Implications of the Theory of Axiomatic Necessity for Artificial Intelligence and Artificial Consciousness

No operational system can internally justify its own admissibility. Current artificial intelligence systems operate only within an operational domain and cannot generate the conditions needed for genuine consciousness, meaning, or ethical normativity. The work formalizes the difference between simulating and actually instantiating these properties, introduces a test for that distinction, and argues that the AI alignment problem stems from this structural limitation. A framework for designing aligned AI systems is proposed, with implications for philosophy of mind and AI ethics.

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Abstract

The Theory of Axiomatic Necessity (TNA) establishes that no operational system can internally generate the conditions that legitimate its own admissibility. This structural theorem has profound consequences for the debate surrounding artificial consciousness. We demonstrate that contemporary artificial intelligence systems operate exclusively within the operational domain ($N_0$) and are structurally incapable of generating the admissibility conditions ($N_1$) required for genuine consciousness, semantic meaning, and ethical normativity. We formalize the distinction between simulation and instantiation through the Bridge Dissipation test, demonstrate that the alignment problem is a direct manifestation of the Failure of Local Closure, and propose a structural engineering framework for the design of aligned AI systems. The implications extend from the philosophy of mind to AI ethics, offering a precise diagnosis of the ontological limits of computational architectures.