Journal of Language and Linguistics Volume 2 Number 1 2003 ISSN 1475 - 8989

1. Introduction

1.1 An Overview

This paper deals with universal quantifiers in Taiwanese, tak 'every', moiN 'every' and takkei 'everyone'. Four issues are addressed in this paper, including whether they allow for a distributive interpretation, whether they allow for a collective reading, their scopal interaction with negation, and with wh phrases. Tak and moiN allows for a distributive reading, but are not compatible with a collective reading. When they interact with negation, they obey the Isomorphism Principle, which basically says that the surface word order determines the scopal relation [Huang, 1981]). When they syntactically precede a wh phrase, they can scope over or under the wh phrase, which result in a Pair-List (PL) reading and a single answer (SA) reading respectively.

Takkei 'everyone' was derived from tak e lang 'every CL person' and presumably it should behave exactly the same as tak 'every'. Examined carefully and compared to moiN chit e lang 'every one CL person', which preserves all the properties of moiN, takkei has its own properties that tak does not have. The first difference is that takkei allows for a collective interpretation, but tak and moiN do not. The second difference is that takkei always scopes over negation, but tak and moiN obey the Isomorphism Principle when interacting with negation. The third difference is that takkei allows for a collective reading when the wh phrase scopes over it and the sentence has the distributive operator long 'all'. Lastly, one sentence can have one takkei only, but tak and moiN do not have this constraint.

To fully understand and explain the syntactic and semantic properties of the universal quantifiers, the distributive operator long 'all' and the collective operator taotin 'together' must be examined first. It will be argued that these two operators project two functional projections, DistP (distributive phrase) and ColP (collective phrase) separately. In addition, based on the fact that plurals always take wide scope, a new tree will be proposed where long and taotin project their functional projections and a PlurP (plural phrase) exists above the DistP and the ColP to encode the wide scope property of plurals. Universal quantifiers in Taiwanese will be argued to move either in overt syntax or in covert syntax to <Spec, DistP>. When they move in overt syntax to <Spec, DistP>, the distributive operator is realized as long in overt syntax. When they move in covert syntax, the distributive operator is not realized in overt syntax. This is why in Taiwanese universal quantifiers can stay in situ but still receive a distributive reading. And, because a collective reading cannot be derived unless the collective operator taotin surfaces in overt syntax and universal quantifiers can receive a distributive reading with or without the distributive operator long, it will be argued that the DistP is the default in Taiwanese.

In addition to their syntactic status, other properties of these two operators will also be discussed. The distributive operator obeys the Leftness Condition, the Locality Condition and the Multiplicity Condition. The Leftness Condition requires that the NP distributed over must be to the left of the operator. This is encoded by the movement of the NP distributed over to <Spec, DistP> in overt syntax. The Locality Condition restricts the distributive ability of the operator in the local clause where the operator is. The Multiplicity Condition requires the NP distributed over must have multiple parts, e.g., plurals, or things like a book which has multiple pages. Besides, the distributive operator obeys a semantic constraint, the exhaustivity of domains condition. This condition requires that the distributive operator long be used as long as all members of a domain are commented, that is, the domain is exhausted. This is why universal quantifiers must co-occur with long as long as they are to its left in overt syntax.

The collective operator taotin shares some of the conditions obeyed by the distributive operator long and has some of its own conditions. Taotin requires that the NP collectivized be plural. This is different the Multiplicity Condition in that entities that have multiple parts such as books cannot be collectivized. It also obeys the Leftness Condition and the Locality Condition. And, unlike long, taotin must surface in overt syntax to derive a collective reading. This is because the DistP is the default and the ColP is not projected unless taotin is realized overtly.

To account the PL reading, Agüero-Bautista (2000) proposes that reconstruction reconstructs the NP argument in the wh phrase back to a position lower than the universal quantifier so that the following reading can be derived:

Since Taiwanese is a wh-in-situ language and hence wh phrases do not move in overt syntax, it will be argued that in Taiwanese it is either the whole wh phrase moves or only the wh determiner moves in LF. When only the wh determiner moves and the NP argument is left behind, the reading above can be derived.

The difference between takkei on the one hand and tak and moiN on the other will be argued to lie in the fact that takkei is a plural universal quantifier and tak and moiN are singular universal quantifiers. Since tak and moiN is just every in English, they can be represented as:

Two semantic representations are proposed for takkei. One is just like the singular one except that the universal quantifier ranges over plural entities:

The other is based on Barwise and Cooper (1981). In that paper, Barwise and Cooper argue that universal quantifier denote the set of all members of a domain, that is, the unique sum individual in lattice-theoretic terms, which is exactly the denotation of definite plurals. Based on the fact that takkei behaves just like definite plurals, which is exactly why one sentence can have only one takkei but tak and moiN do not have this constraint, it will be argued that Barwise and Cooper's denotation of universal quantifiers is a better semantic representation for takkei. But the singular universal quantifiers still remain their traditional denotation because they are different from takkei in that they are not compatible with a collective reading.

1.2 Organization of the Paper

This paper is organized as follows. Section 2 is a description of the syntax of the distributive operator long, the collective operator taotin, and the universal quantifiers. Section 2.1 deals with the syntax of long and taotin. Section 2.2 gives a complete description of the distributivity and collectivity of moiN, tak and takkei. Section 2.3 is devoted to the other properties of long and taotin. Section 3 is about the semantics of distributivity and collectivity. Section 3.1 deals with the semantic representations of the universal quantifiers, where two semantic representations for takkei are proposed. To choose between these two proposals, the syntactic precedence between takkei and moiN chit e lang must be examined, which is done in Section 3.2. Partially based on the discussions in Section 3.2, Section 3.3 deals with the two representations for takkei and picks one that is supported by other evidence. And, then, Section 3.4 deals with the denotations of long and taotin. Section 3.5 is devoted to the interaction between wh phrase and universal quantifiers. The semantic derivations of the possible readings are discussed in this section. And, finally, Section 4 concludes this paper. This paper has two appendices. Appendix A is the detailed semantic derivations discussed in Section 3.3. Appendix B reviews three related previous works.

