issues in linearization: prolegomena for a general theory of communication

Language & Co~~~nica~ion, Vol. 6, No. 4, pp 225-266, 1986. Printed in Great Britain.

0271-5309/86 $3.00 + 00 Pergamon Journals Ltd.

ISSUES IN LINEARIZATION: PROLEGO~NA FOR A GENERAL THEORY OF COMMUNICATION

WILLIAM H. EDMONDSON

This paper presents a review and analysis of the significance of the temporal domain in human communication. Linearization is the term commonly used for the process of placing conceptual or linguistic entities in temporal order, and it is this process which underlies the significance of the temporal domain in communication activity. Our review will necessarily cover a range of topics-semiotic principles, the temporal organization of signed languages, non-linear phonology-and we will analyse in some detail the ways in which various theories of grammar deal with the process of linearization. The conclusions reached will also be a mixture of the general-linearization reveals the underlying similarity between linguistic activity and all other activity-and the p~ticular-the notational insights of non- linear phonology (or autosegmental phonology) generalize to offer a promising account of linearization on the basis of what we can call non-concatenative grammar.’

0.1. In section 1 the concept of linearization is explored from a theoretical perspective. This provides necessary background for section 2 which presents an account of the structure of a signed language such as British Sign Language, and section 3 which presents an account of a generalized form of the notational device of non-linear phonology. Section 4 concludes the review portion of the study which is, in effect, the context for subsequent more detailed discussions. In section 5 we compare various theories of grammar and examine the significance of the projection principle. Section 6 presents some conclusions and pointers for further work.

1 In this section we look at the concept of linearization from a theoretical perspective. The discussion is mostly restricted to spoken language communication-whenever detail seems warranted-but we shall not shy from covering other aspects of communication and semiotic activity in general.

1 .l. Linearization was earlier defined as the term used for the process of placing conceptual or ling~stic entities in temporal order. This usage is umemarkable but ultimately unsatisfactory. Whilst the term linearization succeeds in reflecting the idea of speech as a linear succession of sounds, like beads on a string, it suffers from two drawbacks, In order to form the clearest possible image of the role ‘of the temporal domain in communication we need a couple of new terms, devoid of. inappropriate connotations. Linearization is inadequate as a term because (a) it emphasizes the uni-dimensional (beads on a string) conception of speech, and hence commonly of language; and (b) it only refers to the production of speech, and hence it reinforces the rather lopsided current view of linguistic theorizing as essentially concerned to account for production of linguistic output.

Correspondence relating to this paper should be addressed to Dr. W. H. Edmondson, Centre for Computing and Computer Science, Birmingham University, P.O. Box 363, Birmingham B15 2TT, U.K.

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226 WILLIAM H. EDMONDSON

I propose that instead we use a couple of neologisms which capture the essential characteristics of the role played by temporal order in communication. We need two verbs and henceforth we will use ‘(to) sequence’ and ‘(to) de-sequence’ as terms for the ‘productive’ exploitation of time and the ‘receptive’ exploitation of time. These terms are appropriate because (a) they reflect the notion of temporal order without any implications of uni-dimensionality; (b) they cover output and input; and (c) they convey a sense of symmetry or complementarity-to de-sequence is to undo a sequence and the two processes are thereby intentionally linked through the notion of reversal.

1.2. The significance of the temporal domain, I claim, is not just that languages exploit the processes of sequencing and de-sequencing, but rather that they must exploit these processes-there is no other basis on which to build communication. The study of human communication should, in principle, be concerned with the ‘how’ of this exploitation. Linguistic theorizing is about the ways in which grammatical structures fit into the exploitative activity (this will become clear). Nonetheless it is necessary to have a clear view of the ‘why’ of sequencing and de-sequencing because (a) the question and its answer form an essential part of any complete model of communication; and (b) current models in theoretical linguistics tend to have implicit views of both the ‘why’ and the ‘how’ of temporal organization, views the inadequacy of which can only be appreciated in the light of explicit discussion of the topic.

1.2.1. It is odd that a self-evident characteristic of human activity should be so generally ignored, but in my view that is indeed the situation, so far as the process of sequencing is concerned. One half of the problem facing the human who would do something is as follows: any activity capable of producing observable effects in one’s environment necessarily involves sequences of muscle tensions (i.e. movements). This is a fact, a physiological fact, a reflection of the physical constraints of the musculo-skeletal system. The other half of the problem is that one’s plans of actions, as much as one’s thoughts, indeed all of one’s cognitive entities, are not sequences of muscle tensions. In fact, they are not necessarily sequences of anything at all. A belief in God, awareness of the blueness of a sky, an intention to make a cup of tea, feelings of love for another person, knowledge of a cricket score, a plan to visit a relative-all these (and anything else too) are not inherently sequenced, although they may sometimes be about a sequence. Cognitive entities are essentially atemporal. In the limit this must be universally true, with memories, subdoxastic knowledge, even physiological response patterns all represented in a static and enduring manner; although they may represent sequences they are not sequential in form.2 We will take this as fact also.

The problem we all face, then, is that we must give sequential form to something atemporal; we must produce necessarily sequential muscle actions in response to a cognitive entity which is enduring but inherently atemporal. It is fortunate that our form in space- time is so organized that we can accomplish this with little difficulty if we first transform

the atemporal cognitive entitites into sequences of cognitive entities, because-and this is crucial-we can only ever guarantee a perfect match between an internal/cognitive sequence and an external/physical sequence. The time dimension penetrates the corporeal boundary; or, to slice it differently, the boundary between the external and internal ‘worlds’ does not exist in the temporal domaim or, yet again, a sequence within is that same sequence without.

1.2.2. When we wish to communicate (in the productive sense remember, we have yet

ISSUES IN LINEARIZATION 221

to deal with de-sequencing) we can only succeed insofar as we can transform an atemporal cognitive entity into a temporally structured entity (or succession of entities). It would seem that in the case of linguistic activity this cognitive phase of the process of sequencing is the domain of theoretical linguistics, especially syntax. However, as we shall see in section 5, the situation is more complex because we need to separate the activity of producing sequencible entities from the production of a sequence, something which is not necessarily linguistic. It is important to remember that only when we understand why we must sequence at all can we properly specify the domains of enquiry when we consider how we might do it. The claim that linguistics is a part of psychology (see e.g. Chomsky, 1980) becomes much more obviously good sense when these questions are addressed from the general semiotic perspective. As an example we might note that any theory of syntax which presumes a temporally structured, or ordered, input to the transformational procedures required to produce the sequenced form of a linguistic output must necessarily be incomplete because it does not cover the whole of the cognitive phase of the process of sequencing. It is a matter of definition whether such a theory is complete in linguistic terms, but in cognitive terms it is incomplete.

1.2.3. There is one aspect to the above discussion which we must take explicit note of because it is built into so many theories of grammar without enough care. It was noted above that sequencing involves a cognitive transformation (from atemporal entity to temporally structured entity) as a precursor to muscular output. The question arises as to whether the arrangement of these phases is itself sequential. This is a non-trivial issue, as we shall see later, so it is necessary to have a clear conception of the point being made.

There are two possibilities which need to be considered. The first is that the cognitive transformation involved might not be sequential, although it might be conveniently conceptualized as such. In this case the transformation would be an ‘equivalence’ of some sort. A suitable example is the process of long division. This is conveniently conceptualized as a sequential procedure, an algorithm comprising an ordered set of rules with a defined end state. The reader is invited to tackle an example (176.47/7) as a reminder of what is involved. We must note, however, that the ‘answer’ is a statement of equivalence-enduring and atemporal-despite the fact that we can derive this equivalence via some sequential procedure. It is possible, therefore, to consider that when we sequence a cognitive entity for output as muscular activity there is an equivalence-enduring and atemporal-between the atemporal cognitive entity and the pattern of nerve impulses which produces the sequential muscular activity. This can be true even if our characterization of this equivalence is in terms of some derivational procedure.

The second possibility is that in fact the sequence is derived and the transformation is not a reflection of the contents of an equivalence table but is, rather, the end product of a procedure which is inherently ordered in time. Whilst it is, of course, possible to envisage a mixed system, the extent to which the transformation from atemporal cognitive entity to a sequence of cognitive entities is itself a sequential affair is of considerable theoretical interest. This issue is explicitly addressed in linguistic theories which call upon ordered sets of rules (for example) but is not perhaps discussed in sufficient depth on other occasions (see section 5.2.7).

1.2.4. The epistemological question which arises-how do we recognize which possibility is to be taken seriously? (or, perhaps more realistically, how do we characterize the mixed system?)-reduces in the case of linguistic theorizing to the debate between behaviourists and generativists, and so we may readily accept that the transformational processes employed


linguistically are indeed temporally structured. This does, however, have implications open to empirical investigation (see section 5.2.7). We might also note that although a rule-based linguistic formalism can capture this temporal structure of the transformational procedure itself it is not the only formalism capable of so doing. Interactive activation networks and probabilistic formulations can also yield temporally structured transformations. There is, therefore, no reason to suppose that temporally structured transformations (e.g. derivations) require a particular generative approach (e.g. rule-based formalisms).4

1.2.5. Thus far we have limited our discussion to the production of muscular activity in general and to linguistic output in particular. In this sense ‘sequencing’ and ‘linearization’ seem to be synonyms. That they are not becomes clear when we consider that linearization carries with it the notion of a single stream-the ‘beads on a string’ metaphor is useful here. In principle there is nothing in our discussion so far which suggests that sequencing involves stringing beads on just a single string. Muscular activity obviously involves a great deal of simultaneous activity, despite being inherently sequenced; it is usually possible to walk and chew gum at the same time, and indeed each of these activities involves some simultaneity in muscle coordination.

It is true that speech is characterizable in uni-dimensional terms (the variations in sound pressure at the eardrums, for example) but we should not be seduced thereby into believing that the linguistically motivated patterning of muscular activity does not involve a fair degree of simultaneity. In this sense, then, the process is more aptly called sequencing because this term is neutral as regards the number of strings of beads being produced.

1.2.6. The semiotic implications of the concept of sequencing outlined above are important. The need for sequencing reflects an unavoidable psychophysical constraint; sequencing is independently motivated. This means that sequencing is arbitrarily available for semiotic purposes. Whilst this seems clear as far as the ‘output’ sequence is concerned, where the product of sequencing has no inherent meaning, we should perhaps reserve judgement on the process of sequencing itself, where the sequential derivation may not be free in a semiotic sense (this is taken up later, in section 5.2.7).

The output sequence is actually a complex sequential patterning of simultaneously organized muscular activity, and just as it is possible to walk and chew gum at the same time so is it possible to gesture and speak simultaneously, or to control one’s intonation independently of, but along with, the utterance of words. 5 The semiotics of a linguistic output sequence are correspondingly complex, as we shall see in sections 2 and 3, and it should be evident that the uni-dimensional connotation of the term ‘linearization’ is

misleading.

1.2.7. We have almost completed our general discussion of sequencing; one point remains. I have so far carefully avoided too much specific reference to the sort of cognitive entities I have in mind as being sequenced. Mentioned so far have been specific things like patterns of muscle movements as sequenced in the ‘output’, atemporal thoughts and other cognitive entities, and sequenced cognitive entities as some sort of intermediate form (see 1.2. l-l .2.4). I have also noted that the process of sequencing itself can be sequentially organized.

The model being considered here is that of a sequence of transformations which takes as ‘input’ the ‘to be externalized’ cognitive entity, and yields as output the sequenced pattern of muscle control signals. Within the model the individual transformations may, or may not, take in single entities and put out sequenced (sub-)entities. Consider the discussion of linearization by Levelt (1981) or more generally Brown and Yule (1983). Their use of


the term linearization applies to the activity we might recognize as being near the beginning of the sequence of transformations. If one wishes to describe the interior of one’s house, say, one must begin somewhere; the description starts at a specific location. The describer has to arrange the conceptual structure in a sequence, or, in other words, the cognitive entity [interior of home] has to be broken down into a sequence of sub-entities, say [[hallway] [front room] [hallway] [back room] [hallway] [kitchen] [hallway] [stairs] [landing] [front bedroom] [landing] [back bedroom] [landing] [bathroom]]; and so forth.

The sequence of transformations within the model yields ever more finely structured strings of entities, until one can go no further, and muscular activity is executed. The point, therefore, is that the sequencing applies at all ‘levels’. It is my clear intention that the reader should form as a basic model a recursive notion of transformation which takes single entities and yields ordered strings of (sub-)entities. We will eventually reject this model as too restrictive, but its obviousness is useful for a while, so we will stick with it. In the sense just given, therefore, a transformation is a function from an entity to an ordered string of entities.6 This notion applies at the ‘top’, where we sequence thoughts for output, through to the ‘bottom’ where we sequence phonemes for output.

The model, as just characterized, is conservative in the sense that each transformation yields both a ‘one to many’ structural change and a sequence for the ‘many’. Formally speaking this is not necessary and we must keep in mind the potential for separate specification of both structure and sequence. Note, however, that should we elect to specify structure and sequence separately we may still find that for every structural transformation there is a separate sequencing specification and the two steps yield, as output, the sort of thing we might recognize as the output of a single step in the conservative model. We could call this a pseudo-conservative model. A further option is the independent model, where we find complete independence between structural transformations and sequencing operations. And the last possibility is that we should find a mixture of conservatism and independence. It remains the case, however, that whatever model, or mixture of models, is envisaged as achieving the overall transformation of single entity to a sequence of muscle movements, the essential achievement is that of producing a sequence. It is also necessary, of course, that the sequence should be capable of being de-sequenced. This does not mean that each and every sequencing transformation can be ‘run backwards’ (and in a reverse sequence of transformations) merely that it should be possible to take a sequenced output and derive from it an appropriate de-sequenced cognitive entity.’ These issues are not simple. The difficulty of envisaging the two processes as closely linked will be illustrated in section 2, but first we must address the topic of de-sequencing in general terms.

1.3. When we sequence an entity for output the final step in the process is that of patterning muscle activity. Now that we are concerned with de-sequencing we must consider the ‘first step’, and in particular its difference from muscle control. The first step, obviously enough, is perception and for the purposes of our discussion it is helpful to separate auditory and visual perception.

1.3.1. The auditory perceptual mechanism is ‘designed’ specifically to deal with rapidly varying fluctuations in air pressure at the ear drum. It is pre-eminently a mechanism for ‘de-linearizing’ a genuinely uni-dimensional function of time. If the acoustic waveform represents (results from) the superposition of several different frequencies of sound we can hear these different sounds when we hear the single acoustic stimulus. This is a clear illustration of de-sequencing. As regards speech the de-sequencing is not of the sequence


of muscle movements directly but is, rather, of the evidence of the muscle movements-of the semiotic tokens available as external evidence of the final product of the sequencing process.

