A Set-theoretic Account of English Crossover Effects

In English, whether or not wh-movement creates weak crossover effects depends upon the type of wh-phrases that cross over. A bare interrogative like who shows a typical weak crossover effect whereas which N type (e.g. which girl) and partitive type (e.g. which of these girls) wh-phrases would show mere weaker and weakest crossover effects, respectively. Previous approaches to English crossover phenomena that resort to a binary notion of specificity or D-linking cannot account for the three-way contrast the three different types of wh-phrases show. To overcome this problem, I argue in this paper that specificity should be a non-binary set-theoretic notion and propose the following subset principle and optimal binding relation: Between two lexical nominal expressions A and B, A is regarded as more specific than B iff the denotation of A comes from a more narrowly defined non-singleton set than B. Between two lexical nominal expressions A and B, if A locally binds B, then the non-singleton set from which the denotation of A comes should be a subset of the set from which the denotation of B comes (i.e. B cannot be more specific than A). The smaller the subset (i.e. the wider the specificity gap between binder and binder), the more optimal the local binding relation is. A locally binds B iff A is coindexed with B, and A c-commands B, and there is no such C that does not bind A but binds B. Finally, I show that partitivity functions to carve out a smaller subset and thus make partitive wh-phrases more specific than simple which N type wh-phrases.