Generalized Quantifiers and Ontological Commitments

Abstract: In Generalized Quantifier Semantics for Natural Language, as developed by Montague, Barwise, Cooper and others, singular terms, such as names like “Tom Smith, ” or demonstrative phrases like ‘this man, ’ are treated as (generalized) quanti-fiers. Thus a statement like “Tom Smith is clever ” does not attribute cleverness to that person, Tom, notwithstanding intuition. Rather, it is to cleverness that such a statement will attribute a higher-order property, namely that of belonging among Tom’s properties. In our paper, we raise the following problem for such semantic approaches, a problem that arises from ontological considerations. Singular terms such as names and demonstratives should only commit us to the existence of individuals, hence, given that generalized quantifiers commit us to the existence not only of properties of individuals (or sets, if you prefer), but also to the existence of properties of properties (or classes of sets), such accounts are ontologically questionable. In discussing possible replies, we also raise and address the more general issue of the relationship between semantics and ontology