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Difference between infinity of Space, and Space infinite.       §7. Though our Idea of Infinity arise from the contemplation of
Quantity, and the endless increase the Mind is able to make in
Quantity, by the repeated additions of what Portions thereof it
pleases; yet I guess we cause great confusion in our Thoughts, when
we join Infinity to any supposed Idea of Quantity the Mind can be
thought to have, and so discourse or reason about an infinite
quantity, ( viz. ) an infinite Space, or an infinite Duration: For 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
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endless repetition can never totally represent to it, which carries in
it a plain contradiction.
Locke Hum II, 17, §7, pp. 213-214