Plurals and definiteness

Plurals and definiteness
Charlie Claessen
Internship with Henriëtte de Swart
January 2011
Abstract
The debate revolving around the semantic markedness of plurals is still ongoing. The strong theory of the plural states that the plural is semantically marked,
whereas the weak theory of the plural states that the plural is semantically unmarked. Experimentally, it is hard to distinguish between these two theories, since
they generally make the same predictions about where plurals are read inclusively
and exclusively. Different studies yielded contradictory results, and there is still a
lot to learn from looking at plurals experimentally. I have conducted a study that
compared singulars and plurals with respect to definite- and indefiniteness. In cases
of mixed reference, definites should use a plural to refer to mixed reference, whereas
indefinites are less restricted as to whether to use a singular or a plural. In different
situations of mixed reference, I gave participants the choice between a singular and
a plural. It turns out that there is a natural preference for plurals over singulars,
specifically present in definites: non-mixed situations with only singulars yield 90%
singular answers, but when only one plural item is added to the situation, this rate
drops to 44%. When there is more than one plural item present –both in situations
where the amount of plurals equals, as well as situations where the amount of plurals
exceeds the amount of singulars– the rate of singular answers drops to 20%. I conclude that the singular/plural ratio of a situation influences the inclusive/exclusive
distribution of the plural.
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Contents
1 Introduction
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2 The semantics of plurals: weak or strong?
2.1 The weak view of the plural . . . . . . . . . .
2.1.1 Sauerland, Anderssen, and Yatsushiro,
2.1.2 Spector, 2007 . . . . . . . . . . . . . .
2.2 The strong view of the plural . . . . . . . . .
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2005
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3 Previous experiments on plurals
3.1 Sauerland, Anderssen and Yatsushiro, 2005
3.1.1 Evidence from child performance . .
3.1.2 Evidence from adult performance . .
3.2 Grimm, 2010 . . . . . . . . . . . . . . . . .
3.3 Pearson, Khan and Snedeker, 2010 . . . . .
3.4 Anand, 2010 . . . . . . . . . . . . . . . . . .
3.5 Livitz and Pylkkänen, 2010 . . . . . . . . .
3.6 Farkas and de Swart, 2010 . . . . . . . . . .
3.7 The story so far . . . . . . . . . . . . . . . .
3.7.1 Definites and indefinites . . . . . . .
3.7.2 Predictions . . . . . . . . . . . . . .
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4 Experimental evidence for the influence
4.1 Experiment A: pre-test . . . . . . . . . .
4.1.1 Results . . . . . . . . . . . . . .
4.1.2 Discussion . . . . . . . . . . . . .
4.2 Experiment B . . . . . . . . . . . . . . .
4.2.1 Results . . . . . . . . . . . . . .
4.2.2 Discussion . . . . . . . . . . . . .
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of definiteness on plurals
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5 Conclusion
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Appendices
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A Instruction for experiment A
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B Items for experiment A
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C Instruction for experiment B
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D Items for experiment B
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References
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2
1
Introduction
The semantic difference between the singular and the plural has long been thought a
simple one: at least in languages where the difference is morphologically marked,singulars
can be thought of as denoting ‘one’, as in (1a), while plurals mean ‘more than one’,
as in (1b).
(1)
a. Mary is eating a cookie.
b. Mary is eating the cookies.
Simply stated, singulars refer to atoms, while plurals refer to sums. More recent
views of the plural (Sauerland, Anderssen, and Yatsushiro (2005), Farkas (2006),
Farkas and de Swart (2010), and Bale, Gagnon, and Khanjian (2011), among others)
have challenged this classic view, by stating that there is another kind of plural: one
that can also include atoms in its reference. Consider the examples in (2):
(2)
a. Have you eaten cookies?
b. There are no cookies left in the jar.
The answer to (2a) is true if you have eaten just one cookie; likewise, the statement
in (2b) is false if there is still one cookie left in the jar. The meaning of the plural in
(1b) is called exclusive, since it denotes only sums, and does not include atoms. The
plurals in (2), however, do include atoms in their reference, and are therefore called
inclusive plurals. Note that regular statements, as in (1b), are upward-entailing
(UE), while the environments in (2) are downward-entailing (DE): plurals get an
exclusive interpretation in UE-environments, and plurals get an inclusive interpretation in DE-environments. Even though plurals in questions or in the scope of
negation can receive an inclusive interpretation, the plural form remains sensitive to
the atom/sum distinction, as the oddness of example (3), taken from Farkas (2006),
shows.
(3)
# Have you noticed Sam’s noses?
Singular and plural forms are always in competition: the singular comes with the
presupposition that the presupposed entity is atomic (but this presupposition can be
cancelled, as we will see later). This competition can be treated in two ways: either
the singular is the marked, semantically strong one, or the plural is. The weaker one
of the two can be considered number-neutral: it only arises because the stronger one
is blocked. This leads to two dominant views concerning plurals: the weak theory of
the plural (Sauerland et al. 2005) states the singular has the semantically marked
meaning, that imposes atomic reference. When atomic reference is intended, the
semantically weak plural is blocked by the semantically strong singular. The strong
theory of the plural (Farkas and de Swart 2010), on the other hand states that the
plural is the semantically marked one: singulars have no semantically defined feature,
and are number-neutral. The semantically strong plural includes both inclusive and
exclusive plurals, and blocks the use of the singular if either of these two readings of
the plural is intended. In this paper I will elaborate both views of the plural in section
2. In section 3, I will discuss previous experiments that have been conducted on
plurals to determine which view is more likely to uphold. I conducted an additional
experiment on plurals, focusing on the singular/plural competition with respect to
definiteness, discussed in section 4.
3
2
The semantics of plurals: weak or strong?
The simple view, where singular forms refer to atoms and plural forms refer to sums,
cannot hold, as the examples in (2) illustrate. Because of the inclusive plural, a more
subtle distinction between the singular and the plural has to be found. Two main
views about the semantics of (singulars and) plurals have arisen: the weak and the
strong view of the plural. The weak plural view has a form-meaning asymmetry:
it treats the morphologically unmarked singular as semantically marked and the
morphologically marked plural as semantically unmarked. The strong plural view,
however, has a symmetric form-meaning pairing: it treats the morphologically unmarked singular as semantically unmarked, and the morphologically marked plural
as semantically marked.
Accounts that treat the plural as semantically weak have to distinguish between
semantic and morphological markedness. In different aspects of many languages, the
morphologically marked form also has the semantically marked meaning. Consider
for example the gender difference in (4):
(4)
a. lion
b. lioness
The male lion is morphologically unmarked, while the female lioness is morphologically marked: it has a suffix attachted to the root (male) form. The unmarked form
also has an unmarked meaning:
(5)
a. A group of lions.
b. A group of lionesses.
The unmarked form (5a) can not only be used to refer to a group of male lions,
but also to a group of both male and female lions (and possibly also to a group of
lionesses): its meaning is unmarked. The marked meaning (5b), however, can only
be used to refer to a female group of lions: its meaning is marked.
This symmetrical patterning respects Horn’s division of pragmatic labor: unmarked expressions tend to have an unmarked meaning, whereas marked expressions tend to have a marked meaning. The weak view of the plural has a mismatch
between form and meaning, so it does not respect the Horn pattern. The two views
can therefore also be considered as having the Horn pattern (strong plural) and the
Anti-Horn pattern (weak plural).
2.1
The weak view of the plural
The weak view of the plural treats morphologically marked plurals as semantically
weak (unmarked), and morphologically unmarked singulars as semantically strong
(marked): this view has to distinguish between different kinds of markedness, which
does not respect the Horn pattern. According to the weak view of the plural, since
the plural is divided in both an inclusive and an exclusive reading of the plural,
it must be semantically indifferent to the atom/sum distinction: the plural has
no semantic contribution of its own, and is therefore considered semantically weak.
