This paper, a contribution to the growing literature on virtue ethics as applied to argumentation, makes the case that arguers need two sets of virtues, appropriate for two distinct ends. When mutual understanding is not assured, the ideal of cooperative argumentation is apposite. When it is not, the ideal of adversarial argumentation should be preferred.
The paper is well-written and addresses an important topic. I feel, however, that it is too informal in its approach: several key concepts are nowhere defined or even characterized. We are told that the good of argumentation is that it improves belief systems, but we are not told what that improvement consists in, or what counts as a "good" belief system. It cannot be a system of true beliefs (that has been ruled out). So it has to be simply "better"—but this leaves us none the wiser.
The twin notions of adversarial and cooperative argumentation are characterized several times, often in widely different terms, which introduces confusion. Sometimes the adversarial reasoner is described as "impartial" (section 3.1.) and "charitable"; sometimes on the contrary she is "a knight for her own arguments". I am not saying there is a contradiction here, but clearly the range of interpretations as to what "adversarial" means is wide open.
The notion of "understanding" (which serves to define the turning point where the adversarial ideal becomes more appropriate than the cooperative one) is even more vague. What counts as good enough understanding? When can I be sure that me and my interlocutor see exactly eye to eye? And wouldn't that be the point when argumentation ceases to be necessary?
For these reasons I found the argument rather woolly overall.