(Un)knowability and knowledge iteration

Abstract

Abstract The KK principle states that knowing entails knowing that one knows. This historically popular principle has fallen out of favour among many contemporary philosophers in light of putative counterexamples. Recently, some have defended more palatable versions of KK by weakening the principle. These revisions remain faithful to their predecessor in spirit while escaping crucial objections. This paper examines the prospects of such a strategy. It is argued that revisions of the original principle can be captured by a generalized knowledge iteration principle, Weak-KK, which states that knowing entails the possibility of knowing that one knows. But Weak-KK is vulnerable to an unknowability result and therefore must be rejected. The arguments here suggest that retreating to weaker iteration principles is not an option for the KK enthusiast.