Hostname: page-component-54dcc4c588-sdd8f Total loading time: 0 Render date: 2025-09-23T19:25:59.520Z Has data issue: false hasContentIssue false
  • English
  • Français

MINIMAL TRUTH AND INTERPRETABILITY

Published online by Cambridge University Press:  01 December 2009

MARTIN FISCHER
MARTIN FISCHER*
Affiliation:
Centre for Logic and Analytical Philosophy, University of Leuven
*
*CENTRE FOR LOGIC AND ANALYTICAL PHILOSOPHY, UNIVERSITY OF LEUVEN, LEUVEN, BELGIUM, 3000 E-mail:martin.fischer@hiw.kuleuven.be
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we will investigate different axiomatic theories of truth that are minimal in some sense. One criterion for minimality will be conservativity over Peano Arithmetic. We will then give a more fine-grained characterization by investigating some interpretability relations. We will show that disquotational theories of truth, as well as compositional theories of truth with restricted induction are relatively interpretable in Peano Arithmetic. Furthermore, we will give an example of a theory of truth that is a conservative extension of Peano Arithmetic but not interpretable in it. We will then use stricter versions of interpretations to compare weak theories of truth to subsystems of second-order arithmetic.

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 4 , December 2009 , pp. 799 - 815
Copyright
Copyright © Association for Symbolic Logic 2009

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.)

Article purchase

Temporarily unavailable

References

BIBLIOGRAPHY

Cantini, A. (1989). Notes on formal theories of truth. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 35, 97–130.CrossRefGoogle Scholar
Feferman, S. (1960). Arithmetization of metamathematics in a general setting. Fundamenta Mathematicae, XLIX, 35–92.CrossRefGoogle Scholar
Feferman, S. (1987). Reflecting on incompleteness (draft).Google Scholar
Feferman, S. (1991). Reflecting on incompleteness. The Journal of Symbolic Logic, 56, 1–47.CrossRefGoogle Scholar
Fischer, M. (2008). Davidsons semantisches Programm und deflationäre Wahrheitskonzeptionen. Heusenstamm, Germany: Ontos Verlag.CrossRefGoogle Scholar
Hájek, P., & Pudlák, P. (1993). Metamathematics of First-Order Arithmetic. Berlin: Springer Verlag.CrossRefGoogle Scholar
Halbach, V. (1996). Axiomatische Wahrheitstheorien. Berlin: Akademie Verlag.CrossRefGoogle Scholar
Halbach, V. (1999). Conservative theories of classical truth. Studia Logica, 62, 353–370.CrossRefGoogle Scholar
Halbach, V. (2000). Truth and reduction. Erkenntnis, 53, 97–126.CrossRefGoogle Scholar
Kaye, R. (1991). Models of Peano Arithmetic. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Kotlarski, H., Krajewski, S., & Lachlan, A. (1981). Construction of satisfaction classes for non-standard models. Canadian Mathematical Bulletin, 24, 283–293.CrossRefGoogle Scholar
Krajewski, S. (1974). Predicative expansions of axiomatic theories. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 20, 435–452.CrossRefGoogle Scholar
Lachlan, A. (1981). Full satisfaction classes and recursive saturation. Canadian Mathematical Bulletin, 24, 295–297.CrossRefGoogle Scholar
Lindström, P. (1997). Aspects of Incompleteness, Lecture Notes in Logic, vol. 10. Berlin: Springer Verlag.CrossRefGoogle 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, Germany: Springer Verlag.CrossRefGoogle Scholar
Takeuti, G. (1987). Proof Theory (second edition). Amsterdam, The Netherlands: North Holland.Google Scholar
Visser, A. (1997). An Overview of Interpretability Logic. Logic Group Preprint Series 216. http://www.phil.uu.nl/preprints/lgps.Google Scholar
Visser, A. (2004). Categories of theories and interpretations. In Enayat, A., Kalantari, I., and Moniri, M., editors. Proceedings of the Workshop and Conference on Logic, Algebra, and Arithmetic, October, 2003, pp. 284–341. Logic Group Preprint Series 216. http://www.phil.uu.nl/preprints/lgps.Google Scholar
Visser, A. (2005). Faith & falsity. Annals of Pure and Applied Logic, 131, 103–131.CrossRefGoogle Scholar