Children and Implicature 1

Ad-hoc Implicature in Preschool Children

Alex J. Stiller
Department of Linguistics, University of California, San Diego

Noah D. Goodman
Department of Psychology, Stanford University

Michael C. Frank
Department of Psychology, Stanford University

Thanks to Janelle Klaas for assistance in data collection and to Cindy Fisher and threeanonymous reviewers for helpful suggestions. A previous version of this work waspresented to the Cognitive Science Society in Stiller, Goodman, and Frank (2011).

Please address all correspondence to Michael C. Frank, Department of Psychology, Jordan
Hall (Bldg. 420), 450 Serra Mall, Stanford, CA 94305. Phone: (650) 724-4003. E-mail:mcfrank@stanford.edu

Children and Implicature 2
Abstract
If a speaker tells us that “some guests were late to the party,” we typically infer that not
all were. Implicatures, in which an ambiguous statement (“some and possibly all”) is
strengthened pragmatically (to “some and not all”), are a paradigm case of pragmatic
reasoning. Inferences of this sort are difficult for young children, but recent work suggeststhat this mismatch may stem from issues in understanding the relationship between
lexical items like “some” and “all,” rather than broader pragmatic deficits. We tested
children’s ability to make non-quantificational pragmatic inferences by constructing
contextually-derived “ad-hoc” implicatures, using sets of pictures with contrasting
features. We found that four-year-olds and some three-year-olds were able to make
implicatures successfully using these displays. Hence, apparent failures in scalar
implicature are likely due to difficulties specific to the constructions and tasks used inprevious work; these difficulties may have masked aspects of children’s underlying
pragmatic competence.

Children and Implicature 3
Introduction
Human communicators typically follow general principles of cooperation, such as
being truthful, relevant, perspicuous, and adequately informative. By assuming that theirpartners abide by these conventions, listeners can draw inferences about the meanings
speakers intend to convey (Grice, 1989; Hirschberg, 1991; H. Clark, 1996; Horn, 1998;
Levinson, 2000). For example, consider the following exchange:(1) A: Did you visit your cousins?
B: I visited some of them.
In (1), A may infer that B did not visit all of her cousins. If she had visited all of them,
the word “all” would have been the maximally informative choice. Even though saying“some” would have been true even if she had visited all of them, the choice of “some”
suggests that she has chosen not to say “all,” likely because it is not true. B’s inference,that A’s intended meaning (“some but not all”) is more restricted than the literal meaningof her utterance (“some”), is an example of a pragmatic implicature.
Grice (1975, 1989) introduced a distinction between two types of implicatures:
generalized and particularized. Generalized implicatures, also commonly known as scalar
implicatures (or SIs, the label we adopt throughout the manuscript), involve lexical items
that are ordered with respect to one another, including but not limited to quantifiers(<some, all>), modals (<might, must>), and numerals (<one, two>). A detailed
description of the ordering relations among such terms is given by Horn (1998).
In contrast to SIs, particularized, or ad-hoc, implicatures are cases in which aninference is available due to special features of the context. The important distinction
between the two types of implicatures is that in ad-hoc cases, the relationship between
alternatives relies on context whereas in generalized cases, the set of alternatives is afeature of the language more generally. While some theories emphasize the differences inChildren and Implicature 4
computation between these types of implicature (e.g. Levinson, 2000), others minimize
them (e.g. Sperber & Wilson, 1986). We remain agnostic about the issue; on all accounts,
generalized implicatures differ from particularized implicatures minimally in that theyrequire knowledge of the lexical alternatives (e.g. “some,” “all”) that constitute the scale(though there may be other relevant differences).
Our goal here was to measure preschool children’s ability to make ad-hoc(particularized) implicatures. Even older children have been reported to have difficultywith scalar implicatures. Thus, measuring children’s performance in ad-hoc cases cancontribute to an understanding of whether failures with scalar implicature are due tospecifics of these implicatures per se. If children succeed in making ad-hoc implicatures ata younger age than they perform scalar implicatures, this evidence would rule out broader
pragmatic deficits, such as difficulties computing informativity or going beyond what issaid. To ground this discussion in previous research, we review the literature on
implicature in development below before describing the specifics of our experiment.
Implicature in Development
Implicatures—especially SIs like (1)—have been taken as a paradigm case ofpragmatic inference, and their development has been a subject of considerable interest(Braine & Rumain, 1981; Papafragou & Musolino, 2003; Huang & Snedeker, 2009; Barner,
Brooks, & Bale, 2011). A number of experiments have suggested that SIs, especially those
involving the quantifiers “some” and “all,” are difficult for children until late indevelopment. In one influential study, Noveck (2001) reported difficulties involving modal
operators such as “might” and “must.” These paradigms were both relatively complex,
however, requiring not just an understanding of implicature, but also an understandingthat implicatures could render a statement infelicitous (e.g. “some dogs are animals”) andthat such a statement should be judged false. Even if children made the scalar implicature

