Quantifiers vs. Quantification Theory

The syntax and semantics of quantifiers is of crucial significance in current linguistic theorizing for more than one reason. The last statement of his grammatical theories by the late Richard Montague (1 973) is modestly entitled " The Proper Treatment of Quantification in Ordinary English ". In the authoritative statement of his " Generative Semantics " , George Lakoff (1971, especially pp. 238-267) uses as his first and foremost testing-ground the grammar of certain English quantifiers. In particular, they serve to illustrate, and show need of, his use of global constraints governing the derivation of English sentences. Evidence from the behavior of quantifiers (including numerical expressions 1) has likewise played a major role in recent discussions of such vital problems as the alleged meaningdpreservation of transformations , 2 co-reference, 3 the role of surface structure in semantical interpretation, and so on. In all these problems, the behavior of natural-language quantifiers is one of the main issues. Quantifiers have nevertheless entered the Methodenstreit of contemporary linguistics in another major way, too. (These two groups of problems are of course interrelated.) This is the idea that the structures studied iln the so-called quantification theory of symbolic logic-otherwise know as first-order logic, (lower) predicate calculus, or elementary logic-can serve and suffice 6 as semantical representations of English sentences. Views of this general type have been proposed by McCawley (1971)* and Lakoff (1972)' (among others). A related theory of " Deep Structure as Logical Form " has been put forward and defended by G. Harman (1972). Theories of this general type may be compared with the traditiomal idea that quantification 'theory can be viewed as an abstraction from the behavior