tion is empirical. But empirical knowledge is experience. Hence there can be no a priori knowledge, except of objects that are capable of entering into experience. But although such knowledge is limited to objects of experience, it is not therefore altogether derived from experience. For pure perceptions as well as pure conceptions are elements in knowledge, and both are found in us a priori. There are only two ways in which we can account for a necessary coincidence of the data of experience with the conceptions which we form of its objects: either that experience must make the conceptions possible, or the conceptions must make experience possible. The former supposition is inconsistent with the nature of the categories, not to speak of pure sensuous perception; for the categories, as a priori conceptions, are independent of experience, and to derive them from experience would be a sort of generatio aequivoca. The alternative supposition, which involves what may be called an epigenesis of pure reason, must therefore be adopted, and we must hold that the categories, as proceeding from understanding, contain the grounds of the possibility of any experience whatever. Short Statement of the Deduction. What has been shown in the deduction of the categories is that the pure conceptions of understanding, on which all theoretical a priori knowledge is based, are principles that make experience possible. In other words, they are principles for the general determination of phenomena in space and time, a determination that ultimately flows from the principle of the original synthetic unity of apperception as the form of understanding in relation to space and time, the original forms of sensibility. If the understanding is explained as the faculty of rules, the faculty of judgment consists in performing the subsumption under these rules, that is, in determining whether anything falls under a given rule (casus datae legis) or not. General logic contains no precepts for the faculty of judgment and cannot contain them. For as it takes no account of the contents of our knowledge, it has only to explain analytically the mere form of knowledge in concepts, judgments, and syllogisms, and thus to establish formal rules for the proper employment of the understanding. . . . But although general logic can give no precepts to the faculty of judgment, the case is quite different with transcendental logic, so that it even seems as if it were the proper business of the latter to correct and to establish by definite rules the faculty of the judgment in the use of the pure understanding.. What distinguishes transcendental philosophy is, that besides giving the rules (or rather the general condition of rules) which are contained in the pure concept of the understanding, it can at the same time indicate a priori the case to which each rule may be applied. The superiority which it enjoys in this respect over all other sciences, except mathematics, is due to this, that it treats of concepts which are meant to refer to their objects a priori, so that their objective validity cannot be proved a posteriori. * Reprinted from Immanuel Kant's Critique of Pure Reason, translated by F. Max Müller, London, Macmillan & Co. Ltd., 1881, vol. ii. Our transcendental doctrine of the faculty of judgment will consist of two chapters. The first will treat of the sensuous condition under which alone pure concepts of the understanding can be used. This is what I call the schematism of the pure understanding. The second will treat of the synthetical judgments, which can be derived a priori under these conditions from pure concepts of the understanding, and on which all knowledge a priori depends. It will treat, therefore, of the principles of the pure understanding. CHAPTER I. THE SCHEMATISM OF THE PURE CONCEPTS In comprehending any object under a concept, the representation of the former must be homogeneous with the latter, that is, the concept must contain that which is represented in the object to be comprehended under it, for this is the only meaning of the expression that an object is comprehended under a concept. Thus, for instance, the empirical concept of a plate is homogeneous with the pure geometrical concept of a circle, the roundness which is conceived in the first forming an object of intuition in the latter. Now it is clear that pure concepts of the understanding, as compared with empirical or sensuous impressions in general, are entirely heterogeneous, and can never be met with in any intuition. How then can the latter be comprehended under the former, or how can the categories be applied to phenomena, as no one is likely to say that causality, for instance, could be seen through the senses, and was contained in the phenomenon? It is really this very natural and important question which renders a transcendental doctrine of the faculty of judgment necessary, in order to show how it is possible that any of the pure concepts of the understanding can be applied to phenomena. In all other sciences in which the concepts by which the object is thought in general are not so heterogeneous or different from those which represent it in concreto, and as it is given, there is no necessity to enter into any discussions as to the applicability of the former to the latter. In our case there must be some third thing homogeneous on the one side with the category, and on the other with the phenomenon, to render the application of the former to the latter possible. This intermediate representation must be pure (free from all that is empirical) and yet intelligible on the one side, and sensuous on the other. Such a representation is the transcendental schema. The concept of the understanding contains pure synthetical unity of the manifold in general. Time, as the formal condition of the manifold in the internal sense, consequently of the conjunction of all representations, contains a manifold a priori in pure intuition. A transcendental determination of time is so far homogeneous with the category (which constitutes its unity) that it is general and founded on a rule a priori; and it is on the other hand so far homogeneous with the phenomenon, that time must be contained in every empirical representation of the manifold. The application of the category to phenomena becomes possible therefore by means of the transcendental determination of time, which, as a schema of the concepts of the understanding, allows the phenomena to be comprehended under the category. CHAPTER II. PRINCIPLES OF THE PURE UN DERSTANDING We have in the preceding chapter considered the transcendental faculty of judgment with reference to those general conditions only under which it is justified in using the pure concepts of the understanding for synthetical judgments. It now becomes our duty to represent systematically those judgments which, under that critical provision, the understanding can really produce a priori. For this purpose our table of categories will be without doubt our natural and best guide. Their principle is: All intuitions are extensive quantities.1 I call an extensive quantity that in which the representation of the whole is rendered possible by the representation of its parts, and therefore necessarily preceded by it. I cannot represent to myself any line, however small it may be, without drawing it in thought, that is, without producing all its parts one after the other, starting from a given point, and thus, first of all, drawing its intuition. The same applies to every, even the smallest portion of time. I can only think in it the successive progress from one moment to another, thus producing in the end, by all portions of time and their addition, a definite quantity of time. As in all phenomena pure intuition is either space or time, every phenomenon, as an intuition, must be an extensive quantity, because it can be known in apprehension by a successive synthesis only (of part with part). All phenomena therefore, when perceived in intuition, are aggregates (collections) of previously given parts, which is not the case with every kind of quantities, but with those only which are represented to us and apprehended as extensive. On this successive synthesis of productive imagination in elaborating figures are founded the mathematics of extension with their axioms (geometry), containing the conditions of sen 1 The titles and the statements of the principles of the pure understanding are taken from the second edition. |