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.

The aim of the paper is to propose a unified formal account of dialogical cognitive processes so that it allows the analysis of similarities and differences between those processes. Formal dialogue systems constitute two basic categories or paradigms of modelling communication depending on what cognitive process is described by a given system. The first paradigm consists of designing a set of dialogue rules in a similar manner to Lorenzen’s dialogue logic, and according to which players jointly aim to prove the (...) validity of a formula. In such cases we will say that the system describes formal dialogues and the formal cognitive process of proving the validity of a formula. The second paradigm focuses on building a system similar to Hamblin’s formal dialectics, which “simulates” the real-life communication practice. In the type of dialogues described by those systems, players perform “good” argumentation, i.e. argumentation which fulfils certain requirements of rationality such as e.g. the requirement of not committing a fallacy of circular reasoning. In such a case we will be speaking of a natural dialogue and a natural cognitive process of argumentation. (shrink)

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)

This paper proposes two formal models for understanding real-life dialogues, aimed at capturing argumentative structures performatively enacted during conversations. In the course of the investigation, two types of discourse with a high degree of well-structured argumentation were chosen: moral debate and financial communication. The research project found itself confronted by a need to analyse, structure and formally describe large volumes of textual data, where this called for the application of computational tools. It is expected that the results of the proposed (...) research will make a contribution to formal systems modelling and the evaluation of communication from the point of view of argument soundness. (shrink)

In his book on fallacies, Hamblin built a very simple system for argumentation in dialogue he called the Why Because System with Questions. In his discussion of this system, he replaced the concept of burden of proof with a simpler concept of initiative, which could be described as something like getting the upper hand as the argumentation moves back and forth in the dialogue between the one party and the other. No doubt he realized that the concept of burden of (...) proof was too complex a matter to be dealt with in the limited scope of his chapter on formal dialogue systems. In this paper is shown how an extended version of Hamblin’s dialogue system provides a nice way of modeling the phenomenon of shifting of burden of proof in a dialogue, yielding a precise way of distinguishing between different kinds of burden of proof, and dealing with fallacies like the argumentum ad ignorantiam. (shrink)

In his book on fallacies, Hamblin built a very simple system for argumentation in dialogue he called the Why Because System with Questions. In his discussion of this system, he replaced the concept of burden of proof with a simpler concept of initiative, which could be described as something like getting the upper hand as the argumentation moves back and forth in the dialogue between the one party and the other. No doubt he realized that the concept of burden of (...) proof was too complex a matter to be dealt with in the limited scope of his chapter on formal dialogue systems. In this paper is shown how an extended version of Hamblin’s dialogue system provides a nice way of modeling the phenomenon of shifting of burden of proof in a dialogue, yielding a precise way of distinguishing between different kinds of burden of proof, and dealing with fallacies like the argumentum ad ignorantiam (argument from negative evidence). (shrink)

Current methods to capture, analyse and present the audience participation of broadcast events are increasingly carried out using social media. Uptake of such technology tools has so far been poor amongst older adults, and it has the worrying effect of excluding the demographic from participation. Our work explores whether a common desire to interact with debates can be tapped with technology with a very low barrier to entry, to both support better engagement with broadcast debates and encourage greater use of (...) social media. This paper describes experiments where older adults interact with a BBC radio debate programme: The Moral Maze. As a result, we obtained common interaction patterns which then are used to define recommendations for software-supported interaction with debates based on theories of argumentation. Our goal is to combine research on computational models of argument and user-driven research on human-centred computing in a project with the potential for high-profile impact in addressing older adults inclusion in the digital economy. (shrink)