How to Mistake a Trivial Fact About Probability For a Substantive Fact About Justified Belief

It is sometimes thought that the lottery paradox and the paradox of the preface demand a uniform solution (Hunter (1996) and Foley (1992), for example). Let us see why that appears to be the case. 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. Many books are written sufficiently meticulously that the author is justified in everything he says and in the beliefs that his statements express; a fortiori, this is possible. Still, all but the most arrogant meticulous authors will believe that they have made some errors—and they will be justified in believing that at least one of their statements (and their beliefs so expressed) is false. Such a meticulous author might express this belief that there are errors in his book in the preface rendering his book as a whole inconsistent. So, the story goes, the meticulous author justifiably believes pi where ‘i’ indexes in succession each of the propositions that he expresses in his book and yet he justifiably believes not-(p1& . . .&pn)—