796 LOGIC these, in so far as they make up a concept." 1 But the essential element in the definition the unity of consciousness or unifica tion of differences in a notion is thus left so vague and unde termined 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 sys tem, 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 base any classification and treatment of judgment on the enume ration 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, inter preted the unity involved in the judgment as being a jmerely 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 maybe 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. 5 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 ob servation which is applied in psychology to sensations and ideas, which can be called the notion. Mental facts, which rightly or wrongly 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, conflic- tion, 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 some how given, the cardinal forms of unity in consciousness, and, distin guishing 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, 1 Logilc, 17. 2 Analyttt; 19. 4 See Twesten, Logik, $ 51-57, and 61 ; Hamilton, Logic, i. 230 sq It may here be remarked that Hamilton s mode of translating the relative sections of Ite , . r * i-u i * *"*" *** j uvtfeiuv,iiu t*. 10 u nuo uii; uiJlUJ of A and B in the notion of a given totality or whole A being part of B in on un P Kanti n^ 8 ^ f A " an ther This lelation f whole and part is quit
- It is by this course that the curious phenomenon of an algebraic or symbolic
logic springing from the Kantian groundwork has come about The same result follows, indeed, from any view of thought as merely exercised about facts which are already in themselves completed cognitions. Whether we call these notions <with Hamilton) or irpira (with Antisthenes) or elementary data (with Leibnitz) or simple apprehensions (with the nominalists), the result is the same relation, and modality. The same assumption of distinctions only to be given by the higher researches of transcendental logic is mani fested 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 proposi tion 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 be 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 parti cular 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. 28. As in the Kantian system there were placed, side by side, two diverse conceptions of logical system, that of transcendental logic, and that of formal logic, without any adequate link of con nexion between them, so from the Kantian position there diverged two quite distinct schools of logic, the transcendental or meta physical, and the formal. As regards the second of these, but little requires to be said. The great body of logical treatises written from the Kantian formal point of view contain nothing of interest. In them the traditional logic is handled under the rubrics supplied by the Kantian general philosophy, with more or less of purifica tions from needless detail, according to the acuteness or insight of the writers, with more or less of deviation from the Kantian lines. In but few cases did the real difficulty, that of assigning to formal logic an independent plan and method, lead to a radically fresh treatment. 6 The Kantian transcendental logic, being an analysis of the con ditions under which objectivity in general becomes possible material for cognition, is in a special sense a new theory of thought. For thought is the process mediating the unity of the ego and the multi farious 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 reali zation 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, but have as their content the ] ure 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 the ultimate synthesis through which knowledge becomes possible, and thus express in their organic system the very nature of thought, i e., of the thinking subject. In the Kantian doctrine, however, as it developed itself historically, there are various points of view which disturb the hirmony of the system as thus sketched. Two in parti cular require special notice, as from these the later attempts at a complete revision of logical theory have taken their origin. (1) 6 Generally, the formal logician is compelled simply to take the processes of thought as determined in psychology or metaphysics or what not, and to consider certain aspects of them. His science has, therefore, no independent place, and no method of development. Independence may be striven after, either by attempt ing to develop all processes of thought and their logical peculiarities from an initial definition of thought solely, or by combining with this definition the view that non-contradictoriness is the one logical quality, and thus assigning to logic the discussion of the conditions of non-contradiction in thought. Of the first, Hamilton may be taken as the type; of the second, Twesten, Mai.se], and Spalding.
