According to the Rationality Constraint, our concept of belief imposes limits on how much irrationality is compatible with having beliefs at all. We argue that empirical evidence of human irrationality from the psychology of reasoning and the psychopathology of delusion undermines only the most demanding versions of the Rationality Constraint, which require perfect rationality as a condition for having beliefs. The empirical evidence poses no threat to more relaxed versions of the Rationality Constraint, which only require only minimal rationality. Nevertheless, we raise problems for all versions of the Rationality Constraint by appealing to more extreme forms of irrationality that are continuous with actual cases of human irrationality. In particular, we argue that there are conceivable cases of “mad belief” in which populations of Lewisian madmen have beliefs that are not even minimally rational. This undermines Lewis’s claim that our ordinary concept of belief is a theoretical concept that is implicitly defined by its role in folk psychology. We argue that introspection gives us a phenomenal concept of belief that cannot be analyzed by applying Lewis’s semantics for theoretical terms.