A NEW PRAGMATIC ACCOUNT OF QUANTIFIER-SPREADING
Natalia Rakhlin
University of Connecticut

1. Introduction
1.1. The Errors
In the study reported here, I have investigated the nature of certain interpretive errors
children make with respect to universally quantified sentences well documented crosslinguistically. The aim of this line of research is to gain a better understanding of therelationship between semantics and pragmatics in children’s knowledge of quantification witha broader goal of establishing what type of knowledge is available to children from early on
and what type of competence undergoes development.
It is well attested in a variety of languages that children exhibit non-adult-like behavior
with respect to interpretation of sentences like (1) and (2) under certain experimental
conditions. In particular, it has been found that while children consistently judge (1) true
when it is presented in the context of a picture, in which every boy is paired with a wagon andevery wagon is paired with a boy, if an extra wagon is added to the picture, as in (3), children
often reject (1) as false. Similarly, while they usually accept (2) when the sets of boys and ofwagons pulled by them fully overlap, children may reject it in a situation with an extra, nonwagon-pulling boy, as in (4) (Philip 1995).
(1)

Every boy is pulling a wagon.

(2)

A boy is pulling every wagon.

(3)

(4)

This error has been labeled “quantifier-spreading” or q-spreading, the term I willcontinue to use for convenience. In looking for the solution to the puzzle presented by such
errors, I will propose that by focusing entirely on the universal quantifier we had overlooked
the role of indefinites and their ability to change the meaning of a universally quantified
sentence in triggering such errors. Verifying sentences like (1) and (2) involves making
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judgments about relative quantifier scope. Furthermore, this judgment does not have toinclude any covert scope altering movement operations. The meaning of the sentence changes
depending on how the domain of the indefinite is restricted, namely whether a “plural” or a“singleton” indefinite is chosen. If the singleton option is chosen, then (1) and (2) receive the‘wide scope’ indefinite interpretation and would be false in the context of (3) and (4)respectively. I will suggest that children from early on have the knowledge of the semantics
of quantification including scopal ambiguities, but are less good than adults at coping with
deficient context when resolving them.
1.2. Previous Accounts
1.2.1. Contextual Symmetry Requirement as a Cognitive Property
The research that first brought to light children’s errors triggered by contextual
asymmetry was conducted by Inhelder and Piaget (1964). They discovered that when Swiss
French-speaking children were presented with a visual array of geometric shapes consistingof blue circles as well as blue and red squares and asked “Are all the circles blue”, they often
responded ‘no’ and as an explanation pointed to the blue squares. Inhelder and Piaget called
this response “symmetrical”, and concluded that for young children (“stage II” in Piaget’s
developmental classification), sentences with the universal quantifier require symmetry
between the set denoted by the predicate and the set denoted by the common noun of thesubject. As Inhelder and Piaget put it, “It … looks very much as if the true explanation is thatat stage II children extend the quantifier ‘all’ to the logical predicate of the sentence as well as
to its logical subject” (Inhelder and Piaget 1964, pp. 70-71).
I&P attributed the errors to the immaturity of logical reasoning, namely the child’s
inability to construct hierarchical systems or operate in terms of a schema of class inclusion.
Thus, they claimed that children at this stage, when presented with a question: ‘Are all Xs
Ys?’, where Xs are individuals and Ys are properties, construct two non-graphic collections(as opposed to the more primitive graphic collections “stage I” children operate with), one ofXs and one of Ys. According to I & P, the child, unable to cope with the problem of thequantification of the predicate, is limited to ascertaining whether or not the collection of Xs
coincides with that of Ys. This amounts to reducing the question ‘Are all the Xs Ys?’ to ‘Are
all the Xs all the Ys?’ instead of the correct ‘Are all the Xs some of Ys?’ Thus, according tothis view, the source of non-adult-like responses in children of this developmental stage istheir replacement of class inclusion with equivalence.
Following this explanation, this type of error became known in the literature as the“symmetrical interpretation” error. More contemporary views attributing symmetricalinterpretation to children amount to a claim that there is a fundamental difference between the-240-A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

adult and the child semantics of the universal quantifier: adults require the truth conditions in(5) (simplified), while children require (6):1(5)||every||(A, B) = 1 iff A ⊆ B(6)||every||(A, B) = 1 iff A = B

I&P’s theory offered an elegant explanation of the child data by positing adevelopmental path from the child to the adult interpretation as a transition from being able tohandle a logically simpler operation to a more complex one. However, further researchcomplicated the picture by revealing new conditions that give rise to non-adult responses
inconsistent with (6). Thus, after expanding this line of research to sentences with two-placepredicates, it was found that the lack of symmetry between the members of the agent-set (e.g.
a set of boys) and that of the predicate (a set of wagon-puling individuals) is not what triggers
the highest rate of symmetrical errors for most children, as would be predicted by (6). Rather,
it is triggered by the lack of symmetry between the members of the agent-set (a set of boys)
and that of the theme-set (a set of wagons).
One major study, Philip (1995), reports that for his so-called ‘symmetry’ group, the higherror rate of 56% was obtained on the condition in which the scenario paired with thesentence ’every boy is riding a pony’ contained three ponies ridden by boys and one rider-lesspony. On the other hand, when the scenario contained three pony-riding boys and a ponyriding girl, this group gave adult-like yes-responses close to 100% of the time, showing thatthey do not require symmetry between boys and pony-riders, as would be predicted by I&P’s
account.2
Much subsequent research focused on this type of errors. However, I&P’s hypothesis
about children’s symmetrical interpretation was adopted (in a modified form) as the basic
descriptive generalization for which a new theoretical explanation was sought, one rooted inchildren’s grammar, not in their general cognitive capacity.
1.2.2. Contextual Symmetry Requirement as a Property of a Non-Adult Grammar
Linguistic accounts that followed the influential work of I&P attempted to find agrammatical mechanism that would lead to the “symmetrical” interpretation, which has
subsequently been referred to as ‘exhaustive pairing’ (to emphasize the child’s now
1

The Inhelder and Piaget study involved the French equivalent of the English ‘all’. Most current
research with English-speaking children centers on ‘every’, which is why I use ‘every’ in the formulasin (5)-(6). Since I&P did not discuss lexical differences between ‘all’ and ‘every’ and spoke generally
about children’s logical abilities with respect to universal quantification, I will assume that the formulathey used for ‘all’ would also apply to ‘every’.
2

Similarly, Philip’s ‘perfectionist’ children rejected this sentence at a high rate of 85% in the context
where an extra individual was a rider-less pony. The same group of children exhibited a much lower
rejection rate in the context of an extra pony-riding girl at the rate of 58%.

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established requirement for every member of the agent-set to be exhaustively paired with amember of the theme-set). Various proposals regarding the grammatical origin of the‘exhaustive pairing’ have been made. Roeper and Matthei (1974) suggested that the errors
arise because quantifiers all, some, and every are treated by children as adverbs and thatchildren allow quantifiers to “spread” from their syntactic position as a determiner to theadverbial positions in the sentence (hence another term for this behavior, “q-spreading”).
Similarly, Bucci (1978) suggested that children could not restrict the quantifier to its domain
and allow the domain to spread to other parts of the sentence (cf. also Roeper and de Villiers
1993, Roeper et al. 2004 for extensions).
The adverbial view was further developed by Philip (1995) as the Event Quantificationaccount. He maintained that in child grammar the universal quantifier “alone occupies aposition of sentential scope, rather than the whole quantifier phrase”, and hence is an adverbof quantification rather than a quantificational determiner (Philip 1995, p.3). According to thisidea, for children, the universal quantifier does not quantify over individuals, as it does for
adults, but quantifies over events. The events forming the restrictor are the sub-events of The
contextually relevant event that meet a particular restriction, namely that an individual ofeither the agent-type or the theme-type is a participant in the sub-event.3 Thus, a sentence likethat in (7), which for adults has a semantic structure as given in (8), for the child has themeaning paraphrased in (9) and the semantic structure shown in (10):(7)

Every boy is riding a pony.

(8)

S
Q
∀x

(9)

Restrictorboy(x)

Nuclear Scoperiding-a-pony(x)‘For every event e1, such that e1 involves a boy or a pony (or both) as a participant, ande1 stands in the part-whole relation to an event e2, in which a boy is riding a pony: e1 isan event of a boy riding a pony.’

3

This analysis covers the cases of “classic spreading,” i.e. rejecting (7) in contexts with an unpaired
pony. It does not cover another type errors, namely the ‘perfectionist’ responses, i.e. sentences like (7)rejected in contexts with unmentioned individuals. In Philip’s theory, to cover this type of error, an
additional component had to be added to the restrictor. In addition to stating that participants in the
sub-events are boy, or pony, or both, another type of participant had to be added, namely ‘any
perceived individual’. This addition had the desired result by requiring every sub-event of the event
under consideration that involves any participant to satisfy the truth conditions of the nuclear scope. In
other words, for the perfectionist child, every boy is riding a pony is true if and only if for the event
under consideration every sub-event that involves any participant is a sub-event in which a boy rides apony. Roeper et al. (2004) investigated this type of errors further and gave it an informal name‘bunny-spreading.’ The name comes from the responses when children rejected the sentence ‘every
dog is eating a bone’ paired with a picture containing a number of dogs eating bones plus a bunnyeating a carrot, often accompanied with pointing to the bunny and saying, ‘no, not the bunny.”-242-

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(10)

S
Q
∀e1

Nuclear Scopea boy is riding a pony in e1
Restrictor∃e2 [e1 ≤ e2 &ride(boy, pony, e2) & PART(boy, e1) or PART(pony, e1)]

Roeper et al. (2004) argued for a similar analysis, in which children’s universal
quantifier develops from being an adverb to Floating Quantifier before reaching the adultstage when it becomes a determiner. In the acquisition path they proposed, the child moves
from what they call the “bunny-spreading” (analogous to Philip’s “perfectionist”) stage, when
the child does not project a DP above the NP and interprets subject quantifiers as adverbial
elements in Focus Phrase, to the “classic spreading” stage with every behaving as a Floating
Quantifier, to the adult stage, when every is reanalyzed as rooted in the DP. The final
transition occurs in some children as late as the age of 12.
One alternative approach attributes the errors to children’s treating the strong quantifier
every as weak (Drozd and van Loosbroek 1998, Geurts 2003). Despite their claims of
acknowledging children’s full grammatical competence, these theories still posit certain nonadult-like properties in child grammar. Essentially, they amount to a claim very similar to theone made by the earlier theories (e.g. Roeper and Matthei (1974), Bucci (1978), etc.), which
explained the errors in terms of children’s failure to find a correct restrictor for the universal
quantifier. However, unlike these earlier theories, for the Weak Quantification theories,“spreading” of a quantifier domain is not due to children’s incorrect lexical semantics ofevery or a failure to construct correct semantic representations, but to factors outside ofsemantics proper. Thus, for Geurts, children are said to differ from adults in the following
respects:(i)weak construal of a strong quantifier, resulting in non-canonical parsing at theindependent level of syntax-semantics mapping he assumes;(ii)

allowing the domain of the universal quantifier to be left underdetermined until
after the syntax-semantics mapping occurs;(iii) allowing pragmatic factors alone, namely the perceived salience of sets ofindividuals and information structure, to determine quantifier domains
disregarding the syntactic relations such as sisterhood or constituency.
Even though theories of this type capture the “symmetrical” responses, one may argue
that they underestimate children’s competence since they don’t account for the adult-like
responses researchers have obtained from young children (Crain et al. 1996, Crain et al. 2000,
Gualmini et al. 2001, Meroni et al. 2000, Gualmini et al. 2003, etc.). Another reason for
skepticism with respect to ‘partial competence’ accounts is that the available experimental
data clearly shows that the symmetrical errors are limited for the most part to certain types of-243-

