Episteme (forthcoming)
Authors |
|
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.
|
Keywords | No keywords specified (fix it) |
Categories | (categorize this paper) |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.
Virtues of the Mind: An Inquiry Into the Nature of Virtue and the Ethical Foundations of the Mind.Linda Zagzebski - unknown
Knowledge-How, Abilities, and Questions.Joshua Habgood-Coote - 2019 - Australasian Journal of Philosophy 97 (1):86-104.
The Credit Economy and the Economic Rationality of Science.Kevin J. S. Zollman - 2018 - Journal of Philosophy 115 (1):5-33.
View all 32 references / Add more references
Citations of this work BETA
Epistemic Phase Transitions in Mathematical Proofs.Scott Viteri & Simon DeDeo - 2022 - Cognition 225:105120.
Similar books and articles
A Generation Theorem for Groups of Finite Morley Rank.Jeffrey Burdges & Gregory Cherlin - 2008 - Journal of Mathematical Logic 8 (2):163-195.
Proof, Rigour and Informality : A Virtue Account of Mathematical Knowledge.Fenner Stanley Tanswell - 2016 - St Andrews Research Repository Philosophy Dissertations.
On Superstable Groups with Residual Properties.Abderezak Ould Houcine - 2007 - Mathematical Logic Quarterly 53 (1):19-26.
Probabilistic Proofs, Lottery Propositions, and Mathematical Knowledge.Yacin Hamami - 2021 - Philosophical Quarterly 72 (1):77-89.
Arguing Around Mathematical Proofs.Michel Dufour - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht: Springer. pp. 61-76.
Using Crowdsourced Mathematics to Understand Mathematical Practice.Alison Pease, Ursula Martin, Fenner Stanley Tanswell & Andrew Aberdein - 2020 - ZDM 52 (6):1087-1098.
On Superstable Groups with Residual Properties.Abderezak Houcine - 2007 - Mathematical Logic Quarterly 53 (1):19-26.
Axiomatization of Abelian-by- G Groups for a Finite Group G.Francis Oger - 2001 - Archive for Mathematical Logic 40 (7):515-521.
Dowody komputerowe a status epistemologiczny twierdzeń matematyki.Izabela Bondecka-Krzykowska - 1999 - Filozofia Nauki 3.
Mathematics as a Quasi-Empirical Science.Gianluigi Oliveri - 2004 - Foundations of Science 11 (1-2):41-79.
Informal Proofs and Mathematical Rigour.Marianna Antonutti Marfori - 2010 - Studia Logica 96 (2):261-272.
What's There to Know? A Fictionalist Approach to Mathematical Knowledge.Mary Leng - 2007 - In Mary Leng, Alexander Paseau & Michael Potter (eds.), Mathematical Knowledge. Oxford: Oxford University Press.
Measurable Groups of Low Dimension.Richard Elwes & Mark Ryten - 2008 - Mathematical Logic Quarterly 54 (4):374-386.
Analytics
Added to PP index
2021-05-10
Total views
200 ( #57,189 of 2,499,676 )
Recent downloads (6 months)
76 ( #10,059 of 2,499,676 )
2021-05-10
Total views
200 ( #57,189 of 2,499,676 )
Recent downloads (6 months)
76 ( #10,059 of 2,499,676 )
How can I increase my downloads?
Downloads