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 ...