THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES GIFT OF Professor ^--albone Graham i A SHORT HISTORY OF LOGIC BY THE SAME AUTHOR ROGER BACON : The Philosophy of Science IN THE Thirteenth Ckntuhy. (An Address intro- ductory to the Session 1876-7 at the Owens College, Manchester). Crown 8vo, Is. Manchester: J. E. Cornish. ON THE PHILOSOPHY OF KANT (Shaw Fellow.ship Lectures, 1879). Ex. leap. Svo, 6s. Edinburs'h: David Douglas. FICHTE (Philosophical Classics for English Readers). Crown Svo, Is. net. THE DEVELOPMENT OF MODERN PHILO- SOPHY, WITH other J.ECTUKES AND ESSAYS. Edited, with memorial introduction, bibliography, and notes, by W. R. SoRi.EY. Two vols., demy Svo, 18s. net. THE DEVELOPMENT OF MODERN PHIL- OSOPHY. (Issued separately, witliout the other Lectures and Essays). In one volume, 10s. 6d. net. THE DH:VEL0PMENT of greek PHILO- SOPHY. Edited by W. R. SoRLEY and R. P. Hardie. Demy Svo, 10s. 6d.'net. Edinburgh: William Blackwood & Sons. A SHOET HISTORY OF LOGIC BY ROIJEKT ADAMSON, LL.D. SOMETIME PROFESSOR OF LOOIC AND RHETORIC IN THE UNIVERSITY OF GLASGOW EDITED BT W. R. SORLEY, LiTT.D., LL.D. PROFESSOR IN THE UNIVERSITY OF CAMBRIDGE FELLOW OF THE BRITISH ACADEMY WILLIAM BLACKWOOD AND SONS EDINBURGH AND LONDON MCMXI All Riifhts reserved Be PREFACE The article on Logic which Professor Adamson con- tributed to the ninth edition of the Encydopcedia Britannica consists of a critical survey of the his- tory of logical theory; its value is well known to philosophical students ; and no apology is needed to justify its publication in separate form. It may be mentioned, however, that this publication was thought to be important at the present time, as the work was in danger of becoming less easily accessible owing to the issue of the eleventh edition of the Uncyclopcedia, in which it is not reprinted. The manuscript of the article has been fortunately preserved — alone among the manuscripts of the author's published writings. It is much fuller than the printed article, a number of passages — some fifty in all — having been struck out by the editor with a view to economy of space. These passages aflect both text and notes ; they vary in length from a few words to whole sections ; they vary also in importance ; but the author's own opinion was that the value of his VI PREFACE work had suffered by their omission ; and with this opinion I agree. In the present book these passages have been restored to their place, so that the article as it left the author's hands is now, for the first time, placed before the reader. The manuscript bears no trace of the editorial blue pencil, and the original proof no longer exists : so that a doubt may arise as to whether any particular omission may not have been made by the author himself when he corrected the proofs. But it is clear, from a comparison of manuscript and print, that his proof-corrections were few and unimportant. No real difficulty, therefore, has arisen in deciding upon the restorations. The author's style was so concise that greater brevity could not be attained without sacrifice of the matter. It should be borne in mind that the article on Logic was written and published in 1882. The supplementary articles, by which it is followed in this volume, are all contributions to the history of logic; but the first of these — that on Category, also reprinted from the E'ncyclopcedia Britannica — dates from six years earlier ; and only the last carries the story on towards a more recent development of logical theory. Readers of the author's works do not need to be reminded that his own point of view underwent mr>dification, and that there are some things here which he might have expressed differently had he revised the work himself. PKEFACE VU With the author's manuscript and printed copy before me, my own work as editor has consisted chiefly in selecting the material and seeing it through the press. Some omitted references have been sup- plied ; a few slips of the pen or the press, formerly overlooked, have been corrected ; unwieldy paragraphs have been broken up, and the punctuation has been simplified ; but nothing new has been added to text or notes. I am responsible for the choice of a title. It remains for me to express my grateful thanks to the Syndics of the Cambridge University Press for allowing the publication of the articles on Logic and on Category in the present form. For permission to reprint the critical notices from Mind, with which the volume ends, I am indebted to the kindness of Professor Davidson of Aberdeen, literary executor of the late Professor Bain. W. E. SOKLEY. Kino's College, Cambridge, October 1911. CONTENTS PREFACE ..... I. PROVINCE AND METHOD OF LOGIC . II. THE ARISTOTELIAN LOGIC III. LOGIC FROM ARISTOTLE TO BACON AND DESCARTES IV. LOGIC OF BACON AND DESCARTES . V. LOGIC ON THE BASIS OF PSYCHOLOGICAL EMPIRICISM LOCKE, HUME, MILL, CONDILLAC . VI. LOGIC ON THE BASIS OF METAPHYSICAL PYSCHOLOGY LEIBNIZ AND HERBART VII. THE KANTIAN LOGIC .... VIIL LOGIC AS THEORY OF KNOWLEDGE . IX. LOGIC AS METAPHYSICAL X CRITICISM OF THE CHIEF LOGICAL SCHOOLS PAOE V 1 22 80 85 93 103 110 126 131 139 NOTE A. HISTORIES OF LOGIC NOTE B. HINDU SYSTEMS OF LOGIC NOTE C. RAMUS 164 165 lti8 C CONTENTS SUPPLEMENTARY ARTICLES I. CATEGORY . . . . . .171 II. lotze's logic ..... 190 III. lotze's metaphysic. .... 215 IV. MR BRADLEV'S LOGIC .... 240 I^DEX OF NAMES ..... 263 SHORT HISTORY OF LOGIC PROVINCE AND METHOD OF LOGIC 1. Logic, in the most general acceptation of the term, may be regarded as the systematic study of thought. So wide a definition is certainly sufficient to comprehend all that may have been at various times included within the scope of logical doctrine, but in other respects it is of small value. For it seems essential that to any separate and independent theory there should be assigned a distinct province and a distinct method. But neither province nor method, as in any way special or jicculiar to logic, is marked off by the above description. The terms thought and systevuitic study, indicating the object and method of logical treatment, might, even in similar combination, be appro- priately used in defining, totally or partially, philosophic disciplines not generally viewed as synonymous with logic. They do not serve, therefore, to mark off logic from philo- sophy as a whole, which is unquestionably the systematic exposition of thought, nor from psychology, which includes A 2 HISTORY OF LOGIC within its wider range what may well be described as the study of thought. That some more accurate discrimination of the province and method of logic is absolutely necessary will readily be granted ; for, in default thereof, neither the extent of matter to be included within the study nor the peculiarity of the method by which such matter is treated can be determined. '' The boundaries of logic and its essen- tial constitution must otherwise remain fluctuating and *o vague. Preliminary queries of a similar kind are naturally encountered in the case of all other branches of human knowledge ; and though it is to be acknowledged that many of the sharp distinctions by which one is differentiated from the other are provisional merely, and demand restatement when a somewhat higher point of view is reached, yet their necessity and utility must be allowed. The sciences are not advanced but retarded when their provinces are allowed to overlap and become indeterminate. » There are two methods by which these preliminary questions are generally answered — two methods which in themselves express directions of human thinking and which have at all times occupied a remarkable place in the system of logic. We may refer either to the distinct characteristics of the matter to be treated, or to the essential features of the method of treatment. ■ We may determine the province of a science either by external division, by classification of objects according to their prevailing resemblances and differences, or by internal definition, by exposition of the fundamental characters of the method employed in the science. By neither process, unfortunately, can an unambiguous answer be supplied, at least without much art, in the case of logic. Neither by classification of the sciences, and assign- ment of some specific place in the general hierarchy to PROVINCE AND METHOD OF LOGIC 3 logic, nor hy precise determination of the character of logical analogies as opposed to all other forms of study, can there be readily attained a definition, at once full and exact, of the system of logic. 2. The reasons for the manifold difficulties encountered in the attempt to determine accurately the province of logic, whether by reference to a division of the sciences or by precise definition of the essential features of logical analysis, are not far to seek. The systematic classification 7 of the sciences is not the result of mere observation and comparison ; the selection of the points of agreement and difference involves not only consideration of the contents of the sciences as empirically presented, but also certain leading principles or fundamental views, which are in essence of a philosophical character. According to the general -conception of knowledge which in various kinds is manifested in the special sciences, there will be radically divergent methods of classification, and the province assigned to each member of the ensemble will, for the most part, have its limits determined according to the character of the general view adopted. Moreover, if any of the more prominent specimens of classification of the sciences be critically inspected, they will be found to presuppose a certain body of principles which are wider in scope than any of the special disciplines, and to which no . place in the ensemble can be assigned. In short, a sys- / tematic distribution of human knowledge into its distinctly marked varieties rests upon and presupposes a general philosophy, the character of which affects the place and function of each part of the distribution. Logic, as may readily be imagined, has therefore experi- '•! enced a variety of treatment at the hands of systematisers 4 HISTORY OF LOGIC of scientific knowledge. It has appeared as one of the abstract sciences, in opposition to those disciplines in which the character of the concrete material is the essential fact ; as a subordinate branch of a particular concrete science, the investigation of mental phenomena ; as a nondescript receptacle for the formulation in generalised fashion of the method and logical precepts exemplified in the special sciences. By such processes no more has been effected than to bring into light, more or less clearly, some of the characteristics of the supposed science, without in any way supplying an exhaustive and comprehensive survey of its boundaries and relations to other branches of knowledge. / Thus, when logic is marked off from the concrete sciences and associated with mathematics in the most general sense, as the treatment of formal relations,^ and further differ- entiated from mathematics as implying no reference to the quantitative character of the most general relations under which facts of experience present themselves,- there is certainly brought to the front what one would willingly allow to be a commonplace respecting all logical analysis, namely, that its principles are coextensive with human knowledge, and that all objects as matters of conscious experience have an aspect in which they are susceptible of ^ As, e.g., by H. Spencer, Classification of the Sciences, pp. 6, 12 ; H. QrasBmann, Die Ausdehnungslehre von 1844 (1878), Einleitung, xxii. -xxiii. '■^ Logic and mathematics, under this view, may be regarded either as generically distinct — which is apparently the opinion of Spencer, H. Grassman, and Jevons — or as species of a more comprehensive genua, the theory of formal (symbolic) opei'ations — which is apparently the opinion of R. Grassman (see his PormenUhre, 1872) and Boole (see his Mathematical Analysis of Logic, 1847, p. 4, and Differential Equations, 1859, chap, xvi., specially pp. 388, 389). An admirable treatment of that which is implied in Boole's method is given in Mr Venn's Symbolic Logic, 1881. PROVINCE AND METHOD OF LOGIC 5 logical treatment. But no more is effected. It is still left to a wider consideration to determine what the specific aspect of things may be whicli shall he called the formal and be recognized as the peculiarly logical element in them. There may be selected for this purpose either the general relations of coincidence and succession in space and time, or the fundamental properties of identity and difference, or the existence of classes ; but in any case such selection depends upon and refers to a theory of the nature of knowledge and of the constitution of things as known. In truth, the notions of form and formal relations are by no means so simple and free from ambiguity that by their aid one can at once solve a complicated problem of philo- sophic arrangement. To lay stress upon form, as the special object of logical treatment still leaves undecided the nature and ground of the principles which are to be employed in evolving a science of form, and therefore leaves the logical problem untouched. Still less satisfactory are the results when logic is regarded as in some way a subordinate branch of the psychological analysis of mental phenomena.^ Neither the grounds on which such a classification rests, nor the conclusions deduced from it, seem beyond criticism. The simple facts that certain mental processes are analysed in logic, and that psychology is generally the treatment of all mental processes, by no means necessitate the view that logic is therefore the outgrowth from and a subordinate part of psychology. For it is clear, on the one hand, that logic has a scope wider than psychology, since in any sense of the term it has to deal with all the processes (or with some aspect of all the processes) ^ For this extremely common arrangement, see Hamilton, Lectures on Metaphysics, i. p. 121-3 ; Ueberweg, System der Logik, § 6. 6 HISTORY OF LOGIC by which on auy subject knowledge is formed out of disjointed or disconnected experiences. And, on the other hand, since tlie subordination of one science to another, as species to genus, is fallacious, unless the two agree in fundamental characteristics, the position so assigned to logic would imply that in aim and method it shall be essentially one with psychology, a position equivalent to the negation of logic as a separate and independent discipline. It is not surprising therefore to find that, so soon as logic has been distinguished as arising from psychology, and so dependent on it, the peculiarity of its position and functions compels the recognition of its more general scope and the reduction of its connection with psychology to an amount small enough to be compatible with absolute independence. Strong reasons, indeed, may be advanced for holding that logic is entirely to be separated from psychology, as differ- ing from it in aim, method, and principle, that logical analysis is generically distinct from psychological, and that the two disciplines, while connected as parts of the general body of philosophical reflection, hold to one another a relation the reverse of that commonly accepted. -"^ As to the endeavour to collect from consideration of the sciences in detail a body of precepts, the rules of scientific method, and to assign the systematic arrangement of such rules to one special discipline, called logic, it seems to stand on the same footing and to be open to the same criticism as the allied attempt to treat general philosophy ^ It is to be acknowledged that most of the writers on logic who emphasise the connection of psychology with logic introduce distinc- tions equivalent to the remarks above made, h)ut the grounds for such distinctions and the conclusions to be deduced from them are not generally brought into clear light. PROVINCE AND METHOD OF LOGIC 7 as the receptacle for the most abstract propositions reached in scientific knowledge. There is a peculiar assumption underlying the supposed possibility of distinguishing be- tween scientific method and its concrete exemplifications in the special sciences, and only on the ground of this assumption could there be rested the independence of logic as the systematic treatment of method. It is taken for granted, without examination, that the characteristic features of correct and well-founded thinking are palpable and genera], and that we thus possess a criterion for marking off what is common to all scientific procedure from that which is special and peculiar to the individual sciences. An elaborate philosophic doctrine lies at the root of this assumption, and the position assigned to logic may easily be seen to depend, not on what is apparent in the argument, namely, comparison of the sciences with one another, but on what lies implicit in the background, the philosophic concep- tion of the nature of scientific knowledge in general. With- out reference to the ultimate philosophic view, no definite content could be assigned to logic, and it would remain impossible to distinguish logic from the sciences in detail.^ 3. Thus the various attempts to define the province and functions of logic from general classification of the sciences, to define, in short, by the method of division, yield no satisfactory answer, and refer ultimately to the philosophic view on which classification and division must be based. A similar result becomes apparent when we consider the ^ See, for a clear statement of this impossibility, Comte, PhUos. Positive, i. 34, 35. Definitions of logic as theory of method, which are based on general philosophic views (e.(/., the definition by Sigwart, Logik, i. § 1), stand on a different footing, and are to be examined on difEerent principles. 8 HISTORY OF LOGIC various descriptions of logic tliat have been presented as following from more precise and accurate determination of the essential features of logical analysis and method. " The philosophical deduction or construction of the notion of logic presupposes a comprehensive and well- grounded view, whether of the nature and mode of opera- tion of the human mind, a definite part of which falls under logical treatment, or of the problems and objects of philosophy in general, from among which in due order may be distinguished the particular problem of logic." ^ The most elementary distinctions, by means of which, in the ordinary exposition of logic, progress is effected towards an accurate determination of the province of the science, not only refer to some such ultimate pliilosophic view, but lead to the most diverse results, according to the peculiarity of the views on which they are based. Of these elementary distinctions tlie following are at once the more usual and the more important : — the distinction between the province of logic and the province of the special sciences, as that between general and special ; the distinction between natural growth of knowledge, with its natural laws, and the normal procedure whereby grounded knowledge is obtained, with its normal or regulative principles ; the distinction between knowledge as a whole and its several parts, immediate and mediate, with restriction of logic to the treatment of all or portion of mediate knowledge ; the dis- tinction between the constituents of knowledge as on the one hand given from without (in experience), and on the other hand due to the elaborative action of intellect itself. To one or other of these may be traced the common definitions of logic, and a brief consideration of their contents will be sufficient to show that they severally rest upon more or less ^ Twesten, Die Lor/ik, inabesondere die Anvdytik (1825), p. 2. PROVINCE AND METHOD OF LOGIC 9 developed general philosophic doctrines, and that their significance for accurate determination of the field of logic depends not so much on what is explicitly stated in them as on what is implied in the general doctrines from which they have taken their rise. The distinction of logic from the sciences, as dealing in the abstract with that which is concretely exemplified in each of them, is certainly a first step in the process of de- termination about which there can be little or no doubt. But it is only a step, and progress is not much advanced thereby. For, if the distinction remain vague, it is not sufficient to differentiate logic from many other disciplines, philosophical or philological, and if it be made more pre- cise, the new characteristics will be found to involve some special view as to what constitutes the common feature in the sciences, and to vary with the possible varieties of view. As a rule, too, the added characteristics do not serve by themselves to mark off logical treatment as an independent kind of investigation. They are most fre- quently obtained by a general survey of scientific pro- cedure. Thus it may be said that in all sciences there are implied clearly defined notions, general statements or judgments, and methodical proofs ; logic, therefore, as the theory of the general element in science, will appear as the treatment of notions, judgments, and proofs generally, or in the abstract. If so, then, unless some implied prin- ciple further determine the course of procedure, logic would be regarded as a merely descriptive account of the parts making up scientific knowledge, and it would be not only impossible to assign to it an independent position, but hard to discriminate it from psychology, which likewise deals with the parts of knowledge. If it be understood, however, or explicitely stated, that in 10 HISTORY OF LOGIC all scientific knowledge there is community of method, resting on common principles or laws of knowledge as such, then clearly not only the province of logic, as now made identical with the treatment of the essence of know- ledge, but the special nature of the theorems making up the body of logic, must depend upon the general con- ception of knowledge with which the thinker starts. In ., the view of logic taken, e.g., by ]\Iill, the fundamental idea is that of evidence, under which must be included all the grounds for any judgment not resting on immediate per- ception. So far as verbal statement is concerned, the adoption of this as the root idea would not distinguish in any special way the treatment of logical problems resting on it ; but in fact each problem is dealt with in accordance with the particular theory of what, from the nature of human knowledge, constitutes evidence. Logic thus in- volves, or in truth becomes, a theory of knowledge, and in the end, for general spirit and details of doctrine, refers to an ultimate philosophic view. There seems no escape from I '/this conclusion. Startaswe_jnay^ with ^popular, current distinctions, no sooner do logical problems present them- "t, . selves than it becomes apparent that, for adequate treat- ment of them, reference to' the principles of ultimate / philosophy is requisite, and logic, as the systematic \ handling of such problems, ceases to be an independent ; I discipline, and becomes a subordinate special branch of 1 \ \ general philosophy. ' The attempt to avoid this conclusion must of necessity take form in some discrimination of logic from other varieties which may with it be classed under philosophy in general, and such discrimination is usually effected by laying stress on one or other of the following characteristics. (1) In the whole process of knowledge, it may be said, PROVINCE AND METHOD OF LOGIC 11 we are able to distinyuish and to regard in isolation the metliods according to whicli, from a combination of various elements, cognition of things grows up, and the laws according to which these elements must be ordered, if our subjective consciousness is to represent accurately and faithfully the relations of things. The laws of knowledge — there being understood by knowledge the whole sum of mental determinations in and through which the world of external and internal experience is realised for us — are of two distinct kinds, natural and normal. For the treatment of the natural laws the most appropriate title is psychology ; for that of the normal or regulative laws the title logic is peculiarly appropriate. By the one science knowledge is regarded in its relation to the subjective consciousness, as so much of what enters into and constitutes the world of inner experience ; by the other knowledge is regarded in its relation to truth, to the objective system, as the means whereby, for theoretical or practical purposes, an orderly and verifiable conception of this system is realised. A definite place seems thus secured for logic ; but, if one may judge merely from the various attempts to expound the body of logical doctrines from this point of view, the characteristic feature is not yet sufficient to determine the boundaries of the science or the specific nature of its problems. In fact, the feature selected might be accepted as the distinguishing mark of logical science by writers who would include under that common title the most diverse matters, and who would differ fundamentally in respect to the treatment of isolated problems. The metaphysical logic of Hegel, the empirical logic of Mill, ' the formal logic of Kant, might all claim to be develop- ments of this one view of the essence of logic. So wide a divergence is clear evidence that the criterion selected. 12 HISTORY OF LOGIC though possibly accurate, is not sufficiently specific, and that the interpretation of it, which in truth determines for each the nature and boundaries of the science, depends . upon the view taken respecting knowledge as a whole in its relation to the objective order of experience, respecting the import of the so-called normal laws, and respecting the subjective elements supposed to constitute knowledge. On all sides this particular definition of logic is beset with difficulties, which it cannot alford to dismiss by means of the simple demand that knowledge shall be accepted as somehow given. For, apart altogether from the danger that under so wide a term as knowledge many differences may be accommodated, it then becomes impossible to do more than treat in a quasi-empirical fashion mental facts, the nature and peculiarities of which are to be learned from some external source. In the later, more detailed examin- ation of the view of logic here briefly described, it will be pointed out that the usual formula by which the several logical notions are introduced, viz., that their nature as mental facts is dealt with in psychology, from which logic borrows, is in fact much more than a formula. The logical peculiarities will be found to rest mainly upon the psycho- logical characteristics as borrowed, while it is evident that no substantive, independent existence can be vindicated for a doctrine, the succession of whose parts and their essential nature are given externally.^ ' The following from Drobisch's excellent work {Neue DarstcUung dcr Logik, 3rd ed., 1863) will make clear the view commented upon. " Human knowledge is partly immediate, partly mediate. The former rests on given facta, whether of sense-perception or of consciousness, the latter on that which may be deduced by thought from these facta. . . . Thought may be the object of scientific treatment from a double point of view : first, in so far as it is an activity of mind, ita conditions and laws may be investigated ; second, in so far as it PROVINCE AND METHOD OF LOGIC 13 (2) Some of the perplexities that arise when logic is treated as the theory of the normal laws of knowledge may be obviated by the current distinction between immediate and mediate knowledge. The normal laws of knowledge might be said to apply solely to the process of mediate cognition, and their final aim would be defined as harmony between mediate knowledge and immediate experience. In fact, however, little is gained by the employment of this new characteristic. It is difficult to distinguish with perfect accuracy between the two kinds of knowledge in question ; it is impossible that the treatment of the logical problem should not depend entirely on the view taken as to the nature of that which ditferentiates mediate from is the instrument for acquiring mediate knowledge, an instrument that may be used not only correctly but also incorrectly, and so may lead to true or to false results. There are therefore natural laws of thought and also normal laws, prescripts, rules, according to which it must be directed in order to lead to truth. The investigation of Vthe natural laws of thouglit is a problem of psychology ; the deter- mination of its normal Liwa is the problem of logic. . , . The logical normal laws of thought are not to be discovered by mere observation, for it would then be impossible to decide whether the mode in which we ordinarily think is also valid ; but they must themselves be proved by thought, and so be shown to be necessary, not capable of being other than they are. The warrant for both the thought that proves these laws and the laws proved by it, is to be found in the thorough harmony between the two. Logic thus presents itself as in no way a mere description and analysis of thought, a descriptive science, but as a demonstrative science " (§§ 1, 2, 3). So far, there is little to object to ; but clearly the whole character of the science depends (1) on the significance to be attached to the fundamental term thought, and (2) on the limitations imposed on the conception of laws. It becomes necessary, then, for Drobisch, as for any logician, to define his point of view regarding tliought ; and the definition (§§ 4, 5) at once introduces the further discrimination of form and matter, a discrimination which determines the whole treatment of the forms of logical problems. 14 HISTORY OF LOGIC immediate knowledge. Whether we express this as thought or as belief, its nature then becomes the all- important factor in determining the course of logical treatment, and further progress will manifest divergencies according as stress is laid on the subjective characteristics of thought, the laws to which, from its essential nature, all its products must conform, or on the limitations im- posed by principles which have reference to the most general relations of the things thought about. In the one case a formal logic, of the type commonly known as the Kantian, would be developed ; in the other either an empirical logic, like that of Mill, wherein the nature of notions, propositions, and reasonings is considered from the point of view of the empirical conception of experience, or a transcendental logic, like that involved in the Critique of Pure Reason, or a metaphysical logic, like that of Hegel, or a mixed doctrine, like that of Trendelenburg, Lotze,'and Ueberweg. In short, the general philosophic view of thought is that upon which the character of logic as a science rests. (3) There has above appeared, incidentally, one of the most current methods of solving the logical problem, by procedure from the distinction between that which is given to the mind in knowledge, and that which is supplied by the mind itself. No distinction seems more simple ; none is in reality more complex. The opposition on which, in its popular acceptation, it rests is that between the indi- vidual concrete thinking subject and the world of objective facts, existing, as it were, to be cognised. The full signifi- cance of such an opposition, the forms in which it presents itself in conscious experience, the qualifications which must be introduced into the statement of it that it may have even a semblance of reality, — these are problems not solved by PROVINCE AND METHOD OF LOGIC 15 a simple reference to the distinction as existing. It may well be held that knowledge is, for the individual, the mode (or one of the modes) in which his relation to the universe of fact is subjectively seized, but it is not therefore rendered possible to effect an accurate and mechanical separation of knowledge into its matter and form. Even on lower grounds it may be held that by the employment of this criterion little or no light is thrown upon the logical question. For no determination is supplied by it of the universal characteristic of form as opposed to matter in knowledge, and a comparison of various expositions will show the most startling diversity of view respecting the nature and boundaries of the formal element "IrTkno wledge. It is of course true that in one sense any scientific treat- ment of knowledge is formal. Our analysis extends only to the general or abstract aspect of cognition, not to its actual details. But we are not, on that account, dealing with the form of knowledge. So soon as it is attempted to define more accurately what shall be understood by form, then it is found that various views of logic arise, corre- sponding to the variety of principles supposed to be applied in the treatment of form. Thus the stricter followers of the Kantian logical idea, e.g., Mansel and Spalding, recognise, as sole principles which can be said to be involved univer- sally in the action of thought, the laws of identity, non- contradiction, and excluded middle,^ and in their hands logic becomes merely the systematic statement of these laws, and the exposition of the conditions which they impose upon notions, judgments, and reasonings. Analytical * "Logic," says Spalding (Ency, Brit., 8th edition), "is the regu- lative theory of explicative thought" ; " Logic," says Mansel {Pro- legomena Lorjica, 2nd ed., p. 264), "is the science of the laws and products of pure or formal thinking." 16 HISTORY OF LOGIC consistency, i.e., absence of contradiction, is on this view the one aspect of knowledge wliich is susceptible of logical treatment. On the other hand, the idea of a contribution furnished by the mind itself to knowledge may lead to a more concrete and yet not less exact system of the forms of knowledge, if there be taken into account the real character of the operation by which such contribution is made. Thus in the logic of Ulrici, from the view of thought as essen- tially the distinguishing faculty, by which definiteness is given to the elements entering into knowledge, there follows not simply an iteration of the principle that thought must not contradict itself, but a systematic evolution of the fundamental relations involved in the action of thought, in which the more specifically logical products, the notion, judgment, and reasoning, have a determinate place assigned to them. Not only, then, may quite distinct provinces be assigned to logic by thinkers who start with the same idea of thought as contributing to knowledge, but, as may well be imagined, the treatment of special logical problems presents a most // bewildering variety. The nature of judgment, the prin- ciple of reasoning, the characteristics of thought which is in accordance with logical rule, will be viewed differently according to the special interpretation put upon the func- tions of the subjective factor in knowledge. Here again we find that the really influential fact in the determination of the province and method of logical science is a general philosophic conception of knowledge or thought. i ' In Rosenkranz, Die Modificationen der Logik ahgeleitet aus dem Bcyriff des Denlcens (1846), a similar conclusion is illuBtrated by an elaborate classification of possiljle modifications of the view of logic. Compare also Braniss, Die Logik in ihrem Verhiiltniss zur Pkilosophie geschichUich betrachtet (1823). PROVINCE AND METHOD OF LOGIC 17 4. Although, then, it does not seem practicable to obtain, either by external division or by internal analysis, a clear and sufficient definition of the province and function of logic, there remains yet one method by means of which the desired end may be attained. It may be that the separation of logic from other philosophic disciplines has come about historically, and that the assignment to logic of a special body of problems and a special kind of treatment is due to the accidents of its development. We might therefore hope to gain from a comparative survey of the field of logic, as that has been historically marked out, some definite view not only respecting the specific problems of logical theory, but also regarding the grounds for the isolated treatment of them. That in the history of logic there should be found a certain continuity of doctrine and development may, how- ever, be compatible with entire absence of a common body of received logical matter, and the result of an historical research may be little more than a statement of distinct conceptions regarding the nature and province of the science, leading to the inclusion of very distinct materials within its scope. It requires but a superficial investigation of that which at various intervals has presented itself as logical theory to arrive at the conclusion that the differences in general spirit and in the mass of details far outbalance any agreement as to a few detached doctrines and technical symbols. If the survey were limited even to the period preceding the attempts at radical reformation of philosophy in general, and of logic as included therein, to the period in which the Aristotelian doctrines, as they may be called, formed the common basis of logical treatment, we should be able to detect differences of such a kind as to indicate radically distinct fundamental views. The scholastic logic, which, B 18 HISTORY OF LOGIC even by itself, cannot be regarded as one tbeory with unimportant modifications, is most falsely described as Aristotelian, The technical terminology, the general idea and plan, and some of the formal details are certainly due to the Aristotelian analysis of reasoned knowledge ; but in spirit, in ruling principles, and in the mass of details the method of the scholastic logic is alien to that of Aristotle. It will be shown later that the Aristotelian analysis is saturated with the notions and aims of the Aristotelian metaphysics and general theory of knowledge, and that on that account alone, apart from the introduction of many foreign ingredients, from Stoic, Arab, and Byzantine sources, into the scholastic system, an important difl'erence must' subsist between the original doctrine and that which presents itself as but its historical development. Even more radical is the divergence of modern logic from the Aristotelian ideal and method. The thinker who claimed for logic a special pre-eminence among sciences because " since Aristotle it has not had to retrace a single step, . . . and to the present day has not been able to make one step in advance," ^ has, himself in his general modification of all philosophy, placed logic on so new a basis that the only point of connection retained by it in his system with the Aristotelian may be not unfairly described as the com- munity of subject. Both deal in some way with the principles and methods of human thinking, but as their general views of the constitution of thought are diverse, little agreement is to be found in the special treatment of its logical aspect. So when a later writer prefaces his examination of logical principles with the declaration that " logic is common ground on which the partisans of Hartley and of Reid, of Locke and of Kant, may meet and join ' Kant, Krilik (ed. Hartenstein), Vorrede, p. 13. PROVINCE AND METHOD OF LOGIC 19 hands," ^ WG are not unprepared for the result that, with a few unimportant exceptions, his views of logical principle coincide with those of no recognised predecessor in the same field, diverge widely from either the currently received or the genuine Aristotelian doctrines, and lead to a totally new distribution, in mass and detail, of the body of logical theorems and discussions. Such divergence is, indeed, most intelligible. If one reflects on the significance which would be attached in any one of these logical systems, of Aristotle, of Kant, of Mill, to the universal or universalising element of thought, and on the fact that such universal must manifest itself as the characteristic feature in all the important products of thinking, the notion, the judgment, the syllogism, the con- clusion is inevitable that difference of view in respect to the essence must make itself felt in difterence of treatment of details. The ultimate aim of proof, and the general / nature of the methods of proof, must appear differently according as the accepted ground is the Aristotelian con- ception of nature and thought, the Kantian theory of cognition, or subjective empiricism. - — If, adopting a'simpler method, one were to inspect a fair proportion of the more extensive recent works on logic, the conclusion drawn would be probably the same, — that, while the matters treated show a slight similarity, no more than would naturally result from the fact that thought is the subject analysed, the diversity in mode of treatment is so great that it would be impossible to select by comparison and criticism a certain body of theorems and methods, and assign to them the title of logic. That such works as those of Trendclen])urg, Ueberweg, Ulrici, Lotze, Sigwart, Wundt, Bergmann, Schuppe, De Morgan, Boole, Jevons ^ Mill, System of Logic, i. p. 13. 