mm lligPSBi mm LWHI - HH W dig 1 i JTiSfiMMMdftZttfB^ -■■.•■.; ■:•!.■.• -N J. * ^0* V'-^-V %^v 9 v T -'V %' %/ fa*. %/ *' * i' A ' ^ ^°* '."l§ffi ; ^°^ -SUP* /' V^' *°-v ^°* .^ •. a THE MODALIST OR THE LAWS OF KATIONAL CONVICTION A TEXT-BOOK FORMAL OR GENERAL LOGIC by/ \/ EDWARD JOHN HAMILTON, D.D. h Albert Barnes Professor of Intellectual Philosophy in Hamilton College, N.Y. >>»<< / ( I tow; BOSTON, U.S.A. PUBLISHED BY GINN & CO. 1891 |the LIBRARY OF C ONGR ttSI WASHINGT ON Copyright, 1891, By EDWARD JOHN HAMILTON. All Rights Reserved. Typography by J. S. Cushing & Co., Boston, U.S A. Presswork by Ginn & Co., Boston, U.S.A. PREFACE. This text-book was written under the conviction that the most useful instruction is that which is enforced by the most thorough explanations. It is an attempt to connect the for- mulas of logic with principles, the ultimate character of which will become evident to the faithful student. Besides, the author had an ambition to add something to the science by giving permanent form to views which have been held and taught for years. Logical doctrine and praxis do not now have that place in education which they once had, when the university curriculum was chiefly occupied with the literature and the philosophy of the ancients. But we do not complain of this. Logic receives a fair share of attention in our colleges. In almost all of them it is a required study for at least one term ; while the larger institutions offer advanced courses in theories of knowledge and belief. This is all that could be expected. A pretty thorough indoctrination in logic can be effected in connection with forty or fifty class exercises ; and half as many might suffice for imparling the rudiments. Or may we say that the minimum of required work should include not less than thirty recita- tions, or class-exercises ; after which the young men might be left to their own election as to the further prosecution of this study? So far as we know, Logic is never taught without the help of a text-book ; though professors differ in the degree of their reliance upon this aid. The writer, who has used successively a considerable number of books, has always found it advan- tageous to select, with some freedom, the more important iv PBEFACE. chapters, as subjects of recitation ; aud has supplemented the instruction thus given by a few informal lectures, and by some work required of every member of the class. He has also, of course, encouraged the students to read more than was im- peratively prescribed. He proposes now — so far as there may be need — to deal with his own book as he has dealt with those of others. For the chapters of the "Modalist" are of such a construction as to facilitate this method of procedure. They will be found to have so much independence of one another, that almost any of them could be omitted while the rest would remain compre- hensible. And this is especially the case with certain chap- ters, such as the twenty-first, the twenty-second, and the twenty-third; in which the principles of the new analytic are somewhat minutely expounded. We think that a serviceable knowledge of inferences and syllogisms — so far as these are considered in existing manuals — can be obtained from chap- ters preceding and following those just mentioned. Moreover, it will be noticed that the closing sections of several of the longer chapters are devoted to supplementary discussions ; such as are consigned to small type in the author's metaphysical text-book. 1 In the present work this device, always unseemly, has not been thought necessary. The author is confident that any fellow-teacher who may honor him by employing the new logic as a means of class instruction, will sympathize with it sufficiently not to need specific directions concerning the use of it. Besides, every qualified professor can judge, better than any one else can, what the limitations,, and what the possibilities, of his work may be. Clinton, N. Y., Feb. 1, 1891. 1 A volume entitled " Mental Science." CONTENTS. Prefatory Dissertation ........ PAGE 1 CHAPTER I. Logic Defined ....... 13 II. Belief, or Conviction 21 III. Logic Divided ....... 26 IV. Entities and Conceptions ..... 31 V. General and Individual Notions 37 VI. Predicative Notions; the "Categories" . 45 VII. Predicative Notions; the " Predicables " 52 VIII. The Definition of Notions ..... 61 IX. Logical Division 71 X. Propositions and Predications .... 79 XI. Categorical Predications 89 XII. The Illative Proposition ..... 98 XIII. Inferential Sequence 107 XIV. Orthologic Inference ...... 118 XV. Homologic Inference 130 XVI. Inductive Reasoning ...... 136 XVII. Hypothetical and Disjunctive Reasonings 150 XVIII. Probable Inference ...... 162 XIX. The Opposition of Propositions .... 174 XX. The Conversion of Predications 190 XXI. Contingency and Its Conversion 204 XXII. Syllogisms ........ 222 XXIII. Syllogistic Moods 242 VI CONTENTS. CHAPTER XXIV. Thf Pure, or Dogmatic, Syllogism XXV. The Keduction of Syllogisms XXVI. Fallacies XXVII. Fallacies in Catenate Inference XXVIII. Exterior Catenational Fallacies page 261 279 290 304 318 LOGIC AT THE PRESENT TIME: A PREFATORY DISSERTATION. One hundred years ago the philosopher of Koenigsberg, in the preface to the second edition of his "Kritik," declared that logic had not advanced a step since Aristotle, and was, in fact, a completed science. According to Kant, authors subse- quent to Aristotle had added nothing to logic, but had dis- figured the science by the introduction of topics foreign to it. " For," says Kant, " logic is a science which has for its aim nothing but the exposition and proof of the formal laws of all thought, whether it be a priori or empirical, whatever be its origin or its object, and whatever the difficulties which it encounters in the human mind." But, during this nineteenth century, logical questions have been discussed more earnestly than ever before, and, at the present time, no department of speculative investigation attracts greater interest than that relating to the laws of rational conviction. Differences, moreover, still prevail con- cerning the fundamental doctrines of this science. The only parts of logic on which there is general agreement are certain forms and rules which have descended to us from Aristotle. The philosophy of conviction continues a subject of debate ; for which reason we cannot allow that logic is a completed science. No science can be regarded as complete till its prin- ciples have been established. The treatise now offered to the public is the result of long- continued studies which have had for their object to place the doctrines of logic on satisfactory foundations; and it would be false humility were the author to conceal his assurance that these studies have been successful. He claims to have 2 LOGIC AT THE PRESENT TIME: completed a work which Aristotle left unfinished, and that, too, in a way which would be approved by this great thinker were he now living. For Aristotle's "Organon" does not pretend to set forth a perfected system. It is not a treatise in which unity and simplicity have been reached through the ultimate analysis and the final synthesis of the laws of think- ing ; it is a collection of books written independently of each other, and whose discussions — especially when they relate to forms of argument — elucidate specific operations rather than universal principles. The writings of Aristotle, in gen- eral, reveal little effort at unification ; he aimed not so much to produce systems as to discover and present truth respect- ing important topics. Different discussions show different analyses of the same subject; his statements of related truths occasionally lack co-ordination; and he is content, at times, with primary and superficial generalizations. Therefore, with that lasting strength which results from conformity to the individual and the actual, his philosophy exhibits also the ob- scurities and difficulties and defects of uncompleted doctrines. We are aware that the claim to have reconstructed logic and to have made it a thoroughly satisfactory science is a bold one, and not likely to be immediately allowed. Even though one acknowledge his indebtedness to preceding thinkers ; with- out whose labors success would have been impossible; and though he represent himself, not as a master-thinker, but as a disciple who has been fortunate in his day and opportunities, the author's estimate of his work will be received by many with incredulity and by some with ridicule. Yet he knows what he has been enabled to do; he is certain that he has found the truth on every important point ; and, with this con- fidence, he comes before the public, not at all assured of his immediate reception, but willing to wait, if need be, till his views shall be understood. The reader who may desire to comprehend the spirit and aims of the treatise now submitted to his criticism, should consider some problems which exercise logicians at the present time. First, they desire a clear definition of their science. Aristotle does not give any definition. That already quoted from Kant A PREFATORY DISSERTATION. 6 is the one commonly found in text-books. For instance, Sir William Hamilton says that " logic is the science of the formal laws of thought, or of the laws of thought as thought." This definition is unsatisfactory ; it itself needs to be defined. One might object to it that logic does not have all thought for its subject, but only rational thought ; and also, that logic deals with rational thought not simply as such, but as the instrument and vehicle of conviction. We may, however, accept Kant's definition, provided it be taken to signify that logic is the science of the formal — that is, the essential and necessary — laws of rational conviction. For logic is a science which could be used by the rational beings of any universe. Again, the discussions of our day call for a true determina- tion of the sphere and scope of logic. The Kantian limitation of the science to the formal laws of thought is correct, if it be understood rightly. Pure, formal, or general logic does not consider those modes of enquiry or rules of procedure which are peculiar to any specific sphere of existence or investiga- tion. Nevertheless, though thus limited, logic aims to under- stand all those modes of mental action which reason must employ, under whatever constitution of things, in her pursuit of truth. But if this be so, not only " pure," but also " modal," propositions and reasonings should be considered. That is, those processes of thought which follow the relations of con- tingency and of necessity, as well as those which use only simple assertions respecting classes and portions of classes, should be studied by the logician. Especially contingent and probable, no less than apodeictic, conviction, must be discussed. For contingency and probability are not confined to a specific sphere of being any more than necessity and certainty. They belong to the nature of things, and must be found in any uni- verse. The fact is that problematic inference, though setting forth what is not necessary, is itself as necessary an act of reason, and as truly governed by law, as the apodeictic judg- ment. This was Aristotle's view. He devoted far more attention to " modal " assertions and reasonings than to the " pure." In proof of this it is to be noted that four chapters of that book, 4 LOGIC AT THE PRESENT TIME: the "Prior Analytics," in which syllogistic moods are exam- ined, treat of those moods which are "pure," while fifteen treat of those which are "modal." But these modal syllo- gisms have been neglected by logicians for centuries, and of late years all the teachings, both of Aristotle and of others, con- cerning contingent and necessary sequences, have been "for- mally expelled from the science." In the words of Professor Bowen of Harvard, " The whole doctrine of modality is now rightfully banished from pure logic," as pertaining " not to the form, but to the matter of thought." "Pure" propositions and "pure" syllogisms, only, are considered as lying within the province of the logician. Thus logic has been simplified by the summary process of amputating its more troublesome part. But the question arises, < Can desirable simplicity be obtained by a method which is founded on error, which divorces things most intimately related, and which necessitates superficial and one-sided views ? ' Cannot the difficulties of the case be solved in some better way than this ? Some more natural way ? In this connection the name "Modalist," which has been given to the following treatise, may be mentioned. It is in- tended to indicate that the re-introduction of modality is characteristic of the new logic. Other features may equal this in importance, but none other has so evidently modified the rules and formulae of the science. A third desideratum, in order to a clear and satisfactory logic, is a sound system of metaphysics, or ontology. He who would understand thought as employed in rational conviction must study thought in its relation to objects. For thought, by reason of its very nature, corresponds to the nature of things; and therefore, merely as expressive of this truth, every thought may- be said to have objectivity, whether it have an object or not. Without this characteristic thought could not serve the purposes of knowledge, or be of any logical importance. Conceptions are of interest to the logician only so far as they may, or do, correspond with realities and set forth truth or falsehood about them. Correct thinking is that which has this correspondence, or which, in an hypothetical case, would have it if the antecedent supposed were a reality ; A PREFATORY DISSERTATION. 5 thinking is incorrect when it is wrongly assumed to have this correspondence. Such being the case, the forms and sequences of thought, so far as it is the instrument of conviction, must relate to the nature and laws of things, and should be studied in the light of this relation. It cannot be said that these principles have been rejected by logicians ; neither can it be said that they have been ac- cepted and applied. Certainly their significance has not been realized by those who identify things with our thoughts of them, or who deny that thing are as we conceive them to be, or who say that logic is concerned with thought only and not with things also. The philosophy from which the following chapters derive their force has been named Perceptionalism, because it main- tains, from an analytic and theoretical point of view, that what men call their perceptions are true perceptions of those very things which they say that they perceive. This philos- ophy prizes highly the Aristotelian doctrine of " common sense," or " common perception/' — kolvyj aiaOrjo-Ls, — but differs from it in being a developed system. It was constructed throughout upon a critical investigation of human thought, but, it is to be hoped, with a more exact initial observation of data than seems to have attended the "Kritik" of the illustrious Koenigsberg professor. The author ascribes his success — or what he regards as his success — and his confidence in it, to his metaphysical prepara- tion. He cannot see how a satisfactory logic can be constructed except in connection with a sound ontology. A fourth requisite to the science of rational conviction, and one more specific than those already noticed, is an analytic understanding of the nature of simple judgment and of the knoivl- edge of fact or truth. For these are both modes of mental assertion, and if we use the term "judgment" in its wide logical sense, cognition, the initial act of knowledge, is simply that species of judgment which results in absolute and well- founded conviction. Both knowledge and judgment are expressed by the " prop- osition " in its most general assertive use ; and their radical <3 LOGIC AT THE PEE SENT TIME: nature is to be ascertained by an analysis of the simple asser- tive proposition. Logicians give different accounts of this. Aristotle says that " a proposition is a sentence in which one thing is affirmed or denied of another " ; Locke, that it is a statement setting forth the agreement or disagreement of one idea with another ; Kant, that judgment is the application of a higher conception (the predicate) to a lower conception (the subject). "For example," says Kant, "in the judgment 'all bodies are divisible,' our conception of divisible is applicable to various other conceptions ; among these, however, it is here particularly applied to the conception of 'body.'" All these definitions, and others which might be quoted, are unsatisfactory, Aristotle's, though the best, is superficial and specific when it should be analytic and universal. It does not apply to all judgments, but only to the most common class of assertive propositions. Moreover, it gives a logical division of these rather than a true definition. The correct doctrine affirms judgment to be the mental assertion of the existence or of the non-existence of something; and that there are two modes of judgment. For every assertive proposition is either a simple existential statement, in which the existence or non- existence of the subject is set forth, or it is a predication-proper — an inherential statement — in which the predicate is set forth as existing, or as non-existent, in its relation to some subject. Without this doctrine any account of the laws of belief and conviction must be extremely defective. A fifth essential in logical science is a thorough theory of inference and of illative judgment and assertion in general. Aristotle discusses only that specific mode of sequence which he calls the syllogism. Modern writers for the most part distinguish " mediate " inference — that is, the Aristotelian syllogism — from " immediate " inference. The latter, they say, derives its life from the laws of identity and of contra- diction ; the former, from the dictum of Aristotle, or from some similar principle founded on the relation of the generic to the specific. In addition to this they speak of hypothetical inference as following the law of reason and consequent. Nothing could be more superficial, more inadequate, more A PREFATORY DISSERTATION. T confusing, than any such analysis. Here logic must be wholly reconstructed. The one universal law of inference, to which all others are subordinate,, is that of Antecedent and Conse- quent. The formula "hoc est; ergo Mud est" expresses the nature of every illative sequence, however simple its antece- dent may be or however complex. Then there are two generic modes of inference, the orthologic and the homologic. In the one of these a consequent is inferred from an antecedent without reference to any previous case of similar sequence ; in the other we infer a similar consequent because we perceive a similar antecedent. In the one, following the ontological connections of the elements of entity, we form direct " intuitions " of things as onto- logically related; in the other, we infer a consequent by reason of the recurrence of its antecedent, on the principle that like logical antecedents — whether ontological or cos- mological — are invariably followed by like consequents. This law — the homologic principle — supports not only induction, but all principiation whatever. It is the basis of all reasoning either to, or from, or in the general ; that is, it justifies such reasoning. Further, illative propositions hold an important place in the philosophy of ratiocination. Such propositions, whether they be pure or modal, are modal in meaning, and really express inference. They must be contrasted with simple factual asser- tions, whether singular or general. The subject of an illative predication sets forth an antecedent ; the predicate — or rather the predicate part of the assertion — sets forth the consequent. When Kant says " body is divisible," he expresses the general sequence that " if there is a body, it can be divided." When the statement, " some snakes are venomous," is used as a prin- ciple in reasoning, this proposition, though "pure" because factual in form, is illative in force, and really signifies, " if there be a snake, it may be venomous." The doctrine of the illative — or inferential — proposition bears directly on that of the Aristotelian syllogism. For that syllogism is best explained as the combination of two illative propositions so as to produce a third. 8 LOGIC AT THE PEE SENT TIME: Sixthly, as already suggested, there is need that contingent as well as apodeictic inference should be analytically explained. This has not yet been done, because the metaphysical grounds of contingency have never been accurately determined. Aris- totle distinguishes contingency from necessity, and analyzes many reasonings from contingent premises, but he develops no theory concerning contingent sequence — its nature, its origin, its diverse modes, and its relations to sequences in pos- sibility, probability, and necessity. Nor has any one else given this topic thorough treatment. It is to be allowed, only, that the subject of probability has been handled by modern mathe- maticians with great ability, and that, in this way, some light has been thrown on the theory of problematic sequence in general. Logical possibility — possibility in the widest sense — is the basis of contingency and of probability. The law of this mode of sequence is that a thing is possible when one or more of its conditions exists. By condition we mean a necessary con- dition, a sine qua non. Space, time, and an adequate cause were conditions of the universe. Building materials, a builder and his tools, his plans and his remuneration and other in- ducements, are conditions of a house. Now whatever either is or contains a condition renders the thing conditioned possi- ble, so far as that condition is concerned. Conditions are either causal, or constitutive, or concomitant. The first of these enter into and compose the essential cause of a thing ; the second constitute its nature ; the third are its necessary attendants and consequents. Space, Time, and the Creator are free from causal conditions. This doctrine of conditions is the key to the philosophy of problematic sequence; and explains apodeictic sequence also. For, whenever a thing exists, then each of its conditions must exist, as above, in the cases of the universe and the house. Moreover, though conditions, as such, do not necessitate, but are necessary, they may be said to have a necessitative ten- dency or value. For the core, or vitalizing part, of any ordi- nary logical necessitant is composed of necessary conditions of the consequent. A PREFATORY DISSERTATION. 9 This core is the exact logical antecedent of the consequent, and may be called its necessitant condition, because it both necessitates and is necessary. Whenever an antecedent is constituted exclusively from necessary conditions, it recipro- s^ cates with its consequent, and may be inferred from it con- versely. If either antecedent or consequent exist, the other must exist also ; and if either be non-existent, the other must be non-existent. The occurrence of such reciprocations is especially noticeable in mathematical sequences. A given collection of circumstances — or a case — may con- tain a set of conditions capable of being filled out in any one, but in one only, of a limited number of ways so as to constitute a necessitating condition. When we know that there will thus result an antecedent of necessity in some one way, and have no reason to suppose that this will occur in one way rather than in another, we call each of the possible consequents a chance, and we say that the chances are equal to one another ; because we divide among them the confidence of certainty. Then, should a proportion of these chances support some general specific consequent, we say that this consequent has a prob- ability expressed by the ratio of the chances for it to the whole number of chances. The probability that an odd num- ber will turn up on one cast of a die is one-half, because three out of the six possible individual consequents favor an odd number. Now, when we know only that a certain specific consequent is supported by chances and are unable to determine the ratio of the chances for it to the whole number or to those against it, then the indeterminate probability thus arising is that con- tingency — or contingent sequence — of ivhich logic treats. A most important modification of contingency takes place when it is guarded against a necessity of the opposite. This is effected either when the consequent asserted as contingent is known to have already sometimes accompanied the antecedent, or when the very nature of the antecedent is seen to preclude impossibility. "Man may be wise" is guarded against a necessity of the opposite because men have been wise. This renders it clear that further investigation will not show that 10 LOGIC AT THE PRESENT TIME: man (as such) cannot be wise. So also ace certainly may turn up on the cast of a die, because there is nothing in the nature of a die or in the act of throwing it to prevent ace appearing. Another mode of contingency which is not guarded is fre- quently used by the mind. But guarded contingency is that assumed in the modal syllogisms of Aristotle, and has a just pre-eminence. The theory of sequence based on th Doctrine of Conditions renders possible a simple and intelligible account of modal reasoning, and, indeed, makes the modal syllogism, in its apo- deictic and its contingent moods, the syllogism par excellence, and that to which all syllogizing must be referred. Thus, too, what has long been the terror and despair of scholars has been converted into the crowning part of logical science. Once more, and in the seventh place, we may say that the Aristotelian syllogism calls for more accurate definition than it has yet received. The ordinary description of it as the " mediate inference " is indefinite and unsatisfactory, and the explanation of its process as the comparison of two terms, or two ideas, with a third so as to determine their relation to each other, is a vague, inadequate attempt at the expression of truth. Aristotle himself says that " a syllogism is a sentence in which, certain things being laid down, something else dif- ferent from those things necessarily follows by reason of their existence." This, also, is superficial and inadequate. For the questions arise, ' What is the nature of the things laid down ? and what is the nature and ground of the sequence ? ? There is a lack here similar to that in Aristotle's definition of the proposition. The only mode of inference which possesses all the "acci- dents " of syllogistic figure and mood — the only style of sequence to which all the rules of syllogizing apply — is that which combines two general illative propositions so as to produce a third : it is the process which obeys the law that the ante- cedent of a second antecedent is antecedent also of the second consequent; or (from another point of view) the law that the consequent of a prior consequent is consequent also of the A PREFATORY DISSERTATION. 11 antecedent of that prior consequent, and is therefore a " con- sequent-consequent." We cannot now speak further of this law or of its relations to other principles of inference. Our present object is not to expound the new doctrines, but only to indicate their nature. We must, however, add that no change has been proposed in those forms and rules of syllogizing which have come down to us from ancient times, except in the way of unification and of a slight addition. After the nineteen commonly recognized syllogistic moods have been interpreted by modal laws, twelve other moods, very simple in structure, have been added so as to express conjectural, or unguarded, sequences in contingency. Thus every mode of syllogizing used by the mind has been provided for. These unguarded moods are equal in philosophi- cal, though not in dialectic, importance to those ordinarily allowed ; they have been neglected heretofore. Some of them indicate methods of reasoning which are quite common. One result of the new analysis has been to exalt the general doctrine of inference and its modes above that of the Aris- totelian syllogism. The sphere of the latter has been restricted to "general catenate inference"; while other specific modes of sequence have been assigned distinctive places. This but carries out a tendency in modern logic, according to which various modes of inference have been treated independently of the syllogism and as following principles of their own. Even yet, however, logicians do not make sufficient allow- ance for the fact that different modes of inference may employ the same linguistic expression. A verbal, or superficial, form of sequence should not be taken as the ultimate explanation of inferences essentially diverse. Logical theory should not rest in the secondary and the ministerial, but should point directly to the ultimate. Following this rule, the Aristotelian syllogism will be given a true pre-eminence, yet also a definite and limited place, among modes of inference. In the foregoing remarks no enumeration of new doctrines has been attempted. This preface is intended merely to show the spirit and aim of the treatise which it introduces. Possibly other teachings of the book may seem to some of greater inter- 12 LOGIC AT THE PRESENT TIME. est than those already referred to. But this may be said re- garding every doctrinal modification : it has been introduced without any love for novelty, and only under a sense of neces- sity, and with a profound confidence in that underlying system of philosophy which has suggested the innovation. The posi- tions taken relating to logical definition and division — to the categories and the predicables of Aristotle — to induction — and concerning probable judgment — the specific laws of orthologic sequence, whether mathematical or metaphysical — the specific modes of homologic sequence — the quantification of terms in propositions — the opposition and conversion of predications — and concerning fallacies and their classification, have all been controlled and determined by the analysis of Perceptionalism. We would say, in conclusion, that, in one respect at least, the aim of the present work has been very limited. The history of opinions and the discussion of views which are well worthy of attention, have been quite beyond its scope. The endeavor has been simply to elaborate fundamentals. Perhaps, after a time, some additional chapters may be composed in criticism of important theories and in further elucidation of the system now submitted. Hamilton College, Clinton, N.Y. Nov. 4, 1800. THE MODALIST: OR, THE LAWS OF RATIONAL CONVICTION. CHAPTER I. LOGIC DEFINED. 1. Origin of the name. 2. Not the science of "thought as thought," nor of "inference" only. 3. The science of rational conviction. 4. Reason not radically different from lower faculties, but a special endowment and development. 5. " Discursive " reason is articulate and intentional; "intuitive" reason, habitual and instantaneous. 6. Truth is (a) attri- butal, (6) objectual, (c) subjectual, or propositional. The term "subject." 1. The name "Logic" was originally the Greek adjective corresponding to the nonn Aoyos, which noivn signifies either language or that rational and elaborated thought of which language is the expression. As descriptive of a science the adjective AoyiKo? was employed either in the singular or in the plural. The plural phrase, ra XoytKa, might be translated " the principles of rational thought." It sets forth the science as composed of parts. It is similar in origin to the expression, to. fieTavaiKd, or " metaphysics," a name anciently given to the philosophy of the ultimate in conception and in existence. The singular designation, "tj Aoyi/oj," is that Anglicized by the word " logic." The meaning of it is fully expressed in the original language by adding to it a noun, either eVtorrT/^ or re^vr)-, and the phrase thus formed may be translated "the science, or the art, of rational thinking." The term t£xvv] with the Greeks, like the term "art" with us, is often used to designate a practical science. Logic even yet is sometimes 13 14 THE MODALIST. [Chap. I. called an art because it not merely elucidates truth, but also formulates rules and gives useful directions. 2. This science has been variously defined by modern writers. Most of them say that " Logic is the science of the laws of thought," and some make this statement emphatic by saying " of thought as thought " ; that is, of thought considered simply, or chiefly, as to its own nature. One great objection to this definition, at least as it is commonly given, is that it uses the word " thought " in a narrow and technical sense with- out sufficient explanation. This word is applicable to all our thinkings as well as to those exercised in connection with rational conviction. Memory, imagination, sense-perception, consciousness, have each its own mode of thought ; to say that logic is the science of thought without showing clearly what kind of thought does not satisfy the enquiry of the mind. But a second and more serious fault in the above-men- tioned definition is that it tends to conceal a radical distinction of mental science, namely, the distinction between thought, or conception, and belief, or conviction. This tendency is especially noticeable when we are told that Logic is the science of thought as thought. For, according to the most natural use of terms, Logic does not consider thought simply as thought, but thought always and only as the instrument and vehicle of conviction ; and the laws of thought as the organ of belief cannot be clearly understood if we do not first recognize the distinction between thought and belief. Again, some have defined Logic as the science of reasoning, or inference. For instance, Professor De Morgan calls it "the calculus of inference necessary and probable." This definition is not sufficiently broad ; Logic discusses not only inferences and reasonings, but also conceptions, or notions, and statements, or propositions. Nor are these considered merely in subordi- nation to reasonings, but also as having an independent use of their own. An important part of Logic aims simply to render our notions and statements more adequate and efficient as the embodiments of truth. Another class of writers, desiring to emphasize the practical Chap. I.] LOGIC DEFINED. 15 office of Logic, say that it is the science which teaches "the right use of reason." This definition cannot be greatly con- demned, yet is wanting in completeness. The rules and direc- tions of Logic as an art cannot profitably be separated from the philosophy of our rational operations. To say merely that Logic teaches the right use of reason is not a sufficient recog- nition of that scientific spirit without which any logical sys- tem would be weak and lifeless. Moreover, the term " reason," when used without qualification, covers a wider ground than is surveyed in logical discussions. In particular, that construc- tive imagination which produces poems and works of fiction is something pre-eminently rational ; yet it does not fall within the cognizance of the logician. 3. Perhaps the defmiteness of conception for which we have been seeking may be obtained in connection with the following statement : Logic is the science of the operations and products of the rational faculty in the pursuit and use of truth. The distinction, incidentally assumed in these words, between the operations and the products of the mind is worthy of some attention, because it differs from that existing between material products and the labors in which they originate. In the latter case the things distinguished are of totally diverse natures, whereas the mental conception or conclusion, which results from some rational process, is a thing of essentially the same kind with the steps which lead to it. It is simply a completed thought or conviction which the memory retains, and which the mind can recall and use. Hence, after a mental product has been formed, it may immediately become part of a process which aims at a further product ; as, for instance, when one notion, after being denned, is employed in the definition of another. But the important point in our conception of Logic is, that this science considers reason, or the rational faculty, only so far as it is engaged in the pursuit and use of truth. On this account, if brevity were desired, it might be sufficient to say that Logic is the science of rational conviction ; for belief, or conviction, is always the apprehension by the mind of some- thing as true. That such is the essential character of Logic 16 THE MODALIST. [Chap. 1. will be evident to any one who may examine the various sys- tems of doctrine which have gone under this name. At the same time Logic is not the science of conviction in general, but only of those modes of conviction which depend on the exercise of the reason. Those cognitional convictions, which are not of a rational origin, though recognized by the logician, have only a preparatory and subordinate place in his discussions. One knows, from consciousness, of the pleasure experienced in meeting with a friend, or, from sense-perception, of the size, weight, solidity, roughness, and coldness of a stone ; but such cognitions are not exercises of the reason, and are not investigated by the logician. This is true also of those per- ceptions of times, distances, changes, and relations which ac- company the operation of sense-perception and consciousness. Without any rational process, a person holding two stones, one in each hand, would know that they exist contempora- neously, that they are separate in space, that they are similar to one another, that the one is heavier or rougher than the other, and so on. In short, all presentational cognitions, and the memories consequent upon them, are presupposed or taken for granted, in the science of rational conviction. In speaking of Logic as a science, we would not ignore those practical aims, on account of which it has been called an art. Some authors have discussed logical questions in a purely the- oretical spirit and without any attempt at useful directions. In this they deviate from that conception of the science which the experience of past times has shown to be both reasonable and advantageous. 