CHAPTER 15
QUANTIFIER SPREADING
IT is well-established that young children have difficulties restricting the scope of a universal quantifier (e.g. all, each, or every) to a specific noun phrase. To cite a famous example (Philip, 1995), children often reject the sentence Every farmer is feeding a donkey as a description of a scene depicting a mismatch between the number of farmers and donkeys (see Figure 15.1), presumably on account of the extra donkey. The associated comprehension error is commonly referred to as quantifier spreading, which implies that the scope of the universal quantifier has spread beyond the noun it modifies.
This chapter reviews the literature on quantifier spreading errors and related issues involving comprehension of universal quantification, defined as ‘a complete binding exercised over all members of a set which falls within its scope’ (Freeman, 1985: 240). We first summarize the seminal work of Inhelder & Piaget (1958, 1964a) who first described young children’s errors with universal quantification in relation to the development of logical reasoning (i.e. children’s grasp of class inclusion relations). We then describe early work on quantifier spreading that utilized the truth-value judgement task (Donaldson & Lloyd, 1974; Freeman, 1985), a methodology that would remain popular in studies of quantifier spreading in subsequent decades, complemented by work utilizing picture-choice and act-out tasks. The next section describes early work on deductive reasoning, which tested children on categorical syllogisms and identified conversion errors as a related phenomenon (Bucci, 1978; Johnson-Laird et al., 1986). Following this introduction, we summarize accounts of quantifier spreading that explained errors in terms of structure-neutral representations (Bucci, 1978), incomplete mastery of the mappings between linguistic cues and semantic representations (Brooks & Braine, 1996), quantification over events (Philip, 1995), ‘floating’ quantifiers (Roeper et al., 2004), and shallow processing of syntactic structure (Brooks & Sekerina, 2005/6). We include in our review studies that extended the phenomenon of quantifier spreading to adults (Berent et al., 2009; Street & Dąbrowska, 2010), suggesting that individual differences in language background and educational attainment are predictive of error rates.
The accounts attributing errors to syntactic processing are contrasted with the full competence hypothesis that children have adult-like knowledge of universal quantifiers (Crain et al., 1996). Under this view and related pragmatic accounts of quantifier spreading, children make errors due to the demand characteristics of the truth-value judgement task. We conclude by discussing efforts to identify signature patterns of attention associated with quantifier spreading errors using eye-tracking methodology (e.g. Minai et al., 2012; Sekerina & Sauermann, 2015) and future directions.
FIGURE 15.1. Every farmer is feeding a donkey (Philip, 1995)
15.1 INITIAL DESCRIPTIONS OF ERRORS WITH UNIVERSAL QUANTIFIERS
Inhelder & Piaget (1958, 1964a) noted errors in children’s comprehension of the universal quantifier all in the context of the class inclusion task—an assessment of children’s ability to classify objects on the basis of common features as well as their understanding that sets of objects may be subsets of larger classes; see also Skordos & Barner (Chapter 2 in this volume). In a typical class inclusion task, the child might be shown a set of counters comprising, for example, five blue round discs, two blue squares, and two red squares. When asked Are all the circles blue? young children would typically answer ‘no’ while pointing out the blue or red squares. As an explanation of their misinterpretation of the question, Inhelder & Piaget (1964a: 70) suggested that
It looks as if the child’s thinking is conditioned by a need of symmetry: the extension of the predicate blue must be the same as that of the subject round. <…> What our subjects are doing is to assimilate the expression All As are B to the expression All Bs are A. [Our subjects] substitute equivalence (A = B) for class inclusion (A>B or B>A).
In other words, children interpret All the circles are blue as implying also that All the blue ones are circles. Although Inhelder & Piaget never used the term quantifier spreading, it appears that the concept they described is essentially the same phenomenon, as exemplified in their statement ‘It therefore looks very much as if the true explanation is that at stage II children extend the quantifier all to the logical predicate of the sentence as well as to its logical subject’ (1964a: 70–1). Inhelder & Piaget (1958, 1964a) suggested that young ‘preoperational’ children do not have an understanding of universal quantification until the age of 7 or 8, when concrete operational reasoning emerges. At younger ages, children rely on spatial relations and physical arrangements when dividing objects into sets.
