and one also says, “Double two, double that result, double the doubled result, and so on,” then, if saying that doubling one is less than doubling two means that less doubling has actually been expressed by the tongue or conceived in the mind, this is not conceded when the same starting point and rate of activity are assumed. If a difference is assumed, the greater amount belongs to whichever began earlier and proceeded more vigorously. In that case, doubling one may produce the greater amount.

If, instead, what is meant is that the quantity denoted by one of the two expressions is greater at each stage of doubling, then doubling one five times gives thirty-two, while doubling two five times gives sixty-fourfold. Yet this sixty-four is not a collection of counted things existing either in external reality or in the mind, such that one could say, “Unequal magnitudes have been found in what is infinite.” Rather, expressions denoting finite numbers have merely been uttered; the things counted exist neither in the mind nor in external reality. Thus, even if the numerical expressions belonging to each of these two sequences were assumed to exist in thought and speech, supposing them to be infinite would not entail that they differ in magnitude, given the same starting point and rate of activity.

And if he means that what this expression denotes, were it to exist, would be greater than what the other denotes,