Which Modal Logic Is the Right One?

Abstract

The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, and a more speculative argument for the claim that it does not include S4.2 is also presented

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John Burgess
Princeton University

References found in this work

Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
Modalities and Quantification.Rudolf Carnap - 1946 - Journal of Symbolic Logic 11 (2):33-64.
Extensions of the Lewis System S5.Schiller Joe Scroggs - 1951 - Journal of Symbolic Logic 16 (2):112-120.
Refutation Systems in Modal Logic.Valentin Goranko - 1994 - Studia Logica 53 (2):299 - 324.

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Citations of this work

Possible Predicates and Actual Properties.Roy Cook - 2019 - Synthese 196 (7):2555-2582.
Two-Dimensional Adventures.Lloyd Humberstone - 2004 - Philosophical Studies 118 (1-2):17--65.

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