 The strong Lockean thesis gives rise to the well-known  Lottery paradox, due originally to Kyburg (1961, 1997). The lesson of the Lottery is that the strong thesis is in tension with deductive cogency. Suppose that \(s\) is the universally correct Lockean threshold. Now think of a fair lottery with \(N\) tickets, where \(N\) is chosen large enough that \(1-(1/N) \geq s.\) Since the lottery is fair, it seems permissible to fully believe that  some ticket is the winner. It also seems reasonable to assign degree of belief \(1/N\) to each proposition of the form ‘The \(i^{\text{th}}\) ticket is the winner.’ According to the Lockean thesis, such an agent ought to fully believe that the first ticket is a loser, the second ticket is a loser, the third is a loser, etc. Since cogency requires belief to be closed under conjunction, she ought to believe that all the tickets are losers. But now she violates cogency by believing both that every ticket is a loser and that some ticket is a winner. Since \(s\) was arbitrary, we have shown that no matter how high we set the threshold, there is some Lottery for which an agent must either violate the Lockean thesis or violate deductive cogency. According to Kyburg, what the paradox teaches is that we should give up on deductive cogency: full belief should not necessarily be closed under conjunction. Many others take the lesson of the Lottery to be that the strong Lockean thesis is untenable.