Laws of Nature

This edited collection nicely displays the impressive breadth of philosophically interesting issues pertaining to laws and, as one would expect from this group of contributors, the essays are of high quality. I’ll begin with some general remarks about this collection as a whole before providing an overview of the chapters.

Chapters 1 to 6 are primarily concerned with the historical development of theories of laws in the early modern period. These chapters are nicely organized, so that someone with relatively little historical background on the concepts could read them in succession. This level of attention to historical accounts of laws is a breath of fresh air, in part because of their relevance to contemporary issues (see my comments on Chapter 1, below). If I have a complaint, it’s that this section isn’t longer! The focus on the early modern period isn’t surprising, given its connection to the development of modern science. However, I would have appreciated a chapter on the concept of powers and/or essences in ancient philosophy, especially since some popular contemporary accounts of laws, properties, and kinds—issues that are closely intertwined—explicitly draw their inspiration from Aristotle.

Chapters 7 to 12 feature contemporary topics. There is relatively little overlap among these chapters, and that’s a good thing. As noted above, the range of philosophically interesting questions about laws is vast and these chapters provide a nice sample of contemporary issues. Gaps are inevitable, but I don’t view this as a shortcoming. The point of this book isn’t to introduce readers to laws, but to advance the debates. It does an excellent job. Although many chapters will be accessible to those not familiar with the literature on laws, as a whole this book is best suited to readers acquainted with the main issues concerning laws of nature. (For those looking for an introduction to laws of nature, I recommend (Armstrong [1983]; Carroll [2004]).)

In Chapter 1, Ott and Patton criticize the surprising (well, perhaps not that surprising) failure of contemporary analytic metaphysicians and philosophers of science to attend to the history of the concept of laws. They argue that we must appreciate the history before we can assess various intuitions about lawhood (such as the intuition that laws govern). They do so by tracing the ways in which various intuitions about laws are exemplified in the work of earlier philosophers, noting differences in their goals and methods. These points are very important, but not always appreciated. I did find Ott and Patton’s characterizations of contemporary debates a little frustrating in places—for example, their discussion of Humean theories is piecemeal, and although they discuss objections to some contemporary theories of laws, they don’t mention objections to contemporary powers ontologies—but their historical genealogy and their assessment of contemporary discussions of laws are valuable despite these minor shortcomings.

In Chapter 2, Helen Hattab discusses Descartes’ conception of laws, tracing its lineage through Aquinas and other philosophers in the Aristotelian tradition in order to identify what makes it distinctively modern. These philosophers agree that laws have something to do with God. One difference between Descartes and (most of) his predecessors is familiar: whereas Descartes’s conception of nature is purely mechanistic, theirs is teleological, and this makes a difference for how God imposes structure on the world. Hattab argues (convincingly, in my opinion) that Descartes’ conception of laws differs in other significant respects: laws are universal, causal, and determinative of regularities in nature. However, none of these features originated with Descartes, and Hattab traces their origins in a compelling way. This chapter will be of interest to historians of philosophy, but also to anyone trying to get a better sense of what is involved in the idea that laws govern.

On the surface, Descartes and Newton employ very different methods for the discovery of laws. Descartes derives his laws of motion through a priori reflection on the nature of God, whereas Newton supports his laws of motion through observation (resulting in a limited understanding of laws that accords with human epistemic limitations). In Chapter 3, Mary Domski argues that these surface differences belie deep similarities in their methods. Newton’s laws are a posteriori insofar as they apply to the motions of the sensible world, but they are a priori when taken as mathematical idealizations (pp. 55ff). And for Descartes, our knowledge of laws is qualified in an important sense. They are timelessly true ‘only so far as human reason is able to understand’ (p. 60); our knowledge of laws is limited in that it does ‘not promise the complete and perfect insight into natural bodies and motion that are reserved for God’s infinite intellect’ (p. 52). This chapter is exceptionally clear and well argued. Anyone interested in Descartes, Newton, or the epistemology/methodology of laws should read it.

