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Chinese comparatives and their implicational parameters

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Abstract This paper argues that superiority comparatives in Mandarin Chinese are all phrasal comparatives that can be directly interpreted, and makes a new suggestion of taking the bıˇ-phrase (‘compare-phrase’) to be an adjunct and one constituent, but withbıˇ-shells. This syntactic analysis allows one to combine into one phrase various compared constituents that would otherwise not be analyzed as forming a phrase by themselves. Semantically, in extension of work by Heim as well as Bhatt and Takahashi,bıˇ is taken to compare two sequences of arguments of a gradable predicate along the dimension given by that predicate. It is also suggested that comparatives across languages may be subject to three parameters: (i) argument-dependent comparison vs. non-argument dependent comparison, (ii) phrasal comparison vs. clausal comparison, and (iii) monoadic comparison vs. dyadic comparison.

Keywords Chinese comparatives Phrasal comparatives  Dyadic comparison

1 Introduction

This paper discusses the syntax and semantics of Chinese comparative constructions, such as those in (1), where the gloss ‘COM’ is an abbreviation of ‘Compare’: (1) a. Yue¯ha`n bıˇ ma˘lı` ga¯o 。

John COM Mary tall

‘John is taller than Mary.’

J.-w. Lin&

Department of Foreign Languages and Literatures, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, ROC

e-mail: [email protected] DOI 10.1007/s11050-008-9033-3

Chinese comparatives and their implicational

parameters

Jo-wang Lin

Published online: 10 December 2008

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b. Ta¯ yı¯ngwe´n bıˇ woˇ fa`we´n shuo¯-de ha˘o 。 he English COM I French speak-PART good ‘He speaks English better than I speak French.’

c. Ta¯ zuo´tia¯n za`i xue´xia`o bıˇ woˇ jı¯ntia¯n za`i jia¯lıˇ ka¯ixı¯n 。 he yesterday at school COM I today at home happy ‘He was happier at school yesterday than I am at home today.’

It is argued that the above constructions are all phrasal comparatives rather than clausal comparatives and that Chinese is a dyadic argument comparison language. Based on the data from Mandarin Chinese, it will be suggested that the typology of comparative constructions across languages may be subject to the following parameters:

(2) a. Argument comparison language vs. non-argument comparison language b. Phrasal comparison language vs. clausal-comparison language

c. Monoadic comparison language vs. dyadic comparison language

This paper is organized as follows. Section 2 gives an overview of the syntax and semantics of English comparatives. Section 3 briefly introduces the constructions of Chinese comparatives. Section 4 is a review of previous analyses of Chinese bıˇ-comparatives and their inadequacies. Section 5 proposes an alternative syntactic and semantic analysis of such constructions and the parameters they imply for com-paratives across languages. Finally, Section 6 discusses the implications of the Chinese data in a larger context of language variations, such as the one sketched by Beck et al. (2004), Kennedy (2005), and Bhatt and Takahashi (2007).

2 A brief overview of the syntax and semantics of English comparatives English comparatives are normally divided into clausal and phrasal comparatives, as is illustrated by (3) and (4), respectively.

(3) John is taller than Mary is (tall). (clausal comparative) (4) John is taller than Mary. (phrasal comparative)

The traditional analysis of clausal comparatives is that the -er morpheme and than-clause are analyzed as forming a degree description (DegP) that is a specifier or modifier of AP (Bresnan 1973; Heim 1985, 2000; von Stechow 2005; among others).1 However, the than-clause is obligatorily extraposed at PF and -er is

1 An alternative is to analyze the degree expression by way of the Functional AP Hypothesis, according to which an AP is embedded under a functional DegP (Abney 1987; Corver 1994; Kennedy 1999; among others).

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morphologically attached to the adjective. The than-clause is a wh-construction with a null wh-operator binding a degree gap (Chomsky 1977) and denoting the property of degrees. Moreover, the -er morpheme and the than-clause, though separate from each other at PF, are moved to a clausal scope at LF, leaving behind a degree variable. Therefore, the main clause is also interpreted as a property of degrees, much like the than-clause. The -er morpheme requires that the maximal degree associated with the matrix adjective is greater than the maximal degree associated with the (elided) predicate of comparison in the than-clause. This analysis of comparatives is known as a degree comparison.

In this analysis, the PF and LF of clausal comparatives are as follows: (5) John is taller than Mary is.

(6) PF: a. John is tall-er [wh2than Mary is t2-tall] (clausal comparative)

b. John is tall-er [ wh2than Mary is t2-tall] (phrasal comparative)

(7) LF: [-er [wh2Mary is t2-tall]]1John is t1-tall

The LF of (7) is then interpreted as follows. Gradable adjectives are assumed to be relations between individuals and degrees, as in (8a), in which TALL is a measure function of type <e,d>, which assigns a unique degree to individuals (Cresswell 1976; Klein 1991; von Stechow 2005).

(8) a. ||tall|| =λdλx.TALL(x)  d b. TALL =λx.x¢s height

The morpheme -er takes two <d,t> expressions, P and Q, as its arguments, and requires that the maximal degreed of P exceeds the maximal degree d of Q, as shown in (9). Therefore, the meaning of (5) is equivalent to ‘John’s maximal height exceeds Mary’s maximal height.’

(9) ||-er|| =λP<d,t>λQ<d,t>.the maximal d s.t. Q(d) = 1 > the maximal

d s.t. P(d) =1.

Regarding phrasal comparatives, one view is that they are derived from clausal counterparts through comparative deletion and ellipsis, as the second possible PF in (6b) shows (e.g. Bresnan 1973), and are thus interpreted in the same way as clausal comparatives. (For more recent literature, see Lechner 2001, 2004; Merchant 2006). The advantage of this analysis is the uniformity it maintains for the meaning of -er, i.e., -er is always a two-place operator taking two properties of degrees as its argument.

In contrast to the above reduction analysis of phrasal comparatives, some linguists have argued for a direct analysis of phrasal comparatives (Hankamer 1973; Napoli 1983; Kennedy 1999). On this alternative analysis, a phrasal comparative is comprised ofthan followed by a simple DP, rather than a clause. One difficulty

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raised by this direct analysis of phrasal comparatives is the lack of a description of the second degree because there is no elided material to form such a description. Hence, a different lexical entry for -er is required. One possible such lexical entry was proposed by Heim (1985), who suggested that the direct analysis of phrasal comparatives is not a comparison between two degrees, but rather a comparison between two individuals with respect to a certain dimension. An alternative to Heim’s formulation is to treat -er as a three-place predicate as in (10), taking two individuals and one predicate of individuals and degrees as its arguments, as sug-gested by Bhatt and Takahashi (2007).

