CHAPTER 13
PLURALITY
13.1 INTRODUCTION
PLURAL morphology in English is associated with a ‘more than one’ meaning. For example, a sentence like (1a), in contrast to its singular counterpart in (1b), is generally interpreted as conveying (2). This data point in itself is unproblematic: on the basis of our intuitions about (1a), we might simply conclude that the literal meaning contributed by plural morphology precisely excludes singularities among the possible denotations of the predicate, as proposed for instance by Chierchia (1998).
(1)a. Emily fed giraffes.
b. Emily fed a giraffe.
(2) Emily fed more than one giraffe.
The well-known puzzle associated with these data, however, is the following: if (1a) and (2) share the same meaning, we should expect the negation of the former to be equivalent to the negation of the latter. But this is not the case; the negation of (1a), in (3a), is clearly not equivalent to the negation of (2), in (4). Rather, (3a) is typically interpreted along the lines of (3b), which corresponds to the negation of the singular counterpart in (1b).1
(3)a. Emily didn’t feed giraffes.
b. Emily didn’t feed a (single) giraffe.
(4) Emily didn’t feed more than one giraffe.
The puzzle extends beyond negation, and includes questions such as (5), to which we would intuitively respond affirmatively if Emily fed a single giraffe, in contrast to how we would respond to the question in (6).
(5) Did Emily feed giraffes?
(6) Did Emily feed more than one giraffe?
There are two main kinds of approaches to this puzzle in the literature. One approach argues for an ambiguity in the meaning of the plural, and invokes a principle for selecting between the two possible meanings in different contexts (Farkas & De Swart, 2010; Grimm, 2013). An alternative approach posits that the ‘more than one’ meaning of plural morphology comes about as a pragmatic inference; specifically, the multiplicity inference is proposed to arise as an implicature (Sauerland, 2003; Sauerland et al., 2005; Spector, 2007; Zweig, 2009; Ivlieva, 2013; Magri, 2014; Mayr, 2015).
Most experimental work on plurality to date has focused on testing some version of the implicature-based approach. These studies have typically focused on four aspects of the multiplicity inference: (i) its sensitivity to logical polarity, (ii) its context-dependence, (iii) the possibility of its suspension, and (iv) its development in young children. As we will see, while experimental data from adults regarding (i) and (ii) suggest that the multiplicity inference is indeed a scalar implicature, the existing evidence pertaining to (iii), at least prima facie, provides an argument in the opposite direction. We will argue that the developmental data may provide the critical evidence for adjudicating between the two theoretical approaches. In particular, data obtained from preschool-aged children are generally consistent with the predictions of the implicature-based approach, while they require auxiliary assumptions on the ambiguity-based approach.
The rest of this chapter is organized as follows. In section 13.2, we briefly outline the implicature approach and its predictions, and review the existing experimental work that has investigated the implicature approach. In section 13.3, we briefly consider two implementations of the alternative ambiguity-based approach and the predictions that they make. In section 13.4, we discuss how the two theoretical approaches contend with the experimental findings to date, in particular focusing on the findings related to monotonicity, suspension and context-dependence, and acquisition. Section 13.5 concludes with an outlook for future research.
13.2 THE IMPLICATURE APPROACH
13.2.1 The implicature approach and its predictions
We have already seen that a sentence like (7a), repeated from earlier, gives rise to a multiplicity inference that Emily fed more than one giraffe. We can alternatively refer to the strengthened meaning of (7a) as that in (7b), once the multiplicity inference has been factored in.
(7)a. Emily fed giraffes.
b. Emily fed more than one giraffe.
We have also seen that this strengthened meaning disappears under negation, as (8a) does not seem to convey (8b). This behaviour extends beyond the distinction between affirmative and negative declarative sentences to include questions (9) and antecedents of conditionals (10), suggesting sensitivity to a more general distinction between upward-entailing and downward-entailing contexts (though we will discuss some apparent exceptions in section 13.3.2).
(8) a. Emily didn’t feed giraffes.
b. Emily didn’t feed more than one giraffe.
(9) Did Emily feed giraffes?
(10) If Emily fed giraffes, she will get a prize.
The implicature approach to the data above starts from the observation that this pattern is not unique to plurals, and is in fact parallel to the pattern of scalar implicatures more generally. For instance, a disjunctive sentence like (11a) gives rise to the strengthened exclusive meaning in (11b), but the latter disappears under negation, as shown in (12a—b); under the reading in (12b), (12a) would be compatible with Emily feeding both an elephant and a giraffe.
(11)a. Emily fed a giraffe or an elephant.
b. Emily didn’t feed both a giraffe and an elephant.
(12)a. Emily didn’t feed a giraffe or an elephant.
b. It’s not the case that Emily fed a giraffe or an elephant but not both.
In response to these data, the most prominent proposal in the literature is to treat the multiplicity inference as a form of implicature. Under this approach, multiplicity inferences are not part of the literal meaning of plural morphology, but arise from the comparison of (13a) with (13b). That is, (13a) simply means that Emily fed one or more giraffes, and it is through the negation of the stronger (13b) that we derive the ‘more than one’ meaning.
(13)a. Emily fed giraffes.
b. Emily fed exactly one giraffe.
When (13b) is placed under negation, however, as in (14b), its meaning becomes weaker relative to the assertion in (14a), and therefore the implicature is not derived.
(14)a. Emily didn’t feed giraffes.
b. It’s not the case that Emily fed exactly one giraffe.
The story above can be implemented in various ways, and existing proposals in the literature range from treating the multiplicity meaning as a conversational implicature, arising from a Maximize Presupposition-based comparison with the presuppositional singular (something like (13b)) (Sauerland, 2003; Sauerland et al., 2005), to treating it as a recursive scalar implicature (Spector, 2007; Magri, 2014) or an embedded scalar implicature (Zweig, 2009; Ivlieva, 2013; Mayr, 2015).2 All of these different implementations of the implicature approach predict some sort of uniformity across multiplicity inferences and scalar implicatures, along the lines of (15).
