Abstract

In his influential paper "What numbers could not be", P. Benacerraf argues that numbers could not be objects at all, and that the search for which particular objects the numbers really are is a misguided one. It is widely held that he has given a knock-down argument against a platonistic conception of arithmetic. But, in this paper, I shall try to show first that his argument fails because it depends on too strong an assumption. Second, his criticism is not applicable to the version of platonism that Frege proposed.