Zermelo and Russell's paradox: Is there a universal set?

Abstract

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. © The Author [2012]. Published by Oxford University Press. All rights reserved.