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. The inference is non-deductive. Fa may occur and not be followed by Ga. What is improbable is not impossible.
  2. According to Hempel, the inference is "inductive" and we can only draw the conclusion Ga with a confidence measured by r. Furthermore, r measures the confidence that these premises warrant not the confidence that would be warranted if we had complete knowledge.
  3. Note that "r" is doing two jobs and may mean two different things. In the "law", it is supposed to capture something objective. As a measure of the confidence with which we can draw the conclusion Ga is is supposed to capture something subjective.
  4. Hempel insists that whether something counts as an inductive explanation (unlike deductive-nomological explanation) is "essentially relative to a given knowledge situation" (Aspects, p. 402)
  5. It can be the case that Pr(G/F) = r, that Pr(~G/H) = q, that r and q are both very close to one, and that an individual possesses both properties F and H. So, for example, the probability of a cure (G) given pennicilin (F) may be very high and the probability of a cure given the existence of an antibiotic resistant strain (H) very low, and it can of course be the case that an individual i with an antibiotic-resistant strain is given pennicilin. Hempel calls this "the ambiguity" of statistical explanation.
  6. Hempel distinguishes two versions of the problem discussed in #5, "epistemic" vs. "ontological" ambiguity and offers the requirement of maximal specificity as a solution to the first problem.


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?