# Quantification Puzzles of â€˜Douâ€™

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```					Quantification Puzzles of ‘Dou’

Min Que
0400823

Utrecht University

2006

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Contents

1 General introduction                                                                                                           3
1.1 Syntactic features of ‘Dou’ ... ..................................................................................... 3
1.2 Semantic functions of ‘Dou’ ... .................................................................................. 6
1.3 Outline of this thesis ................................................................................................ 7

2 ‘Dou’ as a distributivity operator                                                                              8
2.1 The account of ‘Dou’ as a distributivity operator’ .................................................... 8
2.2 The problem with quantifier words ........................................................................ 11
2.3 The problem with collective predicates .................................................................. 12

3 ‘Dou’ as a Generalized distributivity operator                                                                         14
3.2 Dou as a Generalized D-operator .......................................................................... 16
3.3 Proper Subset Condition of the use of dou .............................................................. 17
3.4 Mei-CL NP and dou ................................................................................................. 19

4 Dou, all, and quanbu                                                                                                           22
4.1 The relation between all and the Generalized D-operator ..................................... 22
4.2 Is dou really the counterpart of all ? ..................................................................... 24
4.3 Quanbu ‘all’ .............................................................................................................. 26

5 Discussions and Conclusion                                                                                                  30
5.1 Discussions ............................................................................................................ 30
5.2 Conclusion ............................................................................................................ 36

References                                                                                                                   37

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Chapter 1

Introduction

The adverb dou ‘all’ has been much discussed in linguistic literature and there exist
diverse views about dou-quantification. This thesis will review two different
hypotheses on dou-quantification with a particular focus on Lin’s (1998) account of
‘ ‘Dou’ as a generalized distributivity operator’.

1.1. Syntactic Features of ‘Dou’

Though this thesis concentrates on the semantics of dou, it is nonetheless useful to
take certain syntactic characteristics into account as well. Cheng (1995) presents a
summary of the four basic characteristics of dou as follows:

(1) Dou occurs preverbally.

a.      tamen dou lai-le.
they all come-Asp.
‘They all came.’
b.     *tamen lai-le      dou
they come-Asp all
‘They all came.’

(2) Dou quantifies NP to its left and the NP must have plural interpretations.

a.     tamen dou hen xihuan wo
they all very like    I
‘They all like me.’
b.     * ta dou hen xihuan women
he all very like us
‘He likes all of us.’

(3) There is only one dou per clause.

* women dou ba zhexie xuesheng dou ma-ku-le
we all BA these student all scold-cry-Asp
‘We all scolded all of these students, and that made them cry.’

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(4) Dou does not have to be adjacent to its NP, but there are locality restrictions.
a.     zhexie xuesheng wo dou xihuan
these student I all like
‘I like all of these students.’

b.     * zhexie xuesheng zhidao wo dou xihuan guojing.
these student know I all like Guojing.
‘All of these students know that I like Guojing.’

It is interesting to notice the so-called leftness condition on dou-quantification, as
stated in (2). Generally an object NP associated with dou must be moved to the left of
dou at S-structure. Consider (5).

(Lee 1986)
(5)    Naxie shu1 wo dou kan-guo.
‘I read all of those books.’

In virtue of the ‘VP-internal subject hypothesis’ which assumes that subjects originate
inside VP, Lin proposes that the structure of (5) contains two traces inside VP, one
being the subject trace and another the object trace, and the index of dou is free to
select either trace to bind. When dou is associated with the object NP naxie shu ‘those
books’, the property of being read will serve as the argument of dou, which
guarantees that the raised object NP rather than the subject NP wo ‘I’ is the argument
that will be distributed over. It seems that Lin’s proposal nicely captures the problem.

Another very important feature of dou is its locality condition, as briefly mentioned in
(4). Lee (1986) observes that dou must be clause-bound and he puts forward a rule
given in (6) .

(6) Dou-coindexing
Coindex with dou any leftward constituent it c-commands. (A c-commands B iff
neither dominates the other and the first maximal projection dominating A also
dominates B)

According to this coindexing rule, dou in an embedded clause may not be related to
the matrix subject. This is shown in (7) where dou can not distribute over the matrix
subject tamen ‘they’.

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(Lee 1986)
(7)    * Tamen shuo [ zhe ge laoshi dou likai le].
they say this CL teacher all leave asp.
‘ They all said that this teacher had left.’

However, Chiu (1993) has pointed out that it is possible for embedded dou to be
associated with a matrix topic if the topic originates in the same clause as dou. Take (8)
as an example.

(Lin 1998)
(8)    Naxie shu1, Akiu shuo [ List dou du-guo t1].
those books Akiu say List all read-Asp
‘Those books, Akiu said that List read them all.’

The ungrammaticality of (7) is due to the fact that the trace of the matrix subject is too
high for the index of dou to bind, while the only argument trace within the scope of
dou is that of the embedded subject which is a singular NP, not a plural one. So, there
is no argument for the distributive predicate dou likai ‘all leave’. Whereas (8) is
grammatical because the trace of the topic is within the scope of dou, and the topic is
a plural NP, thus the index of dou can bind this trace.

Furthermore, Lin (1998) has found that not only dou in the embedded clause cannot
associate with a matrix argument, but dou in the matrix clause cannot have an
embedded associate either. Sentence (9) is an example.

(Lin 1998)
(9)     * Na-xie shu, wo dou tingshuo [ ta kan-guo t]
that-Cl book I all hear        he read-Asp
‘As for those books, I heard that he has read all of them.’

The trace of Na-xie shu ‘those books’ is within the scope of dou, so it seems that Lin’s
analysis mentioned above permits this sentence, however it is actually very unnatural.
Lin leaves this as an open problem.

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1.2. Semantic functions of ‘Dou’

Semantically, dou has several characteristics, which are summarized below:

(1). When dou occurs, the associated NP can only yield a definite interpretation:

(10)   a.     (You) san-ge ren      likai-le.
(have) 3-CL person leave-ASP
‘There are three persons who left.’

b.      San-ge ren     dou likai-le.
3-CL person all leave-ASP
1. *‘There are three persons who left.’
2. ‘The three persons left.’

(2). In addition to meaning something along the lines of English ‘all’, dou can

(11)   a.     Ta dou      bashi sui le.
‘He is already 80 years old.’

b.     Xiaopang dou tongguo kaishi le, ni que meiyou.
Xiaopang even pass      exam SFP, you but not
‘Even Xiaopang passed the exam, you didn’t.’

(3). In contrast with English ‘all’, dou allows exceptions:

(12)   Haizi-men dou likai le, Xiaoming que meiyou.
Kid-Plu. all leave SFP Xiaoming but not
‘All kids left, but not Xiaoming.’

(4). Sentences featuring dou generally do not allow a collective reading:

(13)   Tamen dou mai-le     yi-ben shu.
‘They all bought a book.’

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(5). The characteristic mentioned above, has exceptions, shown as below:

(14)    Zhangsan, Lisi he Wangwu dou shi tongxue.
Zhangsan Lisi and Wangwu all be classmate
‘Zhangsan Lisi and Wangwu are classmates.’

