they are,
inconsistent, the one side or other always perplexes, whatever
consequences we draw from the other; as an idea of motion not passing on
would perplex any one who should argue from such an idea, which is not
better than an idea of motion at rest. And such another seems to me to
be the idea of a space, or (which is the same thing) a number infinite,
i. e. of a space or number which the mind actually has, and so views
and terminates in; and of a space or number, which, in a constant and
endless enlarging and progression, it can in thought never attain to.
For, how large soever an idea of space I have in my mind, it is no
larger than it is that instant that I have it, though I be capable the
next instant to double it, and so on in infinitum; for that alone is
infinite which has no bounds; and that the idea of infinity, in which
our thoughts can find none.

9. Number affords us the clearest Idea of Infinity.

But of all other ideas, it is number, as I have said, which I think
furnishes us with the clearest and most distinct idea of infinity we are
capable of. For, even in space and duration, when the mind pursues the
idea of infinity, it there makes use of the ideas and repetitions of
numbers, as of millions and millions of miles, or years, which are so
many distinct ideas,--kept best by number from running into a confused
heap, wherein the mind loses itself; and when it has added together
as many millions, &c., as it pleases, of known lengths of space or
duration, the clearest idea it can get of infinity, is the confused
incomprehensible remainder of endless addible numbers, which affords no
prospect of stop or boundary.

10. Our different Conceptions of the Infinity of Number contrasted with
those of Duration and Expansion.

It will, perhaps, give us a little further light into the idea we have
of infinity, and discover to us, that it is NOTHING BUT THE INFINITY OF
NUMBER APPLIED TO DETERMINATE PARTS, OF WHICH WE HAVE IN OUR MINDS THE
DISTINCT IDEAS, if we consider that number is not generally thought by
us infinite, whereas duration and extension are apt to be so; which
arises from hence,--that in number we are at one end, as it were: for
there being in number nothing LESS than an unit, we there stop, and are
at an end; but in addition, or increase of number, we can set no bounds:
and so it is like a line, whereof one end terminating with us, the other
is extended still forwards, beyond all that we can