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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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Now, the facts that space is a formal condition a priori of external experience, that the formative synthesis, by which we construct a triangle in imagination, is the very same as that we employ in the apprehension of a phenomenon for the purpose of making an empirical conception of it, are what alone connect the notion of the possibility of such a thing, with the conception of it. If they adopt the second view of inherence, which is preferred by some metaphysical natural philosophers, and regard space and time as relations (contiguity in space or succession in time), abstracted from experience, though represented confusedly in this state of separation, they find themselves in that case necessitated to deny the validity of mathematical doctrines a priori in reference to real things (for example, in space)--at all events their apodeictic certainty. The first notion of space and extension is derived solely from the senses of sight and feeling; nor is there any thing, but what is coloured or tangible, that has parts disposed after such a manner, as to convey that idea. 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. III. When we say that the intuition of external objects, and also the self-intuition of the subject, represent both, objects and subject, in space and time, as they affect our senses, that is, as they appear--this is by no means equivalent to asserting that these objects are mere illusory appearances. A conception of space and time as quanta may be presented a priori in intuition, that is, constructed, either alone with their quality (figure), or as pure quantity (the mere synthesis of the homogeneous), by means of number. Time and space are, therefore, two sources of knowledge, from which, a priori, various synthetical cognitions can be drawn. But, in order to cognize something in space (for example, a line), I must draw it, and thus produce synthetically a determined conjunction of the given manifold, so that the unity of this act is at the same time the unity of consciousness (in the conception of a line), and by this means alone is an object (a determinate space) cognized.