In this paper, the author discusses Grice's first analysis of non-natural meaning (1957), his notion of a Cooperative Principle underlying human interaction (1975) and his notion of a person (1991). She reformulates Grice's claims about meaning in terms of ascriptions of intentions to the utterer by the audience. It is claimed that by doing so new light can be thrown on some traditional criticism to the definition of meaning, that the use of the Cooperative Principle in the analysis of discourse can be justified and optimized, and that the internal coherence of Grice's philosophy can be better appreciated.