Chapter 2 Literature Review
2.5 Ban ‘half’ and duo ‘more’ in Numeral Classifier Phrases
2.5.2 He’s (2015) Study
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zuo zhe ge dangao wo yong-le yi ge ban apple make this C cake I use-PRF one C half apple ‘I used one and a half apples to make this cake.’
(14) a. *他 從 樹上 摘下 了 ¾ 個 蘋果 ta cong shu-shang zhaixia-le ¾ ge pingguo he from tree-on pick-PRF ¾ C apple
b.*他 從 樹上 摘下 了 一 個 多 蘋果 ta cong shu-shang zhaixia-le yi ge duo pingguo he from tree-on pick-PRF one C more apple c. *他 從 樹上 摘下 了 一 個 半 蘋果 ta cong shu-shang zhaixia-le yi ge ban pingguo he from tree-on pick-PRF one C half apple
Although Zhang (2013) has already clearly described the behavior of ban ‘half’ and duo ‘more’, the syntactic analyses of these sentences are still scarce.
2.5.2 He’s (2015) Study
He (2015), in building the arguments to support the constituency analysis for complex numerals, briefly mentions the analyses of [Num C/M-duo N]. He comments three analyses made under non-constituency analysis and proposes his own analysis based on Hurford’s (1975) work on the linguistic theory of numerals. Taken the sentence (17) as the example, it might be transformed from (18a) by deletion or (18b) by raising.
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(15) 一 百 多 個 學生 yi bai duo ge xuesheng one hundred more C student ‘one hundred and more students’
(16) a. 一 百 個 學生 多 個 學生 yi bai ge xuesheng duo ge xuesheng b. 一 百 ti 多 ti 個 學生i
yi bai ti duo ti ge xuesheng i
Analyzing sentence (17) as (18a) and (18b), we encounter the problem that * duo ge xuesheng ‘more C student’ is ungrammatical and uninterpretable. Even if reconstruction of (18b) does not occur, other problem would arise. That is, yi bai ‘one hundred’ and duo ‘more’ are only two NPs with a structural relation. In this case, duo
‘more’ cannot be assigned a specified interpretation with regard to bai ‘hundred’.
Then, the second analysis regards the projection of (17) as [yi [bai [duo [ge xuesheng]]]]. Under this analysis, we might still face the same problem that the specified interpretation for duo ‘more’ cannot be obtained because bai ‘hundred’ is inaccessible to the composition of duo ge xuesheng. Hence, this analysis might generate incorrect interpretations. Even if He (2015) assigned duo “an interpretation of 50” (195), the whole phrase would then be interpreted as a group of 100 groups of 50 students, a total of 5,000 students. This is quite far away from its conveyed meaning in (17)—101 to 199. The third analysis reviewed by He (2015) is to consider bai-duo a compound base, which can produce two structural analyses, as shown in (19).
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(10) a. [yi [bai-duo [ge xuesheng]]]
b. [yi [bai-duo ge]] xuesheng]
Yet, neither structure generates the correct number. If we suppose “bai-duo
‘hundred-more’ expresses a quantity of 150 (any number from 101 to 150 is possible)”
(195), both structure can only be interpreted as a group of 150 students. After examining these three non-constituency analyses, He (2015) provides one possible constituency analysis with the phrase structure. To fully illustrate how He (2015) analyzes [Num C/M-duo N] sentence under the constituency approach, it is necessary to have a brief remark on Hurford’s (1975) syntax for Mandarin Chinese complex numerals. According to Hurford (1975), the complex numeral phrase (20) would turn out to be a hierarchical structure, as exemplified in (21).
(20) 五 百萬 零 六百 零 一 wu bai-wan ling liu-bai ling yi five million zero six hundred zero one ‘5, 000, 601
(He 2015:200, #45)
There are three points should be noted for interpreting the phrase structure in (21).