Not long after Inhelder & Piaget (1958, 1964a) first described children’s errors in restricting the scope of the universal quantifier all, other researchers launched studies to delineate the phenomenon. These early studies used variants of the Piagetian truth-value judgement task in which children answered a yes/no question about a situation. In the modified tasks, children were instructed to reward (or punish) a puppet for making true (or false) statements about the situation. (Other variants used in later work on quantifier spreading involved sentence-picture verification, with participants asked to compare a sentence with a picture to determine whether they match.) The truth-value judgement task is thought to assess what the participant understands about the situation (or picture) and its relationship to the sentence that describes it, without requiring metalinguistic awareness about the structure of the sentence (Clark & Chase, 1972; Gordon, 1996).
Donaldson & Lloyd (1974) introduced the truth-value judgement task as a methodology for exploring children’s comprehension of the universal quantifiers all and each. Fourteen preschool children (3- to 5-year-olds) were shown an array of four garages and a set of either three or five cars, with the cars arranged in partial one-to-one correspondence with the garages. The children were instructed to tell the toy panda whether he was right (by pressing a bell) or wrong (by pressing a buzzer) after the panda produced a statement as a description of the scene. When there were four garages and three cars, children tended to evaluate the statement All the cars are in the garages as wrong, often justifying their answer by noting the emptiness of the fourth garage. Similarly, where they saw four garages and five cars, they rejected The garages have all got cars in them—stating, for example, ‘Cos not all in them. That police car’s out’ (1974: 79). Notably, although all children made errors on the task, Donaldson & Lloyd (1974) emphasized that the pattern of errors varied across children, with some children’s responses suggesting an insistence on one-to-one correspondence between cars and garages and other children’s responses seeming more random. A decade later, Freeman (1985) would distinguish two different error types, attributing the errors to overexhaustive and underexhaustive search, respectively, although only the former error was described in Donaldson & Lloyd (1974). These terms continue to be used in literature to the present day, with overexhaustive search recognized as the classic quantifier spreading error, involving failure to restrict the scope of the universal quantifier to its subject (e.g. incorrectly rejecting the statement All the cars are in the garages as a description of a scene with an extra garage). Underexhaustive search resulted in a much less common error, involving failure to extend the search for referents within the scope of the universal quantifier beyond the subset in one-to-one correspondence (e.g. incorrectly accepting the statement All the cars are in the garages as a description of a scene with an extra car).
In a second study contrasting two sets of cars and garages (Donaldson & McGarrigle, 1974), forty 3- to 5-year-olds made yes/no judgements about whether one set had more cars than the other, and whether one set had all of the cars. In this study, the cars were arranged on two shelves, one under another, with five cars on one shelf and four cars on the other. Children were first asked whether one of the shelves had more cars on it than the other—a question that the majority could answer quickly and accurately. After that, the row of four cars was enclosed by a row of four garages (i.e. with one car per garage), and the row of five cars was enclosed by a row of six garages (i.e. with one empty garage). When the same question was repeated, about a third of the children changed their answer, indicating that the shelf with four cars (in garages) had more cars on it than the shelf with five cars (and an extra garage). Similarly, when the garages were present and the children were asked Are all of the cars on this shelf? they often agreed that the smaller set (four cars in garages) had all the cars while denying it for the larger set (five cars in garages, with an empty garage). In summarizing the results across studies, Donaldson (1978) emphasized that the salience of the empty garage influenced children’s decisions: ‘The statement which they actually judged, irrespective of the variations in linguistic form, was All the garages are full’ (1978: 65).
As a direct test of the hypothesis that children’s errors were due to the salience of the empty garage, Freeman (1985) modified the design of Donaldson & Lloyd (1974) by positioning a boat in the last (empty) garage, with the boat condition compared with the original empty-garage condition in a between-subjects design. Having a boat in one of the garages was predicted to inhibit overexhaustive errors in response to the question Are all the cars in garages? when there were three cars in four garages. Likewise, when there were five cars and four garages, having a boat in one of the garages was expected to inhibit underexhaustive errors in response to the question Are all the cars in garages? by providing a clue that ‘the set of garages is not be taken as a sure guide to the number of cars to be considered’ (1985: 243). In addition to manipulating the presence/absence of a boat in the fourth garage, Freeman (1985) also examined whether provision of background information would eliminate errors. Half of the children were explicitly told that not all of the garages would be used for housing cars (i.e. not everybody has got a car); this background information was expected to reduce children’s tendency to make overexhaustive errors by giving them an explanation for the empty garage (i.e. there is no car that ought to be there). Four groups of twenty-two children (5- to 6-year-olds) were tested, with the hypothesis that when both extra variables were applied (i.e. boat present in garage, background information provided), children would respond to the questions with higher levels of accuracy. (Note that for each set of cars and garages, children were asked two questions Are all the cars in the garages? and Have all the garages got cars in?) The experiment produced two major findings: first, the background information was irrelevant to children’s responses, implying that, in line with Inhelder & Piaget (1964a), the physical arrangement of the cars and garages was more salient to the children than the verbal information. Second, although the presence of the boat reduced errors (29.5% of children in the boat condition made no errors in comparison to only 2.3% in the empty-garage condition), the fact that the majority of children in the boat condition still made overexhaustive and/or underexhaustive errors indicated that the salience of the empty garage was only one of several factors contributing to task difficulty.
