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Logic and time1

Published online by Cambridge University Press:  12 March 2014


‘In Time rigorous abstraction, in Time the highest, in Time divine knowledge, is comprehended’

Atharva Veda

Following McTaggart [17], we may distinguish two aspects of time: The A-series, running through the past to the present and on into the future, and the B-series, running from earlier to later. In Indo-European languages at least, verbs are tensed, so we cannot help but place whatever we speak of in one of the three divisions of the A-series. But these divisions are not permanent: what is present was future and will be past. Hence a typical statement, e.g. ‘Socrates is sitting’, may well be true at one time and false at another. The instability of truth-value over time was a commonplace among pre-Renaissance logicians, but most modern writers have ‘abstracted from’, i.e. ignored, this feature of ordinary language.

Early logicians were quite interested in time: Aristotle questioned the applicability of the excluded middle to predictions of future contingencies in the famous ‘sea-fight’ passage of On interpretation. Later Greek logicians debated whether that which neither is nor will be can legitimately be called possible, and whether, in order for the conditional ‘if p, then q’ to be true, it is required that ‘not both p and not ∼q’ be true (not just now but) always. Mediaeval logicians in Western Europe struggled with logical difficulties created by the Dogmas of the Church, Omniscience and Free Will. Their counterparts in the Islamic world puzzled over the semantics of the temporal adverbs, ‘always’, ‘usually’, ‘often’, ‘sometimes’, ‘seldom’, ‘never’.

Research Article
Copyright © Association for Symbolic Logic 1979

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An expository paper based on an invited talk delivered at the meeting of the Association for Symbolic Logic in Washington, D.C., 29 December, 1977.



[1]Borges, J. L., The garden of forking paths (translated by Yates, D. A.), Labyrinths (Yates, and Irby, , editors), New Directions, New York, 1962.Google Scholar
[2]Borges, J. L., The theologians (translated by Irby, J. E.), Labyrinth (Yates, and Irby, , editors). New Directions, New York, 1962.Google Scholar
[3]Bull, R. A., An algebraic study of tense logic with linear time, this Journal, vol. 33(1968), pp. 2738.Google Scholar
[4]Burgess, J. P., The unreal future, Theoria (to appear).Google Scholar
[5]Burgess, J. P., Decidability for branching time, Studia Logica (to appear).Google Scholar
[6]Cocchiarella, N. D., Tense and modal logic, doctoral dissertation, U. C. L. A., 1965.Google Scholar
[7]Davies, P. C. W., The physics of time asymmetry, University of California Press, Berkeley and Los Angeles, 1974.Google Scholar
[8]Dummett, M., Elements of intuitionism, Clarendon Press, Oxford, 1977.Google Scholar
[9]Gabbay, D. M., Model theory for tense logics, Annals of Mathematical Logic, vol. 8(1975), pp. 185236.CrossRefGoogle Scholar
[10]Gabbay, D. M., Decidability results in non-classical logics, Annals of Mathematical Logic, vol. 8(1975), pp. 237295.CrossRefGoogle Scholar
[11]Gabbay, D. M., Tense systems with split truth table, Logique et Annalyse, vol. 80 (1978), pp. 140.Google Scholar
[12]Gödel, K., An example of a new type of cosmological solution of Einstein's field equation of gravitation, Review of Modern Physics, vol. 21(1949), pp. 447450.CrossRefGoogle Scholar
[13]Gödel, K., A remark about the relationship between relativity theory and idealistic philosophy, Albert Einstein, Philosopher-scientist (Schilpp, P. A., editor). Harper, New York, 1959, pp. 555562.Google Scholar
[14]Goldblatt, R. I., Diodorean modality in Minkowski spacetime, Studia Logica (to appear).Google Scholar
[15]Łukasiewicz, J., On determinism, Selected works (Borkowski, L., editor), North-Holland, Amsterdam, 1970.Google Scholar
[16]McArthur, R. P., Tense logic, Reidel, Dordrecht, 1976.CrossRefGoogle Scholar
[17]McTaggart, J.M.E., The unreality of time, Mind, vol. 187(1908), pp. 457474.CrossRefGoogle Scholar
[18]Prior, A. N., Time and modality, Clarendon Press, Oxford, 1957.Google Scholar
[19]Prior, A. N., Past, present and future, Clarendon Press, Oxford, 1967.CrossRefGoogle Scholar
[20]Prior, A. N., Papers on time and tense, Clarendon Press, Oxford, 1968.Google Scholar
[21]Putnam, H., Time and physical geometry, Journal of Philosophy, vol. 64(1967), pp. 240247.CrossRefGoogle Scholar
[22]Rabin, M. O., Decidability of second order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141(1966), pp. 135.Google Scholar
[23]Reichenbach, H., Elements of symbolic logic, McMillan, New York, 1947.Google Scholar
[24]Sklar, L., Space, time, and spacetime, University of California Press, Berkeley and Los Angeles, 1974.Google Scholar
[25]Thomason, R. H., Indeterminist time and truth-value gaps, Theoria, vol. 36(1970), pp. 264280.CrossRefGoogle Scholar
[26]Thomason, S. K., Semantic analysis of tense logics, this Journal, vol. 37(1972), pp. 150158.Google Scholar
[27]Thomason, S. K., Reduction of tense logic to modal logic. II, Theoria, vol. 41(1975), pp. 154169.CrossRefGoogle Scholar
[28]Thomason, S. K., Reduction of second order logic to modal logic, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 21 (1975), pp. 107114.CrossRefGoogle Scholar
[29]van Benthem, J.F.A.K., Tense logic as a system of logic, Proceedings of the Tübingen Conference on Formal Semantics, 12 1977 (to appear).Google Scholar
[30]van Benthem, J.F.A.K., Tense logic and standard logic, Logique et Analyse, vol. 80 (1978), pp. 4183.Google Scholar
[31]Whorf, B. L., Language, thought, and reality, M. I. T. Press, Cambridge, 1956.Google Scholar