Fallibilism is ubiquitous in contemporary epistemology. I argue that a paradox about knowledge, generated by considerations of truth, shows that fallibilism can only deliver knowledge in lucky circumstances. Specifically, since it is possible that we are brains-in-vats (BIVs), it is possible that all our beliefs are wrong. Thus, the fallibilist can know neither whether or not we have much knowledge about the world nor whether or not we know any specific proposition, and so the warrant of our knowledge-claims is much reduced and second-order skepticism is generated. Since this is the case in both skeptical and everyday contexts, contextualism cannot resolve the paradox.