Constructive Context

Abstract
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 — employed by Cantor himself in showing that the set of real numbers is uncountable — 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)
Categories No categories specified
(categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,365
External links
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
John L. Bell (1999). Frege's Theorem in a Constructive Setting. Journal of Symbolic Logic 64 (2):486-488.
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.
Analytics

Monthly downloads

Added to index

2010-12-22

Total downloads

8 ( #172,476 of 1,102,742 )

Recent downloads (6 months)

1 ( #296,833 of 1,102,742 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.