Quantificational and modal interveners in degree constructions

Heim (2001) points out that the relational semantics for degrees predicts ambiguities in sentences with comparatives and quantifiers such as _every girl_ that are not observed. She also notes that the same ambiguities do appear with strong modals such as _must_ and _have to_, but not with weaker modals such as _should_, _ought_, and _want_. The problem is to explain why these classes of expressions would behave differently, given that they are all standardly treated as universal quantifiers. I present several counter-examples to Heim's account of this data and then argue that the puzzle involving universal DPs is the same as the puzzle of weak islands in amount wh-expressions, and that it yields to the analysis of weak islands due to Szabolcsi & Zwarts (1993), who argue that degree expressions are restricted in their interaction with the semantic operations meet. This accounts for universal DPs but leaves to be explained the possibility of modal intervention with strong modals. I argue that the split between universal DPs and strong modals supports recent work proposing that modals are not quantifiers over worlds but scalar expressions. An independently motivated scalar semantics for strong modals generates the ambiguity in a way that is compatible with Szabolcsi & Zwarts' theory, and that the predicted truth-conditions are correct for both readings with strong modals. The corresponding account of mid-strength modals explains their lack of ambiguity as merely apparent, due to the fact that the truth-conditions of the two readings are virtually indistinguishable, and neither embodies the missing reading that the quantificational theory leads us to look for. These results support both the scalar semantics for modality and Szabolcsi & Zwarts' semantic approach to intervention constraints.