Introduction

This Element defends mathematical anti-realism against an underappreciated problem with that view—a problem having to do with modal truthmaking.

Part I: Developing Mathematical Anti-Realism

Part I develops mathematical anti-realism, it defends that view against a number of well-known objections, and it raises a less widely discussed objection to anti-realism—an objection based on the fact that (a) mathematical anti-realists need to commit to the truth of certain kinds of modal claims, and (b) it’s not clear that the truth of these modal claims is compatible with mathematical anti-realism.

Part II: Strategies and the Modal-Truth Problem

Part II considers various strategies that anti-realists might pursue in trying to solve this modal-truth problem with their view, it argues that there’s only one viable view that anti-realists can endorse in order to solve the modal-truth problem, and it argues that the view in question— which is here called modal nothingism—is true.