Russell's paradox of the totality of propositions

Russell's "new contradiction" about "the totality of propositions" has been connected with a number of modal paradoxes. M. Oksanen has recently shown how these modal paradoxes are resolved in the set theory NFU. Russell's paradox of the totality of propositions was left unexplained, however. We reconstruct Russell's argument and explain how it is resolved in two intensional logics that are equiconsistent with NFU. We also show how different notions of possible worlds are represented in these intensional logics
Keywords Russell, Bertrand
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DOI 10.1080/08066200050217977
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Modality and Paradox.Gabriel Uzquiano - 2015 - Philosophy Compass 10 (4):284-300.
The Senses of Functions in the Logic of Sense and Denotation.Kc Klement - 2010 - Bulletin of Symbolic Logic 16 (2):153-188.

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