Language Theory: Consensual Selection of Dynamics

Charles Henry
Fondrem Library, MS 44
Rice University
Houston, TX 77005

L.M. Rocha
Computer Research Group, MS P990
Los Alamos National Laboratory
Los Alamos, NM 87545

In: Cybernetics and Systems: An International Journal. Vol. 27, pp. 541-553. Winner of the best paper award of the EMCSR96 and the Gordon Pask Memorial Award.

    Both representational and self-organizing approaches to language avoid, in different ways, the concept of symbol. We argue that representationalism denies the particular aspects of a subject's embodiment, while the self-organizing paradigm refuses to address the utility of the concept of symbol and its evolutionary relationship with an environment. We call for an inclusive approach that considers the syntactic, semantic, and pragmatic aspects of language. We further offer a mathematical structure, defined in terms of fuzzy set and evidence theories, as a model of linguistic categories under this inclusive framework.

1 Introduction

The increased study of natural language during recent decades is biased toward two schools of thought. On the one hand is a focus on syntax [Chomsky, 1965; Jacobson, 1982], which studies the components of language and their arrangements, and how those arrangements might be determined. More recently evolution, and related biological aspects of language, have been adopted to the Chomskian school [Pinker, 1993]. The second approach, which attempts to describe natural language in purely biological terms, such as Maturana [1978], prefers to see language more as a phenomenon governed by autopoietic processes, with the relationship of components within a recursive neural network more a focus than the segregated elements of Chomsky's grammar. Semantics precedes syntax as the more revelatory linguistic feature.

    Interestingly, while these methodologies seem opposed in fundamental ways, they each share a commitment to deny symbols and metaphors as proper aspects of theory, arguing for the inappropriateness of these language constructs [Varela et al 1991; Bickerton, 1990] due to the difficulty of objectively describing metaphor and symbolic expression because each requires a high level of subjective interpretive engagement on the part of the observer.

    We believe that the understanding of natural language is not well served by the prevailing theories and their linguistic descriptions, and offer in this paper a few thoughts on how to rethink natural language as a less idealized, less abstracted phenomenon that requires the incorporation of symbol and metaphor as fundamental and defining properties that can elucidate the nature of human language in previously unrecognized ways.

    Any language can be described as possessing four determining aspects:

    1. All languages are biologically based on the neurological networks of the brain, thus any language inherits the autopoietic machine of the brain as fundamental to its operations.

    2. All languages are a recreated system of structural perturbations.

    3. The use of language continually re-contextualizes the epistemology of the individual; the act of recontextualization allows a leap from one dynamic state to another.

    4. This recontextualization is inherently symbolic and metaphorical

    A language is thus a system of access to the autopoietic machine of the brain, allowing the individual ecology to perturb and reconfigure the existing knowledge states. In other words, we defend that language, with its symbolic and metaphorical attributes, allows a kind of selection of the dynamic states of the brain ultimately related to a subject's interaction with an environment. In this sense, language liberates the brain from its own, continuous, dynamic behavior and grants it a discontinuous leaping from one dynamic stability to another. This "leaping" opens the door to a much larger universe of meaning, unreachable by pure dynamics alone. We elaborate these points next.

2 Self-Organization and Selection

We know a good deal from ethology, enough to realize that one of the prevalent structuring processes of the animal brain is the propensity to deconstruct observable objects or events and then to respond based upon an assessment of the elemental parts. Lorenz [1981], Tinbergen [1951] and others have painstakingly documented the deconstruction process in bees, birds, and primates. As an example, a goose will 'see' not an egg as it will see elements of an egg such as color, speckled pattern, shape, and size. A goose can be easily fooled into sitting on a nest of wooden eggs with these elements exaggerated (a brighter green, a more perfect ovoid, larger speckles, and the like).

    The deconstruction of reality into elements grants obvious and powerful survival potential: an animal will not be focused on one specific egg, but can 'interpret' all eggs within the selected for categorical constraints. The elements can vary _ in fact variety of recognizable phenomena is inherent in this process. Events and situations can have different components (a nest in one field will never be identical to a nest in another field years later) but elicit the same survival responses. Categorical flexibility is an optimum trait; responding only to a singular, uniquely 'perfect' egg would lead to extinction.

