This paper investigates the acquisition of quantity implicatures (QIs) by preschool children. QIs typically arise in examples like The girl started painting the star where the speaker's use of start typically indicates that s/he had reasons not to use a more informative term, e.g. finish. In this case, The girl started painting the star implicates - but does not entail - that the girl didn’t finish painting the star (see Carston 1998, Levinson 2000, Horn 1989, among others).

Although very little is known about how the ability to derive QIs develops, previous research suggests that preschool children - who are otherwise linguistically competent - do not generally show sensitivity to QIs (Noveck, 2001; Chierchia et al, 2001). Other recent results show that, when semantics and contextual conditions conspire in appropriate ways, children do show some success at computing QIs (Papafragou & Musolino, 2002). The present paper focuses on a specific class of scalar expressions, which I will call aspectual terms, such as start and half. It asks, first, whether children are capable of deriving the non-completion QIs associated with such terms, and second, whether these implicatures persist across synonyms (compare start and begin), i.e. whether they are non-detachable.

An experiment tested 40 Greek-speaking 5-year-olds (and 40 adult controls) on four different scalar predicates: arxizo (‘start’), ksekino (‘begin’), kano to miso X (‘do half of X’) and kano to X mexri ti mesi (‘do X halfway’). Ten children were tested on each of the four scalar expressions. In each case, subjects were presented with short stories in which a character completed a certain action, thereby satisfying the truth conditions of an informationally strong term (e.g. The Smurf ate all of the apple). The outcome was then described by a puppet who used a pragmatically infelicitous weaker term (e.g. The Smurf ate half of the apple). Subjects were asked to judge the puppet’s descriptions. It was found that, while adult subjects overwhelmingly rejected the puppet's infelicitous statements, children only rejected the puppet statements 42% of the time. Moreover, it was found that, while the rejection rates of adults did not significantly differ across the four items, children's rejection rate on the half/all scale was reliably higher than on the start/finish, begin/finish and halfway/completely scales (67% vs. 32%, 37% and 32% respectively).

These novel findings offer further evidence for the conclusion that children's ability to derive QIs is fragile and varies considerably depending on the nature of the scalar term. Furthermore, they show that, even though some QIs in child language are non-detachable (cf. start and begin), others are not clearly so (cf. half and halfway). More specifically, half seems to give rise to non-completion inferences more readily than the rest of the aspectual expressions employed in this experiment. A possible explanation for this asymmetry is the fact that expressions of the form do half of X require tracking an object which measures out the completion of an event; by contrast, expressions such as start/begin doing X, or do X halfway require tracking the progress of an event, a process which may be more difficult for our young participants. Some implications about children’s developing pragmatic abilities and their understanding of aspectual distinctions are discussed.