Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T13:02:47.565Z Has data issue: false hasContentIssue false
  • English
  • Français

FOUR BASIC LOGICAL ISSUES

Published online by Cambridge University Press:  05 October 2009

ROSS BRADY  and
PENELOPE RUSH
ROSS BRADY*
Affiliation:
La Trobe Univeristy
PENELOPE RUSH*
Affiliation:
University of Tasmania
*
*DEPARTMENT OF PHILOSOPHY, LATROBE UNIVERISTY, VICTORIA 3086, AUSTRALIA E-mail:Ross.Brady@latrobe.edu.au
†DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF TASMANIA, TASMANIA 7001, AUSTRALIA E-mail:prush@westnet.com.au
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper addresses what we see as the four major issues in logic. The overriding issue is that of the choice of logic. We start with some discussion of the preliminary issue of whether there is such a ‘one true logic,’ but we reserve the main discussion for the first issue of ‘classical logic versus non-classical logic.’ Here, we discuss the role of meaning and truth, the relation between classical logic and classical negation, and whether and, if so, how classical logic should reside at the base world. Given the argument in favor of an overall use of non-classical logic, the second issue is that of the choice of non-classical logic. Brady’s logic MC of meaning containment is argued for, with some comparison made with other relevant logics. For the remaining two issues, we make a case for relevant deduction, in comparison with classical deduction, and we explore possibilities for the appropriate meta-logic, comparing classical and non-classical approaches.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 3 , September 2009 , pp. 488 - 508
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.)

