Lecture 9.

Reduction to the Fundamental

Cartwright, "Fundamentalism vs the Patchwork of Laws" and Hoefer, "For Fundamentalism"

The Fundamental Laws

One sometimes hears science students disparaging each other on the basis of how pure a field of study is. "Your field is just an application of mine" say the most slanderous of such remarks.


This sentiment is not unique to students. Here is the great 20th century physicist Paul Dirac:

Paul Dirac
"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble." (Dirac 1929)

Most academic fields provide their own unique insight into the workings of the world. However, many of us have a strong intuition that some fields of study are more fundamental than others. This is the intuition that there are fundamental laws. It is a common attitude among scientists. Stephen Hawking wrote in his recent book The Theory of Everything,

Stephen Hawking
"It would be very difficult to construct a complete unified theory of everything all at one go. So instead we have made progress by finding partial theories." (Hawking 2005, pg. 121)

Many take our best theories of physics to approximate fundamental laws. The laws of quantum theory and of general relativity probably are not exactly correct, but they appear to be a close approximation to the real laws. Thus, somewhere out there, the fundamental laws are just waiting to be discovered. This view is sometimes called fundamentalism or foundationalism.

What does it take to be a foundationalist? Most tend to adopt some or all of the following prerequisites.

If these things are possible, then it is possible that there might be a law of nature that applies everywhere and to everything. That is what we will minimally mean by a fundamental law, although some authors may additionally mean other things as well.

Does any fundamental law exist? The answer may depend in part on what we mean by "laws." For example, if one thinks that laws capture causal dispositions, one furthermore believes in fundamental causes, then it would seem that there are fundamental laws. On the other hand, if one does not believe in fundamental causes, then this perspective might entail that there are no fundamental laws.

On the Best Systems account of laws discussed last time, the axioms of the best deductive system describing all the facts of the world would seem to form the most fundamental set of laws. However, if one was skeptical about the existence of such a best system, then one might infer that there are no fundamental laws.

Reduction to the fundamental laws

One reason that there might be fundamental laws would be if it were possible to reduce all the known laws to one special set of laws. That is, if all law-like behaviour could be deduced to just one special set of laws, then that special set would be a good candidate for the fundamental laws. This concept of reduction is very common in the philosophy of science, and is sometimes referred to as "Nagelian reduction," having been introduced by philosopher of science Ernest Nagel in his masterpiece The Structure of Science.

Nagelian Reduction. A law X is reducible to another law Y if and only if X can be derived as a deductive consequence of Y.

One reason it seems so plausible that we might reduce many laws to more fundamental ones is that it has happened many times before. The most classic example is Newton's theory of gravity. Before Newton, there were laws known to govern the mechanics of bodies on earth, as well as laws known to govern the mechanics of celestial bodies like planets.


These laws seem quite different. However, Newton managed to show that all these laws turned out to be consequences of just three laws, now known as Newton's laws of physics.

It will be important for us to distinguish between two kinds of reduction. The first is called "Downward" reduction by Nancy Cartwright; I will refer to it here by the more descriptive name of "Whole-to-Part" reduction.

Whole-to-Part (Downward) Reduction

Reduction of the laws governing some phenomenon to the laws governing the component parts of that phenomenon.

For example, some have suggested that the facts about chemistry can be derived from facts about physics, and in particular from the way that quantum mechanics describes the interaction of electron shells. Since chemical phenomena do have quantum particles as component parts, this would be an example of Whole-to-Part reduction.

Chemical bonds in a water molecule

A distinct and independent form of reduction from this is the following, called "Crosswise" Reduction by Cartwright.

Wild-to-Laboratory (Crosswise) Reduction
Reduction of the laws governing complex everyday phenomena "in the wild" to the laws governing highly constrained phenomena taking place in a laboratory.

For example, we know how a plane behaves in a wind tunnel. Indeed, we find that it is a law-like behaviour governed by the lift equation, among other things. But this is a highly constrained environment, much different than what one encounters when, say, flying a plane across the Atlantic. But if the laws describing real planes are reducible to laws describing wind tunnel planes, then we have an example of Wild-to-Laboratory reduction.

