What does it mean to convince? In the pragma-dialectical theory of argumentation, convincing is done by arguments. The perlocutionary act of convincing is fundamentally related to the illocutionary act of arguing. I propose a critical reassessment of this relationship. The arguing-convincing pair presents conceptual difficulties, I argue, both in the pragmatic description based on felicity conditions and in the dialectical one based on intersubjective procedures. To tackle these problems, I develop a proposal that takes the speakers’ non-verbal interaction with evidence, as opposed to their verbal interaction with one another, as the basis for understanding the resolution of differences of opinion. The proposal is compatible with the pragma-dialectical theory, provided some methodological adjustments are conceded.