The role of testimony in mathematics

Synthese 199 (1-2):859-870 (2020)
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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.

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Author Profiles

Line Edslev Andersen
Aarhus University
Hanne Andersen
University of Copenhagen
Henrik Kragh Sørensen
University of Copenhagen

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References found in this work

Evidence, pragmatics, and justification.Jeremy Fantl & Matthew McGrath - 2002 - Philosophical Review 111 (1):67-94.
Epistemic dependence.John Hardwig - 1985 - Journal of Philosophy 82 (7):335-349.
The role of trust in knowledge.John Hardwig - 1991 - Journal of Philosophy 88 (12):693-708.
Epistemic Trust in Science.Torsten Wilholt - 2013 - British Journal for the Philosophy of Science 64 (2):233-253.

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