8. We have no idea of infinite space.
This, perhaps, will be a little plainer, if we consider it in numbers. The
infinity of numbers, to the end of whose addition every one perceives there is no approach, easily appears to any
one that reflects on it. But, how clear soever this idea of the infinity of number be, there is nothing yet more
evident than the absurdity of the actual idea of an infinite number. Whatsoever positive ideas we have in our
minds of any space, duration, or number, let them be ever so great, they are still finite; but when we suppose an
inexhaustible remainder, from which we remove all bounds, and wherein we allow the mind an endless
progression of thought, without ever completing the idea, there we have our idea of infinity: which, though it
seems to be pretty clear when we consider nothing else in it but the negation of an end, yet, when we would frame
in our minds the idea of an infinite space or duration, that idea is very obscure and confused, because it is made up
of two parts, very different, if not inconsistent. For, let a man frame in his mind an idea of any space or number,
as great as he will; it is plain the mind rests and terminates in that idea, which is contrary to the idea of infinity,
which consists in a supposed endless progression. And therefore I think it is that we are so easily confounded,
when we come to argue and reason about infinite space or duration, etc. 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.
