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 This book is DUE on the last date stamped below 
 
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 Form I. 9-5///-7,'23
 
 LOGIC 
 
 OR THE 
 ANALYTIC OF EXPLICIT REASONING 
 
 BY 
 
 GEORGE H. SMITH 
 
 AUTHOR OK "ELEMENTS OF RIGHT AND OF THE LAW," "A CRITICAL 
 
 HISTORY OF MODERN ENGLISH JURISPRUDENCE," "THEORY 
 
 OF THE STATE," AND OTHER WORKS 
 
 i3331 
 
 'QtNAM'S S 
 
 G. P. PUTNAM'S SONS 
 NEW YORK AND LONDON 
 fnucfcerbocfcer prees 
 1901
 
 COPYRIGHT, 1901 
 
 BY 
 
 GEORGE H. SMITH 
 
 Che Ytnicherbocfcer press, flew
 
 v PREFACE 
 
 IT is well known to those conversant with 
 the current literature of Logic that recent 
 logical theories diverge widely from the old 
 Logic of Aristotle and the Schoolmen, and no 
 less widely from each other. From this it hap- 
 pens that, under the common name of Logic, 
 we have many doctrines essentially different 
 from each other ; and the student who desires 
 to enter upon the study of the subject is thus 
 confronted with the preliminary problem of 
 determining under what name the true Logic 
 is to be found. Nor in this case can he expect 
 much help from his instructors; who, like the 
 rest of the logicians, are hopelessly at a loss. 
 Whether he shall study Logic whatever may 
 be his wishes and his determination must 
 therefore be a matter for chance to determine. 
 And, even should he be so lucky as to light 
 on a place where something like Logic is 
 taught, it will probably be taught in so muti- 
 lated a form and so mingled with extraneous, 
 and even inconsistent matter, that it will be
 
 IV PREFACE 
 
 impossible for him to understand it or to ap- 
 preciate its utility. Hence, if the plain truth 
 is to be told, Logic, in the true sense of the 
 term, is no longer taught or learned anywhere; 
 but has become a lost art. 
 
 But while the logicians of the day are thus 
 at variance among themselves, there is un- 
 fortunately one point in which they agree 
 with each other, and also with Whately and 
 others of the older logicians. This consists in 
 the opinion that Logic is a purely formal 
 science, and as such concerned only with the 
 forms, and not with the matter or content of 
 language or of thought; or, in other words, 
 that it does not deal with what is thought or 
 expressed, but with the forms of the thought 
 or expression only. From this it must follow 
 if the view be accepted that Logic, except 
 merely as an improving mental exercise, can 
 be of no practical utility; and this indeed is 
 commonly asserted and always implied in the 
 Logics of the day; which, though essentially 
 different in other respects, agree in this. And 
 from this again it must follow as on this view 
 was irresistibly argued by Locke, Stewart, 
 Reid, and others that the subject is unworthy 
 of the serious attention of rational men ; which, 
 on the premises assumed, has indeed come to 
 be the verdict of the common sense of man- 
 kind. Thus the student is discouraged from
 
 PREFACE V 
 
 the study of the subject not only by the con- 
 fusion reigning over it and the almost insur- 
 mountable initial difficulty of recognizing the 
 true Logic among so many pretenders, but 
 by the conviction impressed upon him by an 
 irresistible argument and by the practically 
 unanimous teachings of logicians, that Logic 
 cannot be put to any practical use. 
 
 The view taken of Logic in this work is dif- 
 ferent. It is what I conceive to be the ancient 
 and orthodox view, that Logic has to deal with 
 the matter as with the forms of thought and its 
 expression ; that it embraces in its scope every- 
 thing that touches the right use of words, as 
 instruments of reasoning, or, in other words, 
 the whole subject of explicit reasoning or ratio- 
 cination ; that it is the science fundamental to 
 all others and essential to all who, in the search 
 after truth, would pass beyond the mere evi- 
 dence of their senses; that, in its educational 
 aspect, it is not only an essential part, but the 
 very foundation of rational education ; and 
 finally that, in use, it is indispensable to the 
 rectitude of thought and of life. Hence, of 
 all branches of learning, I believe it to be of 
 the largest practical utility to man, and that 
 all the learning of the day cannot compen- 
 sate for its loss; and also that its decadence 
 in modern times has been one of the great 
 calamities of mankind. All this I attempt to
 
 vi PREFA CE 
 
 establish and to illustrate practically in the 
 following pages; to which I must refer for 
 the complete proofs; but perhaps something 
 towards this end may be effected in advance 
 by explaining briefly how the work came to be 
 written. 
 
 In the investigation of Jurisprudence, Poli- 
 tics, and Morality generally to which my 
 studies have been principally devoted two 
 important facts were forced on my attention, 
 that seem to establish my present thesis: 
 
 (i) The first of these was that the prevailing 
 errors in the theory of Politics, Sociology, and 
 Morality, and the Moral Sciences, or Science 
 of Human Nature, generally, have their 
 sources, almost always, in merely logical fal- 
 lacies, and may be readily refuted by the ap- 
 plication of familiar logical principles; all of 
 which will be practically illustrated in treating 
 of the fallacies. Here, then, I think, we have 
 a practical proof of the indispensable utility 
 of Logic, and the consequent refutation of the 
 error that it deals only with the forms of 
 thought or expression. For it is known to all 
 logicians that the most serious and pernicious 
 of the recognized fallacies are those that relate 
 to the matter expressed in language, and are 
 therefore called the material fallacies; which 
 by logicians generally are admitted into Logic, 
 but, as it were, on sufferance only.
 
 PREFACE vii 
 
 (2) The second fact I learned was that, 
 though it is impracticable to refute such errors 
 otherwise than by the application of logical 
 principles, yet owing to the logical decadence 
 of the age, and the general disuse of Logic, 
 this mode of refutation is unavailable. Hence 
 under existing conditions, there is no practical 
 means of stemming the tide of moral and politi- 
 cal heresy with which, with increasing violence, 
 mankind is being afflicted; and from this it 
 follows, as a necessary inference, that the first 
 step towards reform of doctrine, or life, in any 
 direction, must be a revival of the study and 
 use of Logic. My work therefore is the result 
 of a profound realization of this practical neces- 
 sity, and of the imperative demand thus result- 
 ing. Nor however interesting the theory of 
 Logic may have been to me have I ever lost 
 sight of what I conceive to be the most import- 
 ant aspect of the subject, namely, its supreme 
 practical utility. 
 
 Generally, the object of the work is to vindi- 
 cate, as against modern innovations, the old or 
 traditional Logic. This constitutes a perfectly 
 definite body of doctrine, rivalling in accuracy 
 and in demonstrative force the Geometry of 
 Euclid. Nor are there wanting treatises in 
 which its theory and application are, on the 
 whole, well explained, as, e. g., notably 
 Whately's work; which, notwithstanding some
 
 Vlil PREFACE 
 
 manifest defects, still remains, not only the 
 best, but the only elementary exposition of 
 Logic, in the English language, that can be 
 recommended to the student. But there are 
 many reasons why a mere reproduction of the 
 older works would be inadequate for our present 
 occasions, to some of which I will briefly ad- 
 vert. 
 
 The first of these relates to the error, already 
 considered, that prevailed with many of the 
 old logicians, as with the new, that Logic is 
 concerned only with the forms, and not with 
 the matter of thought, or its expression. For, 
 though this defect was supplied by the old 
 logicians, at the expense of their consistency, 
 by their admirable exposition of the doctrines 
 of Definition and of Classification and Division 
 and of the Term generally, and of the Material 
 or so-called Non-logical Fallacies, yet their 
 theory of Logic remained incomplete, and 
 Logic was thus mutilated of some of its most 
 vital parts. 
 
 Again, the searching investigation to which 
 the old Logic has been subjected by modern 
 logicians, though its general effect has been to 
 vindicate its substantial truth and to re-estab- 
 lish it on a broader and firmer basis, has yet 
 resulted in several additions to logical doctrine, 
 to which it is essential that the attention of the 
 student should be directed. Hence, while one
 
 PREFACE ix 
 
 of the principal objects of this work is to vindi- 
 cate the truth and the supreme utility of Logic 
 as anciently conceived, it is also contemplated 
 to supply the radical defect I have alluded to, 
 and, at the same time, to incorporate with the 
 old Logic the approved results of modern re- 
 search ; some of which are of great importance. 
 It remains to add a few words as to the 
 method and style with which the subject of 
 the work is treated. Logic is admittedly a 
 demonstrative or apodictic doctrine, and should 
 therefore be treated by the method appropriate 
 to subjects of that nature. This consists in the 
 accurate formulation of our premises, and in 
 reasoning rigorously from them, as in geome- 
 try. But this method demands the use of 
 a style altogether different from that in com- 
 mon use; which may be called the popular or 
 rhetorical. For it is the peculiar characteristic 
 of the logical style that it must be accurate or 
 aphoristic, i. e., that it must express the exact 
 truth without any admixture of error. For 
 the same truth holds good in ratiocination, as 
 in nature generally, that hybrids are unprolific; 
 and hence the slightest admixture of error in 
 our premises will render them altogether use- 
 less for logical inference. Our method will 
 therefore demand the exact analysis of the 
 terms we use and the formal statement of our 
 propositions; which to the general reader is
 
 X PREFACE 
 
 distasteful. For while the logical style ad- 
 mits, and even requires, great brevity of ex- 
 pression, so that, in general, volumes of 
 ordinary disquisition may, by means of it, be 
 compressed into a brief space, yet it demands 
 a degree of attention and independent thought 
 that only a few highly trained or exceptionally 
 gifted minds are willing to give, or perhaps 
 without great exertion are capable of giving. 
 But this is nevertheless essential to the fruitful 
 study of Logic, as of apodictic science gener- 
 ally. There is no royal road to Logic any 
 more than to Geometry. 
 
 The best type of this style is found in the 
 Mathematics, and especially in the writings of 
 Euclid and the geometers, whose style and 
 method I have sought to emulate, with what 
 success remains to be judged. I trust, how- 
 ever, I may, without vanity, say of the result, 
 with Hobbes, that while " there is nothing I 
 distrust more than my elocution, nevertheless 
 I am confident, excepting the mischances of 
 the press, it is not obscure." 
 
 GEORGE H. SMITH. 
 
 Los ANGELES, February 26, 1900.
 
 CONTENTS 
 
 INTRODUCTION OF THE FUNCTION OF 
 
 LOGIC i 
 
 BOOK I 
 
 THE ANALYTIC OF RIGHT REASONING 
 
 CHAPTER I 
 RUDIMENTARY NOTIONS .... 23 
 
 CHAPTER II 
 DOCTRINE OF THE TERM 
 
 I OF THE NATURE OF THE TERM 
 II OF THE SEVERAL KINDS OF TERMS 
 III OF THE ANALYSIS OF TERMS 
 
 CHAPTER III 
 
 DOCTRINE OF THE PROPOSITION . 
 
 I RUDIMENTS OF THE DOCTRINE . 
 II SEVERAL THEORIES OF PREDICATION 
 III OF THE PREDICABLES 
 IV OF THE RELATIONS BETWEEN TERMS 
 
 33 
 
 33 
 
 40 
 
 44 
 
 5 1 
 
 55 
 61 
 
 64 
 
 xi
 
 Xll CONTENTS 
 
 CHAPTER IV 
 
 PAGE 
 
 DOCTRINE OF THE SYLLOGISM ... 74 
 
 I RUDIMENTS OF THE DOCTRINE ... 74 
 
 II THE PRINCIPLE OF SUBSTITUTION . . 77 
 
 III OF MATHEMATICAL REASONING ... 85 
 
 CHAPTER V 
 SUMMARY OF THE TRADITIONAL LOGIC . 91 
 
 I OF THE TRADITIONAL LOGIC GENERALLY . 91 
 II THE TRADITIONAL DOCTRINE OF THE PROP- 
 OSITION ...... 92 
 
 III THE TRADITIONAL DOCTRINE OF THE SYL- 
 LOGISM > ... 104 
 
 BOOK II 
 APPLIED LOGIC 
 
 PART I 
 
 OF THE METHOD OF LOGIC 
 
 CHAPTER VI 
 OF THE LOGICAL PROCESSES . . . 123 
 
 CHAPTER VII 
 THE RULES OF LOGIC 137 
 
 I OF THE RULES OF LOGIC GENERALLY . 137 
 
 II RULES OF JUDGMENT .... 142 
 
 III RULES OF INFERENCE .... 145
 
 CONTENTS Xlll 
 
 PART II 
 DOCTRINE OF THE FALLACIES 
 
 CHAPTER VIII 
 
 PAGE 
 
 DEFINITION AND CLASSIFICATION OF FAL- 
 LACIES ....... 149 
 
 CHAPTER IX 
 
 FALLACY OF NON-SIGNIFICANCE, OR NON- 
 SENSE 157 
 
 CHAPTER X 
 FALLACY OF FALSE DEFINITION . . . 168 
 
 CHAPTER XI 
 ILLICIT ASSUMPTION OF PREMISES (Petitio 
 
 Principii] . . . . . 175 
 
 CHAPTER XII 
 MISTAKING THE ISSUE AND IRRELEVANT 
 
 CONCLUSION (Ignoratio Elenchi} . .188 
 
 CHAPTER XIII 
 ILLICIT CONVERSIONS ..... 198 
 
 CHAPTER XIV 
 
 ILLICIT SUBSTITUTIONS OF TERMS . . 200 
 CHAPTER XV 
 
 EQUIVOCATION 203 
 
 CHAPTER XVI 
 
 THE TRADITIONAL DOCTRINE OF FALLACIES. 210 
 
 I ARISTOTLE'S CLASSIFICATION OF FALLACIES . 210 
 
 II FALLACIES in Dictione (EQUIVOCATION). . 214 
 
 III OF THE FALLACIES extra Dictionem . .219
 
 LOGIC, OR THE ANALYTIC OF 
 EXPLICIT REASONING 
 
 INTRODUCTION 
 
 OF THE FUNCTION OF LOGIC 
 
 i. THE THEORY OF KNOWLEDGE, A DE- 
 PARTMENT OF THE THEORY OF OPINION. 
 The problem of the origin and nature of 
 knowledge has occupied the attention of the 
 philosophers for something over twenty-five 
 centuries without much progress toward solu- 
 tion. This perhaps results from the fact that 
 the problem itself is but part of a larger prob- 
 lem" that should be first considered; for know- 
 ledge is but a species of opinion, which may be 
 either true or false. Hence the inquiry as to 
 the origin and nature of opinion must be the 
 first in order of investigation. Nor until this 
 investigation has been made will we be pre- 
 pared to determine the specific characteristics
 
 2 LOGIC 
 
 by which true knowledge is differentiated from 
 opinion in general. 
 
 2. KNOWLEDGE BUT VERIFIED OPINION. 
 Men generally confound this distinction, and 
 regard all their settled opinions or beliefs as 
 knowledge. This is not merely false, but ab- 
 surd ; for not only do the opinions of men 
 differ, but the opinions of the same man are 
 often inconsistent and contradictory ; and 
 some, it is clear, must be false. And this is 
 apparent also from the nature and generation 
 of our opinions. For, in general, these come 
 to us not from any conscious process, but 
 naturally and spontaneously and from many 
 sources, as, e. g., from testimony, from author- 
 ity, from inaccurate observation or careless 
 reasoning, and even largely from mere pre- 
 judice or bias. Hence, familiar to us as our 
 opinions are, their origin in general is as un- 
 known to us as were anciently the sources of 
 the Nile; nor have we any just notion of the 
 grounds on which they rest, or of the nature 
 and justice of their demands on our belief. 
 Hence, until some means of verifying our 
 opinions be found and applied, we can have 
 no assurance of their rectitude. The first step 
 in Science or Philosophy must, therefore, be 
 to distinguish between verified and unverified 
 opinions. The former constitutes true know- 
 ledge or science ; the latter though it is in
 
 INTRODUCTION' 3 
 
 fact the stuff out of which most of the current 
 philosophy is woven has no just pretension 
 to the name. 
 
 3. THE SOURCES OF OPINION DISTIN- 
 GUISHED. With regard to the source of our 
 opinions, we must distinguish between those 
 derived from our own experience and those de- 
 rived from the experience of others; of which 
 those derived from the common experience of 
 mankind are the most extensive and important. 
 The last have come to us by means of lan- 
 guage, which may therefore be said to be 
 their source; nor could they otherwise have 
 been transmitted to us. The former constitute 
 comparatively speaking but a small and in- 
 significant part of the sources of the mass of 
 our opinions. For the greater part of what 
 we know, or think we know, is not original 
 with us, but has come to us from others by or 
 from language. The distinction, therefore, is, 
 not between opinions derived from experience 
 and opinions not so derived, for it may be 
 said all opinions that are true, or rather that we 
 know to be true, are derived ultimately from 
 experience, 1 but in the manner of their deri- 
 vation ; the one class being those opinions de- 
 rived by us, each from his own experience, the 
 other, those derived not directly from our own, 
 
 1 The distinction made in the text is of fundamental import- 
 ance. The necessity of a constant resort to experience as the
 
 4 LOGIC 
 
 but from the experience of others from or 
 through language. 
 
 4, OF LANGUAGE AS A RECORD OF 
 HUMAN THOUGHT. Of the two classes of 
 opinions, the latter is infinitely the more ex- 
 tensive in scope and important in character; 
 for all that men have seen or thought or felt 
 has been expressed, and is thus preserved to 
 us in language; which thus constitutes, as it 
 were, the record of the results of all human 
 experience and reason. Here, therefore, is to 
 be found the principal source of our opinions, 
 verified and unverified that is to say, not 
 only of our opinions generally, but of our 
 knowledge or science. But, regarding lan- 
 guage as a record and source of opinion, we 
 must distinguish between the forms in which 
 opinion is embodied in it. These forms may 
 be described, with sufficient accuracy for our 
 purposes, as consisting in terms, propositions, 
 and syllogisms. But of these the syllogism in 
 its end and effect is but the reduction of two 
 
 ultimate source of our knowledge cannot be too strongly in- 
 sisted upon. But to construe this proposition as referring to 
 each man's individual experience is to fall into an error of the 
 kind called by Bacon " Idols of the Den" ; and thus to fall 
 under the reproach of Heraclitus " that men search for know- 
 ledge in lesser worlds, and not in the greater or common 
 world," i. e., the great world of the common notions of man- 
 kind, derived from the universal experience and embodied in 
 the common language. (Nov, Org., bk. i., aph. xliii.)
 
 IN TROD UC TION 5 
 
 propositions to one, and, in this connection, is 
 of interest to us merely as exhibiting one of 
 the modes in which opinion is.formed. It will 
 be sufficient, therefore, to distinguish the term 
 and the proposition as the two forms in which 
 opinions, or the elements of opinions, are em- 
 bodied. But the proposition is itself of two 
 kinds, differing essentially in nature. In the 
 one if not an inference it is simply the state- 
 ment of a relation intuitively perceived to exist 
 between two terms or names, that is to say, 
 between the notions or concepts denoted by 
 them, as, e. g., where we say, " Bodies are 
 affected by gravity," or " Two islands cannot 
 be contiguous," or " Fishes live in the sea," 
 or " Man is rational"; in the other, it is a 
 statement of a relation between terms, not in- 
 tuitively perceived or logically inferred but 
 assumed to be true from testimony or other- 
 wise, as, e. g., where we say, '' Brutus was 
 one of the murderers of Caesar," or " Hannibal 
 was conquered by the Romans." The former 
 - in accordance with the definitions used 
 throughout this work will be called a judg- 
 ment ; the latter, an assumption. In the former 
 case the truth of the proposition is involved in 
 the meanings of the terms, i. e., in the nature 
 of the concepts or notions denoted by them ; 
 and this is true also of all inferences, or propo- 
 sitions inferred from judgments. So that with
 
 6 LOGIC 
 
 relation to all such propositions, whether in- 
 tuitively perceived or inferred, the original 
 sources of opinion are the notions or concepts 
 in which they are involved. We may therefore 
 distinguish, as the two sources of opinion af- 
 forded us by language, (i) the notions or con- 
 cepts expressed in terms, and (2) assumptions, 
 or assumed propositions. 
 
 With the truth of the latter, or the evidence 
 on which they rest for credence, Logic is not 
 concerned; nor is it concerned with them in 
 any way, except as premises from which to 
 argue ; or to reject them as such, if they can be 
 shown by logical processes to be false. But 
 where such propositions are justified by experi- 
 ence, and come thus to be generally received, 
 the result universally, or almost universally, is 
 the generation of a new notion, i. e., the 
 notion of the relation perceived between its 
 terms; which is either expressed in a new term 
 or added to the content or meaning of an exist- 
 ing term; and this, indeed, to the extent it is 
 attainable, is the end of science, and, in a per- 
 fect language, were such attainable, would 
 be the general result. Thus the general pro- 
 gress of human thought consists largely in the 
 conversion of propositions into terms or names 
 denoting the relations expressed in them ; and 
 hence, generally, in terms are contained many 
 propositions, as, e. g., in " gravity," ' justice,"
 
 INTRODUCTION / 
 
 etc. in the former of which is contained a large 
 part of Physical Science, and in the latter nearly 
 the whole theory of the State. In this way the 
 stock of the common notions of mankind is 
 continuously accumulated, until it may be said 
 that the great part of all that has been achieved 
 in thought by men is expressed or implied in 
 terms or names. Here,' therefore, are to be 
 found the principal sources of opinion ; and, 
 compared with these, opinions embodied in 
 propositions that cannot be, or have not been, 
 reduced to single notions are limited in ex- 
 tent, and of secondary importance. And this 
 is especially true with regard to the Moral 
 Sciences; under which name I include all the 
 various branches of the science of human 
 nature; for in these sciences it is impossible 
 to conceive of any rudimentary notion or 
 thought that has not, in the long history of 
 man, been conceived by the human mind and 
 embodied in terms. With reference, therefore, 
 to all that has been achieved in science or in 
 popular thought, the sources of all our opin- 
 ions, verified and unverified, that is to say, 
 of all our knowledge or supposed knowledge, 
 are to be sought in language, and, prin- 
 cipally, in the notions expressed in terms or 
 or names ' ; and consequently, with reference to 
 
 1 If the reader will thoroughly apprehend this proposition, 
 he will find in it the key, not only to Logic, but to all Phil-
 
 8 LOGIC 
 
 knowledge or supposed knowledge of this kind, 
 our method must consist in the study of lan- 
 guage. 
 
 5. RECEIVED OPINION DISTINGUISHED 
 FROMTRUE KNOWLEDGE. Our opinions, how- 
 ever, are derived from this source in two ways, 
 which must be distinguished : namely, by tradi- 
 tion, by which our opinions are delivered to 
 us ready made in the form of propositions, 
 and by reasoning upon the notions embodied 
 in terms. For the thought contained in lan- 
 guage is embodied in two ways, namely, 
 explicitly, in the form of propositions, and 
 implicitly, in terms;, and of propositions, as 
 we have seen, many are but explicit state- 
 ments of what is implied in the notions 
 
 osophy. The elements of knowledge, so far as already 
 achieved, we repeat, are the notions or concepts incarnate in 
 terms ; and these must always constitute the principal source 
 of our knowledge ; for, in comparison with the knowledge 
 thus expressed or implied, the original contributions of the 
 most gifted of men to the common stock must be inconsider- 
 able. Nor can any such contribution to the knowledge of 
 mankind be regarded as completely achieved until embodied 
 in definite terms ; and hence the formation of such terms, or, 
 what is the same, of the notions embodied in them, must be 
 regarded as the end of scientific discovery. There is, there- 
 fore, nothing paradoxical in the assertion of Condillac that 
 " Science is but language well made." Hence, to repeat what 
 has been said, it is to the common stock of notions thus gradu- 
 ally accumulated by mankind and permanently secured by ex- 
 pression in terms, that we must resort as the principal source 
 of all knowledge or science. See Appendix A.
 
 INTRODUCTION 9 
 
 expressed in terms, as, e. g., in the prop- 
 osition, " All bodies are affected by grav- 
 ity," etc. With reference to these, though 
 they may be true, their mere reception cannot 
 be said to constitute knowledge; but in the 
 proper sense of the terms we can know them 
 only when we have reasoned them out for our- 
 selves from the primary notions in which they 
 are involved; as, e. g., in the Mathematics, 
 where we cannot be said to have mastered a 
 theorem until we are able to work it out from 
 the premises by the exertion of our own powers 
 unassisted by memory. With reference to all 
 that has been achieved in thought, therefore, 
 our method in the pursuit of knowledge must 
 begin with the apprehension of the notions 
 already formed by men and embodied in terms; 
 and this involves the testing of those notions 
 for ourselves by comparing them with the 
 realities to which they are supposed to corre- 
 spond. 
 
 $ 6. THE PHYSICAL AND MATHEMATICAL, 
 DISTINGUISHED FROM THE MORAL SCIENCES. 
 -These observations apply equally to the 
 Physical and Mathematical as to the Moral Sci- 
 ences ; but there are differences, partly essential 
 and partly accidental, between the two classes 
 of sciences, which must be adverted to ' : 
 
 (i) In the Physical Sciences and in the 
 
 1 See Appendix B.
 
 IO LOGIC 
 
 Mathematics, technical terms expressing ac- 
 curately the concepts or notions involved are 
 exclusively used, but in the Moral Sciences it 
 is otherwise; for there the notions developed 
 by the experience and reasoning of mankind 
 which must always constitute the principal 
 source of our knowledge are in general loosely 
 and inaccurately expressed, and the same vocal 
 sign, or vocable, is commonly used to denote 
 many different notions more or less nearly re- 
 lated ; nor, with reference to these, does the 
 term in general express the notion accurately. 
 Hence the necessity of definition, which is at 
 once the fundamental and the most difficult 
 of the logical processes. But in the Physical 
 Sciences the notion is always accurately defined 
 by the thing itself; and so in the Mathematics, 
 though highly abstract, our notions are always 
 clearly defined. Thus in these sciences the 
 logical processes are so simple that it is impos- 
 sible to err, unless by inadvertence, and all 
 errors are quickly corrected ; and hence a tech- 
 nical knowledge of Logic is but little needed.' 
 But in the Moral Sciences it is different, for 
 here the difficulty of defining our terms is 
 
 1 Hence, from disuse of the more difficult of the logical 
 processes, a man in the former case, may be a competent 
 naturalist without being much of a reasoning creature ; and 
 in the latter, a great mathematician and yet a child in the 
 practical affairs of life, individual and social.
 
 IN TROD UC TION 1 1 
 
 great, and often insuperable, and hence, in the 
 prosecution of these sciences, Logic must 
 always be an indispensable instrument. 
 
 (2) To a certain extent this difference be- 
 tween the two classes of sciences is an essential 
 one, and cannot be altogether removed. But 
 to a large degree the Moral Sciences are sus- 
 ceptible of apodictic treatment, and by such 
 treatment may be indefinitely assimilated in 
 nature to what are commonly called though 
 not exclusively entitled to the name the 
 Exact Sciences; for a large part of the Moral 
 Sciences, including nearly all the fundamental 
 principles upon which they rest, are purely 
 apodictic. For, though it is commonly sup- 
 posed there is an essential difference between 
 Mathematical and what is called Moral Reason- 
 ing, this is not true; all ratiocination (not fal- 
 lacious) is essentially of the same character and 
 equally conclusive. 1 
 
 (3) Hence it may be observed as a corollary, 
 
 1 This is much insisted upon by Locke : " Confident I 
 am," he says, "that if men would, in the same method, and 
 with the same indifferency, search after moral, as they do after 
 mathematical truths, they would find them to have a stronger 
 connection, one with another, and a more necessary conse- 
 quence from our clear and distinct ideas, and to come nearer 
 a perfect demonstration than is commonly supposed " (Essay, 
 bk. iv., chap, iii., 20). "By what steps we are to proceed 
 . . . is to be learned in the school of the mathematicians, 
 who, from very plain and easy beginnings, by gentle degrees,
 
 12 LOGIC 
 
 the principal task before us, with reference to 
 the Moral Sciences, is to reduce them as far as 
 possible to apodictic or scientific form. This, 
 under present conditions, will still leave an im- 
 mense field of investigation in which we must 
 resort directly to experience, and especially to 
 experience as embodied in history and statis- 
 tics; but until all that is susceptible of being 
 so reduced is reduced to scientific form, no 
 progress can be made in dealing with matters 
 depending upon experience. 
 
 (4) With regard to the Physical Sciences 
 another difference is to be noted, namely, 
 between what has been achieved and the dis- 
 covery of new facts; with reference to which 
 the instrument of discovery is mainly experi- 
 ment and observation, or, as it is commonly 
 called, the Inductive Method. In this respect 
 these differ from the Moral Sciences, where, 
 though the same method must always be used, 
 its function is confined chiefly to the process of 
 definition. 1 
 
 and a continued chain of reasonings, proceed to the discovery 
 and demonstration of truths that appear at first sight beyond 
 human capacity " {Id., bk. iv., chap, xii., 7, 8). " This gave 
 me confidence to advance the conjecture which I suggest, 
 Chap, iii., viz., that Morality is capable of demonstration as 
 well as Mathematics." 
 
 1 The nature of Logic, and of the relation of the Inductive 
 Method to Logic, is thus precisely expressed by Bacon : 
 
 " The syllogism consists of propositions, propositions of
 
 INTRODUC TION 1 3 
 
 7. OF THE MODES IN WHICH OPINION 
 is GENERATED. With reference to results 
 achieved and embodied in language, and to 
 our opinions generally, the process by which 
 our notions or concepts are derived is the re- 
 verse of what is commonly supposed. In the 
 discovery of new facts, or the formation of new 
 concepts, we commence with the conception of 
 the concrete, and, the concept being formed, 
 we find the name. But this, in the develop- 
 ment of thought at which we have arrived, can 
 occur only in the Physical Sciences. For, as 
 we have observed, it is hardly probable that 
 in the Moral Sciences any rudimentary thought 
 can ever occur that has not already occurred 
 to some one and been expressed in language. 
 Hence, with regard to all matters dealt with 
 in the Moral Sciences (as also in the Physi- 
 cal Sciences with regard to results already 
 achieved), the order of our cognitions is, first, 
 to learn the words, /. e., the word-signs or 
 
 words, words are the signs of notions. If, therefore, the 
 notions (which form the basis of the whole) be confused and 
 carelessly abstracted from things, there is no solidity in the 
 superstructure. Our only hope then is in genuine induction " 
 (Nov. Org., bk. i., aph. xiv). 
 
 The subject is more fully developed in aph. lix., and beauti- 
 fully illustrated in aph. xcv. See also his doctrine of Idols, 
 aph. xxxviii. et seq. It may be observed here, in passing, that 
 no student of Philosophy, and still less of Logic, can afford to 
 neglect the first book of the Novum Organum or the De 
 A ugmentis.
 
 14 LOGIC 
 
 vocables, and afterwards, the concepts or 
 notions expressed in them.' 
 
 8. OUR SUPPOSED KNOWLEDGE OFTEN 
 NONSENSE. And as the latter function out- 
 side the Exact Sciences is in general very 
 lamely performed, the result is that the greater 
 portion of our supposed knowledge in abstract 
 matters consists of words without definite 
 notions attached to them, and is therefore 
 merely nonsense. For when we reason with 
 undefined or ill-defined terms we are dealing 
 with mere delusions or dreams like Ixion 
 embracing clouds and begetting monsters. 
 Thus, e. g. , when we assert, with Bentham and 
 Austin, that General Utility is the ultimate 
 test or principle by which the just and the un- 
 just and right and wrong generally are to be 
 determined, we are in fact talking nonsense; 
 for it cannot be determined from this expres- 
 sion whether we have in view the welfare of a 
 mere majority, or two thirds, or three fourths, 
 or other proportion of mankind, and hence 
 from this premise all sorts of extravagant 
 opinions are deduced. Hence the mass of us 
 
 1 The logicians, from and including Hamilton, have en- 
 tirely overlooked this distinction, and have thus substituted 
 for the old logical doctrine of Simple Apprehension, the psy- 
 chological doctrine of Conception, a doctrine necessary to be 
 understood, but which is concerned rather with the original 
 formation of language than with its use as an instrument of 
 reasoning.
 
 INTRODUCTION 15 
 
 generally, and all of us in many matters, like 
 Moliere's hero, who was surprised to find that 
 he had been talking prose all his life, have all 
 our lives been talking nonsense. 1 And this is 
 true not only of opinions commonly regarded 
 as nonsensical, but of all opinions involving 
 either undefined notions or notions to which 
 there are no corresponding realities. 
 
 9. THE CRITICAL SPIRIT ESSENTIAL TO 
 WISDOM. Our wisdom is therefore to be 
 measured, not by the extent of our learning, 
 or by knowledge of detached facts, or by vivac- 
 ity of thought or expression, or by the confi- 
 dence of our belief, but chiefly by the capacity 
 to judge our supposed knowledge, and to de- 
 tect its falsity or non-significance. In this way 
 Socrates modestly explained the oracle of the 
 Delphic god, that he was " the wisest of man- 
 kind." For, he said, he alone had discovered 
 that all men were ignorant, including himself; 
 but others mistook their ignorance for know- 
 ledge. 2 We conclude, therefore, as we began, 
 that what we regard as our knowledge consists 
 mainly of unverified opinions or beliefs, and 
 that however firmly these may be established, 
 
 1 See Appendix C. 
 
 2 As explained by Grote (cited infra, 16, App. H), the thesis 
 of Socrates was that " the natural state of the human mind " 
 is "not simply ignorance, but ignorance mistaking itself for 
 knowledge."
 
 l6 LOGIC 
 
 or however passionately they may be asserted 
 and believed, they do not necessarily, or even 
 generally, constitute true knowledge. Hence, 
 until we are enabled to distinguish the true 
 from the false, we can have no assurance of 
 their rectitude or truth. 
 
 10. LOGIC THE ULTIMATE TEST OR CRI- 
 TERION OF TRUTH. We must, therefore, 
 seek some tests or criterions if any there be 
 by which the truth or falsity of our beliefs 
 may be determined ; and of such two only can 
 be conceived ; namely, Experience and Reason- 
 ing, or Logic. Of these the former is more or 
 less efficiently used by men in general ; and in 
 concrete matters and in the ordinary familiar 
 affairs of life, its operation is moderately satis- 
 factory. For thus, by actual contact with the 
 hard facts of our experience, our opinions or 
 beliefs are, to a large extent effectually, and 
 often painfully, modified and corrected. But 
 the function of experience is simply to furnish 
 Reason with materials on which to work; and 
 of Reasoning, or Logic, as Hobbes says: " So 
 far are the mass of men from using it, that 
 they do not even know what it is." 
 
 1 " The most part of men, though they have the use of rea- 
 soning a little way, as in numbering to some degree, yet it 
 serves them to little use in common life ; in which they gov- 
 ern themselves, some better, some worse, according to their 
 differences of experience, quickness of memory, and inclina- 
 tion to several ends ; but especially according to good or evil
 
 IN TROD UC TION 1 7 
 
 ii. THE DECADENCE OF THE AGE IN 
 
 LOGIC AND THE MORAL SCIENCES. And this 
 is true not only of the common people, but of 
 the educated, and even of the philosophers and 
 the professors; who in the last century, owing 
 to the disuse of Logic, have in fact lost the 
 very idea of it; so that in our schools and 
 universities, under the name of Logic, any- 
 thing but Logic itself is taught, and it has thus 
 become a lost art. 1 Yet, obviously, in all 
 abstract matters, and especially in Morality, 
 Politics, and all the different branches of the 
 Science of Human Nature, experience, while 
 useful to us, can go but a little way, and 
 therefore Logic must be an indispensable in- 
 strument. Hence it is to the disuse of Logic 
 that the existing incoherent and chaotic state 
 of the Moral Sciences is to be attributed." It 
 may therefore be confidently hoped that by the 
 renewed use of Logic a revival of these sciences 
 is to be anticipated, vying in extent with that 
 of the concrete sciences in modern times, and 
 
 fortune, and the errors of one another. For as for 'science,' 
 or certain rules of their actions, they are so far from it that 
 they know not what it is" (Lev., chap. v.). 
 
 1 " We live in an age," says De Morgan, " in which formal 
 logic has long been banished from education ; entirely we 
 may say from the education of the habits." The proposition 
 is even truer of the present day ; for in De Morgan's time 
 there still survived some of the old style of logicians. 
 
 * See Appendix D.
 
 1 8 LOGIC 
 
 far surpassing them in practical utility to the 
 human race. 1 
 
 12. OF AUTHORITY AND PREJUDICE. I 
 would not, however, in thus explaining and 
 commenting upon the general dominance of 
 authority and prejudice over men, be under- 
 stood as altogether condemning it. Under 
 existing conditions, and perhaps under all con- 
 ditions, the opinions of the masses of mankind, 
 in Politics and other matters of common con- 
 cern, must be determined mainly by custom and 
 authority. Hence the distinction made by the 
 old philosophers between their esoteric and ex- 
 oteric doctrines; the latter consisting of those 
 that could be taught to the masses, the former, 
 of those that required the peculiar training of 
 the philosopher to comprehend a profound 
 distinction that has been lost in modern times. 
 But though it may not be possible, or perhaps 
 even desirable, to make all men philosophers, 
 yet it is possible to make the masses of them 
 logical in the matters with which they are con- 
 
 1 The argument of Demosthenes in the first Philippic may 
 be readily applied to the proposition asserted in the text : 
 " First I say, you must not despond, Athenians, under your 
 present circumstances, wretched as they are ; for that which is 
 worst in them as regards the past is best for the future. 
 What do I mean? That your affairs are amiss, men of 
 Athens, because you do nothing that is needful ; if, not- 
 withstanding you performed your duties, it were the same, 
 there would be no hope of amendment."
 
 INTRODUCTION 19 
 
 versant ' ; and for those who aspire to be lead- 
 ers of opinion, Logic is essential. For these, 
 if worthy of the function to which they aspire, 
 cannot afford to be deficient in this respect; 
 they must either be logicians, or false prophets, 
 or blind leaders of the blind. 
 
 13. PLAN OF THE WORK. Though I re- 
 gard the study of Logic as essential to the cul- 
 tivation and the use of the reasoning powers, 
 and hence as indispensable to the Moral Sci- 
 ences, yet it is chiefly as a test or criterion of 
 fallacy that I propose to treat it. This use of it 
 will, of course, necessitate some consideration 
 of the elementary principles and rules of Logic 
 as necessary to the understanding of the Doc- 
 trine of the Fallacies. But this part of my essay 
 will be abbreviated to the utmost extent con- 
 sistent with this object ; that is to say, I will 
 try to include everything essential to the under- 
 standing of the rudiments of Logic, but noth- 
 ing more. If I should fail in this, and anything 
 necessary should be omitted, the defect may 
 be readily obviated by reference to the work 
 of Whately, who, among elementary writers, 
 may be regarded (in any true sense of the 
 word) as the last of the logicians. 
 
 The subject will be treated in two books, the 
 first entitled " The Analytic of Right Reason- 
 ing," the second, " Applied Logic " ; the latter 
 
 1 See Appendix E.
 
 2O LOGIC 
 
 of which will include two subjects, namely: 
 ' The Method of Logic " and " The Doctrine 
 of the Fallacies," or " The Analytic of Wrong 
 Reasoning." In treating of the last, the ex- 
 amples of the several fallacies will be taken 
 almost exclusively from current theories of 
 Politics and Morality. Our examples will 
 therefore consist, not of mere trivialities, 
 such as are so common in books on Logic, 
 but of fallacies that, in perverting moral and 
 political theory and in corrupting practice, 
 have dominated, and still continue to domi- 
 nate, the fortunes of mankind. They come 
 to us, therefore, as veterans of what Hobbes 
 calls the " Kingdom of Darkness," crowned 
 with the laurels of victory. 1 
 
 1 Lev., chap. xliv. : see Appendix F.
 
 BOOK I 
 
 THE ANALYTIC OF RIGHT 
 REASONING 
 
 21
 
 BOOK I 
 
 THE ANALYTIC OF RIGHT 
 REASONING 
 
 CHAPTER I 
 
 RUDIMENTARY NOTIONS 
 
 14. DEFINITION OF LOGIC AND OF IN- 
 VOLVED TERMS. Logic is defined by Whately 
 as the science and also the art of reasoning. 
 Reasoning may be defined as consisting in the 
 exercise of the comparative or discursive fac- 
 ulty of the mind that is to say, the faculty by 
 which our notions or concepts are compared 
 with each other, and with the realities to which 
 they are supposed to correspond, and their re- 
 lations with each other, and with such realities 
 are perceived. Or we may define reason as 
 the faculty, and reasoning as consisting in its 
 exercise. 1 But Logic by which I mean the 
 
 1 The terms reason and reasoning, though conjugate, have 
 unfortunately been divorced by logicians, and, following 
 
 23
 
 24 LOGIC 
 
 traditional Logic is not to be regarded as 
 having to deal with reasoning in general, but 
 with explicit reasoning only, or ratiocination ; 
 which may be defined as reasoning expressed 
 in language, or, so far expressed that the miss- 
 ing parts are understood. Hence it is rightly 
 said by Whately that Logic is exclusively con- 
 versant with language; by which is meant, not 
 merely the signs of thought, but also the 
 thought signified. 1 This follows from the 
 definition, and also from considering the sev- 
 eral subjects of which it treats, which, by the 
 universal consensus of logicians, consist of the 
 Doctrines of the Term, of the Proposition, and 
 of the Syllogism. But all these are simply 
 parts or kinds of language. 
 
 15. RATIOCINATION DEFINED. But Ra- 
 tiocination, being a species of reasoning, must 
 consist in the comparison of concepts or 
 notions, and these, in order to fall within the 
 province of Logic, must, ex vi termini, be ex- 
 pressed in terms. Hence, Ratiocination must 
 be defined as consisting in the process of com- 
 
 them, by lexicographers generally ; and accordingly Locke 
 is blamed by Whately for confounding them. But in this 
 Locke is right, and the logicians wrong ; and the usage of the 
 latter has been the source of infinite confusion in Logic. As I 
 use the terms, Reason includes the faculties of Inference, 
 Judgment, and Simple Apprehension ; and Reasoning the 
 corresponding processes. 
 1 See Appendix G.
 
 RUDIMENTARY NOTIONS 2$ 
 
 paring terms, with the view of perceiving their 
 relations. And this necessarily implies, also, 
 the process of determining the meaning of the 
 terms compared, or, in other words, the process 
 of definition. 
 
 16. LOGIC DEFINED. Logic, regarded as 
 a theory, may, therefore, be defined as the 
 Analytic of Explicit Reasoning, or of Ratio- 
 cination meaning, by this expression, the 
 systematized results of an analysis of the pro- 
 cesses involved in ratiocination. 1 And its 
 practical end is to determine the meanings of 
 terms and the relations between the concepts 
 or notions denoted by them. 3 
 
 17. OF THE SEVERAL KINDS OF TERMINAL 
 RELATIONS. The relations between terms are 
 of two kinds, which may be called immediate 
 and inferred ; and the former, again, are of 
 two kinds, that, for lack of better names, may 
 be called intuitive and quasi-intuitive. 
 
