Oyonale - Créations 3D et expériences graphiques
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Cliquer sur les phrases pour les voir dans leur contexte. Les textes de Immanuel Kant et David Hume sont disponibles auprès du Projet Gutenberg.
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We cannot cogitate a geometrical line without drawing it in thought, nor a circle without describing it, nor represent the three dimensions of space without drawing three lines from the same point perpendicular to one another. If we depart from the subjective condition, under which alone we can obtain external intuition, or, in other words, by means of which we are affected by objects, the representation of space has no meaning whatsoever. Now to this presupposition, for which they can have no ground in experience, and which consequently is merely metaphysical, I oppose a transcendental demonstration, which it is true will not explain the difference in the filling up of spaces, but which nevertheless completely does away with the supposed necessity of the above-mentioned presupposition that we cannot explain the said difference otherwise than by the hypothesis of empty spaces. Space has three dimensions--"Between two points there can be only one straight line," etc. But we cannot affirm the converse, that space, as something self-subsistent, can determine real things in regard to size or shape, for it is in itself not a real thing. That is no longer true, thanks to personal computers, increased phone services, fax machines, and the Internet, it is no longer necessary to live in close proximity to Big Business. In the transcendental aesthetic we proved that everything intuited in space and time, all objects of a possible experience, are nothing but phenomena, that is, mere representations; and that these, as presented to us--as extended bodies, or as series of changes--have no self-subsistent existence apart from human thought. Mathematics, too, treats of the difference of lines and surfaces--as spaces of different quality, of the continuity of extension--as a quality thereof. To the question, therefore, respecting the cosmical quantity, the first and negative answer is; "The world has no beginning in time, and no absolute limit in space."