KANTIAN LOGIC, the critical method, which has so influenced general philosophy that all later speculation refers more or less directly to it, has at the same time profoundly modified all later conceptions of the sphere and method of logic. From the Kantiau philosophy there spring directly the three most important modern doctrines of logical theory, - that which, with many variations in detail, regards logic as a purely formal science, the science of the laws of thought or of the laws under which thought as such operates, and of the forms into which thought as such develops; that which, likewise with many variations, unites logical doctrines with a more general theory of knowledge ; and filially that which identifies both logic in the narrower sense and theory of knowledge with an all-comprehensive metaphysic..

It is matter of history that the critical system was developed mainly from the basis of the Leibnitzian logical and metaphysical theories, and it is likewise matter of history that Kant, even in the speculative work which was to so large an extent antagonistic to these theories, remained under the influence of some of their cardinal positions.' In particular the view of logical thought as purely discursive, analytic in character, a view never by Kant harmonized with his general system, is a relic, most significant for the develop- ment of -his logic, from the Wolffian reproduction of Leibnitz's philosophy. This historic basis is not to be lost sight of in attempting to acquire aclear idea of the special place and function assigned by Kant to logical theory.

But a brief reference to the general result of the critical philosophy will suffice to introduce the more special treatment of the Kantian logic. Knowledge, or real cognition, which is analysed in the Kritik in reference to its origin and validity, appears, when subjectively regarded, as a compound of intuition and thought, of sense and understanding. The isolated data of sense experience do not in themselves form parts of cognition, but are only cognized when related to the unity of the conscious subject, when the subject, as it may be put, has consciousness of them. This reflex act, resembling in some respects Leibnitz's apperception, or process of uniting in consciousness, is an act sui generis, not to be mechanically conceived or explained. Only through its means do representations become cognitions. The forms in which the synthetic act of understanding is carried out are, as opposed to the intuitive data on which they are exercised, discursive or logical in character. Essentially they are judgments : all acts of understanding are judgments, and, as judgments, they imply a general element with which the particular of sense is combined, and in the light of which the particular becomes intelligible. In ultimate analysis it appears that no particular, whatever be its empirical character, can become an intelligible fact, save when determined through some specific act of understanding, through combination with some specific notion or general element. Combination of particular and general is thus the very essence of understanding, the mark of knowledge as such. In every item of cognition the same elements may be discerned as necessarily present The consideration of the ultimate modes of intellectualization, of the series of acts by which understanding subsumes the particular, draws the particular into the unity of cognition, may be called in a large sense logic. If the consideration be specially directed to the mode in which, by means of this combination, knowledge arises, and therefore include discussion of the wide problem regarding the relation between understanding and objectivity in general (the matter of knowledge taken generally), the special title transcendental logic may be used. But if, concentrating attention solely on the kind of operation implied in understanding, we endeavour to lay out fully the modes in which understanding proceeds in the construction of knowledge, making abstraction of all inquiries regarding the origin, worth, significance of knowledge itself, the consideration is of a more general character, and may receive the title of general logic.' The understanding, then, like everything else, works according to laws, the laws of its own nature. If we abstract from all that may characterize the matter considered, and take into account solely t he laws according to which understanding must act, we may construct a purely formal doctrine, a theory which is rational both in matter and in form, for the matter consists of the laws of reason, and the form is prescribed by the very nature of reason, - a demonstrative theory, for nothing can enter therein which cannot be shown to have its ground in reason, - a completed theory, for although the matter of thought is infinite and infinitely varied, the modes in which the understanding must operate, if unity of cognition is to result, are finite and capable of exhaustive statement, - and a theory developed from its own basis, standing in no need of psychology or metaphysics, but deducible from the mere idea of understanding as that which introduces unity into representations, whether given (empirical) or a priori (pure).

