Synthese:1-15 (forthcoming)

Authors
Bruno Whittle
University of Wisconsin, Madison
Abstract
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.
Keywords Mathematical anti-realism  Grounding  Explanation
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DOI 10.1007/s11229-021-03066-y
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References found in this work BETA

Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press. pp. 109-36.
Material Beings.Peter Van Inwagen - 1990 - Ithaca: Cornell University Press.
Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.

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