Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T04:24:49.744Z Has data issue: false hasContentIssue false
  • English
  • Français

THE EXPRESSIVE POWER OF TRUTH

Published online by Cambridge University Press:  15 December 2014

MARTIN FISCHER  and
LEON HORSTEN
MARTIN FISCHER*
Affiliation:
MCMP, LMU München
LEON HORSTEN*
Affiliation:
Department of Philosophy, University of Bristol
*
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY FAKULTÄT FÜR PHILOSOPHIE WISSENSCHAFTSTHEORIE UND RELIGIONSWISSENSCHAFTEN LMU MÜNCHEN, GESCHWISTER SCHOLL PLATZ 1 D-80539 MÜNCHEN, GERMANY E-mail: M.Fischer@lrz.uni-muenchen.de
†DEPARTMENT OF PHILOSOPHY 43 WOODLAND ROAD BS83PE, BRISTOL, UK E-mail: leon.horsten@bristol.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

There are two perspectives from which formal theories can be viewed. On the one hand, one can take a theory to be about some privileged models. On the other hand, one can take all models of a theory to be on a par. In contrast with what is usually done in philosophical debates, we adopt the latter viewpoint. Suppose that from this perspective we want to add an adequate truth predicate to a background theory. Then on the one hand the truth theory ought to be semantically conservative over the background theory. At the same time, it is generally recognised that the central function of a truth predicate is an expressive one. A truth predicate ought to allow us to express propositions that we could not express before. In this article we argue that there are indeed natural truth theories which satisfy both the demand of semantical conservativeness and the demand of adequately extending the expressive power of our language.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 2 , June 2015 , pp. 345 - 369
Copyright
Copyright © Association for Symbolic Logic 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Barwise, J., & Feferman, S. (1985). Model-Theoretic Logics. New York: Springer-Verlag.Google Scholar
Caldon, P., & Ignjatovic̀, A. (2005). On mathematical instrumentalism. Journal of Symbolic Logic, 70(3), 778–794.Google Scholar
Cantini, A. (1989). Notes on formal theories of truth. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 35, 97–130.Google Scholar
Craig, W., & Vaught, R. L. (1958). Finite axiomatisability using additional predicates. The Journal of Symbolic Logic, 23, 289–308.Google Scholar
Fischer, M. (2009). Minimal truth and interpretability. Review of Symbolic Logic, 2(4), 799–815.Google Scholar
Fischer, M. (2014). Truth and speed-up. Review of Symbolic Logic, 7(2), 319–340.Google Scholar
Fujimoto, K. (2012). Classes and truths in set theory. Annals of Pure and Applied Logic, 163, 1484–1523.Google Scholar
Hájek, P. (1993). Interpretability and fragments of arithmetic. In Clote, P. and Krajíček, J., editors. Arithmetic, Proof Theory, and Computational Complexity. Oxford: Oxford University Press, pp. 185–196.Google Scholar
Hájek, P., & Pudlák, P. (1993). Metamathematics of First-Order Arithmetic. Berlin: Springer-Verlag.Google Scholar
Halbach, V. (2014). Axiomatic Theories of Truth (revised edition). Cambridge, UK: Cambridge University Press.Google Scholar
Hodges, W. (2008). Tarski’s theory of definition. In Patterson, D., editor. New Essays on Tarski and Philosophy. Oxford: Oxford University Press., pp. 94–132.Google Scholar
Horsten, L. (1995). The semantical paradoxes, the neutrality of truth, and the neutrality of the minimalist theory of truth. In Cortois, P., editor. The Many Problems of Realism. Tilburg: Tilburg University Press, pp. 173–187.Google Scholar
Horsten, L. (2011). The Tarskian Turn. Deflationism and Axiomatic Truth. Cambridge, MA: MIT Press.Google Scholar
Horwich, P. (1998). Truth (second edition). Oxford: Clarendon Press.Google Scholar
Kaye, R. (1991). Models of Peano Arithmetic. Oxford: Oxford University Press.CrossRefGoogle Scholar
Ketland, J. (1999). Deflationism and Tarski’s paradise. Mind, 108, 69–94.Google Scholar
Kreisel, G. (1967). Informal rigour and completeness proofs. In Lakatos, I., editor. Problems in the Philosophy of Mathematics. Amsterdam: North Holland, pp. 138–186.Google Scholar
McGee, V. (1991). Truth, Vagueness and Paradox. Indianapolis: Hackett Publishing Company.Google Scholar
Niebergall, K.-G. (2000). On the logic of reducibility: Axioms and examples. Erkenntnis, 53, 27–61.Google Scholar
Pudlák, P. (1998). The lengths of proofs. In Buss, S. R., editor. Handbook of Proof Theory, Chapter VIII. Amsterdam: Elsevier Science Publisher, pp. 547–637.Google Scholar
Quine, W. V. O. (1970). Philosophy of Logic. Cambridge, MA: Harvard University Press.Google Scholar
Schindler, R. (1994). ACA0, Π1-CA0, and the semantics of arithmetic, and BG, BG + Σ1-Ind, and the semantics of set theory. Available fromwww.math.uni-muenster.de/logik/Personen/rds/.Google Scholar
Shapiro, S. (1997). Philosophy of Mathematics. Structure and Ontology. Oxford: Oxford University Press.Google Scholar
Shapiro, S. (1998). Proof and truth: Through thick and thin. The Journal of Philosophy, 95, 493–521.Google Scholar
Simpson, S. G. (1999). Subsystems of Second Order Arithmetic. Heidelberg: Springer-Verlag.Google Scholar
Suppe, F. (1977). The Structure of Scientific Theories (second edition). Illinois: University of Illinois PressGoogle Scholar
Tarski, A. (1935). Der Wahrheitsbegriff in den formalisierten Sprachen. Studia Philosophica Commentarii Societatis philosophicae Polonorum, 1, 261–405.Google Scholar
Väänänen, J. (2001). Second-order logic and the foundations of mathematics. The Bulletin of Symbolic Logic, 7(4), 504–520.CrossRefGoogle Scholar
Visser, A. (2006). Categories of theories and interpretations. In Enayat, A., Kalantari, I., and Moniri, M., editors, Logic in Tehran: Proceedings of the Workshop and Conference on Logic, Algebra, and Arithmetic, (October, 2003), Number 26 in Lecture Notes in Logic, pp. 284–341. Boca Raton: A K Peters/CRC Press.Google Scholar