On Three Measures of Explanatory Power with Axiomatic Representations

Abstract

Jonah N. Schupbach and Jan Sprenger ([2011]) and Vincenzo Crupi and Katya Tentori ([2012]) have recently proposed measures of explanatory power and have shown that they are characterized by certain arguably desirable conditions or axioms. I further examine the properties of these two measures, and a third measure considered by I. J. Good ([1960]) and Timothy McGrew ([2003]). This third measure also has an axiomatic representation. I consider a simple coin-tossing example in which only the Crupi–Tentori measure does not perform well. The Schupbach–Sprenger and Good–McGrew measures are based on different notions of explanatory power, but both are tenable. 1. Introduction 2. Measures of Explanatory Power 3. The Schupbach–Sprenger Measure 4. The Crupi–Tentori Measure 5. The Good–McGrew Measure 6. Affirmative versus Comprehensive Explanatory Power 7. Coin-Flipping Examples 8. Decomposition 9. Conclusion

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