The human auditory mechanism is so constructed that the range of acoustic fluctuations which are de-sequencible is wider than the range of vocal sounds a human can produce. The evidence is uncontroversial. There exist on the market devices which can ‘speed-up’ speech (this is not merely the fast replay of speech recorded more slowly). Although one could not speak at such rates one can indeed comprehend. Likewise, an orchestra can produce a range of simultaneously present frequencies which can be de-sequenced satisfactorily although no human could produce it vocally. My simple claim here is that when we consider the channel comprising vocal output and auditory input we should recognize the output link as the limiting factor. (One implication of this is that we can understand why the production of speech is so single-mindedly the focus of linguistic attention.) The speech modality, or channel, is in an important sense defined by the properties of the physical output mechanisms and therefore these can be seen as major constraints on the sequencing process. Of course the perceptual mechanisms provide some constraints also, for example one’s speech must be audible, but these are, in the main, unimportant for our enquiry into the de-sequencing of speech.

1.3.3. One other perceptual system is used widely in human communication-vision.* Here too there are some general constraints concerning light levels and such like. However, unlike auditory perception vision involves necessarily mobile sensory apparatus. We can choose not to turn our head for sound location, but we cannot choose a mode of visual perception in which we do not move our eyes (whilst continuing to see, that is) beczuse retinal adaptation sets in and we cease to see anything. The net effect of the necessary mobility is to ensure constantly fluctuating light levels on the retinal receptors. This can be achieved by moving the eyeballs, by moving the scenery, or both, but in practice the eyeballs are constantly on the move.9

The important difference between vision and audition, therefore, is that in vision the sequential nature of the sensory stimulation is largely ‘home-made’, so the processes of de-sequencing have internally available information (about the sequence) with which to

work.

1.3.4. The fact the visual de-sequencing is, in a sense, forced by the sequence of eye movements has three implications for our enquiry. The first is simply that the self-generated exploitation of sequencing and de-sequencing would seem to reinforce the point made earlier (1.2) about the general significance of linearization. The second is that the system is ‘designed’ to cope with atemporal material (the scenery does not have to move to be seen), and even where the visual world contains moving things these are seen as moving things, not sequential things.lO The third point is that the self-generated sequencing imposes a limit on the amount or rate of movement which can be tolerated in the secenery.” We will

see later that the limiting factor in visual communication appears to be the rate at which the visual system can cope with changing stimuli. Thus we can characterize spoken communication as production constrained, and visual communication as perception constrained. However, we will also see that the perceptual system allows visual communication certain freedoms which, although initially surprising, are entirely in accord with the general semiotic principle being invoked.

1.4. We are now in a position to summarize our semiotic viewpoint. All human activity,


without exception, exploits the basic psychophysical constraint that sequence is the only reliably externalizable (or internalizable) property of one’s internal (or external) world. Any activity, communication not excepted, exploits sequencing in order to externalize cognitive entities, and perception necessarily involves de-sequencing. In linguistic communication the processes of sequencing and de-sequencing are more or less related (depending on the modality), but both are always essential. The process of sequencing is sequentially organized in all cases where generativity (of whatever sort) and derivation are reasonably supposed to be operative in the transformation from internal to external form. The sequential organization of de-sequencing of speech cannot be presumed to be the exact reverse of that used for sequencing. Where vision is involved we can say little, at this stage, about the organization of de-sequencing. l2 Other forms of activity, such as tool usage, likewise depend upon sequencing, but their ‘output’ is not de-sequenced in the same way that we find in commu~cation (e.g. when we look at a sculpture we do not try to de-sequence the chiselling activity which yielded the form we see). De-sequencing is nonetheless required for perception, to be sure, but this is not so closely an approximation to undoing the sequencing (as we might reasonably maintain for communication).

We need not be surprised that this characterization of communication as psychophysically constrained semiotic activity does not require the invocation of any special organs or faculties. Communication is not that different from anything else we can do-perception and planned motor activity are required for existence, in all species. The crucial element is probably generativity, and species differences here may simply be a matter of degree. Within the semiotic approach espoused here it is reasonable to suggest that it is incumbent upon those who invoke special language faculties, or whatever, to show that psychophysically constrained patterns of activity and perception, that is, sequencing and de-sequencing (and learning mechanisms which must also be suitable for such constrained activity), cannot in principle be adequate for linguistic activity. Linearization, and all that we have seen this entails, is a good candidate for the ‘general cognitive principles’ mentioned by Chomsky (1980, p. 29)

The study of biologically necessary properties of language is a part of natural science: its concern is to determine one aspect of human genetics, namely, the nature of the language faculty. Perhaps the effort is misguided. We might discover that there is no language faculty, but only some general modes of learning applied to language or anything else. If so, then universal grammar in my sense is vacuous, in that its questions will find no answers apart from general cognitive principles.

It is odd that general semiotic factors such as sequencing and de-sequencing have not been more thoroughly researched in order to show that language can, or cannot, be accounted for in these terms. This would seem to be the only way to demonstrate the necessity of a concept like universal grad. ~though we shall refrain from discussing the achievement of language by children, or learning of any sort, we will discover as we proceed that language is perhaps not so special. In one sense this is simply. because linearization-in the sense we have defined it, that is, sequencing and de-sequencing-is not especially a linguistic issue. It may be true that linguistic activity offers a particularly thorough demonstration of what can (or must) be done with the semiotic psychophysical constraint, but in my view we are ultimately forced to recognize that we are dealing with psychological and cognitive issues. Linguistics may be special in that grammars provide ways of producing sequencible cognitive entities. However, most linguists would consider this a peculiarly pared down concept of linguistics. Yet it is difficult, in the final analysis, to make out a strong case for saying that linguistics is about anything more than this.

The remainder of this study is a justification of the above claim, starting in the next


two sections with some illustrations and moving on to an examination of the way in which several theories fail to address the topic of linearization with sufficient subtlety (section 5).

In this section my intention is to present a brief account of some phenomena in British Sign Language which illustrate the general semiotic outlook sketched in section 1. This is no place in which to present a complete account (always supposing there is a complete account available) and for a variety of partial accounts the reader is directed to the steadily swelling literature on signed languages in general, I3 The two phenomena of interest here are ‘simultaneity’ and ‘reversed signing’. These illustrate, respectively, the psychophysical constraints and the relationship between sequencing and de-sequencing. Some of this discussion is available elsewhere14 so brevity here does not indicate a genuine shortage of discussion.

2.1. Simultaneity has been a much discussed topic amongst signed language researchers.lS As recent research has focused on the fine detail of sequential patterning in signing,16 so has simultaneity diminished in popularity as an issue. This is unfortunate as in fact simultaneity and sequential patterning are not contradictory notions. We will look at three aspects of simultaneity-muscular, grammatical, and spatial.

2. I. 1. In terms of the patterning of muscular activity the simultaneity we encounter in signing is no different from that which we find in speech. ‘The sequential patterning of simultaneously organized muscular activity’, as I described it in 1.2.6, applies just as well to signing as to speech. I7 The fact that ever finer detail of linguistic significance is descernible in signed sequences-apparently making signing more like speech-is irrelevant; it remains the case that more of the muscle activity is observable in signing-the simultaneity is more obvious. This does not make signing ‘more simultaneous’ than speech in any interesting sense. Furthermore, I am not convinced that the arguments presented below (2.1.2, 2.1.3) reduce to such inappropriate attribution of significance to a simple physiological fact (the disposition of the articulators, or rather, the difference in such dispositions for speech and signing).

2.1.2. Grammatical simultaneity does seem to be unique to signing (and, like the point made in 2.1.1, this observation appears to be true of all signed languages). Bellugi writes (Bellugi and Studdert-Kennedy, 1980, p., 134)

there is a significant structural difference between ASL and spoken languages. In spoken languages, the sequencing of segments plays a fundamental role at both the lexical and grammatical levels (albeit the segments are indeed simultaneous bundles of features). In ASL, where the linguistic signal is presented in space as well as in time, the simultaneous presentation of concurrent elements occurs not only at the sublexical level but at the lexical and grammatical levels as well. In the linguistic signal of ASL, sign stems composed of co-occurring elements are displayed emcurrently with inflectional processes composed of co-occurring components concurrently with other grammatical devices such as spatial marking and nonmanual signals.

A simple illustration of this grammatical simultaneity is readily available (although certain grammatical/linguistic facts about signed languages will have to be accepted on trust). In signing {all signing, it would seem) one makes productive and linguistically constrained use of spatial locations (to mark, say, subject, location, indirect object, etc.) and of stylized motions, handshapes and orientations. If one imagines slowly handing a heavy rectangular object (say, a medium-sized box) to another person the sequence of motions involved is clear. The hands form to fit under the edges of the box, and then (with effort) one slowly hands it to someone standing close by. The grammatical simultaneity arises because the indication of size, shape and weight are given simultaneously (and enduringly) and,


furthermore, when the imagined box begins its path from agent to recipient the identification of the subject, object and indirect object is established simultaneously (and enduringly) along with the verb and adverb. Throughout the ‘utterance’, therefore, grammatical information is simultaneously available concerning the verb, adverb, subject, indirect object, direct object, and adjective(s).

2.1.3. Spatial simultaneity is a somewhat more complex notion superficially similar to that discussed in 2.1.1 (as hinted at by Bellugi in the extract above). However, we are not here concerned with the fact that the articulators are spread out in space, (a TV camera positioned a few inches in front of the mouth would convey this impression for speech). What is important is that signed languages use the four dimensions of space-time in a specific way.

The processes of sequencing and de-sequencing, it will be recalled, exploit the time dimension because this ‘penetrates’ the corporeal boundary in a way which the other dimensions do not. In signed languages this has particular significance for perception or ‘reception’ (to which we will return in 2.2) but as regards production there is no sense in which the sequencing required for signing is much different from that required for speech. To be sure, there are physical constraints (mass of the articulators, for example), but the principle is not changed: output activity requires sequencing.

However, there is one difference which is rather significant, although it is not a difference in principle. The articulators in signing are available in four-dimensional space-time, for the construction of four-dimensional semiotic tokens about the four-dimensional world and one’s memories, thoughts, etc., of the four-dimensional world. This is saying something rather different than that the articulators have a fixed disposition in space (as the vocal organs do-constrained by one’s head). Although it is necessary that the semiotic tokens are constructed sequentially, the full dimensionality of space-time is available simultaneously and so we have a spatial simultaneity which is not available in speech. In my view this is very important, and surely contributes to one’s overall impression of signing as being simultaneous and ‘direct’ (a word which is used quite frequently in descriptions of signing, see for example Bellugi’s paper, quoted above). Semiotically speaking, it is surely significant that the process of sequencing for output (necessary in all modalities) should have the freedom to create four-dimensional tokens which match the dimensionality of the ‘real world’. In speech, not only are the tokens actually uni-dimensional but if one extracts extra dimensions like pitch and intensity these can only be analogues of the dimensions of space- time. This difference is noted by Summerfield et al. (1980), although ultimately they

consider it to be insignificant. They write (p. 110): In signed languages, terrestrial space-time is represented within the dimensions of a highly stylized version of terrestrial space-time; the linguistic space-time of the sign space. Nonetheless, the translation is within comparable orders of dimensionality and appears to yield a more isomorphic relation between the world as experienced and the world as expressed in language.

The reader should not be left with the impression that all signing requires such four- dimensional mapping (although it is true that the availability of four-dimensional space- time is not like anything available in speech). Signers exploit spatial metaphors for time, for example, and these can be quite complicated. An illustration (which I observed in natural discourse) is readily described. The metaphor ‘to put off’ or ‘put back’, meaning to postpone, is a spatial metaphor in speech and in signing (BSL). In BSL (and in some natural gesture also, it seems) the sign involves the relocation of a hand (loosely open), from a first position a little in front of the torso to a new location further away (in front of the


torso). This is readily imagined and is an illustration of the use of widespread (possibly universal) cognitive constraint [the body centred ‘time-line’ with ‘future’ in the front, and ‘past’ behind (Brito, 1985)]. This sign can be modified aspectually, as in ‘to put off again and again’. To do this the signer typically moves the non-dominant hand as previously

described, from the position we might here call 1 to position 2, and holds it there whilst placing the dominant hand in position 1 from which it is then moved sideways (distally) in short steps, from position 1 to 3, 4, 5 . . . This establishes the notion of repeated procrastination on a separate time-line orthogonal to the first.

2.2. The above discussion reveals that signing, although intriguingly different from speech in some respects is nonetheless constrained by the need to sequence muscular activity. It is clear that the semiotic use made of such sequences is perhaps not as extensive as in speech (which is forced to use sequencing rather extensively). This will become clearer below, but for now let us rest assured that signing cannot escape the semiotically crucial psychophysical constraint-the need to sequence.

Let us now consider the rest of the gestural/visual modality-visual perception-and the process of de-sequencing. We have already noted (1.3.3) that with regard to de- sequencing visual perception is unlike auditory perception in that visual perception is not so constrained by the sequentiality in the phenomena being perceived. Sequencing is available as a semiotic domain, just as in speech, but vision has access to four-dimensional space- time in a way that speech does not, so sequentiality is potentially less significant (it remains essential for production). What this must mean in practice is that signing can exploit aspects of its simultaneity in both production and perception. Both grammatical and spatial simultaneity are to some degree perceivable in a way which makes sequentiality appear to be irrelevant.

2.2.1. The above remarks receive support from two observations. The first relates to visual constraints on gestural production in signing. It is known that the gestural system is capable of producing rather complex and rapid movements (such as those required when playing the violin). Moreover, such movements can require the hands to move about differently and at different rates. However, such freedom of movement is not permitted in signing. The constraints have been identified by Battison,18 who writes:

The Symmetry Condition requires symmetry if both hands of a sign are moving, in order to limit the complexity of the sign; likewise the Dominance Condition restricts the movements and possible handshapes of the passive hand in signs which have two different handshapes, one on either hand. Bilateral symmetry is thus unmarked, and asymmetry is marked.

Battison also notes that the constraints on the production of signs are forces which shape the changes in signs over time:

Now we see that the changes occurring in sign forms (for whatever reason) are motivated by the same principles-naturalness of signs as dictated by the observed tendency toward symmetry and harmony in articulation, centralization of locations, and the strict limits of movements and executions of signs.

These constraints appear to be widespread in application [for example, see Deuchar (1984), on their relevance to BSL]. Battison is of the opinion that perceptual factors are involved, although I do not agree with what he says concerning linguistic restrictions and redundancy:

The restrictions on possible occurring signs of ASL are motivated by the dynamics inherent in manual articulation and visual perception: The restrictions are linguistic limitations on information coding, partly brought about by a need for systematic redundancy in the signals.

We know that manual articulation is not the limiting factor, and we know that visual limitations constrain the complexity of movement to a de-sequencible rate (and, presumably,


format). One effect of the constraints is to reduce the potential for exploitation of sequentiality. Our semiotic framework, therefore, offers the basis for an explanation of Battison’s constraints, one which does not require appeal to linguistic or information theoretic notions.

