The role of testimony in mathematics
Synthese 199 (1-2):859-870 (2020)
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.Author Profiles
Reprint years
2021
DOI
10.1007/s11229-020-02734-9
My notes
Similar books and articles
Arguing Around Mathematical Proofs.Michel Dufour - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht: Springer. pp. 61-76.
Explanation in mathematics: Proofs and practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11):e12629.
Probabilistic Proofs and the Collective Epistemic Goals of Mathematicians.Don Fallis - 2011 - In Collective Epistemology. Heusenstamm, Germany: pp. 157-175.
Socializing Aspects of Proof Procedure.Jaroslaw Mrozek - 2018 - Proceedings of the XXIII World Congress of Philosophy 56:25-31.
Bevis och övertygelse- om behovet av att bevisa matematiska satser.Kim-Erik Berts - 2011 - Norsk Filosofisk Tidsskrift 46 (4):314-325.
Diversity in proof appraisal.Matthew Inglis & Andrew Aberdein - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. Basel, Switzerland: pp. 163-179.
Knowledge of Mathematics without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.
On the alleged simplicity of impure proof.Andrew Arana - 2017 - In Roman Kossak & Philip Ording (eds.), Simplicity: Ideals of Practice in Mathematics and the Arts. pp. 207-226.
Cognitive islands and runaway echo chambers: problems for epistemic dependence on experts.C. Thi Nguyen - 2020 - Synthese 197 (7):2803-2821.
What do mathematicians teach us about the world? An anthropological perspective.Paul Jorion - 1999 - Dialectical Anthropology 24 (1):45-98.
The non-remedial value of dependence on moral testimony.Paddy McShane - 2018 - Philosophical Studies 175 (3):629-647.
The Argument of Mathematics.Andrew Aberdein & Ian J. Dove (eds.) - 2013 - Dordrecht, Netherland: Springer.
Analytics
Added to PP
2020-06-06
Downloads
28 (#418,925)
6 months
1 (#451,398)
2020-06-06
Downloads
28 (#418,925)
6 months
1 (#451,398)
Historical graph of downloads
Author Profiles
References found in this work
A Treatise of Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning Into Moral Subjects.David Hume & D. G. C. Macnabb (eds.) - 1738 - Collins.
Evidence, pragmatics, and justification.Jeremy Fantl & Matthew McGrath - 2002 - Philosophical Review 111 (1):67-94.
Epistemic Trust in Science.Torsten Wilholt - 2013 - British Journal for the Philosophy of Science 64 (2):233-253.