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E-raamat: Mathematical Anti-Realism and Modal Nothingism

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

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