 H.P. Grice, the father of pragmatic implicatures, offered a very compelling theory of conversational implicatures. (See Grice 1975, 1978, 1981. See also the entry on  implicature.)  But it is unlikely to help the Naive Russellian. Information about the way the believer believes what she believes cannot, it would seem, be carried as a conversational implicature because such information is not calculable by the conversational participants from what is said and the maxims, as Grice’s theory requires conversational implicatures to be. After all, that would require that, at some level, ordinary speakers realize that they are not saying all they mean when they utter, under “ordinary circumstances,” a sentence like (1). But that is implausible. (Schiffer, in his 1987, levels a similar charge, although he does not explicitly present it in terms of Grice’s calculability condition; Salmon responds in his 1989. See also Recanati 1993, chapter 17.)