Cantor's proof in the full definable universe

Abstract
Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the scope of quantifiers reveals a natural way out.
Keywords Cantor’s theorem  Richard’s paradox  definability  countability  quantifiers  indefinite extensibility  constructive ordinals
Categories (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 Laureano Luna, Cantor's proof in the full definable universe
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
W. D. Hart (2010). The Evolution of Logic. Cambridge University Press.
Analytics

Monthly downloads

Added to index

2010-10-05

Total downloads

33 ( #56,616 of 1,101,864 )

Recent downloads (6 months)

8 ( #34,086 of 1,101,864 )

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.