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.
Bibliographical noteFunding Information:
I am thankful to Sharon Berry, David Enoch, Arnon Levy, Alexander Pruss, Joshua Schechter, Assaf Weksler, two anonymous reviewers and to the audiences at my presentations at the 22nd Israeli Philosophical Association conference (2019) and the 93rd Joint Session of the Aristotelean Society and the Mind Association (2019) for very helpful comments and discussion. This article was written with the support of the Martin Buber Society of Fellows at the Hebrew University of Jerusalem.
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- Calling for explanation
- Logical omniscience
- Necessary facts
- Philosophy of mathematics