What philosophers of science and scientists want in scientific explanations is (generally) for there to be some law cited, some universally quantifiable regularity which holds with nomic necessity, an exception-less law. However, it seems to me that scientific laws are all best expressed as conditional ‘if-then’ statements which hold for closed systems (that is, which hold all things being equal or ‘ceteris paribus‘). There is a concern here, however, since if one cites a law of the form if P then Q, and simply adds the caveat ‘ceteris paribus‘ at the end, then the law will not be exception-less, it will not have nomic necessity (at least, this is the concern which somebody like Hempel would seem to have).
First, I’m not sure that the law (P⊃Q, ceteris paribus) is one which lacks nomic necessity. It really does hold under all circumstances, at least if the law is correct. If somebody cannot shake the sense that the ceteris paribus clause is problematic, then what about the following: (P&CP)⊃Q
Here we simply move the ceteris paribus clause from being a caveat after the fact, to one of the antecedent conditions stipulated in the law being cited. Wouldn’t this hold with nomic necessity? If not, then how about this: (P&~O)⊃Q
Take O to stand for ‘open system’ as opposed to a closed system, so that O indicates that there may be factors beyond the ‘idealized’ scenario, which is to say that the system under consideration is not ‘closed’. If the system were closed, then P⊃Q would hold with nomic necessity, but it does so only for closed systems. Here, in our (P&~O)⊃Q form of stipulating the law, the ceteris paribus clause is still being stipulated, but not as obviously. I think that may be the best we can do in science though.
Note that with this definition of a scientific law, a miracle would never be a violation of, or an exception to, any scientific law, since if God acts in the universe in some particular instance, then the ‘universe’ isn’t a closed system in that instance. Scientific laws, I think, must be stated as universal generalizations (regularities) which hold with nomic necessity for closed systems.