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Title: "How did the serpent of inconsistency enter Frege's paradise?"
Author(s): Wright, Crispin
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Editor(s): Ebert, P A
Rossberg, M
Citation: Wright 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.
Keywords: Indefinite Extensibility
Russell's Paradox
Burai-Forti Paradox
Cantor's Paradox
Higher-Order Logic
Issue Date: 15-Sep-2019
Date Deposited: 13-Jul-2016
Abstract: My 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.
Rights: This 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:

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