The creation of human knowledge is not simply the accumulation of facts, skills and ways of making sense of experience. It is also a process of evolution, in which alternative explanations, proposals and solutions compete for survival. As well as providing us with the tools for building common knowledge in a cumulative, co-operative activity, language also offers techniques for setting competing ideas and interests against each other, for ‘arguing a case’ and persuading other people that some courses of action are better than alternatives. The art of persuasive language is sometimes called ‘rhetoric’, a term which has its origins in the skilful argumentative use of language by ancient Greek orators. Today, we still tend to think of rhetoric in terms of the calculated, charismatic performance of individuals: political speakers, evangelists, salespeople and confidence tricksters are obvious examples. The ‘magic’ is assumed to lie in the monologues they perform. In this chapter, I want to take a different perspective on persuasion and argument, one that is based on dialogue rather than monologue. There certainly are people who, through technique and charisma, are particularly effective at making others believe or do what they wish. But effective arguments are those which are accepted by others, and persuasive rhetoric can only really be judged by its effects on an audience. To understand how persuasion and argument are used to get things done, we need to study social interaction.