Bridging Ranking Theory and the Stability Theory of Belief
In this paper we compare Leitgeb’s stability theory of belief (Annals of Pure and Applied Logic, 164:1338-1389, 2013; The Philosophical Review, 123:131-171, ) and Spohn’s ranking-theoretic account of belief (Spohn, 1988, 2012). We discuss the two theories as solutions to the lottery paradox. To compare the two theories, we introduce a novel translation between ranking (mass) functions and probability (mass) functions. We draw some crucial consequences from this translation, in particular a new probabilistic belief notion. Based on this, we explore the logical relation between the two belief theories, showing that models of Leitgeb’s theory correspond to certain models of Spohn’s theory. The reverse is not true (or holds only under special constraints on the parameter of the translation). Finally, we discuss how these results raise new questions in belief theory. In particular, we raise the question whether stability (a key ingredient of Leitgeb’s theory) is rightly thought of as a property pertaining to belief (rather than to knowledge).
KeywordsBelief Probability Lottery paradox Stability theory Ranking theory Knowledge Lockean thesis Odds-threshold
We would like to thank Hannes Leitgeb for his helpful comments on an earlier manuscript, Hans Rott for his suggestions and critical remarks and an anonymous referee for pressing us to focus more on the novelty of the translation and its consequences. They all helped to improve the quality of the paper.
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