Argumentation is often conceived as a rational response to disagreement, even when it does not resolve differences of opinion. Arguing in the face of disagreement has, however, distinctive epistemic effects. Sometimes argumentation achieves convergence of opinion or at least the mutual recognition that a more thorough inquiry is required. But facing disagreement, participants of argumentative exchanges quite often remain steadfast in their initial views or even radicalize them. Can we make sense of these latter situations? To account for their occurrence, it is common to point out that people’s ability to argue is flawed, that an “argumentative culture” is lacking, and that emotional and other non-rational factors often interfere in confrontative situations. But these suggestions do not amount to a thorough satisfactory explanation. In this paper, I provide the outline of a purely epistemic account of these peculiar effects of argumentation in the face of disagreement. I argue that probabilistic models of degrees of confidence (or “credences”) can shed light on the conditions that give rise to several of these effects. This could provide some guidance on how to avoid them.