Radical probabilism

Radical probabilism is a hypothesis in philosophy, in particular epistemology, and probability theory that holds that no facts are known for certain. That view holds profound implications for statistical inference. The philosophy is particularly associated with Richard Jeffrey who wittily characterised it with the dictum "It's probabilities all the way down." Subjective probability Bayes' theorem states a rule for updating a probability conditioned on other information. In 1967, Ian Hacking argued that in a static form, Bayes' theorem only connects probabilities that are held simultaneously; it does not tell the learner how to update probabilities when new evidence becomes available over time, contrary to what contemporary Bayesians suggested. According to Hacking, adopting Bayes' theorem is a temptation. Suppose that a learner forms probabilities Pold(A & B) = p and Pold(B) = q. If the learner subsequently learns that B is true, nothing in the axioms of probability or the results derived therefrom tells him how to behave. He might be tempted to adopt Bayes' theorem by analogy and set his Pnew(A) = Pold(A | B) = p/q. In fact, that step, Bayes' rule of updating, can be justified, as necessary and sufficient, through a dynamic Dutch book argument that is additional to the arguments used to justify the probability axioms. This argument was first put forward by David Lewis in the 1970s though he never published it. The dynamic Dutch book argument for Bayesian updating has been criticised by Hacking, Kyburg, Christensen, and Maher. It was defended by Brian Skyrms. That works when the new data is certain. C. I. Lewis had argued that "If anything is to be probable then something must be certain". There must, on Lewis' account, be some certain facts on which probabilities were conditioned. However, the principle known as Cromwell's rule declares that nothing, apart from a logical law, if that, can ever be known for certain. Jeffrey famously rejected Lewis' dictum.