I 
 
MANUAL 
 
 OF 
 
 ELEMENTARY LOGIC 
 
 DESIGNED ESPECIALLY FOR THE USE OF TEACHERS 
 AND LEARNERS. 
 
 BY 
 
 LYMAN H. ATWATER, D. D., LL.D., 
 
 OV LOGIC AND MORAL AND POLITICAL SCIENCE IN TUB 
 COLLEGE OF NEW JERSEY. 
 
 UNIVERSITY 
 
 OF 
 JF 
 
 REVISED EDITIQN - 
 
 PHILADELPHIA: 
 
 J. B. LIPPINCOTT COMPANY. 
 

 
 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. 
 
 Copyright, 1895, by ADDISON ATWATIB. 
 
CONTENTS. 
 
 Mfl 
 PRKF &.C K ......... ...... 9 
 
 CHAPTER I. 
 
 THE SPHERE AND OBJECTS OF LOGIC. 
 
 SECTION I. Logic the Science of the Laws of Thought IS 
 
 II. The General Nature of Logical Judgments 22 
 
 III. Reasoning as including Conceptions and Judg- 
 
 ments 25 
 
 IV. Pure and Applied Logic 28 
 
 V. Applied Logic further explained 34 
 
 VI. Utility of Logical Study 36 
 
 VII. Fundamental Axioms of Logic... ....................... 40 
 
 CHAPTER IL 
 
 CONCEPTIONS. 
 
 BCOTION I. Conceptions, their Nature and Formation.-. ........ 43 
 
 II. Higher and Lower Conceptions 47 
 
 III. Genus, Species, Essence, Differentia, etc 49 
 
 215198 
 
CONTENTS. 
 
 MM 
 
 BJCT. IV. Other Distinctions in Genus and Species 51 
 
 V. The Three Powers of Conceptions. 53 
 
 VI. Inverse Ratio of Extension and Intension 66 
 
 VII. Denomination of Conceptions 56 
 
 VIII. Various kinds of Terms * 68 
 
 IX. Quality of Conceptions 64 
 
 X. Notativc and Symbolical Conceptions 67 
 
 XI. Logical Division. .............................................. 69 
 
 XII. Definition ... ..... 73 
 
 CHAPTER IIL 
 
 JUDGMENT. 
 
 SBCTION 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 Hypotheticals into Categoricala 103 
 
CONTENTS. 7 
 
 CHAPTER IV. 
 
 REASONING IMMEDIATE INFERENCE. 
 
 PA8B 
 
 SECTION I. Mediate and Immediate Inference Denned 106 
 
 II. Immediate Inference by Opposition 107 
 
 III. Immediate Inference by Conversion 113 
 
 IV. Other 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 142 
 
 , VI. Hypothetical Syllogisms 144 
 
 VII. Conditional Syllogisms 145 
 
 \\ VIII. Disjunctive Syllogisms 146 
 
 IX. The Dilemma 148 
 
 X. Incomplete Syllogisms 152 
 
 XL Complex Syllogisms 153 
 
 \ 
 
 CHAPTER VI. 
 
 APPLIED LOGIC FALLACIES. 
 
 BIOTIOK I. Fallacies, Formal and Material 158 
 
 II. Fallacies, partly Formal and partly Material IM 
 
 III. Logical Puzzles 179 
 
g CONTENTS. 
 
 CHAPTER VII. 
 
 APPLIED LOGIC METHOD. 
 
 VAOB 
 
 SscrioN 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. 22* 
 
 APPENDIX B. 
 
 SYSTEMS OF SYLLOGISTIC NOTATION. 
 
 Notation by Circles 248 
 
 Notation by Straight Lines . 250 
 
 The Hamiltonian Notation.... , 252 
 
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, Hansel, Bayne, De Horgan, 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 IV. 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. 
 
 NOTE TO REVISED EDITION. 
 
 While such minute corrections of the main text of 
 this treatise as have been found needful will be found 
 in this edition of it, the chief improvement consists 
 in the large addition of examples for logical praxis 
 which so greatly facilitate the teaching and study oi 
 Logic. 
 
 PRINCETON COLLEGE, 1879. 
 
ELEMENTARY LOGIC 
 
 CHAPTER I. 
 
 THE SPHERE AND OBJECTS OF LOGIC. 
 SECTION I. 
 
 1. LOGIC IS THE SCIENCE OP THE LAWS OP 
 
 Logic defined, 
 
 THODGHT 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 ^^'^oi,. 
 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 Subject and Ob- 
 adjectives subjective and objective, and the ^ ect define<L 
 
 2 13 
 
14 LOGIC. [Chap. I. 
 
 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 
 needful to discriminate other objects 
 from this subject-object, some writers use the term 
 object-object. The student who under- 
 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 
 Thought de- determine what thought is. 
 
 working and Thought is subjectively the operation, 
 
 product of the an( j 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. Al though 
 
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- 
 
 BionoflnteUeo- 
 
 mory which retains and reproduces tuai 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 fc^tive Fac . 
 through the medium of any process of ^ties 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, mtue* 
 tur, by a direct beholding, and without the inter- 
 vention of reasoning or thinking. 
 
 8. The Intuitive Faculties furnish us 
 
 the 
 the original material of all our know- Thought, 
 
16 LOGIC. [Chap. L 
 
 ledge, '.The Discursive Faculties take the matter 
 The Discursive thus furnished, and proceed from it. 
 
 elaborate it in- 
 to new forms, discurrunt, 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 
 borative. ^^ the Elaborative Faculties. 
 
 9. It is important to observe, that intuitions 
 Intuitions are (aside of exceptions in the region of 
 
 of individual ob- V 
 
 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. 
 l^^dis- To classif 7 is to perform a process of 
 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 latter, not . _ . , 
 
 the former. the sense here intended. It furnishes 
 matter for thought, but is not thought. With 
 this logic does not concern itself, unless casual]} 
 and indirectly. It develops the laws of the think- 
 
Sc. I. ] ITS SPHERE AND OBJECTS. 17 
 
 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 
 fcion, and, by a process of thought, in- 
 
 volving Analysis and Synthesis, reach l J si * an 
 
 thesis to new 
 
 new results. First, 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 A])Stract i on 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 
 
 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- 
 ' *Jte. Observing that, besides extension, they have 
 
 2 
 
18 LOGIC. [Chap. 1. 
 
 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 
 t's 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 ia 
 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 wor<2 
 conception, viz., that act or product of the mind which i denoted 
 by a general term, and is obtained by generalization. In common 
 speech, it has a much broader import, ard 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 bee 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- Conception ex . 
 presents, not all of any individual ob- P lain ed, 
 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 Oon- 
 
 jects, may be abstract, or viewed by ce ptions, 
 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 
 ceptTon Con- ma( ^ e ^ e bject of our thinking. Some 
 oept 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- 
 Generalization 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 O 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. L] ITS SPHERE AND OBJECTS. 21 
 
 will see that lie cannot retain, or employ, to any 
 extent, in judgments and reasonings, the ideas 01 
 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 
 
 ... Extreme views, 
 
 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 conneo- 
 
22 LOGIC. [Chap. j. 
 
 tion, amounting, for practical purposes, to almost 
 Sense in which an identification of thought and lan- 
 
 Whateley's doc- 
 trine is true, guage, there is a sense obviously, in 
 
 which Whateley's doctrine may be regarded as u 
 half truth often the worst form of error.* 
 
 18. The first part of Logic then has to do with 
 Ihe first part of that product of thought which results 
 LTep d t 6 Ss m or h from generalization, called Conception; 
 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- 
 
 PrimitiveJudg- * 4 
 
 ment compared, stituent of every act of 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. II.] 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 J^ ^ 
 conceptions and logical judgments are enoe, 
 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 Judg- 
 tions as both, of its elements. It com- ment defined 
 pares two conceptions, or a conception and an in- 
 tuition, and affirms that they agree or Compares Oon- 
 disagree. Thus it affirms of the con- 
 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 ;" " 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 L 
 
 and the conception, philosopher, do iiot 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 
 
 *nd 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 
 meats to^new" tnem - This is Reasoning, or inference 
 judgments from premises to conclusion. Thus to 
 
 founded npon 
 
 them, conclude from premises is in fact tc 
 
Sec. III.] ITS SPHERE AND OBJECTS. 25 
 
 judge. So all modes of thought, from conceptions 
 to reasonings are in reality forms of ^ Bought b 
 
 reality a form 
 
 judgment. The third and last great O f judgment, 
 province of Logic, therefore, is the laws of rea- 
 soning. 
 
 SECT. III. SEASONING. 
 
 23. This runs into various branches or modes, 
 Mediate and Immediate, Categorical Tie third P ro " 
 
 . vince of Logic is 
 
 and Hypothetical, which need not be Reasoning, 
 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 
 Conceptions, under the name of Propo- Uses, 
 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 terms 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. L 
 
 ing is concerned, while he postpones the considera- 
 Conceptions and ^ on ^ them ' m chief, till he has finished 
 Judgments the analysis of the various forms of the 
 
 have a place in 
 
 Logic in their Syllogism. This shows that these con- 
 own right. 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 * ^HE SCIENCE OF THE LAWS OP 
 
 i*gio. THOUGHT. 
 II. THOUGHT is THE OPERATION, OR PRODUCT 
 
 OF THE OPERATION, OF THE DlSCUB- 
 Of Thought. 
 
 sivE FACULTIES, AS DISTINGUISHED 
 FROM THE INTUITIVE. 
 
Bee. III.l ITS SPHERE AND OBJECTS. 27 
 
 III. THE DISCURSIVE FACULTIES .ARE, 
 
 a. Abstraction and Generalization; the product 
 of which is Conception. 
 
 Enumeration of 
 
 b. Judgment, which out of Concep- Discursive Fac- 
 tions forms Logical Judgments. 
 
 c. Reasoning which from judgments given evolves 
 other judgments founded upon them. 
 
 The thinking and products of think- L e ic deals 
 
 with Ooncep- 
 ing, whose laws Logic unfolds, therefore, tions, Logical 
 
 are, CONCEPTIONS, LOGICAL JUDG- ^tSngs,^ 
 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, theiefore, so far as applicable to Constructive Imagina- 
 tion, are developed in treating of Conceptions, Judgments, and 
 Betsonings. 
 
28 LOGIC. [Chap. 
 
 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- 
 irrespeotive of lied d irrespective of their applica- 
 
 their Applica- 
 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 tho following chapter may be 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. 
 
 ID this Logic classes with Mathematics, and with 
 strict Metaphysics. The rules of Arith- it classes with 
 metic,and the propositions of Geometry ^j^eta" 
 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 ,1 . . , f. Does not In it- 
 
 itself with the original sources of our self give origi . 
 
 knowledge of actual being, or of the nal knwledg< 
 
 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, ID 
 various aspects, come within the province of Psy- 
 chology, Metaphysics, Ontology, or the different 
 
 3* 
 
30 LOGIC. [Chap. . 
 
 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 , ,, -r, 
 
 of necessary truths. By necessary we mean that 
 
 truths, "Neces- ^ e opposite of which, the mind cannot 
 
 aary" 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. I V.I ITS SPHERE AND OBJECTS. 31 
 
 they must be true, as the rules of Arithmetic and the 
 propositions of Euclid must be true in all 
 
 cases. Ilence pure Logic is not only, as eof t e 8 n ^ 
 before shown, the science of the laws, oessar y kwB d 
 
 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 condition^ 
 given, without needing verification from 
 
 Definition of a 
 
 experience. A posteriori knowledge priori and a pos- 
 depends upon experience for proof. 
 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 mv#t be equilateral. So we 
 
2 LOGIC. [Chap. 1. 
 
 kno\t, 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 * 
 
 with the Forms thinking, whatever be the subject-mat- 
 ns> 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 : PURE 
 
 Completed defi- ^OGIC IS THE SCIENCE OF THE NECES- 
 nition of Logic, g^RY AND FORMAL LAWS OF THOUGHT. 
 
J 
 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 Science8 - 
 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 whicli 
 have what, in these relations, is called Form| c^t^t 
 Content, or matter of actual being, Matter ' 
 whether in the realms of body or spirit, are called 
 Material Sciences. The contrast here Material Soien- 
 is not between Material and Spiritual, 068i 
 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 to Physical Sci- 
 
 ences. 
 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 H othetical 
 of actual being only on the hypothesis, Sciences ex- 
 that the conditions of actual being are 
 given to which they are applicable. Thus, that the 
 angle in a semi-circle is a right-angle proves no 
 
34 LOGIC. [Chap. L 
 
 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 no content f 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. 
 
 Application of B 7 ite USe the former Science has made 
 
 Formal Scien- the immense strides which have ad- 
 cos to facts a 
 
 means of dis- vanced it to its present perfection. So 
 
 covering truths, G eometrv an d 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 
 
Bee. 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 ; 
 
 for guiding us to the avoidance of 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 Applied Logio 
 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 
 thought, especially of reasoning, for the ment * 
 things themselves, thus sometimes im- cies and 
 posing upon themselves, or essaying to 
 
 impose on others. 
 
36 LOGIC. [Chap. L 
 
 6 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- 
 
 8iurnnation, . 
 
 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 a means of 
 
 disciplining and invigorating; the mind. 
 Uses of Logic, 
 Intellectual Few studies more effectually promote 
 
 habits of attention, discrimination, and 
 continuous application. 
 
 34. The knowledge thus acquired is of high 
 Imparts valu- va ^ ue on ^ own account. All know- 
 tble knowledge, ledge is precious and elevating ; but cs- 
 
Bee. 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 fcpt 
 
 the products and relations of true Technical 
 Thought, and the nature of the fallacies 
 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 prindpii, ignoratio elenclii, 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 Gdde to right 
 thinking,!, e. of the aimless, erratic, and Thinking, 
 abortive exercise of our faculties. So it is a pro- 
 paBdeutic to all other sciences. It furnishes a 
 needful training for every department of study. So 
 it has been crowned by some, as scientia scienliarum, 
 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, 
 
 and Guide to 
 
 the end of Science is to know, and of Art. 
 
 4 
 
38 LOGIC. [Chap. L 
 
 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 Keasoning, 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- tne knowledge of Psychology, so far as 
 cursive Facul- fa e 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 teacherj with little 
 addition of labor, to compass this portion of psycho- 
 
Bee. 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 refatedl 
 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, 
 
 ; Analogy of 
 
 as to leave it merely to the gramma- Grammar and 
 rians to confer the gift of 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, p. 37. 
 
40 LOGIC. [Chap. 1 
 
 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 way 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.* 
 
 SECT. VII. FUNDAMENTAL PRINCIPLES OR AXIOMS OF 
 
 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. CONTRADIO 
 
 The Four Fun- 
 damental Prin- TION, EXCLUDED MlDDLE, AND 
 
 FICIENT REASON. 
 
 * See Essay on Lord Bacon. 
 
