Open Semantics and the Completeness Problem for Languages of the Third Artificial Nature

The article presents a philosophical and methodological analysis of technical cybernetic languages, focusing on the emergence of a “third artificial nature” – an environment comprising cyber-technical systems capable of self-reflection and self-development. The study traces three evolutionary orders of cybernetics: Norbert Wiener’s first-order cybernetics, Heinz von Foerster’s second-order cybernetics of observing systems, and V.E. Lepskiy’s post-nonclassical third-order cybernetics, which deals with self-developing, poly-subject environments. For each level, the author establishes a mapping between the type of cyber-technical system and the structural characteristics of its descriptive language. The analysis shows that while second-nature computing systems implementing Turing-complete formalisms reach the theoretical limits of machine information processing, they remain fundamentally inadequate for describing systems that can autonomously alter their own semantic rules. The shift toward self-developing technical systems requires adopting a processual approach to semantics (drawing on the work of V.A. Lektorsky and A.V. Smirnov). In this framework, meaning is not a statically defined correspondence, but rather a dynamic, time-bound interpretive process that continuously generates new semantic linkages. To capture this shift, the article introduces and substantiates the concept of “open semantics” as the defining feature of languages belonging to the third artificial nature. The author defines semantic openness as the capacity for recursive-inductive extensions of a language’s semantic domain during technical semiosis, wherein recursion acts as the mechanism by which a system alters the semantic scope of its own syntactico-semantic rules. The article also proposes the concept of “Gödel completeness” to characterize the extensional completeness of such open-semantic languages. This reframes the traditionally negative implications of Kurt Gödel’s incompleteness theorems: the semantic incompleteness of formal languages that allow for self-referential extensions is instead reinterpreted as a positive feature – one that guarantees the evolutionary potential of the linguistic model. The languages of the third artificial nature (Gödel-complete languages of recursive processes) provide a crucial foundation for modeling artificial consciousness, including the representation of both the world and the subject within it (following V.A. Lefebvre). Furthermore, these languages offer a theoretical pathway to overcoming the fundamental limitations of modern large language models, which remain constrained by the static and probabilistic nature of their semantics.

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