Edward Feser

What is a Law of Nature?

Edward Feser

[A lecture given at Fermilab on June 27, 2018] 

The notion of a physical law is perhaps the central concept of modern science.  In their book The Grand Design, Stephen Hawking and Leonard Mlodinow characterize the history of science as “the long process of replacing the notion of the reign of gods with the concept of a universe that is governed by laws of nature.”[1]  They quote Alexander Pope’s famous couplet:

     Nature and Nature’s laws lay hid in night:

     God said, Let Newton Be! and all was light. 

The idea is that it is Newton’s discovery of physical law that made nature at last intelligible, and that Newton’s successors have increased this intelligibility insofar as they have improved upon Newton’s laws and discovered further ones.  Hawking and Mlodinow are, of course, expressing a view that is very common among scientists and admirers of science.

But what exactly is a law of nature?  Hawking and Mlodinow characterize a law as “a rule that is based upon an observed regularity and provides predictions that go beyond the immediate situations upon which it is based.”[2]  Here too their position is no doubt a common one.  But their answer is not terribly informative, because the terms “law” and “rule” are often used synonymously.  Suppose you asked a political philosopher what liberty is and he told you that liberty is freedom.  You would probably respond: “Yes, I already know that much, because the terms are more or less interchangeable.  I wasn’t asking you for a synonym, though.  I want to know the nature of the thing that the words ‘liberty’ and ‘freedom’ refer to.”  In the same way, since the words “law” and “rule” are often used interchangeably, it isn’t very helpful to say that a physical law is a kind of rule.  What we need to know is the nature of the laws or rules that are said to govern the physical world. 

To be sure, Hawking and Mlodinow do say more than merely that a law of nature is a kind of rule.  Again, they tell us that laws are inferred from observed regularities, and that we can derive predictions from them.  They also tell us that “in modern science laws of nature are usually phrased in mathematics,” and that “they must have been observed to hold without exception… at least under a stipulated set of conditions.”[3]  And they tell us that physical laws are “consistent principles,” in contrast with the arbitrary and “inscrutable” whims of the gods in terms of which pre-scientific cultures explain natural phenomena.[4] 

But while somewhat informative, even these remarks still don’t really answer our question.  Suppose you asked a geometer what a triangle is, and he told you that in Euclidean geometry the angles of a triangle summed to 180 degrees, that you could discover various features of triangles by constructing proofs, and so on.  All of that is true, but it doesn’t really answer your question.  What the geometer would be telling you about is a certain property of triangles, and a method for coming to know things about them.  But what you asked about was the nature of the thing that has these properties, and the nature of the thing that can be known in this way.  What you need is what is captured in a definition like: “A triangle is a closed plane figure with three straight sides.”  That tells you what a triangle is, and not merely certain properties of triangles or facts about them.  Similarly, to say that physical laws make natural phenomena intelligible, or that they are stated in mathematical terms, or that we infer them from observed regularities, or that we can derive predictions from them, only tells us about certain properties of laws or facts about them.  It does not tell us what a physical law is, does not tell us the nature of the thing of which these various claims are true. 

Surprisingly, other scientists who comment on the subject are often not much more informative than Hawking and Mlodinow.  Even Richard Feynman’s book on the subject, The Character of Physical Law, for the most part focuses on describing various specific examples of laws of nature and some general features they share, rather than offering a systematic account of what a law of nature is.[5]

However, philosophers of science have explored this issue in considerable depth, and what I want to do in this talk is to examine the five main accounts of what a law of nature is that have been proposed over the centuries.  They are as follows.  First, there is the theological account of laws, according to which a law of nature is a kind of divine command.  Second, there is the regularity theory of laws, which, as the name implies, holds that a law is essentially nothing more than a regularity or pattern found in nature.  Third, there is the Platonic view that a law is a relationship of necessary connection between the properties of things, understood as abstract entities – that is to say, as something like Platonic Forms.  Fourth, there is the instrumentalist view that laws of nature don’t really exist, but are merely convenient fictions useful for making predictions.  Fifth, there is the Aristotelian view that a law describes the causal powers that a material thing or system will tend to manifest given its nature or essence. 

Let me break the suspense by telling you that what I will be arguing is that the first four views are all wrong, and that the last, Aristotelian account of physical laws is the correct one.  Let me also tell you up front one of the reasons why this matters, and it is a reason I suspect you will find surprising.  In recent years, a number of prominent scientists, including Hawking and Mlodinow, Richard Dawkins, Lawrence Krauss, Peter Atkins, and Jerry Coyne, have been vigorously promoting scientism, the view that science is not only a genuine source of knowledge (which no one really denies), but the only genuine source of knowledge.  They have also been using scientism as a cudgel with which to beat theology, and, accordingly, as an argument for what has come to be called the New Atheism.  And they have, into the bargain, sometimes pitted modern science and its method of searching for laws of nature precisely against the Aristotelian tradition in philosophy (as Hawking and Mlodinow do in the potted history of science they provide at the beginning of their book).

Obviously, given what I have already said, I am going to argue against this supposition that there is an incompatibility between modern science and Aristotelian philosophy.  Another implication of my discussion is going to be that scientism is false.  Science certainly gives us knowledge, but it is not the only genuine source of knowledge, and there are serious questions about reality that need to be answered but which the methods of science cannot answer.  And one of those questions is about the nature of laws of nature.

Now, since I have in various writings of mine been very critical of the New Atheist thinkers just mentioned, you might expect that I am going to be deploying these claims in support of some sort of theological conclusion.[6]  Here is where you are likely to find the upshot of my discussion surprising, indeed ironic.  For in fact, while I am certainly no atheist, what I am going to argue is that the Aristotelian account of physical law is the only view on which we can both make sense of how physical laws have the explanatory power that science says they have, and do so without directly bringing God into the picture.  In fact, the Aristotelian view provides something like neutral ground between atheism and theism, at least where the subject of laws of nature is concerned.  And in fact, the alternatives to the Aristotelian view are, in a sense, if anything more favorable to theology, or at least a certain kind of theology, than the Aristotelian view is. 

