Dialogue Types, Argumentation Schemes, and Mathematical Practice: Douglas Walton and Mathematics

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 ({\S}1) and argumentation schemes ({\S}2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.