Page:Kant's Prolegomena etc (1883).djvu/299

 divisible to infinity; that is, its parts can be distinguished to infinity, although they cannot be moved, and consequently cannut be separated (according to demonstrations of geometry). But in a space filled with matter, every part contains the same repulsive force, to counteract all other forces, on all sides; in other words, to drive them back, and in the same way to be driven back by them, that is, to be moved to a distance from them. Hence, every part of a space filled with matter is, movable in itself, and consequently separable from those remaining, as material substance, by physical division. So far, then, as the mathematical divisibility of space filled by a matter reaches, thus far does the possibility of the physical division of the substance that fills it, reach. But the mathematical division extends to infinity, and consequently also the physical; that is, all matter, is divisible to infinity, and indeed to parts, of which each is itself again material substance.

Observation 1.

By the demonstration of the infinite divisibility of space, that of matter has not, by a long way, been proved, if it has not previously been established, that in every part of space material substance exists, that is, that parts in themselves movable are to be met with. For if a monadologist wished to assume that matter consisted of physical points, each of which (for this reason) had no movable parts, but nevertheless, filled a space by mere repulsive force, he would still be able to admit that this space, although not the substance acting in it (in other words, the sphere of the latter's activity, though not the acting movable subject itself), could be divided by the division of its spaces. He would thus compound matter of physical by indivisible parts, and yet allow it to occupy space in a dynamical manner.

But by the above demonstration, the monadologist is entirely deprived of this resort. For, thereby it is clear, that in a filled space there can be no point that does not itself resist repulsion on all sides in the same way as it is repelled; in other words, as a reacting subject, in itself movable, existing outside every other repulsive point; and hence that the hypothesis of a point filling a