Mathematical Pluralism and Indispensability

Erkenntnis 1:1-25 (2023)
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Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology.

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Silvia Jonas
Universität Bamberg

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Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.

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