Infinitesimal Probabilities and Regularity
Speaker: Matt Parker, CPNSS
LAK2.06, Tuesday April 30, 5.30-7pm, all welcome
ABSTRACT: In standard probability theory, probability zero is not the same as impossibility. If an experiment has infinitely many possible outcomes, all equally likely, then all the outcomes must have probability zero, but at least one of them must occur nonetheless. Many have suggested that this should not be so—that probabilities (ontic or epistemic, depending on the author) should be regular: Only impossible events should have probability zero and only necessary or certain events should have probability one. This can be arranged if we allow infinitesimal probabilities, but it turns out that infinitesimals do not solve all of the problems. I will show that regular probabilities cannot be translation-invariant, even for bounded and disjoint events. Hence, for various events confined to finite space and time (e.g., dart throws and vacuum fluctuations), regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable symmetry principles. Moreover, these examples are immune to the main objections against Timothy Williamson’s infinite coin flip examples.