First, simple numerals would directly project numeral phrases. Second, “a multiplicative NumeralP is merged from a numerical base (functional head) and another NumeralP (specifier)” (200). Third, the subscript n for the hierarchies would be determined by the numerical bases. Based on the hierarchical structure in (18) and Xing’s (2003) claims— duo ‘more’ is a numeral particle attaching to the end of numerals, He (2015) proposes the following diagram.
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As indicated by He (2015), this structure needs to work with the formalization in (22), which “guarantees that duo only looks into numeral bases but not whole numeral phrases though syntactically duo combines with the whole numeral phrases” (203).(22) ║duo║=λn[n+1-50%×10 exponent(n)]]
(He 2015:203, #50) In the next section, we will identify the residual problems which were brought out by the studies reviewed in section 2. To be specific, they can roughly be separated into two parts: one is related to the assignment of part-of-speech; the other is about the syntactic structure of ban and duo, including some potential problems of Zhang’s (2013) and He’s (2015) paper.
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Section 3.1 is related to the assignment of part-of-speech and Section 3.2 is about the syntactic structure of ban and duo.
3.1 Problems of Part-of-Speech Assignments
In Section 2.2 and 2.3, we have already summarized the studies related to the part-of-speech of ban ‘half’ and duo ‘more’. To present their ideas wholly, we integrate their claims as in the following table.
Table 2.
The Claimed Part-of-Speech in Previous Studies
Studies Num+C/
Zhang (2013) Quantifier Quantifier Quantifier
He (2015) Quantifier
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Table 2 shows duo ‘more’ is assigned as a numeral adjective or a quantifier. On the other hand, ban ‘half’ is categorized as a numeral adjective, a quantifier, a numeral or a measure word. In this paper, we will later argue that ban ‘half’ is both a numeral and a measure word (M) and duo ‘more’ is a numeral. To provide a solid basis for our claims, we should answer: Why duo ‘more’ and ban ‘half’ should not be regarded as a numeral adjective?
3.1.1 Assigning duo ‘more’ and ban ‘half’ as a Quantifier
To address this question, we have to first examine the part-of-speech “quantifier”.
Since there is scarce study discussing the definition of quantifier, we make the reference from several semantic studies which examine quantifier scope interpretations (Huang, 1981; Huang, 1996; Kuno et al., 1999). In these research, quantifiers in Mandarin include mei ‘every’, youxie ‘some’, duo/xuduo ‘many’, suoyou ‘all’, and etc. If duo ‘more’ and ban ‘half’ indeed are quantifiers, they should be placed in the same position as other quantifiers. Here, we will use the sentence construction of quantifier mei ‘every’ as our replacement test target. According to Lü et al. (1990 [1980]:384), the sentence structures for mei ‘every’ are listed as follows.
(23) Sentence Structures for mei ‘every’ as a quantifier2 a. mei +(Num)+ C/M
每(一)次/每(一)件 mei ci/ mei jian every time/every piece
‘every time/every piece
2 The word mei ‘every’ can also function as an adverb, such as 每隔兩天就休息.
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b. mei +yi+ N
每 一 事物 都 有 自己的 特點 mei yi shiwu duo yiu jide tedian every one thing all have self trait
‘each thing has its own trait.’
To undergo the test of replacement, we replace the above examples with duo ‘more’
and ban ‘half’ in (24) and (25).
(24) a.多(一)次/多(一)件
b. *多一事件都有自己的特點 (25) a.半(一)次/半(一)件
b. *半一事件都有自己的特點
As we can see from the above, duo ‘more’ and ban ‘half’ cannot truly fit in the sentence structures of mei ‘every’. More significantly, (24a) and (25a) are well-formed; however, this is only superficial. This duo ‘more’ and ban ‘half’ are different from the ones in the numeral classifier phrases in lexical meanings.
