Internalizing Meta-Rationality: Rational Worlds, Public Closure and the Conditions of Lawlikeness

Locally correct updating can still fail to function as law. A reasoning system may update well, avoid immediate incoherence, and yet lose stability when its rules are declared, reused, publicized, and asked to govern themselves. The problem taken up here is therefore not which update rule is correct, but what makes a world capable of sustaining lawlike rational practice at all. The argument is transcendental in form: it asks for the structural conditions under which such practice is possible. We propose that rationality be modeled not by a bare rule, but by a package with a public face, an observation structure, and a fibered space of feasible laws together with operations of publicization, canonical completion, and coherent re-entry. Bayes is thereby resituated as an exact boundary law on the public side of such a package rather than as the whole foundation of rationality. Conditions of possibility are treated as genuine only when they survive their own higher-order application, so package-level lawlikeness is formulated as stability under visibility, admissible repair, and recursive reuse. The first theorem-level anchor is finite-tree, which already covers the familiar finite-horizon event-tree settings in which many diachronic Dutch book and dynamic coherence problems are posed. There least rectangularization becomes a reflector, and package-level algebra structure is characterized by coherent re-entry from the descended public shadow. The second anchor is ambient and pointwise. In an internal-diagram setting, canonical governance becomes free completion into lawlike objects, and on a Walker-compatible subcategory public-completion comparison, lifted completion, and generalized re-entry are all proved rather than merely forecast. The fully arbitrary fibrational case remains open, but the central philosophical claim already has substantial mathematical support: rationality is best understood as the closure geometry of worlds that can make their laws public, repair them canonically, and remain stable under re-entry.