Governing laws are thought to be the scourge of Humeanism.1 How remarkable for John Roberts, a philosopher with Humean credentials, to take as his starting point the seemingly metaphysically luscious (and playfully Borgean) thesis:

The laws of nature govern the universe in the sense that the universe cannot but conform to them; their requirements are not merely required but are also inevitable; with them, resistance is futile. (p. 1)

There is no dodge: These governing laws are not all logically necessary truths. Nor is a skepticism or eliminativism lurking; a further epistemological part of the law-governed world-picture is that what the laws are is discoverable by our science. Furthermore, this starting point is not being presented so as to be refuted. Instead, it is the centerpiece of an argument in favor of a certain meta-theoretic conception of laws, the measurability account of laws (MAL, for short), an account that is in fact metaphysically spartan.

Chapter 1 develops the law-governed world-picture. Chapter 2 states and defends some standard, but not uncontroversial, assumptions about laws (e.g. that some laws are contingent). Chapter 3 spells out what the meta-theoretic conception is and some preliminary reasons to think that it is true. Chapter 4 argues that this conception is built into three aspects of the law-governed world-picture: (a) that there are laws, (b) that science is capable of discovering which propositions are laws, and (c) that laws govern. Chapters 5–9 argue that MAL must be true given a different portion of the world-picture: (c) that laws govern and (d) that we can be justified in believing that laws govern. Neither the argument from Chapter 4 nor the one from Chapters 5–9 speaks in favor of any meta-theoretic conception unless the law-governed world-picture is at least in part accurate. Given the strong doubts some philosophers have about its accuracy, Roberts' strategy is to parade MAL's nice Humean features. Just so, the final chapter, Chapter 10, goes on to discuss why MAL is not threatened by arguments used by non-Humeans (like me) against the thesis of Humean supervenience (HS, for short). There is also an appendix that applies MAL to four theories from physics to illustrate how MAL picks out their laws.

According to the meta-theoretic conception, ‘laws of nature are not part of the first-order subject matter about which science theorizes […] the laws of a theory are the propositions that play a certain special role within that theory’ (p. 32). Then, according to MAL, ‘the laws of any theory are the consequences of the reliability conditions of the legitimate measurement methods of that theory’ (p. 323). Interestingly, what the legitimate measurement methods of a theory are is more a matter of commitment than a scientific discovery.

If this is how it is, then the truth values of counterfactuals, and the lawhood of certain propositions, are features of any scientific theory of the world, which are there not because the world being represented by the theory contains objective facts which they reflect, but rather because the methodology and practice of science as such requires that any product of scientific theorizing have such features. On this view, the metaphysics of counterfactuals and laws is ‘post-Kantian’ rather than ‘pre-Kantian’. We cannot (scientifically) understand the world except as governed by laws and containing true counterfactuals—simply because we cannot (scientifically) understand the world without recognizing some methods as good measurement methods […]. (p. 341)

For there to be laws of a theory, the theory has to come packaged with an empirical interpretation that specifies what measurement methods are legitimate. Part of Roberts' development of the meta-theoretic aspect of his account is a contextualist semantics for statements of the form ‘P is a law’. The idea is that ‘P is a law’ is true in context k just in case P is a law of some true theory that is salient in k. (MAL is concisely summarized on pp. 323–5.)

The Law-Governed Universe contains several splendid moments in which keen insight appears in a brief, matter-of-fact manner. One is when Roberts puts to rest an issue that has swum near the surface of discussions of whether laws govern. It can seem puzzling how the same sort of thing that is the reference of a ‘that’-clause, something like the proposition that inertial bodies have no acceleration, could do any governing, seemingly causing the universe to go one way rather than the other, indeed so powerfully that, well, resistance is futile. As Roberts points out, however, this is based on a confusion about what governing amounts to. Even when we consider laws that govern a nation, we see that laws don't do any pushing or pulling of the governed. There is the national government that creates and enforces the laws. ‘The proposition we call the law is not the agent of the governing, but the content of the governing’ (p. 46). Here's another gem: There is a nice analogy offered in support of the meta-theoretic conception. On a first-order conception, lawhood is part of the content of scientific theories.

By contrast, on the meta-theoretic conception of laws, laws are in a certain respect on a par with the postulates of a mathematical theory. It is a postulate of Euclidean geometry that two points determine a line. But it is not part of the content of Euclidean geometry that this proposition is a postulate […]. Euclidean geometry is not a theory about postulates; it is a theory about points, lines, and planes. (p. 92)

Though part of science, lawhood need not be part of the scientific theories. This strikes me as a plausible step toward understanding the absence of ‘law’ and other nomic terms (e.g. ‘cause’) from formal statements of scientific theories.