Children and Implicature 5
in such a case, they might not have taken the step of assuming that the possible
implicature necessarily made the original statement false.
Stronger evidence comes from a series of foundational studies on SI interpretation(Papafragou & Musolino, 2003; Huang & Snedeker, 2009). In one of these, Huang andSnedeker (2009) measured eye movements of children and adults as they listened to SIs.
Participants saw various scenarios corresponding to weak and strong interpretations ofscalar terms, and their relative looking time to the scenes was measured after they heard areference such as “the girl who has some of the socks.” While adults eventually generated
the SI inference (albeit after a delay; though cf. Grodner, Klein, Carbary, & Tanenhaus,2010), five-year-olds did not. Furthermore, adults, but not children, were able todistinguish between scenarios that were consistent with an implicature (e.g. when “thegirl that has some of the socks” described a character with two of the four socks in thedisplay) and those that violated it (e.g. when “the girl that has some of the socks”
described a character with all four of the four socks in the display). These findings provide
the clearest evidence to date that SIs with quantifiers are difficult for children.
These findings are surprising with respect to the broader developmental literature
for at least three reasons: First, there is a large and consistent body of evidence thatchildren learn new words by relying on their understanding of the goals and intentions ofothers, i.e. they learn words “pragmatically” (Baldwin, 1993; Tomasello & Akthar, 1995;
Bloom, 2002; Frank, Goodman, & Tenenbaum, 2009; E. V. Clark & Amaral, 2010). If
children do in fact use pragmatic reasoning to learn new words, why can’t they use thatknowledge to compute SI inferences? Second, an increasingly broad literature suggeststhat toddlers and infants can reason about both the goals (Gergely, Bekkering, & Király,
2002; Meltzoff, 1995; Woodward, 1998; Gergely et al., 2002) and beliefs (Onishi &Baillargeon, 2005; Southgate, Senju, & Csibra, 2007; Buttelmann, Carpenter, &Tomasello, 2009) of other agents. Third, some of the precise abilities involved in pragmaticChildren and Implicature 6
reasoning—in particular a sensitivity to informativeness—are present in younger children
as well. While these first two reasons are speculative, relying on potential links between
implicature on the one hand and social cognition and word learning on the other, the lastis more directly relevant and bears more detailed explanation.
A variety of evidence suggests early sensitivity to informativeness on the part ofchildren (e.g. see Chierchia, Crain, Guasti, Gualmini, & Meroni, 2001; Foppolo, Guasti, &Chierchia, 2012). At age three, children are more likely to produce informative referring
expressions when interlocutors are blind to a scene (Matthews, Lieven, Theakston, &Tomasello, 2006), and at four, they are more likely to provide more information indescriptions when distractors are similar to a target (Matthews, Butcher, Lieven, &Tomasello, 2012). By age five, when they are still failing many scalar implicature tasks,
children show sensitivity to the informativeness of speakers’ statements in the rewards
they give (Katsos & Bishop, 2011) and include supplementary adjectives when needed to
identify a target referent unambiguously (Nadig & Sedivy, 2002).
Results with pointing gestures are even stronger. Twelve-month-olds point to
identify the location of a target object unambiguously (Liszkowski, Carpenter, Striano, &Tomasello, 2006), and two-year-olds know when their own pointing gestures do not
uniquely identify a referent and adjust their communication strategies accordingly (O’Neill& Topolevec, 2001; see also Liszkowski, Carpenter, & Tomasello, 2008, Matthews, Lieven,& Tomasello, 2007, Matthews et al., 2012). Taken together, these findings suggest an early
understanding of informativeness even in production, which typically lags behindcomprehension. If SI follows from an understanding of informativeness (Horn, 1998;
Hirschberg, 1991; Levinson, 2000), then children who know what is—and is
not—adequately informative should be able to use that knowledge to compute SI
inferences, in the absence of other obstacles.
This reasoning has driven a number of authors to consider other factors that mightChildren and Implicature 7
