A Defense of Humeanism about Laws from Methodological Naturalism

Critiquing Emery's Argument for a Governing Account

This essay argues against Nina Emery (2023), that, for a methodological naturalist, a Humean account of laws is at least as preferable as a governing account. Emery maintains that “content naturalism”—that metaphysics should not conflict with the content of our best scientific theories—entails “methodological naturalism,” wherein metaphysics should follow the methodology of science (Emery 2023, 10–11). Accepting this, I argue that the circularity Emery identifies in a Humean account of laws only violates scientific methodology if we assume transitivity between causally-backed and grounding-backed explanations (Loewer 2012; Hicks and van Elswyk 2015). By denying transitivity between these, I propose that a Humean account remains consistent with scientific methodology, and, for reasons of parsimony, even may be preferable.

1 Emery’s Argument

In this section I present Emery’s argument for preferring a governing account of natural laws over a Humean. I explain the terminology and views necessary for her argument, then present a formalized version of it.

Given that any scientific theory is empirically underdetermined (Emery 2023, 66), Emery tries to uncover the “extra-empirical principles” that scientists employ in theory choice (Emery 2023, 72–78). These principles, she argues, are part of scientific methodology.¹ Given methodological naturalism, metaphysics should employ the same extra-empirical principles as science. This further implication of her content naturalism–methodological naturalism link leads her to argue that methodological naturalists should adopt a governing account of natural laws.

Three terms are helpful to establish before moving on to Emery’s argument. First is what she calls a “metaphysically robust explanation” (Emery 2023, 108–111). In its simplest form, a metaphysically robust explanation (hereafter explanation_MR) is an explanation which succeeds in picking out the reason why the explanandum occurred. Such an explanation must not employ a strategy of pattern subsumption; must not explain a pattern by the pattern itself (Emery 2023, 120). We will return to consider explanation_MR further in §2.

Second is what Emery refers to as the “pattern-explanation principle” (Emery 2023, 102–107). The pattern-explanation principle (hereafter PEP) is one of the extra-empirical principles (hereafter EEPs) employed by science in theory choice. She defines PEP as:

When choosing between competing empirically adequate theories, choose the theory that does not leave well-established patterns without a metaphysically robust explanation, even if that theory involves the introduction of some type of entity that is metaphysically weird or novel (Emery 2023, 109).

We return to consider PEP further in §3. For now, it suffices to say that if PEP is an ordinary part of scientific methodology, then methodological naturalists should employ it when choosing between what metaphysical theories to adopt as best.² Empirical adequacy here is simply when a theory accurately predicts some empirical data (Emery 2023, 102).

Finally, under the Humean account, laws are just descriptions of patterns within the “mosaic” of fundamental facts about the world. Specifically, laws are the patterns that figure in the most “informative axiomatization[s]” (Hicks and van Elswyk 2015, 434) of the world. The problem generally pressed here—the circularity objection—arises because it seems that under such a view, the mosaic is the reason why the laws are as they are, but the laws are at least part of the reason why the mosaic is what it is, too (Emery 2023, 120). Emery presses this objection to argue that Humeanism violates scientific methodology:

Emery uses (C2) to argue that a governing account of natural laws should be preferred by methodological naturalists. She defines such an account as:

If it is a law that P, then, according to the governing account of laws, the fact that it is a law that P is the reason why P. (Emery 2023, 112)

In this way Emery secures an explanation_MR of the reason why well-established patterns are what they are; the law determines patterns of events (Emery 2023, 112). It is therefore to be preferred over a Humean account.

This paper will argue that PEP is not the correct EEP to extract from scientific methodology. If succesful, a Humean account of natural laws succeeds in providing an explanation_MR of the well-established patterns.

2 Explanations

I will argue for a lack of transitivity across all of explanation. This argument has the effect of rendering PEP the wrong principle to extract from the historical examples of theory choice in science.

For Emery, explanation_MR is a useful shorthand which reduces to the kind of explanation at play in the historical examples from which she extracts PEP (Emery 2023, 110). We will consider these in §3. From these examples, she argues that an explanation is metaphysically robust if it “identifies the reason why an explanandum occurred.” (Emery 2023, 109) It cannot employ pattern subsumption because it is “pretty clearly [a] no” that such an explanation successfully identifies the “reason why.” Furthermore, pattern subsumption did, even where potentially viable, not play a role in the kind of explanation present in the historical examples (Emery 2023, 110). My argument follows Emery in holding that an explanation_MR cannot employ pattern subsumption.