Since singulars can only refer to atoms, and never to sums, it is not indifferent to this
distinction: they are semantically strong. A pragmatic principle causes the plural
4
never to refer to (just) atoms: the existence of the semantically strong singular,
which has an atomic reference requirement, blocks the use of the semantically weak
plural. This proposal has been worked out in detail in Sauerland, Anderssen, and
Yatsushiro (2005). A different account of the weak plural view comes from Spector
(2007).
2.1.1
Sauerland, Anderssen, and Yatsushiro, 2005
Sauerland, Anderssen, and Yatsushiro (2005) propose a number feature for both
the singular and the plural. The plural feature does not contribute anything semantically, so the plural is semantically weak. The singular feature, however, is
semantically strong, since it contributes a presupposition of atomic reference. Sum
reference is intended when the presupposition of atomic reference is not present.
Sauerland et al. also note the distinction between indefinite plurals in upward
entailing and downward entailing environments. Consider the examples in (6):
(6)
a. Kai has found eggs.
b. Kai has found no eggs.
The sentence in the UE-environment in (6a) is true only if Kai has found more
than one egg. The sentence in the DE-environment in (6b) is false if Kai found a
single egg: the plural marking does not exclude singularity here. This suggests that
number marking on indefinites in DE-environments does not affect truth conditions.
In UE-environments, however, number marking does affect truth conditions. For
example, the plural in (7a) entails that there is more than one egg still hidden,
while the singular in (7b) does not. The distinction between the singular and the
plural is even stronger: the singular in (7b) has an implicature that only one egg is
still hidden.
(7)
a. Some eggs are still hidden.
b. Some egg is still hidden.
Number marking does not affect truth conditions in DE-environments, but it
does in UE-environments. Sauerland et al. differentiate between the singular and
the plural in UE-environments through a principle called Maximize Presupposition:
Maximize Presupposition: between two interpretations, where one has
more/stronger presuppositions than the other, choose the interpretation
with the most presuppositions satisfied in the context.
Since the plural does not come with a presupposition, Maximize Presupposition
interprets the scope of the existential in (7a) as a total function. The singular
alternative, however, is a partial function defined only for atoms. Maximize Presupposition then predicts that the domain of the plural excludes all atoms, from which
it follows that a plurality of eggs is still hidden. Similarly, Maximize Presupposition
applied to (7b) predicts that no more than one egg is still hidden, which is indeed
what was implicated. Simply stated, in UE-environments, Maximize Presupposition
predicts an exclusive interpretation of plurals: if the atomic presupposition of the
singular was satisfied, Maximize Presupposition would have demanded the use of a
singular form. Since the plural form and not the singular is used, we can conclude
that the meaning of this plural does not include atoms.
5
Sauerland et al. weaken the principle of Maximize Presupposition to account for
the inclusive interpretations of the plural:
Maximize Presupposition applies to the scope of an existential if this
strenghtens the entire utterance.
This makes sure that Maximize Presupposition does not apply to plurals in DEenvironments, like in (6b): in a DE-environment, Maximize Presupposition applied
to the scope of the existential would make the entire utterance weaker, and the
weakened principle stated that Maximize Presupposition should only be applied if
this strenghtens the entire utterance.
2.1.2
Spector, 2007
Spector (2007) proposes a different account: like (Sauerland et al. 2005), he also
proposes a number feature for both the singular and the plural. In Spector’s view,
however, both features come with their own semantic contribution. The singular
feature states that the singular has atomic reference; the plural feature states that
the meaning of the plural is inclusive. The exclusive reading of the plural comes
from a scalar implicature. Consider (8):
(8)
Jack saw horses.
The plural in (8) gets an exclusive interpretation, since it includes a scalar implicature that refutes the atomic reading of (8), ‘Jack did not see exactly one horse’.
2.2
The strong view of the plural
The account that Farkas and de Swart (2010) propose is that of a strong plural.
Plural forms are polysemous between an exclusive plural and an inclusive plural, so
both atoms and sums can be included in the reference of a plural. Semantically,
plurals come with a feature [Pl], that has a polysemous semantics (i.e. it includes
both inclusive and exclusive plurals). Singulars do not come with a feature: the
meaning of singulars is derived from the meaning of plurals trough a blocking effect.
Farkas and de Swart use a bi-directional optimality theoretic approach to derive
the optimal form-meaning pairs. A morphologically marked form has more morphological content than a morphologically unmarked form. Likewise, a semantically
(conceptually) marked meaning is conceptually more complex than a semantically
unmarked meaning. This leads to the singular being the unmarked and the plural being the marked form. Conceptually, atoms are less complex than sums, so
reference to atoms is semantically unmarked, while reference to sums is semantically marked. There are two possibilities regarding sum reference: (i) sum reference
that excludes atoms (exclusive sum reference), and (ii) sum reference that includes
atoms (inclusive sum reference). Their approach uses bias constraints for number
(a plural nominal does not have atomic reference, a singular nominal does not have
sum reference), as well as *functN, a markedness constraint on forms, that is an
economy constraint on functional structure in the nominal domain. This leads to
the following form-meaning pairs in (9):
(9)
a. singular form — atomic reference
6
b. plural form — inclusive sum reference
c. plural form — exclusive sum reference
This ensures that plural nominals will always include sums, either inclusively or
exclusively. Singular nominals do not have an inherent denotation restricting the
atom/sum distinction: they do not come with a number feature, whereas the plural
does come with a [Pl] feature. The interpretation of the singular itself is insensitive
to the atom/sum distinction. The interpretation of nominals does have to be interpreted as relating to the atom/sum distinction: the bi-optimal approach makes sure
that a nominal that does not have plural morphology (and therefore lacks the plural
number feature) yields exclusive atomic reference.
In this strong view of the plural, the singular does not pose a potential problem:
it is simply used whenever a plural interpretation (be it inclusive or exclusive) is
not available. The choice between an inclusive or an exclusive reading of the plural,
however, is not a free one. Farkas and de Swart use the Strongest Meaning Hypothesis (SMH), a pragmatic principle, to regulate the choice between the two readings
of the plural. The SMH applies to a set of interpretations, ordered by entailment,
and chooses the strongest element of the set that is compatible with the context.
The exclusive reading of the plural asymmetrically entails the inclusive one: a reference that only includes sums is included in a reference that includes both sums
and atoms. Due to this relation between the exclusive and inclusive reading of the
plural, the SMH can apply. Farkas and de Swart modify the SMH so that it applies
specifically to the plural number feature:
smh pl: the Strongest Meaning Hypothesis for Plurals: for a sentence
involving a plural nominal, prefer that interpretation of [Pl] which leads
to the stronger overall interpretation for the sentence as a whole, unless
this interpretation conflicts with the context of utterance.
In upward entailing environments (10a), the exclusive interpretation of the plural
entails the inclusive interpretation, so the smh pl favors the exclusive interpretation of horses over an inclusive one: the interpretation that Mary saw more than
one horse (exclusive plural) is stronger than the interpretation that Mary saw one
or more horses (inclusive plural). In downward entailing environments, however,
the scale is reversed because the monotonicity is reversed: in (10b), the inclusive
interpretation of the plural entails the exclusive interpretation, so in DE-contexts,
the smh pl favorrs the inclusive interpretation of horses over an exclusive one: the
interpretation that Mary did not see one or more horses (inclusive plural) is stronger
than the interpretation that Mary did not see more than one horse (exclusive plural).
(10)
a. Mary saw horses.
b. Mary did not see horses.
The SMH, and therefore the smh pl as well, is a pragmatic principle: it can be
overridden by contextual factors. Consider the example in (11), that Farkas and
de Swart bring up:
(11)
[Speaker walks into basement, and notices mouse droppings]:
Arghh, we have mice!
7
Even though an upward entailing environment such as in (11) ususally prefers an
exclusive interpretation, the utterance in (11) is felicitous with an inclusive interpretation in situations where the speaker has indirect evidence for the presence of mice,
but is unsure whether it concerns one or more mice. An inclusive interpretation is
the strongest one possible of this sentence in a situation of speaker ignorance: both
atomic and sum reference are compatible with the information the speaker has.
