Applied Logic. Formal Logic, as related to Concep- tions, Judgments, and Reasonings, it remains that we now treat, as briefly as possible, of the applica- tion of these principles, first to the Fallacies. , . , . , _ detection and avoidance of errors m thinking; and next, to the right conduct of the thinking process, when employed in the Method. ,. _ . . discovery ot truth as pertaining to actual being. The former brings us to the doctrine of Fallacies, the latter of Method.* And first, Section I. — Fallacies. 2. A Fallacy is any unsound or delusive mode Fallacies de- °f reasoning, which wears a specious fined. appearance of being genuine, and thus often has power to impose upon men. * For a fuller exhibition of the difference between Formal and Applied Logic, the student is referred to the observations on this subject in Chap. L, Sect. IV. 158 Sec. I.] FALLACIES. 159 3. Fallacies are divisible into Paralogisms and Sophisms. A Paralogism is a fault in Divided into Pa- reasoning unknown to him who em- ralo s isms and Sophisms. De- ploys it. A Sophism, or Sophistical finitionofeach, reasoning, is a faulty argument understood by him who employs it, and used for the very purpose of deceiving. It is is proper to add, how- Both have the ever, that these distinctions have no same Logical logical, whatever may be their moral force ' significance, and that they are often overlooked by good writers who use the terms Fallacy, Paralo- gism, and Sophism interchangeably and indiscrimi- nately. 4. Fallacies are further divisible into Formal and Material. The former are those , . , . Formal and Ma- in Which no Conclusion follows from the terial Fallacies premises, however there may be an ap- disUn s uislie(L pearance of it. These are all cases of more than three terms, Undistributed Middle, II- Instances of licit Process, Negative Premises, affirma- ^ tive conclusion with either premise negative,* * It is important, however, to remember that many proposi- tions, in form negative, are not so in the fact, because the force of the negative particle falls on the subject or predicate instead of the copula. Propositions are in reality negative only when 160 LOGIC. [Chap. VI. making any conclusion from particular premises, or a universal conclusion when either premise is par- ticular, except when Substitutive Judgments furnish the necessary distribution of terms,* from denying the real import of the copula is negative, so dividing the two terms from each other. Thus : " He who has not enough is not really rich, No miser has enough, .*. No miser is really rich." The minor premise is really equivalent to " All misers are persons who have not enough, .-. All misers are persons not really rich." " No person who is not secure is happy, No tyrant is secure = All tyrants are persons not secure, .•. No tyrant is happy." Where both premises are really negative such an experiment will not succeed. " Vicious persons are not happy, A and B are not vicious, .*. No conclusion." All attempts to transfer the negative particle to one of the terms here, will result in Four Terms, or Undistributed Middle, or in altering the meaning of one premise. • Such an exception is the following: " Some mortals are (all) men. Some men are (all the) poets, .-. All the poets are mortal." Sec. I.] FALLACIES. 161 the Antecedent or affirming the Consequent of a con- ditional ; and from violating any of the canons of in- ference in Disjunctives and Dilemmas : inferring A from A, or O from O, by conversion, etc., etc. These have been developed already under Formal Logic, and belong properly to it. They are vices in the very form of thinking, whatever be the premises or conclusion. They do not, indeed, belong to real thought, but only to the counterfeits to • Why introduced which simulate it. They enter into in Applied Applied Logic only as principles of oglc ' Formal Logic which are applied to detect vices in reasoning about matters of actual being. Indeed, they would hardly need to be introduced here at all, were they always put in such phrase as to be palpa- ble. If apparent, the invalidity of the argument in which they occur is self-evident. They are, how- ever, very apt to be disguised under , . ~ Often disguised. equivocal or vague expressions ; or, tor other reasons, to elude the notice of those con- cerned. On this account they require to be noticed in Applied as well as in Formal Logic. 5. Material Fallacies are such as occur when there is no fault in the reasoning process, and M aterial Falla . the conclusion does follow from the pre- cies Defined. 14 * L 162 LOGIC. [Chap. VI. mises. Hence called Material, because they lie not in the form, but the matter of the Syllogism. Is it asked, how is a fallacy possible Groundless pre- mise or irrele- here? The answer is, 1st, that a pre- vant conclusion. . i i i i mise may be unwarrantably assumed, or 2d, the conclusion may be irrelevant. It may fall short of what the reasoner intends or professes to I atio prove. The technical name of this lat- Eienchi. ^er j s Jgnoratio Elmchi — ignorance of the proof of the real issue, the contradictory of your adversary's proposition which you undertake or assume to demolish. This is a fallacy of very frequent occurrence. It is a common defense of criminals to allege that they were insane ; and to attempt to prove this by showing that xamp e ^ acted very unreasonably ! But this is not to the purpose, for if it were, all crimi- nals would be maniacs, and guilt would be impos- sible. So it is a frequent and wicked practice of this fallacy or sophism, to arouse the passions of the tribunal appealed to in regard to the atrocity of an imputed offense, instead of proving it to have been committed by the accused. 6. To this head may be referred various argu- ments which logicians have been accustomed to con- Sec. I.] FALLACIES. 163 trast with argumentum ad rem, i, e. to the point. Such is argumentum ad vereoundiam, or Argumentum ad appealing to the feelings of reverence ., ' ,._ for certain persons or objects, instead of am, proving the point in hand : argumentum " . Adignorantiam, ad ignorantiam, assuming that your posi- tion is correct unless your adversary can evince the contrary : or it is sometimes used to denote any sort of sophism which imposes on men's 7 j Ad populum. ignorance : argumentum ad populum, which is very much akin, being addressed to the passions and prejudices rather than the intelligence of the people ; and finally argumentum ' . Adhominem. ad hommem, an appeal to the practice, principles, or professions of an adversary, as con- firmatory of our own position or fatal to his. This argument is legitimate so far as concerns an adversary, and for the purpose of , , How far valid. silencing him. 11 understood to be limited to this, it is not objectionable. So our Saviour often employed it to silence the cavils of the Pharisees and other adversaries. It is illegiti- mate when employed as if it established any propo- sition absolutely, or were binding upon any besides those whose personal opinions and conduct thus 164 LOGIC. [Chap. VI. make against their positions ; or even upon them, after they renounce such opinions and conduct. 7. The other sort of material fallacy by the un- warrantable assumption of a premise, has some forms that have been signalized by corresponding names. Chief among these is, Petitio Principii or begging the question, which Petitio Princi- * s ^ ne unwarrantable virtual assumption p11 ' of the thing to be proved, or of that by which it is to be proved, without proving it, in the course of the argument. Thus, if one undertake to show that a given tariff will be beneficial because it will promote the public wealth, without proving this latter, he perpetrates a petitio principii. The most deceptive form of this fallacy is, Arguing in a circle — argumentum in circulo — in Arguing in a which the conclusion is virtually used Circle. £ prove the premise, thus going in a circle which returns upon itself, from premise to conclusion and from conclusion to premise. To argue that certain men are good because they be- long to an excellent party, and that this party is excellent because it includes such worthy mem- bers, is to argue in a circle. Some demonstrate Sec. I.] FALLACIES. 165 the immortality of the soul from its simplicity, and then its simplicity from its immortality. 8. Non causa pro causa assumes that to be a cause which is not a cause. Foremost Non cauga among these is the fallacy of post hoc causai ergo propter hoc, taking a mere antecedent of an event to be, as a matter of course, its cause. As if, because night precedes day, it were therefore the cause of day, or because civil war in the United States preceded the continental war between Aus- tria, Prussia, and Italy, it were therefore the cause of that war.* 9. An assumption analogous to this is the taking of non tale pro tali, assuming a resem- Non tale blance without proving it. Thus, " the tali - season is favorable to apples because peaches are abundant," implying such a resemblance between these two kinds of fruit, and the requisites to their growth, as warrants such an inference. "All other * Notwithstanding the elaborate efforts of Mill, Brown, and others to prove that cause is only antecedent or invariable ante- cedent, the intuitive judgment of the human race is well voiced in the following words of Cicero. "Causa est ea quid efficit id cujus est causa. Non sic causa intelligi debet, ut, quod cuique antecedat, id ei causa sit, sed quod cuique efficienter antecedat." — Quoted in Bowen's Logic, p. 306. 166 LOGIC. [Chap. VI. religions are delusions. Therefore Christianity is a delusion." Sect. II. — Fallacies partly formal and partly MATERIAL. 10. By far the most numerous and misleading Semi - Logical class of Fallacies, are those styled by Fallacies. Whateley "semi-logical." This term has been criticized as absurd, as if there were no conceivable medium between a Fallacy purely The term Ex- logical, or non-logical. But whatever plained. ma y ^ e g^ f £} ie term, he employs it to denote a reality which no other term adequately denotes. It denotes the class of Fallacies arising from the ambiguous use of terms in reasoning, or in the syllogism. 11. An Ambiguous Term is equivalent to Two Terms; consequently, if either of the An Amoignous x J Term = Two three terms of a syllogism be ambigu- Terms ous, it amounts to bringing a fourth term into it. But when there are four terms there can be no conclusion. We see then how this Fal- How Semi-Log- lac y of Ambiguous Terms is partly ical - material and partly formal. In order to detect the ambiguity, we have to look at the Sec. II.] FALLACIES. 167 matter of the syllogism as contained in the meaning of its terms. So far it is material. When the am- biguity is detected, the fault which gives rise to the fallacy, is shown at once to be formal, because the syllogism is loaded with four terms which are in- compatible with any conclusion. It is true that, at bottom and in essence, this fallacy is formal. But the discovery of it requires examination of the mat- ter embraced in the syllogism. Thus : " Feathers are light, Light is contrary to darkness, .'. Feathers are contrary to darkness," is a syllogism in reality with four terms, two of which are words spelt with the same letters, but of different meanings. This difference of meaning must be ascertained in order to expose the fal- lacy. 12. Fallacies of this description are far the most specious and numerous of all, and are guc ] 1 F a n ac i es as various as the various causes or kinds s P ecious< of ambiguity in language. We will call attention to a few of the more prominent that logicians have been accustomed specially to designate. 