This may all sound strange, but I think it will sound less so once we have worked through the various theories about the nature of physical law that I referred to earlier.  So let’s get to that.

The theological account of laws of nature

We will start with the theological account of what a law of nature is, because this was, as a matter of historical fact, modern science’s original understanding of what a law of nature is.  Descartes and Newton, for example, famously regarded laws of nature as divine commands.  The idea was that matter has no inherent tendency to behave in any particular manner.  It is simply inert, passive stuff that, by itself, could be ordered this way or that depending on what laws are imposed on it.  The laws discovered by natural science reflect the specific kind of order God has willed to impose on matter.  The laws are universal and inexorable because they reflect the universal and inexorable will of God.  God has decreed that an object at rest will stay at rest and an object in motion will stay in motion at a uniform speed in the same direction unless acted upon by an outside force.  God has decreed that planets will move in elliptical orbits.  God has decreed that radium will have a half-life of 1600 years.  And so on.  Material phenomena are like an army which follows “to a T” the directives of its divine commander-in-chief.

The other accounts of what a law of nature is that we are going to examine can all be seen as essentially reactions to this original theological conception, which at least implicitly and partially define themselves in opposition to it.  Indeed, the physicist Paul Davies has argued that contemporary thinking about laws of nature has never really entirely escaped the theological baggage that was originally associated with the concept.  In a recent essay, he writes:

The orthodox view of the nature of the laws of physics contains a long list of tacitly assumed properties.  The laws are regarded, for example, as immutable, eternal, infinitely precise mathematical relationships that transcend the physical universe, and were imprinted on it at the moment of its birth from “outside,” like a maker’s mark, and have remained unchanging ever since… In addition, it is assumed that the physical world is affected by the laws, but the laws are completely impervious to what happens in the universe… It is not hard to discover where this picture of physical laws comes from: it is inherited directly from monotheism, which asserts that a rational being designed the universe according to a set of perfect laws.  And the asymmetry between immutable laws and contingent states mirrors the asymmetry between God and nature: the universe depends utterly on God for its existence, whereas God’s existence does not depend on the universe…

Clearly, then, the orthodox concept of laws of physics derives directly from theology.  It is remarkable that this view has remained largely unchallenged after 300 years of secular science.  Indeed, the “theological model” of the laws of physics is so ingrained in scientific thinking that it is taken for granted.  The hidden assumptions behind the concept of physical laws, and their theological provenance, are simply ignored by almost all except historians of science and theologians.[7]

The eminent philosopher of science Nancy Cartwright has made similar observations.  In fact, Cartwright goes so far as to say that the notion of a law of nature cannot possibly be made sense of apart from God.[8]  In her view, you can have atheism or laws of nature, but not both.  (Cartwright doesn’t use this thesis as an argument against atheism, by the way, because she does not herself believe there really are any laws of nature.)  In my opinion, Cartwright goes a bit too far.  I think we can make sense of the notion of laws of nature without appealing to God.  But it is true that the notion has theological origins, and as we will see, Davies and Cartwright are correct that even much purportedly secular thinking about the nature of physical law is more beholden to these theological origins than is usually realized.

All the same, in my opinion, the theological conception of physical law ought to be rejected, because it simply gets nature wrong and, into the bargain, it is bad theology.  To see how, consider an analogy.  During a game of checkers, the game pieces on the board will move around in regular patterns.  Perhaps, even if you had never heard of the game before, you could work out some of its rules by observing these patterns.  But it would, of course, be a mistake to think that in discovering them you were discovering something about the game pieces themselves, or about how they tend to behave.  For in fact the game pieces don’t do anything.  Left to themselves, they would just sit there.  It is the players of the game who are doing everything, and in studying the patterns you see on the board you are really only indirectly studying them – in particular, you are figuring out what the players are doing, and what is going on in their minds.

Now, the theological conception of physical law essentially makes of the natural world a kind of checkers board, and God the sole player.  And it makes of natural science a kind of theology.  In searching out the laws of nature, the scientist is not really studying what nature is doing, but rather is studying what God is doing.  For nature itself isn’t really doing anything on this view, any more than checkers game pieces are doing anything.  Only God is really doing anything.

This amounts to a view about causality known in the history of philosophy and theology as occasionalism.  According to occasionalism, it isn’t really the cue ball that knocks the eight ball into the corner pocket.  It is God who knocks the eight ball into the corner pocket, on the occasion when the cue ball makes contact with it.  It isn’t really the sun that causes the ice in your lemonade to melt.  It is God who causes it to melt, on the occasion when the sun is out.  And so on for all other apparent causal connections in nature.  None of them is real.  Only God ever really does anything and the physical world is utterly inert. 

One problem with this view is that if it were true, natural science wouldn’t really be possible.  As we have seen, Hawking and Mlodinow characterize science as in the business of discovering principles in nature that are consistent or exceptionless, as contrasted with the inscrutable or arbitrary whims of the gods.  I think they are right about that.  But if a physical law were nothing more than a kind of divine command, then science couldn’t discover such principles in nature.  That is not because God is arbitrary, but because nature would be.  Go back to the checkers analogy.  There is nothing in the nature of a checkers game piece itself that can tell you how it will behave.  If the players want to use the pieces to play a game of checkers, then the pieces will move around in patterns typical of a checkers game, but they could instead decide to use them in some other way – for example, as money, or to make costume jewelry, or some other use.  We can even imagine that they could have perfectly reasonable and non-arbitrary grounds for doing so.  But the behavior of the checkers game pieces would no longer fit some exceptionless or consistent pattern.

