Ockham’s Razor, Hume’s Problem, Ellsberg’s Paradox, Dilation, and Optimal Truth Conduciveness

Classical Bayesianism represents ignorance, if at all, by flatness of prior probabilities. Such probabilities are an essential part of the standard Bayesian explanation of Ockham’s razor. But flatness as a model of ignorance is called into question by Ellsberg’s paradox, which has led to the consideration of incoherent or inexact degrees of belief, both of which undermine the usual explanation of Ockham’s razor. An alternative explanation of Ockham’s razor is presented, according to which always favoring the uniquely simplest theory compatible with experience keeps one on the shortest or most direct path to the truth. It turns out that minimization of total distance to the truth implies coherent degrees of belief strongly biased toward simplicity. If one focuses on retractions or drops in credence, then a more reasonably moderate bias toward simplicity results but optimal efficiency then demands either incoherence or inexact probabilities, both of which are solutions to Ellsberg’s paradox. Finally, it turns out that dilation, or increasing imprecision in light of new information, is necessary if agents with inexact probabilities are to minimize total retractions. So, in place of paradox and tension, one obtains a unified perspective on Ockham’s razor, Ellsberg’s paradox, dilation, and the justification of inductive inference.