(15) Uniformity Prediction: If multiplicity inferences are implicatures, then everything being equal, multiplicity inferences and implicatures should exhibit similar behavioural profiles.
Now, given this prediction, it is important to note that adults’ rates of implicature computation have been reported to vary quite widely across different lexical scales (Van Tiel et al., 2016). For this reason, some of the studies that we will turn to next involve comparisons across different populations, namely children and adults. This is important because, even if adults do not compute multiplicity inferences and classical scalar implicatures at precisely the same rates, we might expect that children initially exhibit similar performance on the two kinds of inferences, or that they will differ from adults in the same manner for the two kinds of inferences. By comparing across two populations, these studies are informative about the relationship between the two inferences, even if adults do not compute them at exactly the same rates.
13.2.2 Experimental work
We will now turn to a series of experiments that have tested the Uniformity Prediction in (15), both with adults and children.
13.2.2.1 Sauerland et al. (2005)
Sauerland et al. (2005) present one of the first studies comparing adults’ and children’s performance on multiplicity inferences, with the aim of testing whether the latter can be analysed as a form of implicature. If multiplicity inferences are derived as implicatures, one might expect adults and children to treat the two kinds of inferences in a parallel fashion. While there is considerable variability in the results reported across developmental studies of implicature, a fairly robust finding has been that children compute fewer classical scalar implicatures of the kind in (16a,c) than adults do (Gualmini et al., 2001, Chierchia et al., 2001, Noveck, 2001, Papafragou & Musolino, 2003, among others; see also Papafragou & Skordos, 2016, and Skordos & Barner, Chapter 2 in this volume, for relevant discussion and overviews). That is, children have been shown to accept sentences such as (16a) in situations where the stronger alternative (16b) is also true. For the most part, this observation has been taken to indicate that children have failed to compute the implicature in (16c).
(16)a. Emily fed some of the giraffes.
b. Emily fed all of the giraffes.
c. Emily fed some but not all of the giraffes.
More recent developmental research indicates that children can succeed on certain kinds of implicatures, in certain experimental contexts (see, for example, Miller et al., 2005; Barner et al., 2011; Katsos & Bishop, 2011; Stiller et al., 2015; Tieu et al., 2016; Singh et al., 2016; Skordos & Papafragou, 2016; Tieu, Yatsushiro, et al., 2017). There is currently debate in the developmental literature as to the underlying source of children’s apparently selective success across different implicatures; there is also disagreement as to whether nonimplicature responses in children reflect a true absence of implicature. These debates are not necessarily important for the comparison we will make; we will simply rely on the generalization that without facilitatory experimental manipulations or specially selected scales, children behave systematically unlike adults in many apparently scalar implicaturebased tasks. If this is so, and if we further assume that multiplicity inferences are implicatures, we are led via Uniformity to the prediction that children should also exhibit difficulty computing multiplicity inferences. In particular, they should compute fewer multiplicity inferences than adults, under the same kinds of conditions in which they compute fewer standard scalar implicatures than adults.
Sauerland et al. (2005) designed an experiment that involved a puppet playing the role of an alien asking questions about life on Earth. In particular, the puppet would ask participants polar questions such as (17). The expectation was that a reading involving the multiplicity inference (e.g. Does a dog have more than one tail?) would lead to a negative answer, given common knowledge, while a literal interpretation of the question (e.g. Does a dog have one or more tails?) would lead to an affirmative response.
(17) Does a dog have tails?
The authors compared (17) to control questions like (18), in which the literal meaning of the plural is incompatible with world knowledge, and with (19), in which both the literal meaning of the plural and the multiplicity inference are compatible with world knowledge.
(18) Does a boy have beaks?
(19) Does a cat have feet?
The authors tested fourteen children aged 3—5 years, and found the following pattern. Children were adult-like on the control questions, responding negatively to (18) and affirmatively to (19). However, they overwhelmingly tended to produce affirmative responses to target questions like (17), answering ‘yes’ to such questions 96 per cent of the time. This would indicate that children accessed the literal meaning of the question in (17), Does a dog have one or more tails?
The observed non-adult-like behaviour exhibited by the child participants mirrors exactly the differences that have been reported in previous studies of implicatures, with children tending to accept implicature targets more than adults. Sauerland et al.’s (2005) results therefore provide a first piece of evidence in favour of the implicature approach to plurality.
However, as Sauerland et al. (2005) point out (see also Pearson et al., 2011; Tieu et al., 2014), their study has some potential limitations. First, multiplicity inferences are not always computed in polar questions, even for adults. Sauerland et al. (2005) discuss examples like (20), drawn from Krifka (1989), in which a response assuming a multiplicity inference from (20a) seems to be infelicitous.
(20)a. Does your office have windows?
b. Yes (only one though).
c. #No, only one.
Sauerland et al. (2005) attribute the difference between a question like (20a) and one like their experimental (17) to whether the person asking the question already knows the answer to the question, with the relevant distinction between true information-seeking questions and exam-type questions. According to the authors, only exam-type questions systematically give rise to multiplicity inferences. As Pearson et al. (2011) point out, however, the experimental setting in Sauerland et al. (2005) was precisely one in which the puppet was asking true information-seeking questions; the puppet was ignorant about life on Earth and wanted to acquire information by asking the participants questions about life on Earth. It is therefore unclear that this distinction is relevant for explaining how the participants behaved in Sauerland et al.’s (2005) study.
Moreover, Sauerland et al.’s (2005) experimental stimuli involved generic interpretations, which could have been misinterpreted by participants as containing dependent plurals. For example, children might have interpreted (17) along the lines of Do dogs have tails?, in which case yes-responses would be entirely reasonable, independently of the children’s ability to compute multiplicity inferences.
