David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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). 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.
Similar books and articles
Marcus Rossberg & Philip A. Ebert (2010). Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der Arithmetik. History and Philosophy of Logic 30 (4):341-348.
Kevin C. Klement, Russell-Myhill Paradox. Internet Encyclopedia of Philosophy.
Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
Keith Simmons (2005). A Berry and a Russell Without Self-Reference. Philosophical Studies 126 (2):253 - 261.
Kevin C. Klement (2009). A Cantorian Argument Against Frege's and Early Russell's Theories of Descriptions. In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of. Routledge
Kevin C. Klement, Russell's Paradox. Internet Encyclopedia of Philosophy.
Dustin Tucker & Richmond H. Thomason (2011). Paradoxes of Intensionality. Review of Symbolic Logic 4 (3):394-411.
Kevin C. Klement (2010). Russell, His Paradoxes, and Cantor's Theorem: Part II. Philosophy Compass 5 (1):29-41.
Added to index2009-09-08
Total downloads94 ( #45,123 of 1,911,320 )
Recent downloads (6 months)5 ( #142,834 of 1,911,320 )
How can I increase my downloads?