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Remarks on Explanatory Power

Published online by Cambridge University Press:  28 February 2022

Richard C. Jeffrey
Richard C. Jeffrey*
Affiliation:
University of Pennsylvania
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Extract

The idea of using information-theoretical concepts to quantify the notion of explanatory power of theories is an attractive one. Where the theory is adequately represented by a probability measure p on Boolean algebra A of propositions, it is natural to think of measuring explanatory power by some function of H(A), the entropy or uncertainty of p. But recently, Greeno and others have been exploring measures of explanatory power which are suggested by more detailed representations of theories - representations which are themselves suggested by communication-theoretical analogies.

To avoid inessential complications, suppose that the Boolean algebra A is finite, and let ‘a’ range over the atoms of A, viz., the strongest propositions in A which are not logically false. (Any two atoms are logically incompatible, and any proposition in A is expressible as a disjunction of atoms.) Then we have

where we set p(a) logp(a)=0 in case p(a)=0.

Type
Symposium: Theoretical Entities in Statistical Explanation
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1970 , 1970 , pp. 40 - 46
Copyright
Copyright © Philosophy of Science Association 1970

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References

[1] Perez, A., ‘Notions généralisées d’incertitude, d'entropie et d'information du point de vue de la théorie de martingales’, Transactions of the First Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague, pp. 183–208.Google Scholar
[2] Rosenkrantz, R., ‘Experimentation as Communication with Nature’, Information and Inference (ed. by Hintikka, J. and Suppes, P.), Dordrecht 1970, pp. 58–93.CrossRefGoogle Scholar
[3] Watanabe, S., Knowing and Guessing, New York 1969.Google Scholar