David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 71 (2):677 - 712 (2006)
We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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
Hannes Leitgeb (2007). What Theories of Truth Should Be Like (but Cannot Be). Philosophy Compass 2 (2):276–290.
Leon Horsten (2009). Levity. Mind 118 (471):555-581.
Leon Horsten (forthcoming). One Hundred Years of Semantic Paradox. Journal of Philosophical Logic:1-15.
Colin R. Caret & Zach Weber (2015). A Note on Contraction-Free Logic for Validity. Topoi 34 (1):63-74.
Kevin Scharp (2014). Truth, Revenge, and Internalizability. Erkenntnis 79 (S3):597-645.
Similar books and articles
Leon Horsten (2006). Axiomatizing Kripke's Theory of Truth. Journal of Symbolic Logic 71 (2):677 - 712.
Volker Halbach (2001). Disquotational Truth and Analyticity. Journal of Symbolic Logic 66 (4):1959-1973.
Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.
Juan Barba (2001). Trees for Truth. Nordic Journal of Philosophical Logic 6 (1):71-99.
Philippe Schlenker (2010). Super Liars. Review of Symbolic Logic 3 (3):374-414.
Luca Incurvati (2008). On Adopting Kripke Semantics in Set Theory. Review of Symbolic Logic 1 (1):81-96.
Philip Kremer (2008). Supervaluation Fixed-Point Logics of Truth. Journal of Philosophical Logic 37 (5):407 - 440.
D. Skvortsov (1995). On the Predicate Logics of Finite Kripke Frames. Studia Logica 54 (1):79-88.
Volker Halbach (1997). Tarskian and Kripkean Truth. Journal of Philosophical Logic 26 (1):69-80.
Alan Berger (ed.) (2011). Saul Kripke. Cambridge University Press.
John P. Burgess (2011). Kripke Models. In Alan Berger (ed.), Saul Kripke. Cambridge University Press
David Ripley (2013). Paradoxes and Failures of Cut. Australasian Journal of Philosophy 91 (1):139 - 164.
Added to index2010-08-24
Total downloads69 ( #52,423 of 1,779,059 )
Recent downloads (6 months)3 ( #167,974 of 1,779,059 )
How can I increase my downloads?