Freeman & Stedmon (1986) built on these findings by considering further how the presence of a salient boundary influences children’s response patterns. In line with earlier work by Karmiloff-Smith (1979), they elicited underexhaustive errors by splitting the garages into two sets (i.e. two distinct ‘parking lots’). Children often ignored the cars in the more distant lot when asked if all the cars are in a garage, yet when asked to collect all the cars, they readily took the cars from both locations—indicating their grasp of the universal extension of all. Hence, children’s errors in comprehending all were only evident when tasked with judging the alignment of the two sets (cars and garages). Freeman & Stedmon (1986: 33) concluded that ‘children are simply so eager to find a boundary which the word “all” cues them for, that they stop as soon as they reach any marked boundary since that does indeed fulfill the condition of search-up-to-a-boundary.’ In other experiments, Freeman & Stedmon observed error rates that varied as a function of the specific universal quantifier used (every, all, absolutely all, or every single), highlighting the importance of examining semantic distinctions among universal quantifiers in relation to quantifier spreading—a topic addressed in work by Brooks & Braine (1996) and described later in this chapter.
15.2 LOGICAL ERRORS IN SYLLOGISTIC REASONING
Universal quantifiers play a critical role in deductive reasoning (i.e. predicate logic) due to the rich set of inferences they license (Braine & O’Brien, 1998). Hence, research on the development of logical reasoning has centred on children’s acquisition of logical vocabulary (e.g. universal and existential quantifiers, such as all and some; logical connectives, such as if, and, or, not) and children’s ability to use these terms to draw deductive, category-based inferences from sets of premises (Braine & Rumain, 1983). Early studies of syllogistic reasoning identified conversion errors in which a premise, for example All As are Bs, appeared to be interpreted as equivalent to its converse, All Bs are As (Chapman & Chapman, 1959). For example, when adults were given categorical syllogisms of the form shown in (1), conversion of the second premise to All Bs are Cs often resulted in acceptance of the erroneous conclusion All As are Cs.
(1) All As are Bs.
All Cs are Bs.
Newstead et al. (1985) investigated when the adult pattern of responding to syllogistic set-inclusion relations emerged in development. They presented the passage shown in (2) to a total of 288 children, ranging in age from 6 to 16 years:
Children were then asked a series of questions that included valid inferences (e.g. Were all of the round candies large? Correct answer: yes) as well as their converse (e.g. Were all of the large candies round? Correct answer: can’t tell). From the age of 6 years, children’s responses matched the pattern observed with adults in previous research. When the inference was valid, accuracy was highest if the relevant information straddled adjacent premises (e.g. All the round candies are large), and declined when the relevant premises were non-adjacent (e.g. All the round candies are hard). Conversely, if the inference was invalid, performance was lowest when relevant information was contained in adjacent premises (e.g. All the large candies are round), presumably due to higher probability of making conversion errors. Newstead and colleagues concluded that children as well as adults interpret these syllogistic forms as involving transitive and convertible similarity relations; that is, if All As are Bs and All Bs are Cs, then All As are Cs and All Cs are As.
Other research focusing on developmental changes in deductive reasoning examined the role of problem content in constraining children’s ability to follow logical rules. In an early study, Bucci (1978) tested thirty-two children in each of two age groups (6- to 8-year-olds; 11- to 12-year-olds) as well as adults on various syllogistic forms; see Table 15.1 for examples of problem types. Children at both ages demonstrated high accuracy on Modus ponens and Modus tollens, but showed significantly lower accuracy on syllogistic forms requiring a ‘not sure’ response. For the latter problem types, children were much more accurate on problems where they could rely on broad-based factual knowledge than on problems with abstract content (see ‘block’ problems in Table 15.1), which suggests that they prioritized real-world knowledge (e.g. their ability to think of other animals with whiskers besides cats) over logical form when making inferences.