4. Accepting the definition that Logic is the science which discusses the operations of reason in the pursuit of truth, let us consider attentively two leading ideas contained in it ; let us determine exactly what we mean by reason and truth. Reason, or, as it is sometimes called, the rational faculty, is a development of intellectual power which, because of its great importance and wonderful accomplishments, is distinctly no- ticed and named ; yet it is not a faculty radically different in nature from our lower mental capabilities. A man of genius differs from his fellow-men, not in the nature of his gifts, but Chap. L] LOGIC DEFINED. 17 in the natural strength of them and in the degree of their development. In like manner, reason is to be distinguished from those powers of mind which man has in common with the more intelligent brutes rather as a special endowment of strength than as a faculty of a distinct nature. When Locke speaks of " that faculty whereby man is supposed to be distin- guished from the beasts, and wherein it is evident that he much surpasses them," his words must be received with care. Examination shows that reason is not a faculty separate in its nature from our other powers, but only a special endowment of intellectual ability. The perceptions of sense, no less than those of the rational faculty, employ notions, judgments, and inferences; but reason far transcends all sense-perceptions in the grasp of her apprehension and understanding. In like manner, there is an exercise of the faculty of reasoning, or ratiocination, which falls far short of what we call reason. Many brutes exhibit some power even of connected reasoning. Eeason is that gift by which man is capable of language, of civilization, of material social and intellectual progress, of civil government and laws, and of moral and religious life. The superiority of this endowment to the lower powers of mind is manifested principally in two particulars. In the first place, rational conceptions are peculiarly comprehensive ; and secondly, resulting in part from this comprehensiveness of conception, rational judgments are peculiarly penetrative. Eea- son can seize and hold under consideration many things at once, so as to consider fully their nature and relations ; and, while doing so, she reaches a knowledge of things which are invisible to lower powers of thought. So far as sense-percep- tion is concerned, a brute sees the different parts of a locomotive as well as a man ; but no brute can understand the relations, use, and value of each part, and by what process the whole contrivance accomplishes its work. Eational intelligence not only perceives these things, but constructed a locomotive in thought before such an invention ever existed. Philosophers agree that, in the human mind at least, reason is exercised in two modes, the intuitive and the discursive, but they differ concerning the way in which these modes of reason 18 THE MOBALIST. [Chap. 1. are related to one another. Some hold that rational intuition is entirely without a process, or, at all events, wholly different in nature from rational discourse- The better opinion is that the intuition of reason is an instantaneous action the rapidity of which, resulting from the habitual and spontaneous use of certain modes of apprehension, causes the steps of the process to escape detection. Believing this, we must hold the intuitive reason to be a faculty of a very different nature from that power of " intuition " by which necessary relations are imme- diately perceived, and which enters as an element into every phase of human cognition. The discursive mode of reason is that ordinarily employed in all our deliberate investigations. It is distinguished from the intuitive by being more analytical, articulate, and con- secutive, and in being immediately under the guidance of the will. This form of the faculty, also, is the proper subject of logical principles and rules, because it alone admits of direct self-inspection and regulation. Yet an understanding of " the discourse of reason " enables us to understand " the intui- tion of reason," as well ; the two being radically of the same nature. The rapid mode of reason may be compared to that motion of spinning or weaving machinery which is too swift for observation : the more deliberate mode may be likened to the working of a type-writer or a telegraphic instrument, every movement of w T hich is an intentional act of the operator. The intuitive mode becomes understood when the same conclu- sions to which it comes quickly are reached by the consciously directed methods of mental discourse. 5. The question, " What is truth ? " was often asked by ancient philosophers, and with them it mostly had a moral significance and meant, " What is the true end of life ? " The first aim of the thinkers of antiquity was to find some essential principle the knowledge and observance of which might lead men to true happiness. In modern discussions, the term "truth" is more commonly used in that primary and literal sense which it has when we say that a statement is true, or is a truth, and deny that it is false. The truth thus mentioned has been called intellectual truth, and has been distinguished Chap. I.] LOGIC DEFINED. 19 in this way from that more specific kind which is ethical or moral. For truth in general and by reason of its essential nature is closely related to intellect. This intellectual truth is of three modes, or denominations, which are intimately connected with one another. First, there is attributed truth. This is that defined by St. Thomas Aquinas when he says, " The truth of thought is a correspondence of thought and fact according to which thought says that what is, is, or that what is not, is not." (Veritas intellectus est adaequatio intellectus et rei, secundum quod intellectus dicit esse quod est, vel non esse quod non est.) Evidently if a statement — for example, that "the man is rich " — be true, there is a fact existing outside of one's thought, and also a proposi- tion within the mind corresponding to the fact ; and the truth which we ascribe, or attribute, to the proposition, lies in this correspondence. Again, there is objectual truth. This is not any correspond- ence, but it is the fact, or reality, which is the object of the mind's knowledge, and which corresponds to the proposition in the mind. Accordingly we sometimes say, "That is the truth," our meaning being, " That is the fact." In such lan- guage fact, as the basis and object of knowledge, is called truth. Finally, there is subjectual, or propositioned, truth. The term "subject," when opposed to the term "object" in modern philosophy, signifies the mind as the subject of im- pressions from objects and of ideas about them. Subjectual truth, accordingly, is the ideas or conceptions of the mind considered as corresponding with facts or objects known. This may also be styled propositional truth, because when expressed fully it assumes the form of the assertive propo- sition. For belief, or conviction, cannot be exercised on the mere conception of a thing as to its nature, however correct and complete this conception may be. There is always need that we should conceive of a thing as existing or as non-existent. To believe in God is to believe in the existence of God, or in the proposition that God exists ; to believe in the justice of 20 THE MODALIST. [Chap. I. God is to believe in the existence of His justice, or in the proposition that God is just; and to disbelieve in God and His justice is to believe that they do not exist. It is because assertive propositions set forth things either as existent or as non-existent that they are naturally fitted to express subjectual truth. The signification of the noun " subject," referred to above in connection with the adjective "subjectual," belongs chiefly to the discussions of psychology. It is to be distinguished from the ordinary meaning of this word in Logic, according to which it is opposed, not to the term "object," but to the term "pred- icate." In the distinctively logical sense a subject is anything whatever of which anything may be affirmed or denied. But the doctrine of truth pertains to philosophy in general, not to Logic only; and therefore we need not confine ourselves, in the statement of it, to strictly logical terms. When we say that Logic considers the operations of the reason in the pursuit and use of truth, it is clear that the ref- erence is to subjectual, or propositional, truth. This is that which the mind immediately apprehends and employs ; it is only by obtaining possession of this that the mind becomes sensibly related to attributal and objectual truth. C.iap. II.] BELIEF, OR CONVICTION. 21 CHAPTER II. BELIEF, OK CONVICTION. 1. The two primary powers of mind, — thought, or conception, and belief, or conviction. 2. Belief and knowledge defined. 3. Judgment and cognition defined. 4. Inferential judgment, (a) either apodeictic or problematic, (b) either actualistic or hypothetical. 5. The sphere of general, or "pure," logic. Thought, or conception, and belief, or conviction, may be termed the primary powers of the intellect, because, in their exercise, the work of mind is directly accomplished : our other powers, such as attention, association, abstraction, generaliza- tion, synthesis, and analysis, are secondary, because their function is to modify the operation of thought and belief. 1. Of the two primary powers, thought is the more promi- nent in our experience ; for belief is felt only as an accompa- niment of thought. We may have conceptions unattended by convictions, but we cannot have a conviction except as attached to some conception. Moreover, in every enquiry respecting belief, questions respecting the origin and mutual connections of our thoughts are implicated. This close association of belief with thought has led many writers to treat belief as if it were merely a peculiar, or, it may be, a superior, kind of thought. This is a mistake, and the cause of wide-spread- ing confusion. President McCosh ("Scottish Philosophy," p. 384) says truly, "Belief should have a separate place in every system of psychology " ; to which we add, " and in every system of logic also." 2. But, before proceeding farther, we must remark that, in the present discussion, the term "belief" is used in a very wide sense. Ordinarily belief signifies a mode of mental con- fidence which falls short of knowledge, yet which is greater than mere guess-work or presumption. Seeing certain weather indications, one might say, " I believe, though I do not know, 22 THE MOBALIST. [Chap. II. that it is going to rain." We now include under belief every degree of confidence respecting the truth of a thing from the weakest conjecture to the most absolute assurance. According to this signification knowledge is a kind of belief ; for knowl- edge is absolute and well-founded certainty. At present, also, we use the term " conviction " as synony- mous with " belief," though conviction strictly indicates belief, not simply, but as founded on evidence. In like manner, we employ the terms "conception" and "thought" interchange- ably, though a conception properly signifies a thought formed synthetically. The most important point in the doctrine of belief is, not that conviction takes place only in connection with conception, but that belief is possible only when the thought of existence or that of non-existence is united with or included in our con- ception of a thing. This truth has been expressed too strongly by those who say that belief takes place only in connection with propositions. It is the essential and formal function of propositions to set forth things as existent or as non-existent, but any notion may become matter of belief if it only be an existential conception; that is, if it have, as one of its ele- ments, the thought of existence or that of non-existence,, whether this element be prominent in our conception or not. For instance, should one predicate something respecting an existing object, saying, "My friend is faithful," the subject- notion, "my friend," presents the object as existing, and as believed in, though the existence directly asserted by the propo- sition is not that of the friend, but of his faithfulness. 3. The same necessity which leads to a wide use of the term " belief " calls for an equally broad use of the term "judg- ment"; for judgment is the initial act of which belief is the permanent and reproducible product. Ordinarily judgment signifies the formation on evidence of a probable conviction. Hence Locke says, "The faculty which God has given to man to supply the want of clear and certain knowledge is judgment, whereby the mind . . . takes any proposition to be true or false without perceiving demonstrative evidence in the proof." But logicians have found it advantageous to give the name " judg- Chai>. II.] BELIEF, OR CONVICTION. 23 ment " to the assertive faculty in general ; in other words, to that faculty, in the exercise of which we form convictions of any kind, and are led to embody these convictions in propo- sitions or statements. According to this use of language cog- nition, the initial act of knowledge, is a mode of judgment, knowledge being, as we have seen, a mode of belief. If we consider our convictions and the judgments productive of them with reference to their primary origin and mode of formation, they may be divided into two classes, — the presen- tational and the inferential. The former of these includes our cognitions of such things and relations as are immediately present to the soul in space and time ; and with these cogni- tions we may also classify, as things of the same logical re- lations, the simple reproductions of presentational perceptions. Our first perceptions are important because they are the basis of all subsequent knowledge and belief, but the special con- sideration of them belongs to psychology. They furnish those materials of fact which reason uses, but are not themselves distinctively rational. While, the logician recognizes them, he does not make them the subjects of his investigation. Inferential convictions are those which assert the existence or the non-existence of things not immediately present to the soul. It is with them that the discussions of logic are chiefly occupied. They differ from presentational cognitions in that the latter do not depend on any previous knowledge, while inference assumes something as already known to be fact, and then asserts some second thing as a fact connected with the first. 4. Considered with reference to their own nature and opera- tion, inferential judgments are divisible into two principal classes, — the apodeictic, or demonstrative, and the problematic, or contingent. The apodeictic inference leads to an absolutely certain con- clusion, and excludes the possibility of a thing being otherwise than as it is shown to be. Such are mathematical demonstra- tions and all reasonings which infer things as necessarily related to given fact. When a surveyor knows the length of the sides of a field and the angular measurements of its corners, he calculates the area by an apodeictic, or demonstrative, process. 24 THE MODALIST. [Chap. II. Problematic inference is based on the consideration of things as possible or as contingent, and produces forms of conviction weaker than those which result from demonstration. Contin- gency is a mode of sequence approaching probability : it is an expectant possibility. It arises when an antecedent of possi- bility admits only a limited number of possible consequents, some one of which must be realized. Old age is one of several conditions, one or other of which must belong to every man. Therefore it is contingent to man to be old. Contingency is best discussed as a mode of possibility which prepares for probability. Many, following Aristotle, and neg- lecting the distinction between contingency and probability, treat both modes of sequence under the head either of contin- gent or of probable inference ; but a wise use of terms limits " contingency " to those cases in which a thing is looked for, or in any degree expected, as possible, without having its probability determined, and limits " probability " to those cases in which some proportion out of a total number of chances is found or estimated to favor some conclusion. Thus it would be a judgment of contingency to say, " A merchant may prosper, and become wealthy " ; but of probability to say, " The wise and prudent merchant will prosper." Contingency lies between possibility and probability, being more than the one and less than the other. It passes into probability when- ever the ratio of the chances is estimated. Both contingency and probability expect, which accounts for their being often included under the general name " contingency " ; but they are clearly distinguishable. Another division of inferential judgments separates them into the actualistic and the hypothetical. This distinction relates not so much to the internal nature and operation of inferences as to the character of the grounds on which they are based, and of the convictions which they produce. For when an inference, whether apodeictic or problematic, arises from our knowledge of fact or from belief in what we take to be fact, the conclusion of it asserts fact, or at least the possibility or probability of fact ; and the inference is actualistic. But if our reasoning be based on supposition or assumption, the con- Chap. II.] BELIEF, Oli CONVICTION. 25 elusion sets forth only what would be fact (necessarily, or possibly, or probably), provided the supposition were realized. In this case the inference is hypothetical, and asserts what, in the most literal sense, may not be true at all. Should we sup- pose one of the Green Mountains to be of solid gold, we might assert Vermont to be the wealthiest State in the Union, and the inference would be correct ; yet evidently neither premise nor conclusion Avould set forth reality. Hypothetical inferences may be based on antecedents to which no facts ever correspond, but more frequently they pre- sent the abstract operation of some law of existence or of nature. For it is only by an exercise of the imagination that we can conceive of the separate working of a law which never is seen to operate except under a complication of modifying circumstances. Hence hypothetical inferences are largely employed in science. 5. Some writers teach that neither the inference of the actual nor that of the probable or of the contingent lies within the sphere of logic. Rightly conceiving of logic as the general science of our rational operations and as independent of any particular branch of knowledge, they say that the theory either of problematic or of actualistic conviction is necessarily connected with that knowledge of specific classes of things which experience gives us, and that the logic of hypothetical demonstration, alone, is an abstract and ontological science. These views are not well founded. While all the methods of reason should be illustrated and tested by their application to particular cases, the principles of actualistic conviction are not specially connected with any one class of facts or objects, and those of problematic inference are such as must govern finite intellects in their judgments relating to any universe, or system of affairs, in which they can be placed. If the sub- ject of logic as a general science — of "Pure Logic," as it has sometimes been called — be rational conviction in general, then logic must consider actualistic as well as hypothetical, and problematic as well as apocleictic, inference. All these modes of rational conviction, together with their principal varieties, are such as must be followed, by minds like ours, in any uni- verse, or system of things, whatever. 26 THE MODALIST. [Chap. III. CHAPTER III. LOGIC DIVIDED. 1. Logic is objective or subjective. 2. Is general, or abstract, and special, or applied. 3. Is "pure," or "formal," and mixed, or modified — but ambiguously. 4. The terms "directive" and "corrective" proposed. 5. Logic concerns («) notions, or conceptions, (p) judgments, or assertions, (c) inferences, or reasonings. In order to render our conceptions of logic and of the sphere of its instructions more definite, various distinctions and divis- ions have been made. 1. First, objective has been distinguished from subjective logic, or, in the language of the schools, Logica Systematica from Logica Habitualis. The necessity for this distinction arises from the double signification of the word "art." Since this word may indicate either a system of practical principles or an acquired facility in the application of those principles, there are two senses in which one may be proficient in logic. He may be a theoretical logician, well-acquainted with the laws and rules of thought, or he may be a practical logician, skilful in the application of the rules. While habitual logic is a chief end of systematic logic, these two " arts " are distinct acquire- ments, and do not always accompany one another. He who would be in every sense a complete logician must not merely familiarize himself with the principles of correct thinking, but must also sedulously practise them. Nor should he expect to obtain from books, or even from instructors, much more than a useful knowledge of right methods. The foregoing distinction has sometimes been called a divis- ion of logic. But it does not really divide the science. It only explains how the term " logic " may be employed in a secondary sense. Subjective and objective logic cannot natu- rally be regarded as parts of the same whole ; and the logic set Chap. III.] LOGIC DIVIDED. 27 forth in books, which is that commonly spoken of, is wholly objective. 2. Again, general, or abstract, logic has been distinguished from special, or applied, logic. Every department of enquiry is properly subject to various regulative principles connected with the specific character of its investigations ; and these principles, though immediately subordinate to the universal rules of right thinking, constitute a separate system of directions. Mathematical progress is promoted by a knowledge of the correct use of diagrams, in- struments, figures, symbols, modes of notation, and methods of calculation. In courts of law barristers and judges are governed by rules respecting the pertinency and value of dif- ferent modes of proof and the fair interpretation of legislative enactments. The theologian appeals to the canons of Biblical exegesis ; and the psychologist, who would ascertain the laws of mental life, first determines on what sources of knowledge and on what methods of enquiry he may rely. In short, every science has its own principles of procedure, which, as supple- mentary to the rules of right thinking in general, may be called the special logic of that science. But the several regulative codes now described are no part of logic in the ordinary acceptation of the word; for by " logic " we commonly mean that general science which sets forth those forms and laws which rational conviction should observe, no matter what may be the specific nature of the topics considered. The distinction between general and special logic is not properly a division of that general science. Each special logic involves considerable acquaintance with the de- partment of investigation to which it pertains, and is simply that philosophical "introduction," or "methodology," without which great progress can scarcely be hoped for in any branch of knowledge. Every such code is a valuable addition to the science which it is intended to promote, and should be studied as a part of that science. 3. Again, pure, or formal, has been contrasted with mixed, or modified, logic; though logicians differ greatly in their explanations of this distinction. 28 THE MODALIST. [Chap. III. Some say that general, or abstract, logic is " pure," because unmixed with the principles of any specific science, and " formal," because it sets forth the radical methods employed by reason in every sphere of enquiry ; while particular meth- odologies modify the general rules of reasoning by mingling their own directions with them, and therefore constitute mixed, or modified, logic. In other words, Pure, or Formal, Logic is just the same as General, or Abstract, and Mixed, or Modified, Logic is just the same as Special, or Applied. This use of lan- guage is quite common, and is so supported by authority that it cannot be condemned or avoided ; yet it is really undesirable. It repeats a distinction already provided for, and, as we shall see, conflicts with another and better use of terms. Again, those who hold that the " necessary " laws of thought pertain only to hypothetical demonstration, confine the terms "pure" and "formal" to apodeictic logic, and relegate to mixed logic the consideration of actualistic conviction, of probability and contingency, of doubt, and of error. This division of the science and the implications of it cannot be allowed. The theory of demonstration cannot be separated in this way from the rest of logic. The same immutable and ontological laws underlie all modes of sound judgment and correct inference. According to a third method of employing the terms in question, the logic of correct conviction is called " Pure," or " Formal," and that of imperfect and erroneous thinking, Mixed, or Modified. We can conceive of a purely intellectual being, unaffected by any cause of error, and compare him with creatures like ourselves who are subject to mistakes. And our mental action, so far as free from failure or delusion, might be held to obey the laws governing that pure intelli- gence ; while our deviations and delinquencies in the pursuit of truth would be accounted for by influences which mingle with our thinkings and lead them astray. Hence we discrimi- nate between the philosophy of the defective use of reason and that of correct and normal thinking. The distinction thus made is a true division of General, or Abstract, Logic. 4. At the same time, since logicians have disagreed in their Chap. III.] LOGIC DIVIDED. 29 use of terms, two new names may be of service here. Were we, instead of the last distinction, to designate Pure Logic as Directive, and Modified Logic as Corrective, and were we to assign to the one the perfect and normal modes of rational conviction, and to the other the imperfect and abnormal modes, all room for misapprehension would be taken away. But, while dividing logic into the Pure, or Formal, or Direc- tive, and the Mixed, or Modified, or Corrective, Ave do not mean to say that the discussion of correct and that of incorrect pro- cesses should be wholly separated from one another. Clear- ness of statement and an orderly arrangement of details may require some separation, but we must not lose that advantage which accrues from the immediate contrast of perfection and imperfection. The division of logic into the Directive and the Corrective is principally significant as marking two lines of thought which run parallel with each other in logical investi- gations. 5. The distinction between actualistic and hypothetical con- viction, though fundamental in logic, does not yield any divis- ion of the science. The difference of these modes of belief, both as to nature and origin, is very apparent, and the forms and processes of thought in connection with which they are experienced are perfectly similar. To determine whether a conclusion be actualistic or hypothetical, we have only to know whether it be drawn from fact or from supposition. This dis- tinction, therefore, does not give rise to any great variety of discussions. But an important division of logic is based on those three radical modifications of mental action which reason employs. For every exercise of rational thought is either a conception, or a judgment, or an inference ; and every question in logic concerns one or other of these three things. The necessity of grouping according to this division soon becomes evident to the investigator, and it is also perceived that there is a natural order of succession for them, namely, that conceptions should be studied before judgments, and judgments before in- ferences. Hence most text-books contain three principal parts, corresponding to these three general topics. 80 THE MODALIST. [Chap. III. But here we must remark that the logical division of a body of scientific knowledge should not be confounded with the orderly plan of a treatise ; though these things often go by the same name. The object of logical divisions is to impress upon us certain pervasive and fruitful distinctions ; the arrange- ment of a treatise is designed to facilitate our progress in the understanding of doctrines. Accordingly, in a scientific book, several radical divisions may be given, while only one arrange- ment of topics can rightly be adopted. From the nature of the case, indeed, any wise order of discussion must refer more or less directly to logical division, but the work of arrange- ment should not be so controlled by this relation as to be pre- vented from the free pursuit of its own proper aim. These remarks may be illustrated by the plan of procedure chosen for the present treatise. It is essentially the same with that commonly adopted. It is based on the division of our rational states into conceptions, judgments, and inferences, and also on the fact that the doctrine of inference calls for a considerable variety of discussions, and occupies an extended place in logic. Having now finished some necessary introductory disserta- tions we shall apply ourselves, in the next part of this treatise, to questions concerning conceptions, or notions. Then we shall take up judgments, or assertions. After that we shall discuss the radical laws and forms of inference ; whether they belong to the apodeictic (or demonstrative), or to the problematic (or contingent) inference. This will prepare us for the composi- tion of inferences and the conclusions thereby obtainable ; which things fall under the head of syllogisms. Finally, some closing chapters may be specially devoted to fallacies and the causes of error. Chap. IV.] ENTITIES AND CONCEPTIONS. 31 CHAPTER IV. ENTITIES AND CONCEPTIONS. 1. Entities, or objects, and notions, or conceptions. 2. Objectivity and objectuality. Truth and error. 3. Positive and negative (a) facts, (fo) notions, (c) convictions. 4. Schematic conceptions. 5. Categore- matic and syncategorematic words. 6. Subject and predicate. Substance and Accident, or Substantum and Ascriptum. 1. Ax entity is anything whatever that does, or may, exist. Spaces, times, substances, powers, actions, changes, quantities, and relations, are so many kinds of entity. Whatever actually exists is a real entity ; and when a thing does not exist, but is merely conceived of as existing, we use similar language to that which we would employ if it existed, and say that it is a possible, or an imaginary, entity. In the strictest sense that only is an entity which really exists. The essence of entity, however, does not lie in its existence, but in its being that which exists, and which, therefore, also may be of this or that nature. The word "entity " is equivalent to the word " thing " in that wide sense according to which we speak of all beings, or exist- ences, whatever, as things. The advantage of the philosophi- cal term is that it has one signification only, while the word " thing " has many meanings. That action or state of intellect which corresponds to any entity is called a notion, or conception ; the entity of which we conceive is called the "object" of the conception, and the conception, as related to and corresponding with its object, may be said to be objective, or to have objectivity. This objectivity belongs to the essence of thought. Any psychical activity which does not correspond to things, or entities, is not thought, but some other form of experience. To this statement, however, the thoughts of existence and of non-existence, and they alone, present an exception. Existence 32 THE MODALIST. [Chap. IV. and non-existence are not things, or objects, in the full sense of these terms, though they may be thought of just as things are thought of, and must be allowed (that is, in all cases of fact) to have a kind of objectuality. 2. By " objectuality" we mean the character of things as being actually or possibly correspondent to our thought. The objectuality of entity is the counterpart of the objectivity of conception. But this objectivity of thought and this objectu- ality of things do not involve that a thought and the entity corresponding to it are of the same nature, or that they resem- ble one another, or that, if either exist, the other must exist also. They only imply that the nature of the oiie corresponds with the nature of the other. If the existence of a concep- tion always involved that of the corresponding entity, there could be no such things as truth and error. Truth lies in the conformity of thought with fact, or with what, in case some hypothesis were realized, would be fact ; while error is the disagreement, or want of correspondence, between thought and fact. 3. Now fact is of two kinds or modes, — the positive and the negative. According to the first the existence of a thing- is a fact ; according to the second, the non-existence. It is as much a fact that there is no bread in the cupboard, when that is true, as that there is bread in the cupboard, when that is true. Consequently, and corresponding to the positive and negative modes of fact, there are two modes of conception, — the positive and the negative. These are expressed, respectively, by such terms as " bread," "a loaf," and "no bread," "no loaf." Commonly a thing is set forth as existing by a noun without the adjective " no," and as non-existent by the same noun with the word "no" prefixed. At first sight it appears self-contradictory to speak of a thing, or entity, as non-existent ; and it would be so if we intended to speak of a real entity as non-existent. But such is not the case. The only reality perceived and asserted is the fact of non-existence in a case where a certain entity may be imagined or supposed to be. Combining our conception of this entity, considered only as to its nature, with the thought of non-exist- Chap. IV.] ENTITIES AND CONCEPTIONS. 33 ence, we exercise belief in connection with this combination. There is no incongruity in so doing. For we do not think of a thing as both existing and not existing at the same time ; we simply displace from the positive conception of a thing the elementary thought of existence, and replace this by the thought of non-existence. The distinction between positive and negative conceptions shows how we may exercise belief in connection with notions as well as in connection with propositions ; because belief is possible whenever our thought in any way contains the ele- ment either of existence or of non-existence. The forming and holding of conceptions as setting forth fact or truth is what logicians have had in mind in teaching that " simple apprehen- sion" is one of the three logical operations of the intellect. Whether Ave know something as a reality, or assume it to be such for the sake of argument, this apprehending and holding of a thing as true differs from the mere conceiving of a thing. It is even more than the conceiving of it as existing : it in- volves a real or affected belief in connection with our concep- tion. 4. The division of notions, with reference to their fitness to correspond with realities, into the positive and the negative, is not an exhaustive division. There is a third class of concep- tions, — the formal, or schematic. For should we, in conceiving of any entity, think neither of its existence nor of its non- existence, but only of its nature or characteristics, we might express this by saying that we think of it merely as a form, or schema. According to this use of language a " form " includes everything in an entity except its existence. This mode of conception is difficult of deliberate realization ; but it occurs spontaneously sometimes, and especially whenever, after being ignorant about a thing, we learn whether it exists or not. For then, in our assertion respecting fact, we unite the thought of existence, or that of non-existence, with the schematic notion of the entity in question, and exercise belief in connection with this combination. In every pair of conceptions contrasted with each other as positive and negative there is a part common to both; that M THE MODALIST. [Chap. IV. part, when thought separately, is the formal, or schematic, conception. This mode of intellectual action has greatly escaped attention; it should have a place in every system of logic. .