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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 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. 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. [*Footnote; It is evident that what is meant here is, that empty space, in so far as it is limited by phenomena--space, that is, within the world--does not at least contradict transcendental principles, and may therefore, as regards them, be admitted, although its possibility cannot on that account be affirmed.] But, as an intuition there is something (that is, space, which, with all it contains, consists of purely formal, or, indeed, real relations) which is not found in the mere conception of a thing in general, and this presents to us the substratum which could not be cognized through conceptions alone, I cannot say; because a thing cannot be represented by mere conceptions without something absolutely internal, there is also, in the things themselves which are contained under these conceptions, and in their intuition nothing external to which something absolutely internal does not serve as the foundation. If the second part of my system be true, that the idea of space or extension is nothing but the idea of visible or tangible points distributed in a certain order; it follows, that we can form no idea of a vacuum, or space, where there is nothing visible or tangible. Space is essentially one, and multiplicity in it, consequently the general notion of spaces, of this or that space, depends solely upon limitations. Empirical intuition is therefore not a composition of phenomena and space (of perception and empty intuition). We have therefore no idea of space or extension, but when we regard it as an object either of our sight or feeling. [*Footnote; Space is merely the form of external intuition (formal intuition), and not a real object which can be externally perceived.