TY - JOUR

T1 - The Role of Testimony in Mathematics

AU - Andersen, Line Edslev

AU - Andersen, Hanne

AU - Sørensen, Henrik Kragh

N1 - Funding Information:
We are very grateful to the interviewees for their time and support. The paper has benefited greatly from the feedback we received from three anonymous referees. We also thank Mikkel Willum Johansen for valuable feedback. Earlier versions of the paper were presented at: the OZSW Graduate Conference in Theoretical Philosophy at the University of Twente in 2016; the Centre for Logic and Philosophy of Science Colloquium at Vrije Universiteit Brussel in 2016; the Virtue Epistemology of Mathematical Practices workshop at Vrije Universiteit Brussel in 2018; and the Mathematical Collaboration III workshop at the University of Bristol in 2019. We thank the audiences for valuable feedback. Part of the research for this paper was conducted while LEA was a postdoctoral researcher at the Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium. At Aarhus University, she is supported by K. Brad Wray’s Grant, AUFF-E-2017-FLS-7-3.
Funding Information:
We are very grateful to the interviewees for their time and support. The paper has benefited greatly from the feedback we received from three anonymous referees. We also thank Mikkel Willum Johansen for valuable feedback. Earlier versions of the paper were presented at: the OZSW Graduate Conference in Theoretical Philosophy at the University of Twente in 2016; the Centre for Logic and Philosophy of Science Colloquium at Vrije Universiteit Brussel in 2016; the Virtue Epistemology of Mathematical Practices workshop at Vrije Universiteit Brussel in 2018; and the Mathematical Collaboration III workshop at the University of Bristol in 2019. We thank the audiences for valuable feedback. Part of the research for this paper was conducted while LEA was a postdoctoral researcher at the Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium. At Aarhus University, she is supported by K. Brad Wray’s Grant, AUFF-E-2017-FLS-7-3.
Publisher Copyright:
© 2020, Springer Nature B.V.

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85085976537&partnerID=8YFLogxK

U2 - 10.1007/s11229-020-02734-9

DO - 10.1007/s11229-020-02734-9

M3 - Article

VL - 199

SP - 859

EP - 870

JO - Synthese

JF - Synthese

SN - 0039-7857

IS - 1-2

ER -