We will review briefly the route we have taken, and then draw out some threads which have run through the book, mainly in order to consider future prospects. We started by identifying all the number values we could find, whichever type of nominal showed them (chapter 2). Then we kept the values still and looked at the different types of nominal involved in the simplest singular–plural systems. We established that their distributions were constrained by the Animacy Hierarchy (chapter 3). Next we put the possible systems of number values together with the hierarchy and found that this typology covered a great deal of the data and the variation, but had to be elaborated to account for phenomena such as conflated number (chapter 4). Then we turned to the means of expression of number, and again found great diversity (chapter 5). The initially daunting difficulties of agreement in number were made manageable, once we drew a clear distinction between controller and target number (chapter 6). In chapter 7 we examined the ‘other’ uses of number, which are many and varied, and found that they too begin to fit into a typology. And then in chapter 8 we turned to verbal number, showing how different it is from nominal number and examining why.

While we have been able to make considerable progress, it is clear that there are many aspects still to be better understood.

Number is the most underestimated of the grammatical categories. It is deceptively simple, and is much more interesting and varied than most linguists realize. This was recognized by Jespersen: ‘Number might appear to be one of the simplest natural categories, as simple as “two and two are four.” Yet on closer inspection it presents a great many difficulties, both logical and linguistic’ (Jespersen 1924: 188). Lyons too pointed out its interest: ‘The analysis of the category of number in particular languages may be a very complex matter’ (Lyons 1968: 283). This book will illustrate the interest of number, and some first pointers are given in §1.1.We shall also see the challenges which Jespersen and Lyons allude to, one of the trickiest being the need to ensure that as we compare across languages we are really comparing like with like (§1.2). Hence the book is structured so as to work upwards from properties that are safe building blocks for comparison (§1.3). Finally in this introduction a few notes on presentation are needed (§1.4).

The special interest of number

Despite the significance of number, there are still surveys of linguistics where it receives a footnote's worth of attention. This is largely because there are some reasonable but incorrect assumptions about number, which are generally based on the consideration of a rather limited range of languages.

We saw in the last chapter that agreement is one of the ways of expressing number and this will be our main topic here. We first consider agreement and the types of mismatch which occur between the controlling noun phrase and the agreement target. Then we undertake a set of case studies leading to a typology of agreement options in number. There are three typological themes: once again we see the importance of being clear about terms, as we analyse systems where the number values of controller and target differ; we see the importance of hierarchies, this time in syntax; and there is a graphic illustration of how factors which can be identified as being at work in various languages interact in different ways to give very different results.

Controller versus target number

The first notion that we need is ‘agreement’, which is the covariance or matching of feature specifications between two separate elements, such as subject noun phrase and verb. We shall call the element which determines the agreement (say the subject noun phrase) the controller. The element whose form is determined by agreement is the target. The syntactic environment in which agreement occurs is the domain of agreement. And when we indicate in what respect there is agreement, we are referring to agreement categories or agreement features, as illustrated in figure 6.1. Of course, we are primarily interested in agreement in number. The controller of agreement is a noun phrase. Cross-linguistically, the possible targets are more varied than many believe.

We have considered the meanings regularly associated with the different values (plural, dual, paucal and so on). We now come to other uses of number, that is, instances where the regular expression of number is taken over for purposes other than its normal meaning. For instance, in honorific usage, plural forms are often used of a single addressee to indicate respect. The semantic and pragmatic effects of number in such uses cannot be derived in the normal way from the usual meanings of the number values. Given that number is often cited as a straightforward grammatical category, apparently reflecting semantics in a regular way, these other uses are found surprisingly frequently. They occur even in familiar languages: we shall see cases where a particular use identified in some distant language turns out to be rather frequent closer to home.

There are three broad groups of these other uses: first there are honorific uses (§7.1), as just mentioned; second there are unexpected uses in the general area of conjoining (§7.2); and finally there are various special uses, affective ones in the main (§7.3). In analysing these uses, there are three questions which will recur. The first is whether all number values are available for the particular use; often there are restrictions, and for affective use it is never the case that all values are available. The second is why these uses can be available, particularly since number frequently is a relatively clear reflection of semantics.