 18. THE INTUITIVE RELATIONS OF TERMS. 
 Of the former kind are all those relations 
 between terms that are intuitively perceived 
 upon comparing them together, as, e. g., the 
 
 1 See Appendix H. 
 
 2 " Knowledge [is] but the perception of the connection and 
 agreement or disagreement or repugnancy of any of our ideas " 
 (Locke, cited 110 n. g. App. N). " Knowledge is not so 
 much increased by a continued accession of new ideas as by 
 perceiving the relations of those ideas which we have already 
 acquired " (Eunomos, cited Chitty's Blackstone, introd. note).
 
 26 LOGIC 
 
 relation of species and genus between the class 
 of beings denoted by the term man and the 
 class denoted by the term rational, or between 
 the classes denoted by the terms horse and 
 animal, or the relation of mutual exclusion 
 existing between the terms of the proposition, 
 No two islands can be contiguous." 
 19. JUDGMENT DEFINED. The perception 
 of a relation of signification between two terms 
 is called Judgment; which may be defined as 
 the intuitive perception of a significative rela- 
 tion between two terms. The result of the 
 process is called a judgment; which may be 
 defined simply, as a self-evident proposition. 
 
 20. THE QUASI-INTUITIVE RELATIONS 
 OF TERMS. Analogous to the intuitive rela- 
 tions of terms are the relations between the 
 terms of all assumed propositions, or assump- 
 tions; for these, though not intuitively true, 
 are assumed or supposed to be such for the 
 sake of the argument, and used as principles 
 from which to reason ; they may, therefore, be 
 regarded as quasi-intuitive^ Under this head 
 
 1 We borrow this form of expression from the lawyers, who 
 find it indispensable, as, e. g., in the expressions quasi-torts, 
 quasi-contracts" etc. As we are informed by Cicero, the 
 Epicureans held that the gods had not bodies, but quasi- 
 bodies only, i. e., something like bodies. An Indian com- 
 munity, I have read somewhere, were much annoyed by a 
 species of animal something like cows (nie/gkais, I believe 
 they called them) that destroyed their crops, and the question
 
 RUDIMENTARY NOTIONS 2J 
 
 are included all the relations between the terms 
 of propositions assumed as premises, whether 
 upon authority, or from testimony, or other- 
 wise, i. e., between the terms of all proposi- 
 tions other than those that are intuitively 
 perceived to be true, or that are inferred from 
 other propositions. 
 
 21. THE INFERRED RELATIONS OF 
 TERMS. The inferred relations of terms in- 
 clude all relations that cannot be intuitively 
 perceived from an immediate comparison of 
 the terms, or that are not assumed, but that 
 can be inferred by comparing the given terms 
 respectively with a third or middle term, the re- 
 lations of which to the given terms are known. 
 Thus, e. g., we may not be able to perceive 
 from a mere comparison of the two terms, that 
 " Logic is a branch of the Science of Lan- 
 guage," but by comparing the two terms of 
 the proposition respectively with the middle 
 
 arose whether it was lawful to kill them. The pundits to 
 whom the question was referred were of the opinion that, 
 though not cows, the animals were quasi-cows, and therefore 
 not to be killed. The term will be found to be of equal 
 utility in Logic as in the Law. In fact, a very useful book 
 might be written on the subject that might be appropriately 
 termed Quasics. For, outside of concrete notions, all notions 
 denoted by terms are formed by analogy from sensible images, 
 and are quasi-things only, as, e.g., imagination, reflection, 
 perception, etc. We suggest the term Quasics not with a view 
 of seriously recommending it for common use, but simply for 
 the purpose of directing attention to a very important subject.
 
 28 LOGIC 
 
 term, " The Science of the Term, the Proposi- 
 tion, and the Syllogism, ' ' the relation of species 
 and genus between the subject and the predi- 
 cate will be at once perceived. For" Logic is 
 the Science of the Term, the Proposition, and 
 the Syllogism," and " The Science of the 
 Term, etc.," is a species or kind of " the 
 Science of Language," and hence " Logic is 
 a species or kind (i. e., a branch) of the Science 
 of Language." And so we may not be able to 
 perceive from a mere comparison of the terms 
 that " the Thracians were barbarians, " but by 
 comparing these terms with the middle term, 
 " Not -Greeks," the conclusion is apparent ; for, 
 ex vi termini, all " Not-Grecks " were barba- 
 rians. So, generally, using the letters X, Y, Z, 
 etc., to represent the terms of any proposition, 
 we may not be able to perceive intuitively the 
 truth of the proposition that Z is X, yet, if it 
 be intuitively perceived or assumed that Z is 
 Y, and that Y is X, we may infer that Z is X. 
 22. PROPOSITIONS AND SYLLOGISMS. An 
 immediate relation of terms, whether intuitive 
 or assumed, can be expressed only in the form 
 of a proposition which may be defined simply 
 as the expression of such a relation ; and an 
 inferred relation, only in the form of three 
 propositions constituting what is called a syllo- 
 gism. The proposition may be expressed in 
 the formula: Y is X; and all syllogisms in the
 
 RUDIMENTARY NOTIONS 29 
 
 formula: Z is Y, Y is X, . * . Z is X; or, Z is 
 
 Y, Y is not X . . Z is not X the letters 
 standing for terms or names, and the three 
 points (. * .) being the sign of illation, and 
 equivalent to the expression, " ergo," or 
 " therefore." ' 
 
 23. OF APODICTIC AND DIALECTIC. Ra- 
 tiocination may consist wholly of judgments 
 and inferences, or partly of these and partly of 
 assumed propositions. In the former case it is 
 wholly illative, or demonstrative; in the latter, 
 
 1 To define a term (as indicated in the etymology of defini- 
 tion} is in effect to establish the boundaries by which the class 
 of significates denoted by it is separated from all other things ; 
 and these boundaries may be conveniently represented by 
 circles or other enclosed figures. These are known as Euler's 
 symbols, and are extremely convenient and universally used 
 by logicians. A universal affirmative proposition is expressed 
 by a circle contained in a circle, the former representing the 
 subject, the latter the predicate ; the universal negative by 
 two circles excluding each other ; and the syllogism, by thus 
 expressing its several propositions; as, c. g. , in the following 
 diagrams : 
 
 Affirm. Prop. Neg. Prop. 
 
 
 
 Neg. Syll.
 
 3O LOGIC 
 
 only partially so, i. e., only so far as the valid- 
 ity of the inference is concerned. The prin- 
 ciples governing the former kind of ratiocination 
 constitute what is called Apodictic ; those gov- 
 erning the latter, Dialectic. It will be seen as 
 we progress that Apodictic is far more extensive 
 in its scope or use than is commonly supposed, 
 and that it includes, in fact, not only the 
 Mathematical Sciences, both pure and applied, 
 but also a large part of Morality, Politics, and 
 Jurisprudence generally. And especially, it is 
 important to observe, it includes the subject 
 of our present investigations. For Logic, 
 though not so treated by modern logicians, is 
 strictly a demonstrative science, and will be so 
 treated in this essay. 1 
 
 24. VALID RATIOCINATION ILLATIVE IN 
 NATURE. All ratiocination, or reasoning ex- 
 plicitly stated, discloses at once its validity or 
 invalidity that is to say, appears on its face 
 to be either conclusive in its effect, or fal- 
 lacious. Hence, all ratiocination, unless fal- 
 lacious, is illative or conclusive, or, we may 
 say, demonstrative in its nature. On the other 
 
 1 One of the most universal infirmities of the average mind 
 is an incapacity to distinguish (outside the mathematics) be- 
 tween mere opinion and apodictic, or demonstrated truth. 
 With regard to the latter, the man who is conscientious and 
 accurate in his Logic may realize the fine saying of Seneca : 
 " It is truly great to have in one the frailty of a man and the 
 security of a god " (cited Bacon, Essays, " Of Adversity ").
 
 RUDIMENTARY NOTIONS 31 
 
 hand, unless explicitly stated, no reasoning, 
 however apparently convincing, can be re- 
 garded as of this. nature. Hence, from a logi- 
 cal point of view, reasoning in general may be 
 regarded as either valid (i. e., illative), or as 
 invalid; the latter of which may be either fal- 
 lacious or simply inconsequent. The former 
 may be appropriately called Logical Reason- 
 ing, the latter Non-logical or Rhetorical; by 
 which is meant not necessarily illogical or fal- 
 lacious, but either fallacious or simply inconse- 
 quent, i. e., non-illative. 
 
 25. RIGHT REASONING DEFINED. It is 
 with the former only that Logic is directly con- 
 cerned, and to it we may without impropriety 
 give the name of RigJit Reasoning. For the 
 logical quality of the reasoning does not de- 
 pend upon the truth or falsity of the conclusion, 
 but upon the rectitude of the definitions, judg- 
 ments, and inferences. 
 
 26. LOGIC THE ART OF RIGHT REASON- 
 ING. Logic, therefore, regarded as an art, 
 may be simply defined as the Art of Right 
 Reasoning; and it must therefore be regarded 
 as denoting the ultimate test or criterion of 
 truth or error. For until the reasoning is 
 made explicit, it cannot be determined whether 
 it is right or otherwise. It also includes the 
 doctrine of Fallacy, or Wrong Reasoning; 
 but as the latter has for its end simply the
 
 32 LOGIC 
 
 avoidance of error, as a means of assuring the 
 rectitude of our reasoning, it may be regarded 
 simply as one of the practical aspects of the 
 doctrine of Right Reasoning. 
 
 27. LOGIC TO BE REGARDED AS INTEL- 
 LECTUAL MORALITY. Logic must, therefore, 
 be regarded as bearing to reasoning the same 
 relation as Morality to conduct. It may, 
 therefore, be appropriately called Intellectual 
 Morality* 
 
 1 Hence it is that Logic, like Morality, is not popular with 
 those who disregard its precepts ; among whom are to be in- 
 cluded the large majority of writers, and especially of phil- 
 osophers. The principle is as expressed in the adage : 
 
 " What thief e'er felt the halter draw 
 With good opinion of the Law ?"
 
 CHAPTER II 
 
 DOCTRINE OF THE TERM 
 
 I 
 OF THE NATURE OF THE TERM 
 
 28. " TERM," " NAME," AND " WORD" 
 DISTINGUISHED AND DEFINED. These words 
 are often used as synonymous, but the distinc- 
 tion between them is material and important. 
 A word is a vocal sign, or vocable, express- 
 ing a thought, or a thought expressed by such 
 a sign. Under the name " word " is included 
 the substantive or noun, and also other parts of 
 speech, as, e. g., the article, the conjunction, 
 etc. A name (noun or substantive, which may 
 be either simple or complex'} is a word or set of 
 words used to signify an object of thought re- 
 garded as a thing, z. i\, as an existing substance 
 or entity. The knowledge or cognition of a 
 thing by the mind is called a notion or concept ; 
 hence a name may be otherwise denned as a 
 word, or set of words, expressing a notion, or 
 33
 
 34 LOGIC 
 
 as a notion thus expressed. A notion or con- 
 cept is itself a thought, but it differs from 
 other thoughts as being the thought of a thing, 
 i. e,, of something as existing. A term is a 
 name used as a subject or predicate of a pro- 
 position. It is therefore to be regarded merely 
 as an element of the proposition ; and the pro- 
 position as the principal subject in Logic. 
 
 29. "THING" DEFINED. The term 
 thing is used in two different senses that 
 must be carefully distinguished. In its proper 
 sense the term denotes an actual thing or sub- 
 stance, whether material or spiritual, as, e. g., 
 mineral, vegetable, animal, gas, man, soul, 
 God, etc. In this sense things constitute the 
 actual universe, and all notions or concepts 
 whatever, unless false or unreal, are ultimately 
 derived from them. But, in another sense, 
 the term is used to denote, not only actual 
 existences, or, as we may call them, real things, 
 but mere objects of thought, or things existing 
 only in contemplation of mind, and to which 
 there are, in fact, no real things directly cor- 
 responding. 1 These may be appropriately 
 
 1 All true or real notions must correspond to real or actual 
 things, but the correspondence may be either direct between 
 the notion and the real things signified by the term as in 
 the case of concrete terms, <?. g., " man," " horse," etc. ; 
 or indirect as in the case of abstract terms between the 
 notion and the things whose attributes are signified. Thus, 
 taking for example the term " redness ," there is apparently a
 
 THE TERM 35 
 
 called <7?/rt.$7- things; and of this kind are the 
 concepts or notions denoted by all abstract 
 terms; which denote, not real things or in- 
 dividuals, but mere abstractions, as, c. g., 
 such terms as " justice," " the state," the 
 names of the several colors, disease, death, 
 etc. ; where the things denoted are not actually 
 existing things, but mere concepts of qualities 
 or attributes of things objectified by the 
 mind. 
 
 30. " CONCEPT," " NOTION," AND 
 "THOUGHT" DEFINED. The term " con- 
 cept," or " notion," or " thought " (in this 
 connection we may use either indifferently) is 
 a relative term implying or connoting, in its 
 strict or proper sense, an individual thinking 
 mind of which it is the product; and hence 
 the term will have a different meaning accord- 
 ing to the correlative to which it refers. It 
 must therefore have many different senses; of 
 which two must be especially distinguished. 
 In its proper sense it denotes simply a certain 
 affection of the mind of the individual; and 
 in this sense, obviously, it is momentary and 
 evanescent, like the snow falling on the river, 
 described by the poet, as " ae moment white, 
 
 direct correspondence between the notion expressed and the 
 qttasi-\\\\ng signified, though in reality they are the same ; but 
 there is an indirect real correspondence between the notion of 
 redness and the red things of which it is a quality.
 
 36 LOGIC 
 
 then gone forever." For though, it is said, 
 the thought recurs to us, it is not, nor can it 
 be, the same thought, but is merely a copy or 
 image of it. So, when a thought as it is said 
 recurs to us, it is always, or at least almost 
 always, suggested to us by the word in which 
 it is embodied ; and, as to us, so also to others. 
 But Logic does not have to deal with the mo- 
 mentary, fleeting thought of the individual, 
 but with the thought only that is continuously, 
 or we may say permanently reproduced, and 
 communicated by one to another; that has be- 
 come incarnate in words, and is thus, even 
 when lost from the mind, at once preserved, 
 and continuously suggested, or brought back 
 to the consciousness of each and all. Hence, 
 in Logic, the terms, notion, concept, and 
 thought, are to be regarded as used in a 
 secondary or derived sense, as denoting the 
 common notions, concepts, and thoughts of 
 mankind embodied in words. Hence the things 
 or significates denoted by abstract and other 
 universal terms have in fact a kind of exist- 
 ence outside of any and all individual minds; 
 which, as opposed to substantial, may be called 
 logical existence ; i. e., they exist in the word 
 (logos], and their existence is as real and of 
 precisely the same nature as that of the word 
 of which they are an essential part. Hence, 
 though we speak of abstractions as fictitious
 
 THE TERM 37 
 
 (i. c. , feigned) or imaginary things, yet they 
 are real, and in some cases, as, e. g., in the 
 case of death, disease, misery, poverty, etc., 
 terribly real facts. What is meant by the term 
 "fictitious tiling " is, not that the notion signi- 
 fied is false or unreal, but that, for logical pur- 
 poses, it is fictitiously regarded as a thing. 
 
 31. THE NORMAL LOGICAL TERM. 
 Every term legitimate for logical purposes, 
 or we may say every logical term, is therefore 
 to be regarded as involving or implying three 
 essential notions or elements, namely; (i) the 
 vocal sign, or vocable, (2) the notion denoted, 
 and (3) the actual tilings, or objective realities, 
 to which the notion and the vocal sign are sup- 
 posed to correspond. These are all to be re- 
 garded as, in one sense, essential elements of 
 the logical term. For though, where the last 
 is lacking, a term may exist, and it is, there- 
 fore, possible to have an absurd or nonsensical 
 term, yet such a term is not such as is contem- 
 plated when we regard the end of Logic ; which 
 is not to deal with absurdities or ingenious 
 puzzles, but to discover truth and avoid error. 
 Hence, an absurd or nonsensical term, or, in 
 other words, a term whose signification does 
 not correspond to reality, is not the normal or 
 true term, essential to legitimate ratiocination; 
 nor is Los[ic unless in illustrating some of its 
 
 o o 
 
 formal operations in any way concerned with 
 
 43331
 
 38 LOGIC 
 
 it, except to detect and expose its inherent 
 vice and its essential insufficiency for logical 
 purposes. 
 
 32. THE DENOTATION AND CONNOTA- 
 TION OF TERMS. All terms are regarded in 
 Logic as denoting or signifying classes of in- 
 dividuals. 1 The individuals constituting the 
 class denoted by the term are marked or dis- 
 tinguished by certain common attributes, at 
 once common and peculiar to the class, as, 
 e. g., the class " man " by the mark ''rational," 
 by which it is distinguished from other kinds 
 of animals. Accordingly a term is said to 
 denote the individuals designated by it, and to 
 connote the qualities or marks by which the 
 class is determined. Thus, e. g., the term 
 " man-" denotes the class of animals known by 
 that name, and connotes the quality or attribute 
 of rationality by which the class is distin- 
 guished. 
 
 33. THE MEANING AND SIGNIFICATION 
 OF TERMS. The individuals constituting the 
 class denoted by a term are said to be signified 
 by the term, and are called its significates, 
 Thus the term, man, denotes the class, man, 
 as a whole, but signifies each and all of the in- 
 dividual men composing it. The significates 
 of a term may be real, which is the case when 
 they are real individuals or things, existing in 
 
 1 See infra, 35.
 
 THE TERM 39 
 
 nature; or they may be unreal, or fictitious, 
 i. e., existing only in contemplation of mind; 
 which is the case with all abstract terms, and 
 with concrete terms where the classes of indi- 
 viduals denoted are fictitiously regarded as in- 
 dividuals, as, e.g., when we speak of " man " 
 as one of the significates of "animal. " When 
 a term denotes a class of real individuals as, 
 t\ g.," man," regarded as denoting men gener- 
 ally its significates are real ; when it denotes a 
 class of lower classes as, e. g. , the several races, 
 Asiatics, Europeans, etc. they are unreal or 
 fictitious. In the former case the term is said 
 to denote an infima species ; which is to be de- 
 fined as a class made up of real individuals. 
 By the meaning of a term is meant both its 
 denotation, or signification, and its connotation 
 taken together; and the word " meaning" 
 may also be regarded as equivalent to notion 
 or concept. 
 
 34. THE EXTENSION AND INTENSION OF 
 TERMS. The extension of a term corresponds 
 to its denotation, or signification, and is deter- 
 mined by the extent of Ihe class denoted, or 
 by the number of significates signified by it. 
 The intension of a term is but another name 
 for its connotation, both words denoting 
 merely the qualities or attributes, or, in other 
 words, the marks by which the class is deter- 
 mined.
 
 40 LOGIC 
 
 II 
 
 OF THE SEVERAL KINDS OF TERMS 
 
 35. SINGULAR, AND COMMON, OR UNI- 
 VERSAL, TERMS. Grammatically speaking, 
 terms are said to be either singular or common, 
 or, as otherwise expressed, singular or uni- 
 versal. A singular term is one that denotes 
 an individual or single thing, as, e. g. , any par- 
 ticular thing, animal, or man. A common or 
 universal term is one that denotes either a class 
 of individuals or a class made up of other 
 classes. But in the latter case, the subordinate 
 classes may be regarded as individuals consti- 
 tuting the superior class; and conversely the 
 individual may always be regarded as a class, 
 /. e., a class of one. 1 In this work, therefore, 
 the distinction between singular and common 
 or universal terms will be regarded as logically 
 immaterial ; all terms will be regarded as uni- 
 versals, or, in other words, as denoting classes 
 of significates. 
 
 36. ADJECTIVES. Hence also adjectives 
 used as terms will be regarded as nouns or sub- 
 
 1 " By a class is usually meant a collection of individuals 
 . ; but in this work the meaning of the term will be ex- 
 tended so as to include the case where but a single individual 
 exists, as well as cases denoted by the terms ' nothing' and 
 ' universe' 1 ; which as 'classes' should be understood to com- 
 prise respectively 'no beings' and 'all beings.'" Boole, 
 Laws of Thought, p. 28.
 
 THE TERM 41 
 
 stantives; that is to say, where a term is in 
 adjective form (which can occur only with the 
 predicate) it is either regarded as a substantive, 
 or converted into one by adding the substan- 
 tive understood. Thus, e.g., the proposition, 
 " Man is mortal," is to be read: " Man is a 
 mortal," or " a mortal being." 
 
 37. ABSTRACT AND CONCRETE NAMES. 
 A concrete name is one that denotes a class of 
 real individuals. An abstract name is one that 
 denotes qualities or attributes conceived as ex- 
 isting apart from the things in which they in- 
 here, or, in other words, fictitiously regarded as 
 things, as, e. g., whiteness, strength, goodness, 
 humanity, etc.' 2 Abstract names are commonly 
 singular in form, but in their essential nature 
 they are always universal. Thus, when we 
 speak of virtue, the name is to be regarded as 
 
 1 " If we attach to the adjective the universally understood 
 subject, ' being ' or ' thing,' it becomes virtually a substantive, 
 and may for all the essential purposes of reasoning be replaced 
 by the substantive. Whether or not in every particular of the 
 mental regard it is the same thing to say, ' water is a fluid 
 thing,' as to say, ' water is fluid,' it is at least equivalent in the 
 expression of the processes of reasoning." Boole, Laws of 
 Thought, p. 2J. 
 
 ' 2 The distinction between concrete and abstract names cor- 
 responds precisely to the distinction made by old logicians 
 between names of first intention and names of second inten- 
 tion. The former are names that denote real significates ; 
 the latter, names that denote fictitious significates, or quasi- 
 things. See further on this point Appendix I.
 
 42 LOGIC 
 
 denoting, not a quality existing in any par- 
 ticular man, or in itself, but the class of quali- 
 ties by which all virtuous men are distinguished. 
 So, though we may consider the color red, or 
 redness, in the abstract, dismissing from the 
 mind the individuals in which it is manifested, 
 yet, upon analyzing the concept, we cannot 
 fail to perceive that there are as many individ- 
 ual instances of red, or, we may say, as many 
 individual reds or rednesses, as there are indi- 
 vidual things in which the color is manifested; 
 and that red, or redness, is simply the denomi- 
 nation of the class of colors thus manifested. 
 Hence, abstract names, though grammatically 
 singular, are to be regarded as plural, and as 
 differing from concrete names only in this, that 
 the individuals constituting the class are quali- 
 ties, i. e., quasi- things, or fictitious, not actual 
 existences, and that among the marks by 
 which the class is distinguished are the actual 
 individuals in whom alone the qualities exist. 
 An abstract name is therefore to be regarded 
 as denoting a class of qualities ; and as connoting 
 the individuals in which they inhere. 
 
 38. THE DISTINCTION OF FUNDAMENTAL 
 IMPORTANCE. The distinction between con- 
 crete and abstract names, or names of first, and 
 of second intention, is one of fundamental im- 
 portance. In dealing with the former, the 
 things denoted by the names we use are ever
 
 THE TERM 43 
 
 present to the mind, and we may therefore, as 
 is asserted by Mill, be said without violent 
 absurdity to deal with things, rather than 
 with notions or names. But where we deal 
 with abstract terms, the things present to the 
 mind are mere abstractions, fictitiously re- 
 garded as things; and we are, in fact, dealing 
 not with things, but with ^^.yz-things only. 1 
 
 39. POSITIVE AND NEGATIVE TERMS. 
 The distinction between positive and negative 
 terms is also one of fundamental importance 
 in Logic. By this division of terms the whole 
 universe of things, real and fictitious, is divided 
 into two classes, the one marked by having, 
 the other by not having, a certain quality or 
 qualities, as e. g., white things, and things 
 that are not white ; and it is obvious that to 
 each positive there must be a corresponding 
 negative term. 
 
 40. OF THE UNIVERSE OF THE PROPOSI- 
 TION. But ordinarily in speech we have in 
 view a more limited class, and must be under- 
 stood to refer, not to the universe of things, 
 but to some class less than the universe, but 
 superior to the classes denoted by the subject 
 and predicate; and this superior class is said 
 to constitute the universe of the proposition in 
 which the terms are used. Thus, when we 
 speak of " mortal" and " immortal," the class 
 
 1 See Appendix K.
 
 44 
 
 LOGIC 
 
 of " living things" or " beings" is obviously 
 referred to as the superior class, and is, there- 
 fore, said to constitute the universe of the 
 proposition; and the division is to be under- 
 stood to be into " mortal" and " immortal" 
 beings. So, in the proposition, " Brutes are 
 irrational," the superior class we have in view 
 is that of animals, and this class is to be re- 
 garded as the universe of the proposition ; as 
 (denoting " no t " by the Greek privative, a] 
 may be illustrated by the following diagrams, 
 either of which may be used : 
 
 III 
 
 OF THE ANALYSIS OF TERMS 
 
 41. APPREHENSION. As it is the func- 
 tion of Logic to compare the notions de- 
 noted by terms, with the view of determining 
 their relations, a preliminary process is essen- 
 tial . namely, that of apprehending or under- 
 standing the significations of terms; which is 
 called by logicians, " Simple Apprehension." 
 
 1 The operations of the mind involved in reasoning are (i) 
 Simple Apprehension, (2) Judgment, and (3) Inference (see
 
 THE TERM 45 
 
 This is effected by means of what may be 
 called the " Analytical Processes "; which will 
 next be considered. 
 
 42. ANALYTICAL PROCESSES. As pre- 
 liminary to apprehension, it is essential that 
 the sense in which the term is to be used shall 
 be identified, or, in other words, that of the 
 several senses usually denoted by a vocable, 
 one shall be selected. This is often called 
 nominal definition (i. e. , definition of the name), 
 but improperly; for until it is determined in 
 what sense a term is used, there is in fact no 
 name. Hence we call it, Vocal Definition, i. c., 
 Definition of the Vocable. Next, it is necessary, 
 before the two terms can be compared, to ap- 
 prehend, in the case of each of them, the sig- 
 nificates of the term, or the class of significates 
 denoted by it ; for otherwise we will not be 
 able to compare their significations. This is 
 effected by the definition of the term ; which, 
 to distinguish it from vocal, is called nominal 
 or real definition 1 ; and this again involves the 
 process of classification or division. 
 
 Whately, Logic], I have altered the ordinary statement of 
 these operations by substituting for the third "Inference" 
 instead of "Discourse"; which is commonly defined as 
 "reasoning" or "ratiocination." But, as used in this work, 
 these words include both Apprehension and Judgment. 
 
 1 There is some confusion among logicians as to the use of 
 the terms, Nominal Definition and Real Definition. By some, 
 the former term is used as denoting what I have called vocal
 
 46 LOGIC 
 
 43. VOCAL DEFINITION. A word, or vo- 
 cable, i. e. , the vocal sign, has usually many 
 significations; and commonly, in using it, we 
 do not, at first, distinguish between such of the 
 notions denoted by it as are nearly the same, 
 but, instead of regarding it (as we should) as 
 part of several names, use it as though it were 
 a single name. But in thus using a vocable 
 without distinguishing its several senses, it is 
 inevitable that, in the course of the ratiocina- 
 tion, it will be used in a shifting sense, or 
 rather, we should say, in several senses, as 
 suggested by the varying occasion ; and that 
 the coherency of our reasoning will thus be 
 destroyed. This fault in ratiocination is called 
 the fallacy of confusion or of ambiguity, and, 
 as will be seen in the sequel, is one of the most 
 common and most serious of fallacies. Hence 
 it is one of the most important and imperative 
 of logical rules that, in the case of every word 
 we have occasion to use in our reasoning, the 
 sense in which it is to be used shall be clearly 
 
 definition ; but this seems to be incorrect. According to the 
 better usage, a Nominal Definition is a definition of the 
 Notion expressed in a term ; and hence Whately says " that 
 Logic is concerned with nominal definitions only." To this 
 Mansel objects on the ground that " Logic is concerned with 
 real or notional definitions only ; its object being to produce 
 distinctness in concepts, which are the things of Logic " (Man- 
 sel's Aldrich, p. 39). But this is precisely what Whately 
 means ; and says.
 
 THE TERM 47 
 
 distinguished and consistently observed. And 
 this indeed, ex vi termini, is essential even to 
 the beginning of ratiocination; for, until this 
 is effected, we have not even that essential 
 material of ratiocination, a name, with which 
 to deal. The vocal definition of a term may 
 be effected in various ways, as, e. g., by the 
 use of any other term, or phrase, or sentence 
 of equivalent signification ; or, negatively, by 
 rejecting those senses of the word that we do 
 not wish to use; or, often, by an imperfect 
 definition, as by simply specifying the genus of 
 the class denoted by the term ; or, in fine, by 
 any means that may serve to confine the term 
 to one sense only, and thus to prevent am- 
 biguity. 
 
 44. DIVISION AND CLASSIFICATION. - 
 Division consists in distributing the class of 
 significates denoted by a name into subordinate 
 classes, with appropriate names; classification 
 in the reverse process of assigning a class de- 
 noted by a name to a class denoted by another 
 name. 
 
 45. GENUS AND SPECIES. In the former 
 case, the class distributed is called the genus ; 
 the classes into which it is distributed, species, 
 In the latter, the class assigned is a species, the 
 class to which it is assigned, the genus. The 
 genus and species, however, as in the case of 
 synonyms, may be of equal extension.
 
 48 LOGIC 
 
 46. DIVISION. Division is an act of Anal- 
 ysis ; Classification, of Synthesis. But the 
 same principles govern both, and the elucida- 
 tion of one will equally explain the other. In 
 Logic, the analysis of terms is the more im- 
 portant process, and we will therefore adopt, 
 as the subject of explanation, the process of 
 Division. The term to be divided, or, rather, 
 the class denoted by the term, is, as we have 
 said, called the genus; the subordinate classes 
 into which the genus is divided, species. The 
 species must, of course, be exclusive of each 
 other, i. e., they must not overlap; and taken 
 together they must exhaust the genus. Thus, 
 the term thing meaning thereby things and 
 quasi-things may be divided, and subordinate 
 classes subdivided, as follows: 
 
 Things 
 
 Real Things Ouasi-Things 
 
 Bodies Not Bodies 
 
 Organic Inorganic 
 
 Animal Not Animal 
 
 Rational Not Rational 
 etc. 
 
 47. DICHOTOMY. It will be observed 
 that the above division is, in each case, two-
 
 THE TERM 49 
 
 fold, i. e.j into two classes, represented by 
 a term and its negative. This is called Dichot- 
 omy, and, as in using it we are less liable to 
 error than in other modes of division, it is 
 most commonly used. The genus may, how- 
 ever, be divided into three or more species, pro- 
 vided the species taken together exhaust the 
 genus, and be exclusive of each other, as, e. 
 g., in the division of Bodies into (i) Inorganic, 
 (2) Vegetable, and (3) Animal. 
 
 48. NOMINAL DEFINITION OF TERMS. 
 The definition (/. e., the real or nominal defini- 
 tion) of a term consists in assigning the class 
 denoted by it to an appropriate genus, and 
 giving its specific difference ; by which is meant 
 some mark or marks peculiar to it, by which it 
 may be distinguished from other species. It 
 is, therefore, a species of classification, i. e., 
 it consists simply in classifying the given class, 
 or species, by assigning it to a genus, and in 
 adding also the appropriate marks, or specific 
 difference, by which it is distinguished from the 
 other species contained in the genus. The 
 definition of a term is, therefore, to be regarded 
 simply as a complete classification of it; and 
 the classification of it as an incomplete or im- 
 perfect definition. But the latter has the ad- 
 vantage that it can often be used where the 
 former would be inconvenient or impossible. 
 
 49. THE ESSENCE OF THE TERM. A
 
 50 LOGIC 
 
 quality at once common and peculiar to the in- 
 dividuals denoted by a term is called a property 
 of the class denoted ; a quality common to the 
 class, but not peculiar to it, is called an acci- 
 dent* The definition of a term is made up by 
 selecting from the accidents of the term one to 
 serve as a mark for the purpose of determining 
 the genus, and from the properties one to serve 
 as specific difference. These together constitute 
 the essence of the term ; which will therefore 
 vary with the definition, and be determined by 
 it. Thus, e. g., if we define man as a rational 
 animal, "animal" will be the genus; ra- 
 tional" the specific difference; "talking',"' 
 laughing, " " cooking, ' ' etc. , properties ; ' ' mor- 
 tal," " carnivorous," " mammal," etc., acci- 
 dents. But we may, if we choose, define him 
 variously as a talking, laughing, or cooking, 
 mortal, carnivore, or mammal. The essence of 
 a term is therefore but another name for the 
 meaning of the term. Properties not used for 
 specific difference, and accidents not used for 
 genus, do not enter into the essence of the term. 
 
 1 There is much confusion among logicians in the use of the 
 term accident. The definition in the text is that of the best 
 authorities, including Aristotle ; and the term should be con- 
 sistently thus used.
 
 CHAPTER III 
 
 DOCTRINE OF THE PROPOSITION 
 
 I 
 RUDIMENTS OF THE DOCTRINE 
 
 50. PROPOSITION DEFINED. A proposi- 
 tion may be defined as the expression of a rela- 
 tion of signification between two terms; which, 
 of course, implies the expression of the corre- 
 sponding relation between the notions ex- 
 pressed in the terms. 
 
 51. THE GRAMMATICAL PROPOSITION. 
 But here there is a difference between Logic 
 and Grammar, or, we may say, between the 
 logical and the grammatical proposition. In 
 the latter, any of the innumerable relations ex- 
 isting between terms, or, what is the same 
 thing, between the things denoted by them, 
 'whether past, present, or future, may be ex- 
 pressed as existing between the terms; and the 
 relation may be expressed by any copula or 
 connecting word, or the same word may be 
 51
 
 52 LOGIC 
 
 used to express both copula and predicate, as, 
 e. g., " John struck William " ; " The sun will 
 rise at six o'clock to-morrow"; " It rains"; 
 " The Carthaginians did not conquer Rome," 
 etc. But in Logic the only copula used is the 
 present tense of the verb " to be" with or 
 without the negative particle ; and the only in- 
 terterminal relation considered is that of species 
 and genus; which may be either affirmed or 
 denied. 
 
 52. THE LOGICAL PROPOSITION. Ac- 
 cordingly the logical proposition is of two 
 forms, the affirmative and the negative. In 
 the former the relation of species and genus 
 between the terms is affirmed, as, e. g. , " Man 
 is mortal," ' Y is X," etc. ; in the latter it is 
 denied, as, e. g. , " Man is not perfect," ' Y 
 is not X," etc. The affirmative proposition 
 may be read, either, " Y is X," or " Every Y 
 is X," or " All Y's are X's " ; or, to take the 
 concrete example, ' Man is mortal," or 
 " Every man is mortal," or " All men are 
 mortal," these expressions being all equiva- 
 lent, and signifying equally that the subject 
 class or class denoted by the subject is a 
 species of the predicate class. The negative 
 proposition may be read either as above or as' 
 follows: " No man is perfect," ' No Y is X," 
 etc. It is a cardinal postulate in Logic that all 
 propositions may, and indeed for purposes
 
 THE PROPOSITION 53 
 
 of logical analysis must be converted into 
 logical form; as, e. g., the above examples 
 into the following : " John is the man who 
 struck William " ; " Six o'clock is the hour at 
 which the sun will rise to-morrow"; " Rain 
 is falling"; " The Carthaginians are not [or, 
 grammatically, we should say, " were not "] 
 the conquerors of Rome." ' 
 
 53. INTERPRETATION OF THE LOGICAL 
 PROPOSITION. In all logical propositions the 
 copula is to be interpreted as meaning " is con- 
 tained in " or " is a species of," or the contrary, 
 as the case may be. 2 Hence in Logic the only 
 
 1 There are commonly recognized by logicians four forms of 
 the proposition, designated respectively by the letters, A, E, 
 I, and O, and called the " Universal Affirmative" the "Uni- 
 versal Negative" the "Particular Affirmative" and the 
 "Particular Negative" (see infra, 88). But if in I 
 and O we regard the expression "some Y" instead of 
 " Y " as the subject of the proposition, these forms will be- 
 come the same as A and E. Hence, propositions may, as in 
 the text, be regarded as of two kinds only, namely, affirma- 
 tive and negative ; the former affirming that the subject is 
 included in the predicate class ; the latter denying that it is so 
 included. This distinction agrees precisely with our defini- 
 tion, and will be sufficient for our present purposes, and, 
 indeed, for all practical purposes. 
 
 2 The affirmative proposition " Y is X " is to be construed as 
 asserting that the class Y is wholly included in the class X ; the 
 negative, " Y is not X," that it is wholly excluded. But the 
 class Y may denote a part of a class, as, e. g. , " Some A " ; 
 in which case the proposition " Y is X," or " Y is not X," 
 would be equivalent to the ordinary forms, "Some A is X." 
 or " Some A is not X,"
 
 54 LOGIC 
 
 significative relation recognized is the relation 
 of the inclusion or exclusion of the subject 
 class in or from the predicate: and accordingly 
 this may be called appropriately the logical 
 relation. Yet the logical proposition is not less 
 capacious of expression than the grammatical ; 
 for, as the latter may always be converted into 
 the former, it follows that all relations may be 
 expressed in the one as in the other. The 
 only difference is that in the grammatical prop- 
 osition the relations between the notions in- 
 volved may be expressed either in the copula, 
 or in the terms themselves ; while in the logical 
 proposition the only interterminal relation ex- 
 pressed (i. e. y affirmed or denied) by the copula 
 is that of species and genus, and all other re- 
 lations between notions are expressed in the 
 terms, i. e., in complex terms. 1 
 
 54. THE CONVERSION OF PROPOSITIONS. 
 By conversion is meant the transposition of 
 subject and predicate i. e., making the predi- 
 cate the subject, and the subject, predicate. 
 But, such conversion, to be legitimate, must be 
 illative, /. e., the force or conclusiveness of the 
 proposition must not be affected. Thus the 
 proposition, " Y is not X " (since the subject and 
 predicate classes are mutually exclusive), may 
 be converted into the proposition, " X is not 
 
 1 This is admirably illustrated by Mr. Boole's system of 
 signs, of which I append an epitome. See Appendix L.
 
 THE PROPOSITION 55 
 
 Y," which is called simple conversion; and so 
 with all definitions, and other equational proo- 
 ositions; and also with the particular affirma- 
 .tive proposition, " Some Y is X." But the 
 affirmative proposition, " Y is X," cannot be 
 thus simply converted; for the subject class is 
 identical with only " some " of the predicate 
 class, and in conversion the predicate must be 
 qualified by that particle, thus substituting a 
 new term. Or, symbolically, the proposition, 
 ' Y is X," can be converted only into the 
 proposition, " Some X is Y "; which is called 
 conversion per accidens. 
 
 II 
 
 SEVERAL THEORIES OF PREDICATION 
 
 55. THE COPULA. In the logical proposi- 
 tion, as we have seen, the copula is interpreted 
 as meaning "is contained in," or the contrary- 
 and this is the traditional, or, as it may be 
 called, orthodox, theory of predication. But 
 the copula may be otherwise interpreted ; and 
 from these several interpretations several theo- 
 ries of predication will result. Of these, two 
 may be distinguished as requiring some remark, 
 namely, the Equational Theory, in which the 
 copula is interpreted as meaning, " is equiva- 
 lent to," and is expressed by the sign of equiv- 
 alence (=) ; and the Intensive Theory, where it
 
 56 LOGIC 
 
 is interpreted as meaning, " has the quality or 
 attribute" Thus, e. g. , the proposition, " Man 
 is rational," is interpreted according to the 
 Traditional Theory as meaning, " the class 
 man is contained in the class rational" ; ac- 
 cording to the Equational Theory, as meaning, 
 
 the class man is the same as the class 
 rational" ; and according to the Intensive, as 
 meaning, " the individuals constituting the 
 class man have the quality or attribute, rational, 
 or of rationality." 
 
 56. THE EQUATIONAL THEORY. In the 
 logical proposition, the classes denoted by the 
 subject and predicate may be equal ; for, where 
 this is the case, each may be said to be con- 
 tained in the other. Hence in such cases the 
 proposition is always convertible, as, e, g,, we 
 may say indifferently that " man is a rational 
 animal,' 1 or that "a rational animal is a man," 
 or, generally, if Y = X, either that " Y is X " 
 or "X is Y." Such propositions are recog- 
 nized and used in the traditional Logic, as in 
 the case of definitions, and in other cases, 
 but it is not thought necessary to express the 
 equivalence of the terms. Hence in the affirm- 
 ative proposition " Y is X " it cannot be deter- 
 mined from the form of the proposition whether 
 X is of greater extension than Y, or of the 
 same extension. 
 
 57. QUANTIFICATION OF THE PREDICATE.
 
 THE PROPOSITION . 57 
 
 The modern doctrine of " the quantification 
 of the predicate " has for its object to remedy 
 this supposed defect by expressing in every 
 proposition by an appropriate sign the quan- 
 tity of the predicate, or, in other words, by in- 
 dicating whether it is distributed or not ' ; and 
 this is effected by prefixing to the predicate a 
 sign indicating the relation of quantity between 
 it and the subject, and giving to the propo- 
 sition an equational form. Thus, e. g., the 
 proposition, " Y is X," may be expressed in 
 the form " Y = vX," which is the method of 
 Boole; or in the form Y = YX," which is 
 the form proposed by Jevons, and is read, 
 " Y = the part of X that is Y," or " the Y's 
 are the X's that are also Y's." Or, more sim- 
 ply, instead of the proposition, " Y is X," we 
 may say, " Y is a certain species of X " ; or, 
 to take a concrete example, instead of the 
 proposition, " Man is an animal," we may say, 
 
 ' Man is a certain species or kind of animal." 
 Hence, whether an equational proposition shall 
 be expressed in the traditional or in the equa- 
 tional form is a matter of choice to be 
 determined by convenience. Generally the 
 
 1 A term is said to be " distributed" when it is taken uni- 
 versally, i. e., where the other term of the proposition is, or 
 may be, predicated of all the individuals denoted by it, as, e.g., 
 the subject of a universal affirmative, or either subject or 
 predicate of a universal negative proposition (see ^ 87).
 
 58 . LOGIC 
 
 traditional form is sufficient, as we can readily 
 determine from the matter of the proposition 
 whether it is to be regarded as equational or 
 otherwise. But in the mathematics the equa- 
 tional form is much the more efficient, and is 
 therefore always used. 
 
 58. THE INTENSIVE THEORY. The differ- 
 ence between the traditional and the intensive 
 theory of predication is that, in construing the 
 proposition, we have regard in the former to 
 the extension of the terms only ; but in the 
 latter, in construing the predicate, we have re- 
 gard to its intension. Thus, when we say " Man 
 is mortal," we mean, in the former case, that 
 the class man is contained in the class mortal ; 
 but in the latter, that man has the quality or 
 attribute of mortality. But the latter expres- 
 sion means nothing more than that " the qual- 
 ity of mortality is contained in, or among, the 
 qualities of man "; which is itself an extensive 
 proposition. Hence the intensive interpreta- 
 tion of the proposition simply results in an 
 extensive proposition in which the qualities 
 of the original terms are substituted for its 
 original significates, and the terms inverted. 
 Thus, e.g., if we denote by Y' the qualities of 
 Y, and by X' the qualities of X, the proposi- 
 tion, Y is X, may be converted into X' is Y'; 
 which may be called Intensive Conversion, or 
 conversion by Intensive Interpretation.
 
