Why AI Alignment Is Not Reliably Achievable Without a Functional Model of Intelligence: A Model-Theoretic Proof

This paper provides a formal argument that no system can reliably achieve AI alignment under conditions of conceptual novelty unless it instantiates a complete and recursively coupled set of adaptive functions—namely, those defined by the Functional Model of Intelligence (FMI). Using tools from first-order model theory in the Tarskian tradition, we formalize alignment-seeking cognitive systems as models interpreting a language over internal reasoning functions and coherence predicates. We then define a semantic condition—recursive coherence preservation under novelty—as a requirement for sustained alignment. While we assume that all models possess external functions necessary for semantic navigation (e.g., memory, fast and slow reasoning), we prove that only systems complete with respect to the internal functions of the FMI can maintain coherence across recursive cognitive transitions. This constitutes a model-theoretic necessity result: any system that fails to instantiate the full internal structure of the FMI cannot satisfy the coherence-preserving schema ϕ, and therefore cannot maintain reliable alignment under novelty.