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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For, if these objections hold good, we deny to space, and with it to all mathematics, objective validity, and no longer know wherefore, and how far, mathematics can be applied to phenomena. In order fully to convince the reader of this certainty, we shall select a case which will serve to make its validity apparent, and also to illustrate what has been said in SS 3. Suppose, then, that space and time are in themselves objective, and conditions of the--possibility of objects as things in themselves. For, in the first place, we can only represent to ourselves one space, and, when we talk of divers spaces, we mean only parts of one and the same space. 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. Space and time, as conditions of the possibility of the presentation of objects to us, are valid no further than for objects of sense, consequently, only for experience. My purpose, in the above remark, is merely this; to guard any one against illustrating the asserted ideality of space by examples quite insufficient, for example, by colour, taste, etc.; for these must be contemplated not as properties of things, but only as changes in the subject, changes which may be different in different men. The ideas of space and time are therefore no separate or distinct ideas, but merely those of the manner or order, in which objects exist: Or in other words, it is impossible to conceive either a vacuum and extension without matter, or a time, when there was no succession or change in any real existence. If, for example, we take the pure conceptions of relation, we find that (1) for the purpose of presenting to the conception of substance something permanent in intuition corresponding thereto and thus of demonstrating the objective reality of this conception, we require an intuition (of matter) in space, because space alone is permanent and determines things as such, while time, and with it all that is in the internal sense, is in a state of continual flow; (2) in order to represent change as the intuition corresponding to the conception of causality, we require the representation of motion as change in space; in fact, it is through it alone that changes, the possibility of which no pure understanding can perceive, are capable of being intuited. For example, the proposition, "All objects are beside each other in space," is valid only under the limitation that these things are taken as objects of our sensuous intuition.