Page:The Works of John Locke - 1823 - vol 01.djvu/292

216 on all sides pursue those indeterminable lines of number; and reckoning any way from ourselves, a yard, mile, diameter of the earth, or orbis magnus, by the infinity of number, we add others to them as often as we will; and having no more reason to set bounds to those repeated ideas than we have to set bounds to number, we have that indeterminable idea of immensity.

§ 12. And since in any bulk of matter our thoughts can never arrive at the utmost divisibility, therefore there is an apparent infinity to us also in that, which has the infinity also of number; but with this difference, that, in the former considerations of the infinity of space and duration, we only use addition of numbers; whereas this is like the division of an unit into its fractions, wherein the mind also can proceed in infinitum, as well as in the former additions; it being indeed but the addition still of new numbers: though in the addition of the one we can have no more the positive idea of a space infinitely great, than, in the division of the other, we can have the idea of a body infinitely little; our idea of infinity being, as I may say, a growing or fugitive idea, still in a boundless progression, that can stop nowhere.

§ 13. Though it be hard, I think, to find any one so absurd as to say, he has the positive idea of an actual infinite number; the infinity whereof lies only in a power still of adding any combination of units to any former number, and that as long and as much as one will; the like also being in the infinity of space and duration, which power leaves always to the mind room for endless additions; yet there be those who imagine they have positive ideas of infinite duration and space. It would, I think, be enough to destroy any such positive idea of infinite, to ask him that has it, whether he could add to it or no; which would easily show the mistake of such a positive idea. We can, I think, have no positive idea of any space or duration