Habgood-Coote, J orcid.org/0000-0003-3427-3325 and Tanswell, FS (2023) Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups. Episteme, 20 (2). pp. 281-307. ISSN 1742-3600
Abstract
In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), 2021. This article has been published in a revised form in Episteme https://doi.org/10.1017/epi.2021.26. This version is free to view and download for private research and study only. Not for re-distribution or re-use. |
Keywords: | Social epistemology, mathematical practice, proof, group theory, classification of finite simple groups, collective knowledge, mathematical knowledge |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Arts, Humanities and Cultures (Leeds) > School of Philosophy, Religion and History of Science (Leeds) > School of Philosophy (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Jun 2021 09:51 |
Last Modified: | 26 Oct 2023 15:02 |
Published Version: | https://www.cambridge.org/core/journals/episteme/a... |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/epi.2021.26 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:175703 |