A PROBLEM AND A SOLUTION FOR NEO-FREGEANISM

Abstract

I argue that Benacerraf’s famous objection to mathematical realism in his paper “What numbers could not be” can be adapted to present severe difficulties for the Neo-Fregean programme. I formulate an alternative abstraction principle and argue that there is no reason for the natural numbers to be generated by one abstraction principle rather than the other. Independently of this conclusion, the formal comparison of the two abstraction principles involves a result of interest to Neo-Fregeans: I offer a solution to the bad company objection.