Reliability of mathematical inference.
Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundatio...
| Published in: | Synthese Vol. 198; no. 8; pp. 7377 - 7400 |
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| Format: | Article |
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Springer Nature
Aug2021
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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=151648027&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 151648027 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Aug2021 vid: 198 iid: 8 pid: 237 pub: Springer Nature artinfo: ui: 151648027 10.1007/s11229-019-02524-y ppf: 7377 ppct: 23 formats: fmt: @attributes: type: P size: 346KB tig: atl: Reliability of mathematical inference. aug: au: Avigad, Jeremy affil: Department of Philosophy, Carnegie Mellon University, Pittsburgh, USA Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA su: Mathematical proofs Twentieth century Accounting standards Evidence sug: subj: Mathematical proofs Twentieth century Accounting standards Evidence keyword: Formalization Mathematical proof Reliability Robustness ab: Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2021. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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