While the findings of Sauerland et al.’s (2005) study can be taken to provide some initial evidence in favour of an implicature approach, the results are not entirely conclusive for the reasons just discussed.
13.2.2.2 Pearson et al. (2011)
Pearson et al. (2011) tackle the multiplicity-as-implicature hypothesis from a different angle, designing an experiment that aimed to test whether such inferences are cancellable in upward-entailing contexts. The authors used a Covered Box task, modelled on Huang et al. (2013). Huang et al. (2013) presented participants with three boxes; the contents of two of the boxes were clearly visible to both the experimenter and the participant, while the contents of the third box were hidden. On each trial, participants were asked to give the experimenter the box that matched the experimenter’s description. As an example, on one target trial, participants would see one box containing one cookie, one box containing three cookies, and a covered box. The experimenter would direct participants to ‘Give me the box with two cookies’. The expectation was that if the exactly-n meaning of the numeral was a cancellable implicature, participants would select the box containing three cookies, thereby satisfying the experimenter’s request. If, on the other hand, the exact meaning was not a cancellable implicature, but rather part of the semantics of the numeral, participants would necessarily have to select the covered box. Huang et al. (2013) found that adults chose the covered box on the numeral target trials, suggesting, at least prima facie, an exact semantics for the numeral. In contrast to the numeral trials, Huang et al. found that adults were more willing to cancel the scalar implicature of ‘some’, for example selecting the box where Cookie Monster had all of the cookies when asked to give the box where Cookie Monster had ‘some of the cookies’.
If the multiplicity inference is an implicature, just like the one arising from the scalar quantifier some, one should expect that in exactly the same experimental setup adults would also cancel the multiplicity inference in order to give the experimenter one of the visible boxes, just as was observed for some in Huang et al.’s (2013) study. This is precisely what Pearson et al. (2011) set out to investigate. They presented participants with three cards at a time, two visible and one face down. On one critical target, for example, the two visible cards showed Big Bird with no kite and Big Bird with just one kite, respectively. Participants then heard the instruction in (21).
(21) Point to the card where Big Bird has kites.
The expectation was that if participants could cancel the multiplicity inference, interpreting (21) as Point to the card where Big Bird has one or more kites, they would be happy to select the visible picture where Big Bird had only one kite. On the other hand, if participants interpreted (21) with the multiplicity inference (i.e. Point to the card where Big Bird has more than one kite), they would have to select the face-down picture.
Pearson et al.’s (2011) study consisted of two experiments. In the first experiment, sixteen native speakers of English were presented with sentences like (21) in target conditions like the one described earlier. Participants displayed an overwhelming preference for the facedown card on target trials, in parallel with Huang et al.’s (2013) results for the numeral targets but not the some targets. Prima facie, such a finding goes against the implicature approach, which would predict that the multiplicity inference should be cancellable in the same contexts in which the some-not-all implicature is cancelled.
In a follow-up experiment, Pearson et al. (2011) introduced the term ‘only’ into the test sentences, as in (22), and found that participants were much happier to select the visible picture in which Big Bird had exactly one kite.
(22) Point to the card where Big Bird only has kites.
The authors speculate that this result may be due to the fact that on a standard semantics of ‘only’, the multiplicity inference is merely presupposed, and not asserted. Even if this is so, we are nevertheless left with a difference that is puzzling on the implicature approach: when presented in the same experimental setup, the implicature of some, but not the multiplicity inference, is easily cancellable—even in the absence of ‘only’.
In sum, Pearson et al.’s (2011) results offer somewhat mixed evidence, and do not argue conclusively in favour of the implicature account, due to the observed difference between multiplicity inferences and scalar implicatures with respect to the ease of cancellability.
13.2.2.3 Tieu et al. (2014, 2015, 2017)
Building on Sauerland et al. (2005), Tieu et al. (2014, 2015, 2017) conducted another pair of acquisition experiments aimed at detecting multiplicity inferences in preschool-aged children. These authors set out to test the developmental Uniformity Prediction that arises from the scalar implicature approach to multiplicity inferences, namely that the pattern of children’s multiplicity inferences should mirror their performance on standard scalar implicatures. On the implicature account, any observed differences in the acquisition profiles of the two inferences would minimally have to be explained via auxiliary assumptions.
In order to address some of the potential limitations of the Sauerland et al. (2005) study, Tieu et al. (2014) avoided the use of polar questions and instead tested the interpretation of the plural in affirmative and negative declarative sentences. By manipulating monotonicity, the authors could further test the implicature approach advanced by Spector (2007), which would predict the disappearance of multiplicity inferences in downward-entailing environments.3
The authors used a Truth-Value Judgement Task (Crain & Thornton, 1998), in which participants watched a series of short stories and then had to judge a puppet’s descriptions of the stories. A sample target story is provided in (23); in this story, the protagonist fed exactly one pig. Participants were expected to accept the accompanying upward-entailing target sentence (23a) if they accessed the literal existential meaning, but they were expected to reject the sentence if they accessed the multiplicity inference. The downward-entailing counterpart of (23a) can be found in (23b) (though the actual stories and characters were different across the upward- and downward-entailing conditions, to keep the task interesting for the child participants). Participants were expected to reject the downward-entailing target in (23b) if they accessed the literal meaning of the test sentence, since it was false that Emily didn’t feed any pigs (she fed one). They could, however, accept the sentence if they computed the multiplicity inference locally under negation, giving rise to the meaning Emily didn’t feed more than one pig.
