How can necessary facts call for explanation?

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)11607-11624
Number of pages18
JournalSynthese
Volume198
Issue number12
DOIs
StatePublished - 1 Dec 2021
Externally publishedYes

Keywords

  • Calling for explanation
  • Logical omniscience
  • Necessary facts
  • Philosophy of mathematics
  • Probability
  • Strikingness

All Science Journal Classification (ASJC) codes

  • Philosophy
  • General Social Sciences

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