This paper looks at the way some discourse relations interact with the dimension of quantity implicatures. We focus on the relation of contrast as marked by the connective but to argue that it is preferable to assume that the way contrast is established does not take quantity implicatures into consideration. We explore the consequences of this for a set of theories of but which we refer to as being inferential. We demonstrate that the inference used in the interpretation of but is properly captured by the notion of argumentative goal in a multi-layered semantics.
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