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The semantics of the coordinator but does not fit neatly into the traditional distinction between entailments and conversational implicatures. In its counterexpectational use, but can convey an implication relating its two conjuncts, which Grice (1975) classifies as a conventional implicature because its behavior diverges from both entailments and conversational implicatures. I propose that this meaning component arises from but’s interaction with the discourse context – specifically, how it makes conventional reference to the question under discussion (QUD) in the sense of Roberts (1996/2012, 2004). This derives the variable interpretation of the implication in the counterexpectational use, as well as its absence in the corrective and semantic opposition uses of but. This account provides a new perspective on the relationship between the different uses of but as a type of modal polysemy (Kratzer 1981, 1991), and it suggests that other expressions that have been argued to have conventional implicatures might also make conventional reference to the QUD.