168 LOGIC. [Chap. VI. 13. The fallacy of Division and Composition. Division and ^ n t ms the middle term is taken divi- Composition. dedly or distributively in one premise, and collectively in the other. Thus : "All these persons are a crowd, A. and B. are some of these persons, .". They are a crowd." Here persons are taken collectively in the major, and distributively in the minor. " Five is one number, Three and two are five. .\ They are one number." This is composition in the major and division in the minor. 14. This fallacy is of constant occurrence in con- Paliacy of the action with the word " all," which, in word all." fae peculiar idiom of our language, affords great facilities for it. First, as in the ex- amples given above; " All these soldiers are an armv, All these soldiers are individual persons, .*. Individual persons are an army." Here in the major "all" is taken collectively, in the minor distributivelv. Sec. II.] FALLACIES. 169 But the greatest liability to an ambiguous or non-natural sense of the word " all," is where it is the subject of a negative judgment, in which case it is nevertheless impossi- ble to deny the predicate of "all" the subject. Thus : " Not all men are poets, or All men are not poets," is equivalent to " Not every man is a poet, or Some men are not poets." Sometimes there is danger of construing " not all" as equivalent to none, whereas it only amounts to " not some." This is well illustrated by Whateley in the following example : " If all testimony to miracles is to be admitted, the Popish legends are to be believed ; but the Popish legends are not to be believed ; therefore no (for " not all") testimony to miracles is to be admitted." It is important to be on our guard against fallacies arising from ambiguities in this pregnant mono- syllable. 15. A very ensnaring form of ambiguous middle is known as Fallacia Accidentis. or , Fallacia Acci- a clieto secundum quid ad dictum sim- dentis. 15 170 LOGIC. [Chap. VI. pliciter, and vice versa, i. e. of using the middle term considered with reference to some of its acci- dents in one premise, and with reference to its mere essence in the other. " The covering of sheep is what we wear, Undressed wool is the covering of sheep, .*. Undressed wool is what we wear." Again : " Government is a blessing, The most cruel despotism is a government, .". Therefore it is a blessing." 16. A very common form of ambiguous mid- Paiiacy of Ety- dle is that founded on Etymology, or mology. th e assumption that derivative, paro- nymous, or conjugate words have the signification of their roots, and compounds of their originals. It is true indeed, that the meaning of words sometimes remains unchanged through all these variations. Sometimes the changes of meaning are slight, but, for that very reason, all the more liable to be over- looked and to gender fallacies. Thus : " Projectors ought not to be trusted, This man has formed a project, .*. He ought not to be trusted." Sec. II.] FALLACIES. 171 " Artful persons should be shunned, A. B. is a great artist, .'. He ought to be shunned." " Truth is derived from to trow, i. e. believe, But belief is variable, /. Truth is variable, i. e. not immutable." 17. Analogous to this is the Fallacy of Interro- gations, sometimes called Fallacia Plu- p a i lacy of In _ rium Interrogationum. This is prac- terrogations. ticed when, under one question in form, by ambi- guity of meaning, more than one question in reality is put, so that the person questioned is entrapped, whatever answer he may give. This is a trick fre- quently practiced by examiners of witnesses. Law- yers are peculiarly prone to it. They put ambigu- ous and embarrassing questions, and then with great show of sincerity and fairness, insist on a categorical yes or no for answer, as if to refuse such an answer would imply a lack of truthfulness, when in fact, such a categorical answer must be false or inadequate, owing to the ambiguous implications of the interrogation. So the attempt is often made to ensnare or deceive, by a false assertion or implication, in a False i mp iica- question so put as to imply that it is tioI1S, 172 LOGIC. [Chap. VI. beyond dispute. No better instance of this can be found than the celebrated question of Charles II. to the Royal Society, "Why a dead fish xamp ( ^ oeg ^^ though a live fish does, add to the weight of a vessel of water in which it is placed ?" This was put with such apparent assurance that some of the philosophers were, for the time, de- ceived, and busied themselves in seeking an expla- nation of the fact, while they omitted to inquire if it was a fact. So, many an innocent person has been entangled and led to criminate himself, being for the moment unmanned and thrown off his guard, by the very audacity with which such questions were put to him as these : " How long since you left off drinking, swearing, back-biting," etc. ? No duty is more in- cumbent on courts than that of protecting witnesses and parties against such injustice. 18. Quite similar to this is the demand often _ _, made upon witnesses by examiners, not Demand for Dis- x tract and Ade- only for a Clear, but for a Distinct and qnate Cognition. . , ^ ... , -. T -r even Adequate Cognition (see chap. II., Sects. 9, 30) implying that their testimony is to be suspected, unless, besides certainty as to the object testified about, they can also give its Example. marks. Thus, if a witness testifies that Sec. II.] FALLACIES. 173 a certain signature or manuscript is in a given man's hand-writing, it is quite common to insist that he should give some of the marks or distinctive pecu- liarities by which he distinguishes the chirography in question. The same thing is often done in ex- aminations for the purpose of identifying persons, places, and other objects. The fallacy of all this, so far as it implies distrust of the testimony of those who are unable to give the marks, is palpable. In general it is only the few experts, in each p a n acy ^. department, who, besides knowing ob- P osedi jects with certainty, can give the distinguishing marks or definitions of them. There are few things that we know with more certainty than the different hand-writings with which we have been familiar. There are few matters in respect to which those who have not made it a subject of special study, will more certainly and egregiously blunder, than in at- tempting to give the marks which distinguish the chirography of different persons. So with other things. Nothing would sooner nonplus such ques- tioners themselves than to exact of them a logical definition of words, or the marks of conceptions, with which they are perfectly familiar, and which they constantly use with substantial accuracy. 15* 174 LOGIC. [Chap. VI. 19. Another fallacy is the Over-estimation of Probabilities, i. e. of the degree of belief which Over-estimation ou g ht to be produced by evidence less of Probabilities, than certain — especially of supposing that a plurality of probabilities necessarily strengthen each other. A single probability of any uncertain event is ascertained by dividing the number of chances favorable to the event by the total number of chances. Thus the probability that a person blindfolded will take a black ball out of an urn containing 10 white and 2 black balls is yi or h 20. " To find the chance of the recurrence of an event already observed, divide the number of times the event has been observed, increased by one, by the same number increased by two. If an inlander coming to the sea, observed the phenomenon of the tide ten times in succession, the chance to him that at the next period the tide would again rise would be T¥+i == ir^ or 11 to 1. Every certainty is repre- sented by a unit, as has been shown ; and so many units are added to the possible cases (denominator of the fraction) as there have been events, and so many to the favorable cases (numerator) as there have been favorable events. ' Or, if we represent/ says M. Quetelet, 'the number of times that the Sec. II.] FALLACIES. 175 event has occurred by a similar number of white balls that we throw into an urn, adding also one other white ball and one black ball, the probability of the reproduction will be equal to that of drawing a white ball.' "In order to calculate the probability that an event already observed will be repeated any given number of times, the rule is, to divide the number of times the event has been observed, increased by one, by the same number increased by one and the number of times the event is to recur. Thus, if the tide had been observed 9 times, the chance that it would re- cur ten times more would bef4. 10 ;j; T = (-j-J) = %. ' This is the same thing as if each reproduction of the observed event corresponded to putting a white ball in an urn where there were already, before commencing the trials, a white ball and as many black balls as it is supposed that the event observed should re-occur times/ " — Thomson' sLaws of Thought. 21. If two or more probabilities are independent of each other, they do afford mutual -^j^w support. But if otherwise, if they are strengthen and when they probabilities of probabilities, they weak- weaken each en each other. .If the credibility of a other " witness be f so far as his ability to observe aright 176 LOGIC. [Chap. VI. and know the facts is concerned, f so far as his veracity is concerned, then the total probability of his telling the truth is § X f = A, unity being the representative of certainty. 22. If, however, the probabilities are mutually independent, they strengthen each other, and as they increase in number and force, they may come short of certainty by only an infinitesimal distance. Thus, if the probability that A. B. committed a given murder be strong, 1, from certain money be- longing to the victim being found in his possession ; 2, from his boots fitting tracks found near the place of murder; 3, from blood on his clothes; 4, from a piece of knife-blade found in the head of the murdered body fitting precisely the broken blade of a bloody knife found in the pocket of the suspected person ; it is clear that all these separate probabilities confirm each other, and together fall only short of apodictic proof. In this case, the mode of computing the absolute probability, is to sub- tract each separate probability from unity, which gives the probability of the opposite event, or of failure arising from each several cause. But as these several probabilities of the opposite event weaken each other, or are probabilities of probabilities, the Sec. II.] FALLACIES. 177 entire probability of it is ascertained by multiply- ing the separate ones together. This product sub- tracted from unity will give the probability of the original event in question, of which this is the oppo- site.* Thus in the example just given j let the first probability be \, the second \ y the third \ y the fourth J. Subtracting each of these from unity, and multiplying them together, we have iXf XfX \ = ■£$ = j3g-, which, subtracted from 1, gives -^f , as the probability that the suspected person was the real murderer — a probability sufficient to neutralize all reasonable and practical doubt. 