2.2.2. The second observation is altogether more unexpected, unless one follows through the logic of the discussion in 2.1 and 2.2 to some sort of conclusion. The arguments so far clearly point toward the idea that sequentiality is linguistically irrelevant in signing (or at least, it is my intention that this is what the reader should be prepared to countenance, if only temporarily). We have seen that in terms of patterning muscular activity, etc., the need for sequencing in signing is not diminished, but the discussions of simultaneity, de- sequencing and production constraints raise the prospect that psychophysical necessity does not necessarily spill over into linguistic fact.

At face value this prompts the apparently absurd notion that the flow of time in signing is irrelevant. In fact this is readily testable experimentally and the result of carrying out such experiments (on a pilot scale) are reported elsewhere.lg The procedure is simply to play films of signed language conversations in reverse. For the most part the ‘gnising’ is incomphrehensible, but not completely so. Obvious problems occur with verbs in which the direction of motion of an articulator is used to establish the arguments of a verb (so, in the earlier example, GIVE becomes RECEIVE). Nonetheless, the findings are significant; (a) for the most part gnising is not recognized as time reversed signing; (b) after such material has been played with normal forward motion the reversed version is comprehensible (this perhaps depends on the subject matter and the viewer-not enough experimentation has been done). At least one subject managed virtually perfect comphrehension of a time reversed pot-pourri of conversational bits and pieces lasting more than six minutes, having once seen it played forwards.

The significance of this observation is simple enough-the flow of time is important at a general conceptual level (e.g. one doesn’t start the telling of a joke with the punch line) and sequencing is required psychophysically. But is sequencing required linguistically? Is concatenation a necessary property of linguistic systems?

A visual analogue of the above phenomenon is available, and it provides a good illustration of the point. A cartoon strip is a set of drawings, ordered in time ‘thematically’ but not linguistically. Furthermore, each frame has to be drawn and this (as we know) requires the execution of a sequence of muscle movements. Note that when we view such a frame we give it sequential structure (in the de-sequencing process) but this may not bear any relationship to the sequence of penstrokes executed by the artist. When we view an ordered set of four frames we de-sequence them in left to right order-at first. We can go back and look at one (all) of the previous frames should we want to (we don’t have to ‘start again’) and we can even deduce the order if presented with a jumbled set.

Comprehension of some ‘gnising’ following a single exposure to the signing version is not problematic, therefore, if we acknowledge that once we have the thematic order sorted out (in general-we need not be reliant on super-power memory for every detail in some six minutes of film) what we are viewing is much like a sequence of frames, each atemporal in nature. One subject even volunteered the opinion that I had cleverly edited the film so as to reverse the order of the ‘sentences’ (he was unaware that I had reversed the film in its entirety).20

2.3. The conclusion I want to draw, tentatively at this stage, is that I would give a negative


answer to the question posed above: Is concatenation a necessary property of linguistic systems? We cannot avoid the process of sequencing in any activity-that is a psychophysical constraint. Sequencing is necessary semiotically (the ordering of jokes, concepts, or what- have-you), that too seems incontrovertible. But it is far from clear that sequencing has to be exploited linguistically, that is certainly open to question. Even more importantly, however, we can without doubt conclude that a purely concatenative account of language cannot be sufficient. There is much too much about signing which is non-concatenative for anyone to seriously maintain that concatenative linguistic models are sufficiently general to apply to signing. This line of argumentation might be considered esoteric or perverse (or simply indicative of the exceptional or even non-linguistic nature of signing) were it not for the fact that there is plenty of other evidence for non-concatenative linguistic structures. In the next section we shall look at some of this evidence.

3 The line of argument being developed is that proper understanding of the psychophysical

need for sequencing and de-sequencing frees one to ask a general question: What is the linguistic necessity for sequencing (and de-sequencing)? This prompts an enquiry into the significance of concatenation in linguistic structures (as the embodiment of sequence) and this in turn leads to two further issues. Concatenation can be inadequate because structures are ‘simultaneous’ in the sense we have discovered is the case for British Sign Language. However, concatenation may also be inadequate as a basis for accounts of discontinuous linguistic structures which are, nonetheless, sequenced. It is this latter possibility which we consider in this section.

Simultaneity and discontinuity are not directly linked, so it is necessary to consider the two factors separately. The discussion of signing, it will be recalled, made no claims concerning discontinuous structures. We will now consider the treatment of some discontinuous structures and the extent to which simultaneity is, or is not, involved.

3.1. We turn here to work on autosegmental phonology, or non-linear phonology as it is more appropriately called. We will be considering McCarthy’s account of non- concatenative morphology in Arabic (McCarthy, 1981) but first it is necessary to comment upon the formalism of non-linear phonology.

The following section briefly presents arguments that have been given elsewhere to the effect that the current conception of the notational formalism of non-linear phonology is needlessly restricted to spoken languages (Edmonson, 1986). It is important to recognize that the restrictions are inconsistent with the underlying conception of the notation. Once the notation is freed from the modality-specific cast usually given it we can see that the structural insights it affords are appropriate in other linguistic domains-signed languages, grammar in general, even semantics.

3.1.1. Non-linear phonology is based on the idea that the organization of the phonological specification of an utterance can be captured most perspicuously if the segment sequence is abstracted from the complete or integrated description. This is used as a framework, a sequence of empty slots or locations to which are attached or associated the remaining details of the specification. We can consider non-linear phonology to express the controlled or structured fragmentation of disintegration of a phonological account of an utterance, a sort of dissection. However, it is not essential that the sequence of slots represents the sequence of segments.


3.1.2. The segment sequence is variously referred to as the ‘skeleton’, ‘melody bearing tier’, or ‘skeletal tier’. For reasons which will become obvious I will refer to spinal elements, not segments. Associated with elements in the spine are various tiers, or half-planes, which provide the featural details or specifications of the elements. I use the term association plane. The provision is arranged by means of listing, on as many association planes as seems desirable, the various features which make up the specification of each element in the spine, and by associating these lists with the spinal elements concerned. A useful analogy is offered by a spiral- or ring- bound notebook, where the binder is the spine, with the loops or rings representing the elements and the pages representing the association planes. Each page is used for a particular feature, or cluster of features (we will return to the details). On any one page the appropriate features will be listed and connected to one or more loops in the binder (elements) by means of association lines. When the dissection is complete each element (loop or ring) can represent a speech segment, in conventional terms, with the features indicated by the association lines drawn on the various planes (pages). The spinal elements are, as it were, ‘empty segments’ with segmental detail provided by the appropriately linked autosegments (which are not segments either).

3.1.3. In various accounts of linguistic phenomena expressed in terms of non-linear phonology the number and nature of the association planes is an important detail. McCarthy (198 1) refers to ‘some feature or bundle of features’ as defining a single association plane, and he establishes the case for extending the formalism to include planes which are ‘morphologically determined’. Clements and Keyser (1983) argue for a set of tiers (association planes) which encapsulate structural information (specifically, syllable structure) and they propose that a ‘complete phonological representation . . . consists of a composite representation containing both structural tiers and phonetic tiers’. Hayes (1985) outlines a ‘fully autosegmental’ phonology as capturing underlying representations and surface representations, and of the latter he notes that there might be ‘multiple tiers’ (association planes) ‘plausibly one per independently controllable articulator’.

The trend in these accounts seems clear enough. One can invoke association planes freely if convincing justification is offered. The arguments eventually reduce to a debate between two extreme views. On the one hand are those who propose as the simplest standpoint that association planes should be provided freely (e.g. for every articulator and for every structural layer or level) with research aimed at motivating the abandonment of planes or their conflation into clusters with articulatory or linguistic significance. On the other hand are those who favour a gradual increase in the number of association planes, each addition being argued for in the treatment of a particularly intractable linguistic phenomenon.

The formalism of non-linear phonology does not force the issue one way or another. It is the case that argumentation concerned with ‘mechanisms of association’ (the rules which specify the circumstances in which association lines are set up, are spread to adjacent segments, or are deleted) interacts with the above debate. This comes about mainly through the avoidance of crossing association lines by means of the invocation of an extra plane (this is a geometric sleight of hand which always removes crossing association lines). Nonetheless, the general concept which underlies non-linear phonology is not at issue here.

3.1.4. Another important detail of the formalism is the nature of the spine. The spine is defined, in one sense, as the line of intersection of all the association planes (or half- planes, because they radiate from the spine). In accounts of spoken languages, as already

238 WILLIAMH.EDMONDSON

noted, the spine is considered to represent the sequence of segments. It is as if the spinal elements are simply [ + segmental], having the property of specifying the duration or timing of the segments. However, even this simple outline reflects an uneasy compromise between intensely debated points of theory. Also, unlike the debate over the number of association planes the arguments here have important repercussions for the formalism itself.

3.1.4.1. We will consider first the notion that the spine provides or captures timing information. McCarthy (1983) in a discussion of several variants which differ in their ascription to the spine of detailed information, states that there is general agreement that the spine conveys timing information. He refers to the ‘timing level’ as the lowest level in the hierarchy recognized as non-linear phonology, and segments as ‘timing atoms’.

It is clear that ‘timing information’ should not refer to actual durations or temporal values. This is simply because the notational device sets up a specific mechanism for the association of detailed information with spinal elements, and duration is a detail, just like tongue position. There is no reason why we cannot invoke a timing plane and no reason why the spinal elements must be speech segments with specified durations. When we seek to assess the formalism we must recognize that it requires that all detail be put on planes, with the spine left as the featureless maker of the temporal order of distinguishable events. The events (elements) are only characterized through reference to the various association planes. In this sense ‘timing’ means succession or order, and the events ordered in the spine might, or might not, be segments in the conventional sense.

There seems to be no convincing argument to the effect that specification of timing units in the spine permits insightful analysis not obtainable via the alternative specification of succession in the spine and timing on a timing plane. It is clear that in arguing for totally featureless spinal elements we must face the requirement for some mechanism for co- indexing association planes. In fact this may be the only other important structural function of the spinal elements. It seems entirely plausible that endowing spinal elements with specific characteristics is attractive simply because no other proposal has been made for co- indexation of association planes. Put more simply, the issue here is that spinal elements have to be ‘recognizable’ or ‘identifiable’ so that association of spinal elements with features can be made selective or dependent upon the nature of the elements (e.g. in some languages only the segments conventionally identified as vocalic can carry or express high or low tone). Co-indexation is a plausible mechanism for such identification.*’ The conclusion here is a general one. In terms of the formalism it appears that no attempt has been made to show that durational information should not be assigned its own timing plane, or that such information must be incorporated in the spinal element for formal reasons or for linguistic reasons.

3.1.4.2. We can now turn to the second aspect of spinal specification which needs to be questioned. Not content with requiring that the spinal elements are specified for duration, theoreticians offer several contrasting views as to whether even more information should be provided in the spine. This is clearly of fundamental importance for the formal device itself. It is not possible to attempt a review of all the complex reasoning behind the various proposals, but one proposal does merit discussion here.

Clements and Keyser (1983) offer extensive support for a claim made earlier, and notably, but not exclusively, by McCarthy (1981). The substance of the claim is that the spinal elements are, essentially, either consonants or vowels. In fact Clements and Keyser prefer to say that the elements ‘distinguish between syllable peaks and syllable non-peaks (or

ISSUES IN LlNEARlZATION 239

syilable margins)‘, The CV-tier, or CV ‘skeleton’, is central to their approach, and although the elements are most accurately thought of 8s [ + segmental] [ + / - syllabic] the conceptual relation to consonants and vowels is clear, It is appropriate to add that this particular approach is widely adopted and caIIed ‘CV-phonofogy’, because of the centraIny of the CV-tier in its role as the spine. However, we must recognize that when a CV spine (or some other spine with specified elements) is proposed a strong claim is made about alI languages. If, on the other hand, a particular plane is proposed, such as the CV plane, no attendant claim is made to the effect that a successful account of all languages must utiIize that particular ptane. The formaI device does not require that ail planes are utilized in the characterization of all languages; a major attraction of the notational device is precisely that it can cope with widely differing phonologies. To the extent that a plane such as the CV plane is not universally utilized it cannot play a major role in any account of a universaI phenomenon such as syllables (in spoken languages, and maybe also in signed languages, see Edmondson, 1986).

3.1.4.3. In summary, therefore, we must conclude that the spinal elements are completeIy featureless; no single plane provides spinal elements, nor are these elements specified temporally.

3.1.5. The forma3 device of non-Iinear phonology, as set out above in a modified and more general form, is entirely consistent with the notion that discontinuous arrangements of spinal elements may be associated with a feature in a plane. In other words, the formal device provides for the characterization of a sequence of distinguishable events in a way which does not assume sequenti~ity to be a necessary property of that characterization, For example, we might find that a half-plane is only associated with spinat elements we might recognize as vowels, whereas a different half-plane is only associated with spinal elements we might recognize as consonants, Because vowels and consonants are intermingled in speech we find the possibility that two groups (say, vowels and consonants) may be ~scontinuousIy present in the ‘output? afthough they may, on their separate half-planes, be considered to be simultaneously present (in the sense that we have no reason to suppose that vowels and consonants are ordered as groups). On the other hand, it is equally possible that constituents discontinuously represented in the ‘output’, and thus simultaneous in a sense, actually have an underiyingIy concatenative arrangement. The point is that the ordering of elements in the spine does not have any imptications for the ordering of underlying entities. We may consider it reasonable to suppose, for exampIe, that where we have concatenation of the surface forms of the morphemes in wards there must be a matching order in the underlying arrangement of the morphemes. However, this is entirely presumptive of cognitive processes until sufficient empirical evidence can be brought to bear.

3.2. McCarthy’s treatment of Arabic morphoio~ (1981) is a perfect illustration of the structural possibilities just ouiined. (Recall that McCarthy is working in a framework which has the spinal elements identified as vowels and consonants), He argues that the morphological structure of Arabic is best accounted for if the roots-‘three or four consonants which cluster around a single semantic field, like KTB i%rite”‘-are viewed as discontinuous morphemes non-concatenativeiy intermingled with other-vocaiic- discontinuous morphemes. The Classical Arabic verb system, for example, comprises fifteen CV patterns (binyanim) for the non-concateuative intermingling of triiiteral root morphemes with vocalic patterns and affixes, Furthermore, each binyan is itself patterned (vocalic) for voice and aspect. This is iifustrated (briefly) below with some verb stems (the exampIes


are from McCarthy’s extensive tabulations and we should note his reminder that they are ‘abstracted’ in that details of phonology and agreement are ignored):

Perfective Active Passive kaatab kuutib nkatab nkutib

He notes:

III katab (correspond) VII nkatab (subscribe)

Imperfective Participle Active Passive Active Passive

ukaatib ukaatab mukaatib mukaatab ankatab unkatib munkatib munkatab

certain verbal categories such as aspect and voice are marked on the binyanim not by the disarrangement of consonantism but rather by altering the quality of vowels of the stem in a systematic way.

