Conditioning and Evidence

There are many measures of uncertainty out there. Sometimes they appear to conflict. For example, classical or frequency probability supports significance testing. Bayesian probability, in the same situation, would call for conditioning on the evidence. Evidential probability resolves many of these conflicts in an intuitively plausible way, and in a way that admits of real world semantic justification in terms of frequencies. In what follows we will briefly and informally characterize evidential probability, examine some of the situations in which conflict can arise, and explore the tension between classical statistics and Bayesian conditioning. Finally we shall exhibit the semantic justification underlying the resolution of these conflicts.