Research Group
in Analytic Philosophy

One approach to explaining our knowledge of, and our ability to refer to abstract objects is to explain that knowledge and referential ability as arising out of  our grasp of “abstraction principles,” principles which explain the identity conditions of those abstract objects in terms of some conditions with which we are antecedently familiar.  This is the neo-logicist strategy for cardinal numbers, according to which we understand cardinal numbers by understanding identity-statements concerning them, and we understand these in turn by understanding their equivalence with statements about 1-1 mappings. 

Frege seems to have considered just such a strategy, and to have rejected it. The goal of this talk is to clarify Frege’s conception of abstract objects, and to shed some light on its viability, by examining that (apparent) rejection. I will argue that Frege’s reasons for rejecting the now-popular abstractionist strategy are not what they are standardly taken to be, and that the realism about numbers that emerges from Frege’s work is a more nuanced and plausible, if somewhat more tangled, view than is the robustly Platonist one commonly attributed to him.