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Michael G Titelbaum, The Stability of Belief: How Rational Belief Coheres with Probability, by Hannes Leitgeb, Mind, Volume 130, Issue 519, July 2021, Pages 1006–1017, https://doi.org/10.1093/mind/fzaa017
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1.
Sometimes maths makes magic. One builds a formal system, hoping to satisfy certain specifications or capture some abstract notion. Then—seemingly on its own—the system solves other problems, generates fecund principles, or reconciles possibilities previously assumed incompatible.
While there’s nothing quite like experiencing this oneself, a similar serendipity can arise from watching someone else pull the trick. In The Stability of Belief: How Rational Belief Coheres with Probability, our mathemagician is Hannes Leitgeb. Leitgeb develops a formal theory of how all-or-nothing beliefs cohere with degrees of belief. The theory is plausible and has important philosophical precedents. But what’s truly remarkable is the many things it can do: square Bayesian belief update with AGM revision; unite traditional decision theory with a decision theory for full belief; mesh attractive theories of assertability, conditionals, and acceptance; and so on. Leitgeb introduces a hat in the first chapter, then pulls rabbits out of it for 300 pages.