Chen on our access to the physical 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.

I'll explain why I disagree.

It's easy to get bogged down in this debate before we can even begin to discuss the epistemic problem. We could quibble over whether the idea of a Humean mosaic even makes sense. We could argue over the epistemological background theory in which to cast the problem. Fortunately, Eddy and I are on the same board with respect to all these preliminaries, so we can get right to business.

Assume that there's a "mosaic" M. Intuitively, M is the totality of all non-modal truths. We also assume that there is a system L of physical laws. Humeans hold that L is entailed by M. Non-Humeans deny this. Finally, there is our total evidence E. The evidence is compatible with many possible mosaics, and many possible laws. If L1 and L2 are alternative laws, and both are compatible with E, how could we have reason to accept L1 rather than L2? This is the problem.

Eddy's answer is that we should accept a fundamental Principle of Nomic Simplicity (PNS), according to which the laws are probably simple. More precisely, if L1 is simpler than L1 then all else equal it is more likely, in an epistemic sense, that L[L1] than L[L2], where 'L[φ]' says that φ is the true system of laws.

In fact, PNS is part of a more comprehensive Principle of Nomic Virtues (PNV), according to which the laws probably strike a good balance of simplicity, informativeness, and naturalness. (I'll ignore naturalness in what follows, for reasons I won't get into.)

Why think that these are fundamental epistemic principles? Because science would not be possible without them, Eddy says, and there's no way to reduce them to something more fundamental.

Eddy also argues that Humeans and anti-Humeans alike must treat these principles as fundamental. One might have thought that the Best-Systems Analysis guarantees that the laws are simple – after all, the laws are here defined as the best systematization of the mosaic, and simplicity is one of the standards by which candidate systematizations are ranked. But Eddy rightly points out that this doesn't entail that the laws are simple. There are many worlds whose mosaic is such a mess that the best systematization is highly complex.

I agree that friends of the BSA should accept PNV as a fundamental epistemic principle. But I don't think the two views are thereby on a par.

To begin, PNS and PNV are not univocal principles. The Humean and the Primitivist give a different interpretations to the concept of lawhood that figures in the principles. Let's distinguish the two versions of PNV.

This is (in essence) what PNV amounts to for the Humean:

(PNVH) The mosaic has a simple and informative systematization.

This is what it amounts to for the Primitivist:

(PNVP) The primitive laws are simple and informative.

The Humean needs PNVH, the Primitivist needs PNVP. So far, I agree that the two views may seem on a par. But the Primitivist needs further principles.

Recall that our problem is how we can get from our data E to the laws L. Eddy doesn't fully explain how this is supposed to work, on the Primitivist picture. I assume we need some kind of a priori connection between hypotheses about the primitive laws and observable data. PNVP doesn't give us any such connection. The following assumption would help:

(T)If L[φ], and φ entails p, then p.

This says that the primitive laws correctly describe the events in the mosaic. Justifying T is a version of the "inference problem", introduced in van Fraassen (1989). I believe that it is a serious problem for anti-Humeans who posit laws as ontological or typological primitives. If L is a primitive property that attaches to some propositions and not to others, why couldn't it attach to a falsehood? Humeans need no analog of T.

The Primitivist needs something much stronger and stranger than T, once we recognize that many systems of laws are probabilistic. The Primitivist arguably can't accept a Humean interpretation of the relevant probabilities; she must treat them as primitive. Since we never directly observe primitive probabilities, any hypothesis about these probabilities is logically compatible with any observations. We need an a priori link between possible observations and primitive probabilities. Something like this:

(PP)The epistemic probability of p, given that the primitive probability of p is x, equals x, and does so conditional on a wide range of possible observations E.

I've found that anti-Humeans often want to wiggle out of their commitment to T. They insist that T somehow comes for free, given their conception of laws. The case is clearer for PP, which arguably comprises T as a special case. The rules of probability clearly don't entail PP. There are probability measures that deviate wildly from PP. The Primitivist needs a fundamental principle according to which such measures do not qualify as rational prior probabilities. I find this deeply problematic, for the reasons explained in Schwarz (2021). I've also argued, in Schwarz (2014), that the Humean needs no such principle.