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experimental conditions. The tasks resulting in high rates of errors are those in which the test
sentences are given without or with a very limited linguistic context. Instead, children are
shown a visual array of individuals and asked whether the truth or falsity of the test sentenceholds of these individuals. In contrast, when the test involves a rich linguistic context, theerror rate is dramatically reduced (Crain et al. 1996, Drozd and van Loosbroek 1998). These
factors provided a motivation for a new explanation, one that considers the errors to be afunction of the experimental design masking children’s full competence of universal
quantification.
1.2.3. Theory of Plausible Dissent
One of the most influential accounts attributing the errors under consideration to aflawed experimental design is the theory of Plausible Dissent first proposed by Crain et al.
(1996), and argued for in subsequent work by Meroni et al. (2000), Gualmini et al. (2003),
etc. According to this view, the appearance of spreading errors in the contexts of visualasymmetry is purely coincidental. The errors are claimed to be not a response to the extra
individual in the picture, as assumed by all other theories, but children’s reaction to thepragmatic infelicity of how the tests are typically administered. According to Crain et al.
(1996), in order for a truth value judgment to be felicitous, the context has to meet certain
pragmatic conditions, the relevant one for the issue at hand being the condition of Plausible
Dissent. It requires for the addressee to be able to conceive of an alternative outcome in orderto judge the proposition as true or false in a particular context. While adults and older children
are capable of constructing potential alternative outcomes, young children, according to Crainet al., lack the ability to do so and need the context to represent them explicitly. Since thepicture-based tests do not suggest an alternative outcome (e.g. all boys are simply shown
riding ponies, but it is not shown that some of them first had an option of riding an elephantor not riding at all), children cannot judge the truth or falsity of the sentence reliably.
This approach successfully showed how experimental design affects children’s
performance, and demonstrated that given optimal experimental conditions, children arecapable of dramatically improving their performance. This supports the idea of the errors
being a matter of performance and not that of competence. The condition of Plausible
Dissent, however, has been criticized as unnecessary because researchers have beensuccessful in improving children’s performance by contextual manipulations that did not
involve the condition of Plausible Dissent (Drozd and van Loosbroek 1998, Phillip and Lynch
2000, Sugisaki and Isobe 2001).
One interesting manipulation was done by Sugisaki and Isobe (2001). In this experiment,
two groups of Japanese-speaking children were tested using picture contexts only, mirroring
the conditions of the typical q-spreading experiments. Group 1 was presented with pictureswith one extra object (e.g. three cats each bouncing a ball plus one extra ball), and Group 2
with pictures with at least 4 extra objects (three cat-ball pairs plus a group of extra balls).
They found that by increasing the number of extra objects in the picture scenarios given tochildren, they were able to elicit a much higher percentage of adult-like responses: 37.5%-244-

A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)correct for Group 1, in contrast to 87.5% for group 2, a result quite mysterious for the theory
of Plausible Dissent’, as well as for the theories discussed in section 1.2.2.
If we look closer at the reported studies, an interesting picture emerges. First observationis that rich linguistic context (with or without explicitly suggesting potential alternative
outcomes) helps raise the rate of adult-like responses. Secondly, what seems to be playing arole in reducing the rate of errors is a manipulation of the relative visual salience of the sets.
Thus, children’s performance improves under such a wide variety of conditions – satisfying
Plausible Dissent (Crain et al. 1996), creating picture-contexts with multiple rather than single
extra individual (Sugisaki and Isobe 2001), back-grounding of the extra individual (Philip andLynch 2000), de-emphasizing the extra object (Gordon 1996), emphasizing it (Crain et al2000), and emphasizing the restrictor set of the universal quantifier (Drozd and van
Loosbroek 1998).
In the next section, I will present my proposal, in which I will argue that the Full
Competence approach is correct in insisting that children’s semantics for universal
quantification is fully adult-like; however, I will reject the assumption that children’s apparent
reaction to the asymmetry in the visual context is merely coincidental. Nor will I rely on
Plausible Dissent as the primary explanation for the divergent results obtained by various
researchers.
2. A New Pragmatic Account of Q-Spreading
2.1. Hypothesis
In order to explain the pattern of responses reported in the literature, I would like tosuggest that we look at the ambiguity of sentences like (11), due to the interaction of the twoquantifiers, the universal and the indefinite, as a potential cause of the ‘q-spreading’responses.
(11) Every boy is pulling a wagon.
I propose that the crucial source of difficulty lies not in the interpretation of theuniversal, but in the “free” nature of indefinites with regards to how their domain restrictions
can be set - in addition to being permitted to have either a singleton or a non-singleton set as
their domain without any morphological clues about which option has been chosen,
indefinites permit an information gap between the speaker and hearer in having access to thedomain (Schwarzschild 2002, Kratzer 1998). I would like to argue that children have thesemantic knowledge of both the universal and the indefinite; hence, from early on they havethe knowledge of the ambiguity. However, they are less good than adults at resolving it in aminimal context. What appears to be ‘q-spreading’ is not grammatical errors. These responses
are a manifestation of a strategy children use to resolve the sentence ambiguity by restricting
the domain of the indefinite to a singleton set if the situation contains a salient single object.
The presence of the latter, which may be taken as a ‘referent’ for the ‘wide scope’ indefinite,-245-

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often leads the child to assign ‘wide’ scope to the indefinite when adults wouldn’t. In order tounderstand how this works, let’s take a closer look at the semantics of indefinites.
2.1.1. Quantifier Domain Restrictions
As has been pointed out, an important semantic feature of quantifiers is that they range
over relevant individuals. Thus, (12) does not say that every boy in the world rode a pony. If
it did, there would be very few situations in which it were true.
It has been argued that this notion of relevance in quantification is part of the semantics
of quantification and hence has to be part of the formal semantics of quantifiers. Quantifier
domain restrictions have been posited as a formal mechanism of expressing the notion“relevant” (Westerstål 1984, von Fintel 1994, Marti 2003). Under one common view, they are
expressed as silent pronoun-like elements (e.g. a sister to the common NP argument of thequantifier), a common notation for which is shown in (12) and its abbreviated semantics givenin (13):(12) Every boyC rode a pony.
↑context supplies its value: e.g. “those who came to Sam’s birthday party”(13) Every [C & boy][rode a pony] or
Every [ λx.C(x) & boy(x)] [λx.rode-a-pony(x)]This context-dependency is a property that indefinites share with other quantifiers. If thisis correct, interpreting (12) involves not only choosing relevant boys (the value of C), but also
relevant ponies (the value of C’):
(14) ∀x [x is in C & x is a boy →∃y [y is in C’ & y is a pony & x rode y]] ,↑context: “the ponies Sam’s parents hired for the birthday party”
or narrowed to a singleton set: “the white pony”
Furthermore, choosing one relevant pony instead of multiple ponies has importantconsequences for the relative semantic scope of the indefinite and the universal quantifier: itcreates an interpretation identical to the one in which the sentence has the inverse scopeinterpretation: If C’= {P1, P2, P3…}, this yields a non-specific indefinite and allows covariation of boys and ponies. If C’= {P1}, it yields a specific indefinite, truth-conditionallyidentical to the wide scope indefinite resulting in (14) being equivalent to (15): 4(15) ∃y [y is in C’ & y is a pony and ∀x [x is in C & x is a boy and x rode y]]4

I assume the presuppositional ‘every’ (i.e. it presupposes a non-empty set of boys in (12)).

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What this demonstrates is that if the restriction of an indefinite is true of exactly one
individual (what Schwarzschild 2002 calls “singleton indefinites”), it behaves logically like areferential noun phrase. In such a case, in order for the sentence to be true, all of the boys are
required to ride the pony included as the singleton restriction.
Indefinites are notorious for their ‘irregular’ behavior: the seemingly varying
quantificational force, when they appear to be existential quantifiers in certain syntactic
contexts but not in others (Lewis 1975, Kamp 1981, Heim 1982, among others), and theirability to take island-free wide scope (Fodor and Sag 1982, Reinhart 1997, Kratzer 1998,
among others). There have been various approaches proposed to account for the behavior ofindefinites, reviewing all of which is outside the scope of this paper. Although multiple
theories of indefinites may be able to handle the child data under consideration here, forconcreteness I will adopt Schwarzschild (2002), who argues that indefinites are unambiguous
existential quantifiers with their scope derived in a regular way. According to this proposal,
the exceptional wide scope of indefinites can be derived simply by manipulating the
cardinality of their domain restrictions. In the next section, I will review this theory anddiscuss how this approach sheds light on q-spreading.
2.1.2. Deriving the Scope of Indefinites
It has long been assumed that ambiguities observed with sentences with multiple scopebearing elements, such as quantifiers, are derived through a covert movement operation (QR),
which creates operator-variable structures by moving and adjoining the operators to the left ofclausal boundaries (e.g. adjoining to IP), with the operator binding the variables from its
raised position (e.g. May 1977, 1985):(16) [IP … QP …]  [QP [IP … t …]]
Thus, a sentence with an indefinite and universally quantified NPs has the readings witheither the universal or the indefinite taking wide scope, paraphrased in (18) and (19) andwhose abbreviated LFs are given in (20) and (21).
(17) A boy tasted every dish.
(18) For every x, such that x is a boy, x tasted a dish.
(19) There is an x such that x is a boy and x tasted every dish.
(20) [Every dish2 [ a boy1 [ IP t1 … t2…]]](21) [a boy1 [ Every dish2 [ IP t1 … t2…]]]
An important argument for the movement theory of scope comes from the data showingthat QR obeys locality constraints on movement, barring wide scope from within extraction-247-

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islands.5 Thus, Hornstein (1984) observed that while the universally quantified NP can takewide scope from the embedded subject position in the ECM construction, as in (22), it takes
obligatory narrow scope in a tensed clausal complement, as in (23).
(22) A professor expects every student to pass the exam. (a reading with co-varying
professors and students).
(23) A professor expects that every student will pass the exam. (no co-variation)
It has also been observed that the movement theory of scope runs into problem withindefinites, which do not obey island constraints. Consider the example from Fodor and Sag(1982) given in (24), which has a reading in which the indefinite takes wide scope out of an
adjunct island:(24) If a relative of mine from Texas dies in a fire, I will inherit a house.
One can imagine that the speaker has multiple relatives from Texas. If this is the case,
two interpretations are possible. Under one reading, a death in a fire of any one of the
speaker’s relatives from Texas would result in the speaker’s inheriting a house. Under anotherscenario, one specific relative must die in a fire in order for the speaker to inherit a house.
Accounting for this reading with a wide scope indefinite construed as the existential quantifieris problematic since such scope taking would be exceptional (moving out of a syntactic
island) and is disallowed for other quantifiers. To see the contrast, we can look at a minimallydifferent sentence, e.g. with the universal quantifier instead of an indefinite in an adjunctclause, as in (25), which is unambiguous: ‘every’ is not permitted to scope above theconditional (the reading under which every relative of the speaker’s is such that the speaker
will inherit a house in case that relative dies in a fire). The only available reading is the one inwhich death of all of the relatives in a fire is required for him to inherit a house.
(25) If every relative of mine dies in a fire, I will inherit a house.
An even more serious problem is presented by sentences with indefinites that haveintermediate scope readings, as in (26):(26) Every author here despises every publisher who would not publish a book that wasdeemed pornographic.