This thesis will mainly discuss the various interpretations with regard to the
distributivity and collectivity, thus concentrate on the semantic characteristics
illustrated in (4) and (5). Generally, there are two controversial accounts on dou-
quantification. The first is that dou should be considered as a distributivity operator
(Lee 1986, Liu 1990 etc.). The second one is that dou should be rather treated as a
Generalized Distributivity Operator (Lin 1998).

1.3. Outline of this thesis

In this research the semantics of dou will be explored extensively. In the next chapter
an early account of dou by Lee (1986) will be discussed. Its weaknesses will be
revealed at the end of that chapter. In chapter 3 a more advanced theory by Lin (1998)
based on Schwarzschild (1996) will be discussed. In chapter 4 I will show that the
semantics of dou is in fact not similar to that of English all, and I will propose that the
Chinese quantifier quanbu instead behaves like English all. In the end, I will open up
discussions and show that Lin’s account is dissatisfying in a number of respects as
well.

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Chapter 2
‘Dou’ as a distributivity operator

2.1 The account of ‘‘Dou’ as a distributivity operator’

It has been observed that in English, the floating quantifier all may be the force of
distributivity in a sentence. This is shown in example (15).

(15)     a.     ? The girls are wearing a dress.
b.     The girls are all wearing a dress.

Sentence (15a) is actually pragmatically ill-formed because it means that more than
one girl are wearing a single dress; while the well-formed sentence (15b), where there
appears all in a floated position, denotes a distributive reading, that is, each one of the
girls is wearing a single dress separately. It seems that all plays a role in the
distributivity of the predicate in (15b).

This observation of all can be captured by Link’s (1987) proposal in which he
suggests to treat floating quantifiers such as all as distributivity operators operating on
a VP, written as Dvp whose translation is as follows:

(16) Dvp  Xy[ y  X  VP( y)] , where X is a variable over plural individuals and
y a variable over singular atomic individuals.

According to this, all in (15b) distributes the property of wearing a dress over each
atomic individual of the group denoted by the subject NP The girls.

If we translate (15) into Chinese as in (16), a similar contrast will be obtained as well.
Sentence (16a) is also pragmatically ill-formed in Chinese and (16b) allows a

(16)     a.     ?Nvhai men chuan zhe yi-tao lifu.
Girls Plural wear DUR one-CL dress.
The girls are wearing a dress.

b.     Nvhai men dou chuan zhe yi-tao lifu.

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Girls Plural all wear DUR one-CL dress.
The girls are all wearing a dress.

Next, let us consider example (17) , a typical example for distributivity in Chinese.

(Lin 1998)
(17) a.        Tamen mai-le yi-bu chezi.
‘They bought a car.’

b.      Tamen dou mai-le yi-bu chezi.
‘They all bought a car.’

Sentence (17a) indicates that the entire group of people bought one car all together;
whereas (17b) means that each one of the group denoted by tamen ‘they’ bought a car.
Thus (17a) has a collective reading and (17b) a distributive reading. The difference in
meaning in this example is triggered by the occurrence of dou in (17b), just like all in
(15b).

Based on the observations such as (16) and (17), it has been widely acknowledged
that dou should be treated as a distributivity operator (Lee 1986, Cheng 1995, Lin
1998 among others), along the line of Link’s theory of distributivity. The semantic
translation of dou is written as dou  PXy[ y  X  P( y)] . Accordingly, dou in
(16b) and (17b) distribute the property of wearing a dress or buying a car respectively
over the atomic individuals of the subject.

Another evidence supporting the distributivity effect of dou is from Lee(1986), shown
in (18) in which the predicate is a collective type.

(18)   a.      Women heyong yi-ge chufang.
We share one-Cl kitchen
‘We share a kitchen.’

b.      Women dou heyong yi-ge chufang
we all share one-Cl kitchen
‘We each share a kitchen with someone else./ All of us share a kitchen.’

According to Lee, while (18a) only has the meaning that we share the same kitchen
together, which is obviously a collective reading, (18b) has a distributive reading on
which each of us shares a kitchen with someone else. However, Lin (1998) points out
that (18b) can have another reading that all of us share a kitchen, nevertheless, this

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reading seems available only when the plural individual denoted by the subject NP
consists of at least three persons. Compare (19 a) with (19b).

(19)   a.      * Women liang-ge ren dou heyong yi-ge chufang.
We two-Cl person all share one-Cl kitchen
‘We two people all share a kitchen.’

b.      Women san-ge ren dou heyong yi-ge chufang.
We three-Cl person all share one-Cl kitchen
‘We three people all share a kitchen.’

(19b) allows a collective reading with respect to the subject NP, but (19a) does not.
We will discuss this further in section 3.

Besides the above instantiations, Cheng (1995) also observes that when dou co-occurs
with wh-words such as shei ‘who’ and shenme ‘what’, it can have the same function.
Consider (20) below.

(Cheng, 1995)
(20) a.       shei dou hui lai
who all will come
‘Everyone will come.’

b.     zhangsan shenme dou chi
Zhangsan what all eat
‘Zhangsan eats everything.’

In sentence (20a) all distributes over shei ‘who’, meaning each one of what shei
‘who’ denotes will come; in (20b) all distributes over the object shenme ‘what’,
meaning Zhangsan eats everything the latter refers to.

As discussed in chapter 1, dou only quantifies NP to its left and the NPs must have
plural interpretations, and the index of dou is free to choose either the subject trace or
the object trace. That is to say, as a distributivity operator, dou distributes the property
denoted by the VP over the atomic individuals of NPs to its left, which apparently
must have plural interpretations, no matter the NPs are subjects or objects of the VP.
However, Lin(1998) points out that it is important to note that when a VP has more
than one index inside it, the binder index of dou is free to choose any index to bind. If
we consider an example like (21), where both the subject NP and the object NP are
plural, we will find there is ambiguity caused by this feature of dou.

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(Lin 1998)
(21) Naxie shu women dou kan-guo le

a. ‘We have read all of those books.’
b. ‘All of us have read those books.’
c. *‘All of us have read all of those books.’

In this case, dou may not only distribute the property of reading over the subject we,
but also distribute the property of being read over the object those books. However it
cannot distribute the property over both the object NP and the subject NP; thus
prohibiting the meaning in (c).

Until now, we have discussed the widely-accepted hypothesis that dou is a
distributivity operator. However, problems have been found when applying this
analysis to some instances, which will be discussed in the next section.

2.2 The problem with quantifier words

Lin (1998) observes that the occurrence between dou and quantifier words such as
mei-(yi)-ge ‘every’ and dabufen-de ‘most’ gives rise to some problems for the
treatment of dou as a distributivity operator. Consider examples in (22).

(Lin 1998)
(22) a.        Meige ren *(dou) mai-le shu
‘Everyone bought a book.’
b.      Dabufen/daduoshu de ren *(dou) mai-le shu
most/majority DE man all buy-Asp book
‘Most people bought a book.’

The English quantifier words like every or most are generally assumed to be
inherently distributive. If this also applies to their Chinese counterpart mei-(yi)-ge and
dabufen-de, the meanings of these two sentences would be unacceptable. Because we
have supposed dou as a distributivity operator, then, in (22a) and (22b), dou has to
distribute the property denoted by the VPs over atomic individuals which are actually
not distributable. This induces a contradiction. In order to account for the problem,
Lin(1998) suggests that we should reconsider the semantics of these quantifier words.

