— 220 —
No positive Idea of infinite Space.       §18. He that thinks he has a positive Idea of infinite Space, will,
when he considers it, find that he can no more have a positive Idea of
the greatest, than he has of the least Space. For in this latter, which
seems the easier of the two, and more within our comprehension,
we are capable only of a comparative Idea of Smalness, which will
always be less than any one, whereof we have the positive Idea. All
our positive Ideas of any Quantity, whether great or little, have
always bounds; though our comparative Idea, whereby we can
always add to the one, and take from the other, hath no bounds.
For that which remains either great or little, not being compre-
hended in that positive Idea, which we have, lies in obscurity: And
we have no other Idea of it, but of the power of enlarging the one,
and diminishing the other, without ceasing. A Pestle and Mortar
will as soon bring any Particle of Matter to Indivisibility, as the
acutest Thought of a Mathematician: And a Surveyor may, as
soon with his Chain, measure out infinite Space, as a Philosopher, by
the quickest flight of Mind, reach it; or by thinking comprehend it,
which is to have a positive Idea of it. He that thinks on a Cube of an
Inch diameter, has a clear and positive Idea of it in his mind, and so
can frame one of 1/2 a 1/4 1/8, and so on till he has the Idea in his Thoughts
of something very little: but yet reaches not the Idea of that
incomprehensible Littleness, which Division can produce. What
remains of Smalness, is as far from his Thoughts, as when he first
began; and therefore he never comes at all to have a clear and
positive Idea of that Smalness, which is consequent to infinite
Divisibility.
Locke Hum II, 17, §18, p. 220