Because the parts of such an idea not being perceived to
be, as 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.
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