Having been shamed by a friend into posting more on this blog, I thought I'd say a few more things on Christopher Potts' book The Logic of Conventional Implicatures.
According to Potts, "no lexical item contributes both an at-issue and a CI meaning" (LCI, p. 48). In past posts, I have suggested that this is mistaken. Originally I tabled examples like, "Some asshole cut me off" in which the nominal "asshole" seems to be essential to the at-issue meaning of the sentence and it seems to conventionally implicate a negative attitude on the part of the speaker toward this person.
However, a clearer sort of example is the sentence "Dickhead is over by the copier." Lexical items like "dickhead" are a particularly fascinating case. It seems to me that these items are indexicals whose character is partially determined by their expressive content. Roughly, the character is: the contextually salient individual toward whom the speaker has an extremely negative attitude. Suppose that on the occassion in question, the referent of "dickhead" is Joe. Then the the at-issue meaning of this utterance of "Dickhead is over by the copier" is that Joe is over by the copier and the CI-meaning is that the speaker (Jane) things poorly of Joe. Thus, it appears that "dickhead" contributes both an at-issue and a CI meaning, contra Potts' claim.