Sec. VII.] ITS SPHERE AND OBJECTS. \ 
 
 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 contradictories one must ,,,,, 
 
 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- 
 tion, there must be a SUFFICIENT REA- s^^ent j ea . 
 SON OR GROUND. It must be evinced Bon * 
 
 by self-evidence, or other sufficient evidence. 
 
 4* 
 
42 LOGIC. [Chap. X 
 
 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 01 
 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 \\^ 
 that all the details of religion and morals, are btu 
 the logical unfoldings of this simple principle ? 
 
CHAPTER II. 
 
 SECTION I. CONCEPTIONS. 
 
 1. IN unfolding the nature of Conceptions, as 
 , 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, 
 
 whether external or internal, whether Intuition com- 
 boclies or states of consciousness, im- p 
 mediately and intuitively. Conceptions, on the 
 other hand, grasp (con-capio) a plu- 
 
 Conception 
 
 rality in one, through the medium of grasps a piurai- 
 a common sign or mark, whereby ltym 
 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 of ob j ectg or 
 mark or resembling quality, as the marks, included 
 
 under a common 
 whole class of red things are brought name, 
 
 43 
 
$4 LOGIC. [Chap. 1L 
 
 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 
 Expressed by a mar ^ s > rectilineal figure and six sides. 
 General Word, Another aspect of the same truth is, 
 Conception is that act or product of the mind which 
 is oppressed by a General Word. And hence, 
 3. Conception is that product of the mind which 
 
 results from Generalization, whereby many 
 Formal Defini- ... 9 
 
 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 
 
 Involves Ab- un( ^ er * ne name Magnets. It is obvious 
 Btraction, 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 
 order to detect the resemblance of these 
 qualities in the several magnets. Then there is the 
 Classification or Generalization by vir- 
 
 Generalization. ., . -. , T^- 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. 
 
Bee. I.] CONCEPTIONS. 45 
 
 This is Denomination. Thus we have a conception 
 formed as the result of Abstraction, Com- 
 
 . Denomination, 
 
 parison, Generalization, Denomination. 
 
 4. NOTION is a term of wider import than Con- 
 ception. It is used almost as loosely jr ti on , 
 
 as Idea. It includes representations Idea ' 
 
 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 Oon . 
 Wisdom, Virtue. Or they may be viewed oeptions, 
 as, 
 
 CONCRETE, 
 
 i. e. as inhering in some object, as magnet, hot-blood, 
 wise man, virtuous person. These dis- 
 
 Ooncrete, 
 
 tinctious 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 Denf 
 tative, Connotative, and Non-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, 
 Denotative *"' e ' Singular Terms, have this capacity, 
 Terms, Singu- whether they be proper names, or com- 
 
 lar Terms, . . . 
 
 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 
 Comotative or conceptions cfenote objects, and con- 
 Attnbutive, no f. e q ua ]ities 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. 
 
Bee. II.] CONCEPTIONS. 47 
 
 8. Non-connotative words are proper nouna 
 which denote objects simply; also ab- Hon . Conilota . 
 stract common terms, which denote qua- tetfre, 
 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 p w 
 
 r roper a amea 
 
 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, 
 parallelograms, polygons, etc., may all 
 
48 LOGIC. [Chap. I) 
 
 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 andlow- others > is called the Higher. The nar- 
 er Conceptions, rower one s 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, 
 Determination is called Determination. The Concep- 
 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, ^^ ^ ^^ Conception whlch lg 
 
 Abstract when taken by itself alone, becomes Con- 
 
Bee. 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- 
 i ons, 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 
 
 Differentia or 
 
 one species from others under the same Specific Differ- 
 
 Genus. Individual or Intuition is that e 
 
 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 
 
50 LOGIC. [Chap. D 
 
 nevei be a Species or Genus, which is always corn- 
 Essence is Gen P ose< ^ ^ a plurality of individuals. Es- 
 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 
 Logical Defini- that is 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 
 
 Accident, 
 
 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. rv. 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 
 
Bee. IV.] CONCEPTIONS. 51 
 
 Those Species to which any given Species becomes a 
 genus, are relatively to it Subaltern gutaltern GeD . 
 Species. Those Genera which are Species us and Species. 
 of a higher Genus are called Subaltern Genera. 
 Tims 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 Summnmehmtia 
 which is never a species. Infima Species infim* 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 Proximate Gen . 
 ascent or descent. Thus triangle is the era **& 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, 
 
 Being simply ; or it may be Relative to e 
 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 ^J^^ 
 it is sometimes fixed arbitrarily with cies often arbi- 
 reference to the purposes of some parti- ] m y 
 
62 LOGIC. [Chap, a 
 
 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 
 
 Logical and Na- S P ecies in Lo g ic and in Natural History. 
 turai Species In Logic, as has been shown, it means 
 
 distinguished, . 
 
 one of 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. 
 
Bee. V.J 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 Conception*, 
 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, intern 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- 
 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 KATIO OP EXTENSION AND INTENSION, 
 OB COMPREHENSION. 
 
 18 As the Extension of Conceptions increases, 
 their Intension diminishes. It is by ^ Extengion 
 laying aside the distinctive marks of increases, In- 
 
 , tension dimiu- 
 
 lower conceptions, that we rise to higher, ^ QSt 
 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, 
 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 
 Hamilton, that this distinction is without any snffi- 
 
66 LOGIC. [Chap. li 
 
 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 
 
 Kames keep Conceptions. Thus, as the extension is 
 
 pace with the 
 
 Extension and increased, names are employed to denote 
 Conoe tions each enlarged class, till we reach the 
 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 
 
 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 
 
 1 1 
 
 1 1 I 
 
 1 1 1 
 
 5 41 
 
 - s 
 
 M <D 
 
 %l 
 
 & 
 
 
 1 
 
 1 t 
 
 2 ^ 
 
 s . I 
 
 
 
 W 
 
 T3 
 O fl 
 9 c3 
 
 -g 
 
 I " 
 
 <u oT 
 
 H 
 
 OQ 
 
 & 3 
 
 
68 LOGIC. [Chap. II, 
 
 BECT. 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 
 
 oi Terms mark- Terms, or Nouns, so certain features of 
 ing ZttnreiTof Conceptions are usually set forth as 
 Contentions, 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 
 mon, 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, aa 
 this man, a house, some animal. 
 
Bee. VIII.] CONCEPTIONS. 59 
 
 22. The second principal division of nouns is into 
 
 Attributive and Substantive. Attribu- 
 
 ,. ^ Attributive, 
 
 lives are the adjectives 01 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 
 
 they are adjuncts. Substantive Nouns de- 
 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 
 
 . -r^- i T Distributive. 
 
 is Distributive or used distnbutively, 
 
 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 
 
50 iOGIC. [Chap. IL 
 
 say, " these trees amply shade this park," they are used 
 Distribution of objectively. 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 
 
 father and son are called Correlatives. 
 
 In all Relative Conceptions there is a ground of 
 
 Ground of Bela- ^ ne re l a ti n (fundamentum relationis). 
 
 tion - 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 
 
 Oases of several 
 
 Correlatives, Correlatives. Thus, cousin implies not 
 
Sec. VIII.] CONCEPTIONS. Q\ 
 
 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 
 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 aid In- 
 objects. They are for this reason called defillitei 
 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, instated don- 
 Hence such purely Negative Concep- c e P tions ' 
 tions are sometimes classed by logicians as Infini- 
 tated Conceptions. 
 
 6 
 
62 LOGIC. [Chap. ,* 
 
 25. It is not, however, true of most Negative 
 Most Negatives Conceptions, that in their real and 
 definite* or In- cus ^ omar y significance, they have this 
 
 nitee, 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 witaout practical 
 
 importance. In the first place they add 
 
 Importance of .** p ,, ,, 
 
 these Distino- 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. 63 
 
 fcbe 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- Com atiWe 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- Q ogite 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 OP CONCEPTIONS. 
 
 29. By the Quality of Conceptions is meant the 
 degree of perfection with which they Quality of Con . 
 represent to the mind the objects and ceptions defined, 
 
84 LOGIC. [Chap. Ii. 
 
 the marks included in them. In this regard, Con- 
 ceptions, like all cognitions, are perfect in proportion 
 
 When the are aS tn6V ^ aVG tn6 severa ^ virtues of Clear- 
 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, 
 Clear and Ob- w ^ ien ^ ' 1S s i m pty distinguishable from 
 scure, 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 
 
Bee. IX.] CONCEPTIONS. 65 
 
 being able to point out the marks by which they 
 are so distinguished. Such knowledge 
 
 i f -.L T> A. -j. Distinct and 
 
 may be sure as far as it goes. But it is Confused Gog- 
 confused with respect to the marks or nit i ons 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 
 be sure as to the hand- writing of differ- 
 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* 
 
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 
 
 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 
 Adequate and ^* n Adequate an( i Inadequate. It is 
 Inadequate, 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 
 
Bee. X.] CONCEPTIONS. 67 
 
 3xtension. That measure of it which is adequate, 
 cannot be decided by any unvarying No TJnvarying 
 rule. It varies with the exigencies and Buies of Ade- 
 requirements of each particular discus- q 
 sion, and must often be determined somewnat arbi- 
 trarily. 
 
 SECT. X. NOTATIVB AND SYMBOLICAL CONCEPTIONS. 
 
 33. This is a pregnant distinction. A Nota- 
 tive Conception is such that when pre- jr t a tive Con- 
 sented to the mind, it suggests its own eeption, 
 marks (notce) by its very name, so that they are at 
 once and indubitably evident, e. g. quadruped, tri- 
 angle, octagon, oligarchy. A Symbol- Syml)olical 
 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. IL 
 
 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 
 
 Knowledge how imperfections of Obscurity, Confusion 
 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. 
 
OF THE 
 
 UNIVERSITY 
 
 OF 
 
 Boa. XL] CONCEPTIONS. 69 
 
 SECT. XI. LOGICAL DIVISION. 
 
 35. Logical Division divides a Genus according 
 to its extension, i. e. into its constituent Lo ical Divig- 
 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. gu er . ordinate 
 The proximate species into which it is Geims ' 
 divided, are called Co-ordinates. If Co-ordinate 
 either of these be divided into parts or SpecieSl 
 Species, with reference to its superior Genus, it is 
 called Subordinate Genus. Any one of 8^0^^ 
 given Co-ordinate Species, is called, in Genu8 - 
 relation to any one part of a higher or lower Co- 
 ordinate Division under the Summum Disparate 
 Genus, Disparate. Thus, quadruped is Bpedes. 
 super-ordinate to lions, leopards, horses, E xamp i eBt 
 cats, etc. They are co-ordinate with 
 
 each other. They are subordinate to quadnped 
 and animal, while lion, as compared to fish, Shet 
 land pony, or bull-dog, is Disparate. 
 
70 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 
 
 aera to Proxi- once j n o w h a les, sturgeon, etc., without 
 
 mate Species. 
 
 previously dividing them into birds, 
 fishes, etc., would be a violation of this rule. 
 
 b. There must be but one principle of Division, 
 But one 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 Rule, which is, that the Divisions must 
 Divisions Mutu- ^ e mutually exclusive. They must not 
 ally Exclusive, run fafo g^h o ther 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. 7| 
 
 d. All the parts should be exactly equal to the 
 genus divided; any one part, and the gum rf partg 
 sum of any number of parts less than equals Divisum, 
 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 
 
 i . . /. i -r i , 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 _ ,. ., . 
 
 Individuals not 
 
 divides an individual, which is logically logically diviai- 
 
 indivisible, into its component parts, as 
 
 a ship into hull, masts, sails, etc. The test of this 
 
72 LOGIC. [Chap. IL 
 
 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 
 luals. treated as Logical individuals. Often 
 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- ^ nus 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 
 
Bao. XII.] CONCEPTIONS. 73 
 
 SECT. XII. DEFINITION. 
 
 40. This gives the marks of Conceptions, and 
 unfolds their Intension. It thus bounds 1^^ ^ e . 
 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 By esseilt i a i 
 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 this. 
 
 Jtil? 5 ' Let not the student forget when asked what is 
 logical or essential definition, that it is Logical Defini- 
 made up of the genus and differentia. tion< 
 
 b. It must include the objects covered by the 
 definitum, or species defined, neither Not too Broad 
 more nor less. If it include more, it is nor Narrow - 
 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- 
 
 fiion. If it is a good definition of a whale to say that 
 
 7 
 
74 LOGIC. [Chap. IL 
 
 it is a fish, then all fish are whales. A definition 
 
 too narrow is detected by conversion by 
 How Detected. ... ^, . . , 
 
 contraposition. Thus, if 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 
 NotbyNega- avoided. Negatives show what are 
 tives. no ^ 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 clear less language. To say that "truth is 
 Language, the 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 
 
 word defined, or any of its derivatives, or 
 Hot Tautolo- 
 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, circulw 
 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 Surpins- 
 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 [Chat. ii 
 
 defined, because it 'has no differentia, Thus, being 
 can only be defined by some synonym or de- 
 scription casually substituted for it. It 
 ma 7 be defined as a thing, or that which 
 
 Logically Defi- j^ existence. Summuin Genus in any 
 
 nable, J 
 
 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- 
 Simple ideas lion, ^ * ne 7 cann t 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 Eoman 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- (j e nus and Dif- 
 entia may be considered as two com- ferent ' a Teall 7 
 
 two Commtuu- 
 
 municant genera, and the Conception cant Genera. 
 defined that which is included within the sphere 
 
 of their coincidence. Either may be considered 
 
 * 
 
78 LOGIC. [Chap. II 
 
 genus and the other differentia, and vice versa, ai 
 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- lgi 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. Efsolutwn. This resolves the Conception into 
 Eesolution, its marks, genus and differentia, and is. 
 
Sec. XII.] 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 
 Conception of 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, Mollu&ks, 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 Suteti 
 
 virtue and happiness. This last, how- tntion. 
 
80 LOGIC. L Chap. IL 
 
 ever, hardly comes 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 Real Definition, and strangely 
 Nominal and inconsistent accounts have been given 
 real Definition, o fj t> 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 
 its, 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 
 thft 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.J 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 importance of 
 of conceptions, is of fundamental im- Definition. 
 portance in thinking, investigating, and discoursing, 
 An accurate Definition, or presentation of the stcdua 
 questionis, 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 mutnal 
 its proximate species, we, of 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- 
 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 
 
 Mental Act a ligent act is a Judgment. To know ifl 
 
 to discriminate, and therefore to judge. 
 
 Even feeling and sensation, the most rudimental form 
 
 82 
 
Sec. 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 Predia^a ex . 
 or is not; i. e. it affirms that the Concep- ^tence only, 
 tion, Existence, agrees or disagrees with some sub- 
 ject. But beyond the mere predication of Existence, 
 Primitive Judgments do not go. Logi- Logioal Judg . 
 cal Judgments are founded on Concep- mentel 
 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, 
 
 7 All Thought 
 
 Judgments, or Reasonings, in reality resolvable into 
 proceed from and terminate in Judg- u gme 
 rnents. 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. 
 
