An Observation Concerning Porte’s Rule in Modal Logic

Rohan French; Lloyd Humberstone

doi:10.18778/0138-0680.44.1.2.04

Authors

Rohan French Department of Philosophy, Monash University, Victoria 3800, Australia
Lloyd Humberstone Department of Philosophy, Monash University, Victoria 3800, Australia

DOI:

https://doi.org/10.18778/0138-0680.44.1.2.04

Abstract

It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ◊A, or else no consistent normal modal logic contains ◊¬A.

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