What is a law of nature?
Mar 25, 2019
Introduction
Some perceive the objective of science to be to uncover the laws of nature. What is a law of nature? This question has both a metaphysical and epistemological dimension to it. The metaphysical one concerns what characteristics render something a law of nature as opposed to a mere matter of fact, an accidental regularity, or some other type of law. The epistemological question is whether and how a law of nature can be identified. There are a few competing theories of what constitutes a law of nature. For the majority of this essay, I will focus on David Lewis’s systems approach. However, before doing so, I will briefly discuss the interpretative possibilities posed by universals and regularity. Ultimately, I will argue that Lewis’s theory is deficient as a metaphysical account, but, notwithstanding, Lewis’s approach offers substantial value to the scientific enterprise of explanation.
A Few Notable Views
The first view that I will discuss is D. M. Armstrong’s theory of universals. Armstrong holds the realist position that there exist recurrent entities that share identical properties. These universals do not exist as a consequence of semantic concepts. Rather, they exist independently of and logically prior to linguistic description, which is used to identify and characterize universals a posteriori using empirical observation. Moreover, the realm of universals is constrained by what is existent, as nothing lawlike can be said about what does not exist. Laws of nature, according to Armstrong, consist in necessary relations between universals—in all possible worlds. These relations are products of what a universal is. Armstrong is a realist; he believes that these universals are truly existent things with particular properties, not merely mentally imposed constructions.
Another view is what is often referred to as the theory of regularity. This position, famously held by Hume, contends that laws of nature are not physically necessary. Rather, laws of nature are merely pervasive uniformities observed in the world. One criticism often leveled against regularity theorists is that they fail to distinguish between laws and accidental generalizations. One example that van Fraassen offers is as follows (p 27). One generalization that can be made about the world via empirical observation is that all solid spheres of gold have a diameter of less than one mile. Similarly, one could observe that no spheres of uranium exist with a diameter of less than one mile. A regularity theorist might hold that both are matters of law. However, a necessitarian would say that only one is necessarily true—that uranium cannot exist as a sphere with a diameter of one mile. No properties of gold physically prevent it from existing in such a form. It just so happens that gold does not exist in that form. A regularity theorist might respond that additional criteria could be imposed in order to restrict what may be considered a law. Doing so would help to differentiate accidental generalizations from law. For example, some resiliency condition could be established to ensure that whatever regularities are deemed law must be such that they are observed in a wide variety of contexts and circumstances.
There are many other aspects to the debate about what metaphysically constitutes a law. For example, authors disagree about what relationships laws bear to counterfactual statements. Moreover, many scientists and philosophers alike have different priorities when it comes to classifying something as a law or as something else—perhaps a simplifying assumption. Some think laws should help to explain phenomena. However, others counter that things widely considered to be laws do not illuminate some ultimate explanation. Rather, they merely consist in a relationship. For example, Boyle’s Law pertains to the relationship between pressure, temperature, and the volume of an ideal gas, but, it is perhaps not explanatory. As an aside, note that laws of nature should be distinguished from scientific laws. Laws of nature may be thought to be a priori facts about nature whereas scientific laws serve a human purpose. Because this essay focuses on Lewis, I shall set these questions aside and proceed directly to a summary of Lewis’s response to the question of what a law of nature is. Perhaps in explaining the theoretical virtues and flaws in Lewis’s account, some of these questions will be addressed.
Lewis’s Approach
Lewis’s systems approach to the laws of nature also begs a few interesting questions. First, to properly characterize his approach, I will attempt an illustration of how it might work. Consider the solar system with its eight planets in orbit. A set of true statements accurately describes and predicts the orbit of Mercury. Another describes and predicts the orbit of Venus. The same is true for all other orbiting planets. However, it seems apparent from common and field-specific usage that each fact about these planets’ orbits does not constitute a law, as law is conventionally held to mean something other than merely each matter of fact. Instead, one might think that a more concise set of underlying physical principles may causally underlie all of these orbits as well as those for planets in other orbital systems. This more concise set of principles seems to achieve a balance between two criteria that Lewis establishes for an optimal deductive scheme: simplicity and strength.
