So, also, others, after asserting that a line is composed of
points, can produce many arguments to prove that a line cannot be
infinitely divided. Assuredly it is not less absurd to assert
that extended substance is made up of bodies or parts, than it
would be to assert that a solid is made up of surfaces, a surface
of lines, and a line of points. This must be admitted by all who
know clear reason to be infallible, and most of all by those who
deny the possibility of a vacuum. For if extended substance
could be so divided that its parts were really separate, why
should not one part admit of being destroyed, the others
remaining joined together as before? And why should all be so
fitted into one another as to leave no vacuum? Surely in the
case of things, which are really distinct one from the other, one
can exist without the other, and can remain in its original
condition. As, then, there does not exist a vacuum in nature (of
which anon), but all parts are bound to come together to prevent
it, it follows from this that the parts cannot really be
distinguished, and that extended substance in so far as it is
substance cannot be divided.
If anyone asks me the further question, Why are we naturally so
prone to divide quantity? I answer, that quantity is conceived by
us in two ways; in the abstract and superficially, as we imagine
it; or as substance, as we conceive it solely by the intellect.
If, then, we regard quantity as it is represented in our
imagination, which we often and more easily do, we shall find
that it is finite, divisible, and compounded of parts; but if we
regard it as it is represented in our intellect, and conceive it
as substance, which it is very difficult to do, we shall then, as
I have sufficiently proved, find that it is infinite, one, and
indivisible. This will be plain enough to all who make a
distinction between the intellect and the imagination,
especially if it be remembered that matter is everywhere the
same, that its parts are not distinguishable, except in so far as
we conceive matter as diversely modified, whence its parts are
distinguished, not really, but modally. For instance, water, in
so far as it is water, we conceive to be divided, and its parts
to be separated one from the other; but not in so far as it is
extended substance; from this point of view it is neither
separated nor divisible. Further, water, in so far as it is
water, is produced and corrupted; but, in so far as it is
substance, it is neither produced nor corrupted.