— 214 —
We have no Idea of infinite Space.       §8. 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 never 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 compleating the Idea, there we have our Idea of
Infinity; which though it seems to be pretty clear, when we con-
sider 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; ’tis 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, what-
ever 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 inlarging, and Pro-
gression, 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
— 215 —
no Bounds; and that the Idea of Infinity, in which our Thoughts can
find none.
Locke Hum II, 17, §8, pp. 214-215