 According to Stalnaker, this is precisely what is going on in the case of identity claims like the one we have been considering. Daniels’ assertion of ‘Lloyd is I.L. Humberstone’ clearly flouts the proposed maxim. We can assume that Daniels is aware that O’Leary doesn’t know whether he is in a world like i, where the man to whom he’s been introduced is the famous author, or a world like j where they are distinct. Yet Daniels utters a sentence that expresses a different proposition depending on whether the actual world is like i or like j. In such circumstances, the audience should look for an alternative interpretation of the assertion. Daniels’ assertion can be brought back into conformity with the maxim by re-interpreting it as conveying the proposition expressed by the diagonal of the matrix. At a rough intuitive level, we can say that Daniels is trying to get O’Leary to accept that the sentence ‘Lloyd is I.L. Humberstone’ expresses a truth. But the 2D framework also allows us to specify more precisely just what empirical information is conveyed within a given conversational context. Given O’Leary’s and Daniels’ common presuppositions about what the two names represent, Daniels’ assertion also expresses the proposition that the man to whom O’Leary has just been introduced is the author of ‘Direction of Fit’.