Presupposition Projection and Anaphora in Quantified Sentences

Quantified sentences constitute a recalcitrant problem for theories of presupposition projection, and a great number of attempts have been made to explicate the projection properties of quantificational expressions (Karttunen & Peters 1979, Cooper 1983, Heim 1983, van der Sandt 1992, Beaver 1994, 2001, Fox 2008, 2012, George 2008a,b, Schlenker 2008, Charlow 2009, Chemla 2009b, Schlenker 2009, Fox 2010, Sudo, Romoli, Hackl & Fox 2011). Schematically, the main problem is how to predict the presuppositions of sentences of the form QpRqpS q 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, that are potentially presuppositional. For the moment, I will concentrate on cases where the nuclear scope S has a presupposition and the restrictor R does not, and will discuss presupposition projection out of the restrictor in depth in §5. The main challenge comes from the fact that different quantifiers have different projection properties. Consider, for instance, the sentences in (1), where the presupposition is triggered by the predicate criticized herself, which I assume to presuppose that the subject is female.