In this chapter we concentrate on the possible meaning distinctions in number systems. Often the situation in languages like English is taken as normal, whereas it represents only one of the possibilities. We will first consider whether number needs to be expressed; we shall see that for some languages the expression of number is in a sense optional, while in others it is a category which speakers cannot avoid. To investigate these systems we shall first consider the notion of ‘general’ number as a meaning distinction and base a partial typology upon it (§2.1). We then narrow our attention to the cases where number is expressed, and establish the main types of distinction within the category (§2.2). Thus §2.1 is devoted to the opposition of number and ‘non-number’, while §2.2 examines the possibilities within the number domain. In §2.3 we propose a typology, systematizing the material examined so far, and we go on to show that languages may simply not have a number system (§2.4); then we consider approaches to number within formal semantics (§2.5).

Our aim in this chapter is to find all the possible distinctions. At this stage we shall not be concerned about the type of nominal we look at, so long as we find those which show the greatest differentiation. Keeping any particular nominal ‘still’ as it were, we shall see how many different numbers it may have available, in the most favourable contexts.

The place of the lexicon in relation to other components of a complete morphological description is implicit in much of what has already been said above. In particular, from the discussion of the word- (or stem-) based nature of morphology, and of the interaction of morphology with the syntax, the broad outlines of a possible internal organization for the lexicon are fairly clear. However, it is first necessary to say a few words about the notion of ‘lexicon’ itself. We suggest that this is properly construed as a component of linguistic knowledge (parallel in this respect to syntax and phonology), rather than merely as a list of arbitrary items. We then proceed to consider an important class of rules that characterize much of a speaker's lexical knowledge: the traditional domain of derivational processes. Finally, we discuss the issue of productivity, which bears in important ways on the status of particular lexical rules within the grammars of individual languages.

The lexicon

As Aronoff (1988) points out, there are a number of distinct senses that can be (and have been) assigned to the notions ‘lexicon’ and ‘lexical.’ Two of these are the principal concerns of Aronoff's discussion: the notions of the lexicon on the one hand as the locus of idiosyncrasy in language, and on the other as a collection of all of the items that belong to ‘open’ or ‘major’ word classes (typically Nouns, Verbs, and Adjectives).

In chapter 4 we discussed some reasons to believe that ‘inflection’ is a domain of grammar in which morphological and syntactic considerations overlap to a significant extent. In section 4.2 of that chapter, we dealt with one central aspect of a theory of that domain: the content and nature of Morphosyntactic Representations. The point of that exercise was not simply to develop a (possibly obscure) formalism, but rather to explore just exactly what information exists in the interface between syntax and word structure. We saw that this can be reduced to an unordered list of inflectional properties (or ‘morphosyntactic features’), with a minimum of internal structure. A limited internal organization of this information, beyond that of an unordered inventory of properties, is necessary to deal with cases where a single word bears more than one specification for the same dimension. To accommodate these, we proposed the device of ‘layered’ representations (essentially, the hierarchical subordination of some unordered feature sets to others), together with a general convention on how these are created and a restricted set of ways in which their content can be referred to in specific rules.

Recall that in chapter 4 we found a number of substantive areas where morphological properties of words appear to be determined by an interaction with the syntactic environments in which they appear; or of properties that must be visible to syntactic principles for these to perform their intended function.

Up to this point, our attention has focused primarily on the principles by which morphological material is introduced into words (i.e., the operation of Word Formation Rules) and on the interaction of those principles with the regularities of syntactic structure. We have as yet said little about the rules that directly govern regularities of sound structure or phonology. In this chapter, we discuss the interaction of word structure with phonology.

In the general domain of rules determining the phonetic forms of words, we can distinguish two broad classes: Morphological rules (i.e. Word Formation Rules, both inflectional and derivational); and Phonological rules. Morphological rules have a Structural Description referring to morphological material (either a Morphosyntactic Representation or an input lexical item), while phonological rules look exclusively at the phonological composition of a form. We have already seen (in chapter 2) that purely phonological rules have properties that are distinguishable from those sensitive to morphological categories – a conclusion that is probably uncontroversial for the set of clear Word Formation Rules that actually create the markings for such categories. We will suggest below the two sorts of rule may also have very significant similarities with respect to their Structural Changes, though that alone is no reason to doubt that the distinction is still worth making.

