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.

I inquire into argument at the system level, exploring the controversy over whether climate scientists should fly. I document participants’ knowledge of a skeptical argument that because scientists fly, they cannot testify credibly about the climate emergency. I show how this argument has been managed by pro-climate action arguers, and how some climate scientists have developed parallel reasoning, articulating a sophisticated case why they will be more effective in the controversy if they fly less. Finally, I review some strategies arguers (...) deploy to use the arguments of others against them. I argue that only by attending to argument-making at the system level can we understand how arguers come to know the resources for argument available in a controversy and to think strategically about how to use them. I call for more work on argument at the system level. (shrink)