Chapter 70: Kolmogorov as Representation Theorem

Kolmogorov’s axioms for probability theory—non-negativity, normalization, countable additivity—are standardly treated as the foundation of the subject: probability is whatever satisfies these axioms. This chapter inverts the explanatory direction. The Kolmogorov axioms are not ontological primitives but representation conditions: they encode how the internal complexity of τ-constructions projects into numerical measures. Probability is derivative; structure is primary. The axioms are consequences of the kernel’s architecture, not independent postulates, and the synthesis of Bayesian credences with Kolmogorov measures is explained by the fact that both represent the same underlying structural complexity viewed from different angles.