# Gottlob Frege and the Interplay between Logic and Mathematics

# Gottlob Frege and the Interplay between Logic and Mathematics

This chapter explores Gottlob Frege's contribution to logic. Frege has been called the greatest logician since Aristotle, but he failed to gain influence on the mathematical community of his time and the depth and pioneering character of his work was acknowledged only after the collapse of his logicist program due to the Zermelo–Russell antinomy in 1902. Frege, by proving his theorem χ without recourse to Wertverläufe, exhibited an inconsistency (or at least an incoherence) in the traditional notion of the extension of a concept. He prompted our awareness of a situation the future analyses of which will hopefully not only deepen our systematic control of the interplay of concepts and their extensions but also improve our understanding of the historical development of the notion of “extension of a concept” and its historiographical assessment.

*Keywords:*
Gottlob Frege, mathematical logic, Zermelo–Russell antinomy, extension

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