cause children’s failure in SI tasks (Noveck, 2001; Huang & Snedeker, 2009; Barner &Bachrach, 2010). These include difficulties accessing relevant the lexical alternatives (e.g.
“all” when “some” is mentioned; Chierchia et al., 2001; Barner & Bachrach, 2010), andknowing that one alternative in SI tasks negates others (Barner et al., 2011). Apparent
failures may also be due to the methodologies of truth-value or felicity judgment (Guasti
et al., 2005; Papafragou, 2006). These methods, which ask children to judge whether animplicature violation is felicitous or correct, cannot differentiate failure to compute SIs
from general tolerance of pragmatic violations (Katsos & Bishop, 2011).
Barner et al. (2011) conducted an experiment that tested whether access to lexical
alternatives posed a problem for children in computing SIs. They showed children displays
where a property was true of some or all of the members of a set, for example a group of
three animals in which all three were reading. In the critical conditions, the majority of 4
– 5 year-olds endorsed the pragmatically infelicitous “some” in a context where “all” could
have been used, consistent with previous work on SI. But they also endorsed the logicallyfalse statement that “only some” were sleeping. In contrast, when the animals wereenumerated (e.g. “only the cat and the cow are sleeping”), children correctly rejected thisstatement in cases where the modifier “only” made it false, suggesting that they
understood what “only” meant. Barner and colleagues interpreted this set of results assuggesting that children were unable to call to mind “all” as the scalar alternative to“some,” even when it was grammatically required by the word “only.” This interpretation
provides a plausible explanation for previous failures: although children may have beenable to understand that “some” was not maximally informative, they nevertheless could
not summon the relevant alternative to mind to compute a SI.
While Barner et al.’s (2011) study explains children’s failures, there are as yet only
limited positive demonstrations of any implicature abilities in children younger than 5,even though such demonstrations should in principle be possible. Miller, Schmitt, Chang,Children and Implicature 8
and Munn (2005) asked children to select a picture in which a puppet made “some faces
happy” by drawing smiling mouths on some but not all of the available faces (distractor
items included an “all” picture and a “none” picture). In a condition when “some” wasstressed, children chose the SI-consistent “some” picture but not the “all” picture, while
they chose both pictures together most often in the unstressed condition. This result
suggests that a referent-selection task might be promising for eliciting successful
implicatures, but the small sample in each condition (N=8) and broad age range (3;6 –5;10) limit the strength of the inferences that can be made from this study.
Papafragou and Tantalou (2004) also provided some evidence that children could
compute implicatures (both quantificational and ad-hoc), in this case in a competitive
felicity judgment task. Children saw e.g. a tiger who was assigned to eat a set of oranges,
and who reported “I ate some” (in the quantifier condition) or a cow who was assigned to
wrap a set of gifts (a parrot and a doll) and reported “I wrapped the parrot” (in the
ad-hoc condition). While a group of 10 children (mean age 5;2) correctly awarded orwithheld prizes from the puppet based on the performance implied by these statements,
these children were on average fully 20 months older than the 3-year-olds we consider
here. More importantly, new evidence from Sullivan, Davidson, and Barner (2011)
suggests that the children in Papafragou and Tantalou (2004) may have succeeded purely
by relying on the Principle of Contrast—giving prizes when the reported action exactly
matched the assigned action, and failing to give prizes when the reported action
contrasted—rather than computing any pragmatic implicature (E. V. Clark, 1988); thus,
Papafragou and Tantalou (2004)’s results should be interpreted with caution.
The Current Study
In sum, previous work has suggested that SI inferences—and perhaps pragmatic
inferences more generally, though the evidence on this issue is more limited—are difficult

