漢語和英語中的數詞組對比分析

國立交通大學

外國語文學系外國文學與語言學碩士班

碩士論文

漢語和英語中的數詞組對比分析

An Analysis of Numerical Expressions in Chinese and English

研 究 生: 葉怡君

指導教授﹕劉辰生 博士

漢語和英語中的數詞組對比分析

國立交通大學外國語文學系外國文學與語言學碩士班

摘要

數詞詞組表達方式之主張根據 Munn 所提倡的&P 分析，或稱為 Boolean Phrase

(BP)而來，而它所累計的對等連接詞組，則是從右邊節點加接進來 (right node adjunction)。此結構充分適用於英文的數詞詞組，因為對等連接詞 ‘and’ 在 PF 上是不可或缺的；但對於中文的數詞詞組而言，&P 並不能完全符合且通用，其 主要原因為中文數詞表達中的對等連接詞｀又＇是隱藏的。最後，這篇論文試圖 證明&P 這樣的分析方式，將適用於中文和英文的數詞詞組表達方式，並強調就 算在中文數詞詞組隱藏對等連接詞(&)的情況下也適用。 關鍵字﹕抽象名詞，對等連接詞，X-bar 理論，對等連接詞結構， 附加結構

An Analysis of Numerical Expressions in Chinese and English

Student: Yi-Chun Yeh Advisor: Dr. Chen-Sheng Liu

Institute of Foreign Literatures and Linguistics National Chiao Tung University

Abstract

The fundamental assumption of this thesis is that numbers are sums. This means that numerical expressions are primarily composed of notations for the arithmetical operation of addition that exists outside the ordinary syntax of language. Hurford (1975, 2003), the most eminent researcher of numerical expressions, calls this external system “the grammar of numbers,” and he makes little attempt to integrate this external grammar with the ordinary syntax of language. This thesis, however, does attempt to account for numerical expressions within the framework of standard X-bar theory. To do this, it must be recognized that numerals exist as word strings that are free of context and that are arranged as paratactic concatenations. Moreover, it must be recognized that all numerals, even small lexical numerals, should be categorized syntactically as abstract nouns. Furthermore, when numerals are combined through addition they form nominal compounds. It follows, then, that co-ordination offers the best syntactical interpretation of numerical expressions. This thesis argues that numerical expressions can be configured as conjunction phrases (ConjP) of a specifically cumulative type called “and” phrases (&P). Specifically, it is argued that numerical expressions are best configured by following Munn’s (1993) analysis of &P, or what he calls the Boolean Phrase (BP), as right node adjunction. This configuration works well for English numerical expressions, because the conjunction “and” is integral to such expressions at PF, but the &P configuration is problematic for Chinese numerical expressions, because the conjunction you that heads the phrase remains covert. In the end, this thesis suggests evidence that the &P analysis does work for both English and Chinese numerical expressions, despite the apparent problem of the covert & in Chinese numerals.

誌謝 能夠順利完成論文，首先，我要感謝我的論文指導教授劉辰生老師的悉心教 導，他在語言學上有著豐富的學識，而且教導學生非常有耐心，對於句法的熱忱 更讓我很佩服。平時他就很關心學生，在各方面也很會替學生著想，平常和老師 討論問題時，他都會明快而敏銳的點出一些方向，讓我不至於像無頭蒼蠅一樣的 摸索，這篇論文的發想與發展都因為老師的指點而更臻完善，非常感謝劉老師。 其次，我要感謝我的論文口試委員，林宗宏老師和蔡維天老師，感謝他們在 百忙之中抽空擔任我的口試委員，對於論文的論點與分析都提出精闢的見解，更 提供我修正的方向，在他們的斧正之下，我才能針對癥結所在逐一提出修正，讓 自己的分析與立論更具說服力。 接著，要感謝陪我一路走過來的同學們﹕縉雯、雯靜、芳瑩和惠瑜。平時一 起討論功課，也會忙裡偷閒的聚餐抒壓，能夠痛快的宣洩壓力，都是因為有這些 朋友。特別感謝惠瑜在忙於寫作論文的同時，還會撥些出時間和我討論這篇論文 的問題，並提供我一些想法，讓我在論文寫作的路上不再感到孤單徬徨，真的由 衷感謝。還有，謦瑜也是身旁一位活潑可愛的學妹，她的率真與活力常帶給我許 多歡樂，讓我在繁重的課業壓力之下能盡情歡笑，也謝謝她關心我的飲食、擔心 我的健康，真的讓人感到窩心。另外，也要感謝文傑學長，佑慈學姐和靜玉學姐， 謝謝他們不吝於提供我建議和想法，也樂於將他們自己的經驗和我分享。 再來，還要感謝我的室友們﹕小皮、秀涵和宜賢。我很高興自己很幸運地能 和你們住在一起，謝謝你們帶給我的歡樂和支持鼓勵，還有謝謝你們在我心情不 好時，總是能靜靜的聽我發洩情緒。我也會一直很懷念我們徹夜聊天都不想睡的 時光。 當然，我也要感謝加拿大認識的老朋友們，因為你們的鼓勵和不斷的給予我 信心，我才能一直在研究這條路上撐下去，也謝謝你們一直相信我能做得到。 最後，要感謝我最最親愛的爸爸、媽媽和我的家人。謝謝爸爸讓我在生活上 無後顧之憂。還有媽媽﹐當初要不是您的堅持﹐我也無法順利完成碩士學業。這 本論文謹代表我內心最深的感謝，我愛你們﹗

Table of Contents Chinese Abstract……….i English Abstract……….ii Acknowledgement………....iii Table of Contents………..iv Chapter 1. Introduction...1 1.1 Basic Assumptions………...1

1.2 A Preview of the Discussion………2

Chapter 2. The Nature of Numbers………4

2.1 Numerals as Abstract Nouns………....4

2.2 Numerals as Nominal Compounds………...6

2.3 Numerical Expressions as a Form of Discourse……….….9

2.4 English Numerical Expressions……….10

2.5 Chinese Numerical Expressions……….14

Chapter 3. Hurford’s Standard Analysis and My First Response……….18

3.1 Hurford’s (1975,2003) Analysis……….…18

3.2 My First Response to Hurford………....22

Chapter 4. Numerical Expressions as Conjunction Phrase (&P) Adjuncts……. 27

4.1 On Co-ordination………27

4.2 Numerical Expressions as Adjunction………32

4.3 Munn’s (1993) Boolean Phrase (BP) Adjunction Analysis………34

4.4 Alternatives to Munn………..39

4.4.1 Zhang (2006)………...39

4.4.2 Kayne (1994) and Zoerner (1995)……….. 40

Chapter 5. My Proposed Analysis……….42

5.1 Of English numerical Expressions……….42

5.2 Of Chinese Numerical Expressions………45

5.2.1 The Matter of ling………54

5.3 A Brief Summary of My Proposal for Co-ordination Adjunction……...57

Chapter 6. Concluding Remarks………..58

Table of Contents

6.2 Postscript: Hurford Revisited……….…61

CHAPTER 1

INTRODUCTION

1.1 Basic Assumptions

The purpose of this thesis is to propose the idea that numbers are sums. This means that numbers are wholes composed of cumulative parts. Numbers embody a system of notation and operation that exists beyond the grammar of syntax, and yet numerical expressions consist of lexemes that also exhibit syntactical categorization. The matter is further complicated by the fact that the syntactical categorization of numerical expressions is extremely limited. There are neither verbs nor prepositions nor even sentences in numerical expressions. Because of this limitation numerical expressions cannot be said to possess arguments in the normal grammatical sense, nor can they be said to be subject to the case filter rule. Numbers can, however, be seen as nouns and noun phrases, and sometimes numbers seem to behave as if they were adjectives, but it is the position of this thesis that numbers are best categorized as nouns, no matter how they behave. There are simple lexical number nouns, such as “seven,” and there are complex constructed number nouns, such as “three hundred and twenty-five,” that are nominal compounds.

