are, inconsistent, the one side or other always perplexes, whatever consequences we draw from the other; as an idea of motion not passing on would perplex any one who should argue from such an idea, which is not better than an idea of motion at rest.  And such another seems to me to be the idea of a space, or (which is the same thing) a number infinite, i. e. of a space or number which the mind actually has, and so views and terminates in; and of a space or number, which, in a constant and endless enlarging and progression, it can in thought never attain to.  For, how large soever an idea of space I have in my mind, it is no larger than it is that instant that I have it, though I be capable the next instant to double it, and so on in infinitum; for that alone is infinite which has no bounds; and that the idea of infinity, in which our thoughts can find none.

9.  Number affords us the clearest Idea of Infinity.

But of all other ideas, it is number, as I have said, which I think furnishes us with the clearest and most distinct idea of infinity we are capable of.  For, even in space and duration, when the mind pursues the idea of infinity, it there makes use of the ideas and repetitions of numbers, as of millions and millions of miles, or years, which are so many distinct ideas,—­kept best by number from running into a confused heap, wherein the mind loses itself; and when it has added together as many millions, &c., as it pleases, of known lengths of space or duration, the clearest idea it can get of infinity, is the confused incomprehensible remainder of endless addible numbers, which affords no prospect of stop or boundary.

10.  Our different Conceptions of the Infinity of Number contrasted with those of Duration and Expansion.

It will, perhaps, give us a little further light into the idea we have of infinity, and discover to us, that it is nothing but the infinity of number applied to determinate parts, of which we have in our minds the distinct ideas, if we consider that number is not generally thought by us infinite, whereas duration and extension are apt to be so; which arises from hence,—­that in number we are at one end, as it were:  for there being in number nothing less than an unit, we there stop, and are at an end; but in addition, or increase of number, we can set no bounds:  and so it is like a line, whereof one end terminating with us, the other is extended still forwards, beyond all that we can conceive.  But in space and duration it is otherwise.  For in duration we consider it as if this line of number were extended both ways—­to an unconceivable, undeterminate, and infinite length; which is evident to anyone that will but reflect on what consideration he hath of Eternity; which, I suppose, will find to be nothing else but the turning this infinity of number both