23. Strictly, however, this and all positive direc- tions touching: the calculation of proba- _ . , , , x Strictly belongs bilities, belong to the doctrine of Me- to Logical Me- thod. It comes in here very naturally, however, in connection with the correlate fallacy. * " As, in the case of two probable premises, the conclusion is not established except on the supposition of their both being true, so in the case of two (and the like holds good with any number) distinct and independent indications of the truth of some propo- sition, unless both of them fail, the proposition must be true ; we therefore multiply together the fractions indicating the proba- bility of failure of each, — the chances against it; and the result being the total chances against the establishment of the conclu- sion by these arguments, this fraction being deducted from unity, the remainder gives the probability for it." — Whatcley's Logic, Book III., 15. M 178 LOGIC. [Chap. VI. 24. A source of ambiguity, not only in the middle, but other terms, which ought Ambiguity Pic- J ' & tae Universaii- not to be overlooked, although the means of guarding against it, will more fully appear under the head of Induction, has re- ceived the name fictce universalitatis /. L e. of a groundless inference from a few cases to all cases. This is among the most common forms of delusive and fallacious reasoning. Common Ex- amples of this are, that Friday is an unlucky day, because some enterprises begun on that day have suffered disaster: that an epidemic is raging, when only the fewest cases of disease have appeared : that hemorrhage of the lungs is always fatal, because it is often so : that all men are knaves because so many are : that the whole community are of a given opinion, because A. B. and C. have ex- pressed it. Out of such fictitious universals arise Syllogisms like the following : " Men love to be humbugged, The President of the Bible Society is a man, .'. He loves to be humbugged." 25. The sources of ambiguous middle are as numerous and varied as the sources of Sources of Am- biguous Middle, ambiguity in language itself. Their de- Sec. III.] FALLACIES. 179 tection and correction belongs rather to rhetoric, grammar, or philology, than to logic. We have no room to pursue it further here. Those who desire to see it unfolded at greater length, may consult the chapter on Fallacies in Whateley's Logic with in- terest and profit. 26. It only remains that in concluding the sub- ject of Fallacies we present some specimens of Sect. III. — Logical Puzzles. In inventing which the intellectual activity of past times exerted itself, for lack of Logical Puzzles worthier objects. These have been be- more ingenious ■ it -. . , • , than useful. queathed to succeeding generations to task their subtlety, and at once amuse and perplex students in their leisure hours. This however has not been the worst of it. They have gone far to countenance the impression that Logic, instead -of being a genuine or useful science, is little better than a kind of jugglery and legerdemain, for work- ing up seeming demonstrations of manifest absurdity and falsehood. 27. The Dilemma is a favorite instru- . Use of the Di- luent for this sort of logical sleight of lemma for this hand. A sly fault in some member of purpoi 180 LOGIC. [Chap. VI. its complex parts affords the facile opportunity for it, because it is so readily unobserved. The standard examples we are about to quote from the books, will illustrate this. 28. " In sifting a proposed Dilemma," says Krug, "we are to look closely to the three Krug's rules for sifting Dilem- following particulars : — 1. Whether, in the Sumption,* the Consequent is a legi- timate inference from the Antecedent ; 2. Whether the Disjunction in the Consequent is complete ; 3. Whether, in the Subsumption,f the Disjunct Mem- bers are properly sublated. The following Dilemma is faulty in each of these respects. " If Philosophy be of any value, it must procure for us power, riches, or honor. " But it procures neither of them. Therefore," etc. " Here, 1, the inference is wrong, as Philosophy may be worth something, though it does Solution. , p ,, . , not secure any ot these external advan- tages; 2, the Disjunction is incomplete, as there are other goods, besides the three here enumerated ; 3, the Subsumption is false, as Philosophy has often been the means of procuring these very advantages." * Major premise. f Minor premise. Sec. III.] FALLACIES. 181 29. Analogous to this is the old quibble to dis- prove the possibility of motion, which Puzzle about also throws up the horns of a dilemma. Motion ' Thus : " If Motion is possible, a body must move either in the place where it is, or in a place where it is not. " But a body cannot move in a place where it is ; and of course, it cannot move where it is not. " Therefore, motion is impossible." The Major Premise or Sumption is false and in- volves a Material Fallacy. The true statement is that, if motion is possible, a body must move from the place where it is to a place where it will be. This removes every ap- pearance of a puzzle. The Major Premise is false except with regard to one indivisible moment. But that is irrelevant to motion, which in its nature re- quires time, while the cognition of it supposes memory. 30. To the same complexion comes the famous old Puzzle named Ignava Ratio, i. e. the , '« . .. i Ignava Ratio. argument for inaction, because events being predetermined or otherwise fixed, all effort to alter them, or to attain what is desirable and avert 16 182 LOGIC. [Chap. VI. what is evil, is unavailing. Cicero thus states it as urged against calling in medical aid in sickness : " If it is fated that you shall recover from the present dis- ease, then you will recover whether you call in a physician or not. If it is fated that you shall not recover, then, with or without a physician, you will not recover. " But either the one or the other of these is fated. " Therefore, it will be of no use to call in a doctor." The obvious fallacy here, to look no deeper, lies in the fact, that the calling in of the doctor and using his prescriptions, may be the very means by which it is ordered that recovery shall take place; hence the first member of the sumption or major premise is false. And so of all analogous cases. 31. The famous puzzle of Achilles and the tor- Aohfflesandthe toise > which S0 lon g baffled tne 1( >gi- tortoise. cians, aiming to prove, by logic, the logical absurdity, that the swiftest runner can never overtake the slowest, is put thus : " The swiftest runner can never overtake the slowest, if the latter has ever so little a start. Suppose, for instance, that Achilles runs ten times as fast as a tortoise, and that the tor- toise is one mile in advance at the outset. While Achilles is traversing this mile, the tortoise has advanced y^th of a mile farther ; before his pursuer has passed over this T Vth, the tor- toise has advanced j^th, and then, again, xsWth, and so on Sec. III.] FALLACIES. 183 forever, always being some fraction, however small, of a mile in advance." The sophism here is disguised under a false state- ment of the problem. The real ques- The R ..^ tion, when will Achilles overtake the exposed. tortoise ? is kept out of sight, and another wholly different substituted in its place, viz., when the tortoise is at any given point ahead of Achilles, how far will it have gone when Achilles shall reach that point ? This soon runs into infinitesmals which are practical zeros, and, even if theoretically infinite in number, really are all included in that finite length which Achilles will quickly get over, leaving the tortoise behind. 32. Other puzzles abound on which we have no room to dwell. It is the less necessary, * Such puzzles as a careful application of the principles have no chief already laid down, will readily solve pacii -iT;i s o furnished. lorded in a two-iold way. 1. In the application of its principles to test and explicate what is contained implicitly in the matter so fur- nished by the intuitive faculties : 2. By guiding us in such use of our intuitive faculties, as shall be most effective for advancing our knowledge. According to the former, the laws of Conceptions, Judgments, and Reasonings show what is, and what is not, ne- cessarily implied by the facts and truths given us from other sources. In the latter, it helps to guide our inquiries, observations, and experiments towards the search for and intuition of such facts as will tend to elucidate or decide questions in issue, thus 16* 186 LOGIC. [Chap. VII. saving us the waste of our powers in irrelevant and fruitless investigations. Section I. — Original and Derivative Sources op Knowledge. 3. Our Original Sources of Knowledge then are the Intuitive (including Self-Consciousness, Recapitulation of sources of Sense-Perception, Self-Evident, Super- sensual truths), and Testimony. The Derivative are what we derive from them through the power of Discursive Thought, including Ab- straction, Generalization, Conception, Judgment, Reasoning. Some add to these Memory, of whom some class it with the former faculties, some with the latter. It is unnecessary to discuss this question here. It is enough that Me- mory is not itself a direct source of knowledge in- tuitive or discursive. It simply keeps and repro- duces what is known through the other faculties. Some questions too might arise, as to how far Testi- mony is an intuitive, or immediate source of know- ledge. It is not our plan here to go far in the discussion of such extra-logical questions. They are to be relegated to psychology, except so far as may be essential to a due understanding of Logic or Sec. I.] METHOD. 187 its applications. It suffices for our present purpose that Memory, like the intuitive faculties, furnishes, inasmuch as it preserves, material for the discursive faculties, but is not itself discursive. 4. Memory is an essential element in nearly all Testimony. It is rare that any one Memory in- bears witness simply to the cognitions volved in Testi- of the present moment. Almost all tes- y ' timony respects the past. 5. Testimony is a fundamental source of know- ledge. All facts known to us beyond i m p 0rtance f the narrow circle of our own experience, Testlm ° Q y' must be learned from Testimony. And our gene- ralizations and reasonings would be extremely scanty for lack of material, without the results of the ex- perience of other men, added to our own, and au- thentically reported to us. Testimony may be either Oral, or Recorded in historical writings, monuments, memen- 0ra l and Ee- toes, and tokens. The canons for dis- corded « tinguishing true testimony from false, and genuine from spurious, authentic from fictitious history, are manifold and easily accessible. To discuss them is aside of our present purpose and beyond our space. 188 LOGIC. [Chap. VII. 6. There is, however, one species of testimony that is wholly unique, and above the God in his Word plane of all human witnessing. We refer to the testimony of God in his Word. This is absolutely sure and infallible, be- ing the utterance of Him for whom it is impossible to err or to lie. It is the exclusive source and foundation of Christian Theology. It is absolutely true and authoritative. To unfold the rules for the correct interpretation of Scripture would be to trench on the sphere of exegetical theology. 7. It is proper, however, to remark that the first Theolo fo nd- P r ^ nc ^P^ es °f theology do not depend ed on the an- upon any process of reasoning, a priori or inductive, but upon the authority of God who declares them. In a qualified sense, the true process for ascertaining what the Scriptures teach may be viewed as inductive. In other words, it simply ascertains and compares the actual teach- ings of Scripture, instead of deciding a priori what they may and may not teach. 8. The application of the laws of thought or prin- m , , „ ciples of logic to the facts, that are al- The laws of x ° ' thought always ways coming before us in an isolated and unorganized form, is constantly Sec. I.] METHOD. 189 made, consciously or unconsciously, by all men. The power to do it is one of man's chief preroga- tives as compared with the brutes. To think at all is, either consciously or unawares, to conform to the laws of thought. All else called think- Unlogical is ing only simulates and counterfeits it. counterfeit But, in proportion as this application ous fe of the principles of logic becomes comprehensive and complete, in regard to any given department of facts or truths, it becomes a scientific view of them. Thus, a comprehension of the facts con- cerning life, in their mutual relations, their har- mony and unity according to the necessary laws of thought, makes up the science of Physiology ; of the phenomena of the soul, Psychology ; of spatial quantity and relations, Geometry. 