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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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Its relation to objects in space gives us the conception of connection (commercium) with bodies.

 Now, as everything real that occupies a space, contains a manifold the parts of which are external to each other, and is consequently composite--and a real composite, not of accidents (for these cannot exist external to each other apart from substance), but of substances--it follows that the simple must be a substantial composite, which is self-contradictory. 

The principle of continuity forbids any leap in the series of phenomena regarded as changes (in mundo non datur saltus); and likewise, in the complex of all empirical intuitions in space, any break or hiatus between two phenomena (non datur hiatus)- for we can so express the principle, that experience can admit nothing which proves the existence of a vacuum, or which even admits it as a part of an empirical synthesis.

 The idea of space is conveyed to the. [Footnote; They can be perceived only as phenomena, and some part of them must always belong to the non-ego; whereas pure intuitions are entirely the products of the mind itself, and as such are coguized IN THEMSELVES.--Tr] They contain, then, over and above the intuition, the materials for an object (through which is represented something existing in space or time), that is to say, they contain the real of sensation, as a representation merely subjective, which gives us merely the consciousness that the subject is affected, and which we refer to some external object. This synthesis is pure when the diversity is not given empirically but a priori (as that in space and time). It would be unjust to accuse us of holding the long-decried theory of empirical idealism, which, while admitting the reality of space, denies, or at least doubts, the existence of bodies extended in it, and thus leaves us without a sufficient criterion of reality and illusion. The simple but empirically determined consciousness of my own existence proves the existence of external objects in space. just as if it were possible to imagine another mode of intuition than that given in the primitive intuition of space; and just as if its a priori determinations did not apply to everything, the existence of which is possible, from the fact alone of its filling space. The home-based business has been born out of necessity. From what source the conceptions of space and time, with which (as the only primitive quanta) they have to deal, enter their minds, is a question which they do not trouble themselves to answer; and they think it just as unnecessary to examine into the origin of the pure conceptions of the understanding and the extent of their validity.