3.1.2 Assigning duo ‘more’ and ban ‘half’ as a Numeral Adjective
For rejecting the claim of numeral adjective, we have to first clarify the part-of-speech of numeral adjective. That is, we have to know the exact definition of numeral adjective. Is a numeral adjective a numeral or an adjective? Suppose numeral adjective is the subcategory of adjective, several generated sentence constructions of duo and ban cannot be explained. Take the structure of [Num+C/M+ban/duo+N] as an example, shown in (26).
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(26) a. 兩 尺 半/多 花布 liang chi ban/duo huabu two meter half/more printed cloth
‘two meters and half of printed cloth/two meters and more of printed cloth’
b. 兩 尺 小 花布 liang chi xiao huabu two meter small printed cloth ‘two meters and small printed cloth’
From the above sentence replacement test, the adjective xiao ‘small’ perfectly fits the position of duo and ban in numeral classifier phrases. However, this once again is superficial. In (26b), the adjective xiao ‘small’ serves as the adjunct of the following NP; while ban/duo in (26a) actually forms a node with [Num+C/M] firstly rather than the NP. In other words, ban and duo do not possess the same feature as the other adjectives—serving as the modifiers of nouns. Yet, we cannot assert their part-of-speech by merely denying this numeral adjective argument. Thus, in chapter 4, detail discussion of their part-of-speech and the exact structure diagram will be displayed.
3.2 Analyzing the Structure of duo and ban in Numeral Classifier Phrases
In the above sections, we have already tackled the problems for assigning duo
‘more’ and ban ‘half’ as a numeral adjective. Then, we are going to address the syntactic problems that are brought out by the previous studies, including Xing (1993), Zhang (2013), and He (2015).
First, Xing (1993), in his paper, gives us abundant examples to generate the behavior of ban ‘half’. Yet, one crucial structure, the sentence like er-shi jin ban xigua
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‘twenty catty and a half (of) watermelon’, was not discussed. The other problem is that Xing (1993) only describes the position and usage of ban ‘half’ from which we are unable to predict its syntactic constructions. Second, Zhang (2013) also has this same problem; that is, we are unable to recognize the syntactic structure from her descriptions in the paper. The other potential issue in Zhang (2013) is the different behavior of duo ‘more’ and ban ‘half’. She indeed makes a major contribution to construe the occurrence of ban ‘half’ and duo ‘more’ in the structure of [Num+C/M+ban/duo+N]. Nevertheless, she does not further discuss why ban ‘half’ is unable to be adjacent to a base, i.e. *er-shi ban jin xigua. Last, He (2015) provides the structure diagram for [Num+C/M+ban/duo+N]; however, some problems still remained unsolved. The first is that He (2015) only discusses the phrases in which duo ‘more’ is adjacent to a base but not the ones that are adjacent to a C/M. Other problems lie in the presentation of his structure diagram. To clearly pinpoint the drawbacks of his analysis, we should examine his tree structure, as shown in (27).
(27)
(He, 2015:203, #49)
He claims that duo ‘more’ is a suffix attached to the whole preceding numeral phrase so that the quantity of duo ‘more’ depends on its host numeral phrases. On the surface, this tentative statement seems to alleviate some problems raised in previous studies.
However, labeling duo ‘more’ as a suffix only explains the syntactic characteristic of NumeralP3
NumeralP3 Suffix
liu bai duo
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the word rather than its part-of-speech. This is similar to the past tense marking in English traditional transformational grammar. Although the past tense verb is marked with a T, it still has its own category as a verb. Except from this problem, the numerical values of ban and duo is impossible to be directly deduced from He’s (2015) structure diagram. Yet, our proposition later in this paper can overcome this inadequacy.
As a summary, one shared problem among these studies is that the syntactic interpretation for the sentence structure of duo ‘more’ and ban ‘half’ in numeral classifier phrases are unable to be seen. He (2015) though demonstrates the analysis of [Num+C/M+duo+N] with syntactic diagram, some details still need to be settled.
