In this work I argue for the thesis that Grice’s intentional-cooperative analysis of assertion works at three levels: the logical, the epistemological and the normative. I use “conventional implicature” as example. First part shows that other approaches to assertion can’t give an accurate description of semantic content. I point to a general, twofold conclusion: the truth-conditional approach fails by neglecting intentional acts to be the meaning blocks; the rule-oriented approach misses its target by disregarding that all communicative acts are intentional, (...) but many are not conventional. Assertion includes some features of intentional action, the main theme in second part. As rational justification is the basis of intention, the solution of some remaining problems connected to assertion may rest in the justificatory structures underlying intention. Judgment, the epistemic variety of rational acceptability, determines, on one hand, the infelicity in conventional implicature cancellation and, on the other, shows why convention is just a minor component in the theory of meaning. Justification deems a special methodology in which causal explanations of meaning and representation can be replaced by justifications, teleological in character. The rationalist background of Grice’s proposal is thus stressed, as well as his conception of rationality as the body of capacities in charge of identifying and attributing value. Following this interpretation, other problems on meaning and communication, for example the relations between the Cooperative Principle and the conversational maxims, can be dealt with. (shrink)