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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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Thus the categories do in some measure really extend further than sensuous intuition, inasmuch as they think objects in general, without regard to the mode (of sensibility) in which these objects are given.

 For it must be confessed of the categories that they are not of themselves sufficient for the cognition of things in themselves and, without the data of sensibility, are mere subjective forms of the unity of the understanding. Only pure intuitions and pure conceptions are possible a priori; the empirical only a posteriorI. We apply the term sensibility to the receptivity of the mind for impressions, in so far as it is in some way affected; and, on the other hand, we call the faculty of spontaneously producing representations, or the spontaneity of cognition, understanding. On the contrary, the transcendental conception of phenomena in space is a critical admonition, that, in general, nothing which is intuited in space is a thing in itself, and that space is not a form which belongs as a property to things; but that objects are quite unknown to us in themselves, and what we call outward objects, are nothing else but mere representations of our sensibility, whose form is space, but whose real correlate, the thing in itself, is not known by means of these representations, nor ever can be, but respecting which, in experience, no inquiry is ever made. 
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 In the aesthetic, I regarded this unity as belonging entirely to sensibility, for the purpose of indicating that it antecedes all conceptions, although it presupposes a synthesis which does not belong to sense, through which alone, however, all our conceptions of space and time are possible. But in so far as the synthesis of the imagination is an act of spontaneity, which is determinative, and not, like sense, merely determinable, and which is consequently able to determine sense a priori, according to its form, conformably to the unity of apperception, in so far is the imagination a faculty of determining sensibility a priori, and its synthesis of intuitions according to the categories must be the transcendental synthesis of the imagination. 

In transcendental logic we isolate the understanding (as in transcendental aesthetic the sensibility) and select from our cognition merely that part of thought which has its origin in the understanding alone.

 The pure categories, apart from the formal conditions of sensibility, have a merely transcendental meaning, but are nevertheless not of transcendental use, because this is in itself impossible, inasmuch as all the conditions of any employment or use of them (in judgements) are absent, to wit, the formal conditions of the subsumption of an object under these conceptions. The proposition, "I think," expresses an undetermined empirical intuition, that perception (proving consequently that sensation, which must belong to sensibility, lies at the foundation of this proposition); but it precedes experience, whose province it is to determine an object of perception by means of the categories in relation to time; and existence in this proposition is not a category, as it does not apply to an undetermined given object, but only to one of which we have a conception, and about which we wish to know whether it does or does not exist, out of, and apart from this conception. We therefore distinguish the science of the laws of sensibility, that is, aesthetic, from the science of the laws of the understanding, that is, logic.