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Abstract:  The Gricean theory of conversational implicature has always been plagued by data suggesting that what would seem to be conversational inferences may occur within the scope of operators like believe, for example; which for bona fide implicatures should be an impossibility. Concentrating my attention on scalar implicatures, I argue that, for the most part, such observations can be accounted for within a Gricean framework, and without resorting to local pragmatic inferences of any kind. However, there remains a small class of marked cases that cannot be treated as conversational implicatures, and they do require a local mode of pragmatic interpretation.