The Limits of AI Inference: Abduction, Regularization and Non-Public Norm Selection

Contemporary AI is often assessed in terms of performance, interpretability, and alignment. We argue that these debates share a deeper epistemic core: correct inference is underdetermined by evidence, and the norms needed to discipline that underdetermination are not, in general, recoverable from observational success, public behavior, or optimization criteria alone. The formal case study is abductive reconstruction. We frame abduction as a regularized inverse problem, and argue that minimal hidden support is its canonical regularizer: it marks the least hidden structure required to preserve the invariants that make a reconstruction explanatorily adequate. From that starting point, we derive three impossibility results with broader philosophical significance. There is no task-blind regularizer for explanation, no purely public procedure guaranteed to recover the right reconstruction across tasks, and no global simplicity ordering across explanatory roles. The constructive upshot is that these limits do not eliminate normative commitment; they require that it be made explicit, contestable, and structurally disciplined. Better data, better optimization, and better public-facing explanations do not by themselves determine which hidden distinctions should survive reconstruction.