One can neither inquire into what one knows nor into what one doesn’t know. The first leg of this problem has recently been called the Dogmatism Puzzle. If knowledge is incompatible with inquiry, the thought goes, knowledge breeds dogmatism. Call the second leg of the problem the Ignorance Puzzle. Inquiry starts from not knowing what one seeks to know, and yet it cannot simply start from ignorance. A compelling solution, we argue, jointly addresses the Dogmatism and Ignorance Puzzles. Inquirers, we propose, are in Incomplete Ignorance. They have proleptic concepts, which enable them to ask questions. We defend a minimalist account of the complement of questions. Questions, this chapter argues, call for an improvement of the inquirer’s cognitive state regarding the issue. Such improvement may psychologically close off further inquiry. But the inquirer’s cognitive state is not thereby epistemically closed. In principle, it permits further inquiry.