    The self-organizing or connectionist paradigm in systems research and cognitive science, has rightly emphasized these characteristics of mental behavior. A given dynamics, say the neuronal interactions of the brain, will converge to a number of attractor states _ eigenstates in von Foerster's [1977] second order cybernetics terminology. Such a dynamic system will then utilize these attractors to categorize its own interactions with an environment. This emphasizes the constructivist position that a cognitive agent is not free to categorize all aspects of its environment but only those for which it can construct internal stabilities according to the dynamic characteristics of its particular embodiment. The ability to relate internal stabilities to environmental interactions has been referred to in cybernetics as eigenbehavior and in cognitive science as emergent representation. It has lead to the idea of memory without record [von Foerster, 1965] and that symbols are not necessary to explain cognition which is inherently subsymbolic [Varela et al 1991]. In applied domains, we have seen the emphasis turn to connectionist machines which classify their environment by manipulation of a network's attractor landscape.

    Clearly, these self-organizing systems, if not chaotic, will classify similar events in their environments to similar attractor points of their dynamics: the categorical flexibility observed above. However, to effectively deal with a changing environment, systems capable of relating internal stabilities to environmental regularities (organizationally closed systems), must be able to change their own dynamics in order to create new basins of attraction for new classifications. Pask [1992] calls systems with this ability informationally open, while Maturana[1978] would prefer the term structurally open. In any case, to achieve this ability to create new meanings or functionalities, the structure of the dynamics must be changed. In autopoiesis this is achieved through the structural coupling of the system and its environment (which might include other such systems), while in conversation theory it is achieved through the conversational interaction between several participants. In other words, the self-organizing system must be structurally coupled to some external system which acts on the structure of the first inducing some form of explicit or implicit selection of its dynamic representations. Rocha [1995c, 1996a] has referred to this process as selected self-organization relying on some form of distributed memory. In the biological realm, this selection is implicitly defined by surviving individuals in varying (genetic) populations, while in the cognitive realm we may have some form of explicit selection referredto as learning. A simple example in an applied domain, would be an external algorithm for selecting the weights (structural perturbation) of a neural network in order to achieve some desired classification.

3 Improving Structural Perturbation

A relevant question at this point is how effective can this structural perturbation get? Connectionist machines can only classify current inputs, that is, they cannot manipulate their own distributed records. Structural change can alter their classification landscape, but we do not have a process to actually access a particular category at any time. Something similar happens at the biological level. If living systems were purely dynamic, then reproduction would have to rely on components that could replicate themselves in a template fashion, or components that could unfold and fold at will so that copies could be made from available elements. In other words, if life did not have a symbolic dimension in DNA, it would be restricted to those proteins and enzymes that could reproduce in a crystal-like manner, or that could unfold to be reconstructed from available amino acids, and then refold to their original form.

    Indeed, DNA introduces a novel dimension to living systems which allows them to construct any protein from a genetic description, and not only those that can self-reproduce in the above described senses. This way, DNA introduces a kind of random access memory so that living systems have access at any time to the blueprints of their own construction. This ability liberates living systems from purely localized interactions; biological reproduction is not restricted to template reproduction as the genetic, localized, descriptions can be communicated much more effectively from generation to generation, as well as to different parts of organisms. This is what von Neumann [1966] called non-trivial self-reproduction. Pattee [1982, 1995] considers this symbolic dimension of living systems essential for genuine informational openness, or the ability of living systems to undergo open-ended evolution, with his semantic closure principle.

    It can always be argued that the random access memory the genetic system establishes, is nothing but complicated dynamics, and the symbolic dimension is just the result of our subjective observation. However, the argument is also extendable to the dynamic level itself, since it too is constructed by our subjective observations. Ultimately, all models are subjective. Having accepted this, we can now go our way trying to establish models and explanations that can be consensually agreed by most. As Pattee [1982, 1995] has repeatedly pointed out based upon the work of von Neumann [1966], the genetic dimension has established a new hierarchical level in evolutionary systems [Laszlo, 1987] which allows a greater level of control of the purely self-organizing dynamics. Failing to recognize this emergent symbolic level, does not allow the distinction between self-organizing systems with some dissipative structure such as autocatalytic networks [Kauffman, 1993] (perhaps even hurricanes), from living systems whose genetic memory does not require larger and larger autocatalytic networks to develop more and more complicated morphologies. This issue was developed in detail in Rocha [1995c, 1996a].

    Our point here, in simple terms, is that language has likewise opened up a whole new universe of meaning for cognitive systems, as they can access the dynamics of classification beyond local interactions. That is, communication between individuals, as well as internally, is not restricted to only those things we can "show" or otherwise somehow physically mimic: the displacement of local observations. Language may be, as the genetic system, a method to point to and reach a particular dynamics necessary in a particular context. It may allow a (fairly) random access to an otherwise distributed memory, defining a more sophisticated system of structural perturbation.