5

Among semantic arguments for QR are not only that movement creates a transparent structure off
which to read the relative quantifier scope, but also the considerations of interpretability (to avoid typemismatch between the transitive verb and the quantifier as its internal argument), deriving inverselylinked readings: structures in which the more embedded QP takes wide scope (e.g. One apple in every
basket is rotten), ACD constructions, quantifiers that bind pronouns, etc. (see Heim and Kratzer 1998
for a review).

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A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)(27) Possible readings:a.
∀x (author x) >∀y (publisher y) > ∃z (book z): For every x, if x is an author, thenx despises every publisher y who refused to publish some book z or another thatwas deemed pornographic.
b.

∃z (book z) >∀x (author x) >∀y (publisher y): There is a z, such that z is a bookthat was deemed pornographic and for every x, x is an author, x despises every y,y is a publisher who refused to publish z.

c.

∀x (author x) > ∃z (book z) >∀y (publisher y): For each x, x is an author, there isa book z that was deemed pornographic – possibly different books for different
authors – such that x despises every publisher y who would not publish z.

The existence of the intermediate indefinite readings as in (27c) presents a problem forboth the ‘naïve’ quantificational view of indefinites (Russell 1919) because, as discussed
above, unlike other quantifiers in this configuration, they do not respect islands in their scopetaking, as well as the ambiguity view (Fodor and Sag 1982). While the latter theories canhandle the widest-scope reading in (27b), the intermediate reading is problematic for thisapproach.
The analysis of indefinites proposed by Schwarzschild (2002) successfully solves the
problem of exceptional scope including intermediate scope using a mechanism that affects
domain restrictions of all quantifiers.6 It also provides a mechanism that can be used to
explain q-spreading behavior of children, as I will show in section 3.
2.1.3. Singleton Indefinites
Schwarzschild’s insight was that the ambiguity of the indefinites is not lexical but can bederived simply by adjusting the size of their domain restriction, which may consist of a set ofany cardinality (except zero) including one. The reason why exceptional ‘wide scope’ ispermitted with indefinites is because of their freedom to have singleton domains, not true ofother quantifiers. If the domain restriction of the indefinite is a singleton set, it appears tohave wide scope regardless of its surface c-command domain without applying covert
movement. In order to have this reading, the context must provide a unique relevant
individual to fill the value for the covert domain restriction.
This elegant solution to the puzzle of indefinites allows us to account for all of the
exceptional scope readings, including the intermediate scope, without any additional syntactic
or semantic mechanisms. If we correctly construct the restricted domain for the indefinite as a6

Another solution to this problem suggests that exceptional wide-scope indefinites are interpreted as
choice functions (Kratzer 1998, Winter 2001, Reinhart 1997, etc.). A choice function takes as its
argument the set of individuals satisfying the descriptive content of the indefinite NP and returns anelement from this set. This approach is also compatible with the analysis of q-spreading I am
proposing. The problems with the choice function approach were discussed in Chierchia (2001),
Schwartz (2001), Geurts (2000), but these objections do not bear on the data discussed here.

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singleton set and fill in the implicit domain-narrowing restriction, we get the desired truthconditions without having to move the indefinite out of an island, hence avoiding the need toaccount for its apparent exceptional scope. According to this proposal, different readings that
we saw in (27) are due to a differently constructed domain of the indefinite. All of thereadings therefore are narrow scope readings, but in two of them the scope relations aremasked by the fact that the indefinite is a singleton.
In order to illustrate how this works more explicitly, let’s suppose that the set of relevant
authors includes three individuals as shown in (28). Let’s also suppose that for each of these
individuals x there is a distinct single book (e.g. a book that x wrote) that was deemed
pornographic, and that each author x despises every publisher who refused to publish thatbook (i.e. the domain restriction of the indefinite contains a bound variable). The formula in(29) shows that even though the indefinite occupies the lowest position, we get the desired covariation between authors and books seen in the ‘intermediate’ reading.
(28) Authors: {Lawrence, Miller, Nabokov}, Books: CL={Lady Chatterley’s Lover}
CM={Tropic of Cancer} CN={Lolita}, Publishers: …
(29) ∀x [author(x)  ∀y [publisher(y) such that ∃z [z ∈Cx and z is a book and z wasdeemed pornographic and y refused to publish z] x despises y]] where Cx={z: z is abook x had written and z was deemed pornographic}
Another reading, the regular narrow scope reading, is derived with the domain of theindefinite consisting of multiple books, as shown in (30):(30) Authors: {Lawrence, Miller, Nabokov}, Books: C={Lady Chatterley’s Lover, Lolita,
Tropic of Cancer, …}(31) ∀x [author(x)  ∀y [publisher(y) such that ∃z [z ∈C and z is a book and z was deemed
pornographic and y refused to publish z]  x despises y]] where C={z: z is a book thathas been deemed pornographic};
Here the domain may contain all books that have ever been deemed pornographic, or it
may be contextually narrowed to a subset containing multiple relevant ones. Finally, thewidest scope reading can be derived in the same way as a narrow scope indefinite, but with its
domain restricted to a single book:(32) Authors: {Lawrence, Miller, Nabokov}, Books: C ={Lolita}(33) ∀x [author(x)  ∀y [publisher(y) such that ∃z [z ∈C and z is a book and z was deemed
pornographic and y refused to publish z]  x despises y]]
In this example, the domain also contains an implicit restriction. The implicit restrictionin this case, as with any other singleton indefinite, may contain any conceivable property
narrowing the set to a unique book and may be asymmetrically available to the speaker and-250-

A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

not to the listener. What this means is that when uttering a sentence with an indefinite, thespeaker has no expectation that the listener should be able to reconstruct from the context theindefinite’s domain restriction with any specificity (beyond figuring out that it contains asingle individual, whose identity is known to the speaker). In other words, the speaker may
felicitously utter the sentence with a single individual in mind and have no expectation thatthe listener would infer from context what individual it is.
2.2. Implications for ‘Quantifier-Spreading’The observation about the role of the domain restriction in the interpretation of sentenceswith indefinites has important implications for the question we are considering. I havereviewed arguments for the importance of the domain restrictions for quantifiers in generaland indefinites in particular. I have established that in order to evaluate a sentence containing
an indefinite NP with respect to its truth conditions, we need to know not only the relativesyntactic scope of quantifiers, but also the value of the restricted domain for both theuniversal and the indefinite.
The latter presents difficulty because any indefinite can in principle have a domain
restriction of the cardinality of one. The difficulty is magnified by allowing the restriction to
be expressed implicitly, making it asymmetrically available to the speaker, but not thelistener. This creates a possibility of interpreting any indefinite as singleton or non-singleton
and is a reason behind the intuition for the specific/non-specific ambiguity of indefinites in an
out-of-the-blue context. Importantly, this suggests that a sentence that contains an indefinite
NP presented in a relatively poor context is ambiguous regardless of the availability of agenuine inverse scope, and a relatively rich context is necessary for the listener to resolve theambiguity.
If the grammar allows for singleton restrictions in cases like we have discussed in theprevious section, then we have to admit this possibility for simpler cases like those withwhich children typically produce q-spreading responses. Let’s suppose our context contains a
set of three boys and four wagons: Boys = {B1, B2, B3}, Wagons = {W1, W2, W3, W4}, asshown in (24). When the child hears the puppet uttering (25) in this context, she has to make adecision about how to restrict quantifier domains. While it is straightforward for the domainof the universal (the child has no reason to consider anything but the entire set of boys shownin the picture because of their visual uniformity), there are at least two equally plausible
options for the domain of the indefinite, one of which is restricting it with the salient single
wagon:(24)-251-

Nanzan Linguistics: Special Issue 3, Vol. 1(25) Puppet: Every boy is pulling a wagon.
Child: Is he be talking about all of them or just this one?
(26) C’=or

Under the surface scope construal, the sentence would have the meaning as in (27). If thechild constructs C’ to include multiple wagons, then the truth conditions would require thatfor each boy x there exist a (possibly different) wagon y, such that x pulled y.
(27) ∀x [boy(x) & x ∈C  ∃y [wagon(y) & y ∈ C’ & x pulled y]]“For every contextually relevant boy x, there is a wagon y in C’ and x pulled y.”
However, if the domain is narrowed to a singleton set, then the truth conditions for thesentence under the universal wide-scope construal would be effectively the same as under theindefinite wide-scope as in (28); and each boy x would be required to pull the same wagon y.
(28) ∃y [wagon(y) & y ∈C’ & ∀x [boy(x) & x ∈C  x pulled y]]“There is a wagon y in C’ such that every contextually relevant boy x pulled y.”This allows us to explain why children sometimes judge universally quantified sentences
like that in (25) false in the context of a picture analogous to the one in (24): unless sufficient
linguistic context is given, the salient single wagon in the picture leads the child to construe
the expression a wagon as a singleton indefinite, the interpretation under which (25) is false
in this context.
2.3. Discussion
If we adopt this explanation for children’s responses, we are able to explain a large
number of previous empirical findings. One observation has been that children are not limited
to ‘spreading error’ responses, but rather produce them (in minimal-context tasks) onlyaround 57% of the time (Philip 1995). This is not surprising under this analysis because botha Yes- and a No-response are grammatically available alternatives. Thus, the “q-spreading”(“No”) responses are those given when the child focuses on the perceptually salient single
wagon and interprets the indefinite as singleton, resulting in the “collective” reading, when
every boy is required to pull that particular wagon. The adult-like (“Yes”) responses are thosegiven when the child chooses the multiple wagons as the domain restriction for the indefinite,
hence getting the distributive reading.
This approach also provides a straightforward explanation for the contrast in the rate of
q-spreading errors between picture-context and rich context tasks. Since with the former, thechild receives no clues as to what reading the experimenter is expecting, she is left to choose
either option. On the other hand, experiments that provide rich linguistic context, as in the
Truth Value Judgment task, provide the child with pragmatic clues that are used in natural-252-