Given PNVP and T and PP, I can see how Primitivists may explain our access to the laws. But they need yet further principles.

Consider the problem of induction. Eddy mentions it on pp.14ff., but construes it as the problem of justifying the inference from E to all of M and L. I don't know anybody who thinks that this inference is justified. (Our observations surely don't tell us much about every movement of every particle in the remotest galaxies!) The problem, as normally understood, is to justify our belief that observed regularities continue to hold in unobserved cases: having found that the sun rises every morning, we believe it will probably keep rising; having found that several samples of gold melt at around 1064 degrees Celcius, we believe that all samples of gold probably melt at around this point. Whatever we call it, let's focus on this kind of inference.

Notice that the conclusion of the inference is not a claim about laws. It's a claim about the mosaic. (In some versions, it's only a claim about the "next" case in the mosaic that we will observe.)

Such inferences are crucial to science. What makes them rational?

Humeans can gesture towards an answer. I have already committed (on behalf of Humeanism) to the assumption PNVH that the history of events in our universe is, at a fundamental level, regular enough to allow for a simple and informative systematization. This allows us to (largely) disregard worlds in which, say, the melting point of gold varies randomly from planet to planet, or from century to century. It's not immediately obvious how it generalizes to macro-level regularities, but we have at least the beginnings of an understanding of how macro-level order can arise from pervasive stochastic regularities on the micro-level (see, e.g., Strevens (2003)).

The situation for the Primitivist looks much worse. PNVP and T and PP only seem to connect observed regularities to non-Humean whatnots. How do we get to unobserved regularities? The Primitivist may want to move from the observed regularities, via PNVP and T and PP, to the laws, and from the laws to the unobserved regularities. But how does this last step work?

Let S be an arbitrary system of laws. Assume it is simple and informative. What can we infer about the mosaic from the assumption that S is the true system of laws? Even assuming T and PP, we cannot infer that the mosaic is regular enough to allow for a simple and informative systematization. Suppose, for example, that S only specifies the behaviour of material objects. Nothing in PNVP or T or PP rules out that S might be the true system of laws even though the world contains an extra layer of non-material ectoplasma that isn't mentioned in S and resists any attempt at systematization. Similarly, nothing in PNVP or T or PP rules out that S might be the true system of laws even though the world has extra fundamental properties, not mentioned in S, which behave in utterly irregular ways. (Imagine the properties that determine melting points to belong into this class.) Scientific practice requires giving low probability to these hypotheses about the mosaic. PNVP and T and PP don't capture this part of scientific practice. We need to add a further principle.

What we need to add, I think, is a principle according to which the mosaic probably allows for a simple and informative systematization. This is just what PNVH, the Humean version of PNV, says. So the Primitivist needs to add PNVH.

(Here's another way to make the last point. The Best-Systems Analysis renders the equality L = BS(M) analytic: the laws L are, by definition, the Best Systematization of the Mosaic. But even non-Humeans should accept the equality, at least as probable. It is, however, not entailed by PNVP, not even in combination with T and PP.)

In sum, the Primitivist needs three or four fundamental principles, depending on whether we count T as part of PP or not. She needs PNVP, T, PP, and PNVH. The Humean only needs one of these, PNVH.

Chen, Eddy K. 2023. “The Simplicity of Physical Laws.” arXiv.
Chen, Eddy K. 2024. Laws of Physics. Cambridge: Cambridge University Press.
Earman, John, and John T. Roberts. 2005. “Contact with the Nomic: A Challenge for Deniers of Humean Supervenience about Laws of Nature Part I: Humean Supervenience.” Philosophy and Phenomenological Research 71 (1): 1–22.
Schwarz, Wolfgang. 2014. “Proving the Principal Principle.” In Chance and Temporal Asymmetry, edited by A. Wilson, 81–99. Oxford: Oxford University Press.
Schwarz, Wolfgang. 2021. “Knowing the Powers.”
Strevens, Michael. 2003. Bigger Than Chaos. Cambridge (Mass.): Harvard University Press.
van Fraassen, Bas C. 1989. Laws and Symmetry. Oxford: Clarendon Press.


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