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.
"A defense of the rationality of adductive inference from the criticisms of Bayesian theorists"--
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