I must confess, for my part, I have no clear distinct
ideas of the different bulk or extension of those
bodies, having but a very obscure one of either of
them. So that, I think, when we talk of division
of bodies in infinitum, our idea of their distinct
bulks, which is the subject and foundation of division,
comes, after a little progression, to be confounded,
and almost lost in obscurity. For that idea which
is to represent only bigness must be very obscure
and confused, which we cannot distinguish from one
ten times as big, but only by number: so that
we have clear distinct ideas, we may say, of ten and
one, but no distinct ideas of two such extensions.
It is plain from hence, that, when we talk of infinite
divisibility of body or extension, our distinct and
clear ideas are only of numbers: but the clear
distinct ideas of extension, after some progress of
division, are quite lost; and of such minute parts
we have no distinct ideas at all; but it returns, as
all our ideas of infinite do, at last to that of number
always to be added; but thereby
never amounts to any distinct idea of actual infinite
parts. We have, it is true, a clear idea
of division, as often as we think of it; but thereby
we have no more a clear idea of infinite parts in
matter, than we have a clear idea of an infinite number,
by being able still to add new numbers to any assigned
numbers we have: endless divisibility giving
us no more a clear and distinct idea of actually infinite
parts, than endless addibility (if I may so speak)
gives us a clear and distinct idea of an actually
infinite number: they both being only in a power
still of increasing the number, be it already as great
as it will. So that of what remains to be added
(wherein consists the infinity)
we have but an obscure, imperfect, and confused idea;
from or about which we can argue or reason with no
certainty or clearness, no more than we can in arithmetic,
about a number of which we have no such distinct idea
as we have of 4 or 100; but only this relative obscure
one, that, compared to any other, it is still bigger:
and we have no more a clear positive idea of it, when
we [dropped line*] than if we should say it is bigger
than 40 or 4: 400,000,000 having no nearer a
proportion to the end of addition or number than 4.
For he that adds only 4 to 4, and so proceeds, shall
as soon come to the end of all addition, as he that
adds 400,000,000 to 400,000,000. And so likewise
in eternity; he that has an idea of but four years,
has as much a positive complete idea of eternity,
as he that has one of 400,000,000 of years: for
what remains of eternity beyond either of these two
numbers of years, is as clear to the one as the other;
i.e. neither of them has any clear positive idea
of it at all. For he that adds only 4 years to
4, and so on, shall as soon reach eternity as he that
adds 400,000,000 of years, and so on; or, if he please,