Quantifying kids prefer intersecting sets – a pilot study

Abstract

Children between approximately four and five years of age are known to fail in picture matching tasks with verbal stimuli presenting an existentially quantified object NP in the scope of a universally quantified subject NP. In this paper, we suggest an experimentally tested provisional answer to a question that has not been asked in any previous work on the very phenomenon: Would they also fail for the truth-conditionally equivalent stimuli in which the universal quantifier is replaced by a negated existential quantifier (plus a negated predicate, as in Every boy walks with a balloon vs. No boy walks without a balloon).

The experimental results indicate that the latter task is indeed much easier. This lends support to the hypothesis that the primary source of the difficulties lies in the acquisition of a special aspect of compositional semantics, that is, in computing the semantic effects of a universal vs. an existential quantifier as subject in combination with an existential quantifier in the predicate. For a universally quantified subject, the relation between the restrictor set of the quantified subject and the set denoted by the predicate is one of set inclusion. For an existentially quantified subject, it is set intersection. At least for the picture matching tasks, the intersection relation seems to be easier to handle than the inclusion relation, even for semantically equivalent stimuli.