34 LOGIC. [Chap. JIL 
 
 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 tl . , , 
 
 formed and ex- men t, so it is explicated by a Judg- 
 piicatedby ment . Thus "bi-peds are two-footed 
 
 Judgments, 
 
 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. 
 Eeasoning, too, the third great process 
 
 Reasoning also 
 
 is by Jndg- 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 of Judgments, 
 
 ment8 ' 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 
 
8c. L] JUDGMENT fcfi 
 
 in concluding that one Judgment flows from others, 
 form? 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 Judgment, 
 (termini, extremes) of the Judgment. 
 
 That which is spoken of is the Subject of the 
 Judgment. That which is affirmed or g n ^ ect} -p IQ ^_ 
 denied of the other is called the Predi- cate< 
 cate. That which connects the two is 
 
 Copula is verb 
 
 the Copula. This is always the verb "to be "in pres- 
 to be, in the Present Tense Indicative, enttense ' 
 if the Judgment be affirmative : and the same with 
 the negative particle affixed, if the Judgment be 
 negative. Thus : 
 
 Sub. Cop. Pred. 
 
 I The earth I is round. 
 
 Sub. Cop. Pred. 
 
 Oaks I 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 liedi 
 When any other than the Substantive verb is em- 
 ployed as Predicate it includes the Copula. Thus, 
 
86 LOGIC. |Clip. Ill 
 
 Sub. Cop. Prod. 
 
 " he runs," is equivalent to, he is running. " No men 
 
 Sub. 
 
 are sinless/' is the same as to say of |all men| that 
 
 Cop. Pred. 
 
 hey jare not| sinless. 
 When Existence simply is expressed, the verb 
 
 Predicate when * ^ e * s kth Predicate and Copula ; as, 
 
 . ... Sub. Pred. Cop. 
 
 God is = is existing. 
 
 5. When any mood or tense of the verb, except 
 w the present indicative in the Copula, ia 
 
 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, 
 
 Oategorematic or intuitions, cannot of themselves con- 
 ana riyncatego- . 
 
 romatic Words, stitute terms of a Judgment. They caa 
 
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, KELATION, 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- ty> 
 ject Quantity. 
 
 II. With respect to the relation of the predi- 
 cate to the intension of the subject 
 
 ^ r . Quality. 
 
 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 
 
 Modality. 
 
 predicate Modality. 
 
 SECT. III. .QUANTITY OP JUDGMENTS. 
 
 8. With respect to Quantity, Judgments are either 
 Universal, Particular, or Singular. , 
 Judgments are Universal when the Pre- Judgment* 
 
88 LOGIC. [Chap. Ill 
 
 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, ~ ~. 
 
 Governments 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 
 ments "euiva- ^ n them, the whole subject is spoken of, 
 
 lent to Univer- an( J fa ey are su bject to the laws of 
 
 sale. 
 
 Universals. 
 
 In like manner, when any Definite part of the 
 Subject is taken, it may be considered 
 
 Also a Definite ' 
 
 part of the Sub- as a universal. For the whole class 
 denoted by the subject-name with its 
 limiting adjuncts is spoken of Thus " these men are 
 natives of Ireland." 
 
Bee. IV.] JUDGMENT. 89 
 
 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 g . m le and 
 Compound when, though simple in form, Compound 
 by a plurality of subjects or predicates, 
 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 
 
 Quality respects 
 
 Subject and Predicate. Hence in respect Affirmation or 
 of Quality, Judgments are either Affir- Ne s ation * 
 mative or Negative. Jl^ Let the learner remember 
 that the Logical Quality of a Judgment refers to its 
 being Affirmative or Negative. The truth or falsity 
 of a Judgment is of course of supreme importance. 
 
 8* 
 
90 LOGIC. [Cha IIL 
 
 But this pertains to its matter, not to its form, with 
 which alone formal Logic concerns itself. 
 
 11. A Proposition is Affirmative or Negative, ac- 
 cording as it has not or has, a negative Copula; 
 Quality in the * e - when, whatever be the form of ex- 
 Copula, pression, the real force of a negative 
 does not or does, fall on the Copula. Thus, "no 
 iron is silver," is negative, for it asserts 
 of all iron that it is not silver. " A per- 
 son not vicious is virtuous," is affirmative, because 
 the force of the negative does not fall on th*. Copula 
 but on one of the terms. "A few men ar& /dse," is 
 affirmative ; "but few men are wise," is in ^ality ne- 
 gative, for it is equivalent to " most men arr not wise." 
 Judgments then as to Quantity and Quality, as 
 The four Logi- thus unfolded by the old Logicians, 
 
 Mid th^T nt - are ^ our > w kich they have been accus- 
 tol* tomed to mark by the Symbols, A. E 
 
 I O., as follows : 
 
 Universal Affirmative, .... A. 
 
 Universal Negative, E. 
 
 Particular Affirmative, .... I. 
 Particular Negative, .... O.* 
 
 * The additional Judgments recognized by recent Logician! 
 will be noticed in due time. 
 
Sec. VI.] JUDGMENT. 91 
 
 SECT. V. DISTRIBUTION OF TERMS IN JUDGMENTS. 
 
 12. Of the foregoing Judgments all Universal^ 
 and no Particulars distribute the Subject. 
 
 * n TVT , i * (* , Uaiversala dis- 
 
 All Negatives and no Affirmatives tribut etiieSEb- 
 'listribute the Predicate. J ect - Negatives 
 
 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. KELATION 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 o* 
 
 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. IIL 
 
 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 : 
 of the truth or falsity of some other 
 Judgment. Thus, "if crops are large, food is 
 cheap." " This man is either holy or unholy." 
 Th k' f ^' Hypothetical Judgments are of 
 Hypothetical three kinds : Conditional, Disjunctive, 
 
 Judgments, i -r^-i 
 
 and JJilemmatic. 
 
 17. The Conditional Judgment affirms such a 
 Conditional relation between two others, respec- 
 Judgments, tively called Antecedent and Conse- 
 
 Antecedent and <l uent > that > if the former be true, the 
 
 Consequent, ] atter j s true a ] so ^ as ^ if t he 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 
 
 haveaCategori- categorically a certain relation between 
 
 the Antecedent and Consequent ; such, 
 
 that, if the former is true, the latter is true ; and if 
 
Be* VI.] JUDGMENT. 93 
 
 the latter is false the former is false. It often ex- 
 presses the relation of cause and effect. 
 
 Causal Eolation 
 
 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. 
 
 Do not assert 
 
 It may assert, not only a causal rela- the trnth of 
 tion, but the truth of a certain argu- eithel member< 
 ment. Thus, " if drunkards drink what intoxicates, 
 A. B. drinks what intoxicates." This 
 
 xt- J.L j. j i tobn 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, Dig - ullctives M 
 with an alternative indicated by the Bert with an ai- 
 
 .. , .,, , mi ., . ternative, 
 
 particles, either and or. Thus, "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. Ill 
 
 of Excluded Middle. A judgment or its contra- 
 Founded on Ex- dictory must be true, and there is no 
 eluded Middle, middle between them. So conditionals 
 are founded on the law of Sufficient 
 
 Its members 
 
 mutually exciu- Keason. 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. DUemmatic 
 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." 
 
 A 
 
 SECT. VII. SUBSTITUTIVE JUDGMENTS. 
 
 22. Substitutive Judgments are those which being 
 affirmative have a distributed predicate, g^stitutives 
 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. IIL 
 
 men, and is, therefore, co-extensive with it. In all 
 All Definition cases of Definition then, and in all the 
 Substitntive, k[ n <{ s o f Definition which have been 
 pointed out, we have Substitutive Judgments. 
 
 23. Judgments of this kind are called Substitu- 
 Why called *^ ve because the predicate may be sub- 
 Substitutive, 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 say 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 
 
 Either 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- 
 Attrilrative ca ^ e * s undistributed, are called Attri- 
 Judgments, butive, because they affirm an attribute 
 of the subject, without taking this attribute in its 
 whole extent, or substitutively. Thus, " men are 
 rational. 7 ' 
 
Sec. VII.] JUDGMENT. 97 
 
 26. The importance of Substitutive Judgments 
 will appear, when we come to treat of 
 
 Importance of 
 
 the subject of reasoning. They render substitutive 
 many processes of reasoning valid, Jud s ments ' 
 which would otherwise be invalid, owing to the non- 
 ilistribution 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 
 Relation of judgments, or as concerned 
 
 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 Eqnationofgub . 
 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 
 
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- 
 nated by their several symbols a& 
 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 
 
 undertaken to develop two others ; viz., 
 
 Negatives with 
 
 undistributed Universal and Particular Negative 
 Judgments with undistributed predi- 
 cates, which he marks by the respective symbols rj 
 and co. But undistributed negative predicates are 
 BO 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. VIIL] JUDGMENT. 99 
 
 and worthless, being nearly, if not quite incapable 
 of real contradiction.*] 
 
 SECT. VIIL ANALYTIC AND SYNTHETIC JUDGMENTS. 
 
 30. Analytic Judgments are those in which the 
 predicate is involved in the very Con- Ana iyt ic Judg . 
 ception or Definition of the subject. As, ments - 
 " man is rational." " Quadrupeds are four-footed." 
 
 * They cannot, 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 silvei. 
 
 U. Afa, All are all. All men are all rational animals. 
 
 Y. Ifa. Some are all. Some men are all the poets. 
 
 i>. Ani. Not any are some. No planets are some stars. 
 
 w. Ini. Some are not some. Some trees are not some oaks. 
 
 o> ia without force because not contradictory to nor inconsistent 
 with any other proposition. 77 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. Ill 
 
 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 Jndg- predicate adds to the conception or defi- 
 ments, 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 
 Exception in ^ e uo ^) a posteriori. The Formal 
 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 F 
 
 Synthetic Jndg- 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 (avaXua), 
 to take asunder), and synthetic (fftwrlfyfju, to put 
 together), is evident from their etymology. 
 
 The terms Explicative and Ampliative have, for 
 obvious reasons, been employed to de- Explicative ^ 
 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 ^J^ 
 subject. This, however, really belongs L g 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. 
 
 ft* 
 
102 LOGIC. [Chap. III. 
 
 SECT. X. PLURATIVE JUDGMENTS 
 
 33. Plurative Judgments are those in which 
 
 Plurative Judg- more * nau na lf> but not all of the Sub- 
 
 menta defined, j ec ^ i 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. ,. , . , , 
 
 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 HYPOTHETICAL INTO CATEGO- 
 BICAXS. 
 
 34. It has already been shown that in every 
 H otheticals Hypothetical Judgment there is a cate- 
 have a Gate- gorical element, which affirms or de- 
 
 gorical element, . , , , . , , . , 
 
 mes 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- 
 Oonditionals tuting for the particles "if," "when," 
 
 low turned into 
 
 Categorioals, etc., which have a conditional force, 
 
Sec. XI.] JUDGMENT 105 
 
 such phrases as "the case of," tne "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/ 1 
 or c 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- 
 
 .. , r~, ., ,. Abbreviations 
 
 dent and consequent. Thus the condi- ^ tlie case 
 tional, "if Peter is a drunkard, he of only three 
 
 Terms, 
 
 (Peter) is degraded," is equivalent to 
 
 " every drunkard is degraded," otherwise it could 
 
 not be true. 
 
 6. Disjunctives may be turned into Categoricals 
 by using all their members for one of 
 the terms, and the phrase, "possible 
 cases," or the like, for the other, thus forming a 
 judgment by Colligation, which, as we 
 have seen, is the opposite of Logical 7 
 Division. Thus: "This season is eitb*ar Spring, 
 
104 LOGIC. [Chap. IIL 
 
 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 
 
 B first be' ^ e * urne( ^ ^ n * Conditionals, by taking 
 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 
 Judgments to be resolved into these, and each of these 
 may be changed into categoricals, ac- 
 cording to the methods just indicated. Thus, the 
 Dilemmatic Judgment, " If .ZEschines 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 ;" " He was either inconsistent or un- 
 patriotic." These may be turned into Categorical^ 
 by the methods already prescribed. 
 
 
CHAPTER IV. 
 
 IMMEDIATE INFERENCE. 
 SECTION I. INTRODUCTORY KEMARKS. 
 
 1. THE next stage of Thought after the forrna- 
 Kettsoning De- ^ on ^ 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 
 
 Mediate 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, medius terminus, 
 lommon to both the judgments given, by means of 
 i common or opposite relation to which, the two 
 
 106 
 
Sec. II.] IMMEDIATE INFERENCE. 1Q7 
 
 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, L e. infer- Three kinds oi 
 
 ence of one judgment from another, is 38 
 
 of three kinds, termed Opposition, opposition, Con- 
 Conversion, and Equipollence or Infi- version ' 
 
 pollence 
 
 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, 
 <f 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 
 Snbalternans, ca ll e( l the Subalternans, the Particular 
 Subaltemate, the Subalternate. All these forms of op- 
 position are brought compactly and clearly to view 
 by Kbe following ingenious and simple diagram, 
 whhh has been devised by logicians. 
 
 . 
 
 Contraries. 
 
 Sub-contraries. 
 
Bee. II.] IMMEDIATE INFERENCE. 1Q9 
 
 6. The Laws of Inference in the case of judg- 
 ments in opposition are, in brief, as fol- Laws of infer- 
 
 . ence in Opposi- 
 
 1ows : tion. 
 
 a. Of Contradictories one or the other must be 
 true, both cannot be true. And by the Ke -Contradicto 
 law of Excluded Middle no interme- rieSi 
 
 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 
 
 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. 
 
 o. From the truth of a Contrary the* falsity 
 of the opposite Contrary follows. But 
 from the falsity of one Contrary, nothing 
 follows in regard to the other. 
 
 d. From the truth of either Sub-ContraYy nothing 
 follows in regard to the other Sub-Con- 
 
 . . Sub-Contraries, 
 
 trary. But from the negative of one of 
 them, it follows that the other must be true. 
 
