Chapter 4. Numerical Expressions as Conjunction Phrase (&P) Adjuncts
4.4 Alternatives to Munn
4.4.2 Kayne (1994) and Zoerner (1995)
Both Kayne (1994) and Zoerner (1995) base their analysis of co-ordination on left node adjunction for the simple reason that Kayne’s Linear Correspondence Axiom (LCA) bars right node adjunction. The LCA states that asymmetric c-command places liner order on all terminal elements. This means that all phrasal ordering is mapped into precedence relations. This, in turn, means that linear order is not parameterized Like Munn, Kayne combines the conjunction and the second conjunct to form a constituent, but, like Zhang, he places the first conjunct in the specifier position and makes the internal conjunct a simple bar level constituent. Zoerner, like Munn, regards the conjunction as the head of a phrase, which he calls &P.
Thus we see that both Kayne and Zoerner argue a Spec/Head or complementation structure for co-ordination that is similar to Zhang’s interpretation, except that Kayne and Zoerner construct left-branching structures, whereas Zhang constructs (like Munn) a branching structure. (See 4.1 for trees) Interestingly, Zhang provides evidence to validate right-branching structures like Munn’s and her own, while at the same time dismissing left-right-branching structures like Kayne’s and Zoerner’s. Zhang (p. 186) identifies English and Chinese
co-ordinate structures on the one hand and Japanese co-co-ordinate structures on the other hand in (25).
(25) a.
[[X] [&Y]] English and Chinese co-ordination
b.
[[X&] [Y]] Japanese co-ordination
Because both English and Chinese co-ordinate structures are left branching, both Kayne’s and Zoerner’s right branching analyses can be dismissed for the purposes of my argument favouring Munn’s right node adjunction analysis of co-ordination.
CHAPTER 5
MY PROPOSED ANALYSIS
5.1 Of English Numerical Expressions
My original example, given in (17) above, consists of a combination of two phrasal structures joined by Tree Adjunction Grammar Gazdar et al., 1985). The initial structure is illustrated again in (26).
(26) nNP0
nNP1 &P 500
& NP2 and 67
The phrasal structure shows the additive construction of the ultimate NP or nominal compound.
NP1 is pronounced “five hundred.” This is immediately followed by &, pronounced “and,”
which is in turn followed by NP2 , pronounced “sixty-seven.” Put together, this numerical expression is pronounced “five hundred and sixty-seven.” As it stands, this structure represents co-ordination as right adjunction, and it illustrates the fact that complex numerals are
fundamentally sums or nominal compounds.
To account for the fact that most complex numbers are also composed in part by
multiplication requires a second structure. Because of my proposal, stated in generalization (5) above, I consider the numbers 1-99 to behave in numeral expressions as if they were separate lexical entities. This is especially true of numbers following “and.” Thus in (18) and (26) the
number 67 is represented in the structure as a single entity, mainly because it is part of the additive process. The combination of the numbers 1-99 with decimal multipliers is a different matter. Because these numbers usually indicate the overall scope of the numeral, and because they represent the multiplicative process, I believe that they deserve their own structural representation, given in (27).
(27) nNP
500
nN mN
5 100
When this auxiliary structure is combined with the initial structure, the result is the complete phrasal structure for my analysis of numeral expressions, given in (28).
(28) nNP0
nNP1 &P
nN nM
& nNP2
Moreover,as Munn observes, the adjunction structure for conjunction phrases can be iterated as much as desired. This, of course, is essential for large complex numbers. Each new conjunct must be preceded by an &-head that serves as a complement for it. An example of the phrasal structure for such a number is given in (29).
(29) English numeral 313,442
It should be noted that & (“and”) appears twice in this structure, once in string of three digits at the thousands’ level and once in the string of digits at the hundreds’ level. It should also be noted that each occurrence of “and” follows the hundreds’ place. There is a sense that “three hundred and thirteen thousand” means “three hundred thousand and thirteen thousand.” That is, the numeral expression deletes the first “thousand” present at LF. The deleted number is, however, restored in the structure.
Since the tree diagram is drawn based on Munn’s adjunction analysis, the numbers are projected to &P. In English numeral expression, it can be easily seen that there are three multipliers appearing in this number and those are ‘digit’, ‘hundred’ and ‘thousand’. Thus, the number before ‘thousand’ is seen as a modifier for ‘thousand’ and the number before ‘hundred’
is seen as a modifier for ‘hundred’ and so on. Also, English numeral expressions contain both overt and covert conjunction “and.” In the diagram there is an overt “and’ appearing between
‘300’ and ‘13’ in ‘313000’, and there is another overt “and” appearing between 400 and 42, but either or both of these conjunctions could also be covert. The pronunciation of the conjunction is optional in English numerical expressions, but it is usually overt.
Since the &P analysis is headed by &, a difficulty arises if there is no “and” in the numeral expression. An example of such a number is 19, 200, configured in (30).
(30) nNP0
nNP1 &P 19,000
nN nM
19 1000
nNP2 &P
200 nN nM 2 100
& nNP3 ande 0e
In this numeral expression both the place for & and its complement NP are phonetically null for the simple reason that they are not needed semantically, though they are certainly present at LF.
Such a numeral expression represents a small exception to the general pattern of &P adjunction analysis, so I believe it does not invalidate the use of this phrasal structure for English numerical expressions.
5.2 Of Chinese Numerical Expressions
What about Chinese numerical expressions? Since there is no equivalent of English “and” in modern Chinese numerical expressions, it might seem paradoxical to propose that Chinese numerals can be analyzed as & Phrases. Nevertheless, I think this approach can be justified.
The &P analysis appears to work well for English numerical expressions, and Chinese numerical expressions are very similar to their English counterparts. We first need to concentrate on the absence of an equivalent of “and” in Chinese numerical expressions.
How can a numerical expression be represented as an &P if there is no conjunctive
morpheme present in that expression? To answer this we must recall what Hurford has taught us:
Numbers are sums. In other words, numbers consist of at least two smaller numbers being combined through addition. Logically, in terms of syntax, this suggests co-ordination. There is no doubt, then, that numerals are what Zhang (2006) calls “co-ordinate complexes.” I call them nominal compounds. What all this means is that the logic of the syntactical composition of numerical expressions is the logic of co-ordination. This in turn means that we might predict that a conjunction similar to English “and” should appear in Chinese numerical expressions.
Brainerd and Peng (1968) remind us that in Archaic Chinese the morpheme you or yu was used as a conjunction in numerical expressions. Liu and Peyraube (1994) argue that you was originally a verb that grammaticalized, first, to a preposition, then later, to a conjunction. It is possible, therefore to conclude that you is still present at LF in Chinese numerical expressions.
Yang (2005) makes this assumption, and I agree with her. Winter (1995, p. 7) identifies the condition of you in regard to numerals perfectly. “There exist languages with zero conjunction because morphemes like and are not necessary for conveying logical connection.” The fact that you is not present at PF in Chinese numerals does not mean that it was not once present at PF, and that it is not still present at LF. In short, the logic of the composition of numerical
expressions in Chinese demands co-ordination, and co-ordination is normally expressed with conjunctions such as “and” or you. Therefore, I propose that, since phrasal structures are definitively rooted in Deep Structure – that is, language before transformations occur – you, though it is phonetically null and marked youe, may be considered as a legitimate holder of the place & in an &P. This is illustrated in (31).
(31) Chinese 567
It has been argued throughout this thesis that numbers are primarily notations for a system of arithmetical operations. Moreover, the central operation of this system is addition.
Numbers are sums. We have also seen in Section 2.4 that the division of each string of three digits in English into two distinct parts, a hundreds’ place followed by a tens’ and units’ place, mediated by the conjunction “and,” suggests the syntactical binary-branching phrasal structure of X-bar theory. Indeed, my main argument has been that numerical expressions, at least in English, can be adequately accounted for by the requirements and conventions of X-bar theory.
