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This paper argues that traces only range over individual semantic types and cannot be type shifted into higher types to circumvent this restriction. The evidence comes from movement targeting positions where DPs must denote properties and the behavior of definite descriptions in these positions. These constraints on possible traces demonstrate that syntactic operations impose active restrictions on permissible semantic types in natural language.
This paper deals with the conditions under which singular definites, on the one hand, and universally quantified DPs, on the other hand, receive interpretations according to which the sets denoted by the NP-complements of the respective determiner vary with the situations quantified over by a Q-adverb. I show that in both cases such interpretations depend on the availability of situation predicates that are compatible with the presuppositions associated with the respective determiner, as co-variation in both cases comes about via the binding of a covert situation variable that is contained within the NP-complement of the respective determiner. Secondly, I offer an account for the observation that the availability of a co-varying interpretation is more constrained in the case of universally quantified DPs than in the case of singular definites, as far as word order is concerned. This is shown to follow from the fact that co-varying definites in contrast to universally quantified DPs are inherently focus-marked.
Analyses of scope reconstruction typically fall into two competing approaches: 'semantic reconstruction', which derives non-surface scope using semantic mechanisms, and 'syntactic reconstruction', which derives it by positing additional syntactic representations at the level of Logical Form. Grosu and Krifka (2007) proposed a semantic-reconstruction analysis for relative clauses like the gifted mathematician that Dan claims he is, in which the relative head NP can be interpreted in the scope of a lower intensional quantifier. Their analysis relies on type-shifting the relative head into a predicate of functions. We develop an alternative analysis for such relative clauses that replaces type-shifting with syntactic reconstruction. The competing analyses diverge in their predictions regarding scope possibilities in head-external relative clauses. We use Hebrew resumptive pronouns, which disambiguate a relative clause in favor of the head-external structure, to show that the prediction of syntactic reconstruction is correct. This result suggests that certain type-shifting operations are not made available by Universal Grammar.