Reflections on temporal and modal logic

• Authors: Epstein Richard L.
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

temporal logic; modal logic

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2015
• Volume: 24
• Issue: 1
• Pages: 111–139

Dates

published

2015-03-01

online

2014-08-02

Contributors

author

Epstein Richard L.

• Advanced Reasoning Forum, Dogshine, New Mexico, USA

References

• 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”, http://www.AdvancedReasoningForum.org ).
• 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.

Identifiers

DOI

10.12775/LLP.2014.015