Exhaustive interpretation : a discourse-semantic account

The theoretical context developed in this book is chiefly aimed at presenting an alternative solution for the problem of the so-called one- and two-sided readings of various predicates. It is generally assumed that e.g. a numeral x can receive two readings: 'at least x' and 'exactly x'. One very generally accepted view of this problem is the theory based on generalized conversational (scalar) implicatures (Grice, Horn, Levinson). In discussion with this view it is argued that the problem of the one-and two-sided readings is a problem related to the information structure in discourse, specifically, that the meaning, and the truth conditions, of a string of words (a sentence) varies with the context in which it functions (specifically, the question to which it functions as an answer (Van Kuppevelt 1991 and other works)).The hypothes argued for are as follows. With respect to the numerals (but also with respect to other scalar predicates), it is possible to account for both the 'at least' and the 'exactly' readings of numerals under the assumption of a unitary, 'exactly'-semantics (within the context of Discourse Semantics (Seuren 1985, 1996)). If a numeral is in comment position (when it is in a strict sense the answer to a question) it receives the 'exactly' or cardinality reading. This is the result of a process of exhaustive interpretation, which is shown to be fully integrated into the semantics of questions and answers. When a numeral is in non-comment position it receives the 'at least' or existential reading, due to the existential quantifier. The main observational argument for this analysis lies in the fact that cancellation phrases, as used in implicature theory, are in a number of well-defined cases unacceptable, contrary to what implicature theory claims.