then I say there is Body; and in proportion as the
resistance to motion is lesser or greater, I say the space is more or
less pure. So that when I speak of pure or empty space, it is not to be
supposed that the word "space" stands for an idea distinct from or
conceivable without body and motion--though indeed we are apt to think
every noun substantive stands for a distinct idea that may be separated
from all others; which has occasioned infinite mistakes. When, therefore,
supposing all the world to be annihilated besides my own body, I say
there still remains pure Space, thereby nothing else is meant but only
that I conceive it possible for the limbs of my body to be moved on all
sides without the least resistance, but if that, too, were annihilated
then there could be no motion, and consequently no Space. Some, perhaps,
may think the sense of seeing doth furnish them with the idea of pure
space; but it is plain from what we have elsewhere shown, that the ideas
of space and distance are not obtained by that sense. See the Essay
concerning Vision.

117. What is here laid down seems to put an end to all those disputes and
difficulties that have sprung up amongst the learned concerning the
nature of pure Space. But the chief advantage arising from it is that we
are freed from that dangerous dilemma, to which several who have employed
their thoughts on that subject imagine themselves reduced, to wit, of
thinking either that Real Space is God, or else that there is something
beside God which is eternal, uncreated, infinite, indivisible, immutable.
Both which may justly be thought pernicious and absurd notions. It is
certain that not a few divines, as well as philosophers of great note,
have, from the difficulty they found in conceiving either limits or
annihilation of space, concluded it must be divine. And some of late have
set themselves particularly to show the incommunicable attributes of God
agree to it. Which doctrine, how unworthy soever it may seem of the
Divine Nature, yet I do not see how we can get clear of it, so long as we
adhere to the received opinions.

118. THE ERRORS ARISING FROM THE DOCTRINES OF ABSTRACTION AND EXTERNAL
MATERIAL EXISTENCES, INFLUENCE MATHEMATICAL REASONINGS.--Hitherto of
Natural Philosophy: we come now to make some inquiry concerning
that other great branch of speculative knowledge, to wit, Mathematics.
These, how celebrated soever they may be for their clearness and
certainty of demonstr