This chapter explores the role of context in the computation of implicit pragmatic meanings (implicatures). In the classic view of Gricean and neo-Gricean pragmatics, conversational implicatures are triggered by the Cooperative Principle and the maxims of conversation, and are defined as non-contextual, with the exception of particularized conversational implicatures (PCIs). On the other hand, it is assumed that generalized conversational implicatures (GCIs) and conventional implicatures (CIs) are not contextual, although GCIs can be defeated by the context or denied by the speaker. This non-contextual approach to pragmatics (the Gricean turn) has given rise to a default approach to implicatures. The second purpose of this chapter is to tackle the contextual dimension of neo-Gricean pragmatics, which has been developed by exponents of neo-Gricean pragmatics. Their approaches to pragmatics, limited to GCIs as scalar implicatures, are based either on pragmatic principles, the Q-Principle and R- or I-principle (Horn, Levinson), or on the reformulation of conversational maxims and reasoning (Gazdar, Chierchia, Fox). It is argued that the focus on GCIs, although it should minimize the role of context in the generation of implicatures, demonstrates on the contrary the pervasive function of context, which is not limited to implicature cancellation.

This chapter presents the most influential linguistic approaches to presupposition. Going beyond the traditional analyses of the problem of presupposition projection, it also considers recent developments in linguistics that link the analysis of presuppositions to general processes of cognition and reasoning, such as attention, probabilistic reasoning, theory of mind, information structure, attitudes and perspectival structure. I discuss some outstanding questions: whether presuppositions form one coherent group or should be thought of as different types of phenomena, why we have presuppositions at all, and why we see the presuppositions that we see (aka the triggering problem). Overall, the chapter stresses the need to consider the intricacies of the interaction of presuppositions with the broader discourse context.