2018 Alternates 6720

2018 Alternates | Saturday, November 3, 2018 | Poster Session II, Metcalf Small | 3:15pm

The acquisition of quantifiers: the universality and distributivity of each
R. Feiman, D. Barner

Universal quantifiers like all, each, and every specify an abstract relation – ‘universality’ – between entities or properties. For example, “All dogs are animals” indicates that dogs are a subset of animals. Each also has another property – ‘distributivity’ – specifying that the relation holds not just of the group as a whole, but of each individual member. For example, “Each person gathered in the yard” sounds odd because only groups can gather, while “each person” seems to require that gather apply to individuals separately. Following Link (1983), most semantic theories posit universality and distributivity as separable features.1,2 This makes a prediction for acquisition – children may acquire the universality and distributivity features of each separately. A minority of theories3 treat each as a first-order operator, meaning roughly: apply predicate to individual until out of individuals. On this account, the universality of each is dependent on its distributivity, predicting both features to co-emerge.

Previous acquisition studies of each have assumed that children treat it as a universal quantifier from the outset, and ask when each becomes distributive.4 However, these studies do not look at when each acquires a universal meaning, leaving open whether universality actually precedes distributivity.

In Experiment 1, we compare the acquisition of each to other operators using the Give-A-Quantifier task.5 We asked 3-7 year-olds (N=20 each) to give each, every, all, some, a, or dax objects and found that, while 4- and 5-year-olds gave the maximum number of objects for all and every, they did not do so for each, and did not distinguish each from dax (a nonce word estimate of children’s baseline behavior) until age 6 (Fig. 1). Only 6- and 7-year-olds tended to give objects one-by-one selectively when asked for each, suggesting that universality and distributivity emerge together. It is, however, possible that requests to give each are pragmatically odd when there is no reason not to grab all together. Therefore, in Experiment 2 we used a Truth Value Judgment (TVJ) task. Cookie Monster bit 0, 2, or 3 out of a total 3 cookies, and 3-7 year-olds (N=20 each) were asked: “Did Cookie Monster bite the/each/two/dax (of the) cookies?” In answer to each questions, children under age 6 said “yes” equally often whether 2 or 3 cookies were bitten, and did the same for dax and the, but not for two (Fig. 2).

These results suggest that children acquire the universal meaning of each two years later than all and every. This in turn suggests that each is not initially learned as a universal quantifier, to be augmented later by distributivity. Rather, the universality and distributivity of each may be linked, suggesting each as a categorically different first-order operation. Furthermore, children begin to produce every and each at similar ages, inviting the question of what they think each means. Ongoing studies are testing whether understanding of distributivity may precede universality.

References

  1. Winter, (2001). Flexibility principles in Boolean semantics: The interpretation of coordination, plurality, and scope in natural language. Boston MA: MIT press.
  2. Tunstall, L. (1998). The interpretation of quantifiers: semantics & processing (Doctoral dissertation, University of Massachusetts at Amherst).
  3. Szabolcsi, (2010). Quantification. Cambridge University Press.
  4. Pagliarini, , Fiorin, G., & Dotlačil, J. (2012). The acquisition of distributivity in pluralities. In of: Proceedings of the Annual Boston University Conference on Language Development (BUCLD) (Vol. 2, pp. 387-399).
  5. Barner, , Chow, K., & Yang, S. J. (2009). Finding one’s meaning: A test of the relation between quantifiers and integers in language development. Cognitive psychology, 58(2), 195-219.