The Witness Set Constraint

Abstract

This article is initially concerned with a famous constraint on the class of possible determiners in natural languages: the so-called Conservativity Constraint. We shall briefly illustrate the force of this constraint and infor- mally sketch Keenan and Stavi (1986)'s view according to which the Con- servativity Constraint derives from the boolean structure of natural lan- guage semantics. We shall proceed to discuss certain well-known linguistic categories that have been argued to be interpreted by non-conservative functions: only and the relative proportional determiners many and few. We shall take the challenge posed by the existence of these categories in order to propose an alternative to the Conservativity Constraint. This alternative will be dubbed the Witness Set Constraint, which is inspired in Barwise and Cooper (1981)'s considerations on the semantic process- ing of generalized quantifiers. We shall defend that the proposed con- straint does not suffer from the empirical shortcomings that have been attributed to the Conservativity Constraint, and indeed, we shall argue in detail that it correctly predicts (a) the existence of conservative de- terminers, (b) the non-existence of certain non-conservative determiners, such as inner negations, cardinal comparison determiners and the con- verses of non-trivial proportional determiners, and most importantly, (c) the existence of the non-conservative functions denoted by only and the relative proportional determiners many and few. This line of reasoning suggests that the class of functions from properties to sets of properties denoted in natural languages typically by determiners is constrained by a principle that simplifies the semantic processing of generalized quantifiers.