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)

The distinction between telic and atelic predicates has been described in terms of the algebraic properties of their meaning since the early days of model-theoretic semantics. This perspective was inspired by Aristotle’s discussion of types of actions that do or do not take time to be completed1 which was taken up and turned into a linguistic discussion of action-denoting predicates by Vendler (1957). The algebraic notion that seemed to be most conducive to express the Aristotelian distinction appeared to be the (...) mereological notion of a part, applied to the time at which these predicates hold: atelic predicates, like push a cart, have the subinterval property, that is, whenever they are true at a time interval, then they are true at any part of that interval; this does not hold for telic predicates, like eat an apple, cf. Bennett & Partee (1972), Taylor (1977), and Dowty (1979)2. Bach (1986) integrated these insights into a semantics based on events. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)

Cognitive Science, Volume 46, Issue 2, February 2022.

Recent work on the acquisition of number words has emphasized the importance of integrating linguistic and developmental perspectives [Musolino, J. (2004). The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. Cognition93, 1-41; Papafragou, A., Musolino, J. (2003). Scalar implicatures: Scalar implicatures: Experiments at the semantics-pragmatics interface. Cognition, 86, 253-282; Hurewitz, F., Papafragou, A., Gleitman, L., Gelman, R. (2006). Asymmetries in the acquisition of numbers and quantifiers. Language Learning and Development, 2, 76-97; Huang, Y. T., Snedeker, J., Spelke, (...) L. (submitted for publication). What exactly do numbers mean?]. Specifically, these studies have shown that data from experimental investigations of child language can be used to illuminate core theoretical issues in the semantic and pragmatic analysis of number terms. In this article, I extend this approach to the logico-syntactic properties of number words, focusing on the way numerals interact with each other (e.g. Three boys are holding two balloons) as well as with other quantified expressions (e.g. Three boys are holding each balloon). On the basis of their intuitions, linguists have claimed that such sentences give rise to at least four different interpretations, reflecting the complexity of the linguistic structure and syntactic operations involved. Using psycholinguistic experimentation with preschoolers (n=32) and adult speakers of English (n=32), I show that (a) for adults, the intuitions of linguists can be verified experimentally, (b) by the age of 5, children have knowledge of the core aspects of the logical syntax of number words, (c) in spite of this knowledge, children nevertheless differ from adults in systematic ways, (d) the differences observed between children and adults can be accounted for on the basis of an independently motivated, linguistically-based processing model [Geurts, B. (2003). Quantifying kids. Language Acquisition, 11(4), 197-218]. In doing so, this work ties together research on the acquisition of the number vocabulary with a growing body of work on the development of quantification and sentence processing abilities in young children [Geurts, 2003; Lidz, J., Musolino, J. (2002). Children's command of quantification. Cognition, 84, 113-154; Musolino, J., Lidz, J. (2003). The scope of isomorphism: Turning adults into children. Language Acquisition, 11(4), 277-291; Trueswell, J., Sekerina, I., Hilland, N., Logrip, M. (1999). The kindergarten-path effect: Studying on-line sentence processing in young children. Cognition, 73, 89-134; Noveck, I. (2001). When children are more logical than adults: Experimental investigations of scalar implicature. Cognition, 78, 165-188; Noveck, I., Guelminger, R., Georgieff, N., & Labruyere, N. (2007). What autism can tell us about every. . . not sentences. Journal of Semantics,24(1), 73-90. On a more general level, this work confirms the importance of integrating formal and developmental perspectives [Musolino, 2004], this time by highlighting the explanatory power of linguistically-based models of language acquisition and by showing that the complex structure postulated by linguists has important implications for developmental accounts of the number vocabulary. (shrink)

Quantifiers are a test case for an interface between psychological questions, which attempt to specify the numerical content that supports the semantics of quantifiers, and linguistic questions, which uncover the range of possible quantifier meanings allowable within the constraints of the syntax. Here we explore the development of comprehension of most in English, of particular interest as it calls on precise numerical content that, in adults, requires an understanding of large exact numerosities (e.g., 23 blue dots and 17 yellow is (...) an instance of “most of the dots are blue”). In a sample of 100 children 2 to 5 years of age we find that (a) successful most comprehension in cases with two salient subsets is achieved at 3 years, 7 months of age, and (b) most comprehension is independent of knowledge of large exact number words; that is, knowledge of large exact number words is neither necessary, as evidenced by children who understand “most” but not “four,” nor sufficient, as evidenced by children who understand “nine” but not “most.”. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expres- sion (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) We hypothesized that the quantified sen- tences have an abstract underlying representation common to the formulas and their associated sets of dia- grams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people’s as- sessment of how well each of the 5 diagrams expresses the meaning of each of the quantified sentences. We report the results from 3 experiments using Gergonne’s (1817) circles or an adaptation of Leibniz (1903/ 1988) lines as external representations and show them to support the predictions. (shrink)