A key juncture in the book is Roberts' presentation of his (primary) God-case (p. 201). It is meant to show that the NP-sentence doesn't hold for all contexts. NP is a proposition stating a connection between lawhood and the subjunctive conditional. It states (roughly) that Q is a law only if Q would still have held under any antecedent P that is consistent with the laws. This proposition and others like it have played a central role in my own work ([1994], see Principle (SC)) and in Marc Lange's ([2000], [2009]). NP is also central to Roberts' book; he argues that it explicates the thesis that laws govern.

Consider a context in which it is supposed that God exists and that he created the universe with the purpose of providing habitat for intelligent life. It is also supposed in this context that, with the laws as they were created, no life survives where and when temperatures are 500 kelvins or higher. Think of this as a theological context. It is one where God's existence and purposes are taken as givens and held fixed in the consideration of subjunctive conditionals. It seems plausible that the conditional, ‘If the universe were always and everywhere 500 kelvins or hotter, then the laws would be different’ is true relative to this context. If the universe were always and everywhere over 500 kelvins, then given God's desire to provide habitat for intelligent life, he would have created different laws, laws that would permit intelligent life to survive at such extreme temperatures. This shows that the NP-sentence is false in this context: ‘It is consistent with the laws that it is always and everywhere hotter than 500 kelvins' is true in the theological context. Yet, for some sentence ‘Q’ such that ‘Q is a law’ is true in this context, we have found that, ‘If the universe were always and everywhere hotter than 500 kelvins, then Q would still be a law’ is false in the same context. The case is pretty compelling and raises questions about the role NP has played in the literature. As I see it, it raises questions about whether NP and similar principles are correctly thought to be conceptual truths.

Roberts primarily sees the context dependence of the NP sentence as creating a challenge for his own approach. As he sees it, NP explicates what it is for laws to govern. So, in essence, he has shown that there are some contexts where ‘Laws govern’ is not true. Roberts thinks that any threat posed by this conclusion is mitigated by the fact that the NP sentence is true in all scientific contexts. Returning to the God-case, notice there are also contexts where we suppose that God exists, but it is the laws that are held fixed. In such contexts, it is plausible that ‘If the universe were always and everywhere over 500 kelvins, then the laws would be the same and there would be no intelligent life’ is true. There is no reason to think the NP sentence is false in these contexts. One might also reasonably think of these contexts as scientific ones. To avoid triviality, scientific contexts are not characterized by Roberts as ones where the laws are held fixed, but as ones in which the participants in the conversation are engaged in inquiry committed to observation and measurement as the only legitimate sources of evidence (pp. 264–6).

By way of critical discussion, I'll consider the argument from Chapter 4 (pp. 143–7). Let T be any scientific theory that posits at least one law. Label one of the laws ‘L’ and reformulate T as the conjunction that L is a law and X. (So, X is the rest of T aside from the part of T that posits L as a law.) Let T* be the theory that L is true, L is not a law, and X. T and T* are inconsistent because they disagree on L's lawhood. With this background, the argument is easy to state: If laws govern, then no empirical evidence can favor T or T* over the other. If no empirical evidence can so favor T or T* then we cannot discover that one or the other is true. That is an apparent problem for any first-order theorist because Roberts made no assumptions about T other than that it attributes lawhood to at least one proposition. Roberts thinks that no such problem faces the meta-theoretic conception. On this conception, T and T* are not rival scientific theories, because the theories of science don't take a stand on what the laws are. Nevertheless, theories have laws—propositions that play the law role relative to that theory. According to Roberts, whenever we believe a true theory, it would be true in our context that its laws are laws, and so ‘to the extent that we are justified in believing a theory T, we are justified in saying that its laws are laws of nature’ (p. 146).

