Rationally Wrong: A No-Go For Accuracy-First Inquiry Under Misspecification

Accuracy-first epistemology evaluates credences by scoring-rule inaccuracy and often uses a single scalar objective as the central criterion for inquiry within a representational scheme. This paper proves a no-go result under misspecification: an experiment can be epistemically preferred by the agent's own scalar accuracy criterion yet be worse by the same score at the true data-generating process. We isolate the mechanism with a score-divergence decomposition and a template proposition separating internal improvement from external truth-tracking. We prove a baseline binary log-score reversal, a local robustness result under small true correlation, a Brier-score analogue, a finite-outcome log-score generalization, and a score-universal theorem at risk neutrality for all strictly proper scores on finite outcome spaces. For finite risk sensitivity, reversal attenuates but persists. The upshot is structural: within-model accuracy norms are indispensable but not self-sufficient for robust inquiry under model error, which requires additional norms governing representational adequacy and model criticism.