Hawkins et al. (1984) also found young children’s syllogistic reasoning to be influenced by the relationship between problem content and their real-world knowledge. In this study, forty young children (4- to 5-year-olds) were presented with a variety of syllogistic problems, a third of which had incongruent content that violated real-world knowledge, as in example (3).
(3) Birds can fly.
Everything than can fly has wheels.
Do birds have wheels?
Children provided very few correct responses to the problems with incongruent content (averaging only 12.5% correct), and often justified their erroneous responses by referring to their existing knowledge, as in ‘No, birds have wings!’ In contrast, their performance approached ceiling (93.8% correct) on problems with congruent content that matched their real-world expectations. The children also showed considerable success in drawing inferences from problems with fantasy content (e.g. Every banga is purple. Purple animals always sneeze at people. Do bangas sneeze at people?), averaging 72.5 per cent correct overall, with their performance approaching ceiling (93.8%) when the fantasy problems were presented first (i.e. prior to the problems with incongruent content). The authors concluded that under some circumstances preschool-age children could draw deductive inferences from the logical form of premises; however, pragmatic forms of reasoning relying on pre-existing knowledge were more pervasive.
Johnson-Laird et al. (1986) went further to fully reject the notion that children were using formal sets of logical rules to perform syllogistic reasoning. They offered the alternative proposal that children, as well as adults, were constructing mental models of the information provided in the premises, drawing information from these mental representations to construct hypotheses, and scanning the models for alternatives prior to drawing their conclusions. Under this view, the development of deductive reasoning reflected children’s growing skills in constructing and manipulating mental models of problem content. Across two experiments, they presented children ranging in age from 9 to 12 years with syllogisms comprising all of the possible pairs of premises involving the terms all, some, and none (where only twenty-seven of these sixty-four pairs generate valid conclusions). The children were given problems with sensible content (e.g. Some of the footballers are musicians. All of the footballers are runners.) and instructed to state what followed from the premises with the assistance of cards that summarized the possibilities (including no valid conclusion). The authors found problem difficulty to be related to the complexity of creating mental models of each premise as well as the number of distinct models that had to be considered when searching for counterexamples to tentative conclusions. They identified a specific problem type associated with conversion errors, shown in (4), for which children often drew the erroneous conclusion All A are C.
(4) All B are A.
All B are C.
In this and other presumed cases of conversion of a premise to its converse (e.g. All B are A is taken to imply All A are B), Johnson-Laird and colleagues argued that the errors were due to the difficulties of aligning the mental models constructed for each premise. Their account challenged the view that children applied a general rule or logical operation that converted all premises of the form All A are B to entail their converses.
15.3 STRUCTURE-NEUTRAL REPRESENTATIONS OF SENTENCES WITH UNIVERSAL QUANTIFICATION
In addition to testing children’s ability to solve logical syllogisms, Bucci (1978) introduced an act-out task in combination with probe questions to assess children’s grasp of universal quantification. Children (thirty-seven at ages 6 to 8 years; thirty-eight at ages 11 to 12 years) and adults were asked to assemble buildings using multi-coloured blocks, with varied instructions as illustrated in (5):
(5) Make a building where all the yellow blocks are square.
Make a building where all the square blocks are yellow.
After participants completed each building, they were asked questions in relation to different blocks (e.g. blue squares, blue rectangles), such as Could we use any of these in a building in which all the yellow blocks are square? The majority of children in both age groups gave responses that suggested they had adopted a structure-neutral interpretation of the instructions: that is, one in which they failed to make a distinction between the subject and the predicate of the sentence. In other words, it appeared as if they encoded sentences as a string of words without hierarchical relationships; for example, All the yellow blocks are square was encoded as ‘all, yellow, square’. When constructing the buildings, children used only the blocks with both properties (e.g. yellow and square) and often expressed frustration that they were limited to using just a few blocks, as in ‘Why do you keep telling me to make these stupid little buildings?’ (Bucci, 1978: 63). When responding to the probe questions, they rejected blocks that were square but not yellow (e.g. blue squares) as well as blocks that were neither yellow nor square (e.g. blue rectangles). (Note that Inhelder & Piaget (1964a) reported both of these error types on class inclusion problems, for example, with some children justifying their answers to the question Are all the circles blue? by referring to objects that were neither circles nor blue, as in ‘No, there are red squares’.) Bucci (1978) suggested that the lack of information provided by the structure-neutral representation would lead children to rely on the discourse context, real-world knowledge, or guessing, in order to answer the questions. She referred to this strategy as a pragmatic mode of processing that reflected children’s lack of expertise in using linguistic cues to delimit the scope of the universal quantifier.
