7.  Difference between infinity of Space, and Space infinite.

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, as an infinite space, or an infinite duration.  For, as 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 endless repetition can never totally represent to it; which carries in it a plain contradiction.

8.  We have no Idea of infinite Space.

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 ever 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 completing the idea, there we have our idea of infinity:  which, though it seems to be pretty clear when we consider 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; it is 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, &c.  Because the parts of such an idea not being perceived to be, as they