These vowel patterns are themselves morphemes.

3.2.1. The vocalic morphemes and the triliteral root morphemes, each of which is discontinuous on the surface, might be supposed lo be simultaneously present in the underlying representation, along with the morphemes for the affixes. So we might reasonably give the structure for the perfective passive of ‘subscribe’ as:

i’ A n k u t i b

V m”

However, the pattern ‘nCVCVC’ is itself a kind of morpheme-the specification of the VIIth triliteral binyan. The morphologial status of the various binyanim themselves is not necessarily very marked. McCarthy writes:

The first binyan is a possible category for nearly all roots that can appear as verbs. It is relatively unmarked morphologically, at least in finite forms, and it has no special semantic properties But the others, the derived binyanim, generally involve some special modification of the meaning of a related noun or verb or of the basic meaning of the root. So, for instance, the third triliteral binyan is usually reciprocal, while the sixth is usually reflexive or effective of the reciprocal.

We might therefore propose, in line with the earlier discussion, that a more felicitous

notation would show: m’

where yet another planes provide further details of the specification of the spinal elements (as speech segments, say). Co-indexation would permit the planes to ‘know about’ each other, just as in the CV version planes must be sensitive to the specification of the segments as vocalic or consonantal.


3.2.2. The example of non-concatenative morphology in Arabic-whether couched in conventional CV notation or in revised non-linear form-clearly shows how simultaneity and non-concatenativity interact, but not causally. We might suppose that ml, m2 and m3 are simultaneously co-present, for example, but this says nothing about the sequencing or intermingling of the spinal elements. We might also suppose that in other circumstances a set of morphemes, mX, my and mZ might necessarily be sequentially organized-as morphemes. But this could not be interpreted as implying a concatenative organization of the surface representation of those morphemes. All we can say with confidence is that the spinal elements mark events which have properties given by the association half-planes.

3.3. The revised notational device of non-linear phonology discussed here affords a ready- made general purpose notation for all possibilities in the process of sequencing (and de- sequencing). We have seen how underlying simultaneity and surface non-concatenativity are not implicationally related, and likewise, how underlying sequentiality and surface concatenativity are not implicationally related. We are now in a position to combine arguments from the first three sections of this study into a framework within which we can analyse aspects of some theories of grammar.

4 The preceding three sections have developed and illustrated the theme of sequencing and

de-sequencing in communication. We have come to recognize the psychophysical necessity of sequencing and de-sequencing in the externalization of all activity, including semiotic activity. Whenever we produce a linguistic token we involve these two processes. It is readily appreciated that sequencing is necessary in a general conceptual sense, so that there is a literal reading of the phrase ‘to put one’s thoughts in order’ [something which has been recognized for two millenia, see Levelt (198 l)]. Sequencing is also ‘obvious’ at the muscular ‘level’-if we tensed all our muscles simultaneously we might break all our bones. However, the ‘levels in between’ are not obviously under the same constraint. Yet in fact the same point applies-we can only guarantee a match between internal and external sequences, whether these are sequences of phonemes, words, sentences or any other sort of token. Where tokens of one sort (say, words) are made up of sequences of tokens of a different sort we have the freedom to specify the two sequences independently (of course). But this does not mean that the underlying representation of the sentences is a sequence (the notational formalism of non-linear phonology shows us how this is possible). It seems somehow natural to presume that underlying sequences do exist, but it is not semiotically necessary that they should. We can now recognize the limited nature of the model introduced earlier (1.2.7).

The second aspect of sequencing and de-sequencing which we have discussed is also very significant. Because sequencing and de-sequencing are independently motivated-regardless of the ‘level’ we are considering, be it words or whole speeches-the question arises as to whether temporal ordering of linguistic entities has any other specifically linguistic motivation. It is the case that temporal order is available semiotically; we are free to attribute significance to any order because sequentiality is motivated elsewhere. The question, then, is whether the temporal structures we find in linguistics merely reflect the exploitation of this semiotic potential or whether they are linguistically essential.

One other important consequence of adopting the particular semiotic outlook advocated here is that we have to recognize as separate (but relevant) the sequence of derivational procedures required to produce externalizable entities (or ‘receive’ and de-sequence such


entities). I have argued that this is a necessary consequence of the requirement of generativity, but in fact the accuracy of that argument is not crucial. What is important in the context of this discussion is that we should recognize the possibility (if not the probability) that the derivational process is itself temporally organized. We might, by way of illustration only, want to think of such derivations as the repeated (i.e. sequenced) application of a procedure which takes in a single cognitive entity and yields a number of such entities (not necessarily a sequence of such entities). This fits comfortably with the expectations we might entertain concerning recursive structures.

4.1. These three aspects of sequentiality have been illustrated, to varying degrees, in the previous sections. We have seen, for example, that signed languages (at least, BSL) may well reveal that whilst temporal structures are required for psychophysical reasons (semiotic principles, if you will), such structures are not essential linguistically. We have also seen that the notational formalism of non-linear phonology is capable of reflecting the required arbitrariness (after some independently motivated modification of the conventional formalism).

We find that underlying simultaneity and surface concatenativity can co-exist, as can underlying concatenativity and surface discontinuity. If we accept the notion of derivation as a sequence of steps in which cognitive entities at one ‘level’ are decomposed into sub- entities at the next, lower, ‘level’ (and each of these is subsequently decomposed, etc. ‘all the way down’), then we must recognize that the extended formalism of non-linear phonology permits any relationship between units or entities in different levels. Thus in Arabic we can find morphemes (either sequenced or not, as morphemes) surfacing as discontinuous or non-concatenative entities at the phonological level. By contrast, in Turkish nouns the morphemes surface in accord with a fixed order, but we have no way of knowing if these entities are sequenced cognitively.22

4.2. We are apparently faced with an imponderable. In principle the sequential aspects of the surface appearance of semiotic tokens need bear no relation to internal relationships-precisely because sequentiality is a necessary property of the output system rather than of the tokens being produced (I think that this is why morphology is so variable). If this is accepted then it must also be accepted that just because the morphology of, say, Turkish (or even English, to some degree) appears linearly or sequentially patterned that does not imply the existence of any sequential pattern in the cognitive representations of such morphemes, but nor does it imply the lack of such sequential patterning. We simply do not know. Whilst it is possible to point to trends in linear patterning (e.g. category changing morphology tends to be suffixed) it is not possible to make universal claims. The solution would appear to be either that a correspondence is assumed (pending experimental work) to the effect that in some way (to be made precise) the sequential arrangements of linguistic tokens do or do not correspond to or match cognitive sequentiality, or that there are indeed linguistic reasons for asserting the existence of cognitive sequencing of linguistic entities and that either these do surface as matching ordered arrangements, or they do not.

4.3. The theoretical linguist is thus faced with a problem. Although we will examine this in detail below, in the discussion of syntax, the problem can be illustrated quite readily by reference to morphology and to semantics.

The surface organization of morphology cannot in principle indicate the nature of the internal organization. If we presume that it does, however, then the indication is that strictly concatenative structures are not universal. Either way, we have no grounds for preferring


concatenative theories. Similarly, at the semantic level evidence is readily available that the surface arrangement of tokens is inconsistent with the cognitive arrangement (where there are more reasonable, introspective, grounds for presuming cognitive or logical structures). In English there is a class of sentences which provide ~scontinuous intermingled representations of semantic entities which are surely discrete-the ‘respectively’ sentences:

(1) Hector and Harriet are (respectively) three and five (respectively).

The adverb may even be omitted without adding difficulty to the interpretation. My point here is that the surface ordering reveals the non-concatenative intermingling of two propositions:

(2) Hector is three (3) Harriet is five

(where, as in (l), we understand that age is being referred to). We might instead want to claim that these propositions are discontinuously represented in the surface form of (1) without concluding in favour of simultaneous co-existence in the cognitive precursor to (l), any more than we can claim that speakers of Arabic have simultaneously present cognitive representations of the various morphemes which make up a verb. However, I feel sure of my intuitions in this case because the ‘respectively’ construction doesn’t work when one is explaining or working out Harriet’s age on the basis of Hector + 2, a derivational (and hence sequential) origin for the propositions. Such sentences once again caution against the presumption that surface sequence matches closely any underlying structures. But, if the presumption is made the conclusion must be that non-concatenativity is not unusual in cognitive structures.

4.4. The theoretical linguist can do one of three things. S/he can choose to recognize the logic of the arguments and look for a notational framework which can encompass both concatenative and non-concatenative aspects of activity-in this case Iinguistic activity. With this in hand the development of theory to match the phenomena should be facilitated. An extension of this would have the linguist arguing that linguistics is fundamentally about the unordered structures and the language specific ordering we do find is irrelevant (and the regularities are properties of the system in general, not of language qua language). This is my own view. Alternatively, s/he can choose to argue that linguistic theory is necessarily concerned with ordered structures because language (not commu~cation in general) couldn’t work without them.

5 In this section we consider the treatment of sequence in a few theories of grammar. In

5.1 two early dissenting opinions are presented, and in section 5.2 a variety of different theories are examined all of which are predicated upon the need to present a unified grammatical account of ordering in all languages. It appears that heretofore no one has appreciated that sequencing and de-sequencing reflect a psychophysical constraint and that therefore the surface order of tokens is not necessarily a grammatical matter. This bias is readily apparent from the tendency to assume, for example, that pragmatic factors should be included in theories of grammar. The usage of the term grammar will here be more restricted-I have in mind structures, in a general sense not a syntactic sense, or relationships. The primary purpose of grammar is to provide sequencible items or semiotic tokens. In some cases grammatical information can surface in sequential detail but the exploitation of sequence is not an essential part of grammar or a necessary aspect of


grammatical activity. All we have left from the simple model of 1.2.7 is the notion of cognitive entities having sub-structure, and some recursive mechanism for getting at the sub-sub . . . structure. Of course, the entities involved in the grammatical process are nonetheless cognitive entities, so we may not need to invoke special faculties or organs. What is special is the purpose for which the entities are produced (sequencing and de- sequencing) and this, along with requirements concerning learnability, will doubtless constrain grammars (grammars have to be ‘possible’ in this function sense). What may not be special is the recursive mechanism (just think of the ease with which we can find embedded structures in knowledge and activity generally). This attitude frees us to consider sequencing as a separate cognitive, and sometimes semiotic, activity. And this gets us to the point where we can see that linguistic regularities may reflect quite pervasive cognitive constraints rather than grammatical structures or relationships, which latter merely provide the sequencible wherewithal without which the constraints would not be so obvious. This line of argument owes much to recognition of the importance of the modality differences between signing and speaking.

My purpose in this preamble to a look at more conventional grammatical theories is simply to summarize what seems a justifiable linguistic perspective given the preceding discussions. It is the perspective from which I have worked in selecting the material which follows.

5.1. In this section we will look at some work done by Curry and by Staal.

5.1.1. In 1961 Curry’s paper ‘Some Logical Aspects of Grammatical Structure’ was published (Curry, 1961). In his paper Curry explores the linguistic application of combinatory logic. In particular he points out that whereas more standard forms of logic concatenate symbols into strings, combinatory logic yields formal objects which are not ‘strings of atoms’ but ‘structures like a genealogical tree’. He continues (p. 65):

Now of course there are various ways in which such a tree can be associated with a string. Any method such as one-to-one association between the [objects] and a special class of expressions [well formed expressions] is called a representation of the system. In order that a linear language be a representation in this sense it is necessary that each [well formed expression] indicate a unique construction (i.e. a unique tree): in such a case the language will be called monotectonic. Now this situation suggests that we may think of language in an analogous fashion . . we may conceive of the grammatical structure of the language as something independent of the way it is represented in terms of expressions . This gives us two levels of grammar, the study of grammatical structure in itself, and a second level which has much the same relation to the first that morphophonemics does to morphology. In order to have terms for immediate use I shall call these two levels fectogrammatics andphenogrammatics respectively; no doubt someone will propose better terms later.

It is indicative that the terms introduced by Curry have not become commonplace, nor have they been replaced by better terms, despite his important insight. Curry seems keenly aware of the linguistic implications of his approach (p.66):

It is to be expected that grammatical structure will vary less from language to language than does the phenogrammatics. Different languages use entirely different devices for indicating grammatical phrase composition. In some languages word order is important, as it often is in English; but in Latin the three words in ‘Puerpuelkzm amat’ can be arranged in any of six possible orders without changing the structure.

He concludes his paper with a mention of two phenomena of natural languages which are ‘rare in the artificial languages of logic and mathematics’. The first is ellipsis and the second is variation-‘the same phrase may be constructed in different ways’.

It is true that the artificial languages of mathematics and logic have generally the property that every phrase has a unique construction-i.e. these languages are monotectonic. But it is a fallacy to assume a priori that the natural languages have this property. They may be, and I believe most of them are, polytectonic, and


the equivalence of different constructions of the same sentence is one of the features which has to be taken account of in an adequate grammar.

These features . . . can be taken into account. They do not affect the fundamental point, that we can profitably study grammatical structure as such, apart from its representation in terms of concatenation.

Curry’s argument is an interesting one. It has a base in logic, not semiotics, and is, in essence, that following recognition of the distinction between tectogrammatics and phenogrammatics we can recognize the possibiliy that a given grammatical structure can have several surface representations and, vice versa, that a given surface representation can represent several grammatical structures .23 He implies that we cannot attribute grammatical significance to surface (order) structures because no unique grammatical reading of such a representation is possible. This is an important argument to add to the debate; not only is sequence arbitrarily available as a semiotic token for exploitation in languages, we cannot even be sure that where a language makes use of, or gives meaning to, the ordering of, say words, it must necessarily do so in a consistent (monotectonic) way.

5.1.2. Staal’s study of Word Order in Sanskrit and Universal Grammar was published in 1967 (Staal, 1967). In this study he briefly refers to Curry’s work, and in a discussion of Curry’s terms he notes that tectogrammatics and phenogrammatics:

correspond to deep structure and surface structure, respectively, provided order is excluded from the deep structure. For, as Curry observes ‘if phrase structure grammar means the building up of phrases by concatenation of adjacent phrases, then it has a phenogrammatical aspect’.

This is placed in the context of a discussion of early Sanskrit scholars (Panini, Patanjali) who, we are reminded, distinguished between ‘sambandha’-‘the relation of a word to another within a sentence (as shown, e.g. by grammatical inflexion)’ and ‘abhisambandha’-‘the order of arrangement of words (as occurring in actual utterances)’ (quotations from Apte, 1963).

My aim here is not to attempt a precis of all Staal’s argumentation and evidence. Instead I want to point to his conclusions and to one or two remarks which he makes concerning Chomsky’s (Aspectsj work. Staal concludes (p. 60) that Sanskrit is word order free, in the sense that ‘on the whole, word order has no grammatical significance’. Concerning the role of order in grammar, we find (p. 64):

It may be re-emphasized here that Chomsky was aware of the fact that the definition of ‘grammatical relation’ does not presuppose order: ‘the systems of grammatical relations defined in the two cases [i.e. set systems and concentration systems1 are identical’ (Aspects, p. 125).

