Burali-Forti's paradox: A reappraisal of its origins

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Abstract

Using both published and unpublished letters and manuscripts, this article shows that Burali-Forti's paradox, which has long been regarded as the first of the set-theoretical paradoxes to be discovered, was not created by either Burali-Forti or Cantor. It arose gradually and began to take recognizable form only in Russell's The Principles of Mathematics of 1903. Russell's long-standing predisposition to seek paradoxes was a vestige of the Kantian and Hegelian philosophical traditions in which he was schooled. Between 1904 and 1906, Burali-Forti's paradox was nurtured by Jourdain and Poincaré, both of whom considered it to be more fundamental than Russell did. To the end, both Burali-Forti and Cantor maintained that there was no such paradox. © 1981.

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Moore, G. H., & Garciadiego, A. (1981). Burali-Forti’s paradox: A reappraisal of its origins. Historia Mathematica, 8(3), 319–350. https://doi.org/10.1016/0315-0860(81)90070-7

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