Chapter 6. Concluding Remarks
6.1 Summing Up
This thesis is based on the assumption, derived from Hurford, (1975, 1987, 2003), that numbers are sums. This means that numbers are constructed by the operation of addition. Often it is said that numbers are constructed by a combination of addition and multiplication. In fact, Hurford establishes his entire structure for numerical expressions on distinguishing between three arithmetical categories: Numbers (simple digits from 0 to 9), base Multipliers (multiples of 10), and Phrases (sums or combinations of sums). On closer examination, though, it is revealed that all numbers larger than 10 are sums, because even multiplication is a kind of iterated addition.
Moreover, it is immediately apparent that this system is mostly – if not entirely – concerned with arithmetical operations. In other words, numerals embody a system that exists beyond the system of language. Thus, the creation of numerical expressions is an attempt to combine
arithmetical operations with syntactical, semantic, and phonological operations. This is precisely what Hurford, who is the acknowledged expert on the language of numbers, has done.
Nevertheless, I began this thesis with an ambition to improve on Hurford’s analysis of numerical expressions. I intended to do this by identifying the syntactical categories of numbers as abstract nouns. Most authors, Hurford included, have assumed that small lexical numbers behave like adjectives, while decimal multipliers and larger complex numbers behave like nouns.
I think, however, that all numbers – as numbers – are nouns. I have held this view from the beginning, and I still hold it. Secondly, in my attempt to integrate arithmetical operations with syntactical operations, I have argued, again from the beginning, that numerals are nominal compounds. Finally, in recognition of the arithmetical origin of numerical expressions, I have argued that numerals are a unique form of discourse: paratactic word strings that consist entirely of nouns, with the exception of the cumulative conjunction & (“and” in English, you in Chinese).
Numerical word strings are concatenations that exhibit rigid word order.
In my original attempt to expand and revise Hurford’s analysis of numerical expressions I relied too heavily on Hurford’s structural analysis, although I did improve on the terminology that should be used in phrasal analysis. I did this by indicating that all numbers are nouns and then identifying numbers according to their arithmetical functions in the composition of
numerals. But even after I had done this, two serious problems remained. The principal problem associated with Hurford’s phrasal structure is that it has to become trenary to accommodate the
“and” of English numerical expressions, thus violating the binary branching principle, one of the most important rules of X-bar theory. A second problem is that when Hurford’s structure is applied to Chinese numeral expressions, the morpheme ling, or “zero,” is forced to project as what Hurford calls a Phrase, when logically it should project as what he calls a Number. These issues were not resolved satisfactorily in the first draft of my thesis.
The current version of this thesis does, I believe, solve these problems more convincingly.
The reason for the improvement is that, while maintaining my original refinements of Hurford’s terminology for syntactical categories, I have adopted Munn’s (1993) adjunction analysis of the Conjunction Phrase (&P), what he calls a Boolean Phrase. I was led to this analysis by
discovering, through close examination, that the internal composition of English numerical expressions exhibits what might easily be regarded as binary structure. Within each string of three digits in English numerals there is a hundreds’ place, followed by the conjunction “and,”
followed by a combination of the tens’ and the units place. Such an arrangement led me to believe that the most appropriate syntactical categorization for numerical expressions is co-ordination.
In this new analysis, achieved within the framework of X-bar theory, and following Munn’s argument for co-ordinate adjunction, the conjunction “and” conjoins with its
complement, the second conjunct, to form the maximal projection of the &P at the X’’ level.
This phrase is then Chomsky-adjoined to the first conjunct, leaving the Specifier position empty.
The ultimate result is NP0 containing the entire structure. Applied to numerical expressions, this adjunctive &P analysis goes a long way to solving all the problems associated with Hurford’s analysis. There is no more need for trenary branching for the conjunction, since the structure, according to X-bar theory requirements, is hierarchical, not flat. Similarly, ling is easily accommodated within this structure when it is applied to Chinese numerical expressions. In short, the &P analysis offers an especially convincing account of English numerical expressions.
The only remaining problem is the hard fact that there is no longer a conjunction equivalent to “and” at PF in Chinese numerical expressions. There is evidence that in the past the morpheme you was used as a conjunctions in Chinese numerals, but that is no longer the case.
How can Chinese numeral expressions be analyzed as &P if they do not contain the category &?
My answer is that the conjunction you is still present at LF. Moreover, the internal logic of the composition of numerals in all languages is essentially arithmetical addition, which in turn suggests syntactical co-ordination. If this is true, you can be used as a conjunction in Chinese numerical expressions as long as it is marked as phonetically null. If this provision can be accepted, the &P analysis as a whole, based on Munn’s application of right adjunction, provides a satisfactory account of both English and Chinese numerical expressions.
Positing a phonetically null conjunction to head a phrase is not entirely radical. Kayne (1994), for instance, does this to license the first conjunct in his co-ordinate structure, but I am trying to justify the merging of e-& with the second conjunct. Most authors would probably question this possibility. In order to prove that Chinese numerical expressions are headed by a covert conjunction, or e-&, I have relied on two related arguments. The first is related to the concept of isomorphism between syntactical and phonetic forms. There is, no doubt, a possible interface there, and I have argued that intonational pauses between segments of numerical expressions in Chinese allow us to identify or recover the deleted conjunction you. I have also argued, following Tokizaki (2005), that covert conjunction can be used to integrate the various parts of a discourse, even entire sentences, according to the asymmetrical properties of phrasal co-ordination under standard X-bar theory. Since I also argue that numerical expressions are a special kind of paratactic and concatenated form of discourse, I believe that I am justified in concluding that you is covertly present in the & slot of &P in Chinese numerical expressions.
We probably should remember here that, as Haegman (1994, pp. 7-8) observes, what is acceptable in language is not necessarily what is grammatical – and vice versa. An overt &
might not be acceptable in Chinese speech, but it still might be grammatical.
6.2 Postscript: Hurford Revisited
As I have just demonstrated, this thesis is an attempt to come to terms with Hurford’s (1975, 1987, 2003) analysis of numerical expressions. It first seemed to me that his structural interpretation of numerals was syntactically vague and incomplete. And so it is. I have improved it by identifying all the elements as nouns and by combining arithmetical and syntactical operations in my analysis. I have also managed to present what I think is a solid – and at the same time original – argument for analyzing numerical expressions as asymmetrical co-ordinate phrasal structures. Moreover, I have demonstrated that this analysis works for both English and Chinese numerical expressions. Nevertheless, I am left with a profound suspicion that perhaps Hurford really has said all there is to say about numerical expressions, and that he was wise to keep the grammar of numerals separate from the general grammar. One thing is certain: numerals are special words.
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