Abstract
I show that from common views about propositions as sets of possible worlds and knowledge requiring a sufficiently strong safety condition one can derive a condition stating that self-knowledge of belief is only possible if the content of that belief is fully understood. I show this by a reductio. If a subject S lacks full understanding of a proposition p, then S’s belief about believing that p cannot amount to knowledge. Even though my argument is based on particular views about propositions and knowledge, I argue that the same kind of argument is also available for other knowledge conditions that rule out relevant luck and other accounts of propositions. However, for many of these other accounts of knowledge the requirement for understanding p will not be full understanding, but only sufficiently high understanding. These results tell us how self-knowledge, ruling out luck and understanding belief contents relate.