The Bayesian who knew too much
In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid inadequate neutral priors and better handle ignorance. The imprecise model generally agrees with Norton’s representation of ignorance but requires that his criterion of self-duality be reformulated or abandoned.
KeywordsBayesian confirmation theory Imprecise credence Ignorance Indifference Principle of indifference Doomsday argument Anthropic reasoning
I am grateful to Wayne Myrvold for initial discussions, Jim Joyce and John Norton for stimulating exchanges. I am indebted to Chris Smeenk for many comments and suggestions. I also thank an anonymous reviewer for helpful comments.
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