Yi-multiplier

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necessary factor to distinguish classifiers from measure words. The following is a

ge-substitution formula postulated by Her and Hsieh (2010) to distinguish classifiers

from measure words.

(25)Ge-substitution

If [Num XNoun] = [Num geNoun] semantically, then X = C and X ≠ M.

3.4 Yi – Multiplier

In supposing that coding of the operation of multiplication in language is necessary, Her (2011b) thinks that Au Yeung (2005, 2007) makes a convincing case for the essential role of the multiplicative identity, 1, in the emergence of classifiers.

Her (2011b) points out that in the number calling system of both Chinese and

English, all multipliers above the ten are called. Take the number 6543 for example.

(26) 六 千 五 百 四 十 三 (Her 2011b, (50)) liu4 qian1 wu3 bai3 si4 shi2 san1

six thousand five hundred four ten three

‘Six thousand five hundred and forty-three’

While, as Comrie (2006) points out, Chinese numbers are famously regular in their decimal pattern, (n × base) + m, where m < base, Her (2011b) mentions that the

number 6543 can be derived as shown in (27) and (28).

(27) Derivation of the number 6543 in Chinese (I) (Her 2011b, (51)) (6 × 10³) + (5 × 10²) + (4 × 10¹) + (3 × 10⁰)

(28) Derivation of the number 6543 in Chinese (II) (Her 2011b, (52)) (6 × 1000) + (5 × 100) + (4 × 10) + (3 × 1)

‧

Her (2011b) points out that the multiplication, that is symbol ×, and addition, symbol +, in examples (27) and (28) is not pronounced, but that all of the bases, such as qian1 ‘thousand’ (10³), bai3 ‘hundred’ (10²), and shi2 ‘ten’ (10¹) must be. Only, ge (10⁰) will be viewed as a exception as a base but without pronunciation. Such an asymmetry between the rightmost digits such as ge and other digits such as qian1,

bai3, and shi2 has been noted by Au Yeung (2005). Au Yeung (2005) points out that

the only phonetically null but numerically present slot is ge when a number is called in Chinese as shown in Table 6. The single digit 3 in Table 6 is equal to 3 × ge that ge is bound to appear but without pronunciation. Because ge is bound to appear and 3 ×

ge is equal to 3, the only possible multiplier for ge is the multiplier 1. The single digit

3 is thus represented by the multiplication formula as 3×1. Because ge is phonetically

null, ge is marked as silent to represent phonetically null.

Table 6: Asymmetry of the Rightmost Digit (Her 2011b, Table 1)

Number 6543 6 5 4 3 Digit Value Calling Liu6-qian1 Wu3-bai3 Si4-shi2 San1- GE

silent

Number Calling 六 千 五 百 四 十 三 (*個) (6 qian1) (5 bai3) (4 shi2) (3 × ge) Liu4 qian1 wu3 bai3 si4 shi2 san1 GE

silent

As a result, Au Yeung (2005: 201) points out: “The silent classifier in the form of 1GE

in the CL slot could serve as a seed for the noisy sortal classifier to grow”.⁸ However,

Her (2011b) mentions that Au Yeung (2005) does not follow his simple mathematical

8

Note that Au Yeung (2007) does not differentiate classifiers from measure words and uses

‘classifiers’ to include both of them. However, Au Yeung (2005) does differentiate classifiers which

are called as sortal classifiers in his terminology from measure words which are called non-sortal

classifiers in his terminology.

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value of ge as classifiers, which is quite simply the multiplier 1. Instead, Her (2011b) points out that Au Yeung pursues a more complicated formula and takes a classifier as having a numerical value ‘one tokenobjectper unit’ and a measure word as ‘n tokenobject per unit’. Au Yeung (2007) further interprets ‘tokenobject’ as the size of the ‘unit’, or the set.

(1× 1set) in example (29) and (2× 1set) in example (30) are demonstrations of ‘one tokenobjectper unit’ and ‘n tokenobject per unit’, respectively.

(29) 三 個 球 (Her 2011b (53))

san1 ge qiu2 (3×(1× 1set)×qiu2)

three C ball

‘three balls’

(30) 三 對 球 (Her 2011b (54))

san1 dui4 qiu2 (3×(2× 1set)×qiu)

three pair ball

‘three pairs of balls’

From the above two examples and the ‘one tokenobjectper unit’ and ‘n tokenobject per unit’ concepts, Her (2011b) proposes that Au Yeung’s distinction between classifiers and measure words rests on the value of n. If n is equal to 1, it is a classifier. If n is

not equal to 1, it is a measure word. Au Yeung’s formula of is shown below.

