Posts on: Laws
Humean accounts of physical laws seem to have an advantage when it comes to explaining our epistemic access to the laws: if the laws are nothing over and above the Humean mosaic, it's no big mystery how observing the mosaic can provide information about the laws. If, by contrast, the laws are non-Humean whatnots, it's unclear how we could get from observations of the mosaic to knowledge of the laws. This line of thought is developed, for example, in Earman and Roberts (2005). Chen (2023) (as well as Chen (2024)) argues that it rests on a mistake. Eddy suggests that Primitivists about physical laws have no more trouble explaining our epistemic access than friends of the Best-System Analysis.
Gómez Sánchez (2023) asks an important and, in my view, unsolved question: what kinds of properties may figure in the laws of "special science" (chemistry, genetics, etc.)?
For the most part, the patterns captured in special science laws are not entailed by the fundamental laws of physics, nor by the intrinsic powers and dispositions of the relevant objects. Some kind of best-systems account looks appealing: the Weber-Fechner law, the laws of population dynamics, the laws of folk psychology etc. are useful summaries of pervasive and robust regularities in their respective domains. They are the "best systematisation" of the relevant facts, in terms of desiderata like simplicity and strength.
Necessitarian and dispositionalist accounts of laws of nature have
a well-known problem with "global" laws like the conservation of
energy, for these laws don't seem to arise from the dispositions of
individual objects, nor from necessary connections between fundamental
properties. It is less well-known that a similar, and arguably more
serious, problem arises for dynamical laws in general, including
Newton's second law, the Schrödinger equation, and any other law
that allows one to predict the future from the present.
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.
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:
In metaphysics, "Humeans" are people who believe that truths
about laws of nature, counterfactuals, dispositions and the like
(truths about what must or would be the case) are in
some sense reducible to non-modal truths (about what is the
case).
One way to be a Humean is to deny that there are any laws
of natures, non-trivial counterfactuals, etc.: if there are no modal
truths, then trivially all modal truths are reducible to non-modal
truths. On this account, there are no "necessary connections between
distinct existences": eating arsenic might in fact be followed by
death, but it could just as well be followed by hiccups or anything
else.
Let's say that something X is nomologically possible if it is true at some world where the actual laws of nature are true. The actual laws may or may not be laws at this world. All we require is that they are true there.
Now consider a chancy law according to which a coin tossed in some standard way has a 50 percent chance of landing heads. For this to be a law at some world w means that it is part of the best theory of w, or that it represents the actual propensities in w, or something like that. What does it mean for it to be merely true at a world?
Is it metaphysically necessary that like charges repel? One might think so: one might think that "charge" is partly defined by its theoretical role, so that this claim comes out analytic. Or one might think that science reveals to us the essence of properties, and that it is part of this essence of charge that like charges repel.
If that law about charges is metaphysically necessary, one might suspect that quite generally, nomological necessity coincides with metaphysical necessity (though see below for an argument against this suspicion):
So I was given a replacement computer now until the other one arrives. If you're waiting for a sign of life from me, I'll probably contact you soon.
But first some philosophy. I want to argue that necessitarianism is compatible with Humean recombinatorialism because powers aren't intrinsic in the sense relevant to this. I also want to suggest that in an ontology of powers, what's fundamental aren't really the powers, but the causal or nomic relations.
Necessitarianism is the view that properties like mass and spin have their causal or nomic role essentially: if a property doesn't behave like mass, it isn't mass. It follows that the laws about mass are metaphysically necessary. (There are many different views in the vicinity here, maybe more about this later.)
Suppose some thing x turns F, and a little later some other thing y turns G. x is the only F throughout history, so on a Humean account of laws of nature, it may well be just a coincidence that y's being G followed x's being F. Suppose it is.
But now consider another world just like this one except that in the far future, lots of G-turnings follow lots of F-turnings so that in this world, it is a law that whenever something turns F and another thing is suitably related, then that other thing turns G. In such a world, x's turning F caused y's turning G.