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Chapter 4 The Analysis
In the preceding chapter, we have already pinpointed the drawbacks of related studies. That is, previous studies merely describe the behavior of ban ‘half’ and duo
‘more’ and fail to justify their syntactic structures. A notable exception is He (2015), where he does offer a formal account of the structure of [Num+C/M+duo+N], but we propose that his account can be further enhanced. Hence, in this chapter, two major parts will be presented. First, the arguments for assigning duo ‘more’ (as a numeral) and ban ‘half’ (as numeral and measure word) will be deployed. Then, we will provide a complete syntactic structure analysis with detailed explanations in the second section.
4.1 The Part-of-Speech of duo and ban
Here, we follow Xing’s (1993) claim and argue that duo and ban in numeral classifier phrases should be labeled as a numeral. First, we conduct the replacement test as follows. In numeral classifier phrases, ban and duo actually behave exactly the same as other simple numerals, like the ones in (28)
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(28 )a. 三 條 黃瓜 san tiao huanggua three C cucumber ‘three cucumbers’
b. 半/多 條 黃瓜 ban/duo tiao huanggua half of/several C cucumber ‘half of/several cucumbers’
However, the other structures that ban and duo may occur as a numeral classifier phrase are [Num+C/M- ban/duo +N] and [Num-duo+C/M+N], as shown in (29a) and (29b).
(29) a. 五 顆 多/半 橘子 wu ke duo/ban juzi five C more/half tangerine ‘five C and more/half of C tangerine’
b. 十 多 顆 橘子 shi duo ke juzi ten more C tangerine
‘ten and more C of tangerine’
Under the replacement test, we found that simple numerals (1~9) are not possible to be placed in any of the above structure. This inconsistent behavior between ban/duo and other basic numerals might disserve this analysis; however, it is common to find similar examples in languages that words in an assigned part-of-speech tend to have
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slightly different features. For instance, adjectives can be roughly categorized as attributive and predicative adjectives (examples are shown in (30) and (31)), which is arbitrary and unexplainable.
(30) Attributive Adjectives a. This is the main reason.
b. *The reason is main.
(31) Predicative Adjectives a. The child is afraid.
b. *He is an afraid child.
The conditions that ban/duo occurs right after C/M and duo appears after the numerical base can be explained by examining their numerical values. That is, the values of ban/duo appearing after C/M or base in the structure of [Num+C/M+ban/duo+N] and [Num+duo+C/M+N] should gain dependence on their preceding C/M or base. In other words, the interpretation of these two post-C/M and post-base ban/duo should be dependent on their syntactic contexts. For instance, the following sentences in (32) might have dubious values.
(32) a. 兩百 斤 多 牛肉 liang-bai jin duo niurou two-hundred M more beef two-hundred M and more (M) of beef
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b. 兩百 斤 半 牛肉 liang-bai jin ban niurou two-hundred M half beef two-hundred M and half (M) of beef
In these two sentences, the mathematical values might be varied from ban/duo’s preceding unit of measurement, including jin, bai-jin or liang-bai jin. If we regard duo’s dependent unit of measurement as jin, then the mathematical value of the sentence ranges from 200.1 to 200.9 catties of beef. Yet, if duo gains the value from bai-jin, the value can possibly range from 200.1 to 299 catties of beef. The same holds true for the sentences in (32b). In the structure of [ban/duo C/M+N], ban/duo, as in (33), does not have various meanings but one.
(33) a. 多 顆 蘋果 duo ke pinguo several C apple ‘several apples’
b. 半 顆 蘋果 ban ke pinguo half C apple ‘half of the apple’
However, some might argue that the semantic meanings of ban/duo in (32) and (33) are different so that they are supposed to be assigned with different part-of speech.
Evidence from the denotation of gradable adjectives, this doubt can be resolved.
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‘Compared to essay 2, essay 1 is long’
In (34), it is apparent that both chang ‘long’ are adjectives; nevertheless, (34b) denotes long but (34a) is comparatively long. This difference is significantly derived from the context. Hence, although ban/duo in (32) and (33) has different meanings, they are still presumably assigned with the same part-of-speech, numeral.