 THE PROPOSITION 59 
 
 59. TRADITIONAL THEORY OF PREDICA- 
 TION. Even under this theory the proposition 
 seems to be susceptible of several interpreta- 
 tions. Thus, e. g., we have interpreted the 
 copula as meaning " is contained in or " is a 
 species of " ; and again we may interpret it as 
 meaning that the significates constituting the 
 subject class may each and all be called by the 
 name constituting the predicate or, in other 
 words, that the name predicated belongs to 
 the significates of the subject term, or of any of 
 them ; which has been called interpreting the 
 judgment "in its denomination " (Thompson's 
 Laws of Thought, 195). But for all logical 
 purposes these interpretations are practically 
 the same, and it will make no difference whether 
 the proposition be interpreted in the one way 
 or the other. This is sufficiently obvious with 
 regard to the expressions, " is contained in," 
 and " is a species of " ; and is equally true of 
 the interpretation suggested by Dr. Thompson. 
 For, taking as an example the proposition, 
 
 ' Man is an animal," it is obviously indifferent 
 whether we construe it as meaning " the class 
 man is included in the class animal" or that 
 
 ' it is a species of the class animal," or that 
 " the name animal is applicable to all signifi- 
 cates of the name man." These varieties of 
 interpretation will, therefore, not demand a 
 further consideration.
 
 DO LOGIC 
 
 60. COLLECTIVE AND DISTRIBUTIVE IN- 
 TERPRETATION. There is, however, another 
 difference of interpretation it is important to 
 consider; and especially with reference to 
 mathematical reasoning, which is to be con- 
 sidered presently. Common terms, or terms 
 denoting classes of more than one, may be used 
 either collectively or distributively, i. e., the 
 class denoted by the term may be regarded 
 either as a whole made up of individuals, 1 or as 
 a number of individuals constituting a class, or 
 signified by the name. Thus, e. g., the term 
 " man " may be used to denote either the class 
 " man," as when we say, "Man is mortal"; 
 or the individuals composing the class, as 
 when we say, " A man is a mortal," or " Men 
 are mortals." Whether a term is used collec- 
 tively or distributively may be indicated, as in 
 the above examples, by the expression, or may 
 be simply understood ; or the expression may be 
 such as not to indicate either expressly or im- 
 plicitly whether the term is used in the one way 
 or the other. With regard to the subject of the 
 proposition it is logically immaterial in which 
 way the term is used. Thus, in the proposi- 
 tion, " Y is X, " the subject is used collectively ; 
 and in the proposition, " All Y's are X's," or 
 
 1 When a concrete term is construed collectively, it becomes 
 abstract, and is to be regarded as denoting, not a number of 
 real individuals, but one quasi individual only.
 
 THE PROPOSITION 6 1 
 
 ' Every Y is an X," or "A Y is an X," distri- 
 butively ; but the forms are logically equivalent. 
 So with regard to the predicate, where the 
 terms are of equal extension, it is immaterial 
 whether it be construed collectively or distribu- 
 tively, provided, if the predicate be construed 
 collectively, that the subject also be thus con- 
 strued. For to construe a term collectively is 
 to regard the class denoted by it as an individ- 
 ual, and a term thus construed is therefore to 
 be regarded as a singular term. But a singular 
 term cannot be predicated of any but a singu- 
 lar term, with which it must exactly conform 
 in signification; or, in other words, a singular 
 term can be predicated of another singular term 
 only in the equational proposition. Thus, 
 e. g., in the proposition, " Y is X," it is im- 
 material whether we regard Y as denoting the 
 class Y, or as signifying the significates com- 
 posing the class. But the class X cannot be 
 construed collectively unless we also construe 
 the class Y in the same way, and unless also 
 the two classes are co-extensive, or, in other 
 words, unless the proposition can be put in the 
 form, Y = X. 
 
 Ill 
 
 OF THE PREDICABLES 
 
 61. DEFINITION AND DIVISION OF THE 
 PREDICABLES. A predicable may be defined
 
 62 LOGIC 
 
 as a term that may be made the predicate of an 
 affirmative proposition. As explained above, 
 such propositions may be either equational or 
 non-equational. In the former case the predi- 
 cate is of the same extension as the subject ; in 
 the latter, of greater extension. All predi- 
 cables, therefore, may be divided into two 
 classes, namely, those that are equivalent to 
 the subject, and those that are not equivalent. 
 An equivalent predicable may be either defini- 
 tion or property ; for each of these is precisely 
 co-extensive with the subject ( 49). Non- 
 equivalent predicables must be either genera 
 or accidents ; either of which may always be 
 predicated of the subject (/#.). This is the 
 division of predicables used by Aristotle. 
 
 62. TWOFOLD DIVISION OF PREDICABLES. 
 But the distinction between " definition " and 
 " property " seems, with relation to the subject 
 of predicables, to be unimportant; for "prop- 
 erty" differs from "definition" only in the 
 use made of the former (/#.). And so with 
 reference to the distinction between genus and 
 accident (/#.). Hence it has been proposed 
 to abandon, as at least unnecessary for logical 
 purposes" (or rather, we should say, for pur- 
 poses of predication), "the distinctions between 
 property and definition, genus and accident, 
 and to form, as Aristotle has also done, two 
 classes of predicables ; one of predicables taken
 
 THE PROPOSITION 63 
 
 distributively and capable of becoming subjects 
 in their respective judgments without limita- 
 tion ; the other of such as have a different ex- 
 tension. In the former the predicable has the 
 same objects [2. e. , significates] as the subjects, 
 but different marks, or a different way of rep- 
 resenting the marks. In the latter there is a 
 difference, both in the marks and the objects " 
 (Thompson's Laius of Thought, 69.)' 
 
 63. ONE KIND OF PREDICABLES ONLY. 
 But even the twofold division of predicables, 
 into equivalent and non-equivalent, is, from the 
 traditional standpoint, of minor importance; 
 for, as we have seen, the old Logic ordinarily 
 takes no account of equational propositions, 
 but these, like others, are regarded as import- 
 ing simply the inclusion of the subject in the 
 predicate; and in this mode of interpreting 
 the proposition, we have, in effect, a complete 
 doctrine of the predicables. 
 
 1 The division of predicables most commonly used is that of 
 Porphyry (Aristotle's Logical Treatises, Bohn's edition, Intro- 
 duction of Porphyry ; also Jevons's Lessons in Logic, p. 98). 
 According to this division, " Specific Difference" is substituted 
 for the " Definition " of Aristotle's division, and there is added 
 as a fifth predicable, " Species ," as being predicable of individ- 
 uals. But, as observed by Mansel (Aldrich's Logic, Preface), 
 "whether this classification is an improvement, or is consist- 
 ent with the Aristotelian doctrine, admits of considerable 
 question." The view taken in the text is in every respect 
 preferable (Thompson's Laws of Thought, pp. 136 et seq.).
 
 64 LOGIC 
 
 IV 
 OF THE RELATIONS BETWEEN TERMS 
 
 64. OF THE RELATIONS OF TERMS GEN- 
 ERALLY. The end of Logic is to determine 
 the relations, and, as involved in this, the defi- 
 nitions, of terms, or (what is the same thing), 
 of the notions expressed in terms ( 16). Of 
 these notions, the most conspicuous are those 
 existing between what are called relative words 
 as, e. g., father and son, wife and husband, 
 higher and lower, etc., and also the active 
 and passive forms of the verb, and all in- 
 flections of verb or noun, or, in a word, all 
 paronyms, etc. But the term, relative, though 
 applicable, is not peculiar to this class of 
 words, and is, therefore, not altogether appro- 
 priate. Relations, more or less apparent, exist 
 between all terms, and in the development 
 of these consists the raison d'etre of Logic. 
 Hence, properly speaking, no term can be said 
 to be absolute, as opposed to relative. For 
 to consider only one of the most general of re- 
 lations any thing, or class of things (real or 
 fictitious), must always be assignable to one of 
 two classes, namely the class denoted by a 
 given term, or to the class denoted by its 
 negative ' ; and, in addition to this universal 
 
 1 This, of course, is true only on the assumption that we 
 reject Particular Propositions, as proposed ( 52, note).
 
 THE PROPOSITION 65 
 
 relation, there are numerous others, either of a 
 general character, as e. g., the relation be- 
 tween numbers, or other expressions of quan- 
 tity, or such as are peculiar to certain words, 
 as, e.g., between hunger and animal, hunger 
 and edible, gravity and body, fish and water, 
 the sun and the planets, etc. In fine, the re- 
 lations between terms are innumerable, and, 
 when the significations of terms are appre- 
 hended, these relations may, in general, or, at 
 least, in innumerable cases, be either intui- 
 tively perceived, or demonstratively inferred. 
 
 65. OF THE SEVERAL KINDS OF INTER- 
 TERMINAL RELATIONS. The relations of 
 terms are, for various purposes, divided in so 
 many different ways that it would be impracti- 
 cable to enumerate them. But, of these divi- 
 sions, there are three that, either on account of 
 their intrinsic importance, or of the importance 
 attributed to them by logicians, will require 
 our attention. These consist in the distinction 
 made (i) between the Predicables and the Cate- 
 gories or Predicaments ; (2) between the formal 
 and the material relations of terms ; and (3) be- 
 tween the relations that are intuitively per- 
 ceived, and those that are not, or, more briefly, 
 between judgments and assumptions (19, 20). 
 
 66. (i) OF THE PREDICABLES AND OF THE 
 
 Otherwise we would fall into the same fallacy as Jevons and 
 Hobbes (v., infra, 90 and note). 
 5
 
 66 LOGIC 
 
 CATEGORIES OR PREDICAMENTS. The dis- 
 tinction between these corresponds precisely to 
 the distinction we have made between the 
 logical and the grammatical forms of the prop- 
 osition. Etymologically both terms are of the 
 same import, denoting simply terms that may 
 be predicated of other terms, i. e. , that may be 
 made predicates of propositions; but, according 
 to inveterate use, the former term relates ex- 
 clusively to the logical proposition, the latter, 
 to the grammatical. There is, therefore, an 
 essential difference between the Doctrine of 
 the predicables and that of the Categories 
 or predicaments. The former which treats 
 simply of the relation of species and genus be- 
 tween the terms expressed in the logical prop- 
 osition has already been considered. The 
 latter treats of all the various relations that 
 may exist between the terms of the grammati- 
 cal proposition ; and, as these include all rela- 
 tions, whatever, that may exist between terms, 
 or between their significates, it follows that the 
 categories or predicaments are to be understood 
 as denoting the most general classes into which 
 such relations may be distributed. By such a 
 classification if it could be accomplished all 
 relations between terms and between things 
 would be developed, and thus a basis furnished 
 for a classification of all possible predicates. 
 But the subject is one of difficulty, and in the
 
 THE PROPOSITION 6/ 
 
 present state of philosophy, a satisfactory treat- 
 ment of it is impracticable. It would simply 
 serve, therefore, to confuse the student, if we 
 should enter upon it, and we will accordingly 
 omit it. 
 
 67. (2) OF THE FORMAL AND OF THE MA- 
 TERIAL RELATIONS OF TERMS. By informal 
 relations of terms are meant those relations that 
 are universal in their nature, i. e., that exist 
 generally with reference to all terms; as, e. g. , 
 the relation between terms and their contra- 
 dictories, between a term used universally and 
 the same term used particularly, between the 
 subject and the predicate of the proposition, 
 etc. These are all apparent at once from the 
 mere expression, without taking note of the 
 matter of the term, except in so far as it is 
 universal or common to all terms. Thus, e. g., 
 in the expression " not-man " we perceive at 
 once a formal relation between this term and 
 " man," and in this case the privative " not," 
 though part of the matter of the term not- 
 man, is the ground of the relation; which is 
 formal because universal. And so, in the 
 terms " Y " and " some Y," a formal relation 
 is apparent, though the word " some " is in fact 
 part of the matter of the term " some Y." 
 
 Hence, the distinction between the formal 
 and the material relations of terms does not, 
 as is commonly supposed, rest upon the
 
 68 LOGIC 
 
 distinction that, in the former case, the matter 
 of the term is not considered, and, in the latter, 
 that it is ; but on the distinction that the formal 
 relations are based upon such part of the mat- 
 ter or meaning of terms as is common to all or 
 to many terms, and with that regard to the 
 material relations this is not the case. 
 
 Hence, logically, there is, in fact, no essential 
 difference of nature between the two kinds of 
 relation. For the material relations between 
 terms are as apparent and as certain as the so- 
 called formal relations, as, c. g,, the relations 
 between relative terms, as " father " and " son," 
 etc., or those between such terms as " island " 
 and "continent," "island" and "water," 
 "body" and "weight," "five" and "seven," 
 " nine " and " fifteen," etc. ; and they differ only 
 in this, that these subsist only in particular 
 cases, and not universally. Hence the notion 
 that would restrict the functions of Logic to the 
 merely formal relations of terms is based upon 
 an unessential difference of nature between 
 these and other relations, and therefore cannot 
 be sustained. 
 
 68. (3) OF JUDGMENTS AND ASSUMPTIONS. 
 Of the immediate relations between terms 
 some as we have seen are self-evident, or 
 may be intuitively perceived ; others are not 
 of this character. Where the relation between 
 the terms of a proposition is of the former
 
 THE PROPOSITION 69 
 
 kind, it is called %. judgment ; where the rela- 
 tion expressed is of the latter kind (if not 
 an inference) it is called an assumption ( 
 19 et seq,}. This division of propositions is 
 based upon an essential difference of nature, 
 and is one of fundamental importance. It 
 will therefore require our most attentive con- 
 sideration. 
 
 LOGICAL JUDGMENT DEFINED. In the logi- 
 cal proposition, the only relation between 
 the terms expressed is what we have called 
 the significative relation, i. e., the relation 
 of inclusion or exclusion of one of the terms 
 in or from the other. Hence judgment, in 
 the logical sense, may be defined as consist- 
 ing in the intuitive perception of a significative 
 relation between two terms, i. e. , in the in- 
 tuitive perception that the subject class is, or 
 is not, included in the predicate class, as, 
 c. g., where, from our knowledge of the signi- 
 fication of the terms, we affirm that " man is 
 an animal, ' ' or that ' ' fishes are denizens of the 
 water," or that " bodies are affected by grav- 
 ity," or that " fortitude is the only resource 
 against the inevitable," or, in the Latin, 
 " Quidquid crit super anda omnis fortuna ferendo 
 est." 
 
 69. OF THE DISTINCTION BETWEEN 
 JUDGMENT AND ASSUMPTION. The product 
 of this mental process as we have seen is
 
 7<D LOGIC 
 
 called a judgment ; which may be defined as 
 a proposition at once self-evident, and not in- 
 ferred from another proposition or proposi- 
 tions. Hence, the opinion that " propositions 
 are judgments expressed in words" is a de- 
 parture from the logical definition of a judg- 
 ment. A judgment expressed in words is a 
 proposition, but the converse is not true. For 
 where a proposition is based not merely upon 
 a comparison of its terms, or upon an inference, 
 but upon extrinsic evidence, or authority, or 
 other grounds, the forming of an opinion is 
 not a logical process, and the proposition, from 
 a logical point of view, is to be regarded, 
 not as a judgment, but merely as an assump- 
 tion or hypothesis. Of this kind is the prop- 
 osition that Pompey's army was defeated at 
 Pharsalia; that Cicero was murdered by the 
 Triumvirate ; that a given policy as, e. g., 
 protection to home industries, or the remon- 
 etization of silver, will be beneficial, etc. 
 
 70. OF THE DISTINCTION BETWEEN 
 APODICTIC AND DIALECTIC ( 23). Hence 
 it may be readily perceived how inadequate 
 is the conception of Logic that would re- 
 strict its functions to merely fornial infer- 
 ence to the exclusion of judgments; or the 
 conception of demonstrative or apodictic rea- 
 soning that would confine it to the mathe- 
 matics : or to the limited class of sciences that
 
 THE PROPOSITION 71 
 
 rest upon intuitions, in the sense of the term 
 used by modern metaphysicians ; or that would 
 exclude from it all reasoning originating in 
 judgments involving empirical notions or con- 
 cepts. For, logically, a judgment as to a sig- 
 nificative relation between two terms denoting 
 notions or concepts, of which the apprehension 
 is empirical, as, e. g., the judgment that 
 
 bodies are affected by gravity," that " fish 
 live in water," that " food will assuage 
 hunger," etc., is quite as self-evident as the 
 judgment that " two and three are five," or 
 that" sixty-four is the square of eight." In 
 fact, the two classes of judgments are, logi- 
 cally, of precisely the same nature, each 
 being but an intuitive perception of a relation 
 between the significations of two terms; as 
 follows from our definition. 
 
 71. No DISTINCTION IN LOGIC BETWEEN 
 A PRIORI AND EMPIRICAL NOTIONS. Logic, 
 therefore, takes no account of the metaphysical 
 distinction between a priori and empirical no- 
 tions, but regards all judgments as intuitive. 
 Its function is simply to determine the relations 
 existing between the significations of terms; 
 and if the significations of the terms com- 
 pared be apprehended, and be of such nature 
 that the relation between them can be per- 
 ceived, either immediately i. e. intuitively, 
 or by intermediary comparison with other
 
 72 LOGIC 
 
 terms, the conclusion reached which ex- 
 presses merely the relation between the signi- 
 fications of the terms is, so far, absolutely 
 true. 
 
 72. OF THE ERROR THAT RATIOCINATION 
 is ONLY HYPOTHETICALLY TRUE. Hence 
 it is an error to suppose that ratiocination is 
 only hypothetically true, or, in other words, 
 that Logic is not concerned \vith the truth of 
 premises. In many cases this is so; but it is 
 true in no case in which the ratiocination pro- 
 ceeds from judgments exclusively. For in all 
 such cases the premises which, as we have 
 said, merely express significative relations be- 
 tween their terms are not merely assumed, 
 but are intuitively known to be true, and the 
 conclusion is true, not hypothetically but ab- 
 solutely. 
 
 And this is essentially the case even where 
 the notions involved in the original judgments 
 or premises are themselves false or unreal; for 
 the ratiocination has for its direct object only 
 to determine correctly the relation between 
 the significations of the terms of the con- 
 clusion ; and all that is directly asserted in 
 the conclusion is that the signification of the 
 terms are related as expressed ; and hence, 
 when the ratiocinative functions have been 
 rightly performed, the conclusion must be 
 necessarily true. But as it is necessary for
 
 THE PROPOSITION 73 
 
 purposes of ratiocination that grammatical 
 propositions be converted into logical, so also, 
 for practical use or application, all logical con- 
 clusions must be reconverted into grammatical 
 propositions, or, in other words, construed as 
 asserting not merely the significative relation 
 expressed, but also the truth or reality of the 
 notions or concepts denoted by the terms; and 
 when thus construed the conclusion cannot be 
 regarded as being absolutely true, unless the 
 terms express real notions. Hence, it may be 
 said that the conclusions reached in ratiocina- 
 tion proceeding exclusively from judgments 
 are, when construed grammatically, true only 
 upon the hypothesis that the notions involved 
 in the original judgments or premises are true 
 or real, and hence, that such conclusions are 
 true absolutely only as logically construed. 
 Thus, e. g., the judgment that " all bodies 
 are affected by gravity" is intuitive; but of 
 the truth or reality of the notions expressed 
 by these terms, respectively, we have no as- 
 surance but experience. And from these ob- 
 servations it may be perceived how, and in 
 what sense, it is that Politics, Morality, and 
 the Science of Human Nature generally are 
 all to a large extent susceptible of demonstra- 
 tion, and to that extent apodictic in their nature 
 ( 23 et seq.\
 
 CHAPTER IV 
 
 DOCTRINE OF THE SYLLOGISM 
 
 I 
 RUDIMENTS OF THE DOCTRINE 
 
 73. ELEMENTS OF THE SYLLOGISM. The 
 Syllogism consists of three propositions ( 22): 
 of which two are called the premises, and the 
 other the conclusion. It has also three terms. 
 Of. these, two appear as the subject and the 
 predicate of the conclusion, and are called, 
 respectively, the minor and the major term. 
 The other which is called the middle tenn- 
 is used in both premises: in the one with the 
 major, in the other with the minor term. The 
 premise containing the major term is called 
 the major, and that containing the minor, the 
 minor premise. Thus in the syllogism, Y is 
 X, Z is Y, .'. Z is X," Z is the minor, X the 
 major, and Y the middle term ; and the first 
 proposition the major, and the second the 
 minor premise. 
 
 74
 
 THE SYLLOGISM 75 
 
 74. ANALYSIS OF THE SYLLOGISM. The 
 proposition is but the expression of a signifi- 
 cative relation between its terms. Hence the 
 premises of a syllogism are merely statements 
 of the significative relations of the terms of 
 the conclusion (the major and the minor) re- 
 spectively with the middle term ; and the 
 conclusion the significative relation thereby 
 inferred between its terms. The essential ele- 
 ments of the process consist, therefore, in the 
 comparison of the two terms of the conclusion 
 respectively with the third, or middle term, 
 and in inferring a direct relation between them. 
 
 75. DEFINITION OF THE SYLLOGISM. 
 Hence syllogistic inference may be more 
 specifically defined as consisting in the infer- 
 ence of a significative relation between two 
 terms from their known significative relations 
 to a third term with which they are respectively 
 compared. 1 
 
 76. THE PRINCIPLE OF THE SYLLOGISM. 
 The principle of the syllogism (by which is 
 meant the principle or axiom on which de- 
 pends the illative force or conclusiveness of 
 syllogistic inference) is expressed in the Dictum 
 of Aristotle, or, as it is technically called, the 
 
 1 The definition in the text is taken substantially from that 
 of De Morgan ; who defines the syllogism as "the inference 
 of the relation of two names from the relation of each of those 
 names to a third" (Formal Log., p. 176).
 
 76 LOGIC 
 
 Dictum de Omni et Nullo. It is variously 
 stated by logicians, but the several forms are 
 all, in effect, identical. Its best expression is 
 as follows : 
 
 DICTUM DE OMNI ET NULLO. "Where 
 three terms (which we will call the middle 
 and the two extremes] so subsist with re- 
 lation to each other that the one extreme is 
 contained in the middle, and the middle is 
 contained in [or excluded froni\ the other ex- 
 treme, then [as the case may be] the extreme 
 included in the middle will be included in [or 
 excluded front} the other extreme." Where 
 the predication is affirmative the principle is 
 called the Dictum de Omni ; where negative, 
 the Dictum de Nullo. 
 
 Omitting in the form given above the words 
 in brackets, it becomes the Dictum de Omni ; 
 substituting the words in brackets, marked as 
 quoted, for the corresponding expressions, it 
 becomes the Dictum de Nullo. 
 
 The two forms of the Dictum (affirmative 
 and negative) correspond precisely to the two 
 forms of syllogisms called Barbara and Cela- 
 rent? viz. : 
 
 1 This is substantially the form given to the Dictum by 
 Aristotle, Prior Analytics, i., iv. 
 
 * Forms of the Syllogism. There are nineteen forms of 
 valid syllogisms recognized by logicians, which are explained 
 in the next chapter. But if we reject the use of particular 
 propositions ( 52 n.) all may be reduced to the two forms
 
 THE SYLLOGISM 77 
 
 Y is X Y is not X 
 
 Z is Y Z is Y 
 
 .'. Z is X .'. Z is not X 
 
 II 
 
 THE PRINCIPLE OF SUBSTITUTION 
 
 77. RULES OF INFERENCE. The follow- 
 ing practical rules may be deduced from the 
 Dictum : 
 
 (1) In any affirmative proposition we may 
 always (without affecting its illative force or 
 conclusiveness) substitute for the subject any 
 other term denoting the same, or part of the 
 same, significates; and for the predicate any 
 term denoting the same significates, or a class 
 that contains them. 
 
 Or, more briefly, we may always in the sub- 
 ject substitute species for genus ; and in the 
 predicate, genus for species. 
 
 (2) So, in any negative proposition, we may, 
 without affecting its illative force, substitute 
 for either subject or predicate any term denot- 
 ing the same, or part of the same, significates. 
 
 Or, more briefly, we may always, in the 
 negative proposition, either in the subject or 
 the predicate, substitute species for genus. 
 
 above given, which are called Barbara and Celarent. In 
 these forms the several terms may be represented indifferently 
 by any letters ; and the order of the propositions is imma- 
 terial. In the traditional Logic the order of the propositions 
 is always as in the examples given in the text.
 
 78 LOGIC 
 
 (3) To which may be added the following: 
 In any affirmative proposition we may always 
 substitute for the predicate any other term that 
 denotes the same significates as the subject, or 
 a class containing them. 1 
 
 78. EQUIVALENCE OF TERMS DEFINED. 
 In the above rules, it will be observed, the 
 term substituted is not necessarily equivalent 
 in signification to the term for which it is sub- 
 stituted ; but it is equivalent so far as the 
 force of the inference is concerned, or, as the 
 lawyers say, quoad the argument. It may be 
 said, therefore, briefly, that mediate, or syllo- 
 gistic inference consists simply in substituting 
 for the terms of propositions other terms equiv- 
 alent in ratiocinative value. 
 
 79. CONVERSIONS OF PROPOSITIONS. 
 The case of conversion of propositions seems 
 indeed, to be an exception ; for here the pro- 
 cess seems to consist, not in the substitution 
 of terms, but in the substitution of a new 
 
 1 The deduction of these rules from the Dictum is perhaps 
 sufficiently obvious, but as it may not be apparent to all, we 
 subjoin the demonstration : 
 
 In the first syllogism (Barbara) it will be perceived, as ex- 
 pressed in the minor premise, that Z is a species, and X the 
 genus, of Y, and that the conclusion is arrived at by substitu- 
 ting for Y, in the major premise, its species Z ; or, for Y in the 
 minor premise, its genus X. 
 
 In the latter syllogism (Celarent) the process consists in sub- 
 stituting for Y, in the major premise, its species Z ; and so it 
 is obvious we may substitute for X in the major premise any
 
 THE SYLLOGISM 
 
 79 
 
 proposition containing the same terms as the 
 original with the order of terms transposed. 
 But the exception, in the case of negative and 
 equational propositions, is more apparent than 
 real ; for the two forms of the proposition (i. e., 
 the converted and the original proposition) are 
 precisely the same in effect, and there is, in 
 fact, neither term nor proposition substituted. 
 For when we say " Y is not X," we equally 
 and as explicitly say " X is not Y " the mean- 
 ing of either proposition being simply that the 
 two classes denoted by X and Y are mutually 
 exclusive; and so in the equational proposition 
 (Y = X) we say, in the same breath, both that 
 Y is equal to X, and that X is equal to Y. So, 
 
 species of the genus X, as, e. g., A, B, or C, and thus con- 
 clude that " Z is not A, B, or C " (as the case may be) ; as may 
 be illustrated by appropriate diagrams : 
 
 So, in the major premise in Barbara, we may substitute for 
 X the expression YX, or any species of X containing Y, as, 
 e. g., A, and thus conclude that Z is YX, or Z is A, as the 
 case may be.
 
 8O LOGIC 
 
 upon consideration, it will be found that the 
 conversion of the (universal) affirmative propo- 
 sition i. e., conversion per accidens is not an 
 exception to the rule, but an application of it; 
 for the process consists simply in substituting 
 for the predicate another term precisely equiv- 
 alent to the subject in signification, as, e. g., 
 in the proposition Y is X," the expression 
 " some X" for " X," meaning, by the ex- 
 pression " some X," that part of X which co- 
 incides with Y; which is but an application of 
 Rule 3. And when this substitution is made, 
 the proposition becomes equational, and means 
 the same thing whether we convert it or 
 not. 
 
 80. OF IMMEDIATE INFERENCES GENER- 
 ALLY. Propositions derived from other propo- 
 sitions by conversion, and also those derived 
 by opposition (explained infra, 89), are re- 
 garded by recent logicians as inferences, and 
 to distinguish them from syllogistic inferences 
 are called immediate. This innovation we re- 
 gard as unfortunate, though of too general use 
 to be neglected, for, according to our view, 
 only one kind of inference is allowed, namely, 
 syllogistic. This, as we have shown, includes 
 the case of conversion per accidens ; and it also 
 includes other, and perhaps all, cases of so- 
 called immediate inference ; as may be readily 
 shown.
 
 THE SYLLOGISM 8 1 
 
 (i) SUBSTITUTION OF CONTRADICTORY. 
 One of these is what is called by Bishop 
 Thompson, " Immediate Inference by Means 
 of Privative Conceptions" and by other logi- 
 cians, improperly, " Infinitation" It is, in fact, 
 identical with the process treated hereafter 
 under the head of " Conversion by Contrapo- 
 sition " ( 91). It consists in substituting for 
 the predicate its negative, or contradictory, and 
 in changing the quality of the proposition, 
 i. e., making the copula of the negative propo- 
 sition affirmative, or that of 'the affirmative 
 proposition negative. Thus, denoting the 
 terms by the capital letters Y and X, and their 
 negatives or contradictories by aY and aX, 
 the negative proposition " Y is not X " may be 
 converted into the affirmative proposition, " Y 
 is aX " ; and similarly the affirmative proposi- 
 tion, " Y is X," into the negative proposition, 
 " Y is not aX " (i. e., is not Not-X). The 
 validity of the process, as may be illustrated 
 by the following diagrams, rests upon the prin- 
 ciple that any negative proposition, as, e. g., 
 " Y is not X," may always be regarded either 
 as denying that the class Y is included in the 
 class X, or as affirming that it is included in 
 the class aX, or "Not-X"; and conversely 
 the affirmative proposition, " Y is X," may 
 be regarded either as affirming that the 
 class Y is included in the class X, or as
 
 82 
 
 LOGIC 
 
 denying that it is included in the class aX, 
 Not-X." 
 
 or 
 
 But when from the affirmative proposition 
 ' Y is X " we conclude that " Y is not Not- 
 X," there is a syllogistic inference; which, de- 
 noting the negative or contradictory of X by 
 aX, may be thus expressed : 
 
 X is not aX (/. e., not Not-X) 
 Yis X 
 
 .*. Y is not aX. 
 
 The inference, therefore, rests upon the 
 judgment that the term " X " is equivalent to 
 the term " Not-aX," and consists in substi- 
 tuting the latter for the former. Hence the 
 principle of inference involved may be stated 
 generally by saying that a term is always 
 equivalent in signification to the contradictory 
 of its contradictory, or, as otherwise expressed, 
 the negative of its negative ; which is but a 
 different expression of the maxim that " two 
 negatives make an affirmative." 
 
 It is, indeed, said that the major terms in the 
 two propositions are the same the proposi- 
 tions differing only in quantity, and hence
 
 THE SYLLOGISM 83 
 
 that no third term is introduced. But this is 
 incorrect ; for the major term in the former 
 proposition is X, and in the latter " not 
 Not-X " ; and it is a fundamental logical doc- 
 trine that no two terms are identical that differ, 
 .either in denotation or connotation, or vocal 
 sign ; and also that the very essence of ratio- 
 cination consists in the recognition of identity 
 of signification in terms having different con- 
 notations or vocal signs, and in the substitution 
 of the one for the other ( 77 et seg.}. 
 
 (2) IMMEDIATE INFERENCE BY ADDED DE- 
 TERMINANTS, AND (3) THE SAME BY COMPLEX 
 CONCEPTIONS. These kinds of supposed im- 
 mediate inference were introduced into Logic 
 by Leibnitz (Davis, Theory of Thought ; , p. 104). 
 The former is stated in the proposition that the 
 same mark may be added to both terms of a 
 judgment; the latter, in the proposition that 
 the two terms of a judgment may be added to 
 the same mark. Of the former, the example 
 given by Thompson is: "A negro is a fellow- 
 creature," therefore, " A negro in suffering is 
 a fellow-creature in suffering " ; of the latter: 
 " Oxygen is an element," and therefore, " The 
 decomposition of oxygen would be the decom- 
 position of an element." The two processes 
 seem to be in substance the same, and both 
 may be expressed symbolically by saying that 
 " If Y is X," then" ZY will be ZX," or (what
 
 84 LOGIC 
 
 is the same) " YZ will be YX " ' ; as may be 
 thus symbolically illustrated: 
 
 This process is erroneously regarded by logi- 
 cians as an immediate inference; but it is, in 
 fact, mediate, and may be stated in syllogistic 
 form as follows : 
 
 Y is X 
 
 ZY is Y 
 
 .'. ZY is X 
 
 The conclusion " ZY is X," fully expressed, 
 is that ZY is that part of X with which it co- 
 incides ; or, in other words, that " ZY is ZYX." 
 But ZYX is ZX; and hence ZY is ZX. 
 
 In this case the observations made with 
 reference to infinitation (supra) will apply a 
 fortiori ; for here a new term, " ZY," is in- 
 troduced, differing from Y in denotation, in 
 connotation, and in verbal sign. 
 
 1 But the converse is not true, i. <*., from the proposition, 
 ZY is ZX, we cannot infer that Y is X ; as will appear from 
 the following diagram :
 
 THE SYLLOGISM 8$ 
 
 It may therefore be concluded, as already 
 asserted, that all inference consists in sub- 
 stituting, for terms of propositions, other terms 
 of equivalent ratiocinative value. 
 
 81. FORMAL AND MATERIAL SUBSTITU- 
 TIONS. Substitution of terms may be either 
 formal or material. The former includes all 
 cases where the substituted term is the original 
 term in a modified form, as, where the ele- 
 ments of a complex term are arranged in a dif- 
 ferent order, as, e.g., where YX is substituted 
 for XY ; or, as where the original term is 
 qualified by some other word or words express- 
 ing a formal relation existing between the sub- 
 stituted term and the original, as, e. g., where 
 in the proposition " Y is X," we substitute for 
 " Y " " some Y, " or for " X " " not Not-X ' ' ; 
 or, as in the example given above, where we 
 substitute for " negro " and " fellow-creature " 
 the terms " negro in suffering " and " fellow- 
 creature in suffering." Material substitutions 
 are those where a new term is substituted, as, 
 e.g., where we substitute for a term a syno- 
 nym, or species for genus, or genus for species. 
 
 Ill 
 
 OF MATHEMATICAL REASONING 
 
 82. MATHEMATICS THE TYPE OF ALL 
 RATIOCINATION. Hence it would seem that
 
 86 LOGIC 
 
 the most perfect type of ratiocination is pre- 
 sented by the mathematical, and especially by 
 the algebraic methods of demonstration ; and 
 this is, in fact, the case, as may be illustrated 
 by two familiar examples: 
 
 ist Example. Thesis. The angles of a plain 
 triangle are together equal to two right angles; 
 or, referring to the figure, a -f- b -j- c = /K 
 (Euclid, Book I., Prop. XXXII.). 
 
 For 
 
 a + b' + c' = &. (/, Prop. XXIX.). 
 
 But 
 
 b' = b 
 
 c' = C. 
 
 Hence, substituting equivalents, 
 
 a-|-b' + c' = a-)-b-(-c= i\\. Q. E. D. 
 
 zd Example. T/iesis. The formula for com- 
 pound interest, i. e., S = p (1 -f- r) n , in which 
 p = principal, n = number of years, r = rate 
 of interest, and S = the amount. 
 
 At end of first year 
 
 S = p + pr = p (1 + r). 
 At end of second year 
 
 S = p(l + r)+pr(l + r) = p(l + r)-.
 
 THE SYLLOGISM 8/ 
 
 At end of third year 
 
 S = p (1 + r)' + pr (1 + r)' = p (1 + 0. 
 At the end of n years 
 
 S = p (1 + r) n . 
 
 83. A CURRENT ERROR ON THIS POINT. 
 It is indeed asserted by recent logicians that 
 there is an essential difference between ordinary 
 and mathematical, or, as it is otherwise ex- 
 pressed, between qualitative and quantitative 
 reasoning. But this opinion arises from the 
 failure to reflect that the comparison of magni- 
 tudes can be effected only by means of units of 
 measurement that can be applied equally to 
 the magnitudes compared, and that these con- 
 stitute the significates denoted by mathemati- 
 cal terms. Hence mathematical reasoning 
 consists not in directly comparing the magni- 
 tudes considered, but in comparing the units 
 that represent them ; and mathematical terms 
 must therefore be regarded as denoting like 
 other terms collections or classes of individ- 
 uals, /. e. , of the units expressed. 
 
 AN OPINION OF MR. BAIN. On this point 
 we have the following from Mr. Bain: " Logi- 
 cians are aware that the form ' A equals B, B 
 equals C, therefore A equals C ' is not reducible 
 to the syllogism. So with relation to ' greater
 
 88 LOGIC 
 
 than' in the argument a fortiori ; yet to the 
 ordinary mind these inferences are as natural, 
 as forcible, and as prompt as the syllogistic 
 inference." But the first expression is a per- 
 fect syllogism differing from the ordinary form 
 only in the different interpretation given to the 
 copula; and this is true also of the argument 
 a fortiori, if we give it the form, " A < B, 
 B < C . *. A < C." It is strange this is not 
 recognized by the author; or, rather, would be 
 strange were not the error common. What 
 is meant, therefore, is that the mathematical 
 cannot be reduced to the ordinary form of the 
 syllogism. But this is not the case, for mathe- 
 matical reasoning can readily be expressed in 
 the ordinary logical forms, as, e. g., the equa- 
 tional syllogism in the two syllogisms follow- 
 ing: 
 
 a is b b is a 
 
 b is c c is b 
 
 .'. a is c .'. c is a; 
 
 and the argument a fortiori in the following: 
 " a is b, b is c, .'. a is c,"- meaning that the 
 class of units denoted by a is contained in the 
 class denoted by b, etc. 
 
 Or the inequalities may be converted into 
 equations, as, e . g. ," a < b " into " a -f- x = b, " 
 and the argument then be expressed in two 
 syllogisms as above.
 
 THE SYLLOGISM 89 
 
 84. REDUCTION OF EUCLID'S FIFTH 
 PROPOSITION TO SYLLOGISMS. Recognizing 
 the mathematical form of the syllogism, there 
 is no need of the cumbersome method usually 
 adopted for the reduction of mathematical 
 reasoning to syllogistic form, as, e. g., in the 
 ancient example of the reduction of Euclid's 
 Fifth Proposition given by Mansel in his notes 
 to Aldrich ; or the reduction of the same prop- 
 osition by Mill (Logic, p. 142). 
 
 In fact, Euclid's demonstration is itself in 
 syllogistic form, and needs only a slight varia- 
 tion in the statement of it to make this ap- 
 parent, as, e. g., as follows: 
 
 Prop. V. The angles at the base of an 
 isosceles triangle are equal to one another. 
 
 Or, referring to the figure, in the isosceles 
 triangle ABC the angles a and c are equal. 
 
 The figure is constructed by 
 producing the equal sides A B 
 and A C to D and E, making 
 the lines A D and A E equal, 
 and by drawing the lines B E 
 and D C. 
 
 Demonstration 
 
 1ST SYLLOGISM 
 
 Major Premise. Prop. IV. 
 
 Minor Premise. The triangles ABE and
 
 90 LOGIC 
 
 A C D are triangles having two sides of the one 
 equal to two sides of the other, each to each, 
 and the included angle equal. 
 
 Conclusion. They are therefore equal in all 
 their corresponding parts, and hence B E = 
 C D and the angle d = the angle e. 
 
 2D SYLLOGISM 
 
 Major Premise. Prop. IV. 
 
 Minor Premise. The triangles C B E and 
 BCD are triangles having two sides of the one 
 equal to two sides of the other, each to each, 
 and the included angle equal. 
 
 Conclusion. They are therefore equal in all 
 their corresponding parts, and hence the angle 
 f = the angle g. 
 
 3D SYLLOGISM 
 
 Major Premise, a d f. (Judgment, or 
 intuitive proposition.) 
 
 Minor Premise, d f = e g. 
 Conclusion, a = e g. 
 
 4TH SYLLOGISM 
 
 Major Premise, a = e g. 
 Minor Premise, e g = c. 
 Conclusion, a = c.
 
 CHAPTER V 
 
 SUMMARY OF THE TRADITIONAL LOGIC 
 
 OF THE TRADITIONAL LOGIC GENERALLY 
 
 85. As explained in the preface, one of 
 the principal objects of this work is to vindi- 
 cate, as against modern innovations, the old or 
 traditional Logic; and accordingly, in all that 
 has been said with exceptions to be noted 
 presently I have kept close to the traditional 
 view, as expounded by Aristotle and the most 
 approved of the older logicians. I have, in- 
 deed, repudiated the doctrine advocated by 
 Whately, and by modern logicians generally, 
 that would distinguish between the formal and 
 the material relations of terms, and restrict the 
 scope of Logic to the former; but in this also 
 I follow Aristotle and the better authorities. 
 
 The only particulars, therefore, in which I 
 have departed from the traditional view of 
 Logic are: (i) that I reject the " Particular 
 Propositions " of the old Logic and those parts 
 of the old doctrine of the Proposition and of 
 91
 
 92 LOGIC 
 
 the Syllogism that are founded on this view 
 of the proposition ; and (2) that I have adopted, 
 in place of the Dictum, the Principle of Sub- 
 stitution ; which is an obvious corollary from 
 the Dictum, and is more readily understood 
 and applied. 
 
 At the same time, it must be admitted, the 
 old doctrines of the Proposition and the Syl- 
 logism are remarkable for the accurate analysis 
 upon which they rest, and the wonderful ingen- 
 uity and acuteness with which they have been 
 developed. They have thus become part of 
 the accepted philosophy of the world ; and there 
 has thus been developed a technical language 
 that has come to be universally received and so 
 generally used that, without an understanding 
 of it, all the literature on the subject must be 
 a closed book to us. I now propose, therefore, 
 to give a brief exposition of these doctrines. 
 
 II 
 
 THE TRADITIONAL DOCTRINE OF THE PROPOSITION 
 
 86. QUALTITY OF PROPOSITIONS. Prop- 
 ositions are said to differ in quality accord- 
 ingly as they are affirmative or negative. Thus 
 the propositions " All Y is X and " Some 
 Y is X " are affirmative ; the propositions " No 
 Y is X " and " Some Y is not X," negative. 
 
 87. QUANTITY OF PROPOSITIONS. Again, 
 propositions, whether affirmative or negative,
 
 TRADITIONAL LOGIC 
 
 93 
 
 are said to differ in quantity accordingly as the 
 predicate is asserted, or denied universally of 
 all individuals of the class denoted by the sub- 
 ject or only part of such individuals. In the 
 former case the subject is said to be distributed, 
 and the proposition is called universal ; in the 
 latter, the subject is undistributed, and the 
 proposition is said to be particular. Thus, 
 e. g., the propositions, " All Y is X" and 
 4 No Y is X " are both universal; and the 
 propositions, " Some Y is X " and " Some Y 
 is not X," both particular. 
 
 88. TABLE OF PROPOSITIONS. Hence, 
 four forms of propositions are recognized by the 
 old logicians, viz. : (i) the Universal Affirma- 
 tive ; (2) the Universal Negative ; (3) the Par- 
 ticular Affirmative; and (4) the Particular 
 Negative ; which are designated respectively 
 by the letters A, E, I, and O; and, with their 
 expressions in Euler's Symbols, are as fol- 
 lows, viz. : 
 
 A: Y is X (/.<?., All Y is X) 
 
 E: Y is not X (/. e., No Y is X) ' (Y) 
 I: Some Y is X 
 
 O: Some Y is not X 
 1 The above differs somewhat from the ordinary notation ;
 
 94 LOGIC 
 
 In the negative propositions, E and O, it 
 will be observed, the predicate is distributed or 
 taken universally ; in the affirmative proposi- 
 tions it is undistributed. 
 
