Oyonale - Créations 3D et expériences graphiques
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Cliquer sur les phrases pour les voir dans leur contexte. Les textes de Immanuel Kant et David Hume sont disponibles auprès du Projet Gutenberg.
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Take, for example, the proposition; "Two straight lines cannot enclose a space, and with these alone no figure is possible," and try to deduce it from the conception of a straight line and the number two; or take the proposition; "It is possible to construct a figure with three straight lines," and endeavour, in like manner, to deduce it from the mere conception of a straight line and the number three. 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. The reason of this is that in the world of phenomena, in which alone objects are presented to our minds, there are two main elements--the form of intuition (space and time), which can be cognized and determined completely a priori, and the matter or content--that which is presented in space and time, and which, consequently, contains a something--an existence corresponding to our powers of sensation. For geometrical principles are always apodeictic, that is, united with the consciousness of their necessity, as; "Space has only three dimensions." But propositions of this kind cannot be empirical judgements, nor conclusions from them. I cannot say, "The regress from a given perception to everything limited either in space or time, proceeds in infinitum," for this presupposes an infinite cosmical quantity; neither can I say, "It is finite," for an absolute limit is likewise impossible in experience. To apply this remark to space. Transcendental idealism allows that the objects of external intuition--as intuited in space, and all changes in time--as represented by the internal sense, are real. But places always presuppose intuitions which are to limit or determine them; and we cannot conceive either space or time composed of constituent parts which are given before space or time.