Abstract

A statement q is a conclusion intermediate between p and h if and only if (1) p justifies h, (2) p justifies q, and (3) (p and not-q) justifies h to a significantly lesser degree than p justifies h. I contend that Gettier-type counterexamples to definitions of factual knowledge violate the following principle: if one knows that h on the basis of p, then all the conclusions intermediate between p and h are true. This principle does not refer to anyone's beliefs that intermediate conclusions are true. I test my contention against several examples which have been discussed in the literature.