>. Another division of notions, less searching in its thought than the foregoing, distinguishes between the complete and the supplementary. A complete notion is one sufficient of itself to serve as a term — that is, as either subject or predi- cate — in a proposition ; but a supplementary notion can only help to constitute a term. In the sentence " The white flakes of snow are falling gently on the grass," the adjective, the participle, and the nouns express complete notions, while the articles, the prepositions, and the adverb express supplemen- tary notions. Words significant of complete conceptions were called by the old logicians " categorematic," from the Greek Kar-qyopr^ia, which signifies an assertion ; while words whose force is merely supplementary were styled syncategorematic. A term which contains only one complete notion or categorematic word is said to be simple, but when several complete notions are combined in one term, it is called complex. In the above illustration both terms, namely, " the white flakes of snow " and " falling gently on the grass," are complex. The distinction between complete and supplementary con- ceptions, and between categorematic and syncategorematic words, arises rather from our mode of employing ideas than from the essential nature of our thought ; for direct and atten- tive thinking can give an independence to any conception whatever, and fit it for categorematic use. But this distinc- tion prepares us to determine at once whether a proposition be fully formed or not, and what its terms may be. A thorough analysis of the component thoughts out of which terms or com- plete notions are constructed belongs to metaphysical psychol- ogy. Commonly in logic when we speak of conceptions we refer to complete conceptions. 6. This is especially the case in that division which distin- guishes between subjective and predicative notions ; for only a complete notion can be either subject or predicate. Chap. IV.] ENTITIES AND CONCEPTIONS. 35 Ordinarily, in making an assertion, we think of one thing, or entity, as existing, and then present another thing, either as existing, or as not existing, in some relation to the first. In saying "the snow is white," "the snow is not yellow," we think of snow as existing, and then assert that the quality indicated by "white" exists in the, snow, and that the quality indicated by "yellow" does not exist in it. The first entity thought of in the assertion is called the subject, and the second the predicate ; which terms are also applied to the correspond- ing conceptions. In common language, the subject is that about which some assertion is made, while the predicate shows what is asserted about it. Obviously, the meaning which logic thus attaches to the term "'subject," is very different from that belonging to it in psychology, and according to which it signifies a thinking and sentient spirit. The terms "subject" and "predicate" are applied, not only to things thought of in assertions, and to our conceptions of those things, but also to the words expressive of the concep- tions. In the sentence, " The rose is red," the words " rose " and "red" are subject and predicate. But whatever maybe the immediate application of these terms, they always refer- to that use which we make of our conceptions when we affirm or deny one thing of another. Two things which can be thought of as subject and predi- cate, and so as related to the faculty of judgment, may also be thought of simply as related to each other, and without refer- ence to our assertion about them. In that light they have been named substance and accident, these designations being thus employed in a very peculiar way. In logic, any entity whatever of which we conceive indepen- dently and about which we can make assertions — that is, any- thing whatever, as existing in predicable relations — is called a substance. In metaphysics we say that there are two kinds of substance, spirit and matter; in logic, spaces and times, powers and actions, changes, qualities, and relations are sub- stances. When we speak of " the height of the column," " the beauty of the picture," " the wisdom of the judge," the height, the beauty, and the wisdom are logical substances, no less oG THE MODALIST. [Chap. IV. than the column, the picture, and the judge ; for they may be subjects of predication. In some discussions a distinctive name for the logical sub- stance would prove advantageous ; therefore we may occasion- ally speak of it as a substantum. The term "accident," also, has a different meaning in this connection from what it has elsewhere, even in logic. For it is applicable to any predicate entity ivhatever as united in being to a subject entity. According to this sense the necessary prop- erties of a thing, and even its essential attributes, are acci- dents. It would be well if some other word could be found to express this very general idea. Possibly the term " ascript," or " ascriphim" would serve the purpose. Then, when think- ing objectively, the logician might speak of "substanta" and " ascripta " ; though more frequently, and because he con- stantly considers the relation of tilings to thought, he will speak of "subjects" and "predicates." Chap. V.] GENERAL AND INDIVIDUAL NOTIONS. 37 CHAPTER V. GENERAL AND INDIVIDUAL NOTIONS. 1. General notions. 2. The process of generalization. 3. The expres- sion of general conceptions. 4. Realism, Nominalism, and Conceptualising 4> Universals." 5. Individual, or numerical, difference. Specific difference. 6. Identity, numerical and specific. 7. The " principium individuationis." 8. "Individual" notions include (a) the singular, (6) the definite, (c) the. indefinite, (d) the class notion ; and are either unital or plural. 9. "All," distributively and collectively. 10. A restricted application of the term ' ' individual. ' ' 1. Ax important logical distinction divides notions into the individual and the general. A notion is general when it is applicable to any of a class of similars simply on account of their similarity, and when it does not include the thought either of one object or of more than one. In saying "man is mortal " we do not conceive either of one man or of more than one, but only think that general notion, "man," which is applicable either to one man or to many. Should we say, " a man is mortal," or " any man is mortal," the words " a man " or "any man" would express, not a general, but an indefinite individual notion; which, however, is closely allied to the general. 2. Every general conception originates in a process called " generalization " ; and this may be described as consisting of two steps, or stages. First, by an act of abstract thinking, we consider a number of objects so far as they are alike, with- drawing our thought from those respects in which they are unlike. This act is often preceded by a comparison of the objects, that is, by that process in which things are contem- plated together for the purpose of perceiving their points of similarity and dissimilarity. This comparison is not always needed, and is easily distinguished from that act of abstraction in which the work of generalization properly begins. 38 THE MODAL 1ST. [Chap. V. The second step is the more essential one. In it, taking one or more of the objects as a sample or samples of the class of similars, we drop from oar conception all thought of individual difference — all thought of number, whether of one or more than one ; the conception which remains is a general notion. Thus, having perceived the similarity between many pieces of gold, we easily think of those many pieces nnder one plural conception, or we consider one piece as a sample of all ; then, rejecting the element of individuality, we think and speak of " gold " in the general. Some say that, in generalization, we conceive of " the many as the one " and of " the similar as the same." This language is incorrect and misleading. In generalization we do not regard a number of different things as if they were one and the same, but we discard all reference either to diversity and similarity or to unity and plurality, and then think that one thought ivhich remains. 3. General notions, conceived independently, are expressed by common nouns, either without any addition or with the definite article prefixed. We say either " man/' " gold," " wis- dom," or "the pulpit," "the press," "the theatre." This use of the article indicates that the conception belongs to a class of objects well-known, and perhaps known in contrast with other classes somewhat resembling it, and, in so doing, it makes an addition to the general notion. For instance, "the pulpit," "the press," and "the theatre" are general designa- tions applicable to well-known agencies of instruction, which also may be compared with one another. Since it is always possible to conceive, in this distinctive way, of things in the general, a choice is given between the simpler and the more precise form of expression. Some languages prefer the one ; others the other. The above-mentioned modes of conveying general notions by the nse of nouns are the direct and proper methods. Other ways are employed, of which we shall speak presently, and which may be characterized as indirect and improper. 4. In using general thought and language we seem to be speaking about things, and we say that we are speaking about Chap. V.] GEN Eli AL AND INDIVIDUAL NOTIONS. 39 things. This fact is the chief foundation for a doctrine, once very prevalent, that there are real entities corresponding to ■•eneral notions as such. These entities were called " univer- sals," and were considered eternal patterns, which, in some way, prepared for, and contributed to, the existence of indi- vidual entities. Thus it was held that man and tree and life and death and virtue and vice are universals, and that each of these imparts its nature to a large class of individuals as they come into being. The advocates of this doctrine were styled Realists, because they asserted the reality of general objects; they were opposed by the Nominalists, who taught that there are no such things even as general conceptions, and that uni- versality belongs only to those names, or words, which may be applied to all the members of a class. A third doctrine, avoid- ing the extremes both of Nominalism and of Realism, has been called Conceptualism, because, while denying the reality of universals, it maintains that mankind constantly form and use general ideas. These ideas are not in their own nature general entities, but individual mental states. They are styled gen- eral because they are applicable to every member of a genus, or kind; for which reason they are also sometimes spoken of as universal notions. The prevalence of Realism in former times and its influence, even at the present day, have been greatly promoted by the preference of man's mind for positive thinking and belief ; we are naturally prone to believe that there are objects corre- sponding to our conceptions. This tendency favors Idealism, or the theory that the objects of the imagination really exist, as well as Realism. Language, too, falls in with both these delusions ; for the very same words sometimes express actual- istic conviction and refer to real objects, and sometimes express merely modes of thinking — imaginative or rational. Moreover, the fact that general conceptions and language are being continually apjilied to existing individuals with little notice on our part of any change in the method of our thought lends further aid to Realism. For the validity, or truthful- ness, of general statements lies wholly in their applicability. 5. Let us now turn to individual conceptions. These are 40 THE MOBALIST. [Chap. V. distinguished from general conceptions because they are always modified, by the thought of number, whereas a general notion excludes the qualification either of oneness or of plurality. An individual notion, such as "a dollar" or "dollars," always stands for what is, or may be, in strict literality, one thing or a number of things. Every such entity is called an individual because it does not admit of "logical division." The general notion "dollar," as representing a class of things, may be divided into "gold dollar," "silver dollar," and "paper dollar"; and, in like manner, every genus may be divided into its species. But an individual dollar cannot be separated, even in thought, into a number of dollars, or things having the same general nature with itself. When, in the descending process of division, we come to the individual, we can go no farther. The thought of individuality, like those of existence, non- existence, and entity, is simple and incapable of analytical definition. It is nearly identical with arithmetical " oneness " or " unity " ; though oneness, in addition to individuality, in- cludes the characteristic of quantity, and so sets forth every individual as a distinguishable quantum of entity. When, along with a first one, another unit presents itself, we immediately perceive the relation of " otherness " existing between them, and so, considering them as quanta, we say that there are two individuals. All conceptions of number start from this beginning ; hence the relation of otherness has been named numerical difference. Then, by a natural metonymy, that characteristic in every entity which is the basis of this otherness, is also called "difference." In other words, indi- viduality, as the ground of otherness, is styled "numerical difference." So every individual may be said not only to be numerically different from every other, but also to have numerical difference in itself. This difference is easily distinguished from that which exists between objects as being unlike each other. The latter is often called " diversity " ; and it is also styled " specific difference," because it is the ground of dividing entities into species, or kinds. Two rain-drops might be so absolutely Chap. V.] GENERAL AND INDIVIDUAL NOTIONS. 41 alike that they would differ only , numerically ; but there is specific as well as numerical difference between a rain-drop and a pebble. 6. Individual, or numerical, identity is that absence, or non- existence, of numerical difference which is perceived when any entity thought of once is compared with itself thought of again ; it is a necessary attribute of every individual entity ; it is what we mean by " sameness " in the strictest sense of the word. Specific identity, on the other hand, is merely the perfect similarity which exists between two or more entities so far as they are members of the same species or genus ; it is the " sameness " mentioned when we say that a thing may be done twice in the same way, or that all quadrupeds have the same bodily structure. 7. In scholastic times there was great discussion as to the "principiuni individuationis," or origin of individuality. The Kealists held that individuals result from the conjunction of " universal " forms with the otherwise " undifferentiated matter " of being. But such forms and such matter are merely philosophical imaginations. The truth is that everything which exists has both individuality and definiteness in every part of its nature ; these attributes begin and cease to exist as necessary elements of the entity itself. 8. Notions are styled individual because of the individuality of the things corresponding to them, and this equally whether a notion represents one thing or more than one. Hence in common language we might say that individual notions may be either singular or plural, but in logic we must say that this class of conceptions may be either unital or plural. For the term " singular," as we shall soon see, has a signification in logic quite different from that given to it in grammar, and therefore ought not to be used in logic in its grammatical sense. Such expressions as "a man," "men," "some men.'' "any man," "all men," "this man," "that man," "these men." "those men," "the man," "the men," " George," "the Georges," "President Cleveland," "his predecessors," "the presidents of the United States," represent individuals, and therefore set forth individual notions. 42 THE MODALIST. [Chap. V. But while ail miital and all plural conceptions are individual, and, under this title, are contrasted with general notions, the term " individual " is also employed sometimes in a more restricted application, as will be better understood after we consider four kinds, or classes, into which individual notions may be divided. The first of these comprises those conceptions which logi- cians characterize as singular, and in which we conceive of an object as having marks peculiar to it, or of more than one object as having marks peculiar to them severally. For such ideas are unique, or singular, in their composition. These thoughts are often expressed by proper names, as when we speak of Niagara, the St. Lawrence, Washington, Caesar, Lon- don, Paris ; but they are also indicated by the common noun with the definite article or a demonstrative pronoun, it being then understood that the objects are known by means of marks peculiar to each of them, and not merely by some general char- acter. If, in conversation respecting given persons or places, one should say, "I admire that man greatly," "I hope to visit those cities," the words, " that man," " those cities," would represent singular conceptions. This same mode of speech, however, would express another class of notions if the objects mentioned were conceived of as definitely related individuals of a certain kind, yet without thought of peculiarities belonging to each of them. One might speak of "the President who was lately inaugurated," or of "the lawyer who has the case in charge," thinking of each only in his character as president or as lawyer, and con- veying only this conception to others. Such ideas, because presenting objects as singularly related, though not as having peculiar natures, might be regarded as imperfectly singular. But they have been called "definite" individual notions, and, under this name, have been distinguished from singular no- tions ; that is, from those perfectly and internally singularized. A third species of notions to be mentioned here are the indefinite individual, or, more simply, the indefinite. Por we may form a thought of a member of a class, or of more mem- bers than one, without determining our conception to any par- Chap. V.] GENERAL AND INDIVIDUAL NOTIONS. 43 ticular member or members. Such notions are indicated by the indefinite article and by the adjectives "any," "some," "several," "many," and other expressions of like meaning. These conceptions, in themselves, are only the result of an indeterminate kind of thinking ; but they are often used as substitutes for general conceptions. For example, the state- ment " a man — or any man — is mortal " may replace " man is mortal," because what is true of any man, taken at random, may be said of man in general. In like manner, the state- ment, " Some men live to a great age," may serve instead of " Man may live to a great age," because the probability, or contingency, in regard to man in general arises from the fact known indeterminately regarding some. The fourth and last kind of individual conception is the class notion ; and this, like the others, may be either unital or plural. The unital class notion is indicated by the adjective " every " ; the plural, by " all." The word " every " empha- sizes the individuality of the things mentioned; the word " all," the universality of the statement about them : thus only we distinguish " every man must die " from " all men must die." In each case both individuality and universality are included in our thought. 9. For this reason it is important to notice a use of the adjective "all," which does not present the members of a class in their independent individuality, and therefore does not express a class notion. In saying "All the soldiers are brave men," we employ the word " all " distributively, as the logicians say, and consider the soldiers in their independent individuality. But should we say, " All the soldiers are the king's army," we would use "all" collectively, and would con- sider the soldiers, not merely as so many individuals, but as being united together ; for it is only as united that they are an army. The Latin language provides for these two senses of the adjective by the terms "omnes" and "cuncti," this last being a contraction of "conjuncti." Whenever the subject of a proposition is a class notion, it must always be understood distributively, because a class considered collectively is no longer, for the purposes of logic, a class, but only an individ- 44 THE MODALIST. [Chap. V. ual resulting from the union of individuals. "All men," as the family of Adam, or as the human race, are an individual, just as a congregation, a crew, a library, or a vocabulary is an individual. The class notion is often used instead of the general notion when we wish to assert something as necessarily, and there- fore universally, true respecting things of a given nature. When we say, "Every man is fallible," "All men are mortal," we give the form of individuality to the general truths that "man may be deceived," and that "man must die." The individualized assertion is an immediate consequence of the general truth, and has the advantage of being more closely related to actuality. 10. Having defined the four kinds of individual notions, we can now explain, in few words, that restricted application in which the term "individual" is sometimes used. It is that which contrasts the individual with the singular, and which therefore includes under the individual only the definite, the indefinite, and the class notions. For in all these we think of objects simply as individuals possessing a common nature. In this restricted sense individual conceptions are opposed to both singular and general conceptions. Chap. VI.] PREDICATIVE NOTIONS. 45 CHAPTER VI. PREDICATIVE NOTIONS. "The Ten Categories." 1. Subjective notions set forth, substanta. Are of primary and of secondary conception. 2. Improperly distinguished as "concrete and abstract." 3. The ten categories of predication. 4. Substance as predi- cate. 5. Quantity. 6. Quality. 7. Relation. 8. Place, time, posture, condition, action, passion. 9. The substantialization of ascripts. The chief logical significance of conceptions arises from the employment of them as the subjects and predicates of propo- sitions, but especially from their use as predicates. This involves many important modifications of thought. 1. All subjective notions set forth a " substantum," or logi- cal substance ; and their nature as substantal conceptions will be sufficiently illustrated if we divide them into those of primary and those of secondary conception ; or, more simply, into the primary and the secondary. For while everything, of whatever kind, may be conceived of as a logical substance and as a subject of predication, some forms of entity are thought of in this way at once, while others are first conceived of ascriptionally, or predicationally, and only afterwards are treated as substanta. For instance, we think primarily of bodies and spirits — that is, of substances in the metaphysical sense — as substanta, and of the powers inherent in those substances as qualities to be predicated of them. Hence we say, "The scholar is wise," "The horse is strong." In like manner we conceive of a space as a substantum and of its size as an ascriptum, and say, " The room is large." Often, however, after some form of entity has been conceived of in the ascrip- tional way, we are led to think of it independently, and find ourselves doing so even while retaining in our minds a refer- 46 THE MOBALIST. [Chap. VI. ence to our primary mode of thinking. In this way subjective notions of secondary conception arise. Thus from the predi- cates, or ascripta, in the cases given above, we may form the substantal notions " wisdom," " strength," and " largeness," or "magnitude." 2. The foregoing distinction is commonly expressed by the division of nouns, or of substantal notions, into the " concrete" and the "abstract." But these terms, though they indicate a difference, throw little light upon its nature. For the so- called "concrete" notion, if it be a general one — as "man," "animal," "matter," "spirit" — is formed by abstraction ; and the so-called "abstract" notion, if it be complicated, involves a synthesis, or concretion, of ideas. For example, by synthesis we conceive of guiltiness as " a liability to penalty because of an infraction of moral law." Therefore, in a very natural sense, substantal notions of primary conception may be ab- stract, and those of secondary conception, concrete. This infelicity, arising from a conventional application of terms, illustrates a difficulty, which cannot always be avoided, in the expression of philosophical truth. 3. We now turn to the discussion of predicative notions. The earliest classification of these is one given by Aristotle. He says, "The Categories are ten in number, what a thing is (ovata), quantity (iroaov), quality (ttoZov), relation (?rpos t/), Avhere (ttov), when (-ttotc), position (kuo-Ooll), possession (eXeiv), passion (7rao-xeiv), action (7rotav)." The term Kar-qyopia originally meant an assertion, but here signifies a generic class, or summum genus, of things assertible. For, as Aris- totle says, " Every proposition sets forth either ' what a thing is ' or some other category." This enumeration of predicative notions cannot be rejected as incorrect, yet is not closely connected with the laws of con- viction. It belongs to a primary stage of logical theory, and is chiefly valuable as bringing before us, for further considera- tion, every form of ascriptional thought. 4. The first category, "what a thing is," was also named by Aristotle oiWa, which term the scholastics translated by " sub- stantia," or substance. The teachings of logicians regarding Chap. VI.] PREDICATIVE NOTIONS. 47 this substance are confusing in the extreme, but we will arrive at its true nature if we remember that it is the form of predi- cation expressed by a noun — that is, by the " noun substan- tive," as this was formerly distinguished by grammarians from the "noun adjective." In saying, "The man is a mer- chant," "'Honesty is a virtue," the substance "merchant" is predicated of man, and the substance "virtue" of honesty. But while the term " substance " here clearly means a sub- stantum, or logical substance, we cannot but observe that the application of it to the predicate of a proposition is accom- panied by a modification of meaning. The subject of a propo- sition must always be conceived of independently before we can rightly say anything about it; therefore whatever is fit to be the subject of an assertion is a substantum in the full sense of the word. But no such independence of conception belongs to any predicative thought. The first of the ten cate- gories may appear to have it, because this category originates in substantal conception, and is expressed by a noun. But a noun used predicatively is preceded by a mental addition which destroys the independence of its conception. For it then sets forth the predicate-substantum either as identical, or as not identical, with the subject-substantum ; and this is quite a dif- ferent thing from setting forth a substantum simply. When we say that "the man is a thief," or that "the man is not a thief," we assert that the man is, or that he is not, identical (numerically) with a thief; we do not say merely that the man exists, and that the thief exists. Locke, and Leibnitz after him, perceived this mental addition, and hence, in their writings, the category of substance gives place to that of " identity and difference." There is, however, some advan- tage in retaining the old name. For the work of this form of predication is not completed in the assertion of identity or difference. Were that so, the category of " substance " would be only a specific form of the category of "relation." The j true end of the predication of substance is to convey the infor- mation that a subject, already known as having one nature or aspect, has, or has not, another also. The statement, "The man is a thief," asserts that a subject known as a human -V 48 THE MODALIST. [Chap. VI. being has the character of a thief; the corresponding negative statement denies that he has that character. In short, numer- ical identity or difference is here used to set forth the exist- ence, or the non-existence, of a nature, or character, as belong- ing to a subject. Aristotle indicates this when he says that the first category shows "what a thing is," and in the name ovaia ; for ova-La primarily signifies nature, or essence. The secondary application of the term " substance " or " sub- stantum," which we have now considered, gives rise to a secondary use of the corresponding term " ascript " or " ascrip- tum." Strictly and primarily every category of predication is an ascriptum, and, under this name, is contrasted with the substantum, or subject, to which it belongs. But when, in the classification and discussion of predications, we find one category called " substance," we naturally restrict the term " ascript " to the remaining categories, and thereupon we divide predicate notions into two comprehensive classes, the substantal and the ascriptional. Such language is scarcely avoidable when one may be speaking concerning the different kinds of predi- cation, but it need not produce confusion, if we exercise care. 5. The second category — quantity — is used in asserting that something exists in a given degree or amount. In say- ing, "The road is ten miles long; the house is one hundred years old," we ascribe a definite age to the house and a definite length to the road ; referring in each case to an appropriate unit of measure. And even in saying, " The house is old ; the- road is long," there is a tacit comparison with some standard. It is only this measured quantity that calls for a specific cate- gory. Quantity, simply as quantity, belongs to and character- izes every form of entity. It might be regarded as a kind of universal quality. As it may always be assumed, the predica- tion of quantity, simply as quantity, seldom takes place. 6. The category of quality sets forth whatever does or may permanently mark an entity, and so be the ground of its clas- sification with other entities similarly marked. This category is primarily expressed by the adjective, as when we say, "The man is wise; the table is round; the business is urgent." Ordinarily and properly the characterizing entity is attached Ciiaf. VI.] PREDICATIVE NOTIONS. 49 to the subject permanently ; yet this condition may be dis- pensed with, provided only the mark be permanently con- nected with the subject in our conception. A dethroned king may still be thought of as a royal person ; the general who has concluded a war successfully may be regarded for life as a vic- torious commander. In fact, the category of quality, like that of substance, is all-embracing in its power to use material ; for any mode or combination of entity may be so used as to char- acterize the subject to which it is related. 7. The fourth category assumes that there are two or more entities, and then simply asserts (or denies) the existence of a relation between them. Thus setting forth the relation of cause and effect, we say, indifferently, "Fire is the cause of heat," or, "Heat is the effect of fire." The linguistic form of these statements belongs to the category of substance, yet they do not predicate substance, because their aim is simply to assert relation, and not nature, or kind. We may also express relation by saying, "Fire produces heat, or is productive of heat," provided our intention is not to assert that heat is being produced, or that fire can produce it, but the fact that heat is produced by fire. Eelations are primarily expressed by prepositions, but are often set forth in this secondary way by nouns, or verbs, or adjectives. In speaking of relations as existing betiveen entities, our lan- guage is based on the circumstance that the conception of a relation comes intermediately between those of the relata. In strict truth, however, a relation is not an intermediate entity, but is composed of two parts, or relationships, one of which resides in each of the things related. This doubleness, or plurality, appears in the relation of husband and wife, of agent and instrument, of cause and effect, of equals, of un- equals, of the container and the contained, and in all other relations. 8. The next category is that of place. Some have objected to this category that it is merely a specific mode of the cate- gory of relation. But it is, or at least may be, more than this. "The king lives in a marble palace," sets forth both that there is a marble palace and that the king lives in it. In like man- 50 THE MODALIST. [Chap. VI ner, a relation and something more are expressed by the cate- gory of "time." "The marriage took place last Thursday/' indicates both that an event occurred at a certain date, and that a certain time has elapsed since that date. The categories of "position" and "possession" might better be named "posture" and "condition." They also have a doubleness. To say, " John sits," or, " John is resolved," sets forth a posture of body or of mind in which the parts of the body or the thoughts of the mind are adjusted to each other, and are, moreover, externally related. For one sits on some seat, and is resolved on some conduct. In the same way the sentence, "John is well, and John is wealthy," indicates first the existence of health and wealth, and then the con- dition in which John finds himself as the possessor of these blessings. Finally, the categories of "action" and "passion" both set forth the operation of some power, but the one in relation to the agent or instrument, the other in relation to the thing acted upon. Therefore these, also, are duplex. 9. Having familiarized ourselves with the natural forms of predicative thought, as presented in the "ten categories," and having seen that predicative conceptions may be divided into two general classes, the substantal and the ascriptional, we must not fail to note, in conclusion, an important point. This is that either the substantal or the ascriptional mode of predi- cative conception may take the place of the other. Especially we must understand how a statement with an ascriptional predicate may, by a slight addition, be changed into an equivalent statement with a substantal predicate ; for a change of this kind often takes place necessarily in the course of our reasonings. When we say, " Some men are wise ; therefore some wise beings are men," this reasoning is valid only because we replace the ascriptional proposition, " Some men are wise," by the substantal proposition, " Some men are wise beings." So, in the syllogism " Man is rational ; every rational being is accountable; therefore man is an accountable being," the argument would not be conclusive if it were not lawful to replace the ascriptional term, "rational," by the substantal Chap. VI. ] PREDICATIVE NOTIONS. 51 term, " rational being." Moreover, in the final proposition of this syllogism we have found ourselves at liberty to adopt the substantal form of assertion, though the ascriptional form might have been retained. The thought of the " being," or " entity," which is added in these modifications of conceptions is that of the substantum to which the ascript belongs. We have the right to make this addition, because, when any subject has an ascriptional predi- cate, it may, of course, be identified with itself as a substantum having that ascript, and, when it has not a given ascript, we can say that it is not a substantum which has it. This process might be called the substantialization ofascripts. The reverse process, of de-substantialization, consists in dropping the thought of substance. Instead of saying, " Man is a mortal," we say, " Man is mortal." This change occurs frequently, but is of less logical consequence than the other. 52 THE MODALIST. [Chap. VII. CHAPTER VII. PREDICATIVE NOTIONS. "The Five Predicables." 1. Defined and enumerated. 2. Genus and species here signify natures, not classes. 3. Species, essence, definition, and nature, distinguished. 4. Difference, as a predicate, is not the relation, but the ground of it. 5. Property. Generic and specific. Often becomes attribute. 6. Accident. Here opposed to essence and property, not to substance or subject or being. Separable as regards the nature ; separable or inseparable as regards the object. 7. The " predicables ' ' are used only when logical connection is conceived exactly. 8. Attributes. Adjuncts. Qualities. 1. A second division of predicative notions given by Aris- totle is known as " the five predicables." This classifies all the possible predicates of any subject, not with reference to their own differences, as in the categories, but according to their exact connection with the nature of the subject. The distinctions thus presented are quite important ; because the force of a proposi- tion, either as setting forth truth or as a premise in argument, varies with the mode in which the predicate is logically related to the subject, or, as Aristotle would say, with the mode of the inherency of the predicate in the subject. Logicians formerly taught that every predication used in reasoning not only conforms to one of the. ten categories, but also to one of the five ■ predicables — in other words, that it not only asserts substance, quantity, quality, relation, or something else, of a subject, but also presents the predicate, employed as related to the nature of the subject in one or other of five ways. They expressed this by saying that every proposition sets forth either the genus, th-e species, the differ- ence, the property, or the accident, of a thing ; and they held that all reasoning arises in connection with these last-men- Chap. VII. ] PREDICATIVE NOTIONS. 