References

BIBLIOGRAPHY

Ackermann, W. (1956). Begrundung einer strengen Implikation. Journal of Symbolic Logic, 21, 113–128.CrossRefGoogle Scholar
Anderson, A. R., & Belnap, N. D. Jr. (1975). Entailment, The Logic of Relevance and Necessity, Vol. 1. Princeton, NJ: Princeton University Press. [ENT1].Google Scholar
Batens, D., & van Bendegem, J.-P. (1985). Relevant derivability and classical derivability in Fitch-style and axiomatic formulations of relevant logics. Logique et Analyse, 28, 21–31.Google Scholar
Beall, J. C., & Restall, G. (2000). Logical pluralism. Australasian Journal of Philosophy, 78, 475–493.CrossRefGoogle Scholar
Beall, J. C., & Restall, G. (2001). Defending logical pluralism. In Brown, B. and Woods, J., editors. Logical Consequences. Stanmore: Hermes, pp. 1–22.Google Scholar
Brady, R. T. (1982). Completeness proofs for the systems RM3 and BN4. Logique et Analyse, 25, 9–32.Google Scholar
Brady, R. T. (1983). The simple consistency of a set theory based on the logic CSQ. Notre Dame Journal of Formal Logic, 24, 431–449.CrossRefGoogle Scholar
Brady, R. T. (1993). Rules in relevant logic - II: Formula representation. Studia Logica, 52, 565–585.CrossRefGoogle Scholar
Brady, R. T. (1996). Relevant implication and the case for a weaker logic. Journal of Philosophical Logic, 25, 151–183.CrossRefGoogle Scholar
Brady, R. T. (2000). Entailment, negation and paradox solution. In Batens, D., Mortensen, C., Priest, G., and van Bendegem, J.-P., editors. Frontiers of Paraconsistent Logic. Baldock, UK: Research Studies Press, pp. 113–135.Google Scholar
Brady, R. T., editor. (2003). Relevant Logics and their Rivals, Vol. 2. Aldershot, UK: Ashgate.Google Scholar
Brady, R. T. (2006). Universal Logic. Stanford, CA: CSLI Publications.Google Scholar
Brady, R. T. (2007). Entailment logic - A blueprint. In Béziau, J.-Y., Carnielli, W., and Gabbay, D., editors. Handbook of Paraconsistency. King’s College, London: College Publications, pp. 127–151.Google Scholar
Brady, R. T. (accepted subject to revision). Free Semantics, in preparation.CrossRefGoogle Scholar
Brady, R. T. (forthcoming in Brady & Rush, Entailment Logic). Normalized natural deduction systems for some relevant logics -I, -II, -III. Presented in stages to Australasian Association for Logic Conferences in 2001, 2002, 2003 and 2004, with Part I. Journal of Symbolic Logic, 71, 35–66.CrossRefGoogle Scholar
Brady, R. T. (forthcoming). Extending metacompleteness to classical systems. Australasian Journal of Logic, in honour of Robert Meyer, forthcoming.Google Scholar
Brady, R. T., & Rush, P. (in preparation). Entailment Logic: Theory and Application, in preparation.Google Scholar
Bueno, O. (2002). Can a paraconsistent theorist be a logical monist?. In Carnielli, W. A., Coniglio, M. E., and D’Ottaviano, I. M., editors. Paraconsistency: The Logical Way to the Inconsistent. New York, NY: Marcel Dekker, pp. 535–552.Google Scholar
Bueno, O., & Colyvan, M. (2004). Logical non-apriorism and the ‘law’ of non-contradiction. In Priest, G., Beall, J. C., and Armour-Garb, B., editors. The Law of Non-Contradiction: New Philosophical Essays. Oxford, UK: Clarendon Press, pp. 156–175.CrossRefGoogle Scholar
Burgess, J. P. (1983). Common sense and ‘relevance’. Notre Dame Journal of Formal Logic, 24, 41–53.CrossRefGoogle Scholar
Coffa, J. A. (1991). The Semantic Tradition from Kant to Carnap. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
Defletsen, M. (2005). Formalism. In Shapiro, S., editor. The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford, UK: Oxford University Press, pp. 236–317.Google Scholar
Dummett, M. (1978). Truth and Other Enigmas. London: Duckworth.Google Scholar
Dunn, J. M. (1976). Intuitive semantics for first-degree entailments and ‘coupled trees’. Philosophical Studies, 29, 149–168.CrossRefGoogle Scholar
Ellis, B. (1979). Rational Belief Systems. Oxford, UK: Blackwell.Google Scholar
Garfield, J. (2004). ‘To pee and not to pee? ’ Could that be the question?. In Priest, G., Beall, J. C., and Armour-Garb, B., editors. The Law of Non-Contradiction: New Philosophical Essays. Oxford, UK: Clarendon Press, pp. 235–244.CrossRefGoogle Scholar
Hunter, G. (1972). Problems About ‘if’. St. Andrew’s, UK: University of St. Andrews, privately circulated.Google Scholar
Hurley, P. (2000). A Concise Introduction to Logic (seventh edition). Belmont, CA: Wadsworth.Google Scholar
Mares, E. (2004). Logical non-apriorism and the ‘law’ of non-contradiction. In Priest, G., Beall, J. C., and Armour-Garb, B., editors. The Law of Non-Contradiction: New Philosophical Essays. Oxford, UK: Clarendon Press, pp. 264–275.CrossRefGoogle Scholar
Meyer, R. K., & Routley, R. (1977). Extensional reduction I. The Monist, 60, 355–369.CrossRefGoogle Scholar
Nagel, E., & Newman, J. R. (2001). Gödel’s Proof. New York, NY: New York University Press.Google Scholar
Priest, G. (2001). An Introduction to Non-Classical Logic. Cambridge, UK: Cambridge University Press.Google Scholar
Read, S. (1988). Relevant Logic. Oxford, UK: Basil Blackwell.Google Scholar
Routley, R., Meyer, R. K., Plumwood, V., & Brady, R. T. (1982). Relevant Logics and Their Rivals, Vol. 1. Atascadero, CA.Google Scholar
Slaney, J. K. (1984). A metacompleteness theorem for contraction-free relevant logics. Studia Logica, 43, 159–168.CrossRefGoogle Scholar
Slaney, J. K. (1987). Reduced models for relevant logics without WI. Notre Dame Journal of Formal Logic, 28, 395–407.CrossRefGoogle Scholar
van Fraassen, B. (1966). Singular terms, truth-value gaps, and free logic. Journal of Philosophy, 63, 481–495.CrossRefGoogle Scholar
Wright, C. (2004a). Intuition, entailment and the epistemology of logical laws. Dialectica, 58(1), 155–175.CrossRefGoogle Scholar
Wright, C. (2004b). On epistemic entitlement: Warrant for nothing (and foundations for free)? Aristotelian Society, Supplementary Volume, 78(suppl), 167–212.CrossRefGoogle Scholar