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Emergence of semantic and syntactic complexity in language Wolfgang Wildgen

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### Emergence of semantic and syntactic complexity in languageWolfgang Wildgen

LANGUAGE CULTURE AND MIND CONFERENCE (LCM 2)INTEGRATING PERSPECTIVES AND METHODOLOGIES IN THE STUDY OF LANGUAGE , PARIS 17-20 JULY 2006

Structure of the argument

- Introduction
- 1.The perspective of information theory
- 2.Syntactic complexity measures (Chomsky)
- 3.Geometrical deformations as memory (Leyton)
- 4.Semantic archetypes (Thom)
- Conclusions

LCM 2 Paris 2006

Complexity , change in complexity, barriers of complexity

- Several proposals for a complexity measure have been made and have played a role in at least one of the three fields: phylogeny, ontogeny and cultural dynamics. The paper will try to evaluate four of them and ask how they are analyzed in the cases easier to access: ontogeny of language and cultural evolution, and how they may be applied to restrict models of linguistic (semiotic) evolution, to which an empirical access seems to be almost impossible.

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The four measures are:

- Increase of information / informational complexity or negentropy (decrease of entropy). This notion rests on principles of thermodynamics (entropy) and has been elaborated in the mathematical theory of information (Shannon and Weaver, 1949).
- The Chomsky hierarchy of formal languages (finite state grammars, context-free and context sensitive grammars, transformational grammars; cf. Chomsky, 1957).
- A geometrically based transformational measure of complexity (memory) has been proposed by Leyton (2001); it may be compared to Chomsky’s proposal and to Thom’s hierarchy.
- The abutment hierarchy of elementary catastrophes and the hierarchy of semantic archetypes derived from it (Thom, 1972 and Wildgen, 1994).

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Are all languages equally complex?

- In the case of the evolution of language capacity since the LCA (last common ancestor) changes in complexity cannot be dismissed.
- This is also the case (on an smaller scale) for functionally deprived languages like pidgins and jargons.
- Different kinds of diminished functionality must be assumed for mentally retarded, autistic, aphasic persons.

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Different presuppositions

- The four measures I will discuss presuppose different views on semiotic systems and refer to different models of human language and communication.
- For this reason the search for an adequate measure of complexity in semiotic systems is also a search for a general and adequate model of human language and semiosis in general.
- Moreover the measures reflect different analytic strategies: global characterization of a system (its grammar) versus local characterization (the morphogenetic germs or singularities of the system)

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1.The perspective of information theory

- The major concern of information theory is the amount and quality of signs transmitted through a given channel (in a time slot).
- The background is a statistical one, i.e. the probability distribution of states of the world(s) which are referred to by signs.
- Very rare events have high information (cf. the logarithmic measure of the inverse of the probability (p) of an event (e): inf(e) = ld 1/p(e)

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Application to semiotic systems

- Transition probabilities in Markov-chains diminish, if the set of lexical choices available at each step increases (if the probability of each single choice decreases).
- If the (generative) base syntax allows for more alternative structures at each step the probability of each point with structural alternatives decreases (cf. grammars with variables rules or probabilistic grammars as applied in sociolinguistics (HDP 1975, Klein & Dittmar, Developing grammars, 1979)).

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Semantic information

- Applying the measure of semantic information, i.e. the amount of specification of a semantic universe proposed by Carnap and Bar-Hillel (1952), I was able to show that the code-hypothesis of Bernstein may be properly opera-tionalized by a measure of semantic information (cf. Wildgen, 1977a,b).
- A given filler of a syntactic slot has higher information, if the semantic universe of the possible (or experimentally elicited) fillers is more restricted. Example:
- Given three independent predicates appearing as expressions or its components in a given syntactic slot: He, a person, a child, a girl, we may assume 23 =8 states of the universe which are possible.
- If all predicates are (positively or negatively) specified the probability of the filler is 1/8; information = ld 8= 3.

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2.Syntactic complexity measures

In his booklet of 1957 Chomsky argued against linear grammars and probabilistic considerations in grammar. Instead he proposed a hierarchy of grammar formats:

- Type 3 corresponds to transitions networks as those considered in information theory (Markov-chains).
- Chomsky’s hierarchy (or similar ones) introduce a complexity measure on syntactic (generative) rules in the framework of production systems.