Lin introduces Yabushita’s (1989) proposal on the semantics of ‘Most CN VP’, stated

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as (23) below.

(23) The semantics of ‘Most CN VP’:

ZX [*CN ( X ) & Y (*CN (Y )  Y  X ) & Z  X & VP(Z ) & Z ( X  Z )]

By lambda abstraction, we can get the semantics of most as follows:

(24)most  PQZX [ P( X ) & Y (P(Y )  Y  X ) & Z  X & Q(Z ) & Z ( X  Z )]

Lin suggests that the problem we encountered will be solved if we adopt this analysis
of most. Take (18b) as an example. Applying (24) to (22b), we will get the following
result:

ZX [*person( X ) & Y (*person(Y )  Y  X ) & Z  X & y[ y  Z  w[book' (w)
(25)
& buy' ( y, w)]] & Z ( X  Z )]

The point here is that Z is a variable ranging over plural individuals rather than atomic
individuals, so it can be the argument of the distributive predicate dou mai-le shu ‘all
bought a book’. Then the problem seems to disappear even if we remain the
assumption of dou as a distributive operator. With respect to mei--(yi)-ge ‘every’, dou
will be discussed in detail in chapter 3.

2.3 The problem with collective predicates

Another problem Lin (1998) has observed is that when the above-mentioned
quantifier words occur with both dou and collective predicates, the assumption of dou
as a distributive operator would fail to capture the sentence interpretations. Take (26)
as an example.

(26) Dabufen-de yinger dou zhang de hen xiang
most     baby all grow DE very alike
‘Most babies look a lot alike.’

If we apply the semantics of most in (24) to (26 ), we will get a logical form in (27):

(27)
ZX [*baby' ( X ) & Y (*baby' (Y )  Y  X ) & Z  X & Xy[ y  X  look  alike'
( y)](Z ) & Z  ( X  Z )

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In (27) , Xy[ y  X  look  alike' ( y)] represents the predicate zhang de hen xiang
‘look a lot alike’. If we apply lambda conversion, we will get
y[ y  Z  look  alike' ( y)], meaning that the property of looking alike distributes
down to atomic individuals. This is contradictory to the fact that no single person
could look alike. It seems there exists a problem if we still assume dou is a
distributivity operator.

Now let us consider another example in which the subject NP is not a quantificational
NP.

(Lin 1998)
(28) Naxie ren       dou shi fuqi.
Those people all be husband-and-wife.
‘Those people are all husbands and wives (couples).’

On the assumption of dou as a distributivity operator, the sentence would be false,
because dou has to distributes down to the atomic members of the plural individual
denoted by the subject NP naxie ren ‘those people’, which is contradictory again to
the fact that no single person could be a husband-and-wife. Apparently dou should
distribute to pairs of those people in this case, which challenges the above assumption.

In the next chapter, we will see how Lin(1998) solves this problem.

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Chapter 3

‘Dou’ as a Generalized D-Operator (Lin, 1998)

Before we start discussing dou as a Gegeralized D-Operator, it is necessary to
understand the so-called intermediate reading. We have been familiar with both the
strictly distributive readings, e.g. (17b) on which each person bought a different car
separately, and the strictly collective readings, e.g. (14a) on which all of them bought
one car together. However, Gillon (1987) observes that there are some cases that
allow neither the former nor the latter readings. To see this, consider (29)

(29)   The men wrote operas.

Let’s suppose the men denotes Mozart, Handel, Gilbert, and Sullivan. Apparently the
sentence cannot have a collective reading because these four persons never wrote one
opera together. And it also cannot have a distributive reading, because neither Gilbert
nor Sullivan ever wrote an opera on his own. Thus, the sentence only allows an
intermediate reading between the two extremes. In order to account for this
observation, Gillon (1987) proposes (30).

(30)   [S NPplural VP ] is true iff there is a plurality cover C of the plurality P denoted
by NP such that VP is true for every element in C.

Schwarzschild (1996) further provides a formal definition of covers and plurality
covers, given in (31)

(31)   a. C is a plurality cover of A iff C covers A and no proper subset of C covers A.
b. C covers A if:
(i)     C is a set of subsets of A.
(ii)    Every member of A belongs to some set in C.
(iii)   Ø is not in C.

To understand this definition, let’s do an exercise first. Suppose we have a set {a, b, c,
d} as set A. Let’s examine if the following sets are plurality covers of set A:

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1.   {{a, b, d}, {c}}
2.   {{a, b, c, d}}
3.   {{a, b}, {c, d}}
4.   {{a, b}, {c}}

Set 1 is a set of subsets of set A, every member of set A belongs to some set in set 1,
and there is no null set in set 1, therefore set 1 satisfies all the conditions of (31 b) ,
accordingly we may say set 1 covers set A. And we find that there is no proper subset
of set 1 covers set A. Then, the condition (31 a) is also satisfied. Thus we conclude
that set 1 {{a, b, d}, {c}} is a plurality cover of set A {a, b, c, d}. Following this
reasoning, we may come to the conclusion that set 2 and 3 are also plurality covers of
set A, however set 4 is not, because a member, d, in set A cannot be found in set 4,
that is to say, the second condition in ( 31b) is not satisfied

Now if we take {m, h, g, s} as the denotation of the men in (29) , then the set
{{m},{h}, {g, s}}, which shows the actual condition of the supposed situation, is a
plurality cover of {m, h, g, s} under the definition of (31). Along the line of Gillon’s
proposal in (30), the intermediate reading of (29) can be explained in the following
way: the VP wrote operas is true for every element in the plurality cover {{m}, {h},
{g, s}}, namely, it is the case that Mozart wrote operas, Handel wrote operas, and
Gilbert and Sullivan collaborated on writing operas.

If we further apply this analysis to the Chinese sentence (28) discussed at the end of
chapter 2, we will come to an intermediate solution to the problem. (28) is repeated as
(32) below:

(Lin 1998)
(32) Naxie ren dou shi fuqi.
Those people all be husband-and-wife.
‘Those people are all husbands and wives (couples).’

Suppose there are 10 persons and each two of them is a couple, hence there are five
couples. We may have a set A {a, b, c, d, e, f, g, h , i, j} and its plurality cover {{a,
b}{c, d}{e, f}{g, h}{i, j}}. As we have mentioned, it is totally false if dou distributes
down to atomic individuals in this sentence; however, now we find that the problem
would be solved if we assume that dou can distribute to each element of the plurality
cover. Thus, the property of shi fuqi ‘being husband-and-wife’ is true for each of the
five couples, which is exactly what the sentence means in the supposed situation.

Along this line of reasoning, Lin (1998) proposes that dou should be regarded as an
overt realization of a Generalized Distributivity-Operator. Now let us see how a

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generalized D-operator works.

3.2 Dou as a Generalized D-Operator

Schwarzschld (1991,1996) argues that the availability of intermediate readings is a
context-dependent affair and not all covers are equal, and he suggests that the
definition as (33)

(33)    X  D(Cov)( )iffy[( y  Cov & y  X )  y   ]

In (33), Cov is a free variable over covers of the whole domain of quantification, and
D represents a generalized distributivity operator which does not distributes the
property of VP over atomic individuals, but a plurality cover.

Lin (1998) extends this analysis to the Chinese word dou and proposes that dou can
be treated as a generalized D-Operator. (33) discussed above is a typical example in
which quantification is restricted to specified partitions of the domain, namely each
couple, rather than the domain itself, the whole group.

Let us examine another interesting example.

(34)   Zhangsan, Lisi he Wangwu dou cengjing shi tongxue/ tong-guo xue
Zhangsan Lisi and Wangwu all ever          be classmate
‘Zhangsan, Lisi and Wangwu were all classmates once.’

The nominal predicate tongxue ‘classmate’ expresses a symmetric relation, that is to
say, if A is B’s classmate, then B is also A’s classmate, and no single individual can be
‘a classmate’ on his/her own. Sentence (34) apparently does not mean that Zhangsan
was a classmate, Lisi was a classmate, and Wangwu was a classmate; whereas it
means the three of them were classmates. But notice that the sentence is ambiguous.
One of the readings is that the three persons were classmates in the same class. The
assumption of dou as a distributivity operator will fail to account for this reading,
since the predicate cannot be predicated of atomic individuals. However, if we treat
dou as a generalized D-operator, it can be captured nicely. If we take {Z, L, W} as the
denotation of the subject NP, a one-cell plurality cover {{Z, L, W}}can be obtained
and the predicate tongxue ‘classmate’ is then predicated of the single cell of this
plurality cover. Another reading of this sentence is available if we suppose a condition
in which Zhangsan and Lisi were classmates in elementary school, Lisi and Wangwu
were classmates in high school, and Zhangsan and Wangwu were classmates in
college. Thus, we may have a three-cell plurality cover {{Z, L},{L, W},{Z,W}}so

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that the predicate tongxue ‘classmate’ is predicated of each of the cells in the cover.
The generalized D-operator analysis of dou then captures this reading successfully
again.

3.3 Proper Subset Condition of the use of dou

We have seen how the treatment of dou as a generalized D-operator works in some
cases, however, it is very important to note that predicate type also plays a role in the
interpretation of a sentence. Lin further investigates this and puts forward a restriction
on the use of dou.

According to Dowty (1987), the collective predicates can be divided into two
subclasses. One class is those that have distributive sub-entailments such as gather, be
alike, disagree, disperse, etc. , whereas predicates like be a big group, be a group of
four, be numerous, etc. are devoid of any distributive sub-entailments. Consider (35).

(35)   a.        All the students gathered in the hall.
b.   * All the students in my class are a big group.

In (35 a), the fact that all the students gathered in the hall may entail the truth that
some subgroups of the students gathered in the hall. Besides, in English all is assumed
as a distributive determiner. Thus, all can distribute the property of gathering over the
subsets of the subject NP, which licenses the grammaticality of the sentence. However,
in (35b), the predicate are a big group lacks such distributive entailment, hence all
has nothing to distribute to. Due to this, the second sentence is ungrammatical.

Lin (1998) points out that Dowty’s proposal about English all cannot extend to
Chinese dou. Consider (36).

(36)   Suoyou-de ren/ Naxie ren (*dou) he-mai-le    yi-ge dangao song Lisi.
all       man/those man all together-buy-Asp one-Cl cake  give Lisi
‘ All people/ those people bought a cake for Lisi together.’

According to Dowty’s proposal, the predicate he-mai-le yi-ge dangao song Lisi
‘bought a cake for Lisi together’ belongs to the type that has distributive sub-
entailment, as gather. Therefore, it seems that dou can distribute the property of the
predicate to every member of the group. However, this is actually contrary to the fact
that dou is not allowed to occur in the sentence. Because sentence (36) means that
each of the people contributes some money to buy a cake to Lisi as a group, but not as
sub-groups or individuals.

Based on this observation, Lin (1998) proposes a condition on the use of dou as

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follows:

(37)   Proper Subset Condition on the Use of Dou:
Dou only occurs with predicates which have a proper subset entailment on
the group argument.

Under this condition, the absence of dou in (36) can be explained, because the
predicatehe-mai-le yi-ge dangao song Lisi ‘bought a cake for Lisi together’ does not
have a proper subset entailment on the group argument. Suppose there are four
persons who bought a cake together for Lisi, it is not the case that two or three of
them bought a cake for Lisi.

Contrary to (36), sentence (38) allows the occurrence of dou because if four people
share the same kitchen together, then it is also true that two or three of them share the
same kitchen. The predicate he-yong yi-ge chufang ‘use one kitchen together’, which
has a proper subset entailment, licenses the grammaticality of this sentence.

(38)   Suoyou-de ren/Naxie ren dou he-yong      yi-ge chufang.
All       man/those man all together-use one-Cl kitchen.
‘All people use one kitchen together.’

Accordingly, the ungrammaticality of (19 a) mentioned in chapter 2, repeated as (39)
below, can be captured by the condition of dou. The subject noun of (39 a) denotes a
set consisting of two members, so the set only has two proper subsets, each containing
a single atomic individual. However, the predicate of the (39a) is a collective type
which cannot be true of an atomic individual, hence the proper subset condition on
dou is violated. Unlike (39a), (39b) has a subject NP denotes a set , consisting of three
members , which includes some sets with two atomic individuals as their members of
which the collective predicate can be predicated. Thus, the proper subset condition on
dou is not violated.

(39)   a.      *Women liang-ge ren dou heyong yi-ge chufang.
We       two-Cl person all share one-Cl kitchen
‘We two people all share a kitchen.’

b.      Women san-ge ren dou heyong yi-ge chufang.
We three-Cl person all share one-Cl kitchen
‘We three people all share a kitchen.’

18
3.4 Mei-Cl NP and dou

Lin (1998) does not discuss in detail about the sentences with both dou and mei-Cl NP
‘every-NP’. However, it is interesting to examine if his proposals will apply to those

(40)   Mei-ge nanhai dou tai-guo yi-zhang zhuozi.
every-Cl boy all carry-Asp one-Cl table.
‘Every boy carried a table.’

Here the predicate tai-guo yi-zhang zhuozi ‘carried a table’ is a mixed type, namely it
can be a distributive one or a collective one. It is reasonable to claim that this sentence
allows at least four readings. Let us have a look at what readings we will get when the
universal quantifier mei-ge ‘every’ takes wide scope. Suppose there are five boys
involved in the action of carrying a table. First, the sentence may have a strictly
distributive reading on which each of the five boys carried one table single-handedly.
Adopting Lin’s (1998) treatment of dou as a generalized D-operator, the plurality
cover for this reading might be {{a},{b},{c},{d},{e}} and dou distributes the
property of carrying a table down to each atomic individual. Second, the sentence
may have intermediate readings. One possible situation is that two boys carried one
same table together, and the other three carried another table together. Hence the
plurality cover might be {{a, b}, {c, d, e}} and dou distributes the property of
carrying a table to each of the two elements in the set.

