Disimplicature

Speranza

What we may call "asymmetric disagreement" (between A and B, to use Grice's favourite letters) occurs when one agent is in disagreement with another, but not vice-versa. 

We can give an example of and develop a framework for understanding this phenomenon. 

One pivotal feature of the example is that one of the agents in the scenario has a belief about what might be the case—a might-belief. 

We may show, alla Grice, that a traditional account of "might"-beliefs and disagreement cannot explain the initially surprising phenomenon of asymmetric disagreement. 

In order to provide an explanation, one may develop a dynamic account of "might-beliefs and a corresponding account of disagreement. 

We should explore a choice point for our account—showing that the simple dynamic account has some controversial (though, perhaps, true) consequences. 

We may also explore how revisionary notions of validity, inconsistency, and disagreement can allow us to avoid these consequences if we wish.

And even if we don't! (Grice loved an Austin biscuit conditional!)