When epistemic closure does and does not fail: a lesson from the history of epistemology

Abstract

Does the failure of a necessary condition for knowledge to be closed under known entailment imply that knowledge itself is not closed under known entailment? More generally, does the failure of a necessary condition for knowledge to be closed under some relation R imply that knowledge itself is not closed under relation R? An examination of the recent history of epistemology would lead one to think that the answer to these questions is 'yes'. I show in this note that the correct answer to these questions is 'no'. Those who answer 'yes' are committing the fallacy of composition. I also show that the mistake merits correction because it concerns important matters and occurs quite frequently. Near the beginning of his impressive early overview of issues concerning epistemic closure principles and their possible use in sceptical argumentation, Anthony Brueckner asserts that 'Knowledge is closed under known logical implication only if each necessary condition is so closed' (1985: 91). It is likely that in making this remark Brueckner was taking his cue from earlier work on epistemic closure by Robert Nozick. Nozick, (1981/1998), had defended his well known 'tracking' account of knowledge, which in its simplest form says that: S knows that P if and only if