In their first experiment, Tieu et al. (2014) tested twenty-eight English-speaking 4- and 5-year-olds and forty-three adult native speakers of English. The adult participants rejected the upward-entailing targets 92 per cent of the time, and accepted the downward-entailing targets 42 per cent of the time. Given that the computation of the multiplicity inference corresponded to rejection in the upward-entailing condition and to acceptance in the downward-entailing condition, adults computed more multiplicity inferences in upwardentailing than in downward-entailing environments, but also computed multiplicity inferences under negation to some degree.4 Children, on the other hand, computed multiplicity inferences only 40 per cent of the time in the upward-entailing condition, and 19 per cent of the time in the downward-entailing condition.
In a second experiment, Tieu et al. (2015) conducted a more direct comparison of the plurality inference and classical scalar implicatures by including a some implicature condition. The plurality inference condition was similar in structure to that of the first experiment, with the materials modified slightly to ensure maximal parallelism between the plural and some condition. A plural target can be found in (24) and a scalar implicature target in (25). For both kinds of targets, participants were expected to accept the sentence if they accessed the literal meaning, and to reject the sentence if they computed the relevant inferences in (24b) and (25b).
(24) Scenario: Zebra is at the orchard. There are four bananas in one tree and four oranges in another tree. Zebra picks one of the four bananas.
a. Zebra picked bananas.
b. ⇝ Zebra picked more than one banana
(25) Scenario: Lion is at the orchard. There are four oranges and four apples on the ground. Lion carries four of the four apples.
a. Lion carried some of the apples.
b. ⇝ Lion carried some but not all of the apples
Tieu et al. (2015) tested seventeen English-speaking 4- and 5-year-olds and twenty-seven adults. Similarly to the first experiment, adults computed more multiplicity inferences in the upward- than in the downward-entailing environment (75% vs. 19%), and children computed far fewer multiplicity inferences than adults regardless of monotonicity (16% in the upward-entailing condition vs. 4% in the downward-entailing condition). The child participants also computed fewer implicatures from some than adults (adults 81% vs. children 28%), consistent with the pattern from multiplicity inferences. Children’s responses to the two kinds of inference targets were also significantly correlated. On the whole, the results from the two experiments appear to be consistent with the implicature approach to plurality.
13.2.2.4 Patson (2016)
Patson (2016), building on Patson et al. (2014), conducted two picture-matching task experiments with adult participants, aimed at probing the interpretations of sentences containing plural definites like ‘the leaves’. Participants read sentences that implied either a particular spatial distribution of the objects denoted by the definite description (Experiment 1), or different set sizes (Experiment 2). For example, in Experiment 1, ‘the leaves’ could be implied to be spatially gathered, as in (26), spatially distributed, as in (27), or neutral with respect to spatial distribution (28):
(26) The gardener raked up the leaves.
(27) The breeze scattered the leaves.
(28) Thomas was confused about the shape of the leaves.
After reading the test sentence, participants were presented with a picture of the denoted object, and they had to decide if the picture was of an object that had been mentioned in the sentence. Crucially, the picture either matched in spatial distribution, mismatched in spatial distribution, or was neutral with respect to spatial distribution (e.g. a pile of leaves; a group of scattered leaves; a single leaf).
Patson observed high accuracy in the picture judgement task, with participants matching the ‘collective’ pictures with the ‘collective’ sentences, and the spatially distributed pictures with the ‘scattered’ sentences. Patson also collected reaction times for participants’ responses, and found that participants were quicker to accept pictures that matched the sentences in terms of spatial distribution than pictures that mismatched the sentences. Crucially, participants were as fast to accept the matching pictures as they were to accept the singular pictures, suggesting the participants had activated the ‘at least one’ interpretation of the plural definite descriptions.
In the second experiment, Patson manipulated the implied set size of the objects rather than spatial distribution. The test sentences either implied a small or large set size (e.g. The scientist examined the tray of leaves vs. During autumn the yard is full of leaves) or were neutral with respect to set size (e.g. I like the smell of leaves). The pictures accordingly depicted, for example, a small set of leaves, a large (uncountable) set of leaves, or a single leaf. Patson again observed high accuracy rates across conditions. Crucially, the reaction time results replicated those of the first experiment: participants were as fast to respond to pictures that matched the implied set size as they were to accept the singular picture.
These results replicate and extend those in Patson et al. (2014). The findings suggest that when participants represent plural definite descriptions they also activate the corresponding singular meaning. As Patson argues, such findings are in line with the hypothesis that the plural is number-neutral in its literal meaning, and is associated with a multiplicity inference via an implicature. By contrast, the results are much harder to reconcile with a semantic proposal on which the multiplicity meaning is encoded in the literal meaning of the plural definite description. Had the plural definite descriptions only activated representations of multiple objects, one might have expected participants to be slower to respond to the singular pictures than to the pictures containing multiple objects.
13.3 AMBIGUITY-BASED APPROACHES AND THEIR PREDICTIONS
Having examined a set of experimental studies that set out to investigate the implicature approach to the ‘more than one’ meaning of plural morphology, we turn next to ambiguity approaches. These approaches essentially posit two possible meanings for the plural, along with some additional principle for selecting between two possible meanings. Compared to the implicature approach, these approaches have been relatively less investigated from an experimental perspective (see Tieu, Bill et al., 2017, for detailed discussion). In the following subsections we present a brief overview of the existing theoretical approaches and their accompanying experimental investigations where applicable.
13.3.1 Farkas & De Swart (2010)
Farkas & De Swart (2010) propose that plural morphology is polysemous between a weak inclusive meaning and a strong exclusive meaning. A plural sentence like (29), repeated from earlier, can thus be associated with two possible readings: a weak reading along the lines of (30a) and a strong reading along the lines of (30b).
Under negation, the relative strength of the two readings is reversed; the negative (31) can be associated with the strong (32a) or the weak (32b).
As we have seen from our previous discussion, people have rather strong tendencies to interpret (29) as (30b) and (31) as (32a). To explain these interpretive preferences, Farkas & De Swart (2010) assume the Strongest Meaning Hypothesis in (33) (see Dalrymple et al., 1998, Winter, 2001, among others).
(33) The Strongest Meaning Hypothesis for Plurals: for a sentence involving a plural nominal, prefer that interpretation of the plural which leads to the stronger overall interpretation for the sentence as a whole, unless this interpretation conflicts with the context of utterance.
With (33), the ambiguity approach can capture the monotonicity effect we observe: the principle favours the interpretation (30b) for the positive (29) and (32a) for the negative (31), as these correspond to the strongest possible interpretations of the respective sentences.
Note that the principle in (33) will also allow for the weaker interpretations to emerge if the stronger ones are in conflict with the context of utterance. For instance, a weak interpretation can be forced by adding a continuation that is in conflict with the strong reading, thereby blocking it, as illustrated in (34); here the negated plural receives the weak interpretation along the lines of (32b), rather than the strong interpretation in (32a).
(34) Emily didn’t feed giraffes, because she fed only one!
Like the implicature approach, the ambiguity approach can therefore capture the monotonicity effect and the presence of readings like that in (34). That is, the two approaches make the same predictions when it comes to the interpretation of plural morphology in positive and negative sentences, and they likewise make the same prediction regarding the availability of the reading in (34).
The two theories diverge, however, in what they predict about the relationship between multiplicity and implicatures. Unlike the implicature approach, the ambiguity approach makes no particular predictions regarding this relationship, since the two phenomena are not seen as related. This relationship between multiplicity and implicatures therefore in principle provides a fruitful avenue for potentially adjudicating between the two approaches. One complication to note, however, is the observation that there is considerable variation in implicature computation rates across scales (Van Tiel et al., 2016); even if the multiplicity meaning arises as an implicature, we might not expect to observe it occurring at similar rates as standard cases of implicature.
A further avenue for investigating the predictions of the theories lies in child language acquisition. As Tieu, Bill, et al. (2017) discuss, the ambiguity approach makes certain predictions about how plurality should be acquired. On this approach, children must not only acquire the two proposed meanings of the plural, they must also be able to make use of the Strongest Meaning principle in an adult-like manner, in order to resolve the ambiguity. Tieu, Bill, et al. (2017) present three possible learning stages during which children might be observed to be non-adult-like in their interpretation of the plural. First, they might only have the strong meaning of the plural, in which case we should expect them to be adult-like on the plural in upward-entailing environments but not in downward-entailing environments. Second, they might only have the weak meaning of the plural, in which case they should be adult-like only in downward-entailing environments. Finally, they might have both meanings for the plural, but fail to deploy the Strongest Meaning principle as adults do. They might instead, for example, be guided by charity, selecting the interpretation that is made true in the context.
Summarizing, the ambiguity approach of Farkas & De Swart (2010) and the implicature approach both predict more multiplicity inferences in upward-entailing than in downward-entailing environments, but they differ in how they view the relationship between multiplicity and implicatures. Furthermore, they differ in the predictions that they make for how children and adults should perform on multiplicity inferences (and scalar implicatures). In the next subsection, we turn to a different incarnation of the ambiguity approach, based not on monotonicity but rather on the distinction between particularized and general reference.
13.3.2 Grimm (2013)
While many of the pre-existing accounts of the plural meaning place importance on monotonicity, Grimm (2013) presents an ambiguity analysis based on the distinction between particularized and general reference. Grimm points out that the inclusive plural meaning can arise in environments like (35), which can be shown to be neither strictly downward-entailing (36), nor to block scalar implicatures (37).
(35) Sherlock Holmes should question local residents to find the thief.
Sherlock Holmes should question groups of two local residents or more
(36) Sherlock Holmes should question local residents.
Sherlock Holmes should question local residents with red hair
(37) Sherlock Holmes should question three local residents.
Sherlock Holmes should question exactly three local residents
Note that the fact that the multiplicity inference appears to be context-dependent is not per se a challenge to the implicature approach. Indeed, the latter can readily account for context-dependence by appealing to relevance. That is, the data above are challenging only if it can be shown that the exactly-one alternative is relevant in the context against which (35) is evaluated.
Grimm takes a different approach altogether and argues that, rather than downward-entailingness, the relevant property to account for the distribution of the inclusive plural reading is the weakened referential status of the nominal. That is, the inclusive plural reading arises in contexts where the nominal doesn’t presuppose the existence of any particular referents. Specifically, Grimm considers the relevant distinction to be between object-level and concept-level entities.
Grimm sets out to experimentally probe the inclusive meaning of plurals in interrogative contexts, by conducting two experiments involving plural nouns in two kinds of contexts. In the first experiment, participants were presented with pictures which clearly instantiated the object under question. For example, participants would see a photo of a woman holding either one mug or two mugs, and would have to answer the yes/no question Is the woman in this picture holding mugs? In the second experiment, participants were presented with ‘rules-and-regulations’ contexts meant to foster generic or kind-level construals (Carlson, 1995). For example, participants saw questions meant to evoke a corporate environment, such as (38).
(38) Did your team terminate projects this fiscal quarter?
EMPLOYEE FACTS: employee’s team has terminated exactly one project this fiscal quarter
What answer should the employee give? Yes/No
Grimm reports that in the first experiment, participants provided yes-answers 92 per cent of the time when the picture contained multiple objects, but gave yes-answers only 32 per cent of the time when presented with a single object. In contrast, in the second experiment, adults answered yes 99 per cent of the time when the ‘employee facts’ line contained a plural entity like three projects, and crucially still preferred the inclusive interpretation on the critical targets (38), responding yes 78 per cent of the time.
Grimm’s experimental data reveal that participants disfavour inclusive readings of the plural when considering object-referring uses of plural nouns, but favour inclusive readings in contexts that encourage general reference. To capture the data, Grimm proposes an analysis that integrates Krifka’s (1995b) analysis of common nouns and Roberts’s (1996) framework for discourse structure involving the Question Under Discussion (QUD).
First, Grimm draws on Krifka (1995b) to provide the two representations needed for the two possible interpretations for a given plural noun: a quantified object reading and an instance of a concept reading (39b).
These two representations then provide two possible interpretations for a given plural noun. The plural marker can be interpreted as a number marker (which Grimm diverges from Krifka in assuming is interpreted as more than one), as in (40a); in this case the interpretation is true when the noun’s referent is the type of thing named and has cardinality greater than one. Alternatively, the plural noun can enter the derivation as a kind or concept, whereupon the interpretation succeeds when at least one entity realizes the kind dog, as in (40b); in this case, the reading is number-neutral, being true as soon as the noun’s referent is the type of thing named.
Next, Grimm situates his analysis within the discourse framework of Roberts (1996). In essence, distinct QUDs can be derived that query either the existence or the number of objects, respectively:
According to Grimm, the interpretation of the plural noun is then guided by which of (41a,b) corresponds to the immediate QUD that the conversational participants are attempting to answer. When reference to particular entities is not yet determined, the Existential QUD is appropriate, licensing an inclusive reading; when reference to particular entities is determined, it is the Quantitative QUD that is the immediate QUD, and the exclusive reading is licensed. This would explain why, in Grimm’s first experiment, where participants were presented with particular objects (i.e. one or more mugs), participants preferred the Quantitative QUD and therefore the exclusive reading of the plural, whereas in the second experiment, where there was no presumption that any projects were completed, participants preferred the Existential QUD and therefore the inclusive reading of the plural.
13.4 GENERAL DISCUSSION
The existing experimental investigations into the semantics and pragmatics of plurality yield a number of insights, all the while raising new questions for future research. We now turn to these insights and remaining puzzles.
13.4.1 Sensitivity to monotonicity
The multiplicity inference appears to be sensitive to monotonicity, as most clearly evidenced by the data in Tieu et al. (2014, 2015). The adult participants in these experiments generally preferred to reject both positive and negative plural descriptions like (42a,b) in singular contexts, such as those in which Emily fed exactly one giraffe. Such responses indicate that adults interpreted the plural exclusively in the upward-entailing (42a), but inclusively in the downward-entailing (42b).
(42)a. Emily fed giraffes.
b. Emily didn’t feed giraffes.
As we have seen, both the implicature approach and the ambiguity approach of Farkas & De Swart (2010) predict precisely this pattern, the former through implicatures that arise in upward-entailing but not downward-entailing environments, and the latter through a Strongest Meaning principle. What about the ambiguity approach of Grimm (2013)? On Grimm’s proposal, participants’ interpretation of the plural nouns would have been guided by whether they accessed the Existential QUD or the Quantitative QUD. However, Tieu et al. (2014, 2015) used the same kinds of stories for their upward-entailing and downwardentailing targets. Given the stories were the same, presumably the salient QUDs were also equivalent across the two conditions. It is therefore somewhat puzzling that adults, particularly in the second experiment, computed far fewer multiplicity inferences under negation (75% vs. 19%). One would have to say that the positive and negative sentences themselves invoked different QUDs, and therefore different interpretations of the plural, since only the sentences differed between conditions.5
Future research might further investigate the respective roles that the QUD and monotonicity may play in adults’ interpretation of plural morphology, and the interaction between the two factors (if any). For the moment, it is clear that adults distinguish between upward- and downward-entailing contexts when interpreting plural morphology. This sensitivity to polarity is expected under all of the various incarnations of the implicature approach in the literature and on certain implementations of the ambiguity approach.
13.4.2 Suspension and context-dependence
The theoretical approaches we have discussed are not quite so straightforward to reconcile with the experimental evidence pertaining to suspension and cancellability. First, we have discussed the observation that multiplicity inferences are harder to suspend than regular scalar implicatures, as can be seen by the contrast between (43) and (44).
(43) Some of the students came. In fact, all of them did.
(44) Emily fed giraffes. #In fact, she fed exactly one.
This difference is reflected in Pearson et al.’s (2011) results, especially those of their first experiment. While their second experiment reveals that multiplicity inferences are easier to suspend in the scope of a presupposition trigger, the exact nature of the interaction between presuppositions and implicatures in such cases is not very clear, rendering it difficult to draw conclusions regarding suspension of multiplicity inferences from this particular data point.
The challenge for the implicature approach is to account for the difficulty of suspending multiplicity inferences in cases like (44) above, while at the same time accounting for their apparent context-dependency in cases like Grimm’s (35). More generally, it remains an open question how to account for the observed difference in cancellability between scalar implicatures of terms like some and multiplicity inferences, as well as the role played by presuppositions in apparent cases of suspension.
As Pearson et al. (2011) discuss, the observation that multiplicity inferences are difficult to cancel has already been made in the literature. Chierchia et al. (2011), in particular, observe the oddness of a case like (44), and propose that the implicature triggered by (44) is in fact obligatory. That is, the implicature arising from some in (43) is context-dependent and easily suspended, while the multiplicity inference arising from the plural in (44) is not. An outstanding question is how exactly to reconcile this with Grimm’s (2013) data, which suggest context-dependency of the multiplicity inference.
