According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, in which the fundamental norms are traditionally assumed to be logical. Here, we present a major generalization of extant Bayesian approaches to argumentation that (a) utilizes a new class of Bayesian learning methods that are better suited to modeling dynamic and conditional inferences than standard Bayesian conditionalization, (b) is able to characterize the special value of logically valid argument schemes in uncertain reasoning contexts, (c) greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and (d) undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic.