A New Theory of Quantifiers and Term Connectives

Abstract

This paper sets forth a new theory of quantifiers and term connectives, called shadow theory, which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and ?-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary, John or Mary, and not both John and Mary, as well as determiner phrases such as every man, some woman, and the boys, are all of semantic type e and denote individual-like objects, called shadows-- conjunctive, disjunctive, or negative shadows, such as John-and-Mary, John-or-Mary, and not-(John-and-Mary). There is no essential difference between quantification and denotation: quantification is nothing but denotation of shadows. Individuals and shadows constitute a Boolean structure. Formal language LSD (Language for Shadows with Distributivity), which takes compound terms to denote shadows, is investigated. Expansions and enrichments of LSD are also considered toward the end of the paper.