Can we believe things that could not possibly be true? The world seems full of examples. Mathematicians have "proven" theorems which in fact turn out to be false. People have believed that Hesperus is not Phosphorus, that they themselves are essentially incorporeal, that heat is not molecular motion -- all propositions which have been claimed to be not just false, but necessarily false. Some have even seemed to pride themselves on believing the impossible; Hegel thought contradictions could be true, and Kierkegaard seems to have thought that Christianity, in which he fervently believed, was impossible and absurd.