Gettier as Generalization Failure: A PAC–Bayes Approach to Anti-Luck

Gettier cases suggest that justified true belief can fail through luck: a belief may fit available evidence while failing to track truth across relevant alternatives. We formalize a central class of these failures as epistemic overfitting: evidential success without robust truth-tracking under a modeled evidence-generating structure. Technically, we develop an algorithmic PAC--Bayes framework over posteriors, so complexity penalizes the full belief state rather than only a single hypothesis. The result is a finite-sample anti-luck certificate that links evidential fit, posterior complexity, and out-of-sample truth-tracking, with exact and soft forms that remain valid for data-dependent posteriors and practical inverse/square-root corollaries. We show through canonical toy stress-tests how the framework separates two loci of epistemic luck: atypical evidence and inferential contrivance. We also clarify scope: the main guarantees are in-distribution (latent heterogeneity), while worst-case and tail-sensitive anti-luck targets are treated as principled extensions via alternative risk functionals. The claim is not a full solution to Gettier, but a quantitative decomposition that makes one core anti-luck component explicitly auditable.