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Presupposition Projection in Quantified Sentences and Cross-Dimensional Anaphora ̊

Presupposition projection is one of the most widely discussed topics in modern formal semantics and pragmatics, and a multitude of theories in various formal frameworks have been put forward in the literature (for overviews, see Beaver 2001, Chierchia & McConnell-Ginet 2000, Geurts 1999, Kadmon 2001, Beaver & Geurts 2011). Although these theories significantly differ both in empirical predictions and in ways in which they conceive of presuppositional inferences, the problem of presupposition projection through quantificational expressions is a common tantalizing problem, and has been actively investigated in a number of different theoretical set-ups (e.g. Karttunen & Peters 1979, Cooper 1983, Heim 1983, Van der Sandt 1992, Beaver 1994, 2001, Beaver & Krahmer 2001, Fox 2008, 2012, George 2008a,b, Schlenker 2008, Charlow 2009, Chemla 2009b, Schlenker 2009, Fox 2012). Simply put, the problem of presuppositions in quantified sentences is how to explain the presuppositions of sentences of the form QpRqpSq from the meaning of Q and the meanings of R and S, where Q is a quantificational determiner and R and S are its restrictor and nuclear scope potentially with presuppositions. For expository purposes, we will first concentrate on cases where only the nuclear scope S has a presupposition, and will come back to presupposition projection out of the restrictor R later in the paper (Section 5). The main empirical challenge of this puzzle consists in the fact that different quantifiers have different projection properties. Consider, for instance, the sentences in (1), where the predicate criticized herself has a presupposition that the subject is female (Cooper 1983, Heim & Kratzer 1998).