Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

In a post-truth era, taking seriously the assertions of political figures and what other people say on the internet strikes many as irrational and gullible. Let us call this reaction the “incredulous reaction.” In this paper, I consider a common response to the targets of the incredulous reaction: excluding them from activities like debate and discounting their beliefs as relevant to our own. This exclusion is motivated by the assumption that those who continue to place epistemic trust in a post-truth (...) society are acting irrationally. I begin with an argument that we can justifiably exclude irrational persons from our epistemic activities. I then present a conflict that emerges when we take the wellbeing of our epistemic community to be an end in and of itself, and not merely a means for pursuing other epistemic goods. I propose that healthy epistemic communities depend on networks of epistemic trust and on ensuring their members are treated with the epistemic respect they deserve. If we were to adopt the development of a healthy epistemic community as a goal, then excluding others may no longer be a justifiable choice. (shrink)

Over the last decade, research on derogatory communication has focused on ordinary speech contexts and the use of conventional pejoratives, like slurs. However, the use of social media has given rise to a new type of derogatory behavior that theorists have yet to address: internet trolling. Trolls make online utterances aiming to frustrate and offend other internet users. Their ultimate goal is amusement derived from observing a good faith interlocutor engage with their provocative posts. The basis for condemning a pejorative (...) utterance is often taken to be the harm it causes or a defective attitude in the speaker. However, trolling complicates this picture, since trolling utterances are by definition insincere and should be recognizable as such to other trolls. Further, these utterances seem morally questionable even when they cause little to no harm, and they often do not feature conventional pejoratives. I argue that while the potential for negative effects is relevant to ethical assessment, in general trolling is pro tanto wrong because the troll fails to accord others the proper respect that is their due. However, this characteristic wrong-making feature is sometimes overridden. (shrink)

In this paper, I argue that, despite the progress made in recent years, virtue argumentation theory still lacks a more systematic acknowledgment of other-regarding virtues. A fuller recognition of such virtues not only enriches the field of research of virtue argumentation theory in significant ways, but also allows for a richer and more intuitive view of the virtuous arguer. A fully virtuous arguer, it is argued, should care to develop both self-regarding and other-regarding virtues. He should be concerned both with (...) his own development as an arguer and with helping other arguers in that regard. (shrink)