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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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Mathematics, too, treats of the difference of lines and surfaces--as spaces of different quality, of the continuity of extension--as a quality thereof.

 If you are interested or just want some further information, all you have to do is email me back, press reply and put MORE INFO in the subject box, and I shall send you further details.  For the infinity of the division of a phenomenon in space rests altogether on the fact that the divisibility of a phenomenon is given only in and through this infinity, that is, an undetermined number of parts is given, while the parts themselves are given and determined only in and through the subdivision; in a word, the infinity of the division necessarily presupposes that the whole is not already divided in se. The world around us opens before our view so magnificent a spectacle of order, variety, beauty, and conformity to ends, that whether we pursue our observations into the infinity of space in the one direction, or into its illimitable divisions in the other, whether we regard the world in its greatest or its least manifestations- even after we have attained to the highest summit of knowledge which our weak minds can reach, we find that language in the presence of wonders so inconceivable has lost its force, and number its power to reckon, nay, even thought fails to conceive adequately, and our conception of the whole dissolves into an astonishment without power of expression--all the more eloquent that it is dumb. In order to construct the table of ideas in correspondence with the table of categories, we take first the two primitive quanta of all our intuitions, time and space. 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. We represented in these antinomies the conditions of phenomena as belonging to the conditioned according to relations of space and time- which is the usual supposition of the common understanding. Thus the mere form of external sensuous intuition, namely, space, affords us, per se, no cognition; it merely contributes the manifold in a priori intuition to a possible cognition. But in the Critique itself it will be demonstrated, not hypothetically, but apodeictically, from the nature of our representations of space and time. It may, for example, be alleged, that a limit to the world, as regards both space and time, is quite possible, without at the same time holding the existence of an absolute time before the beginning of the world, or an absolute space extending beyond the actual world--which is impossible.