8
3
Previous experiments on plurals
Introspective arguments to support a localist view of embedded implicatures, as
brought up by Chierchia, Fox, and Spector (2008), have been refuted by experimental
evidence, as brought up by Geurts and Pouscoulous (2009) and Chemla (2009). You
cannot make a valid claim about implicatures based on introspective evidence alone,
and similarly, you cannot distinguish between the strong and the weak theory of the
plural based on introspective evidence alone.
Several experimental studies have tried to distinguish between the two theories,
or shed some other light on the debate of the semantics and pragmatics of the plural.
In this section, I will give an overview of previous experiments on plurals.
3.1
Sauerland, Anderssen and Yatsushiro, 2005
Sauerland, Anderssen, and Yatsushiro (2005) ran two experiments on plurals, the
first testing child performance, and the second testing adult performance.
3.1.1
Evidence from child performance
Sauerland et al. presuppose that the singular and the plural involve different interpretive processes: the singular presupposes that a single atomic entity is involved,
while the plural has no presupposition. The plural is interpreted in comparison with
the singular: only when the singular is blocked can the plural be used. A similar
comparison process happens in scalar implicatures: when a weaker scalar item is
used, a hearer can infer that a stronger scalar item is not intended. Experimental work on scalar implicatures has shown that children acquire scalar implicatures
quite late, around age 5. Sauerland et al. hypothesize that children that have not
yet grasped scalar implicatures would not yet understand plural marking the way
adults do as well: the singular has the inherent presupposition of cardinality one,
while the plural does not have an inherent presupposition. The plural is interpreted
only in comparison with the singular, so it is more complex to grasp than the singular. This comparison process is comparable to the process that derives scalar
implicatures, so Sauerland et al. argue that children of the same age group would
not understand plurals the way adults do. They tested 14 children aged 3;4 to 5;9
on English sentences that contained bare plurals. The participants were told that a
space alien toy figure has a lot of questions about life on Earth. Participants were
asked to help the space alien by answering its questions. Critical items included
questions like (12a) – questions to which adults would answer ‘no’. Control items
included both questions to which adults would answer ‘yes’ and questions to which
adults would answer ‘no’. An example control item (to which adults would answer
‘no’) is (12b).
(12)
a. Does a girl have noses?
b. Does a fish have legs?
Sauerland et al. found that children answered the critical items 4% adult-like, while
they answered the control items 97% adult-like. They conclude that young children
indeed do not understand plurality in the way as adults do, corroborating the weak
theory of plurals.
9
3.1.2
Evidence from adult performance
Sauerland et al. tested 43 undergraduates to confirm their own intuitions they used
as the adult standard in the experiment on child performance. They compared the
processing of bare plurals versus plurals modified by a numeral. In total, there were
four types of critical questions: questions where Sauerland et al. expected a ‘no’
response, like (13a) and (13b), and questions where they expected a ‘yes’ response,
like (13c) and (13d).
(13)
a.
b.
c.
d.
Does
Does
Does
Does
a
a
a
a
dog have tails?
dog have two tails?
goat have horns?
goat have two horns?
For all questions, participants shared their intuitions over 85% of the time. It must
be noted that four out of 43 participants consistently interpreted questions like
(13a) as including the singular – so even adults could get an inclusive reading in
these types of questions. Furthermore, this type of questions, (which they also used
in the experiment on child performance) has a lower number of correct responses
compared to the other three question types. Question types (13b, 13c, 13d) had
over 95% correct responses, while question type (13a) only had over 85% correct
responses – excluding the four participants that answered ‘yes’ to these questions
on all items! While these percentages show that a majority of adults does indeed
answer ‘no’ to questions like (13a), they also show that adults find questions like
(13a) harder than questions like (13b, 13c, 13d).
Sauerland et al. mention the difference between two types of questions: true information seeking questions, and exam type questions. The difference is whether
the questioner knows the answer to the question (exam type) or not (information
seeking). For an adult, a typical exam type question would be (13a), here repeated
as (14). An information seeking question would be (15). Both types of questions
mentioned here contain a bare plural referring to cardinality ‘one’, yet the exam
type question is answered differently than the information seeking question: (14)
gets a ‘no’ answer, because a dog only has one tail, but (15) gets a ‘yes’ answer,
because the office does indeed have one window.
(14)
Does a dog have tails?
a. * Yes
b.
No
(15)
Does your office have windows?
a.
Yes (only one though)
b. # No
Recall that in the child performance experiment, children answered questions asked
by a space alien toy figure, who did not know anything about life on earth: children
answering (13a) did not answer the exam type question (14), but they answered
this question as an information-seeking question. Adults, however, would answer
(13a) as an exam type question. Children might not consider the question Does a
dog have tails? to be equivalent to Does a dog have more than one tail? (while
10
adults do consider these two questions equivalent): children answering information
seeking questions could infer a kind reading, and consider the question not to be
about one specific dog, but about dogs in general. In that case, they consider the
question Does a dog have tails? equivalent to Do dogs have tails?. The answer to
the latter question is, of course, ‘yes’. A way to circumvent the kind reading is to use
definite plurals: Sauerland et al. used only bare plurals in their child performance
task, and bare plurals can give rise to a kind reading. Definite plurals have a
maximality requirement, so they should always lead to a plural interpretation. If
children would still get a ‘singular’, non-adult-like interpretation of the plural, then
one could conclude that children do not yet understand plural marking the way
adults do.
3.2
Grimm, 2010
Grimm (2010) presents experimental evidence concerning the inclusive reading of
plurals in downward-entailing (DE) environments. Both Sauerland et al. (2005)
and Farkas and de Swart (2010) relate the inclusive reading of the plural to DEenvironments: plural indefinites in a DE-environment generally include reference to
singular entities, so (16) is false if Ed saw one dog.
(16)
Ed didn’t see dogs.
Grimm claims that the inclusive reading of indefinite plurals is not causally related to
DE-environments, since inclusive readings also arise in some non-DE environments,
such as the ones in (17).
(17)
a. Ed wants to eat sandwiches.
b. Both students who saw spies reported to the police.
Furthermore, he claims that the inclusive reading of the plural can only be associated with a generic, or at least a non-referential reading of the plural. Grimm
presents experimental evidence from two studies to support this last point. In his
first experiment, he presented 40 participants with a picture of a woman asking (18).
(18)
Is the woman in this picture holding mugs?
The picture in this referential context displayed the woman holding either one or
two mugs. When the woman in the picture was holding two mugs, participants
answered ‘yes’ 92% of the time, but when the woman was holding only one mug,
participants answered ‘yes’ only 37% of the time. According to both the weak
and the strong view of the plural, this is unexpected, since the DE-environment
should give rise to the inclusive reading more easily than the 37% that was attested.
Grimm’s second experiment presented participants with questions within a ‘rulesand-regulations’ environment (true information seeking questions), which is a nonreferential environment that easily gives rise to generic readings. Participants were
presented with questions like (19):
(19) Did you take vacations this fiscal quarter?
Employee facts: employee took exactly one vacation
11
What answer should the employee give? Yes/No
Grimm found that 78% of participants answered ‘yes’ to a question like (19), preferring the inclusive reading of the plural. Grimm concludes that on the basis of
these two experiments it can be said that a referential use of the plural (as in his
first experiment) prefers an exclusive reading of the plural, while a non-referential
use of the plural (as in his second experiment) prefers an inclusive reading.
Exam type and information seeking questions lead to different expectations concerning the distribution of the plural. Grimm showed that whether a question is
referential or not also influences the expectations concerning the distribution of the
plural.
3.3
Pearson, Khan and Snedeker, 2010
Pearson, Khan, and Snedeker (2010) use the comparison with scalar implicatures
to give experimental evidence in support for the weak plural view (Sauerland et al.
2005): a weak scalar item is in competition with a stronger scalar item, and likewise,
the weak plural is in competition with the strong singular. Using a plural implicates
that the atomicity presupposition is not satisfied. A scalar implicature can be cancelled, so when this happens, the plural can get an inclusive reading, but usually,
plurals are supposed to mean ‘more than one’.
Pearson et al. (2010) conducted a series of experiments using a covered box task.
Participants are shown three cards. The pictures on two of the cards are visible, the
third card is covered. Participants hear instructions of the form ‘Give me the card
where Big Bird has a flower/flowers’ and are trained to pick the covered card when
neither visible card matches the instruction. In the critical trials, the visible cards
contained (i) no flowers and (ii) a plurality of flowers for the singular condition, and
a single flower for the plural condition.
Their main experiment, testing 36 speakers, consisted of one card with Big Bird
(and nothing else), one covered card, and a card with Big Bird and one flower (for
the plural condition, figure 1) or three flowers (for the singular condition, figure 2).
If the implicature is cancelled, participants will choose the leftmost card, otherwise
they will choose the covered card.
Figure 1: Plural condition
Participants were given the instruction in (20a) for the singular condition, and
the instruction in (20b for the plural condition. A pre-test which was identical to
12
Figure 2: Singular condition
this experiment except for the use of only failed to give concrete results, so Pearson
et al. (2010) added only to the instructions to force participants to choose the
covered card in the singular condition.
(20)
a. Give me the card where Big Bird only has a flower.
b. Give me the card where Big Bird only has flowers.
Given the instructions as in (20), the covered card was chosen 94% of the time in
the singular condition (20a), preferred over the card showing multiple flowers. In
the plural condition (20b), the covered card was chosen only 30% of the time – the
card showing one flower was chosen the remaining 70% of the time. The participants
who did not choose the covered card cancelled an implicature. The influence of only
must be noted: in the experiment without only, the covered card was always chosen
in the plural condition, while in the experiment with only, this card was chosen
30% of the time. Only has presuppositional properties that probably influence the
cancellation of implicatures: claiming that Big Bird only has a flower presupposes
that there are flowers, that Big Bird has at least one flower. Pearson et al. did a
follow-up study on 35 speakers where they replaced only with and nothing else, so
the instructions are now as in (21).
(21)
a. Give me the card where Big Bird has a flower and nothing else
b. Give me the card where Big Bird has flowers and nothing else.
The presupposed content of the previous experiment is now part of the asserted
content. Pearson et al. hypothesize that participants should pick the covered card
in both the singular and the plural condition. They found that the covered card was
chosen 80% of the time in the singular condition, and 70% in the plural condition:
the scalar implicature was usually not cancelled. This shows that a scalar implicature is easier to cancel when it is part of a presupposition (use of only).
When looking at Pearson et al.’s data in another way, support for the strong
theory of the plural could just as easily be inferred: in the singular condition, participants always choose the covered card over the card with more items. Since they
do not pick out the card with the plurality of items, this could indicate that the plural is blocked, and that participants choose the covered card because of this blocking
effect. This is support for the strong theory – use the singular only when the plural
is blocked. Finally, since it is reasonable to assume the questioner knows which picture is on the other side of the covered card, the type of questions Pearson et al. use
13
are referential/exam type questions, where it is harder to get the inclusive reading
of the plural than with non-referential/information seeking questions. The amount
of implicatures (or: the lack thereof) obtained in Pearson et al.’s experiments could
partially be accounted to this distinction.
3.4
Anand, 2010
Anand (2010) looks at both downward- and upward-entailing contexts, to characterize judgments people make in quantified contexts. Anand looks at the restrictor
(22a) and nuclear scope (22b) or quantified contexts.
(22)
a. Each man playing with dogs is bald.
b. Each baby wearing yellow is playing with teddy bears
In simple upward-entailing (UE) contexts, the plural usually gets an exclusive reading, while in downward-entailing (DE) contexts it gets an inclusive reading. Anand
discusses the proposals of Sauerland et al. (2005), Spector (2007), and Farkas and
de Swart (2010), who all give the same judgments concerning inclusive and exclusive plurals in almost all cases: the restrictor (DE-environment) should yield more
inclusive readings than the nuclear scope (UE-environment).
Anand ran an image verification task, that used each in quantified sentences that
contained a bare plural as either the restrictor or the nuclear scope (depending on
the trial). The 24 participants had to decide whether a target sentence matched a
picture.
(23)
a. The baby playing with teddy bears is wearing yellow.
b. The baby is playing with teddy bears.
The critical items in both the restrictor (23a) and nuclear scope (23b) conditions
tested if an inclusive reading was available, so the images paired with the target
sentences showed exactly one teddy bear. The results did not yield any convincing results: only 24% of the restrictor trials gave rise to an inclusive reading (where
more inclusive readings were expected), and even the nuclear scope trials gave rise to
inclusive readings 33% of the time, when no inclusive readings were expected at all.
Anand notes that between participants, there are subjects who predominantly exclusivize and subjects who predominantly inclusivize, and there was only one subject
that showed a monotonicity correlation (which was expected for all participants):
the majority of participants does not show the expected effect.
3.5
Livitz and Pylkkänen, 2010
Livitz and Pylkkänen (2010) ran two MEG experiments to find out whether singulars or plurals are semantically marked. Livitz and Pylkkänen focus on activity
in the ventromedial prefrontal cortex (vmPFC), which is associated with semantic
composition in previous experiments on (mostly) semantic coercion. They assume
that semantically marked forms require semantic composition, and are therefore accompanied by more activity in the vmPFC. According to Livitz and Pylkkänen,
14
the semantically marked meaning will come with more processing activity in the
vmPFC.
Their first experiment presented an NP embedded in a longer sentence, presented word-by-word to 17 participants. The sentences varied only in this NP: it
was either singular (24a) or plural (24b). Participants had to judge whether test sentences elicited a positive or a neutral/negative emotion. The experiment measured
processing time in the vmPFC.
(24)
a. During the canoe trip the old friends captured an enormous lizard in the
lake.
b. During the canoe trip the old friends captured three enormous lizards in
the lake.
Note that in the singular conditions the indefinite article is used, while in the plural
conditions a numeral is used to indicate a plurality. Livitz and Pylkkänen found
more activity for singulars than plurals 500ms after the critical noun onset (lizard/s)
in the vmPFC region.
Their second experiment tested the same predictions as the first, but used a
different experimental design: a picture matching task. The stimuli in this experiment were not long sentences, like in the first experiment, but only the critical NP,
consisting of a numeral, an adjective, and the critical noun.
(25)
a. one red lizard
b. three red lizards
All 6 participants had to judge whether the picture matches the stimulus. Livitz
and Pylkkänen again found more activity in the vmPFC region for singulars than
for plurals, this time 300ms after critical noun onset. Since both experiments show
significantly more activation in the vmPFC for singulars, they conclude that the
singular must be semantically marked, supporting the weak theory of the plural.
They attribute the differences between the results of both experiments not only to
the different task that was used, but also to determiner/numeral mismatch in experiment 1; the use of complex sentences versus (only) noun phrases; and possibly
the use of some non-intersective adjectives in the first experiment, while the second
experiment used only intersective adjectives. Regardless, they claim that the effects
they found are still valid.
Livitz and Pylkkänen’s experiments, as well as their interpretation of the results,
come with some problems. The first – one they also mention themselves – is that
the stimuli of their first experiment are unmotivated: all singular NPs contain the
indefinite article a(n), while all plural NPs contain a numeral. They claim that this
has no influence on the measured results, but it cannot be ruled out that there is
no influence at all: singular and plural nominals differ in the sense that they refer
to a different set of possible referents. Both adjectives and numerals restrict the
set of possible referents, so any difference Livitz and Pylkkänen measured between
singulars and plurals might as well be due to the use of numerals versus the use of
the indefinite article. Their second experiment comes with less problems than the
first, but they only used six participants, which also casts some doubt on the results.