Because numbers are fundamentally notations of arithmetical – not grammatical – operations, efforts must be made to interface the two systems in any meaningful account of the composition of numerical expressions. The arithmetical operation involved in the organization of numbers is extremely simple. Numbers are sums. James Hurford, the most accomplished theorist of numerical expressions to date, expresses this empirical fact clearly and succinctly: “The value of a number is the sum of the values of its immediate constituents” (1975, p. 11). To translate this truth into grammatical terms we might say that numerical expressions are

cumulative statements. Numbers are made by one basic operation: addition. Often there are thought to be two operations involved in the composition of numbers: addition and

multiplication, but we should remember that multiplication is only a shorthand form of addition. The complex number 500 is actually composed by adding 100 plus 100 plus 100 plus 100 plus

100, but we usually say, for the sake of convenience, that 500 is composed by multiplying 100

times 5. In the end, numbers are sums.

Instead of following Hurford’s (1975) analysis of numerical expressions as flat structures with ternary branching, I have turned to recent arguments for conjunction phrase (ConjP) interpretations of ordination. In particular, I have followed Munn’s (1993) analysis of co-ordination as what he calls the Boolean phrase (BP) in which the first conjunct is linked with the merged constituent of the conjunction and the second conjunct through right node adjunction. I am convinced that this additive &P arrangement provides a satisfactory interpretation of

numerical expressions within the framework of X-bar theory. At any rate, this analysis works well for English numerical expressions, because these use the overt conjunction “and” in their composition. The only problem now is that Chinese numerical expressions do not use an overt conjunction such as you (yu, yehao) in their composition. The challenge has been to maintain the &P analysis for Chinese numerical expressions, while at the same time justifying a covert

conjunction as the head of &P.

1.2. A Preview of the Discussion

This thesis presents five interrelated proposals:

1. Numbers are sums composed of the arithmetical operation of addition (including multiplication, a shortened form of addition).

2. Numerical expressions are best interpreted syntactically as co-ordinate structures linking nouns to produce nominal compounds.

3. Numerical expressions exist as independent, context-free word strings that can be regarded as a singular form of paratactic and concatenated discourse.

4. Numerical expressions can be accounted for within the framework of X-bar theory by regarding them as additive or cumulative conjunction phrases (&P).

5. The &P analysis accounts for numerical expressions in both English and Chinese, incorporating both English “and” as a co-ordinator and Chinese ling (‘zero’) as a place holder.

I will first discuss the intrinsic qualities of numbers as arithmetical notations and syntactical nouns. This will be followed by a discussion and critique of Hurford’s classical interpretation of numerical expressions, focusing mainly on his phrasal structure. I will then discuss the characteristics of English and Chinese numerical expressions, paying special attention to the use of “and” in English numerical expressions and ling in Chinese numerical expressions. This will be followed by a discussion of the properties of co-ordination as a syntactical category, suggesting that it is co-ordination that best matches and expresses the arithmetical operation of addition that is central to the composition of numbers. I will then present my argument for regarding numerical expressions as additive conjunction phrases (&P) formed, in the manner of Munn (1993). The discussion concludes with an argument for

CHAPTER 2

THE NATURE OF NUMBERS

2.1 Numerals as Abstract Nouns

Hurford (1975, 1987, 2003) does not categorize numerals syntactically, and this creates a problem for any discussion of the phrasal construction of numerical expressions. Corbett (1978/2000) notes that number, as a categorical feature, is dominantly nominal, though verbs may also be marked for number. Moreover, linguists have often treated simple numbers as adjectives and multipliers and complex numbers as nouns. Nevertheless, Greenberg (1978) observes that numbers as numbers – in other words, abstract, context-free numbers – are always nouns. My thesis assumes that Greenberg is correct. All numerals, therefore, must be regarded as nouns. It follows, then, that when numerals combine to form a phrase, the result will be a nominal compound, a syntactic form that is common to both English and Chinese.

It is often taken for granted by linguists that low numbers – simple numbers, lexical numbers – especially those from 1 to 4 behave syntactically like adjectives, while higher numbers, 10 and all the complex numbers that follow, behave syntactically like nouns. But is this generalization true? Or does it represent an almost superstitious misunderstanding? I would like to propose that the grammatical nature of numbers needs to be examined more closely before we accept the common division of numbers into the categories of low adjectives and high nominals.

Greenberg (1978) states that numbers are either concrete or abstract, suggesting that it is possible to think of numbers in two distinct ways. Concrete numbers are derived from discourse. In other words, concrete numbers quantify things. They refer to nouns. They combine with nouns to form phrases. The contextuality of concrete numbers is especially evident in numeral classifier languages such as Chinese where the appropriate classifier must be used with each noun enumerated. Abstract numbers, on the other hand, are created mentally as intellectual concepts. They exist independently and they are not constrained by discourse, contextuality, or reference to nouns. Abstract numbers are nouns. Their principal uses are counting by recitation and performing mathematical computations. Sometimes a simple number may have different

numeral expressions depending on whether it is concrete or abstract. In Chinese, for instance, 2 is expressed as er as the multiplier for 10 in the absolute system, but 2 is usually expressed as

liang as the multiplier in the contextual system, especially for 100, 1000, and 10,000.

The difference between concrete numbers and abstract numbers has a long history of linguistic implications. The distinction between concrete numbers and abstract numbers is the same as the distinction between concrete nouns and abstract nouns. That is, concrete numbers are physical, because they are fused with nouns, but abstract numbers are not physical -- we cannot see, hear, taste, touch, or smell them -- because they are ideas and they are not fused with any nouns. There can be three books or three doors or three people. The number three is not limited to any one noun. To illustrate the difference between concrete nouns and abstract nouns Poncinie (1993) discusses Aristotle’s “double use” of the common term number. In Physics IV, 11, Aristotle defines number as both something that is counted and something that can be used to count something else. What can be counted is the concrete number, and what can be used to count is the abstract number. This may seem to be a simple distinction, but the more we think about it, the more difficult it is to understand. What happens for example, when we count sheep? If we count three sheep, there is no doubt that the abstract number is three. But what is the term

three sheep? Is it the quantity of the group? Or is it a numbered group? Is it three? Or is it three sheep? This is the concrete number, and it seems to suggest two interpretations.