 10 
 
110 LOGIC. [Chap. IV 
 
 7. From this it appears that the Opposition be- 
 
 tween Contradictories is far the most im- 
 
 Oontradictory 
 
 Opposition most portant and fruitful of inferences. The 
 most available mode of 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- 
 
 Other forms of . -.^ T , ~ , 
 
 Opposition crea- ments A & 1 and O above recognized 
 tedbytheJndg- ty tne o \^ logicians. But if we bring 
 
 mentsUandT, * . 
 
 in the additional substitutive judgments 
 U and Y already considered, they lay a founda- 
 tion for other forms of Opposition. 
 
 a. For other forms of Contrary Opposition. The 
 
 characteristic of this kind of opposition 
 
 Other forms of 
 
 Contrary Oppo- is, that of two judgments opposite in 
 quality whatever their quantity, both 
 judgments may be false, but cannot be true together. 
 Thus A and E may both be false, but cannot both 
 be true together. But the same is true of E and U. 
 Thus, it is false alike that " no men are poets/' and 
 that "all men are all the poets." It is true that 
 " all men are all rational animals," false that " no 
 men are rational animals." 
 
 b. Out of the Opposition of these Substitutive 
 
Sec. II.] IMMEDIATE INFERENCE. \\\ 
 
 Judgments to each other, and to other judgments 
 arises what has been named Inconsistent inconsistent 
 Opposition. This obtains between judg- Opposition, 
 ments opposed in quantity but not in quality, which 
 cannot both be true, though both may be false, at the 
 Bame time. Thus the opposed judgments A and U 
 cannot both be true of the same subject and predi- 
 cate, unless A be considered, as it was by old logi- 
 cians, to include U. It cannot be true that all men 
 are all the animals (U), and that all men are only 
 some animals (A). But A and U may both be 
 false, as in any subject and predicate in which ne- 
 gatives or particulars only are true. 
 
 c. Subaltern Opposition exists when there is more 
 distribution in either term of one judg- New g u |j a i tern 
 ment (the Subalternans) than in the Opposition, 
 corresponding term of the other (the Subalternate). 
 Accordingly, this kind of opposition exists between 
 U and I, also between Y and I, for from positing 
 either U or Y, I may be inferred. But from I 
 neither U nor Y can be inferred. 
 
 9. Applying these principles, and extending the 
 diagram of Opposition already given to include U 
 dnd Y, we have the following result : 
 
112 LOGIC. [Chap. IV. 
 U Inconsistent A Contrary E Contrary ; U 
 
 I /'' |"X'" i x/ I 
 
 V *.. P O \> P VJ . Cl 
 
 F*- .* '. i ..* .* ". f 
 
 : ,." *. t : y* '. % : ..* \ : 
 
 Y.'. Subaltern......**.! '.*... Sub-contrary.. !'.6*... Sub-contrary..". Y* 
 
 10. Opposite Judgments must have the same 
 subject and predicate, not only in sound but in 
 sense. " Bread is heavy," and " bread is not heavy," 
 are not opposed, if in the former case " heavy " be 
 used to denote imperfect fermentation, in the latter 
 to denote specific gravity as compared with lead. 
 
 * Some writers, among whom is Thomson in his Laws of 
 Thought, class the opposition between A and 0, as Contrary in- 
 stead of Contradictory, and admit only E and I to be Contradic- 
 tories. He says, " We cannot tell from the removal of whether 
 we ought to replace it by A or U." This, however, though theo- 
 retically true, hardly calls for a deviation from the established 
 use of terms in practice. Would not this argument abolish the 
 contradiction between E and I? If E be removed, we do not, 
 from that fact, know whether it may not be replaced by A, U, or 
 Y, as well as I. We only know that as much as I is true. In 
 like manner we know that certainly as much as A, and possibly 
 as much as U, is true if be removed. This gives them both the 
 power of contradictories. How much more is true in any cas* 
 must be learned from other sources. Y is a kind of false sut>- 
 ontrary to 0. If it be true, is true. 
 
Sec. III.] IMMEDIATE INFERENCE. ;Q3 
 
 SECT. III. CONVERSION. 
 
 11. A second mode of immediate inference is by 
 Conversion. Propositions or judgments conversion De- 
 are converted when the predicate and fined< 
 
 the subject change places, in such a way that the 
 converse is an inference from the convertend or 
 judgment converted. 
 
 12. In order that Conversion may be illative, or 
 give rise to a legitimate inference, no Law of Di s tri- 
 term must be distributed in the con- button of Terms, 
 verse which was not distributed in the convertend: 
 otherwise more would be spoken of in the conclu- 
 sion than in the premise. This was the rule of the 
 older logicians. 
 
 13. Hamilton and his school, however, maintain, 
 not only that no term should be distri- Hamilton's 
 buted in the converse which was undis- Law - 
 tributed in the convertend, but that all terms dis- 
 tributed in the latter should be distributed in the 
 former. 
 
 14. Conversion, in order to be logical, according 
 to these principles, sometimes requires 
 
 a change in the Quality or Quantity of tity or 
 
 the convertend. Hence result the fol- sometimes 
 
 cessary, 
 
 lowing modes of Conversion. 
 10* 
 
114 LOGIC. [Chap. IV. 
 
 A. Simple Conversion is when there is no 
 Simple Conver- change in either Quality or Quan- 
 8ion - tity. 
 
 B. Conversion by Limitation, sometimes called 
 By Limitation P^ accidens, is when the quantity is 
 or per acciaeas, changed from universal to particular. 
 
 C. When the quality is changed, it is said 
 Negation and to be by Negation or Contra-posi- 
 
 Oontra-position. ^ 
 
 15. Accordingly, 
 
 a. A, which distributes the subject but not the 
 How to Convert predicate, must be converted by Limi- 
 Ai tation from universal to particular, and 
 
 therefore, according to the old Logic, which does 
 By old Logic A, no ^ recognize the distribution of affir- 
 beoomes I, mative predicates, becomes I ; but with 
 a quantified and distributed predicate it becomes 
 Y. Thus, "all men are mortal," becomes in the 
 former method, " some mortals are men," which is I ; 
 and in the latter method, "some mortals are all men," 
 
 In perfect Con- which is Y - It is J ustl 7 argued that 
 version A. be- the latter is the only perfect Conversion, 
 
 oo in 6 s T i 
 
 because it alone enables us, by recon- 
 version to regain the original convertend. This 
 ought to be possible in thorough conversion. From 
 
Sec. III.] IMMEDIATE INFERENCE. H5 
 
 " some mortals are men/' i. e. " some men," we can 
 only get by re-conversion, " some men are mortals." 
 But from " some mortals are all men," we readily 
 get back the original convertend, "all men are 
 
 mortals." Of course from Y comes I, 
 
 , ,, T involvesl, 
 
 its subalternate. 
 
 b. E., which distributes both terms, may be 
 converted simply, and remains E after E converted 
 conversion. If, " no men are angels," ^pty- 
 then " no angels are men." 
 
 c. In like manner I, which distributes neither 
 term, may be converted simply. If 
 
 some Americans are Indians, then some 
 Indians are Americans. 
 
 d. O distributes the predicate but not the subject. 
 Consequently, if it were converted with- n 
 
 converted by 
 out changing its quality, the subject un- contraposition 
 
 distributed in the convertend, would be 
 distributed in the converse by being the predicate 
 of a negative. Thus, " some quadrupeds are not 
 horses," would become " some horses are not quad- 
 rupeds," which is obviously illogical as well as 
 false. 
 
 In order to avoid this, the negative particle is 
 transferred from the copula to the predicate, so that 
 
116 LOGIC. [Chap. IV. 
 
 the couvertend becomes I, which may be simply con- 
 verted. Thus, for "some quadrupeds are not 
 
 Pred. 
 
 or 
 
 horses/' say, "some quadrupeds are [not horses 
 " things not horses." This is I, which converted 
 simply becomes, " some things not horses are quad- 
 rupeds." Here conversion is by contraposition. 
 
 16. A and U, i. e. all affirmatives which have 
 Conversion of A the subject distributed admit of this 
 
 and II by con- . ,-,, 
 
 traposition, sort of conversion. Thus, 
 
 A. " All men are rational," may be converted into 
 
 E. " Whatever is not rational is not a man." 
 
 U. *' All men are rational animals," may become 
 
 E. " Whatever is not a rational animal is not a man." 
 
 17. U may be converted simply. Thus, "All 
 
 men are rational animals." Therefore, 
 
 U converted 
 
 simply and " All rational animals are men." This is 
 ;0 ' U, and by subalternation will give I also. 
 Y may be converted into A, which by subalter- 
 nation yields I. Thus, "Some men 
 are poets" (i. e. all the poets), yields A. 
 All poets are men. 
 
 18. The several kinds of judgments therefore 
 Summation, may be converted as follows : 
 
Sec. IV.] IMMEDIATE INFERENCE. 117 
 
 A may be converted into Y and thence I. 
 E into E, and thence O. 
 I into I. 
 
 O into I indirectly by contraposition. 
 U into U, and thence I. 
 Y into A, and thence I. 
 
 A and U may also be converted by contrapo- 
 sition. 
 
 SECT. IV. OTHER MODES OP IMMEDIATE INFERENCE. 
 
 19. Besides Opposition and Conversion, the 
 standard modes of Immediate Infer- 
 
 Other forms of 
 
 ence formerly recognized by logicians, Immediate In- 
 several other forms of it deserve men- 
 tion. 
 
 A. BY RECIPROCAL CHANGE OF POSITIVE AND 
 PRIVATIVE CONCEPTIONS. 
 
 20. If we take any pair of Positive and Priva- 
 tive, or as they are styled by some, 
 Infimtated Conceptions, as has before tive ^ d Priva , 
 been shown, they comprise, taken abso- *i ve 0onoe P- 
 lutely, all being, or the universe : and 
 
 taken most narrowly, they include all the members 
 of the genus which is the particular object of 
 thought. Thus "virtuous" and "not virtuous/' 
 
118 LOGIC. [Chap. IV. 
 
 taken absolutely, include the universe of actual and 
 possible being. But practically, they are only used 
 in reference to beings capable of virtue, i. e. moral 
 beings, and, in ordinary cases, are applied to none 
 but mankind. Supposing the latter to be spoken 
 of, all are included in the virtuous and non-virtuous, 
 and whatever men are not one are the other. 
 To affirm the Therefore, to affirm a Positive Concep- 
 Positive is to tion of any subject, is the same as te 
 tiveT and ^ce deny its corresponding Privative, and 
 versa, v ^ ce ver sa. It is often convenient it 
 
 such cases, instead of an awkward and confusing use 
 of the particle " not," in order to mark the Priva- 
 tive contradictory, to use the particles in or un to 
 form a single compound privative word as incon- 
 sistent for not consistent, unwise for not wise or to 
 use any word of corresponding privative import, 
 without any explicit negative particle, as foolish for 
 unwise, soft for not hard. 
 
 Rules for such ^1. This sort of immediate inference 
 Conversion, [ s governed by the two following rules, 
 a. If the predicate be changed from Positive to 
 Privative, or the reverse, change the quality of the 
 judgment. Thus, "all men are rational," "no men 
 
Sec. IV.] IMMEDIATE INFERENCE H9 
 
 are (not rational), i. e. irrational/' and by conver- 
 sion, " no irrational beings are men/' 
 
 6. To change the subject in like manner, first 
 convert the proposition : thence change the subject 
 (now become predicate), from positive to privative 
 or the reverse, and change the quality of the judg- 
 ment. Or, (what is the same), convert the judgment, 
 and proceed as in rule first. Thus, 
 
 " Some men are (all the) poets." By conversion, 
 
 " Some (or all) poets are men." 
 
 " Some (or all) poets are not beings who are not men." 
 
 " No trees are stones." By conversion, 
 
 " No stones are trees." 
 
 " All stones are things not trees." 
 
 These methods of immediate inference may be 
 applied to all the varieties of propositions. 
 
 B. IMMEDIATE INFERENCE FROM DISJUNCTIVES 
 OR PARTITIVES. 
 
 22. In a Disjunctive or Partitive Judgment, it is 
 immediately evident that whatever of 
 
 Prom Disjuno- 
 
 the objects included in it belongs to tives and Par- 
 one of its members, is not included in 
 any of the others, and whatever is not included in 
 it, does belong to one of the others. Thus, " The 
 
 Of THE 
 
 UNIVERSITY 
 
 OF 
 
120 LOGIC. [Chap. IV 
 
 seasons are either Spring, Summer, Autumn, 01 
 Winter." "Spring is neither Summer, Autumn, 
 nor Winter," and " whatever seasons are not Spring; 
 are either Summer, Autumn, or Winter." 
 C. FROM A COMBINATION OF PREDICATES. 
 
 23. If it be known of man that he is rational, 
 
 By uniting Pre- a ^ SO that ^ e * s an i ma ^ a ^ so that he 
 
 dioates, laughs, then these Predicates may be 
 
 united in one judgment, which may be A or U, ac- 
 cording to circumstances in the present case U 
 Thus : " Man is a rational animal that laughs." 
 Other Formulae furnish materials for immediate 
 inference too numerous and obvious to 
 require minute specification. "Howard 
 was a philanthropist," therefore philanthropy has 
 a real existence. " The President is the supreme 
 executive," therefore to assail the President is to 
 assail the supreme executive. 
 
 24. Some have maintained thai these processes of 
 
 Immediate Inference are unimportant, 
 of 6 iSediate because the conclusion contains nothing 
 Inference no previously contained in the premise^ 
 
 shown! 
 
 But if this objection be valid it lies 
 against all reasoning. It is further objected that 
 the conclusion is identical with the premise. This 
 
Bee. IV.] IMMEDIATE INFERENCE. 12] 
 
 is an error. It will hardly be claimed in regard to 
 
 inference by opposition, especially con- 
 
 J FJ ^ J Conclusion not 
 
 fcradictory opposition. In conversion identical with 
 
 . T i . T . . , i the Premise- 
 
 the subject or principal notion on tne 
 judgment is changed. Equivalent changes from 
 the premise to the conclusion occur in other forme 
 of immediate inference. Few persons who have not 
 made Logic a study, can state with accuracy the 
 exact illative converse of any, especially of all the 
 fundamental logical judgments, as they understand, 
 who have had experience in teaching Logic. An 
 eminent logician says, "Could any person not accus- 
 tomed to exercises of this kind, draw out fully all 
 his own meaning, when he utters the simplest pro- 
 position? The judgment 'all men Explication of 
 are mortal' (a plainer cannot be found), " A11 men KIQ 
 
 mortal," into 
 
 tells us that man is one species in the other jndg- 
 class of mortal beings that the mark ments ' 
 of mortality should always accompany our notion cf 
 man that the word mortal is a name which may 
 rightly be given to man that, if all are mortal, 
 any one man is that any statement which affirms 
 that no men are mortal, must be quite false that 
 even the statement that some men are not mortal is 
 equally false that since man is contained in the 
 
122 LOGIC. [Chap. IV, 
 
 class of mortal beings, which is a wider class, it 
 would be wrong to say all mortal things are men 
 that, however, the assertion " some mortals are men," 
 would be true enough even " some mortals are all 
 men " that no men can be immortal that any im- 
 mortal beings must be other than men that mor- 
 tality really exists, being found in man, whom we 
 know to exist that a man with immortal hopes i& 
 a mortal with immortal hopes that (since heaven 
 is immortality) a man expecting heaven is a mortal 
 looking for immortality that he who honors a 
 man, honors a mortal. Thus from this simple 
 judgment fourteen judgments have unfolded them- 
 selves, or, as some would say, the judgment has been 
 put in fifteen different ways, in the last three of 
 which only is any new matter introduced. And 
 yet any man of common sense would say that his 
 proposition really implied them." Tlwmon's Lawt 
 of Tkwgld, pp. 191-2. 
 
CHAPTER V. 
 
 REASONING MEDIATE INFERENCES. 
 
 SECTION I. INTRODUCTORY REMARKS. 
 
