Organon F

Volume 26, August 2019, Issue 3, Pages 323–339

ISSN 2585-7150 (online) ISSN 1335-0668 (print)

Research Article | Special issue on Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic

Modal Logic before Kripke

Max Cresswell


100 years ago C.I. Lewis published A Survey of Symbolic Logic, which included an axiom system for a notion of implication which was ‘stricter’ than that found in Whitehead and Russell’s Principia Mathematica. As far as I can tell little notice was taken of this until 1930 when Oskar Becker provided some additional axioms which led Lewis in Symbolic Logic (written with C.H. Langford, 1932) to revise the system he had produced in 1918, and list five systems which could be obtained using Becker’s suggested formulae. The present paper reviews the development of modal logic both before and after 1932, up to 1959 looking at, among other work, Becker’s 1930 article and Robert Feys’s articles in 1937 and 1950. I will then make some comments on the completeness results for S5 found in Bayart and Kripke in 1959; and I will finally look at how modal logic reached New Zealand in the early 1950s in the work of Arthur Prior.


Modal logic, history of modal logic, C. I. Lewis, strict implication, Saul Kripke.

Author(s) and affiliation(s)


Max Cresswell


Victoria University of Wellington


Philosophy (HPPI), Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand


About this article


27 October 2018


30 November 2018

Published online

24 August 2019


Institute of Philosophy of the Slovak Academy of Sciences

Institute of Philosophy of the Czech Academy of Sciences

Cite as


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


Cresswell, Max. 2019. "Modal Logic before Kripke." Organon F 26 (3): 323–339.


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

Copyright information

© Max Cresswell

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