Semantic Containment and Disagreement Resolution: A Unifying Framework for Epistemic Validation

Despite decades of sophisticated theoretical development in disagreement epistemology, a fundamental puzzle persists: why do intelligent, well-trained agents with equivalent evidence systematically reach different conclusions and when do these disagreements resolve? This paper proposes the Semantic Containment Principle (SCP): disagreements originate when Agent A cannot semantically span Agent B's epistemic framework—meaning A lacks sufficient conceptual resources to represent B's reasoning structures, operational procedures, and validation methods. SCP establishes that disagreement resolution requires two necessary conditions: semantic spanning capacity and non-monotonic belief revision—the spanning agent's ability to abandon previous commitments when superior alternatives are validated. Drawing from Gödel's incompleteness theorems and Tarski's undefinability results, which demonstrate that validation requires semantic containment in formal systems, SCP extends these structural constraints to quasi-formal human epistemic systems. The framework reveals that existing disagreement theories—Equal Weight, Steadfast, Justificationist, and Total Evidence views—represent optimal responses to different spanning conditions rather than competing theoretical approaches. Equal Weight applies under mutual non-spanning conditions, Steadfast approaches respond to asymmetric spanning scenarios, while Justificationist and Total Evidence views operate when spanning correlates with evidence strength. SCP generates testable predictions about resolution pathways, expert-novice asymmetries, and domain-specific disagreement patterns whilst providing practical guidance through reference point acquisition and spanning enhancement. Most significantly, the framework transforms disagreement from epistemic failure requiring management into diagnostic information revealing validation capacities and opportunities for cognitive enhancement.