Counting parts and wholes and the mastery of partitive language

Children under age 6 or 7 quantify over objects of a single kind in ways that differ markedly from adults. For example, shown three pieces of a single fork and one whole fork, children say there are four forks, and not one or two forks. Here we explore why children exhibit these phenomena as well as motivating hypotheses of what's changing over ages 5 through 8. We note that partitive language such as "two pieces of a fork" specifies atoms of quantification and provides a context in which a piece of a fork is not a fork. We hypothesize that while children begin learning partitive language early in the preschool years, they assign it a precursor meaning that lacks adult quantificational force. Five experiments provide evidence that children begin learning partitive terms at age 2, but analyze these terms and phrases with precursor meanings akin to subsective adjectives. Experiments 1-4 establish that knowledge of partitive vocabulary is unrelated to quantificational decisions on a part/whole quantification task at these ages. In contrast, this early knowledge of partitive language selectively predicts success at using the contrast between "half/piece" and "whole" in a non-verbal visual working memory (VWM) task that does not involve quantificational ambiguity. Furthermore, the level of success on the half/whole VWM task is comparable to that on small/big VWM task, where "small/big" are indisputably subsective adjectives. These data are consistent with the precursor meaning hypothesis. Experiment 5 directly tests whether 4-year-old children can make sense of quantificational language like "this piece and this piece make one fork" and finds they cannot. These data suggest that adult analysis of the quantificational force of partitive language is not mastered until after age 4. They motivate further research that investigates whether, beginning at age 5, a semantic/syntactic change from a precursor meaning to adult meaning of partitive language may reflect and contribute to a wider change in conceptual quantificational resources.