 89. OPPOSITION OF PROPOSITIONS. Two 
 propositions are said to be opposed to each 
 other when, having the same subject and pred- 
 icate, they differ in quantity or quality, or both. 
 
 Propositions that differ both in quality and 
 quantity, as A and O, or E and I, are called 
 contradictories, as, e. g. , " Y is X," and " Some 
 Y is not X " ; or " Y is not X " and " Some 
 Y is X." Those that differ in quality only, if 
 
 according to which it is thought necessary in A and E to use 
 the signs " All " and " No," in order to indicate that the sub- 
 ject is distributed, as, e. g., "All Y is X," "No Y is X." 
 But, properly speaking, the signs "All" and " No" are un- 
 necessary and redundant. For when we say, e. g., "Man is 
 mortal," or " Man is not mortal" we mean, when we speak 
 properly, that in the former case the class "man" is wholly 
 included in, and in the latter that it is wholly excluded from, 
 the class " mortal " ; or, in other words, as the case may be, 
 that " All men are mortal" or that " No man is mortal" 
 ( 53. n -)- The last expression is also objectionable on ac- 
 count of the liability to confound the expression " No man " 
 with the term " Not-man " in converting either of the above 
 propositions by contraposition (for which see infra, 91) ; 
 or (more generally) the negative proposition "No Y is X " 
 is liable to be confounded with the affirmative proposition, 
 "A T ot- Y is X." Hence it will be preferable to regard the 
 subject as always distributed, except where it is preceded by 
 the adjective " some " ; and, in place of the sign " no" before 
 the subject, to use the particle " not " after the copula.
 
 TRADITIONAL LOGIC 95 
 
 universal, are called contraries, as, e. g., " Y is 
 X " and " Y is not X " ; and if particular, sub- 
 contraries, as, e. g., " Some Y is X " and 
 " Some Y is not X." Where propositions 
 differ in quantity only, as A and I, or E and 
 O, the particular propositions are called subal- 
 terns, as, e. g. , " Y is X " and " Some Y is 
 X "; and " Y is not X " and " Some Y is 
 not X." 
 
 There are, therefore, four kinds of opposition 
 recognized by logicians, viz. : (i) the opposi- 
 tion of contradictories ; (2) that of contraries ; 
 (3) that of subcontraries, and (4) that of subal- 
 terns to their corresponding universals; which, 
 with their relations to each other, are admi- 
 rably expressed in the following table, which 
 has come to us from ancient times: 
 
 !\ /\ 
 I V I 
 
 5 <* "**> 
 
 V \\ 
 
 -SUBCOMTRARY- 
 
 (i) CONTRADICTORIES. The most complete 
 kind of opposition is that of contradictories. 
 These cannot both be either true or false: i. e., 
 if one is true, the other is false; or, if one is
 
 96 LOGIC 
 
 false, the other is true. For if it be true that 
 " All men are sinners," it cannot be true that 
 " Some men are not sinners " ; and, conversely, 
 if it be true that " Some are not righteous," it 
 cannot be true that " All men are righteous." 
 In other words, between contradictories there 
 is no intermediate proposition conceivable ; one 
 must be true and the other false. This is 
 called the law of Excluded Middle. 
 
 (2) CONTRARIES. Contraries cannot both 
 be true; for if it be true that " Every man is 
 an animal," it must be false that " No man is 
 an animal." But both may be false, as, for 
 example, the propositions that " All men are 
 learned," and that " No men are learned"; 
 which are both false, for some are learned and 
 some are not. In other words, contrary propo- 
 sitions do not exclude the truth of either of the 
 particular propositions between the same terms. 
 
 (3) SUBCONTRARIES. Subcontraries are con- 
 trasted with contraries by the principle that 
 they may be both true, but cannot both be 
 false. Thus it may be true that " Some men 
 are just," and also that " Some men are not 
 just " ; but if it be false that " Some men are 
 just," it must be true that " No man is just," 
 which is the contradictory, and, a fortiori, 
 that "Some men are not just," which is the 
 subcontrary. 
 
 (4) SUBALTERNATE OPPOSITION. With re-
 
 TRADITIONAL LOGIC 97 
 
 gard to subaltern propositions, their truth 
 follows from the corresponding universal pro- 
 positions; for if " all men are animals," " some 
 men are animals," and if " no man is an ape," 
 " some men are not apes." But from the truth 
 of a subaltern proposition we cannot infer the 
 truth of the corresponding universal, as, e. g., 
 from the proposition " Some men are false," 
 the proposition " All men are false "; or from 
 the proposition " Some men are not false," the 
 proposition that " No man is false." 
 
 90. OBSERVATIONS UPON CONTRARY AND 
 CONTRADICTORY OPPOSITIONS. Accurately 
 speaking, these constitute the only kinds of 
 opposition. Subcontraries are, in fact, not op- 
 posites; and the same is true of subalterns and 
 their corresponding universals. 
 
 It will be observed it does not follow from 
 the principle of contrary opposition that of 
 two terms regarded as subject and predicate 
 as, e. g. , Y and X either the latter or its 
 negative may always be predicated of the 
 former, or, in other words, that Y must be 
 either X, or not X; for, in fact, some Y may 
 be X, and some Y not X, as will obviously 
 appear from the following diagrams: 
 

 
 98 LOGIC 
 
 Hence there arises, seemingly, a puzzling 
 contradiction between this principle and the 
 law of Excluded Middle as it is often stated. 
 Thus, it is said, " Rock must be either hard or 
 not hard" (Jevons, Lessons in Logic, p. 119), 
 or, generally, " Y is either X or not X." But 
 obviously this, unless accidentally, is not true; 
 for some rock may be hard and some soft ; or 
 some Y may be X, and some not X. And so 
 we cannot say of " men " either that they are 
 learned or that they are not learned ; for some 
 are the one and some the other. But the ap- 
 parent contradiction arises from the misstate- 
 ment of the law of Excluded Middle; which 
 is itself nothing more or less than the principle 
 governing contradictories, as expressed above. 
 We may, indeed, where a subject term (as, 
 e. g., Y) denotes an individual or single thing 
 (real or fictitious), affirm of it that it is either 
 X or not X; but if Y denotes a class of more 
 than one we cannot so affirm. 1 
 
 1 Even Hobbes falls into the error of Jevons on this point. 
 "Positive and negative terms," he says, "are contradictory 
 to one another, so that they cannot both be the name of the 
 same thing. Besides, of contradictory names, one is the name 
 of anything whatsoever (i. e., of any conceivable thing), for 
 whatsoever is, is either a man, or not a man, white, or not 
 white, and so of the rest." But, it may be asked, " Does the 
 name 'biped' denote (universally) either man, or not man?" or 
 " the name 'man', either white man, or man not white?" 
 
 The confusion results from the technical view that regards
 
 TRADITIONAL LOGIC 99 
 
 91. CONVERSION OF PROPOSITIONS. A 
 proposition is said to be converted when its 
 terms are transposed, i. e., when the subject is 
 made the predicate and the predicate the sub- 
 ject ( 54). Such conversion is admissible 
 only when illative, i. e., where the truth of the 
 converse is implied in that of the original prop- 
 osition. When such conversion can be made 
 without otherwise changing the proposition it 
 is called a simple conversion; otherwise, it is 
 called a con version per accidens. Thus A (" Y 
 is X ") cannot be converted simply, because the 
 subject only is distributed; we therefore can- 
 not say that " All X is Y," but only that 
 " Some X is Y," which is called conversion per 
 accidens. But E (" Y is not X ") as both sub- 
 ject and predicate are distributed may be con- 
 verted simply ; or, in other words, we may say 
 
 the Particular Proposition as a form distinct from the Uni- 
 versal, and its source would be removed if, as elsewhere 
 suggested, this form of the proposition should be rejected 
 ( 52, n.). We might then adopt, as equally accurate 
 and profound, the remaining observation of Hobbes, that 
 "the certainty of this axiom, namely, that of two contradic- 
 tory names one is the name of anything whatsoever, the other 
 not, is the original and foundation of all ratiocination, that 
 is, of all philosophy" (Logic, Sec. 8), which is in accord with 
 the view of Aristotle : " For the same thing to be present and 
 not to be present, at the same time, in the same subject, and 
 in the same sense, is impossible. . . . For by nature this 
 is the first principle of all the other axioms " (Metaphysics, 
 R. iii., chap. Hi.).
 
 IOO LOGIC 
 
 that " No X is Y." So with I (" Some Y is 
 X "), as both subject and predicate are un- 
 distributed, the proposition may be simply 
 converted, i. e., if " Some Y is X," then it is 
 necessarily true that " Some X is Y." 
 
 By one or the other of these methods, i. e., 
 either simply or per accidens, all propositions of 
 the forms A, E, and I may be converted. But O 
 (" Some Y is not X ") cannot be thus converted. 
 Thus, e. g., it cannot be inferred from the prop- 
 osition "Some Greeks are not Athenians" 
 that " Some Athenians are not Greeks." But 
 such conversion may be effected by simply re- 
 garding the negative particle (not) as part of 
 the predicate ; by which expedient O is changed 
 into I, and may be simply converted, as, e. g., 
 "Some Greeks are Not-Athenians " ; which 
 may be converted into the proposition " Some 
 Not-Athenians are Greeks. ' ' So from the prop- 
 osition " Some men are not learned," though 
 we may not infer that " Some learned are not 
 men," we may infer that " Some unlearned 
 are men." This is called by the old logi- 
 cians "Conversion by Contraposition," and by 
 Whately, " Conversion by Negation." 
 
 This method of conversion is applicable to 
 A and E as well as O, and, as it is of very ex- 
 tensive use, we append a table of such conver- 
 sions, taken, with some alterations, from De 
 Morgan (Formal Logic, p. 67). In this table
 
 TRADITIONAL LOGIC IOI 
 
 (altering De Morgan's notation) the original 
 terms of the proposition are denoted by the 
 capital letters Y and X, and their contraries 
 respectively by prefixing the Greek privative a. 
 We append also for illustration the symbolical 
 expressions for the several propositions: 
 
 A: " Y is X " ; " Y is not aX " ; " aX is not Y " ; 
 " aX is aY " : 
 
 The righteous are happy 
 The righteous are not unhappy / 
 The unhappy are not righteous ' 
 The unhappy are unrighteous. 
 
 E: "YisnotX"; " Y is aX " ; " Some aX is Y " ; 
 
 " Some aX is not aY." 
 
 " X is not Y " ; " X is aY " ; " Some aY is X " ; 
 " Some aY is not aX " : 
 
 Perfect virtue is not human '' \j \ 
 
 Perfect virtue is unhuman IS~\ /f~\\ 
 
 Y Ca A I X I 
 
 Some unhuman virtue is perfect v^ 
 
 Some unhuman virtue is imperfect. \ , 
 
 ^^ *s 
 
 Human virtue is not perfect 
 Human virtue is imperfect 
 Some imperfect virtue is human 
 Some imperfect virtue is not unhuman. 
 
 O: " Some Y is not X " ; " Some Y is aX " ; " Some 
 aX is Y " ; " Some aX is not aY " :
 
 102 LOGIC 
 
 Some possible cases are. not probable 
 
 Some possible cases are not improb- 
 able 
 
 Some improbable cases are possible 
 
 Some improbable cases are not im- 
 possible. 
 
 It will be observed from the above table that 
 a universal affirmative proposition can always 
 be converted into another universal affirmative 
 between the contradictories of its original terms 
 by simply reversing the order of the terms and 
 substituting for them their contradictories. 
 
 92. OF MATERIAL CONVERSIONS. It will 
 be observed that the conversions of propositions 
 treated by logicians have regard to the dis- 
 tinction, heretofore explained, between the 
 formal and the material relations of terms 
 ( 66 (2)), and are confined exclusively to what 
 may be called formal conversions, i. e., to cases 
 where the equivalence of the converted and 
 original propositions results from the formal or 
 general relations of terms. But conversions of 
 propositions based upon the material relations 
 of terms are of essentially the same nature, as, 
 e. g., where the proposition " John is the son 
 of William " is converted into the proposition 
 
 William is the father of John"; or the 
 proposition" Cain murdered Abel" into the 
 proposition " Abel was murdered by Cain," or 
 into the proposition " Cain is the man that
 
 TRADITIONAL LOGIC 103 
 
 murdered Abel." These, having regard to 
 the received distinction between the formal 
 and the material relations of terms, may be 
 called material conversions ; and are infinitely 
 the more numerous class, and equally deserv- 
 ing of attention. But though conversions of 
 this kind are in constant use, and though, in- 
 deed, we cannot proceed a step in our logical 
 processes without them, yet the subject has 
 received but little attention, and remains as 
 yet a vast, unexplored domain. 1 It can only 
 be said, therefore, in the present condition of 
 logical doctrine, that as the distinction be- 
 tween the formal and the material relations of 
 terms has been found unessential, so must the 
 distinction between formal and material con- 
 versions be regarded. Both classes of conver- 
 
 1 To this domain belong such subjects as the "Categories" 
 "Intensive Propositions,'''' " Hypothetical Propositions" and, 
 in short, all forms of expression that differ from the ordinary 
 logical proposition. With these Logic is concerned only in 
 so far as is involved in their conversion into logical forms. 
 Otherwise, neither the Intensive nor the Hypothetical Logic 
 (if we may give either the name) can be regarded as part of 
 Logic as traditionally received ; which is based exclusively 
 upon the logical form of the proposition and its extensive 
 interpretation. With regard to the Hypothetical Logic, it 
 will be observed, it has no place in Aristotle's treatises ; and 
 Mansel is of the opinion in which I agree that in this he 
 showed a juster notion of the scope of Logic than his suc- 
 cessors. The subject is well treated in the current works on 
 Logic, and is worthy of some attention from the student.
 
 104 LOGIC 
 
 sions rest equally for their validity simply 
 upon judgments as to the equivalence of ex- 
 pressions. 
 
 Ill 
 
 THE TRADITIONAL DOCTRINE OF THE SYLLOGISM 
 
 93. The following epitome of the doctrine 
 of the syllogism as traditionally received, brief 
 as it is, will with what has already been said 
 be found amply sufficient to expound it. 
 It will, indeed, require the same close attention 
 and thought as is usually given to mathemati- 
 cal demonstrations; but it may be said that 
 to those who are unwilling to give, or are in- 
 capable of giving, to it this kind of thought, 
 the study of Logic cannot be of much benefit. 
 
 I . Of the Moods and Figures of the Syllogism 
 
 94. MOODS OF THE SYLLOGISM. The syl- 
 logism is said to be in different moods, according 
 to the occurrence and arrangement in it of the 
 several forms of the proposition A, E, I, and 
 O; as, e. g., in the syllogism Y is X, Z is 
 Y, . *. Z is X, ' ' which consists of three universal 
 affirmative propositions, and is, therefore, said 
 to be in the mood A A A. 
 
 The four forms of the proposition, A, E, I, 
 O, may be arranged, in sets of three each, in 
 sixty-four different ways, but upon examina- 
 tion it is found that of these there are eleven
 
 TRADITIONAL LOGIC 1 05 
 
 arrangements only that constitute valid syllo- 
 gisms; and hence the legitimate syllogism can 
 have but eleven moods, viz. : 
 
 Table of Moods 
 
 A A A, A A I, A E E, A E O, A I I, 
 A O O, E A E, E A O, E I O, I A I, O A O. 
 
 95. FIGURES OF THE SYLLOGISM. Again, 
 syllogisms are said to be of different figures, 
 according to the position of the middle term in 
 the syllogism with reference to the extremes; 
 and as there are said to be four different ways 
 in which the middle term may be thus placed, 
 syllogisms are said to have four figures, viz. : 
 the 1st figure, where the middle term is the 
 subject of the major and the predicate of the 
 minor premise ; the 2d, where it is fa& predicate 
 both of the major and of the minor premise ; 
 the 3d, where it is the subject of both the major 
 and the minor premise ; and the 4th, where it 
 is the predicate of the major and the subject of 
 the minor premise. Thus using the conven- 
 tional symbols the forms of the different 
 figures are usually expressed as follows : 
 
 Table of Figures 
 
 1st Fig. 2cl Fig. 3d Fig. 4th Fig. 
 
 Y X, X Y, Y X, X Y, 
 
 Z Y, Z Y, Y Z, Y Z, 
 
 Z X, Z X, Z X, Z X.
 
 106 LOGIC 
 
 If the eleven moods of the syllogism were all 
 valid in each of the four figures, there would 
 result forty-four different kinds of syllogisms 
 differing in mood or figure. But none of the 
 moods are valid in all the figures; and it is 
 found on examination that there are in fact 
 only twenty-four kinds of syllogisms that are 
 valid ; and that of these five are useless. So 
 that the number of different kinds of legiti- 
 mate syllogisms recognized by logicians is 
 nineteen. 
 
 96. REDUCTION OF SYLLOGISMS. All 
 these forms may, however, be reduced or con- 
 verted without affecting their validity into 
 the form of the first figure ; which is accord- 
 ingly regarded by logicians as the principal, or 
 normal figure of the syllogism. The different 
 figures and moods of the syllogism, and the 
 methods of reduction or conversion from one 
 figure to another, are briefly expressed in the 
 following hexameter verses, constituting what 
 may be called 
 
 The Table of Syllogisms 
 
 Fig. i Barbara, Olar^nt, Dam, Ferioque, prioris 
 Fig. 2 Cesare, Canvstr^s, Festino, Fak^n?, secundae 
 Fig. 3 Tertia, Darapti, D/sam/s, Dat/sz', Fi?lapt<?n, 
 
 D0kam0, Feriso, habet, quarta insuper 
 
 addit 
 Fig. 4 Bramant/p, Camenes, D/man's, Fesapo, 
 
 Fresison.
 
 TRADITIONAL LOGIC IO/ 
 
 In these lines the words commencing with 
 capital letters (except " Tertia ") are the names 
 of the several syllogisms in each figure, and 
 the italicized vowels point out the moods of 
 the propositions constituting the several syl- 
 logisms. Thus, e. g., the vowels indicate that 
 Barbara consists of the three propositions, A, 
 A, A; Celarent of E, A, E; Darn of A, I, I ; 
 Feriso of E, I, O, etc. 
 
 The initial letter in the name of each syllo- 
 gism in the second, third, and fourth, or, as 
 they are called, the indirect figures, indicates 
 that the given syllogism is to be reduced to the 
 syllogism in the first figure commencing with 
 the same letter, as, e. g,, Cesare, Camestres, 
 Camenes into Celarent ; Bramantip into Bar- 
 bara ; Darapti y etc., and Dimaris, etc., into 
 Darii ; Festino, etc., Felapton, etc., and Fesapo, 
 etc., into Ferio. 
 
 The letters s, p, and k indicate that the pro- 
 position indicated by the vowel immediately 
 preceding is to be converted s indicating 
 simple conversion, / conversion per accidens, 
 and k conversion by contraposition, or nega- 
 tion. ' 
 
 1 The use of conversion by contraposition as a means of 
 reduction is a late invention. It is, in general, used only in 
 the two forms, Fakoro and Dokamo, or, as they were origi- 
 nally called, Baroko and Bokardo, as all other forms can be 
 reduced without its aid, i. e., by the use of simple conversion 
 or conversion per accidens. Prior to the use of this method,
 
 io8 LOGIC 
 
 The letter m indicates that the premises are 
 to be transposed. 
 
 The other letters are without significance. 
 
 TABLE OF SYLLOGISMS. By the use of the 
 ' Table of Moods" and the " Table of Fig- 
 ures," all the syllogisms given in the " Table 
 of Syllogisms" may be readily constructed, 
 and the mode of reducing the syllogisms in the 
 second and third and fourth figures to the cor- 
 responding syllogisms in the first figure be 
 readily perceived. 1 
 
 Baroko and Bokardo could not be directly reduced to the first 
 figure, but indirectly only by a process called rednctio ad 
 impossible ; which consisted in substituting for one of the 
 premises the contradictory of the conclusion. 
 
 By this method Baroko is converted into a syllogism in Bar- 
 bara, having the contradictory of the original conclusion for a 
 minor premise, and the contradictory of the original minor 
 premise for a conclusion, which, as the minor premise is true 
 ex hypothese, is an absurdity, viz. : 
 
 (Original Syllogism) (Reduced Syllogism) 
 
 X is Y X is Y 
 
 Some Z is not Y Z is X 
 
 .'. Some Z is not X .'. Z is Y 
 
 By the same method Bokardo is converted into a syllogism 
 in Barbara, having the contradictory of the original conclusion 
 for a major premise, and the contradictory of the original 
 major for a conclusion, e. g. : 
 
 Some Y is not X Z is X 
 
 Y is Z Y is Z 
 
 . ' . Some Z is not X . ' . Y is X 
 
 1 A table of the several syllogisms, with their reductions, 
 illustrated by Euler's symbols, is appended (see Appendix M).
 
 TRADITIONAL LOGIC 109 
 
 97. OBSERVATIONS UPON THE FORMS OF 
 SYLLOGISMS. It will be observed from what 
 has been said that the numerous forms of syl- 
 logisms recognized by the old logicians result 
 from two assumptions the one erroneous and 
 the other unnecessary. 
 
 The first is the erroneous assumption that 
 the symbols Y and X must always be taken as 
 denoting respectively the minor and the major 
 terms; from which results that there areyWr 
 figures of the syllogism, instead of three. But 
 if in the fourth figure we regard X as the minor 
 term and Y as the major, it becomes of the 
 first figure. Hence the fourth figure which 
 was not recognized by Aristotle, but is a late 
 invention is rightly rejected by the best 
 authorities. 
 
 The other assumption is that the particular 
 propositions (" Some Y is X " or " Some Y is 
 not X ") are to be regarded as involving the 
 same terms as the universal (" Y is X " or " Y 
 is not X "), and the expression " some " as a 
 mere sign of quantity; from which (and the 
 first assumption) there result the four forms of 
 the proposition, A, E, I, and O, and the nine- 
 teen forms of syllogism recognized by logicians, 
 Barbara, Celarent, etc. 1 
 
 1 The doctrine of the syllogism, and especially that of its 
 moods and figures, has been elaborated by the logicians per- 
 haps to an unnecessary extent, but as it stands must always
 
 I IO LOGIC 
 
 98. PROPOSED SIMPLIFICATION OF 
 FORMS. But if in the particular propositions 
 (I and O) we regard the expression " some " 
 not as a sign of quantity, but as part of the 
 term, or, in other words, if we regard " Some 
 Y " instead of " Y " as the term, they be- 
 come the same as" A" and " E," i. e., Univer- 
 sal ( 52, n.). By this simple change the four 
 forms of the proposition are reduced to two (A 
 and E), and the nineteen forms of syllogism to 
 the two simple forms of Barbara and Celarent. 1 
 
 2. Of the Dictum de Omni et Nullo 
 
 99. OF THE SEVERAL FORMS OF THE 
 DICTUM. The principle of the syllogism, or 
 the Dictum de Omni et Nullo, has already been 
 considered at length, and what has been said is 
 sufficient to elucidate its nature. It is, how- 
 ever, variously stated by logicians, as indeed 
 by Aristotle himself, and it will be of interest 
 to consider some of its various forms. 
 
 constitute a necessary part of a liberal education. For prac- 
 tical use, however, it is unnecessarily complicated ; and it will 
 be found that when modified, as we have suggested (i. e., by 
 rejecting the particular proposition, and substituting for the 
 ordinary form of the dictum the Principle of Substitution), 
 the simplicity of its application will be largely increased. 
 
 1 More accurately, perhaps, it should be said to four forms, 
 namely, Barbara, Celarent, Cesare, and Camestres. But the 
 last two are essentially the same as the second, and there is no 
 advantage to be gained by distinguishing them.
 
 TRADITIONAL LOGIC III 
 
 Of these, in addition to the form already 
 given, and which is on all accounts to be pre- 
 ferred, there are two others to which we will 
 refer. 
 
 These, as given by Whately, are as follows : 
 Whatever is predicated \i. e., affirmed or 
 denied] universally of any class of things, may 
 be predicated in like manner [viz., affirmed or 
 denied] of anything comprehended in that 
 class " (Logic, bk. i., iv.). 
 
 ' Whatever is predicated of a term dis- 
 tributed, whether affirmatively or negatively, 
 may be predicated in like manner of everything 
 contained under it "(Id., bk. ii., chap, iii., 2). 
 
 In effect, these two statements may be taken 
 as types of all the other forms of the dictum. 
 But, as we have observed, ' ' thing " or " things 
 is an extremely vague and unsatisfactory term, 
 and it would be better to substitute for it the 
 expression " significate," or " significates." 
 
 These two forms of the dictum are in ef- 
 fect the same. For to say, as in the latter, 
 "Whatever is predicated of a term distributed," 
 is in effect to say, " Whatever is predicated 
 universally of any class," etc. Bearing this 
 in mind, and substituting " significates " for 
 " t Jungs," both forms of the dictum may be 
 more briefly expressed by saying that " a term 
 predicated of a term may be predicated also of 
 any or all of its significates." Where the pred-
 
 112 LOGIC 
 
 ication is affirmative the principle, as we have 
 seen, is called the Dictum de Omni ; where it 
 is negative, the Dictum de Nullo. 
 
 It is said by Whately that the dictum " can- 
 not be directly or immediately applied to all 
 even categorical syllogisms, but, as all syllo- 
 gisms may be reduced to the first figure, it may 
 be ultimately applied to all." Hence, " to 
 avoid the tediousness of reducing all syllogisms 
 to that form to which Aristotle's dictum is ap- 
 plicable, it has been deemed necessary to in- 
 vent separate rules or canons for the indirect 
 figures" (Whately, Logic, bk. ii., chap, iii., 2); 
 and in this logicians generally agree. 
 
 100. CANONS OF THE SEVERAL FIGURES. 
 
 These canons of the several figures omitting 
 
 the fourth figure, which is disallowed by the 
 
 best authorities as being a mere perversion of 
 
 the first are as follows : 
 
 First Figure : The Dictum de Omni et Nnllo, 
 as above. 
 
 Second Figure: Dictum de Diverse. If one 
 term is contained in and another excluded from 
 a third term, they are mutually excluded. 
 
 Third Figure: Dictum de Exemplo. Two 
 terms which contain a common part, partly 
 agree, or, if the one term contain a part which 
 the other does not, they partially differ (Devey's 
 Logic, pp. 109-111). 
 
 101. THE DICTUM, RIGHTLY EXPRESSED,
 
 TRADITIONAL LOGIC 113 
 
 APPLICABLE TO ALL THE FIGURES. But if 
 the form of the dictum we have adopted, and 
 which is substantially as given by Aristotle 
 ( 76), be taken, it will be found to apply to 
 all syllogisms universally. But as the form 
 given in the paragraph cited has reference to 
 the division of propositions there adopted into 
 two kinds only (namely, A and E, rejecting I 
 and O), it must now be stated somewhat differ- 
 ently, so as to apply to the ordinary division 
 of propositions into their four kinds, A, E, I, 
 and O: 
 
 ' Where three terms (which we will call the 
 middle and two extremes) so subsist with rela- 
 tion to each other that the one extreme is in- 
 cluded (wholly or partly] in the middle, and 
 the middle is included in or excluded from the 
 other, then (as the case may be) the extreme 
 included in the middle will be (ivliolly or partly) 
 included in or excluded from the other ex- 
 treme." 
 
 Or dividing the proposition, and leaving the 
 terms " wholly " or "partly " to be supplied 
 as required, it may be stated thus: 
 
 Dictum de Omni: (a) If one extreme of a 
 syllogism be included in the middle and the 
 middle in the other extreme, then will the 
 former be included in the latter. 
 
 Dictum de Nullo : (b) If one extreme of a 
 syllogism be included in the middle, and the
 
 1 14 LOGIC 
 
 middle be excluded from the other, then will the 
 former extreme be excluded from the latter. 
 
 In this form the dictum may be readily ap- 
 plied to each of the three figures. 
 
 With regard to the first this is sufficiently 
 obvious; for the syllogisms in this figure are 
 in fact but mere symbolical expressions of the 
 dictum that is to say, Barbara and Darii of 
 the Dictum de Omni, and Celarent and Fcrio 
 of the Dictum de Nullo. 
 
 With regard to the second figure, the Dictum 
 de Nullo is, in effect, identical with the Dictum 
 de Diverso. For to say, as is said in the former, 
 that " the middle term is excluded from the 
 last extreme," is in effect to say, " that ex- 
 treme is excluded from the middle"; and 
 hence the Dictum de Nullo agrees with the 
 Dictum de Diverso in asserting that two terms, 
 the one of which is included in and the other 
 excluded from a common middle term, are 
 mutually excluded. 
 
 So in the third figure the dictum is equally 
 applicable. For in the affirmative forms (Da- 
 rapt i, Disamis, and Datisi] it is asserted that 
 the middle is contained in, and in the negative 
 forms (Felapton, Dokamo, and Feriso] that it 
 is excluded from one of the extremes; and in 
 both it is asserted, in effect, that the other ex- 
 treme is partly included in the middle. Hence 
 the former come directly under the Dictum de
 
 TRADITIONAL LOGIC 115 
 
 Omni, and the latter under the Dictum de 
 Nullo. 
 
 That the dictum agrees with the Dictum de 
 Exemplo, however, cannot be said ; for that, in 
 terms, merely asserts the truism that " two 
 terms which contain a common part " in that 
 respect agree, or, " if one contain a part 
 which the other does not," to that extent 
 differ. But it gives us no information as to 
 the principle by which it is determined 
 whether the two terms have or have not a 
 common part. Whereas the dictum of Aris- 
 totle explains that if one extreme be partly 
 included in the middle, and the middle be 
 either wholly included in or excluded from the 
 other extreme, then the two extremes will or 
 will not agree or have a common part, as the 
 case may be. 
 
 It is therefore obvious that the dictum of 
 Aristotle applies equally to all syllogisms, and 
 that to invent separate canons for the several fig- 
 ures is unnecessary and productive of confusion. 
 
 102. THE DICTUM APPLICABLE TO SING- 
 ULAR AND OTHER EQUATIOXAL PROPOSI- 
 TIONS. It has also been objected to the 
 dictum by several logicians that it is not ap- 
 plicable to syllogisms in which the terms are 
 singular, or to other syllogisms composed of 
 equational propositions; which, it is said, are 
 governed by a different regulating principle,
 
 1 16 LOGIC 
 
 viz., that " notions equivalent to one and the 
 same third notion are equivalent to each 
 other" (McCosh, Logic, pp. 126, 127). But 
 this is obviously not so. For an individual 
 may, for logical purposes, be regarded as a 
 class (i. e., a class of one); and classes that are 
 equal to each other mutually include each 
 other. Hence the dictum applies directly to 
 syllogisms of this character; and we may al- 
 ways express such a syllogism, e. g. , Z = Y, 
 Y = X .'. Z = X, in the usual form: Z is Y, 
 Y is X .-. Z is X. 
 
 103. OF PROPOSED IMPROVEMENTS ox 
 THE DICTUM. Other objections are urged to 
 the dictum of Aristotle by modern logicians, 
 and, to remedy its supposed defects, numerous 
 new dicta or canons have been invented to take 
 its place. But these will be found on examina- 
 tion to be either erroneous or merely different 
 and less satisfactory statements of the old 
 dictum. 
 
 In at least this fundamental aspect of the 
 subject the opinion of Kant with reference to 
 the Old Logic must be accepted, viz., that 
 " Since Aristotle it has not had to retrace a 
 single step, and to the present day has not 
 been able to make one step in advance." ' 
 
 1 In these views I find myself supported by the following 
 judicious observations of Professor Jevons : 
 
 "During the last two or three years," he observes, "the
 
 TRADITIONAL LOGIC 1 1/ 
 
 3. Rules of the Syllogism 
 
 104. STATEMENT OF THE RULES. The 
 following rules, with the fallacies resulting from 
 their violation, are given by logicians. They 
 are all obvious deductions either from the 
 definition of the syllogism or from the dictum 
 of Aristotle. 
 
 (1) Every syllogism has three, and only 
 three, terms, viz., the Major, the Minor, and 
 the Middle term. 
 
 The violation of this rule is called the Fal- 
 lacy of Four Terms (Quarternio Terminorum). 
 It generally results from the ambiguity of a 
 term, and indeed can hardly occur in any 
 other way. 
 
 (2) Every syllogism contains three, and only 
 three, propositions, viz., the Major and the 
 Minor premise and the Conclusion. 
 
 This rule can be violated only by violating 
 the first rule, and is therefore to be regarded 
 as superfluous. 
 
 (3) The Middle term must be distributed 
 once at least in the premises. 
 
 thought has constantly forced itself on my mind, that the 
 modern logicians have altered the form of Aristotle's proposi- 
 tion without making any corresponding alterations in the 
 dictum or self-evident principle, which formed the fundamen- 
 tal postulate of his system. Aristotle regarded the proposi- 
 tion as stating the inclusion of one term or class within 
 another ; and his axiom was perfectly adapted to this view 
 (Pure Logic, p. 86).
 
 Il8 LOGIC 
 
 The violation of this rule is called the Fallacy 
 of Undistributed Middle, as, e.g., in the fol- 
 lowing pseudo-syllogism: X is Y, Z is Y .*. Z 
 is X. 
 
 (4) No term must be distributed in the con- 
 clusion that was not distributed in one of the 
 premises. 
 
 The violation of this rule is called the Fallacy 
 of the Illicit Process of the Major or of the 
 Minor term, as the case may be, as, e. g., in 
 the following syllogism : Y is not X, some 
 Z is Y . '. Z is not X, Nations capable 
 of self-government should not be despotically 
 governed; some nations are capable of self- 
 government; no nation should be despotically 
 governed, which is a case of illicit process of 
 the Minor term ; or as in the following syllo- 
 gism: Y is X, Z is not Y .*. Z is not X, 
 Anglo-Saxons love liberty, Frenchmen are 
 not Anglo-Saxons .'. Frenchmen do not love 
 liberty, which is an illicit process of the Major. 
 
 (5) From negative premises nothing can be 
 inferred. 
 
 The violation of this rule is called the Fallacy 
 of Negative Premises; e. g. , Y is not X, Z is 
 not Y .'. Z is X or Z is not X. 
 
 (6) If one premise be negative the conclusion 
 must be negative; and, vice versa, to prove a 
 negative conclusion one of the premises must 
 be negative.
 
 TRADITIONAL LOGIC 1 19 
 
 The violation of this rule may be called the 
 Fallacy of Affirmative Conclusion, e.g., Y is 
 X, Z is not Y .'. Z is X. 
 
 And from the above rules may be deduced, 
 as corollaries, the following: 
 
 (7) From two particular premises no conclu- 
 sion can be drawn. 
 
 (8) If one premise be particular, the conclu- 
 sion must be particular. 
 
 4. Of Enthymemes and Sorites 
 
 105. OF ENTHYMEMES. An Enthymeme 
 is a syllogism incompletely stated, but in 
 which the omitted parts are understood or im- 
 plied. Most commonly the omitted part is the 
 major premise, which is then said to be sup- 
 pressed, as, e. g. , " Caesar was a tyrant, there- 
 fore he deserved death," where the suppressed 
 premise is the major, " All tyrants deserve 
 death." Or the suppressed premise may be 
 the minor, as, e. g., " Freemen are happy, 
 therefore the English are happy," where the 
 suppressed premise is the minor, " English- 
 men are freemen." 
 
 1 06. OF SORITES. The Sorites consists of 
 a string of syllogisms in the first figure, in 
 which the conclusion of each is made the 
 premise of the next, and so on, till finally in 
 the conclusion the predicate of the last premise
 
 1 20 LOGIC 
 
 is predicated of the subject of the first, as, 
 e. g., A is B, B is C, C is D, D is E . \ A is E ; 
 or, to give a concrete example, " The English 
 are brave, the brave are free, the free are 
 happy, therefore the English are happy." 
 Obviously a Sorites may always be resolved 
 into as many separate syllogisms as it has 
 middle terms, as, e. g., in the above example, 
 the first into three and the last into two syllo- 
 gisms, as follows: 
 
 A is B A is C A is D 
 
 B is C C is D D is E 
 
 /. A is C .'. A is D .*. A is E 
 
 The English are brave The English are free 
 The brave are free The free are happy 
 
 .'. The English are free .'. The English are happy.
 
 BOOK II 
 APPLIED LOGIC 
 
 121
 
 BOOK II 
 APPLIED LOGIC 
 
 PART I 
 OF THE METHOD OF LOGIC 
 
 CHAPTER VI 
 
 OF THE LOGICAL PROCESSES 
 
 107. OF THE METHOD OF LOGIC. The 
 logical processes, as we have hitherto con- 
 sidered them, consist in three operations, 
 namely, Simple Apprehension, Judgment, and 
 Syllogism or Inference; of which the first is 
 an analytical process, the second and third 
 synthetical. Hence the logical processes may 
 be regarded as twofold, and as consisting in 
 Analysis and Synthesis. The first of these, 
 however, is not confined to Simple Apprehen- 
 123
 
 124 LOGIC 
 
 sion or analysis of terms, but extends to the 
 analysis of propositions and syllogisms, and of 
 extended discourse ; of which the elements are 
 syllogisms. It also extends, as preparatory to 
 the expression in logical form of subjects to be 
 investigated, to the analysis of the general 
 facts involved and the determination of the 
 questions to be investigated. The logical 
 method consists in the use of these processes. 
 108. LOGICAL DISTINGUISHED FROM 
 PHYSICAL ANALYSIS AND SYNTHESIS. The 
 terms analysis and synthesis are used in differ- 
 ent senses, according to the subject-matter to 
 which they are applied. Of these, two princi- 
 pal kinds may be distinguished, which may be 
 called, respectively, physical and logical the 
 former dealing with physical substances, the 
 latter with notions or concepts. Of the former 
 kind, the most instructive illustration is pre- 
 sented by chemistry ; where these processes are 
 applied directly to matter, which is analyzed 
 by separating its elements, and synthesized by 
 rearranging those elements so as to form new 
 compound substances. These processes are 
 indeed essentially different in nature from the 
 processes with which we are now concerned, 
 yet the analogy between the two is almost 
 perfect; and hence, in chemical analysis and 
 synthesis, we find the best illustration of the 
 nature of analysis and synthesis of notions or
 
 THE LOGICAL PROCESSES 12$ 
 
 terms, by which in a way very similar to the 
 analysis and synthesis of material bodies 
 notions are analyzed into elementary notions, 
 and these again synthesized into compound. 
 
 109. OF THE WORLD OF THINGS AND 
 THE WORLD OF THOUGHT. The world of 
 things is made up of actual things or sub- 
 stances; the world of thought, of concepts or 
 notions. There is between the two a regular 
 correspondence, i. e., a correspondence deter- 
 mined by invariable law, and yet the two are 
 clearly distinct. For it is obvious that things 
 themselves cannot be in the mind but only, 
 notions or concepts of them. These, as we 
 have seen, if real or true, must correspond, 
 either directly or indirectly, with the things 
 which, or the attributes of which, they are 
 supposed to denote ( 29, n.). Where the 
 correspondence is indirect, the thing denoted 
 is a guast-thing only, and cannot be distin- 
 guished from the notion itself; but where the 
 correspondence is direct, there is a real thing 
 corresponding to the notion, and we may 
 either regard the notion or the thing as the 
 significate of the term ( 37, n.); though even 
 in this case it is really the notion, not the 
 thing, that we have in mind ( 38, n.). So 
 that it may be said that Logic, and science 
 generally, deal directly with concepts or no- 
 tions only that is to say, with the world of
 
 126 LOGIC 
 
 thought only, and with the world of real things 
 only indirectly. 
 
 1 10. LOGIC AS THE DOCTRINE OF SIGNS 
 (SEMEIOTIKE). But the notions or thoughts 
 dealt with by Logic are not the evanescent 
 thoughts of the individual, but the common 
 notions of mankind embodied in language 
 ( 30). Hence, as we have observed, Logic 
 is exclusively conversant with language, or 
 rather, more specifically, with terms and their 
 various ratiocinative combinations ( 14, 16) 
 that is to say, with the signs of the notions 
 or concepts and of their relations ; which 
 cannot be dealt with, at least to any con- 
 siderable extent, except by means of the 
 vocables by which they are signified. Hence 
 Logic must be regarded, in its direct scope, as 
 dealing with the signs by which notions and 
 their relations are expressed precisely as, in 
 the mathematics, the subject-matter dealt with 
 consists of the signs of numbers and of their 
 relations. In both cases, therefore, though 
 the ultimate object of Logic is to determine 
 the notions expressed in terms and their re- 
 lations, and ultimately the nature and the 
 relations of the things corresponding to the 
 notions, yet this is effected by means of signs, 
 which, therefore, constitute the immediate 
 subject dealt with. Hence Locke was quite 
 right in conceiving that a science of this char-
 
 THE LOGICAL PROCESSES 12? 
 
 acter is indispensable, and in giving it the ap- 
 propriate name of " Semeiotike, or the Doctrine 
 of Signs," though quite wrong in supposing 
 that this would be a new kind of Logic. 1 
 
 in. THE METHOD OF LOGIC RESUMED. 
 By the method of Logic is meant the method 
 of its use in reasoning, or, in other words, the 
 method of ratiocination, or explicit reasoning. 
 This, as we have said, consists in two processes 
 or operations, namely, Analysis and Synthe- 
 sis, i. e., of language ( 107). By analysis is 
 meant the separation of a whole whether con- 
 sisting of a term, proposition, syllogism, or 
 larger discourse, or of the general problem 
 or subject to be investigated into its com- 
 ponent parts; by synthesis, the comparison (or 
 placing together) of any of the elements of 
 reasoning, with a view to determining their re- 
 lations; that is to say, in the comparison of 
 terms, in order to form a judgment of their 
 relations of propositions, in order to make an 
 inference; and of syllogisms, in order to make 
 an extended ratiocination or argument. An- 
 alysis and synthesis are, therefore, each the 
 converse of the other. 
 
 ii2. MODES OF APPLICATION OF THE 
 
 1 " The consideration then of ideas and words, as the great 
 instruments of knowledge. . . . Perhaps if they were 
 distinctly weighed and duly considered, they would afford us 
 another sort of Logic and critic than what we have hitherto 
 been acquainted with " (see Appendix N).
 
 128 LOGIC 
 
 LOGICAL PROCESSES. In each stage of ratio- 
 cination analysis and synthesis are used con- 
 jointly, and each is equally indispensable. The 
 order in which their applications occur, how- 
 ever, differs according to the purpose we have 
 principally in view, which may be either In- 
 vention or Criticism; that is to say, either (i) 
 the Discovery of Truth, or (2) the Criticism or 
 Judgment of what is supposed or alleged to be 
 true; or, in other words, the verification of 
 truth and the detection of fallacy. Of these 
 two aspects of Logic, the latter is commonly, 
 and perhaps rightly, regarded as the more im- 
 portant, or, at least, as of the greater practical 
 utility. But the former, though commonly 
 undervalued, is hardly of less utility or less 
 fruitful of practical results. 
 