(10) ||-er|| =λx.λP<d, <e,t>>.λy.9d[P(y,d) ^ : P(x,d)]

3 Basic Chinese data

Our discussion begins with a summary of the work of Tsao (1989), who provides a good survey of the basics of Chinese comparatives.2His starting point is Li and Thompson’s (1981) schema for Chinese comparatives, as given in (11) and illus-trated by (12).

(11) X Comparison word Y (Adverbial) Dimension (12) Yue¯ha`n bıˇ ma˘lı` (ge`ng) ga¯o ˚

John COM Mary even tall ‘John is (even) taller than Mary.’

Assuming his own earlier works (Tsao 1982, 1987a, b), Tsao (1989) suggests that a sentence may contain multiple topics, which are further divided into primary and non-primary topics. He then proposes that the compared constituents X and Y, seen in schema (11), must be topics of an equal rank; or more precisely, the compared constituents X and Y must both be primary topics, secondary topics, or tertiary topics, etc.3According to Tsao, the examples in (13)–(16) all involve a comparison of secondary topics. Moreover, he shows that double-topic or even triple-topic comparison is also possible, as is shown in (17) and (18).

2

In addition to Tsao (1989) and others to be mentioned in the text, there are many descriptive works on Mandarinbıˇ-constructions published in Mainland China. The reader is referred to Liu (2004) and Xu (2007) for a survey and to the references cited therein.

3 Paul (1993) proposed a structural condition on two compared items by suggesting that X, in (11), must c-command or cyclically c-command Y. I agree with Shi’s (2001) view that Paul’s characterization is problematic.

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(13) a. Ta¯ la´nqiu´ bıˇ pa´iqiu´ da˘-de ha˘o 。4 he basketball COM volleyball play-Part good ‘He plays basketball better than (he does) volleyball.’ b. Woˇ da`ishu` bıˇ jıˇhe´ xıˇhua¯n 。

I algebra COM geometry like ‘I like algebra more than geometry.’ (14) Ta¯ duı` nıˇ bıˇ duı` woˇ ha˘o 。

he to you COM to me nice

‘He is nicer to you than (he is) to me.’ (15) Ta¯ jı¯ntia¯n bıˇ zuo´tia¯n shu¯fu´ 。

he today COM yesterday feel-good ‘He feels better today than (he did) yesterday.’

(16) Ta¯ ba˘ qia´n bıˇ ba˘ she¯ngmı`ng ka`n de zho`ng 。

he BA money COM BA life regard DE important

‘He regards money as more important than (he does) life.’ (17) Double-topic comparison

Ta¯ yı¯ngwe´n bıˇ woˇ fa`e´n shuo¯-de ha˘o 。 he English COM I French speak-PART good ‘He speaks English better than I speak French.

(18) Triple-topic comparison

Ta¯ zuo´tia¯n za`i xue´xia`o bıˇ woˇ jı¯ntia¯n za`i jia¯lıˇ ka¯ixı¯n 。 he yesterday at school COM I today at home happy ‘He was happier at school yesterday than I am at home today.’

In addition, Tsao (1989, pp. 172–179) proposes three deletion principles, as given below, in order to generate more comparative sentences.

(19) The Primary Principle

Any compared topic, primary or non-primary, can be deleted if it is identical to another topic of an equal rank, however, only forward deletion is allowed.

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It has been observed by Hashimoto (1971) that a direct object in its postverbal position cannot be a compared constituent.

(i) *wǒ ài zhenlǐ bǐ wǒ-de lăoshī 。 I love truth COM my teacher ‘I love truth more than (I love) my teacher.’

However, Tsao (1989) has argued that if the object is fronted, then it can be compared, subject to some pragmatic and phonological conditions.

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(20) The Present-Time Deletion Principle

A topical constituent referring to the present time can be deleted. (21) The Second Compared Constituent Genitive Deletion Principle

When a genitive NP occurs as the second of a pair of compared constituents and the possessed NP is identical with that of the first compared constituent, then the genitive marker can be optionally deleted after the possessed NP is deleted through identical element deletion.

The Primary Principle is used to explain examples such as (22a) or (22b). The Present-Time Deletion Principle accounts for (23), and the Second Compared Constituent Genitive Deletion Principle explains (24).

(22) a. Ta¯ ya˘njı¯ng bıˇ woˇ ya˘njı¯ng da` 。

he eye COM I eye big

‘His eyes are bigger than mine.’

b. Ta¯ zuo´tia¯n za`i xue´xia`o bıˇ woˇ zuo´tia¯n za`i he yesterday at school COM I yesterday at jia¯lıˇ kua`ile`

home happy

‘He was happier at school yesterday than I was at home.’ (23) Ta¯ xia`nza`i bıˇ ga¯ngca´i lia˘nse` ha˘o 。

he now COM a-while-ago face-color good ‘He looks much better than (he did) a while ago.’ (24) Ta¯-de to´ufa˘ bıˇ woˇ-de cha´ng 。

he-Gen hair COM I-Gen long ‘His hair is longer than mine.’

Although I am conservative regarding the notion of multiple topics, Tsao’s description of Chinese comparatives in my view provides a very good base for those who wish to analyze Chinese comparatives.

4 A review of previous analyses of Chinesebıˇ-comparatives 4.1 Biclausal analysis

The literature has generated many discussions regarding the syntax of comparatives in Mandarin Chinese. Some have suggested thatbıˇ-comparatives are transformationally derived from a biclausal source, similar to what some linguists have proposed for English phrasal comparatives (e.g. Cheng 1966; Hashimoto 1966, 1971; Fu 1977; Tsao 1989). However, the biclausal derivation of Chinesebıˇ-comparatives encounters

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some difficulties. As is well known, English comparatives allow constructions, such as (25), where the main clause and thethan-clause are both full clauses.

(25) This table is wider than that desk is long.

The Chinese counterpart of (25), in contrast, is ungrammatical.

(26) *Zhe`-zha¯ng zhuo¯zi (heˇn) kua¯n bıˇ na`-zha¯ng zhuo¯zi (heˇn) this-Cl table very wide COM that-Cl table very cha´ng 。5

long

‘This desk is wider than that table is long.’

If comparative structures are generated by conjoining two sentences and ‘gapping’ and comparative deletions do not apply, then there is no reason why (26) should be ungrammatical. The process of gapping in bıˇ-comparatives is also problematic because gapping in Chinese, as Paul (1999) pointed out, is quite restricted. In particular, gapping in Chinese does not apply to sentences with an overt conjunction marker.

A similar difficulty arises when thebıˇ-clause is assumed to be an adjunct, and adjoined to VP/AP, as in Liu (1996), who gives (27a) an analysis similar to (27b): (27) a. Guo¯jı`ng jı¯ntia¯n bıˇ Hua´ngro´ng zuo´tia¯n ka¯ixı¯n 。

Guojing today COM Huangrong yesterday happy ‘Guojing is happier today than Huangrong was yesterday.’

b. Guo¯jı`ng jı¯ntia¯n [PPbıˇ [CP Hua´ngro´ng zuo´tia¯n ka¯ixı¯n]] ka¯ixı¯n

This analysis wrongly predicts that (28) is well formed, unless some ad hoc condition is stipulated.

