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.