 113 (i) INVENTION. The operations of 
 Logic, regarded as an Instrument or Organon 
 of Invention, consist in the analysis and conse- 
 quent apprehension of terms (Simple Appre- 
 hension), and in the discovery or invention of 
 judgments and of syllogisms, and of argu- 
 ments which are composed of syllogisms; 
 which is effected by synthesis; and the process 
 of ratiocination proceeds in this order, i. e. , 
 from the term to the proposition, from the 
 proposition to the single syllogism, and from 
 that to the extended discourse or argument. 
 
 114. OF THE DISTINCTION BETWEEN
 
 THE LOGICAL PROCESSES 12$ 
 
 ORIGINAL AND COMMONPLACE THOUGHT. 
 Where the notions expressed in terms are dis- 
 tinctly apprehended, and, with reference to all 
 terms, to the extent they are apprehended, the 
 relations between them are readily perceived, 
 and indeed spontaneously present themselves. 
 Hence with such notions men reason with 
 facility and accuracy; and thus originate the 
 numerous opinions that are common to man- 
 kind, or common at least to men generally 
 under the same conditions of environment; 
 and also those that are common to large classes 
 of men. Of such opinions which may be ap- 
 propriately named Commonplace the current 
 literature and thought of the day largely, or, 
 we may say almost exclusively, consist. Hence 
 the effect of current thought and discourse 
 is simply to disseminate such opinion more 
 widely, and thus gradually to develop and 
 consolidate Common Opinion, or Conscience, 
 which has been called by the Greeks Nomos, 
 and by some philosophers Common Sense. 
 This, indeed, is a useful and essentially neces- 
 sary function; for it is recognized by political 
 writers generally that opinion is the ultimately 
 controlling force in politics, and that when it 
 becomes universal and inveterate, it is supreme. 
 But current thought is marked by an essential 
 characteristic, or, we may say, defect namely, 
 that it is incompatible with originality, either
 
 130 LOGIC 
 
 in the acquisition of new truths or in the ap- 
 preciation of original thought in others. Hence 
 it has happened, throughout the history of 
 mankind, that the results of original thought 
 meet with almost insuperable obstacles to their 
 reception ; and that, even where they have es- 
 tablished their footing, they pass into the 
 hands of commonplace thinkers, who treat 
 them after their own methods. Hence the 
 original works of great thinkers, with their 
 methods of thought and expression, and the 
 vivifying effect of actual example, are sub- 
 merged by the newer and inferior literature. 
 
 On the other hand, where the Analytical 
 Method is rigorously applied to all forms of 
 discourse, and especially when it is applied to 
 the notions or concepts embodied in terms, 
 numerous delicate and important but unsus- 
 pected relations between the notions thus de- 
 termined suggest themselves. For in this also 
 logical is like chemical analysis, where, 
 by the resolution of compound substances, 
 thousands of relations between them and 
 between the elements of which they are 
 composed are developed and disclosed. The 
 perception of these unsuspected relations con- 
 stitutes originality, which is but another name 
 for logical power. Nor is this originality any- 
 where more conspicuously displayed than 
 where men of original genius, as, e. g., Bacon
 
 THE LOGICAL PROCESSES 131 
 
 in \\isEssays, deal with commonplace subjects. 1 
 Hence the use of Logic as an Instrument of 
 Invention cannot be too highly appreciated, 
 for in the capacity to use Logic in this way, 
 or, in other words, in the capacity to apprehend 
 the whole significance of terms by resolving 
 them into their elements, lies the essential dif- 
 ference between the Original and the Common- 
 place Thinker. 1 
 
 115 (2) CRITICISM. In this aspect Logic 
 may be likened to the touch of Ithuriel's spear. 2 
 
 1 Where terms are clearly defined and analyzed into their 
 constituent elements, that is to say, thoroughly apprehended, 
 innumerable relations between them are intuitively per- 
 ceived ; and thus, by the use of this method, we are led on, 
 as Locke says in a passage cited (supra 6, n.), " f rom 
 very plain and easy beginnings, by gentle degrees and a con- 
 tinued chain of reasonings, ... to the discovery and 
 demonstration of truths that appear, at first sight, beyond 
 human capacity." This it was, probably, that inspired the 
 beautiful hymn of Newman : 
 " Lead on, Heavenly Light ; amid the encircling gloom, 
 
 Lead Thou me on " ; 
 
 which may be very properly regarded as in reality an ode to 
 the divine gift of Intuition the only source of perfect 
 knowledge. 
 
 2 "Him there they found 
 Squat like a toad at the ear of Eve. 
 
 Him thus intent Ithuriel with his spear 
 
 Touched lightly ; for no falsehood can endure 
 
 Touch of celestial spear, but returns 
 
 Of force to its own likeness ; 
 
 So started up in his own shape the fiend,"
 
 132 LOGIC 
 
 Commonly the reasoning processes operate 
 unconsciously and automatically, and the rea- 
 soning is more or less inaccurate, and hardly 
 ever consecutive or logically coherent. As 
 observed in the Introduction, proposition fol- 
 lows proposition in our minds, suggested by 
 various principles of association, such, e. g., as 
 experience, habit, authority, inclination, etc. ; 
 and thus the great mass of our opinions and 
 beliefs which we very erroneously call our 
 knowledge comes to us we know not how. 
 Nor, however firmly we may be convinced of 
 them, or however passionately we may assert 
 them, have we any just assurance of their 
 truth; nay, it is matter of familiar knowledge 
 that they are all mingled with error. Hence, 
 we concluded, the necessity is apparent for 
 some test or criterion by which to judge them ; 
 and this, except the sometimes painful test of 
 experience, can be nothing else than Logic. 
 In its critical aspect, therefore, Logic is indis- 
 pensable, not only to save us from errors and 
 absurdities, but to distinguish real from unreal 
 knowledge, and to give us assurance of the 
 former ( 7 et seq.\ Without it, except in 
 concrete matters, no man can know whether 
 he is right or wrong; and while some, happily 
 born, learn by practice the application and 
 use of the logical processes, the great mass of 
 mankind, for the lack of Logic, go through life
 
 THE LOGICAL PROCESSES 133 
 
 mistaking falsehood and even nonsense for 
 knowledge, and yet firmly convinced of their 
 wisdom and of the folly of those who differ 
 from them. Hence, in the critical aspect of 
 Logic, the order of applying the logical pro- 
 cesses is the reverse of what it is in the use of 
 Logic as an organon or instrument of inven- 
 tion. There the order is to commence with 
 the analysis of the term, and then to proceed 
 to the synthesis of terms in propositions, 
 syllogisms, and extended discourse; here we 
 commence with the complex result, and by 
 analysis resolve it into its elements. 
 
 116. OF THE USE OF ANALYSIS GENER- 
 ALLY. In the use of Logic, whether for in- 
 vention or for criticism, analysis and synthesis 
 are equally indispensable; but the latter, after 
 the former has been effected, is largely a 
 natural and spontaneous process, and presents 
 but little difficulty in its performance. On the 
 other hand, analysis, while to a certain extent 
 also spontaneous, requires, for its efficient per- 
 formance, the most vigorous and protracted 
 exertion of the mental faculties, as, e. g., in 
 the mathematics, and hence is at once the 
 most important and the most difficult of the 
 logical processes. It will therefore require 
 our special attention. 
 
 We have distinguished between the inven- 
 tional and the critical functions of Logic, and
 
 134 LOGIC 
 
 also with reference to the use of the logical 
 processes as applied in the performance of the 
 one or the other function ; and with reference 
 to invention, we have regarded the function of 
 analysis as limited to the analysis of terms, 
 with a view to an apprehension of the notions 
 expressed by them. In practice, however, it 
 is difficult to distinguish between the uses of 
 analysis for invention and for criticism. For, 
 as we have observed, the human mind is so 
 constituted that the synthetical process is 
 performed spontaneously and involuntarily. 
 Hence there is no subject that can present 
 itself for our investigation which we can ap- 
 proach unembarrassed by opinions already 
 formed; and, indeed, until such opinions or 
 theories are formed, the process of investiga- 
 tion cannot commence. Hence, as is generally 
 recognized, the method of scientific investiga- 
 tion must consist largely in the forming of 
 theories and their subsequent investigation. 
 We may distinguish, however, between our 
 own theories, either accidentally formed or 
 formed for the purpose of the investigation of a 
 proposed subject, and the theories formally pro- 
 pounded by others, either in writing or speech ; 
 and we may conveniently regard the former as 
 belonging to the function of invention, and the 
 latter to that of criticism. The latter, as being 
 the simpler subject, will be first considered.
 
 THE LOGICAL PROCESSES 135 
 
 117. (i) OF THE USE OF ANALYSIS IN 
 CRITICISM. In this case the function of 
 analysis extends to the analysis of all forms 
 of language, from the term to the extended 
 discourse or argument; and, as we have ob- 
 served, it commences with the latter, which is 
 in fact the most difficult task. For here it is 
 necessary to determine from the loose and in- 
 accurate expressions of ordinary disquisition 
 the precise nature of the conclusions asserted 
 and of the arguments used to establish them ; 
 and this task is always difficult, and sometimes 
 impossible. When these matters have been 
 determined it will be necessary also to analyze 
 carefully every syllogism, proposition, or term 
 involved in the course of the reasoning. But 
 this in general, to the trained logician, presents 
 but little difficulty. 
 
 118. (2) OF THE USE OF ANALYSIS IN IN- 
 VENTION. Strictly speaking, this perhaps ex- 
 tends only to the analysis of the term with a 
 view to simple apprehension, and in a previous 
 passage we have so regarded it. But before 
 this task can be approached, it is necessary for 
 us to determine the nature of the precise ques- 
 tions to be investigated ; and this will require an 
 analysis of the facts involved in the investiga- 
 tion, and also of the opinions or theories with 
 regard to those facts casually existing in the 
 mind. For, as will be explained more fully in
 
 136 LOGIC 
 
 the next chapter, the questions demanding in- 
 vestigation are in general determined by the 
 nature and the conditions of the problems 
 involved ; and it is essential to a rational in- 
 vestigation that the issues thus involved be 
 clearly ascertained. When the issues or ques- 
 tions are thus determined and logically ex- 
 pressed, our investigation is then narrowed to 
 the determination of the truth of one of two 
 alternative propositions, which are called the 
 thesis and the anti-thesis, and of which one or 
 the other must be true; and thus our task is 
 in general greatly facilitated. The use of this 
 sort of analysis finds its best illustration in the 
 practice of the lawyers, with whom it is an im- 
 perative rule that the first step in the investi- 
 gation of a case must consist in settling the 
 issues. In ordinary discourse this task is 
 almost always neglected, and, as will be seen 
 as we proceed, this is one of the most fruitful 
 sources of fallacy. 
 
 119. OF ANALYSIS AND SYNTHESIS GEN- 
 ERALLY. This subject is one of extreme im- 
 portance, and to the advanced student should 
 constitute one of the principal subjects for his 
 meditations; but for the purposes we have in 
 view it may be sufficiently developed by a 
 statement of the practical rules by which the 
 reasoner should be governed, which will be 
 given at length in the next chapter.
 
 CHAPTER VII 
 
 THE RULES OF LOGIC 
 
 I 
 OF THE RULES OF LOGIC GENERALLY 
 
 120. SCOPE OF THE RULES OF LOGIC. 
 According to the view we have taken in this 
 essay, inference is only one of the processes of 
 ratiocination. Judgment is also a ratiocinative 
 process, and, like inference, must have its rules 
 by which false or pretended judgments may be 
 distinguished from the real. Moreover, where 
 our reasoning is not apodictic, we have to use 
 assumed propositions, or assumptions, as prem- 
 ises ; and though it is said that Logic is not 
 concerned with the truth or falsity of these, yet 
 this is true only in a qualified sense. For 
 where the falsity of such propositions can be 
 detected by logical processes, i. e., by defini- 
 tion, judgment, and inference, it is the func- 
 tion of Logic to condemn and reject them ; 
 precisely as in the case of self-contradictory
 
 138 LOGIC 
 
 propositions or propositions otherwise absurd 
 on their face. And in all cases it is its func- 
 tion to determine the logical character of an 
 assumed premise, as being an assumption or 
 hypothesis, and not a judgment. 
 
 121. TWOFOLD DIVISION OF THE RULES 
 OF LOGIC. We propose, therefore, to regard 
 the rules of Logic as legitimately extending to 
 all the processes of ratiocination ; and hence as 
 including all rules necessary to direct us in the 
 right use of terms as instruments of ratiocina- 
 tion. They will include, therefore, not only 
 the rules directly governing the process of in- 
 ference, but also those governing the statement 
 of the premises. The latter which will first 
 be considered will be called the " Rules of 
 Judgment,'" the former, the " Rules of In- 
 ference." 
 
 122. RULES OF JUDGMENT. The rules of 
 judgment have for their object, not the form- 
 ing of right, but the prevention of wrong judg- 
 ments. Judging is a natural and involuntary 
 operation of the mind. But in the ordinary 
 processes of the mind we are apt to go astray 
 in our judgments; and the object of the rules 
 of judgment is to guard against this infirmity 
 by preventing false judgments, or, where they 
 occur, by detecting them. 
 
 123. RULES OF INFERENCE. The rules 
 of the syllogism given in a previous chapter
 
 THE RULES OF LOGIC 139 
 
 cover all cases of inference except conversion 
 per accidens. But these rules are needlessly 
 complex, and may be advantageously replaced 
 by the rules of substitution, which include 
 all inferences whatever, and are simpler both in 
 their expression and application than the old 
 rules, of which they are but another expres- 
 sion. The rules of the syllogism, however, 
 are of such familiar use by logicians, and are so 
 wrought into the terminology and literature of 
 Logic, that a familiar acquaintance with them 
 is essential to the logical student; for whom 
 also it will be necessary to recognize clearly 
 the substantial identity of the two processes. 
 
 124. FALLACIES OF THE SYLLOGISM, ALL 
 RESOLVABLE INTO FALLACIES OF SUBSTITU- 
 TION. This is especially important with refer- 
 ence to the violations of the rules of the 
 syllogism, or, as they are called, the fallacies 
 of the syllogism (104 ct scq.\ These are 
 of frequent occurrence, and are familiarly 
 known by technical names; and as these have 
 become firmly established in logical termi- 
 nology by a use of many centuries, they must, 
 of course, be retained. It will be of advantage 
 to the student, therefore, to have pointed out 
 to him that all these fallacies are simply cases 
 of illicit substitution ; which can be readily 
 shown. 
 
 Thus, e. g<, the fallacy of an ambiguous
 
 I4O LOGIC 
 
 middle term (Quarternio Terminorutri) consists 
 simply in the substitution of a new term, hav- 
 ing the same verbal sign as in the original, but 
 a different meaning as in the examples given. 
 
 The case of undistributed middle as, e. g. , 
 " X is Y, Z is Y .-. Z is X " - consists in the 
 illicit substitution of species for genus in the 
 predicate of an affirmative proposition (i. e., X 
 for Y in the minor premise). 
 
 In the case of illicit process of the minor term, 
 as, e. g., " Y is not X, some Z is Y .'. Z is 
 notX," genus is illicitly substituted for species 
 in the subject of an affirmative proposition 
 (i. e,, Z for " Some Z " in the minor premise). 
 
 In the case of illicit process of the major, as, 
 e. g., " Y is X, Z is not Y .-. Z is not X," 
 genus is illicitly substituted for species in the 
 predicate of a negative proposition (i. e., X for 
 Y in the minor premise). 
 
 In the case of negative premise, if the con- 
 clusion be affirmative, as, e. g. , " Y is not X, Z 
 is not Y .'. Z is X," genus is substituted for 
 species in the predicate of a negative proposi- 
 tion (i. e., Not-X for Y in the minor pre- 
 mise). If the conclusion be negative, as, e.g., 
 " Y is not X, Z is not Y . . Z is not X," the 
 fallacy will consist in the illicit substitution of 
 one for another of two unrelated terms (i. e., 
 X for Y); and the same will be true of the 
 other cases, if any there be.
 
 THE RULES OF LOGIC 141 
 
 125. THE LAWS OF THOUGHT. The 
 rules of Logic are founded upon what are 
 called the primary Laws of Thought, viz. : 
 (i) the Law of Identity (or rather the Law of 
 Equivalence); (2) the Law of Contradiction; 
 and (3) the Law of Excluded Middle; the first 
 of which governs the process of Inference, the 
 last two, that of the Judgment. The corre- 
 sponding fallacies consist in their violation. 
 
 These laws may be enunciated in a form to 
 make them of practical utility, as follows: 
 
 (i) THE LAW OF IDENTITY. 
 
 Significates (i. e., things or quasi-things) re- 
 main the same though denoted by different 
 terms. 
 
 Hence terms denoting the same significates 
 may, to the extent of their equivalence, be 
 used interchangeably, i. e., the one substituted 
 for the other. 
 
 The mathematical axiom that " things equal 
 to the same thing are equal to each other " is 
 merely a special application of this principle, 
 its meaning being simply that terms denoting 
 the same class of significates are equivalent to 
 each other. 
 
 It is obvious, therefore, that this law is not 
 adequately stated (as is sometimes said) by the 
 equation, A = A, but rather by the equation, 
 A = B; both terms being supposed to denote 
 the same class of significates, and the term B
 
 142 LOGIC 
 
 to be either A, or any other vocable or sign 
 denoting the same significates. 
 
 (2) THE LAW OF CONTRADICTION, OR 
 RATHER THE LAW OF NON-CONTRADICTION. 
 
 A term, and its negative, or contradictory, 
 cannot be predicated universally of any term. 
 This law and the next are often misstated. 
 
 (3) THE LAW OF EXCLUDED MIDDLE. 
 
 Of two contradictory propositions, one must be 
 true ; or symbolically : ' ' Either A is It," or 
 ' ' Some A is not B. " l 
 
 II 
 
 RULES OF JUDGMENT 
 
 126. Rule I. TERMS TO BE SIGNIFICANT. 
 
 In every logical proposition by which is meant 
 every proposition to be used in ratiocination the 
 terms must be significant, i. e., must have defi- 
 nite signification. 
 
 This rule follows from the definition of the 
 term and of the proposition ; for unless the 
 word or vocable has such definite signification 
 there is no name, and consequently no term or 
 proposition, or valid ratiocination. The viola- 
 tion of this rule may be called the Fallacy of 
 Non-significance or Nonsense. 
 
 Rule II. TERMS TO BE RIGHTLY DEFINED. 
 
 Terms used in ratiocination must not only have 
 
 1 V., supra, 90.
 
 THE RULES OF LOGIC 143 
 
 a definite signification, but the signification 
 must be legitimate, i. e., they must not be falsely 
 defined. This implies (i) that a term shall not 
 be used in an improper sense, i. e. , in a sense not 
 permitted by the usage of the language ' / and 
 (2) that the term shall be so defined as to signify 
 a real concept ; or, at least, that the contrary 
 shall not affirmatively appear. 
 
 The violation of this rule will be called the 
 Fallacy of False Definition. 
 
 Rule III. PREMISES NOT TO BE ILLICITLY 
 ASSUMED. 
 
 A proposition that is obviously untrue, or that 
 can, on logical principles, be affirmatively shown 
 to be untrue, cannot be legitimately used as a 
 premise. 
 
 The violation of this rule is called the fallacy 
 of " Begging the Question," or Petitio Prin- 
 cipii ; and this and the fallacies resulting from 
 the violation of Rules I. and II. may be 
 classed together under the general head of 
 Illicit Premises. 
 
 Rule IV. PREMISES TO CORRESPOND TO 
 THE THESIS OR ISSUE. 
 
 In all ratiocination if designed to be fruitful 
 
 1 The unnecessary use of a term in a sense not justified by 
 usage is commonly indicative either of mental incapacity or 
 fallacious intent ; and should therefore be forbidden, as to 
 children \ve forbid the use of deadly weapons, or to all the 
 possession of counterfeiters' tools.
 
 144 LOGIC 
 
 the premises, and, consequently, also the con- 
 clusion, must correspond to the Thesis or Issue, 
 ^whether that be expressed or understood, or 
 merely determined by the conditions of the 
 problem. 
 
 By the thesis is meant the proposition to be 
 demonstrated ; by the issue t the thesis and the 
 anti-thesis, or contradictory, considered to- 
 gether with a view of determining whether the 
 one or the other is true. 
 
 With regard to nearly all subjects presented 
 to us for investigation the material question at 
 issue is more or less definitely determined by 
 the conditions of the problem ; and hence it is 
 said, " A prudent questioning is a kind of half 
 knowledge ' ' (Prudens interrogatio est dimidium 
 sapientice}. Where the issue is thus determined, 
 it constitutes the real issue, or thesis and anti- 
 thesis of the problem. In other cases it must 
 be determined by agreement, or by actual in- 
 tention, either expressed or understood. In 
 many cases it is not formally stated, but we 
 ascertain it, for the first time, from the use 
 made of the conclusion. 
 
 The fallacy resulting from a violation of this 
 rule if we assume there is no fallacy in the 
 inference will necessarily involve a departure 
 from the thesis or issue, both in the premises 
 and in the conclusion. With regard to the 
 premises, it is called the fallacy of Mistaking
 
 THE RULES OF LOGIC 145 
 
 the Issue ; with regard to the conclusion, that 
 of Irrelevant Conclusion; and in either case, 
 Ignoratio Elenchi. 
 
 Ill 
 
 RULES OF INFERENCE 
 
 127. All inference, as we have observed, 
 may be resolved into the process of substituting 
 for terms other terms of equivalent ratiocina- 
 tive value. There is an apparent exception in 
 the case of conversions of propositions, but the 
 exception is only apparent ( 79). To conform 
 to usage, however, the rule for conversion will 
 be given, though in fact, as explained, the illicit 
 conversion of a proposition is simply a case of 
 illicit substitution of terms. 
 
 Rule V. CONVERSIONS TO BE ILLATIVE. 
 
 A conversion, to be legitimate, must be illative, 
 i. e, , the truth of tlie converted must be implied 
 in the original proposition. 
 
 The violation of this rule may be called the 
 Fallacy of Conversion, or simply Illicit Conver- 
 sion. It can occur only in the simple conver- 
 sion of a universal affirmative or a particular 
 negative proposition (e. g., " Y is X," " Some 
 Y is not X "). In the former case the fallacy 
 will consist in the substitution of genus for 
 species (X for Y) in the subject, and of species for 
 genus (Y for X) in the predicate of a universal
 
 146 LOGIC 
 
 affirmative proposition, thus doubly violating 
 the first rule of substitution. In the lat- 
 ter (" Some Y is not X ") X is substituted for 
 Y in the subject, and Y for X in the predi- 
 cate, though neither is necessarily, and one at 
 least cannot be, a species of the other; which 
 is a violation of the next rule. 
 
 Rule VI. EQUIVALENCE OF TERMS TO BE 
 OBSERVED. 
 
 In all substitutions the substituted term must 
 be equivalent in signification i. e., equivalent in 
 ratiocinative value to the term for which it is 
 substituted. 
 
 The violation of this rule by the substitution 
 of a new term is called the Fallacy of Illicit 
 Substitution. 
 
 The rule will cover all cases of legitimate 
 substitution of terms whatever ; but it is ob- 
 vious, where an ambiguous term is used in a 
 different sense from that originally adopted, 
 that a new term is in fact illicitly substituted. 
 We must add, therefore, as a corollary the 
 following: 
 
 Rule VII. THE SENSE OF TERMS TO RE- 
 MAIN UNALTERED. 
 
 Every verbal expression, ivJietJier a term or 
 proposition, shall, throughout the ratiocination, 
 be used in the sense originally given to it. 
 
 The violation of this rule constitutes what is 
 called the Fallacy of Equivocation, which is to
 
 THE RULES OF LOGIC 147 
 
 be regarded as a species of Illicit Substitution ; 
 and of this there are two kinds: the first con- 
 sisting in shifting the sense of an ambiguous 
 term, which is called the Fallacy of Ambiguity ; 
 the second, in shifting the meaning of what is 
 called an amphibolous sentence, which is a sen- 
 tence equivocal by reason of its grammatical 
 construction, as, e. g., the sentence, " The 
 Duke yet lives that Henry shall depose"; 
 which may mean either that the Duke shall de- 
 pose Henry, or Henry the Duke. If construed 
 in the former sense, the subject of the proposi- 
 tion is, " The Duke that shall depose Henry " ; 
 for which under the latter construction is sub- 
 stituted, " The Duke that shall be deposed 
 by Henry." This is called the Fallacy of 
 Amphibology, or, perhaps better, of Amphiboly. 
 But these fallacies are of essentially the same 
 nature, and will be classed together under the 
 one head of Equivocation.
 
 PART II 
 THE DOCTRINE OF FALLACIES 
 
 CHAPTER VIII 
 
 DEFINITION AND CLASSIFICATION OF FAL- 
 LACIES 
 
 128. DEFINITION OF FALLACIES. A fal- 
 lacy may be defined as a false semblance of 
 valid ratiocination ; to which it bears the same 
 relation as hypocrisy, conscious or unconscious, 
 to virtue. Fallacy is therefore a species of 
 error, whose specific difference consists in its 
 semblance of right reasoning and its conse- 
 quent liability to be mistaken for it. 1 It may 
 
 1 Hobbes, with his usual acuteness, thus clearly explains the 
 distinction between error a.\\<\ fallacy : 
 
 " When we reason with words of general signification (uni- 
 versalibus} and fall upon a general conclusion (conclusionem 
 universalum) which is false, though it be commonly called 
 error, it is indeed an absurdity or senseless speech (pratio 
 insignificans)" Lev., chap. v. According to this view, all 
 fallacies are absurdities, i. e., they necessarily involve either a 
 contradiction, or the use of non-significant or senseless words. 
 149
 
 1 50 LOGIC 
 
 consist either in a false judgment or a false in- 
 ference. But, it will be remembered, the terms 
 judgment and inference in the logical sense de- 
 note, the one intuitive judgment, and the 
 other illative inference. Hence, when we 
 speak of a false judgment or inference, we do 
 not mean a real judgment or inference that is 
 untrue (which would involve a contradiction 
 of terms), but as when we speak of a false 
 prophet a pretended or simulated judgment 
 or inference that is not really such. 
 
 129. CLASSIFICATION OF FALLACIES. 
 All fallacies must consist in the violation of 
 some one or more of the rules of Logic, and 
 hence may be correspondingly classified. Such 
 a classification has, indeed, already been sub- 
 stantially effected in our statement of the 
 logical rules; where, under each rule, the cor- 
 responding fallacies have been named. It 
 remains, therefore, only to arrange them in 
 convenient order, which is done in the table 
 that follows: 
 
 Table of Fallacies 
 
 130. FALLACIES OF JUDGMENT. 
 
 I. Illicit Premises. 
 
 (1) Fallacies in Definition. 
 
 Nonsense (or Non-Significance). 
 False Definition. 
 
 (2) Illicit Assumption of Premise (Petitio 
 
 Principii ).
 
 CLASSIFICATION OF FALLACIES 151 
 
 II. Mistaking the Issue, or Irrelevant Conclusion 
 (fgnoratio Elenchi}. 
 
 131. FALLACIES OF INFERENCE, OR IL- 
 LICIT SUBSTITUTIONS. 
 
 I. Illicit Conversions of Propositions. 
 II. Illicit Substitutions of Terms ; Scil. 
 
 1 i ) Of Vocal Signs, or Vocables. 
 
 Formal. 
 Material. 
 
 (2) Of Notions, /. e., of Senses of Terms 
 
 {Equivocation, Homonymia et Amphi- 
 bolia) . 
 
 132. OBSERVATIONS ON THE FALLACIES. 
 Of the two principal kinds of fallacies con- 
 tained in the above table, the first excepting 
 the Fallacy of Irrelevant Conclusion consist in 
 the illicit assumption of the propositions to 
 be used as the premises of ratiocination. But 
 false or nonsensical propositions do not of 
 themselves constitute fallacies, but only by 
 reason of their use as judgments; for, accord- 
 ing to our definition, a fallacy is a false sem- 
 blance of ratiocination, and therefore cannot 
 exist except as part of ratiocination. Hence 
 we are not concerned with the truth or falsity 
 or the absurdity of any proposition that may 
 be asserted by any one, unless it be used as an 
 independent judgment or as the premise of an
 
 152 LOGIC 
 
 argument, in which case its pretensions may 
 be examined, and, if found to be baseless, it 
 may be challenged as illicit. 
 
 Where such an assumed premise is either 
 non-significant or involves a false definition, it 
 is in itself a fallacy, and therefore entitled to 
 an independent rank as such. But such fal- 
 lacies are innocuous if the sense of the terms 
 be preserved unaltered throughout the ratio- 
 cination. For all conclusions in which they 
 are involved must necessarily be without sig- 
 nificance, or, in other words, nonsensical, and 
 hence unsusceptible of use. But, as will be 
 seen at large as we proceed, the conclusions 
 from such premises, being in themselves un- 
 susceptible of use, are invariably used as 
 equivalent to other and significant proposi- 
 tions, and thus inevitably result in the Fallacy 
 of Irrelevant Conclusion, or Ignoratio Elenclii, 
 which consists in substituting for the conclu- 
 sion another proposition (i. e., the true thesis); 
 and which, though for convenience treated 
 separately, may itself always be resolved into 
 the Fallacy of Illicit Substitution, i. e., into an 
 illicit conversion, or an illicit substitution of a 
 term. And the same observation is true gen- 
 erally, though not universally, of illicit assump- 
 tions of false premises. These, if regarded as 
 mere hypotheses, and if no misuse be made of 
 the conclusion, are not illegitimate ; but, it will
 
 CLASSIFICATION OF FALLACIES 153 
 
 be seen, a conclusion deduced from such pre- 
 mises almost invariably either comes in conflict 
 with some inconsistent fact, or otherwise fails 
 to be sufficient for the purposes the reasoner 
 has in view; and thus, almost inevitably, it is 
 treated as equivalent to some other proposi- 
 tion, thus again presenting a case of Ignoratio 
 Elenchi. Hence if, as we conveniently may, 
 we regard all assumed propositions as mere 
 hypotheses, and therefore as not illegitimate, 
 unless an ill use be made of the conclusion 
 all illicit assumptions of premises must neces- 
 sarily result in an Ignoratio ElencJii ; which, as 
 we have observed, must necessarily consist 
 either in an illicit conversion or the illicit 
 substitution of a term. Hence, as all valid 
 ratiocination consists in the substitution of 
 equivalent ( 78), so all fallacy must consist in 
 the substitution of non-equivalent terms. 
 
 Hence the simplest and most scientific classi- 
 fication of fallacies would be to regard them 
 all as species of illicit substitution that is to 
 say, as cases, either of illicit conversion of pro- 
 positions or illicit substitution of terms; and 
 that we have adopted a different mode of classi- 
 fication is due simply to the consideration that 
 we may thus more conveniently exhibit the 
 different sources of fallacy. Hence, as we 
 proceed, it will be found that the several fal- 
 lacies all have a tendency, as it were, to run
 
 J54 LOGIC 
 
 into each other; which mainly results from the 
 fact that they are all in their essential nature 
 the same, differing only in the peculiar sources 
 in which they originate; though partly also 
 from the fact that, in general, fallacious argu- 
 ments are not explicit, and the fallacy may 
 vary according to the manner in which we may 
 express them. 
 
 In our classification of the fallacies we have 
 distinguished as a class the fallacy of " Mis- 
 taking the Issue, or Irrelevant Conclusion," 
 thus apparently including two separate fal- 
 lacies. But this is only apparently so. For 
 unless there be some fault in the inference 
 which would constitute another kind of fallacy 
 the conclusion and the premises must neces- 
 sarily correspond, and we may therefore regard 
 either the illicit assumption or the illicit con- 
 clusion as constituting the fallacy. If we re- 
 gard the latter as the fallacy, it necessarily 
 resolves itself into a case of illicit substitution. 
 But, for convenience, we regard it as relating 
 to the premises, and thus regarded, it consists 
 in the illicit assumption of one proposition in 
 place of another i. e., of the actual premise 
 for some other proposition more or less resem- 
 bling it which is admitted. 
 
 In concluding these introductory observa- 
 tions I would refer the student to what is said 
 in the conclusion of the Introduction, and
 
 CLASSIFICATION OF FALLACIES 155 
 
 which, for convenience of reference, is here 
 repeated : 
 
 " In our treatment of the subject, the several 
 fallacies will be illustrated almost exclusively 
 by examples taken from current theories of 
 Politics and Morality. Our examples will 
 therefore consist, not of mere trivialities, such 
 as are so commonly used in works on Logic, 
 but of fallacies that, in perverting moral and 
 political theory and in corrupting practice, 
 have dominated, and still continue to dominate, 
 the fortunes of the world. They come to us, 
 therefore, as veterans in the army of what 
 Hobbes calls the ' Kingdom of Darkness,' 
 crowned with the laurels of victory " ( 13). 
 
 Among these theories there are two fruitful, 
 above all others, in examples of logical fallacy 
 namely, the modern doctrine of Absolute 
 Sovereignty, and the Utilitarian Theory of 
 Morality; the former of which may be ex- 
 pressed in the proposition that " Sovereignty 
 is, in its essential nature, an absolute poiver, 
 and, as such, unsusceptible either of limitation 
 or division"; the latter, in the proposition 
 that " General Utility is the trite and only 
 standard of justice and injustice, and of right 
 and wrong generally." Most of our examples 
 will be taken from these theories; and these, 
 and other current theories used for the same 
 purpose, will be found not only to serve as the
 
 1 56 
 
 LOGIC 
 
 most effective means of illustrating the nature 
 of the several fallacies involved, but also to 
 enable us to perceive the frequent use and 
 formidable influence of fallacy upon political 
 and moral speculation, and to realize how dis- 
 astrously and commonly the most vital affairs 
 of mankind are thus affected.
 
 CHAPTER IX 
 
 NON-SIGNIFICANCE, OR NONSENSE FALLACY 
 OF 
 
 133. The nature of this fallacy is explained 
 under Rule I. of the Rules of Logic. The fal- 
 lacy is of two kinds; namely, (i) where a term 
 is used that has an impossible or absurd mean- 
 ing or no meaning at all which constitutes the 
 Fallacy of Nonsense in the narrower sense of 
 the term ; and (2) where an ambiguous term is 
 used without definition which is called the 
 Fallacy of Confusion. But, logically, the two 
 kinds are of essentially the same nature, and 
 hence are classed together under the general 
 head of Non-significance or Nonsense. For 
 the purpose of illustrating their nature, they 
 will, however, be considered separately. 
 
 i . The Fallacy of Nonsense ' 
 
 134. In dealing with concrete matters, it 
 is difficult to use nonsensical speech without 
 
 1 According to Ilobbes (cited supra, 128, n.), all fal- 
 lacies, in their ultimate analysis, may be reduced to this head. 
 
 157
 
 158 LOGIC 
 
 discovering it; and hence the kind of nonsense 
 to which the term is colloquially applied is gen- 
 erally of an obvious and transparent character. 
 But when we come to deal with abstract terms, 
 or terms of second intention, such as are con- 
 stantly used in Morality, Politics, and Meta- 
 physics, the case is quite different. For here 
 not only are we liable constantly to use non- 
 sensical or non-significant terms, but it often 
 requires the most searching and difficult analy- 
 sis to discover that we have done so. Hence, 
 the nonsense of which we are to discourse is 
 something very different from the nonsense of 
 colloquial speech ; which is generally so obvious 
 that only foolish people can fall into it, or, at 
 least, persist in it. It is a kind of nonsense 
 that constantly imposes itself upon the most 
 eminent statesmen, jurists and philosophers, 
 and even upon the most acute logicians. To 
 escape it altogether a. man must be endowed 
 with more than mortal sagacity, and hence the 
 fallacy may be illustrated by examples from 
 the writings of the most eminent men. 
 
 Examples 
 
 135. SOVEREIGNTY. The most striking 
 example of this fallacy is presented by the 
 modern doctrine of Absolute Sovereignty ( 
 132), a doctrine almost universally received by 
 modern political writers, and which (with an
 
 FALLACY OF NON-SIGNIFICANCE 159 
 
 exception, to be touched upon under the next 
 head) has contributed more than any other 
 cause to the corruption of political philosophy 
 and practice. This will require some explana- 
 tion. 
 
 The term Sovereign, in its original and proper 
 sense, denoted merely a single ruler or monarch, 
 and Sovereignty, the power of this monarch. 
 But in modern times the application of these 
 terms has been much extended, and the latter 
 term is now used in many different ways; of 
 which four may be distinguished, namely : (i) 
 Personal Sovereignty, or the power of an abso- 
 lute monarch otherwise known as "the 
 Divine Right of Kings"; (2) Corporate Sover- 
 eignty, or the Sovereignty of the government, 
 whether monarchic, aristocratic, democratic, 
 or mixed; (3) Popular Sovereignty, or the Sov- 
 ereignty of the state or people ; and (4) The 
 Sovereignty of Right or the Lazu. 1 To which 
 may be added as many other senses as abstrac- 
 tions can be imagined for the purpose as, e. g. , 
 the Sovereignty of Reason, or, in a theocracy, 
 the Sovereignty of God. All these different 
 
 1 This expression originated with Aristotle : " Moreover, he 
 who bids the law to be supreme, makes God supreme ; but he 
 who trusts man with supreme power gives it to a wild beast, 
 for such his appetites often make him ; passion, too, influences 
 those who are in power, even the very best of men ; for which 
 reason the law is intellect free from passion." Politics, iii., 
 xvi.
 
 l6o LOGIC 
 
 senses of the term are inconsistent with each 
 other; and all except the first (now happily ob- 
 solete) are in their direct sense without 
 definite signification, or, in other words, non- 
 sensical. For the government or state, and 
 likewise right or law and reason, are purely 
 imaginary or fictitious persons, existing only 
 in contemplation of mind /. e. , they are quasi- 
 persons only; and the power of such fictitious 
 or imaginary beings must be as imaginary as 
 themselves. For the government or state or a 
 corporation cannot, properly speaking, be said 
 to have rights, or will, or power, or conscience, 
 or other human attribute; and when, other- 
 wise than as a mere figure of speech, we speak 
 of such <5w<7.$7-persons as having such attributes, 
 we talk pure nonsense. And so with reference 
 to the sovereignty of God, though the same 
 observation is not literally true, yet practically, 
 as we can know but little of His will, or the 
 exertions of His power, the term, as generally 
 used, carries with it no meaning. 
 
 The following examples are in effect identical 
 with the above : 
 
 (i) The doctrine of Kant, Rousseau, and 
 others, that the will of the government or the 
 state is to be regarded as " the united will of 
 the people" ; which is obviously a mere fiction, 
 and, construed literally, not only false, but 
 impossible.
 
 FALLACY OF NON-SIGNIFICANCE l6l 
 
 (2) The proposition of Hobbes, that the 
 effect of the institution of government was to 
 create not merely " a consent or concord " of 
 the people, but " a real unity of them all in one 
 and the same person" 
 
 (3) The equivalent proposition of Bluntschli 
 and others, that the state is an " organized be- 
 ing " or "organism," having a soul and a body, 
 a conscience and active powers, and also a will 
 different from the wills of the individuals com- 
 posing it. 
 
 (4) And finally the celebrated theory of the 
 Social Compact or Contract, which served 
 Hobbes, Locke, Rousseau, and others as the 
 foundation of their respective reasonings; and 
 from which, as a premise, their several essen- 
 tially different and antagonistic theories are, 
 with equal felicity, deduced. 
 
 136. OF LEGAL FICTIONS. These are all 
 examples of what lawyers call legal fictions ; 
 which are at least as common with the philoso- 
 phers as with the lawyers. 1 In all of them 
 except the last the government or state is re- 
 garded as a body politic or corporation ; which 
 
 1 The difference between the lawyers and the philosophers 
 in this respect is that by the former the fiction is always recog- 
 nized as such, and used merely as a convenient mnemotechnic 
 device. It is also used, not as a universal, but as a particular 
 proposition its use being restricted by the maxim, " In fic- 
 tione juris semper tequilas." But the use of it by philosophers 
 is often the reverse.
 
 I 62 LOGIC 
 
 is defined as a fictitious or imaginary person, 
 existing only in contemplation of mind, i.e., as 
 a guasi-person, and the definition is, in fact, 
 but a bold metaphor. Hence, as we have said, 
 the power of this fictitious or imaginary being is 
 as imaginary as itself. For human power can 
 exist only in actual human beings; and though 
 for convenience we may speak of the power of 
 the government as of that of any other corpora- 
 tion, yet the expression is always to be under- 
 stood as really denoting the concurrent powers 
 of certain individuals in the government. 
 Hence, when we attribute to the state or gov- 
 ernment, or any other corporation or fictitious 
 entity, will, conscience, soul, body, sex, or other 
 human faculty, feeling, or quality, we speak 
 figuratively, and, as in all cases of figurative 
 language, if literally, absurdly. The examples 
 cited may therefore be more specifically as- 
 signed to the class of fallacies called by the old 
 logicians the Fallacy of Figure of Speech (Fal- 
 lacia Figures Dictionis), (infra, 203). 
 
 With regard to the doctrine of a social 
 compact, it has not the excuse of being even 
 figuratively true. Like the fiction of the Eng- 
 lish law that husband and wife are one, it is 
 simply an undisguised, recognized absurdity, 
 assumed as a first principle. That it should 
 ever be asserted would, were it not for experi- 
 ence to the contrary, be simply incredible.
 
 FALLACY OF NON-SIGNIFICANCE 163 
 
 137. THE DARTMOUTH COLLEGE CASE. 
 A similar example of this fallacy is presented 
 by the decision of Chief Justice Marshall in the, 
 Dartmouth College case (4 Wheat., 518), where 
 it was held that an act of the Legislature re- 
 organizing a collegiate corporation was in con- 
 flict with the provision of the Constitution of 
 the United States forbidding enactment by a 
 State of any law " impairing the obligation of 
 contracts." It was not perceived that a corpo- 
 ration, being a fictitious person, is not capable 
 of having any rights, except as representing 
 real persons, and that its so-called rights are in 
 fact merely the rights of its stockholders or 
 other parties interested in it. But in eleemosy- 
 nary corporations there are no private parties 
 interested, and hence the supposed rights of 
 the corporation are in fact those of the State, 
 and consequently subject to its disposition. 
 For it is absurd to speak of rights that have no 
 real owners; and to such rights the Constitu- 
 tion which was designed to protect the rights 
 of real persons can have no application. The 
 decision was therefore simply a case of the Fal- 
 lacy of Nonsense, of the kind called F. Figures 
 Dictionis. 
 
 138. OBSERVATIONS ON THE FALLACY OF 
 NONSENSE. It may be observed here by the 
 reader, who is somewhat familiar with Logical 
 Doctrine, that the Fallacy of Nonsense is ap-
 
 1 64 LOGIC 
 
 parently a new kind of fallacy, not to be found 
 in the books ; but this is very readily explained. 
 ; For, as we have observed, a conclusion involv- 
 ing a nonsensical term, being itself nonsensi- 
 cal, can in its proper sense, or rather nonsense, 
 be of no use for any purpose, and hence is 
 always used as equivalent to some significant 
 proposition, and thus becomes an Ignoratio 
 Elenchi. Thus the doctrine of Absolute Sov- 
 ereignty, like other nonsensical theories, is in 
 itself innocuous, and becomes otherwise only 
 by illicit use. There can be no harm in saying 
 that Leviathan, the creature of our imagina- 
 tion, is vested with unlimited power, or even 
 to say with Hobbes that he is a " mortal 
 god," and therefore omnipotent. For his 
 power, if left to himself, is no more formidable 
 than that of the wooden or brazen gods of the 
 heathen. But as in the latter case the power 
 of the god is, in practice, the power of the 
 priest, so the imaginary power of Leviathan is 
 but a word used to cover the actual power of 
 some officer or officers of the government; and 
 to them the meaning of the doctrine is: " You 
 must not resist us." Hence, invariably, a non- 
 sensical term is used only in the argument, and 
 the conclusion is always used as equivalent to 
 some other and significant proposition, thus 
 making a case of Irrelevant Conclusion, or 
 Ignoratio Elenchi; under which head it is
 
 FALLACY OF NON-SIGNIFrCANCE 165 
 
 commonly treated. Of this numerous exam- 
 ples will be given in the sequel. 
 