Poncinie claims that the totality of the group, having contingent relations to other numbers, is an extensional use of the abstract number, while the numbered group is a concrete term akin to aggregate or class. What this means, then, is that there are really three kinds of numerical expressions. First, there is the abstract number. But the concrete number can be seen in two different ways: either as a totality referring to a group, or as a totaled group complete with existential features. To understand this split usage of the concrete number, let us return to the sheep. Can we apprehend and comprehend the difference between three sheep and three sheep? It is not an easy thing to do.

To complicate the matter, we probably intuit that three sheep is a different proposition than seventy-eight sheep. It is easier to regard three sheep as a numbered group of sheep than it is to regard seventy-eight sheep in the same manner, and it is easier to regard seventy-eight sheep as the totality of the group of sheep than it is to regard three sheep in that way. Why is this? To answer we must return to the common linguistic assumption that simple numbers are adjectival

and complex numbers are nominal. Menninger (1969/1992) offers an explanation of how this belief probably began. Since only the first four numbers are usually considered to be adjectival, Menninger argues that these numbers correspond to the primitive habit of counting on one’s fingers. In other words, low numbers are intimately connected to the physical reality of the entities they quantify. It is easier to see, touch, and imagine three sheep than it is to see, touch, and imagine seventy-eight sheep. This also means that it is easier to regard three as a word that describes sheep than it is to regard seventy-eight as a word that describes sheep. Thus three seems like an adjective, while seventy-eight seems like a noun.

Menninger provides a compelling reason why numbers – even low numbers – should not be regarded as adjectives. We might be tempted to claim that “three-ness” or even “seventy-eight-ness” are attributes of the counted sheep, the same as whiteness might be an attribute of these sheep. But there is a vast difference between numbers as attributes and colours as attributes. One sheep can be white, but one sheep cannot be three or seventy-eight. Numbers always refer to totalities, and as such they are always conceptual. In other words, numbers are always abstract, always detachable from the nouns they count. Contrary to popular linguistic belief, this is true of simple numbers as much as it is true of complex numbers. Menninger (p. 11) says a number word – a numerical expression – is “a special kind of word.” He means it is an abstract noun that is, by its nature, somewhat mysterious.

Menninger illustrates the importance of abstract numbers by telling how Archimedes proposed measuring the universe by computing the number of grains of sand it would take to fill it. “The whole point of Archimedes’ discussion is that even so inconceivably large a number as that of the grains of sand contained in the universe can not only be clearly understood and verbally expressed, it can even be easily exceeded: the limitless progression of the number sequence has finally been recognized!” (p. 141) One of humanity’s greatest achievements, equaled only by the invention of writing and reading, was the discovery of the abstract nature of numbers. In grammatical terms, this means that numbers are actually nouns that name ideas or concepts that exist far beyond their connections to particular physical entities.

Ultimately, complex numeral expressions are nominal compounds. This means that in the phrasal structure of numerals two nouns – either simple or multiplier or even complex in form – are combined to form a larger complex noun. As Li and Thompson (1981) point out, both English and Chinese make frequent use of nominal compounds. Examples of English numerical nominal compounds are given in (1).

(1) a. 14: nine + five → fourteen

b. 78: seventy + eight → seventy-eight

c. 130: one hundred + thirty → one hundred and thirty d. 60: six x ten → sixty

e. 1700: 17 x 100 → seventeen hundred (or, one thousand, seven hundred)

f. 1,000,000: one thousand x one thousand→ one million

When two numerals are combined in English, either through addition as in (1a - c) or through multiplication as in (1d - f), mathematics determines the resulting number, but the syntactical projection of nouns determines the resulting numeral expression. This is very obvious in (1b) where the two numerals are combined in such a way that the only difference between saying the operation of adding the two numerals and saying the resulting sum is the substitution of a hyphen for ‘and’. In (1c) the meaning of the operational phrase ‘plus’ appears as ‘and’ in the numerical expression. In (1a) and (1d) transformations for -teen and -ty are involved. I will discuss these transformations presently. In (1f) the underlying operation for the product, is transformed by mathematics into a completely different lexical expression for the nominal compound. In (1e) the nominal compound can be pronounced in either of two ways. Hurford (1975) would prefer the second alternative because it conforms to his “packing strategy” concept whereby numerical expressions should incorporate the highest possible multiplier – in this case, one thousand, not one hundred.

(2) a. 16: shi + liu → shi liu b. 20: er x shi → er shi

c. 35: (san x shi) + wu → san shi wu

d. 855: (ba x bai) + (wu x shi) + wu → ba bai wu shi wu

e. 1, 0370: (yi x wan) + ling + (san x bai) + (qi x shi) → yi wan ling san bai qi shi f. 21, 3220 (er x shi x yi x wan) + (san x qian) + (er x bai) + (er x shi) →

er shi yi wan san qian er bai er shi

As in English, numeral expressions in Chinese are composed as nominal compounds through the mathematical operations of addition and multiplication. These two basic operations are illustrated clearly in (2a) and (2b). Moreover, the way the operations of multiplication and addition can be further combined is evident in (2c) and (2d). In (2e) and (2f) we notice two important features of Chinese nominal compounds. First, Chinese numerals are arranged in strings of four, unlike English numerals which are arranged in strings of three. For this reason 10, 000 or wan becomes an important Chinese multiplier. The second distinctive feature of Chinese numeral expressions is the appearance of ling, meaning ‘zero’, as a place-holder to mark the beginning of the last string of numbers if it begins with a 0. I will discuss the importance of

ling in much detail as this thesis unfolds.

There are also other differences between Chinese and English numerals resulting from transformations. For instance, the number 16 is expressed with normal word order in Chinese as

shi liu – literally, 10 + 6. In English, however, the numeral expression for 16 involves switching

the normal word order and changing the morpheme ‘ten’ through inflection to ‘teen’, resulting in ‘sixteen’. These transformations are true of all numeral expressions in English for the numbers 13 through 19, with distinct lexical morphemes for 11 and 12, while in Chinese all the numbers between 10 and 20 are expressed by maintaining both the lexical morpheme shi for 10 and the normal word order of 10 + 1 . . . 9. Moreover, in Chinese the numeral expression for 20 maintains both normal word order and morphological form, resulting in the nominal compound

er shi, representing the multiplicative operation of 2 x 10. Once again, this pattern holds true for

30, 40, and so on, up to the next important lexical morpheme bai representing 100. In English, on the other hand, transformation morphologically changes ‘ten’ to ‘ty’ in ‘twenty’, ‘thirty’, and so on, up to ‘ninety’. Finally, a number such as 35 is expressed in Chinese as san shi wu, literally 3-10-5, whereas in English the numeral expression is ‘thirty-five’, combining the 3 x 10 operation into ‘thirty’, resulting in two morphemes for 35, whereas in Chinese all three basic morphemes are preserved. This is to say that Chinese retains both the base multiplier 10 and normal word order, while English transforms the base multiplier and deletes it in expression.