2. Long, Taotin, and Universal Quantifiers in Taiwanese

This section first discuss the syntax of long 'all' and taotin 'together'. A new tree structure is proposed for this purpose and to explain the scopal interaction between negation and universal quantifiers and plurals. Then, we will discuss the syntactic and semantic properties of tak 'every' and moiN 'every', and those of takkei 'everyone' and moiN chit e lang 'everyone'. And, then we will examine other features of long 'all' and taotin 'together'.

2.1 Syntax of Long and Taotin

Lin (1998) argues that universal quantifiers must move because they carry a strong quantificational feature to be checked and dou must be present to project DistP, whose specifier position is for universal quantifiers to move to, and hence induces a distributive reading. However, this is not the case in Taiwanese.

1	a.	???wo kan le mei yi ben shu
		I read Pfv every one CL book
		'I read every book.'
	b.	*wo dou kan le mei yi ben shu
		I all read Pfv every one CL book
		'I read every book.'
	c.	mei yi ben shu wo dou kan le
		every one CL book I all read Pfv
		'I read every book.'
2	a.	chia e moiN chit pun chu goa long khoaN ke1
		here POSS every one CL book I all read EXP
		'I have read every book here.'
	b.	goa khoaN ke chia e moiN chit pun chu
		I read EXP here POSS every one CL book
		'I have read every book here.'

The examples in (1) are Mandarin. Lin points out that a universal quantifier object cannot stay in situ, as in (1a), and must move to the left of the distributive operator dou, as (1c). As the examples in (2) show, in Taiwanese a universal quantifier object can stay in the object position, that is, in situ, as (2b) shows. And, they can also move to the sentence-initial position, just like the case in Mandarin. And, long 'all', just like dou 'all' in Mandarin, distributes over this universal quantifier object2. This suggests that with or without long 'all', universal quantifiers receive a distributive interpretation in Taiwanese. This generalization can be further supported by the following example about plurals.

3	a.	in boe chhia a
		they buy car Prc
		'They bought a car (individually).'
	b.	goa kayi in
		I like they
		'I like them.'

The plural subject in (3a), in 'they', has a distributive reading even though long 'all' does not occur to provide a distributive interpretation3. (3b) also expresses distributivity. (3b) does not mean that I like them as a group4. Instead, it means I like every single member of them, which is exactly a distributive denotation.

The examples in (2) and (3) suggest that with or without explicit indication of distributivity, which is done by long 'all', universal quantifiers and plurals tend to have a distributive interpretation in Taiwanese. This obligatory distributive interpretation suggests that in Taiwanese DistP is obligatory with or without its head, long 'all', being overtly realized. In addition, (2b) also suggests that universal quantifiers in Taiwanese do not have a strong semantic feature with them since they do not have to move to check any feature in overt syntax. Therefore, they do not have to move in overt syntax, as in (2b). Of course, they can also move in overt syntax, as in (2a).

There is also a collective adverbial, taotin 'together', in Taiwanese. It collectivizes a plural NP and gives the sentence containing it a collective reading, which describes a situation where every member of the plural NP participates in an event denoted by the VP, everyone's participation is part of the whole event and all participations together comprise the event.

4	in taotin boe chit tai chhia
	they together buy one CL car
	'They bought a car together.'

(4) describes a situation where every member of them participated in the car-buying event, i.e., everyone paid for this car. But, a sentence needs taotin 'together' to have a collective denotation. A sentence without either long 'all' or taotin 'together', like (3b), denotes distributivity.

Even though (3a) has a seemingly collective reading, it deos not have a collective interpretation in the sense we discussed above. Let us look at the following examples.

5	a.	[ng ka chueikun kha u chiN a ] [in boe chit tai chhia a]
		[Ng family recently more have money Prc] [they buy one CL car Prc]
		'The Ng's became richer recently. They bought a car.'
	b.	[lan boe chia choe chentouki] [chmma khongkun ko kha lihai a]
		[we buy so many fighter plane] [now air force even more good Prc]
		'We bought so many fighter planes. Now the Air Force is even better.'

(5a) describes the financial situation of the Ng family. This family has more extra money now and this is concluded from the fact that they bought a car. It does not have a collective reading because obviously the young children in this family have no money to pay. (5a), in fact, means that the Ng family bought a car.

(5b) describes a similar situation. If a country bought a lot of fighter planes, its citizens can say something like (5b). Not every citizen participates in the plane buying event. In fact, only a very small portion of the population participates. But, the citizens of this country can still claim 'we bought fighter planes' even though in fact it is this country that bought fighter planes.

These two sentences do not really denote collectivity. The plural NP's are just chosen to refer to a certain kind of group that presumably have several or more members, and, what really participates in the event denoted by the verb is the group, not every member of this group.

Therefore, it can be claimed that a collective reading can surface only when taotin 'together' is overtly realized while a distributive reading is the default with or without long 'all' being overtly realized. That is, the collective operator projects a ColP, Collective Phrase, just like the distributive operator long 'all' projects a DistP only when taotin 'together' is overtly realized.

The following examples show that DistP must precede ColP since long 'all' must precedes taotin 'together'.

6	a.	in ting lepai long taotin khi chia png
		they last week all together go eat rice
		'They went to eat together every day last week.'
	b.	*in tin lepai taotin long khi chi png5
		they last week together all go eat rice
		'They went to eat together every day last week.'

Though plurals are similar to universal quantifiers with respect to distributivity in that both of them allow for a distributive interpretation, they are different with respect with the interaction with negation.

7	a.	goa bo kayi moiN chit e lang
		I no like every one CL person	6
		'I don't like everyone.'
	b.	moiN chit e lang long boai lai
		every one CL person all no come
		'Nobody will come.'
	c.	moiN chit e lang goa long bo kayi
		every one CL person I all no like
		'I like nobody.'
8	a.	goa bo kayi in
		I no like they	NEG precedes PL
		'I don't like them.'	PL > NEG
	b.	in bo kayi goa
		they no like I	PL precedes NEG
		'They don't like me.'	PL > NEG

Universal quantifiers obey the Isomorphism Principle (Huang 1981) when interacting with negation, i.e., the syntactic precedence determines the scopal relation. In (7a), negation syntactically precedes the universal quantifier and scopes over it. In (7b), the universal quantifier syntactically precedes negation, and has scope over negation. (7c) is interesting. Syntactically, the preposed universal quantifier precedes negation. Though it originates from a position lower the negation, the object position, it still scopes over negation since it moves to the topic position, which is higher than negation.