On the other hand, when the existential quantifier yi-ge ‘one-Cl’ takes wide scope, we
may have different stories. First, the sentence may have a strictly collective reading
on which all of the five boys carried the same table at the same time all together. This
reading would be easier to be observed if the sentence is followed by another sentence
like (41)

(41)   Na-zhang zhuozi hen zhong.
that-Cl table very heavy
‘That table is very heavy.’

The corresponding plurality cover for this reading would be {{a, b, c, d, e}}, namely,
the predicate tai-guo yi-zhang zhuozi ‘carried a table’ can only be true of the group
argument as a whole, but not of any proper subset of that group. That is to say that the
truth that the five boys carried one same table does not allow that two or three of them
also carried a table together. This does not satisfy the proper subset condition of dou.

19
However, dou is allowed in this sentence. It seems to be plausible to doubt the validity
of this condition. Second, the sentence may also have intermediate readings. Suppose
there was one table. Two boys carried it for a while and put it down, and then the
other three continued to carry it. The plurality cover for this reading hence would be
{{a, b}, {c, d, e}} and dou distributes the property of carrying a table to each of the
two elements in the set. Notice this plurality cover looks exactly the same as the one
for the intermediate reading when universal quantifier takes wide scope, however, the
interpretations they denote are different.

It is interesting to note that there is an experiential aspect marker –guo in sentence
(40). If we change the aspect into progressive, shown in (42), the readings of the
sentence would be reduced to two.

(42)   Mei-ge nanhai dou zai tai yi-zhang zhuozi.
every-Cl boy all be carry one-Cl table.
‘Every boy is carrying a table.’

Sentence (42) may only have a strictly distributive reading or a strictly collective
concludes that the choice of a particular cover depends not only on pragmatics but
also on other factors, like temporal interpretation.

To further examine the pattern of mei-Cl NP and dou , let us consider example (43).

(43)   Mei-ge nanhai dou die-guo luohan.
every-Cl boy all pile-up-Asp arhat
‘Every boy formed a pyramid.’

It is usually assumed that in English form a pyramid cannot occur with universal
quantifier every, hence (44) is ungrammatical.

(44)   *Every boy formed a pyramid.

However, in Chinese (43) is acceptable and grammatical. Though the gloss of die-guo
luohan is ‘plied-up-Asp arhat’, it is actually the same game as form a pyramid. This
sentence allows three readings. One is a strictly distributive reading on which each
boy had different experience of forming a pyramid with other people who do not
belong to the group denoted by mei-ge nanhai ‘every boy’. One is a strictly collective
reading on which all of the boys had the same experience of forming a pyramid
together. Besides, it may have intermediate readings. One possible situation is like
this: Suppose we have five boys. Two of them participated an activity of forming a
pyramid with other people, three of them participated another activity of forming a

20
pyramid with another group of people. It is important to notice that, just like he-mai-le
yi-ge dangao song Lisi ‘bought a cake for Lisi together’ and tai-guo yi-zhang zhuozi
‘carried a table’, die-guo luohan ‘formed a pyramid’ is also a predicate which have
not a proper subset entailment on the group argument. However, dou can and must
occur in sentence (43). This lends support to our doubt mentioned above.

Now if we change the aspect of (43) into progressive as in (45), it is interesting to
notice that there is no change in readings. The reason why this is different from what
happened in (41) and (42) might be the fact that luohan is not a quantifier NP, but a
bare NP which reduces the complex of the scope interpretations of the sentence.

(45)   Mei-ge nanhai dou zai die luohan.
every-Cl boy all be pile-up arhat
‘Every boy is forming a pyramid.’

With respect to the relation between mei-Cl NP and dou, there is one more point
needed to discuss. Lin(1998) claims that universal quantifier word mei-(yi)-ge ‘every’
must occur with dou in order for the sentence to be grammatical. However, Cheng
(2005, TSSS talk) points out that it is possible to have mei-Cl NP without dou, for
example:

(46)   a.     mei yi-ge chushi (dou) zuo yi-dao cai
MEI one-Cl chef DOU make one-Cl dish
‘Every chef makes a dish’

b.      mei yi-ge-ren (dou) xie yi-fen baogao
MEI one-Cl     DOU write one-Cle report.
‘Everyone writes one report.’

Actually, this co-occurrence can be found easily in standard Chinese. Here are some
other examples:

(47)   a.      Meige nanhai tai zhe yizhang zhuozi.
every-Cl boy carry-Asp a-Cl table.
‘Every boy is carrying a table.’

b.      Meige nanren ju zhe yikuai shitou.
every-Cl man lift-Asp a-Cl rock.
‘Every man is lifting a rock.’

From the above discussion, it seems that the pattern of mei-Cl NP and dou still needs
further investigation.

21
22
Chapter 4

Dou, all, and quanbu

In chapter 3, we discussed the account that dou behaves as an overt realization of
Generalized Distributivity Operator (Lin 1998) and how it can solve the problems we
posed in chapter 2. Based on this idea, in this chapter, we will challenge the
traditional view that Chinese dou is the counterpart of English all and will propose
another word quanbu is actually the real all . But first, let us have a look at some
semantic features of all in English and its relation to Generalized Distributivity
Operator.

4.1    The relation between                      all   and      the     Generalized
Distributivity Operator

Following the theory of distributivity by Schwarzschild (1996), Brisson (2003) claims
that all is not like a standard quantifier, like every, but rather interacts with the
quantification introduced by the D operator to rule out the nonmaximality that a D
operator normally allows. She observed that there is a difference between (48a) and
(48b) concerning maximality. Suppose there are 100 girls and 98 of them jumped into
the lake, it is felicitous to utter a sentence like (48a), which suggests that the definite
determiner allows exceptions. However, when all appears as in (48b), there is no
exception permitted, namely, the sentence strictly means that every girl, in this case
100 in total, jumped in the lake. This contrast shows us that the semantic function of
all here is to make sure that the property of the VP is distributed over to each
individual of the denotation of the definite plural.

(48)   a.      The girls jumped in the lake.

b.      The girls all jumped in the lake.

Brisson proposes a notion of ill-fitting and good-fitting covers to explain this
maximality issue. Recall that in sections 3.1 and 3.2 we introduced what the notion of
cover is. When a generalized D-operator applies to the predicate jumped in the lake ,
as shown in (49), then the sentence will be interpreted as in (50).

23
Di
(49)   The girls        jumped in the lake.

(50)    x[ x  Covi & x  the.girls'  x  jumped.in.the.lake' ]

As shown in (51), suppose we have a universe U and the denotation for girls is G and
that for boys is B, and O, P, and Q are some possible covers of the set of singularities
of U.

