Predictions about the future and unrestricted universal generalizations are never logically implied by our observational evidence, which is limited to particular facts in the present and past. Nevertheless propositions of these and other kinds are often said to be confirmed by observational evidence. A natural place to begin the study of confirmation theory is to consider what it means to say that some evidence E confirms a hypothesis H.

Incremental and Absolute Confirmation

Let us say that E raises the probability of H if the probability of H given E is higher than the probability of H not given E. According to many confirmation theorists, "E confirms H" means that E raises the probability of H. This conception of confirmation will be called incremental confirmation.

Let us say that H is probable given E if the probability of H given E is above some threshold. (This...