20 HISTORY OF LOGIC (and these are but a selection from the most recent), treat of notions, judgments, and methods of reasoning, gives to them indeed a certain common character ; but what other feature do they possess in common ? In tone, in method, in aim, in fundamental principles, in extent of field, they diverge so widely as to appear, not so many different expositions of the same science, but so many different sciences. In short, looking to the chaotic state of logical text-books at the present time, one would be inclined to say that there does not exist anywhere a recognised, currently received body of speculations to which the title logic can be unambiguously assigned, and that we must therefore resign the hope of attaining by any empirical con- sideration of the received doctrine a precise determination of the nature and limits of logical theory. 5. In order to make clear the reasons for this astonishing diversity of opinion regarding the province and method of logic, and so make some advance towards a solution of what may well be called the logical problem, it seems necessary to consider some of the leading conceptions of logic, with such reference to details as will suffice to show how difference of fundamental view determines the treatment of special logical problems. In this consideration the order must be historical rather than systematic. Not, indeed, that it is needful, nor is it proposed, to present an historical account of philosophy at large, or even of logic in particular ; our purpose is merely to disentangle and bring clearly forward the nature of the principles respecting logical theory which have served as basis for the most characteristic logical systems. Such an inquiry will not only assist in explaining the divergencies of logical systems, but throw light upon the essence of logic itself. Thus, for example, PROVINCE AND METHOD OF LOGIC 21 a critical comparison of the Aristotelian and Kantian or Hegelian conceptions of the end, aim, and function of logic may be expected to bring forward in their most abstract form opposed, or at least varied, views of the nature of the subject, and to enable a well-balanced judgment to be obtained on the problem involved,^ In this historico-critical survey, the first section must naturally be devoted to a consideration of the Aristotelian logic. If it were intended to present a complete history, or abstract of a complete history of logic, it would doubtless be necessary to preface the treatment of that from which logic, as we know it, has taken its rise, by a notice of such speculations of a logical character as are to be discovered among Oriental systems. But, however interesting such an historic research might be, its results would have little or no bearing upon the special problems before us. Our notions regarding logic are affected by the Aristotelian analysis of the method of reasoning, and by such systems as have been developed therefrom, but have been modified, and are likely to be modified, in no way by any Oriental systems of a like kind. The records of Oriental attempts at analysis of the procedure of thought are of purely historic value, and may, for our present purpose, be disregarded.^ ^ For a notice of works on the history of logic, see note A, p. 164. ^ For a notice of some of the more developed systems of Oriental logic, see note B, p. 165. 22 II THE ARISTOTELIAN LOGIC 6, In a remarkable passage at the close of the tract called by us the Sophidical Refutations, Aristotle claiins for himself distinct originality in the conception of sub- jecting to analysis the forms or types of argument. Something had been achieved in closely allied matters, in the analysis of rhetorical methods and grammatical forms ; but, in the attempt to generalise and reduce to order and method the very substance of reasoning, nothing, according to this statement, had been effected, nor had the possibility of such reduction been seriously contemplated. " The system I have expounded had not been partially, though imperfectly, elaborated by others ; its very foundations had to be laid. . . . The teachers of rhetoric inherited many principles that had long been ascertained ; dialectic had absolutely no traditional doctrines. Our researches were long, tentative, and troublesome. If, then, starting from nothing, it bears a comparison with others that have been developed by division of labour in successive gen- erations, candid criticism will be readier to commend it for the degree of completeness to which it has attained than to find fault with it for falling short of perfection." ^ ' The above translation, which is somewhat free, is taken from Mr PoBte'B edition of the Sophistici Elenchi, p. 95. THE ARISTOTELIAN LOGIC 23 Although the specific reference in this passage is to the analysis of dialectical argument contained in the Tojnca, the same claim might with justice have been made in regard to the more extensive analysis of the forms of reasoning in general which makes up the substance of the other books of the Organon. There had been, prior to Aristotle, much discussion of problems that would under any view be included under the head of logic ; but no systematic attempt had been made to analyse knowledge as a whole in its formal aspect, to throw under general heads or classes the types of reasoning, whether dialectical or scientific, and to exhibit the general relations in which the elements of all reasoning stand to one another. After Aristotle, it became possible to refer all such discussions to a common head, and to view them as component parts of one systematic doctrine. In a peculiar sense, then, Aristotle may be described as the founder of logical science. The precise nature of the inquiries falling within the scope of the Aristotelian logic may receive some preliminary explanation supplementary to that which can only be given by a careful study of the chief theorems of the system, if there be taken into account (a) the advances towards a theory of logical method contained in the speculations of earlier Greek thinkers, (h) the classification of philosophic disciplines, which underlies the body of Aristotle's writings, and (c) the general conception of the matter of logical analysis which may be deduced from any special or incidental treatment of the question in Aristotle. Of these in order. (a) Logical discussions prior to Aristotle. 7. The inquiries which find a place in the Aristotelian logic are all, in a large sense, problems of the theory of know- 24 HISTORY OF LOGIC ledge. They arise, therefore, only in connection with critical reflection on the nature, grounds, and method of knowledge. The earliest forms of Greek speculation, turning rather upon explanation of natural fact, being in essence attempts to reduce the multiplicity of known fact to unity of principle, contain, as a consequence, problems of a metaphysical character, which might involve problems of strictly logical character, but were logical only in poten- tiality. The difficulties with wliich the early Greek speculators were presented had at first an aspect which was metaphysical only. 2^ot until these difficulties were transferred into the sphere of thought, with the conscious- ness, however undeveloped, of a possible opposition between the determination of things reached by immediate processes of thinking and the characteristics of thought when submitted to critical reflection, could problems of a dis- tinctly logical character come forward for solution. Of aU these metaphysical questions the most important centre round the fundamental opposition between unity of principle and multiplicity of fact, between the one and the many, an opposition which under varied forms pre- sents itself at every stage in the history of philosophic speculation. It is, indeed, an abstract expression for the problem with which philosophy at all times has to deal, though, naturally, the formulae under which it makes its appearance are determined by the more or less developed conceptions of the elements entering into it that may have been attained. In the first period of Greek speculation, the problem presented itself in its simplest, most direct aspect, and, after a few rough attempts at a quasi-physical explanation of the genesis of many out of one, there come forward, as reasoned, ultimate solutions, the Eleatic doctrine that only THE ARISTOTELIAN LOGIC 25 unity has real being, the Heraclitic counter-doctrine that only in change, in the many, is truth to be found, and the Pythagorean notion of number, harmony, as containing in abdracto the union of the opposites, one and many. No one of these philosophic treatments can be said to contain specifically logical elements, but they raise questions of a logical kind, and, especially iu tlio records of the Eleatic views, one can trace a close approximation to the critical reflection which marks the transition to a new order of ideas. Eesults which in these systems are stated with metaphysical reference only, reappear with new aspect among the Sophists and the Socratic schools. The transition stage, indeed, partly aided by the atomic separation of objective fact from subjective sense experience, is mainly the effect of the Sophistic and Socratic teaching. Socrates and the Sophists have this in common that both treat the fundamental problem of philosophy as it had been handed down with special reference to the subjective experience of the individual. In their conceptions of the nature of subjective experience they differ widely from one another, just as in aim, method, and principles both differ from modern views on the same question ; but in both is to be discovered the critical reflection on thought and its essence which marked a ncAv stage of specu- lation and prepared the way for a fresh development of philosophical activity.^ A brief indication of the logical ^ It is an error to strain expressions which, with due qualifications, may be accepted as valuable. One meets repeatedly with the assertion that the characteristic difiference between ancient and modern philo- sophy is that in the former the special problem of the theory of knowledge, the possibility of reconciling subjective thought with ob- jective system of things, was not contemplated. In a certain sense this is true ; but, taken absolutely, it is both erroneous and misleading. The Sophistic discussions, the Socratic theory of the notion, the 2(5 HISTORY OF LOGIC elements involved in this new treatment of the problem will be sufficient. In the teaching of the Sophists generally is to be discerned the opposition between subjective reflection and objective fact ; in that of Protagoras and Gorgias in particular there appear as problems of the theory of know- ledge difficulties for the older metaphysic of Heraclitus and the Eleatics respectively. The Heraclitean principle of change is the general foundation for the doctrine that the momentary perception is the only fact of cognition, and upon it may be based the conclusions that all truth is rel- ative to the individual state of the individual subject, and that judgment, as a mode of expressing truth, is a con- tradiction in itself.^ Thus the extreme Heracliteans, as Cratylus, rejected the proposition or combination of words, as expressing a unity and permanence not to be found in things, and reduced speech to the symbolism of pointing with the finger. Less developed but not less clear is the connection between the brief sceptical theses of Gorgias and the Eleatic doctrine of unity. As knowledge [was impos- sible on the Heraclitean view, since it implied a synthesis not discoverable amidst incessant change, so for Gorgias knowledge was impossible, since in the synthesis was Platonic distinctions of reason, understanding, and opinion, the Aris- totelian treatment of the principles of knowledge, of the universal, and of the opposition between science and opinion, are quite unintel- ligible except under supposition of some such distinction. The difference is not in the problem, but in the new conceptions of the nature of the elements, and of the method of solution which modern philosophy introduces into its discu-seion. ^ However we may interpret the Protagorean maxim in relation to more modem conceptions, there appears no reason to doubt the his- toric accuracy of the connection indicated in the Theoetetus, and in the fourth book of the Metaphysics, between the Heraclitean metaphysic and the Protagorean theory of knowledge. THE ARISTOTELIAN LOGIC 27 involved an element of difference, multiplicity, not recon- cilable with the all-embracing unity of things. It is evident from the treatment of such views in Plato and in Aristotle, how many of the illustrations used in support of the general thesis depended for their apparent strength on neglect of some of the elementary conditions of thought, and how inevitably reflection upon these difficulties led to the construction of a theory of thought. The first outlines of such a theory are to be found in the Socratic principle of the notion (or concept, as we may call it, for the notion as viewed by kSocrates is certainly the concrete class notion, the simple result of generalisation and abstraction), and to Socrates is assigned by Aristotle the first statement of two important logical processes — induction, or the collection of particulars from which by critical comparison a generalised result might be drawn, and definition, or the explicit state- ment of the general elements disclosed by critical comparison of instances.^ In the Socratic teaching, so far as records go, no explicit reference was made to the problems in connection with which those processes are of greatest significance, but in the lesser Socratic schools on the one hand, and in Plato on the other, we find the new principle either brought to bear upon the old difficulties, or developed into a comprehensive method. The Socratic concept contains in itself the union of one and many, but it is in nature subjective ; it is a mode of knowledge. If, then, it be regarded as only subjective, the old difficulties reappear. How is it possible to reconcile, even in thought, an opposition so fundamental as that between unity and plurality 1 Must there not be a like irreconcilable opposition between the subjective counter- 1 Mctaph., 1078b 27-29. 28 HISTORY OF LOGIC parts of these objective relations, between the individual notion, the atom of knowledge, and the proposition or definition 1 How, indeed, can there be a combination in thought of that which is in essence uncombinable ? Whether we take Aristippus, who draws mainly for theory of knowledge on the Heraclitean-Protagorean sources, or Antisthencs, Avho leans towards the Eleatic, or the Megariaus, who also, in accordance with the Eleatic thoughts, devoted chief attention to the polemical aspect of the theory, we find a set of problems appearing, the solution of which imperatively called for a theory of knowledge as the combination of one and many. Perhaps the most interesting of these early thinkers, so far as the history of logic is concerned, is Antisthenes, whose extreme nominalism presents the most curious analogies to some recent logical work.^ According to Antisthenes, the world of cognisable fact consists of combinations of elementary parts {irpthTa). These TrpcuTa appear in cognition as irreducible elements denoted by the simplest elements of speech, names. The name is the mark for the sense-impression by which each Trpwrov is communicated to us, for they are only known by sense, and are strictly individual. A composite thing is known through the combination of names of its parts, and such a combination (crv/xTrXoKr/) is a proposition or definition (Xoyos). Each thing has its specific Xdyos (otKcios Xoyos), and a judgment is merely the expression of this. There is therefore no distinction of subject and predicate possible ; even identical propositions, the only * On Antisthenes, see the third part of the Thcwtetus, which ap- pearB, beyond doubt, to refer to him (comp. Peipers, Untersuchum/en iiber das Systems Plato's, 1874, pp. 124-48), and Aristotle, 3Ieta- physica, 1021b 32, 1043b 24 ; Topica, 104b 21. THE ARISTOTELIAN LOGIC 29 possible forms under this theory, are mere repetitions of the complex name. Predication is either impossible or reduces itself to naming in the predicate what is named in the subjoft. It is the simple result of so consistent a nominalism that all truth is arbitrary or relative ; there is no possibility of contradiction, not even of one's self. The theory of Antisthenes, strange as it may at first sight appear, rested on certain metaphysical difficulties, which lie at the root of all the perplexity regarding the import of propositions, and it is not too much to say that these difficulties were kept continually in mind by Plato and Aristotle in their several attempts to explain the nature of knowledge. Both thinkers bring forward, from various fields, new elements which enter into the consideration of the problem, but both find themselves confronted with the ultimate question, What is the ground of unity in things known, and in what way does thought unite the detached attributes of things into a subjective whole? What is the nature of the unity which binds things, themselves in a sense units, into classes or wholes, and how comes it that in the judgment subject and predi- cate are, in a sense, set at one? The inquiry branches off in varied directions, into discussions on the universal and particular, on form and matter, on the unity of the definition, but nevertheless remains the one underlying difficulty for both thinkers. In Plato, for whom the solution was found in the J J participation in or imitation of ideas by things, we find more distinctly conceived the series of logical processes involved obscurely in the Socratic method. So far as positive statements regarding the ideas can carry one, it may be said that in essence these processes concern only 30 HISTORY OF LOGIC the formation of or deduction from the concrete universal concept or general notion. The ideas, in the Platonic system, at least in reference to the thought which appre- hends them, resemble most closely class notions. A deeper significance often appears to attach to the relative processes of induction, whereby the resemblances of things, the idea in them, is disclosed, definition, whereby the content of the idea is made explicit, and division, whereby the external connection of ideas with one another, their system, is deduced ; but such significance attaches to the more purely metaphysical aspects of the theory, and had no particular bearing on the Aristotelian treatment of the same problems. Xot much is given in Plato towards a theory of the proposition, though sometimes an analysis of its elements is sketched ; and the method of division could yield only a few of the types of deductive reasoning. But, over and above these more definite contributions towards the construction of a theory of knowledge, there are general aspects of the Platonic work of not secondary importance for the Aristotelian logic. In Plato the fundamental difi"erences of earlier philosophic views ap- pear in a new phase, and are elevated to a higher stage. Sophistic method is analysed, not as in forms actually existing, but in its essential features, and the opposition between sophist and philosopher is viewed as the opposi- tion between opinion and knowledge. Heraclitean prin- ciple of change and Eleatic doctrine of unity are resolved into the more comprehensive opposition of the universal and the particular, while hints of an ultimate solution, of a universal which is at once and pe)' se particular, are not wanting. The Socratic method of thought appears as that by which alone a solution of philosophic difficulties is to THE ARISTOTELIAN LOGIC 31 be obtained, and the consideration of thought in its re- lation to facts is marked out for special investigation. A deeper view of thought was thus made at once possible and necessary. (b) Classification of Philoso2)hic Disciplines. 8. Much, then, had been effected by Aristotle's pre- decessors in the way of preparing a definite body of problems and a method of dealing with them, problems and method which might fairly be said to belong to a theory of knowledge as such ; and, from the occasional references in the Organon to opinions of contemporaries, it is evident that many isolated attempts at solution of such questions were being carried on. In Aristotle we find a systematic examination of many of these problems, but it is left by him doubtful what place in the general scheme of philosophic sciences should be assigned to it. The distribution into physics, mathematics, and first philosophy, or the wider classification of doctrines as poetic, practical, or theoretical, in no way enables us to class logic or the body of speculations making up the Organon. That the forms of proof analysed in these writings are of universal scope is unambiguously declared ; that the first principles assumed in all proof are dealt with in first philosopliy is also made clear ; but the relations between the two doctrines so reciprocally related cannot be determined from any statement made by Aristotle himself. That he should have regarded the inquiries of the analytics as propaedeutic in character, and should have held that those who assume to discuss problems of first philosophy ought to have made them- selves acquainted with the general theory of proof, is 32 HISTORY OF LOGIC intelligible ; and more than this significance cannot, we think, be assigned to the passage in the Metaphysics, on the ground of which the logical inquiries have been classed as the general, common introduction to the whole system.^ For the close connection between the analytical researches of the Organon and the inquiry into essence or being as such forbids us to accept, in any strict sense, a separation of these as forming distinct and independent sciences. To metaphysics is assigned the consideration of the principles of proof, and the kind of inquiry making up first philosophy is described by Aristotle in a fashion which assimilates it most closely to the researches of the analytics. That which is left undecided by the Aristotelian classification is the relation of the logical inquiries to the organic whole of which first philosophy is the main or sole part.^ To obtain any fresh light we must turn to the consideration of indications supplied by Aristotle as to the nature of the inquiries grouped under the head of Analytics. (c) General conception of the matter of Logical Analysis. 9. Such indications are unfortunately most scanty. As we probably have not the Metajjhysics in its full extent, actual or contemplated, the want of a clear separation between the inquiries belonging specially to first philosophy and those appropriate to the analytical 1 Metaph., iv. 1005b 2. See Zeller, Ph. d. Gr., u. 2 (3rd ed.), p. 184, n. ; Rassow, De Definit. Not., 46, 47 ; Schwegler, Comment, zur Metaph., iii. 161 ; and, contra, Prantl, Gesch. der Loyih., i. 137. 2ieller maintains the view that Aristotle intends to indicate the place occupied by the analytics in his general scheme of philosophy. ' On Aristotle's use of the term \oyiK6s and its allies, see (in addi- tion to Waltz, Com. in Organ., ii. pp. 353-55) Schwegler, Commenlar zu Ar. Metaph., vol. iv. pp. 48-51. THE ARISTOTELIAN LOGIC 33 researches may bo due in part to tlie deficiency of our materials. There are, however, two lines of separation discernible, from which some useful inferences may be drawn. What we call the logic of Aristotle, i.e., the treatises making up the Organon, is roughly divisible into three parts: (1) The formal analysis of syllogism and its allied types of reasoning, with the more particular "^ discussion of the elementary parts of reasoning = the proposition ; (2) the theory of scientific proof and defini- tion (apodictic) ; (3) the theory of probable arguments, or of reasoning based on currently received opinions and leading to conclusions more or less probable (dialectic). Certainly for Aristotle there was no such distinction be- tween the first and the remaining two parts as would in any way correspond to the modern separation of general or formal logic from the theory of knowledge, or material logic ; the three parts in conjunction make up one body of doctrine. Now dialectic is very specially indicated as being of a formal character, i.e., as dealing with no special matter, but with Koivd, opinions, or types of opinions common to all sciences.i Apodictic, we may assume, is in like manner the formal study of what constitutes know- ledge strictly so called, the nature of the principles on which knowledge rests, the special marks distinguishing it, and the method by which knowledge is framed. yBut in every body of doctrine we may distinguish, according to Aristotle, three things : — the genus or class ^ of objects with which the demonstration is concerned/^ the essential or fundamental attributes, qualities of theseV objects, which are to be demonstrated of them ; and^^ thirdly, certain common axioms or principles of deraon- ^ See Annl. Post., i. 11 ; Jlhct., i. 1, and in many passages. Cf, Heyder, Method, d. Arist., p. 348. 34 HISTOKY OF LOGIC stration, not themselves demonstrable, and not entering as integral parts into the demonstration, but lying in the background as security for the reasoning carried out by thought employing them. Can anything corresponding to these three facts be discovered, if we assume for the moment, what certainly is not explicitly stated by Aristotle, that analytic constitutes a special body of doctrine? The genus or class about which the doctrine is concerned can only be reasoning itself, either as apo- dictic or as dialectic, and the latter for a special reason may be left out of account ; aTroSei^ts, then, is the matter concerning which the doctrine is put forward. But ciTrdSet^ts is a form of knowledge, that is to say, is subjective. The properties, therefore, of apodictic science can only be made clear if we consider on the one hand the objective counterparts of necessity and universality in thought, and on the other hand the nature of universality and necessity of thought itself. The common principles or axioms, finally, can only be such presuppositions as are made in apodictic or reasoning generally respecting thought in its relation to fact, as grasping or apprehend- ing reality. The consideration of such axioms, it has been already seen, jDertains to first philosophy. Analytics then would appear as an independent doctrine, holding of first philosophy on the one hand, both in regard of the com- mon axioms and in regard of the attributes of being, by which it is a possible object of science, and on the other hand referring to the subjective treatment of thought, whether in relation to principles or to fact generally, A very similar result may be attained if we follow out a line of distinction indicated in more than one portion of the MetaphysicsA Separating the modes in which ' Meiaph., vi. 4, v. 29, ix. 10. Of. Schwegler, Com,, iii. 241, iv. 29 $q., 186 ; and Brentano, Bedeutung des Seienden nachArist., 21 sq. THE ARISTOTELIAN LOGIC 36 being is spoken of into four — (1) to ov Kara a-vfxftffiriKo^ ; (2) TO ov a)S d.\r}6€<; kul to fXT] ov w? to i/^evSos; (3) to ov Kara ra axviJi-'J-Ta rrj'S KaTr/yopia^ ; (4) to ov Suvaju-ei Koi iv€pyeia — Aristotle excludes the second from the special researches peculiar to first philosophy, the study of being as being, but neither excludes it from general consideration in metaphysics as a whole, nor handles it at length, deferring it rather for more detailed treatment. A comparatively clear account, however, of what is understood by him under the head of being as truth and non-being as falsity may be extracted from the various passages referred to, and little doubt can remain that being so regarded is in a peculiar sense the matter of analytical (i.e., logical) researches. Being as truth and non-being as falsity refer to and rest upon combination and division of the elementary parts of thought. For truth and falsity have no signifi- cance when applied to things, but only to the connection of thought which is dominated by the one principle of non-contradiction. Nay, thinking has not even immediate and direct reference to being as such, but only to beinai rh -rpiydivov, Sfiws ypa(j>ofJLiv wpicixivov Kara rb iroc6v Kal 6 vowv uffavTODS, K^LV /x^ TToahv voT), TideTai irph ofx/jidTwv iroadv, voft S' ovx fj irnaov. h.v 5' i} (pvcris jj tccv wocrcav, aSptaTou Se, rLBtrai fiev iroabv wptdfifvov, voft 8' ^ iro(T6v ix6vov. Cf. also Met., vii. 10 and 11. Aristotle's view strongly resembles, in this point at least, that of Kant. '^ See Metaph., ix. c. 9, p. 1051a. Some interesting remarks on the process of mathematical construction and its relation to syllo- gistic proof will be found in Ueberweg's System der LogiTc, § 101, p. 273. ^ See generally Awd. Post., chap. 13. Of Aristotle's views on mathematics the best expositions seem to be those of Biese {Ph. d. Arist., ii. 216-34), Brandis {Aristoteles, pp. 135-39, and Aristot. Lehr- fjchdTjde, 7-11), and Eucken {Melhode d. Arist. Forschuny, pp. 56, 66). THE ARISTOTELIAN LOGIC 51 and as bearing upon the particular.^ It is in itself the union of the general and the particular, of the universal and the individual. This fundamental notion of know- ledge is not only the integral element in the Aristotelian theory of science, but also the guiduig principle in his scientific method.^ In all cases we require to keep in mind the necessary correlation of the particular facts and the general grounds, the multiplicity of effects and the unity of cause. The one element is not apart from the other. Universals as such are of no avail either as ex- planations of knowledge or as grounds of existence. Par- ticulars as such are infinite, indefinite, and incognisable. Only in the union of these — a union which objectively regarded is the combination of form and matter, of potentiality and actuality, of genus and ultimate difi"er- ence, subjectively is the combination of the data of sense, imagination, and intuitive faculty of reason — is knowledge possible. And the methods by which knowledge is formed in us regarding things exhibit the same twofold aspect. Syllogism as the form of the process from generalia to the determination of attributes of the individual subject, induction as the method of procedure from the vaguely apprehended individuals to the generalia or principles, alike, when analysed, exhibit the conjunction of the uni- versal and particular. But while this general view is undoubtedly to be ascribed to Aristotle, it is no less undoubted that grave difficulties are felt when his various utterances on the fundamental points of the doctrine are placed side by side and the attempt made to extract from them a harmonious and con- ^ Cf. specially Amtl. Pr., ii. 21. - This is excellently put by Eucken, op. cit., pp. 44-5.^». 52 HISTORY OF LOGIC sistent doctrine.^ That some of these difficulties are due to the fragmentary condition in which the successive treat- ments of the question have come down to us may be allowed ; but, as the question involved is in truth the cardinal difficulty of all metaphysical thought, it may well be said that a quite harmonious view is not to be expected ; and in particular this may be said when one considers the doctrine of perception in which the metaphysical deter- minations of universal and particular come forward in subjective fashion. " 16. Opposing throughout the Platonic doctrines of Ideas, separable from the objects known, and declaring that the assumption of such isolated forms not only involved contra- dictions but was of no service in solving the problems of generation and of knowledge, Aristotle is led to emphasise the individual as the ultimate fact in existence and cognition. Universals as classes have no separate substantive exist- ence : they do not indicate the individual roSe n, but a property or quality common to many individuals, iroiov ti ; their function is predicative. Xo doubt they are oicriai in a sense, for they indirectly refer to individuals — i.e., one cannot overlook the closeness of connection between the individual things having essential attributes in common and the notion of these attributes.^ The individual thing ^ See specially the treatment by Heyder, Methodol. d. Arist., pp. 140-216, which is most instructive and comprehensive. The com- mentaries of Bonitz and Schwegler on the relative portions of the MeUiph. fiii. cc. 4 and 6, vii. and xiii. 10) should be consulted. Zeller {Phil. d. Or., iL 2, pp. 300-313) brings out the fundamental difiBculty, and notes some attempted solutions of it. Kampe {Er- kenrUnissthcorie d. Arist., 160-170) lays special stress on the subjective or psychological aspect. 2 It is probably the most helpful view, and one enabling us alto- THE ARISTOTELIAN LOGIC 53 is the basis of all attributes, it is the underlying reality which presents itself in the natural jjrocess of becoming as the subject determined in existence, quality, quantity, relation, &c.^ But what is the individual thing? It can hardly be said that to this Aristotle returns any single unambiguous reply ; his utterances, in fact, disclose a real difficulty, and point to the presence of a twofold conception of the individual : the individual as the ultimate, unquali- fied, undetermined unit, the last result of abstraction ; and the individual as the concrete thing, qualified and deter- mined to the full extent by its generic and specific marks. "With these diverse conceptions floating before him, now one, now the other becoming prominent according to the special problem in hand, Aristotle's expressions sometimes present apparently irreconcilable divergencies. The diffi- culty specially pressing upon him was one arising from the definition of knowledge. Knowledge is of the general and necessary; how then can there be knowledge of the in- dividual 1 Knowledge is not a process capable of infinite regress; its principles are definite and its method deter- minate. But particulars are infinite ; how then can there be knowledge of them 1 ^ Aspects of the same difficulty present themselves at every stage in which reference is made to the nature of ultimate parts or elements, as, e.g., the parts of definition and of the definiendum. So far as solution is oflered it is the following : — The subject or substratum of predicates is certainly onef mode of describing the ultimate fact in existence and gether to reject the fancied opposition between the Categorixe and the Metaph., to regard SevTepai ovcrlai as specially the concrete general notions, in respect of which there is always confusion possible be- tween the thought-content and the real class referred to. ^ See below, p. 1 76 sq. 2 Met., 999a 20, 1003a 5, and cf. xiii. c. 10. 54 IIISTOllY OF LOGIC knowledge. But this subject, as a concretura or awoXov, contains in itself matter and form. Form when first analysed appears to consist of those very predicates which we have already seen to be secondary in nature, and when abstraction is made of them, there appears to remain noth- ing save undetermined matter. Now matter is precisely that which in itself is incognisable. The truth is our first analysis is imperfect. The connection of vXr] and ctSos in the avvoXov is not mechanical aggregation, nor is etSos to be identified with generic properties regarded as generic. The form is the intelligible universal element in the concretum ; it is that which gives definiteness, actuality to the indefinite- ness and potentiality of matter. It is the formal cause, the notional essence of the thing, and its perfect expression in thouglit is the definition, for in the definition the generic properties of the thing and its ultimate specific difference (8t.a(/)opa TeXcvrata) are the necessary elements. It is notional essence, i.e., it is the unity of the essential properties as grasped by thought and apprehended as really existing. The individual would thus appear in the Aristotelian metaphysic as the union of the universal and definite with the particular and indefinite, and in a sense as the final goal of the determining process of knowledge ; for the rt rjv (Tvai, which is the notion of roSe ti, is expressed in definition, the last result of scientific knowledge.-^ Such ' Such a result, it appears to be said in the chapter of the Meta- physics previously referred to (xiii. c. 10), when supplemented by a special distinction, may yield a solution of the difficulty regarding knowledge as essentially general and things known as essentially individual. " Knowledge, like the act of cognising, is either in potentiality or in actuality. In potentiality, i.e., in the aspect in which it resembles matter, itself universal and indeterminate, know- ledge is universal and indeterminate ; in actuality, as being definite and individualising, it is definite and of the individual," The passage THE ARISTOTELIAN LOGIC. 56 a conception, however, is not carried out consistently, and, in particular, fails to reconcile itself with the doctrine of the individual that comes forward, partly in the meta- physics, but mainly in what one might call the Aristotelian theory of knowledge. 17. It is not possible to hold questions of metaphysic strictly apart from those of theory of knowledge, and in Aristotle's treatment of the universal and particular we find that the main features of interest attach to the con- ditions under which an individual or general is cognisable. Now, throughout the analytical researches, the rhetoric, ethics, and generally the subordinate branches of philosophy, one notes an apparently Avell-defined significance attached to the individual. Ta Ka^' eKaara, the particulars of ex- perience, present themselves as the first given data of knowledge, the basis upon which progress to principles or generalia is founded. Ta KaO' eKacrra are prior or simpler so far as our cognition is concerned; and argu- ments based on apprehension of them, arguments of fact or effect, are more persuasive and more easily grasped than arguments from principles or causes. Apparently, also, if we confined attention to some of the more direct dida on this perplexing doctrine, we might assume that, according to Aristotle, knowledge was to be conceived as first ascend- has never appeared very satisfactory to commentators. Doubtless we might interpret it freely in connection with the distinctions given below respecting knowledge and perception ; but it is specially interesting to notice how this description of cognition as twofold, as of the indefinite, and so universal in one aspect and not in another, as of the individual, and so not universal in one aspect while most truly universal in another, applies to mathematical cognition as above sketched by Aristotle. — Of. Brandis, Arisiotelischcs Lehrgebdudc {Ocs. d. yr.-rom. Phil., iii. : 1), p. 9. 