Russell’s paradox and the Fregean program

Abstract

The aim of this paper is to show the impact of Russell's paradox in Frege's mathemathical and philosophical system. First, it shows that the development of the Begriffsschrift was enough to give a structural definition of natural numbers, but not enough to accomplish Frege's program. For this it was still necessary to make some choices. Second, it reviews how the option taken in Grundlagen may drive to Russell's paradox and why Frege's way out fails. Lastly, it analyses the implicit presuppositions in the basic law V of Grudgesetze and it examines which would be the consequences for Frege of refusing one of them.