Similarly, if the theological account of laws of nature were correct, then there would be no reason to expect exceptionless or consistent patterns in nature.  God could make nature operate according to one set of laws today, and a different set tomorrow.  For example, whereas the sun will tend to melt the ice in your lemonade today, tomorrow it might behave according to different laws, in such a way that it will freeze the lemonade, or turn it into gasoline.  We can even imagine that God would have perfectly rational and non-arbitrary grounds to make this happen.  The point is that nature itself would seem arbitrary and unpredictable.  Yet that’s not in fact how nature behaves, which tells against the theological view of laws. 

Another problem is that if you work occasionalism out consistently, it is hard to avoid a kind of pantheism, the view that the natural world is identical to God.  For if physical things literally do nothing, it is hard to see how they can so much as exist at all.  Our awareness of the natural world turns out to be really just a kind of confused awareness of God and his activity. 

In short, the theological account of laws of nature, when worked out consistently, really seems to deny that there is any such thing as nature and any such thing as law.  There is just the inscrutable will of God.  And one problem with this view is, again, that this is simply not borne out by actual experience.  For physical science has in fact discovered law-like patterns in nature.  Hence, even if God exists – and I think he does, but put that aside for present purposes – a law of nature cannot be understood as a kind of divine command.  Some other account of physical laws must be correct.

The regularity theory of laws

So, let’s turn to the regularity theory of laws of nature.  To state this view in its simplest form, a law of nature is simply a regular pattern that we happen to find in nature.  It’s not that God or anything else causes this regularity to exist in nature.  It is just there in nature, and that’s that.  An object at rest stays at rest, and an object in motion stays in motion at a uniform speed in the same direction unless acted upon.  Planets have elliptical orbits.  Radium has a half-life of 1600 years.  And so on.  That’s just how the world is.  In the philosophy of science, this view is often traced back to David Hume, and it seems to be the view taken by at least many contemporary scientists.  For example, Feynman seems to be committed to something like it when he gives physical laws the following characterization in his book The Character of Physical Law:

There is… a rhythm and a pattern between the phenomena of nature which is not apparent to the eye, but only to the eye of analysis; and it is these rhythms and patterns which we call Physical Laws.[9]

The basic idea of the regularity theory is very simple and many scientists seem to think it obvious and unproblematic.  But philosophers of science who defend it have had to qualify it significantly, because on closer inspection the regularity theory is subject to several serious, and indeed in my opinion insuperable, objections.[10] 

The first problem is that a pattern’s being regular is in fact not sufficient, not by itself enough, to make it a law of nature.  To take a stock example, consider the following two regularities: (1) Every lump of gold is smaller than one cubic mile in size, and (2) Every lump of uranium-235 is smaller than one cubic mile in size.  Both of these statements are true, but there is a crucial difference between them.  Though there is in fact no lump of gold as large as a cubic mile, such a lump is at least theoretically possible.  But a lump of uranium-235 that large is not theoretically possible, because a chain reaction would occur before the lump could get that big.  So, though the regularity concerning uranium-235 plausibly counts as a law of nature, the regularity concerning gold does not.  So there must be something more to a law of nature than merely being a regularity.

Or consider an example like the following, made famous by the philosopher Nelson Goodman.  Suppose it were a law that all emeralds are green and also a law that all sapphires are blue.  (This is not quite correct, but for the sake of simplicity suppose it were.  Or substitute a different example if you wish.)  Now consider the attribute of being grue, which something has if it is observed before December 31, 2050 and is green, or observed after December 31, 2050 and is blue.  And consider further the attribute of being an emerire, which something is if it is observed before December 31, 2050 and is an emerald or is observed after December 31, 2050 and is a sapphire.  Then it will be true that all emerires are grue.  But it seems implausible to regard this regularity as a law of nature.  Of course, you might object that attributes like being grue or being an emerire seem silly and are obviously “made up” rather than capturing some objective feature of nature.  But that’s precisely the point.  Since, precisely because of its artificiality, a regularity like “All emerires are grue” does not plausibly count as a law of nature, there must be more to a law of nature than simply being a regularity. 

The actual existence of a regularity also does not appear to be necessary for something to be a law of nature.  For example, consider a law to the effect that particles of a certain kind have a fifty percent probability of decaying within a certain period of time t.  It might seem that there is a regularity that makes this a law, namely that among any collection of particles of the type in question, a certain proportion will in fact have decayed by time t.  But suppose there happened to be only one such particle.  It is perfectly possible that that particle will not in fact decay by time t.  In that case we would not have a certain proportion of particles decaying by time t, and thus would not have any actual regularity for the law to describe.  But there nevertheless would still be a physical law to the effect that any particle of that type has a fifty percent probability of decaying by time t.

Consider also that there are chemical elements that do not exist in nature but would have to be produced artificially, in the lab or by nuclear explosions, if they are to exist at all.  Fermium would be an example.  As with other elements, there are physical laws that describe the properties and behavior of fermium.  But suppose fermium had never in fact been produced.  Then the laws of nature describing fermium would still be true, even though they corresponded to no actual regularities found anywhere in nature.  For it still would have been true, even under those circumstances, that if fermium were to exist, it would behave in such-and-such a way.

It might seem that some of these problems could be dealt with if we added what philosophers call counterfactual conditionals to our statement of a law.  A counterfactual conditional is a statement about what would have happened if a certain situation that did not in fact exist had existed.  Hence, as I just indicated, even in a world without any actual fermium we could state laws governing fermium by saying that if fermium had existed, then it would have behaved in such-and-such a way.  Or we could say that if we had tried to produce a lump of uranium-235 as big as a cubic mile, it would have caused a chain reaction before it could form.  Since no such counterfactual conditional would be true of a lump of gold the size of a cubic mile, it might seem that we could use counterfactuals to capture the fact that the regularity concerning uranium-235 is a genuine law while the regularity concerning gold is not.

