Reflections on temporal and modal logic

Richard L. Epstein



The most popular method of incorporating time into a formal logic is based on the work of Arthur Prior. It treats tenses as operators on sentences. In this essay I show a serious problem with that approach, a confusion of scheme versus proposition, which makes any system built in that way incoherent. I will compare how other formal logics deal with the scheme versus proposition distinction and find that only for formal modal logics does the same problem arise. I then compare Prior’s approach to other ways of taking time into account in formal logics.


temporal logic; modal logic

Full Text:



Azar, B. S., Understanding and Using English Grammar, 2nd edition, Prentice-Hall, 1989.

Epstein, R. L., Propositional Logics (The Semantic Foundations of Logic), Kluwer, 1900. 2nd edition, Oxford University Press, 1995. 2nd edition with corrections, Wadsworth, 2000. 3rd edition, Advanced Reasoning Forum, 2012.

Epstein, R. L., Predicate Logic, Oxford University Press, 1994. Reprinted by Advanced Reasoning Forum, 2012.

Epstein, R. L., Critical Thinking, Wadsworth Publishing Company, 1998. 2nd edition, 2001. 3rd edition (with C. Kernberger), 2005. 4th edition (with M. Rooney), Advanced Reasoning Forum, 2012.

Epstein, R. L., “Valid inferences”, pages 105–112 in Logic without Frontiers: Festschrift for Walter Alexandre Carnielli on the Occasion of his 60th Birthday, J.-Y. Béziau and M.E. Coniglio (eds.), College Publications, 2012. To appear in Reasoning and Formal Logic by Epstein, 2014.

Epstein, R. L., “Truth and reasoning”, pages 101–127 in Prescriptive Reasoning, R. L.Epstein, Advanced Reasoning Forum 2012.

Epstein, R. L., Logic, Language, and the World, vol. 1: “The Internal Structure of Predicates and Names”, Advanced Reasoning Forum.

Epstein, R. L., Logic, Language, and the World, vol. 2 “Time and Space”. Advanced Reasoning Forum to appear 2016 (previously available as part of a draft called “The Internal Structure of Predicates and Names with an Analysis of Reasoning about Process”, ).

Epstein, R. L., and E. Buitrago-Díaz, “A propositional logic of temporal connectives”, Logic and Logical Philosophy (2014). DOI: 10.12775/LLP.2014.015

Prior, A., Time and Modality, Oxford University Press, 1957.

Prior, A., “Changes in events and changes in things” (preprint). Reprinted: pages 35–46 in The Philosophy of Time, R. Le Poidevin and M. MacBeath (eds.), Oxford University Press, 1993. Also reprinted: pages 7–19 in Papers on Time and Tense by Arthur Prior, Oxford University Press, 2003.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism