What is a Law of Nature?
In this essay, I will draw upon the literature of two schools of thought on the question of what makes a Law of Nature, in order to present a two part answer. Laws of Nature at the general level, are descriptions of patterns that we discern in the mass of experience we have with Nature. At the same time, Laws of Nature at the fundamental level, capture the underlying causal necessities of Nature. Although we do not yet understand just what this “causal necessity” amounts to.
First, some comments about what a Law of Nature is not. The notion of a “Law of Nature” comes originally from the theistic belief that God handed down the rules that the Universe must obey simply because She so willed it, and Her omnipotence was deemed sufficient to ensure that whatever She willed was so. Early science was then understood as an exercise in discovering just what God’s rules are. As in other contexts, a Law was a Law because there was a Law giver. Having more or less dispensed with the theistic framework, we are left with the label of “Law of Nature” for something that is clearly not intended to be understood as the dictate of a law giver, and not intended to be considered as holding by necessity because of some theistic omnipotence. So the question becomes, in the absence of a law-giver, just how do we understand a “Law of Nature”?
The modern debate over this question appears to be taking place between two schools of thought. There is the “Humean” school of the Mill-Ramsey-Lewis view of Laws of Nature as regularities in nature. And there is the “anti-Humean” school of the Dretske-Tooley-Armstrong view of Laws of Nature as relations of necessity between Universals(1). At the metaphysical level, the two sides to the debate have vastly different conceptions of the relation between Nature and the Laws. The Humeans maintain that the Laws are descriptions of matters of fact — the facts determine the Laws. The anti-Humeans maintain that it is the Laws that determine matters of fact.
My take on the debate is that the two sides to the debate are talking somewhat at cross purposes. One can adopt a high-level analysis of the kinds of things we refer to as “Laws of Nature”, and seek to determine how we distinguish mere accidental generalizations from a generality we (do or ought to) honour with the “Law” honorific. And one can adopt a low-level analysis of just what it is that makes a Law such a firm and unvarying regularity of nature. It would appear to me that the Humeans approach the topic from the former point of view, while the anti-Humeans approach the topic from the latter point of view.
Let’s consider first, the lower level question of what makes a regularity of Nature into a Law. What the Humean school undoubtedly has right is that most of the things we honour with the label “Law of Nature” are nothing more than recognized patterns in the mass of experience we have with Nature. From elementary particle physics (QCD – quantum chromo-dynamics) to economics (TANSTAAFL – there ain’t no such things as a free lunch) scientists generate sweeping generalizations, frequently applicable only in “ideal” circumstances, and often understood to hold only “approximately”. Some of these generalizations are graced with the honorific of “Law of Nature”. But as Nancy Cartwright has pointed out(2) these generalizations can be considered to be true only when viewed through the noise and fog of “non-existent idealized circumstances”, “ceteris paribus“, “mutatis mutandis“, and a multitude of similar caveats. Considered literally, all of them are false. Our so-called “Laws of Nature” are just patterns of apparent (and approximate) regularity in the underlying data. Sometimes, of course, the patterns are not really there. We are infamous for seeing faces in random fields of smudges, for example. The patterns need not be (and are not according to Cartwright) clear and crisp patterns of unquestionable regularity. Because we are such consummate pattern recognition devices, they can be (and usually are) rather muddy patterns, that hold only “for the most part”.
On the other hand, what the anti-Humean school undoubtedly has right is that the real, basic, fundamental Laws of Nature have an unmistakable element of necessity about them. Suppose, for example, that the analysis of causation by Messrs. Fair, Dowe, and Salmon(3) is correct, and causation is best understood in terms of the conservation of some small number of key quantities (like energy, momentum, and so forth). Then it would be reasonable, on this basis, to consider the conservation restrictions governing causation, so conceived, to be “Laws of Nature”. (In fact, on this understanding, they would be the only actual Laws of Nature — all the rest of what we refer to as “Laws of Nature” would be just higher level generalizations, subject to all the problems highlighted by Cartwright.) But now one has to ask, just what is it that ensures that energy, say, is conserved across causal interactions? While it is obvious that there is some kind of necessity at work here, it is entirely unclear just how to understand that necessity.
Assuming that the conserved quantity understanding of causality is correct, there is something about the nature of Nature that “demands” that energy (say) be so conserved. But since there is nothing at all in place to do anything like an anthropomorphic demanding (no Law-giver), how do we understand this “demand”? I have couched this argument in terms of one particular interpretation of causation. But the analysis is applicable to any candidate Law of Nature that suggests that some property/entity/event A is always (or probabilistically) associated with some property/entity/event B. The question is why? Claiming that the association is just a brute regularity of Nature, as do the Humeans, merely ignores the problem. Claiming that the association is a relation of Necessitation between Universals as do the anti-Humeans merely labels the problem. The problem remains unresolved.
Now let’s consider the higher level question of what distinguishes a “mere” accidentally true generalization from a Law of Nature. The Humean school of thought maintains that the Laws of Nature are those generalizations that “belong to all the true deductive systems with the best combination of simplicity and strength”(4). In other words, the Laws of Nature systematize our descriptions of our experiences of Nature. The Laws would form a part of a model/theory (or consistent collection of models/theories) that most simply accounts for the widest range of experiences. Laws of Nature will then be the basic theorems or axioms of such a model (or collection).
Hence, the conservation laws would be Laws of Nature because they would be axioms or basic theorems of all the model systems that are deemed the best such structures with regards to their strength (ability to cover the field of experiential data) and simplicity (incorporating the fewest axioms). But the generality that “there are no gold spheres larger than 100 km” is not a Law of Nature because it is hard to see how it would form part of such a system of theories. Adding it to any theory (collection) would not seem to promise an increase in simplicity or strength. The Humean approach nicely minimizes the ontological commitments. As Lewis suggested “all there is in the world is a vast mosaic of local matters of particular fact, just one little thing after another”(5). This model-theoretic approach to distinguishing Laws of Nature from accidentally true generalizations fits nicely into the pragmatic approach to Laws recommended by Mitchell(6). And despite the objections of the anti-Humeans, this deductive-systems approach also appeals to a Conceptualist understanding, since it boils down Laws of Nature into mind-dependent conceptual entities (because of its reliance on concepts of simplicity, strength, and best balance — concepts clearly dependent on our cognitive abilities and interests). I should also note that this deductive-system approach to Laws of Nature neatly fits with the Deductive-Nomological model (or D-N model) of scientific explanation(7).
On the other hand, the deductive-systems approach to distinguishing Laws from accidental generalities appears to ignore the element of causal necessity that we pre-philosophically and intuitively rely upon to mark that distinction. We intuitively accept that Boyle’s Law (about the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system) is a Law of Nature because we believe there is some element of causation at work that ensures the relationship. And we also intuitively reject the “law” that there are no gold spheres larger than 100 km because there seems to be no element of causation at work. We don’t do any logical analysis to see if these generalities impact the simplicity or strength of our collection of accepted theories. There is an intuitive awareness of an element of causal necessity that seems to distinguish a Law of Nature like that of energy conservation from such accidental generalization as that about gold spheres.
According to the anti-Humeans, the Humeans ignore this intuitive element of causation in the Laws of Nature. The anti-Humeans therefore rely specifically upon this element of causal necessity to mark that distinction. It is causally necessary that energy be conserved. It is not causally necessary that all gold spheres are less than 100 km. But as I noted above, the anti-Humeans face the serious, as yet unresolved, metaphysical difficulty of providing an explanation of just what this causal necessity amounts to. Consider the surface of a sphere, for example. It is part of what it means to be the surface of a sphere that dictates that the surface is finite and unbounded. Is it possible that it is part of what it means to be a Universe, that dictates that energy is conserved in all circumstances? They also face the epistemological difficulty of showing how, other than by the Humeans’ route of describing the regularities of nature, we come to discover this fundamental relation of causal necessity. As before, claiming the necessity to be brute is to ignore the problem. And labelling it as the relation of Necessitation is to merely label the problem.
I think it simplifies the debate to impose a hierarchy on what we call the Laws of Nature. There are the General Laws and there are the Fundamental Laws. The Humeans are right to the extent that most of what we label as Laws of Nature are simply descriptive generalizations describing patterns we have detected in the mass of our experiences of Nature. We elevate those descriptive generalizations into Laws of Nature when we can fit them into our best theoretical models – models that are simple (few axioms) and strong (cover a lot of the data). These then, are the General Laws of Nature. And for the General Laws, it is the facts of the matter that determine the laws.
However, the anti-Humeans are right to the extent that at a metaphysical level there is an inescapable element of casual necessity captured in the most basic of the Laws of Nature. These Fundamental Laws form the basis from which all the General Laws derive their element of necessity. But the detailed nature of the metaphysical necessity of these Fundamental Laws of Nature remains to be explained. Even so, for the Fundamental Laws, it is (somehow) the Laws that determine the facts of the matter.
Notes & References
(1) Beebee, Helen; The Non-Governing Conception of Laws of Nature” in Philosophy and Phenomenological Research, Vol 61, No 3 (Nov 2000), pp 571-594.
(2) See for example –
Cartwright, Nancy; How the Laws of Physics Lie, Oxford University Press, Oxford, England, 1983. ISBN 0-19-824704-4.
Cartwright, Nancy; “Models: The Blueprints for Laws” in Philosophy of Science, Vol 64, Supplement. (Dec 1997), pp S292-S303.
(3) See for example —
Dowe, Phil; “What’s Right and What’s Wrong with Transference Theories” in Erkenntnis, Vol. 42, No. 3 (May, 1995), pp. 363-374
Dowe, Phil: “Causality and Conserved Quantities: A Reply to Salmon” in Philosophy of Science, Vol. 62, No. 2 (Jun., 1995), pp. 321-333
Dowe, Phil; “The Conserved Quantity Theory of Causation and Chance Raising” in Philosophy of Science (Supplement: Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers), Vol 66, pp. S486-S501
Dowe, Phil; “Causal Processes” in The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL=<http://plato.stanford.edu/archives/fall2008/entries/causation-process/>.
Fair, David; “Causation and the Flow of Energy” in Erkenntnis, Vol. 14, No. 3 (Nov., 1979), pp. 219-250
Salmon, Wesley C.: “Causality: Production and Propogation” in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9
Salmon, Wesley C.; “Causality Without Counterfactuals” in Philosophy of Science, Vol 61, No 2 (June 1994), pp 297-312.
Salmon, Wesley C.; “Causality and Explanation: A Reply to Two Critiques” in Philosophy of Science, Vol. 64, No. 3 (Sep., 1997), pp. 461-477
(4) Carroll, John W.; “Laws of Nature” in The Stanford Encyclopedia of Philosophy (Spring 2011 Edition), Edward N. Zalta (ed.), URL=http://plato.stanford.edu/archives/spr2011/entries/laws-of-nature/
(5) Lewis, David; Philosophical Papers, Volume II, Oxford University Press, New York, New York, 1986, pg ix.
(6) Mitchell, Sandra; “Pragmatic Laws” in Philosophy of Science, Vol 64, Supplement. (Dec, 1997), pp S468-S479.
(7) Woodward, James, “Scientific Explanation” in The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.), URL=http://plato.stanford.edu/archives/spr2010/entries/scientific-explanation/