Ott argues in Chapter 4 that Bacon and Spinoza endorse a theory of laws according to which ‘a law of a thing’s nature is the set of powers that defines that nature’ (p. 63). He begins by arguing that Francis Bacon endorsed a powers ontology (in which natural necessity is located in objects or their properties) rather than governing laws (in which natural necessity is imposed on things from the outside). The result is that Bacon’s position is not as mechanistic as one might be tempted to think. Ott then defends a similar interpretation of Spinoza’s account of laws. I found the arguments for these interpretations both interesting and provocative. I recommend this chapter for those interested in contemporary debates about where to locate natural modalities in a non-Humean ontology. 

Chapter 5 contains a discussion by Stathis Psillos of the theories of laws of Descartes, Malebranche, Berkeley, Leibniz, Hume, and Newton, in succession, paying attention to both their metaphysics and epistemology. Because this chapter covers so much ground, there’s less depth than in some of the other historical pieces in the collection; but it provides an excellent overview of leading theories of laws in the early modern period. It makes for a great starting point for readers diving into the historical material for the first time, and would work well as a secondary text for those looking to cover laws of nature in an early modern philosophy course. For more depth, and to fill in some gaps, the other historical chapters are a natural next step (as is Ott [2009]).

For Kant, some laws (such as that substance persists through change) are a priori, given the role they play in structuring our experience. Others (henceforth, empirical laws) are discovered a posteriori. But how can empirical laws be both a posteriori and in some sense necessary? There are three main interpretations of Kant’s empirical laws. They could be generalizations in the best systematization of relevant facts, but then it’s not clear how empirical laws are necessary. They could be derived from the a priori laws, but derivations are not always available. Or they could flow from the particular natures of things, but our epistemic access to such natures is unclear. In Chapter 6, Angela Breitenbach proposes a fourth interpretation: our access to empirical laws is both systematic, where the unity required for systematization is understood in an idealized way, and informed by a priori principles that determine the form of empirical laws and related concepts. In blending the first and third accounts in this promising way, Breitenbach argues that we can avoid the aforementioned problems.

Despite its unsettling title, ‘Becoming Humean’, I enjoyed Chapter 7. John W. Carroll offers a refinement of his positive account of laws according to which laws are ‘regularities caused by nature’ (p. 123). I’m pleased to see this development, because I had previously found his account somewhat puzzling. (What is ‘nature’, and what does it mean to say that it ‘causes’ a regularity?) Although I wasn’t fully satisfied with Carroll’s answers to these sorts of questions, this chapter gave me a much better understanding of his view. Along the way, Carroll develops a semantics for sentences involving natural modality, which is of independent interest, and likely to be of special interest to those who are suspicious of non-reductive accounts of natural necessity. The semantics allows a deflationary understanding of governing laws, which may even render Carroll’s theory compatible with Humeanism (pp. 135ff)—hence the title of this chapter—making this recommended reading for anyone interested in the Humean/non-Humean debate.

Humean best systems accounts of laws face various objections. Some object that they involve a problematic sort of subjectivity or that they can’t account for the modal force of laws (Armstrong [1983], Chapter 5). Others complain that some formulations are too metaphysical or that they fail to respect scientific practice (Cohen and Callender [2009]). In Chapter 8, Michela Massimi offers a new Humean best systems account in an effort to block such objections. The central idea is that laws are grounded not in the Humean mosaic alone, but in the Humean mosaic plus certain facts about us—namely, facts about a scientific community’s understanding of simplicity, strength, and balance (p. 140). Massimi’s account will be especially interesting to those who share the concerns of Cohen and Callender. Those with Armstrong’s concerns are unlikely to find Massimi’s account to be an improvement on Lewis’s—if anything, her theory embraces the subjectivity that troubles Armstrong—but her chapter will still be of interest to such readers insofar as it illustrates how variance in scientific standards affects that which we regard as lawlike.

