Suppose that knowledge and ignorance are complements in the sense of being mutually exclusive: for person S and fact p, either S knows that p or is ignorant that p. Understood in this way, ignorance amounts to a lack or absence of knowledge: S is ignorant that p if and only if it is not the case that S knows that p. Let us call the thesis that knowledge and ignorance are opposites the “Complement Thesis”. In this article, I discuss its deployment in an ingenious new argument advanced by Alvin Goldman and Erik Olsson (2009) which, if sound, establishes that there is a kind of knowledge that amounts to nothing more than true belief. I rebut their argument and in doing so delineate some important epistemological lessons brought to light by the contrast between ignorance and knowledge.