(31) Au Yeung’s (2005, 2007) Formula (Her 2011b (55))

[Num X Noun] = [Num × (n× 1set) ×Noun], where X=C if n=1 and X=M if n≠1 Although Au Yeung (2005, 2007) is possibly the first researcher to make the above clear and mathematically precise distinction between classifiers and measure

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words, Her (2011b) further provides a simpler proposal of Au Yeung’s (2005, 2007) formula.

Her (2010) proposes that if a classifier or a measure word is interpreted as having a mathematical value, then the only possible mathematical function is multiplication linking between numeral and classifiers or measure words. Simplifying Au Yeung’s formula, Her (2010) proposes that classifiers represents necessarily multiplier 1 and

1 only while measure words represents other than 1. The precise and simplier

distinction for distinguishing between classifiers and measure words of Her (2010) is

given as (32).

(32)Her’s (2010) Yi-multiplier Formula

[Num X Noun] = [Num×n Noun], where X=C iff n=1, otherwise X=M.

Finally, Her (2011b) mentions that many classifiers in Chinese are all of the same mathematical value which is multiplier 1 and that measure words are the other infinite possible values.

3.5 Remark

Theories to differentiate classifiers from measure words have been outlined in this section. Numeral/adjectival stacking is not a perfect way to differentiate classifiers and measure words because there are many variables. For example, a Mandarin Chinese classifier feng1封

. Under the scope of numeral modification, yi1 xiang1

shi2 feng1 xin4

一箱十封信

is acceptable, but under the scope of adjectival

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modification yi1 da4 feng1 xin4一大封信 is semantically doubtful if it is equal to

yi1 feng1 da4 xin4

一封大信

or da4 feng1 de xin4

大封的信is also semantically doubtful if it is equal to da4 xin4大信. Or, a Mandarin Chinese classifiers, ju4具. Under the scope of numeral modification, yi1 xiang1 shi2 ju4 shi1ti3 一箱十具屍體 is acceptable, but under the scope of adjectival modification yi1 da4 ju4 shi1ti3一大 具屍體 is semantically doubtful if it is equal to yi1 ju4 da4 shi1ti3一具大屍體 or

da4 ju4 de shi1ti3

大具的屍體

is semantically doubtful if it is equal to da4 shi1ti3

大屍體. The above situations in which classifiers are testified as classifiers in one test but where there status is uncertain in others will increase the difficulties and lack of accuracy in determining whether a Mandarin Chinese word is classifiers or measure words. Moreover, it is impossible to have a definite dichotomous distinction for classifiers and measure words.

Although Her (2011b) has already revised the defects of de-insertion, I still found some counter-examples through Google searches. For example, a classifier jian4件 is allowed to have de-insertion such as in yi1 jian4 de mao2yi1一件的毛衣⁹. A classifier mian4面

is also allowed to have de-insertion such as in yi1 mian4 de

jing4zi

一面的鏡子¹⁰. Though I found some counter-examples through Google searches, most classifiers are still not allowed to have de-insertion. Words which are not allowed to have de-insertion must be classifiers, while words which are allowed

9

Data accessed on June 27, 2011.

10

Data accessed on June 27, 2011.

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to have de-insertion are likely to be classifiers. Thus, I think that de-insertion is a sufficient but not necessary property for being a classifier.

Although Tai and Wang (1990) and Tai (1994) suggest that ge-substitution can distinguish classifiers from measure words, Hsieh (2009) mentions some counter-examples. I also found some counter-examples, such as ? yi1 ge dao4cai3 一個稻草. As a result, words which can be substituted for ge個 are certain to be classifiers. However, such substitution does not work the other way as can be seen in some counter-examples. I thus conceive that ge-substitution is also a sufficient but not necessary property of being a classifier.

And the last test, yi-multiplier, the inspiration for which derives from mathematics, offers a dichotomous distinction between classifiers and measure words. Moreover, Her (2011b) points out that many classifiers in Chinese are all of multiplier 1 and measure words are multiplier other than 1. As a result, I think that yi-multiplier is a sufficient and necessary property of being a classifier.

To sum up the above comments that I have made for each of the tests, de-insertion and ge-substitution are sufficient but not necessary properties of being a classifier.

Yi-multiplier is a sufficient and necessary property of being a classifier. And numeral

/ adjectival stacking are optional because some variables are likely to occur. As a result, the decisive test to differentiate classifiers from measure words is the use of

yi-multiplier. De-insertion, ge-substitution and numeral / adjectival stacking are used

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to supplement and reinforce yi-multiplier. So, the order of these tests is yi-multiplier first, then de-insertion or ge-substitution. The last one is numeral / adjectival stacking.

