THE 6-49-LOTTERY PARADOX

The paradox of the preface and the lottery paradox are paradoxes of pr actical certainty sharing certain features. The paradox of the lottery argues that rational agents are at once practically certain that each ticket in a lottery will lose but also practically certain some ticke t will win. The paradox of the preface argues that rational agents are at once practically certain that all facts in a written volume are tr ue, yet are also practically certain that some fact is wrong. A differ ence between real lotteries and prefaces is that a winning lottery tic ket is generally an intended feature of the lottery, whereas incorrect facts are generally unintended. Despite these similarities, Pollock g ives a novel argument suggesting that the preface paradox warrants qua litatively different treatment from the lottery, using as a rationale the differences between real lotteries and prefaces. This draws a clea r line between the work of Pollock and the work of Kyburg, both of who m have had a prominent influence in recent thinking on nonmonotonic re asoning in AI. This note shows there are real lotteries with the forma l structure of the preface paradox and possibly prefaces with the form al structure of lotteries. The surprising conclusion is that within Po llock's framework, the treatment of any problem with a formal structur e resembling the lottery (or the preface) depends on the process by wh ich winning tickets (or publishing errors) are generated. The rational es given by Pollock seem to be unrelated to the actual mechanisms impl emented.