Reichenbach, Reference Classes, and Single Case 'Probabilities'

A systematic appraisal of H. Reichenbach's analysis of single case ^probabilities' with concern for the frequency concepts of statistical relevance & statistical explanation, especially as they may be related to the theories of explanation advanced by C. G. Hempel (the covering-law model), & W. C. Salmon (the statistical relevance model). Supported are the conclusions that (1) the frequency criterion of statistical relevance is theoretically defective in failing to distinguish between relations of inductive relevance & relations of explanatory relevance; & (2) required modifications of the accounts of explanatory adequacy dictate an alternative causal relevance model in which the single-case propensity interpretation of probability displaces its long run frequency counterpart as the basis of an analysis of statistical laws. Discussed are features distinguishing three alternative explications of the character of statistical explanation. Explored are the ramifications of this analysis for the alleged symmetry of explanation & prediction with the result that the appropriate reference class for an explanation of the occurrence of a singular event is neither always the same nor always the best choice of reference class for purposes of prediction. Modified AA.