For the last two and a half millennia or so, most philosophers have devoted at least part of their careers to the study of rationality. They have wondered, for example, how "reason" can override the "passions" in rational conduct, how thought can proceed in accordance with rational laws, what the first principles of reason are (if there are any), whether they can be justified, and if so, how. Only few philosophers, however, have bothered to ask how irrational thinking and acting is possible. One of the first, Aristotle, touched off a still unfinished debate about the weakness of the will (akrasia). He noticed a curious problem that has bedeviled theories of rationality from their very beginnings, the problem that these theories tend to overshoot the mark. They tend to demonstrate, not only how a person can act rationally, but also that, given that she can so act, she cannot but act rationally. Theories of rationality tend to have notorious problems in explaining how irrational conduct is possible.