Direct compositionality on demand 1

This paper starts with the assumption that the expression saw everyone, as inJohn[saw everyone ], is a constituent. After all, it can be coordinated, clefted, focussed, questioned, pronominalized, you name it. According to the hypothesis of Direct Compositionality, just like any constituent, this phrase must have a well-formed semantic denotation. But everyone(typically) takes scope over an entire clause, so the semantics ofeveryonemust somehow gain access to more material than just the constituentsaw everyone . The standard treatment in terms of Quantifier Raising connects the quantifier directly with its nuclear scope, but does not associate any concrete denotation with the verb phrase. Indeed, I will argue that no previous analysis I am aware of adequately reconciles the local syntactic constituency of quantifier-containing phrases with the long-distance aspects of their semantics. This paper proposes an explicit new account that does better in certain precise respects. The main innovation are what I call rules of disclosure, which provide a way for quantifiers to reveal their presence within arbitrary constituents. This allows the formal grammar presented below to link a quantifier directly with its scope, yet still characterize the syntactic and semantic content of intervening constituents. Because the fine-grained semantic analysis of the intervening constituents is optional, and so can be calculated only when we choose to examine the details, we have Direct Compositionality on demand. 1. Two equally valid views of the syntax-semantics interface The problem is that many natural language expression types lead a double life, simultaneously here and there, masquerading as a local lump but somehow interacting directly with distant elements. The two main examples discussed here are bound anaphora, in which an anaphor depends for its value on some distant binder; and quantification, in which some local element takes semantic scope over a properly containing constituent. Such action-ata-distance confronts theories of the syntax-semantics interface with a dilemma: should we 1This paper owes debts to three people: first and foremost, Pauline Jacobson, whose work inspired the workshop from which this paper developed, and who discussed many of the ideas below with me during my sabbatical visit to Brown in the fall of 2003. Second, David Dowty, whose remarks on the formal nature of direct compositionality expressed at the workshop and in conversation planted the seed that grew into this paper. Third, Gerhard J̈ ager, who first introduced me to the display property for type logics (“it is always possible to glue two adjacent constituents together before building the larger constituent. This requires a lot of cut applications.” (in email from fall 2003)), which approximates my on-demand property. (See section 8 for a discussion of the display property in comparison with the DCOD property.) Finally, I would like to point out that the crucial technical innovation that gives the logic presented below the on-demand property, namely, the rule of disclosure for quantification,qLR, was directly inspired by J̈ ager’s (2005) similar rule for his binding analysis. In some sense, then, this paper merely emphasizes the importance of a symmetry already present in J äger’s LLC, and extends the same symmetry to quantification. Substantial improvements over the first draft are due to discussions with Chung-chieh Shan and Anna Szabolcsi.