words, it is 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 non-entity, 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 non-entity 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 it is 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,