The Ubiquity of Moore's Paradox

G. E. Moore and L. Wittgenstein discussed statements of form “A and I do not believe that A,” and offered quite different diagnoses of the apparent absurdity. I will examine logical aspects of this paradox, including variants for subjective probability as well as simple belief. In the end I will argue that both Moore's and Wittgenstein's diagnoses appear when we treat belief as a modality, provided we give the language both a third-person and first-person reading. In this way a classical modal logic can have a non-classical logic hidden inside.