On the other hand, regardless of its syntactic precedence, a plural always scopes over negation, which suggests that plurals should occupy a position higher than universal quantifiers.

We have made the following observations. First, universal quantifiers in Taiwanese do not have to move in overt syntax. Secondly, a distributive reading is the default with or without long 'all' being overtly realized, while a collective reading surfaces only when the collective operator taotin 'together' is overtly realized. Thirdly, DistP is higher than ColP. Fourthly, plurals should occupy a position higher than the position of universal quantifiers and negation.

Based on these observations, and following the idea that each occupies a position higher than every (Aguero-Bautista 2000), and the idea of a functional projection for distributivity and collectivity (Lin 1996, 1998; Beghelli and Stowell 1997; Hsieh 1994; and Li 1992), a new tree structure is proposed:

9

Our observations can be encoded as follows. DistP is always there except when the collective operator taotin 'together' is realized overtly and projects a ColP, which follows from the fact that a sentence with a universal quantifier or a plural always expresses a distributive reading unless the collective operator taotin appears to force a collective interpretation. For (2a), every book moves in overt syntax. It, first, moves to <Spec, DistP> to check a semantic feature and then to <Spec, CP>. This movement is in overt syntax, and the distributive operator is overtly realized as long 'all'. For (2b), every book moves to <Spec, DistP> in LF. Since this movement is in covert syntax, the distributive operator is not realized in overt syntax. For (4), taotin 'together' is realized in overt syntax and projects ColP. The plural NP's move to <Spec, ColP>, and then to <Spec, AgrS>. For (7a), everyone moves to <Spec, AgrS> via <Spec, DistP>. Since the subject position is higher than negation, everyone scopes over negation. For (7c), everyone, though as an object, moves to <Spec, CP>, is higher than negation, and scopes over negation. For (8a) and (8b), plurals must move to <Spec, PlurP> via <Spec, DistP>, and because <Spec, PlurP> is higher than negation, plurals always scope over negation. The discussions above clearly show that (9) successfully encodes the phenomena we observed.

2.2. Tak, MoiN, Distributivity and Collectivity

In Taiwanese, there are two every's. One is tak, and the other moiN. In this section, we examine the semantics of tak and moiN, and then we discuss closely related takkei 'everyone' and moiN chit e lang 'everyone', which manifest interesting differences from other tak + N or moiN + N phrases.

2.2.1 Tak vs. MoiN

The first difference we observe is that moiN 'every' can quantify over plural nouns, but tak 'every' cannot. This has a side effect, that is, the nouns quantified by moiN 'every' can be modified by numbers, but those quantified over by tak 'every' cannot.

10	a.	i e chu moiN go pun goa khoan ke neng pun7
		he POSS book every five CL I read Exp two CL
		'As for his books, I read two out of five.'
	b.	*i e chu tak go pun goa khoaN ke neng pun
		he POSS book every five CL I read Exp two CL
	c.	*tak koa chu
		every CLPL book
11	a.	moiN (chit) pun chu
		every (one) CL book
		'every book'
	b.	tak (*chit) pun chu
		every (*one) CL book
		'every book'

(10a) shows that moiN 'every' can quantify over plural nouns. (10b) and (10c) demonstrate that not only can tak 'every' not quantify over a noun modified by a number but also that it must quantify over a singular noun, since it does not allow for a plural classifier. The contrast between (11a) and (11b) suggests that tak is not only semantically incompatible with plurality but syntactically incompatible with the specification of number, including singular.

The second observation is that both tak 'every' and moiN 'every' are compatible with distributivity. This is not surprising since every is generally assumed to be inherently distributive.

12	a.	moiN/tak pun ni khoaN ke e chu *(long) hon thau-the-khi a
		every CL you read Exp REL book all Passive steal Prc
		'Every book you had read was stolen.'

Just as dou 'all' in Mandarin, long 'all' here is obligatory. The sentence is bad if long 'all' is not there8. The quantifiers with tak 'every' and moiN 'every' can be distributed over by long 'all'.

The third observation is that neither tak nor moiN allows for collectivity9.

13	a.	*tak/moiN chia niao taotin lia niaochu
		every CL cat together catch mouse
	b.	*goa siuNbe ka tak/moiN pun chu taotin boeboe e
		I want DISP every CL book together sell Prc
	c.	gun tao hit koa niao changam taotin lia niaochu
		our house that PL cat last night together catch mouse
		'Those cats at our house caught mice together last night.'
	d.	goa siuNbe ka ni so-u e chu taotin boeboe e
		I want DISP you all POSS book together sell Prc
		'I want to sell all of your books together.'

(13c) and (13d) show that a plural NP can be treated as a collective entity that can be dealt with as a whole. However, though tak + N and moiN + N can comment on all members of a certain group, they cannot be regarded as a plural entity that can be disposed of as a whole.

The fourth observation is about the scope between negation and tak 'every' and moiN 'every'.

14	a.	goa bo chhuhoat tak e haksing
		I no punish every CL student	NEG precedes tak
		'I didn't punish every student.'	NEG > tak
	b.	tak e haksing long bo lai
		every CL student all no come	tak precedes NEG
		'None of the students came.'	tak > NEG
	c.	goa bo chhuhoat moiN chit e haksing
		I no punish every one CL student	NEG precedes moiN
		'I didn't punish every student.'	NEG > moiN
	d.	goa ka e moiN chit e haksing long bohoatto hoeitap chit e buntoei
		I teach REL every one CL student all cannot answer this CL question	moiN precedes NEG
		'None of the students I teach can answer this question.'	moiN > NEG

(14a) and (14b) suggest that the syntactic precedence between negation and tak determines their semantic scope. (14c) and (14d) show that moiN has the same behavior, too. Both tak and moiN obey the Isomorphism Principle, which is assumed to be the general principle for scope taking in the Chinese languages.

