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This chapter argues that the semantic behavior of bare plurals (and some other plural indefinites) provides evidence for the existence of higher-order implicatures, i.e. pragmatic inferences based on the comparison of a given sentence with the pragmatic meanings of its alternatives (and not only with their literal meanings). In a nutshell, I claim that a bare plural noun like horses denotes the set of individuals, be they atomic or complex, whose atomic parts are individual horses, and that the at-least-two-reading that one gets in sentences such as John has seen horses in the garden is an implicature that derives from the comparison of this sentence with John has seen a horse in the garden. In terms of its literal meaning, the latter sentence is true if and only if John has seen at least one horse in the garden, but gets pragmatically strengthened into John has seen exactly one horse in the garden (scalar implicature). As a result , John has seen horses in the garden will implicate the negation of John has seen exactly one horse in the garden, so that it will end up meaning John has seen several horses. I give an explicit formalization of the processes that lead to higher-order implicatures, based on the possibility of iterating an exhaustivity operator. The proposal accounts for the readings of plural indefinites in various linguistic contexts (monotone-decreasing contexts, non-monotonic contexts, and universally quantified contexts) . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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