Discussion Questions on I-S Explanation
According to the simplest of Hempel's models of statistical explanation, statistical explanations are arguments that are in some ways analogous to deductive-nomological explanations. Suppose one wants to explain some happening such as "Ga" -- that is, "a is a G" (for example, "a is a sample of radon in which approximately half the atoms have decayed.") According to Hempel, one can explain Ga by "inferring" it from a probabilistic law "Pr(G/F) = r" and the true statement of an initial condition: "Fa". Provided that r is close to 1, we have something analogous to a DN explanation.
But do we? There are very important differences:
1. Why can we offer statistical explanations only of high-probability occurrences? Is this limitation reasonable?
2. How should we understand the objective and subjective (or "logical") probabilities mentioned in this model?
3. Why does Hempel insist that I-S explanation is essentially relative to a knowledge situation? Why isn't D-N explanation similarly relative? Why can't I-S explanations simply be correct, full stop?
4. Why does the ambiguity of statistical explanation pose a problem? If i (in #5 above) recovers, can one use Pr(G/F) = r and Fi to explain why?
5. What does the requirement of maximal specificity say? How is it supposed to address the problem of ambiguity.
6. Why, in Hempel's view, does the requirement of maximal specificity fail to solve the problem of non-epistemic ambiguity?
7. How exactly does Jeffrey disagree with Hempel? What model of statistical explanation would Jeffrey defend?