9. Science then is not a mere knowledge of dis- jointed unreconciled facts or truths, but g c i ence what it a knowledge of these facts as mutually is * related, harmonized, and unified, under all-inclu- sive principles and laws. But, in the sphere of actual being, of events or phenomena, To find lawg . to ascertain their laws and principles is t0 find causes. commonly to ascertain* their causes. Towards this state all knowledge tends in proportion as it tends 190 LOGIC. [Chap. VII. to perfection. And this, not only in each particu- lar department of inquiry considered Perfect know- ledge is scien- by itself, but in the relation of them all to each other. They are more and more comprehended in their mutual relations and har- mony, until they culminate in absolute unity in the Great First Cause, and the Infinite Mind. 10. This process is actually going forward with All Sciences g rea ^ rapidity as science advances. The tend to Unity, various Physical Sciences are more and more seen as distinct, yet cognate and harmonious, divisions of one great whole. The same is true of the various branches of Psychology and Metaphy- sics, in their mutual coherence and interdependence: while Physics have their deepest ground in Meta- physics, in the ideas of substance and cause, with- out which all being is a chimera, and all science a dream. So the several sciences, physical Scientia Scien- , , , . , .-, tiamm: Philo- and metaphysical, are constantly verging sophy and Onto- towards that scientia scientiarum, which logy. is at once the true Philosophy and the true Ontology. 11. Philosophy and Science have been used very much interchangeably, and very much also in more or less contrast to each other. In the former case Sec. I.] METHOD. 191 they are used for that comprehensive view of facts and truths in the particular departments, or in the whole field of knowledge, above g c i ence f urt her set forth. Thus we speak indifferently Compared and Defined. of the Science of Mind and of the Phi- losophy of Mind, of Natural Philosophy and Phy- sical Science. But the words are often used with a sort of contrast, according to which science is re- stricted to the domain of Physics, and Philosophy is more" particularly referred to Metaphysics. This is especially so when these terms are used alone, without any qualifying adjunct. Thus, if we use the word Science alone and absolutely, we usually mean Physical Science. And when we speak of Philosophy absolutely and eminenter, we mean Me- taphysics, as including mind, which is the prime cause, and those first truths of Causality and Sub- stance, Time and Space, which variously condi- tion being, whether body or spirit. 12. As all effective thinking, or application of the laws of thought, tends, and is indispen- i i , , i , . ,« r- • Logical Method sable, to the construction of science, or j,^^ Defini- thorough knowledge, so Logical Method tion ' Divi sion, and Reasoning. in every department of inquiry involves the three great logical processes which mutually 192 LOGIC. [Chap. VII. supplement and complete each other. Definition, which unfolds the nature of the science according to its attributes or qualities : Division, which unfolds it according to its extension or the objects it includes : and Reasoning, in which we either guide our search for facts and truth, or interpret these facts by showing what can fairly be inferred from them. In regard to Definition and Division, it is unnecessary to expatiate upon them here. It is enough to refer the student to the principles already laid down on „ these subjects. It is only necessary to Importance of ■* J * Definition and add, that exact Division and Definition are of the utmost moment to the suc- cessful investigation and treatment of any subject. We will now fix our attention on the application of the modes of reasoning to the discovery, elucidation, and proof of the truth, in regard to the object- matter so marked out by these processes. These rea- sonings are subject to different conditions, and have a different cogency and force, according as they are applied to Necessary or Contingent Matter. 13. The former, as before defined, is that the , opposite of which the mind cannot con- jNecessary and x x Contingent Dis- ceive without intellectual suicide. The latter is that whose existence is Con- Sac. II.] METHOD. 193 tingent, and the supposition of whose non-existence involves no contradiction or absurdity. These two kinds of truth give rise to the two orders of reason- ing, respectively known as Demonstrative and Pro- bable, and to the three classes of Judgments classed by logicians respectively as, Sect. II. — Problematic, Assertory, and Apodictic Judgments. 14. The two former apply to the region of Con- tingent,* the last to that of Necessary truth. This distinction in judgments concerns the degree of cer- tainty in the connection between the subject and the predicate. A. The Problematic Judgment is neither sub- jectively nor objectively certain ; i. e. it J . . Problematic is not certain to him who holds it, nor Judgment = ! r. ., Opinion. can he enforce its acceptance upon others. It is equivalent to mere opinion. B. Assertory Judgments are true and certain sub- jectively but not objectively, i. e. sure Assertory = to him who holds them, but incapable Faith * of being enforced on the acceptance of others of a * This must not, however, be pressed so far as to impugn the necessary existence of God. 1<" N 194 LOGIC. [Chap. VII. different moral disposition. Of this nature is belief or faith, especially Religious Faith. Its judgments are sure to the believer, although they cannot be enforced upon those of a contrary moral disposition. C. Apodictic or Demonstrative Judgments are subjectively and objectively sure ; sure Apodictic Judg- ments necessa- to him who holds them, and capable of r y true. being enforced upon all of sane mind, who can be made to understand them and the evi- dence for them. Of this nature are the truths in Mathematics, Logic, and some primary axioms in Ethics and Metaphysics. 15. In regard to reasoning in the sphere of necessary truth or apodictic judgments, Reasoning from J * J ° Apodictic Jndg- little need be said. The conclusions ments snrei r» n • s* i_ • J a„ of all reasoning from such judgments to others founded upon them, that conform to the principles of the syllogism in its various forms as set forth in formal logic, are as certain, and as im- possible to be false, as the premises. The Its power in the n -,. r-o i n »n ±. ±i Formal Sciences formal sciences afford fine illustrations illustrated by f the achievements of the logical faculty Geometry. in enlarging our knowledge, without in the least increasing its original materials, but by simply explicating them. The whole science of Sec. II.] METHOD. 195 Geometry is but the logical unfolding of the con- tents of a few primary axioms. So also And all Mathe . of the entire range of pure Mathematics, matics - and of pure Logic. All necessary and a priori truths, intuitive and deductive, afford premises for necessary conclusions. Thus, from the R eason i ng f rom a priori truth that space is illimitable, a priori truths. it follows that it is immeasurable. From the a priori truth, " every event must have a cause," and the minor premise, "thunder has occurred" (or been an event), it follows that this n From one a pn- thunder must have had a cause. Here ori and one Con- ,i tineent premise. the major premise is a necessary, the minor a contingent but certainly proved event; and the conclusion is true, with a necessity condi- tioned on the truth of the minor, i. e. in this sense, with a conditional necessity. In genuine logical reasoning the conclusion is a necessary consequence of the premises. In proportion then as they are necessarily true, the conclusion is so likewise. In this we have the type of all purely 196 LOGIC. [Chap. VII. Sect. III. — Deductive Seasoning. 16. This also applies in all cases of Reasoning from wholes known in whatever way, This the type of J Deductive Rea- whether of Extension or Intension, to the parts included under them; from Genus to Species, and individuals under them, or from the marks of the individual or species to the marks of those marks. So far as we have any generic truths, propositions or judgments established, whether in necessary or contingent matter, these furnish premises whence we can reason with neces- sary certainty, to individuals or classes contained under them. If it be established that, (Intensive Syllogism) — " Polyps are animals, And that Animals have sensation, then it follows of necessity that Polyps have sensation." Deductive Reasoning then is from Generals to Deductive Eea- Particulars — the form, as we shall see, souing is from of nearl all demonstrative and abso- Generals to Par- ^ ticulars. lutely conclusive reasoning. 17. But how do we obtain these universal or Sec. IV.] METHOD. 197 Generic Judgments in Contingent Matter, when all that we know originally of mind is .i . -i. . f ■• « . ,i, t Whence come the individual facts that come under Q enera i j udg . the purview of consciousness, and of ments in Con " tingent Matter? matter, what are cognized through our senses ? facts too, the opposite of which are pos- sible, and which it is conceivable might not be re- peated beyond the sphere of experience thus far had ? From the fact that such persons as we have known die, how do we reach the conclusion that all men are mortal ? From the fact that some water is composed of oxygen' and hydrogen, how do we know that all water is so constituted? This brings us to reasoning from particular facts to a general law or truth, which is, Sect. IV. — Induction. 17. This is the principal instrument of scientific progress, and of all advance in human By Induction, or knowledge, except through Divine Re- reasoning from velation, within the realms of actual n n 7 G-enera. being. For this is a region of facts, Actual beings objects, phenomena of actual existence are Indmduals> which are first known as individuals, and might or might not be, according to the good pleasure of God. 17* 198 LOGIC. [Chap. VII. The Formal Sciences and Metaphysics do not of Scope of Formal themselves discover or prove any actual Sciences. being. They only show certain neces- sary conditions or consequences of any facts of actual being, which may be brought to light by the other cognitive powers. But all advance in the knowledge, and especially . the scientific knowledge of mind, is in All progress in Scientific Know- the way of ascent from particular facts bdng Is^from to S eneral laws - Jt proceeds therefore, Individuals to from what we know in some cases, to Classes, . infer that the like is true in all similar cases. This is induction or inductive generalization. T , a Induction, however, is more than Gen- Indnction more 7 * than Generaii- eralization, which it always includes. There may be generalization without induction, though there can be no induction without generalization. Generalization combines in a class objects having similar qualities, and denotes them In what respect by a class-name. Induction concludes it is so. from the fact that some of a given class already generalized possess some given property, all others of that class possess it — in other words, that because a certain mark A is, in some cases, attended with a certain mark B, it is so in all other cases. Sec. IV.] METHOD. 