n-ary Quantifiers and the Expressive Power of DP-Compositions

Abstract

This paper, extending Keenan’s (1987, 1988) Case-extension of generalized quantifiers, proposes a natural algebraic semantics of DP-coordination and DP-composition. DPs in subject and non-subject positions are uniformly identified as a case-extension of a usual generalized quantifier, and DPs with different semantic cases combine with each other to yield polyadic quantifiers. The paper proves that each set of case-extensions forms a complete atomic Boolean algebra consisting of a full set of unary quantifiers, and it further shows that natural language requires the full power of binary quantification, i.e., the full set of (Fregean) reducible and unreducible binary quantifiers. This result, Type <2> Effability, is derived from the fact that the set of all binary quantifiers can be constructed by taking the meet/join closure of the set of (composed) reducible type <2> quantifiers. This fact is illustrated with non-constituent coordination constructions (e.g., gapping in English and Korean), whose interpretation requires arbitrary meets and joins of reducible binary quantifiers.