 In 1961 Henry Kyburg pointed out that this policy conflicted with a principle of agglomeration: If you rationally believe \(p\) and rationally believe \(q\) then you rationally believe both \(p\) and \(q\). Little pictures of the same scene should sum to a bigger picture of the same scene. If rational belief can be based on an acceptance rule that only requires a high probability, there will be rational belief in a contradiction! To see why, suppose the acceptance rule permits belief in any proposition that has a probability of at least .99. Given a lottery with 100 tickets and exactly one winner, the probability of ‘Ticket \(n\) is a loser’ licenses belief. Symbolize propositions about ticket \(n\) being a loser as \(p_n\). Symbolize ‘I rationally believe’ as \(B\). Belief in a contradiction follows: