According to Timothy Williamson's epistemic view, vague predicates have precise extensions, we just don't know where their boundaries lie. It is a central challenge to his view to explain why we would be so ignorant, if precise borderlines were really there. He offers a novel argument to show that our insuperable ignorance ``is just what independently justified epistemic principles would lead one to expect''. This paper carefully formulates and critically examines Williamson's argument. It is shown that the argument does not explain our ignorance, and is not really apt for doing so. Williamson's unjustified commitment to a controversial and crucial assumption is noted. It is also argued in three different ways that his argument is, in any case, self-defeating – the same principles that drive the argument can be applied to undermine one of its premises. Along the way, Williamson's unstated commitment to a number of other controversial doctrines comes to light.