(28) *[IPZhe`-zha¯ng zhuo¯zi [AP[bıˇ na`-zha¯ng zhuo¯zi cha´ng] kua¯n]]

This-Cl table COM that-Cl desk long wide

Therefore, there seems to be no positive evidence that the constituent followingbıˇis a full clause. In fact, this is also the conclusion of Xiang (2003, 2005), who rightly points out that it would be a surprising fact if the clausal analysis of Chinese comparatives could only allow an elided CP, but not a full CP, and odd if a marked ellipsis construction would be preferred over an unmarked normal clause. Worse, there is no explanation for this fact: it would be a stipulation.6

5 In most contexts, the adverbialheˇn‘very’ is obligatorily present before an adjective, However, (26) is ill formed with or withoutheˇn.

6 Xiang (2005) has offered other arguments against a clausal analysis ofbıˇ-comparatives, which are not reviewed here. Shi (2001) also argues against derivingbıˇ-comparatives from a clausal source.

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4.2 DegP-shell analysis

In contrast to Liu’s (1996) adjunct analysis ofbıˇ-phrases, Xiang (2005) proposes a revised Larsonian (1991) style DegP-shell structure for Chinese comparatives. She posits two degree (Deg) heads in the syntactic structure, one lower than AP and the other above AP. The lower Deg head is a phonologically null degree morpheme, exceed, and the higher Deg head is occupied by bıˇ, as represented in (29).

Xiang argues that the above structure has the advantage of generating a transitive comparative such as (30) by head-movement of the exceedk þ predicate to Deg1

whenbıˇdoes not appear.

(30) Ta¯ ga¯o woˇ sa¯n go¯ngfe¯n 。 he tall I three centimetre ‘He is three centimeters taller than I.’

According to the above analysis, the morphemebıˇand the standard do not form a constituent. This assumption, however, is contradictory to Liu’s (1996) coordination test in (31), which shows thatbıˇ and the standard do constitute a prepositional phrase. (31) Zha¯ngsa¯n bıˇ Lıˇsı` huo`zheˇ bıˇ Wa´ngwu˘ ga¯o 。

Zhangsan Comp Lisi or Comp Wangwu tall ‘Zhangsan is taller than Lisi or (than) Wangwu.’

Xiang (2005) explains (31) by analyzing it as an instance of ellipsis inside VP-coordination or an Across-The-Board movement.

Although reasonable, Xiang’s account of (31) is not an argument against the PP status of abıˇ-phrase. It only shows that the ellipsis or rightward movement analysis is compatible with Xiang’s proposed structure forbıˇ-comparatives.

exceedk+ predicate standardj Deg2′

Deg2 (differential) exceedk (29) Deg1P Deg1 AP b Standardj A′ A Deg2P

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In fact, there are arguments in support of the constituent-hood ofbıˇ+ the stan-dard, in support of Liu’s adjunct analysis.

The first argument is concerned with examples such as those seen in (32).7 (32) a. Ta¯-de she¯nga¯o bıˇ woˇ ha´iya`o a˘i ’ bıˇ Ya´omı´ng’

his height COM I even short COM Yaoming

na` ge`ng shı` tia¯n cha¯i dı` yua˘n le then even be heaven differ ground far Par

‘He is much shorter than I am. If compared with Yaoming, his height is even like the distance between the heaven and the ground.’

b. Zha¯ngsa¯n jı¯ntia¯n pa˘o de´ heˇn bu` lıˇxia˘ng ’ bıˇ woˇ Zhangsan today run DE very not ideal COM I zuo´tia¯n ’ na` jiu` cha¯i de ge`ng yua˘n le 。 yesterday that then differ DE more far Par

‘Zhangsan’ did not run very well today. If compared with my running yesterday, the difference is even greater.’

Example (32a) clearly shows thatbıˇþ the standard can be used as an independent fragment, hence serves to support the claim that bıˇþ the standard form a single constituent in syntax. (32b) is even more interesting because it shows thatbıˇ þ individualþ time also form a constituent.

A second argument is related to the use of the elementdo¯u‘all’ in Chinese. It is well known to Chinese linguists thatdo¯u ‘all’, analyzed as a generalized distrib-utivity operator by Lin (1998), must be associated with a plural entity, as the contrast between (33a) and (33b) shows:

(33) a. Ta¯me´n do¯u bıˇ woˇ ga¯o

they all COM I tall

‘They all are taller than I am.’

b. *Ta¯ do¯u bıˇ woˇ ga¯o 。

he all COM I tall

Now consider (34).

(34) Zha¯ngsa¯n bıˇ Lıˇsı` huo`zheˇ (bıˇ) Wa´ngwu˘ do¯u ha´i ga¯o 。 Zhangsan COM Lisi or COM Wangwu all still tall Lit: ‘Zhangsan is taller than both Lisi or Wangwu.’

What is interesting about (34) is the use ofhuo`zheˇ ‘or’, which in this case is an inclusive interpretation, and therefore is compatible withdo¯u ‘all’. However, on Xiang’s analysis involving ellipsis inside VP-coordination or rightward Across-The-Board movement, (34) should be ruled out just as (33b) is, because in either analysis do¯u ‘all’ would be wrongly associated with a singular individual when the predicate do¯u ha´i ga¯o is reconstructed.

Another potential problem with Xiang’s DegP-shell structure is concerned with Tsao’s examples of multiple-topic comparison. Such sentences would make both the

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DegP-shell structure and AP more complicated than necessary. It is not clear how the three different ‘‘dimensions’’ are moved, and whether some conditions on movement are violated.

As for transitive comparatives, though it is reasonable to link them to the same source structure for bıˇ-comparatives, this approach has some problems. One problem has to do with the distribution of adverbs like ha´i ‘still/more’ in (35a). If a transitive comparative is derived by raising the adjective to the position occupied by bıˇ, it is predicted that (35b) would be a well-formed structure with the adverb ha´i left in situ. However, this prediction is not borne out. The morpheme ha´i must appear before the adjective, as in (35c), casting doubts on a raising analysis of the adjective.

(35) a. Ta¯ bıˇ woˇ ha´i zho`ng sa¯n go¯ngjı¯n

he COM I more heavy three kilogram

‘He is three kilograms heavier than I am.’ b. *Ta¯ zho`ng woˇ ha´i sa¯n go¯ngjı¯n

he heavy I more three kilogram c. Ta¯ ha´i zho`ng woˇ sa¯n go¯ngjı¯n

he more heavy I three kilogram

On the other hand, the examples in (35) have a very simple explanation if both the bıˇ-phrase and the adverb ha´i are adjuncts adjoined to AP. Note that, instead of placing ha´i after the bıˇ-phrase, it is also possible to place the former before the latter. Such freedom of word order is quite normal for adjuncts.

