<i>Laws of Nature and Chances: What Breathes Fire into the Equations</i>

This rich and thought-provoking book should set the agenda for discussion about Humean approaches to the metaphysics of laws and chances for years to come. Its aim is an overhaul of the Lewisian Best System Account (“BSA”) that allows the systematization itself to deliver the fundamental ontology and space-time structure in addition to the laws. The view, which Loewer calls the Package Deal Account (“PDA”), will be familiar in broad strokes to those who are acquainted with his articles on the topic over the last several decades. Still, there is plenty here to think about, even for readers familiar with his work.I won’t try to summarize the entire book. Rather, I’ll focus on some key motivational issues and how they inform the structure of the PDA. I’ll use this discussion to develop an objection, which I’ll call the Value of Standards (“VoS”) problem, that concerns me as a Humean who is otherwise highly sympathetic to Loewer’s overall project.Loewer’s PDA is a development of David Lewis’s (1973) BSA, which Loewer elaborates in chapter 3. The BSA has two main components. First is the Humean mosaic—-the collection of particular matters of fact that constitute the world. For Lewis, these consist of space-time points instantiating perfectly natural properties, which are the metaphysically elite properties that play multiple roles in his metaphysics, epistemology, and philosophy of language.Second is a set of systematizing standards, which we might call the Nomic Formula. These standards are supposed to be the epistemic standards physicists use to decide among competing physical theories; Lewis thought that they consist of a balance of simplicity and informativeness. The laws of nature, for Lewis, were the results of applying the Nomic Formula to the Humean mosaic; doing so generates a systematization of the entire mosaic, the regularities of which are the laws. This makes scientists’ epistemic standards into standards that are constitutive of lawhood, and given the particular Nomic Formula that Lewis advocated, it makes the laws into an efficient summary of the entire mosaic.The BSA has a long history of defenders and dissidents, and in chapter 4 Loewer takes on some of the latter. Space forbids a detailed survey, but this chapter is surely a highlight. Objections are presented and dispatched in rapid succession—-Loewer cuts straight to the point—-and more than once his treatment revealed new angles on issues I thought I knew. This chapter should be required reading for anyone looking to contribute to the debates between Humeans and non-Humeans.With those objections cleared away, Loewer pivots to his central constructive aim: developing the PDA. Earlier I noted that he wants the systematization to deliver not just the laws (as on Lewis’s account) but also the fundamental properties and the space-time structure. Here we should consider both why that result is desirable and how to secure it.Chapter 5 answers the “Why” question. In it, Loewer presents his main criticisms of the BSA, which focus on its reliance on perfectly natural properties. Given the variety of roles they play on Lewis’s approach, they must satisfy a battery of metaphysical requirements—-for example, they must be local, intrinsic, and categorical. Moreover, to avoid a trivialization worry, Lewis also required that the laws be expressed in terms of these properties for the purposes of assessing how well they satisfy the standards in the Nomic Formula.Loewer raises several worries about the metaphysical posit of perfectly natural properties. For our purposes the relevant one is the problem of missing value, lodged by Shamik Dasgupta (2018), who asks, effectively, why we should care about expressing the laws with reference to perfectly natural properties. What value is there in this? What if physicists delivered us a final “theory of everything” that referred to properties that don’t match the profile of Lewisian perfectly natural ones? What would be wrong with that?This worry leads Loewer to suggest that the fundamental properties should not be an independent ingredient that is fed into the Nomic Formula but rather should be a result of the systematization process just like the laws. Ultimately, he proposes that the systematization process itself will deliver the fundamental properties, space-time structure, and laws as a “package deal.” This does away with the brute metaphysical posit of perfectly natural properties and instead ties their value to the value of the systematization itself: as long as the systematization is valuable, there will be value in expressing the laws in terms of whatever properties they reference.Next, we need to consider how to structure the view to achieve this. Loewer addresses this issue in chapter 7. The main obstacle here is that if the fundamental properties and the space-time structure are a result of the systematization process, it is not clear what is left to be systematized by the Nomic Formula in the first place.Loewer’s answer is Quinean: physics begins in medias res with the motions of familiar macroscopic objects—-planets, pendula, projectiles, and so on—-and iteratively develops its ontology as it proceeds. A first pass yields a theory that systematizes those