Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-16T15:04:42.576Z Has data issue: false hasContentIssue false

MULTIPLE-CONCLUSION LP AND DEFAULT CLASSICALITY

Published online by Cambridge University Press:  21 April 2011

JC BEALL*
Affiliation:
Department of Philosophy, University of Connecticut, and Department of Philosophy, University of Otago
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF CONNECTICUT, STORRS USA AND DEPARTMENT OF PHILOSOPHY UNIVERSITY OF OTAGO, NEW ZEALAND URL:entailments.netE-mail:[email protected]

Abstract

Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of ‘default classicality’. With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such ‘default classicality’ is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.

Type
Research Article
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

Anderson, A. R., Belnap, N. D., & Dunn, J. (1992). Entailment: The Logic of Relevance and Necessity, Vol. 2. Princeton, NJ: Princeton University Press.Google Scholar
Asenjo, F. G. (1966). A calculus of antinomies. Notre Dame Journal of Formal Logic, 16, 103105.Google Scholar
Baaz, M., Fermüller, C. G., & Zach, R. (1993a). 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. (1993b). Systematic construction of natural deduction systems for many-valued logics: Extended report. Technical Report TUW-E185.2-BFZ.1–93.Google Scholar
Beall, J. (2009). Spandrels of Truth. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Beall, J. (2010). Logic: The Basics. Oxford, UK: Routledge.CrossRefGoogle Scholar
Beall, J., & Ripley, D. (2011). Supplement to Logic: The Basics. Oxford, UK: Routledge. Available from: entailments.net.Google Scholar
Beall, J., & van Fraassen, B. C. (2003). Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic. Oxford, UK: Oxford University Press.Google Scholar
Belnap, N. D., & Dunn, J. M. (1973). Entailment and the disjunctive syllogism. In Fløistad, F., and von Wright, G. H., editors. Philosophy of Language/Philosophical Logic, The Hague, The Netherlands: Martinus Nijhoff, pp. 337366. Reprinted in (Anderson et al., 1992, §80).Google Scholar
Brady, R. (2006). Universal Logic, Vol. 109. Stanford, CA: CSLI Lecture Notes.Google Scholar
Carroll, L. (1895). What the Tortoise said to Achilles. Mind, 4(14), 278280.CrossRefGoogle Scholar
Dunn, J. M. (1966). The algebra of intensional logics. PhD Thesis, University of Pittsburgh.Google Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Field, H. (2010). Reply to Restall. Philosophical Studies, 147, 460467. This is part of a book symposium on Field (2008).Google Scholar
Goodship, L. (1996). On dialetheism. Australasian Journal of Philosophy, 74, 153161.CrossRefGoogle Scholar
Harman, G. (1986). Change in View: Principles of Reasoning. Cambridge, MA: MIT Press.Google Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690716. Reprinted in ?.CrossRefGoogle Scholar
Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8, 219241.CrossRefGoogle Scholar
Priest, G. (1984). Logic of paradox revisited. Journal of Philosophical Logic, 13, 153179.CrossRefGoogle Scholar
Priest, G. (1991). Minimally inconsistent LP. Studia Logica, 50, 321331.CrossRefGoogle Scholar
Priest, G. (2006a). Doubt Truth to be a Liar. Oxford, UK: Oxford University Press.Google Scholar
Priest, G. (2006b). In Contradiction, second edition. Oxford, UK: Oxford University Press. First printed by Martinus Nijhoff in 1987.CrossRefGoogle Scholar
Priest, G. (2008). An Introduction to Non-Classical Logic, second edition. Cambridge, MA: Cambridge University Press. First edition published in 2001.CrossRefGoogle Scholar
Restall, G. (2004). Laws of non-contradiction, laws of the excluded middle and logics. In Priest, G., Beall, J., and Armour-Garb, B., editors. The Law of Non-Contradiction, Oxford, UK: Oxford University Press, pp. 7385.CrossRefGoogle Scholar
Restall, G. (2005a). Logic: An Introduction. New York, NY: Routledge.Google Scholar
Restall, G. (2005b). Multiple conclusions. In Hájek, P., Valdes-Villanueva, L., and Westerstahl, D., editors. Logic, Methodology and Philosophy of Science: Proceedings of the Twelth International Congress, London: King’s College Publications, pp. 189205.Google Scholar
Ripley, D. (2011). Conservatively extending classical logic with transparent truth. To appear. Presented at a 2010 meeting of the Melbourne Logic Group.Google Scholar