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AXIOMS FOR GROUNDED TRUTH

Published online by Cambridge University Press:  30 October 2013

THOMAS SCHINDLER
THOMAS SCHINDLER*
Affiliation:
Ludwig-Maximilians-Universität München
*
*FAKULTAET FUER PHILOSOPHIE, WISSENSCHAFTSTHEORIE UND RELIGIONSWISSENSCHAFT, LUDWIG-MAXIMILIANS-UNIVERSITAET MUENCHEN, GESCHWISTER-SCHOLL-PLATZ 1, D-80539 MUENCHEN, GERMANY E-mail: thomas.schindler@lrz.uni-muenchen.de
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Abstract

We axiomatize Leitgeb’s (2005) theory of truth and show that this theory proves all arithmetical sentences of the system of ramified analysis up to ε0. We also give alternative axiomatizations of Kripke’s (1975) theory of truth (Strong Kleene and supervaluational version) and show that they are at least as strong as the Kripke-Feferman system KF and Cantini’s VF, respectively.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 1 , March 2014 , pp. 73 - 83
Copyright
Copyright © Association for Symbolic Logic 2013 

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References

BIBLIOGRAPHY

Cantini, A. (1990). A theory of formal truth arithmetically equivalent to ID1 . Journal of Symbolic Logic, 55, 244–259.Google Scholar
Feferman, S. (1991). Reflecting on incompleteness. Journal of Symbolic Logic, 56, 1–49.Google Scholar
Feferman, S. (2008). Axioms for determinateness and truth. Review of Symbolic Logic, 1, 204–217.Google Scholar
Field, H. (2008). Saving Truth from Paradox. New York, NY: Oxford University Press.Google Scholar
Fujimoto, K. (2010). Relative truth definability of axiomatic truth theories. Bulletin of Symbolic Logic, 16, 305–344.Google Scholar
Halbach, V. (2000). Truth and reduction. Erkenntnis, 53, 97–126.Google Scholar
Halbach, V. (2011). Axiomatic Theories of Truth. Cambridge, UK: Cambridge University Press.Google Scholar
Halbach, V., & Horsten, L. (2005). The deflationst’s axioms for truth. In Beall, J. C., and Armour-Garb, B., editors. Deflationism and Paradox. New York, NY: Oxford University Press, pp. 203–217.Google Scholar
Herzberger, H. (1970). Paradoxes of grounding in semantics. Journal of Philosophy, 67, 145–167.Google Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716.Google Scholar
Leitgeb, H. (2005). What truth depends on. Journal of Philosophical Logic, 34, 155–192.CrossRefGoogle Scholar
Meadows, T. (2011). Truth, dependence, and supervaluation: Living with the ghost. Journal of Philosophical Logic (forthcoming).Google Scholar
Vugt, F., & Bonnay, D. (2009). What makes a sentence be about the world? Towards a unified account of groundedness. Unpublished manuscript.Google Scholar
Yablo, S. (1982). Grounding, dependence, and paradox. Journal of Philosophical Logic, 11, 117–137.Google Scholar