The work in this thesis contributes towards answering a simple, important and longstanding question: How do people evaluate informal arguments In Chapter 1, I review existing approaches to informal argumentation, and suggest that the Bayesian approach provides the most appropriate way of capturing informal argument strength. The Bayesian approach assumes that arguments are composed of claims and evidence. When people evaluate informal arguments, they make a probabilistic judgment about how convincing it is - that is, how likely the claim is to be true given the available evidence. The Bayesian approach is normative, because it makes predictions about how convincing different arguments should be. In Chapter 2, I examine the Bayesian claim to...