This issue actually came up while I was reading Hempel's "Aspects of Scientific Explanation". It can be seen as a specific objection to the covering law model as well as a general problem for all explanation.

The problem is even worse than that, because "Sometimes, crows caw" predicts both the hearing of a caw and the non-hearing of a caw. So it does not explain either (at least, based on the default model of scientific explanation).

Think of it as a poorly specified inductive-statistical explanation.

The overall problem you seem to have is that neither of these kinds of explanation gives a causal story for the event (which is a third model for scientific explanations).

Not at all. One problem with Hempel is that there are covering-law predictions that aren't causal stories and therefore don't look like explanations. For example, if some event X always causes Y and Z then we can have a covering law model predicting Z from Y and Laws. But that model doesn't result in an explanation for Z.

But even a causal explanation is going to have general laws which aren't reducible. Thus, the problem would remain. And actually, "crows caw" is a causal explanation so I'm not sure why you would think my problem was the absence of causation. If you did see my last two paragraphs in this reply I think they do a better job explaining the problem than this first post.

And by all means, post anything you think would be insightful.