KK, Knowledge, Knowability

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weak  K¬K, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weak  K¬K are much stronger than they initially appear. Jointly, they entail kk and K¬K. And they are susceptible to variants of the standard arguments against kk and K¬K. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability.