it; since their infinite divisibility
is utterly impossible and contradictory.

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, 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, TOTA, ET TO