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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Speculative reason has thus, at least, made room for such an extension of our knowledge; and, if it must leave this space vacant, still it does not rob us of the liberty to fill it up, if we can, by means of practical data--nay, it even challenges us to make the attempt.* 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 since, according to their hypothesis, the least as well as greatest figures contain an infinite number of parts; and since infinite numbers, properly speaking, can neither be equal nor unequal with respect to each other; the equality or inequality of any portions of space can never depend on any proportion in the number of their parts. Space, therefore, cannot be regarded as absolutely and in itself something determinative of the existence of things, because it is not itself an object, but only the form of possible objects. But the understanding at the same time comprehends that it cannot employ its categories for the consideration of things in themselves, because these possess significance only in relation to the unity of intuitions in space and time, and that they are competent to determine this unity by means of general a priori connecting conceptions only on account of the pure ideality of space and time. Now as every thing, that is contiguous to us, either in space or time, strikes upon us with such an idea, it has a proportional effect on the will and passions, and commonly operates with more force than any object, that lies in a more distant and obscure light. The imagination moves with more difficulty in passing from one portion of time to another, than in a transition through the parts of space; and that because space or extension appears united to our senses, while time or succession is always broken and divided.