Lewis on iterated knowledge

Abstract

The status of the knowledge iteration principles in the account provided by Lewis in “Elusive Knowledge” is disputed. By distinguishing carefully between what in the account describes the contribution of the attributor’s context and what describes the contribution of the subject’s situation, we can resolve this dispute in favour of Holliday’s (2015) claim that the iteration principles are rendered invalid. However, that is not the end of the story. For Lewis’s account still predicts that counterexamples to the negative iteration principle (¬Kp→K¬Kp) come out as elusive: such counterexamples can occur only in possibilities which the attributors of knowledge are ignoring. This consequence is more defensible than it might look at first sight.