University of Minnesota Morris Digital Well University of Minnesota Morris Digital Well Philosophy Publications Faculty and Staff choS larship 10-2013 Hilary Putnam's Consistency Objection against Wittgenstein's Conventionalism in Mathematics Pieranna Garavaso University of Minnesota, Morris,
[email protected] Follow this and additional works at: https://digitalcommons.morris.umn.edu/philosophy_facpubs Part of the Logic and Foundations of Mathematics Commons Recommended Citation Garavaso, “Hilary Putnam’s Consistency Objection against Wittgenstein’s Conventionalism in Mathematics,” Philosophia Mathematica, 21(III), (2013): 1-18. This Article is brought to you for free and open access by the Faculty and Staff choS larship at University of Minnesota Morris Digital Well. It has been accepted for inclusion in Philosophy Publications by an authorized administrator of University of Minnesota Morris Digital Well. For more information, please contact
[email protected]. Hilary Putnam’s Consistency Objection against Wittgenstein’s Conventionalism in Mathematics 1. Introduction Hilary Putnam first published the so-called consistency objection in 1979.1 At that time, the objection was directed against Ludwig Wittgenstein's conventionalist account of mathematics. It was not an objection which Putnam raised and then forgot. (It is common to ask how many Putnams ago a claim was made!) In their Introduction to the revised 1983 Second Edition of the well-known anthology Philosophy of Mathematics, Hilary Putnam and Paul Benacerraf raised this objection against all conventionalist accounts of mathematics: Conventionalists attempt to account for mathematical truth by [reducing it] to the truth of certain conventions (by our fiat) plus the preservation of truth through logical consequence.