Conventional implicature, presupposition, and the meaning of must

The class of meaning known as conventional implicature (CI) has received a great deal of attention in the pragmatics and semantics literature in recent years. While the limits of this class of meaning have been greatly expanded and understood in new ways, this renewed attention has also resulted in a certain amount of confusion in regard to the category. There are now two competing conceptions of conventional implicature, but this fact is not always recognized. This paper addresses these two instantiations of CIs: the original description of the phenomenon in Grice (1975:44-45) and a recent reincarnation of it in Potts (2005, inter alia). It then points out differences between the two CI types, comments on the fact that these differences are not always acknowledged, and then illustrates problems that can arise when this occurs.