A Mathematician Reflects on the Useful and Reliable Illusion of Reality in Mathematics.
Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an exte...
| Publicado en: | Erkenntnis Vol. 68; no. 3; pp. 359 - 380 |
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| Formato: | Artículo |
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Springer Nature
May2008
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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=35076119&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 35076119 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 01650106 5KZ jtl: Erkenntnis issn: 01650106 maglogo: N pubinfo: dt: May2008 vid: 68 iid: 3 pid: 237 pub: Springer Nature artinfo: ui: 35076119 10.1007/s10670-008-9105-2 ppf: 359 ppct: 21 formats: fmt: @attributes: type: P size: 222KB tig: atl: A Mathematician Reflects on the Useful and Reliable Illusion of Reality in Mathematics. aug: au: Devlin, Keith affil: Standford University, CSLI , Cordura Hall, 210 Panama Street Stanford 94305-4115 USA su: Mathematics Mathematicians Axioms Cybernetics Ontology sug: subj: Mathematics Mathematicians Axioms Cybernetics Ontology ab: Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Erkenntnis is a copyright of Springer, 2008. All Rights Reserved. item: Erkenntnis holder: Springer Nature dt: @attributes: year: 2008 holdings: @attributes: islocal: N |
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