This paper addresses the possibility of a cognitive account of argumentation, by focusing on a tentative interplay between one of today's most influential theories of argumentation - van Eemeren and Grootendorst's Pragma-Dialectics - and Relevance Theory. With this purpose, I address the extent to which cognitive approaches to communication are able to incorporate pragma-dialectical insights.Both paradigms share today an assumption of 'soft rationality' allowing a significant departure from formal logic conceptions of communication. These experience difficulties in accounting for successful argumentation relying on logically deficient arguments, i.e. fallacies. Acknowledging Pragma-Dialectics' contribution in this respect, I investigate the model's compatibility with a cognitive agenda based on assumptions entirely different from those of a normative agenda such as Pragma-Dialectics'. The difference between Relevance Theory's internal perspective and Pragma-Dialectics' external perspective on discourse gives evidence of a different approach to communication. In the end, this comes down to evaluating whether these divergences are, in argumentation studies, irreconcilable.