How to mistake a trivial fact about probability for a substantive fact about justified belief

Abstract

I am justified in believing that my lottery ticket—call it t1—will not win, on statistical grounds. Those grounds apply equally to any other ticket, so I am justified in believing of any other ticket ti (let i take values from 2 to 1000000) that it will not win. I am not, however, justified in believing the giant conjunctive proposition that t1 will not win & t2 will not win & . . . & t1,000,000 will not win. On the contrary, I am justified in believing that some ticket will win, hence that one of those conjuncts is false. Suggested solution: justified belief is not closed under conjunction. It does not follow from the fact that I am justified in believing p and justified in believing q that I am justified in believing p & q.

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The lottery paradox, knowledge, and rationality.Dana K. Nelkin - 2000 - Philosophical Review 109 (3):373-409.
The Epistemology of Belief and the Epistemology of Degrees of Belief.Richard Foley - 1992 - American Philosophical Quarterly 29 (2):111 - 124.

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