13. No positive idea of infinity.
Though it be hard, I think, to find anyone 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 which is not made
up of, and commensurate to, repeated numbers of feet or yards, or days and years; which are the common
measures, whereof we have the ideas in our minds, and whereby we judge of the greatness of this sort of
quantities. And therefore, since an infinite idea of space or duration must needs be made up of infinite parts, it can
have no other infinity than that of number capable still of further addition; but not an actual positive idea of a
number infinite. For, I think it is evident, that the addition of finite things together (as are all lengths whereof we
have the positive ideas) can never otherwise produce the idea of infinite than as number does; which, consisting of
additions of finite units one to another, suggests the idea of infinite, only by a power we find we have of still
increasing the sum, and adding more of the same kind; without coming one jot nearer the end of such progression.