15
A second problem is that they base their claims about the increased activity in
the vmPFC region mostly on experiments about ‘problematic’ semantic composition: coercion. They generalize this to saying that increased activity in the vmPFC
indicates semantic composition (in general). They take this even one step further
and assume that the composition of the singular or the plural (the marked one) is
indicated by increased activity in the vmPFC – while the experiments they base this
claim on just state that there is some kind of problematic composition, and there
is no reason to assume that the semantic composition of the singular or the plural
is problematic. The obtained results could just as easily be ascribed to the strong
theory of the plural. Both the weak and the strong theory of the plural claim the
two are in competition with each other: the weaker one is used only when the strong
one is blocked. This would lead to increased activity for the weak item, since an
additional step (going via the strong item) is required to get to this item. Given
that Livitz and Pylkkänen found that the singular came with more activity than
the plural, we can conclude that this is because it is used only when the plural is
blocked, arguing the singular has the weak meaning, and the plural the strong one.
3.6
Farkas and de Swart, 2010
Farkas and de Swart (2010) carried out a very small pilot experiment to test their
view on plurality. They expect a plural in an upward entailing context (the nuclear
scope of the quantifier), as in (26), to favor an exclusive reading.
(26)
Each sportsman is wearing gloves.
They carried out a picture matching task, containing the Dutch translation of the
critical item in (26). Participants were shown a picture of a mixed situation: some
sportsmen were wearing one glove, others were wearing two gloves (corrected for
sport: a baseball player wears one glove, while a boxer is wearing two). Participants
strongly rejected (26) as a correct description of the situation, confirming that a
bare plural in the nuclear scope of a quantifier favors an exclusive interpretation
of the plural. The pilot experiment, however, was too small to say whether these
results would be replicated in a follow-up study.
3.7
The story so far
What this section has shown so far, is that it is extremely difficult to make an experimental distinction between the strong and the weak view of the plural. Different
experiments, using different experimental methods with different items, have different outcomes, and researchers draw different conclusions from the data they have
obtained, that can sometimes be interpreted entirely different. Subtle differences are
difficult to attest experimentally, and even robust differences that have been attested
in simple sentences disappear when the sentence is embedded under a quantifier, for
example. In my experiment, my focus will not be on experimentally distinguishing
the strong from the weak theory of the plural, so I can distance myself from the
experiments summed up in this section, while taking into account what these experiments have shown. While Farkas and de Swart (2010) and Bale, Gagnon, and
16
Khanjian (2011), for example, also presented data from other languages, all experiments mentioned here only looked at English. Secondly, most experiments here did
not distinguish between different kinds of plurals, which leads to debatable results,
especially present in Livitz and Pylkkänen (2010). Definite plurals behave differently
from indefinite plurals, that behave differently from plurals modified by numerals or
quantifiers. I will combine these two things and will look at the difference between
definite and indefinite plurals, in Dutch.
3.7.1
Definites and indefinites
A nominal can be singular or plural, and definite or indefinite. This leads to four
possible options, as (27) shows:
(27)
a.
b.
c.
d.
definite singular
definite plural
indefinite singular
indefinite plural
In English, there is one definite article, the, that is used both for the singular and
the plural. The indefinite article a is only used for the singular: the indefinite plural
has a bare form. The definite article poses a uniqueness/maximality requirement
on its nominal, the indefinite article is neutral in this respect. The indefinite article
only contributes existential quantification. Possessive determiners such as your, his
and her can be considered definite: like the definite article, they have no number
restrictions, since they combine both with singulars and plurals. Likewise, they
pose a uniqueness/maximality requirement on the nominal they combine with. The
requirement that only definites have imposes a restriction on the singular that it
can only refer to (a maximal group of) an atomic entity. The indefinite singular
does not have this requirement, so it does not necessarily have to refer to atoms
only. The singular and the plural are always in competition with each other: as
both theories of the plural state, one of the two can be used only when the other
is blocked: the definite plural is used in situations where the definite singular is
not applicable, and the indefinite plural is used in situations where the indefinite
singular is not applicable. Consider the definite example in (28), and the indefinite
example in (29), taken from Sauerland et al. (2005) and Farkas and de Swart (2010),
respectively:
(28)
a. Every boy invited his sister.
b. Every boy invited his sisters.
In (28), the definite singular can only refer to an atomic entity. The reading you
get is that every boy has only one sister, and that he invited this sister. Because of
the competition between the singular and the plural, the definite plural will be used
for all other cases. This includes cases where every boy has more than one sister,
and that he invited (all) his sisters, but also cases where some boys have one sister,
and other boys have more than one sister, and every boy invited the sisters he has.
In this case, the plural is used inclusively. Sauerland et al. refer to these cases as
mixed reference cases.
(29)
a. Every boy invited a friend.
17
b. Every boy invited friends.
The story for the indefinite is different: the singular does not have a maximality/uniqueness requirement, so there is nothing that requires the indefinite singular
to refer only to atoms. The indefinite singular does have the implicature that not
more than one is intended, but this implicature can be cancelled. The situation
in (29a) can therefore be used not just for situations where every boy has just one
friend and he invited him/her, but also for mixed reference situations where some
boys invited more than one friend. The indefinite plural is again in competition,
here with the indefinite singular, and it can be used only in cases where the singular
is not applicable. When the implicature of the singular is cancelled, the indefinite
plural can only refer to exclusive situations: where every boy invited more than one
friend. However, in cases where the implicature of the singular is not cancelled,
the indefinite plural could also be used to refer to inclusive situations. For mixed
reference cases, both the indefinite singular and the indefinite plural can be used.
Comparing the definite and indefinite plural, I expect the definite plural to always
refer to mixed reference situations, since the singular cannot be used in these situations, and I expect the indefinite plural to sometimes refer to mixed reference
situations, since the singular can also be used.
3.7.2
Predictions
In my experiment, I will compare all four conditions mentioned in (27) above: definite singulars, definite plurals, indefinite singulars and indefinite plurals. I expect
definite singulars to refer strictly to atoms, while indefinite singulars are less strict
in referring to atoms only. Vice-versa, definite plurals can be used to refer to mixed
reference situations, while indefinite pluarls are much more restricted in this respect.
I expect that, when given the choice between a definite singular and a definite plural,
participants will opt for the plural in the case of mixed reference, since the definite
singular cannot be used for mixed reference situations. The choice between the indefinite singular and plural in cases of mixed reference is less straightforward: both
can be used to refer to mixed situations. In my experiment, I will try to capture
these predictions that are brought forth by the competition between singulars and
plurals, and the restrictions that definiteness imposes.
18
4 Experimental evidence for the influence of definiteness on plurals
Since all previous experiments on plurals have been on English, the aim of my first
experiment was to see if the inclusive and exclusive reading of the plural are available
in Dutch as well.
4.1
Experiment A: pre-test
I designed a picture matching task to compare singular nominals with plural nominals, and definite nominals with indefinite nominals. The participants were 26
Dutch-speaking students at Utrecht University. Participants were presented with
questionnaires displaying on each page a task like the one shown in figure 3, where
participants had to choose the picture(s) that matched the question (the original
materials were in Dutch).
(a)
(b)
(c)
(d)
Figure 3: ‘Where is Cookie Monster eating a/his cookie(s)?’
Each trial consisted of four pictures: a picture with no (3a), a picture with one
(3b), a picture with two (3c), and a picture with three or four items (3d). Between
items, the four pictures were presented in different orders. Below the four pictures is
a question about the pictures. Participants had to answer which picture(s) matched
the question. Participans were allowed to choose more than one answer. To stimulate
this, each trial contains two pictures that display a plurality, so that participants
always had to choose multiple pictures in some conditions. Each questionnaire
consisted of 18 items: 6 critical items and 12 filler items. There were four critical
conditions: singular definite, plural definite, singular indefinite, and plural indefinite.
