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This paper deals with inference guided by explanatory considerations –specifically with the prospects for a probabilistic interpretation of it. After pointing out some differences between two sorts of explanatory reasoning – i.e.: abduction and "inference to the best explanation" – in the first section I distinguish two tasks: (a) to discern which explanation is the best one; (b) to assess whether the best explanation deserves to be legitimately believed. In Sect. 20.2 I discuss some recent definitions of explanatory power based on "reduction of uncertainty" (Schupbach and Sprenger 2011; Crupi and Tentori 2012). Even though a probabilistic framework is a promising option here, I will argue that explanatory power so defined is not a convincing characterization of what makes a particular hypothesis better, from an explanatory point of view, that an alternative option. Then, in Sect. 20.3 I will suggest a sufficient condition (rule R1*) as my answer to (a). Regarding (b) I will propose a probabilistic threshold as a minimal condition for entitlement to believe (Sect. 20.4). The rule R1* and the threshold condition are intended as a partial explication of explanatory value (and, consequently, also as a partial explication of "inference to the best explanation").

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