scourse or reason about an infinite quantity, as an infinite space, or
an infinite duration. For, as our idea of infinity being, as I think, AN
ENDLESS GROWING IDEA, but the idea of any quantity the mind has, being
at that time TERMINATED in that idea, (for be it as great as it will, it
can be no greater than it is,)--to join infinity to it, is to adjust a
standing measure to a growing bulk; and therefore I think it is not an
insignificant subtilty, if I say, that we are carefully to distinguish
between the idea of the infinity of space, and the idea of a space
infinite. The first is nothing but a supposed endless progression of the
mind, over what repeated ideas of space it pleases; but to have actually
in the mind the idea of a space infinite, is to suppose the mind already
passed over, and actually to have a view of ALL those repeated ideas of
space which an ENDLESS repetition can never totally represent to it;
which carries in it a plain contradiction.

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