53 tioned modes of apprehension; which, therefore, by way of pre-eminence, were called the predicables. These views are extreme. Predications, and reasonings by means of them, may take place without reference to any predicable. But it is true that these modifications of assertive thought are often employed in our more thorough thinkings, and that they have an important function in the apprehension and statement of truth. 2. The first predicable is genus (yeVos). This term frequently signifies a class of similars in which other classes of similars, differing from one another, are comprehended. According to this sense the genus, " forest-tree," comprehends oaks, beeches, maples, elms, and so on. In the present connection genus means, not the generic class, but that nature which belongs to every member of it. When we say that the oak is a forest- tree, and think of it as having the nature of all forest-trees, and distinguish this nature from the peculiarities of the oak, we predicate genus of it. Since it is part, though not all, of our conception of the nature of the oak that it is a forest-tree, the predication of genus does not, in this case, add to our knowledge of what an oak is, but only makes a part of our knowledge explicit. If, however, we were ignorant concerning the nature of an oak, or of anything else, the predication of genus would enlarge our information, and would not be merely explicative of a con- ception already entertained. The predication of " species " or of " difference " may, also, be employed in either of these ways. The question may be asked, " Is the nature asserted in the predication of genus individual or general ? " We reply that it is either, according to the character of the subject. The predicate of a general subject is necessarily general, and that of an individual subject individual. Should we speak in gen- eral and say, " The oak is a deciduous tree," all our thought would be general ; a similar assertion made about this or that oak would be individualized throughout. We do, indeed, say that the individual tree has a generic nature, but this use of language is secondary and metonymical. It does not mean 54 THE MODALIST. [Chap. VII. that the tree has literally a generic nature, or a general nature of any description, but only that part of the individual nature corresponds to a generic conception. The second predicable is designated "species" (eF8o?). This term often signifies a subordinate class of similars, but, in the present connection, it means the nature which characterizes such a class. We say that, while man is, according to genus, an animal, he is, according to species, the rational animal. Thus it appears that " species " comprehends " genus " together with a " difference," by which the given species is distinguished from other species of the same general kind. 3. The predication of species, however, is not the mere assertion that a subject has a certain distinctive nature united with a generic nature. It implies that the nature predicated {the species) is the ivhole nature which the subject has in common with other entities, so far as that nature may be conceived of by us. It would not give the species of horse to say that the horse is a quadrupedal mammal. This would only present a genus, though it would be a subordinate genus formed by the union of the higher nature " mammal " with the peculiarities of the specific nature " quadruped." To give the species, we must add those particulars regarding form and motion, parts and uses, which complete the conception "horse," as enter- tained by us. It is not, indeed, necessary for the purposes of definite and conclusive thinking that we should give all the particulars that enter into this conception. Very often one or two or three of the distinguishing features are sufficient, as repre- sentatives of all the specific peculiarities ; nevertheless it remains true that the predication of species is the predication of the whole nature conceived of. This was taught by Aristotle when he said that to give the species is to give the definition of a thing ; and it is involved in the doctrine that " species " and " essence " are identical, or nearly so. The predication of species and that of essence pre- sent exactly the same truth ; they differ only in that the former 4. directs the mind to the substantal form of conception, while the latter dwells on the attributal, or qualitative. To say that Chap. VII.] PREDICATIVE NOTIONS. 55 man is the rational animal (giving this predicate its full sub- stantal force) asserts species ; to say that man is rational and animal, or that he has a rational and an animal nature, gives his essence. Either form of statement, however, may be said to set forth either essence or species. Let us note here that, in logic, the term " nature " is closely related to "essence," and has precisely the same meaning whenever we refer to the whole nature, or constitution, of a subject. But we may speak of a generic nature, as when we say that the oak in its generic nature is a forest-tree ; while we do not speak of a generic essence. A nature, therefore, may be only part of an essence. 4. The third predicable, "difference," has been designated also "specific difference," and is thus opposed to "numerical difference." Its office is to present, not the relation of differ- ence between different species, but the foundation of this rela- tion; namely, that peculiarity, or collection of peculiarities, which belongs to a species and distinguishes it from others in the same genus. Among plane figures bounded by curved lines the "difference" of a circle is that every part of the circumference is equally distant from a point within ; and the " difference " of man among animals is "rationality." Aristotle says that genus and difference are interchangeable and identical. In a certain sense this is true. We may think first of the genus " animal," and then of the difference " rational," which distinguishes one species of animal ; or we may think first of the genus " rational," and then of the dif- ference "animal," which distinguishes one kind of rational beings. In like manner, a circle and a sphere have the generic character that in each every part of the boundary is equally distant from a point within, the differences of these figures being that the one is solid and the other plane ; but, were circle compared with square, or sphere with cube, in either case, the genus given above would become difference and the difference genus. Nevertheless, though what is now genus may become differ- ence, and what is now difference may become genus, genus and difference are not the same ; nor is the predication of the one 56 THE MOBALIST. [Chap. VII. *}- the predication of the other. A nature is genus as the founda- tion of resemblance between species ; it is difference as the foundation of diversity ; so that the same nature cannot be both genus and difference in reference to the same two specific classes. Genus and difference as such are not interchangeable with each other, but they may exist together for the same reason that two men, who are related as creditor and debtor, may, in their relations severally to two other men, be debtor and creditor. The " specific difference," now under consideration, is easily distinguished from that " individual difference " which belongs to entities simply as such, and whether they differ in nature or not. Moreover, when two individuals, being of different kinds, are said each to have its specific difference, this differ- ence is a part of the individual and is itself an individual thing. Yet it is not, on this account, what we call "individual" (or numerical) difference. To assert this latter is merely to say that one thing is not another ; but to assert the former is to say that one thing is unlike another. 5. The fourth predicable is named "property," this term being thus used in a strict and technical sense. A property is that which is not included in an essence, or species, but which yet is necessarily, and therefore universally, connected with it. Thus it is the property of man to be a religious being, and of a plane triangle to have its three angles equal to two right angles. Property being inseparable from essence, our conception of an essence may easily be enlarged by incorporating with it that of some property ; upon which addition property ceases to be property and becomes attribute — that is, an essential characteristic. For this reason, and because our conceptions frequently vary in comprehensiveness, it may sometimes be difficult to say whether some necessary ascript be a property or an attribute. For example, since every quadrilateral figure is quadrangular too, one might ask, "Is it a part of the essence, or only a property, of such a figure to have four angles ? " The answer is that this is either a property or an attribute, according to the manner of our conception. Mostly, Chap. VII.] PREDICATIVE NOTIONS. 57 for the sake of simplicity, the mind selects just so many lead- ing and permanent marks as are sufficient to distinguish a class of beings from all others, and excludes all remaining ascripts from its idea of essence. This is especially the case in the forming of definitions. Yet it is not invariably so. In conceiving of a triangle we think of three angles as well as of three sides, and recognize the angles as entering into the essence of a triangle, though they are inseparably involved with the sides. The only way to determine whether a neces- sary characteristic be a property, is to ascertain whether it be something additional to our conception of the object. Accord- ingly, we say that it is the property of a circle to contain a greater extent of surface for the length of its boundary than any other plane figure, and of man to be a member of political society. While property is always attached to an essence, or species, this connection may immediately relate either to that generic part which the species has in common with other species, or to some peculiarity in the "difference" of that one species. Hence properties are of two sorts, the generic and the specific, or differential. Mortality is a generic property of man, as an animal ; the power of using language is a specific property of man, as the rational animal. 6. The fifth, and last, predicable is "accident." It is that which pertains to an object, or entity, yet which is not neces- sarily connected with the nature of the object. The faculty of language and the power of laughter are properties of man, while the act of laughing and that of speaking are accidents ; because a man is not always laughing and speaking. Moreover, we must rank with accidents any ascript concern- ing which we cannot tell whether or not it is necessarily in- volved with the nature, or essence, of the subject; although such an ascript is not an accident in the full and proper sense of the term. For it resembles accident, and it is unlike prop- erty and attribute, in this important respect, that it cannot be inferred from the mere existence of the subject. But, in the full sense of the word, that only is an accident which is known to be separable from a nature, or essence. 58 THE MODALIST. [Chap. VII. This separability, however, means only that an accident is not a necessary consequent or concomitant of the nature of the subject. It does not mean that every accident is insepa- rable from the object which may have the given nature. With respect to this object an accident may be either separable or inseparable. It was accidental to Voltaire, considered as a man or as a genius, to be born in France ; yet this fact was inseparable from the man. It was, also, an inseparable acci- dent of Socrates, as the father of Grecian philosophy, to be a statuary. So, on the supposition that there are no human beings except those born on this planet, it would be an insepa- rable accident of man to be a native of the earth ; for, so far as their nature is concerned, human beings might be born elsewhere. The inseparable ascript of a class of things, how- ever, is seldom conceived of as an accident. It is found to be connected in some way with the nature of the subject, and is regarded as a property. We must not leave this fifth predicable without noting how the term "accident," as here opposed to "genus," "difference," "species," and "property," is much more limited in applica- tion than when it is opposed to "substance," or "being." The accidents of a thing simply as an entity include everything whatever that can be predicated of it. The reason for this is, that an entity, simply as such, is not necessarily one kind of thing rather than another, so that every addition to our thought of it is, in a sense, accidental. This wide signification of "accident" — as equivalent to "ascript"' — is easily distin- guished from its ordinary logical meaning, though the two are by no means disconnected. In discussing the five predicables we have used objective rather than subjective language, following the ancient manner of speaking. We have mentioned genus, species, difference, property, and accident, rather than generic, specific, differen- tial, proprietal, and accidental, conceptions. In the primary and literal sense of words it is not things, but notions, as representative of things, that are predicable. Yet the ancient mode of expression serves to remind us that the logician always considers thought objectively, even while he may be Chap. VII.] PREDICATIVE NOTIONS. 59 studying our varying conceptions of the same thing or kind of thing. For these vary only because we contemplate an object now in one aspect and in one set of connections, and now in another aspect and in another set of connections. 7. The classification of predicative conceptions under the five predicables applies only to those cases in which the exact logical connection of the predicate with the nature of the subject is part of our thought. We can, and often do, make assertions without determining whether the predicate be a genus, or a species, or a difference, or a property, or an acci- dent. The doctrine of the predicables, therefore, is not so widely applicable as that of the categories. Every " predicable " presupposes one of the categories, and then makes an addition to it. For it presents some ascript, not simply, but as related in some one of five ways to the nature of the subject. The predicables, therefore, are of the same radical nature with the category of relation ; yet they are properly discussed by themselves on account of their func- tional connection with all the categories, and because of their logical importance. Evidently the end and use of these complex modes of con- ception is to state the manner in which any ascript is logically related to the nature of a subject ; for they always set forth something, either as the whole essence of a substantum, or as included in the essence, or as attached to it. The predicables are those forms of predicative thought which we naturally employ after obtaining thorough information regarding the logical relations of a subject ; while the categories are those more simple and primary forms of conception by which truth, whether individual or general, is set forth without reference to the logical connection of things. 8. Logicians speak only of five predicables ; yet some other conceptions — especially "attribute" and "adjunct" — are of the same general character. Anything included in either genus or difference — that is, any part of the species, or essence — is, technically speaking, an attribute. Attributes, therefore, are either generic or differential. A nature consists of the sum of its attributes. Whatever is connected with a nature 60 THE MOBALIST. [Chap. VII. without being a part of it, is an adjunct. Every adjunct, of course, is either a property or an accident. " Quality " is also a kind of predicable, and nearly the same as attribute. It is properly that mode of conception which sets forth " what kind of a thing " the subject may be ; that is, which assigns to the subject a generic (or a differential) as distinguished from a specific, nature. But, with a somewhat wider use of language, whatever does or may permanently char- acterize is called a quality. Hence properties sometimes receive this name, because by enlarging our conception they may be taken within the nature. When quality is used to set forth nature or character simply, and without reference to logical connections and classifications, it is a "category," not a " predicable." We have seen that, for most logical purposes, the categories may be reduced to two classes, — the substantal and the ascrip- tional, — and that these may be made to replace one another in assertions. In accordance with this, we now add that any one of the predicables may be expressed by either substance or ascript. We may say either, "John is a man," or "is human"; "is rational," or "is a rational being"; "is a biped," or " has two legs " ; " is a European," or " was born in Europe " ; " wrote that note," or " was the writer of that note," intending by our language to set forth either genus, difference, property, or accident. We more naturally express genus and species substantally, and the other predicables ascriptionally ; but either may be expressed either way. Chap. VIII. ] THE DEFINITION OF NOTIONS. 61 CHAPTER VIII. THE DEFINITION OE NOTIONS. 1. Clearness and distinctness radically the same. Definition and divi- sion defined. 2. Definitions are either essential or accidental. 3. Some, necessarily, are accidental, or relational. 4. Essential definitions are either exhaustive or selective ; 5. Scholastic or notational ; 6. Adequate or inadequate. 7. Nominal and real definitions. 8. The essence of a thing is either (a) its whole form, or constitution, (5) its form so far as conceived of by us, or (c) the prominent and important part of its constitution. 9. " Substantial forms." Singular essences. 1. Clearness and distinctness shonld not be contrasted as radically different. Distinctness is simply clearness consid- ered as enabling ns to make correct distinctions. Whenever a thing is clear, it is also therein distinct. Sometimes, however, we say that an object is apprehended clearly when its several parts and boundaries are perceived ; and that it is apprehended distinctly when these are exactly and perfectly perceived. In this contrast distinctness is the highest attainable degree of clearness. Definition and division are processes whose chief aim is to Tender our conceptions as clear, or distinct, as possible. Each contemplates every object as a whole ; but definition regards in turn the several elements of an object, as they are severally related, and then presents these in v(n<; ovSev fxanqv ttoiovvlv) , and Aristotle's conception of the final cause (to ov-cvcko.), simply formulate a general conviction of mankind in regard to the origin of the phenomena of the Universe. For the Peripatetic division of causes, or rather of causal conditions, into the material, the formal, the efficient, and the final, is not really a theory of causation in the abstract, but a cosmogony. It analyzes the causal antecedent of the Universe into four constituents — one of these being design. Chap. XVI.] INDUCTIVE REASONING. 145 Moreover, it is worthy of remark that Aristotle did not con- sider the world to be itself capable of thinking or deliberation ; for, he says, that would be " as if the art of ship-building were in the timber," or as if any machine had the intelligence to construct itself. Indeed, the fact that Nature, notwithstand- ing her wonderful excellence, sometimes produces abortions and monstrosities, indicates an imperfection which probably is inherent in every created agency. In herself Nature is only a marvellous system of powers and laws which operates throughout the Universe, and which, though unintelligent, may be termed intellectual, because it is the production and the reflection of creative thought. By some philosophers inquiry after final causes has been condemned as fruitless. This objection applies only to cases in which conjectures are made without adequate support in existing analogies, and are rested upon as probable without experimental evidence. Mere theorizing respecting the work for which some arrangement or agency is designed, when separated from the observation and investigation of facts, has originated many strange explanations of natural phenomena ; and is worse than fruitless. But hypotheses formed after the analogy of known adaptations, and followed by investigation, have often led to the discovery of truth. Harvey, observing valves in the veins and in the heart, first conjectured, and then discovered, the circulation of the blood. Physiologists discuss every bodily part in the light of some end for which they suppose it to be intended ; and they declare that every part is an organ, with a function of its own. 11. Let us now glance at those canons of experimental enquiry, whereby hypotheses are tested, and which are used chiefly in the fourth, or critical, stage of inductive reasoning. For rules are not needed when every causal condition of a sequence is clearly perceptible, but only when the exact nature of the cause is in doubt. This is especially the case when the cause of some effect is involved in a confusing complex of circumstances ; then a work of determination and of elimi- nation becomes necessary. A less or a greater number of directions may be given for this work according to the com- 146 THE MODALIST. [Chap. XVI. prehensiveness of each rule, but the following five canons dis- cussed by Mr. J. S. Mill, under the head of "methods of induction," are certainly such as every careful thinker must use. They are all outgrowths of the radical law of causational sequence. The first rule is that which governs the " method of agree- ment." When two or more cases of sequence, which have the same consequent, have only one circumstance, or set of cir- cumstances, in common, the antecedent of the consequent is to be sought for in their common part. If a certain fever prevail in two or more localities, in both of which the air is tainted from decaying vegetation, but which differ in all other respects, we say that malaria is the cause, or an essential part of the cause, of the fever. If cucumbers thrive whenever they are planted in rich mellow earth, and enjoy an abundance of warmth, light, and moisture, and if they call for these con- ditions only, we say that we have found the right way for the cultivation of cucumbers. The second rule controls the ''method of difference" If various cases which produce a sequence differ, severally, from other cases which do not produce it, only in the presence of a certain antecedent which is uniformly absent when the sequence is absent, that antecedent is, wholly, or partly, the cause of the sequence. If, on the other hand, a supposed cause be found present in cases where the sequence does not occur, as well as in cases in which it does occur, it cannot be a true and sufficient cause. Since dew falls always on clear nights, but never when the sky is clouded, we ascribe the formation of dew to the cooling of the surface of the earth by radiation. Since all living things breathe the air, and cease to live when prevented from breathing it, we say that air is essential to animal life. The method of difference presup- poses the method of agreement, and is built on it. It is appli- cable whenever a given consequent fails to occur, and this failure is either in accordance with our expectation or in opposition to it. If the failure take place in accordance with our expectation and along with the absence of the supposed antecedent, our theory is confirmed ; but if it fail in opposition Chap. XVI.] INDUCTIVE REASONING. 147 to our expectation and notwithstanding the occurrence of the supposed antecedent, our theory must be rejected. If a cer- tain compound, expected to explode on ignition, will not explode, our conception of the antecedent is evidently wrong. After learning this, if we still desire to find a new explosive mixture, we must amend our hypothesis, and renew our experi- ments and our examination of instances. Sometimes a single instance of a sequence, being distinct and free from all complication, is sufficient to determine a law. Yet oftener a pair of experiments, or observations, one using an antecedent and the other leaving it out, are sufficient. In such cases we can scarcely be said to need or to follow either the method of agreement or that of difference; we simply decide at once according to the principles of the law of causa- tion. But when elimination and determination are necessary, we are greatly helped by analyzing a number of instances. The third rule sets forth the indirect method of difference. Sometimes no cases of the non-occurrence of a consequent can be found which differ from cases of its occurrence merely in the absence of some antecedent. If then we only can find cases of the non-occurrence, which are more or less similar to the cases of the occurrence except as to the presence of any similar antecedent, we may consider that antecedent to be wholly, or partly, the true cause. No species of quadruped, or other animal that is warm-blooded, differs from the ordinary quadruped, or other animal, in being cold-blooded. But we can find animals that are cold-blooded, and we may reason from their constitution by a kind of negative analogy. Thus, says Mr. Mill, "If it be true that all animals which have a well- developed respiratory system, and therefore aerate the blood perfectly, agree in being warm-blooded, wliile those whose res- piratory system is imperfect do not maintain a temperature much exceeding that of the surrounding medium, we may argue from this two-fold experience, that the change which takes place in the blood by respiration, is the cause of animal heat." This third method is simply a special form of the method of difference; and is guided by a reference to the analogies of Nature. 148 THE MODALIST. [Chap. XVI. The fourth rule presents what Mr. Mill calls the " method of residues" If we subduct from any complex of phenomena such parts as are known to be the effects of certain antece- dents, the cause of the residual phenomenon, or phenomena, is to be found in the residue of the antecedents. This method endeavors to isolate a case mentally which cannot be isolated in fact. The principle of it is that by which we find the weight of a load of hay in subtracting the weight of the wagon from that of the wagon and the load. But by the observation of residues we determine separate kinds of causes or of opera- tions, as well as the respective shares which two or more incre- ments of the same cause may have in producing a result. Newton, wishing to know how far an ivory ball suspended by a cord and allowed to strike a hard surface, would rebound by the force of its own elasticity, first of all caused it to swing freely in the air, and measured the loss of motion produced by the resistance of the air during each vibration. Then adding to the length of the rebound the loss of distance incurred in the half- vibration of equal length, he obtained the entire effect of the elasticity. The observation by astronomers that the planet Uranus was sometimes retarded and sometimes accel- erated in its orbital course, so as not to be in its calculated positions, led to the discovery of the planet Neptune, as the cause of the aberrations. So also the fact that comets gener- ally do not return from their distant journeys till after the expiration of the predicted time, has suggested the existence of some cosmic ether, or other medium, capable of obstructing the motion of such bodies. The fifth rule explains the " method of concomitant 'varia- tions" If a phenomenon which is either continuous or recur- rent, varies in a manner to correspond with the variations of another phenomenon, these phenomena are connected through some law of causational sequence. The mere concomitance of the variations does not indicate the specific mode in which the phenomena are related to each other. It does not, for example, show which is cause and which effect, or whether both are effects of the same cause ; but the nature of the specific relation is com- monly easily determined. When quicksilver was observed to Chap. XVI.] INDUCTIVE REASONING. 149 expand in proportion to the heat about it, no one hesitated to believe that heat is the cause of the expansion. So friction is proved to be the cause of heat, when it is found that heat is evolved exactly in proportion to the amount of force expended in rubbing one substance against another. The law of concomitant variations is a specific application of the principle that every cause and its effect mutually cor- respond — the presence or absence of the one involving the presence or absence of the other. But it enables us to inter- pret a peculiar class of cases, in which the cause never ceases from operation ; and in which, therefore, the ordinary method of difference is not available. The fact that the tides follow the moon, and that the high tides attend the conjunction of sun and moon, indicates that the rising and falling of the ocean results from the attraction of these bodies. The seasons evidently result from the sun's changes in latitude. A corre- spondence in the periodical prevalence of " magnetic storms," of the Aurora Borealis, and of solar spots, with certain recur- rent positions of the planets Jupiter, Saturn, Venus and Mars, has led some to think that these planets are the prime movers in a remarkable set of meteoric phenomena. 150 THE MODALIST. [Chap. XVIL CHAPTER XVIL HYPOTHETICAL AND DISJUNCTIVE REASONINGS. 1. Inference is also actualistic or hypothetical. 2. The so-called hypo- thetical syllogism is translative. 3. The law of logical transfer. 4. Trans- lative inference is either express or implicit. 5. The simple hypothetical, or translative, syllogism has two modes : (a) the ponendo ponens, (6) the ■tollendo tollens. Both explained. 6. Logical disjunction is a complicated style of hypothetical inference founded on either (a) contrariety or (&) contradiction. 7. Contrariety explained. 8. It is the ground of the weak disjunctive syllogism; which has one mode, the ponendo tollens. 9. Contradiction is either categorical or consequential. 10. Two contraries become contradictories when the non-reality of either involves the reality of the other. 11. Only a pair, not a series, of things can be mutually contradictory. 12. The strong disjunctive syllogism has two modes, the ponendo tollens and the tollendo ponens. 13. The dilemma is an hypo- thetical syllogism, with a plural "major" and a disjunctive "minor." It is either (a) constructive or destructive, (If) simple or complex. 1. With reference to the mode of its sequence, inference is either apodeictic or problematic ; with reference to its depend- ence on previous perceptions of logical connection, it is either orthologic or homologic ; and with reference to the character of the conviction produced, it is either actualistic or hypothet- ical. Actualistic inference is founded on what is known or be- lieved to be fact ; and its consequent is accepted as fact, either absolutely or possibly or probably, according to the modality of the sequence. Hypothetical inference rests on mere supposi- tion, and asserts only what would certainly or possibly or prob- ably be fact provided the antecedent were a reality. Every hypothetical proposition is illative, or inferential, in its nature. This is especially evident in the case of fully expressed hypotheticals. "If chlorine be a gas, it is elastic," asserts that a certain consequent must be true if a certain antecedent be true. The only difference between an hypothet- Chap. XVIL] HYPOTHETICAL SEASONING. 151 ical proposition and an hypothetical inference is that the for- mer emphasizes the consequent rather than the antecedent;, while the inference dwells equally on both. 2. That form of reasoning, however, which logicians style the "hypothetical syllogism," should not be confounded with mere hypothetical inference. It is really an hypothetical inference with an addition which has the effect of depriving the process as a ivhole of its hypothetical character. When the statement, " If chlorine be a gas, it is elastic," is followed by the assertion, " chlorine is a gas," the object of this addition is to assert the reality of the antecedent, and thereby to change the character of the inference from hypothetical to actualis- tic. This appears in the conclusion, when we assert, for a fact, that "chlorine is elastic." In consequence of the application of the term " hypotheti- cal " to syllogisms of this kind, some ambiguity arises when this adjective is used with reference to inferences generally. Were a special name desired for inferences and arguments purely hypothetical and unchanged by actualistic addition, they might be distinguished as suppositive. The following* would be suppositive inferences : " If air be a substance, then it occupies space ; if trees spring from seeds, then these trees do so ; if all gases are elastic, and oxygen is a gas, then oxygen is elastic." These inferences would become "hypothetical" syllogisms, if additions were made to them asserting that their premises set forth reality. 3. The law according to which an hypothetical is changed into an actualistic inference is a very simple one, and may be considered a corollary, or supplementary part, of the general law of antecedent and consequent. It recognizes the differ- ence between two radical modes of conviction, and operates whenever we apply hypothetical statement to actual fact. Asserting the reality of the antecedent, it claims reality for the consequent. This law might be styled the principle of logical transfer, becauses it enables us to transfer an assertion from one kind of conviction to another ; and syllogisms whose antecedents are constructed in accordance with this principle, might be called translative reasonings, or inferences. 152 THE MODALIST. [Chap. XVII. 4. The working of this law, may be either express or im- plicit. Its express operation occurs when the minor premise, as it is called, asserts fact immediately and exclusively. This takes place in all translative reasonings concerning existing individuals ; as, for example, in the syllogism, " If Socrates be virtuous, he merits esteem ; he is virtuous ; therefore he mer- its esteem." The implicit working of the law appears when the reasoning immediately concerns general objects, or logical classes. In saying, " If oxygen be a gas, it is elastic : oxygen is a gas ; therefore it is elastic," the minor premise has an actualistic force; yet not simply and directly, but only as implicated with a general truth. In other words, the assertion, " oxygen is a gas," has a double significance ; first, it presents a principle which applies, not only to existing oxygen, but to any that ever may exist or may have existed ; and secondly, it contains the implication that some oxygen actually exists and is a gas. The "hypothetical," or translative, syllogism depends on this assertion, in the second premise, of the reality of the antecedent supposed in the first premise ; and only accidentally uses a general truth or principle for this purpose. The proper force of general principles in reasoning will be considered hereafter, in connection with syllogisms of another nature. Some define the hypothetical syllogism as that mode of reasoning which is governed by the principle of antecedent and consequent ; and say that other modes of reasoning follow other principles. Though this is not true, we must allow that the translative inference is specially related to the generic law of inference; inasmuch as the law of logical transfer is not only, like other principles, subordinate to the law of reason and consequent, but pertains to the operation of that law. 5. The law of reason and consequent works in two ways ; we either assert the consequent with the reason, or we deny the reason with the consequent. Hence, also, the law of logical transfer has a double operation. That is to say, after an infer- ence has been made hypothetically, we may then either assert the reason or deny the consequent actualistically, and there- upon assert the consequent or deny the reason actualistically. Chap. XVII.] HYPOTHETICAL REASONING. 