Mathematical Anti-Realism and Modal Nothingism

This Element solves the problem of modal truthmaking for mathematical anti-realists by providing a novel view of modal truth.

Mark Balaguer (Author)

9781009346016, Cambridge University Press

Paperback / softback, published 5 January 2023

75 pages
22.8 x 15.1 x 0.6 cm, 0.15 kg

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

1. Introduction
2. What is mathematical anti-realism?
3. Mathematical error theory defended
4. Paraphrase nominalism and deflationary-truth nominalism revisited
5. Modal semantics and modal truthmaking
6. Possible worlds
7. Modal primitivism
8. Modal nothingism to the rescue
References.

Subject Areas: Maths for scientists [PDE], Philosophy of mathematics [PBB], Philosophy of language [CFA]