It is significant to note here that the nominal compound form of numeral expressions

occurs because they are constructed in the syntax. In other words, complex numeral expressions are unique. They do not, like simple numerals and multiplier numerals, exist in the lexicon, although, as I will soon argue, the complex numerals 11 – 99 behave, especially in English, as if they were independent lexemes. Is there a limit to the construction of complex numerals as nominal compounds? We have already seen that the ancient Greek philosopher Archimedes believed that it is possible to construct a numeral expression large enough to describe the universe. Given the abstract nature of numbers, this would seem to be entirely possible. Nevertheless, Hurford (1975) points out that numerical expressions need to be well-formed or sanctioned by natural language usage, and extremely large “theoretical” numbers may have no usable expression. Radzinski (1991) agrees and observes that it is the interface of arithmetical operations and grammatical operations that determine which numeral expressions are well-formed or even plausible.

2.3 Numerical Expressions as a Form of Discourse

Isomorphism between syntax and phonology has long been considered dubious, and yet

consideration of numerical expressions raises the possibility that it might be necessary to search the interface of these two linguistic forms to fully comprehend how numerals are composed. We have already seen that numerals are abstract, context-free nouns. Verbs (and therefore adverbs) never exist in numerical expressions. Neither do prepositions. Conjunctions are the only other possible syntactic category to be found in numerical expressions. It should be noted, however,

that the presence of a conjunction – always cumulative, represented by “&” – is regarded by Hurford (1975. p. 50) as an optional transformation. The conjunction “and” is certainly present in English numerical expressions, but a comparable conjunction, such as you, is not overtly present in Chinese numerical expressions. I shall argue, nonetheless, that the conjunction you covertly heads an &P in my binary-branching phrasal analysis of numerical expressions. In order to justify this analysis I shall appeal, to a large extent, to phonological data to support my syntactic interpretation.

Once again, Hurford’s common sense approach to the construction of numerical expressions cannot be ignored. He says, in describing his analysis (ibid.): “I have not made an attempt to integrate the grammar of numerals into a grammar for the rest of the language.” We have already seen that the grammar of numerals involves, more than anything else, the creation of sums through the operation of addition (supplemented by multiplication). We have also seen that the creation of sums results in numerals being, syntactically speaking, nominal compounds. But is now time to observe that numerical expressions may also be regarded as independent forms of discourse whose principal characteristic is that they are composed with an absolutely rigid word order arranged paratactically as unique concatenations. Although they are basically nouns or noun phrases, these word strings do not assign case internally, and they do not exhibit any movement whatsoever – making the Empty Category Principle irrelevant. Hurford also mentions that not all lexical items denote objects. In fact, some lexical items denote

relationships. This is where & enters the grammar of numerals, as overt “and” in English numerical expressions and as covert you in Chinese numerical expressions. Either way, it is important to remember that there is always a distinction to be made between the grammar of numerals and grammar as a whole. As my argument progresses, I attempt to integrate the grammar of numerals into the general grammar, but in order to do this I will have to refer to the fact that the grammar of numerals represents a special form of discourse.

2.4 English Numerical Expressions

In English numerical expressions are divided into strings of three. For example, the number 357 contains a units’ place, a tens’ place, and a hundreds’ place. This first string may be called the

hundreds’ level. This basic ordering of places is repeated in the next higher level or string of three digits, which may be called the thousands’ level. This means that at the thousands’ level there are units, tens, and hundreds (of thousands). Moreover, the same pattern holds true for the next higher level, that is, the millions’ level. Once again, there may be units, tens, and hundreds (of millions). This system may be expanded to subsequently ever higher levels, practically ad

infinitum. These facts are illustrated by the table in (3).

(3) Level of Hundreds Level of thousands Level of millions

Units 0-9 of one thousand 0-9 thousands 0-9 millions

Tens 10-99 of one thousand 10-99 thousands 10-99 millions

Hundreds 100 -999 of one thousand 100-999 thousands 100-999 millions

This system may be illustrated, for example, by the number 716, 429, 357. The strings of three digits are conventionally marked by commas in arithmetical notation. At the hundreds’ level we see 357; at the thousands’ level, 429, and at the millions’ level, 716. In the string of three digits at each of these levels there is a units’ place, a tens’ place, and a hundreds’ place.

When these numbers are given numeral expression, each of the levels contains the conjunction “and.” Thus, the number in our example is pronounced (without the emphasis suggested by the italics, which are provided for purely lexical demonstration) “seven hundred

and sixteen million, four hundred and twenty nine thousand, three hundred and fifty-seven.”

Furthermore, something else is immediately noticeable from this numeral expression. Not only is “and” repeated at each level or in each string of three digits, but “hundred” is also repeated immediately preceding each “and.” This means that each string of string of digits is divided into two parts: the hundreds’ place on the left and a combination of the tens’ place and the units’ place on the right. The conjunction “and” stands in the middle of the division. This arrangement always occurs in English complex numbers, and it suggests a binary phrasal structure of two

constituents combined by co-ordination at each level or in each string of three digits. These observations are summarized in the generalizations given in (4).

(4) a. English numerals are arranged in strings of three digits, consisting of a units’ place, a tens’ place, and a hundreds’ place at each successively higher level of strings, beginning with the level of hundreds and proceeding to the level of thousands, the level of millions, and so on, virtually without limitation.

b. At each of the levels the morpheme “and” occurs following the morpheme “hundred.” The effect of this is to bifurcate the string of three digits and suggest a phrasal structure with the hundreds’ place in the X position and a combination of the tens’ place and the units’ place in the Y position. Moreover, this suggested binary structure appears to be co-ordinated by “and.” Its function is additive.

Not all numbers, of course, contain all the possible places and strings. If (4) is true, what about a number such as 6,022? This number is pronounced “six thousand and twenty-two.” In this numeral expression “and” occurs after the word “thousand,” not the word “hundred.” There is a simple explanation for this. The morpheme “and” occurs after the hundreds’ place, but the hundreds’ place is occupied by “zero,” which is never spoken in English numeral expressions (except as 0 itself). The same might be said of the number 6,002, pronounced “six thousand and two.” Here again, “and” occurs after the hundreds’ place, and after the tens’ place as well, but both these places are phonetically null, though they are still present in LF. Therefore, such examples as these do not invalidate the generalizations in (4). In fact, the higher the number containing “and” but not “hundred” is, the more awkward and possibly ill-formed its expression sounds. For example, 76,000,003 is pronounced “seventy-six million and three,” but such an expression sounds somewhat strange.

Just as some numbers do not contain the morpheme “hundred” in their expression, other numbers do not contain the morpheme “and” in their expression. These numbers can be divided into two classes. The first of these classes contains the numbers 0-100, and the second of these

classes contains numbers over 100 that are composed of multiples of 1-100 combined with

various decimal multipliers, beginning with 100 and continuing with 1,000; 1,000,000; and so on. The first class, numbers from 0-100, needs no illustration beyond random selection, say 4, 19, 42, 75, and so on. The second class, however, needs further explanation and illustration. For a number over 100 not to have “and” in its expression it must contain “zero” in both the tens’ place and the units’ place in the first string or at the hundreds’ level. An example would be 2,900 pronounced either “two thousand, nine hundred” or “twenty-nine hundred.” Hurford (2003, pp. 42-43) would prefer the first expression, because of what he calls the “packing strategy,” the idea that well-formed numerical expressions should contain the highest decimal multiplier, in this case 1000. He does admit, however, that an expression such as “twenty-nine hundred” also appears to be acceptable, though he cannot explain why. The important thing to note here is that the number ends with 0 in both the tens’ place and the units’ place at all levels The numeral could be any number from 1-100, and the multiplier could be any decimal beginning at 100. Further examples would be 53,500 (“fifty-three thousand, five hundred”) and 49,000,000 (“forty-nine million”).