In the following data analysis chapter, the above order of the tests will be adopted to re-classify Mandarin Chinese classifier categorizations.

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CHAPTER IV DATA ANALYSIS

On the basis of the theoretical frameworks discussed in Chapter 3, this chapter will present my data analysis of re-classifying five Mandarin Chinese classifier categorizations which are proposed by representative studies such as Chao (1968) in

A Grammar of Spoken Chinese, Erbaugh (1986), Hu (1993), Huang et. al. (1997) in

the Mandarin Daily Dictionary of Chinese Classifiers and Gao and Malt (2009).

In the following, three aspects will be discussed. First, due to a lack of consentient tests to identify the classifiers in these five categorizations, there are discrepancies in the number of Mandarin Chinese classifiers. Thus, I will make use of four consentient tests mentioned in Chapter 3 to re-classify five Mandarin Chinese classifier categorizations posed by Chao 1968, by Erbaugh 1986, by Hu 1993, by Huang et. al. 1997 and by Malt and Gao 2009. Second, after re-classifying the five Mandarin Chinese classifier categorizations by using the four consentient tests, the aim is to offer a group of true classifiers through using two mathematical methods and a questionnaire experiment. Third, true classifiers can be further classified according to their semantic meanings as given in the Mandarin Daily Dictionary of

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Chinese Classifiers (Huang et. al 1997) in a bottom-up form to represent an explicit

semantic categorization.

4.1 Re-classify Mandarin Chinese Classifier Categorizations

By using the four tests based on linguistic theory to analyze Mandarin Chinese classifier categorizations proposed by representative studies such as Chao (1968) in

A Grammar of Spoken Chinese, Erbaugh (1986), Hu (1993), Huang et. al. (1997) in

the Mandarin Daily Dictionary of Chinese Classifiers and Gao and Malt (2009), I propose that these classifier categorizations should be subcategorized into three portions, classifiers, Xc and Xm and measure words because some measure words like dui4對

and shuang1

雙 the multipliers of which other than 1 are included in these classifier categorizations and ambiguous words which both have classifier functions and measure word functions like ba3把

, pian4

片

and kuai4

塊 do not have any precise classifications. In the following, I will explain the concepts and the reasons for proposing these three portions.

The first portion: classifiers. All of the words in this portion are not only identified as classifiers by Chao (1968), by Erbaugh (1986), by Hu (1993), by Huang et. al.

(1997) and by Gao and Malt (2009), but also proved as classifiers by my analysis through using the four tests mentioned in Chapter 3. All of the words in this portion all have a sufficient and necessary property of being a classifier, which is multiplier 1.

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And all of the words abide by two sufficient but not necessary properties of classifiers, ge-substitution and de-insertion.

The second portion is that of Xc and Xm. The reason for why I propose the portion of Xc and Xm is in order to resolve two situations below. First, Tai and Wang (1990) and Tai (1992) mention that classifiers can be ambiguous in some contexts in that they can be interpreted as either classifiers or measure words. For instance, Mandarin Chinese classifiers like ba3把 in yi1 ba3 dao1zi 一把刀子

can mean either ‘one

knife’ or ‘a handful of knives’. The former ‘one knife’ corresponds to classifier and the latter ‘a handful of knives’ corresponds to measure word. And kuai4塊 in yi1

kuai4 rou4

一塊肉 can stress either the shape of an object or a portion of an object.

The former which stresses the shape of an object corresponds to classifier and the latter which stresses the portion of an object corresponds to measure word. However, Tai and Wang (1990) and Tai (1992) do not propose any precise classification to show how these ambiguous classifiers should be classified as classifiers or measure words.

Second, each meaning of one classifier may contribute to different categories, classifiers or measure words. Thus, a classifier may be a classifier in one meaning, but a measure word in other meanings. For instance, when kou3口 is in the meaning of calculating a well or a spring, kou3口 is a classifier such as yi1 kou3 jing3一口井. On the other hand, when kou3口 has in the meaning of calculating objects in the

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oral cavity, kou3口 is a measure word such as yi1 kou3 zhu4 ya2一口蛀牙. The different meanings of kou3口 contribute kou3口 to be a classifier or a measure word. As a result, a question arises as to whether kou3口 should be regarded as a classifier or as a measure words.

From the above two situations, I find that the similarity in these two situations is that ambiguous classifiers sometimes are classifiers, but are also sometimes measure words. Therefore, whether these ambiguous classifiers should be regarded as classifiers or measure words is an urgent issue that should be solved.