 IMMEDIATE INFERENCE, as we have seen, is of 
 one Judgment from another without the interven- 
 tion of any third judgment or third term. 
 
 1. Mediate Inference is from two judgments 
 given as premises to a third founded Mediate Infer- 
 upon them, in which the two terms of enceisfromt 
 
 Judgments giv- 
 
 the conclusion are found to agree or en to a third, 
 disagree with each other, through a third or middle 
 term with which they have each been Through a Mid- 
 compared in the premises. Thus, alj ffle Tem> 
 M is P, all S is M, /. All S is P. Here all S is 
 declared to be P, because it has previously been 
 affirmed to be M, and all M to be P. Or if we 
 take a negative conclusion, "No stones are trees, 
 This oak is a tree, /. It is not a stone." Here, 
 oak, in the conclusion, is declared not to be a stone, 
 because it is a tree, and no trees are stones. 
 
 123 
 
124 LOGIC. [Chap. V 
 
 2. It is obvious that the ultimate ground of 
 Mediate Inference, as shown in the above examples 
 (and the same may be shown of all others), is re- 
 
 . ducible to the principles of Identity and 
 Founded on [/ ^ r 
 
 Identity and [/ Contradiction or rather Non-contradio 
 
 ' tion. In the first case S and P agree are 
 
 one with each other, because they each agree with, 
 
 are the same as, M. Oak and stone do 
 
 Illustration, .., , ., , ., 
 
 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, <rMo- 
 
 fiap.o^ 9 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 * wo P arts t that which is to be proved, 
 Syllogism, an( j ^hat by which 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 
 Premises are Major and Minor. 
 
 The Major Premise is that in which the Majoi 
 Term is compared with the Middle, 
 whatever may be the order in which aj r 
 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 t Order of Premi- 
 
 gism is arranged in regular logical ses and Oondu- 
 order. Thus: sion ' 
 
 "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 
 
 ad >pt 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* 
 
126 LOGIC. [Chap. V 
 
 quently, in either case, not more than one premise ia 
 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 put 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 
 
 Analytic Syllo- together the premises in order to form 
 
 the conclusion. 
 
 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, t , ~ , . 
 
 the Conclusion. 
 
 The Minor Term is the subject of the 
 
 Minor Term, ~ , . 
 
 Conclusion. 
 
 Hence every Syllogism must have three, and but 
 Has three Jndg- 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- 
 Canon of Affir- 
 
 dle term, both agree with it, they agree mative Conciu- 
 with each other. This underlies all 8] 
 Affirmative Conclusions. 
 
 6. 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 
 
 Negative Pre- 
 
 they agree or disagree with each other, mises give no 
 
 rrri ,1 n ~*~r , T> Conclusion, 
 
 LJns is the case ot JNegative Jr remises, 
 
128 LOGIC. [Chap. V, 
 
 from which there can be no Conclusion. ThuSj, 
 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 
 
 HLiadle ierm 
 
 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- 
 tribnted 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 this 100 are unreflecting, 
 
 60 out of this 100 are restless, 
 .'. 20 restless persons aro unreflecting." 
 
 e. No term may be distributed in the conclusion 
 
Bee. I.] MEDIATE INFERENCE. 129 
 
 which was not distributed in the premises. This, 
 which is Illicit Process, is furtively jf niicit Pro . 
 speaking of more in the conclusion C6SSi 
 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 
 and O of 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 odks. 
 I. Some oaks are white oaks. 
 .'. Some white oaks are trees. 
 
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 must be Particular. In other 
 ticuiar when wor( j s 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 universal. 
 
 If the universal conclusion be E, then both its 
 terms must be distributed in addition to the middle 
 
Sec. I.] MEDIATE INFERENCE. 131 
 
 term in 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 1 
 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 M 
 
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 JB.) 
 
 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 A A A. 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, (54^ J5 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 ^ moo ^ s that are thus invalid, only 
 talid Moods, eleven valid ones remain. And of these 
 only a part are valid in any one figure. 
 
Bee. 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 Fig UreS of Aria- 
 middle term is the subject of the major totlei 
 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. 
 
 8 M. S M. MS. MS. 
 
 S P. S P. S P. S P. 
 
 Sub. Pra. ; Turn Prse. Free.; Turn Sub. Sub.; Turn Pr. Suht 
 
 8. Of the eleven valid Moods, some are Invalid 
 in one figure which are valid in another. y alid and ln- 
 Thus AE E would be valid in the valid Mood* 
 
 second figure, as, 
 12 
 
134 LOGIC. [Chap V. 
 
 " All men are mortal, 
 
 No angels are mortal, 
 Y No angels 
 
 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 figure 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. 
 
 ^ fbArbArA, cElArEnt, dArll, fErlOque prio- 
 rigure !.< 
 
 I ris. 
 
 rcEsArE, cAmEstrEs, fEstlnO, bArOkO (01 
 1 ' \ fAkOrO), secundae. 
 
Bee. III.] MEDIATE INFERENCE. 135 
 
 ftertia, dArAptl, dlsAmls, dAtlsI, fElAptOn, 
 Figure 3. | bOkArdO (or, dOkAmO), f ErlsO, habet, quarta, 
 [ insuper addit, 
 
 rbr AmAntip, cAmEnEs, dlmAarls, fEsApo 
 I frEsIsOn. 
 
 In the foregoing lines the vowels signify the 
 moods of the syllogisms respectively al- _ 
 
 Explanation of 
 
 lowablein each figure. The initial letters itaemonio 
 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, * 
 and p that the proposition denoted by the vowel 
 immediately preceding, is to be converted, s, simply 
 p, per acddens, 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 
 
 Limitations 
 
 may at present be passed by will show upon 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. [Ohap. V 
 
 Figure can prove only negatives, because the mid- 
 dle term, being a predicate in both premises, re- 
 quires at least one negative premise 
 Upon the 3d, ^ disfcribute ^ The TMrd 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 
 woof^re* S rea ^7 modified in the case of the judg- 
 misesUandY, 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. " Kational 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 g i sm , 
 12* 
 
138 LOGIC. [Chap. V. 
 
 substitutive judgment, yield a universal conclu- 
 sion. Thus : 
 
 " X Y Z, are ruminant, 
 X Y Z, are (as good as) all horned animals, 
 .*. All horned animals are ruminant." 
 
 SECT. IV. MAXIMS BY WHICH DIFFERENT LOGICIANS HAVB 
 
 APPLIED THE PRINCIPLES OF IDENTITY AND CONTRADIC- 
 TION TO THE SYLLOGISM. 
 
 12. Most of these are founded on the prin- 
 Genns Predica- ci P le tliat ; 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 
 turn, b e 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 
 Figure, ^ the -p^ Figure> Thug . 
 
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 ^ 
 may be affirmed or denied of a whole PartSt 
 
 (in extension), may be likewise 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 totlus. 
 
 C. To the same effect is the maxim contentum 
 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 notce est nota rei ipsius. 
 This probably has reference to construing and testing 
 Syllogisms according to the Intension of Intensive g Uo> 
 the terms. To this some of the fore- gisma. 
 
140 LOGIC. [Chap. V 
 
 going maxims apply, but in a reverse order, since 
 the whole of extension 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, 
 
 u All conquerors are brave, 
 
 Caesar was a conqueror, 
 .*. He was brave," 
 
 according to intension would be construed thus: 
 
 " Caesar 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^onstr ^ e q ua lly certain and necessary. Some- 
 ana 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- 
 Ulnstration 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.] MEDIATE INFERENCE. 141 
 
 Barbara. Celarent. 
 
 1st Figura 
 
 1st Figure. 
 
 Darii. 
 
 Perio. 
 
 Cesare. 
 
 Camestres etc., etc. 
 
 3d Figure, 
 
142 
 
 3d Figure, 
 
 [Chap. V. 
 Felapton, etc., etc. 
 
 For a fuller view of the different schemes of 
 Syllogistic Notation, see Appendix B. 
 
 SECT. V. UNFIGUKED SYLLOGISM. 
 14. Before leaving this subject, it is proper 
 ow 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.J MEDIATE INFERENCE. 143 
 
 we may more explicitly, though awkwardly, state 
 our meaning thus j 
 
 "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 oi 
 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 ?ney 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- 
 Reago . ment. A syllogism may contain hypo- 
 
 Turns on the thetical judgments in which the rea- 
 soning does not turn upon the hypothe- 
 
 Otherwisethe . . 
 
 Syllogism is S1S > " u ^ simply retains it as one of the 
 
 Categorical, termg Q f the con clusion. 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 author* 
 
 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- 
 thesis, 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 
 
 <^ o^ e v 
 
 " 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 
 
 Grounded in 
 
 called Reason and Consequent. Reason and 
 
 17. The nature of the Conditional Conse l neilt ' 
 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 
 
 Laws of Condi- 
 affirmed in the conclusion. tional Syllo- 
 
 B. If the Consequent be denied, the glsmi 
 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 
 
 A. IfAisBCisD, A is B, /. C. is D. 
 
 B. If AisBCisD, C is not D, /. A is not B. 
 
 r If A is B C is D, A is not B, .*. no conclusion. 
 '" \ If A is B C is D, C is D, /. no conclusion. 
 
 13 K 
 
 ' 
 
 
146 LOGIC. [Chap.V 
 
 The fallacy of any inference in the cases under 
 Fallacies iilas- ^, w ^l appear more plainly from 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. 
 
 Best 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/' 
 
6ec. VIIL] 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- 
 
 LawsoftheDiB- 
 
 firmed in the minor, the other mem- junctive Syl- 
 bers are false. Thus: logism< 
 
 " 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 
 fattens. 
 
 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 modiis tollendo ponens. 
 
 19. It is proper to repeat that a Disjunctive 
 may be turned into a Conditional by T 
 
 J 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 
 fhus: "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- 
 Diiemma De . matic 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 may 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. If A is B, either C is D or E is F. Affirm 
 
 One Antecedent 
 
 and a Disjnnct- 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 ID 
 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 **; 
 
 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 ^ de ^' ^ 
 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. [Ch p.V 
 
 affirmation of the Consequents, nothing can bw i*L 
 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 tl ^ 
 Consequents wholly, would lead to a correspond 
 ing affirmation of Consequents or denial of Ante 
 cedents respectively, appears in the following es 
 ample : 
 
 " If A. B. is diligent he will prosper, 
 And if C. D. 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 
 
 Restriction of t ' 
 
 the Dilemma by plurality of Antecedents in the Major, 
 
 ome Logicians, ^ & dlg j unctive Minor> 
 
 21. The Dilemma has been named the SyUogis* 
 
Sec. IX., MEDIATE INFERENCE. 151 
 
 mus Cornutus, or Horned Syllogism, because it con- 
 fronts an adversary with two assump- Horns of ^ 
 fcions 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 T r ii emma> i e . 
 this sort of Syllogism according to the tralemma, 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 prln 
 which determine the conditionals and ci P le8t 
 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 
 Enthymeme, .,, . , 
 
 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/' 
 
 in 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- 
 
&sc. XL] MEDIATE INFERENCE. 15& 
 
 thymemes, occurring in ordinary speech, are in- 
 numerable. Thus : 
 
 " These men are good and therefore brave," etc., eto 
 
 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 
 
 Or chain-syllogism, in which a number of syllo- 
 gisms in the First Figure are so com- 
 
 , . , ,, , ,, ,. f^& Sorites defined, 
 
 bined, that the predicate of 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 - The 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 
 negai ive minor premise of the next svllogism. Th is 
 
Sec. XL] 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 
 
 T . , Inverted Soritei. 
 
 to view by Goclenms. 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 : 
 
 " Eational 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- 
 sated 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 exception! 
 which might arise from substitutive judgments in any of th 
 premises. So also of the Sorites in every form. 
 
156 LOGIC. [Chap. V 
 
 HYPOTHETICAL SOKITES. 
 
 Hypothetical 29. 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. 
 
 PROSYLLOGISM, EPISYLLOGISM 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 Prosy llogism and 
 Episyllogism are of constant occurrence. 
 
 The Prosyllogism is one whose conclusion fur- 
 Prosyilogism, nishes a premise for the principal argu- 
 Episyilogism, ment. The Episyllogism makes the 
 
Bee. XI.] MEDIATE INFERENCE. 157 
 
 conclusion of the main argument one of its pre- 
 mises. 
 
 " Useful studies ought to be pursued : 
 
 Prosyllogism. 
 
 Logic is a useful study (since it helps to think well), 
 
 Episyllogtem. 
 .*. It ought to be studied, and (hence an educational course 
 
 which omits Logic is deficient)." 
 
 31. Epicheirema denotes a Syllogism which has 
 
 a Prosyllogism to establish each of its 
 
 m1 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 Prosyllogism. 
 
 Polysyllogism is a combination of several syllo- 
 gisms in one argument. The Sorites is 
 
 /. . , Poly syllogism, 
 
 wie species of it. 
 II 
 
CHAPTER VI. 
 
 APPLIED LOGIC FALLACIES. 
 
 1. HAVING brought to view the fundamental 
 Transition to ^ aws f P ure thinking, or principles of 
 Applied Logic, F orma l 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 01 errors in 
 
 thinking; and next, to the right conduct of the 
 thinking process, when employed in the 
 
 Method. . 
 
 discovery of 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- ^ 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 an J 
 Applied Logic, the student is referred to the observations on thil 
 
 subject in Chap. I., Sect. IV. 
 158 
 
Sec. L] 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- * alo f sms * nd 
 
 feopnisnis. 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 proper to add, how- 
 
 * * Both have the 
 
 ever, that these distinctions have no same Logical 
 
 logical, whatever may be their moral 
 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- 
 pearance of it. These are all cases of more than 
 three terms, Undistributed Middle. II- Instances of 
 
 .. . _, _, Formal Falla- 
 
 licit Process, Negative Premises, amrma- c i es , 
 
 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. YL 
 
 making any conclusion from particular premises, 01 
 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 
 terras 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. L] 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 
 
 Why introduced 
 
 which simulate it. They enter into in Applied 
 Applied Logic only as principles of slc< 
 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, for 
 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 jf ater i a i p a y a . 
 the conclusion does follow from the pre- cies Defined, 
 
 14* 
 
162 LOGIC. [Chap. VL 
 
 mises. Hence called Material, because they lie iiot 
 in the form, but the matter of the Syllogism. la 
 Groundless re- ^ ^ked, how is a fallacy possible 
 mise or irrele- here? The answer is, 1st, that a pre- 
 
 vant conclusion, . --*" r^Ti 
 
 mise maj be unwarrantably assumed, ca 
 2d^he_^Qp3usi^nmayJ)e irrelevant. It may ML 
 
 sliort of what the reasoner intends or professes to 
 Ignoratio prove. The technical name of this lat- 
 ElencM. er ' 1S> Jgnoratio Elencld 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 
 they 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- 
 
Bee. I.] FALLACIES. 163 
 
 trast with argumentum ad rem, i. e. to the point 
 Such is argumentum ad verecundiam, or Argnmentumad 
 appealing to the feelings of reverence ' verecundi- 
 for certain persons or objects, instead of am, 
 
 proving the point in hand : argumentum 
 
 7 . ,. ,1 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 
 
 Ad populum, 
 ignorance : argumentum ad populum, 
 
 which is very miicn "akin, bemgaddressed to the 
 passions and prejudices rathj 
 
 of the people ; and finally argumentum 
 -- J7 . ' . Adhominem. 
 
 ad /tominenij 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 
 
 ., . , . T/ > T -. , How far valid. 
 
 silencing him. It 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. VL 
 
 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 
 Fetitio Princi- ' ls ^Q unwarrantable virtual assumption 
 pu ' of the thing to be proved, or of that by 
 
 which it is to be proved, without proving it, in the 
 coarse 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 prindpii. The 
 most deceptive form of this fallacy is, 
 
 Arguing in a circle argumentum in circuloixL. 
 Arguing in a whjchJifiLJ^nclusion is virtually^usfid 
 Circle, O prove the premise, thus going, ia- 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 coma pro causa assumes that to be a 
 cause which is not a cause. Foremost Non cauaa prt 
 among these is the fallacy of post hoc causa " 
 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 rggem- jf on ta i e pro 
 blance withoutjprovingjt. Thus, "the tali> 
 season is favorable to apples because peaches are 
 aEundant," 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 
 euique efficienter antecedat." Quoted in Bowen's Logic, p. 306. 
 
