Numerals denote degree quantifiers: Evidence from child language

A large body of work in both the theoretical and experimental literature suggests that upper bound implications in simple sentences with bare numerals are entailments arising from the semantics of the numeral, rather than scalar implicatures of the sort seen with other scalar terms. However, not all semantic analyses of numerals designed to introduce upper bounding entailments in simple sentences make the same predictions about upper bounding implications in other sentences. Here we focus on the case of upper bounded construals of numerals embedded under existential root modals, which are derived as entailments by a semantic analysis of numerals as generalized quantifiers over degrees (Kennedy 2013, 2015), but can only be derived as scalar implicatures by other semantic analyses. We provide experimental evidence from child language that upper bounding implications in such cases are entailments and not implicatures, thereby providing support for the degree quantifier analysis. 1 Numerals and bounding implications 1.1 Two semantic accounts of upper bounding It is well-known that numerals can be understood as imposing different bounding constraints on the quantities that they pick out in different contexts of use. For example, the numeral three in (1) is most naturally understood as providing both a