In order to solve this urgent issue and provide a simply categorization, I adopt the concept of the relation between lexemes and word-forms and the concept of the relation between word-forms from morphology to provide a precise classification.

Lexemes which are abstract are realized by word-forms which are concrete. And the relation between word-forms is in complementary distribution. The hierarchy of lexemes and word-forms are shown in Figure 2.

Figure 2: The Hierarchy of Lexemes and Word-forms

According to the relationship between lexemes and word-forms and the concept of the relationship between word-forms, I suppose that the above classifiers like ba3把

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and kou3口which function both as classifiers and measure words are actually two word-forms, namely ba3把 as a classifier or as a measure word and kou3口 as a classifier or as a measure word. Because the relation between word-forms must be in complementary distribution, ba3把 and kou3口 as classifiers also have to be in complementary distribution with ba3 把 and kou3 口

as measure words. The

complementary distribution of ba3把 / kou3口 as classifiers and as measure words can be inferred from their two interpretations, namely a classifier interpretation of

ba3

把 or kou3口and a measure word interpretation of ba3把 or kou3口. For example, ba3 把 in yi1 ba3 dao1zi 一把刀子 has a classifier interpretation, ‘a knife’, and a measure word interpretation, ‘a handful of knives’. Kou3口 also has two interpretations, one as a classifier as in ‘a well or spring’ in yi1 kou3 jing3 一口 井and the other as a measure word as in ‘a mouthful of decayed teeth’ in yi1 kou3

zhu4ya2

一口蛀牙. Because hearers or speakers only make one interpretation at one time, namely a classifier interpretation or a measure word interpretation, a classifier interpretation for ba3把 or kou3口 and a measure word interpretation for ba3把 or

kou3

口will not occur at the same time. This shows that a classifier interpretation for

ba3

把 or kou3口 and a measure word interpretation for ba3把 or kou3口are in complementary distribution. As a result, my hypothesis that ba3把 and kou3口as classifiers and measure words are actually two word-forms is provable. Moreover,

ba3

把 and kou3口 are listed as only one lexemes in Mandarin Chinese dictionaries,

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rather as two lexemes such as one lexeme for being a classifier and the other for being a measure word. Thus, I infer again that ba3把 and kou3口

as listed in

dictionaries are abstract lexemes and that ba3把 and kou3口as classifiers and as measure words are actually two concrete word-forms. To sum up the above inferences and in order to have a clear distinction between classifiers and measure words, I propose c mark to symbolize classifiers and m mark to symbolize measure words. Thus, ba3把 as a classifier will be presented as ba3把

c and ba3

把 as a measure word will be presented as ba3把

m. The same situation also applies for kou3

口

c and kou3

口

m. The hierarchy of ba3

把

, ba3

把

c and ba3

把

m and of kou3

口

,

kou3

口

c and kou3

口

m will be shown in below.

Figure 3: The Hierarchy of ba3把

, ba3

把

c and ba3

把

m

Figure 4: The Hierarchy of kou3口

, kou3

口

c and kou3

口

m

According to above inferences and observations, I also find that my propositional

Xc and Xm can be further divided into two subcategories. One is for ambiguous

classifiers like ba3 把. The other is for classifiers like kou3 口 in which each meaning of one classifier may contribute to different categories, classifiers or

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measure words.

The last portion is measure words. All words in this portion are identified as classifiers by Chao (1968), Erbaugh (1986), Hu (1993), Huang et. al. (1997) and Gao and Malt (2009). However, these words are testified as measure words by making use of the four tests mentioned in Chapter 3. None of the words in this portion have a sufficient and necessary property of being a classifier, the multiplier 1. Thus, none of the words in this portion should be included in the classifier categorization. The other three tests in Chapter 3 also support that none of the words in this portion are classifiers.

The following Table 7 shows the relations of these three portions. Briefly, these three portions can be simplified into two categories, classifiers and measure words.

Table 7 presents that the classifier portion and Xc portion are regarded as belonging to classifier category and the measure word portion and Xm portion are regarded as belonging to measure word category. Thus, the classifiers that I discuss in the following sections will include both the classifier portion and Xc portion. And the measure words portion and Xm portion will not be discussed further here because

they are not the focus of this thesis.

Table 7: The Relation of the Three Portions

Categories Classifiers Measure words

Portions classifiers , Xc measure words, Xm

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In analyzing Mandarin Chinese classifier categorizations of the following studies (Chao 1968, Erbaugh 1986, Hu 1993 and Huang et. al. 1997 and Malt and Gao 2009), I will adopt four tests in Chapter 3 in the order of yi-multiplier, then de-insertion or

ge-substitution, and then numeral / adjectival stacking to re-examine their classifier

categorizations and to re-classify the classifiers which scholars have identified further into three portions, classifiers, Xc and Xm and measure words.

