Page:Kant's Prolegomena etc (1883).djvu/303

 as belonging to the existence of a phenomenon exist only in thought, namely, in their division itself. Now though the division proceeds to infinity, it is never given as infinite, and hence it does not follow that the divisible contains an infinite number of parts in itself and outside our presentation merely because its division is infinite. For it is not the thing, but only its presentation, whose division could be continued to infinity, and in the object that is unknown in itself, which has also a cause, and yet can be never completed and consequently fully given, it proves no real infinite number, for this would be an express contradiction. A great man who has perhaps contributed more than any one else to maintain the reputation of mathematics in Germany, has more than once turned aside metaphysical claims to upset the propositions of geometry relative to the infinite divisibility of space with the well-grounded observation, that space only belongs to the phenomenon of external things; but he has not been understood. The proposition was taken as though he meant : space appears to us, otherwise it is a thing or relation of things in themselves, but the mathematician considers it only as it appears. Instead of this he ought to have been understood, [as meaning] that space is no quality appertaining to anything outside our senses, but only to the subjective form of our sensibility, under which objects of our external sense, unknown to us as to their construction in themselves, appear to us, this appearance being termed matter. By the foregoing misunderstanding, space was always conceived as a quality [existing] independently, outside our faculty of presentation, but which the mathematician only thought of according to common conceptions, that is, confusedly (for so appearance [phenomenon] is commonly explained); it ascribed the mathematical proposition of the infinite divisibility of matter, a proposition presupposing the highest clearness in the conception of space, to a confused presentation of space, which the geometrician laid at his foundation. In this way, it remained open to the metaphysician to compound space of points, and matter of simple parts, and thus in his opinion to bring clearness into the conception. The ground of the confusion lies in a