Do laws explain regularities?
Humeans about laws of nature hold that the laws are nothing over and above the history of occurrent events in the world. Many anti-Humeans, by contrast, hold that the laws somehow "produce" or "govern" the occurrent events and thus must be metaphysically prior to those events. On this picture, the regularities we find in the world are explained by underlying facts about laws. A common argument against Humeanism is that Humeans can't account for the explanatory role of laws: if laws are just regularities, then then laws can't really explain the regularities — so the charge — since nothing can explain itself.
But why should Humeans accept that the laws explain the regularities? I don't think I've ever seen a credible argument for that assumption. To be sure, the anti-Humean conception of laws that produce and govern and therefore explain the history of events has a certain intuitive appeal, but obviously Humeans don't endorse that conception.
Does the practice of science assume that laws explain regularities? I don't think so. Science often invokes laws in causal explanations, when a given event is explained by earlier events and general laws. But that's perfectly compatible with the Humean picture. What Humeans deny is only that the regularities corresponding to basic laws are grounded in a deeper and different kind of fact, perhaps involving higher-order relations between universals. As far as I can tell, science doesn't postulate any such grounds. Physics textbook typically don't give any explanation for, say, the fact that opposite charges attract. They certainly don't say that the phenomenon is explained by the fact that it is a law, or by higher-order relations between universals.
The alleged explanatory power of laws is supposed to do other work, and maybe that's why anti-Humeans think it should be accepted. Above all, it is supposed to vindicate inductive inference. The standard argument goes as follows. Suppose we've seen a hundred emeralds all of which were green. If laws explain regularities, we can make an inference to the best explanation and conclude that it's a law that emeralds are green, which in turn entails that all unobserved emeralds are green.
But why isn't the best explanation that all emeralds are grue, from which we could infer that all unobserved emeralds are blue? The argument tacitly assumes that the laws are simple — and simple with respect to properties that we classify as simple. What justifies that assumption? If it is legitimate, why can't Humeans similarly appeal to the assumption that the world displays simple regularities involving properties that we classify as simple?
Of course the anti-Humean thinks that in worlds without underlying non-Humean laws everything is just random chaos, so the probability of finding order in such worlds is miniscule. And so she thinks the Humean's confidence in the orderliness of the world is completely unjustified. But again that's hardly a neutral fact. What's the general epistemic principle at work here? Is it some principle of indifference according to which (in the absence of strong laws) all configurations of events in the world deserve equal probability? If so, why doesn't that principle also apply to laws? Why are we justified to believe that the laws are simple given that there are so many more ways for them to be complicated?
So the alleged explanatory role of laws doesn't help with induction. In general, I don't see any independent reason to accept that laws explain regularities.
(There is also the fact that the anti-Humean "explanations" are rather dubious. You can't just stipulate that one fact explains another. That's not how explanation works. In what sense does "it is a law that opposite charges attract" explain that opposite charges attract? If you wonder how and why opposite charges attract, does the law statement really provide an explanation? Doesn't it rather tell you that there is no deeper explanation to be found?)