Page:Kant's Prolegomena etc (1883).djvu/296

 Proposition 3.

Matter can be compressed to infinity, but it can never be penetrated, by a matter, it does not signify how great its pressing force.

Demonstration.

An original force, by which a matter seeks to extend itself on all sides over a given space occupied by it, must, enclosed in a smaller space, be greater, and compressed into an infinitely small space, be infinite. Now, for any given extensive force of matter, a greater compressive force may be found that compels it into a smaller space, and so on to infinity; which was the first [point]. But for the penetration of a matter, a compression into an infinitely small space, and therefore an infinitely compressive force, is required, which is impossible. Hence, a matter cannot be penetrated by the compression of any other [matter]; which is the second [point].

Observation.

I have, at the commencement of this demonstration, assumed that an extending force, the more it is narrowed, must operate so much the more strongly in the opposite [direction]. Now this would not apply to all kinds of elastic forces, [including those] that are merely derivative; but with matter possessing essential elasticity, in so far as it is matter in general, filling a space, it may be postulated. For expansive force exercised from all points towards all sides, constitutes its very conception, lint the same quantum of expanding forces, brought into a narrower space, must, in every point of the latter, repel so much the more strongly, in inverse proportion to the smallness of the space in which a given quantum of force diffuses its activity.

The impenetrability of matter, resting on resistance, which increases proportionately to the degree of the compression, I term relative; but that which rests on