The filler items were superficially similar to the test items, but contained nominals
modified by numerals, instead of definite/indefinite nominals. Participants received
one of four possible questionnaires, that presented items in a pseudo-random order.
Table 1 lists the questions that were used; for the corresponding pictures I refer to
the appendix.
A written instruction explained the task with an example that contained a numeral instead of a definite or indefinite nominal. The instruction showed the participants that they had to choose multiple pictures in some conditions. The original
instruction can be found in the appendix.
The critical nouns were presented in a question environment, which is comparable to a downward entailing environment in the sense that it can give rise to an
19
Item
Where
is
Koekiemonster
eating . . . ?
Where is Bert feeding . . . ?
Where
is
Elmo
rolling . . . ?
Where does Purk
have . . . in her hair?
Where is Pino playing with . . . ?
Where is Ieniemienie
wearing . . . ?
sg-def
his cookie
pl-def
his cookies
sg-indef
a cookie
pl-indef
cookies
his pigeon
his pigeons
a pigeon
pigeons
his marble
his marbles
a marble
marbles
her bow
her bows
a bow
bows
his doll
his dolls
a doll
dolls
her bracelet
her bracelets
a bracelet
bracelets
Table 1: Sample items used in experiment A
inclusive reading of the plural. Because of the competition between the singular
and the plural, and the contrast between the definite and indefinite form, I expect
participants to behave differently in all four conditions. For the definite singular,
I expect participants to only pick the singular picture, since definiteness requires
uniqueness. The indefinite singular should be able to give rise to a ‘set-reading’: in
pictures where Cookie Monster is eating two cookies, it is entailed that he is also
eating one cookie. Since the definite singular can only be used for singular pictures,
the definite plural in the question should refer to (i) (exclusively) plural pictures, but
can also refer to (ii) a mix of singular and plural pictures: an inclusive plural. Since
the indefinite singular can also refer to plural pictures, the indefinite plural should
be used mostly exclusively. However, there is nothing that in pirinciple excludes the
use of the indefinite plural inclusively. I expect that, the more the indefinite singular
is used to refer to plural pictures as well, the less the indefinite plural will be used
to refer to the singular picture.
4.1.1
Results
I excluded four participants: some made more than one mistake in the filler conditions, others inclusified all conditions. The inclusive reading can be found both
in singular and plural nominals. Table 2 lists the amount of inclusive and exclusive readings per condition. For the singular conditions, ‘inclusive reading’ means
that participants picked not only the singular picture (3b), but also the two plural
pictures, (3c) and (3d). The ‘exclusive reading’ for the singular conditions means
that participants picked only the singular picture (3b). For the plural conditions,
‘inclusive reading’ means that participants picked not only the two plural pictures
(3c) and (3d), but also the singular picture (3b). The ‘exclusive reading’ for the
plural conditions means that they only picked the two plural pictures (3c) and (3d).
No participant ever chose one of the two plural pictures without also choosing the
other.
20
Condition
indefinite singular
definite singular
indefinite plural
definite plural
inclusive reading
72%
35%
30%
19%
exclusive reading
28%
65%
70%
81%
Table 2: Results of experiment A
4.1.2
Discussion
For the singular conditions, my expectations were met: participants used the definite singular mostly to refer to a singular picture only (65% exclusive reading),
whereas the indefinite singular could easily refer to plural pictures as well (72%
inclusive reading). However, it is unclear why participants could use the definite
singular inclusively 35% of the time, where I expected this not to be possible at all.
For the plural conditions, participants interpreted both the definite and indefinite
plural mostly exclusive, contrary to my expectations. In fact, participants did exactly the opposite of what I expected. I expected the definite plural to yield more
inclusive readings than the indefinite plural, which is not the case. According to my
expectations, the definite plural should be able to get an inclusive reading, because
of the competition with the definite singular. It seems that this is not the case:
participants chose the exclusive reading 81% of the time. The competition between
the indefinite singular and plural can explain the amount of exclusive readings of
the indefinite plural: the indefinite singular was used inclusively 72% of the time,
so the indefinite plural should not be used inclusively very often. This is indeed the
case: the indefinite plural is used inlcusively only 30% of the time.
Part of the high rate of exclusive readings of the plural can be ascribed to the
task used. The questions that were used were exam-type questions, that were also
referential: both could have led to a higher number of exclusive readings of the
plural. It is possible that a picture matching task is not a good task to capture
inclusive readings of the plural; it might even be that, even though the critical noun is
presented in a (inclusive-allowing) question, participants single out the critical noun
while picking out the matching pictures. This means that the proper environment is
cancelled, which of course leads to more exclusive interpretations of the plural. The
only valid conclusion I can draw for this experiment is that inclusive readings are
possible in Dutch, but that a better experiment is needed to experimentally account
for the influence of definiteness on plurals. Because my expectations are based on the
competition between the singular and the plural, I need an experiment that makes
this competition explicit: an experiment where participants actually have to choose
between the singular and the plural. I will attempt this in my next experiment.
4.2
Experiment B
In experiment B, I wanted to make the competition between the singular and the
plural explicit. The participants were 62 Dutch-speaking students at Utrecht University. Participants were presented with questionnaires displaying on each page a
task, consisting of four pictures, as shown in figure 4, paired with four potential
21
questions that could be asked about those pictures, as shown in table 3 (the original
materials were in Dutch). I asked participants how they would ask me (using one
of the four questions) which picture I have in mind.
(a)
(b)
(c)
(d)
Figure 4: Sample figure used in experiment B
1.
2.
3.
4.
Where is Bert feeding his pigeon?
Where is Bert feeding his pigeons?
In what city is Bert feeding his pigeon?
In what city is Bert feeding his pigeons?
Table 3: Sample definite questions used in experiment B
The questions differed in two ways, as the four questions in table 3 show: participants had to choose (i) whether they preferred a singular or a plural form (his pigeon
versus his pigeons), and (ii) which question word they preferred (where versus in
what city). The latter was added as a filler option to disguise the actual purpose
of the experiment: I only took into consideration whether participants preferred a
singular or a plural form. The test items included both definite and indefinite items:
the example above shows a definite example, the actual experiment also included
indefinite examples. The definite and indefinite examples did not differ in the pictures used, only in the definiteness of the questions. For example, the same pictures
in figure 4 were also paired with the following indefinite questions:
1.
2.
3.
4.
Where is Bert feeding a pigeon?
Where is Bert feeding pigeons?
In what city is Bert feeding a pigeon?
In what city is Bert feeding pigeons?
Table 4: Sample indefinite questions used in experiment B
The critical pictures differed in three ways, based on the the singular/plural
ratio of the pictures. This ratio in figure 4 is 2:2, since there are two singular
pictures, (a) and (b), and two plural pictures, (c) and (d): I call this condition
‘2sg/2pl’. I expect that, if I change the singular/plural ratio, participants will shift
their preference. I therefore added two conditions: one in which the number of
singular pictures exceeds the number of plural pictures, ‘3sg/1pl’, as shown in figure
5, and one in which the number of plural pictures exceeds the number of singular
22
pictures, ‘1sg/3pl’, as shown in figure 6. I expect that, when the number of singulars
exceeds the number of plurals, participants will shift their preference more towards
the singular, and vice-versa, that when the number of plurals exceeds the number
of singulars, participants will shift their preference more towards the plural.
(a)
(b)
(c)
(d)
Figure 5: Sample figure for the 3sg/1pl condition used in experiment B
(a)
(b)
(c)
(d)
Figure 6: Sample figure for the 1sg/3pl condition used in experiment B
In addition to these six test conditions (three different singular/plural ratios,
differing in definiteness), I also included four control conditions. The control conditions were not mixed reference situations, but situations where all four pictures
were either singular, as in figure 7, ‘4sg/0pl’, or plural, as in figure 8, ‘0sg/4pl’. The
test and control conditions differed from each other only in the singular/plural ratio
of the pictures, the questions remained the same. The questions used in all definite
conditions (both test and control) are the questions in table 3, and the questions
used in all indefinite test and control conditions are the ones in table 4.
