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NOTES ON ω-INCONSISTENT THEORIES OF TRUTH IN SECOND-ORDER LANGUAGES

Published online by Cambridge University Press:  28 October 2013

EDUARDO BARRIO  and
LAVINIA PICOLLO
EDUARDO BARRIO*
Affiliation:
University of Buenos Aires - conicet
LAVINIA PICOLLO*
Affiliation:
University of Buenos Aires - conicet
*
*INSTITUTO DE FILOSOFÍA (UBA) 480 PUAN ST., CITY OF BUENOS AIRES ARGENTINA E-mail: [email protected] and [email protected]
*INSTITUTO DE FILOSOFÍA (UBA) 480 PUAN ST., CITY OF BUENOS AIRES ARGENTINA E-mail: [email protected] and [email protected]
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Abstract

It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-inconsistent theories of truth are considered: the revision theory of nearly stable truth T# and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 4 , December 2013 , pp. 733 - 741
Copyright
Copyright © Association for Symbolic Logic 2013 

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References

BIBLIOGRAPHY

Barrio, E. A. (2010). Theories of truth without standard models and Yablo’s sequences. Studia Logica, 96, 375–391.Google Scholar
Belnap, N. D. (1982). Gupta’s rule of revision theory of truth. Journal of Philosphical Logic, 11, 110–116.Google Scholar
Chapuis, A. (1996). Alternative revision theories of truth. Journal of Philosphical Logic, 25, 399–423.Google Scholar
Dedekind, R. (1996). Was sind und was sollen die zahlen? In Ewald, W. B., editor. From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford, UK: Oxford University Press, pp. 787–832.Google Scholar
Ewald, W. B. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford, UK: Oxford University Press.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 Philosphical Logic, 11, 1–60.Google Scholar
Gupta, A., & Belnap, N. D. (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. (2011). Axiomatic Theories of Truth. Cambridge, MA: Cambridge University Press.Google Scholar
Halbach, V., & Horsten, L. (2005). The deflationist’s axioms for truth. In Armour-Garb, B., and Beall, J. C., editors. Deflationism and Paradox. Oxford, UK: Oxford University Press.Google Scholar
Herzberger, H. (1982). Notes on naive semantics. Journal of Philosphical Logic, 11,61–102.Google Scholar
Leitgeb, H. (2007). What theories of truth should be like (but cannot be). Philosophy Compass, 2(2), 276–290.CrossRefGoogle Scholar
McGee, V. (1985). How truth-like can a predicate be? A negative result. Journal of Philosphical Logic, 14, 399–410.Google Scholar
Shapiro, S. (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. New York, NY: Oxford University Press.Google Scholar
Yaqūb, A. (1993). The Liar Speaks the Truth. A Defense of the Revision Theory of Truth. New York, NY: Oxford University Press.Google Scholar