153 Here we must determine exactly what is meant by asserting and denying ; for it might be supposed that assertion always signifies the setting forth of something as existing, and denial the setting forth of something as non-existent ; whereas the terms have wider meanings. Ordinarily we infer from one positive fact to another, that is, from one case of existence to another. But, in addition to this, we infer from existence to non-existence, from non-existence to existence, and from non- existence to non-existence. There are, therefore, four styles of inference ; which may be illustrated, as follows : " If the man has consumption, he will soon die," (from existence to existence) ; "if the formation be granite, it does not contain coal," (from existence to non-existence) ; "if there be no food, we must suffer hunger," (from non-existence to existence) ; u if there be no fuel, there can be no fire," (from non-existence to non-existence). Now to assert the antecedent or conse- quent in any of these inferences is to present it as a reality, whether it be a fact of existence or a fact of non-existence ; and to deny the consequent or the antecedent is to deny its reality, whether that be the denial of existence or of non- existence. In order to express technically those wide conceptions which we have now explained, logicians sometimes call the assertion of the antecedent, and that of the consequent which it in- volves, the " positing," or " placing," of a statement of fact ; and they have termed the denial of the consequent, as well as that of the antecedent, the "sublation," or taking away, of a statement of fact. They also name that form of inference which depends on the " placing " of the antecedent the " modus ponendo ponens" or more simply, the "modus poiiens" ; and that which follows the sublation of the consequent the "modus tollendo tollens" or more simply, the "modus tollens" This phraseology has the additional advantage of indicating that antecedents arise from assertion and denial, not simply because something is asserted or denied, but because, also, there is a presupposed subject, or case, or set of circumstances, in relation to which the positing or sublation takes place. Moreover, as according to the law of contradiction the denial 154 THE M0DAL1ST. [Chap. XVII. of existence involves the assertion of non-existence, and the denial of non-existence the assertion of existence \ instead of merely denying the consequent, we may, and often do, assert its contradictory ; and thereupon deny the antecedent. Hence the negative part of the law of logical transfer may assume the form, "contradict, or assume the contradictory of, the consequent, and you may deny, or contradict, the antecedent." 6. We have now considered those simple and primary modes of " hypothetical " reasoning which are expressed by the ordi- nary "conditional syllogism." A more complicated style of translative reasoning, which, however, is explainable on the same general principles, appears in what are called "disjunc- tive " reasonings. Logical disjunction is either partial or complete. The first exists when it is impossible that two things should be true together, so that the placing of either involves the sublation of the other. This is the disjunction of contrariety. The second arises when, in addition to the foregoing opposition, two things cannot be un- true together, so that the sublation of one involves the placing of the other. This is the disjunction of contradiction. As con- tradiction presupposes contrariety we shall consider the latter first. 7. The nature of contrariety, and its relation to inference in general, may be understood from the fact that a case of this mode of opposition may be produced by the denial or contra- diction of any consequent of necessity. To illustrate this point let us take the sequences already mentioned : If the man has consumption, he will die soon ; If there be no food, we must suffer from hunger ; If the formation be granite, there cannot be coal in it ; If there be no fuel, there cannot be any fire. The first two of these are sequences of positive necessity, the one with an antecedent of existence, the other with an ante- cedent of non-existence ; the second two are inferences of neg- ative necessity, one having a positive and the other a negative antecedent. If now we deny, or take the contradictory of, the consequent in each sequence, retaining the antecedent un- changed, we shall have the following pairs of contraries : Chap. XVII.] HYPOTHETICAL SEASONING. 155 Consumption — continued life ; No food — no suffering from hunger ; Granite — coal in the formation ; No fuel — fire. Assert any one of these contraries, and you must deny, or con- tradict, its fellow. If the man have consumption, he cannot have continued life ; and if he have continued life, he cannot have consumption : if we have no food, we cannot be without suffering from hunger, but must suffer from that cause ; and if there be no suffering from hunger, we cannot be without food, but must have a supply : and so on with the other contraries. In general, therefore, we say that anything and the contradic- tory of any necessary consequent of it, are contraries. The reason for this is that the consequent of a necessitating antecedent is a condition of that antecedent. Evidently, it is impossible for a thing to exist while the contradictory (or any contrary) of any of its conditions exists ; or for any contradictory (or con- trary) of a condition to exist while the thing conditioned exists. The perception of contrariety, however, does not depend on a previous perception of necessary sequence ; indeed, it com- monly takes place independently. For two things may be directly perceived to be of such a nature that the existence of one of them conflicts with, that is, involves the non-reality of, some condition of the other ; in which case they are, and must be, contraries. This incompatibility of one thing with others is as much a part of the nature and constitution of things as the compatibility of one thing with others is, and may be as directly perceived. For example, it is as immediately evident that two bodies cannot occupy the same space at once, and that if the one is there the other is not there, as that a body must occupy some space, or that it may occupy any sufficient space which would be otherwise unoccupied. Contrariety is especially noticeable when a number of na- tures, or things predicable, which have a common character, have also such peculiarities that no two of them can belong to the same individual subject. Hence the co-ordinate species in a correct logical division are contraries one to another with refer- ence to their inherence in the same subject. For instance, 156 THE MODALIST. [Chap. XVII. if an object is of any one color, say red, it cannot be of any other color at the same time ; if a triangle be isosceles it cannot be equilateral or scalene, or if it be equilateral it cannot be isosceles or scalene. 8. The inference of contrariety can be expressed in the same way as "conditional," or simple hypothetical, inference, but it differs from the latter in the peculiar indirectness with which the sequence is conceived. The consequent of simple, or ordinary, hypothetical sequence is immediately conceived and asserted as true; that of contrary inference is obtained by conceiving first of something and then of the immediate, or categorical, contradictory of that something, and is the asser- tion of this contradictory. Conceiving of " red " as a contrary of "white," and then of its contradictory, "not red," we say that, if the paper is white, it is not red. Contrary inference, also, has a doubleness, because each contrary may be, and com- monly is, conceived of as being, in its turn, antecedent to the non-reality, or to the immediate contradictory, of the other. This doubleness may be expressed with any pair of con- traries, if we follow the formulas, " A cannot be both B and C ; it is B; therefore it is not C," and "it is C; therefore it is not B." " The triangle cannot be both equilateral and scalene ; it is equilateral ; therefore it is not scalene," or " it is scalene ; therefore it is not equilateral." Argument of this form may be distinguished as the weak disjunctive syllogism. It admits only the "ponendo tollens" The ordinary, or strong, disjunctive syllogism, as we shall soon see, has a " modus ponens" as well as a " modus tollens." 9. This brings us to that thorough-going form of disjunc- tion which is technically called " contradiction." For contra- dictory opposition includes contrariety and something more. First, then, we say, negatively, that the disjunction of con- tradiction is not at all limited to that opposition which is based on the law of contradiction and excluded middle. This law relates to any pair of propositions which set forth the exis- tence and the non-existence of the very same thing ; and asserts that if one of them be true the other is false, and that if one be false the other is true. The contradictories of which we Chap. XVII.] HYPOTHETICAL REASONING. 157 have made mention above are of this sort. But contradictory inference in general is chiefly occupied with propositions which set forth the existence or non-existence of tivo different tilings ; and asserts the falsity of either of these propositions because of the truth of the other, or the truth of either because of the falsity of the other. To account for such inference we must assume, not merely the law of contradiction, but also an operation of the general law of antecedent and consequent additional to that which appears in immediately self-evident contradiction. Those propositions which set forth the existence and the non-existence of the very same thing, may be styled categorical contradictories ; for this adjective sometimes indicates that a statement is absolute, or unaccompanied by any reason. Such statements as " the man is guilty " and " the man is not guilty," are categorical contradictories ; because their opposi- tion, though founded on reason, takes place according to a law of whose operation the mind is scarcely conscious. The reason for such contradiction is considered only by logicians ; it is the "law of Contradiction." But those propositions which set forth two different things or natures which conflict with each other both as to existence and as to non-existence, may be called consequential contradictories; for their opposition is asserted by the mind on account of some specific reason in the nature of the things considered. In the case of any collection of units that the number of them should be odd, and that it should be even, are contradictories consequentially related to the nature of odd and even integral numbers. 10. Secondly, we say, positively, that any two contraries become the contradictories of one another ivhen the circum- stances of the case are such that the non-reality of either is the only condition wanting to complete an antecedent necessitating the reality of the other. Evidently in any case the non-reality of either of two contraries is a condition of the reality of the other. Let this now be the only condition needed ; thereupon the two contraries are contradictories. For whenever the non- reality of a first thing necessitates the reality of a second, the law of " the denied consequent " requires that the non-reality of the second must also involve the reality of the first. 158 THE MODALIST. [Chap. XVII. In the case of a plane triangle there are three contraries ; it may be either equilateral, or isosceles, or scalene. If now we limit the case to triangles which have at least two sides equal, only two contraries remain; and these are contradictories. For every triangle with at least two sides equal is either equilateral or isosceles. In general when a case of necessary consequence admits of two, and only two, alternative conse- quents, these become contradictories. If a house is certainly to be painted, and only two colors are obtainable, say brown and white, these are contradictories of each other. 11. Several things may be contradictory to one and the same thing. In a quadrilateral both the inequality of opposite sides and the inequality of opposite angles, are contradictories of its being a parallelogram. But things contradictory of one and the same thing cannot be contradictories of each other. For, being contradictories of one and the same thing, they must all be non-existent together if that thing exist; but things contradictory of each other cannot be non-existent together. Neither can the contradictories of one and the same thing be the contraries of one another: for they must all exist together if their common contradictory do not exist. Therefore we cannot have a series of mutual contradictories ; as we can of mutual contraries. We must deal with contra- dictories in pairs. a The relation of contradictory to direct inference may be illustrated by the fact, that contradictory conceptions may always be found when two things are exact logical necessi- tants of each other. For either of such necessitants and the categorical contradictory of the other, are related to each other as consequential contradictories. To exemplify this, let smoke and fire involve the existence of each other, and the non-existence of either the non-existence of the other; then " smoke " and " no fire," or " no smoke " and " fire," are mutually contradictory. If we assert either we deny the other, and if we deny either we assert the other. The con- ception of contradictories, however, need not be based on that of necessitants ; contradiction, like contrariety, can be per- ceived directly. Chap. XVII.] HYPOTHETICAL REASONING. 159 Moreover, as contrariety is specially noticeable between the species of the same genus, that is, between the specific forms of the same generic nature, so the most prominent mode of contradiction arises when a genus consists, or is made to con- sist, of only two species. In the case of integral numbers to be odd and to be even are natural contradictories ; while to be odd and to be a multiple of four, are merely contraries. But should a collection of numbers contain only odd numbers and multiples of four, in that case, and with reference to the mem- bers of that arbitrary class, to be odd and to be a multiple of four would be contradictories. 12. When translative reasoning is based on the relations of contradiction, it is commonly expressed by the strong "dis- junctive syllogism." This consists of a major premise, setting forth the two contradictories in their double hypothetical opposition to each other ; of a minor premise, in which one of the contradictory conceptions is actualistically asserted or denied ; and of an actualistic conclusion. We say, " The line is either straight or bent," and then "it is straight, therefore it is not bent " ; or " it is not straight, therefore it is bent " ; or "it is bent, therefore it is not straight" ; or "it is not bent, therefore it is straight." The disjunctive major premise is really a condensed statement of four hypothetical propositions ; the minor actualistically asserts one of the four antecedents of those propositions ; the conclusion is the consequent of that antecedent. Evidently contradictory inference has two modes, the "po- nendo tollens" and the " tollendo ponens" : contrary inference has only one, the "ponendo tollens." There is, however, a style of reasoning which might be called that of contradic- tory contrariety, in which, while dealing with contraries, we can regard them to some extent as contradictories ; and can, therefore, use the "tollendo ponens" mode of argument, as well as the "ponendo tollens." This arises ivhenever the con- traries in any given case are enumerated exhaustively ; and espe- cially when a complete division is given of some existing genus. For instance, if we say, " The season was either spring, sum- mer, autumn or winter," we not only can assert any one 160 THE MODALIST. [Chap. XVIL contrary and deny each of the rest, but, if we deny all the rest, we can assert that one ; or, if we deny some and leave some undenied, we can assert these last disjunctively. For, if it is neither spring nor summer, it must be either autumn or winter. In the syllogism, " The man is either a knave or a fool ; he; is not a knave, therefore he is a fool," the " tollendo ponens " holds good, although the major premise does not explicitly enumerate the contraries. The reason is that the conclusion is supported by a suppressed and understood contrary, the- complete enumeration being, " The man is either a knave or a fool or both." We cannot, however, say, " The man is a knave, therefore he is not a fool," using the "ponendo tollens" ; because the suppressed contrary does not support this con- clusion. We see, therefore, that in every case of tollendo ponens, notwithstanding this apparent exception, all the alter- natives are and must be considered. For in the foregoing instance the "tollendo ponens" is justified and the "ponendo tollens " condemned only after consideration of the suppressed alternative. 13. A complicated form of argument involving both direct and disjunctive hypothetical inference has been called the dilemma, or double assumption. Its major premise assumes two or more sequences as hypothetically true. Its minor premise is actual- istic, and either asserts the antecedents of those sequences dis- junctively, or denies their consequents disjunctively : in the- former case the dilemma is " constructive " ; in the latter, " destructive." The conclusion either asserts the consequents disjunctively, unless there be only one common consequent, in which case that is asserted; or it denies the antecedents disjunctively, unless there be only one common antecedent, in which case that is denied. The reasons for these operations are apparent from the nature of hypothetical and disjunctive inference. The constructive dilemma is either complex or simple, according as the sequences given in the major premise have different consequents or one common consequent ; and, in like manner, the destructive dilemma is complex or simple, according as the given sequences have different antecedents, or one common antecedent. Chap. XVII. ] HYPOTHETICAL BEASONING. 161 The following is a complex constructive dilemma : " If a statesman who has discovered his policy to be mistaken, alters his course, he is chargeable with inconsistency ; and if he do not alter it, he is guilty of deceit. But he either does, or does not, alter it ; Therefore he must be either chargeable with inconsistency or guilty of deceit." The following is a simple constructive dilemma : "If a study furnish information, it should be pursued; and if it develop the mind, it should be pursued. But this study either furnishes information or develops the mind ; Therefore it should be pursued." The following is a complex destructive dilemma : " If the man were wise, he would not speak irreverently of Scripture in jest ; if he were good, he would not do so in earnest. But he does it either in jest or in earnest ; Therefore he is either not wise or not good." The following is a simple destructive dilemma : "If the man were wise, he would not speak irreverently of Scripture *n jest ; neither would he do so in earnest. But he does it either in jest or in earnest ; Therefore he is not wise." In these last arguments it will be noticed that a negative consequent is denied by giving its contradictory; which is positive. 162 THE MODALIST. [Chap. XVIII. CHAPTER XVIII. PROBABLE INFERENCE. 1. The tychologic principle. 2. Chances. 3. Their individuality. 4. Their arithmetical value. 5. Their addition and subtraction. 6. Their multiplication and division. 7. Compounded probability explained. 8. The compounding of a series. 9. The addition of compounded proba- bilities. 10. The application of the binomial formula to probabilities connected with recurrent trials. 11. Philosophical probability and im- probability. 12. Probability may be either orthologic or homologic. 13. Analogical and inductive probability. 14. Moral certainty. 1. Probability attaches primarily to single inferences and to illative propositions as the expression of these inferences ; after that, and in consequence of that, it may affect syllogisms, or those inferences which follow upon the composition of propositions. For if either premise of a syllogism be probable, the conclusion must be probable. If we can understand the nature of the single probable inference, no difficulty will be experienced respecting that of probable reasoning. We find the radical law of all probable inference in the principle of " the ratio of the chances " ; which principle may be named the tychologic principle. 2. The nature of " chances " is best explained by consider- ing them, in the first instance, as conflictive consequents of possibility, and as making up a family, or company, of such consequents. The antecedent of an inference in possibility differs from the antecedent of an inference of necessity in that the latter cannot have conflictive consequents, while the former may. If a thing be necessary, nothing that cannot exist along with it can also be necessary. But two or more things may be possible at the same time, even while no two of them can be actual together. When we know simply that a book is a bound volume, we can say that it may be a quarto, or an Chap. XVIII. ] PROBABLE INFERENCE. 163 octavo, a duodecimo, or of some other style ; but if it be any one of these, it cannot be any of the others. The fact that it is a bound volume is an antecedent of contingency, or pos- sibility, with a number of connective consequents. Now, when a case admits of only a limited number of connective conse- quents, one of which must be realized, and when it presents no ground for believing that any one of them, rather than any other, has been, or will be, realized, we call the consequents " chances." The relation between a chance and a consequent of necessity is such that the former changes into the latter whenever the antecedent of contingency is filled out, in any way, so as to make it an antecedent of necessity. Should we know not only that a volume is bound, but also that it is a copy of a book published only as a quarto, then we would say that the vol- ume must be — not that it may be — a quarto. But, although chances are thus related to necessary consequents, they them- selves are never necessary, or real, but only ideal, objects. When a chance is realized it ceases to be a chance ; and its companions, also, cease to be chances in their failure to be realized. 3. Every chance is conceived of as an individual, and not as a general, consequent of contingency. Should a drawing take place from a box containing twenty black, thirty red, and fifty white marbles, there would be three general consequents of contingency, viz., that a black, that a red, and that a white marble, should be drawn. These general consequents would not be chances according to the logical use of language. A chance in the foregoing case would be the possible drawing of any one ball ; and evidently there would be one hundred such possibilities. In determining the " ratio of the chances " we always conceive of these individual and equal possibilities. We cannot, however, always conceive of them as directly and as definitely as in the case just considered. If a postman called at a certain house to deliver letters about four days out of every thirty, one might say at first that on any given day there are only two chances, viz., that he may, and that he may not, call. But properly these are two general 164 THE MODALIST. [Chap. XVIII. events — or rather two events of a general character — each of which is supported by a number of chances. The case pre- sents thirty chances — or individual possibilities of equal cred- ibility. According to four of these the postman will call; according to twenty-six he will pass by. These chances may not be definitely conceived of in our judgment respecting the likelihood of a call ; but they are the real rational basis for such a judgment. The individuality of the chances means little more than that they are the units of measure among which the confi- dence of the mind is equally distributed. In every case of probability there is a necessity that one of the chances should be realized, and, as we have no reason to expect one more than another, we expect each equally, dividing among them the con- fidence of certainty. 4. In order to indicate the value of a single chance mathe- matically we must employ a fraction wJiose numerator is unity and whose denominator is the whole number of chances. In the case of the postman the value of each individual chance is one- thirtieth of certainty, while the two general events supported by the chances have the values -^ and -§£, or -f^ and ||. The application of mathematical methods to the determination of probabilities begins with this employment of fractions ; and it leads to the addition, the subtraction, the multiplication and the division, of fractions representing degrees of probability. 5. When two or more events are specific forms of the same general event, so that, if either of them happen, that will be a happening of the general event, the probability of the gen- eral event is found by adding the probabilities of all the speci- fic events included under it. Should a cubical die whose sides are numbered from 1 to 6 be thrown out of a box, the chance for any one number appearing uppermost is i, and the proba- bility for the appearance of an odd number would be f, this being the sum of the chances for the three sides bearing the three odd numbers. But were the die thrown twice, we could not say that the probability for an odd number appearing on both throws would be £ -f- f , or unity ; for " an odd number on both of two Chap. XVIII.] PROBABLE INFERENCE. 165 throws" would not be a general event possible in either of two specific forms, but a double event rendered possible by a doubled antecedent. We shall see that the probability of such an event is found by multiplication, not by addition. Conversely, if an urn contain 30 white balls, and 70 colored red or otherwise, the probability for the drawing of a colored ball is t 7 ¥ °q-. And if fifty of these 70 chances favor other colors than red, the probability for a red ball must be y 7 -^- — -££$ or m «» \. The foregoing examples illustrate the only cases in which the determination of probabilities calls for, and admits of, the addition and subtraction of fractions. These operations are applicable only when some general event and its specific forms are all conceived of as consequents of the very same antece- dent of contingency. 6. The multiplication of probabilities — that is, of fractions indicating probability — is used when one consequent of contin- gency, in other words, one probable event, is consequent upon another. By means of this multiplication we determine the probability of the compound event which would be composed of both the probable events in case they should happen ; which also is the probability of the conclusion, or of any other part y of this compound event, as part of it. If there be one chance in five that a certain criminal will be caught, and one in three that he will be convicted after being caught, it is plain that now, and until he may have been caught, the probability of his conviction will not be one-third of certainty — for that would involve the assumption that he certainly has been caught, or shall be — but only ^ of ^, or ^ ; which also is the probability of the entire compound event of his being both caught and convicted. Therefore the probability of a com- pound event, or of any part of it as such, is the product of the probabilities of its component events. Conversely, if we know both the probability of an event compounded of two probable events and the independent prob- ability of one of its components, and if we divide the prob- ability of the event by the probability of that component, we shall obtain the independent probability of the other compon- 166 THE MODALIST. [Chap. XVIII. ent. If we know that the probability of a criminal being both captured and convicted is ^ z , and the probability of his being caught is jr, we can say that the probability of his being con- victed, in case he is captured, will be |-. Because ^ divided by -1- is equal to i 7. In the foregoing illustration the events composing the compound event are related to each other as the condition of a result and the result conditioned. Such a relatedness, how- ever, is not necessary in order to a compounding of probabili ties. Any two events which are not of repugnant natures, and which, therefore, may both be realized, may be conceived of as one double event. The event of ace on one throw of a die, with the probability -§-, and that of head on one toss of a penny, with the probability J, may be compounded into the event "ace on one throw and head on one toss," with the probability -jL. It is evident, moreover, that, after two events have been compounded, a third may be compounded with the result ; and that, in this way, any number of events may be made to compose an event whose probability is the product of the probabilities of its parts. 8. An interesting case of compounded probability occurs when the component events may be successively expected according to a regular series of fractions. After the shuffling of a complete pack of playing cards, the probability of a pic- tured card being uppermost is -J-f, there being 52 cards in all, and 12 of these pictured. Then, should this event take place, and the pictured card be laid aside, the probability that the next card will be found to be pictured will be -J^-. If this event occur and the second pictured card be laid aside, the probability for the appearance of a third will be -J-J. And, if the subsequent drawings continue to yield pictured cards, the series will go on till only one such card remains in the col- lection ; and will terminate with the fraction J y , the probability for that card. Such being the separate probabilities for the successive appearances of pictured cards, that for a combined event can be easily determined. For example, the probability that the first three cards will be pictured must be the product Chap. XVIII. ] PROBABLE INFERENCE. 167 of the first three fractions of the series. That is |f • £i • £$-, or 1 1§ 1 8 o ^ or a little less than one in a hundred. But the probability that the first card will be pictured, the second plain, and the third pictured, will be the product ^f • |-2- • ii or xfHro or a k oi rt ■£%. This would be the result also if the plain card were to be expected first, or last, of the three. When the compounded probabilities are not a variable series, but equal to each other, as happens when precisely the same trial, or antecedent of probability, is repeated, the calculation is simpler. For instance, the probability that a pictured card will be uppermost three times in succession after three shuf- flings of the entire pack, would be found by raising the frac- tion ^f- to its third power. It would be 2 ^ 7 , or more than one in one hundred. 9. A more complex class of problems than those hitherto noticed calls for both the multiplication and addition of proba- bilities. For addition is used whenever the probability of a general event is to be determined by uniting the probabilities of its specific forms. Let the question concern the probability of obtaining " ace on two successive throws " of a die. This question is ambigu- ous; it may concern (1) the probability of "ace on both throws," or (2) that of "ace on one throw only," or (3) that of " ace on one throw at least," perhaps on both. In the first of these events, " ace on both throws," the second throw, by which the event may be completed, is not to be allowed unless the first throw is successful. We therefore compound the separate probabilities of these two throws, that is, we multiply i by i and find the probability required, ■£$. This calls for no addition of fractions. But the event "ace on one throw only" may take place in either of two ways; for ace may appear on the first throw only, or on the second throw only ; and the probability of it must be determined by adding to- gether the probabilities of its specific forms. The probability of ace on the first throw and not on the second is i • £, or ^. That of ace not on the first throw but on the second is f • £, or 3 5 g. Adding these together we find the probability sought for, if or T \. Finally, the chances for " ace on one throw at 168 THE MODALIST. [Chap. XVIII. least " (out of the two) comprise those of three possible events, viz. of "ace on first throw only," of "ace on second throw only," and of "ace on both throws." We have just seen that the united probability of the first two of these events is T 5 F . Add to this g 1 ^, the probability of ace twice in succession, and we have ^ as the probability of ace once at least in two throws. 10. An ingenious theorem respecting recurrent probabilities provides for the calculation of the chances for an event happen- ing any given number of times, in any given number of trials. Let an urn contain any number of balls, one third of them being red, and the rest of other colors. The probability that the first ball drawn out by a blindfolded person will be red is -| ; the probability that it will not be red is -§. More- over, if every ball drawn out be immediately replaced, these same probabilities will recur with every subsequent trial. We may now ask " What is the probability of a red ball appearing, say, 4 times, and failing to appear 6 times, in 10 consecutive trials ? Or of its appearing 7 times, and failing to appear 3 times ? " Such questions can be easily answered by the use of a mathematical formula. Let us designate the event, the recurrence of which an exact number of times in a given number of trials is the 'subject of enquiry, by E, and its failure to occur by F, the probability of its occurrence on one trial by p, and the improbability of its occurrence on one trial by q. Then, on two trials, the possi- ble combinations are the following double events : first, EE, with the compound probability p xp, or p 2 ; FF, with the probability q x q, or q 2 ; EF, with the probability p x q, or pq ; and FE, with the probability q xp, or qp, or pq. Evidently no other combination than these is possible. Moreover, EF and FE, as they are alike constituted by one success and one failure, may be considered as varieties of that general com- pound event in which we conceive of one event and one failure without respect to order of occurrence. The probability of that event, therefore, will be pq+pq, or 2pq, this being the sum of the probabilities of the specific events. If, now, we drop either the designation EF or FE and use the other (say EF) Chap. XVIII. ] PROBABLE INFERENCE. 169 for that general event which covers both EF and FE, we shall have only three possible events, EE, EF, and FF, with prob- abilities expressed respectively by the terms of the polynomial p 2 + 2pq + q 2 . For example, ^ being the probability for ace on one throw of a die, and -J the probability for the failure of that event, these values being substituted for p and q in the foregoing polynomial, the several terms give the probabilities for ace twice on two throws, EE ; for ace once only on two throws, EF; and for failure of ace on both throws, FF. Thus - (i) 2 + 2 (J X f ) + (f Y, or ^ + if + M- It should be noticed that the sum of these fractions is unity, or one ; as it ought to be. For, since one or other of the three events must happen, they divide between them all the chances in the case. Should we now make three trials, instead of two, the pos- sible compound events, with their probabilities, will be as follows : EEE with the probability ppp =p B EEF » « ' ppq =p* q EFE " " ' ' pqp=p 2 q FEE " " ' ' qpp=p 2 q EFF " " ' pqq =pq* FEF " " ' ' qpq=pqz FFE " " t ' qqp=pq 2 FFF " " ' qqq = g 3 . Again disregarding the order in which the component events may occur, these eight compound events may be conceived of as four, namely, EEE, EEF, EFF, and FFF; and, evidently, the probabilities of these four events are expressed by the terms of the polynomial, p z + 3p 2 q + 3pg 2 + q s . This is the cube, just as the polynomial first obtained was the square, of the binomial p + q. In like manner the development of this binomial to its fourth power, will give the different probabili- ties that an event with the separate probability, p, will occur, on four trials, every time, or only thrice, or only twice, or only once, or not at all ; — the antecedent of probability being exactly repeated in every trial. And, in general, the development of p + q to the nth power will give all the prob- abilities of the occurrence of an event any number of times on 170 THE MODALIST. * [Chap. XVIII. n trials; p being the probability, and q the improbability, of the event on one trial. For instance, in order to determine the chances for " ace three times only in ten throws," we must raise p -f q to the 10th power, and then find the numerical value of the term whose literal part is p 3 g 7 , after substituting i for p and -f for q. The foregoing theorem belongs to a department of mathe- matics in which men of genius have discussed many interesting problems, and which may be taken as a proof that problematic inference is no less rational in its methods, and no less con- nected with the necessary nature of thought and of things, than apodeictic inference is. In the above discussions the "multiplication" of proba- bilities must be taken to mean their multiplication one by another — the compounding of them. The multiplication of a probability by a whole number is an operation altogether different from this : it is only a short way of adding the equal probabilities of two or more possible specific results, connected with one and the same antecedent, and whose united probability is that of a more general event. 