However, Staal would seem to be papering over the difficulties of fusing his account with Chomsky’s, and thus guilty of pulling his coup de grace. His concluding paragraphs (p. 80) contain the following:

In the theory here envisaged the base of the syntactic component consists of a kernel of ordered rules (including at least one recursive rule) introducing sets of formatives, constituents and dummy symbols (transformations markers). This kernel is the same for all natural languages and hence a linguistic universal which is presupposed by particular grammars. . . In addition to the kernel the syntactic component contains other rules which vary from language to language or from language type to language type. For some languages these rules derive further sets from the sets generated by the kernel; for other languages they immediately generate ordered strings. . . Ultimately ordered strings will be introduced everywhere, and surface structures will be derived from these with the help of other transformational rules. The picture which emerges is not that of a syntactic component with a semantic interpretation (deep structure) and a phonological interpretation (surface structure), but that of a kernel consisting of stratified sets which embodies the universal deep structure and is mapped into particular surface structures.

Essentially such a theory is much more simple and perspicuous than earlier systems, since it permits the generation (or ‘interpretation’) of structures in one way only, viz. from the unordered deep structure expressed by the kernel to ordered surface structures. This is infinitely more satisfactory and constitutes a natural development from the basic ideas that prompted earlier formulations of theories in generative grammar.


However, a careful look at the appropriate passage in Chomsky’s Aspects (1965, pp. 123-127) reveals the following:

We have defined the cutegoriul component as the system of rewriting rules of the base. . [these rules] carry out two quite separate functions: they define the system of grammatical relations, and they determine the ordering of elements in deep structures.

. It has been suggested several times that these two functions of the categorial component be more sharply separated, and that the second, perhaps, be eliminated completely. Such is the import of the proposals regarding the nature of syntactic structure to be found in Curry (1961).

. . Proponents of set-sy.stems [e.g. Curry] have argued that such systems are more ‘abstract’ than concatenation- systems. and can lead to a study of grammatical relations that is independent of order, this being a phenomenon that belongs only to surface structure. The greater abstractness of set-systems, so far as grammatical relations are concerned, is a myth. Thus the grammatical relations defined by [a set-system] are neither more or less ‘abstract’ or ‘order-independent’ than those defined by ]a concatenation-system]; in fact the systems of grammatical relations defined in the two cases are identical. A priori, there is no way of determining which theory is correct; it is an entirely empirical question, and the evidence presently available is overwhelmingly in favour of concatenation-systems over set-systems, for the theory of the categorial component.

Chomsky argues frowardly because it is the definition or specification of the grammatical relations which is more abstract, not the relations themselves. Chomsky goes on to argue that a set-system will always be subject to a set of rules which ‘simply converts a set-system into a concatenation-system’ so as to provide ‘the base Phrase-markers required for the application of the sequences of transformations that ultimately form surface structures’. Furthermore, his claim that set-system proponents do not have a mechanism for converting unordered base structures to ordered surface structures is not satisfactory as his own preferred choice, which is to put order in the base component, is entirely arbitrary. And contrary to his argument that in any case ‘free word order’ languages aren’t really free, so empirical support for set-systems is lacking, Staal claims that Sanskrit is genuinely a ‘free word order’ language.

On this account it is not clear why Staal should try to mute his criticism of Chomsky. If the force of Staal’s argument is accepted then we have, in Curry (1961) and Staal(1967) the development of a theme with its roots in antiquity, a theme which we will encounter later.

5.2. We begin our examination of theories of grammar-in relation to the ordering of components-with Chomsky’s Aspects (1965), following which we will consider recent work in the Chomskian tradition and then various alternatives.

5.2.1. It is clear, from the extracts already given in 5.1.2, that Chomsky is inclined to adhere tenaciously to the view that the base contains ordered structures. Without such a presumption transformations become either structure changing or irrelevant, but with it the transformational account can tackle almost anything. What it cannot deal with satisfactorily is those languages with free word order, because to do this we need to invoke disordering rules, and Chomsky’s arguments about the problems of the introduction of order into a set-systems approach apply-mutatis mutandis-to the introduction of disorder into a concatenation-systems approach. It really is not good enough to imply that free word order is only a superficial, stylistic, ‘performance’ overlay on an underlying order (as Chomsky does in Aspects, p. 127). In fact, given the crucial nature of the presumption of ordering in the base (without which Transformational Grammar would appear to lose much of its force), Chomsky’s justification of base ordering is quite inadequate.

The above criticisms are justified without reference to the more general semiotic arguments presented earlier. When these are taken into account the claims for base ordering and subsequent transformations become quite problematic. We know that at some ‘early’


stage in the derivation of an externalizable form there must be a single cognitive entity without temporally organized sub-structure. To get from this to the ordered base (whence, via transformations, to the surface) poses the very same problems as those which Chomsky considers so damning in his account of the set-systems approach. However, by considering the ordered base as the ‘starting-point’ in linguistic explanations he neatly avoids the issue of where the ordering in the base came from, This is non-trivial as a complaint, for Chomsky cannot fall back to an argument which says that the output has to be given an order somewhere, otherwise why would we bother with ordering at all? This is blocked by the independent motivation of sequencing in the output, so any sequence will do. Sequencing is supplied elsewhere, so particular sequences have to be justified on grammatical grounds specifically, or on cognitive grounds, or order can be accepted as grammatically inessential, which allows free word order languages to be of equivalent status to fixed word order languages. In short, as languages don’t always bother with grammatical ordering, nor should they, there is no need to predicate grammatical theories upon ordered structures.

Another criticism of Chomsky’s approach in Aspects is that ordering specifications are concatenative. Logically speaking it is quite feasible for a fixed order language to have non-concatenative specifications. Consider the following range of data from English.

(4) Hector is driving the car over the cliff. (5) Hector is driving the car over the cliff skilfully. (6) Hector is driving the car skilfully over the cliff. (7) Hector is skilfully driving the car over the cliff. (8) Skilfully Hector is driving the car (over the cliff). (9) Skilfully Hector is driving over the cliff.

(10) Hector is driving skilfully over the cliff. (11) Hector is driving skilfully. (12) Hector is driving. (13) ?Skilfully Hector is driving. (14) The car is driven skilfully (by Hector) (over the cliff). (15) The car is skilfully driven. (16) The car is driven. (17) ?Skilfully the car is driven. (18) The car is being driven. (19) ?Skilfully the car is being driven.

The constituent structure in (4) is straightforward:

NP AUX

I A N

I Hector is driving the car


The problem arises when we look at the constituent structure in (5)-(9). Either we must accept that the manner adverb is part of the VP, in which case (8) and (9) show us non- concatenative VPs, or we must accept that the adverb is a separate constituent, in which case (6) must have a discontinuous VP. Of course, to say that the adverb in (8) or (9) is a separate constituent, whereas that in (5)-(7) is part of the VP is to say that anything goes. Also, the data (lo)-(19) support the notion that ‘skilfully’ is part of the constituent which includes the verb. In fact, the adverb seems rather tightly associated with the verb, in the sense that ‘drive(n) skilfully’ feels like an indivisible constituent when the argument is inferred. This is little more than impressionistic evidence in support of the claim that the adverb is really part of the VP which can, in some instances, surface as a discontinuous entity.

It is not my intention in this study to attempt the development of a complete theory of non-concatenative syntax. It is important, however, to note that such a theory would be valid within the framework being explored. The notion of constituent is, in effect, the presumption of underlying concatenation. As we shall see, it is permissible within the semiotic framework for order to be exploited for the expression of grammatical relations (hence we get fixed order languages). Underlyingly concatenative constituents therefore make perfect sense, as does the possibility of these surfacing in a discontinuous format. And, as with the Arabic morphology we looked at earlier, it is possible for the underlying representation of the constituents not to be serially organized. It is a matter for empirical

research to determine whether the S in (4) has NP & VP ordered or not for grammatical reasons. It is possible, for example, to consider that the ordering of the predicate and argument in English sentences is constrained by non-grammatical forces (e.g. pragmatic). The grammatical device of passivization would then be understandable in terms of ‘raising to argument’ a constituent which the speaker wishes to bring within the domain of the pragmatic order constraint. Thus, in English there might be no grammatical specification of the underlying order of argument and predicate and any non-linear account of the grammar would have to show the NP and VP on separate half-planes, without intrinsic order, although the constituents within NP and VP have to conform to order constraints (which, like the Arabic example, we might want to consider separate morphemes, in this case expressive of grammar). This might seem odd, but there is empirical evidence available to support this sort of argument. In Russian it is quite acceptable to produce an utterance which could be translated as:

(20) By the dog was bitten the man.

In English (20) strikes one as odd rather than ungrammatical. Consider the relative merits of (21) and (22):

(21) The man, but not the woman standing in the flower-bed pruning roses, was bitten by the dog. She was bitten by a beetle.

(22) By the dog was bitten the man but not the woman standing in the flower-bed pruning roses. She was bitten by beetle.

Although not prize-worthy (22) could not be said to be unacceptable for grammatical reasons (at least, this is my judgement). I read (21) as having discontinuous semantic entities- ‘man bitten by dog’ intermingled with ‘woman bitten by beetle’, whereas (22) presents the semantic entities serially. My point here is simply that the grammatical specification of sequencible items does not, in the case of English, necessarily amount to the complete specification of sequences. These can be provided elsewhere. In Russian (for example) this


seems particularly clear. In English the grammmar provides some of the sequence (that which is within NP and VP, for example). My suggestion is that the semiotic framework being considered here, coupled with the non-Iinear notational device derived from phonologic~ theory, affords a clear appreciation of the problems with the entirely concatenative view of things revealed in Aspects.

5.2.2. Moving now to Chomsky’s more recent work, on Government and Binding (Chomsky, 1982, henceforth LGB), we find that the situation regarding the presumption of order in the base has become quite confused.

The model to be considered is more complex than that of Aspects. There are five sub- components of the rule system (p. 5):

(i) Lexicon (ii) Syntax

(a) Categorial component (b) Transformational component

(iii) Phonetic Form component (iv) Logical Form component

and these interact with six sub-systems of principles:

(i) bounding theory (ii) government theory (iii) O-theory (iv) binding theory

$) case theory control theory.

For our purposes it is sufficient to note that the base comprises rule systems (i) and (iia), yielding as output D-structures which are transformed (iib) to S-structures. Both D- and S- structures are therfore ordered. This looks similar to earlier models of Transformational Grammar, except that now there is only one transformation-Move Alpha-which leaves traces co-indexed with antecedents. The various sub-components and sub-systems admit parametric variation, which is to say they constitute a general, universal, grammar (UG) which is particularized by the setting of parameters to become the grammar of one language or another. ‘UG is taken to be a characterization of the child’s pre-linguistic initial state’. The parameter fixed UG is called a ‘core grammar’ (each language thus has its own ‘version’ of UG). One such parameter might, we are told, be fixed by positive evidence concerning SVO order. Another parameter concerns one of the base rules (Chomsky’s numbering, p. 27):

(25) S + NP INFL VP

which specifies (for French and English) ‘obligatoriness of NP and order of the elements’. Chomsky continues (and see also 5.2.3 below):

Other languages might not require that NP is obligatory; the Semitic languages are possible candidates. In such languages, putting aside questions of order, the base rule would then be not (25) but (33):

(33) S --t (NP) INFL VP

The choice between (25) and (33) is a choice with regard to a certain parameter of UC?: namely, obligatoriness of subject in syntactic structure. In addition there are choices with regard to ordering of the elements.

Thus far it seems quite clear that specification of ordering in the base is part of the component (iia). This would seem to be essential because if the base were not ordered then (iib) would have no meaning and the output of (ii) could not be considered syntactic. It


might be possible to redefine (iib) to operate on structures rather than strings, in which

case (iia) need not furnish an order, but then (iib) still does not output a syntactic string.

However, the role of the categorial component in the base is, apparently (p. 31), best reduced to a minimum. ‘It will simply express language-particular idiosyncracies that are not determined by the lexicon’; and a little later we find:

Exactly what properties of the categorial component must be stipulated in a particular grammar is a question to which we return; perhaps such properties as order of major constituents, insofar as this is not determined by lexical properties and other principles of grammar.

The projection principle (to which we will return) is responsible for this reduction. Nonetheless, it is clear that order (‘of major constituents’) is considered a parameter, and specification of this is part of the role of the categorial component.24

The discussion becomes a little more complex with the introduction of Case. ‘Case is assigned to NPs by virtue of the configurations in which they appear. . .’ (p. 49). (This is a structural definition, it does not relate to the order of the constituents.) But the situation is confused because we are asked to consider (p. 94):

Suppose that Case-assignment for English observes a condition of adjacency; that is, Case is assigned by V or P to an adjacent NP, and if an adjacent NP has been assigned Case, to the next NP. But Case-assignment never ‘skips-a-category’ in a string. Then the properties. follow, as well as the fact that adverbs and particles cannot be interpolated between verb and object in English.

. Assuming this condition. . for Case-assignment, it is unnecessary to assign order to the compiements in a lexical entry or in the rules of the categorial component of the base. Unwanted orders will violate Case theory, or the form of it that applies in English.

The violations will be ‘detected’ or blocked, at S-structure, or even by the Case-filter in the PF component.

The ordering of constituents in English is effectively accounted for by two types of mechanism: a base rule (25) determines the SVO order, and a filter (such as the Case-filter) which blocks unacceptable products of an unconstrained generative mechanism.

This seems to offer the worst of both worlds. Ordering in the base is unacceptable for reasons given above (5.2.1) and the filtering out of over-generated but ill-formed products would seem to run counter to the generative spirit. Furthermore, both criteria (at least, for English, the example discussed) clearly express a presupposition that concatenativity is the way to talk about order.

5.2.3. Chomsky briefly mentions (p. 128) the possibility that ‘Classical Arabic, with VSO structure’ has a “kind of ‘discontinuous VP”‘, but this is not discussed in any detail. The possibility rests on the notion of co-indexation of the components of discontinuous constituents, the implications of which Chomsky seems to have missed; it would allow him a way out of all ordering specifications in the base (something he seems keen to achieve). He suggests that the notion has no serious implications and that his analysis isn’t much changed. This might only be the case if the discontinuous components of a constituent are restricted in their order, that is, if the constituent has an underlying order.

It would appear that underlying Chomsky’s approach-whether in Aspects or in LGB- are two presumptions. One is that concatenativity is a structural universal in all languages (this may be a misreading of the psychophysically forced semiotic constraint on the use of sequence). The other is that syntax is a structural universal. Together these imply that all languages are necessarily ordered for grammatical reasons, and that if psychophysically forced sequencing did not exist we would nonetheless express grammar through sequence. This would seem to be a continuing theme in Chomsky’s work, and so Curry’s criticisms are as valid today as they were 25 years ago.