56 HISTORY OF LOGIC ing inductively from particulars to the universal, and then descending deductively from these. This, however, is an altogether inadequate view ; and hints are supplied which, though not enabling a quite coherent doctrine to be formed, yet enable us to understand somewhat more clearly not only the special difficulty experienced by Aristotle, but also his method of solving it. Of those hints but two groups can be here taken into consideration. (1) The particulars, ra Kad' eKaara, arc objects of percep- tion, alo-OrjTa. It has already been seen that roSe tl involves form and matter, and is the concretum of both. Perception then might be supposed to be a complex process, involving in some way apprehension of form and receptivity of matter, and containing subjectively both. Aristotle's analysis of perception is far from complete, but we are able to say with respect to it that in his view ato-^r^o-ts is not to be regarded as a simple process, directly receptive of the individual as such. Such a view of perception is altogether foreign to the Aristotelian psychology in which the subjective pro- cesses of mind, with the objective system of things, are conceived as mutually involving and involved, in which the lower faculties, as we may call them, potentially contain the higher, in which the subjective process of knowledge is the evolution of that which is contained in an undeter- mined, indefinite form in the lower stages of apprehension. Thus Aristotle not only marks that sense-perception as a whole is apprehensive of the KaOoXov, while separate acts of perception are apprehensions of the individual, but he dis- tinguishes in perception aspects or stages which, in more modern phraseology, might be described as (a) receptivity of impression, (b) intuition of sense forms, (c) classification with representations of past experience. In each sense- perception there is apprehension of the proper sensible, THE AiaSTOTELIAN LOGIC 57 and also apprehension of the common forms of sense in- tuition, and iinally, there is apprehension of tlie ulcrOrp-bv Kara o-v/jt/3e/?ry/'<^'''( ^ '6\ov ■n-phs fj-fpos f) ^4pos TTphs oKov «x*"') ; Anal. Post., ii. 3 {kripov 56 kripo. aTrJSei^ts, ihv fjL^ ws nepos ^ t« ttjs {(Atjs. tovto Se Xiyw, '6ti SeSeiKTat rh laoa- KiKis 5i'io opdoii, el irav rpiyuvov SeSetKraf fiepos yap- rh 5' oAof) ; Jxhctorica, i. 2, § 19. The general treatment of syllogism in Anal. Pr., i. 4, as apparently resting on the principle of subsumption or logical substitution, has no precise bearing. But the use of the term '6\ov by Aristotle is not to be regarded as identical with its use by 1 / 62 HISTORY OF LOGIC 20. The general idea of the Aristotelian analytic thus obtained does not require to be supplemented by any detailed survey of the logical system into which it is evolved ; but a brief summary of the most important points and indication of the relation in which the parts stand to the whole may be of advantage. The simplest form of knowledge, that in which being as true or false is apprehended, is the judgment. The con- sideration of the judgment is therefore the first part of the analytical researches. Here Aristotle distinguishes more accurately than any of his predecessors (indeed for the first time with accuracy) between subject and predicate as integral parts, symbolised by the noun and verb, and signifying the relations for us of things as appearing under the schemata of the categories. The material basis of the judgment, as one may call it, is the thing as an object of possible knowledge, i.e., the thing as individual (and there- fore as involving matter and form, the particular and the general), as qualified, specifically, in time, space, quantity, and relation, and existing as one mode in the universal nexus of potentiality and actuality. These metaphysical forms, and, specially, the deep-lying modes of potentiality later logicians, and it is not rashly to be assumed that in Aristotle's view the only logical relation is that between genus and species. The distinction between extent and intent, on which later writers have laid stress, is never suffered in Aristotle to become a distinction in kind; the two elements, extent and content {Kara. TracT^s'aud /cafl' avri), are always involved, and the difference is only in the process by which our knowledge is formed. Probably the relations of extent and content would never have been severed from one another had it not been for the error, almost a necessary failing in the attempt to treat formal logic systematically, of regarding notions and judgments as completely formed and defined products apart from the reasoning in which they appear (see, for a diametrically opposed view, Hamil- ton, Leetv/res on Loi/ic, ii. p. 26G). THE AKISTOTELIAN LOGIC 63 and actuality, reflect themselves in the forms wherehy sub- jectively knowledge is realised in us ; and the resulting knowledge is conditioned partly by them, partly by the modes in which intellect as a reality is developed in us. The proposition has necessarily a reference to them ; and thus, alongside of formal distinctions between universal, particular, singular, and indefinite judgments, wc have the distinctions between necessary, contingent, and possible, which appear partly as given qualities of the judgment, partly as representing dilFerences in the conditions of knowledge, partly as referring to differences of subjective apprehension. The essence of the judgment as the apprehension of truth or falsehood consists in its twofold aspect as affirmative and negative, the former of these in a sense prior and better known, but the latter no less necessary, and both referring to objective relations of things. The affirmative and nega- tive character of judgments, the essential dvTt<^ao-t9 of human thought, is further defined in reference to (a) the quantitative distinctions already recognised (the doctrine of logical opposition), (h) the distinctions of necessary, con- tingent, and possible, which are rightly regarded as real matters ahout which the assertion is,^ and (c), consequent on this, the opposition of modal judgments.^ ' On this account the modality is affirmed not to attach to the copula; thus the opposite of "it is necessary-to-be" is "it is not neces8ary-to-be," and not either "it is necessary-not-to-be," or " it is not-necessary -to-be." - There are obscurities in Aristotle's doctrine of modals which remain even after Prantl's laborious treatment (Gcs. d. Logilc, i. 104- 82). A careful survey is given in Rondelet, Thdorie logiqite des pro- positions modules, 1861. The definitions of eVSex. 91b 34, ouS^ 70^ 6 iwdyuv "(crws aTfoSdKWffiv, oAA' SfitDS StjAoj ti. G8 HISTORY OF LOGIC pasasges, iu the treatise De Partihus Animalium, and in the Posi. Anal., ii. 18.^ As regards the first of these, reference is desirable only to bring out the fact that causal nexus is the KaOoXov in question ; the second is of the utmost importance as clearing up what has always seemed an obscurity in the account of the inductive syllogism. In the chapters 16-18 of Anal. Post, ii., Aristotle considers the relation of cause and effect as the essential basis of proof, and he points out with much clearness the dift'erence between the fact as cause of knowledge and the cause as ground of existence and proof. In some cases cause and efl'ect are so united, so reciprocate, that we may infer from one to the other. But the doubt arises, may there not be more than one cause for any given attribute 1 in which case all such inferences from effect must become problematical. Aristotle's solution is remarkable, both in itself and in its bearing on the inductive syllogism. Suppose the attribute ft is found in all individuals of a class A, and also in individuals of class B, C, &c. In order to discover the cause, investigations must be carried on until we have a defined number of classes A, B, C, &c., in all of which /3 is found, and which comprehend all cases of the presence of (3. Then that Avhich is also common to A, B, C, &c., may be regarded as the cause of /3, say, e.g., an attribute a. If this attribute a be really the cause of /3, it will enter into its definition ; it will be its definition. There might, however, be a connection of a and j3 of this universal and reciprocating kind, and yet a might not be the cause in question ; it might be only a fact from which /S could be inferred ; the real cause y, which gives rise to a, lies in the ^ De Part. Anim., iv. 2. Cf. Hamilton, Lect., iv. p. 358, n. On Anal. Post., ii. lG-18, see the valuable summary by Qrote, i. pp. 366-68. THE ARISTOTELIAN LOGIC 69 background. Characteristic of causation, then, is constant reciprocal conjunction of facts. Even if it be admitted, then, that there may be more causes for a phenomenon than one, it will yet be true that each of these causes will be manifested in one class of phenomena where there will be the universal reciprocating coexistence that is character- istic of the relation in question. Thus the attribute longevity observable in quadruped animals and in birds may be due to different causes, e.g., to absence of gall in the one case, to predominance of solid, dry matter in the other. But in each case there will be a definite species characterised by the constant conjunction of the cause and the causatum ; the whole class long-lived animals and the class gall-less animals will coincide. Turning now to the chapter on inductive syllogism, we find induction defined as inference through the minor that the major belongs to the middle. Here evidently major and middle are regarded not as determined by form only but as naturally distinct, and we must assume that by middle term is to be understood the ground or reason of the attribute (major term) characteristic of a defined species or '^ group (the middle term).. Were our knowledge complete and scientific, we should be able to express this in apodictic form : whatever animal has no gall is long-lived ; man, horse, mule, &c., are animals having no gall ; therefore they are long-lived. The progress of knowledge, however, may be from the empirical details. "We may have given to us the fact of the attribute, long-livedness, in the group of animals, man, horse, &c., and discover that these long-lived animals are also wanting in gall. If, then, in accordance with the rules above sketched, there can be discovered a reciprocating relation between want of gall in animals and long-livediiess, if we can constitute a class distinguished by 70 HISTORY OF LOGIC. conjoint presence of gall-lessness and longevity, we have the basis for an inductive proof. We may infer therefrom that gall-lessness is, in this species, the cause of longevity. Such a reasoning is founded on particulars given, and as the coexistence is given, the conclusion seems to be im- mediately drawn ; there does not appear to be mediation or use of a middle term ; nevertheless the middle term is implied, not in the supposition that the two classes recip- rocrate, but in the transference from empirical coexistence to causal nexus. Aristotle's mode of stating this argument has presented so many difficulties of interpretation that various emen- dations have been proposed. Grote, e.g., who has not apprehended why the class long-lived animals should be taken universally, — "we are," he says, "in no way con- cerned with the totality of long-lived animals," — suggests an emendation, which makes the essence of the inductive reasoning turn upon the extension of what we know re- garding some gall-less animals to all of that class. But this is not the inductive step according to Aristotle. Induction has not to prove or assume that a and /?, found coexisting in some members of the species, coexist in all of them ; Aristotle takes this universal coexistence for granted as the basis of the argument. The inductive step is the trans- ference from this universal coexistence to causal nexus. Apodictically, we should say, if a is the cause of y3, then all A which possesses a possesses /? ; thus reasoning from cause to causatum. Inductively we say, all A which possesses a has /? ; therefore a is the cause of yS.i ^ The following is the relative portion of chap. 23 of bk. ii. of the A nal. Pr. : " Now induction and eyllogiem through induction is the proccBS of concluding by means of the minor term that the major term is predicable of the middle " (that is to say, of concluding from THE ARISTOTELIAN LOGIC 71 Induction, as dealing with particulars, starting with the sense data, and resting upon the more evident fact in order to point towards the essential ground or reason, is therefore more persuasive, more palpable, more adapted for popular given facts that an attribute found in all of them is the effect of some other attribute also found in all of them). " For example, if B be the middle term, A and C the extremes, we show, by means of C, that A is predicable of B ; for this is the inductive process. Thus, let A be long-lived ; B, those wanting gall ; C, individual long-lived, as man, horse, mule. Then A is predicated universally of C " (that is to say, the attribute A is found in all the examples before us), "for also that which wants gall is long-lived " (that is to say, as a given fact, gall- lessness and longevity in the species, group, before us coexist). " B, wanting gall, thus is predicated universally of C. If then B and C be reciprocating, if C do not extend beyond the middle term " (that is, if we do not find other animals than the long-lived animals enumerated which also are devoid of gall), " it is necessary that A should be pre- dicated of B. For it has been shown previously that if two terms are predicable of the same third, and if the extreme reciprocate with one of those, then the other of those predicates will be predicable of that with which the first reciprocated ; but it is necessary to know that C is the complex of all the individual cases." The last sentence is ex- tremely hard to interpret. The expression r6 &Kpov occurring in it is generally the technical word for major term, but as in the syllogism before us the major term is one of the predicates, this signification would seem to contradict the words irpbs ddrepov aiiTuv. Hamilton reads t6 fxiaov, which makes the argument intelligible and coherent with the passage apparently referred to in SiSfiKrai irpoTfpov — viz.. Anal. Pr., ii. 21, p. 68a 21-25. Probably Aristotle uses to iiKpov here as equivalent to C, the &Kpov through which the induction proceeds. According to the view taken above, the essence of the Aristotelian induction does not at all lie in the universalising of C, but in con- necting in one proposition the attributes B aud A found to coexist in the group C. There is thus in one sense no middle, for cause is not reached ; in another sense there is, for C is the material link connecting A and B. Aristotle then might naturally use 6.Kpov for C, and assimilate the process of induction to a syllogism in which there was reciprocation of terms. In fact, however, induction regarded after his fashion results merely in the constitution of a group or class characterised as possessing two attributes in common. 72 HISTORY OF LOGIC inquiries, and relatively more apparent. Syllogistic proof, on the other hand, is more stringent, and more efficacious in establishing a scientific conclusion or position. Aristotle's mode of dealing with induction, in so far at least as any specific process is designated by that term, seems on the surface to diverge widely from modern logical theory, and we look in vain in his analytical researches for consideration of the methods of observation and experiment which has come to be recognised as the essential portion of a doctrine of inductive reasoning. Yet it may fairly be argued that in modern theories the term induction is used with great laxity, so as to cover either all processes connected with scientific method or some one special feature of scientific reasoning, and that the difi'erence between the Aristotelian and modern views lies mainly in the matter, not in the form, of the process. For there are numerous hints in Aristotle respecting scientific procedure,^ and, if we consider what is peculiar to modern views, we shall find that it consists mainly in the increased fulness and com- plexity resulting from long-continued scientific research. Our modern logic of induction has profited mainly by the general advance of scientific method, and tends to increase as these methods, by constant contact with facts, become more refined and accurate. The additional cautions or limitations which we now introduce into our statement of the principles of inductive research concern not so much the form of inductive proof as the character and modes of obtaining evidence which is to satisfy the canons or rules of proof. Such limitations become apparent only through ' See, for example, the diRcussions in Topica, i. 17-18 ; ii. 10-11, on similarity ; in the Post. Anal., i. 13, on deductive and inductive methods ; in Post. Anal,, ii. 13, on the formation of definition ; and in Post. Anal., ii. 12, 11-18, on the relation of cause and eSect. THE ARISTOTELIAN LOGIC 73 actual scientific progress, not by analysis of the form of scientific proof. 21. To Aristotle, as has been above said, proof is essen- tially syllogistic or deductive in character. Not every syllogism is an apodictic proof, but all proof is syllogistic. For proof or adequate knowledge is reference of effects to their causes, and the cause is the general element, to KudoXov, which forms the middle term in apodictic proof. ,- Kow proof by means of the cause or reason implies the existence of the cause ; the inquiry why a thing is is useless unless we know or assume that the thing is. If it exists, then the cause or reason of its so existing is that which gives it a definite character or position ; it is, in technical phrase- ology, the form of the thing. But the form of the thing, regarded apart from the material, accidental element essential to its concrete existence, is that which we express in a definition. Proof and definition are thus most closely connected. The terminus to which proof tends, not realised in all cases of proof but certainly in the most perfect, is the definition ; and, besides, if we closely examine proof, and find that ultimately we can force back the chain of middle terms up to certain ultimate, primary universals, disclosed by vovs, and that the nature of these primary universals is stated in their definition, we see further that definition is connected with proof as the terminus from which proof starts. The exposition of definition is thus the crowning portion of Aristotle's theory of apodictic method, i In it we have ^ It does not seem necessary here to consider in detail the peculiar- ities of apodictic as these are laid out in the first book of the Post. Anal., nor to deal with the doubts raised regarding definition and proof in the first chapters of the second book. The substance of 74 HISTORY OF LOGIC brought into close, though not explicit, relation, the funda- mental notions on which his logic rests — the notions of the essence, universal, genus and specific difi"erence. Definition, as concerned with that which is involved in demonstration, the ground or reason, is, in cases where the reason and con- sequent are separable, the sum of the demonstration ; it is the compressed statement of the connection between a subject and the attribute demonstrated of it, i.e., in a syllogism of the first figure, the major terra. ^ Frequently a definition merely states the demonstrated attribute in relation to its subject, without indicating the rational link." Such definitions, however, are defective, just as the conclusion of a syllogism, if taken 7;er se, is defective.^ A genuine definition is the statement of the essence, which in mediated notions is the cause or middle term of the de- monstration, in immediate notions is directly assumed.* A these difficult chapters can be readily summarised. If definition be taken as a finished result, it seems to stand in no relation to proof, and indeed it is hard to discover how it comes about at all. For definition supposes that which is implied in proof, the existence of the thing defined, and, moreover, it is in a special sense a unity, contain- ing no distinction of subject and predicate, whereas such distinction is of the very essence of a demonstrated proposition. Neither in province, nor in method, nor in result do definition and proof coincide. All this follows, however, from an abstract separation of the form or essence of the thing defined from the concrete nature of the thing. The essence is not to be taken apart ; the definition does not pre- exist as a given fact. The essence is the reason of the fact, and is only discoverable when there is the recognised distinction of fact and reason of the fact. We must consider definition in the same manner as being involved in and resulting from the genesis of scientific knowledge. ' 4ir({8€ifiy QiiTd Stacpfpovcra, Anal. Post., i. 8, p. 75b 32. ^ ffvfiirfpaffixd ti d7ro5«i{€a)j, ibid. ' De Anima, ii. 2, p. 413a 13 sq. * & ht riiv dfUawv 6pis 6tais itrrl rov tL iariv iuaTrdStiKTos, Anal, Post., ii. 10, p. 94a 9. THE ARISTOTELIAN LOGIC 75 merely nominal definition or explanation of what a name signifies is but a preparatory stadium in the progress to- wards real, genetic definition. Definition, then, like demonstration, rests on the essential or rational ground, the notion of the thing. The rational ground or notion has its empirical aspect ; it determines a claSvS, and thus, just as in demonstration we may have forms of reasoning based primarily on the empirical details, so in framing definitions we may proceed from the empirical class, and may formulate rules for defining which bear special reference to the genus or body of individuals. In such procedure there is always involved the general idea of the essence or notion as the determining universal, and without this general idea the subsidiary methods, induction and division, do not yield scientific definition. To frame a definition, then, i.e., to discover the elements whose combination as an essential unity makes up the notion of the things defined, we select the predicates belonging to the things in question, but also attaching to other species of the same genus. The combination of such predicates which is not found in any other species, which is, therefore, reciprocable with the essence or form of the species, is its definition. The definition, therefore, contains the genus and the specific attribute (or combination of attributes). Of these elements, the genus is the least im- portant ; the truly essential factor is the specific difference, and, in order that our definition should be ultimate, we must follow out the line of specific difference by which a genus may be divided until we reach a final, irreducible characteristic or group of characteristics, constituting a lowest species (or natural kind, if one were to employ a term made current by J. S. Mill). The systematic following out of the specific differences is 76 HISTORY OF LOGIC logical division ; the critical comparison of points of simi- larity in species of the same genus, so as to obtain a higher generality, has no special title accorded to it, but it resembles the Socratic and Platonic induction {crwaywryy]). Division preceeds on the oppositions actually found in nature ; and though, doubtless, the division by dichotomy has formal advantages, it has not, as a process of real cognition, any supreme value. The negative as such is the inconceivable, and presents nothing for cognition.^ And division is not dependent on exhaustive knowledge ; it is not necessary that, in order to recognise A as distinct from B, we should know the whole universe of possible objects of cognition. A and B may be recognised as identical or distinct in essence, even though they at the same time possess distinct or identical accidental marks. Knowledge, in other words, turns upon the essential, not upon the numerical universal.^ It is only needful, then, that in the systematic process of indicating the elements of definition, all must be included that concern the essence, that the order must be strictly from determining to determined (or from more abstract or general to more concrete or special), and finally, that the enumeration be comj)lete. The final division or species reached is the notion of the thing, and its expression is the definition. 22. The analytical researches thus manifest themselves as a real theory of knowledge and as forming an integral ^ Just as the ovoixa adptarov is said to have no significance save as the summary of a proposition, while a negative proposition has signifi- cance only in regard to the corresponding positive. ^ The reference is to a theory advanced by Speusippus ; see I'rantl, i. Sf>. Aristotle here touches on a logical problem which has trouVjled many logicians. It is the same difficulty that arises when the question of plurality of causes is considered. THE ARISTOTELIAN LOGIC 77 part of the Aristotelian system. Logical relations are throughout conditioned by the characteristics of the Aristotelian metaphysical conception, and the distinction of the formal or technical from the real in cognition has no place in them. No point is more frequently insisted on by Aristotle than the impossibility of deducing any scientific principles or results from the fundamental axiom of thought, the law of non- contradiction. In the Aristotelian system this axiom appears simply as the generalised expression for the peculiar characteristic of thought, its potentiality of truth or falsehood. Such potentiality accompanies thought throughout, and is the mark of its subjective character, but the actuality of thought is something quite distinct, and is only realised through tlie various processes whereby the world of fact is apprehended. Beyond a doubt knowledge has a general aspect ; and there is thus possible a general theory of knowledge, but this is not to be regarded as merely a development from the fundamental axiom of thought. It is the general statement of wliat constitutes actual cognition, and thus refers on the one hand to the ultimate properties of that which is to be known, on the other hand to the qualities of knowledge as a subjective, though not the less real, fact. For to Aristotle subjective has not the sense which it may be said to have assumed in modern logic, mainly through the Kantian analysis. The activity of thought which realises itself in the consciousness of the individual is not a mere formal process of apprehen- sion, mirroring or depicting reality that is totally distinct from it. It is a reality, one aspect or phase of the total sum of things, and its development is a real process correl- ative with the development inherent in things as a whole. At the same time it is impossible to overlook the difficulties which attach to the Aristotelian conception, 78 HISTORY OF LOGIC and the consequent obscurities or perplexities in his logical researches. To remain always true to the fundamental conception of thought as one factor or phase in things, to trace its forms in such a mode as never to lose sight of its essential correlation to the development of reality, is in itself the hardest task for any thinker, and presupposes a more completed metaphysic than is to be found in Aristotle. Some of these difficulties may be briefly noted, as they form the turning-points of certain later doctrines. The judgment or proposition is taken as the initial, the simplest phase of the activity of thought, and so as having the simplest re- lation to things. But the distinctions of things which are subjectively seized in the judgment are too much regarded as given facts, and Aristotle is thus involved in a difficulty respecting the import, the truth or falsity, of the judgment. The presence of this difficulty is specially discernible when he attempts to deal with the temporal reference in the judgment, with the doctrine of opposition, and with the nature of modality. Thus, he notes that the verb, the essential part of the predicate, has a temporal significance, but he also notes that in universal judgments there is no reference to any specific time, and also that the copula, the verb is, has no existential meaning. He is thus driven to the enunciation of a view, common among recent logicians, that the judgment is a reflective or critical act, pronouncing on the truth or falsity of a contemplated separation or conjunction of facts, while, on the other hand, the very contemplation of conjunction or separation has appeared as the essence of the judgment. So, in dealing with opposition, he distinguishes contradictories from contraries, and is inclined to refer the second to the given nature of facts, wherein extreme oppositions of members falling under the same genus are presented. Modality, likewise, he treats THE ARISTOTELIAN LOGIC 79 confusedly, for the assignment of the modal relations to the predicate docs not [sufficiently determine their place in a theory of judgment, nor explain the relation in which they stand to the judgment as the simplest activity of thought. Further, in dealing with the quantity of judgments, Aristotle is perplexed by his own theory of what constitutes generality. He is compelled to throw together universal judgments of a totally distinct kind — empirical and rational, as one may call them, — and though the underlying view that empirical universality is the expression of, and is dependent on, rational connection is made sufficiently clear in the doctrine of proof, it is not carried out to its conse- quences in the doctrine of judgment. Finally, to note only the crowning difficulty, the theory of proof and of definition turns upon the nature of the essential connection of attri- butes in a subject, but the explanation of essence is precisely the lacuna in the system. Indications of a theory of essence are not wanting, but it does not seem possible so to unite them as to form a consistent whole. The greatest obscurity still hangs over the fundamental part of the system, the nature of the TrpioTa which are apprehended by vous, of the specific relation of attributes Ka6' avrd to their subjects, and of the iSmt dpxat from which particular sciences start. That the TrpoVacret? afiecrot, so frequently ad- duced as integral parts of proof, are analytical judgments ^ cannot be accepted without such qualifications as to render the use of such a term misleading ; but what their precise nature is remains in the Aristotelian system undetermined. 1 As Zeller will liave it ; see Ph. d. Or., ii. 2, 191, n. Doubtless Aristotle does define an essential attribute as being one contained in the subject or one of wliich the subject notion is an integral part, but this relation of entering into the definition is not to be identified rashly with the modern view of the analytical relation of subject and predicate. 80 III LOGIC FROM ARISTOTLE TO BACON AND DESCARTES 23. The long history of philosophic thought from Aris- totle to the beginning of the modern period furnishes no new conception of logic so complete and methodical as to require detailed treatment, but exhibits alterations in special doctrines, additions, and new points of view numerous enough to account for a certain radical change in the mode of regarding logic which is, for our present purpose, the only interesting feature. This change may perhaps be expressed not inaccurately as the tendency towards formalising logic. Gradually logical researches came to have their boundaries extended in one way by the introduction of new matter, and narrowed in another by restriction of logical consideration to one special aspect of knowledge. Much in the history of this movement still remains in obscurity, but the general result is sufficiently clear. The periods into which the historical development of logic throughout this long interval may be naturally divided, with their main characteristics, are the following : — (1) The Peripatetic ScJiool, represented by Theophrastus and Eudemu.s, following in the main the Aristotelian FROM ARISTOTLE TO BACON 81 tradition, but deviating in certain fundamental respects, and on the whole treating the matter of logical research as though it were separate from and independent of the theory of knowledge as a whole. To this school is due the distinct recognition of the hypothetical and disjunctive proposition and syllogism, and the more complete enumera- tion of the possible valid modes of categorical reasoning. In both cases the additions are made to turn upon purely formal considerations. The hypothetical and disjunctive judgments are treated as given varieties, to be discerned in ordinary language and expression, not as resting upon any fundamentally distinct principle or activity of thought.^ The addition of five indirect moods to those recognised by Aristotle as belonging to the first figure proceeds on the purely formal ground of difference in position of the middle term in the two premisses. (2) The Epicurean and Stoic Logics. — Of these the Epicurean presents no points of interest. Logic, in their conception, was merely a practical theory of knowledge. The Stoic logic, on the other hand, is the first example of a purely formal doctrine based on and associated with a thoroughly empirical theory of cognition. In essence the Stoic doctrine is identical with that of Antisthenes, above noted, and it is interesting to observe that, under the purely nominalist theory, logic becomes almost identical with the doctrine of expression, or rhetoric. The theory of naming, and tliat of the conjunction of names in propositions, are the fundamental portions of the body of logic. Naturally ^ The nature of hypothetical inference and its law are recognised with the greatest distiuctnesa by Aristotle. From his theory of essence as causal nexus, any distinction of kind between an apodictic (categorical) syllogism and a hypothetical of the type contemplated by later logicians was impossible and needless. P 82 HISTORY OF LOGIC the Stoic logicians tended to increase the bulk of logic by introducing numerous distinctions of language, and by signalising varieties of judgment dependent on varieties of verbal expression. (3) The acceptation of Logic among the Romans. — Here there must be distinguished the quasi-rhetorical logic, such as is found in Cicero, which is altogether Stoic in character, and the Aristotelian logic, as developed by Boetius with the additions of the later commentators. In Boetius one notes specially the technical or formal character of the treatment, which was of special importance historically, from the fact that the earlier scholastic writers derived their main knowledge of logic from certain of the treatises of Boetius. (4) The Scholastic Logic. — On the details of the scholastic logic it is not necessary to enter, but there must be noted the following points as of interest in determining what may well be called the current conception of the Aristotelian logic in modern times. The earlier scholastics, in possession of but few of Aristotle's writings, added nothing of import- ance to the body of logical researches, and the permanent subject of discussion, the nature of universals, did not, through any of its solutions, affect the treatment of logical doctrines. The introduction of the body of the Aristotelian writings was contemporaneous with the introduction of the Arab writings and commentaries into western Europe, and there grew up therewith a more developed treatment of what may be called the psychological element of logic. The logic of the later scholastics is characterised by two points of interest, historically unconnected, but having a natural affinity — the one, the introduction of an immense mass of subtle distinctions, mainly verbal, making up the body of the Parva Logicalia; the other, the influence of the FROM ARISTOTLE TO BACON 83 nominalist conception of thought. ^ The peculiarity of the nominalist view is the severance of immediate apprehension from discursive thought, the assignment of all matter of knowledge to the one, and of all form to the other. But form, under this conception of discursive thought, can be found only in the generalising function of signs or names ; accordingly the fundamental processes of logical thought are regarded as so many modes of application of names. The later nominalist logicians were thus naturally led to the expenditure of immense subtlety and diligence on the thorny problems of the Parva Loijicalia, while at the same time the peculiar inner difficulty of the theory became apparent as its consequences were worked out. (5) T?ie Reaction against Aristotelianism and the Humanist Modification of Logic. — Little of positive value for logical theory is offered by the numerous works repre- senting this stage of historical development. Valla, Agricola, and Vives, with much good criticism in general spirit and detail, present a rhetorico-grammatical logic that resembles most closely Cicero's eclectic reproduction of Stoicism. Kamus, the only logician of the period with historic renown, contributes really nothing to the history of logic, his innovations consisting mainly in the omission of the most valuable portions of the genuine Aristotelic logic, the insertion of practical and interesting examples, and finally rearrangement or redistribution of the heads under which logical doctrine was expounded. The Ramist school, most numerous and flourishing, produced no logical work of the first importance.2 ^ The first of these is no doubt, as Prantl has laboured to prove, Byzantine in origin, but it still remains doubtful whence the Eastern logicians draw. The most probable source is the Stoic writings. 2 See note C, p. 168. 84 HISTORY OF LOGIC The net result of this whole period was the severance of a certain body of doctrine, formal in character (the theory of second intentions), from theory of knowledge generally, and from all the concrete sciences. The boundaries and even the functions of this doctrine remained unfixed, for difference regarding fundamental points of extra - logical theory led to difference in mode of treatment, as well as to difference in conceptions of the end and value of logic. 85 IV LOGIC OF BACON AND DESCARTES 24. Modern reform of logic, by which may be understood the attempt to place logical theory in a more close and living relation to actual scientific method, begins with Bacon and Descartes. To both the scholastic logic presented itself as the essence of a thoroughly false and futile method of knowledge. Neither had the acquaintance with the genuine Aristotelian system requisite in order to distinguish the elements of permanent value from the worthless accre- tions under which these had been buried, and, as a natural consequence, the views of both have a far closer resemblance to the Aristotelian doctrine than mi"ht be imagined from the attitude of opposition common to them. Both thinkers were animated by the spirit of reformation in science, and both emphasise the practical end of all speculation. For both, therefore, logic, which to neither is of high value, appeared to be a species of practical science, a generalised statement of the mode in which intellect acquires new knowledge, in which the mind proceeds from known to unknown.^ But such a conception of logic is, if the ex- pression be permitted, formal : that is to say, the actual province of logic is not determined thereby, but awaits 1 Comp. Dc Aug. Sc, bk. v. chap. 1, 2; Princip. Phil., pref. 86 IIISTOKY OF LOGIC determination from the further idea of the nature of know- ledge and the ultimate constitution of that which is to be known. When this point is reached, a radical diverg- ence presents itself between the views of Descartes and Bacon, consequent on whieh appears a radically divergent statement of the main processes and methods of logical theory. To Descartes the ideal of cognition is the mathematical, that in which from assured and distinct data we proceed by strict sequence of proof to determine accurately and com- pletely the nature of complex phenomena. Such an ideal, extended so as to embrace knowledge as a whole, dominates the whole of the Cartesian speculation, and, as in the case of the Socratic doctrine of knowledge, is the ground of the Cartesian doubt. Perfect certainty, i.e., clearness and dis- tinctness of principles, logical consecutiveness of deduction from them, and exhaustive enumeration of details — such are the characteristics of completed knowledge. There follow naturally therefrom the main processes of knowledge : intuition, by which the simple data and axioms are appre- hended ; induction, or exhaustive enumeration of the elementary factors of any phenomenon ; deduction, or determination of the complex as the necessary result of the combination of simple factors. To the processes of in- duction and deduction, when viewed more generally, the titles analysis and synthesis may be given. i On other portions of logical theory Descartes does not enter, and the text-books of the Cartesian school, even the celebrated Port Royal logic, do little more than expound with some fresh- ness such of the older material as seemed capable of harmonising with the new conception. ' See ReguLrn (mI dircctioncm inrjcnii, Nos. 2, 3, and especially 7. The celebrated rules of Bpeculation {I)e Methodo) are only a more popular Btatenaent of the same processes. BACON AND DESCARTES 87 Two things only require note in respect to the Cartesian logic, apart from its freshness and completeness : the one is the obscurity which hangs over the nature of intuition ; the other is the step in advance of the scholastic logic effected in the assimilation of deduction to synthesis. As regards the first, the criteria laid down by Descartes — viz., clearness and distinctness — are unsatisfactory and ambiguous. It is evident that he implied under these clear and distinct recognition of necessity in the data or principles, but the nature of this necessity is never made clear.^ As regards the second, it was of importance to signalise, as against the scholastic view, that the universal in thought or reasoning was not only of the nature of the class notion, that genera and species were not the ultimate universals, but were themselves secondary products, formed by reasoning, and based upon essential connection of facts. In this Descartes was but returning to the genuine Aristotelian doctrine, but his view has all the advantage derived from a truer and more scientific conception of what these connections in nature really are.^ 1 His ultimate standard is, no doubt, necessity for a thinking subject. Whatever is so connected with the existence of the thinking being that without it this existence is incomprehensible, is necessary. But to apply this ideal to any proposition save the first, the Cogito ergo sum, is for Descartes the fundamental difiBculty of his philosophy. ^ It is remarkable, however, that neither in Aristotle nor in Descartes do we get many indications of any other kind of essential connection than that presented in the relations of geometrical or mathematical quantity. To both the type of exact reasoning is the mathematical. The difference between the two philosophers is but one example of what was previously remarked : that precise deter- mination of the significance of processes of thought is dependent largelj', if not mainly, on general advance in scientific knowledge. Descartes' conception of nature and of natural processes was in advance of the Aristotelian, and his conception of the method of thought by which knowledge is obtained is by so much clearer and profounder. 