199 Thus, from the fact that some fire tortures living flesh in contact with it, we reason in- ductively that all fire will do it. Here is generalization in this way, and to this extent, that what is found true of some, is extended to all, that have a given mark. 18. The great question then, in regard to this class of cases, which needs to be deter- The great ques- mined, is, when are we warranted in tion regarding taking some instances that have come under our knowledge, as samples or accurate repre- sentatives of a whole class, including;, it ° What are tests may be, like cases innumerable ? What or crucial in- ,i »■ « l • i v .• • i j_i stanceSi are the criteria which distinguish these crucial instances from others which warrant no such inference? 19. There is the test of a complete enumeration of all the instances or individual cases si mp i e Enu- composing the class in question. If deration. these all, without exception, have the property in question, then it of course belongs to the whole class. Thus, if the season of greatest growth is in May, June, July, August, which are the only months whose names are with- out the letter r, then the general conclusion follows 200 LOGIC. [Chap. VII. with absolute certainty, that the months without the letter r are those of greatest growth. If it has been found from actual observation, that each of the planets moves in an elliptical orbit, then it is true beyond a peradventure, that all the planets move in such orbits. This is what Bacon called Induction per simplicem mumerationem, by the mere enumeration of all the cases involved. Why this is Em- pirical Indue- It has also been named Empirical In- duction, because its compass is limited to actual experience, and it detects no cause and . , . . establishes no law reaching beyond And nnimport- & J ant. such experience. It is therefore com- paratively unimportant. That induction alone is Th l fr Lt- fruitf 11 ! which enables us to go beyond fill induction, such cases as have fallen within our experience, to an indefinite number of like cases, i, e. all of the same class not yet brought within the range of our experience. 20. In order to this, it is necessary to ascertain, Requisites to it. not onl y the empirical fact, that, in A Causal such instances as have fallen under our gency ' cognizance, the phenomenon in question has occurred, but that there is a causal agency, or other uniform concomitant, connected with them Sec. IV.] METHOD. 201 which ensures it, and which attends all like instances. Then, when it is settled what is the cause or mark of any given phenomenon, the principle that like causes produce like effects, which is either self-evi- dent, or so nearly so that all mankind act upon it, induces the conclusion that, in all similar cases, we may anticipate a like phenomenon. 21. The difference between such an induction and that which is purely empirical, per smvplicem, emtmerationcm, is strikingly gi mp i e Enume- illustrated in the second example of the ratioE nitra- ted. latter- kind, above given, which was the inductive conclusion that all the planets move in elliptical orbits, from observing that each of them moves in such orbits. This, however, of itself, creates only a moderate presumption, that any planets now unknown and yet to be discovered, move in such orbits. But when it was ascertained that the Centripetal and Centrifugal Causal Force Forces act jointly on all the planets, and Discovered. that the product of this joint action is an elliptical orbit, then the conclusion was indisputable, that all planets observed and unobserved, move in elliptical orbits. 22. What then are the Tests of such Causal 202 LOGIC. [Chap. VII. Agency, or other equivalent concomitant, and proof Tests of Causal of a g iven phenomenon? The proofs Agency, etc. that a given object or agency is, or con- tains in itself, the cause, or invariable concomitant of a given effect, so that we are warranted in asserting that the instances observed are as good as the entire inductive Syllo- class of like instances? The Inductive gism. Syllogism naturally falls into the Third Figure. Thus : "XYZ have polarity, XYZ are (represent quoad hoc) all magnets, .*. All magnets have polarity." It may, however, be put more awkwardly, in the First Figure. Thus : "XYZ have polarity, All magnets are (represented quoad hoc by) XYZ. .*. All magnets have polarity." In either case the question is, when do the parti- The Question re- cu l ar cases X Y Z so represent the garding it. whole class, or when are they so proved to be, or to contain the causes or uniform con- comitants of a given phenomenon, that they fairly represent the whole class, and warrant a universal inductive conclusion ? Sec. IV.] METHOD. 203 1st Criterion, the Method of Agreement. — If, whenever a given object or agency J. St X6St IS tno is present, without counteracting forces, Method of ™ . i i ^i • Agreement, a given effect is produced, there is strong ground that we have found the true cause of the effect, which will always produce it, in the absence of counteracting forces. Thus, it, in all cases ot the application oi given degrees of heat, clay hardens, lead melts, and water boils, it is just to conclude that this is the real cause of these phenomena, and that whenever it is applied in such measure to these several sub- stances, they will re-occur. It is to be borne in mind, however, that the same effect may pro- -, n too , t -t Exception. ceed from different causes. In order to game effect may determine to which of two possible pyoceed from different causes, causes it is due, in any given cases, the distinctive indications of each respectively must be sought. This is usually not difficult. The sensation of heat may arise from the general warmth of the weather, from an artificial fire, from exces- sive clothing, or from fever. It is usually easy, in view of all the circumstances, to determine which. But if not, unreal causes may be eliminated by the 2d Criterion ; the Method of Difference. 204 LOGIC. [Chap. VII. — This is given when, the supposed cause being present the effect is present, and this 2d Test. Me- r ... thod of differ- being absent the effect is wanting, i. e. unless in the former case other coun- xception. ter-agents are present to neutralize it, or in the latter to produce it. Thus, it is double proof that sound is the result of vibra- Example. . . r, . , i i . i , tions oi air excited by the resonant body, if, on the one hand, whenever sound is heard, such vibrations are found; whenever such vibra- tions appear sound is given forth ; and if, on the other hand, a bell or other sonorous body, suspended and struck in an exhausted receiver, yields no sound. It proves that the contact of moisture is the cause of the decomposition of animal matter, if, whenever the latter occurs such moisture is present ; if dry- ness checks or arrests it ; and if salt, which prevents it, acts by detaching the water from the meats which it preserves. If, when reason is present, there is accountability, and when it is absent there is none, then it is a condition of accountability. 3d Criterion — accounting for residual varia- tions without invalidating the proof of 3d Test. Eesid- ual variations the supposed cause. Thus, it was found accounted for. ^ ^^ trayeled fagter than what Sec. IV.] METHOD. 205 seemed the true theory of its law of velocity allowed. It was suspected, however, that the rarefaction of the air, arising from the heat produced by the mo- tion of the sound, accelerated its progress to this ex- tent. Experiments proved this conjecture true, and thus confirmed the original hypothesis.* * The following striking example is given in the words of Tlwmson's Laws of Thought, New York Edition, pp. 262-3, Chap. VII. " In Sir Humphrey Davy's experiments upon the decomposition of water by galvanism, it was found that besides the two compo- nents of water, oxygen and hydrogen, an acid and an alkali were developed at the two opposite poles of the machine. As the theory of the analysis of water did not give reason to expect these products, they were a residual phenomenon, the cause of which was still to be found. Some chemists thought that elec- tricity had the power of producing these substances of itself; and if their erroneous conjecture had been adopted, succeeding re- searches would have gone upon a false scent, considering galvanic electricity as a producing rather than a decomposing force. The happier insight of Davy conjectured that there might be some hidden cause of this portion of the effect; the glass vessel con- taining the water might suffer partial decomposition, or some foreign matter might be mingled with the water, and the acid and alkali be disengaged from it, so that the water would have no share in their production. Assuming this he proceeded to try whether the total removal of the cause would destroy the effect, or at least the diminution of it cause a corresponding change in the amount of effect produced. By the substitution of gold vessels for the glass without any cbange in the effect, he at once deter- 18 206 LOGIC. [Chap. VII. 4th Criterion. Concomitant Variations. — If, as the amount of the supposed cause 4th Test. Con- ' rr comitant Varia- varies, the effect varies proportionally, it is strong evidence of its being the real cause. " That the column of mercury in the Torricellian tube was counterpoised by a column of air, was proved by Pascal when he caused the instrument to be carried up the mountain, and found that as the ascent gradually diminished the height of the column of air above it, so was the column of air it was able to sustain diminished in proportion." mined that the glass was not the cause. Employing distilled water he found a marked diminution of the quantity of acid and alkali evolved; still there was enough to show that the cause, whatever it was, was still in operation. Impurity of the water then was not the sole, but a concurrent cause. He now conceived that the perspiration from the hands touching the instruments might affect the case, as it would contain common salt, and an acid and an alkali would result from its decomposition under the agency of electricity. By carefully avoiding such contact, he reduced the quantity of the products still further, until no more than slight traces of them were perceptible. What remained of the effect might be traceable to impurities of the atmosphere, de- composed by contact with the electrical apparatus. An experi- ment determined this ; the machine was placed under an ex- hausted receiver, and when thus secured from atmospheric influence, it no longer evolved the acid and the alkali." Sec. V.] METHOD. 207 When either of these criteria is found, free from conflicting evidence, and especially when several of them concur, the evidence is clear that the cases observed, are fair representatives of the whole class, and warrant a valid universal inductive conclusion. Sect. V. — Hypothesis. 23. But why make observations and experiments in one direction, or for the purpose of ^ eas011 f or gy- testing one view of the cause of given P 0thesl3 - phenomena, rather than any other ? It can only be because the mind entertains some conjecture or sus- picion that this may correspond with the facts. Thus it is led to institute investigations and trials for the purpose of testing the sona bi e conjec- truth of this conjecture. Such a con- ture or Tenta - • t t tive Theory. jecture so entertained is a Scientific Hy- pothesis, which is thus but a provisional and tentative theory, while a true theory is a proved hypothesis. Such hypotheses, although they have often been abused, by the premature or unwarrantable assump- tion of their truth, are indispensable to effective progress in science. Without such a r a Use and Neees- suide and stimulus, all observations and sity of Hypo- experiments would be aimless, and com- 208 LOGIC. [Chap. VII. monly fruitless. Indeed, for the most part, they would be unattempted. Investigations so guided have led to nearly all the great achievements of scientific progress. 