Recursive Distinction Theory: A First Principles Framework for Intelligence, Generalization, and AI Safety

We introduce Recursive Distinction Theory, a mathematical framework that provides a unified approach to AI capabilities and safety. Starting from three fundamental axioms about the nature of distinction making, we derive a complete theoretical framework explaining the emergence of intelligence and safety guarantees simultaneously. Our theory posits that intelligence emerges necessarily from recursive distinction-making capabilities of sufficient depth, subject to a fundamental Conservation of Relational Information (CRI) principle. Through rigorous category-theoretic derivation, we prove that AI systems require a recursive distinction hierarchy with depth ≥3 to achieve advanced capabilities, demonstrating this threshold emerges necessarily from fixed-point structures in the category of distinction spaces. We derive the CRI principle through a novel thermodynamic formulation, establishing mathematical safety guarantees against unbounded recursive self-improvement. We prove The Distinction Bottleneck Principle, derived directly from information-theoretic first principles, that formally links preservation of distinctions to generalization capacity, explaining empirical scaling laws in AI. Our theory further shows how symbolic logic and Bayesian reasoning emerge necessarily from distinction-preserving transformations, unifying multiple cognitive frameworks under a single axiomatic system. This theory reconciles the apparent tension between capability enhancement and safety, establishing both as emergent properties of the same underlying principles governing information processing in intelligent systems.