Gricean Belief and Desire
Grice argues that speaker meaning is a certain kind of complex intention: the speaker intends to produce in her audience the belief that p by means of the audience’s recognition of that intention—so the act of speaker meaning involves an intention that refers to an intention.  I intend to get you to believe that the sky is blue by uttering the sentence, “the sky is blue” and I intend you to form this belief by recognizing my intention that you form it. Thus we say that speaker meaning involves “Gricean intentions”, meaning such higher-order intentions.
We also describe utterances as “speech acts”, i.e. actions of a certain type. In general, actions are backed by a suitable belief-desire pair: the agent acts as she does because (a) she has a certain desire and (b) she believes that by acting in a certain way she will fulfill that desire. There is a present desire combined with an instrumental belief. So acts of speech should fall under that rubric: there should exist a suitable belief and desire that together “rationalize” the action. It is not difficult to say what these are: the speaker has a desire to communicate that p to some audience a and she believes that by uttering s she will fulfill that desire. I desire you to believe that the sky is blue (I desire to remove your ignorance on the matter) and I believe, instrumentally, that if I utter the English sentence, “the sky is blue” I will succeed in fulfilling my desire—so I perform the speech act of uttering, “the sky is blue”. In principle I could have chosen other means to fulfill my communicative desire, but in the circumstances I chose this particular means. Structurally the case is like my action of going to the fridge and grabbing a beer: I desired a beer and I believed that going to the fridge was the best way to fulfill my desire. Thus we can explain speech acts as we explain other acts—by identifying an appropriate belief-desire pair.
It is also true that agents have intentions corresponding to their beliefs and desires and their consequent actions. I form the intention to go to the fridge for a beer and I act intentionally: my intention is to satisfy a desire by performing an instrumental action. In the case of speech acts the intention has a certain kind of complexity, described by Grice’s analysis, which marks them out as special (I don’t intend the fridge to recognize my intention to get a beer from it). So this Gricean intention must imply corresponding beliefs and desires on the part of the agent. Thus the agent must (a) have a desire to produce in the audience the belief that p by means of recognizing that intention and (b) believe that by uttering s the audience will form the belief that p by recognizing the agent’s intention to produce the belief that p. The agent must have suitable higher-order desires and beliefs to go with his higher-order intentions. So in order to be capable of speaker meaning an agent must be capable of having such complex self-referential desires and beliefs.
By combining the Gricean analysis of speaker meaning with the general belief-desire theory of action we arrive at an account of the belief-desire psychology of an agent capable of what Grice calls non-natural meaning. It is not just the speaker’s intentions that have the complex self-referential Gricean structure but also the desires and beliefs that accompany those intentions. What we desire in relation to others in acts of communication, and what we believe about the way to satisfy these desires, involves the full panoply of Gricean propositional contents. When we explain the actions we call speech acts we invoke desires and beliefs that embed the kinds of content Grice attributed to communicative intentions. A speaker is an agent whose actions are explained by Gricean beliefs and desires. Thus speaker meaning meets action theory: theory of meaning meshes with philosophy of action. Grice is in effect giving us a belief-desire psychology of communicative action, embedding theory of meaning in decision theory.