(a)
(b)
(c)
(d)
Figure 7: Sample figure for the 1sg/3pl condition used in experiment B
The order in which the pictures and questions occurred varied per item. Each
questionnaire consisted of 18 items: 6 critical items, 4 control items and 8 filler
23
(a)
(b)
(c)
(d)
Figure 8: Sample figure for the 1sg/3pl condition used in experiment B
items. The filler items were superficially similar to the critical and control items,
but did not contain a definite or indefinite expression. Participants received one
of six possible questionnaires, that presented items in a pseudo-random order. A
written instruction explained the task to the participants, without using a definite
or indefinite construction. Participants were instructed that they should pick only
one question, namely the one that matches the pictures the best: I tested for their
preference. The instruction also told participants that they should be accurate, but
not hasty. The experiment used six different situations, listed in table 5 (the original
items were in Dutch). The original instruction, as well as additional samples of the
original items, can be found in the appendix.
Pictures of
Koekiemonster eating cookie(s)
Bert feeding pigeon(s)
Elmo rolling marble(s)
Purk having bow(s) in her hair
Pino playing with doll(s)
Ieniemienie wearing bracelet(s)
question word
with who/at who’s place
where/in what city
with who/at who’s place
when/at what time
where/in what city
when/at what time
actual choice
singular/plural
singular/plural
singular/plural
singular/plural
singular/plural
singular/plural
Table 5: Sample sentences used in experiment B
As table 3 and 4 show, the answer that participants had to give had the form of a
question. This was to make sure that the inclusive reading is available at all. Because
I directly juxtaposed a singular with a plural, I expect that in the case of definites
the plural will be the preferred form to refer to mixed reference. For indefinites,
both the singular and the plural form can be used for mixed reference. With respect
to the singular/plural ratio of the pictures, I expect situations with more singular
than plural pictures (3sg/1pl) to yield more singular answers, and situations with
more plural than singular pictures (1sg/3pl) to yield more plural answers. I expect
the evenly distributed mixed reference condition, with two singular and two plural
pictures (2sg/2pl), to have a singular/plural answer distribution that is inbetween
the other two conditions. As for the control conditions, I expect for both the definite
and the indefinite condition that the four singular pictures (4sg/0pl) yield all singular
responses, and that the four plural pictures (0sg/4pl) yield all plural responses.
24
4.2.1
Results
Table 6 presents the results of experiment B. In this table, the definite singular
is in comparison with the definite plural, and likewise, the indefinite singular is in
comparison with the indefinite plural.
Test
Control
Configuration
1sg/3pl
3sg/1pl
2sg/2pl
4sg/0pl
0sg/4pl
Definite
Singular Plural
19% 81%
44% 56%
18% 82%
89% 11%
3% 97%
Indefinite
Singular Plural
21% 79%
31% 69%
27% 73%
92% 8%
0% 100%
Table 6: Results of experiment B
For the control conditions, the results were as expected: the all-singular conditions got around 90% singular answers, the all-plural conditions got even better
results, with 97% plural answers for the definite, and 100% plural answers for the
indefinite. Since all critical items were mixed reference situations, I expected the
definite plural to be preferred more often then the definite singular. This is indeed
the case: in all definite items, the plural is preferred over half the time. My expectation that the 2sg/2pl condition would yield results between the 3sg/1pl and
1sg/3pl conditions, did not hold. In fact, the 2sg/2pl condition behaves much like
the 1sg/3pl condition. Only when the amount of singulars exceeds the amount of
plurals, as in the 3sg/1pl condition, does the plural rate drop.
I expected both the indefinite singular and the indefinite plural to be used for
the critical mixed reference situations. The amount of indefinite singulars is higher
than the amount of definite singulars, suggesting that there is more preference for the
indefinite singular compared to the indefinite plural, than there is for the definite
singular in comparison with the definite plural. However, the indefinite plural is
still used a majority of the time, suggesting a natural preference for the plural. The
pattern observed in the definite conditions by looking at the singular/plural ratios,
is only moderately found in the indefinites.
I used a General Linear Modal Univariate Analysis of Variance to see whether the
observations made above are significant. First of all, the overall difference between
the control items and the test items is significant (p>0.05), meaning the control
items served their purpose: it’s not a coincidence that participants are more in
agreement on the control items than they are on the test items. Table 7 summarizes
the differences between different conditions in terms of significance.
For the definites, two of the three critical conditions, 1sg/3pl and 2sg/2pl, did
not differ significantly from the 0sg/4pl control condition. This is not surprising: I
expected that only the definite plural could be used for mixed reference, just as the
plural is more likely to be used in a situation with only plural referents. What is
interesting is that the 1sg/3pl and 2sg/2pl conditions did not differ significantly from
each other. This means that the difference between these two conditions could be
coincidental, which suggests there is a natural preference for the plural: participants
25
Indefinite
Definite
Configuration
1sg/3pl
3sg/1pl
2sg/2p
4sg/0pl
0sg/4pl
1sg/3pl
—
0.58
0.86
0.00
0.01
Configuration
1sg/3pl
3sg/1pl
2sg/2pl
4sg/0p
0sg/4pl
1sg/3pl
—
0.00
1.00
0.00
0.11
Indefinite
3sg/1pl 2sg/2pl
0.58
0.86
—
0.99
0.99
—
0.00
0.00
0.00
0.00
Definite
3sg/1pl 2sg/2pl
0.00
1.00
—
0.00
0.00
—
0.00
0.00
0.00
0.18
4sg/0pl
0.00
0.00
0.00
—
0.00
0sg/4pl
0.01
0.00
0.00
0.00
—
4sg/0pl
0.00
0.00
0.00
—
0.00
0sg/4pl
0.11
0.00
0.18
0.00
—
Table 7: Significance of between-condition results of experiment B
behave the same, regardless of whether the amount of plurals is equal to the amount
of singulars or whether the amount of plurals exceeds the amount of singulars. The
difference between the 1sg/3pl and 2sg/2pl conditions on the one hand, and the
3sg/1pl condition on the other hand, is significant. This means that, only when the
amount of singulars exceeds the amount of plurals, participants shift their preference
for the plural more to the singular.
For the indefinites, all three critical conditions, 1sg/3pl, 3sg/1pl and 2sg/2pl,
differed significantly from both indefinite control conditions, 4sg/0pl and 0sg/4pl.
This means that it is not just a coincedence that participants are more in agreement
on the control items than they are on the critical items. The differences between
the three test conditions, however, are not significant. This means that the difference between the 1sg/3pl and 2sg/2pl conditions on the one hand, and the 3sg/1pl
condition on the other hand, which was significant when the items were definite, is
not significant when the items are indefinite: the difference could be coincidental.
4.2.2
Discussion
The most noteworthy find of this experiment is that the ‘neutral’ 2sg/2pl condition
actually does not significantly differ from the 1sg/3pl condition (p=1.00 for definites
and p=0.86 for indefinites), meaning the 2sg/2pl condition is not neutral at all. This
suggests that there is a natural preference for the plural over the singular. However,
this preference can be overridden by adding more singular stimuli, but only when it
concerns a definite: the 3sg/1pl condition differed significantly from both the 1sg/3pl
and the 2sg/2pl condition (p=0.00). That this difference is found in definites, not
indefinites, comes as no surprise: the definite singular has the additional constraint
that it involves an atomic entity. This is what we see: in the control condition,
participants choose the singular 89% of the time in a situation with only singular
pictures. The balance shifts if the situation is one of mixed reference, even in cases
where only one plural picture is present (3sg/1pl): participants now choose the
26
singular only 44% of the time. In cases of mixed reference where the number of
singular pictures equals (2sg/2pl) or is exceeded by (1sg/3pl) the number of plural
pictures, we see that the balance shifts even more in favor of the plural: participants
choose the singular less than 20% of the time. Indefinite singulars only come with a
presupposition that an atomic entity is the only option. In cases of mixed reference,
both the singular and plural can be used. The natural preference for the plural is
therefore less present. In the indefinite control condition with all plural pictures,
participants indeed opted for the plural form 100% of the time. In cases of mixed
reference where only one singular picture is involved (1sg/3pl), the plural is still
used 79% of the time. However, when more singular pictures are present (2sg/2pl
and 3sg/1pl), the amount of plurals used drops to around 70%. Regardless, in all
indefinite mixed reference cases, the plural is still used a great majority of the time.
