In response to his message quoted below, I asked John Roberts if we would expand on why he thinks that even allowing the observability of singular causal facts, most leading anti-Humean accounts of laws remain incompatible with Earman and Roberts’ argument. At any rate, John Roberts wrote as follows (it would be interesting to know what supporters of anti-Humeanism about laws have to say about it):
JR: The claim I made is that:
If: HS (as Earman and I defined it in “Contact” part I) is true, and singular causal facts (i.e. facts of the form [c caused e]) are all detectable by empirical measurement procedures (and so, belong to the Humean base),
Then: still, the Armstrong-Dretske-Tooley universals account must be false, and so must be the non-reductive realist view defended by e.g. John Carroll and Tim Maudlin. Let’s call those views “the target anti-Humean views.”
Here’s the argument (I’ve cut-and-pasted this from an unpublished paper with a few modifications):
The question is whether fixing all the singular causal facts, as well as all of the more standard examples of “Humean” facts, will suffice to fix what the laws of nature are, assuming that one of the target anti-Humean views is true. I say that it won’t — and so, if fixing all those facts WILL fix what the laws of nature are, then none of the target anti-Humean views could be true.
So what I have to argue for is this: If one of the target anti-Humean views is true, then there exists a pair of possible worlds that agrees on all singular-causa facts as well as on all more “standard” “Humean” facts, but which differ in their laws of nature.
This is easier to show the looser the connection between singular-causal facts and laws are. So let’s assume that the connection between singular-causal facts and laws is very tight indeed. In particular, let’s assume the nomic subsumption account of causation:
NS: Event c causes event e just in case some description of the occurrence of c, together with one or more laws of nature, entails that e occurs.
Now consider two possible worlds: One is just the actual world, which, we suppose, has some set of laws of nature not too different from the kinds of putative laws we are familiar with from our best scientific theories. Here’s how we construct the second world: First of all, all of the Humean-base facts excluding the singular causal facts are the same in the second world as they are in the actual world; that is, by stipulation, the second world has the same occurrent, non-nomic, non-causal history as the actual world. Now, for every pair of events (c, e) where c causes e in the actual world, there exists a law of nature in the second world to the effect that every event which satisfies a highly specific, gerrymandered description, which as a matter of fact only c satisfies, will be followed by an event of the same kind as e. There are no laws of nature in the second world other than these monstrously gerrymandered laws, together with whatever derivative laws they entail. It is clear that the extension of the singular causal relation will be the same in the two worlds, although the laws of nature are vastly different.
A critic who accepts one of the target anti-Humean views might deny that the second possible world in this little thought-experiment is a genuine possible world. But it is hard to see what principled reason she could give for doing so, given that she has already allowed that the laws of nature could vary independently of the (non-casual parts of the) Humean base.
One disturbing feature about this second world is that in it, each law of nature has exactly one instance. But now consider a third possible world, whose Humean base is vastly different from those of the actual world and the second world, and in which the laws are just those of the second world, and each of these laws has a multitude of instances. In such a possible world, these laws might not even appear to be gerrymandered at all, since each of them has such a large number of instances, and in this world these laws might lead to a remarkable degree of order, vastly different from the order we find in the actual world. It is hard to see what grounds could be given for rejecting the third possible world. But, the Humean base shared by the actual world and the second world is clearly physically possible, relative to the laws of the third world. So what grounds would a supporter of the target anti-Humean views have for denying the possibility of a world that had the laws of the third world, but the Humean base of the first? And such a world would just be the second world.