Dialogue and refutation

Abstract

In this chapter, I provide an overview and argument to the effect that reasoning, including scientific and mathematical inquiry, is inherently both dialogical and dynamic. That is to say, reasoning is social and interactive, and requires an account of history that is not captured by an absolutist and monological account of proofs. I begin by considering the role of dialogue in logic, beginning first with a short analysis of Brandom’s account of dialogue, before discussing the history of logic, and recent approaches to logical games in the work of Jaako Hintikka and Lorenzen. There, I argue that a distinct approach is required where assertion and denial, dialogical response and testing, are central to the dynamics of reasoning and the creation of new knowledge. It is in this light that I go on to discuss the specific role of dialogue in mathematical proofs, with particular attention to the work of Imre Lakatos. Lakatos’ [1] approach to inquiry is understood to operate as a kind of dialogue between “prover” and “refuter”, where a conjecture is considered by means of proof attempts and tests in the form of refutation attempts, disproofs and counter-examples. Such “proofs that do not prove” are part and parcel with the development of inquiry, until a conclusive proof or refutation of the conjecture is reached. I go on to provide a discussion of the broader approach to dialogues, with particular reference to the interactional work of Ginzburg (e.g. [2]). I will discuss a number of constraints over dialogues taking interaction, rather than rules, to be a priori, such that co-operative interactions may be understood to form the basis of the kinds of approaches to inquiry previously discussed. I will also briefly turn to considering how this approach fares in relation to providing a way of accounting for “reasons”, which does not fall into the trap of important criticisms in feminist and post-colonialist theory. I show that the dialogical approach being advocated here is capable of providing a way of moving beyond such criticisms, with particular attention to the role of emotion in interactive reasoning processes as allowing responses to be “framed” adequately. I finish by drawing together the discussion, arguing that interactions may subsequently give rise to propositional meaning under constraints of coherence, convergence, and symmetry.