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.

Current formal dialectical models postulate normative rules that enable discussants to conduct dialogical interactions without committing fallacies. Though the rules for conducting a dialogue are supposed to apply to interactions between actual arguers, they are without exception theoretically motivated. This creates a gap between model and reality, because dialogue participants typically leave important content-related elements implicit. Therefore, analysts cannot readily relate normative rules to actual debates in ways that will be empirically confirmable. This paper details a new, data-driven method for (...) describing discussants’ actual reply structures, wherein corpus studies serve to acknowledge the complexity of natural argumentation. Rather than refer exclusively to propositional content as an indicator of arguing pro/contra a given claim, the proposed approach to dialogue structure tracks the sequence of dialogical moves itself. This arguably improves the applicability of theoretical dialectical models to empirical data, and thus advances the study of dialogue systems. (shrink)