frame an idea of pure Space exclusiv of all body.  This I must confess seems impossible, as being a mos abstract idea.  When I excite a motion in some part of my body, if it be free or without resistance, I say there is Space; but if I find a resistance, 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 demonstration, which is hardly anywhere else to be found, cannot nevertheless be supposed altogether free from mistakes, if in their principles there lurks