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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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The divisibility of a body rests upon the divisibility of space, which is the condition of the possibility of the body as an extended whole.

 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. As regards limitation, therefore, our procedure in space is also a regressus, and the transcendental idea of the absolute totality of the synthesis in a series of conditions applies to space also; and I am entitled to demand the absolute totality of the phenomenal synthesis in space as well as in time. Now as every thing, that is contiguous to us, either in space or time, strikes upon us with such an idea, it has a proportional effect on the will and passions, and commonly operates with more force than any object, that lies in a more distant and obscure light. In our experiences it is easy to observe that it is only the continuous influences in all parts of space that can conduct our senses from one object to another; that the light which plays between our eyes and the heavenly bodies produces a mediating community between them and us, and thereby evidences their coexistence with us; that we cannot empirically change our position (perceive this change), unless the existence of matter throughout the whole of space rendered possible the perception of the positions we occupy; and that this perception can prove the contemporaneous existence of these places only through their reciprocal influence, and thereby also the coexistence of even the most remote objects--although in this case the proof is only mediate. 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. This is just for interest, not counting principle and not counting the compounding of the interest which can add substantial additional income. If phenomena were things in themselves, and time and space forms of the existence of things, condition and conditioned would always be members of the same series; and thus would arise in the present case the antinomy common to all transcendental ideas--that their series is either too great or too small for the understanding. But if I join the condition to the conception and say, "All things, as external phenomena, are beside each other in space," then the rule is valid universally, and without any limitation.