Some key problems with the DN model of explanation seem to result from the fact that it ignores causal dependence and thus apparently allows one to explain causes by their effects. Intuitively, explanation by causes seems fine but by effects, not.
One response would be to add in an extra condition on DN explanation so as to rule out the bad examples. Perhaps: the explanans must cause the explanandum. Another response would be to give up the DN model and just follow the clue the counter-examples suggest. Explanation is giving causal explanation. But so far, we do not have a good reason to favour either of these over the other.
David Lewis
David Lewis defends the idea that explanation is giving causal explanation from some potential problems. Most of his examples stem from putative explanations that depend on future events or goals: teleological explanation. But if there is any genuine teleological explanation (and the Greeks certainly thought there was!) it violates the causal model because future events cannot cause past ones.
Explaining physical processes through future eventual processes or states (least time or the gas laws). This is not explanation but a prediction device. It only counts as explanation if combined with information about the real causal mechanism which underpins the apparently future-directed calculation.
Biological teleology. Lewis can help himself to Darwinian rewrites of biological teleology. What looks like a future tensed goal (or telos) is just a biological function (the function of the long neck is to...). And biological functions are the result of past to future causation. A randomly produced long neck did enable high-up leaf eating which enabled that proto-giraffe to eat more and thus reproduce more, reproducing more long necks. (Though see here for a problem with that.)
Intentional action explanation: even goal directed action can be explained from past to future as long as the future goals / events are encoded or represented in past mental states.
So Lewis can convert apparently teleological explanation, which would contradict his model, into past to future causal explanation. Or, like the future directed calculating heuristics, deny that they really do explain.
Two remaining points on Lewis:
Lewis’ account is consistent with the DN plus extra causal condition view.
If explanation is giving causal information, it is a bit embarrassing that most of the causal history of an event is either unknown or not very explanatory
Peter Lipton
Peter Lipton gives us a reason for 2) why picking up only particular bits of causal information can be helpful and 1) why his approach cannot fit the DN model.
The reason why only some causal history is needed is that explanation is usually an answer not to Why P? but Why P rather than Q? ie contrastive explanation of facts versus foil. One can answer that contrastive question by giving something which explains the difference between them.
To explain why P rather than Q, we must cite a causal difference between P and not-Q, consisting of a cause of P and the absence of a corresponding event in the case of not-Q
The reason why contrastive explanation cannot be reduced to the DN model is that the latter is a deductive argument for a statement. The closest statement to ‘P rather than Q’ for which we can offer a well behaved deductive argument is ‘P and not Q’, to explain which we’d need to explain P and we’d need to explain not Q. But sometimes it is easier to explain ‘P rather than Q’ than it is to explain P and that contradicts that analysis.
(It contradicts the analysis because it must be harder to explain P and to explain not Q than to explain P alone. But it is sometimes easier to explain P rather than Q. So P rather than Q is not P and not Q. But what else can it be? With no other offers in place, Lipton concludes it is an irreducible form of explanation.)