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The First Russell Paradox

  • Irving H. Anellis

Abstract

In 1896, Russell read Arthur Hannequin’s (1895) book Essai Critique sur I’Hypothèse des Atomes dans la Science Contemporaine, which introduced him to Cantor’s work for the first time. Shortly thereafter, in 1897, he read Louis Couturat’s (1896) book De Vlnfini Mathématique and published a review of that book in the journal Mind (Russell, 1897). Couturat gave a very careful exposition of Cantorian set theory and, most unusual for its day, a very favorable one. Russell at first rejected Cantorian set theory, for reasons which I detail in Anellis (1984b). Nevertheless, after reading Russell’s review of his book, Couturat established a correspondence with Russell (1897–1914) that lasted until Couturat’s tragic death. Thanks to Couturat’s efforts, Russell came to appreciate better and understand Cantor’s work, and soon entered into correspondence with Cantor. Cantor soon furnished Russell with reprints of his work including Über die elementare Frage der Mannigfaltigkeitslehre (1892). This new attitude towards Cantorian set theory, however, did nothing to diminish Russell’s critical eye. And after reading Cantor (1892), Russell was able to obtain the first version of the Russell paradox. In §3, which is the heart of this chapter, I use unpublished documentary evidence to show that Russell obtained a version of his famed paradox much earlier than has been commonly assumed, and, with the aid of a work of Crossley (1973) in which the Russell paradox was derived directly from the Cantor paradox, I show how Russell had done the same, as early as December 1900.

Keywords

Mathematical Philosophy Gestalt Switch Great Cardinal Russell Paradox Vicious Circle Principle 
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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Irving H. Anellis
    • 1
  1. 1.Modern Logic PublishingAmesUSA

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