Moreover, because the arithmetical structure of numerical operations is obviously addition, it follows that the syntactical structure of numerical expressions should be co-ordination. As Cormack and Smith (2005) have observed, co-ordination might well be the most primitive of all syntactical operations. If this is true, co-ordination seems to be well suited to accounting for the similarly primitive system of notation to be found in numeral expressions. At the core of this matter is the indisputable fact that both the arithmetical operation of addition and the syntactical operation of co-ordination encode the relation of parts to wholes. Because of the centrality of this relationship to both operations, cumulative conjunctions seem to be indispensible for both addition and co-ordination. Indeed, Hudson (2003) argues that in English “and” does not express dependency but the relationship of parts to wholes in what he calls word strings. All of these
facts suggest that if any X-bar phrasal structure can account for numerical expressions, it must be co-ordination. Moreover, co-ordinate phrasal structures require conjunctions. Therefore, in an English cumulative co-ordinate phrasal structure “and” must appear, either overtly or covertly.
Similarly, in a Chinese cumulative co-ordinate phrasal structure, you, or at least some
conjunction, should appear, either overtly or covertly. Why then is you phonologically null in the adjunctive co-ordinate structure I have proposed for Chinese numerical expressions?
The answer is not likely to be found in standard government and binding rules. The empty category principle, for example, does not apply to e-& in numerical expressions for the simple reason that there is no movement involved in this instance, so there is no trace to be identified. Furthermore, & does not assign case in numerical expressions. In fact, case is not marked on the elements of either English or Chinese numerals. Hurford (2003, p. 65) observes that in some natural languages, such as Finnish, numerals are marked for case agreement, but even in those instances it is not a conjunction that assigns case but the context of the sentence in which the number appears. Kayne (1994) claims that abstract X0 – in effect, e-& – licenses the first conjunct in a co-ordinated phrase, but he makes very little of this in relation to the second conjunct. Alharbi (2002, p. 76) points out that in the phrasal structure of recursive co-ordination e-& occurs as deletion or ellipsis at LF, and it is there, in recursive e-&, that a clue might be found to explain why you is phonologically null in Chinese numerical expressions.
A close examination of the empirical data reveals that & is frequently deleted in recursive co-ordinate structures such as complex numerical expressions. The right node adjunction
analysis I have been using throughout my argument easily accommodates recursivity in various arrangements, as in (32).
(32) a. 3, 567 NP
NP1 &P 3000
NP2 &P 500
& NP3 and 67
b. 3, 567 NP
NP1 &P 3000
NP2 &P 500
& NP3
ande (67)
c. 3, 567
NP
NP1 &P 3000
& &P ande
NP2 &P 500
& NP3
and 67
In (32a) we see the standard structure for the English numeral 3, 567. In this version “and”
occurs in the middle of the final string of three digits, immediately after the hundreds’ place, as is usual in such expressions. In (32b), however, “and” is deleted in this place. Leaving e-& as in Chinese numerical expressions. Dik (1968, p. 272) admits that such an expression as “three thousand, five hundred sixty-seven” is acceptable in English, especially in American English. In fact, this phrase is the English equivalent of the Chinese numerical expression “san qian wu bai liu shi qi.”
We should note here what seems to be a trivial empirical fact, although it is, I think, important to this discussion. In the orthographic or written form of the English numeral in (32b) a comma is used to mark the intonational pause introducing the final string of the digits. In the written form of the English translation of this numeral no comma is used, respecting the fact that Chinese numerals are arranged in strings of four digits – not three, as in English. This suggests that there is no need to mark this Chinese numerical expressions with punctuation because there is no string break in it. I realize, of course, that in Chinese orthography or written form commas are not ever used to mark intonational pauses, but, I submit, such pauses are still present in Chinese at PF. Moreover, if the numeral in (32) is expanded to five digits, then it would be appropriate to write it in an English translation of the Chinese numeral with a comma included, for example: ba wan, san qian wu bai liu shi qi (8, 3567). English punctuation simply supplies a means of identifying such phonological facts in the translation of Chinese numeral expressions.
In (32c) “and” is present as e-& after NP1 (3000). This coincides with the break before the introduction of the final string of three digits. This break is indicated by a comma in both the arithmetical notation and the written form of the numerical expression. The comma also
indicates an intonational pause at this point. All of this suggest that & appears, either overtly or covertly, in co-ordination wherever string intonational pauses are required. In English numerical expressions & appears overtly after the hundreds’ place in each string of three digits, and it also appears covertly between the strings of three digits. In Chinese numerical expressions & only appears covertly – possibly between the strings of four digits, but mainly, I propose, between the hundreds’ place and the tens’ and units’ places in the final string of four digits. If this is true, then Chinese numerical expressions resemble English numerical expressions in that they can both be accounted for by analyzing them as adjoined conjunction phrases (&P).
