Abstract

‘The following sentence is true only if numbers exist: The number of planets is eight. It is true; hence, numbers exist.’ So runs a familiar argument for realism about mathematical objects. But this argument relies on a controversial semantic thesis: that ‘The number of planets’ and ‘eight’ are singular terms standing for the number eight, and the copula expresses identity. This is the ‘Fregean analysis’.I show that the Fregean analysis is false by providing an analysis of sentences such as that best explains the available linguistic data, and according to which no terms in purport to stand for numbers