It is impossible to believe the denial of a proposition one knows to be true, knows that one knows to be true, knows is the denial of a proposition one knows, etc.

But (D3) is also equivalent to (D1), at least if it is impossible to believe the denial of a proposition one knows to be true, knows that one knows to be true, knows is the denial of a proposition one knows, etc. (Oppy (2014: 233) claims, more simply, that it is not possible to know a proposition if one believes its denial.) In the recent literature, Swinburne (1993: 167 and 2016: 175) states a version of (D1) (although in both works he later endorses restricted principles (1993: 181–182 and 2016: 196) to yield what he calls an “attenuated” definition). Zagzebski (2007: 262) endorses (D2). Pla...