A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

discourse to interpret and verify a scope-ambiguous sentence, thus limiting the interpretive
possibilities and resulting in much lower error rates.
Finally, we can also account for the finding that the one-extra-object condition is harderfor children than the multiple-extra-object condition. This is because in the former there is aperceptually salient candidate for the singleton restriction for the indefinite, while in the latter
there isn’t. Hence, in the former, the child may be biased towards the singleton reading, whilein the latter she isn’t and would more consistently choose the distributive reading. This canalso explain why the extra-object-condition is harder than other conditions, such as those inwhich the picture contain an alternative agent.7 This is because according to this proposal, thesource of difficulty is the interpretation of the indefinite object and not the universal subject.
The question arises why adults would almost never give a No-response in the situations
when children do. The difference between adults and children may be due to the differencesin their pragmatic and in their processing flexibility. I suggest that on-line adults go throughthe same calculations as children entertaining the same options, but, due to their greater
pragmatic flexibility, they are more efficient in selecting the correct readings (and/or in
rejecting pragmatically implausible readings). Children, on the other hand, have a weaknessin handling information gaps between them and others (cf. Wimmer, Hogrefe, and Perner
1988, Wimmer, Hogrefe, and Sodian 1988, Ruffman 1996, etc.), which makes it difficult forchildren to manage contextual information. Therefore, it is not surprising that children would
frequently fail to construct the target interpretation for sentences with indefinites, particularlyin those situations when the context given to them is less than optimal.
Another factor that may be causing the difference between adults and children is in theirrespective use of the Principle of Charity (Grice 1975, Davidson 1984). According to thisprinciple, when given a choice between assigning a reading compatible with the presented
situation or the one incompatible with it, adults select the former due to their expectation thatthe speaker is being truthful. It is possible that for a certain reason children do not observe thePrinciple of Charity (cf. Hulsey et al. 2004).
Yet another factor from which the difference between adult and children’s behavior may
stem is their different degrees of processing flexibility. It allows adults to switch from one
reading to another more easily compared with children, who may have difficulty revising
their initial parse because they lack computational resources to evaluate multiple options. As
a result, they select the first grammatical interpretation they access and stay with it (cf. Viau,
Lidz and Musolino 2007, Conroy and Lidz 2007). Thus, the difference between adults andchildren is likely to be due to interplay between various performance factors – both pragmaticand processing, and not in their knowledge of formal semantic.8
7For example, the sentence Every boy is pulling a wagon paired with a picture containing a girlpulling a wagon in addition to boy/wagon pairs.
8

Although without additional research it is impossible to separate children’s pragmatic inflexibility
from their processing inflexibility and to say definitively what is a greater factor in ‘q-spreading’ –-253-

Nanzan Linguistics: Special Issue 3, Vol. 1

There is independent evidence concerning on-line behavior of adults, which comes froman eye-tracking experiment conducted by Meroni et al. (2001) with English-speaking adults.
Their results indicate that adults evaluate alternative domains for the indefinite.9 This study
examined the on-line patterns of fixation duration by adults in response to the extra objects ina picture verification task. Their results indicate that adults not only gazed at the single extra
object, which is irrelevant for the calculations of truth conditions of the sentence under the
distributive reading, but that the duration of their gaze was significantly longer if the picture
contained a single extra object compared with the condition in which there was another object
next to it. This result is reminiscent of the Sugisaki and Isobe (2001) child study, in which thenumber of extra objects in the picture was manipulated. It shows a parallel between adults’
on-line and children’s off-line behavior. For adults, the gaze duration on the extra object
decreases, while for children the error rate decreases if the visual salience of the single extra
object is decreased.
3. Experimental Evidence
3.1 Predictions
I have proposed that instead of focusing on the universal quantifier, as has been done
previously, the so-called q-spreading responses should be explained by children’sinterpretation of indefinites, particularly by their choosing ‘singleton indefinites’ influenced
by the perceptual salience of the ‘extra’ object. As I discussed in the previous section, my
approach relies on the theory of indefinites by Schwarzschild 2002, in which indefinites arealways quantificational, but can appear referential simply because of their ability to havesingleton domain restrictions. Singleton domain restrictions affect the semantic scope
relations independently from any syntactic mechanism of reversing scope. In particular, thoseindefinites that combine with singleton domains, even when syntactically taking narrow scope
and therefore normally receiving the non-specific interpretation, would have the appearance
of being ‘wide scope’ or ‘referential’ and essentially render the sentence scope-neutral (inSchwarzschild’s terminology), thus obscuring the surface syntactic scope relations.
One issue raised in the literature on the acquisition of quantification is whether
children’s inability to cope with sub-optimal pragmatic conditions, their ignorance of the Charity
Principle or their inability to revise their initial parse, I believe the totality of the available datasuggests that children’s pragmatic inflexibility does play a role. Thus, since pragmatic manipulations,such as manipulating the visual salience of the extra object or providing enriched linguistic context,
trigger changes in children’s performance, it suggests that we cannot account for all of children’s
behavior by saying that the errors are due solely to their selecting one interpretation (at random) andnot being able to revise it. Since the experimental data I am reviewing here does not deal withchildren’s on-line behavior, I will leave the role of processing in children’s quantification errors for
future research and discuss only their pragmatic weakness.
9

Although the authors themselves do not make this connection, I believe that their results are
consistent with this explanation.

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syntactically inverse scope readings are available to children from early on. This issue isrelevant for the ‘q-spreading’ debate because it is an issue in which the Full Competence
theories diverge from ‘adverbial’ theories, such as Event Quantification (Philip 1995). The
former are consistent with the claim that children know all and only those scope readings thatare allowed in adult grammar. The latter, on the other hand, maintain that at the initial stage,
the universal quantifier should obligatorily take wide scope since under their proposal theuniversal quantifier occupies the position in which it scopes over the entire sentence. It haseven been suggested that the basic underlying reason for q-spreading is children’s difficultywith QR. Thus, Philip (1995) suggests that the reason why children interpret the universal
quantifier as an adverb instead of as a determiner may be that the children have difficulty withthe operation of QR. According to Philip, applying QR may be problematic for children since
it is an abstract relation (since the movement occurs post-syntactically) and because it resultsin establishing a discontinued dependency between the moved constituent and its trace. Under
this view, because of their difficulty with adult LF, children resort to event quantification,
which is not derived via QR, but with a mechanism described in Heim’s terms as a
“Quantifier Construal Rule” (Heim 1982), and does not require maintenance of an abstract
discontinuous dependency. As Philip put it, “all that matters for semantic interpretation of theuniversal quantifier in such a representation is that this quantifier has scope over the entire
sentence; its original position in the surface structure is completely irrelevant” (p.50).
Hence, under this theory, sentences (30) and (31) for children should have identicalsemantic form derived from an LF in which the universal takes scope over the whole sentence
and hence over the indefinite.
(30) Every farmer rode a donkey.
(31) A farmer rode every donkey.
This predicts that any unpaired individual – a non-donkey-riding farmer or a donkey notridden by a farmer should equally result in a spreading response for either (30) or (31).
Furthermore, if the two sentences have the same LF, distinct from its surface syntax for bothof them, there is no obvious reason why the rate of q-spreading should be different for the twosentence types. In addition, if the adverbial theory is correct and children always require
distributivity and exhaustive pairing between farmers and donkeys for both (30) and (31),both should be rejected in collective contexts, where all farmers ride the same donkey or all
donkeys are ridden by the same farmer, as frequently or more frequently as in distributive
contexts, as long as there are unpaired farmers or donkeys.10
In contrast, my approach makes different predictions. If children have adult-likeknowledge of quantification, we must at least allow a possibility that they have both surface
and inverse scope interpretation for both sentences, given that pragmatic conditions in which
10

For (31), children presumably should allow for one specific farmer to ride all of the donkeys, but
only in case there are no extra farmers. Similarly, for (30) the collective context with no extra donkeys
should result in a “true” response, but a donkey should falsify it.

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the test is administered do not inhibit some reading. In experiment 1, I will test this prediction
with respect to the inverse scope for sentences like (31).
Normally, when sentences of this type are used in ‘q-spreading’ studies, children are
shown a picture with a number of farmers each riding a different donkey and an extra farmer.
When, in this context a child rejects (31) as false and points to the extra farmer, it is taken as
evidence that she assigned the sentence universal wide scope reading, in accordance with theevent quantification semantics, and the unpaired farmer under such reading made the sentence
false for the child (Philip and Aurelio 1991, Philip and Takahashi 1991). However, since inthese studies there are no controls insuring that the sentence does in fact receive universal
wide scope reading for children, we cannot conclusively say what causes them to reject thesentence in that context. It is quite plausible that they reject the sentence because theyinterpret it under the surface scope and look for one specific farmer to be riding every donkey,
and since the context does not contain such a farmer, they reject the sentence. This isespecially plausible given the preponderance of experimental evidence showing that theinverse scope reading is harder to elicit from children than the surface scope and that theformer must be facilitated by more carefully designed experimental conditions (Hulsey et al.
2004). Therefore, it is important to tease apart the surface and the inverse scope interpretationof sentences like (31) and to study whether there is a difference in “q-spreading” rate for eachreading in a better-controlled environment. I will address this issue in experiment 1.
If children in fact prefer the surface scope for (31), we can expect to see a difference inthe rate of ‘q-spreading’ responses between (31) presented in the context consistent with its
surface scope interpretation (e.g. one farmer-multiple donkeys group plus extra farmers) andin the context consistent with its inverse scope reading (a number of farmer-donkey pairs plus
an extra donkey). Children should reject (31) significantly more frequently if it’s presented ina distributive context than when it is presented in the context consistent with the groupreading. Furthermore, just as the presence of extra farmers shouldn’t matter for increasing
errors for the group contexts, the absence of an extra donkey shouldn’t matter in reducing therate of errors for distributive contexts. In other words, I predict that sentence like (31) would
be accepted by children at a high rate in “group” contexts regardless of the presence of extra
agent-type individuals, and rejected by children at a relatively high rate in a distributive
context even if the context contains no extra theme-type individuals.
There is another scope related issue that leads to the same predictions. If children haveadult-like knowledge of quantifier scope, as I propose, one element of this competence shouldbe their knowledge of asymmetric entailment relations between the surface and inverse scope
readings in sentences like (30) and (31). In these examples, the wide-scope indefinite reading
entails the wide scope universal reading. This means that if the sentence is true under theindefinite wide scope, it would necessarily be true under the universal wide scope in the samecontext as well. On the other hand, in those contexts that make the sentence true under theuniversal wide scope reading, the sentence would be false under the indefinite wide scope
construal.

