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.
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