Greg Restall and Tony Roy “On Permutation in Simplified Semantics,” Journal of Philosophical Logic, 38:3 (2009) 333–341.
This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Journal of Philosophical Logic 1993) concerning the modelling conditions for the axioms of assertion A → ((A → B) → B) and permutation (A → (B → C)) → (B → (A → C)). We show that the modelling conditions for assertion and permutation proposed in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent.
In this note, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose a correction.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.