15.4 DISTINGUISHING THE MEANINGS OF ALL AND EACH
Starting from the hypothesis that children’s errors might reflect a lack of knowledge of the linguistic cues to universal quantification, Brooks & Braine (1996) extended the line of research by focusing on children’s acquisition of the lexical semantics of the universal quantifiers all and each. Building on the work of Vendler (1967) and Ioup (1975), they explored linguistic factors that might influence whether children would assign collective or distributive interpretations to sentences containing universal quantifiers. One hundred children, ranging in age from 4 to 9 years, were asked to choose between a collective picture depicting three people acting together in relation to a single object and a distributive picture depicting three people acting individually on three different objects (bears in the example shown): see Figure 15.2.
FIGURE 15.2. Examples of collective (left) and distributive (right) pictures, adapted from Brooks & Braine (1996: Experiment 2)
Children were instructed to point to the picture that went best with a sentence spoken aloud, with the sentences varying over trials in terms of the universal quantifier (all vs. each) and the sentence structure (active vs. passive voice), as illustrated in (6). Note that different sets of pictures were used for each trial, with materials counterbalanced across sentence structures.
(6) All of the men are washing a bear.
A bear is being washed by all of the men.
Each man is washing a bear.
A bear is being washed by each man.
From the age of 5 years, children’s picture choices varied as a function of both the universal quantifier (with more collective pictures selected when the quantifier was all) and the sentence structure (with more collective pictures selected when the sentence was in the passive voice), with response patterns becoming more stable with age. The authors interpreted the findings as suggesting that children acquire sets of linguistic cues that jointly determine sentence meaning, with sensitivity to these cues emerging by 5 years of age.
A subsequent picture-choice experiment focused on quantifier spreading. Sixty children (ages 5 to 9 years) were presented with sets of collective and distributive pictures depicting extra, unattended objects (bears in the example shown) along with a third ‘exhaustive’ picture that showed a set of three people acting on five objects: see Figure 15.3. Brooks & Braine (1996) hypothesized that children who adopted a structure-neutral representation of the sentence All of the men are washing a bear (or Each man is washing a bear) would opt for the exhaustive picture over a collective or distributive picture with extra objects. Contrary to the structure-neutral hypothesis, children from the age of 5 years distinguished the meanings of all and each and associated sentences containing these quantifiers with the collective and distributive pictures, rather than the exhaustive one. These findings were replicated and extended in a cross-linguistic study using translational equivalents of all and each in Mandarin Chinese and Brazilian Portuguese (Brooks et al., 1998). Across samples, children showed sensitivity to lexical semantic cues to universal quantification from about 5 years of age, with responses becoming more consistent with age.
FIGURE 15.3. Examples of collective (left), distributive (centre), and exhaustive (right) pictures, adapted from Brooks & Braine (1996: Experiment 3) and Brooks et al. (1998)
Brooks & Braine (1996) also explored whether children’s errors in restricting the scope of a universal quantifier would replicate in a picture-choice task, and whether errors would be observed outside of the classic context involving sets in partial one-to-one correspondence. Four sentence structures were used, as illustrated in (7):
(7) All of the men are washing a bear.
There is a man washing all of the bears.
Each man is washing a bear.
There is a man washing each of the bears.
For sentences with all, children were asked to choose between collective pictures with two extra objects (bears in the example shown) or two extra actors (see Figure 15.4), whereas for sentences with each, children chose between distributive pictures with two extra objects or actors (see Figure 15.5).
Sixty children were tested, ranging in age from 4 to 10 years. At all ages, children were highly accurate (> 80% correct) in choosing the correct collective picture for the sentences with all, which suggested that they could use the combined set of cues (i.e. the position of the universal quantifier, and singular vs. plural forms of the nouns in subject and object position) to match the sentences with the appropriate pictures. In contrast, children made frequent errors with the distributive sets in partial one-to-one correspondence, with only 9- and 10-year-olds showing success (> 70% correct) in varying their picture choices as a function of the sentence structure (i.e. whether each modified the subject or the object of the sentence). These findings, as well as later work with additional control conditions (Brooks & Sekerina, 2005/6), highlighted the specific challenges associated with using linguistic cues to match sentences with distributive depictions of sets in partial one-to-one correspondence.
