Understanding in mathematics: The case of mathematical proofs.
Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a sim...
| Published in: | Nous (0029-4624) Vol. 58; no. 4; pp. 1073 - 1107 |
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| Main Authors: | , |
| Format: | Article |
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Wiley-Blackwell
Dec2024
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=180703875&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 180703875 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00294624 D97 jtl: Nous (0029-4624) issn: 00294624 maglogo: Y pubinfo: dt: Dec2024 vid: 58 iid: 4 pid: 480 pub: Wiley-Blackwell artinfo: ui: 180703875 10.1111/nous.12489 ppf: 1073 ppct: 34 formats: fmt: – @attributes: type: T – @attributes: type: C – @attributes: type: P size: 494KB tig: atl: Understanding in mathematics: The case of mathematical proofs. aug: au: Hamami, Yacin Morris, Rebecca Lea affil: Philosophy Department, University of Liège, Liège, Belgium Department of Humanities, Social and Political Sciences, ETH Zürich, Zürich, Switzerland Institut Jean Nicod, Department of Cognitive Studies, ENS, EHESS, PSL University, CNRS, Paris, France Independent Scholar, Minneapolis Minnesota,, US su: Mathematical proofs Philosophy of science Agency theory Mathematical forms Philosophical literature sug: subj: Mathematical proofs Philosophy of science Agency theory Mathematical forms Philosophical literature ab: Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Nous (0029-4624) is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Nous (0029-4624) holder: Wiley-Blackwell dt: @attributes: year: 2024 holdings: @attributes: islocal: N |
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