To deny transitivity, I follow Barry Loewer’s distinction between what he calls a metaphysical and scientific explanation. These are defined by what they are expected to identify: respectively what caused an event “in terms of prior events and laws”, and what grounds or constitutes a given fact (Loewer 2012, 131). Hicks and van Elswyk use David-Hillel Ruben’s “backing relations” (Ruben 1990, 151) to argue that the difference between the two kinds lies in the relations that back the explanation; causal/nomic and grounding, respectively (Hicks and van Elswyk 2015, 438–439). Or in Emery’s terms: the explanatory burden that a given explanation has to discharge depends on the relation of the explanans and the explanandum in the world. As concerns science, I argue that a causal explanation is preferred to discharge an empirical explanatory burden. On the other hand, a grounding explanation is preferred to discharge a metaphysical explanatory burden.

This distinction makes it clearer why assuming transitivity could be problematic. Transitivity would predict that if some A explains B, and that B explains C, then the A would also, at least partially, explain C (Hicks and van Elswyk 2015, 435). However, if the kinds of explanation have different burdens to discharge, it does not follow that some metaphysical A → B explanation and scientific B → C explanation gives us A → C. Hicks and Elswyk present their “lion example” to show this:

The position of electron e partially explains the position of lion L, and L explains the number of prey animals in region R (Hicks and van Elswyk 2015, 437)

If transitivity were to hold across this, we would have to say that the position of e is partially what explains the number of prey animals in R. This might seem right, but if the electron had a different position, indeed if all the electrons in L had different positions, L “would still be warding prey animals out of R.” (Hicks and van Elswyk 2015, 437–438) It is thus not this e that explains the number of prey animals in R. This lack of transitivity can be accounted for if we admit that two different kinds of explanation are at play here. Accepting this, and that transitivity does not necessarily hold between these kinds, we can start to see a way for the methodological naturalist to prefer remaining a Humean about natural laws.

As noted, Emery says that explanations_MR is a shortcut to whatever explanation is at play in the examples from which she extracts PEP (Emery 2023, 110). If we can show that science prefers causally-backed explanations to discharge certain explanatory burdens, and we accept multiple kinds of explanation which lack transitivity between them, then PEP does not necessarily follow from the examples.

3 A Different PEP

To argue for the existence of PEP in scientific methodology, Emery considers three historical instances of theory choice; Pauli’s neutrino, Faraday’s electromagnetic field and dark energy. All three show that scientists would rather posit an unobserved entity than leave a pattern unexplained (Emery 2023, 101–127). I will focus on a fourth case, namely dark matter v. MOND, and show that PEP has a hard time accounting for the lack of acceptance of MOND.

MOND (MOdified Newtonian Dynamics) argues that the fact that galaxies spin faster than they should based on the visible mass is not optimally explained by “dark matter,” but by changing the laws of gravity. More specifically that Newtonian gravity holds only when acceleration is significantly higher than a universal acceleration scale (a₀) (Merritt 2020, 43–45). The theory of dark matter (properly called the standard cosmological model) holds that the discrepancy is explained by the presence of matter that generates gravitational force, but does not interact with radiation (Merritt 2020, x). Both theories have succeeded in generating many accurate predictions, and both can arguably be said to be empirically adequate (Merritt 2020, 223–226).³ Granting this, the acceptance of dark matter over MOND cannot be because MOND leaves a well-established pattern without an explanation_MR, as PEP would predict. Neither theory leaves the pattern without an explanation_MR. However, dark matter posits an entity. There is no good way for PEP to account for dark matter winning out.

If this is true, PEP is the wrong principle to extract from the examples, because it assumes that since science is following PEP regarding causally-backed explanations, we should do the same with regard to all kinds of explanations. I propose PEP* instead:

PEP*: When choosing between competing empirically adequate theories, choose the theory that does not leave well-established patterns without an *explanation with the adequate backing relations*, even if that theory involves the introduction of some type of entity.

With “adequate” being a shorthand for the fitness of the explanation with the relation between the explanans and the explanandum in the world (Hicks and van Elswyk 2015, 438). This can be formulated more clearly as the idea that the backing relation is determined by the type of “reasons why” the explanation aims to identify. Thus, if the “why” is causal, science prefers a cause. If the “why” is constitutive—as the regularity of the Humean mosaic—the explanatory burden is not to find a cause, but to provide a grounding reason. PEP* thus succeeds in explaining the scientific preference for dark matter; science prefers the explanatory burden of an empirical anomaly to be discharged by causally-backed explanations.

