Abstract: One of the defining properties of presuppositions is that they are inferences that survive when a sentence is embedded under negation. For example, “John will bring his wetsuit” and “John won’t bring his wetsuit” both presuppose that John has a wetsuit. Karttunen (1973) thus characterized negation as a “hole” for presuppositions: it lets through the presuppositions of its embedded constituent.

However, it has long been noted that presuppositions of negative sentences sometimes vanish. For example, the following sentence has no presupposition at all: “John won’t bring his wetsuit…he doesn’t even have a wetsuit!” To deal with vanishing presuppositions it has been common to assume the existence of mechanisms that can “cancel” a sentence’s presuppositions (e.g., Heim’s 1983 “local accommodation,” or Beaver and Kraemer’s 2001 “floating-A operator).

In this talk I argue that cancellation mechanisms are conceptually and empirically problematic; a theory of presupposition would do better without them. To meet this challenge I propose a revised theory of presupposition projection under which negation is *not* a hole for presuppositions; instead, it is a “plug” that doesn’t let presuppositions through. Following Schlenker (2008), the projection system employs a bivalent semantics as well as reasoning over continuations of a sentence in incremental processing, but unlike Schlenker it derives presuppositions only from the assumption that the sentence has a true continuation. I will argue that the apparent hole-like behaviour of negation and other operators follows from independent considerations (the “proviso-problem”, Geurts 1996).

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