Integrating Numerical and Semantic Knowledge in the Exact Interpretation of Numeral Quantifiers
A great deal of thinking has been dedicated to the role that language plays in the development of children’s counting ability. A smaller body of research has examined the role played by number in children’s use of language, for example, numerical quantifiers in natural language. In particular, numerical quantifiers appear to have different properties in clausal syntax than they do in the conventional count routine. Specifically, in clauses, it is possible to use a numerical quantifier without an exact meaning, while this is not possible in the count routine. A property of the human psychophysics of quantities is expressed by Fechner’s Law, which states that it becomes increasingly difficult to discriminate between two numbers as the difference between them decreases. The law further states that perception of stimuli will be a logarithmic function of the stimuli. Work on visual representations of number presented on a number line has shown that before children learn to count, their estimates are similarly a logarithmic function of the numbers they are given. If numerical knowledge plays a role in children’s interpretations of exactly interpreted quantified noun phrases, children should be more accepting of non-exact interpretations as the cardinality of the objects counted increases. This would be consistent with Fechner’s Law. Further, they should show a relationship between their acceptance of exact interpretations of numerical quantifiers in a natural language semantics experiment and the degree to which their estimates of numbers on the Number Line Task are linear. The more linear your number line estimates are, the more you should insist on exact interpretations of numbers on our semantics test. To test these predictions, 29 six year-old children and 30 adult Spanish-speakers were given a symbolic and a non-symbolic Number Line Task (Siegler & Opfer 2003), as well as a Truth Value Judgment Task (Crain & McKee 1986) of exact numerical quantifier interpretation. Participants were additionally given executive function measures to determine the role, if any, played by domain-general pragmatic reasoning. Results indicated that children’s, but not adults’, acceptance of quantifiers representing set sizes smaller than the one presented in the TVJT was predicted by the cardinality of the quantifier presented. Further, children’s, but not adults’, number line estimates (i.e. how log they were) predicted their acceptance of quantifiers representing set sizes smaller than the one presented. Thus, children (and not adults) appear to be more likely to allow non-exact interpretations as the cardinality of the objects computed increases. This is likely due to increased variance, which is consistent with Fechner’s Law, a property of number, playing a role. Further, the more linear their symbolic number line estimates, the more participants insist on exact interpretations. That is, more linear spatial number line estimates associate with more exact numerical interpretations in language. With respect to the domain-general, executive function abilities that have been argued to underlie the pragmatic reasoning associated with the generation of conversational implicatures, we found no evidence of such associations. In sum, properties of the number faculty appear visible in children’s developing use of numerically-sensitive elements of language.
