David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
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
W. V. Quine (1976). The Ways of Paradox, and Other Essays. Harvard University Press.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
Bertrand Russell (1919/1993). Introduction to Mathematical Philosophy. Dover Publications.
Bertrand Russell (1903). Principles of Mathematics. Cambridge University Press.
Citations of this work BETA
Bryan Pickel (2013). Russell on Incomplete Symbols. Philosophy Compass 8 (10):909-923.
Alexei Procyshyn (2014). Walter Benjamin's Philosophy of Language. Philosophy Compass 9 (6):368-381.
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