The fifth observation is about the scope between wh phrases and tak and moiN.

15	a.	li chhi e tak chia kao long lip ke siaN lang
		you feed REL every CL dog all chase Exp what person
		'Who did every dog you kept chase?'
	b.	A-bin
		'Abin'
	c.	chit chia lip ke a-bin, hit chia lip ke a-hoa, hit chia lip ke a-tai
		this CL chase Exp Abin, that CL chase Exp Ahoa, that CL chase Exp Atai
		'This one chased Abin, that one Ahoa, and that one Atai.'
	d.	!!chia kao pat taotin lip ke abin10
		this PL ever together chase Exp Abin	collective: bad answer
		'These dogs chased Abin together.'
16	a.	li chhi e moiN chia kao long lip ke siaN lang
		you feed REL every CL dog all chase Exp what person
		'Who did every dog you kept chase?'
	b.	A-bin
		'Abin'
	c.	chit chia lip ke a-bin, hit chia lip ke a-hoa, hit chia lip ke a-tai
		this CL chase Exp Abin, that CL chase Exp Ahoa, that CL chase Exp Atai
		'This one chased Abin, that one Ahoa, and that one Atai.'
	d.	!!chia kao pat taotin lip ke abin
		this CL every together chase Exp Abin	collective: bad answer
		'These dogs chased Abin together.'

The second and third observations show that tak and moiN are distributive but not collective. This also applies to wh questions. A collective reading answer is not good for a question like (15a) and (16a). For the other two good answers, the Isomorphism Principle does not work here, i.e., the word order does not correspond to the scopal relations. Though syntactically tak and moiN precede the wh phrase, the wh phrase can either scope under or over these two universal quantifiers. The following chart summarizes what we discussed above.

	tak + N	moiN + N
every + number (every two days)	-	+
distributed over by long	+	+
collectivized by taotin	-	-
negation	Isomorphism Principle	Isomorphism Principle
	DIST/PL reading *collective reading	DIST/PL reading *collective reading

Among the five properties introduced in this section, the fourth and the fifth are syntax-related. The mechanism proposed in Section 2.1 (the tree structure and the movement) can successfully encode the scopal interaction between the universal quantifiers and negation since the examples in (14) are similar to those in (7), and the scopal interaction between negation and the universal quantifiers in (7) are demonstrated in Section 2.1.

However, the mechanism cannot explain the scopal interaction between wh phrase and the universal quantifiers. Even though the universal quantifiers syntactically precede wh phrases, the sentences can have either of the following two readings.

Obviously, we need more than the syntactic mechanism introduced in Section 2.1 to successfully explain this interaction. We will propose other mechanisms to account for this interaction in Section 3.

2.2.2 Narrowing down: Takkei and MoiN chit e lang

Takkei 'everyone' originated from tak e lang 'every CL person'. Two pieces of evidence can support this assumption. The first one is a phonological one. Takkei 'everyone' has a free variant tak-e, which obviously is short for tak e lang 'every CL person' since it is quite normal in Taiwanese to omit some generic, context-derivable head nouns11, 12. No matter how it is pronounced, it has exactly the same syntactic and semantic properties. The second is that native speakers of Taiwanese tend to use takkei 'everyone', and seldom, if ever, use tak e lang 'every one CL person' when they want to comment on everyone, that is, takkei 'everyone' replaces tak e lang 'every one CL person' almost everywhere. Since takkei 'everyone' originated from tak e lang 'every one CL person', it is reasonable to assume that takkei 'everyone' keeps all of properties of tak. However, this assumption is proved to be not entirely correct.

Takkei 'everyone' and moiN chit e lang 'everyone' are both compatible with distributivity and hence both can be distributed over by long 'all'. This is a property tak and moiN share. Again, long 'all' here is obligatory.

17	a.	takkei/moiN chit e lang *(long) li wi to
		everyone all PRG draw picture
		'Everyone is drawing a picture individually.'

But, to our surprise, takkei 'everyone' allows for collectivity, which tak 'every' does not. As for moiN chit e lang 'everyone', it does not allow for collectivity, just like moiN 'every'.

18	a.	takkei taotin li wi haipo
		everyone together PRG draw poster
		'Everyone is drawing the poster together.'
	b.	*moiN chit e lang taotin li wi haipo
		everyone together PRG draw poster
		'Everyone is drawing the poster together.'

The contrast between (18a) and (18b) suggests that though takkei 'everyone' originated from tak e lang 'every CL person', it has undergone some semantic change so that it is compatible with the collective reading while moiN chit e lang 'everyone' does not undergo the same change.

Next, let us look at the scopal interaction between negation and takkei 'everyone' and moiN chit e lang 'everyone'.

19	a.	goa boe chhuhoat takkei
		I no punish everyone	NEG precedes takkei
		'I will punish nobody.'	takkei >NEG
	b.	takkei long bo lai
		everyone all no come	takkei precedes NEG
		'Nobody came.'	takkei > NEG
20	a.	goa bo chhuhoat moiN chit e lang
		I no punish everyone	NEG precedes moiN chit e lang
		'I will not punish everyone.'	NEG > moiN chit e lang
	b.	moiN chit e lang long bo lai
		everyone all no come	moiN chit e lang precedes NEG
		'Nobody came.'	moiN chit e lang > NEG

Takkei 'everyone' always scopes over clausemate negation regardless of its syntactic position relative to negation, as shown in (19a) and (19b). On the contrary, moiN chit e lang 'everyone' obeys the Isomorphism Principle, that is, the syntactic position determines the semantic scope. However, takkei 'everyone' has some positive-polarity like property in the sense that it takes wide scope over negation only but it does not always scope over other non-negative scope-taking elements, such as frequency adverbials.