88 HISTORY OF LOGIC 25. What is peculiar in the logic of Bacon springs like- wise from the peculiarities of the underlying conception of nature. The inductive method, expounded in the Novum Onjanum, is, however, only part of the Baconian logic, and, since it is commonly regarded as being the whole, a brief statement of what Bacon included under logic may here be given. Viewing logic as the doctrine which deals with the use and object of the intellectual faculties. Bacon divides it (in this approximating somewhat to the extended division of the Stoic logicians) into (1) the art of inquiry or invention, (2) the art of examination or judgment, (3) the art of memory, and (4) the art of elocution or tradition. The third and fourth divisions are unimportant ; the first and second might be called respectively the theory of the acquisition of knowledge and the theory of evidence or proof. The art of inquiry is subdivided into the art of the discovery of arts and the art of the discovery of arguments. The second of these Bacon regards as identical with the Topics of the Greek and Eoman dialectic, and therefore as of comparatively slight value. Of the first there are two main branches : (A) Experientia Literata and (B) Inter- pretatio NaturcB. The art of judgment has two sub divisions : the examination of methods of reasoning — induction and syllogism — which resembles the older analytic ; and the examination of errors of reasoning — whether these be sophistical, i.e., the logical fallacies of the older doctrine, or errors of interpretation to be removed by careful criticism of scientific terms, or arising from errone- ous tendencies of the mind (the doctrine of Idola) — which resembles the older treatment of FAencM. The peculiarity of the Baconian logic, then, must be sought in the processes included under the art of discovering BACON AND DESCARTES 89 arts or knowlcdgo. Among these the syllogism is not included. It is a process with no practical utility ; it involves premisses of which the truth is simply assumed, and consequently its conclusions can have no validity beyond that of the premisses ; it affects to determine the particular from the general, but in fact nature is much more subtle than intellect, and our generalisations, which are but partial abstractions, are quite inadequate to afford exhaustive knowledge of the particular ; it throws no light upon the essential part of cognition as"" a procerss^- in- ■fDTffiafiori, viz., the method by which we are to obtain accurate notions of things, and judgments based on these notions. Moreover, the deductive or syllogistic procedure favours and encourages the tendency to rash generalisation, to the formulation of a universal axiom from few particulars, and to the uncritical acceptance of ekperience. If syllogism exist at all, there must be a prior process, that of generalis- ing by rigid and accurate methods from experience itself. Syllogism is not entirely worthless. It is of particular service in some branches of science {e.g., the mathematical), and generally may be employed so soon as the principles of a science are well established ; but it is a subordinate and secondary method. The art of discovery, then, is the method of generalising -^ from experience. What this method shall be depends entirely on the thinker's conception of experience. Now Bacon's conception is perfectly definite. Observation presents to us complex natures which are the results of simpler, more general forms or causes. From the complex phenomena these forms are to be sifted out by a methodical process of analysis and experiment. A general proposition is one stating the connection between complex natures and their simple forms or causes ; it is, therefore, the result of a 90 HISTORY OF LOGIC graduated process. Xo doubt there may be generalisations based only on an ingenious comparison of the complex phenomena as they are presented to us ; such a process Bacon calls Experientia Literafa, and the maxims recom- mended for it much resemble the ordinary methods of experiment ; but truly scientific knowledge is only to be obtained by the complete inductive method. The characteristics of this inductive method follow at once from the nature of the object in view. The form which is sought can be detected only by examination of cases in which the given complex effect is present, in which it is absent, and in which it appears in different degrees or amounts. By a critical comparison of these cases we may be able to detect, and, were the enumeration exhaustive, we must infallibly detect, by process of exclusion or elimination, a phenomenon constantly present when the effect is present, absent whenever the effect is absent, and varying in degree with the effect. Such a phenomenon would be the form in question — the cause of the given fact or attribute. Exhaustive enumeration is, of course, an ideal, and therefore the method of exclusion can never be perfectly carried out ; but all additional aids have signi- ficance only as supplying in part the place of exhaustive enumeration. We may, on the basis of a wide examination, frame a first generalisation {first vintage as Bacon meta- phorically calls it), and proceed to test its correctness by carrying out the critical comparison with it in view. Or we may, under the guidance of our leading principle, take advantage of certain typical cases presented by nature, or force cases by experiment, in such a way as to supersede the enumeration. There are jrrei'ogative instances, critical phenomena, helpful in discovery of the cause of a pheno- menon. Of other adminicula, or aids to induction, only the BACON AND DESCARTES 91 titles are given by Bacon, and it would be hazardous to conjecture as to their significance.^ Th e Baconian logic , then, or at least what is peculiar to it, is thoroughly conditioned by ^e peculiarities of the Baconian metaphysic or conception of nature and natural processes. As to the novelty of the logic, this to us does not appear to lie in the mere fact that stress is laid upon induc tioEu. nor do we tliink it correct to assign to Bacon the introduction of the theory of induction as an integral portion of logic. But it consists in the new view taken of what constitutes the univci-u] in thought, a view whicli may be inadequate,^ but which colours and affects every process of 1 Nov. Org., ii. 21. In addition to prerogative instances there are mentioned — supports of induction ; rectification of induction ; varia- tion of the investigation according to the nature of the subject ; prerogative natures ; limits of investigation ; application to practice ; preparations for investigation ; ascending and descending scale of axioms. ^ A word may be permitted on the objection so frequently raised against Bacon's method of induction, that its mechanical character not only fails to correspond to the actual process of discover}', but demands a wholly impossible enumeration of instances. It is not a little remarkable that this objection should be raised by any logician who accepts the empirical theory of knowledge, who holds therefore that, except in the case of facts immediately apprehended, we have only probability as our guide. For this is the very foundation of Bacon's doctrine. The exhaustive enumeration {i.e., the immediate apprehension of all facts) is an ideal, but whatever falls short thereof, is not exact knowledge, and must be dealt with by other methods. The tables of presence, absence, and degree are no more the whole of the Baconian theory of induction than are the four experimental methods the whole of Mill's doctrine of inductive proof, though a similar misconception is not infrequent in respect to the latter also. Bacon is perfectly conscious of this defect in his ^ method : he advocates the use of hypothesis, though it is hardly surprising that, with certain current hypotheses before him, he does scanty justice to this potent instrument of research ; and almost the whole exposition of the inductive method is concerned with one of 93 HISTORY OF LOGIC thought, and therefore every portion of logical theory. It is but a consequence of Bacon's narrow view of the essence of syllogism that he sliould set induction in opposition to deduction, and regard syllogism as of service only for communication of knowledge. His^ inductive methods are throughout syllogistic in this respect, that they like all processes of thought involve tlie combination of universal and particular. Experience is interpreted, that is to say, viewed under the light of a general idea or notion. the processes supplementary to and necessitated by the impossibility of realising exhaustive enumeration. The names of the other supple- mentary processes contemplated by Bacon at least suggest many of the methods which have been brought forward in recent logics as antithetic to the mechanical induction of the Novum Organum, 93 LOGIC ON THE BASIS OF PSYCHOLOGICAL EMPIRICISM : LOCKE, HUME, MILL, CONDILLAC 26. The universal element in thought which is recog- nised by Bacon as present received from him no special treatment. His theory of the nature of knowledge offered no explanation of the origin, significance, and validity of the notions involved in inductive procedure. The Essay concerning Hwnwi Understanding, which carries out in the domain of inner experience the practical tendency of the Baconian method, supplied from the point of view of individualism the metaphysical theory common to both, a certain psychological theory of the universal element in knowledge, and thereby aUbrded a new foundation for logical doctrine. The Essay contains, in an unsystematic fashion, much that bears directly on logic {e.g., the whole discussion on names, the classification of the signification of judgments, the criticism of syllogistic argument) ; but of more importance than these detached and direct portions is the general principle which underlies the whole view of human knowledge. This principle is briefly that of psychological genesis. All the complex facts of knowledge are regarded as mechanical compounds due to the coherence of simple data, the facts of inner and outer sense. It is 94 HISTORY OF LOGIC true that Locke's effort to carry out the view is full of difficulty and even of contradiction ; it is true also that the specifically logical processes of judging appear, without any warrant, as reflective acts exercised upon the materials furnished by sense, and that generally there is no attempt made to push the ultimate explanation further than to the very complex fact of an individual mind endowed with a multiplicity of powers, by means of which it brings into the isolated impressions of experience the order and logical coherence which are the very characteristics of knowledge. Nevertheless, the method of Locke is that which underlies and determines all the logical work of one very important school of logicians. It is not needful to enter into details of Locke's own contributions to the foundation of logic. But it may be pointed out that from his position |here were two possible lines of development. In his view the primitive impres- sions, the facts of inner and outer sense, were in themselves primitive facts of cognition ; they were cognitions (it is the very essence of Locke's method to identify a simple im- pression of sense with the knowledge of a simple sense fact). The processes of abstraction, comparison, i.e., judg- ing and reasoning, were exercised upon their data, and these products were, in consequence, of a secondary and, so to speak, artificial character. It was natural that a thinker who identified impression of sense with knowledge of a sense fact should maintain that the secondary for- mations of thought (general ideas, general propositions, syllogism) were not indispensable for cognition ; that we could and did reason from particulars to particulars. At the same time Locke admitted the secondary processes as having actual existence, and in one important case (that of the judgment of coexistence, with which may be taken LOCKE, HUME, MILL, CONDILLAC 95 the idea of substance and of real relation) seemed to allow that in judgment SMimthiiiL; was added to the primitive data. It was possildf, then, fur development from Locke's /^f ] position to proceed either by offering an explanation of the a33eoint of view. THE KANTIAN LOGIC 125 is a mere caput morfuum, a descriptive study of some few types of the application of thought to matters of experience. On the whole this is the view of logic developed through Fichte (and in part Schelling) by Hegel, and the Hegelian system shall hero be regarded as its complete and only representative. 126 VIII LOGIC AS THEORY OP KNOWLEDGE 32. The position assigned to logic as theory of know- ledge and the range of problems included in it are determined by the general philosophic view of the dis- tinction between the reality to be apprehended by thought and the subjective nature of thought itself. There may be, therefore, numberless variations in the mode of treating logic with general adherence to the one point of view.^ In the Dlaleldih of Schleiermacher, for example, the fundamental characteristic is the attempt to unite some portions of the Kantian analysis of cognition with Spino- zistic metaphysic. Knowledge is regarded as the complex combination of intellect, the formative, unifying, idealising faculty, and organisation or receptivity of sense. The generality or common validity of cognition rests on the uniform nature of organisation and on the identity of all ideas in the one ideal system. The objective worth of cognition is referred on the one hand to the determined ' It appears an historic error to identify the point of view here referred to with the Aristotelian. The notion of a parallelism between the forms of reality and the forms of knowledge is too definite to be covered liy the mere expression, whether in Aristotle or in Plato, of the doctrine that knowledge is knowledge of being. LOGIC AS THEORY OF KNOWLEDGE 127 connection between the real universe and the organisation through which the individual is part of the real order of things, on the other hand to the ultimate metaphysical parallelism between the system of ideas and reality. The primary forms of knowledge, notion, and judgment, distinct from one another only as being knowledge viewed now as stable now as in process, correspond to the ultimate elements of the real, the permanent force or substance and its variable manifestations. Syllogism and induction, with the subordinate processes of definition and division, analysis and synthesis, are technical modes of the develop- ment of notions and judgments, modes by which inchoate notions are rendered definite, by which incomplete judg- ments are rendered complete.^ That there is much valuable and suggestive material in this mode of regarding logic is undoubted, and in the discussion of isolated forms of knowledge, such as judg- ment, it is always desirable that there should be kept in mind the reference to the ultimate character of objectivity. But the whole point of view seems imperfect and open to such objections as will always present themselves when a principle is not carried out to its full extent. It may, for proj)0edeutic purposes, be desirable to separate the handling of logical forms from metaphysic, but such separation cannot be ultimate. The system of forms of reality to ' Perhaps the most complete treatment of logic from this point of view is tiiat uf George, Lorjik ah Wisscnsc/uiftslehre, 1868. Ueberweg, dissenting from Schleiermacher's view of syllogism and the systematic processes of reasoning, lays out more fully what in his view are the aspects of reality corresponding to the typical forms of knowledge. Trendelenburg endeavours to fill up the gap between real and ideal by emjjhasising the comnmnity of character between motion, as the ultimate reality, and constructiveness in knowledge, the central activity of the ideal. 128 HISTORY OF LOGIC which the forms of knowledge are assumed to correspond must in some way enter into knowledge, and they cannot enter in as an absolutely foreign ingredient, to which knowledge has simply to conform itself. For, if so, these metaphysical categories would be discoverable only by an analysis of concrete knowledge, and they would remain as inferences from the nature of cognition, not as data directly known. The cardinal difficulty which appears in all treat- ments of logic from this point of view is that of explaining how there comes to be known an objective system of things with characteristic forms or aspects, and it is not hard to see that the acceptance of a reality so formed is but a relic of the pernicious abstraction which gave rise to the Kantian severance of knowledge from noumenal reality.^ In short, the position taken by Schleiermacher and his school, as final standing ground, is but an intermediate stage in the development of that which lay implicit in the critical philosophy. Moreover, it is hardly possible to assume this point of view without tending to fall back into that mechanical view of knowledge from which Kant had endeavoured to free philosophy. If there be assumed the severance between real and ideal, it is hardly possible to avoid deduction of all that is characteristic of the ideal order ^ Thus we find in Schleiermacher {Dial., §§ 132-34) that the ulti- mate difference of ideal and real is accepted as simple datum. In Ueberweg (Logik, § 8 and poisim) there is continuous reference to an inner order of things, the forms of which are the metaphysical categories ; but the actual treatment is altogether independent of these forms ; and we may conjecture that, in the last resort; Ueberweg would have explained the characteristics of logical thinking by reference rather to the psychological mechanism than to a supposed nature of things (see Logik, §§ 40-42), and thus ap- proximated to the position of Beneke rather than to that of Schleier- macher. LOGIC AS THEORY OF KNOWLEDGE 129 from the observed or conjectured psychological peculiarities of inner experience. The real appears only as ultimate point of reference, but in no other way determines the form of knowledge. The characteristic relations which give content to notions, judgments, and syllogisms are deduced psychologically.^ In the long run, it would no doubt be found that the real key to the position is the belief, more or less expressed, that the systematic view of thought as comprehending and evolving the forms of reality is an unattainable ideal — that metaphysic, to put it briefly, is impossible. To some extent this is the position taken by Lotze, whose cautious and ever thoughtful expositions are in- variably directed to the elucidation of the real nodi, the real roots of perplexity or incompleteness of doctrine. In his view logical forms are the modes in which thought works up the material, supplied in inner experience by the psychological mechanism of the soul, in conformity to the ultimate presuppositions with the aid of which alone can harmony, or ethical and aesthetic completeness, be gained for our conceptions of things. But with this doctrine, which approaches more clearly than any other of the type to the metaphysical logic, there is coupled the reserve that any actual point of view from which the development of these presuppositions, their rational explanation, might become possible is unattainable. Our confidence in them ^ This tendency, which appears in Schleiermaclier and Ueberweg, and indeed in all the logics of that school (George's Logik, e.g., is hardly to be distinguished from psychology), is prominent in Beneke. It is curious to note a precisely similar result in the logical theory of Herbert Spencer. Spencer supposes himself to be tlirough- out referring to the nature of reality, but in fact all that is specific in the forms of reasoning developed by him is of psychological origin (see Pr. of Psych., ii. §§ 302-9). I 130 niSTOEY OF LOGIC is finally of an ethical character, and depends upon our conviction of the ethical end or purpose of all the sur- roundings within which human life and character is manifested. In logic as in metaphysic we must content ourselves with more or less fragmentary treatment.^ 1 Lotze's whole view of the genetic connection of the forms of thought is peculiar to himself, and deserves separate treatment (see below, p. 194 sq.). 131 IX LOGIC AS METAPHYSICAL 33. The peculiarities of this, the final conception of logic, are not to be deduced from the simple statement that in it no distinction is drawn between logic and metaphysic.i There must be understood the ultimate view of knowledge as that in which thought and reality are united, and of philosophy generally as the attempt to develop the whole system of these abstract determinations of thought by which coherence and intelligibility are given to knowledge. In it there is carried out to the full extent Kant's idea of thought as the ultimate germ of intelligibility. In the critical system, as we have seen, the fundamental idea was continuously disturbed by the intrusion of doctrines which possessed significance only when the prob- lems were treated from a quite opposed point of view. Thus the abstract separation of conscious experience, regulated according to the conditions of the unity of thought, from a supposed realm of reality involved the consideration of the subject as one portion or item of a mechanical whole. In other words, the Kantian system proved itself unable to unite in a comprehensive fashion 1 For there is no such definite understanding as to what these Tiean as would make the statement of their identitication helpful. 132 HISTORY OF LOGIC the two ideas of thought as the universal in experience and of thought as the activity or mode of realisation of the individual subject. The central point of view, that which refers all in experience to the unity of thought, was continuously departed from, and as a natural conse- quence the various forms or modes of thought were treated, not in relation to their ultimate unity, but as isolated facts, to be dealt with by principles resting on a totally opposed doctrine. It is the essence of the Hegelian method to keep continuously in view the concrete unity and totality of thought, to treat each special aspect or determination as an integral portion of an organic whole, a portion which must prove itself unintelligible and contradictory if re- garded apart from its relations to the whole, and so to avoid those mechanical separations and abstractions which had proved fatal to the Kantian doctrine. In the development of a method which rests upon and endeavours to retain so comprehensive a point of view, there must of necessity be much that is tentative and imperfect. Differences of opinion regarding the main stages in the development, regarding the particular content of any one stage, are quite compatible with adhesion to the general principle of the whole. ^ But from this point of view only can justice be done to those forms of thought which have always been regarded as the special material of logical treatment ; from any other, the treatment must be partial, fragmentary, and, so to speak, external. Thus, notion, judgment, and syllogism are not, in this view, ^ Hegel himself fully recognises the tentative character of the numerous divisions and classification of the categories of thought which make up the substance of the Logik, and desires that too much stress be not laid on the formal side of his exposition (see Logik, i. 29). LOGIC AS METAPHYSICAL 133 treated as merely subjective modes in which the individual consciousness apprehends and works up the material of experience, hut as higher, more developed, and therefore richer forms of the determinations of thought in and through which intelligibility of experience is acquired. The whole system of these determinations of thought, the categories, is the matter of logic ; the realisation of them in subjective experience, or the treatment of the successive phases of consciousness in which abstract thought comes to be recognised in and by the individual, is the matter of the philosophy of spirit, of which psy- chology is one portion. Doubtless the logical treatment may be led up to by tracing the modes in which the full consciousness of the determinations of thought as the essence of reality is attained, but such introduction is proppedeutic merely ; and within the logical system itself the starting-point must be the simplest, least definite of those categories whereby for spirit the realm of fact becomes intelligible. The nature of the opposition between this view and that of the ordinary logic, which in the piain rests upon the principle of individualist psychology, that the content of knowledge is derived ah extra, from an entirely foreign world of fact, will become more clear if there be considered specially the treatment which under the two methods is given to the notion. Notions, in ordinary logic, are re- garded as products formed from the data supplied by presentative and representative experience, and the mode of formation as generally conceived is a continuous process of critical comparison, recognition of differences, similarities, and grouping of like facts. Not only then does the notion present itself as relatively poor and meagre in content, a kind of attenuated individual, not only are the only 134 HISTORY OF LOGIC characteristics presented to the operation of thought mechanical and external, but the final product appears as a mere subjective abbreviation of what is given in experience. In the process, however, even as it is ordinarily con- ceived, there is more involved than is apparent on the surface. The individuals subjected to the abstracting and generalising activity of thought aie qualified indi- viduals, i.e., individuals viewed as determined in their own nature and in respect of thought by a whole network of relations, which when stated abstractly are really of the nature of categories. They are individuals only for a unifying intelligence which views them under diverse aspects, and these aspects are the blank forms of intelligi- bility, which it is the very function of logic to consider in system. Moreover, the purely formal acceptation of the notion as a mere mental hieroglyphic or sign stands in sharp contradiction to the view which as a rule ac- companies it, and which, for the most part, receives explicit statement in a so - called applied logic or doctrine of method, that in the notion is contained the representa- tion of the essence or truth of reality. It is impossible to retain with any consistency the merely arithmetical or numerical doctrine of the notion, as containing fewer marks than the individual, of the genus as characterised by a less number of attributes than the species, and so on. Under- lying all genuine knowledge, all classification, and therefore all formation of notions, is the tendency towards the sub- ordination of parts to a law which determines them. The generic attributes are not simply the points of agreement, but the determining characteristics, and the notion of a thing is the explicit recognition of its nature as a particular manifestation of a universal law. LOGIC AS METAPHYSICAL 135 Thus, even within the limits of the ordinary logic, there are problems which force upon it the reconsideration of the view which regards the notion as merely a mechani- cally formed psychical fact. Knowledge, no doubt, is only realised subjectively in and through psychical facts ; but the treatment of it in its nature as knowledge, and the treatment of its psychical aspect, are toto genere distinct. The metaphysical doctrine which keeps consistently in view thought as the essence of knowledge in its own nature has therefore to contemplate the notion in strictest relation to thought, as one mode in which objectivity as such is apprehended, made intelligible, and, in a very special sense, as the mode in which the nature of thought is made explicit. Thus the notion can only appear as uniting and comprehending under a new aspect those intellectual determinations whereby things are related to one another in a cognisable system. The special characteristic of the Hegelian logic, the methodical principle of development of the determinations of thought, requires for its full elucidation a longer treat- ment than is compatible with the scope of a general sketch. But it seems necessary to add a word respecting certain difficulties or objections which apply, not specially to the methodical principle of Hegel's logic, but generally to the idea of a logic which is at the same time metaphysic or a treatment of ultimate notions. These objections may be variously put, according to the special point of view assumed by the critic, but they are in the long run de- pendent on one mode of interpretation of tlie fundamental antithesis between being, or reality, and thought. For, whether we say that it is confusion to identify thought-forms with relations of fact, that it is unphilosophical to assume that being of necessity conforms to thought, that thought 136 HISTOKY OF LOGIC is purely subjective and knowledge the system of forms in and through which the subjective is brought after its own nature to an adequate representation of objective fact, or point to phenomena of perception as showing that even adequate correspondence, not to speak of identity, between subjective and objective must be matter of discussion, or lay stress upon the procedure of science as negativing the preliminary assumption of the logico- metaphysical assumption, we but express in varied ways a fundamental interpretation of the opposition between reality and know- ledge. We assume an initial distinction, the grounds and precise nature of which are never made clear. For the antithesis between thought and reality is an antithesis in and by means of conscious experience, and is not to be comprehended save through conscious experience. If, indeed, we start wnth conscious experience as a mechani- cally formed tertium quid, something which arises out of the correlation of an unknown subject and an unknown object, we may certainly retain, as an ever-recurring and insoluble problem, the possibility of cognising either factor per se. But the problem arises not from the antithesis but from our way of reading or interpreting it. Opposition between subjective thinking and the real world of fact, slow, ten- tative, and imperfect development in individual conscious- ness of knowledge which contains in essential relation the opposed elements, distinction therefore of the metaphysical or real categories which determine the nature of objects as knowable from the ideal or logical categories which express more specifically the fashion in which the knowable object is reduced to the subjective form of cognition, are not only perfectly compatible with, but are strictly reasoned con- clusions from, the ultimate doctrine that in thought alone LOGIC AS METAPHYSICAL 137 is to be found the secret both of knowing and of being. To bring against this doctrine the continuous complaint that it assumes an identity which, if it can be proved at all, at least demands proof, is to misunderstand the very notion of identity which plays so important a part in the objection. Not even in the most judicious and thoughtful critics of metaphysical logic, in Lotze for example,^ does one find a sufficiently careful distinction between a mere question of nomenclature (i.e., whether we shall restrict the title logic to the portion of general system which deals with notions, judgments, and syllogism, while reserving for metaphysics all the other inquiries) and the question of theoretical importance, whether there remains, over and above the difference between the more immediate deter- minations of thought and its more complex or reflective modes, an essential difference in knowledge between thought and reality. In less careful critics the oversight simply leads to the contention that we shall always repeat the problem of knowing and being as insoluble, and shall view knowledge as a mechanical, subjective product. Many of these objections doubtless result from a very simple fact, already more than once alluded to. Partic- ular distinctions, apparently the most elementary, fre- quently involve and are unintelligible apart from a developed, though not necessarily consistent or well- grounded, conception of things in general. Thus the emphasis laid upon thought as essentially subjective, as being merely the system of operations whereby the indi- vidual brings into order and coherence in his own expe- rience what is furnished ab extra through the natural connection in which he is placed to the objective world, 1 See his Logik (1843), pp. 10, H, aud Logik (1874), bk. iii., chaps. 4, 5. 138 HISTORY OF LOGIC seems at first sight the most simple and direct consequence of the actually given distinction between the individual as one natural unit and the sum of things comprehending him and all others. But, on analysing more closely the title for applying to philosophical problems a view which is that of practical life, and doubtless legitimate and necessary within that sphere, we readily become aware of a whole series of speculative assumptions implicit in that view, and possibly without any adequate justification. At all events, whether or not the view be ultimately defensible, and in the same form in which it is at first assumed, it is unphilosophical to start in the treatment of a difficult and important discussion from principles so ambiguous and undetermined. The practical difference between the indi- vidual agent and the external sphere within which his individual operations are realised and which is therefore treated by him, from his point of view, as external, throws no light 7>e?- se on the nature of the ultimate relation between the individual thinker as such and the world within which his thought is exercised. The confusion between ultimate distinctions and practical points of view is productive of most pernicious consequences not only in logic specially but in philosophy at large. 139 X CRITICISM OF THE CHIEF LOGICAL SCHOOLS 34. It will probably be now apparent that determination of the nature, province, and method of logic is, and has always been, dependent on the conception formed as to the nature of knowledge. Discussions regarding the precise // definition of logic are not mere analytical disputes regard- ing the best mode of expressing in terms the nature of a subject sufficiently agreed upon ; variations in the treat- ment of particular portions of logical discipline do not arise from more or less accurate discrimination of the nature and. relations of given material ; nor are differences in respect to the amount of logical matter to be considered mere expressions of difference as to the range of the same funda- mental principles. The grounds for divergence are much more deeply seated ; and, looking back upon the historical survey of the main conceptions of logical science, it seems quite impossible to hope that by comparison and selection certain common points of view or methods may be extracted, to which the title of logical might beyond dispute be applied. It results, moreover, from this fact that criticism of various logical views cannot be conducted by the method of bringing each in turn before a recognised rule or established opinion respecting the contents and methods of logical science. 140 HISTORY OF LOGIC The logic, as one may call it, of each philosophical theory of knowledge is an integral part or necessary consequence of such theory ; and its validity, whether in whole or in part, depends upon the completeness and coherence of the explanation of knowledge in general which forms the essence of that theory. The course of the preceding historical survey has brought before us a variety of conceptions of logic resting on various doctrines of knowledge ; and, had it been possible to include in these historic notes references to the several treatments of details — such as classification of notions, analysis of judgments, system of reasoning, and methods of proof — an equal variety in special points would have been apparent. Any criticism of a general conception of logic or special application thereof, which does not rest upon criticism of the theory of knowledge implied in it, must be inept and useless. It is not possible to include such expanded criticism in the present work. There remains therefore only one aspect of these various logical schemes which may be subjected to special and isolated examination, viz., the inner coherence of each scheme as presented by its author. Naturally such an examination can be applied only to views which imply the separate existence of logic as a body of doctrine developing into system from its own peculiar principles. "When it is a fundamental position that logic as such has no separate existence, but is one with the all- comprehensive doctrine or theory of the ultimate nature of cognition, it is not possible to criticise such conception of logic separately ; criticism of logic then becomes criticism of the whole philosophical system. In most of the views brought before us, however, a special place has been assigned to logic ; it has been placed in various relations CRITICISM OF LOGICAL SCHOOLS 141 to the allied subjects of psychology and metaphysics, but with a certain independence ; and its contents have been assumed to follow in some way from its own special prin- ciples. It is therefore possible to apply internal criticism to the more important of these general views, and to con- sider how far the pretensions of logic to an independent position and method are substantiated. From the foregoing remarks it will also have become apparent that a general classification of logical schools, as opposed to the reference of these to ultimate distinctions of philosophical theory, is impossible. A distribution into formal (subjective), real (empirical, or, as German authori- ties designate it, erkenntnisstheoretisch), and metaphysical conceptions of logic is rather confusing than helpful. For the formal logics of the Kantian writers, of Hamilton, and of Mansel are distinct, not only from one another, but from such equally formal logics as those of Hobbes, Condillac, Leibniz, Herbart, Ulrici, Boole, De Morgan, and Jevons. Logic as theory of knowledge presents quite special features when handled by Mill, or by Schleier- macher, Ueberweg, IJeneke, and Wundt. And it cannot even be admitted that the threefold classification affords room, without violence, for the Aristotelian logical re- searches. There are no points of agreement and differ- ence so unambiguous that by their aid a division can be effected.^ 35. Few conceptions of logic contain, with so little real ground, such professions of completeness and independence ^ Nor are more detailed classifications, such as those of Roseukranz (ZHe Modificationen der Logik, 1842), Prantl {Die Bedeutung der Logik, 1849), Rabus (Neucste Bestrebungen, 18S0), of service, except when historical. 142 HISTORY OF LOPxIC as that developed in the writings of the Kantian school.^ According to this view, logic is a pure science, having as its special material the form of thought, demonstrative in character and with theorems capable of complete deduction from the elementary principles contained in the very notion of form as opposed to matter of thought. But, when one comes to the examination of the system itself, one finds (a) that the notions of form and matter are much too stubborn to lend themselves readily to analysis, and that explanations of what exactly constitutes form fluctuate between a merely negative definition (whatever is not treated in any other science, philosophical or otherwise) and a psychological deduction from the assumed nature of thought ; - (h) that the really important factor in deter- mining the contents of logical science is psychology, from which much more is borrowed than the mere preliminary definition of thought; (c) that demonstrative character rests entirely on an abstract interpretation of the laws of identity and non-contradiction 3 (d) that throughout the whole system there is not a trace of development, but merely the reiterated application of the law of identity and contradiction, or of some confused distinction between form and matter, to logical products — the notion, judgment, and syllogism — whose nature, characteristics, and distribution are arbitrarily accepted from psychology or general criticism or what not. Thus, in the majority of cases, logicians who simply followed the lines indicated by Kant introduced into their ^ Under this head Kant himself, for reasons above given, is not included ; the writers referred to are named in Ueberweg {Logik, § 34). ^ ^ Mill's criticism on Hamilton's confused statements regarding forms {Exam, oj Hamilton, 438-454), is perfectly applicable to the generality of the Kantian treatises on logic. CRITICISM OF LOniCAL SCHOOLS 143 system, without any criticism, the fundamental distinctions contained in the Kritik der reinen Vernunft. The fourfold scheme of quantity, quality, relation, and modality was applied without hesitation, though in varied and always artificial fashion, to notions ;i judgments were accepted as being categorical, hypothetical, and disjunctive in kind, though the differences are altogether foreign to the logical principles applied ; and generally no attempt was made to do more than treat, in an abstract fashion, some aspects of a procedure of thought determined in all its phases by extra-logical considerations. The inevitable result of such a treatment was the undue preponderance given to the doctrine of notions, which, being viewed after the fashion of Kant as given, completed products, appeared as the ultimate units of thought, to be combined, separated, and grouped together in all the higher processes. The peculiarities of the logical system which is commonly associated with the name of Sir W. Hamilton spring entirely from this view of notions. For, if notions be regarded as the elements of thought, then the judgment which elaborates them can only present itself as the explicit statement of immediate relations discernible among notions. These immediate relations reduce themselves, for Hamilton, to one — the quantitative relation of whole and part — and, attention being concentrated on the extensive reference of concepts, the eightfold scheme of propositional forms is the natural consequence. To such a scheme the objections are manifold. It is neither coherent in itself, nor expressive of the nature of thinking, nor deduced truly from the general principle of the Hamiltonian logic. For it ought to have been kept in mind that extension is but an aspect of the notion, not a separable fact upon which the logical ^ See, e.g., Krug, Loyik, § 25 sq. 144 HISTORY OF LOGIC processes of elaboration are to be directed. It is, moreover, sufficiently clear that the relation of whole and part is far from exhausting or even adequately representing the rela- tions in which things become for intelligence matters of cognition ; and it is further evident that the procedure by which types of judgment are distinguished according to the total or partial reference to extension contained in them assumes a stage and amount of knowledge which is really the completed result of cognition, not that Avith which it starts or by which it proceeds.