macroscopic phenomena; a second pass systematizes both the macroscopic phenomena and the posits of the first theory; and so on. At the limit, a final “theory of everything” would knit together every ontology introduced along the way, together with the macroscopic facts we started from, into a single set of fundamental laws, properties, and space-time structure.1This gives us a basic overview of the PDA’s motivations and structure. Now I want to suggest a worry, which is that it’s not clear that the PDA solves the problem of missing value. Recall: as long as the systematization itself is valuable, there will be value in the individual components of that systematization, such as the fundamental properties that it posits. But what is the value of the systematization itself?Loewer gestures at an answer in chapter 3, where he outlines—-but does not fully spell out—-the standards and the goal they serve: “An optimal systematization of the Humean mosaic … organizes and unifies facts so as to enable [us] to understand the world.” Moreover, the systematization should “explain what [we find in the world] in terms of fundamental ontology and fundamental laws” (27). The goal, then, is understanding, where this involves an explanation of the phenomena we find in the world in terms of fundamental ontology and laws. This seems reasonable—-of course we value understanding—-but, as I’ll argue, the proposal sits uneasily with the rest of the PDA.Imagine an alien civilization that likewise engages in the project of systematizing the mosaic, but they systematize according to different standards. (For example, maybe their standards weigh simplicity more than ours do.) As a result, their final theory differs from our own: it posits different fundamental properties, space-time structure, and laws. What is the value of adopting our standards over theirs?Loewer, I think, wants to claim that our standards are valuable because they provide a systematization that facilitates understanding of the world. But what is understanding? The aliens’ standards would likewise provide a systematization that facilitates something like understanding, which we might call understanding*. Still other sets of standards would provide us with understanding**, understanding***, and so on. What is uniquely valuable about understanding as opposed to these alternatives?One tempting answer is intimated by Loewer’s comments about the fundamental explanations provided by the optimal systematization. You might think that our actual standards provide us with genuine understanding (as opposed to faux understanding) because they illuminate the world’s fundamental structure, whereas other standards do not. But this plainly won’t work: according to the PDA, the systematization process itself is what underwrites the truths about the world’s fundamental structure. So it cannot be on account of illuminating that structure that the standards provide us with understanding; this would effectively define “understanding” as that which the standards provide, but it would not tell us the value of the standards.Chapter 7’s solution therefore reopens the very gap it meant to close. To recap: Loewer escapes Dasgupta’s problem of missing value by letting the system choose its own fundamental properties, so their value now rests entirely on the value of the systematizing standards themselves. But why adopt these standards rather than any rival that would yield a different package deal? Pointing to “understanding” does not help, because each rival set of standards would confer its own analog of understanding. One might reply that our standards are privileged because they alone reveal the world’s fundamental structure, and that revelation is essential to understanding. Yet on the PDA the standards themselves determine the fundamental structure; branding the result “understanding” therefore adds no justification—-it just gives a name to whatever package those standards happen to deliver without showing why those standards are privileged. In short, the missing value problem has reemerged one level up, now targeting the standards themselves. This is the Value of Standards (“VoS”) problem.I think the VoS problem is a worry for the PDA, but I don’t think it’s damning. Resolving it will require, first, a fuller catalog of the systematizing standards and, second, an independent account of why the kind of understanding they yield is uniquely valuable—-perhaps by showing that any community of inquirers, alien or human, must converge on these standards to maximize some sort of pragmatic payoff.2The book’s remaining chapters merit more space than I can give them here. To mention just a few: chapter 8 shows how David Albert and Loewer’s “Mentaculus” fits into the PDA framework; chapter 9 considers how the PDA would treat laws of the special sciences; and chapter 10 defends the view from charges of relativism. Each chapter brims with thought-provoking arguments and novel perspectives. Loewer’s talent for finding fresh angles on long-standing issues makes the book a delight even when one disagrees. Whether or not the PDA can ultimately resolve the Value of Standards problem, Loewer has set a demanding research agenda. Anyone working on the metaphysics of laws and chances will need to engage with this bold and imaginative work.