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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The conception of a cubic foot of space, however I may think it, is in itself completely identical. 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. For if even the complete intuition of a determinate space or time is thoroughly real, that is, if no part thereof is empty, yet because every reality has its degree, which, with the extensive quantity of the phenomenon unchanged, can diminish through endless gradations down to nothing (the void), there must be infinitely graduated degrees, with which space or time is filled, and the intensive quantity in different phenomena may be smaller or greater, although the extensive quantity of the intuition remains equal and unaltered. Empirical intuition is therefore not a composition of phenomena and space (of perception and empty intuition). 2. Space then is a necessary representation a priori, which serves for the foundation of all external intuitions. For we perceive that although two equal spaces may be completely filled by matters altogether different, so that in neither of them is there left a single point wherein matter is not present, nevertheless, every reality has its degree (of resistance or of weight), which, without diminution of the extensive quantity, can become less and less ad infinitum, before it passes into nothingness and disappears. And this foundation is itself unworthy of trust, if it leave under and above it empty space, if it do not fill all, and leave no room for a why or a wherefore, if it be not, in one word, infinite in its reality.