^ The utility of basing logical theorems on psychological premisses, a method involved in the procedure of most expositions of formal logic, may well be matter of doubt. For psychology, as ordinarily conceived, has certainly close relations with logic, but in aim and in point of view is distinctly opposed or at all events subordinate to it. The psychological investigation of thought, if carried out con- sistently, must take one of two forms : either that of description, in which thought, like any other mental fact, is regarded ah extra as that upon which attention and observation are to be directed, — in which case therefore any relations of thoughts among themselves must be of such an external nature as can be presented in the field of observation ; or that of genesis, development, in which the ' The extension of a notion has no numerical or quantitative definiteness. To formulate the judgment as expressing definite amounts of extension, therefore, presupposes complete empirical survey of what, by its verj' essence, remains incomplete. This is Bpecially noteworthy in the case of Hamilton's particular judgments. A judgment such as only some A is all B assumes total and perfect knowledge of the whole spheres of A and B. It is in the strictest sense of the word universal, Hamilton, it may be added, finds it completely impossible to work out a coherent doctrine of syllogism from the point of view taken in the treatment of the judgment. CRITICISM OF LOGICAL SCHOOLS 145 subjective processes of mind are viewed as forms of the one great process whereby knowledge is realised in the individual consciousness. Investigations from the first point of view are diametrically opposed to the logical treat- ment of thought ; for in tlie latter the essential feature, the reference in the subject, with his mental forms, to an objective order within his experience, is entirely wanting. Such investigation is abstract ; it proceeds upon and re- mains within the limits of a distinction drawn in and for conscious experience, a distinction the grounds, significance, and modes of which require to be treated by a larger and more comprehensive method. Investigations from the second point of view are subordinate to logic in the wider sense ; for the treatment of the subjective processes therein is illuminated and determined by the general principles regarding the nature and meaning of conscious experience which it is the sole function of logic to bring forward and establish. The psychology which Hamilton generally has in view is that commonly called empirical, and with his conception of it the two sciences, logic and psychology, are really one. 36. A possible exit from the difficulties or assumptions of the current Kantian logic may be sought by following out and consistently applying the hint contained in Kant's distinction of analytic and synthetic thought, analytic and synthetic truth. It may be said that all thinking involves the fundamental laws of identity and non-contradiction ; that in these laws only is to be found the characteristic and most general feature of thought ; that in them only is the form, or element contributed by mind itself, to be detected. Logic would thus be regarded as the explicit statement of the conditions of non-contradictoriness in thought, as the t 146 niSTOT^Y OF LOGIC evolution of the formal element in thought, and, since in analytic truth only can non-contradictoriness be discovered without material aid, as the theory of analytic thought. Such is the position assigned to logic by Twesten, Mansel, Spalding, and some others ; and the consequences to which it inevitably leads are sufficiently interesting to require that some special examination should be given to it. In the first place, then, it seems evident that the funda- mental distinction implied, that between analytic and synthetic thought, is wrongly conceived. That analysis and synthesis are methods of cognition, differing in many important respects, is undoubted ; but such difference lies in a sphere altogether alien to that within which the present distinction is to be sought. Analytic thought, as here conceived, is only to be understood when taken in reference to the judgment, and then also in reference to a peculiarity in the Kantian doctrine. Kant, emphasising the principle that judgment is essentially the form in which the particular of experience is determined by the universal element of thought, but identifying this universal with a formed concept (resembling, therefore, a class notion), con- templated a class of judgments in which the predicate was merely an explication of the subject notion. Such judg- ments, had the matter been more fully considered, would have appeared as far from primary ; and Kant has himself, in the most unambiguous language, indicated the correct view that analysis is consequent and dependent on syn- thesis — that analytic judgments, therefore, are merely special applications of abstracting thought within a sphere already treated, handled, formed by thought. IMansel, too, whose views are generally acute if not profound, has signalised as the primitive unit of cognition the so-called psychological judgment, which is essentially synthetic in CRITICISM OF LOGICAL SCHOOLS 147 character. The logical judgment, in fact, about which his conception of logic centres, is recognised as a posterior act of reflection, directed upon formed notions, and is not in any way to bo regarded as containing what is a common, universal feature of all judgments. In the second place, even granting what cannot be maintained, that the process of thought is mere explication of the content of previous knowledge, and that the theory of logic has to do with a comparatively small and subor- dinate portion of cognition, there is in such a principle no means of development. We may take up in succession class-notions, judgments, reasonings, and in relation to each reiterate, as the one axiom of logic, that the constituent elements shall be non-contradictory ; but such a treatment is only possible in relation to a material already formed and organised. The utmost possiljle value being given to such a view, logic, under it, could be but a partial and inchoate doctrine. Finally, there is involved in the doctrine of analytic thought, and in the consequences to which attention will next be drawn, a peculiar and one-sided conception of identity or of the principle of identity as an element in thought. Historically this conception has played a most important part : it lies at the root of all nominalist logic from Antisthenes downwards, and has found metaphysical expression of the most diverse kinds. That things are tvhat they are is the odd fashion in which a wellnigh forgotten English writer states what is taken to be the universal foundation of all thought and knowledge.^ The 1 John Sergeant. See The Method to Science, by J. S., 8vo., Loud., 1696, pp. 144, 145. This curious book contains much interesting matter. Sergeant regards inference as " the establishment of identity between extremes by identity with the middle " (p. 227) ; 148 HISTOEY OF LOGIC representatives of things in our subjective experience, the units of knowledge, may be called notions, and, accordingly, that each notion should be what it is appears as the cor- responding logical axiom. The whole process of thought is therefore regarded as merely the explicit statement of what each notion is, and the separation of it by direct or indirect methods from all that it is not. The judgment, essentially the active movement of thought, is reduced to the mere expression of the identity of a notion, and in truth, were the doctrine consistently carried out, Antis- thenes's conclusion that the judgment is a fallacious and inept form of thought would be the necessary result. "When such a conclusion is not drawn, its place is generally taken by much vague declamation regarding the limited, imperfect, and uncertain character of our knowledge, which is regarded as asymptotically approaching to the adequate determination of truth. The conception which underlies this view is the abstract separation of thought from things which has been already noted, but the proximate principle is a deduction there- rejects the second and third figures, and indeed figure at all (p. 233) ; reduces all modes of inference, hypothetical and others, to one type (p. 247) ; considers that all truths are identical propositions (p. 267), even the causal relation being of the nature of an identity (pp. 144-5) ; and concludes jwith that which is an inevitable consequence of this doctrine, viz., that knowledge of one fact in nature implies know- ledge of all nature (p. 269). Much modern criticism of plurality of causes is anticipated here, as indeed it rests on the same abstract conception of identity. If the whole universe be the cause at any one moment, it i.s perfectly clear that " plurality of causes " is a contradiction in terms ; but so, for that matter, would cause be under a like condition. Tlie universe is the universe ; things are what they are ; our thinking is ultimately an incessant reiteration of the same, A, A, A. Sergeant is acute enough to see what many modern critics have not perceived, that the notion of change is endangered by such an abstract principle (see pp. 305-6). CRITICISM OF LOGICAL SCHOOLS 149 from. Knowledge or thought is treated externally as a series of isolated units or parts, and the results of cognition — notions, judgments, and reasonings — are viewed as the constituent factors. Thus, e.g., when it is said that a judgment is the expression of an identity, there arc possible only two modes of explanation : the one, that the identity referred to is that between the original notion (subject) as unqualified by its predicates and the same as qualified, in which case manifestly the result of the judgment is taken as being its constituent essence ; the other that the identity is that of the applicability of distinct names to the same fact, in which case we accept without further inquiry and. exclude from logical consideration the processes of thought by Avhich the application of names is brought about, and assume as being the procedure of thought itself that which is its consequence. Under all circumstances, difference is as important an element as identity in the judgment, and to concentrate attention upon the identity is to take a one-sided and imperfect view.^ 37. So soon, however, as the real nature of thought has been thrown out of account as not concerned in the pro- cesses of logic, so soon as the law of non-contradiction in its manifold statement has been formulated as the one principle of logical or formal thinking, there appears the possibility of evolving an exact system of the conditions of non-contradictoriness. The ultimate units of knowledge, Avhatsoever we call them, whether notions or ideas of classes or names, have at least one characteristic : they are what they are, and therefore exclude from themselves ^ On Condillac's attempt to treat judgments as identities (or equa- tions) some excellent remarks will be found in De Tracy, Ideologic, iii. 133-143, cf. Duhumel, Dcs Mithodcs, i. 89-94. 150 HISTORY OF LOGIC whatever is contradictory of their nature. They are com- bined positions and negations, that whicli is posited or negated being left undetermined, — referred, in fact, to matter as opposed to form. With respect to any article of thought, therefore, the only logical requirement is that it shall possess the characteristic of not being self-contra- dictory, and the only logical question is, what exactly is posited and negated thereby. Complex articles of thought viewed in like manner as complexes of positions and nega- tions may have the same condition demanded of them and the same question put regarding them. A judgment and a syllogism, if narrowly investigated, will appear to be merely cemplex articles of thought, complexes of positions and negations. Proceeding from such a conception there may be treat- ments more or less systematic and fruitful. In the hands of Kantian logicians, such as Twesten, INIansel, Spalding, and the like, little is effected, for, as the forms of thought are accepted as giving and as having their characteristics otherwise fixed (by psychology or critical theory of know- ledge), the treatment resolves itself either into repetition, in respect to each, of the fundamental logical condition, or into the erection of a specific kind of thought (analytical) which has no other feature save that of correspondence with the said condition. But it is clear that restriction by any psychological or critical doctrine of thought is an arbi- trary limitation. It is needful only to regard the operation of thought as establishment of positions and negations, and to develop, by whatever method, the systematic results of such a view. Hobbes's doctrine of thought as dealing with names and as essentially addition and subtraction of nameable features, Boole's doctrine of thought as the de- termination of a cla.ss, Jevons's view of thought as simple CRITICISM OF LOGICAL SCHOOLS 151 apprehension of qualities, — any of these will serve as starting-point, for in all of them the fruitful element is the same. The further step that the generalisation of the system of thought must take a symbolic form presents itself as an immediate and natural consequence. 38. By the application of a symbolic method is not to be understood what has been practised by many writers on logic — the illustration of elementary logical relations by numerical or algebraic signs or by diagrammatic schemata. The expression has the signification which it bears in mathematical analysis, and implies that the general rela- tions of dependence among objects of thought, of what- soever kind, in correspondence with which operations of perfectly general character are carried out, shall be repre- sented by symbols, the laws of which are determined by the nature of these relations or by the laws of the cor- responding operations. The mere use of abbreviations for the objects of treatment is not the application of a sym- bolic method ; ^ but so soon as the general relations of, or general operations with, these objects are represented by symbols, and the laws of such symbols stated as deductions therefrom, there arises the possibility of a symbolic de- ^ Thus one would not describe Aristotle's use of letters for the terms of his syllogisms, nor the current logical abbreviations of S, P, and M in like case, as being, in any true sense of the word, symbolic. On the subject generally, the instructive work of Mr Venn {Symbolic Logic, 1S81) should be consulted. Mr Venn has not only in this work expounded the foundations and main theorems of Boole's logic with a care and skill that leave nothing to be desired, but he has, independently of many real contributions to logical analysis, put in its true light the nature of symbolic method in logic. He has ren- dered it impossible, even for the outsider, to complain that symbolic logic is an arbitrary application of mathematical method to logical material. 152 HISTORY OF LOGIC velopment or method of treatment, which may lead to more or less expanded results according as the significance of the symbolic laws is more or less general. Thus quan- tity, whether discrete or continuous, presents, as an aspect of phenomena, relations of a highly general kind, offers itself as object of operations of a highly general kind, and is therefore peculiarly the subject of symbolic treatment. Currently, indeed, the treatment of quantity is assumed to have the monopoly of symbolism ; but such an assump- tion is not self - evidently true, and it is permissible to inquire whether matters non-quantitative do not present relations of such generality that they, too, can be sym- bolically dealt with. It is, however, a further question whether the generality of the relations and therefore the significance of the symbols in such cases, although subject to some special conditions not necessarily involved in the nature of quantity, do not spring from the fact that we treat the matters as quantities of a special kind, and so insensibly find ourselves applying quantitative methods. In other words, it remains to be investigated, after the preliminary definitions and axioms of any symbolic method have been laid down, whether the conception of thought with which we start, or a special feature distinctly quan- titative in character, has been the truly fruitful element in after-development of tlie system.^ The first step in any symbolic logic must evidently be the determination of the nature and laws of the symbols ; and, as these follow from the nature of the operations of thought, the first step is likewise a statement of the essen- tial characteristic of thinking. As above noted, there have been adopted various modes of expressing this character- ' An excellent nolo, on symbolic logic will be found in Lotze, Loyik (2nd ed., IfeSOj, pp. 256-59, Eug. tr., pp. 208-23. CRITICISM OF LOGICAL SCHOOLS 153 istic, and in some cases the mode adopted is not one from which any generally applicable symbolic rules of procedure could have followed.^ Two only require here to be noted, as representing special views : first, that which proceeds from the idea of thought as essentially the process of grouping, classing, determining a definite set of objects by a mark or notion ; and second, that which proceeds more generally from the conception of thought as consist- ing of a series of self-identical units, to be variously com- bined in obedience to the law of self-identity.- Adopting the first view, wc find that processes capable of symbolic representation, by the customary algebraic signs of addition, subtraction, equivalence, multiplication, and division, have a perfectly general significance in reference to the com- bination, separation, equalisation of classes, to the imposi- tion and removal of restriction on a class ; that to the symbols there can therefore be assigned a set of general laws ; and that any peculiarity of these symbolic laws which differentiates them from the laws of like symbols in mathematical analysis is deducible from the notion of thought with which we started, and is consequently to be carried along with them in all the after development.^ ' Some of these, as e.g., Lambert's and Ploucquet's, are noted and discussed by Mr Venn {Symbolic Logic, xxxii. -xxxvi. and passim). - Tlie first is the view taken by Boole (and expounded with great fulness in Venn, as above) ; the second is that of the brothers Grass- mann (in the Forvicnlehre, 1872, especially bk. ii. , Die Bcgriffslchre odcr Logik). I do not specially note Jevous's theory, otherwise one of high interest and leading to many elegant and ingenious processes, for it appears to me, while not absolutely coinciding in statement with that of either Boole or Grassmann, to be covered by what is special to each of them, and to be valuable mainly as a simplification in certain particular directions. * Mr Venn, in his exposition of Boole, has done much to clear up the significance and laws of the symbol for division. 1 am inclined 154 HISTORY OF LOGIC Symbolic representation of relations of classes follows with equal directness from the general notion that by any such relation a new group is determined in reference to the original groups, or rather tliat the position or negation of a new group (or series of groups) is given, definitely or indefinitely, as the result of such a relation. "With the aid of the symbolic laws so reached, the logical problem as such may then be approached. Given any number of logical terms [i.e., classes, or, as it may be better put, positions and negations) connected together by, any relations, to determine completely any one in reference to tlae others, or to express any one in terms of the others. The symbolic procedure, expounded with marvellous in- genuity and success by Boole, may take various forms, and may be simplified by many analytical devices, but consists essentially in determining systematically how given posi- tions and negations, definite or indefinite, combine with or neutralise one another. A more detailed account of these formal processes is beyond our limits. ■"• The first question which suggests itself in connection with Boole's symbolic logic is the necessity or advisability of retaining the reference to classes, or the description of thought as classification. Do the symbolic laws really depend to any extent on the logical peculiarities of class to think that it wuuld be quite in accordance with Boole's idea to assimilate multijdication and division to the familiar logical pro- cesses of determination and abstraction (as indeed is hinted by Mr Venn, I. c, p. 80). For these processes can, from the special point of view, relate only to the subdivision of a class in extension, and have no reference to the usual distinctions of connotation and denotation. ^ Mr Venn's work is here again invaluable. Jevons's Principles of Science and Studies in Deductive Logic should be consulted. Schroder's Operationskreis dcs Lof/iUcalculs contains some very elegant and simple methods. CRITICISM OF LOGICAL SCHOOLS 155 arrangement ] ^Ir Venn, who emphasises this feature in Boole's scheme, has, however, done good service in leading up to a different explanation. The general reference to objects, which is also noted as implied in all iJoole's formula), has nothing to do with the possible difference of conceptualist or materialist doctrines of the proposition ; and, in fact, as all distinctions of thing and quality, re- semblance and difference, higher and lower, subject and predicate vanish, or are absorbed in the more general prin- ciple underlying the symbolic method, phrases such as classification, extension, intension, and the like should be banished as not pertinent. Nay, the usual distinctions of (quantity and even of quality either disappear or acquire a new significance when they are brought under the scope of the new principle. " What symbolic logic works upon by preference is a system of dicliotomy, of x and not x^ y and not y, and so forth." ^ In other words, quantitative differences require to find expression through some com- bination of the positions and negations of the elements making up the objects dealt with,- while the usual quali- tative distinctions are merged in the position or negation of various combinations. The whole phraseology then of classification and its allied processes seems needless when used to denote the simple determination of objects thought. The literal signs express, not "classes," but units, determined in and for thought as self-identical. For this reason then it appears that the view of the foundations of the symbolic methods of logic taken in Grassmann's Begi'iffslehre is more ' Venn, as above, p. 162. '^ Where this is impossible, as in the case of the truly particular or indeterminate judgment, symbolic methods encounter almost insurmountable difficulties. 156 HISTORY OF LOGIC thoroughgoing, and more closely represents the under- lying principles, than that involved in Boole's formulae and expounded in detail by Mr Venn.^ Grassmann, as above stated, deduces logical relations as a particular class of the determinations necessarily attach- ing to all quantities (i.e., determined contents of thought). Abstraction being made of all peculiarities which may be due to their special constitution, quantities exhibit certain formal relations when they are combined (added, sub- tracted, &c.). Each quantity is a unity of thought, a definite positum, and of such units there are but two classes, elements and complexes. Units of thought, which are self-identical, and therefore subject to the specific law ' For this reason we think that Mr Venn's criticism of the inten- sive reading of logical terms is somewhat beside the mark. Beyond a question, if the point of view from which intension has any sig- nificance and importance be adopted, the relations of notions in intension would be impracticable for symbolic handling ; but from this point of view no such separation between extension and inten- sion as Mr Venn contemplates is possible. The objects with which symbolic logic can deal, and the relations of which it can take into account, are determined units, in respect to which difference be- tween their qualities as recognised and things possessing them is inept. A for symbolic logic, is simply a definite position, with the function of excluding not - A, and the capacity for entering into combination with anything that is not A. It might be a class, or an individual, or a group of qualities, or a single quality, and in any case must be dealt with symbolically in connection with others of like kind; i.e., if I call A a quality, I must deal throughout with qualities, and allow no intensive questions as to the results of com- bination on classes, or groups of things. It is evident also that, under any view of logic, our cognition of things or classes must start with attributes ; and the possibility or impossibility of combination, the extent determined by any combination, depend on the relations of possibly combined position or of exclusion between the con- stituent attributes. Much of Mr Venn's criticism of Jevons's method involves oversight of this fundamental point. CRITICISM OF LOGICAL SCHOOLS 167 that addition of each to itself or multiplication of it by itself yields as result only the original unit, are notions. The theory of notions, therefore, is the development of the general formal relations of units under the special restrictions imposed by their nature.^ There appears very clearly in Grassmann's treatment the essence of the principle on which symbolic logic proceeds. Thought is viewed as simply the process of positing and negating definite contents or units, and the operations of logic become methods for rendering explicit that which is in each case posited or negated. To apply symbolic methods, we require units as definite as those of quanti- tative science, and the only laws we can employ are those which spring from the nature of units as definite. Now it seems a profound error to reduce the whole complex process of thinking to this reiterated position of self- identical units. Undoubtedly, if we start from any given fact of thought, as, e.g., a judgment, and inquire what can be exhibited as involved in it, we have before us a problem of analysis, the solution of which must take form in a series of positions and negations ; but our thinking is not therefore as a whole mere analysis. The synthetic process by which connections of thought among the objects of our conscious experience are established is not the mechanical aggregation of elementary parts. The relations which give intelligible significance to our experience are not simply those of identity and non- identity. It is an altogether abstract and external view of thought, resting in all prob- ability on an obscure metaphysical principle,^ that would treat it as in essence the composition and decomposition * See Die Begriffslfhre oder Logik (1872), p. 48. Schroder {op. cit.) follows Qrassmann, though with the use of class phraseology. - Aa above noted, p. 147 sq. 158 HISTOKY OF LOGIC of elementary atoms, of Trpwra as Antisthenes would have called them. It has, indeed, been imagined that a symbolic logic might be developed which should be independent in all its fundamental axioms of any metaphysical or psy- chological assumptions ; but this is an illusion. No logical method can be developed save from a most definite con- ception of the essential nature and modus operandi of thinking ; and any system of symbolic logic finds it neces- sary, if it is to be complete and consistent, to adopt some such view as that above criticised, to regard thought as purely analytic, as dealing with compounds or units which are themselves highly complex products, only to be formed by a kind of thought not recognised among logical pro- cesses.^ 39. Formal logic, then, in the ordinary acceptation of that term, does not appear to furnish any adequate rep- resentation of the real process and method of thought. Any logical theory must of necessity be formal, i.e., abstract or general ; for it can consider only the general elements of thought, not specific knowledge in which are involved the finite, limited relations of one fact or class of facts to another. The distinction between logic and the sciences is therefore precisely that between philosophy in general and the sciences. Attempts have been made to include in logical analysis the treatment of scientific method, i.e., to discuss as matter of logic the varied processes by which scientific results have been attained. It is true that logical consideration must extend to the notions through which scientific experience, like any other, ' The game fact has been noted in regard to formal logic of the K-intian school, as, e.g., in Manael's distinction of psychological and logical judgments. CRITICISM OF LOGICAL SCHOOLS 159 becomes intelligible, and, in so far as scientific method is but the application of the laws of knowledge as a whole, it is a possible, nay necessary, object of logical treatment, liut to include scientific methodology in particular, the consideration of the mechanical devices by which we strive to bring experience into conformity with our ideal of cog- nition, the discussion of methods of experiment and ob- servation, under the one head logic is an error in principle, whether we view logic in its theoretical aspect or in refer- ence to a special propaedeutic aim. Generalisations on such topics are wellnigh worthless ; they can have vitality and importance only when drawn in closest conjunction with actual scientific work. The theory of scientific method is either doctrine of knowledge treated freely or else the application of thought in connection with actual research and the ascertainment of the principles therein employed. In either case it is not susceptible of abstraction and isolated treatment. 40. There remains only, of the possible views noted, that which identified logic with the theory of knowledge, but which so defined theory of knowledge as to distinguish it from metaphysics. Tlu' (l(;signation of logic as theory of knowledge is one to which in words there can be no possible objection. It brings into the foreground what it has been the object of this article, by an historico-critical survey, to establish, that so-called logical laws, forms, and problems are hardly capable of statement, certainly incap- able of satisfactory treatment, except in the most intimate 155hnection with the principles of a theory of knowledge. To include, however, in the signification of this latter term a peculiar conception of the relation between thinking (knowing) and reality is at once to restrict the scope of 160 HISTORY OF LOGIC logic and to place an arbitrary and, one would say, an ill- founded restriction on the kind of treatment to which logical problems may be subjected. If it be really the function of logic to trace the forms and laws of knowledge, that function is all-comprehensive, and must embrace in its scope all the fundamental characteristics of experience as known. But no characteristic of experience is more pal- pable than the distinction, drawn within conscious experi- ence, between knowledge and reality. It is impossible then for a theory of knowledge to start with the assump- tion that these two exist separately, constituted each after its special fashion, but with a certain parallelism between them. In words one may refer for justification of the assumption to metaphysics, or to psychology, but, in fact, the problem so relegated to some other discipline is essen- tially a logical question, and the method of its solution exactly that which must be applied in the treatment of subordinate logical questions. Practical convenience alone can lead to any separation of the problems which under this view are referred in part to theory of knowledge and in part to metaphysics. Other and more serious difficulties of the view have been already commented on.^ 41. In sum, then, the problems and the methods which compose logic in the strictest sense of that term seem to be one with the problems and methods of the critical theory of knowledge. No other title describes so ap- propriately as that of " logical " the analysis of knowledge as such, its significance and constitution, in opposition to the quasi-historical or genetic account for which the title psychological should be retained. Were such analysis to be described as '* transcendental," no objection could be * Above, p. 127 sq. CRITICISM OF LOGICAL SCHOOLS 161 raised other than that bearing on the advisability of using a special term where a more general one is amply sufficient. Were such analysis described as prevailingly "metaphys- ical," the only answer could be that the term "metaphys- ical" has had and has many a signification, and that it is well to avoid the use of an ambiguous and question- begging epithet. Abstract speculations about the nature of reality, essences, and what not are as foreign to a genuine metaphysic as to a commonplace logic. The researches to which we would here assign the title "logical" undoubtedly include all that can supply the place of the older metaphysic, but in aim and method are so distinct that the same title cannot be borne by both. To assign so extensive a range to logical investigations enables us to see that the criteria by which at one time or another a narrower province was determined for logic are but partial expressions of the whole truth. The analysis of knowledge as such, the complete theory of the intelligible elements in conscious experience, does hold a special relation to all other subordinate branches of human thinking, whether philosophic in the ordinary sense of that term or scientific. According as one or other aspect of this relation is made prominent, there conies forward one or other of the various modes for settling the prov- ince of logic ; but these partial conceptions prove their inadequacy when development is attempted from them, and within the systems constructed in accordance with them there is of necessity continuous reference to inquiries lying beyond the prescribed limits. A certain analysis of some methods of ordinary thinking, based to a very large extent on language, and resembling in many respects grammatical study, has long been current in educational practice as logic ; and to those whose con- L 162 HISTORY OF LOGIC ception of the subject has been formed from acquaintance with this imperfect body of rules and formuliB it may appear a violent and unnecessary extension of the term to apply it to the all-comprehensive theory of knowledge. The reasons, however, are imperative ; and, as these would lead one to deny the right of this elementary practical discipline to the possession of the title, it is desirable to conclude by offering a single remark on the place and function of this currently designated logic. Not much trouble is required in order to see that the ordinary school or formal logic can lay no claim to scientific completeness. Its principles are imperfect, dubious, and most variously conceived ; it possesses no method by which development from these principles is possible ; it has no criterion by which to test the adequacy of its abstract forms as representations of the laws of concrete thinking. Accordingly it is handled, in whole and in detail, in the most distractingly various fashion, and, were it indeed en- titled to the honourable designation of logic, the prospects of that science might well be despaired of. But in fact the school logic discharges a function for which exhaustive- ness of logical analysis is not a requisite. It has a raison d'etre in the circumstance that training to abstract methods must needs be a graduated process, and that, whether as a means towards the prosecution of philosophic study in especial, or as instrument of general educational value, practice in dealing with abstract thoughts must have value. Such elementary practice naturally bases itself on the kinds of distinction apparent in the concrete thinking of those to whom it is applied ; and for this reason school logic not only connects itself with and is in a sense the development of grammar and grammatical analysis and synthesis, but CRITICISM OF LOGICAL SCHOOLS 163 may, to a limited extent, include reference to some of the simpler processes of scientific method. In all probal)ility the discord observable among the ordinary treatises on school logic is due to the want of recognition of the true place which can thus be assigned to the subject treated. The doctrine has a propaedeutic but not a scientific value. 164 Note A HISTORIES OF LOGIC No complete history of logic, apart from philosophy in general, exists; and there can be no doubt that any such history, as far at least as modern logic is concerned, must be more or less a historical review of the main philosojihical systems and of the influence they have respectively exercised on logical study. But of the Aristotelian logic, in its system and in its development throughout the ancient and mediteval epochs, we possess a most adequate history. Prantl's great work (Geschichte der Logik im Abe7idlande, i.,lS55 ; ii.,1861; iii., 1867 ; iv., 1870), extending to the close of the medicBval period, is a masterpiece of learned industry and skilled exposition. The following are some of the more important contribu- tions towards a history of logic, whether in independent works or in portions of systematic treatises ; most of them, indeed, of small value : Ramus, Scholce Dicdecticcr, bk. i. chaps. 