Were this the only determination of the province of logic given by Kant, the question which at once arises as to the possibility of any such independent doctrine would receive an easy solution. For it is evident that logic, as a theory of the form of thought, could consist only of a portion of the more general doctrine, by whatever title that be known, in which the nature of understanding as synthetic activity is unfolded. The distinction on which Kant lays stress between matter and form, a distinction employed by all subsequent writers of his school, is ambiguous and misleading. If by matter be meant the particular characteristics of the things thought about, in which sense we might speak of judgments of physical, chemical, grammatical matter, and so on, then to say that logic does not take this into account is perfectly inept. If logic be a philosophic discipline at all, a theory in any way concerned with thinking, it is at once evident that it can in no way deal with the specialities of any particular science. But this distinction between matter and form is by no means identical with another, lying in the background, and too frequently confused with the first, - the distinction of understanding as a faculty per se with its own laws, deducible from its mere notion, and understanding as the concrete real act of thinking. What Kant calls the mere idea of understanding, and what in other writers of his school appears as a definition of thought, is really nothing but a reference to what has presented itself in the wider inquiries of the Kritik as the complex nature of the synthetic activity of understanding. Kant himself never attempts to deduce from the notion of understanding the-varied characteristics of logical forms, and his followers,--e.g., Hamilton, - when they are consistent, start from concepts as expressing the bare notion of thought, and regard all other forms of thought as combinations of concepts.

But Kant does introduce another element into his treatment of the province of logic, one not original to him, but of the utmost importance for later developments from his point of view-. He inquires. what kind of relations among the elements of thought can form the matter of logical treatment, and defines these as two in number - (1) formal consequence, (2) non-contradictoriness. By formal consequence we are to understand the relation between a conclusion and its premisses, no inquiry being raised as to the truth or validity of the premisses. By non-contradictoriness we are to understand that, logically, notions, judgments, or reasonings can be subjected to treatment only in regard to the absence of explicit contradiction among the factors entering into them. Thought, which introduces unity and system into experience, must certainly introduce formal consequence and preserve analytic truth or correctness. Formal logic, then, treats only of these formal qualities of all products of thought,' The detailed treatment of logic, so far as that can be gathered from the very brief summary (Logik, Werke, iii. 269-340), shows with the utmost clearness how impossible it was for Kant to deduce the forms and relations of thought from the mere notion of understanding, even when coupled with the principles of formal consistency and consequence. Assuming that understanding is the discursive faculty, the faculty of cognizing the many particulars through the one concept or notion, Kant deals first with concepts (Beg,ritfe) as general or discursive representations. lie is careful to avoid an error into which many of his followers have fallen, that of regarding Begriffe in a mechanical fashion as a specific kind of Vorstellung, distinguished only by containing a few of the marks making up the single intuitions. He rightly notes that cognition proceeds by subsuming the particulars under the common element contained in them, and that the generality of the concept thus rests upon the relation in which it stands, as reflective ground of cognition, to the particulars. The characteristics of concepts, as possessing extent and content, are treated briefly, after the fashion familiar in the more detailed logics of his school. It is, however, when the doctrine of judgment is reached that the difficulties of his position appear with greatest distinctness. Judgment is defined " as the representation of unity in the consciousness of distinct representations, or the representation of the relation of these, in so far as they make up a concept." 1 But the essential element in the definition - the unity of consciousness or unification of differences in a notion - is thus left so vague and undetermined that it is impossible to deduce from it any classification or any peculiarities of judgments, and possible indeed to proceed on two quite distinct lines of research. The expression, indeed, refers to that which is the fundamental fact in the critical system, the existence of conditions under which only it is possible for detached data of experience to become objects of knowledge for the single conscious subject ; and, had Kant been true to the principles of his system, it would then have been necessary to Lase any classification and treatment of judgment on the enumeration of the functions of unity in conscious experience. In the Kritik 2 emphasis is laid upon the function of unity as the essence of the judgment, but it is a well-known historic fact that Kant makes no attempt to justify in its details the enumeration of such functions on which his divisions rest. His followers in the field of logic,3 misconceiving the real relation of form to matter, interpreted the unity involved in the judgment as being a merely quantitative relation between given notions.4 There is here involved a twofold error, which has exercised