Super liars

Review of Symbolic Logic 3 (3):374-414 (2010)
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)
DOI 10.1017/S1755020310000067
 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
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,440
Through your library
References found in this work BETA
A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
A Revenge-Immune Solution to the Semantic Paradoxes.Hartry Field - 2003 - Journal of Philosophical Logic 32 (2):139-177.

View all 9 references / Add more references

Citations of this work BETA
Sets and Supersets.Toby Meadows - 2016 - Synthese 193 (6):1875-1907.

Add more citations

Similar books and articles
Added to PP index

Total downloads
76 ( #70,357 of 2,180,170 )

Recent downloads (6 months)
1 ( #303,871 of 2,180,170 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums