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To Be and Not to Be: Dialectical Tense Logic

Graham Priest
Studia Logica: An International Journal for Symbolic Logic
Vol. 41, No. 2/3, Proceedings of the 1981 Annual Conference of the Australasian Association of Symbolic Logic (1982), pp. 249-268
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015056
Page Count: 20
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To Be and Not to Be: Dialectical Tense Logic
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Abstract

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 propositional 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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