a most pernicious influence on the fortunes of logical theory. For, in the first place, so to view judgment is implicitly to proceed from the assumption of notions as given elements of knowledge, the relations of which are to be discovered by comparison or analysis of what is contained in them. The notion as empirically given thus becomes the fundamental fact ; all other forms of thought, judgment, and syllogism are regarded as merely the mechanism by which the content of notions is evolved. Such a doctrine puts out of sight the peculiarities of the notion as the product of thought only, inevitably compels a distinction between what we may call the real processes of thinking whereby notions are formed and the elaborative processes by which notions when formed may be treated, and, by regarding notions as simplest data, leads back to the old nominalist doctrine according to which all thinking is but the compounding and separating of simple elements.3 And, in the second place, there is involved in all this the underlying prejudice, which it was the very business of the critical system to destroy, the attempt to treat knowledge, and thought, which is an integral part of knowledge, in a purely mechanical fashion. The Kantian analysis for the first time in the history of philosophy brought into clear light the essential peculiarity of knowledge, the reference of all the manifold details of experience to the unity of the thinking subject. Such reference, and the modes in which it expresses itself, are not to be conceived mechanically, nor can we regard the products of thought, the notion, judgment, and reasoning, in the same fashion in which, with but partial success, we treat, in psychology, the representations or reproductions in idea of actual fact. The essence of thought, the unity in difference of objects known and subject cognizing, is that which constitutes in its several modes the peculiarity of notions, judgments, and reasonings. The notion is simply the work of thought, looked at, if the expression be allowed, statically. There is no single psychical product, to be treated by the method of observation which is applied in psychology to sensations and ideas, which can be called the notion. Mental facts, which rightly or avrongly psychology deals with after its mechanical fashion, present themselves in a new aspect when they are regarded as parts, or rather as organic elements, in cognition. If we endeavour to apply the abstracting, isolating method of observation ab extra to them, doubtless only mechanical, abstract, and external relations will manifest themselves as obtaining among them, and there may thus be deduced a mass of abstract formulae expressing relations of agreement and disagreement, total or partial coincidence, confliction, intersection, or coexistence and sequence, which have abstract truth, but are in no way adequate to express the genuine nature of thought.

Kant himself proceeds, as was said, by simply assuming, as somehow given, the cardinal forms of unity in consciousness, and, distin- g9ishing form of judgment from matter by the apparently simple difference between matters united and form of uniting, draws out the types of judgment under the familiar rubrics of quality, quantity, relation, and modality. The same assumption of distinctions only to be given by the higher researches of transcendental logic is manifested in his treatment of reasoning, the deduction of one judgment from others. Three main types of such deduction are signalized :(1) deductions of the understanding, in which the conclusion follows simply from change in the form of the given judgment ; (2) deductions of reason, in which the necessity of the deduced proposition is shown by reference to a general rule under which it falls ; (3) deductions of judgment, in which the conclusion is reached by the treatment of given experience in reference to a general rule of reflexion upon experience. Under the first of these fall the familiar forms of immediate inference ; under the second, syllogism in its three varieties, categorical, hypothetical, and disjunctive; under the third, inductive and analogical reasoning. The understanding, if one may interpret Kant freely, is the process by Which the worth of what is given is fixed and determined ; it moves not beyond the given fact, and can therefore subject the fact to no other than formal transformation. The determining judgment or reason is the expression of the fundamental fact in knowledge that all experience is subject to general rules or conditions ; there must therefore to a determination of the particular by the general ; there must be ground for subsuming the particular and the universal. The forms of such subsumption and determination of the particular by the general are syllogisms. Syllogism therefore is the mode in which the essence of cognition is made explicit. The reflective judgment is the expression of the tendency to treat the contingent details of this or that given experience after the analogy of the general rule that all experience is subject to intellectual determinations. This analogy does not necessitate the specific determination of the particular by any specific universal, but serves as general directrix in experiential researches. It is sufficiently evident that a remodelling of the older logical doctrine such as this rests upon a wider and more comprehensive philosophical view of knowledge as a whole, that such distinctions cannot flow from either of the principles previously indicated as those on which the formal conception of logic rested, and, finally, that the logical aspect of these distinctions is formal in the only true sense of that word, viz., in that the treatment is of necessity general, applicable to all or any thinking.

