# Studies in the Logic of Explanatory Power **Abstract:** This paper introduces and defends a probabilistic measure of the explanatory power that a particular explanans has over its explanandum. To this end, we propose several intuitive, formal conditions of adequacy for an account of explanatory power. Then, we show that these conditions are uniquely satisfied by one particular probabilistic function. We proceed to strengthen the case for this measure of explanatory power by proving several theorems, all of which show that this measure neatly corresponds to our explanatory intuitions. Finally, we briefly describe some promising future projects inspired by our account. ∗ To contact the authors, please write to: Jonah N. Schupbach, Department of History and Philosophy of Science, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; email: [email protected]. † For helpful correspondence on earlier versions of this paper, we would like to thank David Atkinson, Vincenzo Crupi, John Earman, Theo Kuipers, Edouard Machery, John Norton, Jeanne Peijnenburg, Jan-Willem Romeijn, Tomoji Shogenji, audiences at PROGIC 09 (Groningen), the ESF Workshop (Woudschouten), and FEW 2010 (Konstanz), and especially Stephan Hartmann. Jan Sprenger would like to thank the NWO which supported his work on this article with the Veni grant 016.104.079: “An Objective Guide for Public Policy? Scope and Limits of Data-Driven Methods in Statistical Model Evaluation.” Jonah N. Schupbach would like to thank Tilburg University’s Center for Logic **Authors:** [[Jonah N. Schupbach and Jan Sprenger∗†]]