Grice (1989) and and later Lewis (1969, 1975) offered well-known and influential reductive explanations of linguistic meaning, both taking the linguistic meaning of a sentence in a speech community to be grounded in certain distributions of attitudes (intentions, beliefs, desires) amongst the language using members of the community. This paper addresses three important objections to this general approach: (i) the objection that the account incorrectly requires language users to have higher-order beliefs (Glüer & Pagin 2003), (ii) the objection that the account wrongly locates language processing in the instrumental reasoning part of the mind (Laurence 1996) and (iii) the objection that the accounts idealise inappropriately by assuming that cooperative assertoric language use is central (Keiser 2023). The paper argues that these objections reveal shortcomings in the Grice-Lewis programme, shortcomings that need to be addressed if the programme is to be successful. Finally, the paper proposes to exploit more recent theories of conversation in an attempt to resurrect a reductive explanation of linguistic meaning in terms of Lewisian conventions.