I have two concerns about this argument. First, more needs to be said for me to see how Roberts gets from governing laws to there being no empirical evidence confirming whether L is a law. One might think that this move is backed by a connection between governing laws and a failure of HS. This connection, however, is not available here because Roberts denies that governing laws threaten HS. According to his own meta-theoretic account, a view motivated by the law-governed world-picture, HS is true (see pp. 355–6). Second, it is interesting to ask what is needed to discover that some proposition is a law of a theory according to Roberts. On his view, whether P is a law of T does not follow in a straightforward way from the content of T. His account says that P is a law of T just in case P is a logically contingent consequence of the reliability conditions of the legitimate measurement methods of T, where the legitimate measurement methods of T are specified not by the content of T but by its empirical interpretation. Then, to be a genuine legitimate measurement method, the method must be counterfactually reliable (see bottom of p. 283). Judgments of counterfactual reliability are as problematic as judgments of lawhood. Thus, it is not clear that Roberts' meta-theoretic approach is epistemologically in any better shape regarding being a law of a theory than the first-order theorist is regarding being a law.

Roberts thinks his approach is better off. Within any scientific context, it will be presupposed that certain legitimate measurement procedures specified by the empirical interpretation of the salient theory are maximally counterfactually stable. And, indeed, provided that the theoretical portion of the theory is true, and P is a logically contingent consequence of the legitimate measurement procedures, then in that scientific context ‘P is a law of T’ and ‘P is a law’ will be true. (Presumably, it might also be that, for some S, ‘S knows that P is a law’ is also true in such a context.) What is troubling here is that the epistemological challenge to the first-order theorist was formulated about justified belief, good reason, and discovery. But, when answering the challenge from the perspective of a meta-theoretic account, Roberts makes it about being justified in what we say. While the first-order theorist's feet are held to the skeptical fire, the meta-theoretic account gets an odd sort of contextual pass. It is supposedly enough for the meta-theoretic conception's viability for it to turn out there are some contexts in which lawhood sentences are justifiedly assertable. It is unclear why we should think a first-order theorist can't manage that.2

Changing topics, I feel obliged to point out that Roberts offers a new manner of responding to counterexamples to HS. Here's a simple such counterexample: (Regarding (2), maybe it is a law that F = ma2 instead.) So it seems there are two possible worlds that agree on the Humean base and differ on their laws. Therefore, HS is false.

  1. It is possible that there exist only a single particle traveling at constant velocity throughout all of history and it be a law that F = ma.

  2. It is possible that there exist only a single particle traveling at constant velocity throughout all of history and it not be a law that F = ma.

For Roberts, this reasoning goes wrong because, though Sentence (1) may be true relative to a context and Sentence (2) may also be true relative to a context, that is not enough to challenge HS. These sentences need to be true relative to a single context or else the challenge would be guilty of a kind of equivocation. For Roberts, the truth of ‘is a law’ sentences is always relative to a contextually salient theory. As he sees it, that F = ma cannot be a law and not be a law relative to a single theory, and so Sentence (1) and Sentence (2) cannot be true relative to a single context. What is unique (and for me, uncomfortably compelling) about this reply is that it ‘does not involve saying that any claim about laws and possible worlds that is supported by our intuitions and mobilized in the anti-HS argument is false’ (p. 360). The key here is the context sensitivity that Roberts builds into the truth conditions of lawhood sentences. Other views that take lawhood sentences to be context sensitive, even those of a first-order theorist, might also be able to avail themselves of this move, depending on what exactly those context-sensitive truth conditions are. The equivocation concern seems to me to be the most serious threat to the counterexamples to HS that I ([1994], pp. 57–85) once found decisive.

The Law-Governed Universe is thoroughly original. It is also remarkably accessible given the hard issues in metaphysics, philosophy of language, and philosophy of science that are discussed. On readability, the argument in Chapters 5–9 is a challenge to work through, though I encourage readers to stick with it. Throughout the book, the steadfast reader will find progress that will shape future work on laws. This is a book written by a first-rate philosopher who sets out to solve core problems. The mistakes are ones of a refreshing philosophical enthusiasm. For philosophers who are open-minded, appreciative of recent work on laws, and who still hold to the belief that there are solutions in philosophy, this a top-notch example of our craft.3

1 See, for example (Beebee [2000]; Loewer [1996]).
2 Roberts seems to be a bit unfair to the first-order theorist in the argument of Chapters 5–9 too. The key juncture occurs on p. 313, in the first full paragraph of Section 8.7.1. (The move described there on p. 313 is recounted again on the bottom of p. 321 and alluded to in the middle of p. 327.) Roberts says that, for a first-order theorist, if S is true in a context k, then S is true (simpliciter). That would be a bad inference if the first-order theorist holds that the truth conditions of lawhood sentences are context dependent.
3 As always, thanks to John Roberts and Marc Lange for our on-going conversations about lawhood.

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