Language and Transformational-Generative Grammars
Examples of Integrated, Multi-set Concept Schemes (Annex 12)
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See other Examples of Integrated, Multi-set Concept Schemes. The concept scheme described here is discussed in the paper on: Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation. This was prepared for a sub-project meeting of the Forms of Presentation group of the Goals, Processes and Indicators of Development (GPID) project of the United Nations University (UNU). The annexes were published in Patterns of Conceptual Integration. Brussels, UIA, 1984, pp. 161-204
Each concept scheme is a form of feature of language. Questions concerning the structuring of concept schemes should therefore emerge in investigations of language (although such investigations should themselves give rise to concept schemes in their own right). Of particular interest therefore are recent studies of transformational- generative grammars as they relate to grammatical categories.
0.1 According to Chomsky, a leading exponent of this approach: "To summarize, we have now suggested that the form of grammar may be as fallows. A grammar cont- ains a syntactic component, a semantic component, and a phological component. The latter two are purely interpretive; they play no part in the recursive generation of sentencestructures. The syntactic component consists of a base and a transformational component. The base, in turn, consists of a categorial subcomponent and a lexicon. The base generates deep structures. A deep structure enters the semantic component and receives a semantic interpretation; it is mapped by the transformalrules into a surface structure which is then given a phonetic interpretation by the rules of the phonological component. Thus the grammar assigns semantic interpretations to signals, this association being mediated by the recursive rules of the syntactic component.
The categorial subcomponent of the base consists of a sequence of context-free rewriting rules. The function of these rules is, in essence, to define a cert- ain system of grammatical relations that determine semantic interpretation, and to specify an abstract underlying order of elements that makes possible the functioning of the transformational rules. To a large extent, the rules of the base may be universal, and thus not, strictly speaking, part of particular grammars, or it may be that, although free in part, the choice of base rules is constrained by a universal condition on the grammatical functions that are defined. Similarly, the category symbols appearing in base rules are selected from a fixed universal alphabet; in fact the choice of symbol may be largely or perhaps completely determined by the formal role the symbol plays in the system of base rules. The infinite generative capacity of the grammar arises from a particular formel property of these categorial rules....
The lexicon consists of an unordered set of lexical entries and certain redund- ancy rules. Each lexical entry is a set of features...Some of these are phonological features, drawn from a particular universal set of phological features,...Some of the features are semantic features. These, too, are presumably drawn from a universal "alphabet", but little is known about this today..." (Chomsky, pp. 141-2)
0.2 The traditional sets of grammatical categories of "subject", "object", "verb", etc are now questioned and are no longer listed systematically because they are considered to belong to the "surface structure" of language. It is as yet far from clear what are the components of the "alphabet" of category symbols. Chomsky stresses, for example, that the notion "subject", as distinct from "noun phrase" (NP), designates a grammatical function rather than a grammatical category. It is, in other words, an inherently relational notion. Notions such as subject, predicate, main-verb, and object, being relational, are already present in the "rewriting rules" (as noun phrase, verb phrase, etc) and Introducing them would be reducndant. "More generally, we can regard any rewriting rule as defining a set of grammatical functions...only some of which (namely, those that involve the "higher level", more abstract grammatical categories) have been provided traditionally, with explicit names." (Chomsky, p. 66-9)
0,3 Since the whole field is continuing to evolve, in what follows the intention is simply to intercelate tentatively several dimensions which are of interest in terms of the other annexes. It should be stressed that this is a personal interpretation and does not reflect the manner in which this material is conventionally treated, although possible points of contact are indicated.
0.4 Chomsky argues that a grammar contains "a syntactic component, a semantic component, and a phonological component." The syntacts component includes a lexicon. For the purpose of this discussion, the lexicon as "an unordered set of lexical entries and certain redundancy rules" will be treated as separate from the syntactic component as a set of "rewriting rules". The four components are shown in the diagram below which is designed to draw attention to possibilit ies for misunderstanding and to semantic and ontological aspects of the question which may not be of current interest tolinguists.
