Chapter 23: Law, Regularity, and the Operator

Laws of nature are not mere regularities in the Humean sense, nor brute necessitations in the Armstrong sense. They are admissible continuation operators—structural features of the coherence kernel K_τ that determine which extensions of a given configuration are τ-admissible and which are not. The analytic continuation principle of holomorphy (Book II) provides the formal mechanism: a law is an operator that takes a local datum and extends it uniquely to the maximal domain of coherence. The Operator Realism Theorem proves that the classification of admissible continuation operators is a structural invariant of the kernel—it is mind-independent, convention-independent, and observer-independent. The Humean debate between regularity theorists and necessitarians is dissolved: both sides presuppose substance ontology, and both are superseded by operator realism.