Scalar Implicature or Domain Restriction: How Children Determine the Domain of Numerical Quantifiers

Abstract

A sentence containing a numerically modified noun phrase, e.g., John has read three books for the exam, can be ambiguous; its numeral can mean ‘exactly three’ or ‘at least three’—depending on whether we talk about John’s maximal achievement or on his satisfying some relevant requirement. In the framework of Stanley and Szabó (2000), the ‘exactly n’ and ‘at least n’ readings can be related by domain restriction–domain widening. Children have been found to access the ‘at least n’ interpretation in sentence-picture matching tasks with varying success. The present study tested the assumption that children’s success depends on whether they notice the possibility of domain manipulation, which depends on how rigidly fixed the domain of quantification appears to them. We hypothesized that the more flexible, the less clearly demarcated the domain of quantification appears, the easier it will be for a preschooler to relate the ‘exactly n’ and ‘at least n’ readings. In Experiment 1, the quantifier domain was a fixed set represented on a card. In Experiment 2, it consisted of mobile disks, which facilitated the exclusion of the irrelevant elements. In Experiment 3, the quantifier domain was not clearly demarcated in space; it consisted of real objects mixed with objects of other types in a toy box. Children’s success rate was below 10% in Experiment 1, it was 36% in Experiment 2, and it raised to 87% in Experiment 3. Experiment 4 tested children’s ability to carry out domain restriction/domain widening by an interpretation task involving two seemingly contradictory statements about one and the same visual stimulus.