I've learned a lot at the Lewis workshop, which was also enjoyable in every other respect. One thing I've learned is that my views about theory strength in Lewis's account of laws were rather naive.
Lewis defines a law of nature as a consequence of the best theory, where what makes a theory good is simplicity, strength, and fit (of assigned probabilities to actual occurrences). I claimed that objective standards for strength aren't hard to find: one could, for instance, use something like number and diversity of excluded possibilities (with a meaningful measure for 'number', these two criteria might coincide). But in the discussions, it turned out that this doesn't work, for at least two reasons.
Some accounts of laws of nature make it mysterious how we can empirically discover that something is a law.
The accounts I have in mind agree that if P is (or expresses) a
law of nature, then P is true, but not conversely: not all truths are laws of nature. Something X distinguishes the laws from
other truths; P is a law of nature iff P is both true and X. The
accounts disagree about what to put in for X.
Many laws are general, and thus face the problem of induction. Limited empirical evidence can never prove that an unlimited generalalization is true. But Bayesian confirmation theory tells us how and why observing evidence can at least raise the generalization's (ideal subjective) probability. The problem is that for any generalization there are infinitely many incompatible alternatives equally confirmed by any finite amount of evidence: whatever confirms "all emeralds are green" also confirms "all emeralds are grue"; for any finite number of points there are infinitely many curves fitting them all, etc. When we do science, we assign low prior probability to gerrymandered laws. We believe that our world obeys regularities that appear simple to us, that are simple to state in our language (including our mathematical language). Let's call those regularities "apparently simple", and the assumption that our world obeys apparently simple regularits "the induction assumption".
Lewis defends a kind of best system theory both with respect to laws of nature and with respect to mental content: something is a law of nature iff (roughly) it is part of the best theory about our world; somebody believes that snow is white iff (roughly) this is what best makes sense of his behaviour according to our belief-desire psychology.
In both cases, it looks on first sight as if the theory introduces an implausible relativity into its subject matter: We don't want to say that the laws of nature depend on what we happen to find simple (but simplicity is part of what makes a theory good), and we don't want to say that what someone believes and fears depends on what we think about his behaviour.
I'm confused. It seems to me that the Dense Worlds Argument refutes Lewis' Humean Supervenience thesis: Not all facts about worlds without alien properties are determined by the distribution of fundamental properties over space-time points. But that's not what really worries me.
What worries me is that I don't know what to blame. I don't see any move that doesn't lead into further difficulties. Consider blaming HS. If HS is false, then our world either contains extended things (as opposed to points) that instantiate fundamental properties, or it contains things that stand to each other in fundamental but not spatio-temporal relations. Let's focus on the second possibility. It is certainly conceivable that fundamental properties are instantiated by extended things. But does this help? Suppose all fundamental properties are instantiated by cubes with a volume of 1 nm^3 (or stages of such cubes with volume 1 ns*nm^3). Then the same kind of shuffling as in the dense worlds argument still shows that the interesting facts about our world are independent of the distribution of fundamental properties. But this time HS is not among the assumptoins, so we can't use the argument as a reductio against it.
Assume that all facts in our world are determined by the distribution of basic intrinsic properties at space-time points. Some of the space-time points in our world might be empty, that is, no basic intrinsic property might be instantiated there (either by some particle or by the point itself). If so, consider another world which is exactly like ours except that at all these empty points some basic intrinsic property is instantiated (say, the basic intrinsic property that plays the role of a certain mass in our world -- "some mass", for short) which however has no effect at all on what goes on in the world. (So if that property is some mass, the laws of nature at this world must be different from the laws at our world since our laws don't accept masses that have no effects.) By the definition of "intrinsic" and a rather weak principle of recombination, such a "dense" world is possible. And obviously, it is in principle indistinguishable from our world.