 2. 77^ Fallacy of Confusion 
 
 139. This fallacy is recognized in the books 
 as one of the most common and pernicious; 
 and, indeed, it is a commonplace in philosophy 
 that the use of undefined terms is one of the 
 most fruitful sources of error. The nature of 
 the fallacy is explained under Rule I. of the 
 Rules of Logic. A few examples will be suffi- 
 cient to illustrate its nature. 
 
 Examples 
 
 140. UTILITARIANISM. The most serious 
 example of this fallacy is presented by the 
 theory of Utilitarianism ( 132 ad fin.), which 
 for the greater part of a century has exercised 
 a predominating and pernicious influence over 
 English thought. The theory, briefly stated, 
 is that general utility is the paramount and 
 sole standard of right and wrong and of the 
 just and unjust. But the term " general util- 
 ity " has no definite meaning; because it is im- 
 possible to determine from it who are the people 
 whose utility or welfare is to be considered 
 whether a mere majority or less, or two thirds, 
 or three fourths, or other proportion ; and
 
 1 66 LOGIC 
 
 hence the proposition must be regarded as non- 
 significant or nonsensical. 
 
 141. EDUCATION. So he who asserts the 
 benefit of education is, in general, talking non- 
 sense. For education is but the development 
 of character, mental, moral, and physical, 
 and may be either good or bad. For there is 
 an education of the thief, of the bully, of the 
 tramp, as well as of the honest man, of the 
 hero, of the efficient man, or of the scholar, 
 or statesman, or philosopher. And so, even 
 among legitimate kinds of education, there is 
 an education of the mechanic, of the farmer, of 
 the laborer, of the lawyer, of the doctor, and 
 many other kinds. Consequently, when one 
 asserts the benefit of education generally, 
 without defining the term, the proposition is 
 nonsensical. 
 
 142. PROTECTION. So the man that as- 
 serts that he is in favor of the protection of 
 American industries is, in general, talking pure 
 nonsense. For there are many kinds of pro- 
 tection, as, e. g., (i) The prohibition of all 
 foreign imports that compete with our own in- 
 dustries; (2) the equalization of the cost of 
 production; and (3) the encouragement of in- 
 fant industries; and until we are told which of 
 these various kinds of protection is intended 
 the proposition conveys no definite meaning. 
 
 143. EXPANSION. So when an American
 
 FALLACY OF NON-SIGNIFICANCE 167 
 
 announces himself as an advocate of territorial 
 expansion he is, generally, talking nonsense; 
 for there are many kinds of expansion, among 
 which three may be especially distinguished, 
 namely: (i) The acquisition of contiguous 
 homogeneous territory essential to the safety 
 of the government, as, e. g., in the case of the 
 purchase of Louisiana; (2) the acquisition of 
 contiguous and homogeneous territory desir- 
 able as giving room for the expansion of popu- 
 lation, but not essential to the safety of the 
 government, as, e. g., the acquisition of Cali- 
 fornia, New Mexico, etc. ; and (3) the acquisi- 
 tion of territory far removed from our own, of 
 a climate unsuited to our people, and inhabited 
 by an alien and non-assimilable race. Such a 
 country must be governed by despotic power, 
 and its acquisition must therefore be distin- 
 guished from other kinds of expansion by the 
 name of Imperialism.
 
 CHAPTER X 
 
 FALLACY OF FALSE DEFINITION 
 
 144. The nature of this fallacy is explained 
 under Rule II. of the Rules of Logic. As 
 there explained, the fallacy is of two kinds 
 consisting, the one in the use of a term in an 
 improper sense, i. e., in a sense not permitted 
 by the usage of the language the other, in 
 using a term in an unreal sense, /. e. , as denot- 
 ing a notion to which there is no corresponding 
 reality. 
 
 The former kind of the fallacy is not admitted 
 by logicians generally ; for it is an unfortunate 
 delusion of philosophers that they are at liberty 
 to define a term as they please. But whether 
 this claim be admitted or otherwise, it has been 
 the source of infinite error; so that the viola- 
 tion of the rule, if not regarded as a fallacy, 
 must at least be regarded as a most prolific 
 mother of fallacy. For where a term is used 
 in a novel sense, though clearly defined, it is 
 hardly within the power of the human intellect 
 168
 
 FALLACY OF FALSE DEFINITION 169 
 
 to emancipate itself from the influence of its 
 usual and proper signification. Hence, inevi- 
 tably, the use of improper terms will result in 
 the fallacy of Ignoratio Elenchi. 
 
 Examples 
 
 145. WHATELY'S DEFINITION OF LOGIC. 
 Whately's definition of Logic as " the science 
 and art of reasoning," and of Reasoning as 
 consisting solely in syllogistic inference, pre- 
 sents an instructive example of the Fallacy of 
 False Definition. This definition excludes from 
 the province of Logic the doctrine of Judgment, 
 and, as involved in this, the doctrine of the 
 Term, and also that of the fallacies called Non- 
 logical or Material, thus mutilating it of its 
 most vital parts. But these subjects are in- 
 variably treated of by the logicians, including 
 himself, arid as is now generally admitted 
 belong to logical doctrine ; which is an effective 
 reductio ad absurduin of the definition. 
 
 146. STEWART'S DEFINITION OF REASON- 
 ING. From the same false definition of Logic, 
 and of reasoning, Dugald Stewart deduces the 
 paradoxical conclusion that not only Logic, but 
 reasoning itself, is but of little utility; which 
 constitutes a still more effective reductio ad 
 absurdum of the falseness of the definition. 1 
 
 1 "Of the different elements which enter into the composi- 
 tion of reason, in the most enlarged acceptation of the word,
 
 1 70 LOGIC 
 
 147. LOCKE'S ATTACKS ON LOGIC. 
 Locke's diatribes against Logic had their 
 source in the same false definition of Logic as 
 being merely the doctrine of syllogism. But, 
 strangely enough, at the end of his work he 
 gives a correct definition of it; which, as we 
 have seen, he takes for an invention of his own 
 ( no). 
 
 148. MILL'S DEFINITION or LOGIC. 
 According to Mill's definition, " Logic is not 
 the science of belief, but is the science of proof 
 or evidence," or, as otherwise expressed, " the 
 science of the operations of the understanding 
 which are subservient to the estimation of evi- 
 dence." But bearing in mind the essential 
 difference between judgments and assumptions 
 it will be observed if we leave out of view 
 axioms, which are to be regarded merely as 
 laws or conditions, to which the mind operating 
 intelligently must conform that the former 
 constitute the first principles of all demonstra- 
 tive or apodictic reasoning, and therefore ne- 
 cessarily fall within the province of Logic ; but, 
 with regard to assumptions, that Logic is not 
 concerned with the evidence of their truth. 
 But the term, evidence, in its proper sense, re- 
 lates exclusively to assumptions or propositions 
 
 the power of carrying on long processes of reasoning or deduc- 
 tion is, in point of importance, one of the least." Phil, of 
 the Mind, v. ii, p. 154.
 
 FALLACY OF FALSE DEFINITION l?l 
 
 in which the significative relations of the term 
 are not intuitively perceived; and hence, with 
 regard to such propositions, the respective pro- 
 vinces of Logic and of the other sciences are 
 clearly defined. The latter deal with the evi- 
 dence of the propositions assumed ; the former, 
 exclusively with inferences from them, upon 
 the assumption or hypothesis that they are true. 
 Hence the definition of Mill precisely reverses 
 the several functions of Logic and of the other 
 sciences that furnish it with assumed proposi- 
 tions as premises. 
 
 149. HAMILTON'S DEFINITION OF LOGIC. 
 The definition of Logic as " the science of 
 the laws or forms of thought " may be cited 
 as another example. Logic is concerned, not 
 with all thought, but with a particular kind of 
 thought only namely, reasoning; and it is 
 concerned, not only with \\\z forms, but with 
 the matter of reasoning. The definition is 
 therefore at once too wide and too narrow; it 
 would include, e.g., rhetoric and grammar, 
 and would exclude the best part of Logic. 
 
 150. DEFINITION OF THE LAW. A most 
 striking example of the Fallacy of False Defini- 
 tion is presented by the definition of the Law, 
 invented by Blackstone and adopted as the first 
 principle of jurisprudence by Bentham and 
 Austin. According to this definition, the law 
 is merely an expression of the will of the
 
 1^2 LOGIC 
 
 government an obviously false and illegiti- 
 mate definition. Yet the theory of Bentham 
 and Austin, based on this definition, has abso- 
 lutely dominated jurisprudence in England and 
 this country for nearly a century; and, as the 
 result, English and American jurists and publi- 
 cists have lost mental touch with the jurists of 
 other countries and ages; and have thus, with 
 reference to scientific jurisprudence, been ren- 
 dered incapable of dealing with this great and 
 important subject. And indeed the effect of 
 the theory on the practical administration of 
 justice has been scarcely less deleterious. 
 
 151. THE THEORY OF PRIVATE UTILITY. 
 Another conspicuous example of this fallacy 
 is furnished by the theory of individual utility 
 assumed by Hobbes, Bentham, and Austin as 
 the first principle of Morality and Politics; in 
 which self-interest is regarded as the sole pos- 
 sible motive of human conduct, and right and 
 wrong, just and unjust, and good and evil are 
 defined as consisting in conformity or noncon- 
 formity to that interest. 
 
 152. THE GREATEST GOOD OF THE 
 GREATEST NUMBER. Bentham also incon- 
 sistently held the theory that " the greatest 
 good of the greatest number" is the true stand- 
 ard of Morality ; which must either be regarded, 
 like the theory of General Utility, as simply 
 nonsensical, or as holding that the standard of
 
 FALLACY OF FALSE DEFINITION' 173 
 
 right and wrong and of the just and unjust is 
 the good of the majority. An execrable doc- 
 trine; for it cannot be asserted that the life or 
 faculties or property of an innocent man can 
 be converted to the use of another or of others, 
 except in the case of a clearly defined right in 
 the one and an obligation to submit to it in 
 the other. 
 
 153. MAINE'S DEFINITION OF THE LAW 
 OF NATURE. Another example is presented 
 by the peculiar and curious view taken by Sir 
 Henry Maine of the term Jus Nat ur ale as 
 used by the Roman lawyers, and its equiva- 
 lent, the Law of Nature, or Natural Law, as 
 used by modern jurists and philosophers. This 
 notion, he erroneously assumes, had its origin 
 in the supposed state of nature ; which doctrine, 
 he says, the Roman jurisconsults borrowed 
 from the Greek philosophers. But the term 
 Jus Naturale, or Law of Nature, is one of the 
 comparatively small class of terms whose mean- 
 ing is perfectly definite and settled. As used by 
 jurists, it is but another name for Natural Jus- 
 tice, 1 or Right Reason applied to the jural 
 
 1 Hobbes's Lev., chap. xxvi. "It is not used among them 
 that be learned in the laws of England to reason what thing 
 is commanded or prohibited by the law of nature." But, 
 " when anything is grounded on the law of nature, they say 
 that reason will that such a thing be done ; and if it be pro- 
 hibited by the law of nature, they say it is against reason " 
 (Doctor and Student, chap. v.). "True law is right reason
 
 174 
 
 LOGIC 
 
 relations of men ; which, as universally held by 
 them, " is part of the law of every common- 
 wealth in the world." 
 
 conformable to nature" (Cicero, De Rep.). " Right reason is 
 what we call law" (id., De Leg.). "Natural law is the 
 rule and dictate of right reason " (Taylor, Elements of Civil 
 Law). ' ' The law is intellect free from passion " (Arist. , supra, 
 135 n.).
 
 CHAPTER XI 
 
 ILLICIT ASSUMPTION OF PREMISES (PETITIO 
 PRINCIPII} 
 
 I. Of the Nature and Several Forms of this 
 Fallacy 
 
 1 54. This fallacy may occur in various ways, 
 and it would therefore be an "endless task to 
 enumerate or classify all its different forms; 
 nor would there be any advantage in doing so. 
 There are, however, several forms of the fallacy 
 that, on account of their frequent occurrence 
 and their powerful influence over the minds of 
 men, demand a particular consideration, and 
 to these our attention will be directed. 
 
 155 (i). ILLICIT GENERALIZATION. The 
 most important of these, which may be called 
 the Fallacy of Illicit Generalization, consists in 
 the use of a universal proposition in cases where 
 the corresponding particular proposition is 
 alone admissible. This fallacy is one of the 
 most common and formidable, not only in 
 popular discourses, but in more pretentious 
 
 12 
 
 175
 
 1/6 LOGIC 
 
 works on Politics and Morality; for almost all 
 the wisdom of common sense is embodied in 
 this sort of propositions, i. e., particular propo- 
 sitions assumed to be universal. Such propo- 
 sitions may, indeed, be used with profit by 
 men of sense in practical affairs; as, in general, 
 when a question presents itself it is easy to 
 perceive whether the principle should be ap- 
 plied or not; or, if a mistake be made, it is 
 corrected by experience; but the masses of 
 men are easily misled by them. Hence they 
 serve well for rhetorical purposes; for the 
 hearer, unless of a critical mind, will in general 
 accept them without hesitation. 
 
 Examples 
 
 156. COMMONPLACES. The most impor- 
 tant cases of this fallacy occur in the use of 
 Commonplaces ; by which is meant, opinions 
 current among men generally, or particular 
 classes of men, and used as premises for reason- 
 ing. 1 These are commonly founded upon some 
 truth which they purport to express, and to 
 which they more or less nearly approximate; 
 
 1 Hence Bacon, as a useful rhetorical device, recommends 
 the preparation of tables of Commonplaces, of which he gives 
 an example in his De Augmentis ; wherein should be arranged, 
 for the use of speakers and writers, in parallel columns, argu- 
 ments pro and con, or theses and anti-theses, on all questions 
 of general interest.
 
 ILLICIT ASSUMPTION OF PREMISES 1 77 
 
 so that there is here, as " in all things evil, a 
 soul of truth." But they are hardly ever uni- 
 versally true; and therefore to assume them as 
 universals is illicit. 
 
 157. POPULAR PROVERBS. Of these com- 
 monplaces, the most striking examples are 
 furnished by popular proverbs; and of these, 
 as illustrating precisely the nature of such 
 maxims, two may be cited that, in their literal 
 expression, are contradictory, but, as maxims 
 go, may both be said to be true, i. e., they are 
 each true in certain cases, but neither univer- 
 sally. They are the old adages, " Never put 
 off till to-morrow what you can as well do to- 
 day " and " Never do to-day what you can as 
 well put off till to-morrow " ; the first of which 
 points out the danger of procrastination, the 
 latter, the danger of committing ourselves be- 
 fore necessity requires. It may be readily seen 
 that, according to circumstances, either of 
 these may serve as a useful hint for conduct ; 
 but, in using it, the caution of the nautical 
 philosopher is to be observed, that " the bear- 
 ing of the observation lies in the application 
 of it." 
 
 158. LEGAL MAXIMS. Another striking 
 illustration of the same class of propositions is 
 furnished by what are called the maxims of the 
 law ; which, in general, are true only as particu- 
 lar propositions, /. e., only in particular cases,
 
 178 LOGIC 
 
 but are habitually spoken of by legal writers as 
 " first principles," analogous to the maxims of 
 science; though every competent lawyer is 
 familiar with the fact that they admit of numer- 
 ous exceptions. A very large proportion of the 
 so-called principles of the law, and of the rules 
 founded upon them, are of precisely this nature, 
 z. e., admit of exceptions, and are, therefore, 
 true only as particular propositions. And it is 
 also a fact that many of these principles and 
 rules are opposed by others, equally approved, 
 that are contradictory to them. Hence, if we 
 regard bulk only, the greater part of the law 
 might be readily and advantageously arranged 
 in a table of contradictory commonplaces, i. e., 
 a collection of theses and anti-theses, as sug- 
 gested by Bacon in the De A ugmentis; wherein, 
 under each topic, one column should represent 
 the one side and the other, the other, of the 
 various questions that may arise in litigation. 
 The cases might also be arranged in the same 
 way. 
 
 The above examples are all cases of illicit 
 generalization, and will serve to show how wide- 
 spread is the use of this particular form of illicit 
 assumption of premise. And, it may be added, 
 such is the lack of critical acumen in the gener- 
 ality of mankind, that the fallacy is seldom 
 detected, and consequently it constitutes the 
 most powerful of rhetorical devices.
 
 ILLICIT ASSUMPTION OF PREMISES 1/9 
 
 159(2). OF THE FALLACY OF NON CAUSA 
 PRO CAUSA. Another form of the Fallacy of 
 Illicit Assumption of Premise is presented by 
 the fallacy called " Non causa pro causa" ; 
 which is also called the fallacy of " Post hoc 
 ergo propter hoc." It consists in the illicit as- 
 sumption that an event preceding another 
 event is the cause of the latter, as, e. g., that 
 a change in the moon is the cause of a change in 
 the weather ; or that the fact of thirteen dining 
 together is the cause of any accident that may 
 happen to any one of them ; or that the Dog 
 Star is the cause of heat. This is, indeed, one 
 of the most familiar of fallacies in political 
 arguments, where it is common to argue that 
 the condition of the country, whether good or 
 bad, is caused by some particular policy, as, 
 e. g., where it is argued alternately, according 
 to vicissitudes of events, by the one party that 
 a prosperous, by the other that a depressed, 
 condition of affairs is caused by the tariff or 
 other political measure. 1 
 
 1 It will be observed that there are some differences of 
 opinion among logicians as to this fallacy. A distinction is 
 made between what is called the causa essendi and the causa 
 cognoscendi ; or between the cause of an event and the cause 
 of our knowing it. These may coincide, as, e. g., when from 
 the fact of its raining in the night we infer that the ground 
 will be wet in the morning ; where the rain is both the causa 
 essendi and the causa cognoscendi. But, when, from finding 
 the ground wet in the morning, we infer that it rained during
 
 l8o LOGIC 
 
 160(3). ARGUING IN A CIRCLE. Another 
 common form of the Fallacy of Illicit Assump- 
 tion is presented by the fallacy called arguing in 
 a circle ; which consists in assuming for a prem- 
 ise the very proposition to be proved, or one 
 obviously equivalent to it, or one that is form- 
 ally involved in it. 1 When the argument does 
 not extend beyond a single syllogism it is 
 called a Hysteron Proteron (the First-last). 2 
 
 161 (4). QUESTION-BEGGING TERMS. 
 Another very common and very dangerous 
 
 the night, the causa cognoscendi is the wet ground, from which 
 we infer the causa essendi, i. e., the rain. Logic is, however, 
 concerned with the causa essendi only so far as it constitutes 
 the causa cognoscendi ; and hence logically the distinction may 
 be regarded as immaterial. 
 
 1 This occurs most frequently in the use of synonyms, and, 
 as observed by Whately, is peculiarly favored by the composite 
 character of our language. It can occur only where the prop- 
 osition assumed is so obviously equivalent to the conclusion 
 as to be evidently the result of a trick or inadvertence. In 
 general the premises assumed are equivalent to, or imply, the 
 conclusion ; and the conclusion is arrived at by the substitu- 
 tion of an equivalent term ; which is the very essence of ratio- 
 cination. Such assumptions are not only admissible, but 
 inevitable. Otherwise all syllogisms would be fallacious, as 
 involving a pctitio principii ; and inference, inconceivable. 
 
 2 The following is a striking example of this fallacy : 
 " Since every unjust act is inexpedient, then no unjust act is 
 expedient ; then no expedient act is unjust ; then every expe- 
 dient act is just." This has been given as a valid argument. 
 But the premise is obviously but an inference from the conclu- 
 sion, which is the principle of the reasoning ; and for it the 
 thesis has been illicitly substituted as the premise.
 
 ILLICIT ASSUMPTION OF PREMISES l8l 
 
 form of this fallacy is that of using question- 
 begging terms (which is also a case of the Fal- 
 lacy of False Definition). It consists either in 
 including in the formal definition of a term 
 some unproved assumption, as being of the es- 
 sence of the conception denoted, or in using 
 the term without formal definition, as though 
 such assumption were included in its meaning. 
 By this method, the propositions from which 
 our conclusions are to be deduced, instead of 
 being proved as they ought to be, are uncon- 
 sciously imbibed by the mind, with the defini- 
 tion, or with our conception of the term, and 
 the conclusion thus in effect assumed. The 
 power of this method of persuasion is well un- 
 derstood by many, and unscrupulously used 
 as, for example, by Hobbes and other support- 
 ers of governmental absolutism ; who realize 
 the truth of Rousseau's observation that " the 
 strongest is not strong enough to continue al- 
 ways master, unless he transforms his power 
 into a right, and obedience into a duty." But 
 with the mass of writers the fallacious process, 
 though none the less efficacious, is entirely 
 unconscious. A notable example of this fallacy 
 is usually given by political writers in their 
 definitions of " the State"; which is simply 
 an independent society of men," but is 
 usually defined so as to include in its essence 
 absolute power, or some other theory of the
 
 I 82 LOGIC 
 
 writer. Any recent work on Politics will serve 
 to illustrate the fallacy. 
 
 2. Of tlie Tests of Illicit Assumption 
 
 162. ENUMERATION OF THE TESTS. 
 There are numerous tests by which the legiti- 
 macy of assumed premises may be determined, 
 of which the most important and familiar are: 
 
 (1) the ''Instance,'' 1 or " Extreme Case"; 
 
 (2) the " Burden of Proof," or Onus Probandi ; 
 and (3) the Reductio ad Absurdum. These will 
 next be considered. 
 
 163. THE INSTANCE, OR EXTREME CASE. 
 This test applies most appropriately to the 
 Fallacy of Illicit Generalization, and is most 
 efficacious in its operation ; though, as is ob- 
 served by De Morgan, it is commonly regarded 
 as not only inadmissible, but impertinent. It 
 consists simply in adducing an exception to the 
 proposition assumed. The subject is admi- 
 rably treated by the author cited. 2 
 
 164. THE ONUS PROBANDI. An ex- 
 tremely effective means of testing the truth of 
 
 1 The term ' ' instance " is commonly used as synonymous with 
 '' example," but it is said by De Morgan that by the mediaeval 
 logicians it was always used to denote an inconsistent example, 
 or, in other words, to denote what we would call an instance 
 to the contrary, an expression that would have been regarded 
 by them as tautological. 
 
 2 "The application of the extreme case is very often the 
 only test by which an ambiguous assumption can be dealt
 
 ILLICIT ASSUMPTION OF PREMISES 183 
 
 a proposition, and of thus exposing an Illicit 
 Assumption, is often afforded by considering 
 what is the presumption in the case ; or, con- 
 trariwise, on which side of the question lies the 
 burden of proof , or onus probandi. In general, 
 this is on the party affirming the proposition, 
 and, in the absence of other presumptions, we 
 are always entitled to demand his proofs. This 
 simple test will be sufficient to dispose of all 
 propositions for which proofs cannot be found, 
 but which have been inadvertently assumed ; 
 and this test we should always apply to our 
 own reasoning, remembering that " Slowness 
 of belief and distrust are the very sinews of 
 wisdom." But in certain cases, and especially 
 in Moral and Political Science, the test will 
 often have a conclusive efficacy. For in 
 Morality, Public and Private, or in Jurispru- 
 dence or Right, the questions presented are 
 generally questions, not of fact, but of right 
 and wrong ; and among these there are certain 
 fundamental principles, as, e.g., touching the 
 right of personal liberty or security or self- 
 ownership, with reference to which the pre- 
 sumption is clearly defined, and its contradictory 
 obviously absurd. Of this kind is the general 
 presumption in favor of liberty; which, of 
 
 with ; no wonder that the assumer should dread and protest 
 against a process which is as powerful as the sign of the cross 
 was once believed to be against evil spirits." Formal Logic.
 
 1 84 LOGIC 
 
 itself, is sufficient to dispose of numerous and 
 important political theories that, from a neglect 
 to consider the onus probandi, have been care- 
 lessly or dishonestly assumed. 
 
 165. OF THE REDUCTIO AD ABSURDUM. 
 This consists in reasoning from the conclu- 
 sion deduced from the premises assumed to 
 some absurd, or admittedly untrue, conclusion ; 
 and this method of refutation will apply not 
 only to the fallacy of illicit generalization, but 
 to all forms of petitio principii whatever. It 
 is, indeed, one of the most efficacious means 
 that Logic has at its command for the detection 
 of fallacy, and will therefore repay an attentive 
 consideration. 
 
 Strictly speaking, the phrase would seem to 
 indicate that it applies only to the establish- 
 ment of the contradictory of the proposition 
 under consideration '; but the method has, in 
 fact, a much wider application, and the term, 
 in common use, a corresponding extension. 
 For it is the essential characteristic of all true 
 
 1 In the narrower sense, the term reductio ad absurdiim is 
 equivalent to the reductio ad impossibile ; of which examples 
 are given supra ( 96, n.). But more generally it is used 
 as including all cases where, from the conclusion of an 
 argument, the contradictory of some admitted proposition 
 or, in other words, a conclusion contrary to the hypothesis 
 can be deduced. Hence it is called by Aristotle the "Argu- 
 ment from Hypothesis." (Mansel's Aldrich, App., note I, 
 p. 228.)
 
 ILLICIT ASSUMPTION OF PREMISES 18$ 
 
 propositions that they will be consistent with 
 each other; and it is an almost equally univer- 
 sal characteristic of untrue propositions that 
 they will be inconsistent with other proposi- 
 tions known to be true. 
 
 This is particularly the case in all the 
 different branches of the Science of Human 
 Nature ; all of whose parts and particular prin- 
 ciples are so connected by numerous relations 
 that it is almost impossible to assert an untrue 
 principle without coming in conflict with others 
 that are self-evident, or readily demonstrable, 
 and which have thus come to be universally 
 admitted. Hence it may be said that in 
 Morality or Politics we may set out from al- 
 most any principles, provided we hold them 
 with indifference and are capable of abandon- 
 ing them when shown to be inconsistent with 
 settled principles and known facts. From 
 which it may be inferred that the reductio ad 
 absurdum in fact constitutes not only an effi- 
 cient, but almost an all-sufficient, instrument 
 for the detection of fallacy in Moral and Politi- 
 cal Science. 
 
 General Examples 
 
 166. LOCKE'S THEORY OF SIMPLE IDEAS. 
 A most instructive example of Illicit As- 
 sumption of Premise occurs in the fundamental 
 assumption of Locke's theory of knowledge;
 
 1 86 LOGIC 
 
 which is, that the original notions received in 
 the mind from sensible objects are notions of 
 the qualities of substances, such as color, hard- 
 ness, etc., which he calls simple ideas ; and out 
 of which, he holds, all our notions are com- 
 pounded. But on reflection it will be perceived 
 that the original or primordial notions of the 
 mind are the composite notions of substances 
 or things ; and what Locke calls " simple no- 
 tions " are the result of subsequent analysis. 
 
 167. THE OBLIGATION OF CONTRACTS. 
 It is one of the so-called maxims of the law 
 that contracts are obligatory and ought to be 
 enforced (Pacta quczlibet servanda sunf); and 
 this is commonly assumed as a universal prop- 
 osition, as, e. g., by Bentham and Spencer in 
 the examples given below ( 180, 181). But 
 there are innumerable cases in which it is 
 obviously not right that contracts should be 
 enforced, and in which, in fact, the law does 
 not enforce them ; which is an effectual refuta- 
 tion of the principle. The true principle is 
 that in case of breach of contract the injured 
 party is entitled to compensation as in the 
 case of torts for the detriment suffered by 
 him by the acts of the wrongdoer (i. e., by the 
 making of the contract and its breach). 
 
 168. FALSE ASSUMPTION OF FACT. This 
 includes innumerable cases, which it would be 
 impossible to classify. One of the most in-
 
 ILLICIT ASSUMPTION OF PREMISES 1 87 
 
 teresting is furnished by Tacitus in his account 
 of the mutiny of the Pannonian legions on the 
 accession of Tiberius, in the address of the 
 soldier, Vibulenus, to the general, Bloesus. 
 His brother, he said, coming as a delegate 
 from the German army, had been butchered 
 by the commands of Bloesus. " Answer, 
 Blcesus," he said; " where hast thou thrown 
 away his corpse ? " By which, says Tacitus, 
 he raised such a spirit of frenzy and ven- 
 geance that had it not been quickly manifested 
 that there was no corpse to be found 
 and that Vibulenus never had any brother, 
 they had gone nigh to sacrifice the general." 
 The example, so far as Vibulenus is concerned, 
 was simply a lie, but, in the soldiers, a fallacy 
 that would have been readily refuted by apply- 
 ing the test of the onus probandi.
 
 CHAPTER XII 
 
 MISTAKING THE ISSUE, AND IRRELEVANT 
 CONCLUSION (IGNORATIO ELENCHI) 
 
 169. The nature of this fallacy, which is 
 explained under Rule IV. of the Rules of 
 Logic, is precisely expressed by the first of 
 the names we have given it, which is a techni- 
 cal term taken from the law. This differs from 
 the equally appropriate term Irrelevant Conclu- 
 sion only in this, that the former has regard to 
 the origin, the latter to the outcome of the fal- 
 lacy. Or, in other words, when we regard the 
 beginning of the fallacy, we call it Mistaking 
 the Issue; when the end, Irrelevant Conclu- 
 sion; and, in either case, Ignoratio ElencJii. 
 The two names, i. e., Mistaking the Issue and 
 Irrelevant Conclusion, present, therefore, two 
 different aspects of the same fallacy, under 
 each of which it will be convenient to consider 
 it. 
 
 170. MISTAKING THE ISSUE. This, as is 
 well appreciated by the lawyers, is one of the 
 most formidable and most common of all fal- 
 188
 
 MISTAKING THE ISSUE 189 
 
 lacies. For the most fruitful of all sources of 
 fallacy is bias or logical dishonesty, of which the 
 expedient of mistaking or misstating the ques- 
 tion at issue is one of the most obvious and 
 most potent instrumentalities. And as logical 
 honesty is, in fact, one of the rarest of intel- 
 lectual virtues, it can be readily understood 
 that the fallacy must be common. 
 
 171. FALLACY OF SEVERAL QUESTIONS 
 OR ISSUES. One form of this fallacy may be 
 identified with the technical Fallacia plurium 
 interrogationum ( 197), which consists in mix- 
 ing in one several questions or issues. As 
 defined by Aristotle, it results " from making 
 two questions one, when it escapes notice that 
 there are many, and one answer is given, as if 
 there was one question only." 
 
 The following examples are taken from a 
 recent work : 
 
 Did you steal anything when you broke 
 into my house last night ? ' ' Are you the only 
 rogue in your family ? ' ' Have you quit drink- 
 ing ? ' ' Have you cast your horns ? ' (Hence 
 sometimes called Cornutus.}" (Davis, Theory 
 of Thought, 294.) 
 
 The fallacy is readily solved by separating 
 the compound question into its several compo- 
 nents, as, e. g. , in the following: Menedemus, 
 Alexino rogante, Numquid, pair em verberare 
 desiisset ? inquit, Nee verberavi, ncc desii ; or,
 
 190 LOGIC 
 
 as in the answers of the two thieves to the 
 question: " Did you steal the sheep you have 
 in your possession ?"; to which the one an- 
 swered, " He did n't steal the sheep"; the 
 other, that " He did n't have it." 
 
 172. It is added by the author, " All this 
 seems quite frivolous." And another, gener- 
 ally accurate, logician says: " The so-called 
 ' Fallacia plurium interrogatiomim ' has not 
 been noticed in the text, because it is a rhe- 
 torical artifice rather than a logical fallacy." 
 (Fowler, Deductive Logic, 150.) But it cannot 
 be doubted that the fallacy, as described by 
 Aristotle, consists simply in mixing several 
 questions or issues in one, and therefore comes 
 under the head of mistaking' the issue; or that 
 it is at once a very common and a very for- 
 midable fallacy. And especially, it is to be 
 observed, it is the hard fortune of the citizen, 
 in all ages and countries, that, in general, 
 whether by accident or design, no question in 
 practical politics is presented to him that does 
 not involve this fallacy. 
 
 Thus, in American politics, for some time 
 after the war, several questions (plures intcr- 
 rogationes) were presented at each federal 
 election, namely: (i) as to the expediency of 
 the protective policy; (2) as to that of the re- 
 construction policy; (3) as to that of the con- 
 traction of the currency; and thus practically
 
 MISTAKING THE ISSUE 19! 
 
 the questions presented to each voter were: 
 " Are you in favor of all these policies ? " or 
 " Are you against them all ?" So in the last 
 election, the issues presented were equally 
 numerous namely : (i) as to the policy of 
 protection ; (2) as to the relative advantages of 
 the single gold or a bimetallic standard ; and 
 (3) assuming the desirability of bimetallism 
 as to the practicability of adopting it in this 
 country alone, without the concurrence of 
 other nations. 
 
 In the case put, and in fact in almost all 
 political contests, each question involved is dis- 
 cussed separately, and the conclusion pro- 
 fessedly drawn is simply the affirmative or the 
 negative of the particular question, as the case 
 may be; but the conclusion intended is, not 
 the affirmative or negative of the particular 
 question, but that of all of them taken to- 
 gether thus presenting a case of irrelevant 
 conclusion. 
 
 Hence, generally, in political contests the 
 actual issue presented is simply as to the as- 
 cendancy of one of two parties; while the 
 voters are persuaded, or persuade themselves, 
 that they are deciding some other issue. Hence 
 it results as a general though not as a uni- 
 versal proposition that politics becomes a 
 mere struggle for political supremacy. 
 
 173. IRRELEVANT CONCLUSION. All fal-
 
 IQ2 LOGIC 
 
 lacies of judgment must, as we have observed, 
 take the form of irrelevant conclusion ( 132); 
 which, in turn, becomes a fallacy only when 
 used as an equivalent to some other proposi- 
 tion. Hence the examples of fallacy already 
 given, and many of those to be given hereafter, 
 will equally serve our present occasion. 
 
 Examples 
 
 174. THE DOCTRINE OF ABSOLUTE SOV- 
 EREIGNTY. The use made of this doctrine by 
 its advocates presents a conspicuous example 
 of this fallacy. The doctrine, like all other 
 nonsensical theories, is in itself innocuous, and 
 becomes otherwise only by illicit use. But it 
 is invariably used in some different and signifi- 
 cant sense, as, e. g., Rousseau's theory of the 
 " Sovereignty of the People," which gave rise 
 to the various political doctrines rife in the 
 French Revolution, and to which historians 
 have ascribed the terrible scenes of the Reign 
 of Terror ; from which they draw the infer- 
 ence that it is dangerous to apply Logic to 
 practical politics. But this also is a case of 
 Irrelevant Conclusion. For the conclusion 
 should be only that Fallacy is dangerous, i. e., 
 not Logic, but the want of Logic. 
 
 175. SOVEREIGNTY OF THE LAW. Of the 
 various forms of the doctrine of Sovereignty, 
 that of the Sovereignty of Right, or the Law,
 
 MISTAKING THE ISSUE 193 
 
 as it metaphorically expresses a doctrine at 
 once true and fundamentally important, might 
 seem to be unobjectionable were it not that, in 
 the direct effect of its language, it is merely 
 nonsensical, and therefore liable to be used as 
 equivalent to some other form of the doctrine, 
 as, e. g., in the use made of it by Von Hoist in 
 his Constitutional History of the United States ; 
 where his expressed conclusion is that " Sover- 
 eignty is One and Indivisible the Sovereignty 
 of the Law" ' But his real doctrine to the 
 establishment of which all his arguments are 
 marshalled is that sovereignty is indivisible, 
 and therefore vested exclusively, not in the 
 law, but in the Federal Government, and not 
 to any extent in the States. 
 
 176. AUSTIN'S USE OF THE DOCTRINE OF 
 SOVEREIGNTY. An example of this fallacy is 
 furnished by Austin and his followers in the 
 use made by them of their conclusion, that 
 ' ' Sovereign poiver is incapable of legal limita- 
 tion "/ which, accepting his definition of the law 
 as being merely an expression of the will of the 
 sovereign, is quite true, and altogether inno- 
 cent; for obviously one's power cannot be said 
 
 1 This though, if the sense of the term be observed, a 
 harmless proposition is not a very consistent one ; for, as in 
 the United States, each State, as well as the Federal Govern- 
 ment, has its own independent system of law, it would seem 
 to follow that there are several sovereignties. 
 13
 
 194 LOGIC 
 
 to be limited by his own will ; but the proposi- 
 tion is habitually used in the ordinary sense of 
 the terms. 
 
 177. USE OF THE DOCTRINE BY HOBBES. 
 Another example, precisely similar, is fur- 
 nished by Hobbes, who logically deduces from 
 his premises the conclusion that " the right or 
 just power " of the sovereign over the life and 
 fortunes of the subject is unlimited; and the 
 corresponding duty of the subject, absolute; 
 which, according to his definition of the terms, 
 right, justice, and duty, means simply that the 
 so-called right of the sovereign is an unbridled 
 or lawless power, to which prudence demands 
 of the subject that he should submit for fear of 
 worse consequences. The conclusion, in the 
 sense of the terms defined, is, therefore, quite 
 true; but it is habitually used by him and by 
 modern English jurists as though the terms, 
 right, justice, and duty were defined in their 
 ordinary and proper sense. 
 
 178. BENTHAM'S MISUSE OF THE THEORY 
 OF PRIVATE UTILITY. But the most flagrant 
 example of this fallacy is that of Bentham, who, 
 having established, or professed to have estab- 
 lished, the doctrine of Private Utility, or Utility 
 to the Individual, which asserts that the sole 
 possible motive of human conduct and the 
 only standard of right and wrong is self-inter- 
 est, afterwards assumes as equivalent to it the
 
 MISTAKING THE ISSUE 195 
 
 principle of General Utility, and systematically 
 uses the latter as the premise established. 
 
 179. MISUSE OF THE THEORY OF GEN- 
 ERAL UTILITY. This theory, in the use 
 habitually made of it by Bentham and by 
 utilitarians generally, also presents a most in- 
 structive example of this fallacy. The theory, 
 being non-significant, is in itself innocuous ; but 
 it is commonly used as equivalent to the pro- 
 position that the interest of the majority is the 
 sole test of right, or, as expressed by Bentham, 
 
 as equivalent to the sacred truth that the 
 greatest good of the greatest number is the 
 foundation of morals and legislation." Thus 
 we have the apparently innocuous principle of 
 General Utility converted into the execrable 
 maxim that the good of the majority is alone 
 to be consulted. 
 
 180. BENTHAM'S DEFENCE OF USURY. 
 Bentham's celebrated defence of usury has 
 been commonly regarded ever since its publica- 
 tion as finally settling the question involved ; 
 but in fact it presents a striking example of the 
 fallacy of Ignoratio ElencJii. 
 
 His thesis, as proposed, is to establish " the 
 liberty of making one 's own terms in money bar- 
 gains "/ and his conclusion, which is entirely 
 legitimate, is that no man, not under disability, 
 
 ought to be hindered, with a viciu to his own 
 advantage, from making such bargains in the
 
 196 LOGIC 
 
 way of obtaining money as he sees fit." But 
 obviously this is to mistake the issue ; for the 
 question is, not whether one should have the 
 liberty of making usurious contracts, but 
 whether he should be compelled to perform 
 them ( 167), and hence his conclusion is 
 obviously irrelevant. He fails, therefore 
 (though the world has thought differently), to 
 establish his proposition. 1 
 
 181. SPENCER'S ARGUMENT. Spencer's 
 argument in Social Statics and Justice for 
 liberty of contract is also an example of the 
 same fallacy. His first principle is his well- 
 known law of equal liberty, namely, " that 
 every man is free to do that which he ivills, pro- 
 vided that he infringes not the equal freedom of 
 any other man." From this principle he de- 
 duces, with admirable logic, the several per- 
 sonal rights that may be summed up in the 
 general right of self-ownership, and also the 
 right of property, and, as a corollary to the last, 
 the right of free exchange, and from that (illog- 
 ically, 189) the right of free contract ; but 
 he illicitly assumes, with Bentham, that the 
 
 1 In these observations it will be understood we are con- 
 sidering, not the moral or political question as to the propriety 
 of enforcing contracts for the payment of interest (on which 
 we have nothing to say), but simply the logical question as to 
 the validity of an argument in favor of usury that has served 
 to convince mankind of its righteousness, and that is univers- 
 ally regarded by an unlogical world as conclusive,
 
 MISTAKING THE ISSUE 197 
 
 question is one touching the liberty of contract, 
 and not as to the righteousness of coercing the 
 parties ( 167), which was his thesis. Hence 
 his conclusion is essentially distinct from the 
 real conclusion intended, which is, that men 
 should be compelled to perform contracts. 
 
 182. BERKELEY'S THEORY AS TO THE 
 NON-EXISTENCE OF MATTER. This furnishes 
 another example. His argument is that, if 
 matter exists, it is impossible for us to know 
 the fact, or to know anything about it. But 
 this conclusion he habitually uses as equivalent 
 to the proposition that " matter, in fact, does 
 not exist," i. e., he substitutes the " non- 
 existence of matter" for " ignorance of its 
 existence."
 
 CHAPTER XIII 
 
 ILLICIT CONVERSIONS 
 
 183. SIMPLE CONVERSION OF UNIVERSAL 
 AFFIRMATIVE PROPOSITION. The most usual 
 form of this fallacy occurs in the simple con- 
 version of a universal affirmative proposition, 
 as, e. g., where from the proposition Y is 
 X " we illicitly infer that " X is Y " ; and to 
 this form all other cases may be reduced. The 
 fallacy is so obvious that it might be supposed 
 it could not often occur, but it is in fact very 
 common. 
 
 Examples 
 
 184. CONFUSION OF PROPOSITION WITH 
 JUDGMENT. An example of it seems to be 
 presented by the commonly received doctrine 
 that " a proposition is a judgment expressed in 
 words "; which seems to result from an illicit 
 conversion of the proposition that a " judg- 
 ment expressed in words is a proposition." 
 
 185. ILLICIT CONVERSION BY NEGATION. 
 198
 
 ILLICIT CONVERSIONS 199 
 
 The fallacy frequently occurs in the conver- 
 sion of a proposition by negation or contra- 
 position. Thus, c. g., the proposition " Y is 
 not X " becomes by negation " Y is not-X " ; 
 from which converting per accidens we may 
 infer that " Some not-X is Y " ; but not as is 
 often inferred that " All not-X is Y." 
 
 By this method any universal affirmative 
 proposition (" Y is X ") may be converted into 
 a proposition between the negatives of its terms 
 (i. e., Not X is not Y) ; but not, as is often 
 done, without converting the terms, i. e., 
 from the proposition " Y is X " we may infer 
 that " Not X is not Y," but not that " Not 
 Y is not X " ( 91). 
 
