Cara writes on 'conversational implicature' for Grice's favourite journal: The Pacific Philosophical Quarterly

"The Russellian approach to the semantics of attitude ascriptions faces a problem in explaining the robust speaker intuitions that it does not predict. A familiar response to the problem is to claim that utterances of attitude ascriptions may differ in their Gricean conversational implicatures. I argue that the appeal to Grice is ad hoc. First, we find that speakers do not typically judge an utterance false merely because it implicates something false. The apparent cancelability of the putative implicatures is irrelevant, since cancelability does not indicate conversational implicature. Finally, the appeal assumes, implausibly, that ordinary speakers generally subscribe to a particular philosophical theory about belief."