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A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

This amounts to a situation, when (30) presented in a context consistent with the wide
scope indefinite reading (henceforth “collective contexts”) is unambiguous – true under either
surface or inverse scope configuration. When, however, it is given in contexts consistent withthe universal wide scope (henceforth “distributive contexts”), the sentence is ambiguous –either true if construed under the surface scope, or false if construed under the inverse scope.
The same applies to (31), for which the sentence is true under both readings if presented incollective contexts, but only under the distributive reading if presented in distributive
contexts.
Thus, if my hypothesis is correct in claiming that q-spreading is children’s reaction to thesentence ambiguity and the use of the perceptual salience of the extra object in resolving theambiguity, this state of affairs should result in a distinct error rate for universally quantified
sentences in collective vs. distributive asymmetric contexts. Since in a collective situation,
where every farmer rides the same donkey, there is no possible interpretation of (30) thatwould give a “false” response in that situation, children’s decision of which reading to selectshould not be affected by the visual asymmetry and hence, they should exhibit a low rate of qspreading errors. On the other hand, children should exhibit a higher error rate with sentences
like (30) in distributive asymmetric contexts, particularly in the single extra object condition
since in this situation they are giving truth-value judgments in a situation that requires them toresolve ambiguity. The same pattern should hold for (31), which should be accepted at ahigher rate in the contexts of one farmer riding all of the donkeys even if there are extra
farmers present in the situation, and at a lower rate if there is co-variation between farmers
and donkeys given that there are extra donkeys. On the other hand, ‘adverbial’ theories do notmake these predictions since according to them such sentences are unambiguous for children.
These predictions will be tested in experiments 1 and 2.
Finally, if the main culprit in q-spreading is not the universal quantifier, but theindefinite, we can ask ourselves whether children will respond in a “q-spreading”-like mannerto sentences containing an indefinite and a quantifier of another type, instead of the universal,
given that the sentences are presented under the typical “q-spreading” inducing conditions,e.g. visual context with a salient single “extra” individual. The approach advanced here
predicts that spreading-like errors can indeed be elicited using sentences without the universal
quantifier if such sentence contains an indefinite and the context contains a salient single
individual to be a potential candidate for a singleton domain restriction for the indefinite. We
also predict that the error rate can be manipulated by controlling the degree of visual salienceof the extra individual. This prediction will be addressed in experiment 3.
3.2. Experiment 1
3.2.1. Goal, Participants and Procedure
Goal: To test whether English-speaking children can correctly interpret sentences like(32) under both surface and inverse scope and whether their success in this task is affected byconditions of contextual asymmetry between the number of individuals in the agent and-257-

Nanzan Linguistics: Special Issue 3, Vol. 1

theme sets and and/or satisfaction of the Condition of Plausible dissent.
(32) A girl tasted every cake.
Participants: 21 English-speaking preschool children (median age 4; 6) recruited at thenursery school run by the University of Connecticut. Five children, who failed the training,were excluded, bringing the sample to the total of 16 children. We also tested 16 adultcontrols, who were University of Connecticut undergraduate students. The adults were given
the same materials as the children, but in a paper and pencil form – the written stories were
presented in the same randomized order as the children, and each was followed by the target
sentence, which the subjects were asked to judge as true or false.
Materials and Procedure: the standard Truth-Value Judgment Task (Crain and Thornton
1998). The materials consisted of sentences like (32). The two possible interpretations for thissentence are given in (33) and (34):(33) ∀y [cake(y)  ∃x [girl(x) and x tasted y]]‘For each cake y, there was a (possibly different) x, such that x was a girl and x tasted y.’(34) ∃x [girl(x) & ∀y [cake(y)  x tasted ]]‘There was an x, x is a girl and x tasted every cake.’
Sentences were presented in contexts that satisfied one of the following three conditions,
schematically represented in (35):(i)

compatible with the surface-scope, as well as the inverse scope by entailment;(ii)

compatible with the inverse scope, but not with the surface scope;(iii) incompatible with either the surface or inverse scope(35) a.

Surface scope context b.
A1
O1
A2
O2
A3
O3
B

Inverse scope context
A1
O1
A2
O2
A3
O3
B

c.

False on both readings
A1
O1
A2
O2
A3
O3
B

Under the scenario of type (35a), compatible with both readings, there was one girl who
tasted every cake, while two other girls did not taste any cake. In the situation (35b)compatible only with the reading in (33), the story contained three girls, each of whom tasted
a different cake. Finally, in a situation of type (35c), there was neither a single girl who tasted
every cake, nor an exhaustive pairing between girls and cakes. All scenarios satisfied thecondition of Plausible Dissent by containing an alternative individual (e.g. in the abovementioned scenario, three girls and one boy). The alternative character always considered
performing the activity described in the story, but failed to do so.

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After a training session, which was used to familiarize the children with the TVJ task
and in which unambiguous quantified sentences were used (e.g. Every boy climbed the tree),each child was given four items of each type (12 test items in total) and fillers in a fixed
random order. The testing was divided into two sessions. Each test item was pronounced witha focus-neutral intonation, without stressing either the subject or the object NP. The stories
were acted out with small toys by the experimenter, before the test sentence was presented.
3.2.2. Results
Table 1 below shows the results for each child.11 Table 2 summarizes the results acrosschildren.
Table 1
Mike
Ivan
Jake
Tatiana
Amy
Ron
Cathy
Billy
Valerie
LionelJane
Mathew
Helen
Eva
Nell
Steve

Number of Accepted Sentences in Each Condition
Surface
Inverse
False
Fillers
3
0
0
3
4
4
0
4
3
4
0
4
3
0
0
4
4
4
1
1
4
0
0
4
2
0
0
3
4
3
1
3
3
2
0
3
1
4
1
4
3
0
0
3
4
3
1
4
3
4
0
4
3
0
0
4
4
0
0
3
2
4
0
4

different fillers

Table 2Distribution of Responses in Children (N = 16)
Accepted ≥3 Rej ≥3
Split
Surface1312Inverse
8
7
1
False
0
16
0
12
13
Fillers
15
1
0
11

The names are pseudonyms.

12

Since fillers varied between true and false, the table indicates correct responses in the acceptancecolumn and incorrect in the rejection column.

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As we can see, the children are nearly unanimous in their acceptance/rejection of certain
sentence types, but they are split with others: while children were adult-like in almost
uniformly rejecting false sentences and accepting the surface scope, they fall into two almost
equal groups with respect to inverse scope.
The main goal of the study was to obtain more fine-tuned findings about the rate of “qspreading” with respect to sentences like (32) by teasing apart the two scope readings
available for such sentences. Our results show that indeed there is a sharp difference in therate of incorrect rejections with respect to the two readings. As we predicted, the test
sentences were much more likely to be rejected in ‘distributive’ contexts, despite thecomplete symmetry between the agent and theme sets of protagonists.
The surface scope contexts contained an asymmetry (i.e. they did not contain exhaustive
paring between the members of the agent and theme sets). Recall that under the “non-adultgrammar of universal quantification” view, such asymmetry is expected to cause children to
reject the sentence. Our results indicate, however, that when the context was presented in arich story form, instead of a schematic picture showing agent/theme pairs, the asymmetry did
not cause children to reject the sentence. The children consistently accepted stimuli in‘surface scope’ contexts, demonstrating that they allow wide-scope indefinites, and when thesentence is interpreted that way, asymmetry in the context does not result in errors.
In the ‘inverse scope condition,’ on the other hand, the contexts were symmetrical –there
was an exhaustive pairing between the agent and theme sets. Despite this symmetry, thiscondition presented difficulty for some children. The children in our sample were almost
evenly divided: 8 out of 16 children accepted the stimuli in the inverse scope contexts and 7
rejected them (1 remaining child gave an equal number of yes- and no-answers).
Those who accepted the inverse scope support our hypothesis that adult-like knowledgeof scopal ambiguities is available to children from early on. This experiment does not allow
us to rule out the possibility that the difference between the “inverse” and “no-inverse scope”
groups amounts to a developmental difference between those who have matured into a stage
at which children allow inverse scope vs. those who remain at the isomorphic stage. However,according to independent evidence, children often choose the isomorphic interpretation given
certain pragmatic conditions of the test, and do not lack the inverse scope entirely (Gualmini
2003, Hulsey et al. 2004). In light of such findings, I will adopt the assumption that inverse
scope is generally available to children, but is difficult to access and requires certain
conditions to be met by the task in order to make the inverse scope reading more salient. We
did not address this issue in this experiment, which is presumably why a number of children

13

The child who made errors on the fillers was a pilot case. After running the test with her, we
adjusted the fillers to eliminate unnecessary complications in the story, which had to do with the plot
and not the structure. Since she was very consistent in rejecting the false sentences while accepting
both surface and inverse scope ones, we decided not to exclude her from the result table. However,
eliminating her from the results would not change the general pattern.

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A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

rejected the inverse scope reading. However, I believe that those who rejected the inverse
scope present an interesting finding.
Firstly, as I noted earlier, these children rejected the sentence in the inverse-scope
context despite the fact that this context exhibits symmetry, supporting my claim thatchildren’s quantificational errors are not fully contingent on the contextual asymmetry.
Secondly, the explanations offered by the children for why they rejected the sentence in the
inverse scope contexts were quite revealing. All of such children explained that the puppet
was wrong when he said that a girl tasted every cake because in the story there were three
girls, not one. This explanation for rejecting the sentence supports my hypothesis that typical‘q-spreading’ errors involve interpreting indefinites as singleton.
If we look at the control group of adults, we will see that they were unanimous in theiracceptance of the surface scope, but, interestingly, were also somewhat divided in theiracceptance of the inverse scope: 3 out of 16 adults rejected three or more of the items in the
inverse scope condition (see table 3 for the summary of the results).
Table 3
Adult Controls (N = 16)
Accepted ≥3 Rej ≥3
Surface160Inverse
13
3
False
0
16
Fillers
16
0

Split
0
0
0
0

Since even some of the adult native English speakers rejected the target sentences in thecontexts in which others accepted them, it seems reasonable to conclude that what we found
was a failure of these subjects to access this interpretation rather than a lack of this reading intheir grammar. Such a view is supported by the studies showing a general preference forsurface scope over the inverse scope in monolingual adult English-speakers (Kurzman and
MacDonald 1993).
In K&M’s study, in a self-paced reading task, subjects had to judge whether a sentencewith two quantifiers (a > every) was compatible with a disambiguating continuation. While
over 80% of continuations compatible with the surface scope were accepted, only around
30% of those compatible with the inverse scope were accepted. K&M term this preference‘the single reference principle’. They explain this preference by saying that single reference issimpler to represent than multiple reference, it is always possible and often obligatory (aswhen a is an only quantifier), and to switch from single to potential multiple reference
involves a complex alteration of semantic representation (Kurtzman and MacDonald, 1993).
Thus, they view the ‘single reference’ bias in adults as a sort of a garden path and not agrammatical phenomenon.
A final observation from our results was that satisfying Plausible Dissent was not a-261-

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sufficient condition for some children’s acceptance of the target sentences in the inverse
scope context. The condition of Plausible Dissent was satisfied across all of the experimental
conditions, which, however, did not result in a uniform acceptance of the inverse scope
sentences.
3.3. Experiment 2
3.3.1. Goal, Participants and Procedure
Goal: to test the prediction that children know the asymmetric entailment relations
between the surface and inverse scope and consequently would make fewer “q-spreading”
errors in “collective asymmetric” contexts compared with the “distributive single
asymmetric” contexts.
Participants: 15 preschool and kindergarten children attending University of Connecticut
Child Labs, median age 4; 9.
Materials and Procedure: universally quantified sentences presented in one of thefollowing contexts:i.
ii.

distributive with a single extra item
collective with a single extra item

The contexts were presented as pictures, samples of which are given below:(36) a.

b.