However, this will not work, because it gets the relationship between laws and counterfactual conditionals the wrong way around.  Counterfactual conditionals will be true only given certain background assumptions, including assumptions about what the laws of nature happen to be.  Hence, consider the counterfactual conditional statement to the effect that if a certain object had been set in motion, then it would have continued in motion at a uniform speed.  This counterfactual will be true only on the assumptions that Newton’s first law is in fact true, and that the object in question was not being acted upon by an outside force.  So, we cannot analyze laws of nature in terms of counterfactual conditionals, because we have to analyze counterfactual conditionals in terms of laws of nature.

A way to try to deal with some of these problems that was developed by philosopher David Lewis is to suggest that a physical law is not just any old regularity, but is, specifically, a regularity that covers a broad range of phenomena and yet can be captured in a relatively simple description.[11]  One problem with this approach is that it still doesn’t rule out all regularities that are not plausibly thought of as physical laws.  For example, the regularity captured by the statement that all emeralds are green is no less simple or broad in scope than the regularity captured by the statement that all emeralds are grue.  But while the former is a plausible candidate for a law of nature, the latter is not.  Nor is it clear exactly how we are to evaluate the criterion of simplicity.  Recall what it means for something to be grue.  By one standard of simplicity, the statement that all emeralds are grue is simpler than the statement that all emeralds are green if they are observed before December 31, 2050 and blue if observed after December 31, 2050.  But since these statements amount to the same thing, the greater simplicity of the first formulation hardly makes it a more plausible candidate for a law of nature than the second and more verbose formulation.  A further problem is that simplicity in the statement of a law and the breadth of the phenomena covered by the law may come into conflict.  If we add details to the statement of a law it may cover a wider range of phenomena, but at the same time be less simple in its formulation.

But there is an even deeper and more serious problem with the regularity theory of laws of nature, however many qualifications we add to it.  The problem is that if a physical law is a mere regularity, then it doesn’t really explain anything.  All it does is re-describe things.  Suppose you say: “Planets always move in elliptical orbits.  I wonder what explains that?”  Suppose I answer: “Kepler’s first law explains that.”  You then ask: “Oh, how interesting.  What is Kepler’s first law?”  And I respond by telling you that Kepler’s first law states that planets always move in elliptical orbits.  Obviously, we’ve gone around in a circle.  I haven’t really explained the regularity in question at all, but merely slapped the label “law” on it.

If laws are mere regularities, then slapping a new label on a phenomenon is all I could be doing.  Again, the regularity theory tells us that a law simply describes a regular pattern we find in nature.  To say that it is a law that “All As are Bs” is just a fancy way of saying that as a matter of fact all the As that exist in the world happen to be Bs.  If I tell you that all the chairs in this room are beige, that would obviously be no explanation of the fact that the chair to my left is beige or of the fact that the chair to my right is beige.  By the same token, if I say that all planets move in elliptical orbits, that does not provide an explanation of the fact that Mars moves in an elliptical orbit or that Venus movies in an elliptical orbit.  It merely summarizes the facts to be explained, rather than actually explaining them.

It is useful to compare this to the theological view of laws of nature.  On the theological view, to say that all planets move in elliptical orbits is to say that God has decreed that that is how planets are going to move.  Notice that that does give us an explanation of the regularity.  You might not think it is a good explanation – that is another matter.  The point is that it does at least give us some answer to the question about why the regularity holds.  Recall that I said that the theological view of laws entailed occasionalism, the view that God is the only real cause of anything that happens in the world.  The reason the ice in your lemonade melts when the sun is out is not that the sun causes the ice to melt, but that God does, on the occasion when the sun is present.  The reason the eight ball goes into the corner pocket when the cue ball knocks into it is not that the cue ball caused the eight ball to move, but that God caused it to move, on the occasion when the cue ball was present.  And so on.  David Hume, the father of the regularity theory of laws, is sometimes described as advocating something like occasionalism without God.  For Hume, the sun’s coming out is followed by ice melting, and the motion of the cue ball is followed by the motion of the eight ball, and that’s all we can say.  It isn’t that the sun or the cue ball causes anything, and it isn’t that God causes anything either.  There are just these patterns there in the world, and that’s all that can be said.  There is no causal explanation to be had, and no other explanation either. 

And the trouble with this, of course, is that Hawking and Mlodinow and other defenders of science have told us that it is only with the rise of modern science and its appeal to laws of nature that we have finally gotten genuine explanations of natural phenomena, whereas theological explanations were pseudo-explanations.  If the regularity theory of laws is true, then this turns out to be the reverse of the truth.

Now, you might be tempted to say that the appeal to Kepler’s laws really is a genuine explanation of the motion of the planets, because Kepler’s laws can be interpreted as a special case of Newton’s laws, and Newton’s laws make reference to concepts like force, mass, and acceleration that can illuminate why the planets move.  But if the regularity theory of laws were true, this would be an illusion, because Newton’s laws too would really merely describe regularities rather than explain them, even if the description is a more general one.  Go back to my example of the chairs.  Suppose you ask me why the chair to my left is beige, and I answer “Because all the chairs in this room are beige.”  Suppose you object that this does not really explain the color of the chair at all, and I reply: “But the fact that all the chairs in the room are beige is actually a special case of the more general fact that all the furniture in the room is beige, and to point this out brings in a new concept – the concept of furniture – which illuminates the fact that all the chairs are beige.”  Obviously, this doesn’t really illuminate anything.  And by the same token, even if you can derive Kepler’s laws from Newton’s, and then take Newton’s in turn to be an approximation of Einstein’s laws, you still will not really have explained anything if physical laws are mere regularities.  All you will be doing is describing the phenomena to be explained using more general concepts, rather than actually explaining the phenomena.

