Epistemic Fog: Diachronic Rationality Under Growing Uncertainty

Dutch-book arguments are often presented as one-shot coherence constraints on credences. Their deeper structural content is an extension principle: partial commitments must extend to admissible valuations on larger contract spaces under the relevant settlement rules. This paper develops a temporal version of that principle.

The central invariant is dynamic commutation: extension and temporal backup must compose without order effects. We study this under epistemic fog, where admissible model, language, and backup architecture evolve with temporal distance. Fog is not ordinary risk inside a fixed model class; it is uncertainty about whether the representational architecture itself remains adequate through time.

In a finite-horizon setting, we characterize when dynamic coherence is preserved. The key condition is compositional anticipatability: future admissible uncertainty must remain representable within a paste-stable architecture. We pair this with operational diagnostics (refinement-interval and tower-gap tests) and explicit time-book constructions when compositionality fails.

The philosophical upshot is a conditions-of-possibility claim within formal epistemology: beyond static belief coherence, rational governance requires architectural stability under self-iteration. Rectangularity is a feasibility condition, while evaluator choice is a second-stage normative problem. Bayesian updating is recovered as a flat special case; robust and tropical evaluators appear as conditional counter-curvature responses when admissible expansion remains compositional.