But why should & appear covertly at this place in the final string of four digits in Chinese
numerical expressions? This claim is not merely an assumption of convenience for my argument.
I believe there is a principled reason for proposing this arrangement. Dik (1968, pp. 41, 58) states that if there is to be one conjunction in a recursive co-ordinate structure, it must come before the last conjunct. As we have already seen, & is deleted between the strings of three digits in English numerical expressions, and & is deleted not only between the strings of four digits in Chinese numerical expressions but also at the end of the numeral before the last conjunct. Dik’s placement rule is more obviously true in non-numerical co-ordinate
constructions. Consider the common English phrase “Tom. Dick, and Harry.” Our knowledge of co-ordination allows us to predict that the meaning of this phrase is “Tom and Dick and Harry.” The important thing to note here is that the commas in the written form of the phrase indicate two things. First, the commas mark intonational pauses at PF, and secondly, the
commas alerts us to the fact that there is an e-& between the first two NPs. Taken together these two facts suggest that in recursive co-ordinate structures – especially in numerical expressions – either commas or intonational pauses, or both, signify e-&.
Are there intonational pauses in Chinese numerical expressions? As we have already seen, such pauses are clearly apparent in English numerical expressions. These pauses are marked by the commas between strings of three digits and by the appearance of “and” after the hundreds’ place in each string. Commas are not used in transcriptions of Chinese numerals.
Nevertheless, although it is not noticeable in everyday speech, in formal spoken Chinese there can be intonational pauses after each decimal multiplier. These pauses might be marked with commas in transcription, and the commas, in turn, might indicate intonational pauses, as in (33).
(33) a. ba wan, san qian, wu bai, liu shi qi
b. ba wan [pause] san qian [pause] wu bai [pause] li shi qi
The pause is longer between strings of four digits, but pauses also can occur, in formal speech, after each multiplier throughout the number, and – I believe – the pause before the tens’ and units’ place in the last string of four digits is usually a little longer than the other pauses in the expression – except, of course, the pauses between strings of four digits. It is important to note here that there is no pause between the tens’ place and the units’ place in the final part of the
string. If my assumption is correct here, the intonational pause at PF in formally spoken Chinese before the final conjunct both mirrors English usage and validates the &P analysis of Chinese numerical expressions.
Hurford (1975, 2003) points out that numerical expressions consist of very rigid word orders. As we have seen throughout this thesis, numerical expressions are also paratactical constructions based on the mutually compatible logical assumptions of addition and co-ordination. For these reasons it is possible to regard a numerical expression as an independent form of discourse, with each successive part of the overall number being an element of the
discourse. Specifically, numerical expressions are concatenations of numbers. As Hurford (1975, p. 30) observes, “The operations of addition, multiplication and exponentiation are all defined in terms of simpler operations, and ultimately all in terms of the basic arithmetical operation, counting or incrementing iteratively by 1.” Moreover, numerical forms of discourse are unique in that they consist totally of nouns and conjunctions, which may be either overt or covert
Tokizaki (2005), a proponent of an hierarchical, binary-branching e-& analysis of paratactic discourses, argues for the existence of a strong isomorphism between phonology and syntax. Earlier studies had already predicted this. In an empirical study Grossjean, Grossjean, &
Lane (1979) discovered that the pauses used by speakers performing sentences were not task specific, but were, in fact, related to the grammar of the sentences. But first Tokizaki analyzes co-ordination between sentences as an asymmetrical binary phrase. Tokozaki’s tree structure is the same as the &P we have seen throughout this thesis, except that it uses the Spec/Head complementation arrangement instead of adjunction. This is illustrated in (34).
(34) Sentences 1 and 2: She gave me the key. I unlocked the door.
&P
S1 &’
She gave me the key
& S2
ande I unlocked the door
It is important to note here that Tokizaki has no difficulty positing an e-& in this binary branching phrasal analysis of sentences or discourses – precisely what I have been arguing
It is important to note here that Tokizaki has no difficulty positing an e-& in this binary branching phrasal analysis of sentences or discourses – precisely what I have been arguing