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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).
If we go with "Crows always caw and only crows caw" (along with your extra premises regarding lungs, sound and ears etc), then we might end up with a different model of explanation, one which takes explanation to be showing that what happened had to happen.
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).
(I wrote an essay on these models of scientific explanation earlier in the year for a philosophy of science course which I could potentially edit and post if there's interest.)
Some good, early papers on explanation (i.e., ones which set the future debate going) are:
The Value of Laws: Explanation and Prediction (by Rudolf Carnap), Two Basic Types of Scientific Explanation, The Thesis of Structural Identity and Inductive-Statistical Explanation (all by Carl Hempel).
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.
Think of it as a poorly specified inductive-statistical explanation.
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