Equilibrium explanation

Familiar counterexamples to Hempel's DN model of explanation (e.g., Bromberger's, 1966) strongly suggest that the explanation of a particular occurrence must cite its cause. When a building casts a shadow, the sun's position and the shadow's length do not explain the building's height because, it would seem, they do not cause it. This plausible diagnosis has been made a matter of principle in Salmon's (1971, 1975, 1978) SR model of explanation, in spite of the puzzles posed by so-called laws of coexistence; if the length of a pendulum at a given time explains its period at that time (as Hempel, 1965, believes), then the causal requirement is inappropriate. But intuitions and issues are divided or unclear in this class of cases, so the causal condition remains tenable, if not unproblematic. Equilibrium explanations, as I will call them, present a distinct set of counterexamples for the causal requirement. Or, at the very least, they suggest that more attention needs to be paid to specifying exactly what it is for an explanation to be causal. Additionally, equilibrium explanations have an interesting bearing on the role of the statistical relevance idea in the theory of explanation, in that equilibrium explanations show how the cause of an event can be (statistically) irrelevant to its explanation. R.A. Fisher (1931) formulated an equilibrium explanation of the fact that the sex ratio at reproductive age is 1:1 in many species. The main idea of his characteristically terse formulation (see Hamilton, 1968; Crow and Kimura, 1970; or Maynard Smith, 1979 for elaboration and discussion) is that if a population ever departs from equal numbers of males and females, there will be a reproductive advantage favoring parental pairs that overproduce the minority sex. A 1 : 1 ratio will be the resulting equilibrium point. The ratio of male to female progeny has an impact on a parent's fitness in virtue of the number of grandchildren that are produced. If males are now in the majority, an individual who produces all female offspring will on average