The Kantian transcendental logic, being an analysis of the conditions under which objectivity in general becomes possible material for cognition, is in a special sense a new theory of thought. For thoughtis the process mediating the unity of the ego and the multifarious detail of actual experience • and only through thought, the universal, are objects so determined that they are possible matters of knowledge for a conscious subject. As determinations of objects, the pure elements of thought may be called notions, while the realization of notions in conscious experience is the judgment, wherein the universal of thought and the particular of sense are synthetically united, and the systematization of experience is the syllogism. Notion, judgment, and syllogism are thus, in the transcendental logic, no bare, abstract forms, hut have as their content the pure determinations of objectivity in general. They cannot be conceived mechanically, as mere products differing only in degree of generality and abstractness from the ideas, and connexions of association which appear as due merely to the psychological mechanism of the human consciousness. They are the essential forms of time ultimate synthesis through which knowledge becomes possible, and thus express in their organic system the very nature of thought, i c., of the thinking subject. In the Kantian doctrine, however, as it developed itself historically, there are various points of view which disturb the harmony of the system as thus sketched. Two in particular require special notice, as from these the later attempts at a complete revision of logical theory have taken their origin. (1) Throughout the Kantian work there appears a constant tendency to regard the ego, or central unity of self-consciousness, as merely abstract, as related mechanically, not organically, to the complex of experience in which its inner nature is unfolded. This tendency finds expression in various ways. Thus the synthesis, which has been shown to be the essential feature of cognition, is regarded as on its subjective side a union of intellectual function and receptivity of sense, and the contributions from either side are viewed as somehow complete in themselves.' Knowledge, in accordance with this, might be considered to be the mechanical result of the combination or coherence of the two, a combination which in the last resort must appear to the conscious subject as contingent or accidental. (2) Knowledge, the systematic union of universal and particular in experience, is thought as containing in some obscure fashion a reference to the most real world, the realm of things in themselves, and therefore as being, in antithesis thereto, strictly subjective. The processes of thought, by which unity is given to experience, thus manifest themselves as limited in scope, and as being the very ground or reason of the restriction of knowledge to phenomenal in opposition to noumenal reality.' The presence of these two difficulties or perplexities in the Kantian system, which are, indeed, at bottom but one, led to revision of transcendental logic in two directions. The one line proceeded from the analysis of knowledge as the product of intellectual function and receptivity, and, uniting therewith metaphysical conceptions of varied kinds, culminated in a doctrine of cognition which, retaining the distinction between real and ideal as ultimate, endeavoured to show that the forms of the idea], i.e., of thought, and the forms of reality were parallel. Logic, tinder this new conception, appeared as a comprehensive theory of knowledge, the systematic treatment of the modes in which thought, conditioned by its own nature and by the nature of the reality upon which it is exercised, develops into knowledge, i.e., of the modes in which a representation of things characterized by universality and evidential force is obtained. On the whole this is the position assigned to logic by Schleiermacher, whose view is followed in essentials, though with many variations in detail, by a large and important school of logical writers.' The second direction may be characterized generally as the attempt to develop fully what is involved in Kant's conception of thought as the essential factor of cognition. Any opposition between metaphysic as dealing with the real and logic as dealing with the ideal element in knowledge appears, in this view, as a mere effort of false abstraction. The very nature of reality is its nature in and for thought. The system of pure determinations of objectivity, which Kant had imperfectly sketched, is not to be regarded as a piece of subjective machinery, because it expresses the inmost conditions of intelligence as such. Nothing is more real titan the ego, than intelligence or thought. Transcendental logic, or logic which is at the same time metaphysic, is the only discipline to which the title logic by right belongs. For it contains the complete system of the forms in and through which intelligence is realized. The notion, judgment, and syllogism are doubtless forms of thought, but they have their definite content. They are the modes in which the forms of objectivity are realized for intelligence, and are thus at once abstract and concrete. The so-called formal logic is a mere caput 7nortuum, a descriptive study of seine 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 here be regarded as its complete and only representative.