Four arguments for denying that lottery beliefs are justified

In Douven, I. ed. Lotteries, Knowledge and Rational Belief: Essays on the Lottery Paradox (Cambridge: Cambridge University Press). Cambridge: (2021)
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A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified.
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