Open knowledge and changing the subject

Abstract

Knowledge is closed under (known) implication, according to standard theories. Orthodoxy can allow, though, that apparent counterexamples to closure exist, much as Kripkeans recognize the existence of illusions of possibility (IPOs) which they seek to explain away. Should not everyone, orthodox or not, want to make sense of “intimations of openness” (IONs)? This paper compares two styles of explanation: (1) evidence that boosts P’s probability need not boost that of its consequence Q; (2) evidence bearing on P’s subject matter may not bear on the subject matter of Q.