11. The calculation of chances brings into prominence a wide philosophical use of the words "probable" and "improba- ble " ; which it may be well to define. Ordinarily the proba- ble is that which has the majority of the chances in its favor ; and the improbable is that which only a minority of the chances support. According to common speech the same event cannot be both probable and improbable under the same cir- cumstances. But, philosophically, that is probable which has any chances at all in its favor, whether they be few or many ; and that is improbable which has any chances at all against it. According to these technical meanings the most improbable event has some degree of probability, and the most probable some degree of improbability. In ordinary language we say that " ace on the first throw of a die " is not probable, but highly improbable ; mathematically and philosophically, it has the probability of one-sixth. Chap. XVIII.] PROBABLE INFERENCE. 171 Probable as well as demonstrative inference may take place either orthologically — that is, directly from an antecedent, and without reference to any previous case of similar conse- quence — or homologically. In this latter case, instead of directly estimating chances, we give the consequent of a re- peated antecedent the same probability as in a previous judg- ment. The instances of probable inference discussed above are all orthologic ; but any of them may be the basis for an homo- logic inference. 12. The relation between orthologic and homologic infer- ence is precisely the same in problematic as in apodeictic sequence ; and does not call for special discussion. Some remarks, however, are in place here concerning our probable judgments respecting natural laws and events. These all pass under the generic name of probable induction, but are often divided into two classes, one of which is especially entitled to this name, and the other of which is sometimes known as rea- soning from, or according to, the analogy of Nature. Probable induction, in the specific sense, is essentially a form of prin- cipiation ; and takes place when a consequent follows a causa- tional antecedent, not invariably, but only sometimes, or for the most part. This happens when some power adequate to produce a result is occasionally counteracted ; or when some tendency which needs advantageous circumstances to render it effectual, is only sometimes attended by such circumstances. Ordinarily a wound produces pain ; mental excitement or bod- ily stupor or rapidity of infliction may prevent this. There- fore we only say that a wound is likely to produce pain. Three steps may be distinguished in forming this inference. We say, first, "Most wounds have caused pain"; then, by principiation, " Most wounds produce, or will produce, pain " ; and then, by the tychologic principle, that is, according to the ratio of the chances, "A wound is likely to produce pain." Because any wound, taken at random, may be one of those which are painful. But, in the foregoing process, the tycho- logical judgment may precede the principiation without any change in the result. Thus, having seen that most wounds have produced pain, we may say, first, that any one of these 172 THE MODALIST. [Chap. XYIII. observed wounds was probably painful, and then, inductively, that any wound whatever is likely to be painful. Ordinary judgments of probability are formed in one or other of these ways. 13. The inference from the " analogy of Nature " differs from the foregoing in that it is not supported by the same- ness, or exact similarity, but only by an imperfect similarity, of the new antecedent to that already known to have a certain consequent. It is founded on the principle that whatever in the natural Universe resembles a known cause, or reason, is probably or possibly a true and sufficient reason. Though this inference may terminate in principiation it is mainly paradigm- atic; it is essentially a reasoning from one parallel case to another ; but it is founded on a parallelism which has been only imperfectly established; and which, therefore, is only probable, or not unlikely. Both the inductive and the analogic inference assume confidently that Nature has an intellectual unity, and that her methods are fixed and uniform : but in the former case a law of natural action has been discovered, while in the latter there are only grounds for conjecture. The prob- ability of probable induction arises because, though the ante- cedent is defined and known, the consequent does not follow always, but with exceptions ; that of analogical inference arises because the existence of a sufficient antecedent is only a matter of probability or of possibility. We cannot be sure that other planets or stars are inhabited because our world contains the race of Adam ; for the case presents only a prob- able or conjectural antecedent. 14. When the proportion of the chances in favor of any event, or course of events, is so great that we feel authorized utterly to disregard the chances against it, the event is said to be morally certain. Thus the alternation of day and night, and of the seasons, and the continued earthly existence of the human family, during the coming year, are things of which we have no doubt. For the practical purposes of logic this cer- tainty differs nothing from the conviction of clear memory, or of immediate cognition, or of demonstrative evidence. But it is important to remark that the highest probability can never Chap. XVIIL] PROBABLE INFERENCE. 173 really reach absolute certainty. No matter how extreme the likelihood of a thing may be — no matter how small the pro- portion of the chances against it to the chances for it may be — still, so long as a thing is probable, there is a possibility of the opposite. Were there a thousand millions of chances for an event, and only one against it, that one chance would in- volve the perfect possibility of its non-occurrence. 174 THE MODALIST. [Chap. XIX. CHAPTER XIX. THE OPPOSITION OF PROPOSITIONS. 1. Pertains to illative propositions having the same subject and predi- cate. 2. Dogmatic assertions may be opposed in quantity and in quality. 3. Their subalternation and superalternation. 4. Their contrariety. 5. Their contradiction. 6. Exclusively partitive assertions. 7. Subcon- trariety. 8. Summary of the laws of opposition. 9. Modal opposition essentially corresponds with dogmatic. 10. Modal contrariety. 11. Modal subalternation. 12. Modal contradiction. 13. This last kind of opposi- tion involves a specific kind of contingency in the sub-contraries. 14. Modes, of contingency or possibility : (a) the embedded, (&) the unstable, or un- guarded, (c) the stable, or guarded, (d) the half-stable, or half-guarded.. 15. This last, as positive and negative, becomes encouraging and dis- couraging contingency ; and furnishes the contradictories of necessity and impossibility. 16. Sub- contrariety. 17. Probability participates in the oppositions of contingency. 1. Illative propositions are the most important in logic. Among illative propositions those which are general, and which, therefore, present laws, or rules, of inference, are espe- cially important. Logic is so much concerned with these that it might even be called the science of " Canonics " ; as it was anciently by the Epicureans. These general illative propositions, when expressed cate- gorically, are of two classes ; first, the pure, or dogmatic, in which we make either universal or particular assertions re- specting the members of a logical class; and secondly, the modal, or conditionative, in which we make either apodeictic or problematic assertions respecting a general subject. When two propositions of either of these classes have the same subject and predicate terms, but differ otherwise, they are said to be opposed — immediately opposed, to one another. Sometimes, with a restricted use of language, only propositions which are contrary to, or contradictory of, each other, are- Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 175 spoken of as mutually opposed. But logicians also charac- terize any propositions as being opposed to each other when they have the same subject and predicate terms, but differ otherwise ; whether they conflict with each other or not. The various modes in which propositions may be opposed are worthy of study, because, in every opposition, the truth or the "falsity of at least one of the opposed propositions can be inferred from the truth or from the falsity of the other. Let us enquire first concerning the oppositions of pure, and then concerning those of modal, categoricals. 2. Dogmatic categoricals may be opposed in quantity, or in quality, or in both. They are opposed in quantity when one is universal and the other particular, both being either affirma- tive or negative ; in quality when one is affirmative and the other negative, both being either universal or particular; in both quantity and quality when one is universal and affirma- tive and the other particular and negative, or when one is universal and negative and the other particular and affirmative. The propositions "all men are wise" and "some men are wise," as also the propositions " no men are wise " and " some men are not wise," are opposed in quantity. The propositions " all men are wise " and " no men are wise," as also the propo- sitions " some men are wise " and " some men are not wise," are opposed in quality. The propositions "all men are wise" and "some men are not wise," as also the propositions "no men are wise " and " some men are wise," are opposed in both quantity and quality. For the sake of brevity logicians indicate these different forms of opposed propositions by the vowels A E I and : A stands for the universal affirmative, E for the universal negative, i" for the particular affirmative, and for the par- ticular negative. The oppositions of these propositions have also been sym- bolized by the sides and the diagonals of a square, the corners of which have been marked severally by the four vowels. In short, the eye is made to help the mind, by means of the following figure, which is called "the logical square " : — 176 THE MODALIST. [Chap. XIX. Contrariety Sub-contrariety Eeference to this diagram will be found to assist the appre- hension and the memory. 3. The opposition of subalternation (which also, from a less important point of view, may be termed superalternation) exists between A and I and between E and 0. In this oppo- sition, according to the common view, the subalternate follows if the superalternate be allowed. If "all men are wise," then " some men are wise " ; if " no men are wise," then " some men are not wise." These are immediate orthologic infer- ences ; the law governing them is " Aristotle's dictum," that " whatever is true of a class universally, is true of any number of its members." But this axiom, does not authorize the con- verse inference ; we cannot infer the superalternate from the subalternate, as such. We can, however, on the principle of the " denied consequent," infer the falsity of the superalter- nate from the falsity of the subalternate. Here, however, we must add that the relation of subalterna- tion may be defined in a way which implies that the subalternate cannot be completely and exactly inferred from the superalter- nate. This definition is an improvement on the common view of subalternation, and will be explained later, in the present chapter. 4. The opposition of contrariety, or confliction, exists be- tween A and E. If A be true, E is false ; and if E be true, A is false. If " all men are wise," it cannot be that " no men are wise " ; and if " no men are wise," it cannot be that " all men are wise." This opposition is a consequence of that im- mediate contrariety which exists between each superalternate and the denial of its subalternate. E immediately involves Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 177 the denial of I, which denial is immediately contrary to A ; therefore E involves the denial of A. If " no men are wise/' it is not true that " some men are wise " ; and, if it is not true that " some men are wise," it is not true that " all men are wise." In like manner, A is immediately followed by the denial of 0, and the denial of by the denial of E. A and E, therefore, are the contraries of one another. But E is not the only contrary of A, nor A of E. Each has another — a co-ordinate contrary. For A must be false if only be true, while E is false ; and E must be false if only I be true, while A is false. In either of these cases A and E are false together. A and E, therefore, are only contraries, not contradictories; this latter name being reserved for propo- sitions between which the opposition is more thorough-going. 5. This " contradictory opposition " takes place between A and 0, and also between E and I. We can say, " If A be true, is false ; and if be true, A is false : also, if A be false, O is true ; and if be false, A is true." E and I contradict each other in the same way. To explain this thorough-going contradiction we must par- ticularly note that the designation " some," which belongs to / and 0, indicates an indefinite number which may include the whole class. It does not mean " some only," or " some, not all," but "some at least," "some, perhaps all." Only that un- restricted " some " which may prove to be " all," can form the contradictory of an universal statement. For, in case there be a class of beings called " men," one of three contrary alterna- tives must follow concerning any characteristic of them — say, wisdom. Either " all men are wise," or " some, not all, are wise" (in other words, "some are wise and some are not wise"), or "no men are wise." Now the indefinite statement designated by 0, that is, " some men — some at least, perhaps all — are not. wise" is a general alternative including both the second and third of those just given as the contraries of the universal affirmative. It may, therefore, be regarded as the only alternative of A. But when one or other of two con- flicting alternatives must exist, these are the contradictories of each other. Hence A and are contradictories. In the 178 THE MODALIST. [Chap. XIX. same way E and I are contradictories. For i" is a general alter- native including the first said second of the three mentioned above. 6. Since the "some" of I and does not preclude univer- sality, we cannot argue from i" that A is not true, nor from that E is not true. Sometimes, however, as we have seen, " some " has a strictly partial, or partitive, meaning. In that case the partitive affirmative and the universal affirmative are contraries ; and so are the partitive negative and the universal negative. For if " only some men are wise " it is not true that "all men are wise," and if "only some men are not wise " it is not true that "no men are wise." These partitive, or exclu- sively partial, propositions, are worthy of notice, yet need not be given any formal place in logic. For every such statement is compounded from two particular predications of the ordi- nary kind, made at once and in modification of each other. Should we, in saying, " Some animals are oviparous," so em- phasize " some " as to signify " some only," this would be equiv- alent to saying, "Some animals are oviparous and some are not oviparous " ; and the effect of this double statement would be the same as that of I and operating together. 7. Finally, the opposition of sub-contrariety exists between / and 0. These are styled subcontraries, partly because they are subalternates to the contraries A and E, but also because they have a peculiar contrariety of their own. For, while we infer the falsity of either contrary from the truth of the other, but not the converse of this, so we may infer the truth of either subcontrary from the falsity of the other, but not the converse of this. Contraries cannot both be true, though they may be both false ; subcontraries cannot both be false, though they may be both true. If it be false that "some men are wise," it is true that "no men are wise"; and this justifies the subalternate ^some men are not wise." If it be false that " some — or any — men are not wise," then " all men are wise" ; and this justifies the subalternate "some men are wise." In- asmuch, however, as we seldom use a particular conclusion when the antecedent warrants an universal assertion, the inference of the truth of one subcontrary from the falsity of the other occurs but seldom. Chap. XIX.] THE OPPOSITION OF PBOPOSITIONS. 179 8. Comparing the different modes in which pure categorical propositions may be opposed to one another, we find the most important to be that of contradiction. This yields the follow- ing sequences : A true, then false ; A false, then true. E true, then I false ; E false, then /true. I true, then E false ; / false, then E true. true, then A false ; false, then A true. Next in importance is contrary opposition. This yields : A true, then E false ; E true, then A false. But there is no sequence, in contrariety, from^l false, or E false. Next subordination, or superalternation, yields : A true, then I true ; E true, then true. But it gives no necessary conclusion from / true, or true. Finally, subcontrariety gives : / false, then true ; false, then /true. But it yields no necessary sequence from the assertion of I or of 0. Examining critically all the foregoing modes of sequence it appears that the truth of an universal assertion (whether A or E) involves either the truth or the falsity of every one of the three propositions which may be opposed to it. In like manner the falsity of a particular assertion (whether I or 0) determines the truth or the falsity of every one of the three propositions which may be opposed to it. Therefore to assert an universal and to deny a particular are the strongest modes of predication. The weakest modes are those asserting the falsity of an universal or the truth of a particular ; because each of these determines only one out of the three opposed judgments. 9. If now we turn to the mutual opposition of modal cate- goricals, we shall find in it an essential correspondence to that of pure categoricals, and at the same time, peculiarities arising from the fact that it pertains to more abstract and searching modes of thought. The universal dogmatic proposition ex- 180 THE MOBALIST. [Chap. XIX. presses necessity, either positive or negative; and the par- ticular dogmatic proposition expresses a contingency, either positive or negative. In conformity with this we find, in modal propositions, contrariety between the necessary and the impossible j subalternation between the necessary and the possible to be, and between the impossible and the possible not to be ; contradiction between the necessary and the pos- sible not to be, and between the impossible and the possible to be ; and subcontrariety between the possible to be and the possible not to be. In this statement the terms " necessary " and " impossible " signify the necessary to be and the impossible to be, this latter being only the necessary not to be, viewed in a peculiar way ; just as the necessary to be is the impossible not to be. Let us take the propositions, " The tea-plant must — or cer- tainly will — grow," " The tea-plant cannot grow," " The tea- plant may grow," and "The tea-plant may not grow"; noticing that in this last the negative particle does not qualify " may," but attaches the idea of non-existence to "grow." These asser- tions cannot all be true under the very same antecedent, or set of conditions ; yet each must be true provided its own proper antecedent exist. For, (1) in cases yielding all the needful conditions of soil, climate, cultivation, and so forth, the tea-plant must grow ; (2) in cases where any of the need- ful conditions is wanting, it cannot grow ; (3) in cases where some conditions are known, but others are not known, to exist, we say that it may grow ; and (4) in cases where some of the conditions are not known to exist, though some are known to exist, we say that it may not grow. Let us desig- nate these four styles of assertion by the accented letters A' E' V and 0'. 10. A' and E' are contraries. They cannot be true together, and they may be false together. With the same antecedent it cannot be both necessary and impossible that the tea-plant should grow. Moreover, the facts obtainable in the case may justify neither of these judgments, but only some form of con- tingency. For in all these judgments the antecedent is the tea-plant considered as in some set of circumstances or other; Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 181 and in a contingent judgment the antecedent would be the tea- plant in the cases marked (3) and (4)} which are, in truth, but two aspects of the same case. With this antecedent both A' and E' would be false, that is, unwarranted, judgments ; as they would be after any antecedent which merely justified contingency. If we knew simply that a man was sick, it would be a false judgment to say either that he must die or that he cannot die. The antecedent only warrants " he may die " and " he may not die." For some sick men die and some do not. If, indeed, the man is found to have consumption, we may say, " He must die " ; or, if he has but a headache, we may say, "He certainly will not die"; but in these cases new ante- cedents are used. The simple antecedent of " sickness " does not make death either necessary or impossible. 11. A' and /', as also E' and 0', are respectively superalter- nate and subalternate. For there is a sense in which whatever is necessary is possible to be, and whatever is impossible is possible not to be. Whatever must be so, may be so ; whatever cannot be so, may be not so. In the former case existence, and in the latter non-existence, consists with given surroundings. Yet this inference of contingency from necessity, or from impossibility, is only partial. For possibility and contingency, in the ordinary and proper sense of these terms, involve the possibility of the opposite. They are perceived when some of the conditions of a thing are known to exist, and some are not known to exist. Only the first of these things follows from a known necessity ; only the latter from a koown impossibility. Contingency, therefore, is said to follow from necessity, only because necessity implies the positive part of the foundation of contingency ; and it is argued from impossibility only in that impossibility implies the negative part of the foundation of it. These, however, are the elements which give importance to positive and negative contingency respectively. The inference of the subalternate particular from the uni- versal, in pure categoricals, has this same partial and one-sided character. We cannot fully infer "some, perhaps all, are," from " all are," nor " some, perhaps all, are not " from " none are." The "some " part follows, but the " perhaps" part does 182 THE MODALIST. [Chap. XIX. not. Indeed, as the "perhaps " implies the possibility, or con- tingency, of "not all," it really conflicts with the universal judgment. The inference of subalternation shows only that the par- ticular — or the contingent — proposition has been in the right direction, not that it has expressed the full and exact truth ; and as subordinate to the universal and the necessary, the par- ticular and the contingent cannot be taken to mean that the superalternate proposition may not be true. They set forth only that peculiar particularity and possibility — or partitive- ness and contingency — which are not apposed to, but involved in, the universal and the necessary. 12. Again, the modals A' and ' are the contradictories of each other, as are also E' and I'. For if it is true that a thing must be so, it is false that it may not be so; and if it is true that a thing may not be so, it is false that it must be so : also, if it is false that a thing must be so, it is true that a thing may not be so; and if it is false that a thing may not be so, it is true that it must be so. likewise, if it is true that a thing cannot be so, it is false that it may be so; and if it is true that a thing may be so, it is false that it cannot be so; also, if it is false that a thing cannot be so, it is true that it may be so; and if it is false that it may be so, it is true that it cannot be so. 13. In these inferences, however, two peculiarities are to be observed in the significations of "may not" and "may" — two modifications of meaning which are not always, or necessarily, attached to these words. First, when the falsity of one contradictory follows from the truth of the other, " may " denotes an absolute possibility to be — a possibility which cannot be displaced by impossibil- ity ; so that, with the given antecedent, the thing is certainly not impossible : while " may not " signifies an absolute possi- bility not to be ; so that — the antecedent remaining without addition or alteration — the thing is certainly not necessary. Secondly, when the truth of one contradictory is inferred from the falsity of the other, the word "may" is not used simply, but means "may, perhaps must" (equivalent to "may Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 183 or must"), while "may not" means "niay not, perhaps can- not," (equivalent to "may not or cannot"). Without these significations of " may " and " may not " the inferences of contradiction would not take place. The force of these words as thus modified may be inadequately expressed by saying that " may " means " certainly may, possibly must," while "may not" means "certainly may not, possibly cannot." These meanings — it will be noticed — correspond exactly to the " some, perhaps all," and the " some, perhaps none " of the dogmatic subcontraries. But they belong to a wider and more searching range of thought. 14. In some of the foregoing statements the term contin- gency has been used interchangeably with possibility, the rea- son being that contingency is based on possibility, and by reason of its radical nature, shares in the oppositional relations of possibility. As regards subalternation and contradiction the possible and the contingent are one ; and, as we have seen, each of these modes of opposition may be said to involve a specific form of possibility of its own. A clearer understanding of these teachings can be had if we consider four styles of possibility, in all of which the essential conception of the consistency of the existence — or of the non- existence — of a thing with given circumstances, is modified by some addition. First of all, there is that possibility which is perceived as accompanying necessity, positive or negative — in other words, as accompanying necessity and impossibility. That which neces- sarily exists, is recognized as possible to be ; and that which necessarily does not exist, is recognized as possible not to be. That which must be, may be ; and that which cannot be, may not be. The positive form of this possibility may be said to be embedded, or infixed, in necessity ; and the negative form to be embedded in impossibility. The positive form, therefore, cannot co-exist with impossibility, nor the negative with neces- sity. Yet a denial of the positive form does not warrant the assertion of impossibility, nor a denial of the negative form 184 THE MOBALIST. [Chap. XIX. the assertion of necessity. Each form exists only in its own mode of necessity, positive or negative; and neither exists in case a given antecedent supports neither necessity nor impossi- bility. If death were considered possible only because death is necessary, a denial of this embedded possibility would not involve the impossibility of death. The case might be one of a possibility lying between necessity and impossibility, and not embedded in either. Therefore this embedded possibility is not that according to which the contingent negative contradicts the necessary, and the contingent positive the impossible, but merely that accord- ing to which the contingent is inferred from the necessary and the impossible. For an antecedent of necessity, positive or negative, is taken as proof that the existence — or the non- existence — of a thing is consistent with a given set of circum- stances. We allow that the possibility in such a case is only partial and improper. Ordinarily when we say that a thing is possible we do not mean that it is possible only to be, but that, so far as our knowledge extends, it is possible either to be or not to be. So also contingency commonly excludes the asser- tion of necessity. But if subalternation be taken as a mode of sequence in which the particular follows the universal and the contingent the necessary, it must be explained in the foregoing way ; and with some such use of terms. This mode of opposition, however, may be interpreted to mean that the ordinary particular or contingent assertion — the " some, perhaps all " or the " may, perhaps must " — is to be accepted as partially correct and as made in the right direc- tion, provided the apodeictic superalternate be true. We really prefer this explanation, though it will not permit us any longer to infer the subalternate from the superalternate, but only that the subalternate has a certain logical value. A second, and an entirely proper, form of possibility is recognized, when the very same antecedent which supports a con- tingency may, or may not, siipport a necessity, yet is not perceived either to do so or not to do so. If one knew only that a lion is a quadruped and that a quadruped may and may not be a carnivore, he could say, " A lion may be a carnivore," and, " A Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 185 lion may not be a carnivore." In so doing he would use the antecedent "lion" correctly, but without knowing the full force of it; because, absolutely speaking, the lion is neces- sarily a carnivore. Or should one use an antecedent capable only of supporting contingency, while he yet knew not of this limitation, this would be another species of the kind of infer- ence now mentioned. If one knew only that a merchant is a man, and that a man may and may not be wise, he could say, "A merchant may be wise," and, "A merchant may not be wise." But he could not say whether further knowledge might not warrant " a merchant must be wise " or " a merchant can- not be wise." The contingency thus described may be styled " unstable" because further knowledge of the antecedent may lead one to displace the contingent by an apodeictic judgment. It may also be called " unguarded" because it is not protected, as another form of contingency is, against being displaced by necessity or impossibility. Evidently no unstable contingency can contradict an apodeictic statement ; since the latter may prove to be supported by the very same antecedent which is employed to support the contingency. A third form of possibility or contingency is the stable, or guarded. This is recognized when the antecedent is perceived to be of a nature to support contingency only; so that no further knowledge of the antecedent can justify a judgment in necessity or in impossibility. In this case we say that a thing is neither necessary nor impossible, but possible to be and possible not to be. Every judgment in contingency may, on further information, be displaced by an apodeictic judgment. This may happen to an unstable contingency while the antecedent remains the very same ; but it cannot happen in stable contingency so long as the antecedent be not essentially modified, or replaced by a new antecedent. That ace may appear and may not appear on the throw of a die, and that frost may and may not occur on New Year's in latitude 40°, are stable, or guarded, possibilities ; they cannot, with the antecedents given, become certainties. Stable contingency is also perceived when the antecedent has been seen to be sometimes accompanied, and sometimes not accom- 186 THE MODALIST. [Chap. XIX. panied, by the consequent. Knowing that man sometimes is wise and sometimes not wise, we assert, as a stable contingency, " man may be, and may not be, wise." The observed instances preclude us from saying that man is necessarily wise, or that he is necessarily not wise. It is especially when determined in this way that stable contingency may be called guarded. This contingency — that is, the assertion of it — denies both necessity and impossibility ; because neither necessity nor im- possibility can result from one of its antecedents. By it the possible to be is opposed to impossibility, and the possible not to be to necessity ; and so the positive side of it contradicts impossibility, and the negative, necessity; but the force of the contradiction comes from that stability which affects both sides alike and together. In the same manner necessity and impossibility contradict this contingency ; that is, are the con- traries of it. But a denial of stable contingency does not compel the assertion of necessity or of impossibility; it only involves that one or other of these is true. The denial of necessity, moreover, involves only that the contingency or impossibility is true — not that the contingency is true ; and the denial of impossibility involves only that the contingency or the neces- sity is true, not that the contingency is true. Thus the stable contingency, " a quadruped may, and may not, be a carnivore " conflicts with both positive and negative necessity ; as each of them does with it. But were it false, this would not justify us in saying either that a quadruped must be, or that a quad- ruped cannot be, a carnivore ; we could only say that one or other of these is true ; nor would the falsity of one only of these apodeictic statements justify the assertion of the contin- gency. Therefore thorough-going contradictory opposition to necessity or to impossibility cannot be obtained from stable con- tingency. There is, however, a fourth style of contingency which does yield this opposition. It may be called half-stable, or half- guarded, contingency. It is perceived when an antecedent of contingency has been seen sometimes to be actually followed by a consequent, and has never been seen without the conse- Chap. XIX.] THE OPPOSITION OF PBOPOSITIONS. 187 quent; or when an antecedent lias been seen sometimes to occur without the consequent, while it has never been seen to be followed by it. In the former case the contingency is guarded against impossibility, but may be displaced by neces- sity ; in the latter it is guarded against necessity, while it may be displaced by impossibility. 15. A half-stable contingency guarded against impossibility may be said to lean, or tend, towards necessity. It is expressed exactly, though indirectly, by a particular affirmative asserted alone. Thus, " some men are wise " means " man may be wise, perhaps must be, and certainly is not incapable of wisdom" A half-stable contingency guarded against necessity leans, or tends, towards impossibility; and is expressed similarly by the particular negative. Thus, " some men are not wise," as an isolated statement, means " man may not be wise, perhaps cannot be, and certainly is not necessarily wise." No terms have been used to designate these two modes of half-stable possibility. Let us call that which leans towards necessity encouraging possibility, or contingency; and that which leans towards impossibility discouraging contingency. These somewhat arbitrary terms are the best which suggest themselves. We are prepared, now, to state what forms of contingent assertion are the thorough-going contradictories of necessity and of impossibility. Necessity is thoroughly antagonized by discouraging contingency, and impossibility by encouraging con- tingency. If we assume simply that " some men are wise," we can assert the encouraging contingency "man may be wise." Then we can say, if it is true that " man may be wise," it is false that " man cannot be wise " ; if it is false that " man may be wise," it is true that " man cannot be wise " ; if it is true that "man cannot be wise," it is false that "man may be wise " ; and if it is false that " man cannot be wise," it is true that "man may be wise." In short, encouraging contingency and impossibility thoroughly contradict each other ; and so do discouraging contingency and necessity. The main object of the foregoing discussion has been to bring out the inner nature and meaning of those particular prop- 188 THE MOBALIST. [Chap. XIX. ositions which are the thorough-going contradictories of universals. Evidently they are at heart a peculiar kind of contingent modals. Hence, too, it should be noticed that the symbols /' and 0', as used to indicate the contingent equivalents of par- ticular propositions, relate only to half-stable contingency, and not to contingency in general. The prominence thus given to half-stable contingency is not unreasonable : dialectically this is the strongest mode of contingency; and it is of peculiar value when we are seeking the actual, and not merely the possible or the probable. 16. Finally, the relation of subcontrariety exists between the propositions just described, that is, between I' and 0', as half-stable contingencies. For if either of these be false the other is true. Yet, critically speaking, this sequence does not take place exactly. The exact sequence is from the falsity of I' or of 0' to the truth of the opposite embedded contingency. A corresponding inaccuracy appears when we say that the falsity of a particular proposition involves the truth of the opposed particular. For the falsity of "some, perhaps all, are," does not involve the doubtful conclusion that "some, perhaps all, are not," but the absolute conclusion that " some, as a part of all, are not " ; and the corresponding inference from the falsity of "some are not," is that "some, as apart of all, are." The falsity of one subcontrary shows that the other has been made in the right direction, though it has fallen short of the truth; this is all that the logical rule can be taken to mean, whether the propositions be pure or modal. For the subcontraries are really, not embedded, but half- guarded, contingencies. These modal subcontraries agree also with the pure subcon- traries in that the truth of either does not involve either the truth or the falsity of the other. That " some (perhaps all) men are wise " does not involve that " some (perhaps all) men are not wise," because the first of these statements implies that we may find all men to be wise, in which case " some men are not wise" would be entirely false. But the two particular propositions will be true together, so far, at least, as regards their " some are " and " some are not," in case we do not find Chap. XIX.] THE OPPOSITION OF PROPOSITIONS. 