Lotteries, Knowledge, and Inconsistent Belief

Mylan Engel, Jr.

Northern Illinois University

Bob holds ticket t_n in a fair lottery, and he believes that t_n will lose [L]. What is the appropriate epistemic appraisal of Bob and his belief that L? Is he justified in believing that L? Does he know that L? Back when Foley and Klein were writing on the subject, the prevailing view was that Bob is justified/rational in believing that L, but does not know that L. Today, this view has fallen out of favor. Contemporary assessments of Bob and his belief that L typically fall into one of two camps, those who argue that Bob is not justified/rational in believing that L and hence does not know that L (Ryan; and Nelkin), and those who favor contextualist appraisals, according to which the ascription ‘Bob is justified in believing and knows that L’ is true in ordinary low-standards contexts, but is false (on both counts) in the high-standards contexts typically evoked by reflecting on lotteries. (Cohen, and Lewis). The view that Bob is not only justified in his belief that L, but indeed knows that L has not been taken seriously, because it is thought to lead to paradox, both respect to justification and with respect to knowledge. I defend this latter view. Along the way, I identify four different but related versions of the lottery paradox—The Paradox for Rationality, The Paradox for Knowledge, The Paradox for Fallibilism, and The Paradox for Epistemic Closure—and offer a unified resolution of each of them.