Quantifier ScaleChildren and Implicature 9“all”"##! (“some”$%&'! ())

“none”(%)' !
!

!

!

!

Ad-hoc Scale(Experimental
Stimulus)!

!

Figure 1. Example stimuli from our referent selection task. The middle item represents
the pragmatically enriched interpretation of “My friend has glasses.” The implicature hasa similar logical structure to the conventional some-not-all implicature (top).

for young children. But in light of the arguments reviewed above, such findings present atbest an ambiguous picture of children’s pragmatic reasoning abilities. A positive
demonstration of ad-hoc implicature in younger children would help to clarify this picture
by suggesting that the challenges of scalar implicature do not extend to this domain. The
current work attempts to provide such a demonstration.
We created a novel, child-friendly referent-selection paradigm, pictured in Figure 1.
In this context, a speaker who asserts, “My friend has glasses” (in the experimental,“label” condition) implies that her friend is wearing only glasses. This inference isformally identical to the quantificational inference that “some” implies “only some,” butto facilitate comprehension, our stimuli create an ad-hoc scale in which scalar alternatives

!
!
!
!

Children and Implicature 10
are concrete nouns (“hat” and “glasses”) rather than abstract lexical items such as
quantifiers or modal operators. Our paradigm also mitigates possible difficulties
associated with calling to mind relevant alternatives by presenting the possible referents
side by side. Finally, to address the fact that truth-value judgment tasks and felicity
judgment tasks do not distinguish between pragmatic failures and mere pragmatic
tolerance (Katsos & Bishop, 2011), our referent-selection task conveys that when one
alternative is selected, the others cannot be the case (Barner et al., 2011).
As a control against baseline differences, we created a further “no label” conditionin which we asked children to choose one stimulus (e.g. the “friend”) but did not give any
further information. This method, referred to in Frank and Goodman (2012) as the“contextual salience” method, allows us to measure children’s baseline belief that one or
the other of the items is most likely to be the puppet’s intended referent. If children in theexperimental condition are making pragmatic enrichments to their linguistic input, thenwe would expect them to pick the target (i.e. single-feature) item less frequently in theabsence of this input.
Methods
In this report, we provide data from two independent samples. We initially collected
a planned sample of 24 children per age group across three ages (2 – 3 year olds, 3 – 4
year olds, and 4 – 5 year olds) and two conditions (Nsample 1 = 147). Due to the loss ofvideo tapes and records for a subsection of the sample we were unable to recodeparticipants’ responses for their choice patterns (see below). We therefore conducted an
independent replication with a second planned sample (Nsample 2 = 144).
Participants
Data in the first sample were collected from 147 children: in the label condition, 25
two-year-olds (M=2.6 years), 26 three-year-olds (M=3.5 years), and 24 four-year-olds (MChildren and Implicature 11= 4.5 years) participated at Bing Nursery School of Stanford, CA and the Children’s
Discovery Museum (CDM) of San Jose, CA. In the no-label condition, an additional 24
two-year-olds (M=2.6 years), 24 three-year-olds (M=3.5 years), and 24 four-year-olds(M=4.5 years) participated at the same locations. Data in the second sample werecollected from 144 children, all recruited at the CDM. In the label condition, there were
23 two-year-olds (M=2.6 years), 24 three-year-olds (M=3.5 years), and 25 four-year-olds(M = 4.5 years), and in the no label condition there were 24 two-year-olds (M=2.5 years),
24 three-year-olds (M=3.5 years), and 24 four-year-olds (M = 4.5 years). Experimenters
recruited children for a “storybook activity.” Parents were present during data collection
at CDM, and they watched quietly from across the room.
In the second sample, 33 additional children contributed data but were not includedin the final sample because of reported English exposure in the home being less than 75%(25), because of parental interference (5), because they failed to complete the study (2), or
because they had a self-reported developmental language disorder (1).
Adults in the label and no-label conditions were 48 participants recruited using
Amazon’s Mechanical Turk web-based crowd-sourcing platform (24 in each condition).
Stimuli
Stimuli for children were arranged in a binder containing materials for six trials:
four inference trials (such as those described above and pictured in Figure 1) and two filler
trials.
The unambiguous filler trials consisted of three different colored cars and threedifferent kinds of fruit. These trials were included as a check to ensure comprehension. In
the second sample, three children each made a single mistake on a filler trial (onetwo-year-old, one three-year-old, and one four-year-old), yielding 98% performance overall.
We do not discuss the filler trials further.