Still another difficulty with Xiang’s approach, as pointed out by Erlewine (2007), is that transitive comparatives always require the presence of a differential phrase; however,bıˇ-comparatives do not have such a requirement. This indicates that the argument structure for adjectives in transitive comparatives might be different from the argument structure for adjectives in bıˇ-comparatives. Moreover, as noted by Xiang herself, only a limited number of adjectives in Mandarin Chinese have the usage of transitive comparatives.8This confirms the necessity to address idiosyn-crasy in the lexicon rather than in the syntax.

4.3 Event-based analysis

Most analyses of Chinese bıˇ-comparatives have focused on syntax rather than semantics. Erlewine’s (2007) master’s thesis was the first study to discuss the compositional semantics of Chinese bıˇ-comparatives in detail, and is therefore worthy of review.

His analysis of Chinese comparatives is comprised of two novel ideas. Syntac-tically, roughly in the same spirit as Xiang’s (2005) analysis, he proposes thatbıˇis a functional head subcategorizing for a voicev¢, which in turn, subcategorizes for the predicate of comparison, as is shown in (36).The lowerbıˇ in (36) is raised to the position of the higherbıˇ to obtain the correct surface word order.

8

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Semantically, he explores a novel neo-Davidsonian eventuality semantics of comparison, and uses the metavariable e to represent both events and states (s). Following Kratzer (1996), he assumes that predicates have only internal arguments, and that external arguments are introduced as the Agent or Experiencer of an eventuality via the voice head. A sentence such asYue¯ha`n xıˇhua¯n Ta¯ngmu˘ ‘John likes Tom’ is thus computed as follows:

(37) a. [[voiceactive, experience]] =λxλe.Exp(x,e)

Bıˇ, on the other hand, performs three functions:

It uses two eventuality variables, e1 and e2, and establishes two external arguments (to be selected) as their external arguments, respectively; it exis-tentially binds the standard’s eventuality e2; and, finally, it establishes the comparative semantics ofe1being greater thane2along a scale established by the predicate. (Erlewine 2007, p. 32)

Notice that Erlewine does not use explicit degree variables. Instead, the comparison proceeds by means of an intensity ordering relation, as defined by ‘[[[’, between eventualities. The semantics ofbıˇ, as proposed by Erlewine, is as follows: (38) [[bıˇ]] =λG<e, <e,t>>λyλxλe1.9e2(G(x,e1)^ G(y,e2)^ e1>>>e2)

On the above assumptions, a comparative sentence, such as (39), obtains its semantic interpretation from the following:

b. v x s.like(TOM,s) Exp(x,s) v VP s.like(TOM,s) voiceactive,experience xihuan Tangmu x s.like(x,s) TOM (36) S b vP v v b v VP voice target predicate of comparison standard

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(39) Yue¯ha`n bıˇ Ma˘lı` xıˇhua¯n Ta¯ngmu˘

John Bi Mary like Tom

‘John likes Tom more than Mary does.’

According to Erlewine, the above semantics has some advantages. First, it explains the so-called Internal Argument Prohibition. The object ofxıˇhua¯n ‘like’, namely, TOM, cannot be a standard of comparison because it has to first combine with the verb xıˇhua¯n ‘like’, making it impossible for the internal argument to be a free variable bound later by an argument ofbıˇ . Another advantage of the eventuality-based semantics of comparison is that the clausal comparative is also analyzed as an instance of individual comparison, rather than degree comparison. Consider the example in (41), adopted from Erlewine (2007).

(41) [Woˇ qu`] bıˇ [nıˇ qu`] ha˘o

I go bi you go good

‘It would be better if I went than if you went.’

(40) S s1 s2[like(TOM,s1) Exp(JOHN,s1)

like(TOM,s2) Exp(MARY,s2) s1 s2]

Tnonpast s1. s2[like(TOM,s1) Exp(JOHN,s1)

like(TOM,s2) Exp(MARY,s2) s1 s2] DP x s1. s2[like(TOM,s1) Exp(x,s1) like(TOM,s2) Exp(MARY,s2) s1 s2] Yu hàn John DP v y x s1. s2[like(TOM,s1) Exp(x,s1) M lì like(TOM,s2) Exp(y,s2) s1 s2] Mary x s.like(TOM,s) Exp(x,s) bi G<e,< ,t>> y x 1. 2 [G(x, 1) G(y, 2) 1 2] predicate of comparison

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Erlewine has analyzed predicates such asha˘o ‘good’ in (41) as proposition-taking predicates, suggesting that they take a proposition with an unsaturated Davidsonian eventuality argument and return a state description (cf. Kratzer’s 2000, 2005 analysis of resultatives and target state passives). In other words, such predicates are of semantic type <<e,t>, <s,t>>, as in (42) below. In order to compute the semantics of a clausal comparative, Erlewine also introduces another version ofbıˇ, given in (43). The semantics of (41) is thus computed as in (44).

(42) [[ha˘o]] =λE<e,t>λs.9e[good(e,s) ^ E(e)]

(43) [[bıˇclausal]] =λG<e,t>,<s,t>>λF<e,t>λE<e,t>λs1.9s2[G(E,s1)^ G(F,s2)^ s1o s2]

Erlewine’s proposal is very enlightening, but it is not without problems. I begin with his construal of the verbal syntax, in whichbıˇinvolves avP-shell structure and forms a constituent with the predicate of comparison rather than with the standard of comparison. As argued above, there is evidence that bıˇ and the standard form a constituent, but in the structure proposed by Erlewine, they do not.9

(44) S s1 s2 e1[good(e1,s1) go(e1) Ag(I,e1)]

e2[good(e2,s2) go(e2) Ag(you,e2) s1 s2]

Tnonpast S e.go(e) Ag(I,e) S v w qù e.go(e) Ag(you,e) F< ,t> < ,t> s1. s2 [ 1[good( 1,s1) E( 1)] 2[good( 2,s2) F( 2)] s1 s2]] v VP E< ,t> s. [good( ,s) E( )] bclausal G<< ,t>,<s,t>> F< ,t> < ,t> s1. s2 [G( ,s1) G(F,s2) s1 s2] predicate of comparison 9

Erlewine actually provides five pieces of evidence againstbıˇand the standard of comparison forming a constituent and functioning as an adjunct. However, his evidence either raises counterarguments or is subject to an alternative explanation, and, hence, is not conclusive. Due to space restriction, those arguments will not be reviewed here.

