The role of testimony in mathematics

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Standard

The role of testimony in mathematics. / Andersen, Line Edslev; Andersen, Hanne; Sørensen, Henrik Kragh.

I: Synthese, Bind 199, 2021, s. 859-870.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Andersen, LE, Andersen, H & Sørensen, HK 2021, 'The role of testimony in mathematics', Synthese, bind 199, s. 859-870. https://doi.org/10.1007/s11229-020-02734-9

APA

Andersen, L. E., Andersen, H., & Sørensen, H. K. (2021). The role of testimony in mathematics. Synthese, 199, 859-870. https://doi.org/10.1007/s11229-020-02734-9

Vancouver

Andersen LE, Andersen H, Sørensen HK. The role of testimony in mathematics. Synthese. 2021;199:859-870. https://doi.org/10.1007/s11229-020-02734-9

Author

Andersen, Line Edslev ; Andersen, Hanne ; Sørensen, Henrik Kragh. / The role of testimony in mathematics. I: Synthese. 2021 ; Bind 199. s. 859-870.

Bibtex

@article{ff5b011c15da45b0a7b369c188327455,
title = "The role of testimony in mathematics",
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{\textquoteright} attitude towards relying on testimony.",
keywords = "Epistemic dependence, Mathematical practice, Mathematics, Testimony",
author = "Andersen, {Line Edslev} and Hanne Andersen and S{\o}rensen, {Henrik Kragh}",
year = "2021",
doi = "10.1007/s11229-020-02734-9",
language = "English",
volume = "199",
pages = "859--870",
journal = "Synthese",
issn = "0039-7857",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - The role of testimony in mathematics

AU - Andersen, Line Edslev

AU - Andersen, Hanne

AU - Sørensen, Henrik Kragh

PY - 2021

Y1 - 2021

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.

KW - Epistemic dependence

KW - Mathematical practice

KW - Mathematics

KW - Testimony

U2 - 10.1007/s11229-020-02734-9

DO - 10.1007/s11229-020-02734-9

M3 - Journal article

AN - SCOPUS:85085976537

VL - 199

SP - 859

EP - 870

JO - Synthese

JF - Synthese

SN - 0039-7857

ER -

ID: 244998172