Before proceeding to look at other theories it is necessary to examine again the notion of constituent. We might want to consider that in the general case continuous constituents need have no specification for the order of their sub-components. However, we should then note that in a hierarchically organized structure composed of such constituents the structure imposes constraints on the order of the terminal elements; in such systems word order cannot be completely random. Completely free word order, whilst it does not require the abandonment of the notion of constituent (these can be orderless and discontinuous) does require the abandonment of any relation between constituent structure and surface structure. Constituents may turn out to be irrelevant in the grammars of some languages, although still definable. This accords with our outlook-which has at its foundation the notion that order is not a necessary part of grammar-but does not accord with prevailing linguistic philosophy-which holds that grammar must in all cases account for order. In fact, we might consider that our framework releases us from the obligation to consider constituents as essential grammatical components.

5.2.4. Marantz (1984), working very much in the same vein as Chomsky, presents a clearer view of the way in which semantic relationships relate to surface structures. Like Chomsky, he relies upon the notion of the projection principle (p. 292):

The present theory falls into the class of theories containing projection principles. According to such theories, the syntactic relations of a sentence are projected from the semantic relations it encodes.

The theory developed has several levels, a logical-semantic (l-s) level with semantic relations and a constituent structure reflecting the hierarchial organization of semantic structures. We find (p. 41):

The linguistic evidence for semantic relations must be separated from the evidence for a level of l-s structure. One posits semantic relations because they can be shown to play an essential role in determining the syntax of sentences. One posits l-s structure as a structure because it encodes certain linguistic constraints.

This maps onto the syntactic (s) level, which (p. 46): . . . stands between l-s structure and surface structure. As l-s structure encodes the logico-semantic relations between constituents of a sentence, so s structure displays the grammatical relations between constituents.

. . To each l-s relation and constituent type of l-s structure there corresponds a grammatical relation and constituent type of s structure; that is there is a one-to-one-type correspondence between semantic and grammatical relations and constituent types.

In his view these levels and structures are universal (p. 69): No matter what the sentences of a language look like in terms of the ordering of constituents or phrase structure regularities, the language will have s structures and l-s structures like those described.

But, as regards the relation between surface structure and s structure, we are told (lot. cit.): Though the theory makes claims about constituency in the syntactic analysis of sentences, it does not, as thus far developed, imply anything about constituency in the phrase structure of languages. For example, every language has s structure VPs (grammaticalizations of predicates), but a language may lack phrase structure VPs. I have assumed that the surface of a sentence in a given language, like the other syntactic levels in the present model, consists of a list of constituents and relations accompanied by an associated constituent structure tree.

Despite this announcement of independence between s and surface structures the argument develops within a few paragraphs into something quite different. From a statement like (p. 70):

Unlike the constituent structure trees of l-s and s structure, the ordering of elements within a surface structure tree is significant and is phonologically interpreted.

we move in the next paragraph to: The list of constituents and relations at surface structure is constrained not only by the mapping relation between s and surface structure but also by the relation of Move Alpha. Basically, Move Alpha is the relation between a constituent bearing a relation not mapped from s-structure and a trace standing in a relation that is mapped from s structure.


Of course, Move Alpha is part of the eventual mapping because it is structurally circumscribed, not random, in its valid application (see 5.2.5). The next paragraph completes the account:

The possible surface structures for a given language are determined by the rules mapping from s to surface structure. In a highly configurational language, s structure Government (i.e. grammatical relations. . .) is expressed in surface structure government and in linear order-in certain types of structural relations within a constituent structure tree. In the so-called nonconfigurational languages, s-structure Government is expressed via case marking and agreement, rather than structural government. Thus the mapping between sand surface structures places fewer demands on the constituency of surface structure, allowing for more freedom in the ordering of words.

It appears that Marantz, like Chomsky, is unwilling to relinquish the generality of constituency or to entertain the idea that the order of words in non-configurational languages could be entirely random (from a grammatical point of view). This is not entirely surprising, as we shall see below (5.25).

If any notion of surface structure constituency is adhered to (within the general X-bar theoretic notions of constituency Marantz invokes for l-s and s structures) there is an implication of partial ordering, because discontinuous constituents are not tolerated. Marantz discusses the need to specify a requirement for adjacency (deciding in favour) in order to account for certain phenomena in French (p. 72):

forms like du (from de + la) and au (from a + le) seem to require the postulation of a distinct adjacency relation.

But this cannot be read as implying that the ‘proximity’ or ‘locality’ relations obliged by structural relations are not also restrictions on the randomness of ordering. That is, we must not lose sight of the fact that regardless of specific claims about adjacency the existence of continuous constituents forces a partial ordering.

Marantz’s account is thoroughly structural-one might almost characterize it as underlying structuralism tempered by the projection principle. He justifies l-s structure as follows (p. 42):

I wish to claim that the only purpose of a structural representation of l-s structure-for a distinct level of analysis called l-s structure-is to impose theta-criterion-like constraints on semantic relations. I reject the G-B version of the theta criterion entirely, relying on independent constraints to derive the same effects. There are constraints on the ability of constituents to bear multiple semantic roles, but those constraints may be encoded in restrictions on the structural representation of semantic relations.

This follows an argument to the effect that constituent structures automatically achieve a useful constraint-the prohibition on ‘a given nominal’ serving:

both as the logical object of a verb and as the logical subject of the predicate that this verb heads. If it did bear both these relations, the nominal would have to appear in two positions in the constituent structure representation of l-s structure simultaneously. . But a given item cannot be in two places at the same time.

This is only a problem if one assumes a certain sort of structural representation. The argument is effectively that duplicative nominal reference (we are dealing with the semantic end of things) is undesirable, which is just as well because the notation cannot cope with it. The notation captures, or expresses, or represents, the constraint. But what then of reflexive constructions (which Marantz does not discuss)? Consider the semantics of the following examples:

(23) I pinched myself. (24) I pinched the man. (25) I pinched myself on the arm. (26) I pinched the man on the arm. (27) I myself pinched the man on the arm.


(28) I pinched myself and the man, on the arm. (29) I pinched myself, and the man on the arm.

It is surely not possible to argue against the reading, of all these examples, which has the referent for ‘I’ and the referent for ‘myself’ as one and the same person. This is as obvious (for me) in (27) as it is in (28/g). So we can find examples with ‘a given nominal’ serving as logical object and logical subject. Furthermore, the non-linear formalism can capture such structures because being ‘in two places at the same time’ is not structurally impossible. We have already seen, in the case of the non-concatenative account of Arabic morphology, how it is possible for a single underlying morpheme to be associated with discontinuous surface elements.

Within Marantz’s three level theory there is a double strand composed of argument structure and role assignment (p. 48):

I have introduced and argued for two basic semantic relations, that between an argument-taking item and its arguments, and that between a semantic role assigner and its semantic role assignee. According to the hypothesis of a one-to-one relation between semantic and grammatical relations, there should be two basic grammatical relations, that between a syntactic argument-taking item and its arguments and that between a syntactic role assigner and its syntactic role assignee.

As we have seen, non-configurational languages do not give (much) surface expression to the structural strand, and it would seem reasonable to suppose that in such languages the role assignment strand would take the weight of accounting for surface forms. This does not seem to be contemplated. We are told that in regard to l-s and s structures:

It is a hypothesis of both Government-Binding theory and the current work that there are constituent structure constraints on the assignment of semantic and syntactic roles. However this is a substantive hypothesis that cannot be derived from the characterizations of role assignment and argument structure within the theory.

Furthermore, in the discussion of surface structure we find that the expected mapping of role assignment onto case and agreement is not pursued. Instead we are offered a complex direct grammatical link between l-s structure and surface structure-with s structure required (perhaps even influential) but ultimately not directly involved. This allows ‘non- configurational’ to be interpreted as ‘structurally uninfluenced by s structure’ but this does not mean that s structure is not necessary, or that the surface is without structure, because l-s structure is intimately involved with both. This permits, for example, the projection principle to apply universally. The account of configurational languages is then very straightforward-the projection principle furnishes structure for l-s and thus for s and eventually surface structure levels. For ‘so-called nonconfigurational’ languages the surface form is not derived, or mapped, from s, but in a complicated way from l-s, and is therefore nonetheless a structural projection from the lexicon. Nonetheless, s structure may be influential in that constraints formulated in s structure can (presumably) shape the non- configurational expression of the correspondingly constrained l-s structure.

5.2.5. It is appropriate here to look more closely at the projection principle. Chomsky’s LGB formulation (p. 29) is:

Representations at each syntactic level (i.e. LF, and D- and S- structure) are projected from the lexicon, in that they observe the sub-categorization properties of lexical items.

This is restated, more complexly and in accord with various observations relating to 8- marking (p. 38), but we are assured (p. 39) that:

. it suffices to have clearly in mind the intuitive idea it is intended to express: that representations at each of the three syntactic levels are projections of lexical properties.

Marantz (1984), as we have seen, puts the projection principle to good use, and in his


concluding chapter he discusses ‘theories with projection principles’, as well as theories without such principles. He writes (p. 304):

projectionless theories provide no principled account of the relation between compositional semantic relations and structural relations.

Marantz does not discuss Hale’s (1983) attempts to provide a projection principle based treatment of the non-configurational language Warlpiri. Hale produces a restricted version of the projection principle:

If VERB selects ARC at Li then VERB selects ARG at Lj (where Li, Lj, range over the ‘levels’ LF, D-structure, S-structure in the syntactic representations of clauses).

He then goes on to argue for a Configurationality Parameter in UG, which he states as follows:

(a) In configurational languages, the projection principle holds of the pair (Lexical Structure, Phrase Structure).

(b) In non-configurational languages the projection principle holds of Lexical Structure alone.

Whilst (a) is straightforward, (b) appears to be meaningless. The interpretation we are offered is:

The CP, in short, determines a tight connection between LS and PS in configurational languages. But for non-configurational languages, by contrast, the CP does not determine any connection at all between LS and PS (leaving that to other principles of grammar).

It emerges from the discussion thus far that desperate attempts are being made to provide a universally valid account of the way languages work, an ‘underlying structure’ account based on X-bar theory and associated notions of constituency and concatenativity. The notion of configurationality is invoked as a way of having one’s cake and eating it. Non- configurational languages are explained as being, in effect, underlyingly configurational and thus a uniform structural account can be made to work for all languages despite surface appearances to the contrary [for, as Chomsky reminds us (p. 28) ‘a survey of surface forms is quite uninformative’]. Yet we are also reminded by Chomsky (p. 128) that the achievement of free word order cannot be the result of abandoned application to Move Alpha:

He [Hale] has also suggested that in non-configurational languages there are no empty categories, hence no transformational rules in the syntax, assuming trace theory. Hale suggests that Japanese is essentially of the non-configurational type; in fact, as has often been noted, there is little if any reason to suppose that rules of the type Move Alpha apply in Japanese.

We are left with over-generation and filtering as means of achieving the sort of word order found in Japanese, 25, or over-generation in general as a way of achieving genuinely free word order. In either case it is not entirely clear that invoking the projection principle has achieved anything.

However, within the general terms of this study there is a more serious reason for concern over the projection principle. We have seen that via the projection principle an appeal can be made to include in UG an X-bar theoretic constituency account of grammatical structures, with perhaps a Configurationality Parameter to fix things for odd languages like Sanskrit or Warlpiri. This amounts to a commitment to concatenation of continuous constituents, and thus to the notion that ordering is a necessary property of linguistic structures.

To my mind this reveals unnecessary and partisan fondness for theoretical uniformity in the face of counter-evidence. Discontinuous constituents are evidenced in Dutch (and perhaps more widely, cf. the English examples given in 5.2.1). Furthermore, Sanskrit, and to some extent Warlpiri, has free word order. (And there are, doubtless, other examples too.)

It would appear that the conventional grammatical components-morphology and syntax-have been replaced by a generalized syntactic account of everything, even (underlyingly) of morphological factors which are so predominant in non-configurational


languages. It is as if the projection principle in fact reflects the projection of syntactic structures onto all grammatical theorizing.

By contrast, the non-linear formalism discussed earlier, with its base in morphologica and phonological enquiry, offers a way of embracing with equal ease rigorously configurational accounts [canonical configurational languages like Chinese (Hale’s example)] with non-concatenative, and possibly simultaneous, arrangements of morphemes expressive of semantic relations. It is noteworthy that regardless of the nature of the representation selected for semantic relations the non-linear formalism permits the simultaneous expression of non-concatenatively organized entities (i.e. discontinuous constituents)-all the way down-as readily as the sequential expression of concatenated continuous constituents- all the way down-or any mixture of the two. There is no need to presuppose that one of these styles of arrangement should depend upon the other. Rather, we should work toward a rather simple set of constructional principles which are not motivated by the need to make one style of arrangement do the work of the other. Alongside concatenative grammar we should accept non-concatenative grammar, with a single notational formalism for both. In this way the more immediately accessible notions of linear order of uninflected morphemes, and random order of inflected morphemes, can co-exist without the need to presume that one is somehow more ‘basic’. I can do no more here than point out how and perhaps why it is that conventional approaches to theories of grammar are unnecessarily restrictive in their theoretical basis (and hence elaborate in their theoretical formalisms?). Non-linear formalism will be developed and will doubtless reveal new simplicities. It is not clear that the projection principle will have a role in such a form~ism.

5.2.6. As regards linearization-our starting point-we are not yet done. We will look briefly at three other theories -GPSG, FUG, FG-which reveal biases of the type already discussed (and thus they provide further illustrations), but this list is clearly not exhaustive. Furthermore, there is an aspect to sequencing which was raised much earlier but which so far has not been mentioned in connection with any specific theory of grammar, This is the notion that the derivational process itself is organized in time. In our discussion of this (5.2.7) we will come to recognize that the rather non-specific claims above, concerning the independence and variable admixture of two styIes of arrangement, can be given some substance.