166 LOGIC. [Chap. VL 
 
 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 c ^ ass ^ 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, mav j^ sa j ( j O f t ne 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 Ambiguous 
 
 Term = Two three terms of a syllogism be ambigu- 
 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- 
 Hcw Semi-Log- lacv of Ambiguous Terms is partly 
 ted* material and partly formal. In order 
 
 to detect the ambiguity, we have to look at the 
 
flee 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 g^ Fallacies 
 as various as the various causes or kinds s P ecions - 
 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. VL 
 
 13. The fallacy of Division and Composition. 
 Division and ^ n * m ' s * ne middle term is taken divi- 
 Oomposition, dedlv or distributive^ 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 these persons are taken collectively in the 
 major, and otherwise 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- 
 Fallacy of the auction with the word " all," which, in 
 word "all," the peculiar idiom of our language, 
 affords great facilities for it. First, as in the ex- 
 amples given above; 
 
 " All these soldiers are an army, 
 
 All these soldiers are individual persons, 
 .*. Individual persons are an army." 
 
 Here in the major "all" is taken collectively, in 
 the minor distributively. 
 
Bee. E.] FALLACIES. 169 
 
 But the greatest liability to an ambiguous or 
 non-natural sense of the word " all." is 
 
 Of "not all," 
 
 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 he 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 Fallada Accidentis, or 
 
 t allacia Acci* 
 
 a dido secundum quid ad dictum sim- dentis, 
 
 15 
 
170 LOGIC. [Chap. VI 
 
 plieiter, 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- 
 Fallacy of Ety- dle i 8 that founded on Etymology, or 
 moiogy. fljg 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 Fcdlacia Plu- p^locy of In- 
 rium Interrogationum. This is prac- terrogationa, 
 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 
 question so put as to imply that it is tion8 ' 
 
172 LOGIC. [Chap. VI 
 
 beyond dispute. No better instance of this can be 
 found than the celebrated question of Charles II. to 
 the Koyal Society, "Why a dead fish 
 does not, 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- J 
 
 tinct and Ade- only for a Clear, but for a Distinct and 
 
 qnate Cognition. . , ~ .,. , -.-,. 
 
 even Adequate Cognition (see cnap. 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 fdbaay E X _ 
 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. VL 
 
 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 -f% or -J-. 
 
 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 
 yj +-|- = }-!; 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. l Or, if we represent/ 
 says M. Quetelet, 'the number of times that (Vj 
 
Bee. 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 bef+io+T^ (W) i- 
 ' 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 
 
 support. But if otherwise, if they are strengthen and 
 probabilities of probabilities, they weak- weaken each 
 en each other. If the credibility of a other> 
 witness be J 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 f X J 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; let the 
 first probability be J, the second J, the third \, the 
 fourth f . Subtracting each of these from unity, 
 and multiplying them together, we have JXfXf X 
 J = -fa = 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- bins 
 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." Whateley's Logic, 
 Book III.. 15. 
 
178 LOGIC. [Chap. VL 
 
 24. A source of ambiguity, not only in the 
 i middle, but other terms, which ought 
 
 t Universal!- not to be overlooked, although the 
 means of guarding against it, will more 
 fully appear under the head of Induction, has re- 
 ceived the uamefictce universalitatis /. i. 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 humbuggecl 
 
 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- 
 
 Hignoua Middle, ambiguity in language itself. Their de- 
 
See. III.J 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 
 
 i -I . T ,. 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- 
 
 ment for this sort of logical sleight of lemma for thx* 
 hand. A sly fault in some member of pnrpos< 
 
l8Q LOGIC. [Chap. VL 
 
 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 
 
 .King's rules for 
 
 lifting 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 
 not secure any of 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 aboilt 
 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, ifmotion 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 famoua 
 old Puzzle named Ignava Ratio, i. e. the 
 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. VL 
 
 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 01 
 without a physician, you will not recover. 
 
 " But eithei 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- 
 Achilles and the toise ? which so lon g baffled the logi- 
 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 ^th, the tor- 
 toise has advanced j^th, and then, again, T^th, and so on 
 
Bee. 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 $ vhian. 
 tion, when will Achilles overtake the ex P sed - 
 tortoise ? is kept out of sight, and another wholly 
 diiferent substituted in its place, viz., if 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 P lacemLo s 10t 
 them. The propounding and solution of such 
 quibbles may be a casual diversion, it cannot be a 
 principal object of pursuit, in any science worth 
 serious study. 
 
CHAPTER VII. 
 
 LOGICAL METHOD. 
 
 1. METHOD, //e06oc, is the way by which we pro- 
 
 ceed to a given goal. Logical Method 
 
 Method Defined. . A , , . Al _ . . , - 
 
 is the way 01 applying the principles of 
 
 Logic to the discovery, confirmation, or elucidation 
 of the truth. 
 
 In order to this, it is necessary to determine 
 
 the sphere and matter, the extension 
 
 vision* 5 S Defini- an( ^ intension, the objects and thequal- 
 
 tion, and Eea- ities, w ith which we have to do. The 
 
 eoning. 
 
 former is accomplished by Logical Divi- 
 sion, and the latter by Definition, which have been 
 duly treated in their respective places, in the Chap- 
 ter on Conceptions. To this we refer the student 
 as sufficient for present purposes, while we pass to 
 consider more especially the use of Reasoning in 
 the search and proof of truth. 
 
 184 
 
Sec. I.] METHOD. 135 
 
 2. It must not be forgotten that Logic does not 
 give us the original facts, axioms, or _ 
 
 Logic not the 
 
 first principles, which constitute the Original source 
 
 -i i / of Knowledge. 
 
 primary matter or groundwork of our 
 knowledge. These are furnished by Its sources m , 
 Intuition, either 1. Of the phenomena merated - 
 of consciousness, i. e, psychological facts : or 2. By 
 sense-perceptions, i. e. of facts pertaining to the 
 material and external world or, 3. By supersensual 
 intuitive truths, i. e. self-evident axioms : or finally, 
 by testimony either spoken or recorded. . 
 
 Logic deals with the matter thus af- with the matter 
 forded in a two-fold 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. [Cnap. VIL 
 
 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, 
 
 of sources of Sense-Perception, Self-Evident, Super- 
 Knowledge, gensual truthg ^ and TestimonV4 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 
 
Bee. 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 
 
 ' t Memory in 
 
 bears witness simply to the cognitions volved in Testi. 
 of the present moment. Almost all tes- mony ' 
 timony respects the past. 
 
 5. Testimony is a fundamental source of know- 
 ledge. All facts known to us beyond i mpor tance of 
 the narrow circle of our own experience, Testimony, 
 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 ip 
 historical writings, monuments, memen- 0^ and Ke> 
 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. VIL 
 
 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 
 
 principles of theology do not depend 
 
 Theology found- * 
 
 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- 
 
 ciples of logic to the facts, that are al- 
 
 The laws of 
 
 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- 
 
 TJnlogical la 
 ing only simulates and counterfeits it. counterfeit 
 
 But, in proportion as this application thou s htf 
 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 w h a tit 
 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 filld ljan ^ 
 to ascertain their laws and principles is to find cause8 - 
 commonly to ascertain their causes. Towards this 
 state all knowledge tends in proportion as it tencba 
 
190 LOGIC. [Chap. VIL 
 
 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- , , . , 
 
 tiarum : 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. 19] 
 
 they are used for that comprehensive view of facia 
 and truths in the particular departments, 
 or in the whole field of knowledge, above g c i ence f ur thei 
 set forth. Thus we speak indifferently Compared an-i 
 
 r ; 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- 
 
 ,, ., ,. f . Logical Method 
 
 sable, to the construction of science, or i nc i u( j es D e fini- 
 thorough knowledge, so Logical Method tion Division 
 
 and Seasoning, 
 in every department of inquiry involves 
 
 the three great logical processes which mutually 
 
J92 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 
 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- 
 Necessary and 
 
 Contingent Dis- ceive without intellectual suicide. The 
 guls latter is that whose existence is Con- 
 
Sec. 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, ASSEBTORY, AND APODICTIC 
 JUDGMENTS. 
 
 14. The two former apply to the region of Con- 
 dngent,* 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 
 
 * Problematic 
 
 is not certain to him who holds it, nor Judgment ~ 
 
 can he enforce its acceptance upon pm] 
 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. 
 17 
 
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 
 meats necessa- to him who holds them, and capable of 
 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, 
 
 Apodictic Judg- little need be said. The conclusions 
 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 
 Formal Sciences f rma l sciences afford fine illustrations 
 illustrated by o f t h e 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 ^ jj ath( ,. 
 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 eUJoning from 
 a priori truth that space is illimitable, a P riori tnlth8 
 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 
 
 From one a pri- 
 
 thunder must have had a cause. Here ori and one Con- 
 the major premise is a necessary, the tm s ent P rei 
 minor a contingent but certainly proved truth ; 
 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, la 
 this we have the tvpe of all purely 
 
196 LOGIC. [Chap. VIL 
 
 SECT. III. DEDUCTIVE SEASONING. 
 
 16. This has place in all cases of Reasoning 
 
 . from wholes known in whatever way. 
 
 This the type of J ' 
 
 Deductive Eea- 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, 
 ?**"*.** * om of nearly all demonstrative and abso- 
 
 GeneralstoPar- ' 
 
 ticulars, lutely conclusive reasoning. 
 
 17. But how do we obtain these universal or 
 
Sec. IV.] METHOD. 197 
 
 Generic Judgments in Contingent Mattel, when all 
 that we know originally of mind is 
 
 -T *i t i ji T Whence come 
 
 the individual tacts that come under Q enera i 
 
 the purview of consciousness, and of ments ** 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 01 truth, which is, 
 
 SECT. IV. INDUCTION. 
 
 17. This is the principal instrument of scientific 
 progress, and of all advance in human 
 
 By Induction, OT 
 
 knowledge, except through Divine Re- reasoning fnui 
 velaiion, within the realms of actual ^ 18 * 
 
 being. For this is a region of facts, Actual beings 
 objects, phenomena of actual existence are Mvid 18 - 
 which are first known as individuals, and might or 
 
 might not be, according to the good pleasure of God. 
 17* 
 
198 LOGIC. [Chap. VIL 
 
 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 actual 
 
 All progress in 
 
 Scientific Know- is by ascent from particular facts to 
 
 being is aC from g enera ^ ^ aws - ^ proceeds therefore, 
 Individuals to from what we know in some cases, to 
 
 infer that the like is true in all similar 
 cases. This is induction or inductive generalization. 
 
 Induction, however, is more than Gen- 
 
 Induction more 
 
 than Generali- 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 ^7 a class-name. Induction conclude* 
 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, 
 
Bee. IV.i 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 qnea- 
 orined, 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 testa 
 
 may be, like cases innumerable ? What or crucial in- 
 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 gi mp i e Elm- 
 composing the class in question. If m eration, 
 these all, without exception, have the property in 
 question, then it of course belongs to the whr>le 
 class. Thus, if the season of greatest 
 
 Example. 
 
 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 enumerationem, 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 
 Andimimport- establishes no law reaching beyond 
 ** such experience. It is therefore com- 
 
 paratively unimportant. That induction alone is 
 The oni fruit- ^ ru i^ u ^ which enables us to go beyond 
 fnl Induction, suc h cases as have fallen within oui 
 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 7 the em P irical fact ; that > in 
 
 A Causal such instances as have fallen under our 
 
 Agency ' cognizance, the phenomenon in question 
 
 has occurred, but that there is a causal agency, or 
 
 other uniform concomitant, connected with them 
 
\ 
 
 OF THE 
 
 { UNIVERSITY / 
 
 Pec. 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 
 
 7 . ,. .,.,., Difference from 
 
 simphcem enumerationem, is strikingly gi mp i e 
 
 illustrated in the second example of the ratio11 
 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 Oangal 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 Causa! 
 
202 LOGIC. [Chap. Vii. 
 
 Agency, or other equivalent concomitant, and proof 
 Tests of Causal ^ a gi yen phenomenon? The proofs 
 Agency et<? fl^ 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 
 * hm ' 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 sase the question is, when do the parti- 
 TheQuestionre- cular cases X Y Z so represent the 
 garding it, whole class, or when are they so proved 
 to be, or *o contain the causes or uniform con- 
 comitants of a given phenomenon, that they fairly 
 represent the whole class, and warrant a universal 
 inductive conclusion ? 
 
Bee. IV.] METHOD. 203 
 
 1st CRITERION, IHE METHOD OF AGREEMENT. 
 If, whenever a given object or agency lgfc Tegt ^ ^ 
 is present, without counteracting forces, Method of 
 
 , , ,, . Agreement. 
 
 a given effect is produced, there is 
 strong evidence that we have found the true cause 
 of the effect, which will always produce it, in the 
 absence of counteracting forces. Thus, 
 if, in all cases of the application of 
 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- 
 ceed from different causes. In order to ga m ? e ffect may 
 determine to which of two possible P roceed fnm 
 
 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 
 thod of differ- being absent the effect is wanting, L e. 
 unless in the latter case other coun- 
 ter-agents are present to neutralize it, 
 or in the former to produce it. Thus, it is double 
 proof that sound is the result of vibra- 
 tions of 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 
 SdTest, Eesid- 
 ual variations the supposed cause. Thus, it was found 
 
 accounted for, ^ gound trave l e( J 
 
Bee. 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 
 Thomson'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 change in the effect, he at once deter- 
 18 
 
206 LOGIC. [Chap. VII 
 
 4th CRITERION. CONCOMITANT VARIATIONS. 
 If, as the amount of the supposed cause 
 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 tht 
 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 mercury 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 j 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 ^eason f or fly. 
 testing one view of the cause of given pothesfe, 
 phenomena, rather than any other ? It can only be 
 because the mind entertains some conjecture or sus- 
 picion that this may correspond witJ the facts. 
 Thus it is led to institute investigations 
 and trials for the purpose of testing the 
 
 truth of this conjecture. Such a con' ture or 
 
 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 _ 
 
 Use and Neawu 
 
 guide and stimulus, all observations and sity of Hypo. 
 experiments would be aimless, and com- 
 
208 LOGIC. [Chap. VI. 
 
 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 
 
 flow far Theory 
 
 and Hypothesis use them so as to avoid all shades of 
 
 are synonymous^ T> J.T 
 
 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. 
 
