Abstract: The typical characteristic of moral assertions is to “express”speakers' moral attitudes. Conventionalists claim that the producing of moral attitudes relies on the compositionality of moral assertions, because the attitude triggers (like “good”, “right” or “wrong”) can denote either natural or moral properties in virtue of which utterers' attitudes are manifested directly or indirectly. However, for conversationalists, moral attitudes are viewed as a sort of generalized conversational implicature (GCI), since moral attitudes stem from "what is implicated" in moral utterances and share basic features of GCI. Therefore, this paper aims to reveal that, in interpreting moral assertions, both the conventionalist methodologies and their resulting views are questionable for the reason that they can neither define the natural properties clearly nor expound the moral properties without involving conversational implicature. In contrast, conversationalist argumentation is preferable in that it not only explains the practicality of moral assertions but also provides a new resolution to the amoralist puzzle.