FIGURE 15.4. Examples of collective pictures showing sets with extra objects (left) or extra actors (right), adapted from Brooks & Braine (1996: Experiment 1)
FIGURE 15.5. Examples of distributive pictures showing sets with extra objects (left) or actors (right), adapted from Brooks & Braine (1996: Experiment 1)
15.5 THE EVENT QUANTIFICATION HYPOTHESIS AND RELATED SYNTACTIC ACCOUNTS OF QUANTIFIER SPREADING
In a widely cited dissertation, Philip (1995) used the truth-value judgement task to explore preschool children’s errors with the universal quantifier every in contexts such as the one described at the beginning of this chapter and depicted in Figure 15.1. Based on findings that over half of preschool children rejected Every farmer is feeding a donkey as the description of a picture where there was one extra donkey, Philip proposed the event quantification hypothesis that errors stemmed from children misinterpreting the universal quantifier as an adverbial modifier of events, as opposed to a determiner modifier of individuals. Under this hypothesis, preschool-age children fail to construct the standard semantic representation of the sentence Every farmer is feeding a donkey, shown in Figure 15.6. Instead, they assign an event quantification representation, shown in Figure 15.7, wherein every event (within a specified discourse context) that involves a farmer and a donkey consists of a farmer feeding a donkey. In support of the event quantification hypothesis, Philip found that substituting a state description (e.g. Every farmer is a donkey-feeder) for an event description (e.g. Every farmer is feeding a donkey) led to a significant decrease in the number of children rejecting the sentence as a description of the picture with the extra donkey.
FIGURE 15.6. Standard semantic representation of the sentence ‘Every farmer is feeding a donkey’, adapted from Drozd & Philip (1993)
FIGURE 15.7. Event quantification representation of the sentence ‘Every farmer is feeding a donkey’, adapted from Drozd & Philip (1993)
Roeper et al. (2004) proposed a three-stage model of the development of syntactic competence with universal quantification. According to this model, at the initial stage universal quantifiers are interpreted as adverbial modifiers, leading children to extend the scope of a universal quantifier broadly to encompass all events within a specified discourse context. This results in errors such as answering ‘no’ to the question Is every bunny eating a carrot? in relation to a picture of three rabbits, each eating a carrot, and a dog eating a bone. Roeper and colleagues referred to these errors as bunny spreading, where the scope of the universal quantifier extends to all events within the discourse context, including events that involve neither a bunny nor a carrot. At the next stage, children acquire the syntactic operation of quantifier ‘floating’ wherein the universal quantifier may be separated from the material within its scope, as in the sentence The children all had pizza. At the ‘floating’ stage, children no longer make the bunny-spreading error, but are prone to make the classic quantifier spreading error. This error occurs because the universal quantifier has been lifted out of its noun phrase (i.e. the quantifier is c-commanding the whole sentence), which leaves its interpretation ambiguous. Finally, in middle childhood (10 to 12 years of age), children enter the adult stage wherein universal quantifiers are treated as determiners.
Roeper et al. (2011) further developed this account, while contrasting children’s acquisition of every and each. In an adaptation of the picture-choice task of Brooks et al. (2001), thirty-eight English-speaking children (4- to 9-year-olds) and forty adults were shown three pictures of flowers in vases: a collective picture of three flowers in single vase along with two extra vases, a distributive picture with three flowers each in its own vase along with two extra vases, and an exhaustive picture with five flowers arranged in three vases (with no flowers or vases left over). Participants were asked which picture or pictures matched the sentences Every flower is in a vase and Each flower is in a vase, and to explain why. Children showed a strong preference to match the exhaustive picture with the sentence with every, whereas 94 per cent of adults indicated that all three pictures were okay. For the sentence with each, over 60 per cent of the children rejected the distributive picture that 90 per cent of adults had indicated was the preferred interpretation. Taken together, the results suggested that exhaustivity (inclusion of all of the items in both sets) was a more salient aspect of the meanings of these universal quantifiers than distributivity (one-to-one correspondence); see Syrett (Chapter 9 in this volume) for more on distributivity. Roeper and colleagues interpreted children’s justifications of their preferred interpretations as evidence for quantifier floating, as children often paraphrased the sentences by shifting the position of the quantifier, such as pointing to the exhaustive picture and saying ‘it’s the only one with flowers in every vase’. Moreover, unlike adults, 40 per cent of the children did not distinguish their interpretations of every and each, which suggested incomplete mastery of lexical information.
