@MISC{Maher93bettingon, author = {Patrick Maher}, title = {Betting on Theories}, year = {1993} }

Share

OpenURL

Abstract

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 threshold remains to be specified but is assumed to be at least one half.) According to some confirmation theorists, “E confirms H ” means that H is probable given E. This conception of confirmation will be called absolute confirmation. Confirmation theorists have sometimes failed to distinguish these two concepts. For example, Carl Hempel in his classic “Studies in the Logic of Confirmation ” endorsed the following principles: (1) A generalization of the form “All F are G ” is confirmed by the evidence that there is an individual that is both F and G. (2) A generalization of that form is also confirmed by the evidence that there is an individual that is neither F nor G. (3) The hypotheses confirmed by a piece of evidence are consistent with one another. (4) If E confirms H then E confirms every logical consequence of H. Principles (1) and (2) are not true of absolute confirmation. Observation of a single thing that is F and G cannot in general make it probable that all F are G; likewise for an individual that is neither