According to some philosophers, we are “cognitively closed” to the answers to certain problems. McGinn has taken the next step and offered a list of examples: the mind/body problem, the problem of the self and the problem of free will. There are naturalistic, scientific answers to these problems, he argues, but we cannot reach them because of our cognitive limitations. In this paper, we take issue with McGinn’s thesis as the most well-developed and systematic one among the so-called “new mysterians”. McGinn aims to establish a strong, representational notion of cognitive closure: a principled inaccessibility of a true theory of certain properties of the world, but he offers arguments that only bear on difficulties with psychologically grasping the correct answers. The latter we label psychological closure. We argue that representational closure does not follow from psychological closure, and that McGinn’s case therefore falters. We could very well be able to represent the correct answer to some question, even without being able to grasp that answer psychologically. McGinn’s mistake in deriving representational closure from psychological closure rests on a fallacy of equivocation relating to the concept of ‘understanding’. By making this distinction explicit, we hope to improve our thinking about the limits of science in particular and human knowledge in general.