The proper treatment of quantification in ordinary English

The aim of this paper is to present in a rigorous way the syntax and semantics of a certain fragment of a certain dialect of English. Patrick Suppes claims, in a paper prepared for the present workshop [the 1970 Stanford Workshop on Grammar and Semantics], that at the present time the semantics of natural languages are less satisfactorily formulated than the grammars ¼ [and] a complete grammar for any significant fragment of natural language is yet to be written.'' This claim would of course be accurate if restricted in its application to the attempts emanating from the Massachusetts Institute of Technology, but fails to take into account the syntactic and semantic treatments proposed in Montague (1970a, b). Thus the present paper cannot claim to present the first complete syntax (or grammar, in Suppes' terminology) and semantics for a significant fragment of natural language; and it is perhaps not inappropriate to sketch relations between the earlier proposals and the one given below. Montague (1970b) contains a general theory of languages, their interpretations, and the inducing of interpretations by translation.