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dc.contributor.authorWright, Crispinen_UK
dc.contributor.editorEbert, P Aen_UK
dc.contributor.editorRossberg, Men_UK
dc.description.abstractMy project here is the appraisal of Michael Dummett's diagnosis that the inconsistency of Frege’s system in Grundgesetze is attributable to his neglect of the indefinite extensibility of fundamental mathematical concepts. I address a problem that obscures the usual intuitive characterisations of the notion of indefinite extensibility, and offer thereby what I believe to be the correct characterisation of the notion. En passant, some issues are reviewed about the "size" of indefinitely extensible concepts. And that will bring us into position to scrutinise the connections of the notion as characterised with paradox, and specifically the paradox that Russell found for Frege’s Basic Law V. It will be argued that Dummett’s diagnosis is apt for the Burali-Forti paradox, wrong for Cantor’s paradox, and correct for the paradox inherent in Law V only on the assumption that full classical imperative higher-order logic is indeed wholly logical.en_UK
dc.publisherOxford University Pressen_UK
dc.relationWright C (2019) "How did the serpent of inconsistency enter Frege's paradise?". In: Ebert PA & Rossberg M (eds.) Essays on Frege's Basic Laws of Arithmetic. Oxford UK: Oxford University Press, pp. 411-436.
dc.rightsThis item has been embargoed for a period. During the embargo please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study. In Ebert PA & Rossberg M (eds.) Essays on Frege's Basic Laws of Arithmetic. Oxford UK: Oxford University Press, pp. 411-436 reproduced by permission of Oxford University Press:
dc.subjectIndefinite Extensibilityen_UK
dc.subjectRussell's Paradoxen_UK
dc.subjectBurai-Forti Paradoxen_UK
dc.subjectCantor's Paradoxen_UK
dc.subjectHigher-Order Logicen_UK
dc.title"How did the serpent of inconsistency enter Frege's paradise?"en_UK
dc.typePart of book or chapter of booken_UK
dc.rights.embargoreason[Gg Companion FINAL version-2.pdf] Until this work is formally published there will be an embargo on the full text of this work.en_UK
dc.type.statusAM - Accepted Manuscripten_UK
dc.citation.btitleEssays on Frege's Basic Laws of Arithmeticen_UK
dc.publisher.addressOxford UKen_UK
dc.subject.tagPhilosophy of Logicen_UK
dc.subject.tagPhilosophy of Mathematicsen_UK
rioxxterms.typeBook chapteren_UK
local.rioxx.authorWright, Crispin|en_UK
local.rioxx.projectInternal Project|University of Stirling|
local.rioxx.contributorEbert, P A|en_UK
local.rioxx.contributorRossberg, M|en_UK
local.rioxx.filenameGg Companion FINAL version-2.pdfen_UK
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