To be and not to be: Dialectical tense logic

Studia Logica 41 (2-3):249 - 268 (1982)
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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 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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Author's Profile

Graham Priest
CUNY Graduate Center

Citations of this work

Logic of paradox revisited.Graham Priest - 1984 - Journal of Philosophical Logic 13 (2):153 - 179.
Characterizing Belnap's Logic via De Morgan's Laws.Alexej P. Pynko - 1995 - Mathematical Logic Quarterly 41 (4):442-454.
Boundary.Achille C. Varzi - 2013 - Stanford Encyclopedia of Philosophy.
Unsettledness in times of change.Martin Pickup - 2022 - Synthese 200 (2):1-20.

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References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Science of Logic.M. J. Petry, G. W. F. Hegel, A. V. Miller & J. N. Findlay - 1970 - Philosophical Quarterly 20 (80):273.
Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.

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