The Role of Testimony in Mathematics

Line Edslev Andersen*, Hanne Andersen, Henrik Kragh Sørensen

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the proof contains no substantial errors increases because different experts will validate the proof in different ways depending on their background knowledge and individual preferences. If this is correct, there is much to be gained for a mathematician from requiring that a number of experts have checked the proof of p before she will rely on p in her own proofs without checking the proof of p. In this way a mathematician can protect her own work and the work of others from errors. Our argument thus provides an explanation for mathematicians’ attitude towards relying on testimony.

Original languageEnglish
JournalSynthese
Volume199
Issue1-2
Pages (from-to)859-870
Number of pages12
ISSN0039-7857
DOIs
Publication statusPublished - Dec 2021
EventVirtue Epistemology of Mathematical Practice - Vrije Universiteit Brussel, Brussels, Belgium
Duration: 13 Jul 201814 Jul 2018

Workshop

WorkshopVirtue Epistemology of Mathematical Practice
LocationVrije Universiteit Brussel
Country/TerritoryBelgium
CityBrussels
Period13/07/201814/07/2018

Keywords

  • Epistemic dependence
  • Mathematical practice
  • Mathematics
  • Testimony

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