lottery paradox

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Suppose a lottery with a large number of tickets. Then it is rational to believe of each particular ticket that it will lose. If it is rational to hold two beliefs separately, then it must be rational to hold their conjunction. But if we conjoin all these beliefs and we know that we have considered each ticket, then this is equivalent to believing that every ticket will lose, which is irrational. The structure is similar to the preface paradox.

Subjects: Philosophy.

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