Philosophia Mathematica 24 (1):30-49 (2016)

Patricia Blanchette
University of Notre Dame
This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; and the prospects for a logical grounding of arithmetic in the wake of the paradox
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DOI 10.1093/philmat/nkv038
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References found in this work BETA

The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.
Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.

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