The other part of our system is a consequence of this. The parts, into which the ideas of space and time resolve themselves, become at last indivisible; and these indivisible parts, being nothing in themselves, are inconceivable when not filled with something real and existent. The ideas of space and time are therefore no separate or distinct ideas, but merely those of the manner or order in which objects exist; or, in other words, 'tis impossible to conceive either a vacuum and extension without matter, or a time when there was no succession or change in any real existence. The intimate connexion betwixt these parts of our system is the reason why we shall examine together the objections which have been urged against both of them, beginning with those against the finite divisibility of extension. I. The first of these objections which I shall take notice of, is more proper to prove this connexion and dependence of the one part upon the other than to destroy either of them. It has often been maintained in the schools, that extension must be divisible, _in infinitum_, because the system of mathematical points is absurd; and that system is absurd, because a mathematical point is a nonentity, and consequently can never, by its conjunction with others, form a real existence. This would be perfectly decisive, were there no medium betwixt the infinite divisibility of matter, and the nonentity of mathematical points. But there is evidently a medium, viz. the bestowing a colour or solidity on these points; and the absurdity of both the extremes is a demonstration of the truth and reality of this medium. The system of _physical_ points, which is another medium, is too absurd to need a refutation. A real extension, such as a physical point is supposed to be, can never exist without parts different from each other; and wherever objects are different, they are distinguishable and separable by the imagination. II. The second objection is derived from the necessity there would be of _penetration_, if extension consisted of mathematical points. A simple and indivisible atom that touches another must necessarily penetrate it; for 'tis impossible it can touch it by its external parts, from the very supposition of its perfect simplicity, which excludes all parts. It must therefore touch it intimately, and in its whole essence, _secundum se, tota, et totaliter_; which is the very definition of penetration. But penetration is impossible: mathematical points are of consequence equally impossible.