(51)   U= {g1, g2, g3, b1, b2, b3,{g1,b1},{g2, g3},{g1,g3,b2,b3}…}
G = [[the girls’]] = { g1, g2, g3}
B = [[the boys’]] = { b1, b2, b3}
O = {{g1},{g2},{g3},{b1,b2}}
P = {{g1},{g2},{g3, b2, b3}}
Q = {{g1}, {g2}, {g3}, {b1}, {b2},{b3}}

In P, g3 is in a cell with two boys, i.e. b1 and b2 are not in the denotation of the girls,
but in that of the boys. Brisson calls P as an ill-fitting cover with respect to the set of
girls, as there is no set of cells whose union is equivalent to the set of girls. The
consequence of assigning P to Covi is that no matter whether g3 did or did not jump in
the lake, the sentence can still come true. The set of { g3, b2, b3} is not a subset of the
set { g1, g2, g3} and there is no such a cell containing g3 which satisfies the restriction
of the quantifier, hence as long as g1 and g2 jumped in the lake the sentence would
turn out to be true. On the contrary, O is a good-fitting cover. In this cover, as each
girl occupies a singleton set of the cover assigned to Covi , each girl is asserted to be
in the extension of jumped.in.the.lake. Brisson defines a cover as a good fit if there is
not any element or member of the set that is stuck in a cell with some non-members.
The formal definition is as follows: (Brisson 2003 : p141)

(52)   Good fit: For some cover of the universe of discourse Cov and some DP
denotation X, Cov is a good fit with respect to X iff
y y  X  Z Z  Cov & y  Z & Z  X 

As we mentioned above that (44a) is a case of nonmaximality which may be caused
by an ill-fitting cover like P where the fact that one of the individuals in the set of {g1,
g2, g3} shares a cell with non-girls makes this individual to be excluded from the
extension of the predicate jumped.in.the.lake. But when all appears in (48b), it
requires a good-fitting cover as O in which each individual in the set of {g1, g2, g3}is
not left out but included in the extension of the predicate. Hence Brisson proposes
that the function of all is to disallow the choice of an ill-fitting cover, or in another
way, all requires a good-fitting cover.

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4.2    Is dou really the counterpart of all ?

It is common practice in the literature to gloss dou as all. However, this turns out to be
confusing and misleading, because not only syntactically but also semantically these
two words have crucial differences.

Syntactically speaking, similar to each, all can both occur to the left of DPs and to the
left of VPs, as shown in (53), hence they are considered as floating quantifiers.

(53)   a.      All the students went home.

b.      The students all went home.

There are similar floating quantifiers in Chinese, e.g. daduoshu ‘most’, illustrated in
(54).

(54)   a.      Daduoshu xuesheng dou likai le.
Most       student all leave Asp
‘Most students left.’

b.      Xueshengmen daduoshu dou likai le.
Student-plu.     most all leave Asp
‘Most students left.’

However, dou is not a floating quantifier since it can only occur preverbally, as
illustrated in (1 a) which is repeated as (55 a) below. If it occurs in the DP, the
sentence is ungrammatical, as shown in (55 b).

(55)   a.      Tamen dou lai-le.
they all come-Asp.
‘They all came.’

b.      *Dou tamen lai-le.
All   they come-Asp
‘They all came.’

The fact that dou does not float should be paid much more attention, since being
glossed as all in the literature potentially causes the misunderstanding that dou is a
floating quantifier.

25
Semantically speaking, there are much more essential differences between dou and
all . Based on the maximization property of all, Brisson comes to the conclusion that
all is dependent on the generalized D-operator, constraining the domain of distributive
quantification. However, dou lacks the characteristic of maximization. Compare (56)
and (57).

(56)   The boys all had lunch.

(57)   Nanhaimen dou chi-guo            wufan le.
Boy-plu.       all   eat-Asp     lunch Asp

Similar to (48b), (56) implies that each of the boys had lunch without any exception.
But (57) does not ensure a maximality effect and allows exceptions. Example (57)
may be understood as allowing exceptions. It is a bit difficult to get the latter reading
directly, but if we suppose there are 50 boys and 48 of them had lunch, then we could
say a sentence like (57). It would be more obvious if we add a jiu ‘only’ -clause to it,
shown as (58).

(58)   Nanhaimen dou chi-guo wufan le, jiu   Xiaoyong he Xiaogang mei chi
boy-plu.  all eat-Asp lunch Asp, only Xiaoyong and Xiaogang not eat.
‘The boys had lunch. Only Xiaoyong and Xiaogang did not.’

Moreover, since all is dependent on a generalized D-operator which is covert in
English (Brisson 2003), and dou is an overt realization of the generalized D-operator
in Chinese (Lin 1998), it would be contradictory if we still consider dou as a
counterpart of all.

Finally dou is obligatory when the quantifiers quanbu or suoyou are used which
roughly mean ‘all’:

(59)   a.      Quanbu xuesheng *(dou) likai-le.
All       student      dou leave-ASP
‘All the students left.’
b.      Suoyou laoshi *(dou) lai-le.
All       teacher dou come-ASP
‘All the teachers came.’

If dou would really be the counterpart of English ‘all’, the above sentences would
contain an extra all and would be parallel with the English phrases below:

26
(60)   a.      *All the students all left.

b.      *All the teachers all came.

It is obvious that the English sentences in (60) are highly ungrammatical. If we
translate dou as ‘all’ we would have expected the same ungrammaticality in Chinese.
But in fact the sentences in (60) are perfectly licit which proves the fact that all and
dou are not the same.

Based on the syntactic and semantic evidence discussed above, I propose that dou is
not the counterpart of all and we should gloss dou just as ‘Dou’ henceforth to avoid
confusion.

But now, there appears another question. Is there a Chinese word which shares its
function with all in English? We will have the answer in the next section.

4.3     Quanbu ‘all’

In this section, I will argue that quanbu in Chinese has similar syntactic and semantic
functions to all in English, and it constrains the domain of quantification introduced
by generalized D-operator and demands good-fitting covers.

Similar to all in English, quanbu ‘all’ can occur both in the DP and the VP. See
example (61).

(61)   a.      Quanbu xuesheng dou huijia    le.
All       student Dou go-home Asp
‘All the students went home.’

b.      Xuesheng quanbu dou huijia       le.
Student     all      Dou go-home Asp
‘The students all went home.’

In (61a) quanbu quantifies the noun right to it, while it quantifies the noun left to it in
(61b), hence we can conclude that it is a floating quantifier, resembling all in English.

Now let us take a close look at the relation between quanbu and dou and how each of
them contributes to the meaning of a sentence. Compare (62 a) and (62b), we will find
the same difference as we see before between (48a) and (48b), repeated as (63a) and
(63b) respectively.

27
(62)   a.      Xueshengmen dou xihuan zhege laoshi.
Student-plu.     Dou like         this teacher
‘The students like this teacher.’

b.      Xueshengmen quanbu dou xihuan zhege laoshi.
Student-plu. all         Dou like     this teacher
‘The students all like this teacher.’

(63)   a.      The girls jumped in the lake.

b.      The girls all jumped in the lake.

Recall that (63a) allows exceptions while (63b) disallows exceptions due to the
function of all which eliminates the nonmaximality. Similarly, if we have 99 out of
100 students who like this teacher but only Xiaomao does not, (62a) is still felicitous,
while (62b) would be infelicitous since the latter has an extra quanbu which, as all,
requires good-fitting covers and hence rule out the nonmaximality that the generalized
D-operator dou normally allows. Example (64) lends support to this argument, as (64b)
means each of the girls helped him, while (64a) could have an interpretation that one
of the girls didn’t help him.

