Oyonale - 3D art and graphic experiments
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Click on the phrases to see them in context. The original texts by Immanuel Kant and David Hume are available from the Gutenberg Projet.
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On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition a priori, under which alone the schema of a pure conception of external intuition can exist; for example, "be tween two points only one straight line is possible," "two straight lines cannot enclose a space," etc. 4th. This philosopher's celebrated doctrine of space and time, in which he intellectualized these forms of sensibility, originated in the same delusion of transcendental reflection. In order fully to convince the reader of this certainty, we shall select a case which will serve to make its validity apparent, and also to illustrate what has been said in SS 3. Suppose, then, that space and time are in themselves objective, and conditions of the--possibility of objects as things in themselves. [*Footnote; Space represented as an object (as geometry really requires it to be) contains more than the mere form of the intuition; namely, a combination of the manifold given according to the form of sensibility into a representation that can be intuited; so that the form of the intuition gives us merely the manifold, but the formal intuition gives unity of representation. But to show reasons for this peculiar character of our understandings, that it produces unity of apperception a priori only by means of categories, and a certain kind and number thereof, is as impossible as to explain why we are endowed with precisely so many functions of judgement and no more, or why time and space are the only forms of our intuition. For, in the contrary case, it would be limited by a void time on the one hand, and by a void space on the other. It is therefore from the human point of view only that we can speak of space, extended objects, etc. The schema of the triangle can exist nowhere else than in thought, and it indicates a rule of the synthesis of the imagination in regard to pure figures in space. The categories are not based, as regards their origin, upon sensibility, like the forms of intuition, space, and time; they seem, therefore, to be capable of an application beyond the sphere of sensuous objects.