21	a.	I invite everyone to dinner often.
	b.	possible reading (i):		(all are invited at the same time and this happens often)
	c.	possible reading (ii):		(not all are invited at the same time, but all are invited over a period of time, and this happens often)
22	a.	goa tiaNtiaN chhiaN takkei lai chia ampng
		I often invite everyone come eat dinner
		'I often invite everyone to dinner.'
	b.	takkei tiaNtiaN khi hit king chhamtiaN chia png
		everyone often go that CL restaurant eat rice
		'Everyone often goes to that restaurant to eat.'

Suppose that (21a) has two different readings. When everyone scopes over often, (21a) means that everyone is included when the speaker makes an invitation and the speaker often makes an invitation like this. If often scopes over everyone, the sentence means that the speaker can invite one or two or more per invitation and over a period of time everyone is invited, and the speaker does this quite often. But, (22a) does not have two readings. The only reading it has is:

(22b) is not ambiguous, either. But, the reading it has is:

That is, in (22a) everyone is invited per invitation, but in (22b) it is not the case that everyone has to go to the restaurant together. It is clear that the Isomorphism Principle is at work here. When tiaNtiaN 'often' syntactically precedes takkei 'everyone', the former takes scope over the latter; if tiaNtiaN 'often' follows takkei 'everyone', it scopes under takkei 'everyone'. Therefore, takkei 'everyone' does not always take wide scope, and its wide scope taking property is positive-polarity like, which is something tak 'every' does not have.

The next observation is about the interaction between wh phrases and takkei 'everyone' and moiN chit e lang 'everyone'.

23	a.	takkei long boe siaN be ho abin
		every all buy what want give Abin
		'What did everyone buy for Abin?'
	b.	goa boe chu, i boe wei, ahoa boe saN	PL: Distributive
		I buy book, he buy shoes, Ahoa buy clothes
		'I bought a book, he a pair of shoes, and Ahoa clothes.'
	c.	takkei long boe chu	SA: Distributive
		everyone all buy book
		'everyone bought books individually.'
	d.	!!abin ahoa boe chu, achhin atai boe wei	PL: Collective
		Abin Ahoa buy book Achhin Atai buy shoe
		'Abin and Ahoa bought books together, and Achhin and Atai shoes.'	[bad answer]
	e.	takkei taotin boe chit tai chhia be ho i	SA: Collective
		everyone together buy one CL car want give he
		'Everyone bought a car together for him.'
24	a.	lan chit cho moiN chit e lang long boe siaN be ho abin13
		we this group everyone all buy what want give Abin
		'What did everyone in our group buy for Abin?'
	b.	goa boe chu, i boe wei, ahoa boe saN	PL: Distributive
		I buy book, he buy shoes, Ahoa buy clothes
		'I bought a book, he a pair of shoes, and Ahoa clothes.'
	c.	moiN chit e lang long boe chu	SA: Distributive
		every one CL person all buy book
		'Everyone bought books individually.'
	d.	!!abin ahoa boe chu, achhin atai boe wei	PL: Collective
		Abin Ahoa buy book Achhin Atai buy shoe
		'Abin and Ahoa bought books together, and Achhin and Atai shoes.'	[bad answer]
	e.	*moiN chit e lang taotin boe chit tai chhia be ho i	SA: Collecitve
		everyone together buy one CL car want give he
		'Everyone bought a car together for him.'	[bad answer]

When takkei 'everyone' precedes wh phrases, as (23a), it allows for both kinds of distributive readings, SA distributive (23c) and PL distributive (23b), and one kind of collective readings, SA collective (23e). If it is is moiN chit e lang 'everyone' that precedes wh phrases, it also allows for both kinds of distributive readings, (24b) and (24c), but does not allow for any kind of collective reading, (24d) and (24e).

Though semantically takkei always takes wide scope, syntactically it does not have to always precede moiN chit e lang. In addition, one sentence cannot have two takkei's but it is acceptable to have two moiN chit e lang's.

25	a.	takkei long chin koansim lan simbiN e moiN chit e lang14
		everyone all very care we body side DE everyone
		'Everyone (here) care very much about everyone around us.'
	b.	lin chhu e moiN chit e lang long e pangcho takkei kiampoi e
		you house DE everyone all will help everyone lose weight Prc
		'Everyone in your family will help everyonei (here) lose weight.'
	c.	???takkei ai pangcho takkei
		everyone must help everyone
		'Everyone must help everyone.'
	d.	chia-e moiN chit e lang long bat hia-e moiN chit e lang
		here every one CL person all know there every one CL person
		'Everyone here knows everyone there.'

What we should bear in mind is that, though takkei and moiN chit e lang can precede each other in syntax, it is not clear whether they have any scopal interaction since both of them are universal quantifiers and which one precedes which one does not influence truth conditions of the sentences at all.

In this section, we have discussed six properties of takkei and moiN chit e lang, including whether they can be distributed, whether they can be collectivized, their scope relation with negation, wh phrases and other scope-taking elements, e.g., tiaNtiaN 'often', and the syntactic precedence between takkei and moiN chit e lang, which does not cause any scope ambiguity because the phenomenon that one universal quantifier scopes over another does not cause any semantic difference.

The following chart summarizes all of the phenomena we discussed in this section.

From the discussions above, it can be found that takkei 'everyone' behaves in parallel to plurals. They share the following properties.

First, both of them allow for collectivity.

26	a.	in toatin khi khoaN tienyaN
		they together go see movie
		'They went to a movie together.'
	b.	takkei toatin khi khoaN tienyaN
		everyone together go see movie
		'All of the persons (everyone) went to a movie together.'

Secondly, both of them scope over negation regardless of their syntactic positions relative to negation.

27	a.	goa boe chhuoat in
		I no punish they	NEG precedes PL
		'I will punish none of them.'	PL > NEG
	b.	in boe lai
		they no come	PL precedes NEG
		'They will not come.'	PL > NEG
28	a.	goa boe chhuoat takkei
		I no punish everyone
		'I will punish nobody.'
	b.	takkei long boe lai
		everyone all no come
		'Nobody will come.'

Based on these two similarities, takkei 'everyone' can be claimed to be a plural quantifier. Since takkei is a plural quantifier, its interaction with negation can be easily explained by the mechanism proposed in Section 2.1.

