This distribution principle looks awfully plausible:
- A explains (B and C) iff (A explains B and A explains C).
But I think it might be false, at least in the right-to-left direction.
A potential counterexample comes from Aristotle. A bandit is lingering by a road, and a farmer is walking home down the same road. By chance (as we would say), they meet at place X at time T. There is a telic explanation in terms of the bandit’s purposes for his being at X at T, and there is a telic explanation in terms of the farmer’s purposes for his being at X at T. But there is no telic explanation for their meeting, even though I take it that their meeting just consists in both of them being at X at T. The meeting is just a coincidence.
Slightly more carefully: let BP be the bandit’s purposes and FP be the farmer’s purposes, and let BXT and FXT be the relevant location facts. Assuming that antecedent strengthening holds for “explains”, this means that (BP and FP) telically explains BXT, and (BP and FP) telically explains FXT. But since their meeting is coincidental, it seems plausible that (BP and FP) does not telically explain (BXT and FXT).
If distribution fails for telic explanation, then perhaps it fails for nomic explanations as well, for the same kind of reason.
Why does this matter? It’s relevant to my criticism last week of Lewis’s “best system” account of laws (not just my criticism). Briefly, I said: on Lewis’s account, the qualitative facts explain what the laws are, but the laws should explain the qualitative facts. That makes a very tight explanatory circle, and that’s bad.
A response might go: it’s true that the conjunction of the qualitative facts explain the laws. It’s also true that the laws explain each individual qualitative fact. But it doesn’t follow that the laws explain the conjunction of the qualitative facts—since the distributive principle fails—and so there is no bad explanatory circle.