Before concluding this section, another important sentence structure of ban should also be discussed; that is, the structure of [Num+ban (N)] which Xing (1993) states this ban is M denoting the quantity of one-second. We propose, following Xing (1993), that the ban in the structure of [Num+ban (N)] is M and thus analyzed ban as a case of jianlei3. To be more specific, we consider ban as the lexical entry which subsumes more than one grammatical category—numeral and M. As a result, in the numeral classifier phrases, the syntactical category of ban is the same as duo—numeral. In the structure of [Num+ban (N)], ban is then an M.
In the next section, we will offer a detailed formal account of the structure for duo and ban in numeral classifier phrases. Also, we will tackle the question of why
3 The related studies about jianlei can refer to Hopper and Thompson (1984) and J.-X. Shen (2007).
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ban is unable to be adjacent to the numerical base.
4.2 The Syntactic Structure of duo and ban in Numeral Classifier Phrases
In the last section, we have already shown that assigning duo and ban as numeral is inferred since it is most economical and predicts the exact numeral values of duo and ban. Next, we will turn our attention to the second purpose of this study—proposing a unified syntactic structure diagram for duo and ban in numeral classifier phrases. To set a solid foundation for our syntactic structure diagram, we need to draw our attention to the universal constraint on numeral systems (the Packing Strategy). After that, one simplified syntactic structure diagram of duo and ban in numeral classifier phrases can be facilitated.
4.2.1 The Review and Extension of the Packing Strategy in Mandarin Numeral System
The Packing Strategy is a constraint on the arithmetical combinations which widely applies to most numeral systems. In Hurford’s (2007) study, he clearly introduces the universal phrase structure rules of the Packing Strategy as follows:
(35)
DIGIT
NUMBER→ (Interpreted by addition) PHRASE(NUMBER)
PHRASE→ (NUMBER) M (Interpreted by multiplication)
(Hurford, 2007:2)
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(36) Two Practical Principles
1. “Go as far as you can with the resources you have’’
2.‘‘Minimize the number of entities you are dealing with’’
(Hurford, 2007)
With the phrase structure rules in (35) and two natural principles in (36), the complete ideas of the Packing Strategy are clearly shown. However, as pointed by Hurford (2007) himself, the Packing Strategy “says nothing about linear order, but only about the hierarchical dominance relationships between constituents of numeral expressions”
(2). Grasping this notion, doubts about the expressions in spoken Mandarin Chinese, such as (37), are aroused.
(37) 三百 六十 = 三百 六 san-bai liu-shi san-bai liu three hundred sixty three hundred six ‘three hundred and sixty’
In spoken Mandarin Chinese, the counting expression san-bai liu-shi can be reduced to san-bai liu without changing the quantity. Within the Packing Strategy, we can get the linear order of san-bai liu in (38).
(38) The linear order of san-bai liu [NUM[PHR[NUM san [M bai]]] &[NUM liu]]
If we only consider the formalization above without knowing its hierarchical dominance relationships between the constituents, we found that the linear order of san-bai liu fit neatly with the number of twenty-something, see (39).
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(39) The linear order of er-shi wu [NUM[PHR[NUM er[M shi]]]&[NUM wu]]
Given the similarities between these two phrase structure rules, we should enhance the simplicity of interpreting these numeral phrase structures. That is, the reading of the final digital in numeral phrases similar to (38) is one-level lower than its preceding base (marked as M in Hurford’s (2007) study). In this logic, ba in the reduced expression wu-qian ba can be easily understood as ba-bai ‘800’ because the base preceded by ba is thousand. With this deduction, one interesting fact further emerges: If we are able to get the final digital reading dependent on the preceding base, then we need not to mark the unit digits as the other bases
In next two sections, we will justify this analysis step by step. First, the reasons
In next two sections, we will justify this analysis step by step. First, the reasons