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Mathematical Anti-Realism and Explanatory Structure

Whittle, Bruno (2021) Mathematical Anti-Realism and Explanatory Structure. [Preprint]

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Plausibly, mathematical claims are true, but the fundamental furniture of the world does not include mathematical objects. This can be made sense of by providing mathematical claims with paraphrases, which make clear how the truth of such claims does not require the fundamental existence of mathematical objects. This paper explores the consequences of this type of position for explanatory structure. There is an apparently straightforward relationship between this sort of structure, and the logical sort: i.e. logically complex claims are explained by logically simpler ones. For example, disjunctions are explained by their (true) disjuncts, while generalizations are explained by their (true) instances. This would seem as plausible in the case of mathematics as elsewhere. Also, it would seem to be something that the anti-realist approaches at issue would want to preserve. It will be argued, however, that these approaches cannot do this: they lead not merely to violations of the familiar principles relating logical and explanatory structure, but even to reversals of these. That is, there are cases where generalizations explain their instances, or disjunctions their disjuncts.

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Item Type: Preprint
Whittle, Brunobwhittle@wisc.edu0000-0002-5374-0286
Keywords: Mathematical anti-realism paraphrase grounding
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
Depositing User: Mr Bruno Whittle
Date Deposited: 15 Feb 2021 18:17
Last Modified: 15 Feb 2021 18:17
Item ID: 18713
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
Date: 14 February 2021

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