It has been noted in the literature that NPIs are degraded if there is an intervening element (typically, a non weakest member of a scale) between them and, in traditional terms, their licensor (in our terms, the exhaustifying operator). This chapter discusses this phenomenon and investigates several arguably related cases of intervention by presupposition triggers. The proposal is that this effect follows as a case of minimality. If. in probing for a Polarity Sentitive item, O finds along its path a closer alternative bearer (i.e. a scalar term), it is forced to activate the alternatives of the scalar term. In negative contexts, this brings about a positive implicature that makes exhaustification fail. Relativized minimality explains why phrasal interveners (e.g. strong quantified NPs) are generally more disruptive than heads (e.g. modals). This approach is extended to presuppositional intervention (diagnosed by V. Homer) in two ways. Some presuppositional triggers (most prominently factives) turn out to be a special case of scalar triggers (as argued by J. Romoli). Others are argued to take on the behavior (and featural make up) of strong NPIs. In all three major cases of intervention considered in this chapter, syntactic locality plays a crucial role exposing the interconnected nature of the syntax and semantics of exhaustification.
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