(64)   a.      Nvhaimen dou bangzhu-guo ta.
Girl-plu.    Dou help-Asp him
‘The girls helped him.’

b.     Nvhaimen quanbu dou bangzhu-guo ta.
Girl-plu.   all       Dou help-Asp him
‘The girls all helped him.’

Another piece of evidence that quanbu shares the same function as all comes from the
relation between dou/quanbu and the quantifiers like mei ‘every’ and daduoshu
‘most’.

In English, sentences like (65a) and (65b) are ungrammatical.

(65)   a.      *Every boy all slept.

b.      *Most boys all slept.

Why is it so? Let us try to analyze this. In English, every and most are both considered
as inherently distributive quantifiers. Suppose we have a set of boys {b1, b2, b3, b4,b5}.

28
In the every case, the extension of slept with a subject as every boy should be a set of
singletons {{b1 }, {b2}, {b3 }, {b4 }, {b5}} so that the property of the predicate slept
distributes over each individual of the set of boys. In the case of most, suppose 3 of
the 5 boys slept, then the extension of slept with a subject as most boy could be a set
of singletons {{b1 }, {b2}, {b3 }}. According to the good-fit definition (52), these two
sets are good-fitting covers with respect to the set of boys {b1, b2, b3, b4, b5}. Hence
we may come to a conclusion that every and most can automatically provide good-
fitting covers due to the fact that they are inherently distributive, therefore there is no
need to have all to require good-fitting covers. Along this line of reasoning, now we
may understand why (65 a) and (65b) are ungrammatical in English.

If we translate these two sentences into Chinese with quanbu contained, we will
obtain the same observation. This is shown in (66) where both of the sentences are
ungrammatical.

(66)    a.     *Mei-ge nanhai quanbu shui le.
every-CL boy       all sleep ASP
‘Every boy all slept.’

b.    *Daduoshu nanhai quanbu shui le.
most        boy      all sleep ASP
‘Most boys all slept.’

However if we change quanbu into dou , the sentences will become grammatical,
shown as (67).

(67)   a.      Mei-ge nanhai dou shui le.
every-CL boy       Dou sleep ASP
‘Every boy slept.’

b.      Daduoshu nanhai dou shui le.
most       boy     Dou sleep ASP
‘Most boys slept.’

Interestingly, (67 a) and (67 b) are grammatical parallels to their English counterparts
as in (68). Both the Chinese and the English constructions consist of a quantifier + a
noun and a D-op (either covert or overt) + a verb: [[quantifier, noun] [D-op verb]].

(68)   a.      Every boy slept.

b.      Most boys slept.

29
To conclude, Chinese quanbu has similar semantic function as English all and it
constrains the domain of quantification introduced by the generalized D-operator dou
in Chinese.

30
Chapter 5

Discussions and Conclusion

5.1 Discussions

Although the account of ‘dou as a generalized D-operator’ nicely solves some
quantification puzzles in Chinese, there are still some problems.

5.1.1 Is there a covert generalized D-operator in Chinese?

Schwarzschild (1996) claims there should be a generalized D-operator in natural
languages operating on VPs. Following up this idea, Lin (1998) proposes that there is
an overt realization of the generalized D-operator which is dou. This brings us a
question: is there a covert generalized D-operator in Chinese?

Let us look at example (69) first.

Lin (1998: p 201)
(69)   a.      Tamen mai-le          yi-bu      chezi
‘They bought a car.’
b.      Tamen dou mai-le              yi-bu      chezi
‘They all bought a car.’

Notice that in Lin’s paper, dou is glossed as all. What (64 a), where there is no dou ,
means that the entire group of people denoted by tamen ‘they’ bought a car
collectively. When dou is used as in (69 b), the meaning of the sentence is that each of
them bought one car. What concerns us most is (69 a). If there is a covert generalized
D-operator in Chinese, there must be an atomically distributive reading in (69a), as

31
the reading in (69 b), however, (69 a) only has a collective reading. Does this prove
there is no covert generalized D-operator in Chinese? This is a bit too hasty. Let us
look at example (70).

(70)   Tamen chi-le         yi-kuai pisa   jiu   qu shuijiao le.
They      eat-Asp one-CL pizza then go sleep            Asp
‘After they ate a pizza, they went to sleep.’

Sentence (70) may have a collective reading on which there is only one pizza which
was consumed by the entire group of people denoted by tamen ‘they’, or an extremely
distributive reading on which each of them ate a (mini-) pizza. This example shows us
it seems there is a covert generalized D-operator in Chinese, otherwise we can have

Now let us go back to example (69 a) but change the object yi-bu chezi ‘one-CL car’
into san-bu chezi ‘three-CL car’, shown as (71).

(71)   Tamen mai-le          san-bu   chezi
‘They bought three cars.’

It is interesting to note that example (71) may have the cumulative type of reading
other than a collective reading. Suppose tamen ‘they’ denotes a group of 5 people.
One of the readings (71) has is that the 5 persons bought 3 cars collectively.
It also has a reading on which those people bought 3 cars cumulatively as separate
groups, for example, 2 of them bought 1 car and another 2 of them bought 1 car and
the other 1 bought 1 car, so there are 3 cars in total. Notice that it can not have an
extremely distributive reading on which each of them bought 3 cars. This observation
tells us that there should not be a covert generalized D-operator in Chinese in
contradiction with what we see from example (70). It seems there should be some
other unknown covert operator; otherwise we cannot get a cumulative reading.

32
5.1.2 Other problems for regarding dou as a generalized
D-operator

From the previous section it has become clear that regarding dou as an overt
generalized D-operator cannot explain additional readings of dou, nor can it explain
its distribution in some environments like the fact that it is not present in (70) even
though the distributive reading can be accommodated. Other environments in which
an approach regarding dou as a generalized D-operator fails are shown in (72) below:

(72)    Wo dou jie-yan-le,                ni        zenme hai    mei jie?
I    dou quit-smoking-ASP, you how               already not quit
‘Even I quit smoking. Why didn’t you?’

The semantics of dou in this case reads as ‘even’ or ‘already’. As of yet I cannot give
an explanation for this additional function of dou. However as was already noted by
Cheng (1995) dou can only appear once in a sentence:

(73)   a.      * Haizi-men dou dou tiao-jin hu-li le.
Kid-Plu.      dou dou jump-in lake-in SFP
Intended meaning: ‘Even the kids all jumped into the lake.’

b.      Shenzhi Haizi-men dou tiao-jin hu-li le.
even       Kid-Plu.    dou jump-in lake-in SFP
‘Even the kids all jumped into the lake.’

Since the ‘even’ dou participates in this effect it proves that the dou in (73 a and b) is
not an entirely different word happening to have the same sound as the dou under
discussion in this thesis. If it would have been the same than it remains a mystery why
it takes part in the syntactic constraint that there can only be one dou in a sentence.
Therefore it must be assumed that both the ‘even’ dou and the ‘all’ dou are one and

33
the same. Whatever this additional function of dou accommodating for the ‘even’
reading might be, it cannot be captured by the generalized D-operator.

