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Quitting Certainties: A Bayesian Framework Modeling Degrees of Belief , Michael G. Titelbaum . Oxford University Press , 2013, xii + 345 pages.
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On the standard Bayesian picture, agents rationally change their beliefs by becoming certain of more and more facts. If we were to read this normatively, we would have to contend that it is irrational to forget. Michael Titelbaum wants to cure Bayesianism of this counterintuitive consequence by providing a new formal framework which he dubs the Certainty Loss Framework (CLF). The CLF is meant to offer the Bayesian answer to problems involving memory loss and, what is more, to problems exhibiting context-sensitivity. In this review, I shall briefly present the main ingredients of the CLF and illustrate it by Titelbaum's analysis of the Sleeping Beauty Problem, that familiar 'test bed' for formal frameworks that model memory loss and context-sensitivity. I shall conclude by mentioning some of the other topics the CLF can help clarify.
But first, a general comment on style. Quitting Certainties is entirely self-contained. The formal machinery is introduced in detail and the reader is only assumed to be familiar with set theoretical notation and some introductory logic. The proofs are all in the Appendices, making the book easy to read for someone who is not interested in the formal nitty-gritty and is only looking for the philosophical import of the results. Moreover, all references to the wider literature are succinctly and clearly explained and all puzzles the book sets out to solve are introduced at length. Titelbaum is meticulous in laying out his framework and makes astute observations along the way with regards to how formal frameworks should be used in philosophy - these remarks alone make the book worth reading for any student of formal philosophy.
The CLF comprises a model together with some systematic and extrasystematic constraints and an interpretation. A model consists of a set of time points (T) and a modelling language (L). Over the set of time points and the set of sentences, Titelbaum defines a probability function capturing the agent's credences at time i (Pi).
The extrasystematic constraints stipulate that the model assigns an agent a credence of 1 in a claim...