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.

Robustness Analysis as Explanatory Reasoning

“…All of these measures are explicitly meant to gauge the strength of the explanatory relation between an explanans and explanandum. While it is beyond the scope of the present paper to argue for measure E 's special merits, the interested reader may refer to (Schupbach and Sprenger [2011]), which argues that this measure uniquely satisfies a set of intuitive conditions of adequacy related to the concept of explanatory power, and to (Schupbach [2011]), which demonstrates experimentally that this measure provides a close fit with our preformal intuitive judgments about explanatory power -at least in the tested, experimental contexts. Though I work directly with E , all of the substantive results derived using this measure in this paper also hold using any of the alternative measures defended in the works cited above.…”

“…To make the logical implications of these conditions more precise, we can make use of recent work on the "logic of explanatory power". Schupbach and Sprenger ([2011]) recently develop and defend the following probabilistic measure of "the explanatory power that a particular explanans [h] has over explanandum [e]:" 12 E (e, h) = Pr(h|e) Pr(h|¬e) Pr(h|e) + Pr(h|¬e)…”

Two Impossibility Results for Measures of Corroboration

“…This condition prominently figures in several explications of evidential support and explanatory power (e.g., Kemeny and Oppenheim 1952;Schupbach and Sprenger 2011 However, once we add an utterly irrelevant proposition h = "the chicken came before the egg" to the hypothesis, it seems that e corroborates h ∧ h -the conjunction of GTR and the chicken-egg hypothesis-not more than h, if at all. After all, h was in no way tested by the observations we made.…”

On structural accounts of model-explanations

“…Others have attempted to capture explanatory depth by other means (Schupbach & Sprenger, 2011;Strevens, 2008;Weslake, 2010), but few if any have offered concrete measures of structure. One of the aims of offering a structural account is to preserve autonomy of higher level explanations, and to allow some highly-idealized and non-causal models, such as those of semiclassical mechanics, to be considered explanatory.…”