Super liars

Review of Symbolic Logic 3 (3):374-414 (2010)
Abstract
Kripke’s theory of truth succeeded in providing a trivalent semantics for a language that contains its own truth predicate and means of self-reference; but it did so by radically restricting the expressive power of the logic. In Kripke’s analysis, the Liar (e.g. This very sentence is not true) receives the indeterminate truth value; but the logic cannot express the fact that the Liar is something other than true: in order to do so, a weak negation not* would be needed, but it would also make the logic inconsistent (because the ‘Super Liar’ This very sentence is not* true could not be assigned any truth value). Taking a hint from the quantificational form of the problematic sentences (… is something other than true), we define a hierarchy of negations which each quantifies over a domain of truth values, assimilated to ordinals. The resulting logic has as many negations and truth values as there are ordinals. Unlike Kripke’s logic, it enjoys a form of expressive completeness. And although the logic is not monotonic, we show that under broad conditions we can construct a variety of fixed points; one of them emulates Kripke’s ‘least fixed point’, while another one assigns a different truth value to each Super Liar.
Keywords No keywords specified (fix it)
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
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,337
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
Solomon Feferman (1984). Toward Useful Type-Free Theories. I. Journal of Symbolic Logic 49 (1):75-111.

View all 9 references

Citations of this work BETA

No citations found.

Similar books and articles
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

48 ( #32,561 of 1,096,612 )

Recent downloads (6 months)

3 ( #102,815 of 1,096,612 )

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.