Topic-sensitivity and the hyperintensionality of knowledge

It is natural to assume that knowledge, like belief, creates a hyperintensional context, that is, that knowledge ascriptions do not allow for substitution of necessarily equivalent prejacents salva veritate. There exist a variety of different proposals for modelling the phenomenon. In the last years, the topic-sensitive approach to the hyperintensionality of knowledge has gained considerable traction. It promises to provide a natural account of why knowledge fails to be closed under necessary equivalence in terms of differences in subject matter. Here, we argue that the topic-sensitive approach, as recently put forward by Franz Berto, Peter Hawke, Aybüke Özgün, and others, faces formidable problems. The root of these problems lies in the approach's prediction that a mere grasp of subject matter may help to provide insights into necessary implications that it would seem to require more substantive epistemic work to gain.