Distributive asymmetric:
Every baby is inside a flowerpot. (∀ < ∃: true; ∃ < ∀: false)

Collective asymmetric:
Every girl is pushing a car. (∀ < ∃: true; ∃ < ∀: true)

Each condition consisted of 4 items plus fillers, presented in a fixed random order. The child-262-

A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

was shown a picture, after which the puppet uttered a test sentences. The task of the child was
to judge whether the puppet’s statement was true of the picture.
3.3.2. Results
As predicted, we found a distinct rate of error across the two experimental conditions.
The findings are summarized in figure 1. We can see that there is a highly significant contrast
in the rate of errors in the distributive and the collective contexts: the former resulted in a rateof errors more than twice that in the latter condition despite the presence of a single extra itemin both types of context.
Figure 1:

Paired t-test: t(13)=3.61, two-tailed p=.003
This observation is in concert with the hypothesis attributing ‘classic spreading’ to a
pragmatic strategy used by children to resolve an ambiguity in contexts that have a single
extra individual because its presence suggests to the child that a singleton reading for theindefinite should be considered and therefore resulting in a certain percent of rejections.
According to this explanation, the extra individual triggers errors in conjunction with anumber of agent/theme pairs because such context is maximally ambiguous: it contains two
sets of individuals across which the event is distributed, which suggests the distributive
reading, and the single individual of the sort denoted by the indefinite, which suggests the
singleton indefinite reading. In this situation the child has to make a decision about whichreading the speaker intends for the sentence. Consequently, the responses are not limited toeither ‘true’ or ‘false,’ but are split between both. On the other hand, in the ‘collective’context, the ambiguity is minimized because, as we discussed earlier, the indefinite wide
scope reading entails the universal wide scope reading. The two readings are essentiallyindistinguishable since the only possible judgment for both of them is “true”. Consequently,
presence of an extra item does not matter to the same extent as in the ‘distributive’ contexts
because it doesn’t stand for a potentially different reading.

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3.3.3. Independent Support
One major goal of the two experiments presented above was to refute the claim that forchildren sentences like (30) and (31) have identical LFs. In this section, I would like to review
some independent evidence that children are sensitive to the syntactic position of theuniversal quantifier. Gualmini et al (2003) showed that children possess knowledge of theasymmetry between internal and external arguments of the universal quantifier with respect tothe property of Downward Entailment (DE) (allowing inference of the truth of a proposition
predicated of a set to its subset). In adult language, the two arguments of the universal
quantifier every differ with respect to this property. The quantifier is downward entailing onlyin its internal but not in its external argument, i.e. an inference from a set to its subset islicensed only for the internal argument of the universal quantifier, as in (37), but not theexternal one as in (38):(37) Every [boy who rode an elephant] [fell off]  Every boy who rode a wild elephant fell
off.
(38) Every [boy who fell off] [rode an elephant] * Every boy who fell off rode a wild
elephant.
One diagnostic of DE is that the disjunction operator or can receive a conjunctive
interpretation in the internal, but only the exclusive disjunctive interpretation in the externalargument of every.
(39) Every [boy who rode an elephant or a zebra] [fell off] ⇔ Every boy who rode anelephant fell off and every boy who rode a zebra fell off.
(40) Every [boy who fell off] [rode an elephant or a zebra] *⇔ every boy who fell off rodean elephant and every boy who fell off rode a zebra.
Gualmini et al. tested whether English-speaking children know the difference between
the internal and external arguments of every with respect to the licensing of conjunctive or.14
They report that children know that or can be used conjunctively in the internal argument of
every, but only as exclusive or in the external argument.
Further support for the view that children are sensitive to the syntactic position of thequantifier, comes from the study that showed that the rate of children’s errors is affected bywhether the universal is in the subject (“right-spreading”) or object (“left-spreading”)

14

Whether children allow conjunctive use of or in the internal argument of every was also tested by
Gualmini and Crain (2001).

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A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

position.15 Thus, H-K Kang (1999) reports a significant difference between the rate of theright-spreading (51%) and the left-spreading error (73%) in English-speaking children.
One other interesting piece of evidence that children are sensitive to the syntactic
position of the universal quantifier comes from the study of quantification in child Catalan(Gavarro and Escobar 2002) and Spanish (Escobar 2002). In their study, G&E were testing
the Event Quantification hypothesis with respect to sentences like (41) and (42). In bothSpanish and Catalan, a grammatical property (precise nature of which is not crucial for thequestion at hand) would require sentences like (41) to have frozen scope, where the universal
quantifier takes wide scope. When children were asked to judge the truth value of suchunambiguous sentences in the contexts like those outlined in a and b, their responses closely
mirrored those of adults, and they accepted sentences like (41) in the contexts analogous to(a) despite the ‘extra’ individuals, which typically elicit ‘spreading’ responses. At the sametime, they correctly rejected the sentence in the context of (b).
(41) Is an elephant carrying all the balloons?
Contexts: a picture showinga) elephant1 carries ballon1, balloon2 and balloon3 b)elephant2
elephant3
boyelephant1 carries ballon1
elephant2 carries ballon2
elephant3 carries ballon3boy

In G&E, 94% of the children accepted the surface scope reading (situation a) and 94% of
3- and 4-year olds (as well as 100% of older children) rejected the inverse scope reading(situation b). If in these children’s grammar, the universal quantifier was an adverbial
quantifier over events, we would expect to find the opposite: children should have rejected thesentence in (a) since it has elephants not carrying balloons, but accepted it in situation (b),since it exhaustively pairs elephants and balloons.
Interestingly, we find a different pattern of responses for G&E’s children when the test
sentences have a universally quantified subject and indefinite objects. When children wereasked to judge the truth-value of (42), their responses across all of the experimental
conditions had a higher error rate than what we saw with respect to (41).
(42) Are all the elephants carrying a balloon?
Thus, the younger group (3-4-year-olds) accepted (42) in the situation shown in (43b), a“classic spreading” context, at the rate of 72%. Even more striking was the fact that their
responses were only 56% correct in the situation shown in (43a), the so-called ‘under-15

The term left-spreading and right-spreading error comes from the direction in which the child isclaimed to ‘spread’ the domain of the quantifier from its sister NP: if it is in the subject position, it
spreads rightwards, and if it is in the object position, it is leftwards.

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exhaustive’ error.16 Results in the Spanish study by Escobar were very similar to the Catalan
results by G&E.
Context: picture showing(43) a.
elephant1 carries ballon1b.
elephant2 carries ballon2
elephant3 carries ballon3
elephant4 carries umbrella1

elephant1 carries balloon1
elephant2 carries balloon2
elephant3 carries balloon3
horse1extra balloon4

I believe that these results can be easily accommodated under my approach, since in(42), but not in (41) there is an ambiguity in how the indefinite can be interpreted. In (41), theindefinite is obligatorily specific and children make very few errors judging the truth-value of
this sentence regardless of the presence of extra individuals in the picture. In (42), on theother hand, one may interpret the indefinite object as either specific or non-specific depending
on how its domain restriction is construed. The ambiguous stimuli trigger a higher rate oferrors than the non-ambiguous ones.
This approach explains the errors not by appealing to children’s lack of certain semantic
knowledge, but by their full semantic competence, which leads them to recognize thepotential ambiguity and, presumably for reasons independent from their linguisticcompetence, handle the ambiguity resolution differently from adults.
There is independent evidence that Spanish children have full knowledge of the semantic
properties of indefinites, which comes from the study conducted by Miller and Schmitt(2003). The goal of their study was to see whether Spanish-speaking children are able to haveboth specific and non-specific interpretation of indefinites under negation. They studied
Chilean Spanish-speaking children’s responses to sentences containing indefinites, which areambiguous, as in (44), and bare singulars, which are obligatorily non-specific, as in (45):(44) El niño no se compró un perro.
The boy neg rfl bought a dog(neg > a; a > neg)

“The boy didn’t buy a dog.”(45) El niño no se compró perro.
The boy neg rfl bought dog(neg > a; *a > neg)

“The boy didn’t buy a dog.”
When children were asked to judge the truth-value of sentences like (44) and (45) in thesituation compatible only with the inverse scope (e.g. the protagonist bought a number ofdogs except one), there was a significant difference in the rate of ‘false’ judgments between
16

Their study included an addition type of context, analogous to the one that may give rise toperfectionist errors in English-speaking children. The rate of correct responses in this condition was
78%.

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A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)(44) and (45). While with respect to the unambiguous (45), the rate of ‘false-judgments’ wasas high as 76%, it was a low 36% with respect to the ambiguous (44). In comparison, adults’‘false-responses’ were 99% and 43% for the bare singular vs. indefinite respectively, thepattern the children essentially mirrored. It is plausible then that G&E’s children’s ‘spreading’responses were due to specific indefinite readings intruding into how they interpret (42) andcausing them to make the errors.
In short, the data reviewed in this section, as the results of the experiments presented in
the previous sections shed some light on the mechanism that creates ‘spreading’ errors. On
the one hand, they show that children have sophisticated semantic knowledge ofquantification (including the knowledge of very subtle properties as shown by their sensitivity
to a potential ambiguity due to scope interactions between the universal quantifier andindefinites and their differential treatment of the internal and external arguments in auniversally quantified sentence with respect to the property of Downward Entailing). On theother hand, we can see that children’s weakness (presumably lying outside of theirgrammatical competence and underlying their weak ability to compensate for insufficient
context), makes them prone to errors when the context provided is insufficient for dealing
with the complexity created by their sophisticated grammar.
3.4. Experiment 3
3.4.1. Goal, Participants, and Method
The experiments that report high rates of q-spreading typically present target sentences
paired with a picture showing participants and their schematic relationships with each other inthe event referred to in the target sentence (e.g. boys pulling wagons). Typically there is a
distribution of participants across sub-events, but a lack of exhaustive pairing between theagent- and theme-sets. Why such contexts result in a high rate of q-spreading errors has been
widely debated in the literature. I have proposed that “classic spreading” responses result
from children’s strategy of using asymmetry in the visual context as a pragmatic clue forselecting domain restrictions for the quantified phrases. If the picture contains a salient single
individual with the property denoted by the indefinite (i.e. a salient single wagon in case of asentence “no boy is pulling a wagon”), children are likely to see its salience as an indicationof its relevance for the speaker and construct the domain restriction for the indefinite toinclude exactly one individual (the extra wagon). Consequently, the sentence ‘no boy ispulling a wagon’ would receive “wide scope” indefinite interpretation, true in the situation
depicted in the scenario in which some boys are pulling wagons, but one salient wagon is not
being pulled. This predicts that errors similar to classic q-spreading can be elicited withsentences that instead of the universal quantifier contain another quantifier given that they arepresented under the typical “spreading” inducing conditions, e.g. visual context with a salient
single “extra” individual. Thus, in such contexts children should be able to judge sentenceswith the negative determiner true.

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Hypothesis:Children will accept as true sentences with the negative determiner and an indefinite incontexts that contain a salient single individual they can use as a value for a singletondomain restriction.
The error rate can be manipulated by controlling the degree of visual salience of theextra individual.