24. Some confound Theory with Hypothesis, and accurate writers often find it difficult to How far Theory and Hypothesis use them so as to avoid all shades of are synonymous. . -r> , ,1 synonymous meaning. But neverthe- less, correct use points towards the difference we have indicated. Hypothesis could not be well substituted for Theory, when we speak of Wells' theory of dew, or Dalton's theory of definite chemical proportions, or the Newtonian theory of universal gravitation. And yet theory is often used for hypothesis, i. e. for an unproved doctrine or speculation, or a tenta- tive and provisional, but uncertain explanation of phenomena. Thus we speak of Smith's Theory of the Moral Sentiments ; the exploded phlogiston and anti-phlogiston theories. Some use theory for a provisional and unproved explanation of a large group of facts. This however is but an hypothesis regarding such a group of facts. Definition f ^ n re g arc ^ *° * ne distinction be- some Scientific tween Theoretical and Practical Judg- Terms. Judgments. ments, and other Scientific Terms, we Sec. -V.] METHOD. 209 quote the following from Thomson's Laws of Thought: " Judgments that relate to speculation only, are called Theoretical ; those which refer to T , . _ 7 Judgments Tne- practice are Practical. Judgments oretical, Practi- pn l TjpTn on ^i"Tfl~ that require or admit of proof, are ble ' i n a e mon- called Demonstrable; those which are strable - manifest from the very terms, are Indemonstrable. Thus much being premised we can define certain subordinate parts of a science. An Axiom is an indemonstrable theoretical judg- ment. A Postulate is an indemonstra- ^ iom Postu- ble practical judgment. A Theorem is late > Tlieorem ' a demonstrable theoretical judgment. A Problem is a demonstrable practical judgment. A Thesis is a judgment Thesis. proposed for discussion and proof (but with Aris- totle it sometimes means an axiom of some special science or disputation). An Hypothesis is a judgment provisionally accepted as an explanation of some group of facts, and is liable to be discarded if it is found inconsistent with them. A judgment which follows immediately from an- other, is sometimes called a Corollary or Consectary. One which does not 18* 210 LOGIC. [Chap. VII. properly belong to the science in which it appears, but is taken from another, is called a Lemma. One Lemma. which illustrates the science where it ap- ScMion. pears, but is not an integral part of it is a Scholion." 25. The great distinction of Scientific Genius lies Chief mark of chiefly in this insight which, with keen Scientific gemus. discernment of analogies, anticipates the truths or laws of nature, and devises observations and experiments to prove or disprove them. So Newton suspected that the same force which causes the falling of an apple, propels all matter, and pro- duces the revolution of the planets; Franklin, that lightning is a discharge of electricity. They proceeded to verify these hypotheses by experiments and observations which proved them. While the legitimate use of hypothesis is thus advantageous and essential to science, the cautions needful to be observed to prevent the abuse of it are, Cautions in Ee- A. No hypothesis should be assumed 5" ■ t( \ I?\ to account for what can be otherwise thesis, 1, Must be needed. accounted for, on existing and known principles. B. It should be adequate to account 2. Adequate. n ,, , . ,. for the phenomena in question. Sec. VI.] METHOD. 211 C. The facts to be accounted for should be real and not imaginary, as the question be- fore mentioned of Charles II. to the be explained Koyal society, why a live nsh in water would increase its weight, while a dead fish would not, and quite perplexed some of its members, until it occurred to them to inquire if the fact were so. D. It should be independent of -$ subsidiary subsidiary hypotheses — it should not Hv P otheses ' require other hypotheses to account for itself. E. It should not be assumed to be To be accepted true until proved to be so. when proved. Sect. VI. — Analogy. 26. When it is argued from a known resemblance between objects or classes in some known Reasoning from particulars, that they resemble each Analogy defined. other in other respects, this is reasoning from analogy. It has been common to define analogy as a proportion between objects. When ,-, . , , j Example. we reason that because men resemble animals in having life and sensation, they therefore resemble them in the power of locomotion, or in the grade of their intelligence, we reason from 212 LOGIC. [Chap. VII. analogy, or the relative proportion of objects.* It is obvious that this is a very uncertain argument, Has only a pro- and can > in n0 CaSe > rise hi g her than babie force. mere probability. This probability will be weaker or stronger according to circumstances. The argument for future retribution, from the pre- sent evils visited upon sin, is certainly stronger than the argument that brutes have reason because other conscious beings have it. But in neither case is it conclusive. The argument from analogy may be well employed to add a cumulative May strengthen x J other argu- force to other arguments. It is not, mentSi ■, . i ■ *» • > 1 /» however, in any case conclusive of itseli. 27. Its most important service, however, is in „ , , . refutation of fallacious arguments. It Most useful in » refutation. often has in this way a powerful nega- tive force. Thus, if it be objected to the doctrine of future punishment that the infliction of pain is inconsistent with the benevo- Examples. lence of God, this argument is refuted by the fact * To reason from Analogy, is to reason from the Intension of that to which it relates. To reason by Induction is to reason in extension from one or some objects in a class to all in that class. In analogical reasoning, we argue from a resemblance in some qualities to a resemblance in other qualities. Sec. VII.] METHOD. 213 that God does inflict pain, or so order and permit events that it is undeniably inflicted, in this life. The alleged impossibility of the future life and immortality of the body on account of its death, is disproved by the fact that in all nature life is evolved from death, and the seed which we sow " is not quickened except it die." 1 Cor. xv. 36. Sect. VII. — Categories. 28. These are summa genera of predicables. Logicians and metaphysicians have Definition of sought to give complete lists of these Categories. summa genera, to which all particular predicables and classes of predicables might be referred. It has, however, been hard to find any such exhaus- tive enumeration. Says Whateley, " The Categories enumerated by Aristotle, are odaia, Aristotle's Cate- izbaoVy Tidlov, jrpoazc, ~oi) y trove, xetadat, S ories ' e%£iv, TtoiEiv, Ttdayziv ; which are usually rendered, as adequately as, perhaps, they can be in our lan- guage, substance, quantity, quality, relation, place, time, situation, possession, action, suffering. The catalogue (which certainly is but a very crude one) has been by some writers enlarged, as it is evident may easily be done by subdividing some of the 214 . LOGIC. [Chap. VII. heads ; and by others curtailed, as it is no less evi- dent that all may ultimately be referred to the two heads of substance, and attribute, or (in the language of some logicians) accident." Some, however, per- haps justly, translate e/£*v, " mode of action," in- stead of " possession." Aristotle's Categories are rather metaphysical than logical. 29. Kant's celebrated four triplets of Categories Kant's Cate- are cer tainly ingenious, and, if not ab- gories. solutely exhaustive, in a metaphysical view, go far to show the nature and a 'priori basis of the several logical judgments. According to him all judgments must connect the predicate with the subject so as to involve under the head of, 1. Quantity. 2. Quality. 3. Relation. 4. Modality. Unity, Affirmation, Substance and Accident, Possibility, Plurality, Negation, Cause and Effect, Eeality, Totality. Limitation. Action and Eeaction. Necessity. It may be observed that the first of these triplets corresponds to Singular, Particular, and Universal Judgments; the second to Affirmative, Negative, and Kestrictive* Judgments; the third to Categori- * Restrictive Judgments "are such as contain a negative in the predicate-conception, e. g., God is infinite. The human soul is immortal. In respect to their contents, they are negative ; but Sec. VII.] METHOD. 215 cal, Conditional, and Disjunctive Judgments; the fourth to Problematic, Assertory, and Apodictic Judgments. 30. Tables of Categories are almost as various as the writers on Logic and Metaphy- sics. McCosh gives the following as a provisional summary of primary judgments. 1. Identity and Difference. 5. Quantity. 2. Whole and Parts. 6. Resemblance. 3. Space. 7. Active Property. 4. Time. 8, Cause and Effect. 31. J. S. Mill in his Logic gives the following classification of nameable things in the spirit of the Positive Philosophy. J. S. Mill. 1. Feelings or states of consciousness. 2. The minds which experience these feelings. 3. The bodies or external objects which excite certain of these feelings, together with the power or properties whereby they excite them. in respect to form, they are affirmative. Logically considered, therefore, they belong to the class of affirmative judgments. These judgments are also called infinite, or more properly indefi- nite, because, by means of a predicate involving a negative, the subject is transferred from the sphere of definite conception to that of indefinite conception, a sphere to which it does not pro- perly belong." — Gerhart's Philosophy and Logic, p. 214. 216 LOGIC. [Chap. VII. 4. The successions and coexistences, the likenesses and un- likenesses between feelings and states of consciousness." — Logic, I. 111. 32. Thomson (Laws of Thought, p. 315) just attempts the following : TABLE OF THE CATEGORIES. ID fcJD J2 ' 3 S3 .i-H o c o o Substance ' Quantity Attribute i Quality . Kelation of Time of Space of Causation of Composition of Agreement and Eepug- nance of Polar Opposition of Finite to Infinite. Sec. VIII.] METHOD. 217 Sect. VIII. — Harmony and Co-ordination of Sciences. 33. As the application of scientific method to any given and mutually related set of phenomena or truths develops a science of these facts, like the Science of Botany, Anatomy, Ethics, etc., so many of these sciences are related to each other as Genus and Species. Thus Ornithology, Piscatology, etc., under Zoology. Various attempts have i i , t •/» ,i n ■ Classification been made to classify the Sciences so and u utua i as to show their Mutual Harmony and Ha ™ony of . the Sciences. Interdependence. It is plain that they might be logically divided and sub-divided from various stand-points, which have been taken ac- cording to the respective aims and purposes of the authors. Thus they may be divided into the Speculative and Practical, or the Phy- gpeculative and sical and Metaphysical, or the Formal Pra ctical, etc. and Material, etc., with their respective subdivisions. Attempts of this sort have often been made, with considerable success and utility. 