1-8 ; Keckermann, Systema Logicce, 1598 ; Gassendi, Ojjera, i. 35-66 ; Fabricius, Specimen elenchicum historue logicce, 1699 ; Walch, Parerga Academica (1721), pp. 453- 848; Darjes, Via ad Veritatem, appendix, 1755; Bnhle, in Commentat. Soc. Gotting., vol. x. ; Fiilleborn, Beitrdge z. Gesch. d. Phil. (1794), pt. iv. pp. 160-80; Eberstein, Gesch. d. Logik u. Metaphysik hei den Deutschen von Leibnitz his a%if qejjenwdrtige Zeit (2nd ed., 1794), useful as a survey of the Wolffian logics; Calker, Denklehre (1822), pp. 12-198; Bachmann, Sys^tem der L^ogik (1828), pp. 569-644; Muss- mann, De Logicw ac Dialectics notione historica, 1828 ; HINDU SYSTEMS OF LOGIC 165 Troxler, Logik (1830), vol. ii. ; Sigwart, De historia lof/iccv inter Grcecos usque ad Socratem, 1832 ; St Hilaire, De la Loyique d'Aristote (1838), ii. pp. 93-312; Franck, Esquisse d'une histoire de la logique, 1838 ; ReifiFeiiberg, Principes de lugique, 1833 (with bibliograi)hy) ; Trendelenburg, Gesch. d. Kategorienlehre, 1816 ; Blakey, History of Lngir^ and Essay on Logic (2nd ed., 1848), with bibliographical appendix ; Hoflfniann, Grundziige einer Geschichte der liegrijf der Logik in Deutschland von Kant his Baader, 1851 ; K. Fischer, Logik u. Metaphysik (2nd ed., 1865), pp. 16-182, a valuable critique of some modern doctrines ; Rabus, Logik und Metaphysik (1868), i. pp. 123-242, excellent; Ueberweg, System der Logik (4th ed., 1874), pp. 15-66, excellent critical account ; Ragnisco, Storia critica delle Kategorie^ 1871, 2 vols. ; Rabus, Die neuesten Bestrehungen auf dem Gebiete der Logik bei den Deutschen, 1880; Harms, Ges- chichte der Logik, 1881 ; Venn, Symbolic Logic, 1881 (introduction, and pp. 405-444), a valuable contribution to the history and bibliography of the application of symbolic methods in logic. The only good bibliography of logic is that given by Rabus in his Logik u. Metaphysik, i. pp. 453- 518. Some of the older lexicons, e.g., Lipenius, Bibliotheca Realis (1685), s. vv. " Logica," " Organon," " Dialectica," contain great store of bibliographical references. A com- plete bibliography is a desideratum. Note B hindu systems of logic In almost all the Hindu systems of philosophy, as these are classified by the most recent authorities, indications are to be found of a more or less developed analysis of the process or method of reasoning, and therefore of a certain amount of logical theory. In two systems in particular the logical element is the most prominent feature. The XyAya, or logical doctrine of Gotama, is in a very special sense the Hindu logic, while in the Vaiscschika, or Atomist system of 166 HISTORY OF LOGIC Kauada, there are many expansions of or additions to the Nyihja, though the prevailing interest is not logical. The most accessible sources of information regarding the Hindu logic, Colebrooke's Essays, and Professor M. MuUer's abstract (in the appendix to Archbishop Thomson's Laws of Thought), tend to mingle in an undesirable fashion what is special to the Nyaya doctrine, and what is added by Kanada and his followers. In order to appreciate the extent to which the analysis of reasoning has been carried in these early systems, it is advisable to restrict attention to the original exposition of the Nydya. The aim of Nyaya is the attainment of perfection, of bliss, through knowledge. But, to have knowledge in a systematic and complete fashion, it is requisite that the individual should know (or should be capable of organising his know- ledge in reference to) the sixteen great topics or heads of discussion. These, as enumerated by Gotama, are — (1) proof ; (2) the objects of proof ; (3) doubt ; (4) motive ; (5) the illustration or example for discussion ; (G) the final assertion ; (7) the enumeration of the five members of the final assertion ; (8) confirmatory argument ; (9) the con- clusion, the defined judgment; (10) the objection; (11) controversy; (12) deceptive counter argument; (13) ap- parent reason or sophism ; (14) fraud or wilfully deceptive argument, ruse; (15) futile argument or self-contradictory counter argument; (16) conclusive refutation. Inspection of these at once shows that they represent stages in dialectic or in the process of clearing up knowledge by discussion. The generalia, i.e., the kinds of proof, described as four in number — sense-perception, inference (either from cause to effect, from effect to cause, or from community of nature, i.e., in a wide sense, analogy), comparison (analogy in a stricter significance), tradition — and the things about which proof may be exercised, under which a twelvefold division is given by Gotama, and enlarged in endless detail by his commentators, who introduce thereunder much of Kanada's system, are fir.st laid down as the basis for the whole. Then follows (Nos. 3-6) the progress from doubt, which first calls for reasoning or proof, through motive, to position of the problem in the form of an example or case, and to the general a.ssertion, as having valid grounds. HINDU SYSTEMS OF LOGIC 167 The analysis of the grounds of assertion is then given, and here we have what corresponds more particularly to the syllogism as known to us. Five members are signalised : (1) the thesis or proposition to be proved; (2) the reason, or intermediate ground by which the subject of the propo- sition is linked on to an explanatory principle ; (3) the explanatory principle ; (4) the application of this explanatory principle ; (5) the statement of the conclusion as following from the application. Thus, in the example usually given — (1) thesis, this mountain is fiery; (2) intermediate ground, because it smokes ; (3) explanatory jyrincijjle, whatever smokes is fiery, as, for instance, a hearth ; (4) a]>plication, therefore this mountain is fiery ; (5) statement of conclusion, the mountain, then, is fiery, because it smokes. There can be no doubt that in this somewhat unsystematic arrangement we have the outlines of syllogistic argument. Considerable obscurity, however, rests over the third member, and it is only partially cleared up when we proceed to the next topic, which may perhaps be translated confirmatory argument. Here the essence of the argument appears to be a regress from the known mark to the fundamental quality from which it follows. Thus, e.g., if it were said the mountain is not fiery, then the argument would be adduced, but the mountain smokes, and what is not fiery does not smoke. Apparently there is involved the assumption that the mark is a necessary consequence of the primary quality, but the exposition is obscure, and, doubtless, connects itself with the principles of causal connection recognised by Hindu thinkers. (See Williams, as below, pp. 73-4). When the conclusion has thus been confirmed, when the negation of the ground has been shown to fail in explaining the observed fact, the thesis may be stated in an absolute and definitive form (topic 9). The remaining seven topics are then concerned with the discussion which may arise when an opponent brings forward objections to the con- clusion. This he must do by positing his antithesis (10), whereupon issue may be joined (11). Should the adversary be unable to establish his antithesis, he may resort to deceit, bringing forward arguments, illogically arranged and devoid of force (12), which soon leads to the employment of sophisms (13) or merely apparent arguments, and even to 168 HISTORY OF LOGIC deceitful ruses (14). Under these topics the Nydya signalises and discusses various well-known forms of fallacy. The destruction of all these fallacious arguments reduces the opponent to the employment of futile, irrelevant responses, which undermine his own position (15), and the exposure of which completes his discomfiture and reduces him to silence (IG). Expositions of this dialectic system are not yet available in such kind and amount as would enable one to do full justice to it. Evidently much patience and a very consider- able knowledge of the current philosophical view would be requisite in order to ai)preciate at their true worth many apparently formal, and in some cases dubious, divisions. Of accounts which may be consulted the following seem the more important : Colebrooke's Essays on the Reiigion and Philosophy of the Hindus, from which the expositions in Hitter {Ges. d. Phil., iv. 382 sq.), Hegel (Werke, xiii. 161- 167), and Cousin (Ilistoire Generale, Lecon ii.) are taken; Ward's Account of the History, Literature, and Religion of the Hindoos (4 vols., 1811 ; later editions, with tiule altered, in 1815, 1817, 1821) ; Windischmann, Philosoplde irii Fort- gange der Weltgeschichte (1834), specially pp. 1895-1920; M. Miiller, appendix to Thomson's Laws of Thought ; Rozenkranz, Die Modificationen der Logik (1846), pp. 184- 97. Williams, Indian Wisdom, pp. 71-88 ; St Hilaire, articles " Indiens," " Gotama," " Nyaya," " Kanada," in the Dictionnaire Philosophique, and translation, with com- mentary, of part of Gotama's " SUtras," in the Memoires de V Academie des Sciences Morales et Politiques, torn. iii. Note C RAMUS The logical theories of Ramus acquired for a brief period a factitious importance from their connection with the general revolt against Aristotelianism, and with the Protestant struggle against the Roman Catholic authority. RAMUS 169 In themsolves they have no particular value, nor indeed much originality, and the exposition of them by their author, always rather literary than philosophic, adds nothing of strength or interest. In comparison with the Aristotelian analysis of the forms and methods of thinking, the few alterations of statement, and generally the thin residuum of logical theory, which characterise Kamist work, appear as singularly insignificant. Nor have any of the si)ecial peculiarities of tlie Kamist logic exercised influence on the history of logical doctrines. The keenness of the controversy which raged in so many of the centres of learning between the Aristotelians and the total or partial Ramists is explic- able only as having reference to differences which were merely symbolised by the apparent difference in logical doctrine. In the Protestant universities and seminaries generally the Kamist logic obtained, and for some time kept, a firm footing. In Scotland, through Melville, Buchanan, and the Earl of Murray, who had been a pupil of Kamus, his system was installed as the orthodox staple of logical training, and such records as remain of Scottish university education during the troubled sixteenth century would undoubtedly exhibit the traces of this new movement. In England, Cambridge alone, always disposed to reject the authority of Aristotle, and generally more open to new ideas than the sister university, was a stronghold of llaniism, and, apart from special works of Kamist tendency, the influence of the new doctrine is discernible in the writings of more than one Cambridge alumnus. William Temple, a friend of Sir Philip Sidney, and an official of the university, published a volume of Scholia in Kami Dialeclicam, 1591 ; George Downam, praelector on logic, wrote commentaries In Petri Rami Dialecticavi, 1606; and Milton, in 1672, expanded the Dialectica in his Artis Logicce Plenior Instittciio. Mar- lowe's Faiishcs, and his Massacre of St Bartholomew, show how familiar Kamist phraseology and the personality of Kamus must have been to an alumnus of Cambridge, while Bacon, with well-grounded objection to much of the Kamist method, expounds the system of logic with unmistakable reference to the Kamist principles and method of arrange- ment. There is a monograph on Kamus by Ch. Waddington 170 HISTORY OF LOGIC with a good bibliography — Ramus {Pierre de la Ramee) : sa Vie, ses Ecrits, et ses Opinions, Paris, 1856 — and a slighter work, mainly biographical, by Ch. Desmaze (P. Ramus, Professeur au Colle;8e/xtav o-vfMTrXoKijv Xeyo/xevoiv), each signifies either Substance (ouo-ia), or Quantity (iroa-ov), or Quality (ttolov), or Eelation (■n-p6<; tl), or Where (i.e., Place, ttoS), or When (i.e., Time, ttotc), or Position {Kua-Oai), or Possession (€xe"')j or Action {iroulv), or Passion (Tratrxctv). Ovcxia, the first category, is subdivided into irpoWr] ovaia or primary sub- stance, which is defined to be roSe n, the singular thing in which properties inhere, and to which predicates are at- tached, and SevTepai ovcriai, genera or species which can be predicated of primary substances, and are therefore ovo-ta only in a secondary sense, N'evertheless, they too, after a certain fashion, signify the singular thing, ro'Se n (Cafeg., p. 3b 12, 13). It is this doctrine of Trpwrr) ovo-ta that has raised doubts with regard to the authenticity of the Cate- gorice. But the tenfold classification, which has also been captiously objected to, is given in an acknowledged writing of Aristotle's (see Tojnca, i. 9, p. 103b 20).^ At the same time it is at least remarkable that in two places where the enumeration seems intended to be complete (3Iet., p. 1017a 25 ; An. Pos., i. 22, p. 83a 21), only eight are mentioned, ex€iv and KiiaOai being omitted. In other passages^ six, five, four, and three are given, frequently with some addi- tion, such as KoX at aXAttt Karqyopiai. It is also to be observed that, despite of this wavering, distinct intimations are given by Aristotle that he regarded his list as complete, and he uses phrases which would seem to indicate that the division had been exhaustively carried out. He admits certainly that some predicates which come under one cate- gory might be referred to another, but he declines to deduce ' Against this passage even the cross-grained Prantl can raise no objection of any moment ; see 6es. der Lorjik, i. 206, n. "^ See Bonitz, Index Arislotclicus, s.v., and Prantl, Oeg, d. Log., i. 207. CATEGORY 177 all from one highest class, or to recognise any relation of subordination among the several classes. The full import of the categories will never be adequately reached from the point of view taken up in the Categorice, which bears all the marks of an early and preliminary study. For true understanding we must turn to the Aleta- pJiysics, where the doctrine is handled at large. The dis- cussion of Being in that work starts with a distinction that at once gives us a clue. To ov is spoken of in many ways ; of these four are classified — to ov Kara avfjifiifirjKos, to w ws a\r}6€<;, to oi' Swdfia kol ivfpycLa, and to ov Kara to. crx^fiaTa toiv KaTrjyopiwv. It is evident from this that the categories can be regarded neither as purely logical nor as purely metaphysical elements. They indicate the general forms or ways in which Being can be predicated ; they are determinations of Being regarded as an object of thought, and consequently as matter of speech. It becomes apparent i also why the analysis of the categories starts from the singular thing, for it is the primary form under which all that is becomes object of knowledge, and the other cate- gories modify or qualify this real individual. IlavTa 8e to. yiyv6fx.€va viro t€ tivos ytyveTat Koi Ik tivos /cai Tt. To oe Tt' Acyco KaG' €KacrTr]v Karqyopiav rj yap roSe -q irocrov t] ttolov rj TTov {Met., p. 1032a 13-15). . . . The categories, there- fore, are not logical forms but real predicates ; they are the general modes in which Being may be expressed. The definite thing, that which comes forward in the process from potentiality to full actuality, can only appear and be spoken of under forms of individuality, quality, quantity, and so on. The nine later categories all denote entity in a certain imperfect fashion. The categories then are not to be regarded as heads of predicates, the framework into whicli predicates can be M 178 HISTOKY OF LOGIC thrown. Thoy are real determinations of Being — allgemeine Bestimmtheiten, as Hegel calls them. They are not summa genera of existences, still less are they to be explained as a classification of nameable things in general. The objections Mill has taken to the list are entirely irrelevant, and would only have significance if the categories were really — what they are not — an exhaustive division of concrete existences, Grote's view (Aristotle, i. 108) that Aristotle drew up his list by examining various popular propositions, and throw- ing the different predicates into genera, " according as they stood in different logical relation to the subject," has no foundation. The relation of the predicate category to the subject is not entirely a logical one ; it is a relation of real existence, and wants the essential marks of the proposi- tion al form. The logical relations of to ov are provided for otherwise than by the categories. Aristotle has given no intimation of the course of thought by which he was led to his tenfold arrangement, and it seems hopeless to discover it. Trendelenburg in various essays has worked out the idea that the root of the matter is to be found in grammatical considerations, that the categories originated from investigations into grammatical functions, and that a correspondence will be found to obtain between categories and parts of speech. Thus, Substance corresponds to noun substantive, Quantity and Quality to the adjective. Relation partly to the comparative degree and perhaps to the preposition. When and Where to the adverbs of time and place. Action to the active, Passion to the passive of the verb, Position (Kcto-^at) to the intransitive verb, ex^'"^ ^° ^^^ peculiar Greek perfect. That there should be a very close correspondence between the categories and grammatical elements is by no means surprising; that the one were deduced from the other is CATEGORY 179 both philosophically and historically improbable. Eefer- ence to the detailed criticisms of Trendelenburg by Ritter, Bonitz, and Zeller will be sufficient. Aristotle has also left us in doubt on another point. Why should there be only ten categories 1 and why should these be the ten? Kant and Hegel, it is well known, signalise as the great defect in the Aristotelian categories the want of a principle, and yet some of Aristotle's expres- sions would warrant the inference that he had a principle, and that he thought his arrangement exhaustive. The leading idea of all later attempts at reduction to unity of principle, the division into substance and accident, was undoubtedly not overlooked by Aristotle, and Brentano has collected with great diligence passages which indicate how the complete list might have been deduced from this primary distinction. His tabular arrangements (pp. 175, 177) are particularly deserving of attention. The results, however, are hardly beyond the reach of doubt. There was no fundamental change in the doctrine of the categories from the time of Aristotle to that of Kant, and only two proposed re-classifications are of such import- ance as to require notice. The Stoics adopted a fivefold arrangement of highest classes, yeviKwraTa. To 6v or rt. Being, or somewhat in general, was subdivided into vttoku- [xeva or subjects, Troia or qualities in general, Avhich give definiteness to the blank subject, ttws exovra, modes which further determine the subject, and irp6<; tl ttws ix'^vra, definite relative modes. These categories are so related that each involves the existence of one higher than itself, thus there cannot be a Trpo's n Trwg cxov which does not rest upon or imply a ttws ^x^v, but ttw? txov is impossible with- 1 Brentano, Bedeutung des Scienden nach Aristotcles, pp. 148- 178. 180 HISTOKY OF LOGIC out TToioV, which only exists in inroK^i^evov, a form or phase of TO OV?- Plotinus, after a lengthy critique of Aristotle's categories, sets out a twofold list. To Iv, Klvrj. 577. CATEGORY 189 meaning, and the subordinate categories evolve themselves by no principle, but are arranged after a formal and quite arbitrary manner. They are never brought into connection with thought itself, nor could they be shown to spring from its nature and relations. J. S. Mill has presented, " as a substitute for the abortive classification of Existences, termed the categories of Aris- totle," the following as an enumeration of all nameable things : (1) Feelings, or states of consciousness ; (2) The minds which experience these feelings ; (3) Bodies, or external objects which excite certain of those feelings ; (4) Successions and coexistences, likenesses and unlikenesses, between feelings or states of consciousness. -"^ This classi- fication proceeds on a quite peculiar view of the categories, and is only presented here for the sake of completeness. Trendelenburg, Geschichte der Kategorienlekre, 1846 ; Ragnisco, Storia critica delle Categoine, 2 vols. 1871. For Aristotle's doctrine the most important, in additicm to Brandis, Zeller, and the above, are llonitz, Sifzicngsher. d. kun. Akad. d. Wisseu., Wien, 1853, pp. 591-645; Prantl, Ges. d. Logik, i. ; and Brentano, Bedeutung des Seienden nach Aristoteles, 1862. See also Schupi)e, Die Kategorien des Aristoteles, 1866 ; Grote's Aristotle, i. ; and the trans- lations of the Categorice by Maimon, 1794, and Heydenreich, 1835. * Logic, i. 83 ; cf. Bain, Deductive Logic, App. C. 190 n LOTZE S LOGIC The translation of the volumes in which Lotze, towards the close of his long career as thinker and teacher, began to arrange in systematic form the ripest fruits of his reflection, is a contribution of the highest value to English philosophical literature. The Logic and the Metaphysic — the untimely death of the author has deprived us of his work on Practical Philosophy — contain a treatment of the main speculative problems distinguished by acuteness, breadth of knowledge, critical caution, and profound sense of the deep importance of the questions discussed. The historical position of the author gives to these volumes a unique interest. For Lotze might fairly have been de- scribed as the one remaining link of connection between the great epoch of systematic speculation in Germany and the more recent age of detailed, scientific research. The character of his mind reflected his historical position, ^o thinker of any time has more thoroughly combined the speculative instinct of the constructive philosopher with the cautiou.s, practical attitude of the trained scientific investigator. If it be the ideal of the philosopher to work ' Mintl, Januarj' 1885. — A critical notice of the English transla- tion of Lotze's Lofjic (Oxford, 1884), lotze's logic 191 into a harmonious conception those thoughts which are the deepest,' most far-reaching, most characteristic of his age, it would be hard to point to any one who has realised the ideal more thoroughly than Lotze. Lotze's very excellences as a thinker, however, have their consequent defects. His training had given him a profound distrust of constructive metaphysics, a distrust so strong as to be sometimes, if not unintelligent, at least unjust. Yet he is animated by the true speculative impulse, and through the panoply of his cautious reserve the reader of his earlier works could obtain partial glimpses of a comprehensive, well-knit metaphysical idea. The excessive caution of the writer rendered it hard to form any complete notion of his deepest views, and the several parts of his work had, therefore, all the obscurity that belongs to the isolated fragments of an imperfectly known whole. Even in these latest volumes, in which the manner is more scholastic, more regularly expository than was Lotze's wont, something of the same obscurity is to be detected. The various assumptions, distinctions, views, through which the exposition proceeds, wait for justifica- tion from the completed whole ; even his metaphysic is not fairly before us, since we still want his treatment of the philosophy of religion. The close interdependence of the several parts of Lotze's work is certainly in no sense an objection to them. On the contrary, Lotze's writing has no more valuable lesson to give the student of philosophy than to teach him the impossibility of abstracting and isolating within its magic sphere. But the continuous feeling of interdepend- ence renders the exposition difficult, and in the Logic these difficulties seem to me of a very peculiar and instructive kind, 192 HISTORY OF LOGIC Before proceeding to give some account of what Lotze embodies under the old title of Logic, I may be allowed to express to the translators and editor of the volume the feelings of gratitude and respect for their labour which I feel assured all students of Logic in this country will share with me. The volume ought to do much for the study of Logic in England, and the translation, if not positively attractive as a piece of English, will at aU events not repel or unduly baffle a reader. Lotze's style is never easy to reproduce ; it always has considerable force and eloquence, while in his latest work it is unusually compressed and full of meaning. An elegant version in English could not be forced within the bounds of the original, and the present translation, which, so far as I can judge, is extremely faithful and accurate, suffers only from the inevitable evil of compression. The translators— for the task has been co-operative — have done their work with great ability, and the editor is to be congratulated on the wonderfully uniform style which the whole presents. I have not examined the whole translation minutely, but a selection of certain chapters yielded so small a number of weaknesses, and these of so unimportant a kind, as to confirm the general impression derived from inspection of the whole. The rendering of technical terms has also been very success- fully achieved, though due uniformity is not always main- tained. The rendering " conception and association " for " Fassung und Verkniipfung " (p. 406) is somewhat misleading. The Logic, as the title specifically indicates, falls into three books or sections. The first of these, Pure Logic, or Thought, is a systematic exposition of the forms in which the logical activity of mind proceeds. The second, Applied Logic, or Investigation, is a much less .systematic lotze's logic 193 treatment of the various ways in which the confused, entangled mass of concrete experience is brought into conformity to the ideal forms of logical connection. The third, Methodology, or Knowledge, is a free discussion of the fundamental problem which emerges from the exposi- tion of the logical activity of mind, the problem of the foundation of knowledge, of the relation between the forms of connection making up the logical ideal and the nature of the real to which experience points. In all three books the reader will find not merely much that will throw light upon logical difficulties, much that will suggest problems of a subtle and profound character, much that may correct hastily adopted theories, but also, to put it generally, a quantity of philosophic thinking so elevated in tone, so sagacious in procedure, as to afford mental exercise of the mo.st improving kind. There is no logician who will not learn much from Lotze's work. On the multitude of interesting detailed questions that appear throughout the volume I do not propose to say anything, and in particular, I must here omit all that concerns the treatment of the commonly called Inductive Logic in the Second Book. The general point of view from which the methods of research are regarded seems to m.e most excellent ; indeed, the only point from which they can be consistently and with profit regarded. And I merely call attention to the weighty and well-expressed note in which Lotze gives his opinion on the logical calculus. With regard to the whole Second Book, however, one must take the advice Lotze offers in his preface, " to regard it as an open market, where the reailcr may simply pass by the goods he does not want." It is more critical than systematic, and the treatment strengthens the opinion, which one might defend on general grounds, that the methods of scientific investiga- N 194 HISTORY OF LOGIC tion and proof are not capable of being thrown into a rigidh^ coherent and logical form. The main interest of the work is to be found in the general idea of the logical activity of thought which inspires the whole, and out of which the characteristics of the familiar logical forms are developed. It is by no means easy to give a complete account of this general idea, and Lotze has himself preferred to allow its features to become apparent in and through the details of the exposi- tion. He deliberately declines to formulate his view as an introduction, either in the way of describing and assigning its exact position to the logical act or in the equivalent way of discussing the place Logic is to hold in a systematic scheme of philosophy. It is of service for the reader of the present work to consult the earlier treatment of Logic which the author put forward under the mors immediate influence of the philosophical tendencies of the last genera- tion, and which in essentials is reproduced in the first book of his later treatise. In the introduction to the small but richly suggestive Lorjic of 1843, Lotze discussed two main conceptions of Logic, those of Herbart and Hegel, by comparison with which he was enabled to define the two main features of his own doctrine, features which reappear, though less explicitly put forward, in the later work. On the one hand, while sharing with Herbart the view that the logical forms are to be assigned to the activity of thought, an activity of one specific mode of mental exist- ence, he dissents from the conclusion which Herbart drew, that these logical forms had no validity or significance other than that which belonged to them as specially complicated expressions of the psychological mechanism. From psy- chology, from the natural history of the mental life, no light, he held, could be thrown on that which is the very essence lotze's logic 195 of the activity of thought. The same dissent led him to reject the purely formal functions which by Herbart were assigned to the logical connections of ideas. It would do injustice to the meaning of the notion, the judgment, the syllogism, if these were regarded simply as ways in which consistent ideas were put together, or inconsistent ideas held asunder. When we reflect over the real content of the several acts of conceiving, judging, reasoning, we cannot resist the conclusion that their significance is not exhausted by the mere statement of the mechanical conditions under which psychical facts combine or oppose one another. The unique objective reference which is essential to thought is not explicable in the terms ap propriate to the natural history of ideas. On the other hand, Lotze as strongly dissented from the Hegelian conception of Logic, in which it appeared to him an arbitrary and indefensible identification of thought and reality was the mother-error. Thinking and reality are in essence distinct ; however close may be their relations to one another, and however the two may stand as parts of the sum total of being, they are not rashly and as a first step to be identified. The conception of a Logic which should be at once an exhibition of the ways in which thought proceeds and of the essential forms of reality seemed to him confused and misleading. Thought after all is reconstructive in character ; as he puts it in his later Avork, " the human mind does not stand at the centre of things but has a modest position somewhere in the extreme ramifications of reality." The formation of knowledge is a gradual process, and it would be absurd to suppose that there is even a precise correspondence, much less a sub- stantitd identity, between the tentative eilects of thinking and the modes of real existence. 196 HISTORY OF LOGIC As in contrast to these opposed conceptions of Logic, Lotze contemplates the middle course which at once recognises the essentially siihjedive or formal character of the activity of thought, and at the same time gives full justice to the claim, which thought at all events makes for itself, to be in close relation with reality. " Logic is certainly formal in the sense that it is a theory of the operations of thinking through which the subject works its thought into knowledge ; it is as certainly not formal in the sense that these forms of thought are mere psychical facts standing in no express relation to the problem of knowing the real. Logic is certainly not real, in the sense that its forms are elements of the essence of things, but it is real, in so far as these forms depend on elements of the essence of things, in that there lie in the nature of things motives which constrain the thinking spirit to take in the movement of its own thought exactly those forms of apprehending and conjoining objective fact " (Zo^^Vi:, 1843, }). 13). In the introduction to the present work, a sliorter course is taken to define provisionally the scope of Logic, and the needful explanations appear only in the course of the detailed expositions. Thought as a specific function of the thinking spirit, operating on the material supplied in and through the mere mechanism of the soul, is taken to be a means to knowing. As means or instrument, it unites characteristics of its own and of that which stands as its correlate, the real to be known. It needs hardly to be said that even a provisional statement, the import of which is so grave, demands the most careful scrutiny. In terras it reads like much that one has been accustomed to meet in the ordinary text-books ; the signifi- cance which Lotze attaches to it can only be understood when the whole of his work is taken into account, and it LOTZES LOGIC 197 is possible that a critic, with the utmost desire to be fair, may do injustice to a proposition so many-sided and subtle. The earlier Locjic was rather more open in its explana- tions. We read there that thought has its own specific nature, and therefore its forms have a character distinguish- ing them from the real which under any supposition is contrasted with thought. At the same time, these forms of thought, the acts of thinking, have a colouring due to the nature of the real or to something which is even more closely connected with the real than thought itself. This something is more closely defined as the metaphysical categories, the ultimate assumptions ( Voraussetzungen is the term used) which reason finds itself compelled to make in regard to the real. Thus thought holds a peculiar and intermediate position. On the one hand, it is opposed to, and distinct from, the mere sequence and combinations of psychical experience, which the natural laws of mind bring forward ; in each of its acts and forms there may be traced the special feature of critical reference to a ground or determining condition ; and the succession of logical acts may be regarded as a series of steps through which the critical activity of thought proceeds in the attempt to arrange the whole material of experience as a coherent, determined reconstruction of reality. On the other hand, the forms of thought are not identical with the fundamental assumptions of reason in respect to the nature of the real ; they are but ways in which the psychical experience, the Vorstcllungen of the thinking spirit, is brought into con- formity with these assumptions [Logik, 1813, pp. 18, 23). The later work is less ex})licit in its introductory state- ments, but its procedure manifestly turns upon the same considerations. There is implied throughout, and more fully defined in the detailed discussion, a comprehensive 198 HISTORY OF LOGIC conception in which no opposition of the real and the spiritual experience of the individual is involved. Thought, as belonging specifically to the individual thinking spirit, may, indeed must, stand in such relations with the real as follow necessarily from their conjoint existence in the sum total of being. But its nature generally, and the characteristics of its particular forms, exhibit, when scru- tinised, clear marks of the fundamental difference that obtains between them. The world of thought is the changeless, dateless realm of ideas, in which is no becoming, no development, no existence as fact. Ideas have validity, but not factual reality. They are true, but not existent. And though the animating principle of thought is, in the later work, expressed more cautiously, as the act of "adding to the reproduction or severance of a connection in ideas the accessory notion of a ground for their coherence or non-coherence," yet the exposition of the successive stages through which the principle finds realisation is dominated by the reference to metaphysical assumptions regarding the real. Much of the later work, the Third Book in particular, is but a free, semi-historical defence of the peculiar position assigned to thought. Without ofiFering for the present any criticism on the ultimate view which is involved in Lotze's method of regarding Logic, I Avould point out that Lotze finds himself in some difficulty when the question arises how the forms of this logical activity are to be discovered. It is by the notion of ground, applied to the conception of the contents of perceptive and representative experience, that is to say, by a rather easy psychological reflection, that he helps himself along, and makes the first all- important step. The mere notion of a ground for the combination or severance of ideas that may have come lotze's logic 199 about mechanically through the natural laws of mind, implies the consciousness of a tlistinction between the simi)ly subjective play of thought and the content of those thoughts which seem to enjoy a peculiar species of objective being. No question with regard to validity or truth can possibly arise until the psychological data have undergone the remarkable process to which Lotze, following earlier thinkers, gives the name of Objectification. The object, be it remarked, and Lotze is careful to remark, is not to be simply identified with the real ; it is for thought, in thought, and by thought. More closely examined, it will be seen that the act of objectifying is at once an act of positing, i.e., setting a content before one, distinguishing and comparing. The characters of the posited content, the distinctive marks by wliich one object is opposed to another, the possibility of comparing, are given, not made by thought. In particular, Lotze thinks, it is a merely fortunate fact, that the world of cognisable stuff affords means of comjmring and universalising. That things should present themselves as comparable in degree, number, and extensive quantity, is no necessity of reason, but a fact which thought has thankfully to accept, and without which its most complex acts would be deprived of their essential basis. These elementary processes, through which per- ceptive and reproductive experience receives form as knowable matter, have left traces of themselves in the fundamental types of grammatical forms ; but they are to be viewed as preceding the specifically logical acts, as pre- requisites for the critical activity of thought rather than as forming part of it. The main types of the logical act Lotze takes without further discussion. Concept, judgment, and syllogism are ways in which the problem thought sets before itself, that of reducing experience to a systematic 200 HISTORY OF LOGIC whole in which each combination or separation shall have its ground, is gradually solved. The activity of thought, which finds successively expression in the form of concept, judgment, syllogism, is a higher development of the same function through which the idea of an objective order became possible, and in its development presupposes and rests upon the results of that function. Logical thought, in fact, is to be regarded as a continuous criticism of the crudely formed experience in which ideas of individual facts and vague general representations of similarities are already given, a criticism animated by the single principle that for the conjunction or severance of facts in presentation adequate grounds can and must be disclosed. The concept, the judgment, the syllogism are modes in which coherence as opposed to mere conjunction of fact is represented. That it should be possible to obtain a coherent representa- tion is a fortunate accident, depending on an arrangement of the real contents of experience which is not itself a necessary truth ; for it is quite conceivable that, even to a spirit animated by the principle of logical connection, experience should offer a dislocated mass of isolated facts which would allow no exercise to its logical function. The same general consideration lends strength to the conclusion, for which other grounds may be adduced, that the forms of logical coherence are not to be rashly viewed as in them- selves modes of connection of the real. The relations of universal and particular, of condition and consequence, have no existence as facts. They are valid forms of thought, and have a content of their own, but they have not existence as things or even as reciprocal modes of things. What their content is Lotze allows to appear only in the course of the exposition which traces their development ; and he leaves much more obscure in the later treatise than lotze's logic 201 in the earlier Logik the answer which might be offered to the question, What determines the varieties of content? For it is not immediately apparent why the merely formal demand for coherence should obtain practical satisfaction in the way of concept, judgment, syllogism, or rather in the assumed relations of which these are the subjective modes of realisation. In the earlier Logik the reference to the ultimate metaphysical assumptions supplied a partial key to the difficulty : the concept there appeared as the mode of apprehending the logical substance ; judgment as the way in which the relations of universal and particular, of determining rule and determined instance, of conditions and consequences, relations implicit in the content, were subjectively expressed ; and syllogism as the mode of representing the systematic whole in which universal and particular, ground and consequence, rule and case are the isolated, abstract parts. In the later work, the scrutiny of the logical forms proceeds with greater freedom, and though it follows the same path, it makes less distinct reference to the underlying metaphysical question. The essence of the Concept Lotze finds in the peculiar thought which accompanies the presented or represented features, whether mere singulars of perception or generalities formed by the unconscious operation of the discursive activity, the thought of the determining rule or basis. In the process of conceiving, the object, whether a genus or an individual, is viewed as containing in its content the determining rule from which folloAvs the combination of marks making it up. This rule or logical basis is a higher universal than the mere generic image, and it is not formed by the mere omission of marks, which the ordinary logic takes to be the mode of formation of notions. Nor is the relation of rule to determined particulars exhaustively 202 HISTORY OF LOGIC given in that of whole and parts ; there fall therefore to be rejected, as but clumsy adumbrations of the truth, many of the " properties of notions " with Avhich formal logic has delighted itself. The concept, however, is an imperfect expression of the logical activity. It is itself but a transitory form, midway between the immediate, confused, and incoherent knowledge of the object which is appropriate to perception and the completed cognition in which all that enters into the object would have its value, position, and relations adequately determined. Moreover, it simply places the determining rule alongside the specific features, whether constant or variable, of the objects conceived, and leaves it undecided how, precisely, we are to understand the relation of the universal to its particulars, of the logical substance to its accidents. A more definite attempt to express the nature of the thought-relation between the opposed elements is found in tlie Judgment. The essential factor in the judgment, the copula, has no other function than to convey the notion which we form of the relation which binds the material contents of experience into conceivable coherent form. The instructive survey of the forms of judgment, occupying the two chapters of Lotze's First Book, raises many points of interest to the logician, but it is the less necessary to dwell on them since the theory has already been brought before the English reader, partly in Mr Bosanquet's " Logic as the Science of Knowledge," in Eifsays in Philosophical Criticism, partly in Mr F. H. Bradley's Principles of Logic. The main object of the survey is to determine the value of the form of judgment as a mode of expressing thought - relation among the contents of ideas {i.e., of psychologically given experience). lotze's logic 203 It is a kind of criticism hut little familiar to logicians ; Hegel only, to whom Lotze owes here and throughout much more than he is disposed to acknowledge, has subjected the form of judgment to a similar anal3'sis. Lotze himself is probably much influenced in his grouping of the modes of judgment by the general consideration of the successive grades of knowledge, from its crude in- determinate beginnings to the ideal goal of completed systematic insight ; and this consideration supplies a serviceable key to the distribution adopted. The im- personal judgment, the simplest form, while bearing on its surface the mark of the distinction into subject and predi- cate, which is at once the essence and the perplexity of the judgment, yet leaves the subject entirely undetermined, and so throAvs little or no light on the kind of relation which in judgment as such is contemplated as uniting subject and predicate. The ordinary categorical judgment, asserting that the subject is the predicate, finds itself at once met and baifled by the question. How can one determined and distinct content of thought he another? Keferences to the relation of substance and accident, thing and property, do but throw the difficulty forward and convert the simply assertive judgment into a more complex form. In his criticism of the categorical judgment Lotze traces the perplexity mainly to the contradiction between the form of judging and the law of identity ; for while the one asserts that S (which is a determinate content) U P (another determinate content), thought, proceeding under the law of identity, refuses to contemplate an S which is anything but S, a P which is anything but P. It does not seem to me that the criticism is at all furthered by the appeal to this so-called law of thought ; for the solution of the difficulty is to be found, and is found by Lotze, in 204 HISTORY OF LOGIC showing that the abstract conception of identity has no real application to the case in question. A thought which could proceed by affirming only identity of content is no thought at all. It would have been better simply to insist on the patent fact that the merely assertive judgment, the qualitative or positive judgment, fails to express what it proposes to express, fails to show how a unity is possible between the diverse logical marks of its two factors, the subject and the predicate. That the universal is in some way the particular, and vice versa, that the individual is only a determinate, fully kno^\Ti fact when more than an isolated unit, — aU this is implicit in the mere assertion contained in the simple, qualitative judgment ; but the form of the judgment is wholly inadequate to the thought which is implied in it. Lotze, however, constantly tends to view the world of thought, of ideas, as that in which the bare, abstract rule of identity is the all-supreme law, and finds in this a peculiarity of thought which effectively dis- tinguishes it from reality. Escape from the perplexity of the categorical judgment Lotze finds, first, in the transformation which the assertion undergoes when it is quantitatively determined as expressing of all, or some of the subject, the previous predicate. Even here, however, as he insists, the logical form is unequal to the task thought has imposed on it. We find ourselves either in the position of reasserting a blank identity, or reduced to a repetition of the impersonal existential judg- ment. It is only in the hypothetical judgment, which, by its very form, denies the supreme validity of the abstract rule A = A, that the logical form of thinking finds for itself a means of expressing a relation of differences that is at once a unity for thought, and yet not a blank identity. The law of sufficient reason thus stands alongside of and lotze's logic 205 supplementary to the law of identity ; yet Lotze, true to his preconception of the nature of thought, will have it that the superior and fruitful principle is of but inferior validity, that it is no necessity but a fortunate fact, an assumption " the truth of which is guaranteed by the concentrated impression of all experience." One hardly knows what to make of this, or how to understand the curious property of thought, which, subject in its own nature to an absolute law of a most stringent, but perfectly worthless character, shall yet make an assumption violating its own law and delightedly find that the thinkable world conforms thereto. It is a specimen of Lotze's excessive caution, and perhaps the consequences that would seem to follow from it might be invalidated by some portion of his metaphysical theory of the real. I note it here as bearing on the general view which animates much of the author's polemic against other philosophies. The final, most developed group of forms of judgment appears as supplying a much - needed addition to the hypothetical. In the latter, there appeared, in the only way which could satisfy thought, the principle that the individual is determined by the universal. The individual is not the universal, but it is individual only through conditions or grounds, the interconnection of which is itself represented only by a universal proposition. This inter- connection justifies and explains the quantitative determina- tion which appears in the general (or, as we might call it, abstract) judgment, in which the predicate P is asserted of S, -i.e., of any individual S, because this participates in the general characters of S from which follow as consequence the predicate P. And since it is not P vaguely or gener- ally that follows a vague, indeterminate S, but a particular modification Pj, Pg, or P^ which follows a modification of 206 HISTORY OF LOGIC S — S], S.