A long line of epistemologists including Sosa (Epistemic explanations: a theory of telic normativity, and what it explains. Oxford University Press, Oxford, 2021), Feldman (The ethics of belief. Philos and Phenomenol Res 60:667–695, 2002), and Chisholm (Theory of knowledge, 2nd edn. Prentice-Hall, Englewood Cliffs, 2007) have argued that, at least for a certain class of questions that we take up, we should (or should aim to) close inquiry iff by closing inquiry we would meet a unique epistemic standard. I argue that no epistemic norm of this general form is true: there is not a single epistemic standard that demarcates the boundary between inquiries we are forbidden and obligated to close. In short, such norms are false because they are insensitive to the potentially ambitious epistemic goals that agents may permissibly bring to bear on an inquiry. Focusing particularly on knowledge-oriented versions of the norm, I argue that beliefless ignorance has a positive role to play in epistemic life by licensing prolonged inquiry into questions that we especially care about. © 2022, The Author(s).