On Russell's vulnerability to Russell's paradox

History and Philosophy of Logic 22 (4):207-231 (2001)


Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ?the most important event? in ?the most important year in my intellectual life?. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell was thus vulnerable to (at least one version of) Russell's paradox and hence that the paradox exposes a pre-existing difficulty in Russell's Moorean philosophy. Contrary to Hylton, I argue that the Moorean Russell adhered to views which insulated him against the paradox. Further, I argue that Russell became vulnerable to his paradox as a result of changes in his Moorean position occasioned, first, by his acceptance of Cantor's theory of the transfinite, and, second, by his correspondence with Frege. I conclude with some general comments regarding Russell's acceptance of naïve set theory

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References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford, England and New York, NY, USA: Oxford University Prress.
Logic and Knowledge: Essays 1901-1950.Bertrand Russell - 1956 - London, England: Macmillan.

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The Origin of the Theory of Types.Ryo Ito - 2018 - Annals of the Japan Association for Philosophy of Science 27:27-44.

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