„ or S3 — the general judgment finds its comple- ment in the disjunctive. The disjunctive judgment, again, while the completest form in which, by judgment, the unity of subject and predicate can be expressed, has its mark of imperfection in the undetermined choice of alternatives which it offers. It shadows forth the union in thought of subject and predicate ; but as it at the same time, while explicitly pointing to a systematic inter- connection as the basis of such union, does not contain the interconnection, it finds its supplement in the Syllogism, the mode of thought in which the interconnections of the conditions with that which they bring into a unity of thought is formally expressed. The serial arrangement of judgments finds its counter- part in the distribution of syllogistic forms; liut here the material for discussion is too rich to allow of any thorough examination. It is good that attention should be drawn, as Lotze's chapter cannot fail to draw it, to the precise character of the forms of inference familiar to ordinary logic as the categorical, inductive, and analogical syllogisms, and to the inadequacy of these to discharge all the work which thought has to perform in framing a logically coherent conception of experience. The more complex forms, the quantitative and the classificatory, present problems of a special character ; and on the whole one's feeling sometimes is that Lotze's method of transition is arbitrary and artificial. One misses the stringency of a connecting idea from which these varieties Avould follow, and tliough one thankfully accepts what Lotze frankly offers regarding the ideal type of completed, systematic cognition, it is not easy to understand its full drift or to perceive its bearing on other portions of his exposition. AVithout discussing these points, I proceed to notice the lotze's logic 207 general prol)lem which underlies the whole work, and which is formally though unsystematically discussed in the Third l>ook, the problem of the relation between the structure of thouglit and the nature of reality. Lotze has chosen to develop his views in a semi-historical fasliion, criticising various conceptions of value that have come forward in tlie history of speculation, and defining his position in reference to the aspects of the whole problem so presented. The problem itself may be variously defined as an inquiry into the worth for reality of the forms of thought, or as an investigation of the nature and grounds of certainty in knowledge. The discussion of Scepticism yields two important results, on one of which at least there can be little misunderstanding. That the sceptical view of knowledge implies the i)rinciple that reason is capable of attaining truth, criticising its own procedure and determin- ing the worth of grounds, is an argument not less strong because it is familiar and direct. But the radical notion of scepticism, that knowledge, by its very nature as a mediating process, as a connecting link between reality and the thinking spirit, is for ever incapable of attaining to a perfect cognisance of the real, is subtle and many-sided, requiring no small care in handling, if any result of value is to follow. Lotze, so to speak, turns the flank of the sceptical doctrine, by insisting that, after all, knowledge can be nothing but a mediating process, can be nothing but the systematising of what is given in the experience of the thinking spirit, and therefore that any question regarding the trutli of knowledge must be expressed and discussed in terms that are appropriate to the matter in hand. The abstract nature of things, which presents itself as an element in the sceptical reasoning, is after all a conception, the notion of what the order of things must be ; 208 HISTORY OF LOGIC and -the problems which scepticism had formulated in an uniutelligitDle and unanswerable fashion must be restated. It must be asked, what are the characteristics of assured and certain cognition within that world of knowledge in which only the venue lies'? One form of answer, a signifi- cant and far-reaching thought, Lotze finds in the Platonic theory of a world of Ideas ; and the discussion enables him to advance a further position of his own doctrine. The Ideal world may be the home of certain and consistent contents of thought; but the mode of existence of these thoughts, it must be definitely recognised, is not that of real being as things, or even of occurrence as events. They have validity, but not factual existence. Within themselves they may form a concatenated system, from point to point of which the thinking mind may proceed with the certainty of insight ; but Plato could not explain, nor does it seem within the scope of the theory to explain, the kind of relation which must be thought between the realm of the eternally valid ideal contents and the reality of things. Even if we allow that in the Ideas is to be found a system of interconnected parts, the Platonic teaching afforded no answer to the deeper question, What are the ultimate elements or principles, and how are they related to the dependent portions of the system 1 The attempt to answer this new problem Lotze takes to be the gist of the opposed doctrines of modern philosophy in respect to the origin of knowledge, the a priori and the empirical. His criticism rests upon a general assumption or metaphysical principle applied to the special case of interaction between the reality of things and the thinking mind (§§ 325ff.). The result of action on the mind is invariably conditioned by the nature of mind itself, and only in the special forms in which that nature expresses itself can the result make its appearance. lotze's logic 209 Experience, tlierefore, must always exliibit an a priori side, and only in experience can the a priori truths, the formulations of what is the essence of the thinking mind in its contributory function, he discovered. The necessity and universality, the self - evidence, characterising these truths, cannot he exhi])ited as resulting from isolated psychological events ; nor is it by the psychological method that insight into the peculiarity of knowing can be obtained. Throughout these discussions there has been quietly growing in strength the doctrine that the formed product, knowledge, depending as it does on the peculiar nature of the thinking spirit, has a special mode of existence, and that its modes, though doubtless corresponding to elements in the reality of things, are not themselves to be taken as forms of the real. In the fourth chapter this doctrine receives explicit statement and ample illustration. The reality which appears in the formed content of thought is " wholly dissimilar to existence and can only consist in what we have called Validity or in being predicable of the Existent." Nay, even the content apprehended in know- ledge has the peculiar timeless and changeless mode of being expressed in the Platonic Idea. It is indifferent both to the subjective movement of thought and to the changes of the empirically presented world of perception in which the real seems to be directly given. In this last clause is found the final problem for Lotze's view of thinking. How can we represent any relation between the world of thought-contents (about which we can make only one assertion as necessary for thought itself, viz., that each thought-content is itself and no other) and the changing stream of perceptive experience 1 Having brought the separations of knowledge to their ultimate form, how are we to understand the junction which appears to take 210 HISTORY OF LOGIC place 1 The answer which Lotze makes depends to a large extent on the manner in Mhich the separations have been expressed, but it is fairly given in the three positions signalised by him. First, any assertion within the sphere of knowledge regarding real existence is hypothetical. Secondly, we must assume that the empirical, perceptive world has law in itself. Thirdly, we may obtain, by a scrutiny of perceptive experience itself, certain directly given synthetical truths, on the basis of which thought, discursively proceeding by its own formal rules, may confidently hope to erect a structure of knowledge that shall not only be consistent but in harmony with the laws of fact. On the first and second of these positions I offer no remark ; they are simple statements in appearance, but in reality conceal a whole philosophy. The third is the most interesting, for it brings to the front the question which throughout the Logic has been in the background : To what extent has Lotze succeeded in justifying his restriction of the functions of thought to the discursive, mediating act of passing from premisses to conclusion? On this limitation depends the worth of his separation between logical and metaphysical relations, and the validity of his general view of the logical forms. Thought has been placed in opposition to the real, as antithetical to, though corresponding in some way with, it ; in the move- ment of thinking the apprehended content has inevitably found expression in the forms of concept, judgment, syllogism ; yet these forms, it is insisted, are in no way relations of the real. Now we find Lotze introducing a new distinction, from which would follow a far more .serious restriction of the function of thought, a much more limited notion of the significance of the logical forms. Dealing with knowledge, he reinstates the Kantian doc- lotze's logic 211 trine of synthetical a x>^iori judj^Tnents, assigns these, however, in a thoroughly un-Kantian fashion to a perception which does not contain the element of thought, and regards them as self-evident, intuitively grasjjcd data, from which the discursive, claborative activity of thouglit may proceed in the construction of a knowledge that adequately rep- resents the real. One would raise little or no objection to what is said regarding the self-evidence of these data, and the necessity in the long run of resting knowledge on self- evidoncing judgments ; there is here, doubtless, one of those fruitless problems of philosophy which owe their origin and interest to the enormous difficulties of stating simple facts. But one cannot avoid asking, What, then, in their nature, are these primitive data? Are they judgments, apprehensions of a connection in real fact, which by inherent light approve themselves as being connections in fact and not merely subjective modes of apprehending 1 Only the affirmative answer can be yielded by Lotze, though, as was said, he prefers to disguise the answer by using the term " perception." If then we insist that thought has only to deal in the fashion of elaboration with such formed products, we must recognise that, in so using the term " thought," we refer not to that which is responsible for the specifically logical forms of concept, judgment, and syllogism, but to the mode in which thinking as a phase of the concrete psychical life of the individual mind is carried out. We can no longer maintain that to thought are assignable the fundamental arrangements that make up the essence of concept or judgment ; by thought can only be meant the special exercise of dealing with material already formed, in the modes which we have called the forms of judgment and concept. That there may be such a discursive exercise may pass without further question ; the restriction of the 212 HISTORY OF LOGIC word " thought " to it has no justification, and it excludes us from regarding the logical forms as in any way expressing the essence of thought. It is not from one portion only of Lotze's exposition that one would reach the same result. Looking back on his account of the procedure of thought, we find that he starts his survey of the logical activity with the presupposition that material for thought has already received a special handling, has already been formed into definite objects, with distinguishable and comparable marks ; and, moreover, in the history of the logical activity, the somewhat vague notion of ground has been made to play a very remarkable part. For under its cover there have been quietly introduced into the contents of thought, of the concept, e.g., the all- important features, aspects, of determining and determined, of essence and appearance, of law and modifying circum- stance. If one asks, — "What, then, are these aspects of the objective content conceived (apprehended in form of a concept) % Are they thoughts ? — • no explicit answer is given. Lotze has been consistent in holding that under- neath the logical operation of thought, in the wider sense in which he used that term, there have always lain the metaphysical assumptions ; but he has never fairly faced the question whether these are not in their essence thoughts. The difficulty of accommodating the logical activity to these ultimate determinations of objective reality becomes still greater when his narrower conception of thought, as a merely elaborative, mediating process, is to the front. For then one may fairly ask : If knowledge, the whole structure that is due to the operation of discursive thinking, be based on immediate data, which are in form judgments, but which cannot be exhausted by the one law of discursive thought ; if the procedure of thought involve throughout lotze's logic 213 determinations that are not traceable to the activity by which notions, judgments, and syllogisms as modes of elaborating come about ; if, finally, the ideal which thought involves cannot be expressed as the reduction of experience to an analytical whole, — is it not entirely without justifica- tion to identify the discursive activity with thought? Are not the accompanying features of this discursive process the genuine characteristics that make up the essence of thought 1 and is not the discursive process itself but a phase of the concrete life of spirit, the analytical effort of understanding ] It is the opposition between the apparently timeless and changeless content of thought, and the changing, temporally modified content of perceived reality that weighs most with Lotze and causes him to distinguish so sharply Logic from Metaphysic ; yet without diminishing the opposition, one may well doubt the interpretation he has given of it and the conclusion he draws from it. "Were one to allow to the fullest extent that the essential aspects of the real, those by which it is intelligible for us, are in their nature "thoughts," and that " thought " is but another name for the system of such thoughts, one would still recognise that, when thought is taken in abstraction from the concrete reality of thinking mind and external reality, it presents the timeless and changeless character of the Platonic Idea. But such result is due to the abstraction that has been made ; it is we who make the opposition, not the nature of things ; and the characteristic of the realm of ideas attaches to it not as an entity in itself, existing in isolation from the real, but as an ahdradum with no independent, factual exidence, not even existence of a kind different from that of the real. The world of thought per se is truly a " king- dom of shadows " when we compare it with the full reality of concrete existence, but not on this account should we 214 HISTORY OF LOGIC suppose that thought is somehow divorced from things and has but a formal function in their regard. The perplexities to which such a supposition leads take ample vengeance for the error of mistaking a distinction in thought for a distinction of thought from things. The minor oppositions which prey upon Lotze seem to connect themselves with the same fundamental consider- ation. The life of the individual subject contains no perfect picture of the world of being; that there shauld be much in it which but imperfectly represents the real relations of things — that the human mind should pursue many a devious path and be liable to varied error — is hardly surprising; and one need not on that account suppose an original and impassable separation between reality and knowledge. The consideration of the ways in which our thinking attains to knowledge, of the methods by which crude imperfect experience is transformed, belongs to Psychology rather than to Logic. In sum, what Lotze has marked off as Logic seems to be no independent doctrine, but in part the fragment of a larger whole, the treatment of thought, which is Metaphysic, in part belonging to the history of the development of knowledge in the individual mind, which is Psychology. That Lotze uses Psychology in a narrower sense, that he tends to contrast the psychical mechanism with thought, may be regarded as an expression of the deep-seated disinclination he throughout manifested to contemplate a constructive, systematic philosophy. Justification for the view can be found only in his final metaphysical conception, which, at all events in large part, is accessible in the Metajjhysic. In a subsequent notice of that work, I propose to consider farther the bearings of his general philosophical position on his treatment of Logic. 215 III lotze's metaphysic ^ In the Metaphysic Lotze sums up, with ample historical auci critical detail, views which in many other fuiius he had already laid before the world. If, however, it is to be said that the work contains little absolutely new to the readers of his earlier philosophic productions, it is to be added that only in it is there given the fulness of state- ment required to make a speculative thought intelligible, and that in this, his latest efl'ort, Lotze's remarkable powers of subtle expression, wide knowledge of the mani- fold issues raised at every step in speculative construction, and keen sense of the bearings of metaphysical thought on real experience find their amplest scope and bear their richest fruit, i^o word need be said of the value of the Metaphysic as mere discipline. Instructive as Lotze's method always is, whatsoever be the matter to which it is applied, it is here more than ever of significance. The work is a monument of careful, profound, and comprehensive thinking. But it is sufficiently recognised that in Lotze, Germany and the world have lost the last representative of a great philosophical tradition, and that his works must be taken to heart by any student who desires to know how ^ Mind, October 1885. — A critical notice of the English translation of Lotze's Metaphysic (Oxford, 1884). 216 HISTORY OF LOGIC the problems of speculation still connect themselves with the ever increasing mass of special knowledge that the labours of the new generation have accumulated. Our business, at present, is solely with the one closely knit view of things that forms Lotze's metaphysical conception, a view that has given connectedness to his researches in many special fields, that has grown with his growth, and that finds here its most explicit statement. " Except in rare cases," Lotze has said,^ " a prolonged philosophical labour is nothing else but the attempt to justify, scientifically, a fundamental view of things which has been adopted in early life." There is certainly a wide difference, in form and in detail of treatment, between the Metaphysik of 1879 and the early, little appreciated work with the same title of the year 1841 ; yet the slightest comparison of their contents enables us to see that the fundamental conception has remained the same, and that the difference arises, in part, from a relinquishment of the method which in the earlier work exhibits clear traces of the then prevailing philosophy in Germany, in part, from the increased fulness of special experience with which the fundamental thought is connected. In both the funda- mental conception is that of ethical or teleological idealism — the view of the sum total of things as the unfolding of a plan, of which the significance is spiritual, of which the fixed traits are the general laws of order and connection in nature, and of which the manifestation is the varied realm of things. The manner in which a thinker arrives at his deepest conviction or is led to give definite form to his thought has always more than mere personal interest. The influences which have weighed with him, and which enter as com- ' Contemporary Review, January 1880, p. 137. lotze's metapiiysic 217 ponents into his view of things, are not to be regarded as mere external accidents ; they form the very substance and in some ways the most signiticaiit element of his views. The function of a metaphysical doctrine is to give a unity to experience, and the character of the experience taken in is an essential constituent of the doctrine itself. Lotze has not left to conjecture the task of determining what in his case were the historic circumstances under which his thought was developed. In the interesting account of his early speculative impulses given in the Streit!), with that of Lotze, Metaphysic, bk. i, cc. 4, 5. 224 HISTORY OF LOGIC but in the external form of his method he imitates Herbart, and throughout the Metaphrjsic the conceptions which he bears most constantly in mind are those of Herbart. Nor is this unnatural ; for Herbart's metaphysic has a prevail- ing air of scientific realism. Herbart's treatment of such fundamental conceptions as those of change, substance, and cause comes near to the exacter determination of ordinary thought that characterises the best scientific method, and in some departments at least, as in psychology, the results are of the most excellent kind. It is possible at the same time — and for the view one would claim the support of Lotze — that the best results of the Herbartian treatment in the concrete spheres of research are independent of the peculiarities of the Herbartian metaphysic and can be combined with a conception of the Avhole nature of reality difi'ering widely from that of Herbart. The treatment of the first fundamental notions of Ontology — being, quality, reality, and change (Book I, cc. 1-4) — is directed so consistently against Herbart's doctrines that some notice of the latter seems needful in order to seize the full meaning of the result to which Lotze slowly works up. To Herbart, the task of Ontology was the elaboration or clearing up of the notions involved in or connected with the indirect affirmation of real being given in sense-perception. Philosophy, in his view, has to start from a foundation supplied to it, has to accept something as given, and has then to endeavour so to determine the nature of the involved thoughts as to bring them into conformity with the absolutely valid laws of our thinking — the laws of identity and non-contradiction. Experience in its simplest phase, sensuous perception, no doubt ofi'ers us much that is incoherent, self-contradictory, and standing in need of elaboration ; but of one lesson it lotze's metaphysic 225 teaches there can be no doubt : it teaches that something is. Even if all the content of experience be characterised as phenomenal, even if we admit tliat sensuous perception as qualitative state of a percipient can in no way be identified with the quality — the v:hat — of the real cor- responding to it, yet the fact of perception, the order and method of perceived content — order and method which are as much given as the content ordered — force upon us the thought of an independent real from which they follow. The course of philosophy is thus arc-like : it starts from the groundwork of experience, is driven onwards and upwards to the conception of a reality that is not in experience, and has to descend again in explanation of experience with the wealth of notions that it has gathered in its progress. But the course of thought is never other than subjective. The contradictions inherent in the crude notions of experience drive us to supplement these notions and to form more complicated conceptions which allow thought without self-contradiction to deal with experience ; but the supplementing remains a work of thought merely and indicates nothing in the nature of the real itself. The related elements of a complex conception, the ways in which we consider now this, now that, aspect of the real, remain external to the real itself. Objective we may call them, if we understand by that only — valid for all finite intelligences to whom experience comes as a compound effect of the relations in which intelligence, itself a real, stands to other realities ; but they are subjective in the deeper sense, that in themselves they express only move- ments of thought, i.e., transitory states of a subject over against and inclusive of whom the realm of reality stands in unchanged, stable, motionless self-identity. The motives which animate a great thought are always P 226 HISTORY OF LOGIC SO numerous, and the value which one assigns to it depends so much on its applicability to special problems, that a brief statement can convey but little of its deepest signifi- cance. It must suffice here to draw attention to the main outlines of the conception which Herbart, following the older Eleatic and Atomist thinkers, placed in opposition to the dominant philosophy of his time. For him as for the Eleatics, the real was characterised by changelessness of being, simplicity, and permanence ; but with the Atomists, he admitted multiplicity of being. The real he found in the absolutely simple, positive, specifically qualified essences, to the notion of which he thought we were driven in order to make consistent our empirical conceptions. The real existence which seems to be given in sense-perception, the more compHcated experiences of things with qualities, of change, of interaction, seemed to him conceivable, if viewed as resulting from, or expressing, certain relations of the ultimate realities that lie beyond experience. That the real is, we affirm as a necessary supplement to experience ; what the real is, we do not know by direct perception, but we are driven to conceive of such real after the fashion of a simple quality, such as might be given in presentation. Having so determined the real, we have then to discover how, in conformity with its notion, to explain the most general conceptions of experience, the forms of our empirical knowledge, i.e.. Space, Matter, Movement, and Time, and finally Experience itself, as a series of states in a subject, which yet claims to have a peculiar relation with the real. Apart from its general speculative importance, Herbart's view derives much of its interest from the apparent cor- respondence it maintains with the popular, common-sense, everyday conception of things. It represents one line along which thought, starting from the ordinary practical lotze's metaphysic 227 mode of regarding,' the world, is compelled to proceed. We naturally and easily take as initial position the practical conception of ourselves as real, existent subjects, variously affected in consequence of the varying relations in which we stand to other real existences. The position or affirma- tion of reality in any presented content, offers itself naturally as the correlative of self-position, conviction of our own real being. An easy reflection, which doubtless conceals under its simple guise a highly complicated move- ment of thought, leads us to admit that the nature, the characteristic features of the posited real, cannot be identical with the qualitative content of the experience with which the position is connected ; but we are just as ready to maintain that nevertheless the fact of our experience, the occurring of any presented content, is sufficient warrant for the position in question. We readily allow that the apparent unity of the things, to the conception of which we have accustomed ourselves, need not be absolute ; scientific analysis renders familiar the view of apparently simple but really complex effects arising from the combina- tion of simple antecedents ; and, still carrying with us our conviction of reality as the substratum, we are willing to regard the varied field of experience as phenomenal result of unknown and unknowable real elements. Our realism easily transfigures itself. And equally simple reflections enable our first conception of things to yield certain provisional characteristics of these real elements. The diti'erence between the fulness of direct sensuous percep- tion and the unfulfilled content of a wish or purpose would be sufficient of itself, were it not confirmed by many similar distinctions, to lead us to the important discrimin- ation between subjective and objective reality and to de- termine the latter as relatively independent, permanent. 228 HISTORY OF LOGIC self - existent. Now of these and like reflections the metaphysic of Herbart contains the precise and explicit formulation. Like them, it starts from the conviction of the real nature of the affected subject ; admits that the qualitative content of affections must be viewed as de- pendent on the subject ; maintains, however, that the fact of the occurrence of these affections, and the independent ways in which they come and go, are sufficient to justify the retention of our first, primitive belief in reality ; and endeavours to give an exact formulation of the results to which reflection on the form of experience must lead. One might ask, with regard to it, whether these results do follow as supposed ; or one might ask whether the results themselves satisfy the demands of thought from which they are assumed to have followed. The latter is the line of inquiry followed by Lotze, and, although something may be lost by adopting it to the exclusion of the other, we may here consider the substance of the criticism he offers. Does the conception of the existent as made up of a multiplicity of ultimate reals, each characterised by the marks of positive quality, simplicity, independence, enable us to understand the world of experience 1 Does not the attempt to make this conception conform to the demands of thought itself lead, even in Herbart's hands, to such a transformation of it as practically to destroy its peculiar features'? One might say here that the Herbartian con- ception of the real corresponds point for point to his conception of the mental life, and most of the difficulties of the one are the difficulties of the other. There the varied flow of inner experience is viewed as the continuously altering result of the mutual interference of the several isolated Vorstellungen, each of which is and remains per- manently what it is. But it was impossible for Herbart lotze's metaphysic 229 to avoid just such an alteration of his psychological doctrine as appears to be called for in regard of the metaphysic, — an alteration, as one might briefly express it, from the mechanical conception of a multiplicity of isolated units to the conception of a real altering spiritual life. Consider, in the first place, the bare demands made in the notion of Being. Sensuous experience may appear to involve the positing, the aflirming of a single, isolated, unit of reality ; but it does so only if we allow ourselves to make a wholly false abstraction in its regard. The sensuous experience which might be conceived to have as its correlate the posited unit of reality would not be sense-perception as an act of knowing, but an abstract idea of the hypo- thetical simplest element in the psychical life. Kowhere do we find a sensuous experience which involves the position of an unrelated, absolute, real. The common-sense view of things goes no further than to the assertion that reality somehow is and is made known to us through sense-experience, nor does it ever involve the thought of real being as consisting in the absolute unrelated position of real elements. What determines for any element of existence its being is the relations in which it stands. The thought of pure being is, if we look to its genesis, an abstraction ; if we look to its content, a mere abstract. Nor does it avail to insist that relations imply related parts, the being of which must therefore be allowed as independent of the relations. Common-sense here is in complete accord with speculative thought. Being is a connected system of which the parts taken in isolation are not. And if we allow ourselves to revel in abstractions, to hypostatise, as llerbart does, unconsciously perhaps but not unfrequently, and to speak of these isolated elements as existences which enter into relations with one another, we sufler the fate 230 HISTORY OF LOGIC inevitable on all abstract procedure : we are presented with incompatible features, with a disjunction that is to be united but refuses all combination. The relatedness of being is not an internal accident of being itself ; elements wliich have not relatedness in themselves cannot enter into relations in general. Herbart, however, had the courage of his opinions. He insisted that relatedness is an external accident of the reals, that the world of true being remains for ever intact, unaffected by change, and that the ground of change, phenomenal change, is not to be sought in any mark of the real itself. But careful analysis of his procedure makes clear to us that an important modification is introduced, and necessarily introduced, into the conception of the real. Phenomenal change we accept as an experience, which, though offering insuperable difficulties to thought, is never- theless given ; and the notions involved in it must somehow be capable of explanation. Herbart's explanation appears at first sight to be merely the more exact interpretation, the translation into metaphysical terms, of the criticism which scientific analysis of the common-sense view easily yields. One readily allows that the phenomenal thing, the complex of attributes united in our apprehension as one thing, exists not as it is at first conceived ; that the multiplicity of attributes points to a multiplicity of real antecedents ; and that the unity indicates no featureless substance, but merely the identity of one and the same real in varied relations with others. Any given real. A, may be placed in relation to any number of other reals ; out of each such relation will emerge, for a spectator who is not directly cognisant of the reals but himself stands in relations, the apprehension that we call a quality or attribute ; and ])opular thought readily accommodates itself lotze's metaphysic 231 to the admission that the unity of the empirical complex is provisional. Change, in like manner, must be interpreted as the phenomenal indication of the coming and going of real relations, lint, having gone so far with Herhart, one is compelled to ask, not only whether more has been done than to express in a vivid way the primary conviction that experience rests upon reality, but whether the new inter- pretation is compatible with the metaphysical conception of the nature of the real. If the real is to be conceived as a multiplicity of simple unchangeable elements, capable of entering into relations with one another, what, for the reals themselves, is the significance of these relations'? It is in vain that Ilerbart endeavours to retain the two opposing sides of his doctrine. He cannot at once claim for the real elements their characteristic features of unchanging self- identity and find in their varying relations the ground of phenomenal change, substantiality and causality. Even if it be granted that, for a subject that stands as one real among others, varying relations will take form, will find schematic representation in the ways familiar to perceptive experience as alteration, determined sequence of states and of events, — it remains impossible to interpret the nature of these real relations in conformity with the Eleatic view of Being. Herbart himself has another mode of interpreta- tion. Change is not in any one real ; but it may follow from the reciprocal relations of the reals. For these, he thinks, may be legitimately viewed as opposing one another, and as preserving each its own identical being in the midst of opposition. Each real maintains itself against disturbance or suppression from other reals, and in this self-maintenance is to be found the secret of real action. In any one real there may thus be a series of states or conditions, expressing the ways in which it preserves itself over against the other 232 HISTOKY OF LOGIC reals that oppose themselves to it. The elaborate criticism which Lotze offers of this new conception leads directly to the heart of his own view, and it may be briefly summed up as follows. If Ave preserve our first conceptions of the reals as simple, self-identical posited contents, then opposi- tion or any kind of relation between the reals can only be thought as subjective mode of relating on the part of a conceiving mind, from which there follows no explanation at all of real action. If we desire to explain real action, and so allow that relation of the reals is more than subjective result of comparison — is something in the real world itself — then we must resign our conce})tion of the world of reals as a multiplicity of independent, distinct, self-identical units. It is not that we require to suj^plement in any way our conception of real action in order to attain this result ; we simply require to make plain to ourselves the implication of the thought. He who posits real relatedness must at the same time allow that the independence of the related elements ceases, that they become no longer changeless, permanent centres of relation, but merely the relatively fixed points in one continuously altering system. The unity and self-identity which wo demand of the real must be transferred from the hypothetical monads to the whole in which they are members. Of the substantial soundness of Lotze's criticism no reasonable doubt can be entertained. The same line of thought, though with differing form of expression, lies implicit in Kant and in Hegel. For Kant is practically expressing the same view when he insists that, so long as we attempt to conceive objects as merely logical units, interconnection of them is impossible. Objective relation is only possible in an experience connected together in the unity of a thinking subject. The very gist of Hegel's lotze's m eta PHY sic 233 philosDphy lies in the antithesis to Herbart's conception of the real nature of things as an aggregate of simple, un- changing points of relation. Lotze has his own quarrel with both Kant and Hegel, but it is animated by quite special consideratii^is and is of small importance as compared with his agreement with them on this cardinal point.