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Type 2 grammars are called context free; they allow for the construction of abstract structures without direct reference to terminal elements (at each step).

- Type 1 grammars consider (left, right) contexts of rule applications.
- Type 0 grammars allow for transformations of structures (partial trees) with deletion and other rather unrestricted operations (e.g. move-operations).

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The measure first concerns the computational strategy of sentence generation / analysis, secondly it involves dependencies between linguistic events with different scope, i.e. local (step by step from left to right) for type 3, global for type 0 grammars. Barriers may further restrict the scope of move-operations.

- Practically the computational grammars proposed after 1957 tended to solve the problem of sentence generation at lower levels (type 3; cf. ATN-networks or type 2).
- As the measure is restricted to formal grammars of a certain type, its relevance for human language is not evident (formal language is not natural language).
- One may assume that a protolanguage with a very small lexicon (below 50 items) and simple syntactic rules at the level of two word utterances (no or primitive morphology) may easily be generated by type 3 grammars (this stage corresponds roughly to the competence of a two year old human child).

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Criticism

- The Chomsky hierarchy is only a segment of a net of different restrictions on replacement rules (in the semi-Thue-format).
- The rule formats are highly dependent on conceptions of grammar writing and have been changing rather quickly (since Chomsky’s proposals in 1957). Therefore they are rather technical features of grammars (therefore artifacts) than a characteristic for real languages.
- Some of the features asking for more complex grammars are rather infrequent (not necessarily relevant for all language users; cf. Chomsky’s mirror-language argument in Chomsky 1957).

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3.Geometrical deformations as memory (complexity =degree of deformation)

Deformation of a circle by forces () and resultant indentations (cf. Leyton, 1997: P2).

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Deformations of complexity 3

This process may be continued to any level of complexity

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The patterns of deformation (active forces and indentations) have different effects:

- They refer to some ideal form; e.g. a circle,
- They are an index of forces which apply to the ideal form,
- They are a memory of the deformations.

The amount of deformations (transforma-tions) may serve as a complexity measure (of shape memory)

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Early object-symbols as precursors of writing

One can see some geometrically ideal forms like spheres, disks, pyramids and deformations, the composition with lines and holes etc.

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Application to symbolic forms

- The (shape) is the number of deformations applied to it; the asymmetries added (by symmetry breaking).
- As the deformations are the traces of processes which have acted on the (ideal) figure at the start, they constitute a memory inscribed in the figure.
- The forces of deformation may be power fields in different medias (brushes in a painting, strokes in a sculpture, physical forces in an architecture).
- In phonation a basic vowel (e.g. [ə] may be deformed to obtain the field of vowel phonemes, a regular r pace may give a rhythm, etc.

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4.Semantic archetypes (Thom)

- The set of semantic archetypes proposed by Thom (1972) and elaborated by Wildgen (1982) are abstract pictures of possible scenes
- The basic semantics of sentences can be derived as specific applications (interpretations) of these archetypes.
- The abutment hierarchy of elementary catastro-phes is therefore a mathematically founded complexity measure for schematic pictures/actions/sentences.

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The abutment hierarchy of catastrophe theory

Our examples referred to A3 (complexity 2), A5 (complexity 3) and D4 (compactified in X9; cf. Wildgen, 1985)

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- The action-concept involves two stable entities: the body (the hand) and the object. Every point on the lines is an attractor.

The book

The father (having the book)

The father

Catastrophe of capture

Derived from the cusp (A+3)

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Valence (complexity) 4

Object (pebble)

Substractedpiece

Instrument

Agent

Schema of shaping an object with an instrument via subtraction.

