Chapter 3. Hurford’s Standard Analysis and My First Response
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
Fifteen million four hundred thirty eight thousand three hundred and fifty three
(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 is a plausible revision 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
connected to a constituent formed by the conjunction and YP.
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
The traditional flat structure, as in Jackendorff (1977).
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
The conjunction phrase with right node adjunction, as in Munn (1993).
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
5 100 60 7
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
Munn’s argument for favouring the right node adjunction analysis of co-ordinate