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.
© The Author . Published by Oxford University Press. All rights reserved.
Garavaso, “Hilary Putnam’s Consistency Objection against Wittgenstein’s Conventionalism in Mathematics,” Philosophia Mathematica, 21(III), (2013): 1-18.