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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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3. On this necessity a priori is also founded the possibility of apodeictic principles of the relations of time, or axioms of time in general, such as; "Time has only one dimension," "Different times are not coexistent but successive" (as different spaces are not successive but coexistent). We have already traced to their sources the conceptions of space and time, by means of a transcendental deduction, and we have explained and determined their objective validity a priorI. Geometry, nevertheless, advances steadily and securely in the province of pure a priori cognitions, without needing to ask from philosophy any certificate as to the pure and legitimate origin of its fundamental conception of space. The attributes of necessity, infinitude, unity, existence apart from the world (and not as a world soul), eternity (free from conditions of time), omnipresence (free from conditions of space), omnipotence, and others, are pure transcendental predicates; and thus the accurate conception of a Supreme Being, which every theology requires, is furnished by transcendental theology alone. The attributes of necessity, infinitude, unity, existence apart from the world (and not as a world soul), eternity (free from conditions of time), omnipresence (free from conditions of space), omnipotence, and others, are pure transcendental predicates; and thus the accurate conception of a Supreme Being, which every theology requires, is furnished by transcendental theology alone. Thus space and time were the intelligible form of the connection of things (substances and their states) in themselves. Nevertheless, space is so conceived of, for all parts of space are equally capable of being produced to infinity. It is therefore from the human point of view only that we can speak of space, extended objects, etc. On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition a priori, under which alone the schema of a pure conception of external intuition can exist; for example, "be tween two points only one straight line is possible," "two straight lines cannot enclose a space," etc.