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For lottery believers and non-believers

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The Lottery Paradox

The Lottery Paradox, originally noticed by H.E. Kyburg in his 1961 Probability and the Logic of Rational Belief, is studied by epistemologists interested in justification.

The paradox can be simply put. Let us imagine that one wishes to enter a local lottery along with thousands of other participants. However, it is immediately recognizable that the chance of one's ticket losing is so high that one is justified in believing that it will not win. Probability seems to confirm the justification for such a belief. Yet, it is not just one's individually purchased ticket that has such a high probability of losing, but any ticket that has been bought in a fair lottery. Furthermore, since one seems justfied in believing that each individual ticket will not win, one also seems justified in believing that the conjunction of all tickets, or that every ticket, will not win. On the other hand, one must also remember that in all lotteries there is the slight probability that a ticket will win. After all, there is always at least one winner. Following this, one does not seem justified in believing that the conjunction of all tickets, or every ticket, will not win. Therefore, one is paradoxically justified in believing that every ticket will not win, and also not justified in believing that every ticket will not win.

The Lottery Paradox was also construed slightly differently in David Lewis' "Elusive Knowledge." Let us imagine that one knows how many thousands or millions of tickets there are, and one also knows the number of losing tickets as well as the number of winning tickets, one. Under his interpretation, there are so many tickets and possibilities of losing that no matter how many tickets you know will lose, it is still not great enough to turn your justified belief into knowledge.

[The information in this blog entry was taken from several sources on the 'net. (wikipedia.org, about.com, answres.com, etc.) A simple search will yield numerous sites offering the same information.]

Entry #36

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