Below, there is a re-examination of Mandarin Chinese classifier categorization proposed by Chao (1968) in A Grammar of Spoken Chinese in Section 4.1.1, of that proposed by Erbaugh (1986) in Section 4.1.2, of that proposed by Hu (1993) in Section 4.1.3, of that proposed by Huang et. al. (1997) in the Mandarin Daily

Dictionary of Chinese Classifiers in Section 4.1.4 and of that proposed by Gao and

Malt (2009) in Section 4.1.5.

4.1.1 Chao (1968)

The fifty-one classifiers in A Grammar of Spoken Chinese edited by Chao (1968) will be re-examined by making use of the four tests mentioned in Chapter 3 and re-classified into three portions on the basis of the concepts of the three portions in Section 4.1. In the following, I will give one or two prototypical examples for each portion and then list the rest of words. Last, some words that I exclude from these three portions will be listed individually.

4.1.1.1 Classifiers

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All of the words in this portion are proved to be classifiers not only by Chao (1968) but also by my analysis. The prototypical examples listed here are mei2枚 and ding3 頂. Finally, all words in this portion are listed in 4.1.1.1.3.

4.1.1.1.1 Mei2

枚

For example, yi1 mei2 jiang3 zhang1一枚獎章

‘one medal’.

Yi-multiplier:

(33) 一 枚 獎章 = 一 × 1 獎章

yi1 mei2 jiang3zhang1 yi1 yi1 jiang3zhang1

one C medal one one medal

‘one medal’ ‘one medal’

By using yi-multiplier, mei2枚 is tested to be a classifier.

Ge-substitution:

(34) 一 枚 獎章 = 一 個 獎章

yi1 mei2 jiang3zhang1 yi1 ge jiang3 zhang1

one C medal one C medal

‘one medal’ ‘one medal’

Ge-substitution shows that mei2

枚is a classifier.

De-insertion:

(35) 一 枚 (*的) 獎章

yi1 mei2 (* de) jiang3zhang1

one C DE medal

‘one *C medal’

The semantic meaning of mei2枚

in de-insertion shows that mei2

枚is a classifier.

Numeral/adjectival stacking:

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(36) *一 枚 十 個 獎章

yi1 mei2 shi2 ge jiang3zhang1

one C ten C medal

(37) 一 大 枚 獎章 = 一 枚 大 獎章

yi1 da4 mei2 jiang3 zhang1 yi1 mei2 da4 jiang3 zhang1

one big C medal one C big medal

‘one big medal’ ‘one big medal’

(38) 大 枚 的 獎章 = 大 獎章

da4 mei2 de jiang3 zhang1 da4 jiang3 zhang1

big C DE medal big medal

‘big medal(s)’ ‘big medal(s)’

(39) 大大的 一 枚 獎章 = 一 枚 大 獎章

da4da4de yi1 mei2 jiang3 zhang1 yi1 mei2 da4 jiang3 zhang1

big one C medal one C big medal

‘one big medal’ ‘one big medal’

(40) *一 大 枚 小 獎章

yi1 da4 mei2 xiao3 jiang3 zhang1

one big C small medal

*‘one big small medal’

Mei2

枚is also a classifier by applying the test of numeral/adjectival stacking. By using the above four tests to examine mei2枚

, mei2

枚

is proved as a classifier.

4.1.1.1.2 Ding3

頂

For example, yi1 ding3 cao3 mao4一頂草帽

‘one straw hat’.

Yi-multiplier:

(41) 一 頂 草帽 = 一 × 1 草帽

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yi1 ding3 cao3mao4 yi1 yi1 cao3mao4

one C straw hat one one straw hat

‘one straw hat’ ‘one straw hat’

By using yi-multiplier, ding3 頂 is shown to be a classifier.

Ge-substitution:

(42) 一 頂 草帽 = 一 個 草帽

yi1 ding3 cao3mao4 yi1 ge cao3mao4

one C straw hat one C straw hat

‘one straw hat’ ‘one straw hat’

Ge-substitution shows that ding3

頂

is a classifier.

De-insertion:

(43) 一 頂 (*的) 草帽

yi1 ding3 (*de) cao3mao4

one C DE straw hat

‘one *C straw hat’

Ding3

頂in de-insertion shows that ding3頂is a classifier.

Ding3

頂in de-insertion shows that ding3頂is a classifier.

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