ABSTRACT
This final chapter applies the relative-divergence format of epistemic evaluation to solve the problem of equal likelihood, and then to solve Cartesian skepticism. Let us recall how the problem of equal likelihood arises to challenge the practice of induction. When some hypothesis h is supported by the actual body of evidence e A obtained so far, we rely on h to predict an occurrence of some event o. For example, we predict that the sun will rise in the east tomorrow morning because the past observations support the hypothesis that the sun rises in the east in the morning. However, when it seems reasonable to predict an occurrence of o based on some hypothesis h, the skeptic constructs an alternative hypothesis h* that has the same likelihood as h does in the sense that P(e A | h ∧ b) = P(e A | h* ∧ b), but is inconsistent with o. For example, that the sun rises in the east in the morning till today but rises in the west in the morning thereafter. This hypothesis entails all the past observations of the sunrise, just as the original hypothesis does, but it predicts that the sun will rise in the west tomorrow morning.