4 Metaphor and Evolutionary Constructivism

We can thus say that the existence and use of a language is thunderously transformational. The categorical constraints of, purely classifying, instinct-level autopoiesis can be accessed and recontextualized through the consensual, willful exercise of a system of perturbations. It is the recognition of the access to and limited control over a previously closed, interior ecology of largely autopoietic processes that more than likely gave rise to the myths, prevalent in all ancient cultures, that language was a gift of the gods and made human beings god-like in its acquisition [Cassirer, 1946].

    We thus see language as a systematic influence in the recontextualization of an existing epistemology (moment to moment, year to year, in waking and in dreams) that allows for the leap from one dynamic state to another. It is also critically important to note that any language, because it resides upon the neurological structure of the brain as its chief biological processor, is necessarily constrained by the autopoeitic machine that it soperturbs and disrupts. We believe that the most efficacious means to explore the constraints and at the same time the leap of dynamic states is precisely in symbols and metaphors, which are properties that must occur as products of open-ended dynamic state transition.

    Symbols, metaphor, and analogy recapitulate the ontogeny of a dynamic state through contestation with another, resulting in a new synthesis within the epistemological domains of those states that are consequently re-formed. Metaphor, symbol, and analogy all share the key characteristic of synthesis of apparent and, in more advanced utility, non-apparent elements of objects and events. A metaphor is thus a heightened degree of routine association made remarkable because it involves the juxtaposition of apparently dissimilar phenomena. This contributes significantly to our survival, enabling us to transfer solutions across problems with similar goal structures. In the most advanced stages of brain development, we achieve true system mapping, in which we far surpass other species in our capability to transcend perceptual similarity. Discerning correspondence in non-similar phenomena is one of our highest achievements [Holyoak and Thagard, 1995]. This point was developed in greater detail in Henry [1995].

    Constraints are integral to this selected cognitive strategy. A language is by nature open ended and capable of infinite combinations, but its semantic value would be null if there were no categorical restrictions. The variety and richness of semantics depends on the tension between the language as a means of leaping dynamic states while constrained by the inherited neurological processes upon which those states reside. Meaning, in large part, emerges from this tension, from the continual intersection of an abstracting system of organization that must relate by nature of its associative propensities to the external world.

    The metaphoric/symbolic quality of language production is inevitable because meaning must be constructed from the associations of often disparate elements and events. To say language or its component words are 'representational' misses a critical point: words cannot represent singular objects or events without recourse to a variety of associations. Essentialism is impossible in linguistic constructs. On the other hand, cognitive categories must relate to the external world, or an organism would not efficiently categorize (and thus survive in) its environment, in other words, the construction of categories must be evolutionarily, and consensually, viable.

    This evolutionary constructivism [Rocha, 1996a, 1996b] calls for an integration of representational and connectionist (autopoietic) models of cognition, under an evolutionary epistemology framework. Neither open intentionality nor closed construction can alone explain cognition. Representationalism and constructivism must be brought together under an evolutionary model that includes syntax, semantics, and pragmatics.

    Evolutionary constructivism accepts that cognition is constructed, that is, it is constrained by its own dynamical embodiment and development, but this form of constructivism also acknowledges the pragmatic, functional, necessity of its representational dimension established through natural selection. In other words, it merely accepts the obvious need for an evolutionary constraint of cognitive categories. Mental categories are certainly constructed by brains, but if the classification power of such categories in a given environment is null, then the biological systems associated with such brains will most probably not survive in the environment they misclassify. This does not mean that cognitive categorization should be seen as open-ended; not at all, a given material system will only be able to classify certain aspects of its environment, those for which it can construct dynamic stabilities. But it must be able to classify well enough in order to survive. An artificial neural network will also not be able to solve any problem, and we will choose different kinds of networks, with different dynamics, to solve different problems. Thus, models of cognitive categorization need to include the contextual influence of dynamic, developmental, and pragmatic (selective) constraints [Rocha 1995d, 1996b].

    Radical constructivism, based as it is on the dynamic and developmental cybernetic explanations of cognition, often seems to either explain away the notion of representation or avoid it altogether. The same trend takes place in connectionist cognitive science. But we also do not have to pursue a naive realist avenue if we wish to study the notion of representation. It does not have to be seen as the unconstrained one-to-one mapping of real world categories to brain categories. Quite the contrary, evolutionary constructivism demands the understanding of cognition and representation as emerging from several dimensions that are mutually constraining: dynamics, development, and pragmatics. The representational aspects of categories have to do with the existence of a pragmatic (selective) dimension. But representation is also constrained by the dynamic and developmental dimensions. It is a truly inclusive approach.

