On Blum’s Argument for the Soundness of the S5 Axiom

Abstract

In a recent paper, Blum argues that the characteristic axiom of S5 is sound when the modal operators are interpreted as logical necessity and logical possibility. In this paper, I show that this interpretation eliminates the modal dimension: logical necessity, whether understood as validity or provability, is a global property of formulas, so the argument collapses to a triviality.