Plane in a wind tunnel

Whole-to-Part reduction provides just one reason to think that some laws are more fundamental than others. However, it is not the only reason; one can believe that there are fundamental laws without accepting Whole-to-Part reduction. It turns out to be practically impossible to describe all of chemistry in terms of the laws of fundamental physics, let alone the incredible complex of everyday phenomena. It might even be a theoretical impossibility. But as we will see later, there remain other reasons to think that there might be fundamental laws.

On the other hand, Wild-to-Laboratory reduction provides a reason to think the laws apply to our world at all. It is hard to imagine how one could believe in the existence of fundamental laws while denying Wild-to-Laboratory reduction. The kinds of fundamental laws that are compatible with this denial seem undeserving of the name.

Nancy Cartwright

Nancy Cartwright has challenged the possibility of Wild-to-Laboratory reduction. This is perhaps one of the most serious challenges to the foundationalist perspective on laws, and has formed a leading part of the resurgence of anti-foundationalist philosophy of science. Let's have a look at her challenges.

Denying Wild-to-Laboratory Reduction

The physicist Richard Feynman suggested that in spite of the simplicity of the fundamental laws, the actual happenings of the real world are a rather complicated and accidental mess.

Richard Feynman
"I must say immediately that one does not, by knowing all the fundamental laws as we know them today, immediately obtain an understanding of anything much. It takes a while, and even then it is only partial. Nature, as a matter of fact, seems to be so designed that the most important things in the real world appear to be a kind of complicated accidental result of a lot of laws."

Much of the world consists of such messy, complicated facts, like the way a pile of papers fall. In fact, things are often so messy that it's hard to recognise the fundamental laws from among the morass. Given this pervasive messiness of the world, might one doubt that there are fundamental laws at all?

Cartwright suggests we think through this situation with a simple example: take a bank note falling from a height. Have a look at it in slow motion to see the incredible complexity of such a fall.

The fundamental law involved here would appear to be Newton's equation, that the force is proportional to the acceleration of a body, F=ma, where the principal force is gravity. And yet, Cartwright points out, if the only force is gravity then Newton's equation is not a good description of the system, since it fails to describe the air and wind blowing the bank notes about. What Newton's equation with only the gravitational force describes perfectly is just the motion of a body falling straight down in a vacuum.

Falling Ball

There is an immediate objection: there are other forces in play in the bank note system! Thus, the foundationalist will respond, when one accounts for all the forces effecting the bank note, such as the force of air pressure, the internal forces holding the bank notes together, and so on, one finds that this total set of forces is described by Newton's equation, F=ma.

Cartwright responds with a question: how do you know that? You don't seem to be able to write down the relevant forces, since they're too complex. That is, you have no good model that exactly describes this system. In fact, one has hardly any idea what kinds of forces would even be involved, since the internal forces of the bank note are only ever heuristically described.

To take another example: a simple force diagram like the one below is an idealisation that holds only in the highly constrained environment of a laboratory. In "the wild" there are many unaccounted for forces on the plane that makes this description strictly incorrect. According to Cartwright, if we do not have a correct description of the system, then we do not have any evidence that the system satisfies Newton's equation.

Forces on an airplane

According to Cartwright, there is no evidence

In short, the argument is that one has no evidencee for believing that a complete description of the system will satisfy Newton's equation. This is Cartwright's "No Force/No Model" objection: without being able to describe the forces or model the system in exact detail, she says, we have no evidence that the object will fall according to Newton's equation. She thus rules the foundationalist belief to the contrary a fundamentalist faith.

Cartwright's argument may be generalised as follows.

Cartwright's Argument Against Wild-To-Laboratory Reduction
  1. Outside the laboratory, there are no direct tests of the fundamental laws, i.e. no real-world systems that are described with perfect precision by a fundamental law.
  2. Without a direct test, we have no reason to believe a putative law is true.
  3. Therefore, we have no reason to believe the fundamental laws are true outside the laboratory.

The crucial step is the second premise, which Cartwright argues is true due to the fact that there are always external causes that influence a system in a way that is not described by the putative fundamental laws. Thus, Cartwright ends up with the dramatic conclusion that there are no fundamental laws after all.

Instead, Cartwright advocates a view on which there is a patchwork of laws describing many different things, no one of which is particularly privileged. A "messy and imprecise" law like "The bank notes will go roughly down" is not intrinsically different than Newton's equation; it just occupies a different role in the patchwork.