5.2.6.1. Generalized Phrase Structure Grammar (Gazdar et al., 1985) is an approach to grammar in which a clear distinction is drawn between structure and linear order. The two components of the theory which reflect this distinction are Immediate Dominance rules and Linear Precedence statements. Convincing examples are offered which show that some sets of phrase structure rules are more concisely and perspicuously captured in ‘ID/LP format’. The authors offer a set of rules such as might be produced in accounting for Makua, and these are reproduced here (with numbering added):

Z!) (iii) (iv)

I$ (vii) (viii)

VP -+ v VP-rVS VP --) V NP VP * NP V VP -t NP V NP VP + NP NP V VP -* V NP NP VP-tVNPS

fix)

E!) (xii) (xiii) (xiv) (xv) (xvi)

VP-tVSNP VP+NPVS VP + NP V PP VP + PP V NP VP-‘PPNPV VP -+ NP PP V VP + V PP NP VP -+ V NP PP


They point out that this ‘can be replaced by a more compact ID/LP formulation’:

:,y (ii) (iii) (iv)

:s

VP-tV VP -* V, NP VP -t v, s VP + V, NP, NP VP * V, NP, PP VP -t V, NP, S

;; v << s

The Linear Precedence statement captures the generalisation that Vs must precede Ss. Gazdar et al. go on to point out that if (xi) in the original set were of a different form, say:

(ix) ’ VP z S V NP

then the set of rules (i) ’ -(xvi) ’ could not be reformulated in ID/LP format. They note (p, 49):

There is a formal property that distinguishes grammars [such as (i)-(xvi) from (i) ’ -(xvi} ‘I. It is that in [the former] the set of expansions of any one category observes a partial ordering that is also observed by the expansion of all other categories. We will refer to this property as the Exhaustive Constant Partial Ordering (ECPO) property. A CF-PSG can be put into ID/LP format if and only if it has the ECPO property.

. . Exhaustive Constant Partial Ordering is a very astract property of grammars. As the examples above suggest, many plausible-looking sets of CF-PSG rules do not possess it. Indeed, it is a statistically unexpected property. If we consider the set of possible grammars defined on the same vocabulary as [(i) ‘-(xvi) ’ 1, with the same number of rules, and the same upper bound on the size of rules, then only a tiny proportion of this set will have the ECPO property (because from any grammar that has the ECPO property a large number of distinct grammars could be made by varying one or more orderings within specific rules in a way that destroyed the ECPO property). It would therefore be interesting and surprising if ECPO turned out to be a linguistic universal. Clearly, anyone adopting ID/LP as their format for stating grammars, as we do, k committed to the rather strong claim that it will turn out to be a universal.

The discussion above is presented at length simply because the conclusion apparently reached in the final two sentences represents something of a non-sequiter. It is clearly the case that any attempt, such as they make, to treat immediate dominance and linear order as separate components, is to be considered a step in the right direction. However, the authors are so committed to a linear concatenative framework that their logic slips. Adopting an ID/LP format does not commit one to accepting ECPO as a universal, simply because the use of the format does not force every language to have any Linear Precedence, let alone one which conforms to ECPO.

The format is independent of ECPO, or to put it differently, ECPO is a separate additional constraint because Linear Precedence statements could have a form which does not conform to ECPO-for instance, in terms of adjacency. An example could be the set of PS rules (i)’ -(xvi) ’ where the LP statement might be ‘PP, but not S, may separate V and NP’26. In fact their motivation is explicit, for we find (p. 47):

. . . treating immediate dominance and linear precedence separately is an idea with a long history. Many linguists have suggested something of this sort. But in fact none of the previous work does exactly what we are proposing here. We are not proposing any nonlinear levels of syntactic structure or nonlinear stages in the derivation of linearized structures. Rather, we wish to separate dominance and precedence in a set of statements that directly determine linearized structural representations.

Although they note the work of Curry, Staal, and others, a very clear distinction is drawn between on the one hand the value of separately representing structure and linear order, and on the other the need to contemplate unordered structures. GPSG embraces ID/LP format but does not admit the possibility of free constituent order, free word order, or discontinuous constituents. Yet Curry’s critical comments remain valid because GPSG does not comprise separate tectogrammatic and phenogrammatic components.

In this respect Falk’s account (1983) is equally unsatisfactory, although somewhat more attention is paid to the problems posed by free word order languages. Falk argues that


free word order is actually free constituent order and linear precedence is then restricted to ‘within’ constituents. Thus for Japanese Falk concludes that within constituents the order rule is just Head First, but with ‘almost total freedom of constituent order’. Falk also discusses Hale’s:

. . . bifurcation of the world’s languages into two camps:‘)<-bar’ languages and ‘W-star’ languages. . . W- star languages, on the other hand have the rule:

E+W

(i.e. an expression consists of a string of words).

This earlier account (from Hale 1979) is not favoured in Hale’s more recent work (1983) where we find the concern is rather to avoid over-attention to phrase structure accounts.27 Ultimately, in my view, Hale does not succeed in avoiding phrase structure bias.

The conclusion to be drawn from the above discussion is simply that Curry’s original insight has either been misunderstood or ignored. Either way the distinction between tectogrammatics and phenogrammatics has not been sufficiently widely discussed. We are left with the overwhelming impression that a great deal of ingenious theoretical enquiry is motivated by the desire to show that grammatical structures are, underlyingly, constituent structures (and hence, inevitably, partially ordered) and even that these are part of UG. It is worth pointing out here that although our overall enquiry is motivated by the exploration of the implications of independent motivation for sequence, the specific criticisms made against grammatical theories such as GPSG rely upon the detection of internal inconsistencies, something to which our semiotic framework sensitizes us.

5.2.6.2. A completely different type of theoretical approach is motivated by functionalism-the belief that some social or general communicative purpose motivates linguistic structures, and that we can only look for explanations in this way. For example, Kay (1985) writes (p. 251):

Language is a system for encoding and transmitting ideas. A theory that seeks to explain linguistic phenomena in terms of this fact is a functional theory. One that does not misses the point. In particular, a theory that shows how the sentences of a language are all generable by rules of a particular formal system, however restricted that system may be, does not explain anything. It may be suggestive, to be sure, because it may point to the existence of an encoding device whose structure that formal system reflects. But, if it points to no such device, it simply constitutes a gratuitous and wholly unwelcome addition to the set of phenomena to be explained.

Kay then sets out to offer a theory-Functional Unification Grammar-of which he says (p. 253):

The claim that this theory makes on the word ‘functional’ in its title is therefore supported in three ways. First, it gives primary status to those aspects of language that have often been called functional; logical aspects are not privileged. Second, it describes linguistic structures in terms of the function that a part fills in a whole, rather than in terms of parts of speech and ordering relations. Third, and most important for this paper, it requires its grammars tofunction; that is, they must support the practical enterprises of language generation and analysis.

In FUG, therfore, we can expect to find a clear alternative to the sort of preoccupations with concatentative constituent accounts seen earlier. However, we are ultimately disappointed.

Kay’s proposal, in essence, is (p. 255): . . functional unification grammar knows things by their functional descriptions, (FDs). A simple FD is a set of descriptors and a descriptor is a constituent set, a pattern, or an attribute with an associated value. I shall come to the form and function of constituent sets and patterns shortly. For the moment, we consider only attribute-value pairs.

The list of descriptors that make up an FD is written in square brackets, no significance attaching to the order. The attributes in an FD must be distinct from one another so that if an FD ‘F’ contains the attribute ‘a’ it is always possible to use the phrase ‘the a of F’ to refer unambiguously to a value.


Unification of FDs is the carefully defined process of blending sets of descriptors-the aim being to work up to the appropriate FD for a language (i.e. a grammar). Yet it seems that the notion of Pattern (the specification of linear order) does not look general enough. Once again it emerges that concatenation is assumed underlyingIy (p. 263):

The purpose of constituent sets and patterns is to identify constituents and to state constraints on the order of their occurrence. . . The patterns are templates that the string of immediate constituents must match.

One problem is that if two FDs are to be simply unified the terms or symbols given as the value for a given common attribute (say ‘Pattern’) must be compatible. Thus if an FD includes:

Pattern = (subj verb) and another includes:

Pattern = (verb obj) unification will give:

Pattern = (subj verb obj). Simple unification fails, however, if the two values are incompatible, for example, the Patterns ‘(subj verb)’ and ‘(verb subj)’ cannot be unified simply. Complex FDs result where incompatible Patterns are given as part of the alternative FDs (given as parts of the complex FD). This is shown as:

yli: : ~~~~~~~~~1

! r;/ :;1

where the curly brackets signify alternatives.

It is a rule of unification that within an FD an attribute (i.e. $, which is read as Pattern) can only have a single value. Thus complex unification requires a multiplicity of FDs as alternatives. Of course, FDs which are components of FDs may have ‘local’ values for attributes differing in kind (and thus incompatible in a different sense) with values given in the more ‘global’ FD. So the following is unremarkable:

1

$ = (topic contrast) 1 r $ = (verb. . . adverb)! : t I where the constituents specified as ordered are different properties (see Karttunen and Kay, 1985, p. 291). Difficulties arise when complex unification is attempted because it may make no sense to suggest that, say, a syntactic specification of order is an alternative to a pragmatic specification, and other than embedding (which implies hierarchical precedence) there is no way to unify Patterns specified in different terms. In fact, the example given by Karttunen and Kay of a fragment of Finnish comes unstuck exactly for this reason-they list within a single FD the following two Patterns (p. 296):

$ = (._. FiniteVerb. . . TensedVerb. . . MainVerb. . .) $ = ((#[New = Noj)#l)

where the second ‘incorporates the idea that NPs introduce new discourse referents only in the last position’ by attributing ‘the property [New = No] to all but the last immediate constituent’, an ‘unsatisfactory solution, but it serves here as an example of a non-trivial pattern’.

No mechanism is provided for saying that both Patterns are specified simultaneously at one and the same ‘level’, that is, in a single FD. The implication is that serial organization


is itself serially organized (assuming, reasonably, that the nesting of FDs reflects the derivation, with terminal elements most deeply embedded) and that therefore simultaneous specification is ruled out. Discontinuous structures (such as verb complement structures in Dutch) seem also to be problematic, because it is not clear how the Pattern specification mechanism can cope with the non-random intermingling.

Once again we see that despite the best of intentions concerning the development of genuinely agnostic theory (in relation to presumptions about the nature of ordering) what is on offer turns out to have underlying presumptions about ordering. One basic presumption would seem to be that a complete FD (i-e. a grammar) must have a Pattern, other presumptions concern the style of ordering itself, as we have seen.

5.2.6.3. A different functional approach is offered in Functional Grammar (FG), (Dik, 1980, 1981). As before our interest focuses on expression within this theory of concepts of ordering. It is not necessary to work through complex deductions-Dik himself is quite explicit (1981, pp. 20121):

FG contains a rather specific hypothesis about linearization of functional structures. Predications are linearized by means of rules which bring their constituents into the so-called ‘functional patterns’ which in turn are based on the following language independent pattern schema:

P2, Pl (V) s (V) 0 (V), P3

In this schema, S and 0 stand for the neutral or unmarked positions of Subject and Object. The Vs indicate the possible positions of (finite and infinite) verbs. PI, P2, and P3 indicate ‘special positions’ used for special purposes, and the commas stand for breaks in intonation.

. . . The functional patterns and the rules for mapping predication structures onto them can account for those constituent orderings which are determined by the syntactic and the pragmatic functions of constituents. It will be shown, however, that in many languages categorial differences between constituents interfere with these functional determinants of constituent order. In order to account for this in a general way, I shall develop the hypothesis of a language independent preferred order of constituents (LIPOC). According to LIPOC, preference is in principle given to orderings in which categorially less complex constituents precede catgorially more complex ones, with clitic pronouns as the least complex, and complex subordinate clauses as the most complex constituents.

However, this is not the whole story. The process of making an utterance requires the construction of predications and the appropriate filling of argument slots (in this sense the theory seems to incorporate a projection principle). A Semantic Function Hierarchy governs the order in which arguments are assigned to predicates, and in another clear statement concerning order we find (p. 176):

We interpreted Subj and Obj assignment as a method of defining a perspective on the state of affairs designated by the predication, starting with one of the entities involved (the Subj), through a second entity involved, (th Obj), to the other entities involved. It stands to reason, then, that this perspective is mapped onto the linear structures of the sentence in the order Subj-Obj-Other rather than in some other order.

FG, then, is rather similar to accounts discussed earlier. The manner in which lexically specified predi~te-argument structures are filled out is functional, but the approach is syntactic-it deals with concatenative organization of continuous constituents. We might note here that in terms of the semiotic approach I am taking functionalism is quite acceptable-one might almost say that my approach is summarized by the question ‘How might communication function?‘. More interestingly, perhaps, it also seems that we can accept that functionalism in Dik’s sense provides some constraints on, and motivations for, token sequences. What is wrong, in my view, is to incorporate such things into theories of grammar-we should be seeking to avoid a synecdochical view of the significance of grammar in linguistics. Pragmatic and semantic issues, along with, say, other cognitive or stylistic factors, phonological aspects, in fact anything which we might consider distinctive

about communication, combine with grammar to constitute the subject matter of linguistic


theory (in the sense linguistic behaviour or language use). It is only when we cut the domain of grammatical theory down to a sensible size that we can envisage linguistic behaviour as being explicable in general cognitive terms. Our semiotic outlook is a good alternative to the myopia which afflicts so many linguists.

5.2.7. The FG developed by Dik gives explicit indications about the way in which the derivation of the form of an utterance maps onto its form. The Subj-Obj-Other order of assignment is reflected in surface order (other orders being exceptions requiring explanations).

Intriguingly, this topic is explicity discussed in Marantz (1984), in terms of Subject-Object asymmetries which arise from asymmetric predicate-argument structures (p. 23):

. . . constituents are assigned their semantic roles in the present theory; they do not receive their roles by virtue of occupying slots in predicates.

. . Since P-A structures of verbs are functions from arguments to predicates, which arguments one inserts into P-A structures determines what predicate the function will yield. As the predicate assigns the logical subject its semantic role, choice of arguments for P-A structures determines the semantic role of the logical subject.

This can be read as ‘subject last’ assignment, something which, we learn from a discussion of a criticism by Bresnan (see Marantz, 1984, p. 28) is also found in ‘Dowty’s theory’. The detail of the argument put forward by Marantz (or for that matter by Dowty) or of Bresnan’s criticism, is not relevant. It is enough that some theories seek to say something about the order in which details are supplied in derivations of surface forms, and one, at least, seeks to match this directly with surface order itself.

In terms of our general discussion the serial ordering, or otherwise, of the derivational process is considered only in the light of considerations of generativity. Such ordering seems in fact to be a requirement of generative mechanisms, whether these involve networks or recursive rules. Without some ordering the notion of derivation and generation collapses and we are left with enduring and atemporal equivalences (learnable in the best behaviourist manner) between ideas and sound patterns. Specific details of such ordering-such as subject first-are open to debate but even more worrying is the presumption that the ordering is semiotically available. Dik offers no reason for suggesting that the sequential property of a derivation is itself available for semiotic exploitation; the process may be inscrutable.

