This paper evaluates whether and to what extent modal constraints on knowledge or the semantics of ‘knows’, which make essential reference to what goes on in other possible worlds, can be considered non-epistemic factors with epistemic significance. This is best understood as the question whether modal factors are non-truth-relevant factors that make the difference between true belief and knowledge, or to whether a true belief falls under the extension of ‘knowledge’ in a context, where a factor is truth-relevant with respect (...) to S’s belief that P iff it bears on the probability that P is true. To the extent that these factors are non-epistemic, epistemologies that endorse them—modal epistemologies—stand in conflict with intellectualism. I focus on three modal epistemologies: safety, sensitivity, and David Lewis’s epistemic contextualism. I argue that prima facie, safety and sensitivity allow that non-epistemic changes in a context can shift the closeness ordering on worlds, and in so doing make a difference to whether S knows P, while Lewis’s contextualism allows that non-epistemic changes in a context can shift the relevant domain of not-P possibilities that must be eliminated for ‘S knows P’ to be true in that context. Then to make her theory compatible with intellectualism, the modal epistemologist must say much more about the notion of probability at play in the definition of ‘truth-relevant’. I suggest that either accepting or rejecting that modal epistemologies are intellectualist has significance consequences for debates between pragmatists and purists, which radiate into wider contemporary epistemology. (shrink)