Excursus on laws and explanation

Before moving on to the next theory of what a physical law is, I want to pause over this issue of the explanatory power of laws of nature, because some interesting things have recently been said about it by a couple of scientists of note.  Consider first the views of physicist Sean Carroll, who appears to endorse the regularity theory of laws and directly addresses the objection that given such a theory, physical laws “might describe what the universe does, but they don’t explain the reason why it does those things.”[12]  Carroll’s response is essentially to bite the bullet and acknowledge that on his account, the fundamental laws of nature are simply “brute facts” without explanation.  He rejects what is traditionally called the Principle of Sufficient Reason (PSR), according to which, for anything that exists or any event that occurs, there must be some explanation sufficient to account for it, to make it intelligible.  Carroll, like others in the tradition tracing back to Hume, holds that at bottom the world simply is the way it is in a way that is not intelligible or explainable.

One problem with this that Carroll seems insufficiently sensitive to is that it entails a massive comedown from the bold claims made about science by scientists like the ones I referred to earlier – Hawking and Mlodinow, Dawkins, Krauss, Atkins, Coyne, and many others.  Again, they claim that science and science alone has finally given us genuine explanations of natural phenomena in a way that, they claim, philosophy and theology do not.  But if the regularity theory of laws is true and PSR is false, then it would turn out that even science doesn’t really provide explanations at all.  It only seems to because we usually don’t think very carefully about the implications of the regularity theory of laws and the rejection of PSR.  (This is actually a common problem.  Many amateur philosophers who thrill to Hume’s criticisms of theology and metaphysics don’t realize that Hume’s skepticism, followed through consistently, takes down everything – science no less than religion and traditional philosophy.)

Another problem, though, is that Carroll is simply wrong to reject PSR.  For one thing, considered even just as an inference from experience, PSR is as well-supported as any law of nature.  For we do in fact tend to find explanations when we look for them, and even when we don’t we tend to have reason to think there is an explanation but just one to which, for whatever reason (such as missing evidence), we don’t have access.  Furthermore, the world simply doesn’t behave the way we would expect it to if PSR were false.  Events without any evident explanation would surely be occurring constantly and the world would simply not have the intelligibility that makes science and everyday common sense as successful as they are.  That the world is as orderly and intelligible as it is would be a miracle if PSR were not true.

But even that is putting it mildly, because PSR is in fact more certain than even the best-supported empirical hypothesis can be.  For on close analysis it turns out that any position that denies PSR will ultimately be incoherent, especially if (as with Carroll) the denial is made in the name of science.  One way to see this is suggested by some remarks made by philosopher Alexander Pruss, who was in turn developing a point made by Robert Koons.[13]  Denying PSR, Pruss notes, entails radical skepticism about perception.  For if PSR is false, then there might be no reason whatsoever for our having the perceptual experiences we have.  In particular, there might be no connection at all between our perceptual experiences and the external physical objects and events that we suppose cause those experiences.  Nor would we have any grounds for claiming even that such a radical disconnect between our perceptions and external reality is improbable.  For objective probabilities depend on the objective tendencies of things, and if PSR is false then events, including perceptual experiences, might occur in a way that has nothing to do with any objective tendencies of things.  Hence one cannot consistently deny PSR and at the same time trust the evidence of sensory perception, including the observational and experimental evidence upon which science rests.  For we could have no reason to trust that evidence if PSR were false. 

But the Pruss/Koons line of argument can be pushed further than they push it.  Consider that whenever we accept a claim that we take to be rationally justified – as scientists do when they judge a theory to be well-supported by the available evidence, or consider a hypothesis to have been falsified experimentally – we suppose not only that we have a reason for accepting it (in the sense of a rational justification for doing so) but also that this reason is the reason why we accept it (in the sense of being the cause or explanation of our accepting it).  We suppose that it is because the rational considerations in favor of the claim are good ones that we are moved to assent to the claim.  We also suppose that our cognitive faculties track truth and standards of rational argumentation, rather than leading us to embrace conclusions in a way that has no connection to truth or logic. 

But if PSR were false, we could have no reason for thinking that any of this is really the case.  For all we know, what moves or causes us to assent to a claim might have absolutely nothing to do with the deliverances of our cognitive faculties, and our cognitive faculties themselves might in turn have the deliverances they do in a way that has nothing to do with truth or standards of logic.  We might believe what we do for no reason whatsoever, and yet it might also falsely seem, once again for no reason whatsoever, that we do believe what we do on good rational grounds.  Now, this would apply to any grounds we might have for doubting PSR as much as it does to any other conclusion we might draw.  Hence to doubt or deny PSR undercuts any grounds we could have for doubting or denying PSR.  The rejection of PSR is thus self-undermining.  Indeed, to reject PSR is to undermine the possibility of any rational inquiry.

There is another way in which science implicitly presupposes PSR.  It might be suggested that there can be genuine explanations, including scientific explanations, even if PSR were false.  Carroll seems to take this view, and one finds it taken also by philosophers like J. L. Mackie and Bertrand Russell.[14]  The idea is that we can explain at least some phenomena in terms of laws of nature, those laws in terms of more fundamental laws, and perhaps these in turn in terms of some most fundamental level of laws.  The most fundamental laws would, however, lack any explanation.  That the world is governed by them would just be an unintelligible “brute fact.” 

But this is incoherent.  Suppose I told you that the fact that a certain book has not fallen to the ground is explained by the fact that it is resting on a certain shelf, but that the fact that the shelf itself has not fallen to the ground has no explanation at all but is an unintelligible brute fact.  Have I really explained the position of the book?  It is hard to see how.  For the shelf has in itself no tendency to stay aloft – it is, by hypothesis, just a brute fact that it does so.  But if it has no such tendency, it cannot impart such a tendency to the book.  The “explanation” the shelf provides in such a case would be completely illusory.  Nor would it help to impute to the book some such tendency, if the having of the tendency is itself just an unintelligible brute fact.  The illusion will just have been relocated, not eliminated.

By the same token, it is no good to say: “The operation of law of nature C is explained by the operation of law of nature B, and the operation of B by the operation of law of nature A, but the operation of A has no explanation whatsoever and is just an unintelligible brute fact.”  The appearance of having “explained” C and B is completely illusory if A is a brute fact, because if there is neither anything about A itself that can explain A’s own operation nor anything beyond A that can explain it, then A has nothing to impart to B or C that could possibly explain their operation.  The notion of an explanatory regress of physical laws terminating in a brute fact is, when carefully examined, no more coherent than the notion of an effect being produced by an instrument that is not the instrument of anything.

So, Carroll’s attempt to salvage the regularity theory of laws by denying PSR will not fly.  But that brings us to the views of another contemporary physicist, Lee Smolin.  Like Carroll, Smolin appears to conceive of laws as regularities.[15]  But unlike Carroll, Smolin also endorses PSR.[16]  So, unlike Carroll, he cannot try to bite the bullet and take the fundamental laws of nature to be unintelligible “brute facts.”  He has to find some way to make them intelligible or explicable despite being mere regularities.  The way Smolin does this is in terms of evolution, and he attributes a similar view to Paul Dirac, John Wheeler, and Richard Feynman.[17]  The idea is that the laws that now govern the universe may have arisen from previous, different laws, and those in turn from yet other laws.  Smolin proposes that a kind of “cosmological natural selection” guides this process.[18] 

However, there are serious problems with this view.  First, we need to ask if this proposed evolutionary process is itself law-governed.  If it is not, then it seems that this process has no explanation but is just a brute fact.  But this would violate PSR, which, as I have said, Smolin himself endorses.  So, we have to say that the evolutionary process in question is law-governed.  But now we have another problem, which is that the laws that govern the evolutionary process now themselves stand in need of explanation.  If we say that they have no explanation, then we not only would once again violate PSR, but we will have rendered pointless the initial appeal to evolution.  For if we are going to allow that the laws that govern the evolutionary process have no explanation, then we might as well say that the laws of nature that now govern the universe, which we were proposing to explain in terms of evolution, have no explanation.  But if instead we say that the laws that govern the evolutionary process do have an explanation, and posit some further, higher-order evolutionary process to explain those laws, then it seems we are led into a vicious regress.

Smolin recognizes that his positon faces this problem, which he labels the “meta-laws dilemma.”[19]  He proposes two possible solutions.  The first would be to posit what he calls a “principle of the universality of meta-law.”  The idea here is that it might turn out that all the possible meta-laws that could govern the proposed evolutionary process are equivalent to one another insofar as they would generate the same results.  But it is hard to see how this solves the problem.  For one thing, no reason is given for believing that there is any such principle.  It appears to have no motivation other than the ad hoc one of solving the meta-laws problem. 

For another thing, the principle wouldn’t solve that problem even if it were true.  The most it would show is that, if there is an evolutionary process governed by a meta-law, then any meta-law will be as good as any other.  But that doesn’t explain what makes it the case that there is in fact such a process.  If you see me eating vanilla ice cream and ask me why I am eating it, I would not be giving a complete explanation if I told you that the only ice cream available was vanilla.  That would explain why I am eating vanilla ice cream, specifically, but not why I am eating any ice cream at all.  Similarly, the most that Smolin’s proposed principle could explain would be why the evolutionary process is governed by such-and-such a meta-law, specifically.  What remains to be explained is why there is any evolutionary process in the first place.  And if Smolin appealed to a meta-meta-law in order to answer that question, that would simply land him in a higher-order version of the same problem.

Smolin’s other proposed solution to the meta-law dilemma is to propose “a marriage of law and configuration.”[20]  The idea here is that there are not two things, the evolutionary process and a distinct meta-law that governs it.  Rather, there is just the process itself, with the meta-law being immanent to it.  Now, there are two ways one could interpret Smolin here.  He might mean that the meta-law governing the evolutionary process is simply to be identified with the regularity exhibited by the process.  This would be a straightforward application of the regularity theory of laws to the analysis of meta-laws.  Meta-laws too are just regularities.  But if this is what Smolin means, then the problem should be obvious.  If a meta-law is identical to a regularity, then it cannot explain the regularity.  We will be back where we started, with the fundamental laws (or in this case meta-laws) as inexplicable brute facts, whereas the whole point of Smolin’s theory was supposed to be to allow us to avoid that.

Another way to read Smolin here, though, would be as saying that, given its nature or essence, the physical universe manifests a power or capacity to give rise to new laws, and the meta-law is a description of the operation of this power or capacity.  But on this interpretation, Smolin would be taking something like the Aristotelian view of the nature of physical law (or of the meta-law, in this case), and no longer defending a regularity theory.  He would be saving the regularity theory at the cost of abandoning it.

The upshot of this long excursus, then, is that the regularity theory simply has no way to get around the problem that if laws are just regularities and nothing more, then they do not explain anything. 

The Platonic view of laws

Let us turn, then, to the third view of laws of nature, which I referred to earlier as the Platonic view.  The easiest way to explain this view is as follows.  Suppose we think of the key properties referred to in a scientific theory as something like the Platonic Forms familiar from Plato’s famous theory.  For example, suppose we think of mass, force, and acceleration as Platonic Forms.  There is the Form or abstract pattern of having mass, the Form or abstract pattern of having force, and the Form or abstract pattern of having acceleration.  All the particular physical objects that there are participate in these Forms.  Then laws of nature, on this view, can be thought of as necessary connections holding between these Forms.  For example, Newton’s second law of motion, F = ma, would be understood as describing a necessary connection holding between the Form of mass, the Form of force, and the Form of acceleration.  The law is like a higher-order Form in which these Forms participate.  So, since all physical objects participate in the Platonic Forms of force, mass, and acceleration, they also participate in the higher-order Form that we call Newton’s second law.

This is an oversimplification, and not everyone who endorses this sort of view would take Platonic Forms to be the best model for the properties that laws of nature relate to one another.  For example, philosopher David Armstrong conceives of the properties in question in a way that is closer to Aristotle’s understanding of forms than it is to Plato’s conception.[21]  If we go in that direction, then we end up with a view that is, in the respects relevant to the concerns of this talk, closer to the Aristotelian account of physical laws that I will be discussing in a moment.  

But if we do think of the properties in question on the model of Platonic Forms or abstract entities, then we have a problem.  For this Platonic account really doesn’t explain why the natural world behaves in accordance with physical laws.  Consider that, if Platonism is true, then there are Forms corresponding to all sorts of things that don’t in fact exist.  For example, there is a Form of being a unicorn and a Form of being a Tyrannosaurus Rex, just like there is a Form of being a lion.  The difference, of course, is that there actually are things that participate in the Form of being a lion, but there are no longer things that participate in the Form of being a Tyrannosaurus Rex, and there never was anything that participated in the Form of being a unicorn.  Now, by the same token, not only the laws that actually govern the world, but also alternative possible physical laws that don’t in fact govern it, all presumably exist together in the Platonic realm of abstract objects.  So, what explains why the world participates in just the specific physical laws it does, rather than one of the alternative sets of laws, or no laws at all?  Abstract objects are causally inert.  By themselves they don’t do anything, and so if we think of laws of nature as Forms or abstract objects, we still need to appeal to something in addition to the laws in order to explain why the world actually participates in these Forms.

Suppose we say that we can explain this in terms of higher-level laws of some sort, again understood on the model of Platonic Forms.  The trouble with this, of course, is that we would now need to explain why the world operates according to these higher-order laws, which raises the same problem all over again and threatens an infinite regress.  Suppose instead that we say that God causes the world to operate according to the laws, using the Forms as a blueprint for creation, as Plato suggested in the Timaeus.  Then we’re essentially back to the theological conception of laws of nature, with all of its problems.  Or suppose we say that it is just an inexplicable regularity that the world operates according to physical laws conceived of in Platonic terms.  Then we’re essentially back to the regularity view of laws, with all of its problems.  On close inspection, then, the Platonic view isn’t any better than the alternatives we’ve already rejected.

The instrumentalist view of laws

Now we come to the instrumentalist view about laws.  Instrumentalism in philosophy of science is the approach that says that the theoretical entities posited by scientific theories do not really exist, but are merely convenient fictions useful for organizing experience and making predictions.  In the present context, the idea would be that laws of nature are merely useful fictions and do not really exist.

The debate between instrumentalism and scientific realism is a large topic and I’m not going to attempt to address it in any depth here.  Suffice it for present purposes to say that the main argument for scientific realism in general is an argument for the reality of laws of nature in particular.  And that is what is called the “no miracles” argument.  The idea is that physical theories that posit unobservable entities like atoms, fermions, bosons, and all the rest are so successful in making accurate predictions and supporting technological advances that it would be a miracle if these entities did not exist.  Similarly, since the laws of nature posited by modern physical science are an essential part of this story of predictive and technological success, it would be a miracle if they did not correspond to reality.

Of course, if it were a literal miracle, that would entail divine action, which would bring us back to the theological account of laws.  If we leave out literal miracles, the point is that the success of science would be a massively improbable coincidence if laws of nature were mere useful fictions.  And if we leave this coincidence unexplained, we will be back to the problems we saw faced the regularity theory of physical law.

The Aristotelian view of laws of nature

Notice that all of the views I have been criticizing have something in common.  None of them holds that there is anything in the physical world itself that explains why it has the order it does.  For the theological and Platonic views about laws of nature, this is because the order that exists in the world is to be explained by reference to something outside it – God’s commands in the one case, Platonic abstract entities in the other case.  For the regularity and instrumentalist theories of laws, this is because there is no explanation at all to be offered, either by reference to something outside the world or by reference to anything else.

The central idea of the Aristotelian view is that the explanation of the order exhibited by the physical world is to be found precisely within the physical world itself, in the natures or essences of physical objects and systems.  For example, uranium-235 will reach critical mass well under a cubic mile, not because of some arbitrary divine command, not because of some Platonic Form it participates in, and not as a matter of some inexplicable brute fact regularity, but rather because of the essence or nature of uranium-235, something internal to this particular kind of physical substance itself.  The physical laws governing uranium-235 are, on the Aristotelian view, to be understood as descriptions of the way something having the essence or nature of uranium-235 will tend to behave.  More precisely, they describe the active and passive causal powers that follow from the essence or nature of uranium-235 – the ways it will tend to affect or be affected by other things.

Now, there is a standard objection to this sort of view which goes back to early modern philosophy and science, and is enshrined in Molière’s famous mockery of attempts to explain how opium causes sleep by attributing to it a “dormitive power.”  The claim is that to appeal to the inner nature or essence of a thing or to its causal powers is merely to utter a tautology and explains nothing.  Common though this objection is, however, it is not a good one, and rests on a misunderstanding of what the Aristotelian is saying.[22] 

Note first that the appeal to natures or powers is not in fact a tautology.  If I were to say that opium causes sleep because it brings about slumber, that would be a tautology – saying exactly the same thing in different words.  But to say that opium causes sleep because of its essence or its causal powers is not a tautology, it does not merely repeat the same thing in different words.  It tells us, for example, that there is something in opium itself that brings about sleep – that it is not just the circumstances in which it is taken that cause sleep, and that it is not an accidental feature of this or that particular sample of opium that causes sleep but rather reflects opium as such.  Now, it is true that that is not terribly informative.  But it is not uninformative.  It does have some content.  And the Aristotelian is not claiming any more than that.  He is not denying that, if you want to know exactly what it is about opium that brings about sleep, you need to do chemistry and not just talk vaguely about causal powers.  He is saying merely that even if a complete explanation has to do much more than merely refer to the essence and causal powers of opium, it has to do at least that much.

And one of the reasons it has to do so is that there is no other way to make sense of laws of nature.  For if we don’t think of a physical law as a description of how a physical object will behave given the essence and causal powers internal to it, then either we have to think of a law as having its explanatory force by reference to something external to the world of physical objects (God or Platonic Forms) or as having no explanatory force at all (as in the regularity theory and instrumentalism).  And I have argued that none of those options can be right.  The Aristotelian view wins by process of elimination.

But there are other things to be said for it as well.  As Nancy Cartwright has famously argued, a curious feature of the laws of nature we know of is that they are not in fact universal regularities.[23]  Or to be more precise, if interpreted as universal regularities, laws turn out not to be strictly true; whereas if they are interpreted in a way that makes them come out true, they are no longer strictly universal.  For example, the law of universal gravitation will not correctly describe the behavior of bodies that are charged or subject to air friction.  Newton’s law of inertia holds only in circumstances where no forces are acting on a body – circumstances which never in fact obtain.  Kepler’s first law tells us that planets move in ellipses, but this is only approximately true insofar as planets are always acted upon by the gravitational pull of other bodies.  And so on.  Laws are true only ceteris paribus, only when certain conditions obtain.  In that case, though, they correctly describe the behavior of the entities they govern only under those particular conditions, and are not true of the entities universally.

This makes perfect sense if we think of physical objects and systems as having active and passive causal powers or capacities, because the manifestation of a power or capacity can be blocked.  For example, the law of inertia, on Cartwright’s interpretation, describes the natural capacity of any physical object to continue in uniform rectilinear motion, where the manifestation of this capacity can be blocked by interference from outside forces, such as those that result from friction or the gravitational influence of other bodies.  The law describes something real insofar as physical objects really do have such a capacity, even though the law does not describe a regularity that ever actually occurs in the world, because outside forces always are in fact interfering and thus blocking the manifestation of this capacity.

The Aristotelian view also accounts for some of the problems that face other theories of what a law of nature is.  For example, we saw that a problem with the regularity theory is that it cannot explain why odd and artificial regularities like “All emerires are grue” are not genuine laws.  The Aristotelian would say that the reason is that genuine laws reflect the causal powers and capacities a physical thing will manifest given its nature or essence.  But there are, for example, no physical things that have the capacity to be green before December 31, 2050 and blue afterwards, so that there is no such feature as being “grue” that a law of nature might describe.

Let me end by coming back to the implications of my discussion that I alluded to at the beginning.  The first implication is that there is greater continuity than meets the eye between modern science and the older, Aristotelian view of the world it is usually thought to have supplanted.  Of course, Aristotle and his medieval successors got a lot of things wrong, in particular where empirical details are concerned.  But what they got right, according to the neo-Aristotelian position I am describing, is the broadest outlines of nature.  They were correct that natural phenomena all have essences and causal powers, even if they sometimes were wrong when trying to identify exactly what those causal powers were.

Here is a second implication.  As I have said, the Aristotelian view takes a law of nature to be a description of the powers and capacities a thing will tend to manifest given its nature or essence.  That entails that laws of nature are not the fundamental level of reality, because they presuppose something else, namely the existence of the physical objects and systems that the laws of nature describe.  This reverses the order of things that appears to be taken for granted by many scientists.  The assumption seems to be that ultimate explanation will involve tracing all of physical reality down to some set of laws of nature, where the laws will in some sense be what exists fundamentally or primordially.  On the Aristotelian view, this gets things backwards.  No matter how far down we take laws of nature, the existence even of the most fundamental laws will itself always necessarily presuppose the existence of something else, namely the physical system that the laws describe.

What this entails, in turn, is that scientism is false.  Scientism holds that only scientific knowledge is real knowledge.  But if scientific explanation always terminates in an appeal to laws of nature, then there is always going to be something science cannot explain, namely the existence of the fundamental laws themselves.  But that scientism is false should also be clear from the whole discussion to this point, and whether or not one agrees with the Aristotelian position.  For whether one accepts the regularity theory of physical law, or the Platonic theory, or some other theory, one will always be taking an essentially philosophical position rather than a scientific one.  Since science presupposes the notion of laws of nature, the investigation of what a law of nature is will, whatever conclusion one reaches, always be a philosophical rather than a scientific investigation, and that entails that there is more to be known about reality than science can reveal.

Finally, if the existence of laws of nature presupposes the existence of a physical reality that is described by those laws, that obviously raises the question of why that physical reality exists.  Now, one could at this point bring God back into the picture.  One could argue that, even if laws of nature are not divine commands but instead just descriptions of the way physical things will behave given their nature or essence, still, the fact that these physical things exist at all requires a divine cause.  But one could argue instead that a divine cause is not necessary.  That is not a debate I am going to get into here.  Suffice it to say that on the Aristotelian view, what directly grounds the laws of nature are the essences of physical things, so that for the purposes of analyzing the character of physical law, one can bracket off the question of whether physical things themselves have a divine cause.  In that sense, the Aristotelian view of laws of nature is neutral between theism and atheism.