We discuss the ‘problem of convergent knowledge’, an argument presented by J. Schaffer in favour of contextualism about knowledge attributions, and against the idea that knowledge-wh can be simply reduced to knowledge of the proposition answering the question. Schaffer's argument centrally involves alternative questions of the form ‘whether A or B’. We propose an analysis of these on which the problem of convergent knowledge does not arise. While alternative questions can contextually restrict the possibilities relevant for knowledge attributions, what Schaffer's puzzle reveals is a pragmatic ambiguity in what ‘knowing the answer’ means: in his problematic cases, the subject knows only a partial answer to the question. This partial knowledge can be counted as adequate only on externalist grounds.