As mentioned, Grimm’s (2013) observation that multiplicity inferences are contextdependent is not in and of itself a problem for the implicature approach. The multiplicity inference could be treated as an optional implicature, the presence of which is dependent on the context. In particular, the presence of the implicature would depend on whether the exactly-one alternative is made relevant in the context. In Grimm’s first experiment, this alternative was made relevant in the context, while in the second experiment it was not. In this way, the implicature approach can explain both the sensitivity to polarity and the context-dependency displayed by the multiplicity inference. One would, however, have to work through the details of how to reconcile cases where context-dependence is evident (like Grimm’s (35)) with the apparent lack of suspension in cases like (44). Notice that the same issue arises on the ambiguity approach of Farkas & De Swart (2010), which would need to explain why the Strongest Meaning principle appears to be violable in cases like (35) but not in cases like (44).
13.4.3 Children’s development of plural meanings
The data pertaining to monotonicity, suspension, and context-dependence do not unequivocally argue for one approach to multiplicity over the other. However, considerations of language acquisition and learnability may be able to shed light on the debate. Let us consider how each approach might explain the experimental results we have discussed.
We have observed that children do not compute as many multiplicity inferences as adults do (e.g. Sauerland et al., 2005; Tieu et al., 2014, 2015). What could be missing, according to the implicature approach? On the implicature analysis, the child must learn the relevant alternatives, contrasting the plural form with some version of the singular; otherwise no inference can arise from the plural. Children who cannot yet compute multiplicity inferences may lack knowledge of or access to the required alternatives. In fact, access to alternatives has been proposed to be a problem for children’s generation of implicatures more generally; in cases where children do have access to the required alternatives, research indicates they are fully capable of generating implicatures and implicature-like meanings (see, for example, Barner et al., 2011; Stiller et al., 2015; Tieu et al., 2016; and Singh et al., 2016). On the implicature approach, the multiplicity inference may be particularly challenging for the child learner of English, given that neither the plural morpheme -s nor the (enriched) singular alternative correspond to standalone lexical items that the child can easily contrast with each other (unlike the cases of, for example, ‘some’/‘all’, ‘or’/‘and’, ‘might’/‘must’, and numerals).
How might the ambiguity approach of Farkas & De Swart (2010) contend with the developmental data? On the whole, the child data appear to pose a challenge to this approach. While the ambiguity approach is not incompatible with similar developmental profiles for multiplicity inferences and standard implicatures, it would not appear to readily account for children’s behaviour across the polarities, that is, in positive and negative sentences. Recall that on the ambiguity approach, the positive (45a) is ambiguous between the readings in (45b) and (45c), while the negative (46a) is ambiguous between the readings in (46b) and (46c). The Strongest Meaning hypothesis is expected to favour (45b) for (45a) and (46c) for (46a).
As we discussed in section 13.3.1 (following discussion in Tieu, Bill, et al., 2017), there are three main developmental scenarios that might give rise to non-adult-like behaviour on the ambiguity approach. Children might access only the weak meaning of the plural; they might access only the strong meaning of the plural; or they might have both meanings but fail to apply the Strongest Meaning hypothesis in an adult-like way. Yet what the child data in Tieu et al. (2014, 2015) reveal is that children in fact favour the weak reading of the positive (45a), but the strong reading of the negative (46a). It is unclear how the ambiguity approach might capture this observed pattern across the two polarities. As suggested by Tieu, Bill, et al. (2017), for example, the ambiguity approach might posit that children engage with the Strongest Meaning principle differently from adults, obeying the principle only in downward-entailing contexts. But while it is plausible that children at a certain age might differ from adults in the deployment of a pragmatic principle like the Strongest Meaning hypothesis, it’s not clear why their application of such a principle would vary systematically with the polarity of the context.
Alternatively, the ambiguity approach might explain the data by positing that children in this age range have only mastered the weak inclusive meaning of plural morphology, hence accessing a globally weak reading of the positive (45a) but a globally strong reading of the negative (46a). But as Tieu, Bill, et al. (2017) discuss, such a scenario raises a potential learnability problem, in the form of a subset problem (Berwick, 1985; Crain et al., 1994; Gualmini & Schwarz, 2009). In particular, if a child has acquired the weak meaning of the plural morpheme, any evidence they encounter for the strong meaning will also be compatible with the weak meaning, given that the strong meaning entails the weak meaning. What evidence would then prompt the child to move from a weak to a strong meaning for the plural morpheme?
Finally, let us consider what the child would have to learn on an account like Grimm’s. One possible explanation for children’s difficulty with multiplicity inferences, under Grimm’s proposal, might lie in a difficulty with selecting the correct QUD, and thereby accessing the target meaning of the plural. In this scenario, what the learner needs to develop is something more general than a particular kind of inference; the child has yet to become adult-like in her management of the discourse structure.6 In the Tieu et al. (2014, 2015) experiments, for instance, one might posit that children favoured the Existential QUD, while adults favoured the Quantitative QUD; what would develop over time is an alignment with the adult-like selection of the target QUD.7
Alternatively, as on the ambiguity approach of Farkas & De Swart (2010), Grimm’s approach might also posit that children simply haven’t yet mastered both meanings or representations of the plural. Given their preference for the inclusive meaning of the plural, one might posit that children acquire the kind reading earlier than the quantified object reading. Future work might more closely investigate the developmental connection between plurality and genericity.8
Summarizing, the existing experimental data from children appear to be more straightforwardly accounted for under the implicature approach. However, as we have discussed, both approaches to multiplicity inferences provide possible avenues for further investigating the developmental path that children may take to an adult-like understanding of plural morphology.
