The Role of Testimony in Mathematics

Line Edslev Andersen*, Hanne Andersen, Henrik Kragh Sørensen

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer 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.

OriginalsprogEngelsk
TidsskriftSynthese
Vol/bind199
Nummer1-2
Sider (fra-til)859-870
Antal sider12
ISSN0039-7857
DOI
StatusUdgivet - dec. 2021
BegivenhedVirtue Epistemology of Mathematical Practice - Vrije Universiteit Brussel, Brussels, Belgien
Varighed: 13 jul. 201814 jul. 2018

Workshop

WorkshopVirtue Epistemology of Mathematical Practice
LokationVrije Universiteit Brussel
Land/OmrådeBelgien
ByBrussels
Periode13/07/201814/07/2018

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