Mathematical Anti-Realism and Modal Nothingism

Mark Balaguer

doi:10.1017/9781009346030

Series: Elements in the Philosophy of Mathematics

Mathematical Anti-Realism and Modal Nothingism

Published online by Cambridge University Press: 02 December 2022

Mark Balaguer

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Mark Balaguer: Affiliation:
California State University

Summary

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.

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mathematical anti-realism modality error theory truthmaking abstract objects

Type: Element
Information: Series: Elements in the Philosophy of Mathematics

DOI: https://doi.org/10.1017/9781009346030 [Opens in a new window]

Online ISBN: 9781009346030

Publisher: Cambridge University Press

Print publication: 05 January 2023

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Mathematical Anti-Realism and Modal Nothingism

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