In recent years the homogeneity clause of Article 2 TEU has gained concretization of its scope and content due to enforcement of values vis-à-vis EU Member States violating the rule of law. Every instance of such enforcement must necessarily assume the presence of certain ‘epistemic minimum’ shared by the conflicting constitutional authorities. Any conception of such a minimum however seems problematic or at least begging profound theoretical questions. At stake are the conditions of mutual inter-systemic cognition. The paper refers to the reinterpreted epistemically oriented versions of the constitutional pluralist theory. It is suggested that the ‘vertical’ application of Article 2 does not invalidate questions about conflicts between competing constitutional orders. The paper’s goal is then to explore the epistemic limitations of EU’s values enforcement through the prism of assumptions and understandings of conflict which lie behind such supranational interventions.