Children and Implicature 12
In each inference trial, three copies of the same base object were present, with two
features varying across the set. Inference trial materials were sets of faces (with glasses
and hats as features), houses (with trees and flowers), plates of pasta (with meatballs andsauce), and beds (with a teddy bear and a stuffed penguin). One object from the base set
had neither feature (“distractor”), one had exactly one feature (“one-feature”), and one
had both features (“two-feature”).
Positions of the three objects and which feature was used for the one-feature object(e.g. only hat vs. only glasses) were counterbalanced such that the position of each item
and named feature occurred an identical number of times. To accomplish this, six orders
were necessary. The assignment to one of the six orders was random and identical for thechildren in the control and test conditions. All orders began with a filler trial to ensurethat children understood the task.
Procedures
The task was administered by an experimenter, who used a stuffed animal as aconfederate. In the first sample, the stuffed animal was a green monster named “Furble,”while in the second sample, the stuffed animal was a red dog named “Clifford.” Theexperimenter asked participants to help the stuffed animal identify various people andobjects. In the Label condition (experimental), each inference trial consisted of the stuffedanimal using a description, “My X is/has Y,” that was ambiguous between the one-featureand two-feature objects. For example, in a trial like the one pictured in Figure 1, thestuffed animal would say “My friend has glasses.” Children were then asked to point tothe appropriate item and their response was recorded. On filler trials, the stuffed animal
simply referred to one of the items unambiguously, e.g. “My car is red.”In the No Label (control) condition, the procedure was identical, but children heard
a revised story in which the stuffed animal would say something unintelligible. In the firstChildren and Implicature 13
sample, the cover story was that Furble had eaten too much peanut butter to speak. In
the second sample, the cover story was that Clifford was a dog and could only bark. Thus,
instead of saying, “My friend has glasses,” the stuffed animal would simply mumble orbark. Children were again asked to pick out the item they thought belonged to the stuffedanimal. There was no correct answer on filler trials in the no-label condition.
Adults completed an equivalent task embedded in a webpage, picking alternatives
from each set of objects by clicking on corresponding radio buttons. The adult version
used the same script with a picture of Furble substituting for the stuffed animal in the live
action version. Adults in the control condition saw strings of hash marks instead of thenames of features. Adult participants were informed that the task was designed forchildren.
Results
The primary question of interest in our analysis was whether participants’ choices
indicate a successful pragmatic inference: in other words, whether they chose theone-feature object (e.g., the face with glasses but no hat) in contrast to the two-feature
object (e.g., the face with glasses and a hat). We begin our analysis by examining theinfluence of different factors on this primary measure of interest (one-feature choice);
subsequently we consider different ways of answering the question of whether participant
judgments reflect pragmatic inference. We end by considering our adult control data.1
Initial Analyses
Because of the large number of participants we tested, we were able to divide oursample into half-year age groups. Means and standard deviations for these age groups are
given in Table 1 and are plotted in Figure 2. Throughout this section we used logistic
1

Data and code used in these analyses are available at http://github.com/langcog/scales.

Children and Implicature 14

Proportion One-Feature Choices

1.00

Label
0.75

0.50

0.25

No Label

0.00
2

3

4

Age (Years)

Figure 2. Mean proportion of choices indicating the one-feature (implicature-consistent)
object on inference trials in the Label (light gray) and No Label conditions (dark gray)across ages. Error bars show 95% confidence intervals computed via subject-wise nonparametric bootstrap.

mixed-effects models to quantify effects of different factors on implicature-consistent(one-feature) responding. In all of these models, we estimate the influence of various
factors on this dependent variable with crossed random effects of participant and item
(Gelman & Hill, 2007), the maximal random effects structure justified by ourexperimental design (Barr, Levy, Scheepers, & Tily, 2013).
Our first analysis used a model that included age (as a continuous factor),
condition, and their interaction. We found a positive effect of age (β = .72, p < .0001), a
negative effect of the No Label condition (β = 1.65, p = .005), and a negative interactionof the two (β = −.99, p < .0001). In other words, older participants were more likely tochoose the implicature consistent response, but primarily in the Label condition. An

Children and Implicature 15

Label (Experimental)

No Label (Control)