Moreover the problem noted in the previous paragraph runs deeper. Since there is
some syntactic constraint which prevents dou to appear more than once in a sentence
there occur problems with sentence (21), mentioned in chapter 2 and repeated below:

(Lin 1998)
(74) Naxie shu women dou kan-guo le

a.      ‘We have read all of those books.’
b.      ‘All of us have read those books.’
c.      *‘All of us have read all of those books.’

As can be seen in (74) the meaning (c) is not possible by using only one instance of
dou. This seems quite plausible since if it indeed is a generalized D-operator it makes
sense that only one NP can make use of this feature. This means that we would need
two instances of dou to account for meaning (c). However as was reported before,
such a construction is syntactically impossible. This might be regarded as simply a
syntactic problem, but it would have been nice if the generalized D-operator would be
able to give us more insight in this phenomenon, which it doesn’t.

But in fact there is a much bigger problem concerning the generalized D-operator
which I would like to point out. Recall some of the possible denotations provided by
the generalized D-operator:

1. {{a, b, d}, {c}}
2. {{a, b, c, d}}
3. {{a, b}, {c, d}}

It seems that the generalized D-operator permits quite a lot of readings. But in fact it
permits almost any reading, even the collective one. Of course such a notion nicely
solves a lot of problems concerning dou. However since the generalized D-operator is
so free in its interpretation it is hardly a surprise that it can capture most of the
readings of dou. We could wonder what use we have of an operator that permits

34
almost any reading. Such an analysis gives us little insight in the workings of dou.
Less technically we could phrase the meaning of dou as: some operator playing a roll
within distributivity. Of course that is not very informative. Conceptually a more
specific operator would be desirable.

Furthermore it is no wonder that this operator is covert in many languages like
English. After all if the semantics of such a thing is very thin we could wonder
whether such an operator exists at all. Since there is little empirical proof that this
operator is realized in languages and the only word applying for this function is
Chinese dou, which seems to appear in places that have little to do with distributivity
and does not appear in some cases that would require it, evidence is extremely slim.

Nonetheless I do not wish to claim that the generalized D-operator does not exist.
However it is shown that a more specific account for dou is much desired.

5.1.3 Mei ‘every’ and dou

Lin (1998) tries to argue that, different from English every which is inherently
distributive, mei ‘every’in Chinese is not inherently distributive, hence NPs with mei
has plural denotations. Let us compare (75a) and (75b).

Lin (1998: p 236)
(75)   a.      Nei-yi    zu     (de) xiaohai       dou hua-le    yi-zhang hua
That      group DE     child        [dou] draw-Asp one-CL      picture
‘That group of children all drew a picture.’
b.      Mei-yi    zu     (de) xiaohai       dou hua-le     yi-zhang hua
every     group DE children [dou] draw-Asp one-CL               picture
‘Every group of children all drew a picture.’

The crucial difference between (75a) and (75b) is that the former means that each of
the children in that group drew a picture, while the latter means that each group of the
children drew a picture together. Lin argues that if mei ‘every’ in Chinese is
inherently distributive, (75b) should implies that each of every group of children drew

35
a picture single-handedly, which is obviously not what the sentence means. So he
assumes that mei ‘every’ is not inherently distributive and that mei-yi-zu xiaohai
‘every group of children’denotes a plurality that is made up of groups of children.
Then Lin finds evidence to his assumption from reciprocal sentences, e.g. (76).

Lin (1998:p237)
(76)    Mei-ge ren      dou huxiang      qingwen-le yixia
Every       man [dou] reciprocally kiss-Asp       once
‘Everyone kissed each other.’

Since reciprocal predicates require a plural subject, mei-ge ren ‘every man’ has to
denote a plurality.

Besides, Lin also finds support from Beghelli and Stowell (1997) who observed that
in at least one context, contrary to each, English every seems able to serve as a non-
distributive quantifier, as shown in (77).

(77)    It took all the boys/every boy/*each boy to lift the piano.

Lin thinks it is the same as Chinese mei ‘every’ as in (78).

Lin (1998:p 238)
(78)    Yao tai-qi      zhe-jia gangqing xuyao suoyou            ren/mei-ge ren/ *ge-ge ren
Want lift       this-CL piano        need   all          man/every man/ each man
de hezuo.
DE cooperation.
‘To lift this piano needs all persons’/ every person’s / each person’s
cooperation.’

However Lin (1998) made a wrong observation that mei ‘every’ has to co-occur with
dou. In fact there are plenty of examples in Chinese where they do not have to appear
together, as illustrated in (79).

36
(79)   Mei-ge ren        mai-le     yi-liang che
‘Everyone bought a car.’

What (79) asserts is that each person bought one car separately, which is an extremely
distributive reading. If we consider mei-ge ren ‘every person’ as a plurality, the
sentence should mean that all the people bought one car together, which is obviously

Hence we have to reconsider whether or not mei ‘every’ in Chinese is inherently
distributive.

5.2 Conclusion
In this thesis, two semantic analyses on dou , which are D-operator and Generalized
D-operator, are reviewed. It has been discussed that the latter account is more
advanced. Moreover, a new proposal has been made which is that dou is not English
all , whereas quanbu is more parallel with English all. In the end, some problems of
the second account are discussed and further questions are raised.

37
References:

Beghelli, Filippo and Tim Stowell: 1997. Distributivity and Negation: The Syntax of
Each and Every. In A. Szabolcsi (ed.), Ways of Scope Taking, Kluwer, Dordrecht,
pp. 71-107.
Brisson, C.: 2003. Plurals, All, And The Nonuniformity of Collective Predication.
Linguistics and Philosophy 26: 129-184.
Cheng, Lisa L.-S: 1995, On Dou-Quantification, Journal of East Asian Linguistics 4,
197-234.
Cheng, Lisa L.-S.: 2005, presentation, On each and every type of quantificational
structure in Chinese.
Chiu, Hui Chun: 1993, The Inflectional Structure of Mandarin Chinese, Ph.D.
dissertation, University of California, Los Angeles.
Dowty,David: 1987. A Note On Collective Predicates, Distributive Predicates, and
All. In F. Marshall (ed.), Proceedings of the Third Eastern States Conference on
Linguistics, The Ohio State University, Columbus. pp. 97-115.
Gillon, Brendan S: 1987. The Readings of Plural Noun Phrases in English. Linguistics
and Philosophy 10, 199-219.
Lee, Thomas H.-K. 1986. Studies on Quantification in Chinese, UCLA: PhD
Dissertation.
Lin, Jo-Wang :1998, Distributivity in Chinese and its implications. Natural Language
Semantics 6: 201-243.
Link, Godehard: 1987, Generalized Quantifiers and Plurals, in P. Gardenfors (ed.),
Generalized Quantifiers: Linguistic and Logical Approaches, Reidel, Dordrecht,pp.
151-180.
Schwarzschild, Roger: 1991. On the Meaning of Definite Plural Noun Phrases. Ph.D.
dissertation, University of Massachusetts, Amherst.
Schwarzschild, Roger: 1996. Pluralities. Kluwer, Dordrecht.
Yabushita, Katshiko: 1989. The Semantics of Plurality Quantification: The Proportion
Problem Is a Pseudo-Problem. ESCOL, pp.301-312.

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