 Grice is probably best known in the philosophy of language for his theory of implicatures. It is surely his most influential body of work for those parts of linguistics, psychology, cognitive science and computer science that share philosophy’s interest in language. His theory of meaning, however, is indispensable for understanding his overall philosophical vision and his ‘big picture’ of language and communication. We will not explain this project, which consists in part of ultimately reducing all semantic notions to psychological ones. But we will say a bit about its central concept of ‘M-intentions,’ in order to develop an important aspect of his pragmatic theory, the concept of a communicative intention.