Knowledge of Ignorance in Epistemic Puzzles

Three epistemic puzzles are analyzed in the article: the puzzle discovered by Williamson (the puzzle of visual measurement), Fitch's paradox (the paradox of knowability), and the surprise exam paradox. It is demonstrated that an essential part of each of them is the assumption that agents can have negative reflexive knowledge, i.e. knowledge of one's own ignorance. In Williamson's scenario, an agent tries to visually estimate how tall a tree is. Negative reflexive knowledge ascribed to the agent in the scenario is to the effect that he knows that, for any natural n, if the tree is n inches tall then he does not know that it is n - 1 inches tall. In Fitch's setting, the possibility of knowing one's own not-knowing a state of affairs is considered. Finally, in various versions of the surprise event puzzle (such as the surprise exam puzzle), it is presupposed that people expect an event but know that, a day before the event, they will not know that it is going to take place next day. These observations can be generalized to the claim that negative reflexive knowledge-formally, assumptions of the form ...K(...K...) -are an essential part of many (if not all) epistemic puzzles. It is shown that negative reflexive knowledge plays the same role in epistemic puzzles as alethically negative self-reference plays in semantic paradoxes, namely the Liar paradox and Yablo's paradox (the latter is taken in the interpretation proposed by Priest). Alethically negative self-reference is the fact that paradoxical sentences ascribe to themselves the property of being untrue. Both negative reflexive knowledge and alethically negative self-reference, produce (within relevant settings) unwelcome effects: paradoxicality in semantic paradoxes and counter-intuitive consequences in epistemic puzzles.

Keywords

Authors

References