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Bayesian confirmation theory is rife with confirmation measures. Many of them differ from each other in important respects. It turns out, though, that all the standard confirmation measures in the literature run counter to the so-called “Reverse Matthew Effect” (“RME” for short). Suppose, to illustrate, that (H_{1}) and (H_{2}) are equally successful in predicting E in that (pleft( {E,|,H_1 } ight) /pleft( E ight) =pleft( {E,|,H_2 } ight) /pleft( E ight) >1). Suppose, further, that initially (H_{1}) is less probable than (H_{2}) in that (p(H_{1}) < p(H_{2})). Then by RME it follows that the degree to which E confirms (H_{1}) is greater than the degree to which it confirms (H_{2}). But by all the standard confirmation measures in the literature, in contrast, it follows that the degree to which E confirms (H_{1}) is less than or equal to the degree to which it confirms (H_{2}). It might seem, then, that RME should be rejected as implausible. Festa (Synthese 184:89–100, 2012), however, argues that there are scientific contexts in which RME holds. If Festa’s argument is sound, it follows that there are scientific contexts in which none of the standard confirmation measures in the literature is adequate. Festa’s argument is thus interesting, important, and deserving of careful examination. I consider five distinct respects in which E can be related to H, use them to construct five distinct ways of understanding confirmation measures, which I call “Increase in Probability”, “Partial Dependence”, “Partial Entailment”, “Partial Discrimination”, and “Popper Corroboration”, and argue that each such way runs counter to RME. The result is that it is not at all clear that there is a place in Bayesian confirmation theory for RME.

DOI: 10.1007/s11229-016-1286-7

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