The first class of numerals that does not contain “and” is especially interesting. Conventionally, the numbers 0-9 are considered to be simple numbers whose function it is to combine with other numbers, either through addition or multiplication, to form complex numbers (Hurford, 1975; Greenberg, 1978; and many others since). In other words, a complex number is either a sum or a product of two other numbers, one of which is usually a simple number and one of which is usually a decimal multiplier. Thus the number 37 is composed of multiplying the simple number 3 by the multiplier 10, attaining the product 30, and then adding the simple number 7, attaining the final sum 37. Nevertheless, in the light of this discussion there seems to be some justification for considering the numbers 0-99 as a distinct category of numbers in numerical expressions, mainly because they never contain “and.” These numerals are not separate lexical items, but within numerical expressions they behave as if they were lexical because they frequently occur both before multipliers and after “and” at the end of numbers Examples would be “twenty-three million,” “sixty-four thousand,” and “five hundred and twenty-four.”.

(5) Within numerical expressions the numbers 1-99 often may be treated as separate lexical items. They often appear before higher multipliers beginning with 100, combining with them in phrasal structures. Their function here is multiplicative. The numbers 1-99 also appear after “and” at the ends of complex numbers. Their function in this case is additive.

Combining this generalization with the generalizations stated in (4) yields all the information needed to proceed with an interpretation of English numerical expressions within the framework of X-bar theory. To summarize: 1) English numerals are arranged in strings of three digits with a units’ place, a tens’ place, and a hundreds’ place; 2) the morpheme “and” appears after the hundreds’ place, suggesting an additive phrasal structure with two constituents joined by co-ordination; 3) numbers from 1-99 often appear before decimal multipliers and at the ends of complex numbers and can be treated as single lexical items in a multiplicative phrasal structure. At the core of the English system of numerical expression is the frequent appearance of “and” and its location after the hundreds’ place in strings of three digits at all levels.

2.5 Chinese Numerical Expressions

Chinese numerical expressions are similar to English numerical expressions in many ways. They are formed by a combination of multiplicative and additive arithmetical operations, and they are arranged in strings of digit places at successively higher levels. But Chinese numerical

expressions are arranged in strings of four places instead of strings of three places, as in English. This means that 10,000, pronounced wan, becomes an important multiplier in Chinese, though it does not exist at all as a multiplier in English. Thus the English notated number 23, 417 would be notated 2, 3417 in Chinese, and instead of being pronounced er san qian (“twenty-three thousand”) at the beginning it is pronounced er wan (“two ten-thousand”) at the beginning. The remainder of the number is pronounced san qian (“three thousand”) si bai (“four hundred”) shi

qi (“seventeen”). Each Chinese numeral contains four places: a units’ (ge) place, a tens’ (shi)

place, a hundreds’ (bai) place, and a thousands’ (qian) place. These four places are repeated at successively higher levels. This illustrated in (6).

(6) Level of ge Level of wan Level of yi

1-10,000 10,000 – 10,000,000 100,000,000 – 100,000,000,000

ge place 0-9 0-9 ten-thousands 0-9 ten-millions of ten thousand

shi place 10-99 10-99 ten-thousands 10-99 ten-millions

of ten thousand

bai place 100-999 100-999 ten-thousands 100-999 ten-millions of ten thousand

qian place 1000-9,999 1000-9999 ten-thousands 1000-9999 ten-millions

of ten thousand

The most important difference between Chinese and English numerical expressions is that, unlike English, Chinese does not use any conjunction equivalent to “and” at any point in the composition of the expression. There is, however, diachronic evidence in Brainerd and Peng (1968) that in ancient times Chinese did use the morpheme you (or yu) equivalent to “and” in English as a co-ordinate conjunction in numerical expressions. According Liu and Peyraube (1994), grammaticalization first transformed the verb you, meaning “give,” to a preposition and then later to a conjunction. Li and Thompson (1981) observe that you now occurs mostly in pairs, meaning “both . . and” Zhang (2006, p. 180), however, notes that the first you of the construction you . . . you is deletable, suggesting that if you did occur in Chinese numerals, it would do so in the middle of a string. It is also significant to note here that Yang (2005. p. 45) assumes that you is part of the internal logic of the composition of Chinese numerical

expressions. This idea has merit, I believe, and I will develop it in Section 5.2.

The other major difference between Chinese numerical expressions and English numerical expressions is that Chinese sometimes incorporates the morpheme ling, meaning “zero,” whereas the digit 0 is always phonetically null in English, except when it stands alone. In Chinese numerals ling always appears in the place of a multiplier when the value of that

multiplier is 0, but ling only appears once in any string of four digits. For example, the number 56, 0000, 0025 is pronounced wu shi liu yi ling er shi wu. There are six zeros in this numeral, but only one ling is pronounced. According to Brainerd and Peng (1968), the ling that is pronounced is the one nearest to the end of the number. It would seem, therefore that the principal function of ling is to hold the place(s) of the absent multipliers. In this example it would be difficult to process and redundant to pronounce the fact that all the multipliers between

yi and er shi wu have been omitted. In English the number 56,000,025 is pronounced “fifty-six

billion and twenty-five.” Here too mention of the multipliers between “million” and “twenty-five” has been omitted. And yet there is an intervening morpheme, namely the conjunction “and.” It is tempting, in this example, to equate the English use of “and,” with the Chinese use of ling, becauseboth these morphemes seem to hold the places of intermediate multipliers and to signal that something has been omitted. Nevertheless, we have already seen that the use of “and” in English numeral expressions appears to be predictably related to the function of co-ordination, and it therefore seems to exhibit phrasal qualities within the framework of X-bar theory. This is not immediately apparent in the case of ling, which is essentially a place holder. I will have more to say about the similarities and differences between “and” and ling when I present my analysis in Section 5.

In the meantime, the phonological rules in (7) may be said to govern the use of ling:

(7) a. Although ling appears medially in Chinese numerals, it is always a number, not a conjunction equivalent to “and,” which appears medially in English numerals.

b. When ling appears in the coefficient position before any multiplier, the multiplier is phonologically null at PF. For example, 305 is pronounced san bai ling wu, not

san bai ling shi wu.

c. When we have more than one consecutive ling, only one of them is pronounced because of phonological haplology. For example, the number 56, 0000, 0025 is pronounced wu shi liu yi ling er shi wu. There are six zeros in this numeral, but only one ling is pronounced.

d. If ling appears at the end of a numeral, it is phonologically null at PF. For example, 1500 is pronounced as yi qian wu bai or yi qian wu, not yi qian wu bai ling ling.

e. If a number ends with a multiplier, pronunciation of the multiplier is optional. Thus, 3500 is pronounced either as san qian wu bai or san qian wu.

