Do factive mental states come in degrees? If so, what is their underlying structure, and what is their theoretical significance? Many have observed that ‘knows that’ is not a gradable verb and have taken this to be strong evidence that propositional knowledge does not come in degrees. This paper demonstrates that the adjective ‘aware that’ passes all the standard tests of gradability, and thus strongly motivates the idea that it refers to a factive mental state that comes in degrees. We (...) will explore a range of structural questions that have been overlooked in regard to our awareness of facts, showing that the degreed structure of awareness has significant implications for our understanding of knowledge. (shrink)