However, again, the mechanism alone cannot explain the scopal interaction between takkei and wh phrases, just like it cannot explain the interaction between tak 'every', moiN 'every' and wh phrases. We will deal with this issue in Section 3.

2.3 The Distributive and the Collective Operator in Taiwanese

In this section, we briefly discuss the distributive operator long 'all' and the collective operator taotin 'together'. Since distributivity and collectivity play an important role in the semantics of tak 'every', moiN 'every', takkei 'everyone' and moiN chit e lang 'everyone', which we discussed separately in the last two sections above, it is definitely helpful to devote some space to these two operators.

2.3.1 The Distributive Operator Long

Several works (Lin 1996, 1998; Hsieh 1994; Li 1992; Gao 1994; and Huang 1994 among others) are devoted to the Mandarin distributive operator, dou 'all'. It is generally accepted that dou has four properties: it is a distributive operator, it obeys the Leftness Condition, the Locality Condition, and the Multiplicity Condition. The Taiwanese distributive operator long shares these four properties.

The Leftness Condition requires that the NP distributed over by long must be to its left. Sentences are ungrammatical if the NP distributed over is not to the left of long as long as long appears.

29	a.	gun long boe chhia a
		we all buy car Prc	(distributing over gun 'we')
		'We all bought a car.'
	b.	chit koa chu goa long khoaN ke a
		this PL book I all read Exp Prc	(distributing over chit koa chu 'these books)
		'I've read all of these books.'
	c.	*goa long khoaN ke chit koa chu
		I all read Exp this PL book	(distributing over chit koa chu 'these books')
		'I've read all of these books.'

(29c) is bad because the NP, chit koa chu 'these books', that is distributed over by long does not move to the left of long.
The Locality Condition requires that long can only distribute over elements in the local clause where long exists, as shown in (30).

30	goa ka i khokheng in mai long chhuhi
	I and he urge they no all go out
	'He and I urged them not to go out both.'
	*'He and I both urged them not to go out.'

The Multiplicity Condition15 requires that only things with multiple parts16 can be distributed over by long, and only predicates that have a proper subset entailment on the group argument can occur with long, as shown in (31a), (31b), (31c), (31d) and (31e).

31	a.	*goa long boe chhia
		I all buy car	(distributed over goa 'I')
		*'I all bought a car.'
	b.	chit pun chu goa long khoaN ke a
		this CL book I all read Exp Prc	(a book has many pages.)
		'I've read every page of this book.'
	c.	chiat tua kuan e chiu ni long lim khi a
		so big bottle DE wine you all drink go Prc	(potentially a big bottle of wine has parts.)
		'You finished such a big bottle of wine!'
	d.	*taipohun e lang long paowi chongthonghu
		most DE person all surround Presidential Office
		'Most people surrounded the Presidential Office.'
	e.	taipohun e lang long pat paowi ke chongthonghu
		most DE person all ever surround Exp Presidential Office
		'Most people have the experience of surrounding the Presidential Office.'

Consider the contrast between (31d) and (31e). Suppose there are one hundred out of 120 people participated in the surrounding of the Presidential Office. For (31d) to be true, it should be true that these one hundred persons as a whole surrounded the Presidential Office. That is, it is a collective effort of the one hundred persons. No proper subset (part) of the one hundred persons can be said to surround the Presidential Office. In (31e), paowi ke 'surround Exp', different from paowi 'to surround', has a temporal interpretation. While paowi 'to surround' denotes groups of individuals located at the same time in the same event, paowi ke 'surround Exp' can denote groups of individuals located at different times and in different events. It allows that only paowi ke 'to surround Exp' can be true of some subset of the denotation of the subject noun phrase. Both things with multiple parts and predicates that need proper subsets mean some kind of multiplicity. This is what the Multiplicity Condition captures.

As explained in Section 2.1, long is the overt realization of the distributive operator. The overt realization of long is due to the overt movement of universal quantifiers or plural to <Spec, DistP>. However, (27b) and (28a) point out an interesting asymmetry between plurals and universal quantifiers, that is, universal quantifier subjects require long while plurals do not. While plurals also have to move to <Spec, DistP>, long is not obligatory. This suggests that overt movement is not the only trigger for long to be overtly realized.

To know what else is needed to explain the obligatoriness of long, let us examine the following examples.

32	a.	tiuN-e li-e ong-e (long) li chia png
		Tiun Li Ong (all) PRG eat rice
		'Mr. TiuN, Mr. Li and Mr. Ong are (all) eating.'
	b.	tiuN-e li-e ong-e goa (long) u khoaN ke
		TiuN Li Ong I (all) have see Exp
		'I have seen Mr. TiuN, Mr. Li and Mr. Ong (all).'
	c.	chit koa chu (long) li pangking
		this PL book (all) at room
		'These books are (all) in the room.'
	d.	chit koa chu goa (long) khoaN ke a
		this PL book I (all) see Exp Prc
		'I have read these books (all).'
	e.	in (long) khoaN ke chit chhu tienyiaN
		they (all) see Exp this CL movie
		'They (all) saw this movie.'
	f.	in, goa (long) u khoaN ke
		they I (all) have see Exp
		'I have seen them (all).'

The six examples above seem to be suggesting that long is optional with respect to plural NP's. However, this is not true. In fact, whether long can or cannot appear in these examples is determined by a semantic condition, exhaustivity of domains. Let's look at (32a). If a manager calls his secretary and asks to see five persons, TiuN, Li, Ong, Ko, and Go. The secretary wants to tell him that the first three are eating their lunch now and the others are on leave. In this case, the secretary will use (32a) without long to report about the first three men. But, if the manager asks to see three persons only, TiuN, Li and Ong, the secretary will use (32a) with long to report about these three men. In these two situations, what the manager does is to set up a domain. In the first situation, the domain includes five persons. When the secretary reports part of the domain, long cannot be used. On the contrary, in the second situation, the domain includes three persons only. When the secretary reports the entire domain, long is obligatory. That is, when the domain is exhaustively commented on, as the second situation introduced above, long is obligatory; while the domain is not exhaustively commented on, as the first situation above, long cannot be used.

