Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T07:14:15.681Z Has data issue: false hasContentIssue false
  • English
  • Français

TRUTH WITHOUT CONTRA(DI)CTION

Published online by Cambridge University Press:  07 November 2011

ELIA ZARDINI
ELIA ZARDINI*
Affiliation:
Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, and Northern Institute of Philosophy, University of Aberdeen
*
*INSTITUTO DE INVESTIGACIONES FILOSÓFICAS, UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO, MEXICO CITY, 04510, MEXICO, NORTHERN INSTITUTE OF PHILOSOPHY, UNIVERSITY OF ABERDEEN, ABERDEEN, AB24 3UB, UK. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between ‘ ‘P’ is true’ and ‘P’, is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively “unstable”. I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between ‘ ‘P’ is true’ and ‘P’ (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 4 , December 2011 , pp. 498 - 535
Copyright
Copyright © Association for Symbolic Logic 2011

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

Beall, J. C. (2009). Spandrels of Truth. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Blizard, W. (1989). Multiset theory. Notre Dame Journal of Formal Logic, 30, 36–66.Google Scholar
Brady, R. (2006). Universal Logic. Stanford, CA: CSLI Publications.Google Scholar
Curry, H. (1942). The inconsistency of certain formal logics. The Journal of Symbolic Logic, 7, 115–117.CrossRefGoogle Scholar
Field, H. (2006). Truth and the unprovability of consistency. Mind, 115, 567–605.CrossRefGoogle Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Gabbay, D. (1985). Theoretical foundations for non-monotonic reasoning in expert systems. In Apt, K., editor. Logics and Models of Concurrent Systems. Berlin: Springer, pp. 439–457.CrossRefGoogle Scholar
Gentzen, G. (1934). Untersuchungen über das logische Schließen I. Mathematische Zeitschrift, 39, 176–210.CrossRefGoogle Scholar
Gupta, A., & Belnap, N. (1993). The Revision Theory of Truth. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Herzberger, H. (1982). Naive semantics and the liar paradox. The Journal of Philosophy, 79, 479–497.CrossRefGoogle Scholar
Kripke, S. (1975). Outline of a theory of truth. The Journal of Philosophy, 72, 690–716.Google Scholar
Laertius, D. De vitis, dogmatibus et apophthegmatibus clarorum philosophorum.Google Scholar
López de Sa, D., & Zardini, E. (2007). Truthmakers, knowledge and paradox. Analysis, 67, 242–250.CrossRefGoogle Scholar
López de Sa, D., & Zardini, E. (2011). No-no. Paradox and consistency. Analysis, 71, 472–478.CrossRefGoogle Scholar
Maudlin, T. (2004). Truth and Paradox. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
McGee, V. (1991). Truth, Vagueness, and Paradox. Indianapolis, IN: Hackett.Google Scholar
Meyer, R., Routley, R., & Dunn, M. (1979). Curry’s paradox. Analysis, 39, 124–128.CrossRefGoogle Scholar
Priest, G. (2006a). In Contradiction, second edition. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Priest, G. (2006b). Doubt Truth to Be a Liar. Oxford, UK: Oxford University Press.Google Scholar
Troelstra, A., & Schwichtenberg, H. (2000). Basic Proof Theory, second edition. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Zardini, E. (2008). Truth and what is said. Philosophical Perspectives, 22, 545–574.CrossRefGoogle Scholar
Zardini, E. (2011a). The role of utterances in Bradwardine’s theory of truth. Recherches de théologie et philosophie médiévales. Forthcoming.Google Scholar