Street & Dąbrowska (2010) examined individual differences in susceptibility to errors in interpreting universal quantifiers among adults, comparing performance of individuals with high versus low educational attainment on a picture-choice task. The authors observed poor performance in the group with low educational attainment, which they attributed to their lack of knowledge of the grammatical constructions (e.g. Every dog is in a basket vs. Every basket has a dog in it). The participants’ performance on the task improved dramatically after a brief training was used to provide an explanation of the sentence structures; note that a control group trained on passive sentences did not show improvements in understanding universal quantification. Using a novel version of a sentence-picture verification task to examine acquisition of universal quantification, Berent et al. (2009) compared performance of three groups of college students: native speakers of English, deaf students, and second language (L2) learners of English. Deaf speakers and L2 learners performed similarly and, like children, exhibited quantifier spreading errors (referred to as symmetric errors in this paper). Berent and colleagues attributed the errors to participants’ underdeveloped pragmatic knowledge of English, which was a likely consequence of restricted access to English language input.
Based on observations of quantifier spreading in college students in studies utilizing picture-choice (Brooks & Sekerina, 2005/6) and sentence-picture verification tasks (Brooks & Sekerina, 2006), Brooks & Sekerina suggested that errors might stem from shallow syntactic analysis, as opposed to faulty grammar. Shallow processing is a term used to describe a quick-and-dirty sentence-processing mode that generates representations ‘good enough’ for current purposes but lacking in details (Sanford & Sturt, 2002; Sanford & Graesser, 2006). When presented with an ambiguous sentence like Every flower is in a vase, the listener will often select a candidate interpretation based on contextual factors, rather than generate multiple interpretations (e.g. three flowers in one vase, three flowers in individual vases, five flowers in three vases, as in Roeper et al., 2011). Shallow processing resonates with Bucci’s (1978) pragmatic processing mode in which children arrive at a semantic interpretation based on pragmatic factors, or even guessing, while ignoring syntactic information.
15.6 CHILDREN’S ERRORS MAY REFLECT TASK DEMANDS, NOT FAULTY GRAMMAR
In contrast to the abovementioned accounts that treat quantifier spreading as involving the misinterpretation of a universal quantifier, Crain et al. (1996) argued that such errors are a manifestation of inappropriate testing conditions—that is, the failure to meet pragmatic felicity requirements for yes–no questions in studies utilizing the truth-value judgement task. For a yes–no question to make sense, the child should have an opportunity to consider an alternative outcome that differs from the one presented—in other words, the condition of plausible dissent should be satisfied. Crain and colleagues showed that preschool-age children who exhibited quantifier spreading (in a replication of Philip’s 1995 study) accepted the correct interpretation 88 per cent of the time when the condition of plausible dissent was satisfied. To set up this condition, Crain et al. embedded the truth-value judgement task in a scenario in which story characters were engaged in decision-making (i.e. between drinking soda or hot apple cider after skiing). Based on preschoolers’ correct acceptance of the statement Every skier drank a cup of hot apple cider as a description of a scenario where there were leftover cups of cider, Crain and colleagues concluded that young children have full grammatical competence with universal quantification and that interpretive errors result from flaws in testing procedures.
More recent work has highlighted other features of the truth-value judgement task that may inadvertently elicit errors. O’Grady et al. (2010) observed a sharp decrease in quantifier spreading among Japanese preschool children when they were asked to act out the sentences (e.g. Every cat is biting a fish) rather than make yes-no truth-value judgements in the typical context of a picture showing an extra object (e.g. fish). O’Grady and colleagues’ argument that the critical factor is the salience of the extra object is reminiscent of Donaldson’s (1978) emphasis on the salience of the empty garage in her studies. Similarly, Kiss & Zétényi (2017) have argued that quantifier spreading is an ostensive effect elicited by the features of the pictures. A line drawing is an abstraction of the depicted situation and may be perceived by the viewer as providing relevant clues for interpreting the sentence. When naturalistic photographs were used instead of line drawings, children exhibited markedly lower rates of quantifier spreading, presumably because the extra objects were less salient in the photographs.