Participants: Our sample consisted of 19 preschool age children (3- and 4-year old)attending UConn Child Labs. After the training session, 3 of them were excluded after theyfailed the training, bringing the sample to the total of 16. Five adult control subjects have also
been interviewed.
Method: We used a version of the standard Truth Value Judgment Task. Children wereshown pictures and were asked to judge the truth-value of target sentences like those in (46)(47). The variable property across two of the experimental conditions I will present first was
the degree of visual salience of the extra individual in the object set - single extra object andnon-salient multiple extra objects. Each experimental condition consisted of 4
sentence/picture pairs presented in a fixed random order plus fillers. No linguistic context wasgiven (no background story) to replicate the contextual paucity that typically gives rise to qquantifier-spreading errors. Prior to presenting the target sentence, children were asked topoint out who was in the picture to ensure its full comprehension. After that, the puppet
uttered the test sentence, and the child was asked to judge whether the puppet’s description of
the picture was correct.
Materials: target sentences with a negative determiner presented in one of the following
contexts:(46) salient extra object: No boy is hugging a dog.

(47) non-salient (multiple) extra objects: No girl is holding a cat.

(48) controls: No boy is hugging a dog/ No boy is hugging a cat.

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3.4.2. Results
The children were divided into the following two groups:


The adult-like group, who correctly rejected all but the control sentences - 6 children(and all of the adult controls).

The ‘spreading’ group - 10 children, who judged as true at least three out of 4 items of atleast one type. For convenience, I will refer to these non-adult-like responses‘spreading’ responses

The results in the three conditions across all children are summarized in figure 2. As we
can see, the ‘salient extra object’ condition produced the highest rate of errors. Similar to‘classic spreading’ children, the children who gave “yes” responses often explained their
judgment by pointing to the extra individual in the picture and saying “not this one” or “hemeans this one”. The ‘yes’ responses were given even though the children had successfully
pointed out the multiple dog-hugging boys before the test sentence was presented.

3.4.3. Discussion
We can ask whether an adverbial theory of universal quantification, such the Event
Quantification (Philip 1995), can be extended to account for these errors. The answer seems
to be that we cannot, at least not without drastically modifying the lexical semantics of “no”.
If we simply adopt the event quantification semantics for sentences with the negative
determiner, we would get the semantic form like that in (49):(49) ∀e [a boy or a dog participate in e] [it’s not the case that boy hugs dog in e]“For every event in which a boy or dog (or both) is a participant, it is not the case that a
boy hugs a dog.”
The sentence construed this way would be falsified by any dog-hugging boy, which leaves the‘yes’ responses we elicited unexplained. The correct truth conditions can, however, becaptured by means of a contextually narrowed quantifier domain without altering the regular
adult semantics of the negative determiner. For those children who accepted the target-269-

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sentence, it is interpreted as containing an implicit domain restriction, something like the one
given in (50) with its meaning shown in (51):(50) No boy is hugging a fluffy white dog over here.
(51) ∀x [boy(x)  ¬∃y[dog(y) and y is in C and x is hugging y]]C={x: x is a fluffy white dog}
A conclusion that we can make is that the visual asymmetry is responsible for the negative
determiner errors, particularly when the asymmetric individual is highly salient. The visualcontext serves as a pragmatic clue, particularly when the experimental design offers nolinguistic context to supply that information. This asymmetry is interpreted as an indication of
the relative relevance of the individuals in the picture: the salient extra dog is perceived as themost relevant and included into the singleton domain restriction for the indefinite. This allows
for a yes-response, since there clearly is a dog such that no boy is hugging it.
3.5. Finding Values for the Domain Restriction Variables in Adults and Children
If children’s semantics of the negative determiners is adult-like, we can ask why adults
don’t make the same type of errors. The answer has to do with the observation that for adults,
the sentence “no boy is hugging a dog” uttered in the context of the picture with boys anddogs is most readily understood as talking about all of the individuals in the picture. As wasobserved by Kratzer (2004) in her discussion on covert domain restrictions in adult grammar,
the utterance in (52) is most readily understood as talking about everybody in the room where
the sentence is uttered. It would be judged false if only a subset of the people present in theroom is smiling, even if there is a highly salient feature distinguishing the group of smilers(e.g. everyone who is smiling is wearing a red hat). Likewise, (53) would be judged false if
there are any smilers in the room, even if the non-smilers share a highly salient feature.
(52) EverybodyC is smiling.
(53) NobodyC is smiling.
These examples show that for adults, properties of individuals, even very salient ones,
are not readily picked up as values for domain restriction variables. This is, however, exactly
what I claimed occurred with children in experiment 3. The contrast between adults andchildren becomes less drastic if we consider the following observation: the difficulty ofpicking up sub-properties as values for covert domain restrictions holds true only in an out-of
the-blue context. Thus, if one utters ‘every boy is smiling’, and points at a picture, the listener
would obligatorily interpret ‘every’ as ranging over all of the boys in the picture, and not any
subset thereof, regardless of any visually distinctive features some of them may share.
However, such narrowing is possible in natural discourse. Let’s imagine the example given in(54) uttered in the following situation:-270-

A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)(54) Situation: department meeting where both students and faculty are present. The head ofthe department announces that according to the new regulations, the students who missgenerals’ deadlines will no longer receive department funding.
(55) A person present in the room: Now everybody is worried.
There is the intuition that the sentence may be judged true even if only the students
present at the meeting are worried. From this, we see that in a natural discourse, there arecontextual clues when domain restrictions are narrowed. Without overt clues, adults assume
that the maximal set of individuals present in the situation has to fill the value for the domain
restrictions. Children, on the other hand, do not always obey this strategy and may adjust
domain restrictions without overt linguistic context. This may be, as I stipulated earlier, due totheir over-interpreting the visual information as pragmatic clues that can be read by theinterlocutors. One additional piece of evidence that this unexpected domain narrowing occurs
comes from the so-called under-exhaustive errors, another type of errors usually included
under the umbrella term of quantifier spreading. The error is illustrated in (56):(56) Experimenter: Is every boy riding a bike?
Child: Yes.

While it is difficult to explain this type of response under the Event Quantification theory, it
can be straightforwardly analyzed as the child’s having narrowed the domain for ‘every’ toinclude only the boys deemed relevant, something an adult would do only if the context
contained explicit clues for such narrowing.
I have found additional evidence of under-exhaustive errors in children that clearlysuggest that children’s domain restrictions are more flexible than those of adults. In an
experiment reported in Rakhlin 2007, when children were shown pictures like those in (57)
and asked to judge the truth of the sentence below, most accepted it as true:(57) Puppet: One jaguar is reading a book, but every jaguar is playing baseball.
Child: True (78% in the 15 preschool and kindergarten aged children tested).

In contrast, their responses to the following controls were nearly 100% corect. The differenceis that for ‘both’, the size of the quantifier domain restriction is fixed by lexical semantics,
and “both” requires it to consist of exactly two individuals:-271-

Nanzan Linguistics: Special Issue 3, Vol. 1(58) Puppet: One cat is eating, but both cats are sleeping.
Child: No, only one is sleeping.

In contrast, adults responded to (57) with ‘squeamishness’ equal to that with which they
responded to (58), judging both as contradictions. This suggests that a major difference
between adults and children likely responsible for “q-spreading”, is not in the formal
semantics of quantification, but in the freedom children have when making assumptions aboutnarrowing domain restrictions in situations of contextual paucity.
3.5.1. Experiment 3, Part II: the Extra Subject Condition
In addition to the general ‘flexibility’ of quantifier domains, there was another non-adultlike property I have uncovered in experiment 3, namely in the ‘extra subject’ condition.
In this condition, the target sentences had the same structure as in the two conditions
discussed above, but the pictures contained an extra individual of the same sort as the agent,illustrated in (59)-(60):(59) Puppet: No boy is hugging a dog.
Child: Yes (points to the extra boy)(60)

In our sample, this type of response was given at the rate of 26.56 %, lower than in the‘extra dog’ (salient extra object) condition, but higher than in the non-salient extra object
condition (a picture with multiple extra dogs). Here again, the non-adult-like children seem tonarrow the domain, but in this case it is the domain of the negative determiner that isnarrowed to include a single boy, an option normally rejected by adults. This suggests another
difference between adults and children: children allow singleton domain restrictions for thosequantifiers that disallow them in adult gramamar. Thus, for adults, sentences with thenegative determiner denote empty intersections, in our example between a set of boys and aset of dog-huggers, and require the set of boys to be non-singleton. The sentence is odd in asituation in which there is only one boy as a denial that the one contextually present boy
hugged a dog (it is acceptable if understood as ‘non-specific’, denying that any boy huged adog). Children do not seem to have this ‘anti-uniqueness’ requirement.

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There is independent evidence that children do not obey the ‘anti-uniqueness’ foranother quantifier that requires it for adults, namely the universal quantifier ‘every’. In the
study by Yatsushiro and Sauerland (2004), children were shown to allow singleton domain
restrictions for “every”, an option disallowed by adults. In their study, Y&S investigatedchildren’s knowledge of the presuppositions of ‘every’ – the existence and the anti-uniqunesspresuppositions. The former requires the context for a universally-quantified sentence tocontain a non-null set of individuals of the sort denoted by the common noun of theuniversally quantified NP. The latter requires this set not to have the cardinality of one. These
properties of the universal quantifier are illustrated in the following example. Both (62) and(63) are true in the context of (61), but each violates one of its presuppositions:(61) Context: a boy named Johnny, his parents, his one red-headed sister, two brothers, no
grandparents.
(62) Johnny: Every grandma of mine is wearing red pants. (existence presupposition isviolated).
(63) Johnny: Every sister of mine has red hair. (anti-uniqueness presupposition is violated).
Y&S found that while children had a high rate of correct responses with (62) - 72%
correct, with (63) there was only a low 32% of correct responses. The explanation offered by
Y&S was based on Heim’s theory of presuppositions. It holds that some presuppositions are
inherent in the lexical semantics of the expressions, while others are implicated. The two
types of presuppositions follow separate acquisition paths, with the implicatedpresuppositions acquired later than the semantic presupposition. Thus, the existence
presupposition, which children know, is lexically encoded for “every”, while the antiuniqueness is derived as an implicature via Heim’s principle “Maximize Presupposition”(Heim 1991). It states that if there are logically equivalent expressions that differ only withrespect to their presuppositions, the one with the strongest presuppositions that are satisfiedmust be used. Consequently, using the expression with a weaker presupposition entails thatthe stronger presuppositions are not satisfied. According to this, the anti-uniqueness of“every” (and ”no”) arises as an implicature because a potentially more informative alternative(“the”) is not used. Children do not reliably calculate implicatures and hence lack the antiuniqueness requirement for “every” and “no.”4. Conclusion
The ‘big question’ behind the experiments reported here was the question of how thegenerative theory should deal with the well-documented inconsistencies between childlanguage and the properties of the adult grammar. One approach to this question attributes the
pre-adult characteristics of child language to the neurological maturation in certain
grammatical mechanisms. A competing approach seeks to handle linguistic development
within the Strong Continuity assumption (Pinker 1984) by accommodating any
inconsistencies between the hypothesized grammar and the target grammar as incorrect (or-273-Nanzan Linguistics: Special Issue 3, Vol. 1

