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In the present study we are using a conceptualization of a General Theory of Systems of Symbolic Expressions and Representation to discuss complementarity in language. This conceptualization reconciles our factual knowledge of neuronal control in biological systems with notions of computability and decidability in artifacts as well as living organisms. We thereby identify cognition with computation on representations (i.e. structures of symbolic expressions, — possibly containing existential predicates and projecting on the truth values) in domains of symbolic objects closed under allowed operations (i.e. in autonomous or self-defining systems). It will be argued that "linguistic complementarity", defined in terms of a distinction between "description" and "interpretation" of language, exists in language processing when symbolic expressions are considered partial objects which are related to each other as elements in a complete lattice structure. The formal theory developed by Dana Scott (1976) as a model for the Type Free Lambda Calculus is used in relation to this Theory of Systems of Symbolic Expressions and Representations. We argue that all non-trivial systems of symbolic expressions are "comprehended" by this model and have inherent incompleteness properties by which any description must proceed by the iterative specification of sub-languages. It is shown that continuous domains insure this. Type Freeness is taken to mean that every distinct expression is a unique type sui generis, but the dichotomy of rules in combinations, where every object can be either operator or operandi, implies a complementarity by which value elements and functions, as constant courses of variation, are mutually defining. Meaning is considered from the point of view of denotation or representation by converging sequences of monotonically ascending continuous expressions that approximate objects of infinite ("real") type as limits. The methodology of defining a partial order over domains of expressions is also considered.

DOI: 10.1007/978-94-011-2779-0_9

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