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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.


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.

 The world has a beginning in time, and is also limited in regard to space. 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. For example, if we take away by degrees from our conceptions of a body all that can be referred to mere sensuous experience--colour, hardness or softness, weight, even impenetrability--the body will then vanish; but the space which it occupied still remains, and this it is utterly impossible to annihilate in thought. Of time we cannot have any external intuition, any more than we can have an internal intuition of space. Space and time themselves, pure as these conceptions are from all that is empirical, and certain as it is that they are represented fully a priori in the mind, would be completely without objective validity, and without sense and significance, if their necessary use in the objects of experience were not shown. And so would it really be, if the pure understanding were capable of an immediate application to objects, and if space and time were determinations of things in themselves.