## Models of laws

In *The Metaphysics within Physics*, Tim Maudlin raises a
puzzling objection to Humean accounts of laws. (Possibly the same
objection is raised by John Halpin in several earlier papers such as
"Scientific law: A perspectival account".)

Scientists often consider very different models of putative laws. Such models can be understood as miniature worlds or scenarios in which the relevant laws obtain. On Humean accounts, the laws at a world are determined by the occurrent events at that world. The problem is that rival systems of laws often have models with the very same occurrent events. Whether this is a problem depends on what we mean by "the relevant laws obtain". Maudlin:

Let's suppose (and how can one deny it) that every model of a set of laws is a possible way for a world governed by those laws to be. (Maudlin, p.67)

To see the problem this creates, assume H is a history of occurrent events which fits two incompatible systems L1 and L2. For Humeans, H is a complete model, so presumably it is a model of both L1 and L2. By Maudlin's supposition, H is then governed by both L1 and L2, which is impossible.

But why should we follow Maudlin's "supposition"?

Imagine it is a law that all ravens are black, and let L be this
law. We must distinguish two propositions: (a) that all ravens are
black, and (b) that it is a law that all ravens are
black. Correspondingly, we must distinguish two sets of worlds, or
models: those where (a) is true and those where (b) is true. (This is
not controversial; nobody thinks that lawhood is the same as truth.)
The *content* of our law L is (a), the proposition that all
ravens are black. So what is a *model* of L? The most natural
proposal, I would have thought, is to say that a model of L is a
situation in which the content of L is true. Any situation in which
all ravens are black is therefore a model of L. Maudlin's "undeniable"
supposition is instead that only those situations should count as
models of L in which L is a law: the situation must be "governed by
those laws".

Of course it doesn't really matter how we use the word 'model'. We
could call situations in which L is true *models of L in the weak
sense*, and situations in which it is a law *models of L in the
strong sense*. As I said, I think the weak sense is more
natural. Maudlin himself slips into it on the very next page, where he
reminds the reader of the crucial point that "different laws share the
same models".

More important is whether we really have a conflict between
Humeanism and scientific practice. When physicists consider models of,
say, Newtonian mechanics, they consider hypothetical situations in
which the laws of Newtonian mechanics are *true*. According to
Maudlin, they further restrict their attention to situations in which
the Newtonian laws are *laws*. But do we really need to assume
this in order to make sense of scientific practice? I don't see
why. On the contrary, I think it is plausible that physicists only
care about what kinds of hypothetical situations satisfy the relevant
equations: the content of the relevant laws.

(Perhaps Maudlin's argument is based on a simplistic conception of
the logic of nomic possibility. It is plausible to say that a model of
a physical theory should be a situation that is *nomically
possible* on the assumption that the theory is true. I suspect
Maudlin takes nomic necessity to be an S5 modality. It then follows
that if w is nomically possible relative to L, then L must be a law at
w. It also follows that if some proposition p (say, that I had salad
for lunch) is *not* nomically necessary, then it is nomically
necessary that p is not nomically necessary. But these assumptions are
highly controversial. On Humeans accounts of lawhood, they are false,
and I don't think this can be regarded as a cost. If it is a law that
all ravens are black, does it really follow that it is also a law that
it is a law that all ravens are black?)