Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-02-04T17:37:47.478Z Has data issue: false hasContentIssue false
  • English
  • Français

CONSERVATIVELY EXTENDING CLASSICAL LOGIC WITH TRANSPARENT TRUTH

Published online by Cambridge University Press:  26 March 2012

DAVID RIPLEY
DAVID RIPLEY*
Affiliation:
Department of Philosophy, University of Connecticut and School of Historical and Philosophical Studies, University of Melbourne
*
*DEPARTMENT OF PHILOSOPHY, 101 MANCHESTER HALL 344 MANSFIELD RD., UNIVERSITY OF CONNECTICUT STORRS, CT 06269-2054, USA AND SCHOOL OF HISTORICAL AND PHILOSOPHICAL STUDIES, OLD QUAD, UNIVERSITY OF MELBOURNE PARKVILLE, VIC 3010 AUSTRALIA E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper shows how to conservatively extend a classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth-involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system features admissible Cut, but the other does not.)

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 2 , June 2012 , pp. 354 - 378
Copyright
Copyright © Association for Symbolic Logic 2012

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

Baaz, M., Fermüller, C. G., & Zach, R. (1992). Dual systems of sequents and tableaux for many-valued logics. Technical Report TUW-E185.2-BFZ.2–92.Google Scholar
Baaz, M., Fermüller, C. G., & Zach, R. (1993). Systematic construction of natural deduction systems for many-valued logics: Extended report. Technical Report TUW-E185.2-BFZ.1–93.Google Scholar
Barwise, J., & Etchemendy, J. (1987). The Liar: An Essay on Truth and Circularity. Oxford, UK: Oxford University Press.Google Scholar
Beall, Jc. (2009). Spandrels of Truth. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Beall, Jc, & van Fraassen, B. C. (2003). Possibilities and Paradox: An Introduction to Modal and Many-valued Logic. Oxford, UK: Oxford University Press.Google Scholar
Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2011). Tolerant, classical, strict. Journal of Philosophical Logic. To appear.Google Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Frankowski, S. (2004). Formalization of a plausible inference. Bulletin of the Section of Logic, 33, 41–52.Google Scholar
Halbach, V. (2011). Axiomatic Theories of Truth. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Hyde, D. (1997). From heaps and gaps to heaps of gluts. Mind, 106, 641–660.CrossRefGoogle Scholar
Kremer, M. (1988). Kripke and the logic of truth. Journal of Philosophical Logic, 17(3), 225–278.CrossRefGoogle Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72(19), 690–716.CrossRefGoogle Scholar
Leitgeb, H. (1999). Truth and the liar in De Morgan-valued models. Notre Dame Journal of Formal Logic, 40(4), 496–514.CrossRefGoogle Scholar
Malinowski, G. (1990). Q-consequence operation. Reports on Mathematical Logic, 24, 49–59.Google Scholar
Maudlin, T. (2004). Truth and Paradox. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Priest, G. (2006). In Contradiction. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Priest, G. (2008). An Introduction to Non-Classical Logic: From If to Is (second edition). Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Restall, G. (2005). Multiple conclusions. In Hajek, P., Valdes-Villanueva, L., and Westerståhl, D., editors. Logic, Methodology, and Philosophy of Science: Proceedings of the Twelfth International Congress. London, UK: Kings’ College Publications, pp. 189–205.Google Scholar
Ripley, D. (2011a). Paradoxes and failures of cut. Australasian Journal of Philosophy. To appear.Google Scholar
Ripley, D. (2011b). Sorting out the sorites. In Berto, F., Mares, E., and Tanaka, K., editors. Paraconsistency: Logic and Applications. Dordrecht, Netherlands: Springer. To appear.Google Scholar
Shoesmith, D. J., & Smiley, T. J. (1978). Multiple-conclusion Logic. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Takeuti, G. (1987). Proof Theory. (second edition). Amsterdam: Elsevier Science. Studies in Logic 81.Google Scholar