What does ‘might’ mean? One hypothesis is that ‘It might be raining’ is essentially an avowal of ignorance like ‘For all I know, it's raining’. But it turns out these two constructions embed in different ways—in particular, as parts of larger constructions like Wittgenstein's ‘It might be raining, and it's not’ and Moorean sentences like ‘It's raining, and for all I know it's not’. A variety of approaches have been developed to account for those differences. All approaches agree that both Moore sentences and Wittgenstein sentences are classically consistent. In this article I argue against this consensus. I adduce a variety of data that I argue can best be accounted for if we treat Wittgenstein sentences as being classically inconsistent. This creates a puzzle, since there is decisive reason to think that ⌜Might p⌝ is consistent with ⌜Not p⌝. How can it also be that ⌜Might p and not p⌝ and ⌜Not p and might p⌝ are inconsistent? To make sense of this situation, I propose a new theory of epistemic modals that aims to account for their subtle embedding behavior and shed new light on the dynamics of information in natural language.