Affine Shadows: Accuracy-First Bayesianism and Its Limits

Accuracy-first arguments show that Bayesian updating uniquely minimizes expected inaccuracy relative to a fixed, scoreable evidential representation. Accepting that theorem-level result, we ask a different question: what philosophical burden can such derivations bear? We argue that the strongest foundational reading of accuracy-first Bayesianism presupposes more than the mathematics itself establishes. Proper-scoring arguments require evidential content to inhabit an affine space on which inaccuracy is well defined, but diachronic coherence does not itself force affineness. Moreover, coherent global evidential order can be non-affine when locally Bayesian evidential regimes fail to descend to a single global public structure. In such cases one may still recover a canonical affine shadow of the evidential order, and Bayes may be vindicated on that shadow. But the result is then conditional: it is a theorem about the affine approximation, not yet a full foundational vindication of the original evidential order. We therefore distinguish internal from foundational vindication, argue that accuracy-first succeeds at the former, and identify the further bridge condition under which vindication on an affine shadow can lift to the original evidential order.