Page:Kant's Prolegomena etc (1883).djvu/301

 cases where a larger or smaller space is to be conceived as entirely tilled by the same quantity of matter, that is, by an identical quantum of repulsive forces. By an infinitely divisible [thing], therefore, no real distance of parts, which, with all extension of the space of the whole, always constitute a continuum, may be assumed, although the possibility of this extension can only be made comprehensible under the idea of an infinitely small distance.

Observation 2.

Mathematics can indeed, in its internal employment, be quite indifferent to the chicane of a mistaken metaphysics, and rest in the certain possession of its evident assertions of the infinite divisibility of space, no matter what objections a sophistry, clinging to mere conceptions, may throw in its way; but in the application of its propositions, which apply to space, to substance, which fills it, it must rely on a test according to mere conceptions; in other words, on metaphysics. The above proposition is itself a proof of this. For it does not follow necessarily that matter is physically divisible to infinity, although it is so in a mathematical connection, every part of space being again a space, and hence always including within itself parts external to one another; but this cannot prove that in every possible part of this filled space, there is substance, which, consequently, separated from all the rest, exists as in itself, movable; something has been wanting then hitherto, to the mathematical demonstration, without which it can have no certain application to Natural Science, and this defect has been obviated in the proposition above given. But as concerns the remaining attacks of metal physics on the at present physical proposition, of the infinite divisibility of matter, the mathematician must entirely resign himself to the philosopher, who, apart from this, through these objections, betakes himself into a labyrinth, out of which it is difficult for him to find his way, even in questions immediately concerning him, and hence has enough to do on his own account, without the mathematician mixing himself up in the business. If, namely, matter be infinitely divisible, then (concludes the dogmatic