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As for the semantics ofbıˇ-comparatives, Erlewine’s analysis ofbıˇ states that only lambda-abstracted variables can be compared items, and only one variable is lambda-abstracted withinv¢ before v¢ combines with bıˇ. The consequence of this is that the system will allow comparison across only one dimension. This limitation is a weakness of Erlewine’s theory, however. As seen from Tsao’s (1989) examples, sometimes the subject and object can be simultaneously compared, as long as the object NP is fronted, as in (13b). The proposed semantics is not able to capture Tsao’s cases of double-topic comparison, let alone triple-topic comparison.

Another problem with Erlewine’s semantics of Chinese comparatives is the need it gives rise to for different lexical entries for normal individual comparison and proposition comparison. A better alternative is to unify the apparently different cases under the same meaning ofbıˇ. Such a proposal will be made later.

5 An alternative analysis

5.1 Argument-dependent comparison

As was noted earlier, some examples, such as (26) and (28), reproduced below, are ungrammatical, suggesting that proposition comparison in Chinese is not allowed. (26) *Zhe`-zha¯ng zhuo¯zi (heˇn) kua¯n bıˇ na`-zha¯ng zhuo¯zi (heˇn) cha´ng 。

this-Cl table very wide COM that-Cl table very long ‘This desk is wider than that table is long.’

(28) *[IPZhe`-zha¯ng zhuo¯zi [AP[bıˇ na`-zha¯ng zhuo¯zi cha´ng] kua¯n]]

this-Cl table COM that-Cl desk long wide

‘This desk is wider than that table is long’.

However, it is not true that clausal propositions cannot be compared. The following examples clearly show that proposition comparison is possible in Chinese: (45) [CPNıˇ qu`] bıˇ [CPwoˇ qu`] ha˘o

you go COM I go good

‘It’s better for you to go than for me to go.’

(46) [CPTa¯ za`i tu´shu¯gua˘n nia`n shu¯] bıˇ [CPta¯ za`i jia¯lıˇ

he at library read book COM he at home

nia`n shu¯] re`nzhe¯n read book serious

‘He studies more seriously in the library than he does at home.’

The contrast between (26) and (28), on the one hand, and (45) and (46), on the other hand, must be accounted for by any adequate syntactic analysis of Chinese com-paratives.

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A crucial distinction between (26), (28) and (45), (46) is that the two compared clauses linked bybıˇin the former are independent clauses that are not arguments of any predicate, whereas the two compared clauses in the latter can be regarded as the external arguments of the predicate of comparison. This observation is obvious for (45) becausenıˇ qu` ‘you go’ and woˇ qu` ‘I go’ are normally analyzed as the sen-tential subject, hence an argument, of the adjectiveha˘o ‘good’. (46) is a bit more complicated, because it does not seem intuitive to say that the propositionta¯ za`i jia¯lıˇ nia`n shu¯ ‘he studies at home’ is the sentential subject of the predicate (hen) re`nzhe¯n ‘(very) serious’. Its argument-hood, however, can be ensured once it is assumed that verbs have an event argument, as Davidson (1967) proposed, and that (manner) predicates, such as (hen) re`nzhe¯n ‘(very) serious’, are predicated of properties of events, i.e., type <<e,t>, <e,t>> expression as in Parsons (1990). Under the above assumptions, the meaning of a sentence such as (47) is something like (48).

(47) Ta¯ nia`n shu¯ heˇn re`nzhe¯n he study book very serious ‘He studies seriously.’

(48) a. ||ta¯ nia`n shu¯ || =λe9x.[study¢(x)(e)(he¢) & books¢(x)]

b. ||heˇn re`nzhe¯n || (||Ta¯ nia`n shu¯||) =λe9x[study¢(x)(e)(he¢) & books¢ (x) & serious¢(e)]

From the above analysis, the propositionta¯ za`i jia¯lıˇ nia`n shu¯‘he studies at home’ in (46) is an argument of the predicateheˇn re`nzhe¯n ‘serious’, and, therefore, can be analyzed as a sentential subject as well. It can be safely concluded, then, that what distinguishes (26) and (28), on the one hand, and (45) and (46), on the other, is whether the compared items function as arguments of a gradable predicate.

Based on the above proposition comparison, the examples discussed by Tsao (1989) are reanalyzed below. Recall that his generalization with respect to Chinese bıˇ-comparatives is that the morphemebıˇ must be flanked by constituents of equal rank, and that these compared constituents can be individuals, times, or locations. From his examples, it is not difficult to conclude that both external and internal arguments of a predicate can be compared, as long as they occur before the pred-icate. Some examples are reproduced below.

(49) Comparison of external argument Yue¯ha`n bıˇ ma˘lı` (ge`ng) ga¯o 。

John COM Mary even tall

‘John is (even) taller than Mary.’

(50) Comparison of various internal arguments a. Woˇ da`ishu` bıˇ jıˇhe´ xıˇhua¯n 。

I algebra COM geometry like ‘I like algebra more than geometry.’

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b. Ta¯ duı` nıˇ bıˇ duı` woˇ ha˘o 。

he to you COM to me nice

‘He is nicer to you than (he is) to me.’

c. Ta¯ ba˘ qia´n bıˇ ba˘ she¯ngmı`ng ka`n

he BA money COM BA life regard

de zho`ng 。

PART important

‘He regards money as more important than (he does) life.’

In addition to external and internal arguments, we have found, from Tsao’s examples, that times and location can be compared, as in (51) and (52).

(51) Comparison of time

Ta¯ jı¯ntia¯n bıˇ zuo´tia¯n shu¯fu´

he today COM yesterday feel-good ‘He feels better today than he did yesterday.’ (52) Comparison of location

Ta¯ za`i xue´xia`o bıˇ za`i jia¯lıˇ kua`ile` 。 he at school COM at home happy ‘He is happier at school than at home.’

Moreover, the different kinds of compared constituents can all appear simulta-neously, giving rise to what Tsao called multiple-topic comparison, as in (53). (53) Triple-topic comparison

Ta¯ zuo´tia¯n za`i xue´xia`o bıˇ woˇ jı¯ntia¯n za`i jia¯lıˇ ka¯ixı¯n 。 he yesterday at school COM I today at home happy ‘He was happier at school yesterday than I am at home today.’

There is no doubt that external and internal arguments are true arguments, but what about times and locations? Traditionally, times and locations are treated as adjuncts. However, there are reasons to believe that times and locations are more like arguments than adjuncts with respect to wh-extraction (see Tsai 1994 for Chinese wh-extraction). Semantically, it is often assumed, especially in works studying tense and aspect, that time is an argument of a predicate (e.g. Lin 2003, 2006 for Chinese). Linguists occasionally lump time and location together as one single argument. For example, Kratzer (1988), when discussing the distinction between stage-level and individual-level predicates, suggests that stage-level predicates have a spatial-temporal argument in their argument structure, though this argument only optionally appears in overt syntax. If it is true that times and loca-tions are part of the (perhaps optional) argument structure of a predicate, a clear generalization about Chinese comparatives is (54).

