1. Davood Bahjat Fumani

    Dear all,

    Just a quick reminder about the next session of our EXRE Colloquium, which takes place tomorrow: we’ll have the pleasure of hearing Francesco Praolini’s talk on “The Revenge Lottery Paradox” at 17:15, room MIS02, 2122.
    Please find his abstract below.


    It is intuitive to think that rational belief is closed under conjunction introduction; that is, more perspicuously, (Conjunction Closure) for any two propositions, p and q, if it is rational for one to believe that p and it is rational for one to believe that q, then it is rational for one to believe their conjunction. At the same time, Bayesians insist that rationality requires of agents that they have probabilistically coherent degrees of confidence in propositions; that is, more perspicuously, (Probabilism) at any given time, a rational credence function is a probability function. Further, it is natural to hold that there exists a relation between rational categorical beliefs and credences. The following is a popular thesis about their relation: (The Lockean Thesis) there is a threshold value v (where v is a real number and 1/2 < v < 1) such that, for any proposition, p, it is rational for one to believe that p if and only if one’s rational credence in p is equal to or greater than v. As we know, however, not all of Conjunction Closure, Probabilism, and The Lockean Thesis are true: a version of Henry E. Kyburg Jr.’s lottery paradox shows that these three theses are jointly inconsistent. A popular solution to this and other versions of the lottery paradox is to deny Conjunction Closure. I argue in this paper that we can reach paradoxical conclusions from cases like or analogous to those presented in traditional versions of the lottery paradox even if we assume that Conjunction Closure is mistaken. As I show in this paper, these paradoxes arise when we assume standard Bayesian updating rules and we ask which beliefs, if any, belong to an agent’s body of evidence.