It is widely believed that for all p, or at least for all entertainable p, it is knowable a priori that (p iff actually p). It is even more widely believed that for all such p, it is knowable that (p iff actually p). There is a simple argument against these claims from four antecedently plausible premisses.

The argument is given below. Here ‘A’, ‘E’, ‘K’, ‘□’, ‘◊’ stand for ‘Actually’, ‘Someone entertains’, ‘Someone knows’, ‘Necessarily’ and ‘Possibly’, while ‘→’ and ‘↔’ are the material conditional and biconditional. In addition, q is any (entertainable and expressible) proposition that no one actually entertains, while r is ¬Eq, the proposition that...