Simplicity refers to the magnitude of axiomatic content contained within a deductive system. Strength refers to the amount of information and detail that the deductive system provides about the world. One criticism commonly leveled at Lewis’s approach is that it is indeterminate what the criteria of simplicity of strength entail. A deductive system may be the most simple in one language but incredibly informationally burdensome in another. Is there one language that should supersede all others in choosing between deductive systems? Moreover, even if such a language could be identified, even within said language, what does the simplicity of a deductive system consist in? After all, predicates could be constructed that are defined in terms of a vast number of properties. Does the unification of these properties under one predicate count as simplicity or complexity? Regarding strength, how is one piece of information extrapolated from a deductive system weighted in relation to another piece of information? A further problem is posed by this notion of achieving a balance between simplicity and strength. Some suggest that the problem can be solved simply by using a curve fitting or optimization technique and weighting the two criteria equally. However, again, notions of simplicity and strength are subjective, and a deductive system’s position along a curve is a matter of perspective. Clearly, Lewis’s approach entails vast indeterminacy regarding what is a law and what is not.
About Lewis’s approach, I make two claims: first, that it is deficient as a metaphysical account of what a law of nature is, and, second, that it may nonetheless hold practical value in surmising causal principles in the universe probabilistically.
Regarding this first claim, it appears that Lewis’s systems theory is mind-dependent, as it is not clear how simplicity and strength can be identified objectively. Simplicity seems to denote a cognitive burden, which is apt to differ between beings. Strength also seems to require a mind because the process of deduction—how information is derived from a Lewisian system—is mind-based. Thus, it is unclear how Lewis’s position accounts for the existence of laws outside the mind, which seems, on face, to be inconsistent with Lewis’s endorsement of realism, the notion that laws and phenomena exist independently of subjective conceptual schema. If the view were instead adopted that order is imposed by the mind and that laws do not govern some external reality, this would be to deny the existence of natural laws and suggest that only regularities can be observed. In this case, the notion of laws as deductive axioms seems to make little sense; phenomena cannot be deduced from regularities. Moreover, if it is true that the simplicity and strength of deductive systems are mind-dependent notions, then the aforementioned problems regarding the indeterminacy of simplicity and strength become even more pronounced, as differences in a subject’s language or conceptual operating system may result in completely different deductive systems being optimally simple and strong to different subjects. In other words, laws of nature would be different for different subjects, which contradicts Lewis’s realist position.
An example offered by van Fraassen begs additional questions about Lewis’s approach. Van Fraassen describes a world in which all the best true theories include the statement that all and only spheres are gold (pp 46-47). In said world, there are also smaller iron cubes lying on the surface of these gold spheres. However, it is not the case that gold is spherical by necessity; it just happens to be so in all instances across time and space. With different initial conditions, two of the spheres may have collided and produced gold of a different shape. Lewis’s approach would entail that it is a law that gold must be spherical, and it is a physical necessity in this possible world. Van Fraassen seems to point to Lewis’s failure to explicitly differentiate between initial conditions and governing axioms as a theoretical flaw in his position. This concern is a salient one, but the question arises of how it is possible to metaphysically differentiate between necessity that is a product of initial conditions and that which is manifested in laws of nature. Perhaps Lewis’s failure to distinguish between the two is a theoretical virtue of his position. After all, laws too might be seen as mere initial conditions of a possible world, and initial conditions might be seen as laws governing what may happen thereafter. To make this overlap more clear, consider what might be meant by “initial conditions”. It seems perhaps arbitrary to assign these to a point in time, as a possible world without the dimension of time is conceivable. Alternatively, one could imagine a universe without a temporal beginning. In these cases, it seems that initial conditions refers to a set of attributes about a possible world that are primitive or logically prior to its existence. Both spatial laws governing spheres as well as the geography of the universe at some temporal starting point may be seen as preexisting attributes of the universe—initial conditions. Moreover, deductions cannot be made about the spatiotemporal evolution of a world without both knowledge of governing axioms and cross-sectional data from a given time. Maybe, the two are no different—merely specifications of one kind or another about the nature of the universe. As such, perhaps only an account of physical necessity like Lewis aims to provide can appropriately unify these notions of initial conditions and laws of nature.
