Let's say that the proposition that p is transparent just in case Kmp for every m, where Km abbreviates m iterations of the epistemological operator 'it is known that'. I show that, given Timothy Williamson's margin for error semantics for such epistemological operators, the existence of transparent propositions, (for example B(0), which abbreivates 'any man with 0% scalp coverage is bald') requires (in a large class of models) that certain higher-order predicates (such as KmB(x) for some sufficiently large m) have known boundaries – a fact which is apparently incompatible with the epistemicist theory of vagueness.