 In regard to the distinction be- 
 
 Definition of 
 
 some Scientific tween Theoretical and Practical Judg- 
 Jndgments, 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 _ 
 
 Judgments The- 
 
 practice are Practical. Judgments oretical, Practi- 
 
 ., . , .. /, cal, Demonstra- 
 
 tliat require or admit of proof, are ble> 
 
 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- AT1 - nm> p ogtu . 
 ble practical judgment. A Theorem is late ' Theorem, 
 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. \IL 
 
 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- 
 
 Schoiion. pears hut 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 genius, 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 Re- A. No hypothesis should be assumed 
 thesis ^i Must ^ accoun ^ ^ or what can be otherwise 
 be aeeded, accounted for, on existing and known 
 principles. 
 
 B. It should be adequate to account 
 for the phenomena in question. 
 
Bee. 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 
 Royal Society, why a live fish 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 NO Subsidiary 
 subsidiary hypotheses it should not H yP theses ' 
 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 1^0^ f rom 
 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 
 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 
 
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- anc ^ can > ^ n no case ^ r ^ se higher than 
 table 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 
 
 Stay strengthen 
 
 other argu- force to other arguments. It is not, 
 however, in any case conclusive of itself. 
 27. Its most important service, however, is in 
 Most useful in refutation of fallacious arguments. It 
 refutation, often has in this way a powerful nega-r 
 tive force. Thus, if it be objected to the doctrine 
 of future punishment that the infliction 
 of pain is inconsistent with the benevo- 
 lence of God, this argument is refuted by the fact 
 
 * To reason from Analogy, is to reason from the Intension ot 
 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 cw 
 u 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 obaia, Aristotle's Gate- 
 7ro<7ov, 7ro2ov, TtpboTt, Ttou, ^3re, xetffdac, ries> 
 efyefv, noeeiv, nd0%ew 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. TO, 
 
 heads ; and by others curtailed, as it is no less evi- 
 dent that all may ultimately be referred to the two 
 neads of substance, and attribute, or (in the language 
 of some logicians) accident" Some, however, per- 
 haps justly, translate fv, " mode of action," in- 
 stead of "possession." Aristotle's Categories are 
 rather metaphysir al than logical. 
 
 29. Kant's celebrated four triplets of Categories 
 
 Kant's Gate- are certainly 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, 
 
 I. Quantity. 2. Quality. 3. Relation. 4. Modality. 
 
 Unity, Affirmation, Substance and Accident, Possibility, 
 
 Plurality, Negation, Cause and Effect, Eeality, 
 
 Totality. Limitation. Action and Reaction. Necessity. 
 
 It may be observed that the first of these triplets 
 corresponds to Singular, Particular, and Universal 
 Judgments; the second to Affirmative, Negative, 
 and Restrictive* 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 
 
Bee. VII.] METHOD. 216 
 
 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. Besemblance. 
 
 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. 
 
 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 
 thej 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 on- 
 likenesses between feelings and states of consciousness." 
 L)gic, I. 111. 
 
 32. Thomson (Laws of Thought, p. 315) just 
 attempts the following : 
 
 TABLE OP THE CATEGORIES. 
 
 SUBSTANCE 
 
 Attribute 
 
 QUANTITY 
 
 QUAXITY 
 
 Relation 
 
 ' Of TIME 
 
 of SPACE 
 
 of CAUSATION 
 
 of COMPOSITION 
 
 of AGREEMENT and BEPUO- 
 
 NANCE 
 
 of POLAR OPPOSITION 
 of FINITE TO INFINITE. 
 
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 T , . ., c* . Classification 
 
 been made to classify the Sciences so and Mutual 
 as to show their Mutual Harmony and Harm n 7 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- SpeCTl i at i V e and 
 sical and Metaphysical, or the Formal Practical etc - 
 and Material, etc., with their respective subdivisions. 
 Attempts of this sort have often been made, witk 
 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. 
 
21$ 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 mo*i 
 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. Physic, being 
 th, science, or rather group of sciences, Thich is 
 conversant with the general laws of the irotld, so 
 far as they relate to beings without life or organiza- 
 tion, would come next; and it imports, in addition 
 to +iie 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. 
 
 III. PHYSICS Theoretical. 
 
 IV. CHEMISTRY Theoretical. 
 
 V. PHYSIOLOGY Theoreti cal. 
 
 VI. ANTHROPOLOGY Theoretical. 
 
 VII. SOCIAL SCIENCE Theoretical. Historical. Applied. 
 
 Historical. Applied. 
 
 Historical. Applied. 
 
 Historical. Applied. 
 
 Historical. Applied. 
 
 Historical. Applied. 
 
 KELIGIOUS PHILOSOPHY." 
 
 19* 
 
APPENDIX. 
 
 APPENDIX A. 
 
 EXAMPLES FOE PRAXIS. 
 
 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 whether 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. 
 
 6. Quadrupeds are animals, 
 Worms are animals. 
 
 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 FOE 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, 
 
 .*. 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 by alleged 
 
 miracles, 
 
 Christianity sustains its claims by alleged miracles ; 
 .'. It is a false religion. 
 
 25. The minute-hand can never overtake the hour-hand of a 
 clock, because while it is passing to the point where the hour- 
 hand is at any given moment, the latter will have advanced 
 
EXAMPLES FOR^PEAXIS. 227 
 
 some distance : and when the former has passed over this dis- 
 tance the hour-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 mest 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 
 is 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 FOE 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 been a law that could have given life, then 
 
 verily righteousness should have come by the law, 
 But righteousness did not come by the law." 
 / Gal. iii. 21. 
 
 * The fallacy here is that the Disjunction is incomplete. There 
 is another horn, viz : that Protagoras had no cause of action, 
 because before the bringing of this suit, Euathlus had no case in 
 court. See Chap. VI., 28. 
 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. 
 
 46. 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 | that he would tell the truth if he did know it. 
 
 48. What is the probability that B. B. wrote a certain anony- 
 mous letter, where the separate probabilities are 
 
 From chirography, |, 
 
 From the sentiments, ^, and 
 
 From his known meanness of character, \ ? 
 
 49. All plants contain cellular tissue, 
 No animals are plants, 
 
 .*. No animals have cellular tissue. 
 
 50. A fungus is a plant, for it is either a plant or an animal, 
 and it is not an animal. 
 
 51. If this man were wise, he would not speak irreverently 
 of Scripture in jest ; and if he were good, he would not do so 
 in earnest ; but he does it, either in jest or earnest ; 
 
 52. Magnets attract iron, and they have polarity, 
 
 53. Insects are not winged, because birds are winged, and 
 insects are not birds. 
 
 54. Insects are not fishes, because fish live in water, and in- 
 sects do not. 
 
 55. What is the probability of a recurrence next year of a 
 fire in one of our great cities, consuming millions of property, 
 from the fact that such fires have occurred on an average once 
 a year for the last ten years ? 
 
232 APPENDIX. 
 
 56. All these students form a powerful body, 
 A. B. is one of these students, 
 
 He forms a powerful body. 
 
 57. What inferences by opposition can be obtained from 
 
 All men are fallen, 
 
 Some trees are oaks, 
 
 Some stones are not diamonds. 
 
 All triangles are three-sided figures ? 
 
 58. Convert logically 
 
 Some men are not cultivated. 
 Some men are cultivated. 
 All plants are living things. 
 All pure men love God. 
 
 59- What do you say of dividing college studies into chem- 
 ical, classical, rhetorical, theoretical, practical, those taught by 
 text-book, and those taught by lecture, as a sample of Logical 
 Division ? 
 
 60. What do you say of defining a square as a rectangular 
 parallelogram, a quadruped as a dog, a triangle as a three- 
 sided figure whose angles are equal to two right angles? 
 
 61. Point out the subject, predicate, copula, quanity, and 
 quality of the following judgment: 
 
 All students decline in scholarship who become indolent* 
 
 62. Body is space-filling substance, 
 Body has mobility, 
 
 .'. Whatever has mobility is space-filling. 
 
EXAMPLES FOE PRAXIS. 233 
 
 63. Discontented persons are not wise, 
 Abstemious persons are wise, 
 
 /. Discontented persons are not abstemious. 
 
 64. Whatever promotes the public good should receive the 
 attention of government, 
 
 Dram-shops do not promote the public good, 
 /. They should not receive the attention of government. 
 
 65. Animals are sensitive beings, 
 Sensitive beings have life, 
 Beings having life are organized, 
 
 /. Animals are organized. 
 
 66. Useful pursuits ought to be encouraged ; 
 
 Farming, since it produces food for man and beast, is such ; 
 .'. It ought to be encouraged, and consequently what de- 
 presses it ought to be opposed. 
 
 67. If the earth does not revolve on its axes, existing pre- 
 nomena cannot be accounted for; 
 
 It does so revolve, 
 
 68. Silver is money, 
 Gold is money, 
 
 69. Perseverance enables us to conquer, 
 Therefore it is useful. 
 
 70. All gold is precious, 
 This mineral is precious, 
 
 20* 
 
234 APPENDIX. 
 
 71. Warm countries alone produce oranges, 
 Florida is a warm country, 
 
 .*. Florida produces oranges. 
 
 72. The earth moves either in a circle, ellipse, or straight line, 
 It does not move in a straight line, 
 
 73. If the atheists are right the world exists without a cause, 
 But the atheists are not right, 
 
 74. A religion attended by miracles is from God, for none 
 but God can work miracles, and he would not work them in 
 behalf of an impostor; 
 
 The Christian religion was attested by miracles, for in- 
 dubitable evidence proves it ; 
 
 /. The Christian religion is from God. 
 
 75. Point out the subject, predicate, copula, and distributed 
 terms in the following judgments : 
 
 He that believeth hath eternal life. 
 Civil office is either legislative, executive, or judicial. 
 Circles are figures equidistant at every point from a point 
 within. 
 
 76. What can you infer by Opposition and Conversion from 
 
 All men are liable to become gray, 
 Some stars are (all the) planets, 
 Some persons are not cheerful ? 
 
 77. Although animals feel, perceive, remember, and have 
 instinct like men, they do not know axioms above sense, nor 
 have articulate speech, nor increase their knowledge from gen- 
 
EXAMPLES FOR PRAXIS, 235 
 
 eration to generation, which are higher gifts than the former. 
 Men do this, and therefore have more than brute intelligence. 
 
 78. All plants have life, 
 
 But none have consciousness, 
 
 79. If I am to succeed in life, no conduct of mine will pre- 
 vent it ; 
 
 If I am to fail, no conduct of mine will prevent it ; 
 But one or the other of these is true ; 
 .'. All effort on my part is useless. 
 
 80. The predictions of weather from Washington having been 
 true four days out of five, and it being proposed to increase their 
 accuracy one-tenth by better instruments,one-tenth by increased 
 skill in the observers, and one-tenth by the increase of stations 
 of observation what measure of probability may we expect in 
 the predictions of next year? 
 
 81. Many defalcations and breaches of trust have recently 
 been discovered, and therefore nobody is worthy of confidence. 
 
 82. What can you infer by all modes of Logical Inference, 
 mediate and immediate, from the following judgments, taken 
 singly or in any mode of combination ? State and analyze also 
 the kind of reasoning, or of syllogism, employed in each in- 
 stance : 
 
 A., B., and C. are scholars, 
 
 All scholars are studious, 
 
 All studious persons are diligent. 
 
 83. 1. The following definitions of Logic have been given. Test 
 each of them by the proper logical canon for good definition : 
 
236 APPENDIX. 
 
 a. Logic is the science of reasoning. 
 
 b. Logic is the art of reasoning. 
 
 c. Logic is the science of thought. 
 
 d. Logic is the science of discursive thought. 
 
 e. Logic is the science of the laws of discursive thought. 
 /. Logic is the art of improving the mind. 
 
 2. Give a logical division of conceptions according to 
 their quality, as clear, distinct, etc. (See Chap. II., 9.) 
 
 3. What can you conclude by any form of inference, 
 mediate or immediate, from 
 
 Men are capable of religion, 
 Apes are not capable of religion ? 
 
 84. " The gospel which was preached by me is not after man, 
 for I neither received it, neither was I taught it [by man] ; but 
 by revelation of Jesus Christ." Gal. i. 11, 12. 
 
 85. " I do not seek to please men, for if I did, I should not 
 be the servant of Christ [as I am]." Gal. i. 10. 
 
 86. " But that no man is justified by the law in the sight of 
 God is evident : for, the just shall live by faith, and the law is 
 not of faith." Gal. iii. 11, 12. 
 
 87. The government cannot outlive the prevalence of Chris- 
 tianity among the people, because it is a republic, and republics 
 are governed by the people, and only virtuous people are fit to 
 govern ; but all experience proves that a people will not remain 
 virtuous after it has rejected Christianity. 
 
 88. Paganism, Mohammedanism, Judaism are false ; 
 These (according to infidels) are representative of all 
 
 religions ; 
 
EXAMPLES FOR PRAXIS. 237 
 
 89. Reason, conscience, and free-will are requisite to account- 
 ability, because all possessing them, whether angels or men, are 
 accountable ; while those destitute of either of them, as infants, 
 idiots, and maniacs, are not accountable. 
 
 90. What can you infer from each of the following judgments, 
 singly, or from any combination of some or all of them ? 
 
 All men are rational creatures, 
 Kational creatures are progressive, 
 Brutes are not progressive. 
 
 91. The ice-crop has failed in a certain region three times in 
 twenty years. Compute the probability of its not failing the 
 present winter. 
 
 92. Analyze the two following, and point out their different 
 logical force, with reasons : 
 
 1. Parallelograms are plane figures, 
 Circles are not parallelograms, 
 
 2. Parallelograms are four-sided plane figures whose opposite 
 sides are parallel, 
 
 Circles are not parallelograms, 
 
 93. Men are bipeds, so also are birds, and therefore birds are 
 ien. 
 
 94. Men of genius are eminent poets, and 
 Men of genius are eminent philosophers, 
 
238 APPENDIX. 
 
 95. All adequate cognitions are distinct, 
 All distinct cognitions are clear, 
 No clear cognitions are obscure. 
 
 What can you infer from each of the foregoing? 
 