CHAPTER 3

HURFORD’S STANDARD ANALYSIS AND MY FIRST RESPONSE

3.1 Hurford’s (1975, 2003) Analysis

The phrase structure rules given by Hurford identify three constituents of numerical expressions: Phrase, Number, and M(ultiplier). The value of a Phrase is the product of its constituents, and the value of a Number is the sum of its constituents. The value of an M is always 10 or a multiple of 10. Hurford’s structure rules state that both Number and M are recursive. His basic phrase structure rules are given in (8).

(8) DIGIT

NUM →

NUMPHRASE (NUM)

NUMPHRASE → NUM M

In Hurford’s own words (2001, p. 10758): “Here, `NUM' represents the category Numeral itself, the set of possible numeral expressions in a language; `DIGIT' represents any single numeral word up to the value of the base number (e.g., English one, two, . . ., nine); and `M' represents a category of mainly noun-like numeral forms used as multiplicational bases (e.g., English -ty,

thousand, and billion). The curly brackets in the rules enclose alternatives; thus a numeral may

be either a DIGIT (e.g. eight) or a so-called NUMPHRASE (numeral phrase) followed optionally by another numeral (e.g., eight hundred or eight hundred and eight). If a numeral has two

immediate constituents (i.e., is not just a single word) the value of the whole is calculated by adding the values of the constituents; thus sixty four means 60-4. If a numeral phrase (as distinct

from a numeral) has two immediate constituents the value of the whole is calculated by multiplying the values of the constituents; thus two hundred means 2 – 100.”

There are three problems associated with Hurford’s structure:

1. The first problem is the simple fact that his categories of Phrase, Number, and M are not related to the standard syntactical categories of Noun, Verb, Adjective, and Preposition. Hurford claims (1975, p. 19) that Phrase, Number, and M are syntactical categories, but all that he specifically mentions in regard to syntax is that Multipliers are always nouns.

2. The second problem is that his phrasal structure incorporates ternary branching to include the conjunction “and.” This violates a major principle of X-bar theory, which states that phrasal structures must be binary branching (Kayne, 1984; Pollard, 1984; Kornai & Pullum, 1990). This flaw is illustrated in (9) below.

3. The third problem involves the placing of ling, meaning “zero,” when the structure is applied to Chinese numerals. This morpheme is placed in the Phrase category when logically it should appear in the Number category. This problem is illustrated in (10) below.

(9) English numeral 230, 567 

NUM

230 567

PHR NUM

NUM M PHR CONJ NUM

PHR CONJ NUM NUM M PHR NUM

NUM M PHR

Two hundred and thirty thousand five hundred and sixty seven

2 100 30 1000 5 100 60 7

The problem of ternary branching is obvious here. This seems to occur because of the attempt to combine nouns and a conjunction syncategorematically through his conjunction insertion rule (p. 50), but this violates the principles of X-bar theory. It is also interesting to note that Hurford makes no attempt to incorporate in his structure the multiplicative composition of two complex Phrases, 30 and 60. Apparently this operation has been left out because it is necessary to pronounce “thirty” and “sixty” as integral parts of the overall numerical expression. In other words, the operations of multiplying the Numbers 3 and 6 by the Multiplier 10 to form the Phrases 30 and 60 are phonologically null. Hurford has omitted these operations in his structure because he is only interested in representing the actual pronunciation of the numerical expression.

(10) Chinese numeral 23, 0567       NUM 23 0567 PHR NUM PHR PHR NUM NUM M PHR PHR NUM PHR NUM M PHR PHR PHR NUM

NUM M NUM M PHR NUM M NUM M NUM

er shi san wan ling wu bai liu shi qi

2 10 3 1,0000 0 5 100 6 10 7

.

The only possible justification for Hurford’s structure here is to say that ling combines with the deleted M qian at LF to form a Phrase and that is what is projected. There seems to be some plausibility for this when we note that in Hurford’s structure of the English numerical expression in (8) he projects both “thirty” and “sixty” as phrases, presumably because the numbers 3 and 6 have already combined with the M 10 and these operations are phonetically null.

3.2 My First Response to Hurford

The phrasal structure I first considered is compatible with Hurford’s generally accepted analysis. At the same time, my proposal is more precise than Hurford’s in its terminology, and it therefore more accurately describes the ways that numeral expressions are actually generated.

In my proposed analysis all the constituents are nouns, so in the beginning I believed it to be important to distinguish the unique feature of the different kinds of nouns and nominal

compounds used in the proposed phrase structure. This was done in the following ways.

1. A noun that serves as multiplier (10, 100, 1000 and so on) is designated [mN]. 2. A simple number (0-9) is designated [sN].

3. A complex number – that is, a number made by multiplication or addition – is designated [cN]. However, all complex numbers are categorized, as in (4) and (5). 4. A complex number that is a product of multiplication is designated [pcN].

5. A complex number that is the sum of addition is designated [scN]. 6. A complex number that is combined by [scN] and [mN] is [mP].

Labeling all the numbers and numerical expressions as nouns indicated their major phrasal category, and sub-labeling them according to their functional characteristics indicated the exact and complete ways that they operate in the phrase structure. Hurford’s terminology for nominal phrase structure rules may be more parsimonious; but my terminology was more extensive, precise, and meaningful.

The fundamental phrase structures for the proposed nominal compounds of numerical expressions are given in (11).

(11) a. The Multiplicative Structure pcN

sN mN

b. The Additive Structure scN

pcN/ mP (and) scN/ sN

At first I was willing to accept Hurford’s flat and ternary branching additive structure with the insertion of the conjunction “and”, even though it is difficult to combine this part of the structure with the multiplicative part of the structure. Just the same, I suspected that ternary branching is somehow inappropriate for analyzing the structure of numerical expressions.

The full phrasal structures I first considered for the construction of numerical expressions as nominal compounds in English and Chinese are presented in(12) and (13).

(12) English numeral 15,438,353 scN scN mP scN scN pcN CONJ scN mP pcN scN scN mN sN mN pcN sN mN sN mN pcN sN

(13) Chinese numeral 1543,8353 scN mP scN scN scN scN scN scN pcN pcN pcN mN pcN pcN pcN sN mN sN mN sN mN sN sN mN sN mN sN mN sN

yi qian wu bai si shi san wan ba qian san bai wu shi san

I think that my first revision of Hurford’s phrasal analysis of numerical expressions does have a certain amount of merit. Not only does my revision clarify Hurford’s terminology and make it more exact, but my revision also challenges a basic assumption on which Hurford builds his system. From the outset I have assumed that all numbers are abstract nouns, and therefore they should be regarded as absolutely context free. This assumption represents an important departure from Hurford’s somewhat tentative assumption that small numerals from 0 to 9 behave as adjectives, while larger numbers behave as nouns. For example, in a note on Corbett’s (1978) statement that the higher numbers are, the “nounier” they become, Hurford (1980, p. 247) says, “I believe that he is right.” And yet Hurford does not incorporate the syntactical category of adjective into his proposed phrasal structure for numerical expressions. The most that he says in regard to syntactic categories is that his Phrases are nouns. I am convinced, however, that all numbers are abstract nouns, and that my precise – though, admittedly, complicated – system for labeling all numerical nouns according to their arithmetical functions is, at the very least, an improvement on Hurford’s nomenclature.