If we accept that derivational ordering might map onto surface order we are faced with the additional problem that the timing may not coincide. For the mapping notion to make sense we must stipulate that the derivational process is synchronized with the output process. If it is not there must be some sort of buffer store, in which case the argument for mapping virtually disappears (because buffers are good places in which to map one order onto a different one; they contain atemporal representations). Or else, yet again, one ends up saying something very precise and not very plausible about the process of producing utterances, namely, that such processes are filtered through a last-in-last-out shift register arrangement which maintains order but manipulates duration. Such proposals look unnecessarily restricted to fixed order spoken languages. If the derivation is slow we might get observable psycholinguistic effects, but if it is fast we may not be able to learn anything. If a language has free word order it is clear that derivational order cannot be mapped onto surface order at all (without some rather bizarre assumptions). If a language has partially fixed order then both theoretical research and psycholinguistic experimentation might throw light on whether or not a mixed system (see 5.2.5, 5.2.6) can be arbitrarily mixed. In addition, it is noteworthy that in this sort of account the attempt is being made to find


a structural reason for surface order, rather than to consider structure and order as separate factors. So we end up with our familiar complaint, that one style of grammar (syntactic) is presumed to be basic.

6 In this study I have shown why we should consider sequencing and de-sequencing as

fundamental aspects of all communication behaviour, motivated by psychophysical constraints. I have also shown how it is that a wide range of grammatical theories, although preoccupied with linear order, fail to reflect any real underst~ding of the fact that ordering may only be a property of linguistic communication by virtue of the psychophysical realities of the production mechanisms (especially). Sequencing need not be linguistically relevant, but it is available for semiotic exploitation and so can be expected to be given linguistic relevance. What is not at all clear is that we should entertain any expectation that a uniform manner of semiotic exploitation will be found to underlie all languages (or even any language). Yet this is what seems to be assumed by theory builders.

To my mind Curry’s criticism can be restated in terms of the need to separate grammatical structural principles from the linguistic and communicative exploitation of the psychophysically motivated requirements of sequencing and de-sequencing. What appears to be wrong with current theorizing (in general) is the influence of surface form (stereotypically characterized as sequences of words) on structural concepts; it is almost as if the underlying belief is that underlying all languages are (typologically) analytic rather than synthetic-and SVO as well!

Non-linear phonology offers the prospect of a notation with which a linear structure can be characterized as the linear or simultaneous combination of many different influences and structures yielding an output which, although sequenced at some levels, does not have to be sequenced everywhere. Discontinuous constituents are in no way exceptional. Concatenative or simult~eous output (in terms of muscle patterns} can also be contemplated (e.g. we have separate control of larynx pitch and word order). One of the linguistician’s tasks is thus to characterize the manner(s) in which sequencing and de-sequencing are exploited to convey grammatical structures, structures which may be non-concatenative.

6.1. We can put some detail into the above outline. We can envisage the process of sequencing-taking a cognitive entity and yielding a muscular patterned output-as comprising the following two processes.

Semantic entities and structures are mapped onto grammatical entities and structures- where ‘entities and structures’ reflects the cognitive duplexity found generally (whereby, for example, we can consider a VP to be an entity and/or a structure depending on our viewpoint, and likewise a ‘noun’ may be considered a nominal entity but its morphology may reflect semantic and/or grammatical structure). This mapping represents the interface between individual, idiosyncratic and circumstantial cognitive entities on the one hand and linguistic cognitive entities (much more ‘socially’ defined, and thus less individualistic)28 on the other. It is the linguistic cognitive entities which are eventually externalized and it is the business of grammar to provide the structural coherence which is necessary if the sequencing process is not to be anarchic. Notice, the grammar does not provide the sequencing-that is motivated elsewhere-but it facilitates the exploitation of sequencing in such a way as to ensure that complex n-dimensional representations can map onto sequences in a recoverable manner. We can therefore consider the output of the grammatical


phase to be sequencible items, not sequences, where an item might be a sentence, a phrase, a word, a morpheme, or a phoneme.

Alongside this cognitive mapping we have the process of sequencing itself. Recall that the sequence of tokens is available for semiotic exploitation. Independently of the grammatical provision of those tokens or items we have to consider what it is that we might want to map onto a sequence of items. The nature of the sequence is independently specifiable because (a) there is nothing about grammar which necessarily provides specification of temporal order (grammar provides orderable items); (b) sequentiality is psychophysically, not linguistically, motivated. All the obvious ordering influences are in fact found. Order can be specified semantically, in the sense that ‘natural order’ or ‘event structure’ can surface in the order of items, and this may also surface in an order such as the Semantic Function Hierarchy. Functional specification of order can surface as theme- rheme order, for example, and this (like perhaps many order influences?) has cognitive/communicative overtones-it is ‘helpful’ to organize communication so that the topic precedes the comment. Order can also be specified grammatically-grammatical cognitive structures are just like any other and can ‘claim a slice of the action’, in terms of specifying sequence, alongside other cognitive structures. But it is in no sense grammatically necessary that grammatical influence on ordering should be found.

6.2. What is intriguing is that the ‘slice of the action’ metaphor exactly fits the formalism of non-linear phonology. The formalism permits (or to be precise, it looks as though it can be made to do so with little effort)29 the influence of many different domains (i.e. half-planes) on the final ordering. These influences may be ‘competitive’, in that the items being ordered are the same for two or more different influences. Word order is obviously influenced by separate factors. Also, ordering influences may not be competitive, if the items being ordered are very different one from another-so word order can be specified independently of the ordering of morphemes within the word (cf. the account of Japanese above, 5.2.5).

6.3. The non-linear formalism is exactly what is required to capture the complexity of the specification of ordering. Language typology, as hinted above, takes on new significance in that through discovery of trends and patterns (see e.g. Greenberg, 1966; Hawkins, 1983) we can uncover the cognitive, pragmatic, social, contextual etc., influences at work. My own suspicion is that in fact these influences may themselves be cognitively constrained. It may even be possible to detect the influence of a general ‘head-first’ constraint on communication’s exploitation of order-in that ‘head-’ can be read as theme-, agent-, head- (in ‘head-modifier’, where heads are nouns (NP), verbs (VP), adpositions (adP)), or lexeme- (in ‘syntactic’ morphology, where the tendency is for grammatical suffixation, see e.g. Selkirk, 1982). It also seems probable that we can profitably look at other phenomena through ‘non-linear’ eyes. For example, agreement mechanisms look like prime candidates for non-linear description. Which is to say, we might consider agreement to be the discontinuous surface expression of underlying morphology.

6.4. The programme for further research is now clear. We need to develop a non-linear formalism, and non-linear phonology looks like an excellent starting point. We need to do theoretical psycholinguistic work to provide more precise specification of cognitive ordering influences. We need to do further typological and theoretical work, for example on agreement, and possibly also experimental work, to provide data for the psycholinguist. Work in theoretical psychology is also needed to provide additional specification of the


mechanisms of grammar. We need to develop the semiotic framework to provide better specification of the role of grammar in linguistic activity. And within this range of efforts we can locate the efforts of theoretical linguists who should be trying to formulate grammatical theories which are underlyingly non-concatenative, because if there is one presumption to be made concerning underlying order in grammar it is that there isn’t any.

7 Our conclusion is simple enough. We must work toward a theory of grammar devoid

of any presumptions of concatenativity, continuity or sequentiality-whether explicit or implicit. Only by understanding the general semiotic and psychological significance of linearization can we abstract from grammar the obligation to offer explanations in that domain. It seems clear enough that with a full appreciation of the significance of linearization must come a recognition of the need to re-examine existing theoretical work, not just because it may be missing the point but because the formalism used may be based on a misconstrual of the phenomena (as one might suspect of X-bar theories, for example, where the formalism is derived from a model of ordered surface structures). In this sense, then, we can go beyond Curry or Staal, and advocate a much more self-conscious theoretical style in which formalisms are examined in relation to the phenomena. One might look again at FUG (an example, surely amongst many) where purely formal restrictions render very difficult something which should not be so-the simultaneous blending of different ordering specifications which the notation obliges us to consider incompatible. FUG exemplifies the difficulties we face in not being meta-theoretically broad-minded enough.

It is my view that the time is ripe for a return to the idea of studying Human Communication, as an interdiscipline if necessary, because we need to look again at the phenomenon. This is not an irrelevant comment. Information theoretic models and von Neumann computer architectures-not to mention the linear organization of writing systems, for logic as much as for English-have squeezed our thinking into a sequential mould. I think that this is especially true of our thinking about language and communication. Non-linear phonology offers us a way of breaking out of that mould, as I believe I have demonstrated in this preliminary study.

NOTES

’ The term non-linear phonology is chosen because, unlike the frequently used alternatives-pluri-linear phonology, autosegmental phonology-it expresses most directly the concept of non-concatenative structures. The term non-concatenative grammar is virtually self-explanatory but a more detailed account is given below in section 5.

’ One is reminded here of the old ‘delay-line’ type of memory system in early computers-bits of data were constantly recirculated in, or through, some medium such as a column of mercury or a length of tensed wire. If such a principle (i.e. constant recirculation) were shown to be the basis of neurophysiological memory then my presumption would be unreasonable in detail. However, for this to be a significant problem for the theoretical framework being developed here we would need to be sure that the circulation time in such memory ‘cells’ (?) was linked to or governed by the timings elsewhere in the system. If the two systems (i.e. memory and sequencing/de- sequencing) were asynchronous then circulating memory would not constitute a problem.

3 There may be a change of scale.

4 We should recognize that generativity does not imply a need for a particular formalism although it does seem to imply a need for temporally structured derivational transformations. Atemporal transformations can always be contained in a look-up table of equivalences (of arbitrary complexity) in which case sequencing is simply a mapping and generativity is not available. Temporally structured derivations are, by definition, not in any table of equivalences, so generativity-the result of concatenation of derivational procedures-is assured. Thus

264 ~ILLIM H.EDM~NDsoN

generativity, although necessary, is not sufficient for the definition of an appropriate formalism. The argument is perhaps complicated (but not fundamentally altered) when we recognize that neural mechanisms have finite response times which can contribute to sequential patterning of the transformational process itself,

On a different point, my use of the word ‘transformation’ is not unthinking. To those who would argue that it is confusing because the term has a special meaning in linguistics I would reply that (a) everyday words cannot be hijacked by jargon addicts-the jargon users are responsible for any misreading or misrepresentation which their jargon may cause; (b) my intention is that the reader should be reminded not of TG specifically but of why it is so called-the underlying notion is that of transformation from some ‘deep’ structure to a ‘surface’ structure, and so I consider the motivation behind the term is not unlike the reasons for its employment here.

’ We should take note here that output sequences directed toward the achievement of some physical goal (walking, chewing, making a cup of coffee or tea, etc.) are available, but not arbitrarily, for semiotic purposes. In particular, the manner of physical activity is available semioti~ally. In this domain also the question of inherent meaning arises, both as regards the sequential aspects of the derivation and the sequential output itself. We will touch upon this again, in our discussion of signing, but space limitations preclude a full treatment.

6 I am being coy about whether the output entities are sub-entities of the input entity. They have their ‘sub-’ ness specified only by the transformation. All cognitive entities are members of the set of cognitive entities and so transformations may apply to certain sub-sets and/or may yield sub-sets.

’ It would be possible to extend this discussion deeply into the field of language learnabilty-for example, should the individual transformations themselves be ‘reversible’?, does the sequencing procedure have to be derivable from the de-sequencing procedure?

* I am aware that touch plays a significant role in some circumstances (e.g. with the deaf-blind) but is seems appropriate here to restrict our attentions to the two modalities most generally employed. Vision is employed in spoken commutation both to monitor gaze and natural gesture, and to assist comprehension in noisy conditions (by means of lip-reading).

9 The saccadic movements are abrupt and discontinuous-the changes in the point of fixation are rapid, with brief unwavering intervening fixations. More explicity directed vision, such as is achieved in response to an instruction to ‘look at X’, is similar-a rapid head/eye movement followed by ‘looking at x’ which involves small saccadic changes in fixation.

lo This point should not be missed. Movement is, I suggest, treated as quality, such as colour; it is an attribute of an object. We do see a car when we see a moving car.

” I am not sure how this can be calculated but my reasoning is to the effect that Nyquist’s sampling restriction must have some analogue in the visual system as I have outlined it-the saccadic movements constitute time samples.

I2 I have not substantiated the claim that sequencing and de-sequencing are reiated. Clearly they are to some degree, and the visual constraints on the production of signs provide empirical support for this (see below, section 2.2.1). If de-sequencing was not somehow the reverse of sequencing then evidence regarding self-monitoring and correction (like, that it takes place at ail) would require rather convoluted explanation. (See also section 1.2.7 and note 7.)

I3 See for example, the journal Sign Language Studies (published by Linstok Press, MD). Also, and the list is not ekhaustive, Deuchar (1984), Klima and Bellugi (i979), Liddell (1980), Wall et al. (1981).

I4 See e g Edmondson (1985). A more detailed account is available in an unpublished manuscript, Edmondson (198lb). ’ .

Is See for example, Bellugi’s paper: Clues from the similarity between signed and spoken language, in Bellugi and Stu%ddert-Kennedy (1980). 16

17

18

19

20

21

See, for example, Liddell (1984), and Edmondson (1986).

Or, in fact, to any other activity.

See Battison (1978), pp. 55, 56, 74, 78, 89, and Klima and Bellugi (1979), p. 76.

See Edmondson (1985).

It is not clear that this sort of comprehension is available if the material is ASL.

Clearly this mechanism has to be worked out, but it is self-evident that a form of co-indexation can be devised which would allow a spinal element to be identifiable as, say, vocalic, by virtue of having associated with it a half-plane which specifies the feature [vocalic]. In fact, this approach allows a spinal segment to be identifiable in terms of any plane or combination of planes associated with it, rather than just in terms of some pre-ordained label.

22 It is possible to imagine that psycholinguistic experiments would provide some evidence of internal ordering.

23 This may seem to go beyond Curry’s argument, but I think it does not. Curry uses monotectoni~ to refer to one-to-one mappings between grammatical structures and representations. Tectogrammatics refer to grammatical


structures, so the claim that natural languages are polytectonic should mean they exhibit mappings of the form ‘many grammatical structures to one representation’ (this is unremarkable). He also illustrates his argument with an example of the mappings which fit a ‘one grammatical structure to many representations’ definition (e.g. Puer puellam amat). This too is unremarkable.

24 See also pages 34, 39, and 41 of I&B.

*s Chomsky’s example on p. 129 makes use of English type case assignment, see 5.22.

26 See Falk, 1983.

27 See especially his Introductory Remarks, pp. 5-l 1.

** One might want to lay the lack of individualism at the door of innateness, but see also Edmondson (198la).

29 I am presuming that the non-linear formalism will turn out to have representations of hierarchial structures with different sized ‘units’ or spinal elements corresponding to, say, phonemes, morphemes, words, etc. This can be achieved via co-indexation in a way which seems clear enough-the OCP (Obligatory Contour Principle) can operate so as to (effectively) coalesce elements into elements specific to a plane (or cluster of planes), because the OCP is itself plane specific. Or to put this differently-spinal elements can carry the indices of association lines in a way which is accessible to OCP. A new half-piane can then be created (‘by OCP’) on which spinal elements are single entities as defined by con~tenative coalesence of identically co-indexed elements (as regards some other half-plane).

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issues in linearization: prolegomena for a general theory of communication

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