 1. By Opposition ; 
 
 2. By Conversion; 
 
 3. By the combination of any two of them ; 
 
 4. By the combination of all of them. 
 
 96. The cases of bad drainage known are cases attended with 
 much sickness, 
 
 These cases are (as good as) all cases of it, 
 
 97. Bad weather is followed by good weather, and good 
 weather by bad weather, 
 
 .*. The one is the cause of the other. 
 
 98. Supposing the prospects of the completion of a proposed 
 building in six months to be nine-tenths from the known prompt- 
 itude of the architect and builder, three-fourths from the possi- 
 bilities of rapid work in winter, and three-fourths from various 
 other contingencies, what is the total chance ? 
 
 99. If it is our destiny to be saved, we shall be saved what- 
 ever we do or omit to do ; and if we are to be lost, we shall be, 
 whatever we may do about it. But we are destined to be saved 
 or lost ; whatever we do, therefore, will not affect our destiny. 
 
 100. Moisture is a chief cause of animal putrefaction, because 
 
 a. It is present where such putrefaction occurs. 
 
 b. Putrefaction is arrested in a perfectly dry atmosphere. 
 
EXAMPLES FOR PRAXIS. 239 
 
 c. Any variations from this are accounted for by the action 
 of other agents. 
 
 101. What do you say of the following as specimens of 
 Definition ? 
 
 a. The United States are composed of the territory and its 
 inhabitants, whose central government has its seat at Washington. 
 
 6. The United States are composed of the New England, 
 Middle, Southern, South-western, North-western, and Pacific 
 States. 
 
 102. Give your opinion of the following definitions and 
 divisions of, or under, Applied Logic : 
 
 a. A Fallacy is an unsound mode of reasoning. Logical 
 Method is the true mode of reasoning. 
 
 6. Fallacies are divisible into Formal and Material, illicit 
 process, argumentum ad verecundiam, and post hoc ergo propter hoc. 
 
 103. What can you infer from the first of the folio wing judg- 
 ments by Conversion ; from the second by Equipollence or In- 
 finitation ; from the third by Opposition ; from any combination 
 of them by Mediate Inference ? 
 
 The precious metals are gold and silver, 
 Gold and silver are fusible, 
 Fusible metals are evenly divisible. 
 
 104. What can you infer by any mode of Mediate or Im- 
 mediate Inference from the following judgments, whether taken 
 singly or in any possible combination of some or all of them ? 
 
 Some animals are birds, 
 
 All birds are winged creatures, 
 
 No winged creatures are reptiles. 
 
240 APPENDIX. 
 
 105. The Bible is a revelation from God if it is attested by 
 adequate miracles, 
 
 It is a revelation from God, 
 
 106. Having for a major premise, 
 
 " Money is either gold, silver, nickel, copper, or paper," 
 what can you infer from it with either of the following as a 
 minor premise: 
 
 a. This money is gold. 
 
 b. This money is not copper. 
 
 107. If wars enrich many people, they promote the public 
 welfare ; 
 
 If they impoverish many people, they are hostile to the 
 public welfare ; 
 
 But they both enrich many people and impoverish many 
 people, 
 
 108. Very lavish expenditures in railway construction in this 
 country preceded, and therefore caused, the financial crisis of 
 1873. 
 
 109. The Middle States include a large territory, 
 New Jersey is a Middle State, 
 
 110. Inductive reasoning is that which proceeds from par- 
 ticular cases to general laws, and is eminently instrumental in 
 the discovery of truth. 
 
EXAMPLES FOR PRAXIS. 241 
 
 The argument that because A., B., and C. achieved eminence 
 without a college education, and therefore a college education 
 does not help in attaining eminence, is a case of reasoning from 
 particular facts to a general law, and is therefore inductive, and 
 hence conclusive. 
 
 Point out any fallacies you discover in the foregoing argu- 
 ment, whether in respect to the laws of Formal or of Applied 
 Logic, especially in reference to the criteria of a valid inductive 
 conclusion. 
 
 111. No one is free who is enslaved by his appetites, 
 Every sensualist is so enslaved, 
 
 112. David slew Goliath, 
 
 David was the sweet Psalmist of Israel, 
 
 113. Every liar is vile, 
 
 A vile pei-son should be contemned, 
 
 114. Religion is the greatest blessing to man, 
 Mohammedanism is religion, 
 
 115. It will be clear weather if the clouds rise from the hill* 
 tops, 
 
 The weather will not be clear, 
 
 116. Barns are structures for the accommodation of animate 
 Barns are not bird-cages, 
 
 21 
 
242 APPENDIX. 
 
 117. In Opposition, prove the relation of the sub-contraries 
 from that of the contradictories. 
 
 118. What can you get by opposition from "Benevolent 
 actions are commendable " ? By conversion from " Commend- 
 able actions are right " ? By conversion from " Bight actions 
 ought to be performed"? By any mode of mediate inference 
 from any combination of any two or more of the foregoing 
 judgments? In every case of such combination name the 
 kind of Syllogism resulting, and analyze it according to the 
 laws of that kind. 
 
 119. Free-will, reason, and conscience are requisite to and 
 constitute accountability. For wherever they are accountability 
 is ; where they are wanting there is no accountability ; and as 
 they increase in strength accountability increases. 
 
 120. Men are sensitive and rational, 
 
 .*. Brutes, being sensitive, are rational. 
 
 121. Within the last fifteen years the gold dollar has been 
 worth two and a half times a legal-tender irredeemable paper 
 dollar. It is now equal to such paper dollar. 
 
 .'. Gold is extremely fluctuating in value, and so unfit to 
 be used as a measure of value. 
 
 122. Define Science, also Philosophy, and show how they 
 differ from each other and from other kinds of knowledge. 
 
 123. Rose-water is a decoction of roses, 
 Bose- water is a sweet perfume, 
 
EXAMPLES FOR PRAXIS. 243 
 
 Besides resolving the foregoing as a Syllogism, show which 
 judgment is analytic and which synthetic, and why ; also, whether 
 rose-water represents a notative or symbolical conception, and 
 why. 
 
 124. What can you infer from " Man is rational," by Oppo- 
 sition? "Man is accountable," by Conversion? "Man is im- 
 mortal," by Reciprocal change of positive and privative con- 
 ceptions ? 
 
 Also from the combination of all or any two of these judg- 
 ments by any form of inference, mediate or immediate ? 
 
 125. Meat and drink are necessaries of life, 
 
 Meat and drink are what drunkards and gluttons spend 
 their substance upon, 
 
 126. Logic is worthy to be cultivated if Aristotle is infallible, 
 But he is not, 
 
 127. A. B. is a successful demagogue, 
 
 A successful demagogue must know how to hoodwink 
 (he people, 
 
 He who knows this must understand their weaknesses, 
 He who understands these must lose his respect for them, 
 
 128. All the fish taken in the net were an indiscriminate 
 mixture of various kinds, 
 
 Salmon and mackerel were fish that the net enclosed. 
 
244 APPENDIX. 
 
 129. Nothing is heavier than platinum, 
 Feathers are heavier than nothing, 
 
 .*. Feathers are heavier than platinum. 
 
 130. If it is certain that students will be diligent, academic 
 honors are useless ; 
 
 And if it is certain they will be idle, such incitementa 
 are useless ; 
 
 But one or the other of these is true ; 
 /. Academic honors are useless. 
 
 131. Compute the entire probability that the gentleman who 
 died with an insurance on his life amounting to a quarter of a 
 million of dollars, procured within the previous three months, 
 intentionally sought his own death in order to leave this amount 
 to his family, the probabilities of this hypothesis being 
 
 (1) From the enormous amount insured 
 
 (2) From the insurance being effected within three months 
 
 of his death J 
 
 (3) From his imprudent exposure of himself to attacks 
 
 of disease \ 
 
 (4) From his previously having lost his wife's large 
 
 patrimony in speculation \ 
 
 The counter-probabilities being 
 
 (1) From his unblemished character \ 
 
 (2) And from his having carried very heavy life insur- 
 
 ance at former periods of his life } 
 
 132. Find the genus and differentia, if there be any, an<J giv 
 the logical character of the following definitions : 
 
EXAMPLES FOR PRAXIS. 245 
 
 Dew is a natural deposit of water on the earth which Is 
 neither rain nor fog. 
 
 Logic is a mental science. 
 
 Conversion of Judgments is making the subject and predicate 
 change places. 
 
 A category is a predicable. Also, 
 
 Define Logic by the method of Eesolution, also of Colligation. 
 
 133. Give a Logical Division of Applied Logic, descending 
 through the divisions and subdivisions of Fallacies. Also of 
 Kant's categories. 
 
 134. What Inference free from all Fallacy can you get a, by 
 Opposition ; 6, by Conversion ; c, by Mediate Inference from 
 
 All civilized persons are educated, and 
 None but civilized persons are Christians, 4~-> 
 / ?W, { *..< 6 
 
 135. The tastes of men are variable, but what is according to 
 the constitution of nature is invariable, 
 
 136. Seasoning by Analogy is inconclusive, 
 Butler's Analogy is such reasoning, 
 
 137. Cloven feet being found universally in horned animals, 
 we may conclude that this fossil animal was horned, since its 
 feet are cloven. 
 
 138. Hypotheses have often proved a fruitful means of dis- 
 
 21 
 
246 APPENDIX. 
 
 covering and testing truth, and therefore they ought to be 
 accepted. 
 
 239. Taking the definition of Dew above given, analyze logi- 
 cally the following argument, to prove that it results from the 
 condensation of moisture in the air by contact with the earth 
 when colder than such air: 
 
 I. This is the universal law of such contact of warm air upon 
 colder surfaces, as is proved 
 
 x. From the water formed on the outside of ice-pitchers, 
 
 y. Also on the surface of stones colder than the air, 
 
 z. On walls of unfurred rooms, 
 
 w. From water or ice formed on the inside of window-glass 
 suddenly chilled. 
 
 Again, no water is deposited on surfaces as warm as the air 
 in contact with them, as appears 
 
 x. From pitchers or crockery as warm as the surrounding 
 air, 
 
 y. Panes of glass when it is warm outside, 
 
 z. Stones warmed by the sun. 
 
 II. The earth at night in a clear atmosphere, such as that in 
 which dew is formed, is made cooler than the air in contact with 
 it by the radiation of its heat through the atmosphere in all ob- 
 served instances x, y, z, to. 
 
 Again, no dew is formed in case of the earth being as warm 
 as the air, as is shown 
 x. In cloudy nights, 
 y. At mid-day, 
 . In decidedly cold weather. 
 Still further, the amount of dew formed varies with th 
 
EXAMPLES FOR PRAXIS. 247 
 
 amount of moisture in the atmosphere and the extent to which 
 it is warmer than the earth, as appears, because 
 
 x. When the air becomes suddenly hot and surcharged with 
 moisture the dews are heaviest, 
 y. There is little dew in time of drouth, 
 n. There is average dew in average clear weather. 
 
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( j ^ re i at i ons O f thought respectively in- 
 logistic Nota- 
 tion, 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 , ,, , . 
 
 b Circles drawn tor purposes of casual illustration. 
 
 (See Chap. V. 13.) 
 
 2. Three circles are employed to denote respectively the 
 Maj or, Minor and Middle Terms. Affirmative judgments are 
 symbolized by the total or partial mclusion 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 denote re 
 gpectively the minor, middle, and major terms, represents, 
 248 
 
SYLLOGISTIC NOTATION. 
 
 24.9 
 
 i. The moods A A A. 2. AEE. 3. AIL 4. EIO.aD 
 of the First Figure. 
 
 1. Barbara. 
 
 2. Gelareni 
 
 
 
 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* 
 
250 APPENDIX. 
 
 NOTATION BY STRAIGHT 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," i. e. "some mortals," 
 mortal is undistributed. But we take that definite portion 
 of it which is co-extensive with the class man. Thus : 
 
 mortal, 
 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 iu 
 their quantity and other relations. 
 
SYLLOGISTIC NOTATION. 25 1 
 
 P 
 
 M 
 
 8 
 
 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 ia P, 
 
 All S is M, 
 
 i 
 
 .-. No S is M. 
 
 Substitutive Judgments are indicated by two equal and 
 parallel lines. Thus : 
 
 Judgments of Logical Division or Colligation (chap. II. 43) 
 rnay be expressed thus : 
 
 Division, Colligation, 
 
 S __ 8 i r 
 
252 APPENDIX. 
 
 THE HAMILTONIAN NOTATION. 
 
 5. Quite the most expressive and complete system oi 
 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 : 
 
 b read, C and r are equal. 
 
 may be read in two ways; Extensively, C is included und& 
 
SYLL GISTIC NO TA TION. 253 
 
 I ; Intensively, r is 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 : 
 
 E3n.mii.! This is a Syllogism in the Second 
 
 ' * ' 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 som* C; 
 
 .'. Some r is some C; or .'. Some C is some r; or 
 
 .'. Some C is some r. /. Some r is some C. 
 
 22 
 
254 APPENDIX. 
 
 C, ' "", M: i *: r "This is a negative Syllogism 
 J ^ in the First Figure, which may be 
 
 read it either of the following ways; but in either way, it 
 has only one direct or immediate Conclusion, though a 
 Second Conclusion may be obtained from, it (iwtititu'^/, ty 
 converting simply the propex 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 
 
SYLL G IS TIC NO TA TION. 
 
 255 
 
 sailed the Fourth Figure is here identified with the Indirect 
 Moods of the First 
 
 14 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. 
 
256 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\ o>. 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 amrma- 
 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, arc 
 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. 
 
SYLLOGISTIC NOTATION. 257 
 
 In which A signifies a term distributed, I a term undistri* 
 bated, 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. t 1. Afa. All are all 
 
 All are some. 
 Some are all. 
 Some are some. 
 Some are not some. 
 Some are not any. 
 Not any is some. 
 Worst. * 8. Ana. Not any is any. 
 
 14 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 s -^-', placed beneath a Conclusion, 
 indicates that, when the Premises are converted, the Syllo- 
 gism remains in the same Mood; ^><C shows that the two 
 Moods between which it stands are convertible into each 
 
 other by converting their Premises. The Middle Term if 
 22 R 
 
258 
 
 APPENDIX. 
 
 THE HAMILTONIAN ANALYSIS AND SCHEME 
 
 TABLE OP 8YLLO- 
 
 A. AFFIRMATIVE HOODS. 
 
 Fm. n. 
 
 and 11. are Balanced. B. The other mood* are Unbalanced. Of theae, 
 
SYLLOGISTIC NOTATION. 
 
 259 
 
 OF NOTATION FIGURED SYLLOGISM* 
 
 QISTIC MOODS. 
 
 A. AFFIRMATIVE MOODS. 
 FlG. III. 
 
 X 
 
 X 
 
 X 
 
 0: 
 
 B. NEGATIVE HOODflL 
 
 ?ffl. 
 
 rii. 
 
 ML and IT. are unbalanced in termi only, nat in propositions; the rct io btk. 
 
260 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." 
 
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