Document Type

Article

Publication Date

10-2013

Publication Title

Philosophia Mathematica

Volume

21

Abstract

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.

Issue

3

First Page

279

Last Page

296

DOI

https://doi.org/10.1093/philmat/nkt003

ISSN

0031-8019

Comments

This is a pre-copyedited, author-produced version of an article accepted for publication in Philosophia Mathematica following peer review. The version of record:

Garavaso, “Hilary Putnam’s Consistency Objection against Wittgenstein’s Conventionalism in Mathematics,” Philosophia Mathematica, 21(III), (2013): 1-18.

is available online at: https://doi.org/10.1093/philmat/nkt003

Rights

© The Author [2013]. Published by Oxford University Press. All rights reserved.

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