The Problem of Nearly Convergent Knowledge is an updated and stronger version of the Problem of Convergent Knowledge, which presents a problem for the traditional, binary view of knowledge in which knowledge is a two-place relation between a subject and the known proposition. The problem supports Knowledge Contrastivism, the view that knowledge is a three-place relation between a subject, the known proposition, and a proposition that disjoins the alternatives relevant to what the subject knows. For example, if knowledge is contrastive, (...) I do not simply know that the bird in front of me is a goldfinch; instead, I know that the bird in front of me is a goldfinch rather than a raven or eagle or falcon. There is, however, a binary view of knowledge that overcomes even the Problem of Nearly Convergent Knowledge. I will give this binary view, show that it is motivated by the same considerations that motivate Knowledge Contrastivism, and argue that it avoids problematic consequences for our epistemic lives that Knowledge Contrastivism cannot. (shrink)