David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophy Compass 5 (1):16-28 (2010)
In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes.
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References found in this work BETA
C. Anthony Anderson (1987). Semantical Antinomies in the Logic of Sense and Denotation. Notre Dame Journal of Formal Logic 28 (1):99-114.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.
Nino B. Cocchiarella (2000). Russell's Paradox of the Totality of Propositions. Nordic Journal of Philosophical Logic 5 (1):25-37.
Nicholas Denyer (2003). Rieger's Problem with Frege's Ontology. Analysis 63 (2):166–170.
Citations of this work BETA
Bryan Pickel (2013). Russell on Incomplete Symbols. Philosophy Compass 8 (10):909-923.
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