The same condition applies to the other examples in (32). Assume a situation below for (32b). A detective shows five pictures with names on them to a witness, and asks whether the witness saw any one of these five persons. The witness saw three of them, say TiuN, Li and Ong, but not the other two. In this case, the witness will use (32b) without long to report the fact. But, if the detective shows only three pictures to the witness and asks the same question, the witness recognizes all of them: TiuN, Li and Ong. Then, he will use (32b) with long to report his knowledge. What the detective in this situation does is just like what the manager in the previous situation does, i.e., to set up a domain. When the witness wants to make a comment on only part of the domain, he does not use long. While the witness wants to comment on all of the members in the domain, he must use long.

In sum, the exhaustivity of domains condition can help predict when long is obligatory. When the domain is exhaustively commented on, long is obligatory; while only part of the domain is commented on, long cannot be used.

This semantic condition can explain why overt movement of universal quantifiers requires long but overt movement of plural NP's does not. Universal quantifiers refer to every member of a domain. When a universal quantifier are used, it means that the domain is exhaustively commented on, which is exactly when the exhaustivity of domains condition requires long must be used.
Overt movement of NPs and the exhaustivity of domains condition cooperate with each other to explain the occurrence of long. Overt movement of NPs provides a syntactic reason and the exhaustivity of domains condition provides a semantic reason. Neither of them alone can explain the syntactic property of long.

2.3.2 The Collective Operator Taotin

Little attention, if any, has been paid to the collective operator. We find that some of the syntactic properties of taotin 'together' are parallel to those of long, and some are not. First, not surprisingly, taotin requires a plural NP that it can collectivize.

33	a.	*goa toatin khi khoaN tienyian
		I together go see movie
	b.	goa ka i toatin khi khoaN tienyian
		I and he together go see movie
		'He and I went to a movie together.'
	c.	*goa be ka chit pun chu taotin boeboe e
		I want DISP one CL book together sell Prc
	d.	goa be ka chit koa chu taotin boeboe e
		I want DISP this PL book together sell Prc
		'I want to see these books together.'

Goa 'I' in (33a) and chit pun chu 'this book' in (33b) are singular and hence cannot be collectivized by taotin. On the contrary, goa ka i 'I and he' in (33b) and chit koa chu 'these books' in (33d) are plural and can be collectivized. This explains the (un)grammaticality of the four examples in (33).

This point is a little different from the Multiplicity Condition in that plurality is only part of the Multiplicity Condition. Things with multiple parts, such as books, cannot be collectivized; only plurals can be collectivized.

34	a.	*chit pun chu goa taotin khoan wan a
		this CL book I together see finish Prc
	b.	chit koa chu goa taotin khoan wan a
		this PL book I together read finish Prc
		'I finished reading these books together.'

Secondly, taotin also requires the Leftness Condition.

35	a.	*goa siuNbe taotin boe chit koa chu17
		I want together sell this CL book
	b.	goa siuNbe ka chit koa chu taotin boeboe e
		I want DISP this PL book together sell Prc
		'I want to sell these books together.'	(these books as a whole)
	c.	chit koa chu goa toatin boekhi a
		this PL book I together sell Prc
		'I sold these books together.'	(these books as a whole)
	d.	goa ka i ka chit koa chu taotin boekhi a
		I and he DISP this PL book together sell Prc
		'He and I sold these books together.'	(these books as a whole or do the selling together)

(35a) is bad because chit koa chu 'these books' does not precede taotin. (35b) and (35c) are both good since the Leftness Condition is obeyed. (35d) is ambiguous because two potential candidate, goa ka i 'I and he' and chit koa chu 'these books', are in the right positions to be collectivized.

Thirdly, taotin also obeys the Locality Condition.

36	a.	goa ka i taotin khokheng [IP in mai chhukhi]
		I and he together urge they no go out
		'He and I together urged them not to go out.'
		*'He and I urged them not to go out together.'
	b.	goa ka i khokheng in [IP mai taotin chhukhi]
		I and he urge they no together go out
		*'He and I together urged them not to go out.'
		'He and I urged them not to go out together.'

In (36a), taotin is in the matrix clause and it can only collectivize something in the same clause. This is why it cannot have the 'to go out together' reading. On the other hand, in (36b), taotin is in the lower clause and it can collectivize something in the lower clause, not the matrix clause. This is why it cannot have the 'to urge together' reading.

Fourthly, a collective interpretation surfaces only when the collective operator taotin is overtly realized. We have shown that sentences without the distributive operator or the collective operator receive a distributive interpretation in (3a) and (3b), which are repeated below.

3	a.	in boe chhia a
		they buy car Prc
		'They bought a car (individually).'
	b.	goa kayi in
		I like they
		'I like them.'

The observations above suggest that to get a collective reading, the collective operator taotin must be overtly realized to project a ColP and NPs must move to <Spec, ColP> to get a collective interpretation. If taotin is not overtly realized, no ColP is projected and NPs have no place to move to get a collective denotation. Therefore, a collective reading is impossible when taotin is not overtly realized.

3. The Semantics of Distributivity, Collectivity and Universal Quantifiers

In this section, we want to discuss the semantic representations for the quantifiers, the distributive operator long 'all', and the collective operator taotin 'together'. And then we will demonstrate how these semantic representations work with the tree structure proposed in Section 2.1.1 to derive the readings we can get and block the readings we cannot get.

3.1 The Semantic Representations for the Universal Quantifiers

We discussed the following universal quantifiers in the previous section: tak 'every', moiN 'every' and takkei 'everyone'. We have established that the first two are singular universal quantifiers18 and the last one a plural universal quantifier. For the singular ones, we make the default assumption that they are just like every in English and denote.

In this representation, the universal quantifier ranges over atomic individuals.

As for the plural one, we propose the following semantic representation along the same line of the singular ones:

37

* is an operator that pluralizes predicates in the sense of Link (1983). * takes a one-place predicate P as its argument to form all the possible sum individuals from the member of the extension of P, *P. Suppose the model has three people, a, b, and c. [man] is {a, b, c}. Then [*man] is

the set of all sum individuals. The capital variables in the formula are variables over plural entities.

