The Status of Prior Probabilities in Statistical Explanation

Citation: Salmon, W. C. The Status of Prior Probabilities in Statistical Explanation. Philosophy of Science 32(2) (RSS)
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Summary

In this article the author deals with the two different kinds of explanation types, deductive-nomological explanation and statistical explanation based on Hempel and Oppenheim (1948)’s classification. Deductive-nomological explanation represents deductive relationship between premise and conclusion, statistical one shows inductive relationship.

Salmon indicates the two explanations in a mathematical way, premise and conclusion such as a structure of ‘if and then something’. When it comes to the relationship of premise and conclusion, there are certain logical and empirical conditions of adequacy which make the relationship reasonable and the adequacy might be corresponded with deductive-nomological explanation. To make this explanation logical and reliable, some decisive manner or factor would be needed in the structure of the explanation. The structure is consisted with three different factors (multiplicity of potential explanation), statements of antecedent conditions (C), lawlike generalization (L), and statement describing phenomenon to be explained (E). Salmon asserts that lawlike generalization is most important factor in the explanation and it makes the structure more schematized. Therefore at least one lawlike generalization is needed in the structure, and if C and L are reasonable and firmly mentioned, E isn’t required. Selection of generalization among some candidates is also important. The generalization should be tested by deducing with additional premises.

The limitation of statistical explanation or inductive explanation is its vagueness. Because the phrase of ‘All’ could not be used in this explanation, rather ‘Almost all’ is used. In this explanation, lawlikeness is not need because generalization in it is already lawlike. Likewise the case of deductive-nomological explanation, making (or selecting) generalization is important. In this case, the potential generalization would have more actual explanatory power based on observed frequencies.