34. Compte and the positive school of philoso- phers, however, amidst their enormous errors, have unfolded a scheme of classification and co-ordination among the sciences, at once beautiful and fruitful, 19 218 LOGIC. [Chap. VII. which has commanded wide acceptance among those who have attended to the subject. Starting with Descartes' suggestion, that the order of arranging the sciences should be from the simplest to the more complex, he adopts the fol- lowing, which at once commends itself by its sim- plicity, naturalness, and beauty, and which we give, as we find it, in a form most available for our pre- sent purpose, in Thomson's Laws of Thought, pp. 316-19. " Mathematics, or the science of quantity, is at once the most simple in its elements and the most general in its application, entering more or less into all the sciences of nature, and constituting almost the whole of that which comes next it in the order of dependence. Astronomy, or the science of the heavenly bodies, is the application of mathematical truths to the laws of matter and motion ; matter and the motions of material bodies being the new con- ception which belong to this science. Physics, being the science, or rather group of sciences, which is conversant with the general laws of the world, so far as they relate to beings without life or organiza- tion, would come next ; and it imports, in addition to the conceptions of Astronomy, those of light, of Sec. VIIL] METHOD. 219 heat, of sound, of electricity, of magnetism, and many others. Chemistry would rank next, which is the science of the decomposition and combinations of the various substances that compose and surround the earth. Next in order of complexity would rank Physiology, founded on the additional conception of vegetable and animal life. To this would suc- ceed Anthropology, or the science of man's nature; and to this Social Science, which ascertains the laws that govern men when combined in cities and na- tions. Each of these departments may be divided into many branches; as Physics into Acoustics, Optics, Electricity, and the like; or Social Science into Morals, Politics, Political Economy, Law, and the like. " On comparing scientific works, differences in the mode of teaching the same subject become appar- ent. In one the pure theory of Astronomy is presented; in another the striking features of its historical progress as a science, with speculations on the historical sequence of the phenomena themselves ; in a third the practical applications of which the science admits in respect to the comfort and progress of mankind. This threefold mode of treatment runs through all the sciences; and in a table of 220 LOGIC. [Chap. VII. them might well be expressed. The classification would thus embody all that is valuable of another system of classes, that according to the purpose towards which the science was directed. "A classification which advances on Descartes' principle, from the more simple to the more com- plex subjects, which commences from the notions of extension and quantity, and proceeds through ma- terial things, up to living, intelligent, and moral agents, ought to coincide with the order in which the sciences themselves have reached maturity. And this it certainly does. Mathematics had made good its ground when astronomy was yet in its infancy; physics began to obtain a sure footing later than either • whilst the sciences which relate to life are still very immature; and some of the main problems of social science are yet matter of contro- versy even in our own days. "There is besides a general correspondence between this classification and the order in which the various objects of science came into being. The heavenly bodies were first appointed their paths in the celes- tial spaces; then the surface of our earth was pre- pared for living creatures ; then they were created after their kind, and man the last. The social life Sec. VIII.] METHOD. 221 of man grew up last of all, when his race was mul- tiplied on the globe ; and ever as new elements ap- pear, the conditions of society are being modified even to the present time." Hence emerges the following "classification of the sciences. Group. Mode of Treatment. I. Mathematics Theoretical. Historical. Applied. II. Astronomy Theoretical. Historical. Applied. III. Physics Theoretical. Historical. Applied. IV. Chemistry Theoretical. Historical. Applied. V. Physiology Theoretical. Historical. Applied. VI. Anthropology.... Theoretical. Historical. Applied. VII. Social Science Theoretical. Historical. Applied. V , Eeligious Philosophy." 19* APPENDIX. APPENDIX A. EXAMPLES FOR PRAXIS. ffl^ The following examples may be used for 'practical exercise in Conceptions, Judgments, and Reasonings of all kinds. In analyzing Syllogisms, let the student complete them when un- finished, and point out their kind, whether Categorical or Hypothetical; if the former, give their Mood and Figure; if the latter, show whether they are Conditionals, Disjunctives, or Dilemmas. Mark the Enthymemes, Sorites, Prosyllogisms, and Episyllogisms. In all cases show ivhether the Syllogism is valid or invalid, and if invalid, indicate the kind of Fal- lacy. 1. Body is extended substance, This inkstand is a body, .*. It is extended substance. 2. Plants are bodies with organization, Potatoes are plants. 223 224 APPENDIX. 3. Animals are bodies having organization and sensation, Frogs have organization and sensation. 4. Bodies having organization, sensibility, and reason are men, The poets are men. »•••••«•• 5. X Y Z, are ruminant, X Y Z, are (as good as) all horned cattle. ••••••••a 6. Quadrupeds are animals, Worms are animals. i 7. Oaks are vegetable, Oysters are not oaks. 8. Beasts are animals, Birds are not beasts. ••••••••• 9. These emigrants are either Scotch, Irish, or German, They are not Germans. •••••*•« 10. These people are patriots because they are free. 11. If the classics teach how to produce wealth they ought to be studied, They do not so teach. <•*.... EXAMPLES FOB PRAXIS. 225 12. If we can prevent what occurs we ought not to fret about it, If we cannot prevent what occurs we ought not to fret about it, But either we can or cannot prevent it. • •*<*••••> 13. A Christian nation is brave, A brave nation is free, A free nation is happy. •••••••» 14. A plane triangle is a rectilineal figure having three sides, A plane triangle is A B C. • •••••*••• 15. All these trees make a thick shade, This catalpa is one of these trees, .*. It makes a thick shade. 16. Whatever study gives knowledge relative to either of the three learned professions ought to be a part of liberal education ; Geology and Mathematics do not give such knowledge, .*. They ought not to be studied. 17. If all men are liars then nothing can be proved by human testimony ; But some things can be proved by human testimony, .*. No men are liars. 18. Typhoid fever is epidemic, Because A. B. and C. have it. P 226 APPENDIX. 19. An inflated currency promotes national prosperity, be- cause it enables persons to make rapid fortunes. 20. What we eat grows in the fields or is the flesh of animals, Cooked food is what we eat, 1 .'. Cooked food grows in the fields or is the flesh of animals. 21. The rumor that A. B. has committed a given crime is universal, for I heard it from Mr. A and Mr. B. 22. If we say the Baptism of John was from heaven we con- demn ourselves for not believing him ; If we say it was of men, the people will stone us ; But we must, if we say any thing, confess it was from heaven or of men ; .*. If we say any thing, we must either condemn ourselves, or the people will stone us. Luke xx. 4-6. 23. Some flowers are (all the) tulips, All flowers are beautiful, .*. All the tulips are beautiful. 24. All false religions have sustained their claims bv alleged miracles, Christianity sustains its claims by alleged miracles ; .*. It is a false religion. 25. The hour-hand can never overtake the minute-hand of a clock, because while it is passing to the point where the minute- hand is at any given moment, the latter will have advanced EXAMPLES FOR PRAXIS. 227 some distance : and when the former has passed over this dis- tance the minute-hand will have advanced still further ; and so on ad infinitum. 26. This man has an excellent character because he belongs to an excellent church, as appears from its being composed of such excellent men. 27. He who is most hungry eats most, He who eats least is most hungry, .'. He who eats least eats most. 28. If the taking of an oath to discharge our duty tends to secure its performance, then it ought to be repeated in refer- ence to every duty of life ; if it does not, then the civil oaths administered are superfluous. But one or the other of these are true. .*. The oaths commonly administered are superfluous, or they should be repeated in connection with every duty of life. 29. No man is rich who is not content, No miser is content (i. e. every miser is one who is not content), .*. No miser is rich. 30. Men can live without animal food, and they can live without vegetable food, as has been often demonstrated, But all food is either animal or vegetable, .*. Men can live without food. 31. He who calls you a man speaks truly, He who calls you a fool calls you a man, .*. He who calls you a fool speaks truly. 228 APPENDIX. 32. Useful studies ought to be encouraged, Logic, since it helps us to reason accurately, is such, .'. It ought to be encouraged. 33. X Y Z have polarity, X Y Z are (as good as) all magnets, for polarity appears wherever magnets are ; it disappears when they are withdrawn, unless other polar forces are present, and it increases with the power of the magnet ; .*. All magnets have polarity. 34. Some men of genius are (all) the poets, Some poets are melancholy. 35. The mind is a thinking substance, A thinking substance is a spirit, A spirit has no composition of parts, That which has no composition of parts is indissoluble, That which is indissoluble is immortal, Therefore the mind is immortal. 36. Protagoras engaged to teach Euathlus the art of pleading for a large reward, one half to be paid at once, the other half when the latter should have gained his first cause in court. After a short time Protagoras sued Euathlus. for the unpaid moiety, enforcing his claim by the following Dilemma: If the case is decided in my favor, the sum will be due to me according to the finding of the court ; If it is decided in your favor, the sum will be due to me according to our contract, EXAMPLES FOR PRAXIS. 229 But it must be decided either in my favor or yours. .'. Whether I gain or lose the cause I shall be entitled to the reward. * Euathlus thus answered . If I gain the cause, nothing will be due you according to the decision of the court, If I lose it nothing will be due you according to our contract ; But I shall either gain or lose it, .*. In neither case shall I pay you the reward. 37. A policy which promotes the national wealth ought to be adopted ; But the education of the people increases their wants and expenditures, and therefore does not increase national wealth ; .'. It ought not to be adopted. 38. All is not gold that glitters, Tinsel glitters, .'. It is not gold. 39. If there had beer, a law that could have given life, then verily righteousness should have come by the law, But righteousness did not come by the law." • • #•••••••• ' . X ,' ( I , 111* _- 1 , * The fallacy here is that the Disjunction is incomplete. There is another horn, viz : that Protagoras had no cause of action, be- cause before the bringing of this suit, Euathlus had no case in court. See Chap. V., 29. 20 230 APPENDIX. 40. Poets are men, Orators are men. 41. Plants are bodies with life, and without consciousness, Geraniums are such bodies. 42. All trees bearing acorns are oaks, Some trees do not bear acorns. 43. All men are rational animals, Apes are not men, /. They are not rational animals. 44. Some men are orators, Some bipeds are (all) men, .*. Some bipeds are orators. 45. The following answer was given to Pyrrhus' assertion that nothing can be certainly known : If you certainly know this, your assertion is disproved, If you do not certainly know it, you have no right to affirm it, But you either do or do not know it, Therefore your doctrine is untenable. 4G. Most people are careless, Most people are destitute of perfect health. 47. It is almost certain that C. D. is a true witness because there is a probability amounting to f that he saw and ob- EXAMPLES FOR PRAXIS. 