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(54) Argument requirement of Chinese comparatives

In Mandarin Chinese, compared constituents must be arguments of a gradable predicate of comparison.

The above generalization predicts that true adjuncts like manner expressions are not comparable constituents. This prediction is borne out, and thus, sentences like (55) are not acceptable.

(55) a. *Woˇ-de she¯ngrı` huı` ma`nma`ndi bıˇ kua`ikua`dı` da`o 。 my birthday will slowly COM quickly arrive ‘My birthday will come more slowly than quickly.’

b. *Ta¯ mia˘nqia˘ngdi bıˇ xı¯n-ga¯n-qı´ng-yua`n-di da¯yı`ng zuo`

he reluctantly COM willingly promise do

na`-jia`n shı` 。 that-Cl thing

‘He promised to do it more reluctantly than willingly.’

This is in contrast with English, which allows manner adverbs to function as compared constituents. The following three examples are all real life sentences, as found on the internet.10

(56) a. Although there may be a $ 100 million picture out there, I think that its day will comemore slowly than quickly, so that the market will be allowed a chance to grow moreslowly than swiftly.

b. In this sense, cultural organizations – for the most part public or at least dependent on public funding – take part,more reluctantly than willingly, in this process of. . .

c. He sighs, butmore happily than sadly.

Manner adjuncts, more often than not, are analyzed as functions, which take VPs as their arguments. In this sense, manner adjuncts are predicates rather than argu-ments. The generalization in (54) thus excludes them from comparable constituents. In fact, the same generalization also excludes normal predicates from being comparable. Therefore, examples such as (57) are ruled out.

(57) *Zha¯ngsa¯n (heˇn) yo`nggo¯ng bıˇ (heˇn) co¯ngmı´ng 。 Zhangsan very diligent COM very clever

‘Zhangsan is more diligent than clever.’

10An anonymous reviewer remarks that the examples in (56) need to be understood as ‘rather than’, thus casting doubt on the distinction between English and Chinese. However, it is not clear that the remark is correct. The examples in (56) can be easily paraphrased as degree expressions. For example, the sentence Its day will come more slowly than quicklyis equivalent to ‘The degree to which its day will come slowly exceeds the degree to which its day will come quickly’. Such paraphrases are standard paraphrases of comparative constructions. Another objection to the reviewer’s suggestion is that the expression ‘rather than’ implies a total negation, but examples such as (56a) and (56b) do not seem to have such an implication.

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Predicates are not arguments. Therefore, they are not comparable. However, the English counterpart of (57), as indicated in the translation, is grammatical, showing that predicates in English are, after all, comparable.

Likewise, it is predicted by (54) that reason clauses are not comparable in Chinese, and this prediction is borne out, as evidenced by (58).

(58) *Ma¯ma yı¯nwe`i Xia˘omı´ng shuo¯hua˘ng bıˇ yı¯nwe`i ta¯ mother because Xiaoming say-lie COM because he

to¯u qia´n ge¯ng she¯ngqı`

steal money more angry

‘Mother was angry more because Xiaoming told a lie than because he stole money.’

Again, this is in contrast to English comparatives, which allow reason clauses to be compared items. Below are two examples from the internet.

(59) a. However, this westward movement took placemore because the English were searching for better land than because the population was increasing.

b. . . . for doubtless many persons have suffered more because someone else has said ‘‘don’t’’ to them than because they themselves gave up and said ‘‘die.’’

The above contrasts between English and Chinese point to the following parameter of comparative constructions across languages.

(60) Argument dependence parameters of comparatives

Comparatives in a given language may be argument-dependent or non-argument-dependent.

In argument-dependent languages, such as Mandarin Chinese, only arguments of gradable predicates can serve as compared constituents, while in non-argument-dependent languages, compared constituents are not restricted to arguments. Later, it will be shown that the restriction to argument comparisons in Chinese can be derived from a proper semantics of the morphemebıˇ.

5.2 The syntax of Chinesebıˇ-comparatives

As noted earlier, there seems to be no positive evidence for the existence of clausal comparatives in Mandarin Chinese, in that the morphemebıˇmay not be followed by a full clause. Therefore, bıˇ-comparatives in Mandarin Chinese are truly phrasal underlyingly, rather than reduced constructions derived from clausal comparatives. There are also indications thatbıˇ and subsequent constituents form a syntactic unit. This assumption has no problem whenbıˇ is followed by a single phrase, no matter whether that phrase denotes an individual, time, or location. However, whenbıˇ is followed by two or more phrases, it becomes more challenging to maintain the assumption. The most challenging cases are sentences like (53) where a time and a

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location phrase are compared in addition to the external argument. It is usually assumed that the subject of a sentence does not form a constituent with a temporal and/ or location modifier. Perhaps for this reason, sentences such as (53) are sometimes analyzed as cases of reduced comparatives wherebıˇ is followed by a full clause with an empty predicate elided. In what follows, however, a proposal will be made that allows the subject and a temporal and/or location modifier to form a constituent.

The idea pursued here is a variant of Xiang’s (2005) DegP-shell, or Erlewine’s (2007) vP-shell structure, in the sense thatbıˇis a functional head that can move. However, unlike Xiang and Erlewine, we propose that DegP-shell is an adjunct adjoined to the predicate of comparison in the spirit of Liu (1996), rather than a functional projection in which the predicate of comparison is embedded. Moreover, bıˇ is analyzed as a dyadic degree operator, which is like an adverb of quantification in being able to quantify over more than one indefinite (Lewis 1975; Heim 1982). The structure, as proposed for the triple comparison in (53), is (61):

According to the above analysis, the innermost argument of bıˇ is the location phrase, which appears in the complement position of the lowest Deg head. Both time and individual arguments are the specifiers of recursive DegPs. The degree headbıˇ is raised from the lowest Deg position to the highest Deg position. Under this analysis, the stringwoˇ jı¯ntia¯n za`i xue´ xia`o ‘I today at school’ forms a con-stituent to the exclusion of the main predicate AP and the whole recursive DegP, includingbıˇ is a constituent. This analysis of bıˇ-comparatives will be referred to as the dyadic DegP-shell analysis, which belongs to the family of direct phrasal comparatives. As shown later, the dyadic DegP-shell analysis may interpret the bıˇ-phrase directly once a proper semantics is assigned to bıˇ.

(61) S NP AP t he NP AP zuóti n yesterday PP AP zài xuéxiào at school DegP AP k ix n Degi DegP happy

b NP Deg w I Deg DegP ti NP Deg j nti n today Deg PP ti zài ji l at home

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Assuming the above analysis of bıˇ-comparatives to be correct, this points to another possible parameter of comparatives across languages, namely:

(62) Adicity of comparative degree heads

A comparative degree head in a language may be dyadic or monoadic. The Chinesebıˇis an instance of dyadic comparison, whereas the English-er is an instance of monoadic comparison.

