Why Is Proof the Only Way to Acquire Mathematical Knowledge?
This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition's truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowle...
| Publicado en: | Australasian Journal of Philosophy Vol. 102; no. 2; pp. 333 - 354 |
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| Formato: | Artículo |
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Taylor & Francis Ltd
Jun2024
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=178152299&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 178152299 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00048402 BHK jtl: Australasian Journal of Philosophy issn: 00048402 maglogo: N pubinfo: dt: Jun2024 vid: 102 iid: 2 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 178152299 10.1080/00048402.2023.2233540 ppf: 333 ppct: 21 formats: fmt: – @attributes: type: T – @attributes: type: P size: 1.5MB tig: atl: Why Is Proof the Only Way to Acquire Mathematical Knowledge? aug: au: Lange, Marc affil: The University of North Carolina at Chapel Hill su: Mathematics Research Proposition (Logic) Induction (Logic) Evidence sug: subj: Mathematics Research Proposition (Logic) Induction (Logic) Evidence keyword: evidence explanation induction knowledge mathematics proof ab: This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition's truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we can justly expect that if the mathematical proposition is actually false, despite the evidence for its truth, then this fact has an explanation. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Australasian Journal of Philosophy is the property of Taylor & Francis Ltd 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: Australasian Journal of Philosophy holder: Taylor & Francis Ltd dt: @attributes: year: 2024 holdings: @attributes: islocal: N |
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