Been re-reading this very fine paper recently (in order to be a responsible dissertation director!), and noticed something puzzling. Schaffer aims to discredit the reductive view that knowledge-wh constructions are reducible to knowledge that constructions. The basic idea of the reductive view is that the former construction encodes a question, and the reduction can go through correct answers to such questions. So, you know whether the caged bird sings, when the caged bird sings, iff you know that the caged bird sings.
The fundamental problem Schaffer raises for this reductive view is the problem of convergent knowledge: where two different questions have a common correct answer. As in: S knows whether it is a wolf or german shepherd vs. S knows whether it is a poodle or german shepherd. When it is a german shepherd, a correct answer to the two embeddded questions is: it is a german shepherd. But the first knowledge is hard and the second is easy, so a reductive view that replaces both knowledge-wh attributions with knowledge that it is a german shepherd is in trouble.
It strikes me that this argument plays off a too simplistic version of the reductive view. Some versions of it allow the reduction through any correct answer to the question (see, e.g., Higginbotham), but that’s a special case.
To see alternatives, note that there are lots of correct answers to the questions “is it a GS or W?”, “is it a GS or P?”. Among them are: “it is a GS”, “it is a GS and not a W”, “it is a GS and not a P”, and (a favorite among logicians) “yes”. There is no answer such that it is the correct answer to these questions. There are multiple correct answers. So which answers should the reductive view exploit in trying to reduce knowledge-wh to knowledge that?
I would think one would begin with the idea of informative and responsive answers to the question. So if the question is “is it a GS or a W?”, the answer that it is a GS and not a W is more informative and responsive an answer to the question than the answer that it is a GS. In short, I would think that a reductive view would want to exploit answers to questions that involve all the central conceptual elements involved in the question.
I don’t pretend that this is formally precise or an adequate form of a reductive view as it stands. It’s more like a pointing in the direction that I expect the best reductive view to be found. If so, however, it looks like the problem of convergent knowledge is going to have to be formulated differently, if it is to raise a problem for the reductivist view. For knowing that it is a german shepherd and not a wolf is knowing something different from knowing that it is a german shepherd and not a poodle.