189 all men to be wise. In like manner, " man may be, perhaps must be, wise " does not involve " man may not, perhaps can- not, be wise," because, if man should prove to be necessarily wise, this would show that the discouraging contingency had been falsely asserted. Indeed, in the strictest sense, encourag- ing and discouraging contingency conflict with each other. Yet, should we find that, though man may be wise, he is not necessarily wise, then both the positive and the negative con- tingency would be true so far as the "may" and the "may not " are concerned. 17. Probability has not been mentioned in the above dis- cussion. The oppositional relations of this mode of sequence are essentially those of possibility ; and belong to probability as being based on possibility. Probability presupposes some form of contingency proper ; and may be divided into unstable, stable, and half-stable, according to the style of contingency on which it is based. In unstable probability the ratio of the chances is determined provisionally and temporarily ; because the very same antecedent which yields probability may be found to yield certainty. In half-stable probability the ratio of the chances is guessed at roughly ; because our knowledge extends only to instances favoring one side. Permanent, duplicating, or recurrent probability, which is the leading form of this mode of assertion, is " stable " ; and as such, while not justifying either the subalternation or the thorough-going con- tradiction of judgments, conflicts with both necessity and impossibility. The importance of modal opposition relates to the con- tradictions between possibility (including contingency) and necessity; it is not connected with the specific nature of probability. 190 THE MODALIST. [Chap. XX. CHAPTER XX. THE CONVERSION OF PREDICATIONS. 1. The conversion of dogmatic, or "pure," propositions. 2. Requires a substantialized and quantified predicate. Proceeds on the principle of Identity. 3. The ordinary conversion of affirmatives. 4. And of the uni- versal negative. "Not," as the exclusive particle. 5. Particular negatives must be converted by "contraposition," or " infinitation." 6. Conversion "per accidens," or "by limitation." Conversion "per differentiam," or by "the retained-necessitant." " Simple " conversion. 7. The quanti- fication of modals. 8. The universal- necessary and the particular-con- tingent. 9. The universal- contingent. 10. The particular- necessary. 11. Quantity is non-essential to modal thought. The ordinary converse of a necessity is a simple contingency ; but sometimes we convert with the retained-necessitant. 12. The ordinary converse of an impossibility is an impossibility. 13. The conversion of contingency. Always follows " the asserted-consequent.' ' 14. Contingent and particular conversion compared. 1. Conversion, or, more expressly, conversional sequence,, takes place whenever from a given proposition another is inferred in which the same terms appear but with an exchange of places. Like oppositional sequence it is not dependent on any reference to a previously perceived similar sequence ; and is, therefore, orthologic. The antecedent proposition is called the convertend; the consequent proposition, the converse. The subject of the convertend furnishes the predicate of the converse, and the predicate of the convertend the subject of the converse. For example, from " all men are mortal " we infer that " some mortals are men." Propositions purely factual, or historical, may be converted. Because "Mr. Harrison is president elect," we can say "the president elect is Mr. Harrison." From " some rogues are on that jury " it follows that " some on that jury are rogues." Such inferences not only follow the law of Identity (Chap. XV.), but are entirely explained by means of it : no study is required Chap. XX.] THE CONVERSION OF PREDICATIONS. 191 to understand them. The conversion now to be discussed per- tains to those illative propositions which may be used as prin- ciples in reasoning, and especially to categorical predication as expressing general hypothetical sequence. Let us consider, first, the conversion of pure, or dogmatic, categoricals ; and, after that, the conversion of modal predications. Before commencing this discussion it should be observed that not all propositions are convertible ; only those which have been distinguished as inherential statements, or predica- tions proper. Presentential propositions cannot be converted, because they never set forth a sequence, nor any relation between things, but merely the existence or the non-existence of the subject. 2. The conversion of a dogmatic predication takes place only after the predicate of the convertend has been both substan- tialized and quantified. Substantialization is effected when the predicate is changed from the ascriptional form of thought, such as adjectives and verbs express, to the substantal form, which is expressed by nouns or their equivalents. In this way " all horses have four feet " becomes " all horses are quadrupeds " ; and, instead of " no horses eat flesh, or are carnivorous," we say, "no horses are flesh-eaters, or car- nivora." Then, also, the predicate, which is commonly un- qualified in the original proposition, must be given that quantity, whether universal or particular, which the nature of the sequence warrants. We must say — in thought, at least, — "all horses are some quadrupeds," and, "no horses are any flesh-eaters." After this quantification every ordinary affirmative statement asserts that all, or some, of the subject class, are identical with some, at least, of the predicate class ; and every negative statement asserts that all, or some, of the subject class, are different from any — and, of course, from all — of the predicate class. Thereupon conversion follows on the principle of Identity. Because, so far as verbal thought goes, the converse of a thoroughly quantified dogmatic propo- sition presents essentially the same truth as the convertend. But, as ordinary assertion aims only to characterize the sub- ject, and does not quantify the predicate, the subject of the 192 THE MODALIST. [Chap. XX. convertend loses its quantity after it becomes the predicate of the converse. "All horses are some quadrupeds/' and "no' horses are any carnivores/' become, simply, "some quadrupeds are horses/' and "no carnivores are horses." The ordinary purposes of predication do not require us to think and say "some quadrupeds are all (the) horses" and "no carnivores are any horses." 3. The converse both of the universal affirmative and of the particular affirmative proposition, is a particular affirmative j because ordinary affirmation only identifies the subject with a part of the predicate class. "All men are wise" and "some men are wise " alike yield " some wise beings are men." The converse of the universal, however, may be said to be a stronger assertion than that of the particular. Quite in consistency with the foregoing, certain universal affirmatives are convertible into universal affirmatives ; because they are statements which contain more than the ordinary uni- versal affirmative. To indicate this, they have been symbol- ized by the vowel U, instead -of A ; and we are told that {/may be converted into U. This class of propositions comprises all those in which the subject is an exact logical necessitant of the predicate. Accordingly, " all spirits are sentient " yields " all sentient beings are spirits " ; provided the convertend be under- stood to teach that spirits have sentiency as a distinguishing attribute, or as a specific property. Definitions, also, belong to the class U, because they give the exact analytic equivalent, of a thing. If " every moral law is a rule of right action," then " every rule of right action is a moral law." 4. Passing to negative propositions, it is evident that all of these, when quantified,, assert that all, or some, of the subject class, are not any of the predicate class. In other words, they entirely exclude from the predicate class all or some of the subject class. On this account the particle "not," properly enough, has been called "the exclusive particle" ; though this designation does not set forth its essential meaning. The principle of Identity requires the converse of the universal negative to be an universal negative. Hence "no four-stomached animal is carnivorous," yields "no carnivore has four stomachs."' Chap. XX.] THE CONVERSION OF PREDICATIONS. 193 5. The particular negative is commonly said to be incapable of conversion ; it is more exact to say that the negative propo- sition obtained by converting the particular negative has no predicative force. " Some colored men are not negroes," with quantified predicate, becomes " some colored men are not any negroes." The converse of this, " not any — or no — negroes are some colored men," is a true converse, yet useless because of the indefinite "some" For while negroes are not some colored men, they may be some other colored men. This converse does not enable us to say either that negroes are, or that negroes are not, colored; it does not characterize the subject either positively or negatively ; therefore it fails of the essential end of predication. But while the particular negative does not directly yield any usable converse, its contrapositive does ; and, employing this, we convert the particular negatively indirectly. " Some colored men are not negroes," by contraposition (Chap. XV.), becomes " some colored men are men not negroes," a particular affirm- ative ; from which we obtain " some men not negroes are colored." Not only 0, but A, may be, converted by contraposition. The contrapositive of "all horses are quadrupeds," is "no horses are animals not quadrupeds " ; from which we obtain the con- verse, " no animals not quadrupeds are horses." E also may be converted in this way. " No men are perfect," yields " all men are beings not perfect," and then "some beings not perfect are men." But this converse of E is a weak assertion, and is seldom used. The particular affirmative alone cannot be con- verted by contraposition ; because its contrapositive is a par- ticular negative. The contrapositive of " some men are happy " is "some men are not unhappy" ; this has no usable converse. In every contraposed proposition the original predicate con- ception is displaced by its contradictory, and, because this contradictory is generally a negative conception, contrapositive conversion has been called " conversion by infinitation ; " that is, by the formation of negative conceptions. The original conception, however, is occasionally negative, and is then dis- placed by a positive conception. In this case the conversion 194 THE MODALIST. [Chap. XX. does not depend on infinitation, but on the reverse process ; which might be called re-finitation. 6. The ordinary conversion of A into I was styled by old logicians " conversio per accidens" ; which phrase signifies that, in the subject of the converse, the predicate conception of the convertend is not used simply, but with reference to some " accidental " addition. For, in saying conversely, " some ani- mals are men," we do not mean that any animals, simply as such, are men, but only that certain animals which have char- acteristics not necessarily connected ivith the nature of animals in general, are men. The same idea is presented when A is said to be converted "by limitation." Ordinarily, in this conversion of A " per accidens," or " by limitation," the subject of the converse loses its universality ; it drops part of its force. The converse " some animals are men" means only that "some animals are (at least) some men." But occasionally, especially in syllogizing, the subject of the convertend, as predicate of the converse, retains its universality; so that we regally assert "some animals are all the men." This mode of converting an universal or apodeictic proposition might be styled conversion " per differentiam," or. more exactly, conversion "by the retained-necessitant." For the subject of the convertend, as predicate of the converse, retains its necessitant value, and its " specific " membership in the class designated by the other term. The conversion of / into /, and that of E into E, are com- monly called "simple conversion," because the converse has the same quantity and quality with the convertend. This language should not be allowed to conceal the fact that these conversions depend upon entirely different laws, so far as their quantifications are concerned. I is converted on the same principle as A, that is "per accidens," or by limitation; E is converted on the principle of negational exclusion. Let us now turn from the conversion of pure categorical propositions to that of modals. Modal conversion reveals the Chap. XX.] THE CONVERSION OF PREDICATIONS. 195 inner significance of dogmatic conversion; and explains the conversion of all illative propositions whatever. 7. At this point we meet the fact that modal propositions often quantify their subjects in the same way that dogmatic propositions do ; and are compelled to enquire into the mean- ing of this quantification. We sometimes say, not simply " man must die ; man cannot reach perfection," but " all men must die ; no men can reach perfection " ; sometimes, not simply " a professor of religion may be a hypocrite ; a liquor- dealer may not be a bad man," but "some professors of religion may be hypocrites ; some liquor-dealers may not be bad men." In short, necessary statements are occasionally given universal quantity, and contingent statements particular quantity. Not only so; we sometimes "distribute" the subject in contingent statements, and employ "undistributed" subjects in necessary statements. We say, "all soldiers — or any sol- dier — may exhibit bravery; some soldiers must die in battle." Let us consider, first, universal statements of necessity ; secondly, particular statements of contingency; thirdly, uni- versal statements of contingency; and fourthly, particular statements of necessity. 8. The universal necessary proposition differs from a simple general statement of necessity only in being more explicit and emphatic. "All men must die" means that "man, as such, must die." If man, simply as man, is mortal, then all men must die. But if man were necessarily mortal only when sub- jected to influences from which some of the race are free, we could not say that "all men must die," or that, absolutely speaking, " man must die." In that case we could only say, " some men must die," and, with regard to man as such, " man may die." Hence the universality of an apodeictic propo- sition shows that the statement is made unreservedly, and without mental qualification or limitation. It arises from, and is used to indicate, the absolute necessity of the statement. Therefore, also, when any proposition is given and accepted as a rule of necessary sequence and of demonstrative inference, the universality may be dispensed with. 196 THE MOBALIST. [Chap. XX. For a similar reason the particular contingent proposition need not be regarded as a necessary logical form. " Some pro- fessors of religion may be hypocrites," as a general contingency, differs as to strength only from the assertion that "a pro- fessor of religion may be a hypocrite." Its meaning may be expressed without the "some" if we give the word "may" a questioning emphasis. It states that a professor of religion may be a hypocrite, but suggests also that the realization of this contingency is not to be expected under ordinary circum- stances. It is consistent with the proposition that many pro- fessors of religion cannot be hypocrites. In short, a particular contingent proposition respecting a logical class sets forth such a weakened contingency as is suggestive of improbability. It should be recognized among the forms of modality. Yet the weak contingency which it embodies may be conceived and expressed without the quantification ; we can therefore sim- plify our discussion — so long, at least, as it relates to mere contingency — by dispensing with this quantification. 9. The universal contingent proposition, as might be ex- pected, has a force opposite to that of the particular. It expresses a strong contingency ; especially when the universality is emphasized. " A professor of religion may be a hypocrite " is a contingent assertion applicable to every member of the class spoken of considered simply as a member of the class. This contingency is strengthened when we say, " All professors may be hypocrites." The first assertion would consist with the knowledge that some professors are not, and cannot be, hypo- crites, though not of course, with such knowledge respecting any whose character is in question; the second assertion excludes such knowledge altogether. The same thoughts are expressed by contrasting " any professor may be a hypocrite " and "every professor may be a hypocrite." But should we omit the contrast and emphasize "any" there would be no difference between these statements. In short, there is no difference between an universal contin- gency and an unquantified contingency, if the latter be under- stood absolutely, or as excluding all knowledge of exceptions. The statement, " It may be that every liquor-dealer is a bad Chap. XX.] THE CONVERSION OF PREDICATIONS. 19T man," would express a strong contingency; for it would imply that one could not say that the rule has any exceptions. 10. Finally, propositions which set forth necessity (or im- possibility) concerning an undistributed subject, are really con- tingent assertions respecting the subject viewed simply. " Some- soldiers (that is, some of the logical class ' soldiers ? ) must die in battle " expresses the contingent rule, " a soldier may die in battle." The contingency thus expressed, however, is affected by two additions. First, we are informed that the antecedent of con- tingency, " a soldier in battle," is sometimes filled out so as to- become an antecedent of necessity. This, also, is the essential thought expressed by the dogmatic proposition, "some soldiers die in battle." Hence, — as necessity conflicts with impossi- bility — we are informed that the contingent rule "a soldier may die in battle," cannot be supplanted by the apodeictic rule " a soldier cannot die in battle " ; it is guarded against impossibility. In like manner, the principle of reasoning that " some soldiers cannot — or not all soldiers can — be killed in. battle," and which, so far as it is a general contingency, is expressed by " a soldier may not be killed in battle," cannot be supplanted by " a soldier must be killed in battle " ; it is guarded against necessity. This addition, whereby a con- tingency is guarded against impossibility, or against necessity, — or, in general terms, against a necessity of the opposite — is important, and cannot be neglected in the opposition and conversion of predications. The quantification employed in making the addition instrumentally determines and expresses the essential character of the proposition as regards modality. In short, the " some" of particular necessary propositions sets- forth contingency in precisely the same way as the " some " of particular dogmatic propositions ; and, in each case, the verbal thought should be distinguished and separated from its mental meaning. Secondly, the " some " of the particular necessary proposition indicates that an appreciable proportion of the class '-soldiers" are certain to die in battle, and, in so doing, brings before us, indirectly, the essential nature of contingency as distinguished 198 THE MODALIST. [Chap. XX. from possibility in general. For, while contingency admits of various degrees, all contingency, even the weakest, is a strong possibility, circumscribed and determined by a necessity ; and therefore such as justifies expectancy. It is possibility con- fined to a sphere in which only a limited number of conse- quents are possible. As in every battle, or set of battles, some soldiers die while the rest survive, and there are thus as many events as there are soldiers, it follows that any soldier, taken at random, has so many chances to be killed and so many to live through the battle or the war. One of the deaths may be his or one of the survivals ; and one out of the limited total of events must be liis. Therefore the possibility of his being killed or not, is a circumscribed, or determined, possibility — a contingency. This contingency is further strengthened in case the "some " of the proposition respecting the class " soldiers," is conceived to be a considerable proportion of the " all." If the ratio of the " some " to the " all " were fixed and given, a regular judgment of probability would take place. But that being unsettled, there is only a contingency, which approaches a probability without reaching it ; or, if you please, a contin- gency which is an undetermined probability, while it is itself a determined possibility. Such is the significance of the par- ticular assertion of necessity. Yet not all contingency asserts that a certain event neces- sarily happens to a number of a logical class, and that any one in the class may be of that number. If some appreciable pro- portion of the balls in a box were red, there would be a con- tingency of corresponding strength that the ball first drawn out would be a red one j and were a thousand boxes similarly supplied, the contingency would be the same for box after box. This contingency would assume that one out of the limited number of balls in each box must appear ; but it would not be based on any knowledge that red balls have appeared, or that red balls must appear, any number of times. Yet this contin- gency would be guarded, if we knew that there was nothing to prevent any ball from being drawn on any repetition of the trial; and it would become a definite probability, if we Chap. XX.] THE CONVERSION OF PREDICATIONS. 199 knew the exact number of balls of each, color. Such contin- gency differs from that expressed by the " particular " proposi- tion in its origin ; but not in its nature, and as a ground and mode of judgment. And this being the case, it is plain that particular quantification is not necessarily connected with guarded contingency, but only with the origin of a certain form of it ; which also it naturally expresses. 11. The foregoing analysis shows how quantification may strengthen and weaken, modify and define, modal assertion, while yet quantity is no proper part of modal thought, and has only a secondary and ministrant place in the expression of modality. The essential meaning of any modal proposition dispenses with quantification. Such being the case, we proceed to the conversion of modals ; beginning with the conversion of apodeictic assertions — that is, of propositions setting forth unqualified necessity and im- possibility. The converse of a necessity is a contingency. For, if a man must be a mortal, a mortal may be a man. To speak more accurately, it is a contingency guarded against impossibility. For if man, as such, must be a mortal, then a mortal, as such, H- may be a man, but is certainly not iyicapable of being so. This exclusion of impossibility, which results from the necessity asserted in the convertend, is often implied when we use the word " may " alone ; and the exclusion of necessity may be implied in using "may not" alone. Then what "may be " cannot, on further information, be found impossible, and what " may not be " cannot be found necessary. The word " may " sometimes indicates an unstable possibility, in which case there is no exclusion of impossibility ; it expresses the converse of necessity only when this exclusion is understood. Moreover, the contingent converse of a necessity is exclusive with reference to its subject. The full statement of it is, not that " a mortal may be a man," but that " only a mortal may be a man." Commonly this exclusion, being unnecessary to the course of one's reasoning, is allowed to drop out of thought. But sometimes it is essential; and then it must be retained and recognized. 200 THE MODALIST. [Chap. XX. a This full conversion of necessity might be distinguished as differential conversion." It is expressed dogmatically when we say, " some mortals are all men." It is a peculiar case of limitative, or contingent, conversion. It might be named con- version with " the retained necessitant." The contingency produced by the conversion of a necessity arises from the circumstance that the consequent of a necessary sequence conditions its antecedent : because, whenever we can assert that a condition of a first thing exists in a second thing, Ave can say that the first thing, so far forth, may be — or is possible. As the use of this law depends on the assertion of the consequent, it may be called the principle of tlie asserted consequent. The common rule is, that we cannot assert the antecedent because the consequent is asserted ; this, however, means only that the antecedent cannot be asserted absolutely, or apodeictically ; it can be asserted contingently. This prin- ciple is a part of the general theory of conditions. 12. The converse of an impossibility is an impossibility. "A horse cannot fly" ; therefore "a flying animal cannot be a horse." This converse has the same modality as the conver- tend ; there is no change either from necessity or from nega- tion: hence the conversion is called "simple." The simplicity, however, is superficial ; there is really a great change. In the convertend we reason from an existing subject to a non-existing predicate — from an existing horse to the non-existence of a flying animal in the horse. In the converse we no longer con- ceive of the original subject as existing, and of the original predicate as non-existent; but do just the reverse. We reason from the existence of the predicate to the non-existence of the sub- ject — from the existing flying animal to the non-existence of a horse in it. This is a radical change. The law governing this conversion is the principle of the denied consequent, that is, the principle which requires us to contradict the antecedent, if we contradict the consequent, of a necessary sequence. That such is the nature of the conversion will be evident, if we remember that the impossible and the necessary not to be, are the same. "Man cannot be perfect," means "man necessarily is not perfect." If now we contradict the conse- Chap. XX.] THE CONVERSION OF PREDICATIONS. 201 quent, "not perfect/' by asserting "perfect," we must contra- dict the antecedent "man/' in other words, man as existing. Therefore we say, "a perfect being necessarily is not — or cannot be — a man." An impossibility is also convertible on the principle of the asserted consequent. " a man cannot be perfect " has " man " for antecedent, and " not perfect " for consequent. Asserting this consequent, we have, "a being not perfect may be a man." This converse, because of its contingency and of its negative subject, does not compare in value with the other, " a perfect being cannot be a man." Necessity, also, may be converted on the principle of the denied consequent. " A war requires an army " has the con- verse, "where there is no army, there can be no war." So, since a plain must be extended, what is not extended cannot be a plain. This converse is apodeictic and absolute; and, notwithstanding its negative subject, is quite useful. It gives & test for the existence of any subject whose attributes or properties are known : if any of these do not exist, the subject cannot exist. It also furnishes the means of reducing a false statement of necessity to an absurdity. For if, in any instance of an assumed antecedent, its alleged necessary consequent can be shown to be wanting, this would lead to the contradiction and impossibility, that the antecedent known to exist does not exist. 13. The conversion of contingency, positive and negative, presents far more difficulty than that of necessity and impossi- bility. The laws of contingent conversion can be simply stated ; but the intelligent use of them involves an understand- ing of the subtle compounded nature, and of the delicate vari- ations, of contingent sequence. Besides, the ambiguity of lan- guage adds to the inherent obscurity of this subject. This especially attaches to the word "may," which sometimes denotes a naked, or bare, possibility, such as excites no ex- pectancy ; sometimes a clothed, or invested, possibility, which alone deserves the name of a contingency ; and sometimes a specific mode of contingency : so that the meaning of this word must often be a matter for consideration. 202 THE MOJDALIST. [Chap. XX= The general rule for the conversion of a true contingency is that we must follow the pvinciple of the asserted, and not that of the denied, consequent. " Man may be wise," of which the consequent is wise as existing in man, has the converse, " a wise being may be a man " ; while " man may not be wise," of which the consequent is wise as non-existent in man, has the converse " a being not wise may be a man." But should we apply the " denied consequent " to the first of these convertends, the result, " one not wise may not be a man" — though in a certain sense a correct inference — would have no predicative force. It sets forth a possibility which not only is unguarded against either necessity or impossibility, but is also unsupported by any ground for believing that the negative sequence contingently asserted has ever at any time been realized, or that it ever will be. A precisely parallel con- version would be, " a quadruped may be an elephant," there- fore "an animal not an elephant may not be a quadruped'' — an inference entirely nugatory, because, for aught that the convertend teaches, it may" be true that all animals not ele- phants are quadrupeds, or that none of them are quadrupeds ; and we are given no reason to suppose that any one of them ever has not been, or will not be, a quadruped. In like manner, applying "the denied consequent" to the convertend " man may not be wise," we have " a wise being may not be a man," a possibility wholly unprotected, inde- terminate, and without predicative force. Because, for aught that is given in the convertend, it may be true that a wise being must be a man, or that he cannot be a man, and we have no reason to believe that any wise being ever was not, or will not be, a man. A parallel conversion to this would be, "a quadruped may not be an elephant," therefore, " an elephant may not be a quadruped." 14. The conversion of contingent modals is closely related to that of particular dogmatic propositions. These latter, in- ternally and essentially, are simply the most common and im- portant forms of contingent sequence. They are contingencies guarded against the necessity of the opposite. Hence the rules for their conversion can be explained by the laws of modal con- Chap. XX.] THE CONVERSION OF PREDICATION IS. 203 version, even while they exhibit an apparent contrast to these laws. For contingent propositions, positive and negative, are converted according to one principle (the asserted consequent) which applies to both alike ; while particular dogmatic propo- sitions are converted by two rules. I — the particular affirma- tive — is converted by "limitation," and — the particular negative — by " contraposition." Thus " some men are wise," converted by limitation, yields " some wise beings are men " ; and " some men are not wise, " converted by contraposition, yields " some beings not wise are men." This contrast is a result of that form of thought which neg- ative propositions ivith a substantal predicate naturally assume, and which is especially observable in the pure, or dogmatic, negative. In all such propositions we aim to assert the non- existence of cm identity. But, ordinarily, the mind, clinging to positive conception, instead of asserting that non-existence immediately, first conceives, though without assertion, of the identity as existing, and then denies its existence. This mode , of conception resembles that according to which negative neces- sity becomes impossibility. Contraposition destroys the indi- rectness of such assertion by immediately attaching the thought of non-existence to the predicate, and then substantializes the negative conception thus produced. After this change, the predicate, "not wise being," truly sets forth the contingent negative consequent ; which the original predicate, " wise being," did not. Thereupon the contraposed proposition, as a consisting of antecedent and consequent, is converted on the same principle as the particular affirmative, that is, "by limi- tation"; which is equivalent to "the asserted consequent," as applied to guarded contingencies. 204 THE MODALIST. [Chap. XXL CHAPTER XXI. CONTINGENCY AND ITS CONVERSION. A SUPPLEMENTARY CHAPTER. 1. Contingency distinguished from possibility. 2. Possibility denned. 3. Contingency, a circumscribed possibility. 4. Either empirical or mathe- matical. 5. Involves an opposite possibility, but not an opposite contin- gency. 6. Is either guarded (i.e. half-guarded) or unguarded. When double, may be doubly guarded. 7. When combined with a prior sequence, produces a contingency unguarded, i.e. unassured, against a necessity of the opposite. 8. Unguarded mathematical (or intuitional) contingency. 9. Embedded contingency, is contingency only in an improper sense. 10. Possibility is converted only by the asserted- consequent ; and according to (a) the law of contained-conditions, and (&) the law of the unascertained- necessitant. 11. The converse by the denied- consequent has no force, or value. 12. The conversion of contingency. Violently rejects the denied- consequent. 13. Is effected by the asserted-consequent. 14. Assumes a numerical limitation of the predicate of the convertend. 15. Not ordinarily, nor necessarily, double. 16. The converse of an encouraging — or guarded affirmative — contingency, is an encouraging contingency with a positive subject. 17. That of a discouraging — or guarded negative — contingency is an encouraging contingency with a negative subject. 18. These unite in the double converse of a double guarded contingency. 19. The conversa of unstable contingencies are unstable. 20. The conversion of improper— or embedded— contingency follows that of the necessity in which it lies. 21. A scheme of symbols. 1. The perplexity which has hitherto obscured the exposi- tion of modal assertion and reasoning has arisen principally in connection with contingent propositions. The nature of apodeictic statements is easily understood. He who would cut plain roads through the labyrinth of modality must set forth the forms and laws of contingent predication. We have already attempted this ; but an additional and somewhat inde- pendent discussion will be found useful. Chap. XXI.] CONTINGENCY AND ITS CONVERSION. 205 Contingency, as a ground of inference, is that mode of possi- bility which excites expectancy ; it may be distinguished from simple possibility by the conditions under which it is produced. 2. Possibility, in the widest sense, is the consistency of the existence of a thing with given surroundings. What is con- sistent with given circumstances is not impossible in those circumstances. This wide possibility shows that the question as to the reality of a thing is not absolutely absurd. Ordinary logical possibility, however, is more than mere consistency, or non-repugnancy. It is the compatibility, or con- gruity, of the existence of a thing, with given circumstances. Hence it is suggestive of the question of reality, even, while it may suggest no answer to this question. For when we say that B is possible because A exists, meaning that the existence of A involves the existential compatibility of B with the cir- cumstances assumed with A, the question arises, "Does B exist ? " The compatibility, or congruity, of B with given surround- ings, rests on the fact that A, as one of those circumstances, contains some, at least, of the necessary conditions of B. A broken line composed of three straight lines on a plane renders a triangle possible because it contains three conditions of a tri- angle. But, in order to a suggestive sequence of possibility, the conditions contained in the antecedent must be such as specially connect themselves with B, the consequent. If they are of a very general character, they will not imply the possi- bility of B specifically. It would not be a suggestive sequence to say that space renders a line, or a triangle, or a field, or a house, possible. Such judgments are metaphysical rather than logical. But the specific judgments, " a line may be straight," " a triangle may be scalene," " a house may be of four stories," might prove suggestive and useful. Whenever an antecedent of possibility is perceived to con- tain such a combination of conditions as necessitates the conse- quent, it becomes an antecedent of necessity, as well as of possibility. Ordinarily, however, the antecedent of possibility either does not have a necessitant force or is not perceived to have it ; so that the question of reality is left undetermined, 206 THE MODALIST. [Chap. XXL and even untouched. For, as already said, possibility per se suggests no answer to this question. Its judgments result in the harmonious construction of thought, but are only negatively helpful towards the ascertainment of truth. 