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AXIOMATIZING SEMANTIC THEORIES OF TRUTH?

Published online by Cambridge University Press:  26 January 2015

MARTIN FISCHER ,
VOLKER HALBACH ,
JÖNNE KRIENER  and
JOHANNES STERN
MARTIN FISCHER*
Affiliation:
MCMP, LMU München
VOLKER HALBACH*
Affiliation:
University of Oxford
JÖNNE KRIENER*
Affiliation:
Birkbeck College, London
JOHANNES STERN*
Affiliation:
MCMP, LMU München
*
*LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY GESCHWISTER-SCHOLL-PLATZ 1 80539, MÜNCHEN, GERMANY E-mail: [email protected]
†NEW COLLEGE OXFORD, OX1 3BN, UK E-mail: [email protected]
‡DEPARTMENT OF PHILOSOPHY, BIRKBECK COLLEGE LONDON, WC1E 7HX, UK E-mail: [email protected]
LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY GESCHWISTER-SCHOLL-PLATZ 1 80539, MÜNCHEN, GERMANY E-mail: [email protected]
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Abstract

We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 2 , June 2015 , pp. 257 - 278
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

BIBLIOGRAPHY

Burgess, J. P. (1986). The truth is never simple. The Journal of Symbolic Logic, 51(3), 663–681.Google Scholar
Burgess, J. P. (2009). Friedman and the axiomatization of Kripke’s theory of truth. Unpublished manuscript, delivered at a conference in honour of the 60th birthday of Harvey Friedman at the Ohio State University, 14–17 May 2009.Google Scholar
Cain, J., & Damnjanovic, Z. (1991). On the weak Kleene scheme in Kripke’s theory of truth. The Journal of Symbolic Logic, 56(4), 1452–1468.CrossRefGoogle Scholar
Cantini, A. (1989). Notes on formal theories of truth. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 35(2), 97–130.Google Scholar
Cantini, A. (1990). A theory of truth formally equivalent to ID1. Journal of Symbolic Logic, 55, 244–258.Google Scholar
Cantini, A. (1996). Logical Frameworks for Truth and Abstraction. Amsterdam: Elsevier Science Publisher.Google Scholar
Davidson, D. (1990). The structure and content of truth. The Journal of Philosophy, 87(6), 279–328.CrossRefGoogle Scholar
Davidson, D. (1996). The folly of trying to define truth. The Journal of Philosophy, 93, 263–278.Google Scholar
Feferman, S. (1991). Reflecting on incompleteness. The Journal of Symbolic Logic, 56, 1–47.Google Scholar
Feferman, S., & Sieg, W. (1981). Inductive definitions and subsystems of analysis. In Dold, A. and Eckmann, B., editors. Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies, Lecture Notes in Mathematics, Vol. 897. Berlin: Springer, pp. 16–77.Google Scholar
Field, H. (2008). Saving Truth from Paradox. New York: Oxford University Press.Google Scholar
Fujimoto, K. (2010). Relative truth definability of axiomatic truth theories. Bulletin of Symbolic Logic, 16(3), 305–344.CrossRefGoogle Scholar
Gupta, A. (1982). Truth and paradox. Journal of Philosophical Logic, 11, 1–60.Google Scholar
Gupta, A., & Belnap, N. (1993). The Revision Theory of Truth. Cambridge, MA: MIT Press.Google Scholar
Halbach, V. (1994). A system of complete and consistent truth. Notre Dame Journal of Formal Logic, 35, 311–327.Google Scholar
Halbach, V. (2014). Axiomatic Theories of Truth (second edition, revised ed.). Cambridge: Cambridge University Press.Google Scholar
Halbach, V., & Horsten, L. (2006). Axiomatizing Kripke’s theory of truth. The Journal of Symbolic Logic, 71, 677–712.Google Scholar
Herzberger, H. (1982). Notes on naive semantics. Journal of Philosophical Logic, 11, 61–102.Google Scholar
Horsten, L., Leigh, G. E., Leitgeb, H., & Welch, P. (2012). Revision revisited. The Review of Symbolic Logic, 5(04), 642–664.Google Scholar
Kremer, M. (1988). Kripke and the logic of truth. Journal of Philosophical Logic, 17, 225–278.Google Scholar
Kripke, S. (1975). Outline of a theory of truth. The Journal of Philosophy, 72, 690–716.CrossRefGoogle Scholar
Leitgeb, H. (2005). What truth depends on. Journal of Philosophical Logic, 35, 155–192.Google Scholar
Leitgeb, H. (2007). What theories of truth should be like (but cannot be). Philosophy Compass, 2, 276–290.Google Scholar
McGee, V. (1991). Truth, Vagueness, and Paradox: An Essay on the Logic of Truth. Indianapolis, Cambridge: Hackett.Google Scholar
Patterson, D. (2012). Alfred Tarski: Philosophy of Language and Logic. Palgrave New York: Macmillan.Google Scholar
Pohlers, W. (2009). Proof Theory: The First Step into Impredicativity. Berlin: Springer.Google Scholar
Rogers, H. (1967). Theory of Recursive Functions and Effective Computability. New York: McGraw-Hill.Google Scholar
Simpson, S. G. (2009). Subsystems of Second Order Arithmetic (Second edition). Perspectives in Logic. Cambridge: Cambridge University Press.Google Scholar
Tarski, A. (1956). The concept of truth in formalized languages. In Corcoran, J., editor. Logic, Semantics, Metamathematics (1983, second edition). Indianapolis: Hackett Publishing Company.Google Scholar
Turner, R. (1990b). Truth and Modality. London: Pitman.Google Scholar
Welch, P. D. (2014). The complexity of the dependence operator. Journal of Philosophical Logic. Online First DOI 10.1007/s10992-014-9324-8.Google Scholar