 1 86. AN ARGUMENT OF HOBBES. A 
 striking example of this fallacy is presented by 
 Hobbes, that prince of logicians. Justice he 
 defines as the keeping of covenants, and injus- 
 tice as the failure to keep them. But, accord- 
 ing to his theory, covenants become valid only 
 upon the institution of government, from which 
 they derive their validity. Hence in a state of 
 nature there is neither justice nor injustice. 
 But he says also: " Whatever is not unjust is 
 just," and this conclusion which is contra- 
 dictory to his main position is obviously 
 arrived at by an illicit conversion of the univer- 
 sal affirmative proposition, " Whatever is just 
 is not-unjust."
 
 CHAPTER XIV 
 
 ILLICIT SUBSTITUTIONS OF TERMS 
 
 187. Substitutions of terms may consist 
 either in the substitution of a new vocable or 
 vocal sign, or in the substitution of a new 
 sense to the same vocable. The latter is always 
 illicit, and constitutes the Fallacy of Equivoca- 
 tion. The former will be considered in this, 
 the latter in our next chapter. 
 
 The substitution of new terms of equivalent 
 signification for terms originally occurring is 
 the most common and extensive in application 
 of all the processes involved in ratiocination; 
 and the corresponding illicit processes if we 
 include equivocation may be regarded as in- 
 cluding all fallacies whatever. Hence the 
 examples already given, and especially those 
 given under the head of Irrelevant Conclusion, 
 will serve equally well to illustrate the fallacy 
 now under consideration. 
 
 Examples 
 
 188. AUSTIN'S ARGUMENT. Many ex- 
 amples of this fallacy are furnished by Austin,
 
 ILLICIT SUBSTITUTION 2OI 
 
 as, e. g., in substituting for the predicate of the 
 proposition that " The sovereign power is in- 
 capable of legal limitation ," the term " legally 
 despotic," and thus inferring from the former 
 proposition that government is vested by law 
 with despotic power; which is not only untrue, 
 but upon his own theory impossible. For, if 
 law is but an expression of the will of the 
 sovereign, it is equally absurd to say either 
 that the sovereign power " is limited" or that 
 " it is conferred" by law. 
 
 189. SPENCER'S ARGUMENT. Another 
 example is furnished by Spencer in inferring 
 from the " right of free exchange " the " right 
 of free contract," which is in effect to substitute 
 genus for species in the subject of a universal 
 affirmative proposition. For exchange is only 
 a species of contract (v. supra, 181). It is true 
 that the right of free contract cannot be 
 doubted, but the substitution is none the less 
 a logical fallacy. 
 
 190. FLETCHER vs. PECK. Still another 
 example of this fallacy is furnished by Chief- 
 Justice Marshall (the greatest and most logical 
 of American jurists) in Fletcher vs. Peck, 6 
 Cranch, 135 ; where it was decided that an act 
 of the Legislature of Georgia revoking a grant 
 of land was in contravention of the provision of 
 the Constitution of the United States forbid- 
 ding the States to pass any act " impairing
 
 202 
 
 LOGIC 
 
 the obligation of contracts.'" The argument in 
 effect was that a grant is a contract, and that 
 this was impaired by the act ; which was in 
 effect to substitute " Contract" for " Obliga- 
 tion of Contract."' The fallacy is the more 
 glaring from the fact that a grant is an exe- 
 cuted contract, which carries with it no obliga- 
 tion. Hence the constitutional provision must 
 be held to refer only to executory or obligatory 
 contracts.
 
 CHAPTER XV 
 
 EQUIVOCATION 
 
 191. The ambiguity of terms and sentences 
 (Homonymia et AmpJiibolid) is undoubtedly the 
 most prolific of all sources of fallacy. This is 
 recognized by all logicians, and, indeed, by 
 philosophers generally ; but we doubt that 
 many appreciate the extent of the evil or the 
 universality of the danger to which men are 
 exposed by reason of it, or (especially) their 
 own infirmity in this respect. 
 
 ' Instances of this fallacy," says Mr. Mill, 
 " are to be found in most all the argumentary 
 discourses of imprecise thinkers"; a proposi- 
 tion true in its literal statement but false in its 
 obvious implications; for it implies that the 
 proposition is not true of precise thinkers, and 
 also (though with becoming modesty) that it is 
 not true of the author. But in fact the most 
 precise, or, as we would prefer to say, the 
 most logical thinkers are liable to fallacy, and 
 especially to this kind of fallacy ; and none 
 203
 
 204 LOGIC 
 
 more so than Mr. Milh 1 In this respect, if 
 fallacies be regarded as intellectual sins, we 
 may say: " There are none righteous. No, 
 not one." For it is with logicians as with 
 generals: the best that can be said of them is, 
 that the greatest are those who commit the 
 fewest blunders. Hence the only difference, 
 other than degree, between the more precise or 
 logical thinker and the unprecise is, that the 
 fallacies of the latter are difficult, those of the 
 former easy to expose. Hence it may be said 
 that, while it is the greatest achievement to be 
 right, it is no mean achievement to be clearly 
 and unequivocally wrong, i. e., perspicuous in 
 our errors. Hence the value of the political 
 theories of Hobbes and Austin, the most logi- 
 cal of modern writers; which, though false, 
 and even pernicious, are yet full of instruction. 
 Nor is the proportion of men of great logical 
 genius so large as is generally supposed. They 
 are in fact as scarce as great generals, or great 
 statesmen, or great poets. Nor is it to be as- 
 sumed that philosophical writers are less liable 
 to this and other fallacies than the less preten- 
 tious classes. ' For it is most true, as Cicero 
 saith of them somewhere, that there can be 
 nothing so absurd but may be found in the 
 books of the Philosophers" (Hobbes, 
 
 1 This is very fully shown by Mr. Jevons (Pure Logic and 
 Minor Works, p. 201).
 
 EQUIVOCATION 
 
 v.). So, as observed by the author cited, the 
 educated classes generally are inferior to the 
 vulgar in this respect. For " those men that 
 take their instruction from the authority of 
 books, and not from their own meditations, 
 [are] as much below the condition of ignorant 
 men as men endued with true science are above 
 it. For between true science and erroneous 
 doctrines, ignorance is in the middle " (/</., 
 chap. iv.). Hence no one should imagine him- 
 self free from this general infirmity of mankind ; 
 and he who most thoroughly realizes his weak- 
 ness in this respect may, like Socrates, be justly 
 pronounced the wisest of mankind. All are 
 liable to it; and he who supposes he is not is 
 simply unaware of his infirmity. 
 
 The nature of the Fallacy of Equivocation is 
 obvious, and has been sufficiently explained. 
 It remains, therefore, only to illustrate it by 
 appropriate examples, and for this purpose the 
 examples already given under other heads will 
 with one or two others be sufficient to serve 
 our purposes. 
 
 Examples 
 
 192. EQUIVOCAL USE OF NONSENSICAL 
 TERMS. Some of the most important cases of 
 this fallacy occur from the use of nonsensical 
 terms. The very nature of these is that they
 
 2O6 LOGIC 
 
 cannot be used for any practical purpose, ex- 
 cept by changing their meaning and thus 
 giving them a definite sense; and hence, for 
 the propositions in which they occur, significant 
 propositions are always substituted. Thus, as 
 we have seen, the term Sovereignty varies es- 
 sentially in meaning, as used in the several 
 doctrines of Personal Sovereignty, Corporate 
 Sovereignty, the Sovereignty of the People or 
 State, and the Sovereignty of Right or the Law ; 
 all of which different senses of the term are in- 
 consistent with each other, and all, except the 
 first, in their direct sense, without definite 
 signification, or, in other words, nonsensical. 
 Yet the term is habitually used by political 
 writers without distinguishing the sense in 
 which it is used, or without attempting to give 
 it any definite signification. But in the prac- 
 tical application of the doctrine of Sovereignty 
 the term is invariably used as equivalent to 
 such definite conclusions as the occasions of 
 the writer may require, or as a premise from 
 which such conclusions may be deduced; and 
 thus the most extravagant doctrines are ap- 
 parently established. Of which, as we have 
 seen, a striking example is furnished by Prof. 
 Von Hoist ( 175); and others equally ap- 
 propriate may be easily collected from almost 
 any work touching the subject. 
 
 The same observation will apply to the
 
 EQUIVO CA TION 2O/ 
 
 theory of general utility, or Utilitarianism, 
 and also to the notions that the will of the 
 government is the united will of the people ; 
 that the State is an Organism ; that it is 
 founded on compact, etc. ; all of which are, in 
 their direct sense, in themselves nonsensical, 
 and therefore innocuous, but are habitually 
 used as premises to establish all sorts of ex- 
 travagant conclusions. 
 
 193. OF EQUIVOCATION GENERALLY. 
 The above will suffice for examples of equiv- 
 ocations consisting in giving significance to 
 nonsensical terms. In illustrating other equiv- 
 ocations, the only embarrassment consists in 
 the number of examples that crowd upon 
 our attention ; but the following may be 
 sufficient. 
 
 194. ARGUMENT OF AUSTIN. One of the 
 most striking of these is furnished us by the 
 argument of Austin in support of his famous 
 position that judicial decisions are in their 
 essential nature laws or statutes, and the judges, 
 in fact, legislators; and another by his equally 
 remarkable position that " Custom does not con- 
 stitute part of the law" ; both of which rest 
 upon the equivocal use of the ambiguous term 
 " Law " ; which may denote either a law or 
 statute (lex], or the Law (Jus). 
 
 195. AN ARGUMENT OF BAIN. An ex- 
 tremely effective example of this fallacy is also
 
 208 LOGIC 
 
 furnished by Mr. Bain in his statement of the 
 doctrine of Utility. It consists in using the 
 term "party " in the double sense of a natural 
 and of a corporate person. Utility, he says, is 
 " the tendency of actions to promote the happi- 
 ness and prevent the misery of the party under 
 consideration; which party is usually the com- 
 munity in which one's lot is cast." ' 
 
 196. AN ARGUMENT ATTRIBUTED TO 
 PROFESSOR HUXLEY. Still another example 
 is presented by an argument attributed to Pro- 
 fessor Huxley. It consists in the equivocal use 
 of the term "power,'" which is commonly used 
 in two senses, namely, as denoting actual power, 
 or might, and as denoting rightful, or jural, 
 power, or right. The argument is as follows: 
 ' The power of the State may be defined as 
 the resultant of all the social forces within a 
 definite area. It follows, says Professor Hux- 
 ley, with characteristic logical thoroughness, that 
 no limit is or can be set to State interference " 
 (A Plea for Liberty, Donisthorpe). 
 
 This fallacy is common to all the Austinian 
 school of jurists, and, indeed, constitutes the 
 common fundamental infirmity of all their dis- 
 quisitions. These jurists, according to their 
 theory, have, indeed, no right to use the term 
 in any but the former sense; but, as we have 
 
 1 Bentham is guilty of the same fallacy (Principles of Legis- 
 lation).
 
 EQUIVOCATION 
 
 209 
 
 seen, after establishing their conclusions they 
 habitually use it as though equivalent to right, 
 in the proper sense a notion that can properly 
 have no place in their system.
 
 CHAPTER XVI 
 
 THE TRADITIONAL DOCTRINE OF FALLACIES 
 
 I 
 ARISTOTLE'S CLASSIFICATION OF FALLACIES 
 
 197. The received classification of fallacies, 
 adopted by the schoolmen from Aristotle, 
 though remarkable for its profound insight, has 
 but few pretensions to scientific accuracy; and 
 it is to be suspected that much of the obscurity 
 and confusion that surround the subject results 
 from the undue authority given to it by logi- 
 cians. It has, however, so profoundly affected 
 logical doctrine and nomenclature that, apart 
 from its intrinsic value, it must always remain 
 one of the principal subjects for the student's 
 attention. 
 
 198. TABLE OF FALLACIES. According 
 to this scheme, fallacies are divided into two 
 classes, called by the schoolmen and by later 
 logicians, Fallacies in Dictione, or in Voce (i. e., 
 in diction or speech), and Fallacies extra Dic- 
 tionem, or in Re (i. e., not in diction, but in 
 
 210
 
 DOCTRINE OF FALLACIES 211 
 
 matter). Of the former class six forms or 
 examples are given, and of the latter, seven, 
 which are as follows: 
 
 Aristotle ' s Division of Fallacies 
 
 I. FALLACIES IN DICTIONE : 
 
 (i) Homonymia (Ambiguity of Terms). 
 (*) Amphibolia (Ambiguity of Sentence). 
 
 (3) F. Compositions (F. of Composition). 
 
 (4) F. Divisionis (F. of Division). 
 
 (5) F. Accentus (F. of Accent). 
 
 (6) F. Figures Dictionis (F. of Figure of 
 
 Speech). 
 
 II. FALLACIES EXTRA DICTIONEM : 
 
 (1) F. Accidentis (F. of Accident). 
 
 (2) F. a Dicto Secundum Quid ad Dictum Sim- 
 
 pliciter (Illicit Substitution of Unquali- 
 fied for Qualified Terms). 
 
 (3) Ignoratio Elenchi (Irrelevant Conclusion). 
 
 (4) F. Consequents (Non-Sequitur). 
 
 (5) Petitio Principii (F. of Illicit Premise). 
 
 (6) Non-Causa pro Causa (Mistaking Cause). 
 
 (7) F. Plurium Interrogationum (F. of Several 
 
 Issues in One). 
 
 199. OBSERVATIONS UPON THIS CLASSI- 
 FICATION. As will be seen presently, all the 
 fallacies In Dictione are simply cases of Equivo- 
 cation, and of the fallacies Extra Dictionem all 
 except the 4th (F. Consequentis) are Fallacies 
 of Judgment ; under which head most of them 
 have already been considered at large. The
 
 212 LOGIC 
 
 excepted fallacy (the F. Consequentis) includes 
 all the Fallacies of Inference, except Equivoca- 
 tion. It is obvious, therefore, that the current 
 expressions (In Dictione and Extra Dictionetn) 
 whether from being a mistranslation of Aris- 
 totle's language or otherwise do not truly ex- 
 press the nature of the distinction between the 
 two kinds of fallacies, and are, therefore, cal- 
 culated to mislead us as they have Whately 
 and others with regard to it. 
 
 200. The true scheme of division is as fol- 
 lows: 
 
 Table of Fallacies 
 
 I. FALLACIES IN DICTIONE (EQUIVOCA- 
 TION). 
 
 (Including the six forms specified in the 
 first table.) 
 
 II. FALLACIES EXTRA DICTIONEM. 
 (i) Fallacies of Judgment. 
 
 (Including all fallacies Extra Dictionem 
 given in the table, except F. Conse- 
 
 (2) F. Consequentis (JVon-Sequitur). 
 
 (Including all Fallacies of Inference ex- 
 cept Equivocation.) 
 
 (a) Formal Fallacies (/. e., of Inference). 
 (Including Undistributed Middle, Il- 
 
 licit Process.) 
 
 (b) Material Fallacies. 
 
 (Including Illicit Substitutions of New 
 Terms.)
 
 DOCTRINE OF FALLACIES 213 
 
 The terms "Formal" and " Material Fal- 
 lacies" correspond to the "Logical" and 
 " Material Fallacies " of Whately, whose 
 " Semi-logical Fallacies " correspond precisely 
 to the fallacies In Dictione of Aristotle, or, in 
 other words, to the Fallacy of Equivocation. 
 This division of Whately's has, since his time, 
 been very generally adopted ; but, as is re- 
 marked by Mansel, it " is not the ancient prin- 
 ciple of distinction which is stated with more 
 or less clearness by several logicians," as, e. g., 
 in the following definitions of Sanderson: 
 
 Every fallacy In Dictione arises from some 
 ambiguity (mnltiplicitate} of expression." 
 ' Fallacies Extra Dictionem are those in which 
 the deception happens, not so much from some 
 ambiguity latent in the words themselves, as 
 from ignoring things " (i. e., the notions ex- 
 pressed). ' The former arise," says Mansel, 
 "from defects in the arbitrary signs of thought, 
 and hence are generally confined to a single lan- 
 guage, and disappear on being translated into 
 another. The latter are in the thought itself, 
 whether materially, in the false application of 
 notions to things, or formally, in the violation 
 of the laws by which the operations of the 
 reason should be governed ; and thus adhere 
 to the thought in whatever language it may be 
 expressed. Under this head are thus included 
 both false judgments and illogical reasonings"
 
 214 LOGIC 
 
 (i. e., both Fallacies of Judgment and Fal- 
 lacies of Inference) (Mansel's Aldrich, p. 132). 
 
 II 
 
 FALLACIES IN DICTIONS (EQUIVOCATION) 
 
 2OI (l) (2). HOMONYMY AND AMPHI- 
 BOLY. These are both cases of the Fallacy of 
 Equivocation, the former consisting in the 
 illicit use of ambiguous terms, the latter in the 
 illicit use of ambiguous sentences. They are 
 essentially of the same nature; and we, there- 
 fore, as is most in accord with the usage of our 
 language, class them together under the com- 
 mon name of Equivocations. This fallacy 
 has already been fully considered. 
 
 202 (3) (4). COMPOSITION AND DIVISION. 
 These fallacies are essentially of the same 
 nature. They consist in using a term succes- 
 sively in a distributive and in a collective sense, 
 or, in other words, in substituting for a term 
 used distributively the same term used collect- 
 ively, or vice versa. The former constitutes the 
 Fallacy of Composition, the latter the Fallacy 
 of Division. 
 
 The following are examples of the Fallacy 
 of Composition : 
 
 3 and 2 (distributively] are two numbers ; 
 
 5 is 3 and 2 (collectively)-, 
 
 .'. 5 is two numbers. 
 
 He who necessarily ^tv-y or stays (i. e., either
 
 DOCTRINE OF FALLACIES 21$ 
 
 necessarily goes, or necessarily stays) is not a 
 free agent ; 
 
 But every one either necessarily ^w.? or stays 
 (i. e., necessarily does one or the other); 
 
 . . No one is a free agent. 
 
 The following are examples of the Fallacy of 
 Division : 
 
 5 is one number; 
 
 3 and 2 (collectively) are 5 ; 
 
 . *. 3 and 2 (distributively) are one number. 
 
 The angles of a triangle are equal to two 
 right angles ; 
 
 A B C is an angle of a triangle ; 
 
 . . A B C is equal to two right angles. 
 
 All the black and white horses of the de- 
 ceased (/. e. , all the black, and all the white 
 horses) are the property of the legatee ; 
 
 The piebald horses are black and white 
 (/. e. , each is black and white); 
 
 . . The piebald horses are the property of 
 the legatee. 1 
 
 Obviously these fallacies (Composition and 
 Division) constitute merely a species of equivo- 
 cation, i. e., of either Homonymy or Amphiboly. 
 
 1 The last example is suggested by the celebrated Moot case 
 of the legacy of "all the testator's black and white horses." 
 The question was, whether the legatee was to have the black 
 and the white horses, or the piebald horses, i. e., the horses 
 that were each black and white. The legatee claimed that he 
 was entitled to both classes ; and, hence, in the one or the 
 other of his claims, was guilty of this fallacy.
 
 2l6 LOGIC 
 
 203 (5). THE FALLACY OF ACCENT OR 
 PROSODY (F. ACCENTUS F. PKOSODI^E}. 
 This fallacy is also a species of equivocation, 
 i. e., either Homonymy or Amphiboly. It con- 
 sists in varying the meaning of a term or 
 proposition by change of accent, tone, or 
 punctuation. 
 
 The most extreme case of this is that of 
 irony, by which the sense is precisely reversed, 
 as, e. g., in the speech of Job to his friends: 
 " No doubt but you are the people, and wis- 
 dom shall die with you." In this way, i. e., 
 by ironical use afterwards forgotten, the name 
 of the subtle doctor, Duns Scotus, has come 
 to be the peculiar name of a fool (i. e., dunce). 
 The fallacy resulting from changing the sense 
 of an ironical expression is too obvious to be 
 dangerous, but if it should occur would be a 
 case of F. Figures Dictionis. 
 
 204 (6). FIGURE OF SPEECH (F. FIGURE 
 DICTIONIS}. This fallacy (which is also 
 merely a species of equivocation) consists in 
 the illicit use of figures of speech, or, in other 
 words, in substituting for the indirect or fig- 
 urative, the direct or literal sense, as in the 
 following example: 
 
 " Herod is a fox ; 
 A fox is a quadruped ; 
 .'. Herod is a quadruped."
 
 DOCTRINE OF FALLACIES 21J 
 
 Or as in the following example, which was 
 given by a student called on for a syllogism. 
 The logical Professor, it may be explained, 
 was of corpulent habit, and known as " Old 
 Boll." 
 
 " All flesh is grass, the Scriptures say, 
 And grass when cut is turned to hay ; 
 Now if Death's Scythe Old Boll should take, 
 Golly ! What a haystack he would make ! " 
 
 But more serious examples may be found 
 among those already given, as, e. g., the 
 equivocal use of the term poivcr in the argu- 
 ment attributed to Professor Huxley, and also 
 in the misuse of the propositions that " the 
 State is a person," that "it is an organism," 
 that " its ivill is the united will of the people," 
 that " it has an interest or ivelfare distinct 
 from that of the people," etc., as heretofore ex- 
 plained. A striking example of this fallacy is 
 also presented in the famous case of Dart- 
 mouth College vs. Woodward ( 137). The 
 fallacy consisted in regarding the college as 
 a person ; which was only figuratively true. 
 For a corporation is a qua ^z'-person only, i. c., 
 is regarded as a person for certain purposes 
 only. 
 
 205. Hamilton strangely speaks of this as 
 " a contemptible fallacy," and as though to 
 furnish an example at once of confusion of
 
 2l8 LOGIC 
 
 things essentially different and of misappre- 
 hension of the nature and scope of Logic he 
 couples with the Fallacy of Figure of Speech 
 that of Equivocation, as being, the latter, a 
 species of the former, instead of vice versa, as 
 is in fact the case. ' These fallacies," he says, 
 (" ' sophismata equivocationis, anipliibolia, et ac- 
 centus) may easily be reduced to sophismata 
 figures dictionis ; they are only contemptible 
 modifications of this contemptible fallacy." 
 
 But, as is in effect observed by the author to 
 whom we are indebted for the above quota- 
 tion, when we reflect that nearly all words 
 denoting mental or moral qualities or acts 
 which is but to say nearly all terms used in the 
 different branches of the science of human 
 nature are in their origin metaphors, derived 
 from sensible objects or events as, e. g,, intui- 
 tion, perception, appreJiension, inference, induc- 
 tion, deduction, reflection, education, justice, 
 right, wrong, straight, power, organic, etc., 
 and that these terms still carry with them, to 
 a large extent, their material associations, by 
 which, as the history of philosophy shows, we 
 are continually being misled, we can hardly 
 fail to agree " that the sophism Figure Dic- 
 tionis, so far from being contemptible, is 
 worthy of our closest and most watchful 
 consideration" (Theory of Thought, Davis, p. 
 27).
 
 DOCTRINE OF FALLACIES 21$ 
 
 III 
 
 OF THE FALLACIES EXTRA DICTIONEM 
 
 206. OBSERVATIONS. Of these fallacies, 
 all except the fourth are Fallacies of Judgment ; 
 and four of them, namely, Ignoratio Elenchi, 
 Petitio Principii, Non Causa pro Causa, and F. 
 Plurium Interrogationum, have already been 
 considered in detail under that head. The 
 others, namely, the Fallacies of Accident, of 
 Secundum Quid, and of the Consequent of 
 which the first two are also Fallacies of Judg- 
 ment remain to be considered. 
 
 Logicians are widely at variance with refer- 
 ence to the nature of these fallacies; and, if 
 we may judge from the translations and from 
 the confusion reigning over the subject, Aris- 
 totle's own explanation of them must be re- 
 garded, in some particulars, as hopelessly 
 obscure. Hence, though I have attempted to 
 interpret his meaning correctly, I am by no 
 means sure that I have succeeded in this better 
 than others. It may, however, be claimed for 
 the exposition of the subject here given that it 
 is at least intelligible and consistent, and that, 
 in connection with the rest of Aristotle's 
 scheme, it renders his classification of the fal- 
 lacies complete. And, it may be added, it is 
 in accord with the best authorities.
 
 22O LOGIC 
 
 207. THE FALLACY OF ACCIDENT CF. Ac- 
 CIDENTis}.T:\\\s fallacy has its source in the 
 assumption that an accident of some of the 
 significates of a term, or of all its significates 
 for a certain time, is an accident of the term, 
 and therefore predicable of it without qualifi- 
 cation (v. supra, 49.) This assumption in 
 the case of an inseparable accident of all the 
 significates of the term is, indeed, legitimate; 
 for obviously such an accident may always be 
 predicated of all the significates of the term, 
 and hence of the term. But with separable ac- 
 cidents of the significates of a term, it is other- 
 wise; for, though these are commonly spoken 
 of as accidents of the term, they are not such 
 in fact, for their relation to the term is tem- 
 porary or transient. 1 Hence such an accident 
 can be predicated of the term only for so long 
 as it continues to be an accident of it, or, in 
 other words, only with relation to some par- 
 ticular time expressed or understood. For in 
 the logical proposition the copula has no rela- 
 tion to time, but expresses simply a permanent 
 significative relation between the terms, and 
 
 1 The terms separable and inseparable accidents can apply 
 only to real individuals, and hence only to concrete terms or 
 terms of first intention. With relation to these the distinc- 
 tion is sufficiently obvious. Thus, e. g., with reference to 
 Socrates, " Stagyrite" is an inseparable accident ; "standing," 
 "sleeping," etc., separable the last being predicable of him 
 only at times.
 
 DOCTRINE OF FALLACIES 221 
 
 hence a separable accident cannot be predi- 
 cated generally of a term. For, as is said by 
 Aristotle, " it is uncertain when [i. e., at what 
 times] an assertion can be made of a thing 
 present from accident"; or, in other words, 
 whether at any given time the accident con- 
 tinues to exist (Soph. Elenc/i, chap. xxiv.). 
 Thus, e. g,, an attacking party might be rightly 
 informed at a given time that the enemy was 
 sleeping, and hence conclude that it would be 
 safe to attack him; but it might be a fatal 
 error to assume the truth of the premise as 
 continuing to exist an hour later. 
 
 208. DEFINITION OF THE FALLACY. The 
 fallacy may therefore be defined as consisting 
 in predicating of a term a separable accident of 
 its significates without qualifying it by refer- 
 ring to the time at or during which it is inher- 
 ent ; or, in other words, in assuming, in place of 
 a proposition of which the predicate is an ac- 
 cident thus qualified, another proposition of 
 which the predicate is the accident unqualified ; 
 as if, e. g., from knowing a man is lame we 
 should assume that he is permanently lame. 
 Or the subject may be more generally illus- 
 trated as follows: Let Y denote the subject 
 (" John "), A the accidental predicate (" tem- 
 porarily lame," i. e., "lame for the time being"), 
 and X the general predicate (^'permanently 
 lame "); then we may be entitled to say " Y
 
 222 LOGIC 
 
 is A " ; but to assume, in place of this, that 
 Y is X would be to substitute for A the term 
 X, i. e., species tor gemis in the predicate of a 
 universal affirmative proposition. For the 
 class of " temporarily lame" will include all 
 the "permanently lame," and many others. 
 
 It will be noted here that there is necessarily 
 a significative relation between the accidental 
 and the general predicate, namely, that of 
 partial coincidence. Hence, to substitute X 
 for A is, in effect, to substitute AX (i. e., 
 " Some A ") for A, which presents a case of 
 illicit substitution of species for genus in the 
 predicate of an affirmative proposition. 
 
 It will also be observed that the Fallacy of 
 Accident is defined as consisting in the illicit 
 assumption of a premise. But, where the same 
 fallacy occurs in a formal inference, it con- 
 stitutes the Fallacy of Undistributed Middle, 
 which is a case of Non-sequitur or F. Consequen- 
 tis, as may be thus illustrated : 
 
 Some A is X 
 
 Y is A 
 
 .'. Y is X 
 
 The stock example of this fallacy, which I 
 have taken from Aldrich, is as follows: 
 
 ' What you have bought you have eaten ; 
 you have bought raw meat; therefore you
 
 DOCTRINE OF FALLACIES 22 3 
 
 have eaten raw meat " (Quod emisti comedisti ; 
 crudum emisti ; ergo crudum comedisti); which 
 may be expressed in the following syllogism, 
 which, in form, is unobjectionable: 
 
 The meat you buy is raw ; 
 The meat you eat is the meat you buy ; 
 .'. The meat you eat is raw. 
 
 The fallacy here may be regarded as a case 
 of equivocation, consisting in the use of the 
 term " raw " in the major premise in the sense 
 of " raw when bought," and in the conclusion 
 in the sense of " raw when eaten." But if the 
 term " raiv " be construed simply in both 
 cases (/. e., as used without qualification), the 
 fallacy must be regarded as a case of F. Acci- 
 dentis, consisting in the illicit assumption of 
 the major premise. For all that can be right- 
 fully affirmed is that the meat bought is raw at 
 the time of purchase; instead of which it is 
 assumed that it is permanently raw. For, 
 as we have observed, in the logical prop- 
 osition the copula includes both the future 
 and the past, and the significative relation be- 
 tween the terms is asserted, not as true only 
 at the moment of assertion, but before and 
 afterwards; and hence a universal proposition 
 may always be negatived by showing an in- 
 stance to the contrary, either in the past or in 
 the future.
 
 224 LOGIC 
 
 The following examples are furnished us by 
 Aristotle, and are given as paraphrased in the 
 notes of Mr. Owen's translation : 
 
 " Do you know what I am about to ask ? 
 No. But I am about to ask whether virtue is 
 good. Therefore, you know not whether virtue 
 is good." 
 
 " Do you know who approaches ? No. 
 But Socrates approaches. Therefore, you do 
 not know Socrates." 
 
 Here in each case the most obvious source 
 of the fallacy is in the use of the equivocal 
 terms, " What I am about to ask " (in the 
 first case), and " Who approaches " (in the 
 second). But this ambiguity may be removed 
 and the arguments expressed syllogistically in 
 unobjectionable form as follows: 
 
 1 i ) The question, I am about to ask, is unknown to 
 
 you. 
 The question whether virtue is good is the question 
 
 I am about to ask. 
 
 .'. The question whether virtue is good is unknown 
 to you. 
 
 (2) The man approaching is unknown to you. 
 Coriscus is the man approaching. 
 
 .'. Coriscus is unknown to you. 
 
 Indeed, even as thus expressed, the most 
 obvious solution of both these fallacies is still 
 to regard them as cases of equivocation, con-
 
 DOCTRINE OF FALLACIES 22$ 
 
 sisting in using the term " unknown to you " in 
 a double sense, i. e., in the major premise in 
 the sense of " unknown to you before you are 
 told," and in the conclusion in the sense of 
 " unknown to you after you are told," But if 
 the term be regarded as used in the same sense 
 in both places, the case is evidently one of F. 
 Accidenlis, consisting in the illicit assumption 
 of the major premise, or, in other words, in 
 the illicit substitution of the unqualified term, 
 " unknown to you," for the qualified term, 
 " unknown to you before you are told," which 
 alone was admissible as a predicate. 
 
 209. THE FALLACY OF SECUNDUM QUID 
 (F. A DIC TO SECUNDUM QUID AD DICTUM 
 SIMPLICITEK], This fallacy consists in as- 
 suming an unqualified in place of a qualified 
 proposition. But as the copula has but one 
 meaning, a proposition can be qualified in no 
 other way than by qualifying one or both of 
 its terms. Hence the fallacy must consist in 
 substituting for an unqualified a qualified term. 
 
 But a term can be qualified (i. e., its signifi- 
 cation or extension altered) only by coupling 
 with it another term that partly, but not 
 wholly, includes it, thus making a new term of 
 less extension, as, e. g., men by white, which 
 gives us for the new term, white men; or, 
 more generally, Z, Y, or X, by A, which 
 
 gives us, for new terms, AZ, AY, and AX, all 
 
 15
 
 226 LOGIC 
 
 included in, but of less extension, than the 
 originals; or, in other words, the class denoted 
 by a qualified term will always be a species 
 of the class denoted by the unqualified term. 
 Hence the Fallacy of Secundum Quid is simply 
 a particular case of the illicit substitution of 
 genus for species in the subject of an affirmative, 
 or in either the subject m predicate of a negative 
 proposition. 
 
 Where the illicit substitution occurs in the 
 inference, the fallacy belongs to the general 
 class of fallacies that go by the name of F. 
 Consequentis or Non-scquitur ; but if in one 
 of the premises, it constitutes the Fallacy of 
 Secundum Qiiid, now under consideration; 
 which must, therefore, like the F. Accidentis, 
 be regarded as a case of Illicit Assumption of 
 Premise, or of Petitio Principii. The Fallacy 
 of Secundum Quid may therefore be defined as 
 consisting in the illicit assumption of a premise 
 in which there is an unqualified term in place 
 of another in which the same term is qualified ; 
 or, as expressed by Aristotle, is assuming that 
 " what is predicated in part is spoken simply " 
 (Soph. Blench., chap. v. , 2). 
 
 210. OF THE RELATION BETWEEN THE 
 FALLACIES OF ACCIDENT AND SECUNDUM 
 QUID. The Fallacy of Secundum Quid will 
 therefore include the Fallacy of Accident, which 
 is but a particular case of it. Or, in other
 
 DOCTRINE OF FALLACIES 
 
 words, the latter is a species of the former, its 
 specific difference being that the qualification 
 omitted relates exclusively to time ; whereas, 
 in the case of Secundum Quid generally, the 
 omitted qualification may relate either to time 
 or to place, quantity, or any other quality or 
 attribute. 
 
 The following examples of the F. Secundum 
 Quid are taken from various sources : 
 
 (1) Pernicious things are things to be forbidden; 
 The use of wine is pernicious ; 
 
 Therefore the use of wine is a thing to be for- 
 bidden. 
 
 (2) Things productive of bad effects are unfit for 
 
 use ; 
 
 Antimony is a thing productive of bad effects ; 
 .'. Antimony is unfit for use. 
 
 (3) Things productive of bad effects are to be dis- 
 
 couraged ; 
 
 Eloquence is a thing that produces bad effects ; 
 .'. Eloquence is to be discouraged. 
 
 (4) Things destructive to human life are to be 
 
 avoided ; 
 
 Medicine is a thing destructive to human life ; 
 .'. Medicine is to be avoided. 
 
 (5) Y is X 
 Z is Y 
 
 /. Z is X.
 
 228 LOGIC 
 
 In each of these arguments all of which are 
 regular in form the fallacy consists in the 
 illicit assumption of the minor premise, consist- 
 ing in substituting in the subject an unqualified 
 in the place of a qualified term, viz., in the 
 first, the term " use " for " excessive use"; in 
 the second, " antimony" for " antimony when 
 misapplied" ; in the third, "eloquence" for "elo- 
 quence when abused" ; in the fourth, " medi- 
 cine" for " medicine when used by ignorant 
 doctors" ; and in the fifth, denoting by A any 
 term qualifying Z, Z, for AZ. The fallacy, 
 therefore, in each case consists in the substitu- 
 tion of genus for species in the subject of an 
 affirmative proposition, and hence differs from 
 the corresponding fallacy of inference simply 
 in being an illicit assumption instead of a 
 formal inference. 
 
 211. ERRONEOUS VIEWS OF LOGICIANS 
 AS TO THESE FALLACIES. The F. Accidentis 
 was defined by Aldrich, and probably by the 
 old logicians generally, as in the text. But 
 Whately, who is followed by most of the later 
 logicians, defines it as the converse of the 
 Fallacy of Secundum Quid ; and since then the 
 subject has been involved in the greatest con- 
 fusion. The prevailing view is thus expressed 
 by De Morgan : 
 
 " (i) The Fallacia Accidentis and (2) that 
 a dicto sccundum quid ad dictum simplicitcr.
 
 DOCTRINE OF FALLACIES 229 
 
 The first of these ought to be called that of 
 a dicto simpliciter ad dictum sccundum quid, for 
 the two are correlative in the manner described 
 in the two phrases. The first consist in infer- 
 ring of the subject with an accident that which 
 was premised of the subject only, the second in 
 inferring of the subject only that which was 
 premised of the subject with an accident " (For- 
 mal Logic, p. 250). 
 
 The latter process is undoubtedly fallacious, 
 but the former/, e., inferring of the subject 
 ^vitJl an accident that which was premised of 
 the subject only ; or, in other words, of infer- 
 ring that what is predicated of a term generally 
 may be predicated of the term as qualified by 
 an accident is entirely legitimate. For to 
 qualify a term, either by an accident or other- 
 wise, is simply to diminish its extension, and 
 thus to create a subclass or species of the class 
 denoted by the unqualified term; and accord- 
 ing to the dictum whatever may be predicated 
 of the unqualified term or genus may be predi- 
 cated of the qualified term or species; or, in 
 other words, in any universal proposition of 
 which the unqualified term is the subject, the 
 same term qualified by an accident may be legiti- 
 mately substituted for it; that is to say, sym- 
 bolically, denoting by AY, Y as thus qualified, 
 if Y is X, then AY is also X; as may be thus 
 illustrated :
 
 230 LOGIC 
 
 In illustration of the supposed fallacy (F. a 
 dicto simpliciter ad dictum secundum quid] De 
 Morgan and others give us the story of the 
 stork, from Boccaccio, which, as quoted by 
 Professor Davis, is as follows : 
 
 A servant who was roasting a stork for his 
 master was prevailed upon by his sweetheart 
 to cut off a leg for her to eat. When the bird 
 came upon the table the master desired to 
 know what was become of the other leg. The 
 man answered that ' the stork never had but 
 one leg.' The master, very angry, but deter- 
 mined to strike his servant dumb before he 
 punished him, took him the next day into the 
 fields, where they saw storks standing each on 
 one leg, as storks do. The servant turned 
 triumphantly to his master, upon which the lat- 
 ter shouted, and the birds put down their other 
 leg and flew away. 'Ah, sir,' said the servant, 
 but you did not shout to the stork at dinner 
 yesterday ; if you had done so, he would have 
 showed his other leg too.' 
 
 The gist of which, the author says, " is the 
 assumption that what can be predicated of 
 storks in general can be predicated of roasted
 
 DOCTRINE OF FALLACIES 2$ I 
 
 storks, a dicto simpliciter ad dictum secundum 
 quid" But undoubtedly (assuming for the 
 sake of the argument that dead and roasted 
 one-legged storks belong to the genus stork) 
 whatever may be universally predicated of 
 storks may, unless the dictum be a delusion, be 
 predicated of roasted and one-legged storks as 
 well as of others. The error, therefore, con- 
 sists, not in an incorrect inference of the 
 particular proposition from the universal prop- 
 osition including it, but in the illicit assump- 
 tion of the universal proposition that whenever 
 you shout at a stork it will put down a second 
 leg, though it may have only one leg, and be 
 dead and roasted. 
 
 212. F. Consequentis. There is much dis- 
 pute as to the nature of the fallacy intended by 
 Aristotle under this name. De Morgan and 
 other logicians following Aldrich regard it 
 as consisting in the " affirmation of a conclu- 
 sion " which does not follow from the premises, 
 or, in other words, as but another name fora 
 Non-scquitur, which is at least the most con- 
 venient view. 
 
 213. CLASSIFICATION OF FALLACIES OF 
 THIS KIND. According to this view, the F. 
 Consequentis will include (i) the merely formal 
 fallacies, commonly known as fallacies of the 
 syllogism ; and (2) all the material fallacies of 
 inference except Equivocation. The former
 
 232 
 
 LOGIC 
 
 have been sufficiently treated in considering 
 the rules of the syllogism ; the latter, under 
 the head of Substitution. The former as well 
 as the latter, and also the fallacies of Equivoca- 
 tion (or In Dictione), are also, it will be remem- 
 bered, fallacies of Substitution.
 
 APPENDIX OF NOTES 
 
 A- 4 
 
 Perhaps, when men understand that the main 
 sources of Philosophy are to be found in the 
 study of words, we may hope to escape the dreary 
 treadmill on which philosophers have hitherto been 
 exercising themselves. All progress in Philosophy 
 that has been made has been the result of the un- 
 conscious observation of this method as, e. g., the 
 work of Locke, which, though weak in its meta- 
 physics, constitutes the greatest contribution to 
 philosophy made in modern times; and which, as 
 shown by Home Tooke, is merely an essay on lan- 
 guage. " Perhaps," he says, " it was for mankind 
 a lucky mistake (for mistake it was) which Mr. 
 Locke made when he called his book an Essay on 
 the Human Understanding. For some part of the 
 inestimable benefit of that book has, merely on ac- 
 count of its title, reached to many thousands more 
 than, I fear, it would have done had he called it 
 "A Grammatical Essay," or "A Treatise on 
 Words or Language " {Diversions of Pur ley). 
 
 B 6 
 
 Comparing the physical sciences and the mathe- 
 233
 
 234 LOGIC 
 
 matics with the moral sciences, the latter are infi- 
 nitely the more difficult of achievement; and also 
 infinitely more important to the welfare of man- 
 kind. For under the name of the moral sciences 
 are included all the several branches of the 
 Science of Human Nature; which is obviously the 
 principal concern of mankind, and as such the sci- 
 ence to which all others are to be regarded as sub- 
 sidiary. This was the distinguishing characteristic 
 of Socrates' philosophy. It was expressed in the 
 injunction written over the portals of the Delphic 
 god: " Know thyself! " and in modern times has 
 been finely rendered: " The proper study of man- 
 kind is man." It is also embodied in the fine old 
 term, the Humanities, which signifies those parts of 
 education that have for their end the development 
 of our manhood or humanity, and which must 
 therefore constitute the essential elements of a 
 rational general education. 
 
 This was the great discovery of Socrates; to the 
 preaching of which, as the gospel most needed by 
 men, his life was devoted. Nor have there been 
 wanting, in succeeding ages, philosophers and 
 those the greatest to continue his mission. But so 
 averse are men to being convinced of their errors 
 that nothing is more odious to them than the at- 
 tempt. Hence, generally, all means of defence are 
 regarded as legitimate, that is to say, not only fal- 
 lacies, but falsehoods and slanders, and, at times,
 
 APPENDIX OF NOTES 235 
 
 the prison, or the rack, or death. Thus Socrates 
 was poisoned for this offence only; which, though 
 otherwise atrocious, was creditable to the Athen- 
 ians, as at least proving an uncomfortable mental 
 susceptibility to the power of reasoning or Logic. 
 For in modern times we have invented a better 
 method of dealing with such fellows, and have 
 developed a mental integument as impervious to 
 the weapons of reason as that of the elephant or 
 rhinoceros to the weapons of the primitive hunter; 
 and against which the Socratic wit would batter 
 in vain. Thus we are enabled to dispose of those 
 who would disturb our mental peace and compla- 
 cency, by simply refusing to listen to them, and by 
 extolling our own idols, like the Ephesians; who, 
 in answer to the preaching of the apostles, "all 
 with one voice, about the space of two hours, cried 
 out: Great is Diana of the Ephesians." By these 
 two means which have been aptly called "the 
 conspiracy of silence," and " the society of 
 mutual admiration " our opinions are now im- 
 pregnably buttressed. Thus we live in a sort of 
 Fools' Paradise ; though, as Bacon says, " the 
 apotheosis of error is the greatest evil of all, and 
 when folly is worshipped, it is, as it were, a plague- 
 spot upon the understanding " (Nov. Org., bk. i., 
 aph. Ixv.). 
 
