Lotteries Knowledge and Rational Belief

We talk and think about our beliefs both in a categorical (yes/no) and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious near-platitudinous claim is known to give rise to a paradox commonly known as the ''lottery paradox'' at least when it is coupled with some further seeming near-platitudes about belief. How to resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject all of which provide compelling reasons for rethinking many of the fundamentals of the debate.