CRITICISM OF LOCICAL SCHOOLS, 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 regarding the best mode of expressing in terms the nature of a subject sufficiently agreed upon ; variations in the treatment 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 fundamental 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. 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. 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 an article like the present ; 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 develop. bug 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 criticize 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 is therefore possible to apply internal criticism to the more important of these general views, and to consider 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 certain German authorities 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, Leibnitz, Herbart, Ulrici, Boole, De Morgan, and Jevons. Logic as theory of knowledge presents quite special features when handled by Mill, or by Schleiermaeher, Ueberweg, Beneke, and Wundt. And it cannot even be admitted that the threefold classification affords room, without violence, for the Aristotelian logical researches. There are no points of agreement and difference so unambiguous that by their aid a division can be effected.' 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 consistently, must take one of two forms, either that of description, in which thought, like any other mental fact, is regarded ab 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 subjective processes of mind are viewed as forms of the one great process whereby knowledge is realized in the individual consciousness. Investigations from the first point of view are diametrically opposed to the logical treatment of thought, for in the 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 remains 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. Investiga- tions from the second point of view arc 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 i nature and meaning of conscious experience which it s 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.

Irm, the hint contained in Kant's distinction of analytic and synt letic thought, analytic and synthetic truth. It may be said that all thinking iuvolves 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 evolution of the formal clement 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 fundamental 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, emphasizing 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 judgments, 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 synthesis, - that analytic judgments, therefore, are merely special applications of abstracting thought within a sphere already treated, handled, formed by thought. Manse], too, whose views are generally acute if not profound, has signalized as the primitive unit of cognition the so-called psychological judgment, winch is essentially synthetic in character. The logical judgment, in fact, about which his conception of logic centres, is recognized as a posterior act of reflexion, directed upon formed notions, and is not in any way to be 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 subordinate 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 organized. The utmost possible 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, 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 nomin alist logic from Antisthenes downwards, and has found metaphysical expression of the most diverse kinds. That things are what they are is the odd fashion in which a well-nigh forgotten English writer states what is taken to be the universal foundation of all thought and knowledge.' The 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 corresponding 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, Antisthenes'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 therefrom. 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. This, e.g., when it is said that a judgment is the expression of an identity, there are 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 qualilied, 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 which 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 vie w.2 So soon, however, as the real nature of thought has been thrown out of account as not concerned in the processes 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, whatsoever 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 whatever is contradictory of their nature. They are combined positions and negations, that which 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-contradictory, 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 negations 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 complex articles of thought, complexes of positions and negations. Proceeding from such a conception there may be treatments more or less systematic and fruitful. in the hands of Kantian logicians, such as Twesten, Mansel, Spalding, and the like, little is effected, for, as the forms of thought are accepted as given and as having their characteristics otherwise fixed (by psychology or critical theory of knowledge), 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 arbitrary 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 determination of a class, Jevons's view of thought as simple 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 generalization of the system of thought must take a symbolic form presents itself as an immediate and natural consequence.

By the application of a symbolic method is not to be understood what has been practised by many writers on logic - time 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 relations of dependence among objects of thought, of whatsoever kind, in correspondence with which operations of perfectly general character arc carried out, shall be represented by symbols, the laws of which are determined by the nature of these relations or by the laws of the corresponding operations. The mere use of abbreviations for the objects of treatment is not the application of a symbolic 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 development 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 quantity, 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 assumption is not self-evidently true, and it is permissilde to inquire whether matters non-quantitative do not present elations of such generality that they, too, can be symbolically 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 quantitative in character, has been the truly fruitful element in after-development of the system.2 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 essential characteristic of thinking. As above noted, there have been adopted various modes of expressing this characteristic, and in some cases the mode adopted is not one from which any generally applicable symbolic rules of procedure could have followed.3 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 consisting of a series of self-identical units, to be variously combined in obedience to the law of self-identity.; Adopting the first view, we find that processes capable of symbolic representation, by the customary algebraic signs of addition, subtraction, equivalence, multiplication, and division, have a perfectly general sig,niticance in reference to the combination, separation, equalization of classes, to the imposition 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 carded along with them in all the after development. 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 that 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 all of the symbolic laws so reached, the logical problem as such may then be approached. Given any number of logical reruns (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 the others, or to express any one in terms of the others. The symbolic procedure, expounded with marvellous ingenuity and success by Boole, may take various forms, and may be simplified by many analytical devices, hut consists essentially in determining systematically how given positions and negations, The first question which suggests itself in connexion 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 arrangement? Mr VC1111, 4010 emphasizes 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 Boole's formulae, 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, resemblance and difference, higher and lower, subject and predicate vanish, or are absorbed in the more general principle 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 dichotomy, of x and not x, and not y, and so forth." 6 In other words, quantitative differences require to find expression through some combination of the positions and negations of the elements making up the objects dealt with,7 while the usual qualitative 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 determinivCcn 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 tl.e symbolic methods of logic taken in Grassmann'sBegrIP/chre is more thoroughgoing, and more closely represents the underlying principles, than that involved in Boole's formula. and expounded in detail by Mr Venn.

Grassmann, as above stated, deduces logical relations as a particular class of the determinations necessarily attaching to all quantities (i.e., determined contents of thought). Abstraction being made of all peculiarities winch may be due to their special constitution, quantities exhibit certain formal relations when they are combined (added, subtracted, &c.). Each quantity is a unit of thought, a definite posibtm, 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 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.8 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 quantitative science, and the only laws we can employ arc 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 connexions 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 probability on an obscure metaphysical principle,3 that would treat it as in essence the composition and decomposition of elementary atoms, of IrpErra, as Antistfienes 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 psychological assumptions, but this is an illusion. No logical method can be developed save from a most definite eon, ception of the essential nature and siodus operandi of flunking, and any system of symbolic logic finds it necessary, if it is to be complete and consistent, to adopt some such view as that above criticized, 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 recognized among logical processes.' Formal logic, then, in the ordinary acceptation of that term, does not appear to furnish any adequate representation 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 there- fore 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, 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. But 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 cognition, the discussion of methods of experiment and observation, under the one head logic is an error in principle, whether we view logic in its theoretical aspect or in reference to a special propredeutic aim. Generalizations on such topics are well-nigh 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 connexion with actual research and the ascertainment of the principles therein employed. In either case it is not susceptible of abstraction and isolated treatment.

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. The designation 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 incapable of satisfactory treatment, except in the most intimate connexion 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 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 palpable than the distinction, drawn within conscious experience, between knowledge and reality. It is impossible then for a theory of knowledge to start with the assumption 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 essentially 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.2 3S. 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 appropriately 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. 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 male prominent, there conies forward one or other of the various modes for settling the province of logic ; but these partial concep, The same fact has been noted in regard to formal logic of the Kantian school, in 31ansel's distinction of psychological and logical judgments.

tions 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 conception of the subject has been formed from acquaintance with this imperfect body of rules and formula,' 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; aud, 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 entitled 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 exhanstiveuess of logical analysis is not a requisite. It has a raison d'être 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 may, to a limited extent, include reference to some of the simpler processes of scientific method. in all probability 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 propredeutie but not a scientific value.