David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
One of the most familiar uses of the Russell paradox, or, at least, of the idea underlying it, is in proving Cantor's theorem that the cardinality of any set is strictly less than that of its power set. The other method of proving Cantor's theorem Ã¢â¬â employed by Cantor himself in showing that the set of real numbers is uncountable Ã¢â¬â is that of diagonalization. Typically, diagonalization arguments are used to show that function spaces are "large" in a suitable sense. Classically, these two methods are equivalent. But constructively they are not: while the argument for Russell's paradox is perfectly constructive, (i.e., employs intuitionistically acceptable principles of logic) the method of diagonalization fails to be so. I describe the ways in which these two methods..
|Keywords||No keywords specified (fix it)|
No categories specified
(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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Laureano Luna & William Taylor (2010). Cantor's Proof in the Full Definable Universe. Australasian Journal of Logic 9:11-25.
Mauro Ferrari & Pierangelo Miglioli (1993). Counting the Maximal Intermediate Constructive Logics. Journal of Symbolic Logic 58 (4):1365-1401.
Timothy Bays (2009). Skolem's Paradox. In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy.
Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
John L. Bell (1999). Frege's Theorem in a Constructive Setting. Journal of Symbolic Logic 64 (2):486-488.
Bart Jacobs (1989). The Inconsistency of Higher Order Extensions of Martin-Löf's Type Theory. Journal of Philosophical Logic 18 (4):399 - 422.
Kevin C. Klement (2010). Russell, His Paradoxes, and Cantor's Theorem: Part I. Philosophy Compass 5 (1):16-28.
Wolfram Hinzen (2003). Constructive Versus Ontological Construals of Cantorian Ordinals. History and Philosophy of Logic 24 (1):45-63.
George Boolos (1997). Constructing Cantorian Counterexamples. Journal of Philosophical Logic 26 (3):237-239.
L. H. Kauffman (2012). The Russell Operator. Constructivist Foundations 7 (2):112-115.
Seiki Akama (1996). Curry's Paradox in Contractionless Constructive Logic. Journal of Philosophical Logic 25 (2):135 - 150.
John Bell (1999). Boolean Algebras and Distributive Lattices Treated Constructively. Mathematical Logic Quarterly 45 (1):135-143.
Added to index2010-12-22
Total downloads8 ( #187,002 of 1,413,163 )
Recent downloads (6 months)1 ( #153,719 of 1,413,163 )
How can I increase my downloads?