^ That the real cannot be conceived after the fashion of perceived object, but only in the systematic order peculiar to the content of a notion, is a conclusion from which one may rapidly proceed to a statement of Lotze's ultimate metaphysical view. Retaining as he does the opposition between our subjective thinking and reality, Lotze is careful to maintain that the various thoughts by which we gradually correct our first conception of things are not to be taken as themselves constituting the nature of reality, but as the ways in which we construct for ourselves a view that satisfies the problems reflection brings before us. The being of things we cannot reconstruct ; we must accept the given fact of existence, and resign the inherently hopeless task of accounting for the fact that anything exists. But since we have seen that the ultimate nature of things is not to be sought in an aggregate of simple qualities, that the position characteristic of things is not to be taken as distinct from their content, that change and relatedness belong to the very essence of reality, — we are driven to conclude that the being of things is not a doom thrust upon them from without, is not the result of a union between qualities and an underlying substratum of realitj', is not a law external to the cases of its manifestation, but ^ One of the briefest s^tatements of Lotze on the problem of the nature of real relatedness will be found in the Grundziige der Religionsphilotiophic, §§14 fl'. •234 HISTORY OF LOGIC can be interpreted only as the ability to act and suffer, only as the position ■which the so-called thing occupies in a systematic whole of interconnected and mutually deter- mining reality. And. if we push further our attempt to make clear the notion of this interconnected system, we are forced to the conclusion that the absolute independence of things is an erroneous exaggeration of a truth correct enough in its proper place, and that relatedness of things is conceivable only if the so-called things be viewed as members of one fundamental unit or substance, or Absolute. Philosophy has sought out many forms of expression for the notion to which Lotze, by his own path, thus attains ; and, on the whole, criticism of them does but force upon one the extraordinary difficulties which attend any attempt to sum up in one brief formula the content of the most complex thought with which we interpret experience. It is hardly possible to avoid the abstractness attaching to the employment of any one notion as explanatory of a wide and varied complex of facts, and frequent injustice must be done in the criticism of other solutions by overlooking the inevitable narrowness of the notions through which definite formulation of a view has been sought. It is by closer scrutiny of the conception of real inter- action among so-called things that Lotze advances to a more complete determination of the chara(;teristics necessarily involved, in the thought of the all-embracing reality. If relations obtain among things, if the thought of reciprocal determination is to be taken as more than a subjective term of comparison, these relations cannot remain external to the things themselves, but must indicate changes, recipro- cally determining, in the inner states, the modes of existing, of the things them.selves. That this should be so, is but a special application of the thought which Lotze throughout lotze's METAPHYSIC 235 insists upon, tyic thought of reality as no meclianical compound of matter and form, but as itself the living, developing whole. If, further — recalling the conclusion reached, that the independence of things is but an abstrac- tion of our own thinking, and that the possibility of a reciprocal determination of inner states exists in the unity of the real in wliich all such states are — we ask what mode of existence we can ascribe to the absolute real attained, we have simply to consider what insight we possess into the possibility of a union, a real union, of manifold states in one being. With Leibniz, Lotze answers, there is given one, and there is only given one, instance of such unitas in vaHetate : spirit or mind. We can only conceive of the absolute, the uniting bond of the varied states of so-called things, after the fashion of spirit or mind. Reality, in the full sense, is only for the unit conscious of its own unity in multiplicity. Doubtless such a conclusion raises many special problems, but it furnishes the sole comprehensive answer to those more abstract inquiries that fall witliin the scope of Ontology. It is not possible to do more than indicate in the brief- est fashion the nature of the discussions which fall under the remaining rubrics of the Mefaphydc. Generally, the purport of these may be said to be the attempt to .show that the forms of experience, more or less complex, which at first glance appear more particularly to connect themselves with the realist view of the universe, are susceptible of as exact and more profound interpretation on the idealist hypothesis. For example, the reality of space, which is a necessity for the realist view in one fashion or another, whether in the crude fashion of naturalist speculation or in the finer metapliysic of Herbart, may retain all its signifi- cance when interpreted as signifying merely that in the 236 HISTORY OF LOGIC nature of the inter-related activities of so-called things are involved features which are capable of apprehension by us only in tlie fashion of the space-schema. Space is thus a mode of intuition, or rather a mode of the intuited : for its relations appear in the content of the apprehension, not in the mode of apprehending. Time, in like manner, must be conceived not as something external to the real life of the one absolute being, but as the mode in which, in the experience of the finite spirit, the orderly connection and continuous development of reality is apprehended. There is in the chapter of Time, and in the treatment of the same point in the Grundzilge der Metapliysik and Grundziige der Religionspliilosopliie, much matter that would deserve careful and detailed handling. Of special interest, in my opinion, is the manner in which Lotze has to connect with the metaphysical difficulties of the notion of Time the psychological problems that arise from consideration of memory and of the limit of simultaneous consciousness. The further the Cosmological speculations are pushed, the more nearly do they approach a question familiar to British philosophy. When space has been interpreted as a mode of intuition, when a reading in terms of conscious experience has been attempted in regard to the fundamental characteristics of matter, when the independent existence of so-called things has been denied, — the question naturally arises. Are things and their relations more than the orderly experience of finite minds 1 Is there no existence in the universe of reality save the conscious experience of minds ? Unfortunately the answer to such a question has too often been attem]jted with the aid of notions altogether inadequate to it, and with an almost total forgetfulness of the true metaphysical significance of the question. One cannot but feel sympathy with llerbart in his indignation at subjective lotze's metaphysic 237 idealism ; for if ever there was an empty formula, parading itself as full of meaning and value, it is the fancied philosophical truth that since all that we know is in self - conscious experience, our varied presentations and representations compose the total of reality. It is a prejudice, though an inveterate prejudice, that the spiritual, inner life has no other function than to reflect in fashion of a mirror a real world, complete in existence and function independently of mind. The contrast that obtains under any metaphysical conception between the larger life of the whole and the inner modes of being and acting which make up the individual's self-consciousness, is too readily interpreted as a contrast between two radically unlike phases of being ; and the simple truth that the being of even the hypothetically assumed thing is not identical with the phase of individual thought in which it is directly apprehended or indirectly represented, is taken to mean that the being of things is complete and absolute apart from the spiritual realm of self-conscious mind, that existence breaks up into two unlike spheres. But we rob the thing in no way of its reality for all the practical ends of life (and these for the most part determine our conception of reality) Avhen, on purely ontological grounds, we deny to it self-existence and independence, and interpret it as but a form of the process through which the absolute, itself spiritual in nature, takes expression. Just as little need we hesitate to say, on grounds more jisychological, that things are not in the fulness of their being save when forming, with and in relation to the mner life of self-conscious minds, parts of that to which we can assign reality of existence. Things are not modes of apprehension of finite minds ; the external world is no spectral illusion or projection of individual minds ; but the existence of things, of an external world, is 238 HISTORY OF LOGIC not a summed up, completed fact, apart from the existence and tliought of finite minds. We must interpret the world as one whole, not as an incoherent juxtaposition of opposed parts. A world in which there is an inner life, directly and immediately given, cannot be interpreted after the realist fashion, whether in its crude or more refined form. And here, one may be permitted to say, lies the oversight in the quasi-metaphysical schemes that have been based on modern scientific conceptions. We need not only the most exact and complete history of the ways in which the real course of things has proceeded, but to interpret the whole in the light, not of what is lowest, least independent in it, but of what is highest, most complete in being. It is but a step from this conclusion to a new series of thoughts which Lotze, wrongly one may think, does not specifically include under Metaphysic. In accordance with his stubborn antagonism to the term Thought, Lotze, insisting that the function of thought is but formal, finds in the concrete life of spiritual activity, as contrasted Avith the cold, colourless mechanism of thought, the vehicle through which the real existence of things is brought down to us. It is Experience in the largest sense of that vague term — real apprehension, feeling, and acting — that gives us a place among things and indeed makes these things to be for us. And in this concrete life, there are features, feelings and estimates of worth, of which the pure con- templation of the world by thought could give us no inkling, but which force upon us a new and larger inter- pretation of the sum total of things. In fact, Lotze arrives by his own path at the point long before reached by Kant in the Krilik d&t' Vrtheihkraft, and like Kant, though with more modern phraseology, offers a final reading of the universe in tenns of ethical idealism. Things are, not lotze's metapiiysic 239 merely in order to be the parts of a mechauism, but as the instruments whereby the ultimate good is wrought out; our knowledge has objective value because it brings before us no mere purposeless play of phenomena, but gives us a world the interconnections of which are subordinated to the final and sole reality in it, the Good. Of the manner in which Lotze handles the difficult problems raised by these thoughts, nothing need here be said, for Lotze has himself with his usual caution excluded the treatment from Metapiiysic proper. The ninth book of the Mikrolcosiitus and the (Iruwlziuje der Relvjionspliilosophie contain his most matured expressions. A notice like the present can convey but a very imperfect idea of so complicated a work as the Metaphysic. There exists in the English language no other work at all resembling it, and one may hope for good results from its appearance among us. Very sincere gratitude is due to the translators, who seem to have executed their difficult task with the most conscientious care and with a high measure of success. Our stubborn tongue does not lend itself readily to the expression of subtle thoughts, and at times the sentences of the translation have a Teutonic awkward- ness, but on the whole the book appears to me by far the most successful of the unfortunately few translations we possess of German philosophical works. The editor, Mr Bosanquet, is to be congratulated on the successful termina- tion of what must have been difficult and delicate work. 240 IV MR Bradley's logic ^ 'Mr Bradley's work comes very opportunely. It is a characteristic feature of much of the best philosophical work of the present time that it consists in the main of revision of fundamental principles. A period of eminently constructive work lies behind us, and it is not impossible that much of the present stir may signify only the process of coming to understand what has been done. But it is true now, as at all times, that a philosophic view is only to be attained from one's own position, and that a compre- hensive philosophic method can only become living and fruitful if it connects itself and is penetrated with the thoughts of the present. There is no simple tradition in philosophy, and, if a method or system is accepted, the ground must lie in the fact that its leading idea has proved itself capable of expanding so as to cover the new aspects under which the perennial problems have appeared. It is but natural that the process of scrutinising first principles and testing them by application to the great body of questions that has always formed the material of philosophy should appear, when regarded from a somewhat external point of view, like a chaos of disjointed and ' Mind, January 1884. — A critical notice of The Principles of Logic, by F. H. Bradley (London, 1883). MR BRADLEY'S LOGIC 241 mntnally opposing tendencies. Certainly the present state of the study of Logic has this appearance. If one takes only the representative English writings in that depart- ment, one cannot but be struck by the apparently bound- less diversity of view in regard to every matter of funda- mental importance. Province and method of the science, auxiliary principles with which to make the approach to logical doctrines, theory of the doctrines themselves — in no one of these points is there anything like an established view, a common basis. It is not many years since one might have said that, on the whole, putting aside the merely historical teaching of what is erroneously entitled the Aristotelian logic, English writing on the subject might have been fairly distributed under two main heads : on the one hand, a purely formal logic, basing itself, though per- haps unwittingly, on an extremely imperfect psychology, supporting itself by appeal to the high authority of Kant, and claiming to have effected, if at a cost of rejecting the most in- teresting questions, a purification and scientific limitation of the sphere of logical discussions ; on the other hand, a general theory of knowledge, likewise involving much disputable psy- chology, but rightly claiming to represent more truthfully than its rival the actual process of thought as exemplified in scientific work, and so extending its boundaries as to be able only by arbitrary refusal to reject the deeper questions inevitably raised by any discussion of the nature of know- ledge. In a multiplicity of ways, complete dissolution of the one, and partial dissolution of the other of these ap- parently compact doctrines has been brought about, and now the state of Logic is like that of Israel under the Judges : every man doeth that which is right in his own eyes. Even when a writer is aware that fundamental difficulties lie in the way of the view upon which he is Q 242 HISTORY OF LOGIC proceeding, he claims the right to act as did the prudent divine, to look the difficulty in the face and pass on. The reader is perplexed by continual references to a distinction between logical and non-logical, a very phantom on which he can lay no hold, but which in some strange fashion appears to regulate his author's proceedings and to extricate him when any formidable danger is at hand. Each Logic presents some new arrangement of material, some fresh classification of notions, judgments, and the like, some novel way of getting over an old familiar stile, but it is rare indeed that in any such treatment a really vigorous effort is made to show the grounds for all tliat is advanced and so allow the reader to form what our German friends call an objective opinion. Affairs are no better, perhaps to some they may appear worse, among the German logicians. In that speculative domain. Logics swarm as bees in spring-time. Many of them, it is true, do not aspire to more than merely academic honours ; they are text-books from which the reader may learn a little, and by which he may to some extent be disciplined in thinking. But, these apart, there have been supplied by German writers within the last few years quite half a dozen treatises of a much higher order, comprehensive, elaborate, based on principles of some sort, and each giving an altogether individual and new reading of the funda- mental logical processes. He who endeavours to extract from the Logics of Lotze, Sigwart, Bergmann, Schuppe — even if he does not extend consideration to the somewhat earlier but yet living works of Ulrici, Trendelenburg, and Ueberweg — a systematic representation of logical doctrines, has before him a task to which the labours of Hercules were simple. He will doubtless be able to discover that in some fashion all are treating of the same fact, whether it MR BRADLEY'S LOGIC 243 be described as tbought or knowledge ; more of agreement than this he will hardly find. In the mass and in detail, each treatment pursues its own way, and supports itself by a more or less explicit reference to something else, whether psychology, or metaphysics, or common-sense, or philology, or anthropology, or what not. Classifications and dis- tinctions are introduced, on grounds sufficient or insufiicent but invariably diverse, and thus, in so cardinal a matter as the distribution of the forms of judgment, we are presented not only with such rearrangement of the comparatively familiar types as indicates a novel point of view, but with a variety of new forms, substantial and accidental, descriptive and explanatory, substitutive, co-ordinative, subsumptive, &c., the number of which seems practically indefinite, and to be determined merely by the extent to which current modes of speech have been taken into consideration by the writer. The limits of the subject as a whole are equally indeterminate. Inquiries rejected by some are admitted and treated as fundamental by others ; the ground of rejection or inclusion appearing really to be whether or not the writer has handled elsewhere or proposes to handle elsewhere these problems. Chaotic as are the phenomena on which an opinion with respect to Logic has to be based, the general character of that opinion can hardly be matter of doubt. This turmoil of conflicting views is a most hopeful sign. For it indi- cates that we are beginning to form a logic which shall in some way represent the laws and methods of our thought, and that the stage of preparation, the attainment of some more precise conception of what is truly the function of thought, has been reached. We have, one would trust for ever, given up the conception of thought as a mere formal activity, dissevered from the body of that which makes up 244 HISTORY OF LOGIC our knowledge, indilferent to content, and obeying only the law of one and two, of Identity and Difference. Probably no theory of thought has ever been so empty and so destruc- itive of genuine thinking as the Formal Logic, miscalled Kantian, which endeavoured to proceed upon that basis. Really, that logic, taken strictly, must resolve its whole , contents into one simple practical maxim : " Let thinking be consistent with itself." Whatsoever else it contains must come from without, in the shape of psychological proposi- tions regarding the elements of thinking, or metaphysical assumptions regarding the conditions of wliat is thought. But, though we are perhaps able to see how futile is the purely formal logic of thought, there is sufficient evidence supplied by our current logical works that we have not yet succeeded in marking off logical discussions proper from general psychology or grammar or merely popular thinking. Even where the view is taken that Logic is a real theory of knowledge, an attempt to unfold completely the processes and laws by which knowledge is formed and systematised, there is an almost constant confusion between the psycho- / logical and the logical analysis of knowledge. Knowledge ' being confessedly a subjective affair, a matter of mind, it is instantly assumed that the same predicates which apply to facts of mind regarded as such are to be found and are operative as logical peculiarities. The doctrine of notions, e.g., tends to become a mere receptacle for psychological discussions regarding the modes of forming ideas, their kinds and the properties of each class — subjects no doubt of psychological interest, but not truly involved in the logical inquiry. The doctrine of judgment is confused by having imported into it a whole mass of disputable matter reganling the nature of belief, or conviction of reality ; and theories of the judgment, which are almost as numerous as Mli BRADLEY'S LOGIC 245 treatises on Logic, turn for the most part on psychological differences. Only a vigorous effort to determine generally the fundamental characteristics of the points of view from which Logic and Psychology respectively contemplate know- ledge, or a detailed criticism of the several doctrines witli this general aim in view, can aid us in coming to a really fruitful decision as to the function and scope of logical science. It is as making a large and powerful contribution towards this end that one hails Mr Bradley's work. He does not profess to work out in systematic completeness a doctrine of logic; but, partly by polemical discussion of views, partly by presentation of results based on a more sound and pene- trating analysis of the functioji of thought, he has not only cleared the way of much that for long has been an almost insuperable obstacle, but has also drawn attention to the real nature of logical problems and raised the discussion of them to a platform indefinitely higher than that occupied by our current logical thinking. His work is not one of which it is easy to give any brief and connected account, and the difficulties of a reviewer are somewhat aggravated by the peculiarities of the author's style and method. In a matter of this kind, no doubt, much must depend on the individual's turn of thinking ; but I should fear that some part of the good efTect that ought to be produced by Mr Bradley's work will not be realised because the reader will fail to seize the leading idea of the whole. The discussion grows in complexity as it is developed, and partial views are taken up into and superseded by the more comprehen- sive solutions. But there is throughout implied a method of regarding the whole business of thought that is not brought with sufficient clearness to the front, and the point of many isolated treatments may in consequence be missed. Mr Bradley has chosen his own way, and has 246 HISTORY OF LOGIC worked towards a theory of judgment and inference, by taking up, comparing, setting against the current teaching, and carefully sifting empirically selected types of judg- ments and reasonings. Such a method has its advantages for teaching purposes, but it is apt to mislead unless the underlying principles which guide the whole discussion are clearly discerned. Mr ]jradley hardly brings these forward into sufficient prominence, though he might well have done so, and it requires a long-breathed reader to accompany him through his devious course. Perhaps this one complaint may connect itself with the remark in Mr Bradley's pre- face that critics of different tendencies may object that the treatment contains too much or too little metaphysics. I cannot think that Logic as a whole is in any way inde- pendent of Metaphysics, though I fully admit that, as meta- physics covers a multitude of problems, it is not necessary that into every section all the rest should be dragged ; nor do I imagine that the occasional distinctions drawn by Mr Bradley between logic and metaphysics indicate a contrary opinion. ^Vhat is alone of importance is the ultimate view of reality and thought, which is common to all such problems and binds logic and metaphysics into a unity, I do not find that Mr Bradley makes the view on which he proceeds clear, and it appears to me that the force of many of the discussions, in particular that with which the book closes, on the validity of inference, is weakened by the want of some definite statement. Mr Bradley begins his inquiry with the treatment of the central problem of logical theory, the significance or import of the Judgment, and to this the whole of Book I is devoted. Book II begins the discussion of Inference, and in its first part, expounds certain general types and principles of reasoning as substitute for the rejected syllo- MR Bradley's logic 247 gisni. The second part of the book is entirely critical, and is devoted to an examination of the doctrine of Associ- ation with its natural se([uels, the idea of reasoning from particulars and tlie Inductive methods, and to an apprecia- tive though hostile review of Jevons's Equational Logic. Jiook III resumes the discussion of Inference, brings for- ward in the lirst part the main processes in which the essential characteristics of inference are to be detected, and endeavours to reduce these to their most general expression, and in the second part handles the ultimate problem, fore- shadowed throughout all the discussion, of tlie relation between logical tr'ith and real, objective connection. The work, it will be seen, is at once comprehensive and has a certain systematic idea in it. Apart from the main inquiry, moreover, it abounds in good thinking, and no reader can fail to derive benefit from the acuteness with which isolated questions of psychological or metaphysical interest are handled. In truth, one is somewhat embar- rassed witli Mr Bradley's riches, and would feel inclined at times to wish that he had pruned his work more closely. A little dissatisfaction is inevitable when a promising problem is only hinted at, even though the glance given be one of undeniable acuteness. The frequency with which Mr Bradley is compelled to make brief excursions into psychology and what he chooses to call metaphysics, and the importance of the relative matters, lead us to desire that he had substituted for much occasional disquisition one serious and careful statement of the way in which he regards thought as subject of psychological, logical, and meta- physical treatment respectively. Such a statement is called for, not only in order to illumine his own results, but also as furnishing some guiding thread to his criticism of other views. 248 HISTORY OF LOGIC Xaturally, it is in the theory of Judgment that a logician's fundamental point of view comes to the front, and the judgment is here handled with great elaboration and much subtlety. Experience must have taught every one who has made the attempt how difficult it is to express in other language the results a thinker has come to on a question of the greatest complexity ; and I can hardly hope to have succeeded in adequately apprehending all that enters into Mr Bradley's view of what constitutes a judg- ment. So far, however, as I can determine, his opinions would be somewhat as follows. Judgment is clearly a mental function, that is to say, it can only be understood as part of the complex in which thought and reality stand as opposed to, yet depending on, one another. But as a mental function, judgment is not to be taken as having the characteristics of a mental fact. However valuable may be the results of a psychological investigation of judgment as a fact in the mental life, however much light may be indirectly thrown on its logical nature by tracing the history and conditions of its appearance, the judg- ment as an element of knowledge, as the very mode of apprehending the real, is not simply a psychical fact, nor can the logical theory of judgment admit any determination of either idea or reality as these are treated for psychology. The constituents of the judgment, idea and reality, are equally necessary and require special definition. The idea is not the mental fact, taken as such ; it is part of the general content of the real as appreliended, separated off, fixed and used as a sign or symbol. Eelatively to the real, which is substantival, the idea is adjectival. It is known as not itself the real, but it has significance, meaning ; and this meaning is definitely referred to the real. In any judgment the idea or ideal content is connected with, MR BRADLEY'S LOGIC 249 attached to, the real, and the new relation resulting is perceived not to be made by the act of judging but to be independent thereof. This highly general description of judgment can hardly be quite intelligible until it has received fiUing-in from contrast with opposed views and from consideration of the new features which complex experience introduces into it. Jiut the view deserves warm recognition as an attempt to see through the thick veils of current doctrine and to seize the very essence of the act of judging. I do not know how far Mr Bradley's illustrations and explana- tions of the term idea will throw light upon the meaning in which it is to be employed ; for there is danger, despite his precautions, that the mutter will be viewed psychologically; and this danger is perhaps aggravated by the attempt to give a genetic account of the way in which we may suppose judgment to have come about in a developing intelligence. There is a correlative danger, attaching to the term reality, on which a word will be said later. What one would desire to insist more strongly upon, is the essential con- junction of the two factors, reality and idea, in judgment, and the impossibility of taking these apart from one another. Popular thinking and psychological considerations tend constantly towards a contrast which is fatal to any theory of thought ; and the employment of the term idea at all emphasises the contrast in a most hurtful manner. Provisional acceptance of the general description of judgment enables Mr Bradley to deal summarily with certain definitions of judgment, which err either by ab- stractly isolating the factors of the judgment or by ac- cepting part for the whole. Such, e.g., are all definitions of judgment as comparison of ideas, under which fall the current explanations of judging as referring to a class, 250 HISTORY OF LOGIC as asserting identity of subject and predicate, or definitions which are merely adequate or inadequate psychological theorems. The criticisms here are to the point and felicitously expressed. The discussion of the more abstruse questions regarding the judgment is led up to from the familiar doctrine that, in a categorical judgment, existence of either subject or predicate is not asserted. " All S is P " by no means forces the assertor to the admission that eitlier S or P exists. S and P are merely ideal contents, and the judgment is no more than the statement that these are so connected that if the one, tlien the other as qualified by the first. Difficulties of this kind have recently begun to find their way into our current logical discussions, not without most hopeful results, ■*■ Clearly, if a solution is to come at all, and is to affect our distribution of logical judgments, it must be arrived at by a more profound con- sideration of the reference to reality that has appeared as a constituent of the judgment. Mr Bradley advances to the task by contrasting in a general way the char- acteristics of reality and truth. The real is individual, self-existent, substantival. Truth on the other hand, as having to do with the idea, has no one of these char- acteristics. At first sight, then, it would seem that all truth is hypothetical merely, that it expresses only well or ill founded connections of ideal contents in our minds. To come closer to the problem, there is introduced a pro- visional classification of categorical assertions, into (1) analytic judgments of sense, in which the given is merely ' See, e.g., Mr Venn in Symbolic Logic, and Mr A. Sidgwick's very thoughtful treatment of Abstract and Concrete T^ropositions in Fallacies. MR BRADLEY'S LOGIC 251 described by one of its parts, (2) synthetic judgments of sense, in wliich the real of sense-perception, involved in the assertion, transcends what is immediately given, (3) those in whicli the real referred to is not a fact of per- ception. Scrutiny of these yields as result the important principles, that the real, even when taken in the sense of the real in perception, is not identical with its momentary appearance in perception, said momentary appearance, in- deed, being an incognizable atom when taken in isolation ; that the real, taken in more or less limited fashion, is ideally determined and directly referred to in the analytic judgments ; that the real is indirrctly referred to in syn- thetic judgments and is in them taken to be a continuous identity underlying the momentary phenomenal appear- ance. All such judgments are singular and appear to be categorical, to imply assertion of the real and of its elements as appearing in the judgment. Universal abstract judg- ments and hypotheticals, on the other hand, appear to assert merely necessary connection of ideal content, and therefore point only to that in the real which is the ground of the consequence necessarily following. In the judg- ment, " If S, then P," we only assert that if the real be qualitied. as S, then it will present also the qualihcation P ; we do not assert that the real is either S or P. But to rest content with such a view is to do grave injus- tice to the function of thought and to take an extremely imperfect and abstract aspect of the real as the whole of its significance. In the concluding sections of his second chapter Mr Bradley advances towards a completer doctrine of the kinds of propositions. He has little trouble in showing that synthetic judgments of sense, which trans- cend the given, proceed on a principle not distinguishable 252 HISTORY OF LOGIC from that wliich characterises the hypothetical, while analytic judgments of sense, though professing to give the real, do so only by a process of mutilation that is con- cealed by ordinary language but is fatal to their claims as absolutoly and simply triie. The terms of ■which the singular analytic judgment consists are universal, are wholly inadequate to express the concrete reality that is assumed. Such judgments are in fact the poorest and most abstract, giving the least expression of reality. Like all other judg- ments they do refer to reality, but they refer in the least definite, most hypothetical fashion. Abstract judg- ments, though on one side to be described as hypothetical, for they do not assert the existence of their elements, are on another side categorical, for they do imply a quality of the real and express the nature of the real as the realm of law, of systematic connection of facts. The negative judgment (ch. iii), Mr Bradley regards as resting essentially on the recognised exclusion by the real of a suggested ideal determination. It implies, therefore, in all cases a recognised ground of exclusion, a positive element, though the nature of this ground need not be the same in all cases of negation. It is with satisfaction that one sees the blank form Not-A assigned to its true place (pp. 118-9, cf. pp. 147-8), but the whole tenor of this chapter and occasional special statements (pp. 109, 116) tend rather strongly towards the purely subjective inter- pretation of judgment which is the gulf always yawning beside the logician. The disjunctive judgment (ch. iv) is shown to involve a categorical assertion regarding the disparate members of a whole predicate, a hypothetical determination of the subject in reference to these dis- parates, and a general assumption or inference regarding the totality of the sphere which is divided. MR BRADLEY'S LOGIC 253 Chapter v, on the Princij)les of Identity, Contradiction, Exchided Middle, and Double Negation, is perhaps one of the least satisfactory, not because there is much in it from which one would dissent, but because it does not seem possible to discuss with any proHt these principles from the point of view which tlie author is taking. If we regard judging as part of the subjective process of knowing, these principles have only relative significance. In their abstract and general form they can only be handled in what we think Mr Bradley would call metaphysics. Not much is to be gained by treating truth in isolation, and so render- ing the Law of Identity, e.rj., as that it merely expresses the abstractness of truth (p. 133), and, similarly, the dia- lectic method requires not to be compared with Contra- diction and Excluded Middle when these are taken from the same point of view. Chapters vi and vii, on Quantity and Modality, raise a multiplicity of questions. Want of space prevents my doing more than call attention to the excellent treatment of the general basis of probable reasoning which is given in ch. vii ; to a general statement of the chapter I shall have occasion later to refer. The treatment of quantity raises two problems — first, that of extension and intension, second, that of the meaning to be assigned to universal and particular. In respect to both, the ordinary logic has accepted partial doctrines either from uncritical ex- perience or from psychology, and Mr Bra-(1 by WILLIAM K.NKHIT, LL.U., Pidlessor of Moml Philosophy in the University of St Andrews. Jic-Usue in Shilling Volumes net. Descartes . . . Prof. Mahaffy. BOTLER . . Rev. W. L. Collins. Beukelev . . Prof. Campbell Fra.ser. FiciiTE . . . Prof. Adamson. Ka-vt .... Prof. Wallace. Hamilton .... Prof. V^itch. Heoel . . Prof. PMward Caird. Lribniz . . .John Theodore Merz. Vice Prof. Flint. HoBBES . Prof. Croom Robertson. Hume .... Prol. Knight. Spinoza . . . Principal Caird. Bacon— Part L . . Pnjf. Nichol. Bacon— Part n. . . Prof. Nichol. Locke . . Prof. Campbell Fiaser. WILLIAM BLACKWOOD & SONS, Edinburgh and London. UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles BC 13. A22' 3 1158 00093 7333 CoD 1