Philosophia Mathematica 21 (3):279-296 (2013)

Pieranna Garavaso
University of Minnesota, Morris
Hilary Putnam first published the consistency objection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that a conventionalist can explain the consistency of T and suggest that an analogous explanation can be provided for the consistency of Peano arithmetic
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DOI 10.1093/philmat/nkt003
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Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.

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