Confirmation Theory

We first discuss several qualitative properties of confirmation as analyzed in a probabilistic framework. Some of these properties are classical, while others are relatively novel; some are shared by absolute and incremental confirmation, others are distinctive for each kind. We then proceed to address axiomatic characterizations of major classes of probabilistic measures of incremental confirmation. This treatment includes an original result displaying how conditions which single out the traditional probability difference measure up to ordinal equivalence. Finally, we argue that the longstanding project of a compelling confirmation-theoretic generalization of logical entailment (and refutation) can be achieved, provided that the right explicatum is adopted (to wit, a relative distance measure). This conclusion, we submit, dispels concerns that have been aired in the literature up to recent times.