Zermelo and Russell's Paradox: Is There a Universal set?

Philosophia Mathematica 21 (2):180-199 (2013)


Zermelo once wrote that he had anticipated Russell's contradiction of the set of all sets that are not members of themselves. Is this sufficient for having anticipated Russell's Paradox — the paradox that revealed the untenability of the logical notion of a set as an extension? This paper argues that it is not sufficient and offers criteria that are necessary and sufficient for having discovered Russell's Paradox. It is shown that there is ample evidence that Russell satisfied the criteria and that Zermelo did not

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Gregory Landini
University of Iowa

References found in this work

Basic Laws of Arithmetic.Gottlob Frege - 2013 - Oxford, England: Oxford University Press.
The Ins and Outs of Frege's Way Out.Gregory Landini - 2006 - Philosophia Mathematica 14 (1):1-25.
On Frege's Way Out.P. T. Geach - 1956 - Mind 65 (259):408-409.

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Citations of this work

Frege's Cardinals Do Not Always Obey Hume's Principle.Gregory Landini - 2017 - History and Philosophy of Logic 38 (2):127-153.
Review of Terence Parsons, Articulating Medieval Logic. [REVIEW]Paul Thom - 2015 - History and Philosophy of Logic 36 (2):178-181.

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