However, in the literature, another representation for universal quantifiers is argued. Barwise and Cooper (1981) argue that quantifiers correspond to NPs, not to determiners and quantifiers denote families of sets. In their definition, quantifiers such as

denote a set of entity that satisfies some property, which can be informally represented as

in their formalism. So, they define ||the n||(A) = ||every|| (A) if |A| = n, and undefined otherwise. that is, in their formalism a universal quantifier denotes the unique sum individual, which the NP the + plural N denotes.

Though this definition does not work for the singular universal quantifiers, moiN and tak, because their syntactic and semantic behaviors are very different from those of definite plurals, this definition works for the plural universal quantifier takkei, which does share the same behavior with (definite) plurals. Therefore, it is a likely assumption that instead of functioning like a traditional plural universal quantifier, takkei behaves like the quantifiers in Barwise and Cooper's (1981) sense. According to this idea, takkei denotes (38).

38

We have argued that takkei takes a presupposed domain with it, which is contextually determined. The D in the denotation captures this fact. *person(y) is the plural object of person, which is represented as a lattice, with respect to D. (38) says that the denotation of takkei is the super of the lattice *person(y), that is, the unique sum individual.

To choose between the two representation for takkei, we need to look at the syntactic precedence between takkei and moiN chit e lang, which show syntactic evidence for our choice. Therefore, in the next section, we discuss the syntactic precedence between these universal quantifiers.

3.2 The Syntactic Precedence between Takkei and MoiN chit e lang

The fact that tak-kei cannot precede tak-kei but moiN chit e lang can precede another moiN chit e lang is related with the domains of the two universal quantifiers. We mentioned that tak-kei comes with a presupposed domain, but moiN chit e lang does not. (Footnote 1 and 14) That is why moiN chit e lang can be generic and it usually needs a modifier that sets up a domain for it. Since moiN chit e lang can have different domains and hence can peacefully coexist in a sentence. Tak-kei comes with a presupposed domain, which cannot be altered in the same sentence. That is, if two tak-kei appear in the same sentence, they will refer to the same group of persons. According to Principle A, a reflexive anaphor should be used in this case.

39	a.	goa chhiaN takkei toto koansim lan simbiN e moi chit e lang
		I ask everyone more care we body side De everyone
		'I ask everyone (here) to care more about everyone around us.'
	b.	goa e chhiaN lin chhu e moiN chit e lang pangcho takkei kiampoi e
		I will ask you house DE everyone help everyone lose weight Prc
		'I will ask everyone at your home help everyone (here) lose weight.'
	c.	???takkei ai pangcho takkei
		everyone must help everyone
		'Everyone must help everyone.'
	d.	gun chit cho e moiN chit e lang e ka lin hit cho e moiN chit e lang
		we this group DE everyone will DISP you that group DE everyone taosankang e help Prc
		'Everyone in our group will help everyone in your group.'
	e.	takkei ai pangcho kai (bo siaN e le)
		everyone must help self (otherwise who will Prc)
		'Everyone here must help themselves. Otherwise, who will?'

(39c) and (39e) illustrate the discussion about tak-kei. Since tak-kei refers to the same group of persons, a reflexive anaphor should be used as in (39e), instead of using tak-kei again, (39c). (39d) illustrates the discussion about moiN chit e lang. Since the two moiN chit e lang's refer to two different groups of people, it is fine for moiN chit e lang to precede another moiN chit e lang.

That is, takkei is just like an r-expression, e.g. a proper name. Its referent does not change as long as the referent is not reset. In longer sentences as follows, this can be seen more clearly.

40	a.	takkei long linwi abin kayi *takkei/i
		everyonei all think Abin like *everyonei/hei
		'Everyonei thinks that Abin like himi.'
	b.	lan chia moiN chit e lang long linwi abin kayi in hia moiN chit e lang
		we here everyone all think Abin like they their everyone
		'Everyone here thinks that Abin likes everyone there.'
	c.	inwi takkei tui goa ho, goa ma tui takkei ho
		because everyone to I good, I also to everyone good
		'Because everyone is good to me, I am good to everyone.'
	d.	Johni thinks that Mary likes *Johni/himi.
	e.	Because Johni is good to Mary, Mary is good to Johni.

As we can see, takkei in (40a) and (40b) behaves just like the proper name John in (40d) and (40e). These examples further support that argument that takkei is like an r-expression and hence no two takkei can occur in the same sentence.

3.3 Choosing Between the Two Representations of Takkei

Two representations for the plural universal quantifier takkei are proposed Section 3.1.

One is:

which is just like a traditional regular universal quantifier except that the universal quantifier ranges over plural entities, the capitalized letter X. The other is Barwise and Cooper's (1981) definition of universal quantifier, represented as:

where universal quantifiers are defined as the set of all of the individuals in a domain, that is, the unique sum individual in lattice-theoretic terms, which is exactly what definite plurals denote.

It can be argued that the Barwise and Cooper's definition is better for takkei, but not for moiN and tak, based on the following observations.

First, the singular universal quantifiers are not compatible with a collective reading, but the plural universal quantifier is. If both kinds of universal quantifiers denote a set of entities, then it is difficult to explain why one kind allows for a collective interpretation but the other does not. Especially, if both kinds denote a set, it is very difficult to argue against that a set of entities cannot work together and allows for a collective interpretation.

Secondly, the syntactic behavior of takkei and moiN chit e lang discussed in Section 3.2 also suggests that takkei denotes the set of all members in a domain, just like a definite plural, and hence it behaves like a definite plural, e.g., it obeys Condition C, but moiN chit e lang does not behave, in any way, like a definite plural. The traditional universal quantifier definition for takkei does not capture this similarity between it and a definite plural.

Given the argument that universal quantifiers have the same denotation as definite plurals (Barwise and Cooper 1981) and given the observation that syntactically and semantically takkei is exactly like definite plurals, as discussed in Section 3.2, then the better semantic representation for takkei should be