Quantification and Second-Order Monadicity

treatment of quantification is rightly regarded as a major advance in the study of logic and language. But it led Frege and others to some views that we can and should reject, given developments in the study of transformational grammar and compositional semantics. Once these views are put aside, the developments suggest that the common logical form of sentences like (1) and (2) (1) Every bottle is red (2) Pat kicked every bottle is '›O[EVERY(O) & õ(O) & ö(O)]'; where 'O' ranges over ordered pairs of a special sort, but not ordered pairs of sets. If this is correct, some familiar conceptions of logical form must be modified. Pace Frege, there is no important mismatch between the structure of a sentence like (2) and the structure of the proposition (Thought, potential premise/conclusion) expressed by using the sentence. This point— about grammatical form, logical form, and the need to revise pre-Fregean conceptions of both—will be familiar to specialists. But it has not yet pervaded the wider community that learned, often via Russell (1905, 1918), about the alleged mismatch. Correlatively, many philosophers have held that logical forms are regimentations of sentences in a natural language. So given a preference for first-order regimentation, appeal to second-order logical forms can seem misguided. But as Boolos (1998) shows, quantification into monadic predicate positions is motivated and unobjectionable, when it is construed as plural quantification (over whatever first-order variables range over) as opposed to quantification over sets. We can also reject the idea that transitive verbs are associated with functions from pairs of entities to truth values. Instead, we can adopt the following view, motivated by extensions of Davidson's (1967, 1985) event analyses: all verbs are semantically monadic; combining verbs with other expressions corresponds to predicate-conjunction; and grammatical relations that verbs bear to their arguments are semantically associated with participation relations, like being an Agent of, that individuals can bear to things like events. Schein (1993) adopts this approach to plural constructions like (3).