5 Time and Religion

Because language systematically perturbs an existing autopoietic process by re-combining the ontogeny of dynamic states, it thus has access to and recreates memory. An interesting paradox can be extrapolated from this. A closed system of instinctual dynamic states that function on a pre-set code of deconstruction and response would be atemporal: it is restricted to local observations. Language, as it names and often recategorizes/resynthesizes external and internal objects and events, is a process of abstraction that coheres upon the instinctual deconstructed elements and thus further removes those objects and events away from their source. It, too, is atemporal: the random access memory. Yet the combination of these atemporal phenomena creates in us our sense of time and passing because it refers to objects and events that are usually invisible.

    This may be directly a result of the recognition of the leaps of dynamic states themselves. Once the invisible can be conjured through language, and non-apparentness likened in disparate phenomena as a means of learning and survival, then remembrance and utility of the invisible becomes itself integral to and selected for survival. Once the invisible is selected for as a survival mechanism, it is not difficult to see the relationship to organized religion. Indeed, the metaphorical and symbolic aspect of language as a product of interacting with and transforming dynamic states itself reflects universal religious tenets. On one level language is thus a consensual ritualization of the autopoietic machine of the brain.

6 Evidence Sets as Linguistic Categories

Evidence sets [Rocha, 1994, 1995b, 1995d] are mathematical extensions of interval valued fuzzy sets (IVFS) through the Dempster-Shafer theory of evidence (DST) [Shafer, 1976]. A fuzzy set A on a universal set X is defined by a membership function A(x): X -> [0,1]. An IVFS is given by A(x):  X ->  I([0,1]), where I represents the set of intervals in [0, 1]. An evidence set A of X, is defined by a membership function of the form:

A(x): X ->  B[0, 1]

where, B[0, 1] is the set of all possible bodies of evidence ( Fx, mx) on I(Y ) = I[0, 1]. Such bodies of evidence are defined by a basic probability assignment function mx on I(Y), for every x in X. A body of evidence is defined by a class F of sets of a universal set Y weighted by a set function m with the following restriction:

Rough Equation

sum from {B in Y} m(B)~=~1

    In the case of evidence sets, class F is restricted to intervals of [0, 1]. From function m, belief and plausibility measures can be obtained which generalize probability theory [Shafer, 1976; Wang and Klir, 1993; Klir and Yuan, 1995]. Figure 1 shows an evidence set with three intervals for each element x of X, with respective belief weights obtained from function m.

    We propose that evidence sets are viable tools for models of cognitive categories under this form of evolutionary constructivism or, to adopt another descriptive term, contingent anaplasis. The interval based membership values offer an uncertain representation of categories, that is, a numerical, unconstrained, interval valued membership in a category/set. Nonetheless, these intervals of membership are constrained by the basic probability assignment function from the DST of evidence. In other words, the membership value of an element in an evidence set is defined by interval membership values and an account of belief constraining this membership. The several weighted intervals of membership is equivalent to the membership of an element in an evidence set according to a set of subjectively defined contexts [Rocha, 1994,1995b, 1995d]. Each interval of membership is associated with a particular context.

    The contexts that constrain evidence sets are understood as subjective in that they may depend not only on higher level cognitive constraints, but on material and developmental constraints. They can be obtained by associating them with a genetic algorithm or boolean network [Rocha, 1995a], or within a higher level modeling of cognitive categories through an extended theory of approximate reasoning based on set theoretic operations between evidence sets [Rocha, 1994, 1995d; Zhu et al, 1995]

    Evidence sets are mathematical set structures defined in two distinct levels: membership and belief. Intervals define membership in an unrestricted, open-ended, way, while the basic probability assignment function constrains membership within a belief based, subjective framework. The unrestricted membership is associated with the traditional representationalist, objectivist, framework of cognitive science, artificial intelligence, and fuzzy approximate reasoning [Lakoff, 1987]. The belief framework, as defined by Shafer [1976], defines a formal, higher level, account of subjective, contextual, representation, which attempts to model the evolutionary (dynamic and selective) constraints of cognitive systems in a mathematical framework. Notice that evidence theory can be made equivalent to some forms of modal logic [Resconi et al, 1993]. Furthermore, evidence sets capture all the main forms of uncertainty recognized in generalized information theory: fuzziness, non-specificity, and conflict [Rocha, 1995b, 1996b].

    The modeling capabilities of evidence sets thus make them an appropriate starting point to more deeply explore the consensual selection of dynamics as it applies to natural language theory.


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