Age

Mean

SD

N

Age

Mean

SD

N

2.0

0.37

0.21

15

2.0

0.29

0.23

21

2.5

0.55

0.22

33

2.5

0.27

0.20

27

3.0

0.61

0.24

26

3.0

0.24

0.23

27

3.5

0.70

0.28

24

3.5

0.25

0.23

22

4.0

0.79

0.27

21

4.0

0.17

0.14

26

4.5

0.79

0.22

28

4.5

0.18

0.23

22

Table 1
Summary statistics for one-feature responses by age group for each condition. Age indicateshalf-year age bins (e.g. 2.0 indicates children from 2 years 0 months to 2 years 6 months).

examination of the random effects suggested that there was some item-level variation(βbeds = .17, βf aces = −.04, βhouses = −.16, βpasta = .04), but all four items showed thesame basic developmental trends.
We examined differences between our two independent samples by adding sample asa factor to our previous model, and adding all two- and three-way interactions between
sample and other variables. We found that there was a negative coefficient for the second
sample that was almost reliable (β = −1.49, p = .06) but no reliable interactions withsample (p > .14). This trend towards a main effect of sample suggested slightly lower
performance in choosing the implicature-consistent target for children in the second
sample. We speculate that this may be due to the composition of the first sample, which
included some children from an on-campus nursery school where younger children
especially may have felt more comfortable in the testing situation. Nevertheless, a modelChildren and Implicature 16

Proportion One-Feature Choices

1.00

0.75

SampleOriginal
Replication

0.50

Condition
Label
No Label

0.25

0.00
2

3

Age (Years)

4

Figure 3. Mean proportion of choices indicating the one-feature (implicature-consistent)
object on inference trials in the Label (light gray) and No Label conditions (dark gray)across ages, divided by sample. Error bars show 95% confidence intervals computed via
subject-wise non-parametric bootstrap.

that included only the second sample showed exactly the same pattern as the model that
included both, with reliable effects of age (β = .87, p < .0001), condition (β = 2.33,
p = .003), and their interaction (β = −1.09, p < .0001). The two samples are compared in
Figure 3.
We next modeled the effects of demographic factors on responding in our second
sample, for which we had available a short demographic information sheet given to allparents participating in research at Children’s Discovery Museum. A model including
gender showed a reliable negative coefficient for males’ responses (β = −.94, p = .02)
suggesting that male children made fewer implicature-correct responses; there were no
reliable interactions between gender and age or condition. We did not find an effect ofself-reported percentage exposure to English in the home (main effect β = .003, p = .80,

Children and Implicature 17

Label

Proportion Choices

1.00

No Label
One-Feature

0.75

0.50
Two-feature

0.25

0.00

No-feature
2

3

4

2

Age (Years)

3

4

Figure 4. Mean proportion of choices indicating the one-feature (implicature-consistent),
two-feature, or no-feature object on trials in the Label and No Label conditions, across ages.
Data are from second sample only. Error bars show 95% confidence intervals computed via
subject-wise non-parametric bootstrap.

no reliable interactions), presumably because we excluded children with percentages lower
than 75% and hence our range was restricted. We also did not find any main effect orinteraction with parent education (main effect β = −0.03, p = .69).
To summarize, we found a consistent pattern in our data: a developmental increase
in responding in the Label condition but not the No Label condition. The developmental
increase was marginally earlier in our first sample than our second, and appeared to bestronger for girls than for boys, but overall all analyses yielded a consistent picture of thedata.
Evidence for Pragmatic Inference
We next turn to an examination of whether—and when, developmentally—our data
yield evidence of pragmatic inference. In order to do so, we start with the observation

