David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 41 (2-3):249 - 268 (1982)
The paper concerns time, change and contradiction, and is in three parts. The first is an analysis of the problem of the instant of change. It is argued that some changes are such that at the instant of change the system is in both the prior and the posterior state. In particular there are some changes from p being true to p being true where a contradiction is realized. The second part of the paper specifies a formal logic which accommodates this possibility. It is a tense logic based on an underlying paraconsistent prepositional logic, the logic of paradox. (See the author's article of the same name Journal of Philosophical Logic 8 (1979).) Soundness and completeness are established, the latter by the canonical model construction, and extensions of the basic system briefly considered. The final part of the paper discusses Leibniz's principle of continuity: Whatever holds up to the limit holds at the limit. It argues that in the context of physical changes this is a very plausible principle. When it is built into the logic of the previous part, it allows a rigorous proof that change entails contradictions. Finally the relation of this to remarks on dialectics by Hegel and Engels is briefly discussed.
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References found in this work BETA
Dag Prawitz (1965/2006). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
Nicholas Rescher (1971). Temporal Logic. New York,Springer-Verlag.
M. J. Petry, G. W. F. Hegel, A. V. Miller & J. N. Findlay (1970). Science of Logic. Philosophical Quarterly 20 (80):273.
Graham Priest (1979). Logic of Paradox. Journal of Philosophical Logic 8 (1):219-241.
Citations of this work BETA
Dimiter Vakarelov (1989). Intuitive Semantics for Some Three-Valued Logics Connected with Information, Contrariety and Subcontrariety. Studia Logica 48 (4):565 - 575.
Alexej P. Pynko (1995). Characterizing Belnap's Logic Via De Morgan's Laws. Mathematical Logic Quarterly 41 (4):442-454.
Jean Paul van Bendegem (2014). Inconsistency in Mathematics and the Mathematics of Inconsistency. Synthese 191 (13):3063-3078.
Joseph Wayne Smith (1986). Logic and the Consistency of the World. Erkenntnis 24 (2):105 - 114.
Seiki Akama, Tetsuya Murai & Yasuo Kudo (forthcoming). Partial and Paraconsistent Approaches to Future Contingents in Tense Logic. Synthese:1-11.
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