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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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Of this we find a striking example in the cognitions of space and its relations, which form the foundation of pure mathematics. A substance which is permanently present in space, yet without filling it (like that tertium quid between matter and the thinking subject which some have tried to introduce into metaphysics), or a peculiar fundamental power of the mind of intuiting the future by anticipation (instead of merely inferring from past and present events), or, finally, a power of the mind to place itself in community of thought with other men, however distant they may be--these are conceptions the possibility of which has no ground to rest upon. 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. Space is essentially one, and multiplicity in it, consequently the general notion of spaces, of this or that space, depends solely upon limitations. It is therefore not merely possible or probable, but indubitably certain, that space and time, as the necessary conditions of all our external and internal experience, are merely subjective conditions of all our intuitions, in relation to which all objects are therefore mere phenomena, and not things in themselves, presented to us in this particular manner. Now to this presupposition, for which they can have no ground in experience, and which consequently is merely metaphysical, I oppose a transcendental demonstration, which it is true will not explain the difference in the filling up of spaces, but which nevertheless completely does away with the supposed necessity of the above-mentioned presupposition that we cannot explain the said difference otherwise than by the hypothesis of empty spaces. But if it is a phenomenon in space, it has a place not merely in the understanding (among conceptions), but also in sensuous external intuition (in space), and in this case, the physical locale is a matter of indifference in regard to the internal determinations of things, and one place, B, may contain a thing which is perfectly similar and equal to another in a place, A, just as well as if the two things were in every respect different from each other.