This book has suggested that the only quantifier determiners in English with interpretations corresponding to generalized quantifiers are those which give rise to dependency-inducing scope inversion, do not combine with collective predicates such as gather in the library, exhibit singular agreement only, and are characterized by distributive conjunction. All other so-called quantifier determiners are entirely not quantificational, with the existentials instead denoting various types of individual, represented by generalized Skolem terms. The asymmetry with respect to collective verbs implies that English true quantifiers have no plural readings, at least in certain dialects. Under present assumptions, syntactic derivation in Combinatory Categorial Grammar alone, together with an “anytime” operation of Skolem term specification of the uninterpreted terms associated with indefinite noun phrases (NPs), can be used to directly compute the available scoped readings, including certain notorious cases involving inversion out of NPs.
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