Children and Implicature 18
that there are two differences between the Label and No Label conditions. First, in the
Label condition, children can use the name of a feature (e.g. “glasses”) to narrow down
the reference set logically, that is to the two objects that possess that feature. Second,
they can make a pragmatic inference that the name refers to the object with only thatfeature. It is only this second difference that we are interested in.
To examine this second factor, we look to the distribution of children’s responses
across possible targets (Figure 4). (All analyses in this section use only the second sample,
for which response data was available). In the Label condition, the youngest 2-year-olds
were close to random in their responses. For the 2.5 – 3 year-olds, responses to the
no-feature object were lower and responding was approximately even between the
logically-possible alternatives. In the 3 – 3.5 year-olds, responding was noticeably higher
for the one-feature than the two-feature object (52% vs. 37%); and this pattern was evenstronger for older groups.
We next attempt to quantify these differences. In these analyses, we model only thesubset of responses in which children did not choose the no-feature distractor, again using
a logistic mixed-effects model. Chance responding for this analysis was 50%, and a reliable
positive coefficient is a signal of pragmatic inference. We pursued two alternativemodeling approaches: modeling the Label condition independently, and modeling the two
conditions jointly.
Pursuing the first approach, we used a mixed model to compare one-feature
responding to chance in the Label condition alone, reasoning that individual participants
could show clear evidence of greater-than-chance responding by choosing the one-feature
response at above chance levels. In this analysis, the youngest age group for which there
was a significant bias to choose the one-feature object was the 3.5-year-olds (β3.5 = 1.07,
p = .03); 4 and 4.5 year olds were highly reliable in their one-feature responding(β4.0 = 1.99, p = .0003 and β4.5 = 1.70, p = .0008 respectively).