incomplete) parameter setting without positing any ad hoc stages or arbitrary changes in the
linguistic development. Within this approach, any remaining discontinuity is handled byattributing it to performance factors, such as children’s pragmatic or processing inflexibility,
which may obscure the full extent of their adult-like grammatical competence.
The phenomenon of child language that I have focused on here, the so-called “qspreading,” has been seen as evidence of discontinuity – representing a stage at whichchildren possess certain grammatical mechanisms that are not found in the adult grammar,
and which the child eventually ‘grows out of’. The responses elicited from children seemed toindicate that children imposed on the universally quantified sentences the truth conditions that
require their semantic structure to include non-UG elements, such as restrictors formed by aconjunction of NPs in which only one forms a syntactic constituent with the quantifier (oreven by the elements that are not mentioned in the sentence at all in case of the so-called
perfectionist children).
However, there is strong evidence that the seemingly odd truth conditions arise under
predictable conditions and can be manipulated by the experimental technique. A sharp
decrease of errors can be produced by various types of manipulations. Yet, one generalization
seems to hold across all experiments: children’s performance with respect to q-spreading isfacilitated by providing a richer context (either linguistic or visual). As I have argued, the roleof the enriched context is that it supplies clues about the intended value for domain
restrictions of quantifiers, or, in other words, provides information as to what contextual
elements are relevant. According to my proposal, the source of children’s difficulty and thecognitive module in which development takes place is not their semantic competence, but thearea in which meaning and context intersect. As I discussed in section 2, the meaning ofquantified sentences is partially determined by context, and the child, who has full semantic
knowledge of universal quantification and scope ambiguities, gets into trouble when asked tointerpret such sentences without sufficient context.
To summarize my main conclusions, I have argued that children are adult-like in:i. formal semantics of quantification;ii. allowing all and only those quantifier scope relations that are permitted in
adult grammar;iii. knowing that quantifier domain restrictions are contextually determined;
I have also argued that children are different from adults in:a)judging what is relevant to others under sub-optimal pragmatic conditions;b)allowing the covert domain restriction variables to pick up their values from a salientfeature of a subset of the given individuals, even if the context is too poor for suchdomain narrowing for adults;-274-

A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)c)

not recognizing ‘implicated presuppositions’, such as the anti-uniqueness of ‘every’ and‘no’;

I would like to put forward the hypothesis that children show the behaviors enumerated
in the second list due to their developing ‘mind-reading’ abilities, i.e. their weak ability torepresent the content of other minds in a given situation. More specifically, the relevant
property is children’s insufficient ability to negotiate the relationship between the information
discernable by other interlocutors in a given context and each speaker’s (including self’s)
contribution to the discourse.
That there may be a connection between pragmatic tasks in general and ToM is not
surprising. Understood broadly, pragmatics deals with those areas of interpreting an utterance
that involve aspects of meaning beyond the truth conditions, namely various ways of using
context for reconstructing the speaker’s meaning (i.e. the proposition that the speakerintended to convey with both explicit and implicit information). Consider the following
examples of this (from Wilson 2005):(64) Peter left the party. (political group or festive gathering)(65) The teachers told the students they (the teachers or the students) needed more time tofinish the task.
(66) I saw no one in town. (no one I knew or no one interesting)(67) Some of the talks were interesting (not all of them)
In order to decide what proposition the speaker intended to convey, the listener may haveto lexically disambiguate (as in 64), establish co-reference (as in 65), fix quantifier domains(as in 66), or understand intended implications (as in 67) to list just a few examples ofpragmatic tasks involved in sentence interpretation. Other examples of this involverecognizing context- based conditions on the felicitous use of an expression (presupposition
accommodation) and discerning the speaker’s communicative intentions for recognizing
flouting implicatures. All these tasks require the hearer to have a sophisticated ability toreason about the content of other minds. This connection between pragmatics and ‘mindreading’ goes back to Grice (Grice 1957, 1967, 1969, 1989). Thus, his ‘working out schema’for deriving conversational implicatures involves making a series of conjectures about the
speaker’s desire/belief psychology. Following this schema, in order for speaker A to infer the
implicated meaning of B’s utterance, A has to go through a very complex reasoning process
involving a sophisticated ability to “read” other minds given in (68):(68) A: Is Sally coming to the meeting?
B: Her car broke down. ⇒ Sally is not coming at the meeting.

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Nanzan Linguistics: Special Issue 3, Vol. 1(69) He said that P; he could not have done it unless he thought that P; he knows (and knowsthat I know that he knows) that I will realize that it is necessary to suppose that Q; hehas done nothing to stop me from thinking that Q; so he intends me to think, or is atleast willing for me to think, that Q. (Grice 1989: 30-31)
There is a wealth of independent evidence that children undergo development withrespect to their ‘mind reading’ abilities. It is fair to say that some questions within the field of
the Theory of Mind development have not been settled, including precisely what set of
abilities constitutes this cognitive module or whether it is a module in the Fodorian sense orrather something that Fodor considered a “central inferential cognitive system” (Fodor 1992).
However, it is widely accepted that there is a developmental schedule according to which
various pieces of ToM come on line, including evidence that children’s ability to makeaccurate inferences about epistemic effects of particular situations on others does not become
adult-like until at least the age of 8. Thus, Taylor (1988) demonstrated that children until thisage exaggerate how much information can be inferred about a mostly obscured picture by anaive observer. In her experiment, children readily assumed that the puppet looking at amostly covered up picture of an animal would know what animal was in the picture, evenwhen only a small unrecognizable detail of the animal was left uncovered for the puppet tosee.
In another experiment, Ruffman’s (1996) ‘two colors’ task, the child and a puppet areboth shown two dishes each filled with a different color candy – one with red and one withgreen. The puppet is told that one candy (without specifying which color) will be taken andplaced in the box. The puppet then leaves, and the child observes the experimenter take one of
the red candies and put in a box. The puppet returns and the child has to answer a series ofquestions, including “what color does the puppet think is in the box”. Ruffman reports that alarge majority of children between the ages of 5 and 8 incorrectly answered ‘green’, i.e.
instead of realizing that the puppet was merely agnostic, they ascribed it false belief. This lineof research shows that when asked to judge how much a third person knows from observing
certain evidence, children often over-attribute as well under-attribute knowledge (cf. also
Wimmer, Hogrefe, and Perner 1988, Wimmer, Hogrefe and Sodian 1988, etc.). If thisweakness generalizes from visual information to communicative situations in general, thiswould predict that children are not be able to cope well with the types of tasks illustrated in(64) through (67).
For instance, working out conversational implicatures relies not just on the speaker’s
ability to know that the listener will be able to compute the implicated meaning in a given
situation, but on the listener’s ability to infer that the speaker knows that the listener would
know that he knows that the implicated meaning can be computed. Certain aspects ofmeaning of sentences in context are derived by the listener from considering a set ofalternative options the speakers had for expressing his intentions. For instance, scalar
implicatures rely on the hearer considering possible alternatives, and assessing whichalternative entails another and is thus more informative. Then, given the assumption thatspeakers would be maximally informative (or that the context is such that being maximally-276-

A New Pragmatic Account of Quantifier Spreading (N. Rakhlin)

informative is required), the hearer would infer that the speaker has avoided the more
informative option because his intention is to express an implicated meaning – negating thealternative that wasn’t used.
It is not surprising then that children have been shown to fail in computing scalar
implicatures (e.g. Noveck 2001, Gedalyovich 2002). These results coexist with the findingsthat show that with improved experimental design, e.g. making the speaker’s communicative
intention to be maximally informative explicit, children are able to compute scalar
implicatures (Papafragou and Tantalou 2005).
Children were also shown to use presuppostional expressions (e.g. definite determiners)
in contexts in which their presupposition was not satisfied and couldn’t be accommodated by
the listener (Maratsos 1976, Karmiloff-Smith 1979). However, there is also evidence fromcomprehension tasks that children’s semantics of definites is presuppositional (Maratsos
1976, Syrett, Kennedy, and Lidz 2007) and that the problem in production tasks is in their
misjudging how much the listener can infer in a given situation in order to accommodate thepresupposition rather than in failing to recognize that definites require a certain context inorder to be interpreted. Thus, young children may use a definite NP in a context in which
there is more than one object of the sort denoted by the NP. This is because they fail to realizethat what they perceive as unique (e.g. a red car in an array containing black, brown and whitecars), would not be perceived as unique by the listener unless the domain restriction is madeexplicit.
Now let’s return to the cases of classic q-spreading and see whether we can draw aconnection between these responses and reasoning about the content of other minds. I haveproposed that verifying sentences like (70) involves making judgments about how the domainof the indefinite should be restricted since the meaning of the sentence relies on whether the“plural” or the “singleton” indefinite is chosen. If the singleton option is chosen, then (70)receives the ‘wide scope’ indefinite interpretation and would be false in the context of (71).
(70) Speaker: Every boy is pulling a wagon.
(71)(72) Listener: Does he mean all of these?

or just this one

Presumably, both adults and children go through this type of reasoning, but adults
quickly abandon the singleton option for object indefinites unless there is overt context-277-

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requiring them to choose it.17 Many children, on the other hand, are almost equally likely to
go with either option, particularly when the single extra item in the picture is highly
perceptually salient, and hence they produce both adult-like ‘yes’- and “q-spreading” ‘no’responses (at the rate of 44% and 56% respectively in Philip 1995).
I suggest that what causes the difference between adults and children is having to use a‘working out schema’ that requires one to consider the content of other minds, somethingalong the following lines:(73) The speaker could mean the multiple X’s or the single X for the domain restriction of
the indefinite. Since the singleton X is more marked, if she means the single X, she has
to assume that I know that she means the single X. However, she has no reason toassume that I would know that she means the single X since there have not been any
overt clues given to me to inform me that she means the single X. Therefore, she mustmean the multiple X’s.
If we are correct in claiming that such type of reasoning is involved in making thisdecision, it is entirely plausible to suppose that q-spreading would disappear as children fully
develop their ToM. Until that happens, they are unable to complete the inference in (73) andresort to guessing (or perhaps some other pragmatic strategy, such as using visual prominenceof the objects in the picture as their guide).
Further research is necessary in order to demonstrate more directly the ToM/ Qspreading connection. Perhaps, the Taylor-task (judging whether a partially obscured picture
can be reconstructed by another observer) can be a good non-verbal predictor of a child’s
success with universal quantifiers.
If this conclusion about the ToM and children’s pragmatic competence is correct, thismeans that we do not only have strong empirical reasons to adopt a pragmatic account of qspreading that I have developed here, but we have a good theoretical justification for favoringsuch an account. It allows us to maintain the Strong Continuity Assumption, which provides astrong explanatory force to the acquisition theory. It also provides an explanation for ‘why
pragmatics should be different’.

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17

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