Why safety doesn’t save closure

Abstract

Knowledge closure is, roughly, the following claim:

For every agent S and propositions P and Q, if S knows P, knows that P implies Q, and believes Q because it is so implied, then S knows Q.

Almost every epistemologist believes that closure is true. Indeed, they often believe that it so obviously true that any theory implying its denial is thereby refuted. Some prominent epistemologists have nevertheless denied it, most famously Fred Dretske and Robert Nozick. There are closure advocates who see other virtues in those accounts, however, and so who introduce revisions of one sort or another in order to preserve closure while maintaining their spirit. One popular approach is to replace the “sensitivity” constraint at the heart of both of those accounts with a “safety” constraint, as advocated by Timothy Williamson, Duncan Pritchard, Ernest Sosa, Stephen Luper, and others. The purpose of this essay is to show that this approach does not succeed: safety does not save closure. And neither does a popular variation on the safety theme, the safe-basis or safe-indicator account.