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dc.contributor.authorLarvor, Brendan
dc.date.accessioned2019-07-17T11:51:26Z
dc.date.available2019-07-17T11:51:26Z
dc.date.issued2019-07-15
dc.identifier.citationLarvor , B 2019 , ' From Euclidean Geometry to Knots and Nets ' , Synthese , vol. 196 , no. 7 , 10.1007/s11229-017-1558-x , pp. 2715-2736 . https://doi.org/10.1007/s11229-017-1558-x
dc.identifier.issn0039-7857
dc.identifier.otherPURE: 10719061
dc.identifier.otherPURE UUID: 313ac255-f1d0-4820-bd51-07ce95eda818
dc.identifier.otherScopus: 85029597867
dc.identifier.urihttp://hdl.handle.net/2299/21444
dc.descriptionThis document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.
dc.description.abstractThis paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.en
dc.format.extent22
dc.language.isoeng
dc.relation.ispartofSynthese
dc.rightsEmbargoed
dc.subjectEuclidean geometry
dc.subjectKnot theory
dc.subjectMathematics
dc.subjectProof
dc.subjectTopology
dc.subjectPhilosophy
dc.subjectSocial Sciences(all)
dc.titleFrom Euclidean Geometry to Knots and Netsen
dc.contributor.institutionSchool of Humanities
dc.contributor.institutionPhilosophy
dc.description.statusPeer reviewed
dc.date.embargoedUntil2018-09-19
dc.identifier.urlhttp://www.scopus.com/inward/record.url?scp=85029597867&partnerID=8YFLogxK
dc.identifier.urlhttps://link.springer.com/article/10.1007/s11229-017-1558-x
dc.relation.schoolSchool of Humanities
dc.description.versiontypeFinal Accepted Version
dcterms.dateAccepted2019-07-15
rioxxterms.versionAM
rioxxterms.versionofrecordhttps://doi.org/10.1007/s11229-017-1558-x
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
rioxxterms.licenseref.startdate2018-09-19
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue
herts.date.embargo2018-09-19
herts.rights.accesstypeEmbargoed


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