Tim Maudlin has a paper, "Why be Humean?", which criticizes the Lewis doctrine of Humean supervenience. Maudlin is an advocate of some kind of non-Humean account of laws of nature specifically. Most of the paper argues that there are problems for the Humean account, but he ends by considering, and rejecting, such arguments as he finds that can be given in its favor.
He identfies 4 pro-Humean arguments. First, he says that there is a semantic argument, which he attributes mostly to the Logical Positivists; this argument says that because we have no way to experience non-Humean laws, we have no way to refer to them. Second, and relatedly, he identifies an epistemological argument. We have no way to know whether there are non-Humean laws or not, so we should keep them out of our theories. Third, there is a methodological argument, that we have no need of non-Humean laws so we should exclude them from our metaphysics on the basis of parsimony. Fourth, there is the prejudicial argument, that non-Humean laws are simply too weird to believe in.
The only argument which gets any respect from Maudlin is the methodological argument, and he doesn't think it's strong enough to support the Humean view. I believe he underestimates the methodological argument. However, Barry Loewer has some very good discussion of that argument, so I would like to instead examine one of the other arguments. The semantic argument seems to me to be parasitic on the epistemological argument, and the prejudicial argument seems to me to have been included by Maudlin primarily as an ad hominem against the Humeans, but I think the epistemological argument deserves to be taken much more seriously than Maudlin is willing to allow.
I advocate a view which I am inclined to call anti-realist. One of the ways of describing what I mean by anti-realism, which I believe connects with traditional debates about realism, is in terms of how closely a view ties epistemology and metaphysics together. Realism involves making a sharp divide between the two; questions of what there is, on a realist view, depend little or not at all on what we know or can know. Anti-realism brings the two closer together, insisting that it makes little sense to construct theories of what there is without considering whether there's any way we could know about those things.
Maudlin's rejection of the epistemological argument involves his commitment to a strong form of realism in my sense. He explicitly rejects my kind of anti-realism on the basis of a sort of slippery slope argument. He says, reasonably enough, that a theory which said only what we actually know to be true is true would be absurd. Thus, any view which ties existence to knowledge must involve appeal to things being knowable in some sense, rather than actually known.
So far, so good. However, Maudlin thinks that ultimately there is no reasonable way to make sense of knowability. His way of putting this is that knowability, for a Lewis-style Humean, must involve the truth of counter-factuals, which depends on goings-on at nearby, similar worlds. So, to take one of his examples, the truth or falsity of the claim "Socrates had blood type O" depends on what happens at possible worlds where a sample of Socrates' counterpart's blood survives until blood type tests are developed, or perhaps where the technology to test blood types is developed in ancient times. Maudlin says that this is absurd; "Socrates had blood type O" is either true, or false, as the case may be, because of the Socrates in our world, even though there is no way anyone in our world will ever know whether it is true or false.
I believe this is a highly misleading and prejudicial way of representing the Lewis position. Certainly I do not think it adequately represents mine. What makes "Socrates has blood type O" a claim that I would categorize as knowable is that it is very similar to claims that are known or that it is very easy to come to know, namely claims about the blood types of present and future people. The primary evidence of knowability is similarity to the known. This is not particularly different from the Lewis view on the matter; part of what makes the closest possible worlds where the blood type of Socrates is actually tested similar to ours is that they contain a Socrates counterpart who is a human being like us, so it is the fact that Socrates is a human being like us, and so with a blood type, that makes the weird possible world story which Maudlin finds so irrelevant true.
In contrast, it is not clear that non-Humean laws are similar to anything at all in our experience. Thus, it seems to me that a case can be made that it is possible to divide the knowable from the unknowable in such a way that the ordinary facts everybody wants to save end up on the knowable side, while non-Humean laws end up on the unknowable side.
Of course, Maudlin could, and probably would, still insist that knowability should not constrain metaphysics, but I don't think he can use the argument that knowability can't be a criterion because it unavoidably excludes what uncontroversially must be included.