A Bayesian approach to argumentation has, arguably, made great strides in illuminating long-standing questions about argument quality. In particular, the Bayesian framework allows nuanced evaluation of content-based differences in argument strength for individual arguments –both for arguments about facts and for practical arguments. It also provides a principled approach to summary evaluation in contexts of multiple, both mutually supporting and competing arguments, in final reckoning. What it has not done, however, is contribute systematically to an understanding of the dialectical process of argumentation, either in dyads or across large collectives. The talk reviews the literature on argument quality, but then focusses on recent work within the Bayesian framework to address this dialectical challenge.