Even if Lewis cannot provide an adequate metaphysical account of laws, perhaps there is some value in his theory from a practical standpoint (pertaining to the goal of identifying relations that are most likely to be laws of nature). Before explaining how Lewis’s systems approach can be applied practically, I will explain the related concept of models, discussed in the context of economics. Like Lewis’s systems approach, an economic model aims to simplify the enterprise of prediction/explanation by making particular assumptions about the world. In choosing an appropriate model, predictions generated by the model are compared to empirical data. If these predictions are discordant with what is observed, the assumptions of the model are refined to better fit further observations. There is some controversy among economists of whether the field of economics should prioritize prediction or explanation. After all, economists often use assumptions or abstractions that are predictively efficacious but unrealistic. For example, perfect competition is unattainable in the real world, but the assumption is considered predictively efficacious for modeling the behavior of a variety of industries. Perhaps this assumption could be tailored to fit the competitive layout of every industry, but the virtue of the assumption is its simplicity (lack of an informational burden) and strength. To assess the competitive layout of every industry would represent a great cost to an analyst, and, by using abstraction, as some economists would argue, one is better able to perceive the strength of causal patterns and relationships in markets. If one can explain/predict more with less, perhaps that less is more meaningful than extraneous details that add comparatively little predictive power to the model. Note, however, that detail certainly adds predictive power to a model, but it comes with an informational and explanatory cost; some specifications with a weak amount of influence on the model’s predictive success are perhaps not very explanatory but are mere details or surface phenomena. I take it that this is the intuition behind Lewis’s systems approach. If some deeper axiom is able to explain the phenomena of the world without the need for additional specifications, then this axiom is perhaps more causally potent or explanatory. If law is understood to be that which is causally or explanatorily fundamental or primitive, then perhaps to seek the true deductive system that is ideally balanced between simplicity and strength is to shoot at the right target. Thus, maybe the intuitions behind Lewis’s metaphysical theory of law can be applied in building explanatory scientific models, and, in doing so, one gets a continually improving estimation of that which is truly law.
What is thought to be a law does, in fact, depend on the breadth of data available, information processing capacity, and cognitive power of some individual subject or collective entity. For example, what modern humans probabilistically infer to be law is probably different from what some other intelligent alien species might take to be law. The fact that simplicity is relative to the cognitive subject is perhaps a virtue of the Lewisian approach in practical terms. Perhaps computers and processing power changes what humans perceive to be optimally simple and informative, as the ability to code multiplies the linguistic possibilities of how deductive frameworks and models can be constructed. Moreover, there are vastly more ways to compare the predictions of said deductive systems with empirical data. What results is a continually improving capacity to approximate a true deductive system with the best balance of simplicity and strength. Whether something is chosen as a more useful body of axioms than that which was previously accepted is in part determined by the collective cognition of scientists, consisting of computers and people. For the reasons articulated above, even if Lewis’s systems approach is deficient as a metaphysical account, it has value in the scientific enterprise of probabilistically assessing what is most likely to be a law of nature.
Conclusion
I find that Lewis’s metaphysical account of laws of nature does not accord well with his realist position. Furthermore, if one were to instead consider the regularity theorist’s position, so too is Lewis’s approach problematic. However, if laws are taken to be primitive causal forces with explanatory value, employing ideas implicit in Lewis’s approach can produce a useful approximation of what the laws of nature are likely to be, given humans’ cognitive and perceptive limitations. Furthermore, the blurred line between initial conditions and laws of nature calls for a theoretical approach that treats both as comparable or parallel specifications of a possible world. It seems, therefore, that to seek an appropriate balance of simplicity and strength—though it is indeterminate what that balance might be—is to aim at the right target in the identification of what are likely to be laws.