Abstract

This chapter deals with objections to mathematical conventionalism, focusing especially on technical objections. To make things easier to follow and more self-contained, the chapter begins with a brief overview of arithmetization. Then a technical argument alleging incompatibility between the factuality of conventions and the conventionality of arithmetic is discussed followed by discussion of a related but more general worry about circularity. Then an anti-conventonalist argument from Pollock is discussed and related to Montague’s paradox. Finally, Gödel’s argument against conventionalism is critically discussed. Ultimately the chapter demonstrates that there is no incompatibility between conventionalism and metamathematical results and methods.