I present two arguments that aim to establish logical limits on what we can know. More specifically, I argue for two results concerning what we can know about questions that we cannot answer. I also discuss a line of thought, found in the writings of Pierce and of Rescher, in support of the idea that we cannot identify specific scientific questions that will never be answered.

It is widely thought that education should aim at positive epistemic standings, like knowledge, insight, and understanding. In this paper, we argue that, surprisingly, in pursuit of this aim, it is sometimes necessary to also cultivate ignorance. We examine several types of case. First, in various circumstances educators should present students with defeaters for their knowledge, so that they come to lack knowledge, at least temporarily. Second, there is the phenomenon of ‘scaffolding’ in education, which we note might sometimes involve (...) the educator quite properly ensuring that the student is ignorant of certain kinds of information. Third, if ignorance is lack of true belief, as a number of commentators have claimed, then in those cases in which students believe something truly without knowing it and teachers show that they lack knowledge, students may abandon that belief and thus become ignorant. In examining the role of ignorance in education, we explore exactly which kinds of ignorance are valuable in teaching situations and draw attention to important epistemic differences between ignorance on different levels. (shrink)

When moral philosophers study ignorance, their efforts are almost exclusively confined to its exculpatory and blameworthy aspects. Unfortunately, though, this trend overlooks that certain kinds of propositional ignorance, namely of the personal costs and benefits of altruistic actions, can indirectly incentivize those actions. Humans require cooperation from others to survive, and that can be facilitated by a good reputation. One avenue to a good reputation is helping others, sticking to moral principles, and so forth, without calculating the personal costs of (...) doing so, e.g., saving someone from a burning building without calculating how personally costly or beneficial it would be. These actions are indirect moral benefits (partly) resulting from that kind of propositional ignorance. (shrink)

I argue that the Standard View of ignorance is at odds with the claim that knowledge entails truth. In particular, if knowledge entails truth then we cannot explain away some apparent absurdities that arise from the Standard View of ignorance. I then discuss a modified version of the Standard View, which simply adds a truth requirement to the original Standard View. I show that the two main arguments for the original Standard View fail to support this modified view.