Synthese:1-18 (forthcoming)

Authors
Dan Baras
Hebrew University of Jerusalem
Abstract
While there has been much discussion about what makes some mathematical proofs more explanatory than others, and what are mathematical coincidences, in this article I explore the distinct phenomenon of mathematical facts that call for explanation. The existence of mathematical facts that call for explanation stands in tension with virtually all existing accounts of “calling for explanation”, which imply that necessary facts cannot call for explanation. In this paper I explore what theoretical revisions are needed in order to accommodate this phenomenon. One of the important upshots is that, contrary to the current consensus, low prior probability is not a necessary condition for calling for explanation. In the final section I explain how the results of this inquiry help us make progress in assessing Hartry Field's style of reliability argument against mathematical Platonism and against robust realism in other domains of necessary facts, such as ethics.
Keywords calling for explanation  strikingness  necessary facts  probability  logical omniscience  philosophy of mathematics  reliability arguments
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DOI 10.1007/s11229-020-02817-7
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References found in this work BETA

Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Rational Self-Doubt and the Failure of Closure.Joshua Schechter - 2013 - Philosophical Studies 163 (2):428-452.

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