27
5
Conclusion
The debate concerning the markedness of plurals, with on the one hand proponents
of the weak theory of the plural, and on the other hand proponents of the strong
theory of the plural, is still undecided. Previous experiments on plurals have led to
some insights, but could not convincingly distinguish between the two theories of
the plural. What these experiments have shown, is that the task used is important:
referential questions, compared to non-referential questions, lead to a lower number
of inclusive plurals (Grimm 2010). The question type is also important: exam-type
questions, compared to information seeking questions, also lead to a lower number
of inclusive plurals (Sauerland et al. 2005). All previous experiments on plurals
have looked at English. In my experiment, I have looked at Dutch, and used a task
that has not been used before in the study on plurals. I compared not only singulars
and plurals, but also looked at the influence of definiteness.
In cases of mixed reference, definites should only be able to use the plural to refer
to a mixed situation, since the definite singular has an atomicity requirement, and
cannot be used for these situations. Since the indefinite singular is less restricted
than the definite singular, there should be no preference for indefinite singulars
or plurals in mixed situations. In my experiment, I presented participants with
different configurations of mixed reference (varying the singular/plural ratio), and
tested their preference of singulars and plurals. It turns out that there is a natural
preference for plurals over singulars, clearly visible in definites. Definite non-mixed
situations with only singular pictures yield almost 90% singular answers. However,
when there is only one plural picture added to the situation, participants opt for
the singular only 44% of the time. When the amount of plurals exceeds the amount
of singulars, and even when the amount of plurals equals the amount of singulars
depicted in a situation, participants only choose the singular about 20% of the time.
The differences between these three definite mixed reference situations are significant. In indefinites, the natural preference for plurals is less visible: in an indefinite
non-mixed situation with only plurals, participants prefer the plural 100% of the
time. However, when the situation changes to a mixed reference situation and one
singular condition is added, participants prefer the plural 80% of the time. When
the amount of singulars equals or exceeds the amount of plurals, participants prefer
the plural 70% of the time, but this does not differ significantly from the other mixed
reference condition: in all indefinite mixed reference cases, the plural is used a great
majority of the time. This difference between the definite and the indefinite could
be due to the strict interpretation of the definite singular, whereas the indefinite
singular is less restricted. I can conclude that the division between the amount of
singular and plural items in a mixed situation influences the inclusive/exclusive distribution of the plural. There are still some questions left unanswered: for one, the
difference between the definite and indefinite should be looked in to, possibly with
a task similar to mine, where not only the competition between the singular and
the plural is made explicit, but also where participants are given a choice between
definites and indefinites.
28
A
Instruction for experiment A
In dit experimentje krijg je telkens vier plaatjes te zien, gevolgd door een vraag over
deze plaatjes. Aan jou de vraag welke plaatjes de vraag beschrijft. Ik ben op zoek
naar alle mogelijke plaatjes die bij de zin passen: kies dus niet alleen het plaatje dat
het beste past, maar kies ieder plaatje dat bij de zin past.
Er zijn in totaal 18 vragen. Voordat het experiment begint krijg je een voorbeeld:
(a)
(b)
(c)
(d)
Waar speelt Grover met minstens één hond?
De verwachte plaatjes zijn hier (b) én (c) én (d): op alle drie deze plaatjes speelt
Grover met één of meer honden.
29
B
Items for experiment A
(a)
(b)
(c)
(d)
Figure A: Waar eet Koekiemonster zijn koekje/zijn koekjes/een koekje/koekjes?
‘Where is Koekiemonster eating his cookie/his cookies/a cookie/cookies?’
(a)
(b)
(c)
(d)
Figure B: Waar voert Bert zijn duif/zijn duiven/een duif/duiven?
‘Where is Bert feeding his pigeon/his pigeons/a pigeon/pigeons?’
30
(a)
(b)
(c)
(d)
Figure C: Waar rolt Elmo zijn knikker/zijn knikkers/een knikker/knikkers?
‘Where is Elmo rolling his marble/his marbles/a marble/marbles?’
(a)
(b)
(c)
(d)
Figure D: Waar heeft Purk haar strikje/haar strikjes/een strikje/strikjes in het haar?
‘Where does Purk have her bow/her bows/a bow/bows in her hair?’
31
(a)
(b)
(c)
(d)
Figure E: Waar speelt Pino met zijn pop/zijn poppen/een pop/poppen?
‘Where is Pino playing with his doll/his dolls/a doll/dolls?’
(a)
(b)
(c)
(d)
Figure F: Waar draagt Ieniemienie haar armband/haar armbanden/een armband/armbanden?
‘Where is Ieniemienie wearing her bracelet/her bracelets/a bracelet/bracelets?’
32
C
Instruction for experiment B
In dit experimentje krijg je telkens vier plaatjes te zien. Ik neem één van de vier
plaatjes in gedachten. Onder de plaatjes staan vier mogelijke vragen die je kan
stellen over de plaatjes. Hoe zou je vragen welk plaatje ik in gedachten heb?
Kies slechts één van de vier opties per vraag, ook als je van mening bent dat er
meerdere opties mogelijk zijn.
Er zijn in totaal 18 vragen. Blijf niet te lang bij elke vraag stilstaan, en kom
niet terug op reeds gegeven antwoorden. Voor het experiment begint krijg je een
voorbeeld.
(a)
(b)
(c)
(d)
1. Wanneer eet Koekiemonster twee koekjes?
2. Wanneer eet Koekiemonster een koekje?
3. Hoe laat eet Koekiemonster twee koekjes?
4. Hoe laat eet Koekiemonster een koekje?
Koekiemonster eet in elk plaatje twee koekjes, dus misschien vind je twee koekjes
een betere keuze dan een koekje. De vier plaatjes verschillen in het tijdstip, dus
misschien vind je hoe laat een betere keuze dan wanneer. In dit geval kies je optie
(3), ook al is dit niet het enige mogelijke antwoord.
33
D
Items for experiment B
Each item pictured here was included in the experiment in more conditions: distributed over six different lists, the distribution of the four pictures was 4sg/0pl
(control), 3sg/1pl, 2sg/2pl, 1sg/3pl, 0sg/4pl (control). All these conditions had
both a definite and an indefinite version. Here I included only one version of each
of the items I used.
(a)
(b)
(c)
(d)
Figure G: Met wie/bij wie eet Koekiemonster een koekje/koekjes?
‘With who/at who’s place is Koekiemonster eating a cookie/cookies?’
(a)
(b)
(c)
(d)
Figure H: Waar/in welke plaats voert Bert zijn duif/zijn duiven?
‘Where/in what city is Bert feeding his pigeon/his pigeons?’
34
(a)
(b)
(c)
(d)
Figure I: Met wie/bij wie rolt Elmo een knikker/knikkers?
‘With who/at who’s place is Elmo rolling a marble/marbles?’
(a)
(b)
(c)
(d)
Figure J: Wanneer/hoe laat heeft Purk haar strikje/haar strikjes in het haar?
When/at what time does Purk have her bow/her bows in her hair?’
35
(a)
(b)
(c)
(d)
Figure K: Waar/in welke plaats speelt Pino met een pop/poppen?
‘Where/in what city does Pino play with a doll/dolls?’
(a)
(b)
(c)
(d)
Figure L: Wanneer/hoe laat draagt Ieniemienie haar armband/haar armbanden?
‘When/at what time is Ieniemienie wearing her bracelet/her bracelets?’
36
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