Probability and Decision Theory

A number of further paradoxes involving probability, decision theory, and infinity are adduced. Some, like Satan’s Apple and Beam’s paradox, only provide weak evidence for causal finitism. But a particularly interesting paradox allows an agent who has from eternity been playing a fair die-guessing game, which game will one day come to an end, to leverage information from past rolls to ensure that shemakes only finitely many wrong guesses.This is absurd: leveraging past information in fair rolls should be just as irrational as the Gambler’s Fallacy. The game involves infinite causal histories, however, and so the causal finitist can reject its possibility.This provides rather more evidence for causal finitism.