An anonymous reviewer of this paper questions this conclusion, noting that Chineses does seem to allow comparisons parallel to the English examples below. (63) a. He is taller than I thought.

b. I have written more papers than he has read. c. I own more books than he does CDs.

If constructions parallel to those in (63) exist in Chinese, then that challenges the claim of argument-dependent comparisons in Chinese.

In my estimation the Chinese constructions that are closest to the English sen-tences in (63) are as follows:

(64) a. ta¯ (she¯nga¯o) bıˇ woˇ yua´nla´i xia˘ng de ha´i ga¯o 。 He height COM I originally think DE more tall ‘He is taller than what I thought (originally).’

b. woˇ xieˇ de we´nzha¯ng bıˇ ta¯ du´ de

I write Rel article COM he read Rel

(we´nzha¯ng) ha´i ge`ng duo¯ 。

article more even many

‘The articles that I have written are more than the articles that he has read.’

c. woˇ yoˇngyoˇu de shu¯ bıˇ ta¯ yoˇngyoˇu de CD ha´i

I own Rel book COM he own Rel CD more

ge`ng duo¯ 。 even many

‘The books that I own are more than the CDs that he owns.’

However, none of the above sentences involves a clausal comparison. In (64b) and (64c), the two items being compared are two noun phrases with a relative clause. Therefore, they are examples of individual (noun phase) comparisons.

(64a) may look more like a clausal comparison, but the nominalization markerde in this example, which is homophonous to the relative clause markerde as in (64b) and (64c), immediately rules out this possibility. The function of the nominalization marker de turns a clause into something very close to a free relative in English. Therefore, the meaning of (65a) can be paraphrased as (65b).

(65) a. woˇ bu` xıˇhua¯n ta¯ ma˘i de 。

I not like he buy DE

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It is sometimes assumed that a nominal constituent, which is phonologically empty and whose content can be reconstructed from the context, actually follows the nominalization marker. Therefore, the phrasewoˇyua´nla´i xia˘ng de ‘what I originally thought’ is actually a noun phrase or a nominal constituent denoting the wrongly assumed height, rather than a clausal constituent denoting a property of degrees. Under this analysis, it is easy to treat (64a) as a case of argument comparison, because the subject NP and the nominalized constituent can both be regarded as an argument of the predicatega¯o ‘tall’, as one can say either ta¯ heˇn ga¯o ‘He is tall’ or ta¯ de she¯n ga¯o heˇn ga¯o ‘His height is tall’. Similar remarks apply to (64b) and (64c).

It is also worth noting that if the nominalization markerdein (64a) is deleted, the sentence becomes grammatically incorrect, as shown in (66), further supporting the view that (64a) does not involve a clausal comparison.

(66) *ta¯ (she¯nga¯o) bıˇ woˇ yua´nla´i xia˘ng ha´i ga¯o 。 He height COM I originally think more tall ‘He is taller than what I thought (originally).’

5.3 Semantics ofbıˇ

Recall that Heim (1985) and Bhatt and Takahashi (2007) provided methods to directly interpret phrasal comparatives. The lexical entry of -er, as suggested by Bhatt and Takahashi, is recast as follows:

(67) ||-er|| =λx.λP<d, <e,t>>.λy.9d[P(y,d) ^ :P(x,d)]

According to (67), -eris a three-place operator, which takes two individuals, one predicate of individuals and degrees as its arguments. Interestingly, the argument structure of -er, as in (67), corresponds exactly to the syntactic structure given in (68b), which is proposed in this study for Chinese comparatives such as (68a). (68) a. Yue¯ha`n bıˇ ma˘lı` co¯ngmı´ng 。

John COM Mary clever

‘John is cleverer than Mary.’

However, the semantics of -er, as stated in (67), is a monoadic -er, which is not able to cover examples of multiple comparison involving individuals, times, or locations. In order to capture dyadic comparison, a more general semantics forbıˇ is required.

b. S NP AP Yu hàn DegP AP c ngm Deg NP b m lì

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The following proposes a generalized version of -er, which may directly interpret phrasal comparatives.

To begin with, let us assume that gradable stage-level predicates, as opposed to individual-level predicates, allow (optional) time and location arguments, in addi-tion to individual ones. Thus, in addiaddi-tion to individuals of typee, and degrees of typed, we have semantic type i for time, and l for location, in our system. Under these assumptions, adjectives such asco¯ngmı´ng ‘clever’ and ka¯ixı¯n ‘happy’ may have the following denotations, respectively:

(69) a. ||co¯ngmı´ng || =λdλx.CLEVER(x)  d b. CLEVER =λx.x¢s intelligence

(70) a. ||ka¯ixı¯n|| =λdλlλiλx.HAPPY(l)(i)(x)  d

b. HAPPY =λlλiλx.x¢s happiness at location l at time i

In order to explain examples such as (68a), the semantics ofbıˇcan be defined as in (71).

(71) Semantics of bıˇ – preliminary version I:

||bıˇ|| =λx.λP<d,<e,t>>.λy[imaxd[P(d)(y)] >imax d [P(d)(x)]]

However, the semantics ofbıˇas given in (71) is not able to cover comparison of times, locations, or those across different domains, such as exemplified in (72). (72) a. Ta¯ zuo´tia¯n bıˇ jı¯ntia¯n ka¯ixı¯n 。

he yesterday COM today happy ‘He was happier yesterday than today.’

b. Ta¯ za`i jia¯lıˇ bıˇ za`i xue´xia`o ka¯ixı¯n 。

he at home COM at school happy

‘He is happier at home than at school.’

c. Ta¯ jı¯ntia¯n bıˇ woˇ zuo´tia¯n ka¯ixı¯n 。

he today COM I yesterday happy

‘He is happier today than I was yesterday.’

d. Ta¯ za`i xue´xia`o bıˇ woˇ za`i jia¯lıˇ ka¯ixı¯n 。

he at school COM I at home happy

‘He is happier at school than I am at home.’

e. Ta¯ jı¯ntia¯n za`i xue´xia`o bıˇ woˇ zuo´tia¯n za`i jia¯lıˇ ka¯ixı¯n 。 he today at school COM I yesterday at home happy ‘He is happier at school today than I was at home yesterday.’

In order to explain all of the above examples, a generalized meaning ofbıˇ, such as (73), is required.

(73) Semantics of bıˇ – preliminary version II: ||bıˇ|| = (λl)i(λi)jλxλ}<d, <(l), <(i), <e,t>>>>(λl¢)

i

(λi¢)jλy[imax d[} (d)(l¢)(i¢)

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In (73), parentheses are used to indicate that the element within the parentheses is optional. Symbols with the same superscript index must match in their presence or absence. Therefore, when the left ‘λl’ appears, the right ‘λl¢’ must appear with it, and similarly for ‘λi’ and ‘λi¢’. This analysis covers all examples in (72), with (71) as a special instance of (73). In particular, it guarantees that the comparative degree morpheme bıˇ is always flanked by constituents of the same type, thus capturing Tsao’s (1989) generalization that compared items must be ‘‘topics of an equal rank’’. We thus directly account for the semantics of bıˇ-constituents, without resorting to any reduction analysis.

Two points are worth mentioning, however. One feature of (73) is the require-ment that the external argurequire-ment, i.e., the variablesx andy, is always a compared item. At first glance, this prediction seems to be wrong because of examples, such as (74a), where the external argument is not being compared.

(74) a. Zha¯ngsa¯n za`i xue´xia`o bıˇ za`i jia¯lıˇ ka¯ixı¯n 。 Zhangsan at school COM at home happy ‘Zhangsan is happier at school than at home.’

b. Zha¯ngsa¯n za`i xue´xia`o bıˇ ta¯ za`i jia¯lıˇ ka¯ixı¯n 。

Zhangsan at school COM he at home happy

‘Zhangsan is happier at school than at home.’

This apparently wrong prediction is not serious. As proposed by Tsao (1989) and discussed earlier, Chinese comparatives are subject to a forward deletion principle, which deletes the second compared item. Therefore, the structure of (74a) does contain an empty individual argument afterbıˇ, which is equivalent to the pronoun in (74b). This empty argument will fill the value of the variable x, which is co-referential with the value of the variabley.

A real inadequacy of (73) is that it only allows one individual argument of a predicate to be compared. However, Chinese bıˇ-comparatives may compare external and internal arguments at the same time when the internal argument is fronted, as (75) shows.

(75) Ta¯ la´nqiu´ bıˇ woˇ pa´iqiu´ da˘-de ha˘o 。 he basketball COM I volleyball play-Part good ‘He plays basketball better than I play volleyball.’

In order to cover examples such as (75), one more individual variable must be added to (73), and thus, (73) is revised to (76a).

(76) Semantics of bıˇ – final version:

a. ||bıˇ|| = (λl)i(λi)j(λw)kλxλ}<d, <(l), <(i), <(e), <e,t>>>>>(λl¢)i(λi¢)j(λz)kλy

[imaxd [}(d)(l¢)(i¢)(z)(y)] > imaxd [} (d) (l)(i)(w)(x)]]

b. ||bıˇ|| =λ!a iλ}<d,< ! a;t>>λ!ai0[imaxd [}(d)( ! ai0)]>imaxd [} (d) ( ! ai0)]], where |!a |  1.

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However, (76a) is complicated and would be more desirable if simplified, as in (76b), where the symbol ‘!a ’ indicates a sequence of arguments of a gradable predicate, <!a > is the corresponding semantic type, and |!a | is the number of arguments in the sequence. Moreover, the matching subscript index i in (76b) replaces the matching indices in (76a); and it is required that the sequence of arguments must contain at least one element. This reformulation maintains the essence of (76a) and appears simpler and more elegant.

6 Concluding remarks: implicational parameters of comparatives

Recently, several linguists have begun to pay attention to crosslinguistic variations in the expression of comparison (Beck et al. 2004; Kennedy 2005; Bhatt and Takahashi 2007). Kennedy (2005) has addressed this issue in detail by suggesting that languages may differ with respect to two potential parameters in expressing comparison. One is explicit versus. implicit comparison; and the other, individual verses. degree comparison.

 Explicit versus implicit comparison:Does the comparison involve specialized morphology that expresses arbitrary ordering relations (explicit comparison), or does the comparison involve taking advantage of the inherent context sensitivity of the positive (unmarked) form (implicit comparison).

 Individual versus degree comparison: Do the comparatives express orderings between arbitrary individuals (individual comparison), or do they (also) express orderings between individuals and arbitrary (linguistically explicit) degrees? (Kennedy 2005:1)

For the individual/degree comparison distinction, the following two parameters are suggested by Kennedy:

 The Degree Abstraction Parameter: A language {does, does not} have binding of degree variables in the syntax.

 The Standard Type Parameter: Languages may differ in whether the com-parative morphology selects a standard of typed (degree comparison) or of type e (individual comparison)

Bhatt and Takahashi (2007), on the other hand, suggest that universal grammar may allow a language to interpret phrasal comparatives either by ‘‘reduction analysis’’ or ‘‘direct analysis’’.

This concluding section aims to link our discussion to the picture of comparatives across languages, as sketched by these authors. To begin, recall that Chinese does not have clausal comparatives, and all comparatives can be analyzed as (multiple)-phrasal comparatives using ‘‘direct analysis’’ to interpret them. From here, a clear implicational universal is:

 If a language does not have clausal comparatives, it does not have degree comparison, i.e., it does not have the binding of degree variables in the syntax.

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Therefore, even if ‘‘reduction analysis’’ is sometimes available for phrasal com-paratives in some languages (Bhatt and Takahashi 2007), this strategy is not available for Chinese. Thus, Chinese, as Kennedy (2005) has suggested, is a lan-guage of individual comparison.

However, also according to Kennedy (2005), when a language is an individual comparison language, the standard type of parameter is of type e. This is prob-lematic. As discussed earlier, in addition to normal individuals, times, locations, and even propositions can be a standard of comparison in Mandarin Chinese, as long as they are arguments of the predicate of comparison. In view of this, an independent parameter of comparison, such as the following, might still be needed:

 Comparatives in a language can be argument-dependent or non-argument-dependent.

Individual comparison of typeeis a special case of argument-dependent com-parison. Perhaps argument-dependent languages may allow different types of arguments to serve as standards of comparison. This parameter needs further investigation in the future for languages other than Mandarin Chinese.

Another parameter discussed in this article is dyadic comparison vs. monoadic comparison. This parameter can be stated as follows:

 If a language has phrasal comparatives, the construction may allow comparison of one phrase (monoadic comparison) or more than one phrase (dyadic com-parison).

Undoubtedly, this parameter is a lexical matter. For some languages, the comparative morpheme may allow only one standard, but for some languages, it may allow more than one. Since the author does not know enough languages to confirm more cases of dyadic comparison, this parameter must await further confirmation in the future.

Acknowledgements Parts of this paper were presented at GLOW VI on Dec 27–29, 2007, The Chinese University of Hong Kong, and at IACL-16, May 30–June 2, 2008, Beijing University. I would like to thank the audiences there for their questions and comments. Special thanks to Ting-chi Wei, Cheng-sheng Liu, and Wenjie Wang for their examples and discussions. I also wish to thank an anonymous reviewer ofNALS for comments and suggestions on how to improve this paper. The research leading to this article was sponsored by the National Science Council of Taiwan (Grant Number NSC96-2411-H-009-015-MY2). I am solely responsible for any remaining errors.

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