231 served correctly what he testifies about, and another proba- bility of f that he would tell the truth if he did know it." What is the probability that B. B. wrote a certain anony- mous letter, where the separate probabilities are, From chirography, £, From the sentiments, i, and From his known meanness of character, \. APPENDIX B. SYLLOGISTIC NOTATION. 1. Various methods have been adopted to represent to the eye the different forms of the Syllogism, Meaning of Syl- an( i ^ re i a ^ ons f thought respectively in- t,i on , volved in them. This is done through linear diagrams analogous to the figures of Geom- etry. It greatly assists the mind in discerning at a glance the quantity, the mutual relation, and the quality of the different terms and judgments of the syllogism, together with its figure and mood. One of the most celebrated schemes of notative symbols is that by means of circles in- vented by Euler, upon which we have already Euler's Method , ,, « , .,, , ,. v «■ i drawn tor purposes or casual illustration. (See Chap. V. 13.) 2. Three circles are employed to denote respectively the Major, Minor and Middle Terms. Affirmative judgments are symbolized by the total or partial ?^clusion of the circle signi- fying the subject in that which stands for the predicate. Negatives are signified by the total or partial exclusion of the former from the latter. The following diagram, in which A B and C denote re- spectively the minor, middle, and major terms, represents, 232 8YLL GISTIC NO TA TION. 233 1. The moods A A A. 2. AEE. 3. A 1 1. 4. E I 0, all of the First Figure. 1. Barbara. 2. Celarent. 3. Darii. 4. Ferio. Of course, this method, mutatis mutandis, is applicable to the other figures. This clearly and beautifully represents the Syllogism according to extension, as also the distribution or non-distribution of different terms. 20* 234 APPENDIX. NOTATION BY STKAIGHT LINES. 4. According to this scheme, a horizontal straight line denotes a term distributed. The letters S, P, or M attached, indicate that it is respectively minor, major, or middle term. S P Dots are used to signify an undistributed term as noting its indefiniteness. M Any definite portion of an undistributed term is indicated by a line not dotted inserted in one that is dotted. Thus in the judgment "men are mortal," & e. "some mortals," mortal is undistributed. But we take that definite portion of it which is co-extensive with the class man. Thus : p mortal. S men. Affirmative judgments are symbolized by lines, one above the other — the former being the predicate, the latter the subject. Negative judgments are represented by parallel lines drawn so that one is not under the other. Thus : S To complete the syllogism, of course three lines must be employed to represent the three terms and judgments in their quantity and other relations. SYLL GISTIC NO TA TION. 235 P M . S . This represents A A A, of Fig. 1. Thus : All horses are quadrupeds, All Shetland ponies are horses, .". All Shetland ponies are quadrupeds. If there be one negative premise in the Syllogism, it can be thus represented. The following is E A E, Celarent, of Fig. 1. P M S No M is P, All S is M, .*. No S is M. Substitutive Judgments are indicated by two equal and parallel lines. Thus : P S Judgments of Logical Division or Colligation (chap. II. 43) may be expressed thus : - . . P x y z P Division, Colligation, S S x — v z 236 APPENDIX. THE HAMILTONIAN NOTATION. 5. Quite the most expressive and complete system of Notation, and one of his important contributions to Logic, is that invented by Sir William Hamilton. It is so con- trived as to exhibit, at a glance, all the characteristics of the valid Syllogism, both according to intension and exten- sion, in all the figures. This is done by means of lines, wedge-shaped in the figured Syllogism, and of uniform length and breadth in the unfigured Syllogism, and in all substitu- tive judgments, these latter lines denoting the perfect equality of subject and predicate. 6. The wedge-shaped figure or line denotes a judgment — its thick end the subject of extension which is contained extensively in the predicate : its thin end the subject of in- tension, or predicate of extension, which is contained inten- sively in the other. Most of what follows is so well put in Bowen's Logic, that we transfer it with little modification. "As the employment of letters following upon each other in the same alphabet might suggest that one was invariably subordinated to the other, instead of being its subordinate in one Quantity and its superordinate in the other, Hamil- ton uses for the Extremes the Latin C and Greek r, each being the third letter in its own alphabet; as usual, M stands for Middle Term. Thus : is read, C and r are equal. may be read in two ways ; Extensively, C is included under SYLL GISTIC NO TA TION. 237 r ; Intensively, vis included in C: — or, in the usual manner, C is r, and r is C, merely remembering, without saying so, that Extension is signified in the former case, and Inten- sion in the latter. 7. ''Negation is indicated by a perpendicular stroke drawn through the line, thus: ■— { — . The line without this stroke may be regarded as the Affirmative Copula; with the stroke, as the Negative Copula. A colon ( : ) annexed to a Term shows that it is distributed, or taken universally; a comma ( , ) so annexed, that it is undistributed or Parti- cular. When a Middle Term has a colon on the right, and a comma on the left, it is understood that it is distributed when coupled in a Judgment with the Term on the right, and undistributed when coupled with the other. 8. "A line drawn beneath or above three Terms indicates the Conclusion (or the Copula of the Conclusion) deduced from the two Premises which those Terms constitute. In the Second and Third Figures, since there may be two equally direct or immediate Conclusions, they are represented by two such lines, the one above, and the other below the Premises. Thus : This is a Syllogism in the Second r Figure, which may be read in either of the following ways. Extensively. Intensively. Some C is some M ; All M is some T; Some r is all M ; Some M is some C; .*. Some r is some C; or .'. Some C is some T; or .'. Some C is some r. ,\ Some r is some C. 938 APPENDIX. C, — — «, M: — I"- •: r "This is a negative Syllogism j— — in the First Figure, which may be read in either of the following ways; but in either way, it has onty one direct or immediate Conclusion, though a Second Conclusion may be obtained from it indirectly, by^ converting simply the proper or direct Conclusion. Extensively. Intensively. Some M is some C ; No M is any r ; No r is any M ; Some C is some M ; No r is some C ; or, Some C is not any r ; or, indirectly. indirectly. Some C is not any r ; Not any r is some C. 9. "The following diagram presents the whole Hamil- tonian doctrine of Figure, together with the distinction between the Analytic and the Synthetic order of enounce- ment. After the explanations which have been given, it will be easily understood. "As a Judgment has been designated by a line, a Syllo- gism, which is a union of three Judgments, is appropriately typified by a triangle, a union of three lines, of which the base represents the Conclusion, and the other two lines, the Premises. As the direction of the arrows indicates, we may proceed either in the usual or Synthetic order, from the Premises to the Conclusion, or in the reverse order, which is Analytic, from the Conclusion to the Premises. As there is no valid reason for always placing the Major Premise first in order, the diagram shows that either Premise may have precedence in this respect, so that what has been SYLLOGISTIC NOTATION. 239 called the Fourth Figure is here identified with the Indirect Moods of the First. * * * "The Unfigured Syllogism is properly represented as in- cluding all the others, as any Syllogism of either Figure may be easily expressed in this form. In like manner the triangle representing the First Figure is made to include the two typifying respectively the Second and Third, as either of the latter may be readily reduced to the former. And again, the essential unity of the Syllogistic process, and the unessential nature of variation by Figure, are appropriately signified by a single triangle comprehending all the varieties of form. 240 APPENDIX. "The double Conclusions, both equally direct, in the Second and Third Figures, are shown in the crossing of two counter and corresponding lines. The Direct and Indirect Conclusions in the First Figure are distinctly typified by a common and by a broken line; the broken line is placed immediately under the other, and may thus indicate that it represents only a reflex of — a consequence through the other." 10. It will be remembered that the four fundamental judgments hitherto recognized by logicians, viz., A E I 0, yield sixty-four conceivable moods. Excluding from these all that are invalid as offending against the laws of the syllogism, only eleven moods remain that are valid in the fourteen syl- logisms of the first three figures, or nineteen, if the fourth figure be recognized. But Hamilton, as we have seen, recog- nizes eight judgments, adding to the four already named, U Y i oi. The possible combinations of these are five hundred and twelve. Of this number, however, only thirty-six will bear the tests of valid syllogisms, of which twelve are affirma- mative and twenty-four negative. Thus, on this system, each affirmative mood has two corresponding ones that are negative, as each of its premises may be made negative. Since each of the moods on this system can be put in either of the three figures, there arise three times thirty- six, or one hundred and eight valid syllogisms in the several figures. The changes in the different figures, however, are for the most part unessential and insignificant. The follow- ing table by Hamilton exhibits the eight judgments re- cognized by him, very ingeniously in their relative strength, SYLL GISTIC NO TA TION. 241 in which A signifies a term distributed, I a term undistri- buted, f an Affirmative, and n a Negative copula. A par- ticular is accounted weaker than a universal, and a negative weaker than an affirmative. Best. Worst. { -5 6 1. Afa. 2. An. 3. Ifa. Ifi. Ini. Ina. Ani. All are all. All are some. Some are all. Some are some. Some are not some. Some are not any. Not any is some. -8. Ana. Not any is any. " With these explanations, the following list of the twelve valid Affirmative Moods in each of the three Figures, and the twenty-four valid Negative Moods in the First Figure, all expressed in the Hamiltonian notation, will be found intelligible,. 11. "In this Table, the Quantity of the Conclusion is marked only in the cases already considered, wherein the Terms obtain a different Quantity from that which they held in the Premises ; accordingly, when not marked, the quantification of the Premises is held as repeated in the Conclusion. The symbol w ^— ', placed beneath a Conclusion, indicates that, when the Premises are converted, the Syllo- gism remains in the same Mood ; ^>P U |. . I-...— C : ,i ; M : E3H c,- ■3BB V«W W<- ' M, X B. NEGATIVE MOODS. r a C,- [b C «a : M , i— ■, T iii. and iv. are unbalanced in terms only, not in propositions: Hip rest in both. 244 APPENDIX. said to be balanced, when it is Universal in both Premises. The Extremes, or Terms of the Conclusion, are balanced, when both alike are distributed ; unbalanced, when one is, and the other is not, distributed. Accordingly, of the Moods, in this Table, numbers I. and II. are balanced as respects both terms and propositions ; in III. and IV. , only the terms are unbalanced; in the remainder both terms and propositions are unbalanced." • Date Due , ' & V 1 ^j* 00 * g-p#l ^ • f) BC71.A88 Manual of elementary logic Princeton Theological Seminary-Speer Library 1 1012 00008 2828