A second look at the logic of explanatory power (with two novel representation theorems)

We discuss the probabilistic analysis of explanatory power and prove a representation theorem for posterior ratio measures recently advocated by Schupbach and Sprenger. We then prove a representation theorem for an alternative class of measures that rely on the notion of relative probability distance. We end up endorsing the latter, as relative distance measures share the properties of posterior ratio measures that are genuinely appealing, while overcoming a feature that we consider undesirable. They also yield a telling result concerning formal accounts of explanatory power versus inductive confirmation, thereby bridging our discussion to a so-called no-miracle argument. © 2012 by the Philosophy of Science Association.