My first response to Hurford’s analysis was that he is not willing to make the attempt to fully integrate the grammar of numerals with the grammar of language. Because of this apparent reluctance Hurford is not able to analyze numerical expressions according to X-bar theory, and, since I am personally committed to acceptance of this theory, I found Hurford’s analysis to be unsatisfactory. I felt that there must be a way to construct a phrasal structure for numerical expressions that did not violate the rule of binary branching simply because it had to incorporate the transformation of conjunction insertion in English. Besides, Chinese numerical expressions do not even exhibit conjunction insertion at PF. The only solution appeared to be the

construction of a binary branching phrase that incorporates conjunctions as part of the phrase. Therefore, I propose that numerical expressions should be analyzed as additive or cumulative Conjunction Phrases (&P). Throughout the remainder of this thesis I will advance my argument for this interpretation of numerical expressions, providing what I believe isa plausiblerevision of Hurford’s phrasal analysis.

CHAPTER 4

NUMERICAL EXPRESSIONS AS CONJUNCTION PHRASE (&P) ADJUNCTS

4.1 On Co-ordination

We have seen so far that, in both English and Chinese, in the most fundamental manner possible, numbers are always sums. Therefore, numerical expressions encode, first and foremost, the arithmetical operation of addition. Intuitively, then, we must expect that the most appropriate syntactical operation for the construction of numerical expressions is co-ordination. In my first response to Hurford’s classic analysis I attempted to improve upon the nomenclature of

Hurford’s phrase structure by identifying the various noun phrases involved in the arithmetical operations of numeral expressions, giving these noun phrases specific functional names. But that was not sufficient to really expand or revise Hurford’s analysis. In order to do that we need to interpret numerical expressions according to X-bar theory, but before we proceed in that direction, we need to examine certain matters related to co-ordination in general.

According to Carston and Blakemore (2005), the central issue in the current discourse on co-ordination is the matter of symmetry versus asymmetry. There is an intuitive sense whereby co-ordinated elements possess both similar semantic values and similar syntactical status. Moreover, the meaning of “and” appears to suggest that in terms of truth-conditional

propositions, P & Q is equivalent to Q & P, though pragmatics suggests that in some cases P &

Q is actually P & then Q. For these reasons, early interpretations of co-ordination, such as that

of Jackendorff (1977), tended to be represented by flat structures, either non-headed or multi-headed, with the conjunction mediating between or among symmetrical syntactic elements. This symmetrical interpretation of co-ordination is still favoured by some authors. Even early X-bar theorists sometimes claimed that co-ordination is an exception to the conventions of the X-bar schema. Nevertheless, with the development of Chomskeyan Principles and Parameters theory and Minimalism in the 1990s, most authors have come to accept the phrasal structure of ConjP whereby the two conjuncts of a co-ordinated structure are not symmetrical in that XP is

Kubo (2007) points out that it is impossible to ignore the problematic nature of co-ordination in relation to the ambivalence of its symmetrical and asymmetrical features. Of particular interest to Kubo is the fact that co-ordinate constructions are paratactically construed, suggesting that they possess a fundamental symmetry. But the suggestion of symmetry is not the only significant feature of paratactical arrangement. For the purposes of my overall argument in this thesis it is the centrality of the conjunction, particularly “and,” in parataxis that I would like to emphasize. If numerical expressions are co-ordinate structures, as I assume they are, their paratactical construction, in their context-free status as a miniature independent form of

discourse, implies that adjunctive “and” is required in their formation. While I contend that the paratactical construction of co-ordinate structures reveals the centrality and necessity of “and” in numerical expressions, I do not, however, argue that numerical expressions – or, indeed, co-ordinate structures in general – are to be interpreted as phrasally symmetrical. On the contrary, I assume that numerical expressions, like all co-ordinate structures, are best accounted for as asymmetrical phrases following the binary branching and strong endocentricity principles of X-bar theory. In fact, Kubo also points out two additional characteristics that display the

asymmetry of co-ordinate structures: they exhibit c-command relations between the first and second conjuncts, and they exhibit co-ordination internal consistency, as in Ross (1967). I assume that these two features are also evident in numerical expressions.

As Carston and Blakemore (2005) observe, most linguists today accept the asymmetry of co-ordinate structures. This is true even of authors working outside the paradigm of X-bar theory, Principles and Parameters Theory, and Minimalism. Hudson (2003), for example, a proponent of Word Grammar, assumes that in English the conjunction and the second conjunct in a co-ordinate structure form a constituent that is combined with the first conjunct

asymmetrically. Zhang (2006) calls the first conjunct the external conjunct and the combination of the co-ordinator and the second conjunct the internal conjunct. I shall use this convenient terminology throughout the remainder of this thesis. Ross (1967) first proposed the constituency of the conjunction and the second conjunct on phonological grounds, arguing that an intonational pause is possible between the first conjunct and the conjunction, but not between the conjunction and the second conjunct, as in (14):

(14) a. John left, and he didn’t even say good-bye. b. John left. And he didn’t even say good-bye. c. *John left and. He didn’t even say good-bye.

Another solid argument for asymmetry in co-ordinate structures comes from pragmatic

processing whereby the logic of co-ordinate truth statements is not always (P & Q) / (Q & P), but sometimes (P & then Q), as in Hudson’s (2003) example, given in (15):

(15) a. She gave him the key, and he unlocked the door. b. *He unlocked the door, and she gave him the key.

Not only do the conjunction and the second conjunct form a constituent in each of these sentences, but the semantics and pragmatics of the co-ordinated statement indicate that word order cannot be altered without changing the meaning. (P & Q) is not symmetrical with (Q & P). This simple fact has important implications for the asymmetrical and rigidly ordered structure of numeral expressions, as I will illustrate in Section 5.

Cormack and Smith (2005, p. 395) sum up the complexity of co-ordination precisely: “Coordination appears to be symmetric, but the grammar is only capable of providing asymmetric structures. In a standard Principles and Parameters version of projection, two phrasal categories can be related in either of two ways. They may be linked (asymmetrically) to a particular head as specifier or complement of that head, or they may be linked (again

asymmetrically) as adjunct and host.” A convenient overview of the possibilities of phrasal tree structures for co-ordination is given in (16).

(16) a. XP

XP1 and XP2

b. XP

XP XP

and XP1 and XP2

The flat structure with adjoined conjunctions, as in Sag et al. (1985).

c. ConjP

XP1 Conj’

and XP2

The conjunction phrase with specifier-complement relation, as in Zoerner (1995), Johannensen (1998), and Zhang (2006).

d. XP

XP1 ConjP

Conj’

and XP2

e. ConjP

Conj’ XP2

XP1 and

The conjunction phrase with left node adjunction, as in Kayne (1994).

