Seminar on History and Philosophy of Science

Abstract: In this talk I consider two families of principles for generalized probabilistic learning, reflection principles and martingale principles, in the setting of measure theoretic probability. Roughly speaking, these principles assert that your current opinions should cohere with your anticipated future opinions. I will show that both principles can be justified by three types of arguments, which are based on expected accuracy, diachronic coherence, and the value of information. Together these arguments establish reflection and martingale principles as important guides to rational learning.