Given the proliferation of findings indicating that even preschool children are highly sensitive to contextual manipulations of the truth-value judgement task, researchers have offered various pragmatic accounts of quantifier spreading (e.g. Kang, 2001; Rakhlin, 2007); see Brasoveanu & Dotlačil (Chapter 14 in this volume) for discussion of other factors influencing the processing of quantifier scope. It is now well-established that familiarizing children with the intended domain of quantification through a storyline or other contextual support drastically decreases error rates (e.g. Crain et al., 1996; Philip, 2011). Drozd (2001; Drozd & Van Loosbroek, 2006, see also Geurts, 2003) proposed that without such contextual support, children will fail to consider presuppositions constraining the use of universal quantifiers, and thus are prone to interpret them as weak rather than strong quantifiers (see Schwarz, Chapter 6 in this volume). Weak quantifiers, which include vague quantifiers, such as few, some, or most, are interpreted in a context-dependent way, by factoring in expectations about what would be considered normative in a given situation (Moxey & Sanford, 1993). For example, the expression some would likely denote a larger amount in the context of a school purchasing some new books than in the context of an individual purchasing some new books. Unlike weak quantifiers, strong quantifiers, such as the universal quantifiers all, each, and every, do not specify a range of possible values, and must be interpreted in relation to a set under discussion. It may be too cognitively demanding for a child to think about two sets (e.g. cars and garages) to compare them or, alternatively, ‘It may never occur to a child who is presented with an exhaustive pairing task that she should be distinguishing and comparing sets’ (Drozd, 2001: 36). Rather, the child may treat the universal quantifier as if it were a weak quantifier, allowing a sentence such as Every car is in a garage to be interpreted in accordance with situational expectations (e.g. how many cars should there be given the presence of five garages).
15.7 EYE-TRACKING STUDIES OF QUANTIFIER SPREADING
In recent years, research on quantifier spreading has supplemented behavioural designs focusing on response accuracy with eye-tracking measures of visual attention. In the first such study, Minai & colleagues (2012) tracked the eye movements of 4- to 5-year-old Japanese children and adults in the context of a sentence-picture verification task. They ran two versions of the task, varying the number of extra objects in the scene: for example, three turtles each holding an umbrella along with either three extra umbrellas or one extra umbrella. In line with previous work (e.g. Freeman & Stedmon, 1986), quantifier spreading occurred more often when there was only a single extra object, highlighting its salience as a distractor. Analysis of eye movements revealed that children tended to fixate more on the extra object than a control group of adults did. Note, however, that the increased fixations to the distracting object occurred prior to the onset of the sentence rather than simultaneously with sentence processing. Following Rakhlin (2007) and O’Grady et al. (2010), Minai and colleagues attributed this finding to children’s inability to ignore the salience of the extra object due to undeveloped skills in executive control of visual attention.
FIGURE 15.8. Fixations to the extra containers as a function of accuracy in sentence-picture verification for sentences of the form ‘Every apple is in a bowl’; quan = quantifier, npo = noun phrase for object, v = verb, p = preposition, npc = noun phrase for container
Sekerina & Sauermann (2015, 2017) identified a signature pattern of visual attention associated with quantifier spreading in adult heritage speakers of Russian and Russian children performing the sentence-picture verification task. Sekerina et al. (2018) extended these findings to school-age children (forty-one native English speakers, ages 5 to 12 years). On trials designed to elicit quantifier spreading (i.e. with containers and objects in partial one-to-one correspondence, such as apples in bowls), children performed at chance (53.3% correct) in verifying Every apple is in a bowl as a description of a picture showing three apples each in a bowl with two extra bowls. As shown in Figure 15.8, quantifier spreading was associated with increased fixations (visual attention) to the extra bowls in the picture relative to correct responses. Note that the increased fixations appeared after the children had processed the quantified noun phrase (every apple): that is, the fixations were time-locked to the occurrence of the verb phrase (is in a bowl). Moreover, incorrect responses were associated with faster reaction times than correct responses—consistent with the view that quantifier spreading occurs when individuals engage in shallow processing of sentence structure. Sekerina and colleagues (2018) suggested that quantifier spreading is associated with cognitive overload in real-time sentence processing, such that participants whose processing resources are taxed exhibit lesser control of visual attention, concurrently with exhibiting the error.
15.8 CONCLUSION
For half a century, researchers in the fields of developmental psychology and linguistics have puzzled over young children’s difficulties in grasping universal quantification, focusing on their tendency to extend the domain of a universal quantifier beyond the noun phrase it modifies. Using a broad range of methodologies, researchers have emphasized children’s reliance on contextual and pragmatic factors to produce what appear to be sensible, if not logical, responses to questions about set relationships that constitute violations of one-to-one correspondence. Despite a great deal of progress in exploring this topic, the extant studies have tended to rely on similar cross-sectional designs that fail to provide a comprehensive account of individual differences in sentence processing skills over the course of language development. Given evidence that adults as well as children are susceptible to quantifier spreading, future studies should place greater emphasis on online measures that assess the dynamics of sentence processing in real time. Future work using longitudinal designs is needed to evaluate how the development of pragmatic competence influences sentence processing and interpretation of universal quantification.
ACKNOWLEDGEMENTS
The authors thank Elizabeth Che for creating the original artwork for this chapter.