Lexical repertoire of words/signs Level of verbailizable meaning: any partic ular case Progressive fragmentation into analytical elem- ents which cannot be meaningfully verbalized Progressive integration into semantic gestalts which cannot be adequately verbalized Degree of integration beyond conceptual capacity using three dimensions of space and one of time
The outermost circle is the level of the individual elements of each of the four components as broken down to their lowest level by analysis. The next circle inwards is the level of any specific verbalaized statement -- it is the level at which meaningful speech is possible. Moving inwards from that level integration should be understood to increase in the three following senses:
0,5 This integration abandons dependence on three-dimensional Euclidean space and the associated time dimension, as argued by Rene Thom: "We therefore endeavor in the program outlined here to free our intuition from three-dimensional experience and to use much more general, richer, dynamical concepts, which will in fact be independent of the configuration spaces." (p. 6) Such methods "appeal to the ideas of the morphogenetic field and chreod associated with singularities of the bifuraction set of an infinite-dimensional space....the problem of integrating these local models into a stable global structure (dynamical topology)...remains wide open." [Annex 3, p. 324) And in relation to Chomsky's focus on linear sequences, it is useful to note Thom's point: "It is sometimes said that all information is a message, that is to say, a finite sequence of letters taken from an alphabet, but this is only one of the possible aspects of information; any geometric form whatsoever can be the carrier of information, and in the set of geometric forms carrying information of the same
type the topological complexity of the form is the quantitative scalar measure of the information....it is possible that a language, a semantic model, consist- ing of topological forms could have consideravle advantages...over the linear language that we use...Topological forms lend themselves to a much richer range of combination...than the mere juxtaposition of two linear sequences." (Annex 3 p. 144-5]
0.6 The centre of the diagram may therefore also be partly understood in Thom's terms: "It may seem difficult to accept the idea that a sequence of stable transformations of our space-time could be directed or programmed by an organizing centre consisting of an algebraic structure outside space-time itself. The important point here, as always, is to regard it as a language designed to aid the intuition of the global coordination of all the partial systems controlling these transformations." (Annex 3, p. 119]
0.7 Without attempting to relate the perspective of Chomsky's generative grammar to the diagram, an indication can be given of the kinds of conceptual sets which might be examined for comparison with those of the other annexes.
a. Lexical sets :Here the focus would be on0.8 Clearly the four groups of sets above are intimately interwoven, (in fact the diagram should be "folded up" in some special way to reflect this.) This may be used to illustrate the successive articulation of the sets discussed in the other annexes and to indicate constraints on what can be communicated with only N categories or words:
1.1 "Ward-at-level-one" This is the original "Verbum" in which verb-noun-adjective- adverb-etc are integrated in a single meta-level, proto-state- ment/sound/sign pregnant with possibility
2.1 "Word-at-level-two" The two "words" at this level may possibly be considered as resulting from a single high level distinction between "subject" and "object", with their nature modified by the connotations of such notions as "verb", "adjective", etc as yet embedded in the two categories. The power of this first distinction is indicated by logician G Spencer Brown's comments:
"An oberserver, since he distinguishes the space he occupies, is also a mark...We see now that the first distinction, the mark, and the observer are not only interchangeable, but in the form, identical." (Laws of Form, 1969, p. 76)
3.3 "Word-at-level-three" The three "words" at this level may be considered as resulting from the separation of "verb" from "subject" and "object" which are thus distinct in meaning from those at level 2 above.
This procedure could be continued with the separation out of the other parts of speech. Note that in this sense the categories are no longer part of the surface structure in Chomsky's sense, because implicit at each level are:
a. the rules whereby the elements at that level are to be combined, b. the "proto-sound" with which they are associated, and c. the "proto-significance" of the words
However only by reaching set levels characterized by about 20-50 elements is there sufficient specificity to construct a sign alphabet (although artificial languages may of course be constructed with less) . Only by reaching about 70 elements is there sufficient specificity to distinguish the range of sounds associated with any such alphabet. Much higher numbers (e.g. 10 ) are required to constitute a set of basic words (sound combinations, rule combinations., meaning combinations) in an operational language. It is perhaps no wonder that concept schemes with a small number of elements have considerable difficulty in "grounding" their insights and "meshing" them in operational reality.
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