Mathematical Anti-Realism and Modal Nothingism

ISBN-13: 9781009346016 / Angielski / Miękka / 2023 / 75 str.

Mark Balaguer (California State University)

Opis

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.

Spis treści

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.