Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.

Number terms and quantifiers share a range of linguistic (syntactic, semantic, and pragmatic) properties. On the basis of these similarities, one might expect these 2 classes of linguistic expression to pose similar problems to children acquiring language. We report here the results of an experiment that explicitly compared the acquisition of numerical expressions (two, four) and quantificational (some, all) expressions in younger and older 3-year-olds. Each group showed adult-like preferences for “exact” interpretations when evaluating number terms; however they did not (...) use the corresponding upper bounded interpretation when evaluating the quantifier some. Apparently, children follow different procedures for learning and evaluating numerals and quantifiers. These findings have implications for theories of number representation in child and adult grammars. (shrink)

Abstract Proportional quantifiers have played a central role in the development of formal semantics because they set a benchmark for the expressive power needed to describe quantification in natural language (Barwise and Cooper Linguist Philos 4:159–219, 1981). The proportional quantifier most, in particular, supplied the initial motivation for adopting Generalized Quantifier Theory (GQT) because its meaning is definable as a relation between sets of individuals, which are taken to be semantic primitives in GQT. This paper proposes an alternative analysis of (...) most that does not treat it as a lexical item whose meaning is accessible without the help of compositional processes. Instead, proportional most is analyzed as the superlative of many (cf. Bresnan Linguist Inq 4(3):274–344, 1973). Two types of empirical evidence are presented in support of this view, both exploiting the fact that only a decompositional analysis of proportional quantifiers provides the means to generate different logical forms for seemingly equivalent statements of the form most A B and more than half of the A B. (shrink)

Children's comprehension of the universal quantifiers all and each was explored in a series of experiments using a picture selection task. The first experiment examined children's ability to restrict a quantifier to the noun phrase it modifies. The second and third experiments examined children's ability to associate collective, distributive, and exhaustive representations with sentences containing universal quantifiers. The collective representation corresponds to the "group" meaning (for All the flowers are in a vase all of the flowers are in the same (...) vase). The distributive representation implies a pairing (e.g., each flower paired with a vase for Each flower is in a vase). The exhaustive representation exhausts both sets (e.g., for The flowers are in the vases all the flowers are in vases and all the vases have flowers in them). Four- to 10-year-olds children had little difficulty restricting the quantifier all to the noun it modified in a task which required them to attend to the group feature of all. In contrast, only 9- and 10-year-olds were able to solve the task when the quantifier was each and the pictures showed entities in partial one-to-one correspondence. Children showed a preference for associating collective pictures with sentences containing all and distributive pictures with sentences containing each. The results suggest that between the ages of 5 and 10 years, children's semantic representations undergo less radical changes than others have proposed. Instead, developmental change may occur gradually as children acquire linguistic cues which map onto existing semantic representations. (shrink)

Number terms and quantifiers share a range of linguistic (syntactic, semantic, and pragmatic) properties. On the basis of these similarities, one might expect these 2 classes of linguistic expression to pose similar problems to children acquiring language. We report here the results of an experiment that explicitly compared the acquisition of numerical expressions (two, four) and quantificational (some, all) expressions in younger and older 3-year-olds. Each group showed adult-like preferences for “exact” interpretations when evaluating number terms; however they did not (...) use the corresponding upper bounded interpretation when evaluating the quantifier some. Apparently, children follow different procedures for learning and evaluating numerals and quantifiers. These findings have implications for theories of number representation in child and adult grammars. (shrink)