Prospects for Using Information Dialectics to Improve AI: The Concept of Galois-Field-Based Intrinsic Explainability

The rapid development of artificial intelligence in recent years has been driven primarily by engineering advances, while the philosophical foundations of the concept of “intelligence” itself have been reconsidered much more slowly. This paper proposes a conceptual research program based on the thesis that philosophical analysis can serve not only as a means of interpreting existing technologies but also as a source of architectural principles for artificial intelligence. The main thesis of the paper is that an artificial system that aspires to functionally approximate human conceptual thinking must not only statistically process natural language utterances but also adequately interpret the place of the concepts used within the structure of natural language. Specifically, the meaning of fundamental concepts should be determined through their interrelations with one another, rather than through a set of vocabulary features. The simplest example of such an interrelation is the opposition through which paired philosophical categories are defined in objective dialectic. A dialectical concept of information is used as a substantive example. This concept, based on the basic opposition between the categories of “matter” and “information,” constructs derivative concepts (“alienated information,” “signal,” etc.). The work builds on the existing relational bottleneck paradigm. The distinctive feature of the proposed approach lies in its transfer of the bottleneck to semantically interpretable relations between concepts and the requirement that this layer be computationally sufficient to obtain the result. On this basis, the concept of Galois-field-based intrinsic explainability (GFIE) is proposed. Galois fields are viewed not as a natural “algebra of meaning,” but as a potential computational substrate for the implementation of predefined finite semantic operations. A minimal proof-of-constructibility is provided: a three-valued semantic operation is first defined independently, then encoded in GF(3) and implemented by a polynomial function. This example demonstrates the “semantics first, algebra second” principle, excluding the direct attribution of meaningful meaning to the addition or multiplication of field elements. This paper presents a conceptual framework and research program, not a report on a constructed and empirically validated AI architecture. Existing results in the algebraization of multivalued operations, finite-field computations, partial digital convolutions, and modular computing architectures are considered as individual, potentially applicable components, but not as proof of a complete technical implementation of GFIE.