The Reference of Indefinites

Abstract

In this paper I argue that indefinite NPs have a more complex referential nature than is usually supposed, and that this structure must be reflected in their semantic representation. According to the classical view due to Frege and Russell, an indefinite NP is represented by an existential quantifier, a variable, the restriction and the occurrence of the variable in the argument position of the main predicate. Hence, there is no clear correspondence to the indefinite NP on the surface. Sentence (1) is translated into the formula (2a), in which the indefinite NP a man corresponds to the variable x in the argument position of the predicate walk and in the predication man(x). The formula specifies that the intersection of the two sets denoted by the predicates is non-empty. The model-theoretic interpretation (2b) links the variable x to an object d that fulfills both predicates, treating the attributive material man on par with the assertive material walk. Hence, at the representational level, the indefinite NP is not represented as an independent expression. This conception has been widely accepted in semantics and can be found in current semantic theories.