Children and Implicature 19
On the other hand, the reason we included the No Label condition in our
experiment was to provide a baseline measurement of the salience of different alternatives(Frank & Goodman, 2012). In previous work, we have shown that this salience can affectparticipants’ baseline responding. Thus, a more sensitive test for pragmatic inference
might be having overcome that baseline responding bias. To quantify this effect, we fit alogistic mixed model with data from both the Label and No Label conditions (again,
excluding no-feature responses). This model contained both coefficients for each age groupand interactions between age and condition. We set responses in the No Label condition
as the baseline; thus an interaction between condition and age group would be a signal of
greater-than-baseline responding for a particular condition. In this model we found atrend towards such an interaction in the 3.0 age group (β3.0 = .83, p = .07), indicatingthat there was some baseline bias that participants might be overcoming. Coefficients forall subsequent age groups were reliable (β3.5 = 1.11, p = .03; β4.0 = 2.66, p < .0001;
β4.5 = 1.81, p = .0003).
In summary, we found reliable evidence for pragmatic inference beyond the literalinterpretation of a linguistic description in children from 3.5 – 4 years old, with suggestive
evidence of an effect in 3.0 – 3.5 year-olds. In contrast, we saw no such evidence in
two-year-olds. Was this lack of positive responding due to difficulties that thetwo-year-olds had with the task? The number of trials might have been taxing on theattention spans of two-year-olds, and we did not actively control the level of the
vocabulary items that were used in the stimuli. In addition, we saw substantial (25%)
incorrect responses (choosing the no-feature item) for the youngest two-year-olds in the
Label condition, suggesting that they were not able to succeed in the basic language
interpretation component of the task with high reliability.
In a pilot follow-up experiment, we created a version of the task that tested thecontribution of these factors to younger children’s performance. In this version, weChildren and Implicature 20
included one fewer trial, added a common grounding phase in which objects were named(Barner et al., 2011; Papafragou & Musolino, 2003), and used only vocabulary items thatwere very likely to be known to young children. We still saw no sign of above-chance
responding from a group of 12 two-year-olds, so we suspect that for younger children there
may be obstacles to success in the particular paradigm we used here. One such obstacle isthat the one-referent implicature target is relatively less salient than the two-referent
distractor, simply by virtue of having one rather than two features. Thus, whether ourcurrent data signal a true developmental change or simply a limitation of ourexperimental methods will be a question for future work.
Adult Control Data
Adults performed at ceiling in the online version of our task, choosing theone-feature object 96% of the time in the Label condition (95% CI: 91% - 100%) and 23%of the time in the No Label condition (95% CI: 15% - 30%). This level is substantiallyhigher than that of the older four-year-olds in our study. But we caution against a strong
interpretation of this finding. Adults expressed explicit understanding of the pragmatic
nature of the task (in the Label condition, 29% of the responses to our debriefing question“What did you think this study was about?” made direct or indirect mention of
informativeness or the dichotomy between what is said and what is meant).
In followup work using the same task as we introduced here, we have found greaterlevels of explicit metacognition when participants perform multiple trials in a row, as in
the results reported above. (In contrast, we find no such order effects in data fromchildren). Thus, most of our experiments with adults have relied on asking a single
question to each participant (Frank & Goodman, 2012; Vogel, Emilsson, Frank, Jurafsky,& Potts, 2014). In one study that used substantively identical displays, but only asked asingle question to each participant, we found levels of implicature that were almost exactlyChildren and Implicature 21
the same as those shown by the 4-year-olds: 75%. Though many factors may affect thestrength of adults’ implicatures (Goodman & Stuhlmüller, 2013; Degen & Tanenhaus,2011), we suspect that the level of inference shown by the oldest children in our task here
is not anomalous from the perspective of adult judgments.
Discussion
We began by describing preschool children’s puzzling difficulties with one type ofpragmatic inference: scalar implicature. We then went on to test their ability to makecontextually-grounded, ad-hoc implicatures—inferences that do not rely on linguistic
scales using quantifiers or modals. Our experiments provide evidence that children by age
3.5, and perhaps even slightly earlier, can make such inferences. These data provide
evidence for preschool children’s pragmatic capacities and delimit the class of explanations
that can account for failure in scalar implicature more specifically.
Together with work by Barner et al. (2011), this finding begins to suggest a possible
resolution to the puzzling pattern of failures in scalar implicature experiments: Children
are sometimes capable of computing implicatures, but these implicatures are sensitive tothe availability of the inferential alternatives. On the classic Gricean account, inferringthat “some” means some but not all requires considering the counterfactual scenario in
which the speaker wanted to talk about all and chose the message “all.” Barner et al.
(2011) argue that it is this computation that proves troublesome for preschool children:
they cannot summon all (and its matching message “all”) to mind as alternatives thatare relevant in the pragmatic computation—at least not in time to have this inference
inform their judgements.
The prediction of this account is that when the inferential alternatives are moreavailable, the implicature computation should be easier. An item can be more available
for a number of reasons. One reason is that the relationship between the target item andChildren and Implicature 22
its alternative might be well-practiced. For example, numbers seem to elicit strong scalarinferences even for young children (e.g., “two” could mean two or more but iseffortlessly narrowed to two and no more, presumably because of an inference from thealternative “three”). For children, “three” is highly associated with “two” because of theirpositions in the highly-practiced count list (cf. Huang, Spelke, & Snedeker, 2013). In
contrast, children are not taught to recite the quantifier list “none,” “some,” “all” (Barner& Bachrach, 2010).2 Another, perhaps more straightforward case of accessibility is when
the alternative interpretations are pictured in the context. In the case of standard scalar
implicature tasks, a “some”-consistent display is shown and children are asked to makejudgments about it (Papafragou & Musolino, 2003). There is no display showing “all” inthis case. In contrast, in referent selection tasks like ours (or like the Miller et al., 2005
study cited above), the alternative interpretations are physically pictured and hence
presumably easier to reason about. Thus, across the number and ad-hoc implicature casestudies, there is some prima facie support for the “availability of alternatives” hypothesis.
Other aspects of our experimental design likely played a role in younger children’s
success in our task as well, however. Tasks that ask for truth-value or felicity judgments
impose considerable demands on children beyond their comprehension of an utterance. In
contrast, referent selection is a task that children are called upon to perform nearly every
day of their lives. By its nature it implies that responses are likely to be exclusive, afeature that may also have pushed children to consider the contrasting modes of referringto the different possible targets in our task (e.g. “if he had wanted this one he would havesaid ‘hat,’ but instead he said ‘glasses.’ ”). Future work should capitalize on design
features of our task to probe further the sources of previous failures in SI (Miller et al.,2005). Nevertheless, the success of four-year-olds and older three-year-olds in our study
2

We acknowledge that this interpretation of numbers as being pragmatically upper-bounded iscontroversial, but cite it for the sake of completeness.

Children and Implicature 23
suggest that children’s difficulty with some scalar implicatures should not be interpreted
as a more general difficulty with pragmatic reasoning.
Pragmatic reasoning is a central area in human cognition where language
understanding and social cognition come together to enable sophisticated feats ofcommunication. Because of this centrality, the results on children’s limited pragmaticabilities present an important experimental puzzle. Our work here places one piece byshowing that some pragmatic inferences are within the capabilities of young children.
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