3. Possibility excites expectancy only when it is strength- ened into contingency. For contingency is a ground for believ- ing, not simply that a thing is abstractly possible, but that it actually may be true. This latter mode of sequence is often asserted in an unrea- soned way, or, rather, by an intuitive and practical exercise of the reason. Perceiving that one certain kind of fact or event is occasionally followed by another, we not only associate the latter with the former, but regard it as contingently connected with the other, and to be looked for, with more or less expecta- tion, whenever the other occurs. But when we reflect on such a judgment, so as to make it understandingly and place it on a foundation, we find that the possibility — the contingency — which it asserts, is confined to a sphere in which only a limited number of events are possible, and in which one of these events must take place. Contingency, therefore, is a circumscribed, or determined, possibility. The essential nature of contingency may be understood from the two following illustrations. Should we know that some of a limited number, say of a hundred, balls are red, without knowing how many, it would be a contingency to any ball taken at random to be red. The fact that the ball is one of the hundred is the antecedent of contingency; and it has a. hundred possible consequents, of which an undetermined pro- portion favor the appearance of a red ball. It would be a variation of this illustration if there were an indefinite aggre- gation of balls, composed of many equal sets in each of which there were some red balls ; in this case also it would be con- tingent to a ball taken at random to be red. Again, if we knew that some snakes are venomous, without knowing what proportion, it would be contingent to any snake, taken at random, to be venomous. The antecedent here is membership in a class of things which sometimes have a cer- Chap. XXI.] CONTINGENCY AND ITS CONVERSION. 207 tain character — in other words, the possession of that snake nature, which sometimes is venomous. 4. So far as the foregoing judgments assert contingent sequence they both arise in the same way : they both make an indeterminate use of the tychologic principle — " the ratio of the chances." But they differ as to the process by which each forms and accepts the conception of favoring chances. That snakes are sometimes venomous has been ascertained from observation, and is the ground for an homologic inference. An indefinite proportion of all snakes hitherto seen having been found venomous, this may be asserted concerning snakes not yet seen : so we say that some of the whole logical class are venomous. This justifies the general judgment "a snake may be venomous." The contingency, thus expressed, is per- ceived only after a previous perception of actual sequences, and, with reference to this, may be named inductive, or empirical, contingency. But the contingency that any ball of the hun- dred or more may be red, rests on our immediate knowledge respecting a set, or an aggregation, of balls, that some of them are red, and has no connection with any previous experience. It does not assume that, in some previous trials, the ball chosen at random has turned out red. Contingent judgments of this latter formation are less fre- quent than those based on the observation of past sequences, yet they illustrate better the essential principle of contingency; for they make no addition to it. This form of contingency is that assumed by mathematicians, and may be distinguished as intuitive, or mathematical. J. S. Mill and the Associationalists teach that all contingent judgment is empirical, or based on observation of the past ; their doctrine gives no satisfactory account of mathematical contingency. Such is the nature of contingency, not as a general, but as a specific, mode of logical sequence. It lies between possibility and probability, and is more determinate than the former, and less determinate than the latter. 5. Two characteristics of contingency are closely connected with its nature. In the first place, such sequence is always ac- companied with a " possibility of the opposite." The " opposite " 208 THE MOBALIST. [Chap. XXL here means the contradictory of that which is contingently asserted. When we judge that the ball selected at random may be red, or that the snake met accidentally may be venom- ous, it is also felt that the ball may not be red, and that the snake may not be venomous. This doubleness arises because the antecedent of possibility both assures us that some condi- tions of the consequent exist, and leaves us in doubt whether or not others do ; it therefore justifies both a positive and a negative sequence in possibility. But contingency is double only when both sides of the possibility are supported by known facts or instances. Consequently we cannot say that contingency is always double, but only that it is always accompanied by a possibility of the opposite. Knowing that some snakes are venomous, but not whether any snakes are not venomous, we can assert a negative possibility, but not a negative contingency, concerning snakes. This negative possibility accompanies the positive contingency, like a shadow. So also a positive possi- bility accompanies a negative contingency. These possibilities differ from the contingencies which they accompany in that they are not grounds of expectancy. Because, for aught we know, it may be true that they never have been — or that they never can be — realized in any case. It may be said that the opposite of the contingency asserted is supported by any chances that remain after those favoring the assertion have been subtracted from the total number; and that, therefore, the opposite of a contingency is also necessarily a contingency. This, however, is not so. The denial of the opposite of the asserted contingency is supported by the same chances which support the original assertion, and is also a contingency. But the assertio?i of that opposite is not really supported by any chances at all. For, as the remainder above mentioned may be either some chances or none, we have no right to depend upon any. In short, the opposite of the contingency asserted, being wholly unsupported by facts or instances, is only a naked possibility. 6. The second characteristic of contingent sequence is that it may be either guarded or unguarded. Naturally and prima- rily positive contingency is- guarded against impossibility, but Chap. XXL] CONTINGENCY AND ITS CONVERSION. 209 not against necessity j while negative contingency is guarded against necessity, but not against impossibility. Each of these, therefore, may be* termed half-guarded, or — more simply — guarded, contingency ; and, as we shall see, each of them may become unguarded. Knowing simply that some snakes are venomous we have the guarded contingency, " a snake may be venomous " : knowing simply that some snakes are not venom- ous, we have the guarded contingency, "a snake may not be venomous." These contingencies may combine in the double sequence, "a snake may, and may not, be venomous,'* which appeals to both positive and negative instances. This, as guarded against both impossibility and necessity, may be described as doubly guarded. 7. Contingency loses its guarded character if it be not * immediately based on facts, but inferred from the combination of a contingency with a prior sequence. Knowing that "a lion is a quadruped," and that "a quadruped may be a carnivore," we say, " A lion may be a carnivore." Also knowing that " a lion is a quadruped," and that " a quadruped may not be a carni- vore," we say, "A lion may not be a carnivore." Further infor- mation displaces both of these deduced contingencies by a necessity. In like manner the similarly inferred contingencies, "an ox may be a carnivore" and "an ox may not be a carni- vore," give place to an impossibility. Again, some reptiles being snakes and some snakes venomous, we say, "A reptile may be venomous " ; and, for like reasons, " A reptile may not be venomous." Here are two unguarded contingencies ; addi- tional knowledge renders each as guarded as those from which it has been inferred. An exception to the rule now explained will be noticed hereafter. Unguarded contingency may be single or double, according as the contingency from which it is deduced is single or double. In the above illustrations, if we unite the opposite single asser- tions, we can say, "A lion may, and may not, be a carnivore," "An ox may, and may not, be a carnivore," and, "A reptile may, and may not, be venomous." But it is not so important to distinguish between the single and the double mode of unguarded contingency as it is to distinguish between that 210 THE MOBALIST. [Chap. XXI. guarded contingency which is double, being both positive and negative, and that guarded, or half-guarded, contingency, which is single, being either positive or negative. Ordinarily con- tingency is single, and guarded only on one side. 8. Mathematical unguarded contingency may be illustrated thus : let there be 100 balls of ivory, all of these being white 5 100 of wood, some of these being red ; and let all the balls be placed in one collection. Then if one knew not that all the ivory balls are white, but only that (a) they are all among the 200, and that (b) some of the 200 are red, it would be a con- tingency to an ivory ball to be red. Or, if he knew only that (a) all the ivory balls are among the 200, and that (6) some of the 200 are white, it would be contingent to an ivory ball to be white. Investigation would displace either of these con- tingencies by the certainty that every ivory ball is white. But if the ivory balls were some white and some red, and this should appear on investigation, then the contingent judgments respecting the color of any ivory ball (taken at random) would become guarded, and stable. For unguarded contingency may be termed unstable ; guarded (or doubly guarded) contingency, stable ; and the half -guarded, half-stable. 9. In addition to the foregoing modes of contingency, we must mention that fixed, or embedded, possibility, which may sometimes be called contingency ; and which is that compati- bility of the existence, or of the non-existence, of a thing with given circumstances, which may be inferred from necessity, or from impossibility. This mode of sequence is possibility or contingency only in an improper sense ; for it excludes the possibility of the opposite ; but it has a place in logic. Comparing with each other the different modes of contin- gency proper, we find that guarded contingency is the most developed and complete sequence ; half-guarded contingency is the most frequently used in reasonings ; and unguarded contin- gency is the purest, but also the weakest and least determinate, mode of contingent sequence. Chap. XXL] CONTINGENCY AND ITS CONVERSION. 211 The Conversion of Contingency. 10. The general rule for the conversion of possibility and of contingency is that either may be converted by the asserted- consequent, but not by the denied-consequent. To understand this rule we must discuss first the conversion of possibility, and then that of contingency. With respect to possibility let us first show that the asserted- consequent yields a logical converse, and then that the denied- consequent does not do so. The following specific formulas exhibit the conversion of possibility by the asserted-consequent : (1) If the existence of one thing (A) render possible the existence of another thing (B), then will the existence of B render possible the existence of A. (2) If the existence of A render possible the non-existence of B, then will the non-existence of B render possible the exist- ence of A. (3) If the non-existence of A render possible the existence of B, then will the existence of B render possible the non- existence of A. And (4) If the non-existence of A render possible the non-exist- ence of B, then will the non-existence of B render possible the non-existence of A. The non-existence mentioned in these formulas always relates to, and is included in, a case in which something is non-exist- ent ; it is not non-existence per se. Non-entity, of itself, is never either antecedent or consequent ; but cases occur in which the non-existence of one thing makes something else possible to be, or possible not to be. Those antecedents which assume non-existence, are cases of existence modified by the non-existence of some element which might have been present. Therefore, for the sake of simplicity, we may disregard the difference between positive and negative antecedents, and retain only the first two of the foregoing rules ; after which these may be combined in the one rule that " if the existence of A render possible the existence, or the non-existence, of B, then will the existence, or the non-existence, of B render possible the exist- 212 THE MODALIST. [Chap. XXI. ence of A." That is to say, any antecedent of possibility may be made the consequent of its own consequent. In other words, every sequence in possibility may be converted by "the asserted consequent." This formula may be justified, first, with reference to affirma- tive possibility, and then with reference to negative possibility. The principle which gives vitality to affirmative possibility may be called " the law of contained conditions " ; and the con- version of this mode of possibility by the asserted consequent follows upon the fact that the law of contained conditions has a reciprocal action. For the antecedent of possibility always contains a condition, or conditions, of the consequent ; and the consequent, a condition, or conditions, of the antecedent. Let A be antecedent of possibility to B, because A involves c, which is a condition of B. Then, first, c is a condition of A, as being involved in A ; and secondly, c is involved in B, as being a con- dition of B. This being so, B, as involving c, which is a condi- tion of A, may be antecedent of possibility to A. Take the sequence, "man (A) may be wise (B)." Here wisdom is pos- sible because man has intellect (c), which is a condition of wisdom. But intellect is a condition of "man," as being a necessary part of him ; and it is involved in wisdom as being a condition of wisdom. Therefore, conversely, " a wise being may be a man." A coin may be a piece of silver, and a piece of silver a coin, because each of these involves "valuable metal." A long walk and a wide plain render each other logi- cally possible, because each involves the element of "distance." The principle which gives vitality to negative sequences in possibility is a corollary, or concomitant, of "the law of contained conditions " ; it may be named " the law of the unas- certained necessitant " ; and this principle, like that which it accompanies, has a reciprocal action. In every assertion of pos- sibility proper, while knowing that some conditions of an entity exist, we are ignorant whether such and so many exist as con- stitute a logical, or necessitating, condition. We may know that the antecedent, considered per se, does not contain a logical condition (or necessitant), or we may be ignorant whether it does or not ; in the one case we assert a settled or stable, in the Chap. XXI.] CONTINGENCY AND ITS CONVEBSION. 213 other, an unstable, possibility of non-existence ; in either case we assert the possible non-existence of B, because A {either as known, or so far as known) does not contain a necessitant of B. But the non-existence of B, though involving the non-existence of any necessitant of B, and of any antecedent containing that necessitant, is consistent ivith what does not contain the necessi- tant. Therefore the non-existence of B is consistent with the existence of A : " man may be wise " yields, first, " man may not be wise," and then the converse possibility, "a being not wise may be a man." Therefore, though there is silver there may be no coin, and though there be no coin there may be silver. Ordinarily A is known not to contain a necessitant of B ; so that the contingency, " A is possibly not B — man is possibly not wise " is guarded against necessity. In this case the con- verse, "Not-.B is possibly A — not-wise is possibly man" is guarded against impossibility. But should A be only not known to contain a necessitant, the convertend would not be guarded against necessity, nor the converse against impossi- bility. Knowing that a carnivore may not be a quadruped, and that a lion is a carnivore, we may say, " A lion may not be a quadruped." Further knowledge will displace this by a necessity : and the converse, " a non-quadruped may be a lion " will be displaced by impossibility. But commonly the con- vertend is understood as guarded, so that the converse, also, is guarded. So much for "the asserted-consequent." 11. We are now prepared to ask whether possible sequence can be converted by " the denied-consequent," as well as by " the asserted-consequent." This point may be discussed as a question respecting the validity of two formulas, if, as before, we neglect the distinction between positive and negative ante- cedents, and so reduce four formulas to two. These are : 1. If the existence of A render possible the existence of B y then the non-existence of B will render possible the non-exist- ence of A. 2. If the existence of A render possible the non-existence of B, then will the existence of B render possible the non-exist- ence of A. Expressed categorically, these conversions are, 214 THE MODALIST. [Chap. XXI. (1) A is possibly B; therefore, what is not B is possibly not A ; and (2) A is possibly not B; therefore, B is possibly not A. Coin is possibly silver ; therefore, what is not silver is possibly not coin. — Coin is possibly not silver ; therefore, silver is pos- sibly not coin. In these proposed inferences, as the method of " the denied-consequent " requires, the contradictory of the consequent is used for antecedent and the contradictory of the antecedent for consequent. The conversion of a positive sequence is attempted, in this way, on the principle that the absence, or contradiction, of the antecedent renders the absence of its consequent possible — that is, shows it to be possible. For the absence of the antecedent puts us in doubt whether even those conditions of the conse- quent respecting which the antecedent would give assurance, are present or not ; inasmuch as, if they are, it must be in some other antecedent. Beyond question the law of "the unascertained necessitant " applies here in a very literal way ; and so we say, first, "A is possibly B" ; then, "What is not A is possibly not B " ; after which, using " the asserted- consequent," as with any negative possibility, we obtain the converse, "what is not B is possibly not A." "Coin is possibly silver — what is not coin is possibly not silver — what is not silver is possibly not coin." This sequence is correct ; and yet it is entirely nugatory and useless. Though supported by the fact that the denial of an antecedent of possibility leaves no ground for conjecturing that the consequent exists, so that, until we learn more, we can say that, so far as we know, the consequent may not exist ; it is open to two objections. The fatal objection is that the secondary, or intermediate, convert end, from which the con- verse is immediately produced, is without convictional value, because it is founded purely on "the unascertained necessitanV ; which principle is useless except as a concomitant principle. All logical force disappears when we form that secondary conver- tend, by using contradictory conceptions. Hence no connection of congruity or compatibility is perceivable in the converse, between antecedent and consequent. Chap. XXL] CONTINGENCY AND ITS CONVERSION. 215 Then, secondly, while the original convertend may be a guarded possibility, the converse is unguarded. We correctly say, "A quadruped may be a lion — a non-quadruped may not be a lion — a non-lion may not be a quadruped." But, notwithstanding all this, it might be true that every " non-lion " is a quadruped. The conversion of a negative sequence by "the denied-conse- quent " may be attempted as follows. " A is possibly not B. — jSTot-J. is possibly B. — B is possibly not A." Coin is pos- sibly not silver ; what is not coin is possibly silver ; silver is possibly not coin. Here, as before, the operation of " the denied- consequent " is equivalent to that of the asserted-consequent after contradictory conceptions have been employed. This conversion, like that just considered, is without con- victional force. In saying, " What is not coin may be silver," because " coin may not be silver," we base a sequence simply on the removal of an antecedent of possible non-existence; we assert a possibility because we have no reason either for or against it, except the removal of that antecedent. Such an assertion is entirely indeterminate ; and so is the converse of it, " silver may not be a coin." Moreover, while the original possibility may be — and commonly is — guarded, this converse is unguarded. Should we say, " A quadruped may not be a lion ; therefore a lion may not be a quadruped " ; this converse will be displaced, on further knowledge, by a necessity. 12. We pass, now, from the conversion of possibility in general to that of contingency. By this we mean the inference of a converse contingency from a convertend contingency ; for to infer a possibility conversely from a contingency, would only be a conversion in possibility, and not, distinctively, a convex sion in contingency. While the conversion of contingency follows the same rule as that of possibility in general, it has some noteworthy pecu- liarities. In the first place, the method of the denied-consequent is more violently rejected by contingency than by possibility. This method leads to a formal but useless converse in possibility, but produces no converse whatever in contingency. The reason for this is that the facts or instances which sustain the original contingency, do not support the proposed converse contingency. 216 THE MODALIST. [Chap. XXI. The contingency, " a snake may be venomous/' rests on the fact that " some snakes, at least, are venomous." This fact yields no support to the converse, that " an animal not venomous may not be a snake " ; it is not a fact relating to such animals. So also the contingency, "a snake may not be venomous," rests on the fact that " some snakes are not venomous " ; and this does not support any converse contingency respecting " ven- omous " animals. In short, the conversion of contingency by the denied-consequent, results only in a useless indeterminate possibility. 13. On the other hand, the asserted-consequent produces a true conversion ; because the same facts which support the con- vertend, support the converse also. The same instances justify the contingency, " a snake may be venomous," and the contin- gency, " a venomous animal may be a snake." In like manner, the contingencies, "a snake may not be venomous," and "a non-venomous animal may be a snake," are supported by the same instances. Mathematical contingency, equally with the empirical, is convertible by the asserted-consequent. Let some balls in a collection of one hundred be red. Then it is contingent to any ball, selected at random, to be red, and to any red ball to be the one so taken. Or, if some of the balls be not red, it is contingent to any ball selected at random, not to be red, and to any ball not red to be so selected. Convertend and converse originate together, and are supported by the very same facts. 14. But, in this connection, it should be remarked that con- verse does not follow convertend so absolutely — so perfectly as a matter of course — in contingency as in possibility. A converse contingency, unlike a converse possibility, depends on a limitation which, ordinarily and naturally, attaches to the predicate of the convertend, yet which is not necessarily in- herent in it. For the class or set of things, to which the sub- ject of the converse refers must be numerically limited in order that some indefinite proportion — or ratio of chances — may be assumed between the "some" and the "all." Without this limitation, at least in our first apprehension of the converse contingency, no basis of expectancy could be formed. But the Chap. XXI.] CONTINGENCY AND ITS CONVERSION. 217 class thus numerically limited is the same as that to which the predicate of the convertend refers. In converting " a snake may be venomous," we assume that the venomous animals which are snakes belong to a class "venomous," and constitute an appreciable proportion of that class. In the converse of the negative contingency a similar ratio is assumed between the "non-venomous," which are snakes, and the whole class "non-venomous." So, in converting the mathematical contin- gencies, the " red balls " and the " balls not red " are thought of as belonging to the collection in the box ; and not as being any red balls whatever, or any balls not red. This numerical limitation somewhat resembles "quantifi- cation " of the predicate, but is quite another thing j for it is not exclusively related to a logical class. 15. Another difference between contingency and possibility is that the conversion of possibility always admits of a doubleness, ivhile this is not the case ivith contingency. Every antecedent of possibility proper justifies both a positive and a negative con- sequent. Hence every positive sequence in possibility is accom- panied by a negative sequence, and every negative, by a positive. This being so, the converse of a positive possibility is accom- panied by the converse of the negative, and the converse of the negative by that of the positive. Therefore "a man may be wise," as a possibility, has the double converse, "a wise being may be a man," and " a being not wise may be a man." And, in the same way, both these conversa may be inferred from the negative possibility, " a man may not be wise." But the positive contingency, " a man may be wise," justifies only its own single converse ; and the negative contingency, " a man may not be wise," only its own single converse. Neither of these contingencies can claim the converse of the other along with its own ; because the facts supporting it justify only one converse contingency. When a positive and a negative contingency are united so as to form a double contingency, the converse of the double contingency is also double ; but this is not because each con- tingency warrants the converse of the other, but only because each is followed by its own. 218 THE MODALIST. [Chap. XXI. 16. In addition to the supreme law for the conversion of contingency some subordinate rules claim attention. These pertain to the different modes of contingency according as it is proper or improper, guarded or unguarded. In discussing them we need not continue to contrast possibility and contingency ; for we must employ principles freely applicable to both. The most common modes of contingency are that affirmative sequence which is guarded against impossibility, and which has been styled "encouraging," and that negative sequence which is guarded against necessity, and which we have named " discouraging." These correspond with the half -guarded modes of possibility, positive and negative ; and are based on these possibilities. Both may be styled "guarded" in the sense that each is guarded against a necessity of the opposite. The converse of an encouraging contingency is an encourag- ing contingency with a positive subject. If "a man may be wise," then " a wise being may be a man." The same instances sup- port both these contingencies, and guard both against impossi- bility. The strength of the converse depends on the ratio of the men who are wise to the whole class " wise " ; and varies with our estimate of that ratio. 17. The converse of a discouraging contingency is an encour- aging contingency with a negative subject. If " a man may not be wise," then " a being not wise may be a man." The same facts justify both these contingencies. The converse is guarded against impossibility ; because, by reason of the law of Contra- diction, if any subject— A — be not a given predicate — B, then A is something which is no't B. Therefore, on the same basis of fact, we say, "A man may not be wise — A man may be a being not wise — A being not wise may be a man." This last assertion is an encouraging contingency. A discouraging contingency does not yield a discouraging converse, because this would involve " the denied consequent." 18: Encouraging and discouraging contingency are the two modes of half-stable contingency. Stable, or double-guarded, con- tingency is the compound from their conjunction. Accordingly the converse of stable contingency is tivo-fold, and includes the con- verse of each of the constituent parts. Knowing that some men Chap. XXL] CONTINGENCY AND ITS CONVERSION. 219 are wise and some men not wise, we have the stable contingency, " a man may, and may not, be wise," with the double converse, " a wise being may be a man, and a being not wise may be a man " ; each of these assertions being a half-stable encouraging contingency. But we cannot say, conversely, " A wise being may, and may not, be a man," because the negative part of this converse would involve the denied-consequent. 19. The converse of an unstable contingency is an unstable contingency. The original assertion being only mediately and contingently supported by facts, this must be the case with the inferred proposition also. Knowing simply that "some carnivores are quadrupeds, and some quadrupeds lions," we say, "A carnivore may be a lion." This is an unstable contin- gency ; further information might show that a carnivore cannot be a lion, or that it must be a lion. For the same reason the converse, " a lion may be a carnivore," is unstable ; and further knowledge will show that lions are necessarily carnivorous. Again, knowing merely that " all oxen are quadrupeds and that some quadrupeds are carnivores," we have the unstable contingency, " an ox may be a carnivore," and its converse, " a carnivore may be an ox." Further information displaces both convertend and converse by an impossibility. Once more, knowing only that " some mammals are quadru- peds and some quadrupeds are carnivores," we have the con- tingency, , " a mammal may be a carnivore," and its converse, " a carnivore may be a mammal." Both are unstable ; further knowledge renders both stable. For it is neither necessary nor impossible that a carnivore should be a mammal, or that a mammal should be a carnivore. The foregoing contingencies are single. Should we say, " An ox may, and may not, be a carnivore," because " a quad- ruped may, and may not, be a carnivore," we should assert a double unstable contingency ; and its double converse, " a car- nivore — as also a non-carnivore — may be an ox," would consist of two unstable assertions. 20. The foregoing laws of conversion are those of contin- gency proper in its various modes, and do not control fixed, or 220 TBE MODALIST. [Chap. XXI. embedded, contingency. This lias the peculiarity that it may be converted either by the asserted consequent or by the denied consequent — by the former because it participates in the nature of contingency (though not a true contingency); by the latter because it shares in the relations of necessity. The possibility, "man may be mortal, because man must die," yields not only "a mortal may be a man," but also "what is not a mortal may not be a man." For this latter contingency is embedded in the converse, "what is not a mortal cannot be a man"; which is obtained by the denied consequent from the original under- lying necessity. In like manner, the possibility, "man may not be perfect, because man cannot be perfect," yields, not only "a being not perfect may be a man," but also "a perfect being may not be a man." This is embedded in the converse of the underlying impossibility. Such being the case, it is plain that the converse of a fixed contingency by the denied consequent is another fixed contin- gency. But this is not the result when the asserted conse- quent is used. Then tlie converse of a fixed contingency is the same as the ordinary converse of necessity (Chap. XX.). More specifically, the converse of a positive fixed contingency is an encouraging contingency with a positive subject, while that of a negative fixed contingency is an encouraging con- tingency with a negative subject. Thus the embedded con- tingency, "man may be mortal," yields the encouraging contingency, "a mortal may be a man" : and, in like manner, "man may not be perfect" yields "an imperfect being may be a man." 21. Some advantage might result if the various modes of possibility and contingency were indicated by symbols. In particular the student might construct for himself a useful scheme of those oppositions and conversions in which possi- bility and contingency are concerned. To this end we make the following suggestions. Let the small Greek vowels i and o indicate the positive and negative modes of unguarded, or unstable, possibility ; that being the purest form of possibility proper. Let possibility as guarded against impossibility be marked by the grave accent, thus, I and 6 ; as guarded against Chap. XXL] CONTINGENCY AND ITS CONVERSION. 221 necessity, by the acute accent, thus, C and 6 ; and as guarded against both impossibility and necessity, by the circumflex accents, thus, 2 and 5. In possibility proper t and o always accompany each other. So, also, in the modes of guarded possibility, do t and 6 ; I and 6 ; and t and 8. The two modes of embedded possibility might be indicated by the same letters •enclosed in parenthesis — (t) and (o) . These do not accom- pany each other. The different modes of contingency might be symbolized by ■circumscribing with a circle those proper possibilities on which contingencies are based. Thus, © and © may indicate single unstable contingencies ; © -f- © a double unstable contingency ; © and © are half-guarded contingencies ; © -f © is stable contingency. But, for the sake of simplicity, let the diphthongs ei and ov take the place of the circumscribed vowels. Then a and ov and et -f- ov indicate the forms of unstable contingency ; et and ov the half-guarded contingencies ; and ei + 6v the guarded ; that is, the doubly guarded. Every single contingency embraces a corresponding possibility and is attended by a possibility of the opposite; but not by a contingency of the opposite. Thus et and ov do not necessarily accompany each other ; but et embraces t, and is attended by 6, and ov embraces d, and is attended by L So, in unstable contingency, et involves t and o, but not ov ; and ovy o and t, but not et. The foregoing discussions show that the logician is com- pelled to employ the conception of contingency more specifically and definitely in connection with the conversion, than in con- nection with the opposition, of predications. We account for this, because opposition deals with given propositions, while conversion is the formation of a new statement ; and because, while contingency and possibility, by reason of their common nature, may be used in similar dialectic oppositions, their con- versions differ by reason of the specific differences belonging to them as modes of sequence. 222 THE MODALIST. [Chap. XXII. CHAPTER XXII. SYLLOGISMS. 1. Syllogisms denned. 2. The syllogism-proper. 3. Relational syllo- gisms : (a) immediate, (b) mediate. 4. Homologic syllogisms : (a) para- digmatic, (&) principiative, (c) applicative. 5. Hypothetical syllogisms. 6. The consequent-consequent is the first and supreme law of syllogisms- proper. 7. The principle of the separating-consequents. 8. The principle of the common-antecedent. 9. The principles of syllogistic reciprocation. 10. These are less independent in their operation than the other laws. 11. The three propositions, and the three terms, of the syllogism. 12. To analyze a syllogism, begin with the conclusion. 13. The four " figures." The order of the propositions. 14. Syllogistic moods. 1. " A syllogism/' says Aristotle, " is a statement in which, certain things being laid down, something else, different from the premises, necessarily follows in consequence of the prem- ises" ("Topics," I. 1). The "things laid down," or "prem- ises," are propositions known, or assumed as true; and the " something else " is a proposition, either apodeictic or proble- matic, necessarily believed in consequence of the premises; but the main teaching of the definition is that syllogistic infer- ence arises from more than one premise. This, indeed, is the essential meaning of the noun vrov KpLTiKrjv, yv KaXovatv ouaOrjcnv ; — and he finishes the discussion by saying that first principles are obtained by induction from this perception ; — Srjkov S?) otl rj/juv ra irpwTa lirayoiyrj yvwpt^uv ava.yKa.iov ' koX yap kol aicr0r)O~i