The 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)|
|Through your library||Configure|
Similar books and articles
Jordan Howard Sobel, On the Storeyed Revenge of Strengthened Liars, and the Contrary Finality of No-Proposition Resolutions.
Christopher Gauker (2006). Against Stepping Back: A Critique of Contextualist Approaches to the Semantic Paradoxes. [REVIEW] Journal of Philosophical Logic 35 (4):393 - 422.
Ahmed Alwishah & David Sanson (2009). The Early Arabic Liar: The Liar Paradox in the Islamic World From the Mid-Ninth to the Mid-Thirteenth Centuries Ce. Vivarium.
Bradley H. Dowden (1984). Accepting Inconsistencies From the Paradoxes. Journal of Philosophical Logic 13 (2):125-30.
Alexandre Billon (2011). My Own Truth ---Pathologies of Self-Reference and Relative Truth. In Rahman Shahid, Primiero Giuseppe & Marion Mathieu (eds.), Logic, Epistemology, and the Unity of Science, Vol. 23. springer.
Philip Kremer (2009). Comparing Fixed-Point and Revision Theories of Truth. Journal of Philosophical Logic 38 (4):363 - 403.
Philip Kremer (2008). Supervaluation Fixed-Point Logics of Truth. Journal of Philosophical Logic 37 (5):407 - 440.
Adam Rieger (2001). The Liar, the Strengthened Liar, and Bivalence. Erkenntnis 54 (2):195-203.
Nobu-Yuki Suzuki (1999). Algebraic Kripke Sheaf Semantics for Non-Classical Predicate Logics. Studia Logica 63 (3):387-416.
Matt Leonard (2012). Burge's Contextual Theory of Truth and the Super-Liar Paradox. In Michal Pelis Vit Puncochar (ed.), The Logica Yearbook 2011. College Publications.
Added to index2009-01-28
Total downloads45 ( #28,909 of 722,813 )
Recent downloads (6 months)1 ( #60,541 of 722,813 )
How can I increase my downloads?