This paper investigates the tentative compatibility of two pragmatic approaches, Pragma-Dialectics (PD) and Relevance Theory (RT). The development of pragmatics historically led to conceptions of communication that supplied answers formal logic approaches had trouble capturing. Within argumentation studies, PD took this pragmatic turn while at the same time pursuing a normative agenda. This gives evidence of an external approach to language (in that argumentation follows norms imposed by the theorist) excluding, though not closing the door to cognitive insights. The purpose of this paper is to discuss the extent to which PD can operate from an internal cognitive perspective — i.e., with explicit ambitions of dealing with cognitive mechanisms of meaning construction and belief fixation.