 D it 
 
 The disuse of Logic must necessarily affect the 
 teaching of Moral and Political Science, Metaphys- 
 ics, and the Science of Human Nature generally;
 
 236 LOGIC 
 
 for the investigation of which it is indispensable. 
 Hence, as the proper study of mankind is man, it 
 may be said that the universities of the day have 
 fallen behind their predecessors in efficient perform- 
 ance of their most essential function. It should 
 not be forgotten that the task of reorganizing Euro- 
 pean society as it emerged from the chaos of the 
 dark ages was mainly effected by such men as 
 Lanfranco, Suger, Anselm, and other churchmen 
 graduates of the mediaeval schools and universi- 
 ties, and consequently educated in Logic and Law; 
 studies the art of teaching which has been lost by 
 our modern universities, and which yet surpass all 
 others as means of a rational education. That this 
 is the case with Logic, it is the aim of this woik to 
 show; with regard to the Law, the opinion of Burke, 
 by those competent to judge, has been generally 
 accepted, that it " is one of the first and noblest 
 of human sciences a science which does more to 
 quicken and invigorate the understanding than all 
 other kinds of learning put together." Though, 
 he adds, "it is not apt, except in persons happily 
 born, to open and liberalize the mind exactly in 
 the same proportion." 
 
 E 12 
 
 The peculiar merit of Logic, as one of the Hu- 
 manities, is its perfect cognoscibility, and the 
 consequent facility with which it can be taught. 
 Arnauld in the preface to the Port Royal Logic 
 tells us that he undertook to teach a young noble-
 
 APPENDIX OF NOTES 237 
 
 man all that was useful in Logic in four days, and 
 successfully performed the task. The claim is 
 seemingly extravagant, but as his notion of Logic 
 was confined mainly to the doctrine of the syllo- 
 gism, and to so much only of the doctrines of the 
 term and of the proposition as was incidentally 
 necessary, and as the student was a young gentle- 
 man of remarkable ability, it may very well be 
 credited. Nor will a more complete and compre- 
 hensive study of the subject add much to the labor 
 of mastering it ; if indeed it will not facilitate the 
 task. The general diffusion of logical culture can- 
 not be regarded, therefore, as a vain aspiration. 
 The subject requires no preliminary culture other 
 than the studies usually taught in the common 
 schools, and may be readily mastered by almost 
 any young man of average ability and the proper 
 age say sixteen or seventeen. And this will espe- 
 cially be the case with one who has thoroughly 
 mastered the elements of algebra and geometry. 
 Thus it is quite possible to devise a very brief 
 course of study sufficiently thorough to train the 
 student as a reasoning creature, and to make him 
 equally competent with the graduates of our great 
 universities to grapple with all the great problems 
 of Politics and Morality; and, indeed, until our 
 modern university education be reformed, even 
 more so. This was illustrated by the mediaeval 
 universities, to whose graduates, as we have ob- 
 served, the reorganization of society at the close of 
 the dark ages was entrusted, and by whom the 
 task was successfully accomplished; nor do I think
 
 238 LOGIC 
 
 it extravagant to say that alongside of them in prac- 
 tical politics our modern graduates would be but 
 children. Of the subjects taught outside of The- 
 ology the principal, as we have said, were Logic and 
 Law, and these must be regarded as the most essen- 
 tial parts of a rational education. The latter will 
 require long and persevering study, but a thorough 
 logical training will render the student competent 
 to master it; and without such training either 
 systematically taught to him at the outset, or grad- 
 ually acquired in the study of the law itself its 
 mastery is impracticable ; and the same observation 
 is true with reference to Political Science generally. 
 
 I have been admonished by a friend that the use 
 of examples of this kind in an elementary work 
 may be hazardous; and this, I understand, on the 
 double ground that the younger student may find 
 it difficult to understand them and the older, regard 
 them as disputable; and that thus they must prove 
 to the one a stumbling-block, and to the other fool- 
 ishness. With regard to the last objection, it is to 
 be admitted that if any of the examples are in fact 
 disputable, the objection is well taken. But I am 
 persuaded that, if they appear so to any one, it is 
 only because of the universal bias of men in these 
 unlogical times in favor of their opinions, and that 
 any one who will provisionally reject all prejudice 
 will see at once that the argument is in every case 
 demonstrative. Or if in any case I am deceived,
 
 APPENDIX OF NOTES 239 
 
 then my own reasoning will serve for example. 
 With regard to the younger student, the opinion 
 seems to be that it would be better to illustrate 
 the nature of the fallacies by the more familiar 
 examples of the character commonly used in the 
 current logics. But this, I think, to be a great 
 mistake. The fallacies are themselves sufficiently 
 simple to be readily understood, and trivial 
 examples merely serve to lead the student to 
 suppose that he is in no danger of falling into 
 them. I have therefore thought it far better to 
 take my examples from theories that have played 
 and are now playing a great part on the stage of 
 history. Nor are these, when treated logically, at 
 all difficult, with a little reflection, to understand; 
 and indeed it is to be assumed that, if a young man 
 has arrived at the age at which he can study Logic 
 profitably without some familiarity with these ques- 
 tions, his education has been much neglected. 
 Neither this nor any part of my work can, indeed, 
 be understood without the independent thought of 
 the reader; but this also I consider not only a great 
 advantage, but an essential condition to the right 
 exposition of the subject. For though the princi- 
 ples of Logic are extremely definite, and therefore 
 readily cognoscible, yet, as already observed, they 
 require for their mastery the same kind and degree 
 of study as is required by the mathematics; and 
 there is no royal road to Logic any more than to 
 geometry. If the student, therefore, will take the 
 trouble to work out thoroughly these examples, and 
 others of the same character (of which many will
 
 240 LOGIC 
 
 suggest themselves), he will achieve not only a 
 mastery of the principles involved in them, and of 
 the practical use of Logic, that cannot be otherwise 
 attained, but also an accurate, though limited, 
 knowledge of all the great political, social, and 
 moral questions involving the welfare of mankind; 
 which, better than anything else, will serve as 
 an introduction to those studies. I have also, 
 in the use of these examples, another point in 
 view, which is, that, by means of the application 
 of logical principles, these apparently difficult 
 problems are readily solved, and the most im- 
 portant heresies in Politics and Morality that 
 afflict mankind exposed; and thus are proved, by 
 practical illustration, the theses with which I com- 
 menced, that in all the moral sciences the use of 
 Logic is essential, and that the confused and un- 
 satisfactory condition of the literature of these 
 subjects is due to the decay of Logic. 
 
 In conclusion, however, I would say that while 
 regarding the current examples used in the logics 
 as inadequate for the illustration of the subject, I 
 have not neglected them, but, in the chapter on 
 the Traditional Doctrine of Fallacies, have con- 
 fined myself mainly to them. 
 
 G 14 
 
 This is strenuously objected to by Hamilton. 
 " Dr. Whately, " he says, " is contradictory. . . . 
 In some places he makes the operation of reasoning 
 not only the principal, but the adequate object of
 
 APPENDIX OF NOTES 241 
 
 Logic. ... In others, he makes this total or 
 adequate object to be the language. But as there 
 cannot be two adequate objects, and as language 
 and the operation of reasoning are not the same, 
 there is therefore a contradiction " (Logic, u). 
 
 But though language and reasoning are not the 
 same, yet they are the same so far forth as Logic 
 is concerned with either; for, as Logic has to deal 
 only with reasoning expressed in language, it is 
 necessarily concerned with both to the same extent; 
 and we may say, with equal propriety, that the 
 subject-matter of Logic is either language or 
 reasoning. 
 
 The error of Hamilton lies in the illicit assump- 
 tion that the term " language " is equivalent to the 
 external logos, i. e., the expression, as opposed to 
 the inward thought. But if language be construed 
 as denoting both the thought and the expression, as 
 it should be, the only objection disappears; and 
 when thus construed, the proposition that Logic is 
 concerned wholly with language is too clear to be 
 disputed. 
 
 H 1 6 
 
 The name given to the subject by Aristotle was 
 the " Analytics." The name Logic seems to 
 have been first applied to it in the time of Zeno, 
 the Stoic. Many names have been invented to sig- 
 nify the scope of Logic, as, e. g., the Architectonic 
 Art; the Organon, or Instrument; the Ars Artium, 
 or Disciplina Disciplinarum; Heuristic, or the Art 
 of Discovering Truth; the Medicina Mentis, or the 
 
 16
 
 242 LOGIC 
 
 Cathartic of the Mind, etc. (Thompson, Laws of 
 Thought, 35); and to these should be added the 
 name given by Socrates to his own doctrine (which, 
 though the fact is commonly overlooked, was noth- 
 ing else than Logic), namely, the Obstetrics of the 
 Mind (Maieusis), 
 
 Of these, the last two names express precisely 
 the two main functions of Logic, that is to say, 
 ist, to serve as a cathartic of the mind to rid it of 
 the false persuasion of knowledge; for, as has been 
 well said, " the natural state of the human mind " 
 is " not simply ignorance, but ignorance mistaking 
 itself for knowledge " (Grote's Plato, i., p. 373) ; 
 and, 2d, to bring forth from the mind " answers of 
 which it is pregnant" (Id., p. 367); or, in plain 
 language, to develop and formulate the unformed 
 ideas in our minds, whether innate or acquired 
 from without. See Socrates' own account of this 
 function, as given in the Thesetetus (Id., iii., p. 
 112). 
 
 I-37 
 
 There is much confusion with modern logicians 
 with regard to the nature of first and second inten- 
 tions or notions, but the above definition seems to 
 accord with the best authorities and expresses a 
 distinction of fundamental importance. According 
 to this definition, Notions of Second Intention 
 will include all abstract notions, and also notions of 
 classes of real individuals construed collectively; 
 in which case they become abstract. 
 
 The following is the definition of Aquinas (Opus-
 
 APPENDIX OF NOTES 243 
 
 cula, cited Krauth, Voc. of Phil. Art., " Intention, 
 First and Second "): 
 
 " Nouns of first intention are those which are 
 imposed upon things as such, that conception alone 
 intervening by which the mind is carried imme- 
 diately to the thing itself. Such are man and 
 stone. But nouns of the second intention are those 
 which are imposed upon things not in virtue of 
 what they are in themselves, but by virtue of their 
 being subject to the intention which the mind 
 makes concerning them, as when we say that man 
 is a species and animal a genus." Which seems to 
 accord with our definition : that is to say, if we 
 speak of man as denoting the class of individual 
 men, the name is of the first intention, but if we 
 regard man collectively as a significate of the class 
 animal, the name is of second intention; and so 
 with reference to all other abstract names. Names 
 of second intention are precisely denoted by the 
 term " univer sales a parte ret," /. e., universal 
 notions considered apart from things, or, in other 
 words, abstract notions, and also by the term 
 " beings of reason," as quoted infra. 
 
 The division of names into names of first and of 
 second intention was obviously intended to com- 
 prehend all names; and hence, if names of first 
 intention are identical with concrete names, as they 
 evidently are, names of second intention must in- 
 clude all abstract names; and it is not admissible 
 to confine them (as Mansel does) to some of that 
 class only. Accordingly a universal (ens unum 
 in multis] is defined by Aldrich simply as a
 
 244 LOGIC 
 
 predicable, /. e. , as "Nomen Commune, Univocum, 
 Secundce Intentionis, uno verbo, Predicabilis, Sive 
 Vox apta prcedicare, i. e. , Univoce did de multis ' ' 
 (Aid. Log., p. 23). 
 
 It is singular that in the Port Royal Logic this 
 distinction should be regarded as unimportant, and 
 even made the subject of ridicule. " No one, 
 thank God! " it is said, " now takes any interest in 
 ' the universal a parte rei,' or ' beings of reason,' or 
 in ' second intentions.' Thus, there is no ground 
 to apprehend that any one will be offended at our 
 having said nothing about them." But it may be 
 safely said that no one can have an adequate con- 
 ception, either of the nature or use of Logic, until 
 the notion expressed in the term " second inten- 
 tions," and the other phrases cited (which are 
 similar in meaning), are thoroughly grasped. 
 
 K- 3 8 
 
 Even where we use concrete terms, it is not the 
 thing itself, but the notion of the thing that is pres- 
 ent to the mind. For, as is said by Hobbes, 
 " seeing names ordered in speech (as is defined) 
 are signs of our conceptions, it is manifest they are 
 not the signs of the things themselves." Hence, 
 as Mansel says, " concepts (or notions] are the things 
 of Logic." On this point Max Miiller's Laws of 
 Thought (the opening chapters) may be read with 
 profit. For without acceding altogether to his the- 
 ory, that thought is impossible without language, 
 this is certainly true (ex vi termini), as to ratioci- 
 nation, or explicit reasoning, and may therefore be 
 accepted without error, and much to his profit, by
 
 APPENDIX OF NOTES 245 
 
 the logician. According to Home Tooke " thing " 
 and " think " are but the same word spelt differ- 
 ently; and hence, he says, " the vulgar pronuncia- 
 tion of ' nothink ' instead of ' nothing ' is not so 
 very absurd." 
 
 L-53 
 BOOLE'S LOGIC 
 
 " All the operations of language, as an instru- 
 ment of reasoning, may," it is claimed by Mr. 
 Boole, " be conducted by a system of signs com- 
 posed of the following elements," viz. : 
 
 ist. " Literal symbols, as x, y," etc., represent- 
 ing names or terms. 
 
 2d. " Signs, as -|-, , X," representing relations 
 to each other of the substantive elements of com- 
 plex terms. 
 
 3d. " The sign of identity ( = )," or, as I should 
 call it, the sign of equivalence, /. e., of significative 
 equivalence, or equivalence of denotation. 
 
 The names signified by signs of the first class 
 may be either single names denoting classes, as, 
 e. g., man, horse, good, white, etc., or they may 
 be composed of several names, denoting classes 
 that partially coincide as, e. g., good men, black 
 sheep, etc. In the latter case the signs may be 
 combined together precisely as the words denoting 
 the terms. Thus, if we represent the class men 
 by x, and the class good by y, " good men " will 
 be denoted by the expression yx. So if x stands 
 for sheep, y for black things, and z for horned things, 
 zyx will denote " horned black sheep." But it is 
 obvious that in the expression " black sheep," the
 
 246 LOGIC 
 
 order in which the component terms are placed 
 makes no difference ; or, in other words, that it is 
 the same thing whether we say " black sheep" as in 
 English, or " sheep black" as in Spanish and other 
 languages. Consequently, the class " black sheep " 
 may be written either yx or xy, which may be ex- 
 pressed by the following equation: 
 
 (i)yx = xy. 
 
 In which the complex term yx or xy denotes a 
 class of individuals that is at once included in the 
 class 7 and the class x. On the same principle, if 
 we represent by z the adjective " horned," zyx will 
 stand for the term "horned black sheep" and we 
 will have the following equations: 
 
 (2) zxy = xyz = yxz. 
 
 If, in the equation xy = yx, we suppose y to be 
 wholly included in x, as, e. g., if it denote the 
 black sheep in the flock x, then we will have the 
 equation : 
 
 (3) xy = y. 
 Again, if x = y, then xy =x a . But a class is not
 
 APPENDIX NOTES 247 
 
 enlarged or diminished by repeating the term de- 
 noting it. Thus, " white white " or "sheep sheep " 
 mean nothing more than "white" or "sheep." 
 Hence we have the equation: 
 
 (4) x' = x. 
 
 If the class denoted by a term is composed of 
 two classes, denoted respectively by x and y, as, 
 e.g., " men and women," it may be expressed by 
 the complex term x + y. But obviously, the ex- 
 pressions, " men and women," and " women and 
 men," are equivalent in meaning. Hence the 
 equation: 
 
 (5) x + y = y + x. 
 
 Again, if we qualify the term ' ' men and women ' ' 
 by the adjective "Asiatic," we have the expres- 
 sion "Asiatic men and women "; but this is equiv- 
 alent in meaning to the expression " Asiatic men 
 and Asiatic women." Hence, denoting men by x, 
 women by y, and Asiatic by z, we have the equation : 
 
 (6) z(x + y) = zx + zy. 
 
 If we denote the adult population of a city by x, 
 and the women by y, then x y will denote the 
 men. But it is indifferent whether we express the 
 excepted class first or last, provided it be distinctly 
 represented as the exception. Thus the expres- 
 sion, " the adult population less the women," and 
 the expression, "excepting the women, the adult
 
 248 LOGIC 
 
 population," are equivalent in meaning to each 
 other, and botli to the expression " the men." 
 Hence we have the equation: 
 
 (7) x - y = - y + x. 
 
 But the expression, " the white population, less 
 the women," is equivalent in meaning to the ex- 
 pression, " the white population, less the white 
 women." 
 
 Hence, representing " while " by z, we have the 
 equation: 
 
 (8) z (x y) = zx zy. 
 
 If, in the proposition, " The stars are the suns 
 and the planets," we denote stars by x, suns by y, 
 and planets by z, we shall have the equation : 
 
 (9) x = y + z. 
 
 But, if the stars are the suns and the planets, the 
 stars, except the planets, are suns. Hence we have 
 the equation: 
 
 (10) x z = y. 
 
 If the terms x and y are equivalent, it is obvious 
 that those of the class x, or, as we may say, the x's, 
 that possess a given quality, must be identical with 
 the y's that possess it. Hence, if x = y, we have 
 the equation: 
 
 (n) zx = zy.
 
 APPENDIX NOTES 249 
 
 But, per contra, it cannot be inferred from the 
 equation, zx = zy, that x = y. ( 82 (2) n.) 
 
 For, " suppose it true that those members of a 
 class x which possess a certain quality, z, are iden- 
 tical with those members of a class y, which possess 
 the same quality, z, it does not follow that the 
 members of the class x universally are identical 
 with the members of the class y." Thus, return- 
 ing to our sheep, let x denote one portion of a 
 flock of sheep, and y another, and let z denote 
 "horned" ; then zx will denote the horned sheep 
 in one portion of the flock, and zy the horned sheep 
 in the other; and, if we suppose these to be equal, 
 we shall have the equation: 
 
 zx = zy. 
 
 But it will not follow that the two portions of the 
 flock are equal in number, and we therefore can- 
 not say x y ; as may be thus illustrated : 
 
 Adverting to the above equations, it will be per- 
 ceived that the laws governing the convertibility of 
 the different forms of expression are, to a certain 
 extent, identical with those obtaining in mathe- 
 matics. Thus, in the equations (i) and (2), the 
 symbols are commutative like the symbols of algebra. 
 The logical process here involved is, therefore, 
 expressed in the same manner as in the correspond-
 
 250 LOGIC 
 
 ing algebraic expression ; and this expression, 
 whether regarded as logical or algebraic, will be 
 subject to the same law. There is, therefore, in 
 the process involved in these equations, (i) and (2), 
 a certain resemblance or analogy to the process of 
 multiplication; and this is also true of equation 
 
 ("). 
 
 In equations (6) and (8) a process is exhibited 
 closely resembling that of factoring in algebra. 
 
 In equations (5), (7), (9), and (10), we have 
 illustrated a principle of conversion of symbols 
 apparently identical with the corresponding process 
 in algebra. Hence we may affirm as logical axioms: 
 ist, that if equals be added to equals the wholes 
 will be equal; and, 2d, that if equals be taken from 
 equals, the remainders will be equals. 
 
 Hence, with regard to the equations specified 
 (i, 2, u, 6, 8, 5, 7, 9, and 10), we may affirm gen- 
 erally that the logical symbols may be transposed 
 or converted precisely in the same way as in the 
 operations of addition, subtraction, and multiplica- 
 tion in algebra. But with regard to the analogy 
 between multiplication and the corresponding 
 logical operation, it will be observed that in one 
 respect it fails, namely, in equation (4), x 2 = x; 
 which is good in Logic, but not generally true in 
 algebra. Also, it will be observed, there is appa- 
 rently no logical process corresponding to the alge- 
 braic operation of division. Thus, as we have 
 seen, we cannot infer from equation (n), " zx = 
 zy, " that x = y, as we may in algebra. 
 
 But if we conceive of an algebra or arithmetic
 
 APPENDIX NOTES 251 
 
 that deals only with the two numbers, i and o, this 
 discrepancy will altogether disappear. For on such 
 hypothesis, equation (4), x 2 = x, will be true, both 
 in Logic and in mathematics. And in equation 
 (u), zx = zy, if z = i, the proposition, x = y, 
 may be inferred, both in Logic and in mathe- 
 matics. But if z be equal to zero, it cannot be 
 thus inferred, either in Logic or algebra. Hence, 
 if we conceive of an algebra in which the symbols 
 x, y, z, etc., " admit indifferently of the values of 
 i and o and of those values alone," then " the laws, 
 the axioms, and the processes of such an algebra 
 will be identical in their whole extent with the laws, 
 axioms, and process of an algebra of Logic." 
 
 Accordingly, Mr. Boole's system is founded on 
 this hypothesis, and " the logical value and signifi- 
 cance " of the terms dealt with (i and o) are thus 
 explained. In algebra, the equation oy = o is true, 
 whatever the value of y. So, in Logic, if o be re- 
 garded as a class, whatever class may be denoted 
 by y, the equation oy = o will be true; for, as we 
 have seen, oy denotes the class of individuals that 
 are at the same time included in the two classes, 
 /'. e., o and y. But none are included in the class 
 o, and therefore, oy = o. 
 
 So in algebra, the equation ly = y is true, what- 
 ever the value of y may be, and this is true in Logic 
 also, if i be regarded as including y. For as we have 
 seen (equation 3), if one of the two terms making a 
 combined term is included in the other, the com- 
 bined term is equal to the term of least extension. 
 But this condition may be satisfied by regarding i
 
 252 LOGIC 
 
 as denoting the Universe. " Hence, the respective 
 interpretations of the symbols, o and i, in the sys- 
 tem of Logic, are Nothing and Universe. ' ' Denoting 
 the Universe by i, and men by x, the expression 
 i x denotes the class " not-men," /. e., all 
 animals that are not men. 
 
 The equation x 2 = x may be put in the form, 
 x" x = o, and this again in the form, x (i x) 
 = o; of which the interpretation is obvious; for, 
 if x denotes " men," and i x " not-men," it is 
 clear that there can be no individuals belonging at 
 once to the two classes, x and i x, or, men and 
 not-men. So if we denote by x any class charac- 
 terized by the possession of any quality whatever 
 the same result will follow. 
 
 It is observed by Mr. Boole that the principle of 
 analysis and classification involved in his system is 
 " division into pairs of opposites, or, as it is techni- 
 cally said, Dichotomy " ( 47), and this is in fact the 
 fundamental process in Logic. And this, it will 
 be observed, agrees with the opinion of Hobbes 
 and of Aristotle ( 90 n.). 
 
 In equation (5), it will be observed, there is a 
 certain ambiguity in the expression x -)- y. In 
 common speech the classes denoted by the sym- 
 bols x and y may either be exclusive of each 
 other, or they may overlap, as, for instance, in the 
 proposition, " Scholars and men of the world de- 
 sire happiness," or, " Useful things are those that 
 either produce pleasure, or prevent pain." In 
 Mr. Boole's system this ambiguity is removed. 
 
 If the two classes are intended to include each
 
 APPENDIX NOTES 253 
 
 other, the expression to denote the aggregate class 
 will bex(i y) + y( I x ); which is to be read 
 x's that are not y's,- and y's that are not x's. 
 
 If we intend two classes that overlap, then the 
 full expression should be, xy + x (i y) -j- y (i x). 
 
 " The result of these investigations may be em- 
 bodied in the following rule of expression: 
 
 " RULE. Express simple names or qualities by 
 the symbols x, y, z, etc., their contraries by i x, 
 i z, etc. ; classes of things defined by common 
 names or qualities, by connecting the correspond- 
 ing symbols as in multiplication; collections of 
 things consisting of portions different from each 
 other, by connecting the expressions of those por- 
 tions by the sign +. In particular, let the expres- 
 sion, ' Either x's or y's ' be expressed by x 
 (i y) + y (i x) when the classes denoted by 
 x and y are exclusive; by x -[- y (i x) when they 
 are not exclusive. Similarly let the expression, 
 ' Either x 's or y's or z's ' be expressed by x 
 (i - y) (i - z) + y (i - x) (i - z) + z (i - x) 
 (i y), when the classes denoted by x, y, and 
 z are designed to be mutually exclusive; and by 
 x + y (i z )+ z (i x) (i y), when they are 
 not meant to be exclusive, and so on." 
 
 For illustration, " let us assume 
 
 x hard, y = elastic, z = metals; 
 
 and we shall have the following results: 
 
 " ' Non-elastic metals ' will be expressed by 
 
 zO - y);
 
 254 LOGIC 
 
 ' Elastic substances with non-elastic metals ' by 
 y + z(i - y); 
 
 ' Hard substances, except metals,' by x y; 
 " ' Metallic substances, except those which are 
 neither hard nor elastic,' by z z (i x) (i y), 
 or by z[i - (i - x) (i -y)]." 
 
 The above brief account of the elements of Mr. 
 Boole's system is given for the purpose of illus- 
 trating the laws that govern the convertibility of 
 terms, and of substantive elements of terms; or, in 
 other words, that govern the formal substitution of 
 equivalent expressions, ( 67 (2)) a purpose for 
 which it admirably serves. It will require some 
 attention to understand it, but with such attention, 
 no difficulty will present itself. 
 
 It may be readily perceived that by the use of 
 fhe above data a very extensive calculus may be 
 developed, and such a one has in fact been devel- 
 oped by Mr. Boole; but with regard to its utility, 
 opinions may widely differ. 
 
 ' The idea of a logical calculus," says Lotze, 
 "has been often taken up and often abandoned; 
 but the Englishman Boole has recently made an 
 elaborate and careful attempt to carry it out, which 
 is beginning to attract attention in Germany, as 
 well as in his own country. Though I freely 
 admit that the author's ingenuity makes his able 
 work very charming, I am unable to convince my- 
 self that this calculus will help us to solve problems 
 which defy the ordinary methods of Logic." 
 (Logic, vol. ii., 277.)
 
 APPENDIX NOTES 
 
 M 96 
 
 TABLE OF SYLLOGISMS 
 
 255 
 
 
 
 rYX 
 
 ist Figure < ZY 
 ( ZX 
 
 A: 
 
 Barbara 
 V is X S^i 
 
 v\ 
 
 A: 
 
 z is Y nf^ 
 
 
 A: 
 
 .'.ZisX V_ 
 
 JJ 
 
 E: 
 
 Celarent 
 
 Y is not X / 
 Is 
 
 \' \ 
 
 A: 
 
 Z is Y (( z 
 
 
 E: 
 
 Y"" 
 
 .'. Z is not X > 
 
 -S 
 
 
 Darii 
 
 Ferio 
 
 A: 
 I: 
 
 Y is X / 
 Some Z is Y I t 
 
 ^~X**\ E: Y is not X ^_^^ 
 ^T\l I: Some Z is Y \_//v\ * J 
 
 I: 
 
 \ 
 
 .'. Some Z is X 
 
 V.5/ O: .'. Some Z is not X ^ * 
 
 
 
 rXY 
 
 ^</ Ft git re < ZY 
 (ZX 
 
 
 Cesare 
 
 Cif/iS^M/ 
 
 E: 
 A: 
 E: 
 
 X is not Y 
 Z is Y 
 .'. Z is not X 
 
 x ^ E: Y is not X 
 
 (0 Y ) 
 
 V*' J E: .'. Z is not X
 
 256 
 
 LOGIC 
 
 
 Came sir es 
 
 
 
 
 Celarcnt 
 
 A: 
 
 X is Y 
 
 
 
 E: 
 
 Y is not Z 
 
 E: 
 E: . 
 
 Z is not Y 
 '. Z is not X 
 
 
 
 
 A: 
 E: 
 
 X is Y 
 .'. X is not Z 
 
 
 
 
 
 
 or Z is not X 
 
 Festino 
 
 E: XisnotY 
 
 I: Some Z is Y 
 
 O: .'. Some Z is not X 
 
 Fakoro 
 A: X is Y 
 
 O: Some Z is not Y 
 O: .'. Some Z is not X 
 
 Ferio 
 
 E: YisnotX 
 
 I: Some Z is Y 
 
 O: .'. Some Z is not X 
 
 Ferio 
 E: Not-Y is not X 
 
 I: Some Z is not Y 
 O: .'. Some Z is not X 
 
 
 rYX 
 
 
 
 
 
 jd Figure -j YZ 
 
 
 
 
 
 (zx 
 
 
 
 
 
 Darapti 
 
 
 Darii 
 
 
 A: 
 
 YisX /^~~/*\^\ 
 
 A: 
 
 Y 
 
 isX 
 
 A: 
 
 YisZ (z /(7)J x J 
 
 I: 
 
 Some Z 
 
 isY 
 
 I: 
 
 .'.SomeZisX Vj^Lx 
 
 I: 
 
 .'. Some Z 
 
 isX 
 
 
 Disamis 
 
 
 Darii 
 
 
 I: 
 
 Some Y is X / ^N, 
 
 A: 
 
 Y 
 
 is Z 
 
 A: 
 
 Y is Z /f> /jX 
 
 I: 
 
 Some X 
 
 is Y 
 
 I: 
 
 .-. SomeZisX \S-K / X ) 
 
 I: 
 
 .'. Some X 
 
 is Z 
 
 
 ^V y 
 
 
 or Some Z 
 
 isX
 
 
 APPENDIX NOTES 
 
 257 
 
 
 Datisi 
 
 Darii 
 
 A: 
 
 Y isX /^S^^rx 
 
 A: Y is X 
 
 
 /( Y /) \2\ 
 
 
 I: 
 
 Some Y is Z ( V_J()/ 
 
 I: Some Z is Y 
 
 
 \ X y' 
 
 
 I: 
 
 .'. Some Z is X ^~-^*/ 
 
 I: .'. Some Z is X 
 
 
 Felapton 
 
 Ferio 
 
 E: 
 
 Y is not X /^~^>< ~x K: 
 
 Y is not X 
 
 A: 
 
 Yis Z O( ) X] I: 
 
 Some Z is Y 
 
 O: 
 
 . '. Some Z is not X ^~_3<^ >/ O: 
 
 .'. Some Z is not X 
 
 
 Dokamo 
 
 Darii 
 
 O: 
 
 Some Y is not X / ^^ A: 
 
 YisZ 
 
 A: 
 
 Yis Z [C y Q)x\ ^ 
 
 Some not X is Y 
 
 
 
 Some not X is Z 
 
 O: 
 
 .'. Some Z is not X \^2^^ or 
 
 Some Z is not X 
 
 
 Ferison 
 
 Ferio 
 
 E: 
 
 Y is not X /'TN / \ E: 
 
 Y is not X 
 
 
 ( * JL-L x i 
 
 
 I: 
 
 Some Yis Z V^Vy I: 
 
 Some Z is Y 
 
 O: 
 
 .'. Some Z is not X ^ / O: 
 
 .'. Some Z is not X 
 
 
 /XY 
 
 
 
 4th Figure -| YZ 
 
 
 
 (zx 
 
 
 
 Bramantip 
 
 Barbara 
 
 A: 
 
 Xis Y /""""X 
 
 A: Y is Z 
 
 A: 
 
 Y is z /fer\ \ 
 
 A: X is Y 
 
 I: 
 
 .'. Some Z is X \&jj 
 
 A: .'. X is Z 
 
 
 v^_/ 
 
 or Some Z is X 
 
 
 Camenes 
 
 Celarent 
 
 A: 
 
 X is Y /TX 
 
 E: Y is net Z 
 
 E: 
 O: 
 
 Y is not Z /V" X \ x"~x 
 
 .-. z is not x \v x y / ( z y 
 
 A: X is Y 
 E: .'. X is not Z 
 or Z is not X
 
 258 
 
 LOGIC 
 
 Dimaris 
 
 I : Some X is Y 
 A: Y is Z 
 
 I: .'. Some Z is X 
 
 Fesapo 
 
 E: XisnotY 
 
 A: Y is Z 
 
 I: .'. Some Z is not X 
 
 Fresison 
 
 X is not Y 
 Some Y is Z 
 O: .'. Some Z is not X 
 
 Darii 
 
 A: Y is Z 
 
 I: Some X is Y 
 I: .'. Some X is Z 
 or Some Z is X 
 
 Ferio 
 
 Y is not X 
 Some Z is Y 
 O: .'. Some Z is not X 
 
 Ferio 
 
 E: Y is not X 
 
 I: Some Z is Y 
 O: .'. Some Z is not X 
 
 N no 
 
 The opinion of Locke cited, which occurs at the 
 end of his essay, may be taken as the consumma- 
 tion and final generalization of his theory of knowl- 
 edge. In the body of the work the conclusion 
 reached by him is, that the elements of all knowl- 
 edge are ideas (by which is meant what are now 
 commonly called notions or concepts), and that 
 " knowledge [is] but the perception of the connec- 
 tion and agreement, or disagreement, or repugnancy 
 of any of our ideas " (Essay, b. 4, c. i). 
 
 This definition, it will be observed, is too nar- 
 row, as it excludes the knowledge derived directly 
 from the perception of concrete objects. But al- 
 lowing for this defect it is accurate and profound 
 and must be taken as the foundation of all science. 
 In the beginning it seems that Locke had no
 
 APPENDIX NOTES 259 
 
 conception, or at least a very inadequate conception 
 of the intimate connection between language and 
 thought, and of the indispensability of the former 
 as an instrument of thought. But as he proceeded 
 he seems gradually to have realized this great truth, 
 which is treated of in his third book; and upon 
 the conclusions thus reached is based his theory of 
 knowledge and his general philosophy as developed 
 in his fourth book, and as generalized in the conclu- 
 ding chapter, to which we have referred. His theory 
 of knowledge, therefore, is to be regarded as based 
 to a great extent expressly, and otherwise implicitly, 
 upon the notion that all knowledge beyond that 
 coming from experience consists in the perception 
 of the agreement, or disagreement, of our ideas, or 
 notions; and hence that all reasoning must consist 
 in the comparison of notions or concepts; that 
 practically this can be effected only by means of 
 the names of the concepts or notions; and hence 
 that Logic must consist in Analysis and Synthesis 
 of names or terms; which is the theory of this 
 work. (See observation of Home Tooke, Appen- 
 dix A.)
 
 INDEX 
 
 Abstract and concrete terms, 37 
 
 Accent, fallacy of, 203 
 
 Accident and genus distinguished, 49 
 
 Accident and secunJum quid, relation between, 2IO 
 
 Accident, fallacy of, 207, 208 
 
 Adjectives regarded as substantives, 36 
 
 Amphiboly, 201 
 
 Analysis and synthesis, logical and physical, distinguished, 108 
 
 Analysis, use of, 116 
 
 Analytical processes, 42 
 
 Apodictic, 23, 70 
 
 Apprehension, 41 
 
 A priori, and empirical notions, 71 
 
 Arguing in circle, 160 
 
 Aristotle, his dictum, 76 ; his classification of fallacies, 197 
 
 Bain, an opinion of, 83 
 Burden of proof, 164 
 
 Canons of the several figures of syllogism, 100 
 Categories and predicables distinguished, 66 
 Classification, division and, 44 
 Collective and distributive interpretation, 60 
 Commonplace and original thought distinguished, 112 
 Commonplaces, 156 
 
 The numbers refer to sections. 
 26l
 
 262 INDEX 
 
 Common terms, singular and, 35 
 
 Composition and division, fallacy of, 202 
 
 Concept defined, 30 
 
 Concrete terms, abstract and, 37 
 
 Confusion, fallacy of, 139 
 
 Connotation and denotation of terms, 32 
 
 Consequent, fallacy of the, 212 
 
 Consequentis, F., 212 
 
 Contradiction, the law of, 125 
 
 Contradictory, substitution of, 80 
 
 Contraposition, conversion by, So 
 
 Conversion by intension, 58 
 
 Conversion of propositions, 54, 70, 91 
 
 Conversions, material and formal, distinguished, 92 
 
 Copula, the, 55 
 
 Criticism, 115 
 
 Definition, vocal, 43 ; nominal or real, 48 
 
 Denotation and connotation of terms, 32 
 
 Dialectic, 23, 70 
 
 Dichotomy, 47 
 
 Dictum, Aristotle's, 76 ; forms of, 99 ; applicable to all fig- 
 ures, 100, 101 ; and to singular and other equational 
 propositions, 102 ; proposed amendments of, 103 
 
 Division, 46 
 
 Division and classification, 44 
 
 Enthymemes, 105 
 
 Equational theory of predication, 56 
 
 Equivalence of terms, 78 
 
 Equivocation, fallacy of, 127, 191, 201 
 
 Essence of term, 49 
 
 Euclid, his fifth proposition reduced to syllogisms, 84 
 
 Excluded middle, the law of, 125 
 
 Extension and intension of terms, 34 
 
 The numbers refer to sections.
 
 INDEX 263 
 
 Fallacies, classification of, 129 ; definition of, 128 ; observa- 
 tions on, 132 ; extra dictionein, 206 ; in dictione (equivo- 
 cation), 201 ; of inference, 131; of judgment, 130; of 
 the syllogism, 104, 124 
 
 False definition, fallacy of, 126, 144 
 
 Figiirce dictio nis, F., 204 
 
 Figure of speech, fallacy of, 204 
 
 Figures of the syllogism, 95 
 
 Formal and material conversions, 92 
 
 Formal and material relations of terms, 67 
 
 Formal fallacies, 104 
 
 Genus and accident, 49 
 Genus and species, 45 
 Genus of term, 49 
 
 Ilomonymy, 201 
 
 Hypothesis, argument from, 165 
 
 Hysteron proteron, 160 
 
 Identity, the law of, 125 
 
 Ignoratio elenchi, fallacy of, 126, 169 
 
 Illicit assumption of premises (petitio principit), 154 ; tests 
 
 of, 162 
 
 Illicit conversions, 127, 183 
 Illicit generalization, 155 
 Illicit substitution, fallacy of, 127, 187 
 Immediate inferences, 80 
 Inference, rules of, 77, 123, 127 
 Inferences, immediate, 80 
 Infinitation, 80 
 Instance, or extreme case, 163 
 Intension and extension of terms, 34 
 Intensive conversion, 58 
 Intensive theory of predication, 58 
 Intuitive propositions or judgments, 18, 19 
 
 The numbers refer to sections.
 
 264 INDEX 
 
 Invention, 113 
 
 Irrelevant conclusion, fallacy of, 126, 169, 173 
 
 Judgment, defined, 19 ; rules of, 126 
 Judgments and assumptions distinguished, 68 
 
 Knowledge defined, i, 2, 5 
 
 Language, as record of human thought, 4 ; as source of 
 opinion, 3 
 
 Laws of thought, the, 125 : the law of identity, 125 ; the 
 law of contradiction, 125 ; the law of excluded middle, 
 125 
 
 Legal maxims, 158 
 
 Logic, definition of, 14, 16 ; the traditional, 85 ; decadence 
 of the age in, n ; method of, in ; the morality of in- 
 tellect, 27 ; the art of right reasoning, 26 ; the ultimate 
 criterion of truth, 10 ; as the doctrine of signs, no 
 
 Logical processes, 107, 112 
 
 Logical term, elements of the, 31 
 
 Material and formal conversions, 92 
 Material and formal relations of terms, 67 
 Mathematical reasoning, 82 
 Meaning and signification of terms, 33 
 Method of logic, in 
 Mistaking the issue, 169, 170 
 Moods of the syllogism, 94 
 
 Moral sciences, distinguished, 6 ; decadence of the age in the, 
 ii 
 
 Name defined, 28 
 
 Negative terms, positive and, 39 
 
 Nominal or real definition, 48 
 
 Non causa pro causa, fallacy of, 159 
 
 Nonsense, fallacy of, 126, 134, 138 
 
 Notion defined, 30 
 
 The numbers refer to sections.
 
 INDEX 265 
 
 Onus probandi, 164 
 
 Opinion, its modes of generation, 7 ; language as source of, 3 
 
 Opposition of propositions, 89 
 
 Original and commonplace thought distinguished, 112 
 
 Petltio prin fipii, fallacy of, 126 
 Plurium inter rogationum, F., 171 
 
 Popular proverbs, 157 
 
 Positive and negative terms, 39 
 
 Post hoc ergo propter hoc, 159 
 
 Predicahles, definition and division of, 61 ; and categories dis- 
 tinguished, 66 
 
 Predication, theories of, 55, 60 
 
 Property and specific difference distinguished, 49 
 
 Proposition, defined, 22, 50 ; the grammatical, 51 ; the logi- 
 cal, 52 ; interpretation of the logical, 53 ; the traditional 
 doctrine of the, 86 
 
 Propositions, conversions of, 54, 91 ; kinds of : intuitive, 18, 
 20 ; quasi-intuitive, 20 ; inferred, 21 
 
 Proverbs, popular, 157 
 
 Quality of propositions, 86 
 Quantification of the predicate, 57 
 Quantity of propositions, 87 
 Quasi-thing defined, 29 
 Question-begging terms, 161 
 
 Ratiocination, defined, 14, 15 ; not merely hypothetical, 72 
 
 Real things defined, 29 
 
 Reasoning, defined, 14 ; supposed distinction between quali- 
 tative and quantitative, 82 
 
 Rcductio, ad absurdum, 165 ; ad impossibile, 165 
 
 Reduction of syllogisms, 96 
 
 Relations of terms, immediate ; intuitive relations or judg- 
 ments, 18, 19 ; quasi-intuitive, or assumptions, 20 ; in- 
 ferred relations or syllogisms, 21 
 
 The numbers refer to sections.
 
 266 INDEX 
 
 Right reasoning defined, 25 
 
 Rules, of logic, twofold division of, 121 ; of inference, 77, 
 123, 127 ; of judgment, 122, 126 ; of the syllogism, 104 
 
 Secundum quid, fallacy of, 209 
 
 Semeidtike, or the doctrine of signs, no 
 
 Several questions, fallacy of, 171 
 
 Significates of terms, 33 
 
 Signification and meaning of terms, 33 
 
 Simple apprehension, 41 
 
 Singular and common terms, 35 
 
 Sorites, 106 
 
 Species, genus and, 45 
 
 Specific difference, 49 
 
 Substitution, the principle of, 77 ; formal and material, Si ; 
 of contradictory, 80 
 
 Syllogism, analysis of, 74 ; definition of, 22, 75 ; elements of, 
 73 ; moods and figures of, 94, 95 ; principle of, 76 ; re- 
 duction of, 96 ; rules of, 104 ; the traditional doctrine of, 
 93 
 
 Term, defined, 28 ; kinds of, 35 
 
 Terminal relations, generally, 64 ; kinds of, 17, 65 
 
 Tests of illicit assumption, 162 
 
 Thing defined, 29 
 
 Thought defined, 30 
 
 Traditional doctrine of fallacies, 197 
 
 Traditional theory of predication, 59 
 
 Universe of the proposition, 40 
 Vocal definition, 43 
 
 Word defined, 28 
 
 The numbers refer to sections.
 
 UC SOUTHERN REGIONAL LIBRARY FACILITY 
 
 A 001 401 248 8 
 
 CALIFORNIA 
 
 LIBRARY, 
 
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