Kubo (2007) points out that all such phrasal interpretations share the assumption that a conjunction like “and” is merged in the narrow syntax. But Kubo also observes that not all natural languages use an overt conjunction for syntactical co-ordination. Drawing on Haspelmath (2005), Kubo identifies languages that use conjunctions as having syndetic co-ordination and languages that do not use conjunctions as having asyndetic co-co-ordination. Most European language, such as English, use syndetic co-ordination, while many other natural languages, particularly ones that do not have a long traditional of writing, use asyndetic co-ordination. Such languages rely strongly on intonational pauses to indicate co-ordination at PF. It is interesting to note here that, according to Ross (1967), intonational pauses before the conjunction are an important reason for believing that the conjunction and the second conjunct form a constituent. It seems reasonable to assume that in some languages the conjunction has been deleted after the pause because it seems to be redundant. I shall discuss the possibility of isomorphism between syntax and phonology in some detail in Section 5. In fact, Kubo’s empirical observations about asyndetic co-ordination are crucially important to my thesis. I assume that numerical expressions are co-ordinate structures that can be analyzed as conjunction phrases. English numerical expressions use the conjunction “and,” but Chinese numerical

expressions do not use an equivalent conjunction, usually transcribed as you. I assume, therefore, that the “&” slot in Chinese numerical phrase structure in covert. According to Kubo, the

conjunction phrase analysis cannot account for co-ordination in languages that use only asyndetic co-ordinate structures. In such languages “. . . the whole meaning of co-ordinate

structures cannot be determined by a non-existent co-ordinate conjunction” (p. 8). I will dispute this assertion in Section 5.

4.2 Numerical Expressions as Adjunction

To reiterate Hurford (1975, p. 11), “The value of a number is the sum of the values of its immediate constituents.” This simple but important fact needs to be kept in mind whenever we are considering the syntactical composition of numerical expressions. Essentially, numbers are sums. They express addition much more than multiplication. Recall that multiplication might be seen as a kind of addition. To say “10 times 3” is actually to say “10 plus 10 plus 10.” Sums require at least two components, called summands: one number and another number. Thus, it appears that the syntactical operation of co-ordination should be especially appropriate for the composition of numerical expressions. This in turn suggests that conjunctions such as “and” should be an integral part of numerical expressions. Though desirable, this is not an easy thing to accomplish for those who wish to work within the parameters of X-bar theory.

The problem is illustrated very well by Hurford himself (2003). The phrasal structure in (17) is taken from his argument (p. 42).

(17) NUM

PHR CONJ NUM

NUM M PHR NUM

five hundred and sixty seven

It is clear from this structure that the number 567 represents a sum of its two principal elements, 500 and 57. This diagram also shows the multiplicative process at work in attaining 500, what Hurford calls a Phrase, and the additive process at work in attaining 67, what Hurford calls a Number. The Multiplier 100 is also included in the structure, though the Multiplier 10 involved in calculating 67 is not included. Besides the fact that this structure represents the sum of 500 and 67 it also represents the fact that these two numbers are added. This is done by the inclusion of the conjunction “and.” Here is where the problem occurs for proponents of X-bar theory. In Hurford’s structure, the branch leading to “and” makes the entire structure ternary branching, not binary branching, as X-bar theory requires (Pollard 1984; Kayne, 1984; Kornai and Pullum, 1990). Duarte (1991, p. 33) states this explicitly: “A further requirement on syntactic

configurations assumed in this framework [of X-bar theory] is binary branching: a mother node cannot have more than two daughters.”

The solution I propose is based on Munn’s (1993) argument for a phrasal projection of a conjunction such as “and” through right node adjunction. According to this approach, Hurford’s number example 567 would be configured as in (18).

(18) nNP0 nNP2 &P 500 nN mN 5 100 & nNP1 and 67

The first thing to note is that this structure incorporates a revision of the labeling of constituents from that presented in my thesis. In this new notation “nNP” signifies “numeric Noun Phrase,” “mN” signifies “multiplier Noun,” and “nN” signifies “numeric Noun.” Finally, “&” signifies “and,” and, following Hartmann (2000), “&P” signifies “and Phrase.” From the example above,

based on the generalization given in (5), it can be seen that the category “nN” includes numbers from 0-99. It also should be noted that this system of labeling makes no distinction between simple numeric Nouns (0-9) and complex numeric Nouns (those higher than 10). Nor does this system mark numerals as products or sums, since it is superficially evident which is which. This system does, however, retain my original assumption that all numbers are nouns.

Another important feature of my proposed adjunction analysis is that it combines the three major characteristics of English numerical expressions: the additive function, the

multiplicative function, and the co-ordinate function of “and” – all within the framework of X-bar theory. Thus this phrasal structure not only solves the problem of trinite branching apparent in Hurford, but it also simplifies – and therefore improves – the system of labeling I used in my original revision of Hurford, while at the same time it retains my original improvement on Hurford’s labeling by indicating syntactical categories where he had not done so. Before proceeding to apply this new analysis to numerical expressions in both English and Chinese it is necessary to outline and discuss Munn’s (1993) treatment of co-ordination as adjunction.

4.3 Munn’s (1993) Boolean Phrase (BP) Adjunction Analysis

Munn’s (1993) analysis is based on his belief that co-ordination should be incorporated into X-bar theory. Jackendorf f (1977) presents co-ordination as a flat structure with either multiple heads or no heads, as in (19).

(19) XP1

XP XP and XP

According this analysis “and” is syncategorematically linked to a series of XPs so that all the elements are equal. Munn observes that such a flat structure violates both binary branching (as we have already seen with Hurford) and endocentricity, two of the principal features of X-bar

theory. Nevertheless, the flat structure analysis has had a long history and is still being

advocated at the present time. Its proponents include Chomsky (1965), Dik (1968), Dougherty (1969), Gazdar et al (1985), Goodall (1987), Johnson (2002) and Phillips (2003). In the meantime, Munn’s analysis has independently duplicated by Collins (1988) and subsequently supported by Bošković and Franks (2000) and Alharbi (2002).

At the core of Munn’s analysis is the conviction that the two conjuncts of a co-ordinate phrase are not equal semantically, nor is the conjunction empty of meaning. Following Ross (1967), Munn argues that the conjunction and the second conjunct form a phrasal constituent. Given this interpretation, Munn observes that there are two possibilities for configuration of what he calls the Boolean Phrase (BP). These are illustrated in (20).

(20) a. BP NP B’ B NP Spec/Head BP b. NP NP BP B NP Adjoined BP

The question is, where should the first conjunct be placed? Munn at first decided to place it in the Specifier position, while placing the second constituent in the complement position. This is illustrated in (20a). Munn’s later choice was to adjoin the first conjunct to the constituent formed by the conjunction and the second conjunct. This is illustrated in (20b). Munn believes that adjunction supplies the most accurate interpretation of co-ordination, the principal reason being the asymmetry that exists between the two conjuncts. In Munn’s adjunction analysis the head B and its complement, the second conjunct, form the maximal projection of the BP. This means that B, or “and,” is the head of its own phrase. Moreover, the first conjunct NP1 and the

second conjunct NP2 are of the same category and at the same bar level. The B and the second

conjunct project to an X’’ level, and the Specifier place is left empty as a landing site for the null operator. This is illustrated in (21)

(21) NP

NP1 BP

B’

B NP2

Munn’s argument for favouring the right node adjunction analysis of co-ordinate

structures over the Spec/Head analysis is focused mainly on binding criteria. But first he points out that in co-ordinate structures the second conjunct – that is, the internal conjunct consisting of the co-ordinator and the second conjunct – can be extraposed, while the first, or external