= 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 axioms. This argument was first put forward by David Lewis in the 1970s though he never published it. 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, can ever be certain, if that. Jeffrey famously rejected Lewis' dictum and quipped, "It's probabilities all the way down." He called this position radical probabilism. In this case Bayes' rule isn't able to capture a mere subjective change in the probability of some critical fact. The new evidence may not have been anticipated or even be capable of being articulated after the event. It seems reasonable, as a starting position, to adopt the law of total probability and extend it to updating in much the same way as was Bayes' theorem. Pnew(A) = Pold(A | B)Pnew(B) + Pold(A | not-B)Pnew(not-B) Adopting such a rule is sufficient to avoid a Dutch book but not necessary. Jeffrey advocated this as a rule of updating under radical probabilism and called it probability kinematics. Others have named it Jeffrey conditioning. It is not the only sufficient updating rule for radical probabilism. Others have been advocated including E. T. Jaynes' maximum entropy principle and Brian Skyrms' principle of reflection. Jeffrey conditioning can be generalized from partitions to arbitrary condition events by giving it a frequentist semantics. See also Bayesian epistemology Selected bibliography Formal Logic: Its Scope and Limits. 1st ed. McGraw Hill, 1967. 2nd ed. McGraw Hill, 1981. 3rd ed. McGraw Hill, 1990. 4th ed., John P. Burgess (editor), Hackett Publishing, 2006, The Logic of Decision. 2nd ed. University of Chicago Press, 1990. Probability and the Art of Judgment. Cambridge University Press, 1992. Computability and Logic (with George Boolos and John P. Burgess). 4th ed. Cambridge University Press, 2002. Subjective Probability: The Real Thing. Cambridge University Press, 2004. References External links His website at Princeton; includes several manuscripts, including Subjective Probability Bibliography Curriculum Vitae From a defunct page devoted to the memory of Richard Jeffrey by