This contribution bridges three fields—pragmatics, argumentation, and law. Arguments can be seen as the verbal formulation of inferences that articulate justificatory relationships, meaning that behind every argument is at least one argumentative inference. As an argumentative activity and verbal practice, legal discourse has gaps to be filled by pragmatic inference. Neo- and post-Gricean frameworks can thus tentatively be used for its analysis. Based on these frameworks, this contribution asks whether argumentation in the interpretation of statutory law is the same as in international law. More precisely, it looks at judges’ legal interpretations, which function as justifying arguments because they are constrained by rules/canons of interpretation. It is shown that neither a pragma-dialectical hierarchy of statutory canons nor a hierarchy of related presumptions carries over to international law where there is no such hierarchy.