Greg Restall and Tony Roy “On Permutation in Simplified Semantics,” Journal of Philosophical Logic, 38:3 (2009) 333–341.

doi:10.1007/s10992-009-9104-z

 download pdf

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 → ((AB) → B) and permutation (A → (BC)) → (B → (AC)). 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.


Do you like this, or do you have a comment? Then please  share or reply on Twitter, or  email me.


← A Priori Truths | Writing Archive | Models for Substructural Arithmetics →

about

I’m Greg Restall, and this is my personal website. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews.

elsewhere

subscribe

To receive updates from this site, you can subscribe to the  RSS feed of all updates to the site in an RSS feed reader, or follow me on Twitter at  @consequently, where I’ll update you if anything is posted.

search