Under PEP*, MOND fails acceptance because it does not provide a causally-backed explanation of why gravity behaves as it does. If you are not persuaded that this is the reason MOND fails acceptance, I argue that, as predicted by PEP*, a grounding-backed explanation would not either have satisfied the explanatory burden of the beta decay data that Pauli’s causally-backed neutrino explanation did. Explaining the neutrino data by saying “The reason the violation of the law of conservation of energy occurred is because of a law that governs how energy must be distributed” would have been insufficient to discharge the explanatory burden of the violation of the law in the empirical data.

If PEP*, as opposed to PEP, is part of scientific methodology, a Humean account of laws fares much better. Because (P1) comes to require a metaphysical explanation, and (P2) a scientific explanation. With no transitivity between the two, it does not employ pattern subsumption, and a Humean account succeeds in providing an explanation_MR without positing an entity. If we take parsimony to be an EEP,⁴ the Humean account is to be preferred over a governing account, which introduces a metaphysical entity into our ontology.

4 Objections

There are multiple objections to making this sort of move. I will engage with three of what I see as the most fatal possible objections to my argument.

One could argue for transitivity across all of explanation, as Lange does (2018). For my argument to succeed we do not need to adopt the entirety of Loewer’s distinction. In fact, the only crucial thing that has to hold is that there are different explanations which lack transitivity between them, and that science prefers one to discharge certain explanatory burdens. I think the lion example is effective in showing that we intuitively operate with this understanding of explanation. Lange disagrees, however, arguing his point by the principle of “contrastive transitivity.” That is, transitivity holds, but it is in a misalignment between what is rather than what is not that transitivity fails to obtain. The reason we do not observe transitivity in the lion example is that the presence of electron e rather than its absensce is not what explains the lion’s presence rather than its absence. Were that the case, transitivity would exist from e to the amount of prey animals in R (Lange 2018, 1342–1343). My reply is that this seems exactly like it creates a distinction between kinds of explanation, kinds which lack transitivity between them. And indeed we can have alignment between contrasts without necessarily having transitivity, as shown by Isaac Wilhelm’s boulder counterexample: Boulder falling (rather than not) partially explains hiker ducking (rather than not), hiker ducking (rather than not) partially explains hiker surviving (rather than not). It seems wrong to say that the boulder falling partially explains the hiker surviving (Wilhelm 2024, 91).

In response to an objection that PEP* is the wrong principle to take from the examples, I will say that a defender of such an objection would need to show how the explanatory power that e.g., Pauli was looking for could be satisfied with a non-causally backed explanation. That is, they would have to show why the methodological naturalist should follow PEP or some PEP** for non-causal explanations, if the explanatory burden in these scientific cases is exclusively discharged by causally-backed explanations.

It could be objected that PEP*’s requirement of “adequacy” is too vague, and potentially ad hoc. I have tried to connect Hicks and Elswyk’s correspondence-with-the-relation-in-the-world to the adequacy of an explanation consisting in the kind of “reason why” it is trying to identify. If this definition is unsatisfactory, “adequacy” might gain greater clarity by being identified with the distinction between Michael Streven’s “event explanations” and “basing generalizations” (Strevens 2008, 41–45, 2008, 228–244). This is all to say that “adequacy” can be further defended and expounded. Future work in this would benefit from a more principled account of the term, as well as more thoroughly matching it against the historical record of theory choice. As a closing note here, it should be mentioned that an objection that adequacy reintroduces a methodological difference between science and metaphysics is unfounded, for each is free to use both kinds of explanation.

5 Conclusion

I have argued that the kind of explanation at play in the examples from which Emery extracts the pattern-explanation principle is one with a causal-backing relation, and that for certain explanatory burdens, such explanations are preferred over non-causally-backed explanations. I have argued that transitivity between these two different kinds is unlikely.

Given this, I offer up PEP*. Under this principle, the kind of explanation required to explain a well-established pattern must correspond with the kind of backing relation required to discharge the explanatory burden of the pattern. A Humean account of laws thus employs two different kinds of explanations to explain the mosaic and the laws respectively.

As such, the circularity in the Humean account of natural laws disappears, and it fails to violate scientific methodology. This has the result that it becomes reasonable for a methodological naturalist to remain a Humean about natural laws.

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