Chapter 3 Unsolved Problems
3.2 Analyzing the Structure of duo and ban in Numeral Classifier Phrases
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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 why marking the unit digits is unnecessary. Second, two alternative structural diagrams will be shown and discussed.
4.2.2 The Marking of the Unit Digits
In Mandarin Chinese, we refer to the position for simple numbers as gewei shu
‘unit-digit numeral’. However, do we need this marking in the numeral system? This is the question that will be addressed in this section. In He’s (2005) paper, he follows Hurford’ s (1975) theory and draws out the following hierarchical structure (40) for the complex numeral phrase (41).
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structure [X dian Y], such as yi dian wu ‘1.5’ for instance. This shows that fractional numerals are different from the Packing theory’s predictions. If fractional numerals do not share the same phrasal structure with other numerals, then the position for simple numerals is the last level in the structure. In this way, the necessity of marking its position is obviated because it is the terminal node. Furthermore, He (2005) puts forward that simple numerals “directly project numeral phrases” (200) as his explanations for the hierarchical structure of Mandarin Chinese numerals. This meansNumeralP5
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that simple numerals are the heads forming the non-branching structure by themselves.
Hence, other multiplicative NumeralPs (except from the simple numerals) are all merged from a numerical base (functional head) and another NumeralP (specifier).
Although He (2005) has firmly declared that the position for simple numbers is not marked in the structure, we still cannot deny the possibility—a functional head to mark the unit-digits. Also, an undeniable fact of 1 is that numeral 1 is equal to ten to the power of zero ‘100’. With the marking of the unit-digits, the entire syntactical diagram will be consistent in both the syntactical structure and the decimal system. As a result, we hypothesize Mandarin Chinese numeral system might have another possibility for the marking of simple numerals; that is, the marker does exist but it is silent, marked as ONE. Under this hypothesis, we suggest that the NumeralP1 for the simple numbers is also merged from a functional head Num1 marking the position of unit-digit and another NumeralP as its specifier. Below are two separate structures displayed in (42) and (43) for numeral wu ‘5’.
(42) No Marking
4 Hereafter, we will later mark numeral phrase as NumP rather than NumeralP for the following two purposes. First, we would like to distinguish our analysis from He’s (2015). Second, considering the marking of noun phrase as NP, it is more consistent if we mark numeral phrase as NumP.
NumP14
Num1′
Num1
Wu
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(43) Silent Marking
In (42), the structure is pretty simple which forms Num1P itself. The structure in (43) has a silent marking for the unit-numerals as the functional head and then merges with another NumP. By solely examining these two structures, we can only tell (43) works better in syntactical aspect; however, we are still unsure which one is better for our analysis of duo and ban in numeral classifier phrases. Thus, in the following sections, we will predict two different analyses based on these two possibilities. On the one hand, we can verify these two hypotheses; on the other, we reach our aims to propose a unified syntactic structure diagram for duo and ban in numeral classifier phrases.
4.2.3 duo and ban with Silent Marking of Unit Digits
In this section, we intend to propose the possible syntactic structures for duo and ban in numeral classifier phrases with a silent marking to mark unit-digits. As we have mentioned in previous sections, the lexical meaning of duo and ban in the structure of [Num+C/M+ban/duo+N] or [Num+duo+ C/M+N] are dependent on their preceding unit of measurement. That is, duo gets its reading of the base if it is placed right after it; however, duo gets its reading of C/M if it follows a C/M. As a result, we
5 With this analysis, wu is possible to form a Num P itself firstly and then merge with the functional head. However, this is not the main focus in this structure so the details are omitted.
NumP1
Num1′
Num1
wu5
ONE
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suppose that duo/ban is conjoined with either a numeral base or a C/M. First, we will deal with the structure of [Num+C/M+ban/duo +N], as shown in (44).
(44) 二十 五 斤 半/多 葡萄 er-shi wu jin ban/duo putao twenty five catty half/more grapes ‘twenty-five catties and half/more of grapes’
In sentences like (44), we understand them as [er-shi wu jin+ ban/duo JIN] so that we predict the hierarchical structure of the above sentence as (45).
(45)
In the diagram, for the structure of NumP, we follow He’s (2005) proposition in his study: Num2 is the functional head and merges with other numeral phrases as its
CLP
CL′
CL′
& CL′
NumP2 CL′ CL′ NP
NumP
Num2′ CL CL N′
& NumP1 jin duo/ban JIN
Num2 Num1′ N
er shi Num1 putao
wu ONE
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specifier. Then, CL′ would firstly combine with NumP and forms a CL′ node. Then, this CL′ node is in conjunction with the other CL′ node formed with the numeral ban/duo and a silent C/M. As for the mathematical value of ban/duo, we have mentioned that they are dependent on their preceding unit of measurement which can be jin, wu jin or er-shi wu jin. That is, the value of ban/duo can be derived from any node above the CL′ node formed by ban/duo. The whole structure in arithmetic formula is [(2×10+5] ×jin+ ban/duo ×JIN] which resemble natural number, e.g.
[[8×10] +3].
Apart from the above structure, duo is also possible to be adjacent to a numerical base. In our example (46), duo appears right after the base shi ‘ten’ and gets its value accordingly. That is, duo displays the value ranging from more than 0 to 9 catties of grapes6.
(46) 二十 多 斤 葡萄 er-shi duo jin putao twenty more catty grapes ‘twenty and more catties of grapes’
Because duo in this structure (46) has to get its reading from the base, we propose that duo is conjoined with er-shi. Yet, as our assumption in this section—a silent marking occupies the position of simple numerals, duo is logically the specifier of NumP1. The hierarchical structure of (46) can be seen in (47).
6 As indicated above, the denoted values of these approximants numerals might be diverged from person to person.
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(47)
This arrangement is not only directly corresponding to the denoted values of duo, but also shows that it is attached on the numerical base one-level lower than the last NumP in the hierarchical structure. To be more specific, in the sentence like san-bai duo jin putao ‘three hundred and more catties of grapes’, duo would be the specifier of Num2, a level lower than NumP3 (detailed presented in (48)).
CLP
CL′
NumP2 CL′ NP
Num2′
Num2 & NumP1 CL N′
Er shi Num1′ jin
duo Num1 N
ONE putao
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(48)
However, we encounter the first problem by examining this structure. Although the value of duo can correctly be generated by this tree, it will generate the ungrammatical sentence *san-bai duo shi jin putao, even if, we tentatively suggest a stipulation that the numerical base occupied by duo will turn out to be silent. No satisfying reasons can be found to explain this stipulation. Second, under this analysis, we are unable to explain why ban is unable to be adjacent to a numerical base. Since both duo and ban are numerals which display approximant quantity, they should logically behave the same in syntax.
In summary, we have to clearly pinpoint the advantages of this syntactical structure, comparing to He’s (2005) analysis. First, it successfully presents the correct
In summary, we have to clearly pinpoint the advantages of this syntactical structure, comparing to He’s (2005) analysis. First, it successfully presents the correct