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MODALITY AND AXIOMATIC THEORIES OF TRUTH I: FRIEDMAN-SHEARD

Published online by Cambridge University Press:  01 April 2014

JOHANNES STERN
JOHANNES STERN*
Affiliation:
Munich Center for Mathematical Philosophy, LMU Munich
*
*MCMP, FAKULTÄT FÜR PHILOSOPHIE WISSENSCHAFTSTHEORIE UND RELIGIONSWISSENSCHAFTEN LMU MÜNCHEN, GESCHWISTER-SCHOLL-PLATZ 1 D-80539 MÜNCHEN, GERMANY E-mail:johannes.stern@lrz.uni-muenchen.de
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Abstract

In this investigation we explore a general strategy for constructing modal theories where the modal notion is conceived as a predicate. The idea of this strategy is to develop modal theories over axiomatic theories of truth. In this first paper of our two part investigation we develop the general strategy and then apply it to the axiomatic theory of truth Friedman-Sheard. We thereby obtain the theory Modal Friedman-Sheard. The theory Modal Friedman-Sheard is then discussed from three different perspectives. First, we show that Modal Friedman-Sheard preserves theoremhood modulo translation with respect to modal operator logic. Second, we turn to semantic aspects and develop a modal semantics for the newly developed theory. Third, we investigate whether the modal predicate of Modal Friedman-Sheard can be understood along the lines of a proposal of Kripke, namely as a truth predicate modified by a modal operator.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 2 , June 2014 , pp. 273 - 298
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

BIBLIOGRAPHY

Asher, N., & Kamp, H. (1989). Self-reference, attitudes and paradox. In Chierchia, G., Partee, B. H., and Turner, R., editors. Properties, Types, and Meaning. Vol. I: Foundational Issues, Dordrecht, Netherlands: Kluwer, pp. 85–158.Google Scholar
Belnap, N., & Gupta, A. (1993). The Revision Theory of Truth. Cambridge, MA: The MIT Press.Google Scholar
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge, UK: Cambridge University Press.Google Scholar
des Rivières, J., & Levesque, H. J. (1986). The consistency of syntactical treatments of knowledge. In Halpern, J. Y., editor. Theoretical Aspects of Reasoning about Knowledge. San Mateo, CA: Morgan Kaufmann.Google Scholar
Fitting, M., & Mendelsohn, R. L. (1998). First-Order Modal Logic. Dordrecht, Netherlands: Kluwer Academic Publishers.Google Scholar
Friedman, H., & Sheard, M. (1987). An axiomatic approach to self-referential truth. Annals of Pure and Applied Logic, 33, 1–21.Google Scholar
Gupta, A. (1982). Truth and paradox. Journal of Philosophical Logic, 11, 1–60.Google Scholar
Halbach, V. (1994). A system of complete and consistent truth. Notre Dame Journal of Formal Logic, 35(3), 311–327.Google Scholar
Halbach, V. (2001). Disquotational truth and analyticity. The Journal of Symbolic Logic, 66, 1959–1973.Google Scholar
Halbach, V. (2002). Modalized disquotationalism. In Halbach, V., and Horsten, L., editors. Principles of Truth. Frankfurt, Germany: Ontos Verlag, pp. 75–101.Google Scholar
Halbach, V. (2011). Axiomatic Theories of Truth. New York: Cambridge University Press.Google Scholar
Halbach, V., Leitgeb, H., & Welch, P. (2003). Possible-worlds semantics for modal notions conceived as predicates. Journal of Philosophical Logic, 32, 179–222.Google Scholar
Halbach, V., & Welch, P. (2009). Necessities and necessary truths: A prolegomenon to the use of modal logic in the analysis of intensional notions. Mind, 118, 71–100.Google Scholar
Herzberger, H. (1982). Naive semantics and the liar paradox. The Journal of Philosophy, 79, 479–497.Google Scholar
Horsten, L. (2002). An axiomatic investigation of provability as a primitive predicate. In Halbach, V., and Horsten, L., editors. Principles of Truth. Frankfurt, Germany: Ontos Verlag, pp. 203–220.Google Scholar
Kripke, S. (1975). Outline of a theory of truth. The Journal of Philosophy, 72, 690–716.Google Scholar
Leitgeb, H. (2006). Towards a logic of type-free modality and truth. In Dimitracopoulos, C., Newelski, L., Normann, D., and Steele, J. R., editors. Logic Colloquium 05, Lecture Notes in Logic. New York: Cambridge University Press, pp. 68–84.Google Scholar
McGee, V. (1985). How truthlike can a predicate be? A negative result. The Journal of Philosophical Logic, 14(4), 399–410.Google Scholar
Monk, J. D. (1976). Mathematical Logic. New York: Springer Verlag.Google Scholar
Montague, R. (1963). Syntactical treatments of modality, with corollaries on reflexion principles and finite axiomatizability. Acta Philosophica Fennica, 16, 153–167.Google Scholar
Peacocke, C. (1976). Truth definitions and actual languages. In Evans, G., and McDowell, J., editors. Truth and Meaning. Oxford: Oxford University Press, pp. 162–188.Google Scholar
Quine, W. V. O. (1977). Intensions revisited. Midwest Studies in Philosophy, 2, 5–11.Google Scholar
Sheard, M. (1994). A guide to truth predicates in the modern era. The Journal of Symbolic Logic, 59, 1032–1054.Google Scholar
Sheard, M. (2001). Weak and strong theories of truth. Studia Logica, 68, 89–101.Google Scholar
Stern, J. (2012). Toward Predicate Approaches to Modality. PhD thesis, University of Geneva, 2012.Google Scholar
Stern, J. (forthcoming). Montague’s theorem and modal logic. Erkenntnis, DOI 10.1007/s10670-013-95237.Google Scholar