Before closing this section, it is worth noting that the acquisition studies by Sauerland et al. (2005) and Tieu et al. (2014, 2015) pertained specifically to preschoolers’ knowledge of multiplicity inferences. This age range (3–5 years) is apt for investigating connections between multiplicity inferences and scalar implicatures, as previous studies of implicature have likewise targeted this age range, and shown that preschoolers typically compute fewer standard implicatures than adults do. On the face of it, the findings of Sauerland et al. (2005) and Tieu et al. (2014, 2015) appear to support the hypothesis that multiplicity inferences are a form of implicature, with similar developmental profiles. However, the observation that 4-year-old children may not be fully adult-like in their interpretation of plural morphology is prima facie at odds with the findings of studies conducted with much younger children. In particular, it has been reported that children begin producing plural morphemes at 22 months of age (e.g. Brown, 1973; Mervis & Johnson, 1991; Fenson et al., 1994; Barner et al., 2007),9 and that 24-month-olds are sensitive to plural marking in comprehension (Wood et al., 2009; Davies et al., 2016). For example, Wood et al. (2009) used a manual search paradigm in which 2-year-old children were prompted to search for objects in a box. The authors found that the 24-month-old participants searched longer in the plural condition, suggesting they were expecting to see ‘more than one’ object in such cases. More recent work by Davies et al. (2016) also suggests that English-acquiring 24-month-olds have an understanding of plural morphology (in particular, of the voiceless /s/ allomorph).
Tieu, Bill, et al. (2017) attempt to explain the difference in the findings from 2-year-olds and 4-year-olds by identifying differences in the experimental paradigms used to test the two age groups. Studies like Wood et al. (2009) (and the more recent Davies et al., 2016) allow toddlers to derive a meaning for the linguistic description, and require the toddler to execute an action (or look to a particular object) based on that interpretation. By contrast, the Truth-Value Judgement Tasks in Tieu et al. (2014, 2015) presented 4-year-olds with situations in which only a single object was depicted. The acceptance of a plural description in such a situation doesn’t necessarily mean that children didn’t expect there to be more than one object. The 4-year-olds may simply have been willing to override their expectation, and accept the use of plural morphology in a context in which they themselves would not have produced the plural. As Tieu, Bill, et al. (2017) point out, this acquisition scenario is quite consistent with a recent proposal regarding children’s so-called pragmatic tolerance in the domain of scalar implicatures (Katsos & Bishop, 2011). According to Katsos & Bishop (2011), preschoolers are simply more tolerant and charitable than adults when forced to accept or reject under-informative scalar descriptions.
13.5 CONCLUDING REMARKS
In this chapter, we have presented an overview of recent experimental work investigating the semantics and pragmatics of plurality. These studies have examined the ‘more than one’ meaning that is seemingly contributed by plural morphology, referred to in the literature as a plurality or a multiplicity inference. As we have discussed, theoretical treatments of the multiplicity inference include deriving the ‘more than one’ meaning as a kind of implicature (Sauerland, 2003; Sauerland et al., 2005; Spector, 2007; Zweig, 2009; Ivlieva, 2013; Magri, 2014; Mayr, 2015), or treating the plural as ambiguous between two possible meanings (Farkas & De Swart, 2010; Grimm, 2013). Recent findings from experiments conducted with children and adults reveal that the plural meaning is sensitive to monotonicity, context-dependent, suspendable under certain conditions, and computed by preschool- aged children on a par with standard implicatures (Sauerland et al., 2005; Pearson et al., 2011; Tieu et al., 2014, 2015; Grimm, 2013). As we have discussed, the implicature approach to multiplicity inferences, in all of its different incarnations, is largely consistent with the experimental evidence accumulated in the literature in recent years, in particular that arising from the comparison between preschool-aged children and adults. This body of experimental work, however, has also introduced certain challenges, arising in particular from the way these inferences can be suspended, their apparent context-dependency, and the relationship between multiplicity inferences and presuppositions. In addition, while some initial attempts to compare multiplicity inferences and classical scalar implicatures have suggested that the two exhibit similar behavioural profiles, more work is needed in order to understand the exact relationship between multiplicity inferences and standard cases of implicature, in both the developing and adult grammar.
1 There is a marked reading of (3a) that makes it equivalent to (4), as supported by the continuation in (i). This generally requires stress on the syllable containing the -s morpheme. We will return to this reading.
(i) Emily didn’t feed giraffes, she fed only one!
2 See Stateva et al. (2016) for experiments in Italian designed to test diverging predictions of a Maximize Presupposition-based theory (Sauerland et al., 2005, Sauerland, 2008) and a higher order implicature theory (Spector, 2007), concerning the interpretation of plural nominals in the scope of universal and non-monotonic quantifiers.
3 An exception to this pattern could arise through the presumably less preferred computation of the multiplicity inference in the scope of negation, a point we return to later.
4 A less plausible source of the yes-responses to the negative sentences would be a wide scope reading of the bare plural above negation, although bare plurals are generally assumed to resist wide scope (cf. Carlson, 1977).
5 See Tian & Breheny (Chapter 12 in this volume) for an overview of experimental studies investigating negation processing and the pragmatic effects of negation.
6 See Zondervan (2007, 2009, 2010) for discussion of the role of the QUD in implicature computation, and Gualmini et al. (2008), Conroy etal. (2009), and Lewis (2013) for relevant discussion of the role of the QUD in child language experiments.
7 It is worth pointing out, however, that the critical stories in the Tieu et al. experiments were such that the protagonist engaged with a particular entity that was explicitly mentioned; according to Grimm (2013), this therefore should have activated the Quantitative QUD as the immediate QUD. The justifications that children provided for accepting (the inclusive reading of) the plural in sentences like Emily fed pigs (where Emily fed exactly one pig), do not seem consistent with this (e.g. Because she feed a pig / Because she said the pig has been feeded, and that happened).
8 See Sneed (2005, 2008) and Lazaridou-Chatzigoga et al. (2015) for discussion of children’s acquisition of generic noun phrases.
9 There are also reports, however, that children do not always produce the plural in required contexts (for discussion, see Berko, 1958; Cazden, 1968; Brown, 1973; Winitz et al., 1981; Mervis & Johnson, 1991; Marcus et al., 1992; Marchman et al., 1997; Zapf & Smith, 2008).