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Interpreting adverbs as quantifiers in this way open up new difficulties in determining what in natural language is to be taken as a quantifier and what is not. No longer do we need the explicit determiner-restrictor formation we observed earlier in natural language quantified noun phrases. Nor do we need any observable variables bound by such quantifiers. 12 Intensional Operators as Quantifiers The remarkable success of the possible worlds semantics given by [Kripke 1958, 1963] in aiding our comprehension of modal and other intensional logics has led some ⎯ notably [Lewis 1968] ⎯ to take seriously the metalinguistic quantification over worlds employed in the semantic analysis of ' ', '◊', and other intensional operators.

As we will come to see throughout our discussion, noun phrases are quite a complex class, and much philosophical ink has been spilled in attempting to understand how various types of noun phrases function. We will be interested at various points in almost every type of noun phrase, but for now I want to advance the suggestion that the best starting point for a theory of quantification is the field of quantified noun phrases. 20 This is not an uncontentious assumption ⎯ as noted above, the cases of definite and indefinite descriptions, which I rule by my syntactic test to be quantificational, are taken by many to be referential.

The neo-Fregean view is, in essence, a formal implementation of the Fregean idea that quantifiers are predicates of predicates. Frege's thought was that, in a sentence like (26) All men are mortal. one could see the universal quantifier as attributing a certain property to the (complex) property of being mortal if a man. The property to be attributed was that of universal instantiation ⎯ that property which a predicate has if it is true of everything. Similarly, the existentially quantified (25) Some men are mortal.

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