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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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- Geometry is a science which determines the properties of space synthetically, and yet a priorI. What, then, must be our representation of space, in order that such a cognition of it may be possible?
For, if these objections hold good, we deny to space, and with it to all mathematics, objective validity, and no longer know wherefore, and how far, mathematics can be applied to phenomena. Consequently, even the perception of an object as phenomenon is possible only through the same synthetical unity of the manifold of the given sensuous intuition, through which the unity of the composition of the homogeneous manifold in the conception of a quantity is cogitated; that is to say, all phenomena are quantities, and extensive quantities, because as intuitions in space or time they must be represented by means of the same synthesis through which space and time themselves are determined. Precisely similar is the case with our notion of space. For inasmuch as only by means of such pure form of sensibility an object can appear to us, that is, be an object of empirical intuition, space and time are pure intuitions, which contain a priori the condition of the possibility of objects as phenomena, and an a priori synthesis in these intuitions possesses objective validity. Thus much only can we say; "The image is a product of the empirical faculty of the productive imagination--the schema of sensuous conceptions (of figures in space, for example) is a product, and, as it were, a monogram of the pure imagination a priori, whereby and according to which images first become possible, which, however, can be connected with the conception only mediately by means of the schema which they indicate, and are in themselves never fully adequate to it." On the other hand, the schema of a pure conception of the understanding is something that cannot be reduced into any image--it is nothing else than the pure synthesis expressed by the category, conformably, to a rule of unity according to conceptions. Nothing further is necessary, then, for the solution of the first cosmological problem, than to decide, whether, in the regress to the unconditioned quantity of the universe (as regards space and time), this never limited ascent ought to be called a regressus in infinitum or indefinitum.