In Chapter 9, James Woodward articulates an invariance-based account of laws (roughly put, laws are patterns that are invariant/resilient across many sorts of transformations), and argues that it is superior to various Humean and non-Humean accounts of laws. He does a superb job of articulating the details of the invariance-based account—that is, of describing the ‘superstructure’ or ‘architecture’ of laws—and in so doing, he has (at the very least) helped to articulate some important desiderata that metaphysical accounts of laws ought to satisfy in order to respect scientific practice. It’s less clear to me that Woodward succeeds in arguing that the invariance-based account is a genuine competitor to various Humean and non-Humean accounts on offer. Upon learning that laws are patterns of invariance, one might wonder why these patterns of invariance hold, whether they are compatible with a Humean ontology, or the like. These sorts of considerations play a significant role in the Humean/non-Humean debate. Although Woodward offers some preliminary arguments for thinking that we needn’t (or shouldn’t) engage with such considerations, I’d like to have seen the arguments developed in more detail. In any case, I highly recommend this chapter to anyone interested in the architecture of laws or in the extent to which we need to do metaphysics in order to answer questions about what laws are.

Suppose a seesaw tips to the right. We can explain this in terms of the masses (m) on either side and their respective distances from the fulcrum (x). Thus, it tips to the right because its m_rx_r – m_lx_l > 0. However, we would not be inclined to say that it tips to the right because its x_r – m_lx_l/m_r > 0. Both properties of the seesaw are reducible—indeed, they are mathematically equivalent—but one seems more natural and explanatorily powerful than the other. In Chapter 10, Marc Lange tries to make sense of this difference. His basic proposal is that a reducible property, P, is natural if and only if there is an explanation of the law in which P figures in terms of P itself. So, for example, we can articulate a (non-fundamental) tipping law, and one good way of doing so invokes the property centre of mass (which involves m_rx_r – m_lx_l) rather than its algebraic equivalent x_r – m_lx_l/m_r. This chapter is full of interesting examples, and the argumentation is careful and precise. I recommend it to anyone interested in scientific explanation or the metaphysics of non-fundamental laws and properties.

Many laws—perhaps all of them—seem to admit of exceptions, and to be rendered most perspicuously as involving ceteris paribus clauses. On the surface, this seems be in conflict with the fact that laws are supposed to be universal. In Chapter 11, Stephen Mumford proposes a solution: laws describe what is disposed to happen, not what does happen. As Mumford recognizes, this type of move isn’t new, but he articulates it carefully and forcefully and offers a nice defence against various objections that might be levelled against it. If he’s right, this suggests a potential advantage for dispositionalist accounts of laws. (I’ll note that it seems possible to modify Mumford’s account of ceteris paribus clauses so that it is consistent with other non-Humean theories of laws. If so, his solution to the problem is broader than he admits.)

In Chapter 12, Nancy Cartwright and Pedro Merlussi begin by providing a taxonomy of ways in which laws of nature might be said to be contingent. This is important on its own, because some theories of laws (for example, Humean reductionism and the Dretske–Tooley–Armstrong theory according to which laws are relations among universals) are motivated in part by the idea that the laws should be contingent, but what this means is not always made clear. They then explore the extent to which four leading metaphysical theories of laws—Humean reductionism, relations between universals, dispositional essentialism, and capacities à la Cartwright ([1999])—can accommodate contingency in its various forms. They argue for the conclusion (no doubt surprising to some) that all four theories can accommodate contingency in most of its forms. I recommend this chapter for anyone interested in the modal attributes of laws. It also contains some interesting applications to matters of free will and determinism.

As my summaries suggest, to get the most out of the individual essays some background knowledge would be helpful. Nevertheless, given its breadth of coverage and the strength of the contributions, I recommend this collection to anyone with an interest in laws, their history, as well as their metaphysics.