A Modal Translational Semantics in Prior’s “Symbolism and Analogy”

Main Article Content

Jeremiah Joven Joaquin

Abstract

This paper explores a modal semantics Arthur Prior developed in his 1957 lecture, “Symbolism and Analogy.” Prior’s semantics employs a translational scheme where certain modal axioms are translated as sentences in an easily understood language. Using Prior’s semantics, we show that one can distinguish between modal logics like D, M, T, S4, and S5 without recourse to possible worlds. Finally, given the current conception of what a semantics ought to be, we consider whether Prior’s modal semantics is indeed a semantics.

Article Details

Section
Articles

References

Carnap, R. (1946). Modalities and Quantification. The Journal of Symbolic Logic, 11(2), 33-64. https://doi.org/10.2307/2268610

Carnap, R. (1947). Meaning and Necessity: A Study in Semantics and Modal Logic. University of Chicago Press.

Copeland, B. J. (2002). The Genesis of Possible Worlds Semantics. Journal of Philosophical Logic, 31(2), 99-137.

https://doi.org/10.1023/A:1015273407895

Copeland, B. J. (2016). Prior, Translational Semantics, and the Barcan Formula. Synthese, 193(11), 3507-3519. https://doi.org/10.1007/s11229-015-0955-2

Cresswell, M. (2016). Prior on the Semantics of Modal and Tense Logic. Synthese, 193(11), 3607-3623. https://doi.org/10.1007/s11229-015-0949-0

Cresswell, M. (2019). Modal Logic before Kripke. Organon F, 26(3), 323-339.

https://doi.org/10.31577/orgf.2019.26302

Feys, R. (1950). Les Systèmes Formalisés des Modalités Aristotéliciennes. Revue Philosophique de Louvain, 48, 478-509.

https://doi.org/10.3406/phlou.1950.4310

Hintikka, J. (1961). Modality and Quantification. Theoria, 27(3), 119-128. https://doi.org/10.1111/j.1755-2567.1961.tb00020.x

Kripke, S. A. (1959a). A Completeness Theorem in Modal Logic. The Journal of Symbolic Logic, 24(1), 1-14. https://doi.org/10.2307/2964568

Kripke, S. A. (1959b). Semantical Analysis of Modal Logic. The Journal of Symbolic Logic, 24(4), 323-324. https://doi.org/10.1017/S0022481200123321

https://doi.org/10.1017/S0022481200123321

Lepore, E., & B. Loewer. (1981). Translational Semantics. Synthese, 48(1), 121-133.

https://doi.org/10.1007/BF01064631

Lewis, C. I., & C. H. Langford. (1932). Symbolic Logic. Dover.

Lewis, D. (1970). General Semantics. Synthese, 22(1/2), 18-67.

https://doi.org/10.1007/BF00413598

Markoska-Cubrinovska, A. (2016). Possible worlds in "The Craft of Formal Logic". Synthese, 193(11), 3459-3471. https://doi.org/10.1007/s11229-015-0912-0

https://doi.org/10.1007/s11229-015-0912-0

Meredith, C. A., & A. N. Prior. (1956). Interpretations of Different Modal Logics in the "Property Calculus" [Unpublished manuscript].

Prior, A. N. (1951a). The Craft of Formal Logic [Unpublished manuscript].

Prior, A. N. (1951b). The Ethical Copula. Australasian Journal of Philosophy, 29(3), 137-154. https://doi.org/10.1080/00048405185200171

Prior, A. N. (1952). In What Sense Is Modal Logic Many-Valued? Analysis, 12(6), 138-143. https://doi.org/10.1093/analys/12.6.13

Prior, A. N. (1955a). Diodoran Modalities. The Philosophical Quarterly (1950-), 5(20), 205-213. https://doi.org/10.2307/2957434

Prior, A. N. (1955b). Formal Logic. Oxford University Press.

Prior, A. N. (1956). Modality and Quantification in S5. The Journal of Symbolic Logic, 21(1), 60-62. https://doi.org/10.2307/2268488

Prior, A. N. (1957a). Time and Modality. Oxford University Press.

Prior, A. N. (1957b). The Necessary and the Possible. The Listener, 627-628.

Prior, A. N. (1957c). Symbolism and Analogy. The Listener, 675; 678.

Prior, A. N. (1957d). Many-valued Logics. The Listener, 717-719.

Prior, A. N. (1962). Possible Worlds. The Philosophical Quarterly, 12(46), 36-43. https://doi.org/10.2307/2216837

Prior, A. N. (1976). What is Logic? In P. T. Geach & A. Kenny (Eds.), Papers in Logic and Ethics (pp. 122-129). Duckworth.

Wright, G. H. von. (1951). An Essay in Modal Logic. North-Holland Publishing Company.