Derived from the parabolic umbilic (D5) (compactified)

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Schema complexity and the evolution of symbolic behavior

The complexity of schemata may be applied to different symbolic forms (Cassirer):

- Lithic industries and the process of manufacturing tools (cf. Wildgen, 2004)
- Art, e.g. the composition of a figure by manual traits or the structure of abstract signs
- Mythical structures, e.g. action schemata of heroes/ghosts/gods on objects and other actors
- Valence schemata of verbs in a protolanguage (cf. Wildgen, 2004)

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In order to produce such an hand axe in the early Paleolithic, on had to use both hands and systematically subtract pieces (which could be tools themselves); as a consequence positive tools and negative ones may be distinguished

Abbévillien= 600.000-350.000, second glacial period;

Acheuléen= 350.000-100.000; third glacial period

(above) Abbévillien-Biface (Le Stade) Le Champs de Mars

(below) Middle Acheuléen (Saint Acheul) (cf. Weiner, 1972: 130)

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Handmotion and basic drawing techniques

Monochro-me drawing of a horse(Peña de Candamo)

The drawing may be decomposed into a number of traits:

Broad curves (semicircular), lines, small strokes, points, etc.

The compositionality principle is a Gestaltist one

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Handaxe in the early Paleolithicum

(above)

Abbévillien-

Biface (Le Stade)

Le Champs de Mars

(below)

Middle

Acheuléen

(Saint Acheul)

(cf. Weiner, 1972: 130)

Abbévillien= 600.000-350.000, second glacial period; Acheuléen= 350.000-100.000; third glacial period

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Evolution as transition to higher levels of complexity (=emergence)

- The complexity measure must first allow for levels of complexity, i.e. there must be barriers to transition, which define plateaus.
- The nature of the barrier must be such its transition has costs, which must be evaluated in a Darwinian context.
- If we assume parallel channels of symbolic processes, a level of complexity may be reached in one symbolic form and possibly enable the transition (at lower costs) in another one.

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Strategic conclusion

- As a complexity measure is crucial for a whole family of models in language and cognition, one should not mix it with spurious complexity introduced by the technicalities of specific descriptive devices. Thus basic intuitions of the Chomsky hierarchy should be freed from their restriction to generative grammars.
- The complexity measure must allow a translation to measures applicable to natural systems (i.e. in physics, chemistry, biology). This criterion is only fulfilled by the information measure and the catastrophe hierarchy.
- The concept of emergence should be defined either in the context of a morphogenetic theory or in the framework of a theory of (stochastic) self-organization.

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Conclusions

- The proposal of Leyton may be easily applied to visual semiotics; its application to semantics asks for a kind of morphodynamic theory, as developed by Thom.
- Only catastrophe theory allows for a natural restriction to valence 3 (4 with special conditions).
- The abutment hierarchy imposes a very general restriction on model complexity; a feature which Leyton’s theory is lacking and which is totally absent in the algebraic/logical tradition (with the exception of Peirce’s diagrammatic logic, but he could not derive the restriction logically).

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References:

- Chomsky, Noam, 1957. Syntactic Structures, Mouton, Den Haag.
- Cumming, Graeme S. and John Collier, 2005. Change and Identity in Complex Systems, in: Ecology and Society 10 (1); online: www.ecologyandsociety.org/vol10/iss1/art29
- Leyton, Michael. 2001. A Generative Theory of Shape, Springer, Heidelberg.
- Shannon C.E. and Weaver, W., 1949. The Mathematical Theory of Information, University of Illinois Press, Urbana.
- Thom, R., 1972. Stabilité structurelle et morphogenèse (2e édition, revue et corrigée, 1977), Interéditions, Paris.

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Wildgen, Wolfgang, 1977a. Differentielle Linguistik. Entwurf eines Modells zur Messung von semantisch-pragmatischer Variation, Niemeyer, Tübingen.

- Wildgen, Wolfgang, 1977b. Kommunikativer Stil und Sozialisation. Eine empirische Untersuchung, Niemeyer, Tübingen
- Wildgen, Wolfgang,1982. Catastrophe Theoretic Semantics. An Elaboration and Application of René Thom's Theory, Benjamins, Amsterdam.
- Wildgen, Wolfgang, 1994. Process, Image, and Meaning. A Realistic Model of the Meanings of Sentences and Narrative Texts, Benjamins, Amsterdam.
- Wildgen, Wolfgang, 1999. De la grammaire au discours. Une approche morphodynamique, Reihe: Sémiotique européenne, Lang Verlag, Bern.
- Wildgen, Wolfgang, 2004. The Evolution of Human Languages. Scenarios, Principles, and Cultural Dynamics, Benjamins, Amsterdam.

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