2018 Friday Session C 1000
Friday, November 2, 2018 | Session C, Terrace Lounge | 10am
Acquiring the universal quantifiers: every part together or each part on its own?
T. Knowlton, J. Halberda, P. Pietroski, J. Lidz
The universal quantifiers each, every, and all differ in whether they give rise to distributive or collective readings. Sentences with each are mandatorily interpreted distributively [1-2], explaining why each cannot occur with collective predicates like gather in (1a).
- *Each (of the) student(s) gathered
- ?Every student gathered
- All (of the) students gathered
Sentences with every and all are likewise amenable to distributive readings, as in (2a). But, unlike sentences with each, they also allow collective interpretations, as in (2b).
- {Each/every/all the} student(s) ate a pizza by themselves
- {*Each/every/all the} student(s) ate a pizza together
Acquiring an adult-like competence with these quantifiers entails understanding this subtle difference. Quantifier spreading errors have been argued to arise precisely because 4-to-9 year-olds do not have an adult-like understanding of distributivity [3-5]. Although preschoolers can access both collective and distributive interpretations, they are not sensitive to each’s strongly distributive meaning when used in sentences like two boys each pushed a car [6]. One possibility is that learners start with a common “core” meaning for each and every (e.g, they apply to all members of a domain) and gradually acquire universal quantifiers’ distributivity properties. An alternative is that children pair the correct individual- based meaning with each when they first learn it, but performance limitations mask their underlying competence.
Here, we use a novel paradigm to test whether learners have an individual-based meaning for each that differs from their group-compatible meaning for every. To make the task as simple as possible, we did not probe collective or distributive interpretations of each– and every-sentences directly. Instead, we asked if what participants remember about a scene differs depending on which type of statement they evaluate. Specifically, how well were they able to recall a group-based property: center of mass [7]?
Twenty-six participants aged 3;2-8;7 (mean=6;3) were shown displays consisting of circles, triangles, and squares on an iPad (Figure 1) and asked whether each/every circle is blue. The correct answer was always “no”. After responding verbally, the screen turned blank and participants were asked to “touch where the middle of the circles was” from memory. If participants attended to and represented the circles as a group when evaluating the statement, they should have better estimates of its center [8]. If they focused more on the individual circles and did not attend to or represent the group as a whole, they should have worse estimates.
Participants who evaluated an every-statement were able to recall the center of the circles with less error than participants who evaluated an each-statement (t(23.6)=2.11, p<.05; Figure 2). This was true despite the fact that the images were identical across both conditions. Moreover, participants did not improve with age (Figure 3). This result is well explained if (i) the meaning of each – but not every – is specified in terms of individuals, giving rise to obligatory distributivity and (ii) this subtle group- individual distinction is present from the time learners first acquire the universal quantifiers.