Only a few years ago, Lightfoot (1979) could correctly note that most of what passes for the study of syntactic change in the literature of linguistics is really concerned with change in morphological rather than syntactic properties. As the opposite side of the same coin, much of the literature on phonological change is similarly devoted to essentially morphological problems. This state of affairs doubtless derives today from the early generative program of reducing word structure either to syntax or to phonology, but in any case, the revival of synchronic morphology as a viable object of enquiry calls for corresponding study of the nature of change in morphological systems.

The present chapter discusses some basic issues of change in morphological systems, in the context of the theory developed in this book. We begin with a short excursus on the role of the study of change in the development of a synchronic theory of word structure, arguing that an adequate theory of what structures are possible in natural languages probably cannot be provided on a purely synchronic basis. Rather, we must view “what there is” as the product of “what is possible” with the range of possible diachronic developments. Linguistic structures do not simply spring into existence ex nihilo: most linguistic forms and regularities are inherited either directly or through the lens of linguistic change from previous states of the language; or else borrowed from the systems of other languages.

We saw in the preceding chapters that it is at least worth investigating a theory of word structure based not on the classical notion of the morpheme, but rather on the premise that words are related to one another through the operation of processes called Word Formation Rules. It seems clear that the intuition of relatedness among words, captured on the traditional view by saying that they share a morpheme, can be reconstructed satisfactorily within this alternative approach by saying either that they share a base, that they share a morphologically relevant property such as [+ Plural], or that their derivations involve the same rule. Indeed, in separating these subtypes of ‘relatedness’ we arrive at a more nuanced view of the matter than one on which words simply do or do not share one or more entire morphemes. The question of how to reconstruct the internal relations of scope among the parts of a word, represented traditionally by an organization of its component morphemes into a constituent-structure tree, will be postponed until chapter 10, when more of the substance of a rule-based view has been developed. As pointed out at the end of chapter 3, there are a number of aspects of such a theory that need to be fleshed out.

In this final chapter, we turn to a different area in which the choice of an appropriate theory of word structure is important. This is the problem of how a computational system might be designed to ‘parse’ individual words in a natural language. The notion of computational parsing is most familiar in the syntactic domain, of course, where it refers to the process of recovering structural descriptions for natural-language sentences from a string of words in light of the system's representation of the syntax and lexicon of the language in question. Analogously, ‘parsing’ in morphology is the process of retrieving the information carried by particular words, as they contribute to the meaning and the structure of larger linguistic constructions within which they appear.

Reasons to study morphology as parsing

When we ask in a computational system for an account of the information carried by individual word forms, there are two rather different sorts of motivation we might have, and the extent to which we want to pursue a linguistically well-motivated analysis will depend on the goals of the analyst. An understanding of this difference, in turn, is important in determining the sorts of criticism of a given system that might be appropriate. The first set of motivations can be identified (somewhat pejoratively, perhaps, in a work devoted to questions of general linguistic theory) as ‘technological’ reasons. In these cases, the question of what information a word form carries is posed because we want the answer.

This chapter is devoted to the question raised above of whether it makes theoretical sense to distinguish principles of morphology from those of other parts of a grammar. In section 2.1 we will look more closely at the system of a single language, Kwakw'ala, in which the grammar of words is particularly well developed. Among its many interesting features, Kwakw'ala allows us to examine the relation between morphology and syntax in some detail, because the language displays at the same time a rich and highly structured syntax, and an equally developed and highly structured system of word formation. When we look closely at the facts in these two domains, we will see that they are governed by rather different principles. The point of such a demonstration in the present context is to show that two quite separate rule systems govern Kwakw'ala ‘grammar’ (in the generalized sense of ‘morphosyntax’), and that the line between them corresponds to the difference between principles operating within a word and those organizing words into higher-level units.

Following this demonstration that an individual language may distinguish the grammar of words from the syntax of phrases, we consider the issue in more general terms. If we take seriously the suggestion that a system of principles governs the construction of words and their relations within a lexicon, and a different system governs the syntactic structure of phrases, clauses, etc., we would expect some systematic differences to obtain between the two systems.