Note that Cartwright's conclusion does not imply antirealism, at least not by itself. In fact, Cartwright says that she actually advocates a certain form of realism about objective knowledge, since she thinks it is the only way to explain our ability to successfully manipulate and make predictions about the world using experiments.

Nevertheless, this argument does recommend we adopt a radical revision of the nature of laws. It is a revision that Cartwright also believes has policy implications, since it suggests that the laws of fundamental physics don't have any particularly privileged status, and thus do not warrant the allotment of so many billions on underground particle accelerators like the Large Hadron Collider at CERN.

Large Hadron Collider

Cartwright compares her view to the foundationalist view using a parable involving St. Peter, who is writing the book of nature.

Book of Nature

On the foundationalist version of the parable, God carefully creates the fundamental laws of the universe as well as the initial state of the universe. And all St Peter has to do to write down the book of nature is to patiently calculate the consequences of the fundamental laws and the initial state.

On Cartwright's view, God instead wrote down a giant set of overlapping law-like regularities. St Peter is then tasked with the problem of ensuring that the patchwork of laws overlaps consistently in order to write the book of nature.

The religious figures in these stories are irrelevant of course. In the stories, "God" just plays the role of identifying the objective facts, while "St Peter" plays the role of identifying contingent or accidental facts. The stories thus illustrate how it is possible to believe in an objective patchwork of laws while denying the existence of fundamental laws.

Concerns about Cartwright's argument

1. Messiness is compatible with fundamental laws.

Let us return to the original idea of a "messy world" of complex phenomena. It is first worth noticing that, if something is "messy," that does not necessarily mean that it escapes the domain of simple fundamental laws. Just look at the double pendulum below. It is described by nothing more than Newton's law of gravity together with the constraints of the pendulum's motion, a relatively simple thing. And yet it gives rise to an incredibly complex motion in the lower bob. Have a look at the video.

If all that we could observe were the motion of the lower bob traced out by the light bob, it might seem hard to believe that there was a simple fundamental law governing th emotion — but there is. It is important not to conflate the simplicity of a law with simplicity of the phenomenon it describes.

2. Causes are nowhere to be found

Bertrand Russell wrote of "causes" that,

To me, it seems that ... the reason why physics has ceased to look for causes is that, in fact, there are no such things. The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.

Whether or not we should eliminate them from our philosophical vocabulary, Russell is correct that the word "cause" is conspicuously missing from the basic entities and influences described by most sciences. In particular, it is clearly completely absent from physics, normally instead standing as a substitute for more precise terms like "force" or "interaction."

If our description of the world does not include cause, then it is somewhat more difficult for Cartwright to make the general claim that there is always a confounding cause for every attempt to describe the world using fundamental laws.

3. There can be knowledge without direct tests

A crucial aspect of Cartwright's argument is her claim that without a direct test, we have no reason to believe a putative law is true. However, it seems that in many cases we can believe something even when a direct test is lacking.

For example, we might be able to test just one consequence of a law, such as that Newton's law with the force of friction says that a sliding body will roll to a stop.

Force of Friction

Or, we might be able to test a good approximation of a law, and use the fact that it is a good approximation to infer that the law is likely to be true. This is exactly what occurs, for example, when we do tests of Galileo's law of freefall when there is air in the room. But it seems Cartwright's account lacks any room for the kinds of approximations that we discussed in lecture 7.

The central problem here is that knowledge normally includes inductive inferences. An inductive inference is one that goes outside what we have strictly observed. For example, we might induce from observations about hundreds of sunflowers that they all contain golden spirals in the centre.


The claim that all sunflowers have this property of course goes beyond what we have strictly observed. Nevertheless, most of science hinges on this kind of reasoning, which has a schematic form that looks something like the following.

inductive schema

How exactly does this induction work? That is a very deep philosophical question that we will come back to later in this course. For now, it is sufficient to notice that it is very pervasive in science, and yet seems to be ruled out by Cartwright's claim that we cannot infer that our fundamental laws hold outside the confines of the laboratory.

For fundamentalism

If these replies to Cartwright stand up to scrutiny, then there may yet be reasons to be a foundationalist. Let us discuss a few of them.

The first is an historical reason. The basic components of nature are already known to be made up of parts governed by law-like equations. If preservative realism is correct, then there is good reason to expect those equations to get ever more accurate, but not to be replaced (at least not the successful parts) altogether.

There is also a mereological reason. Namely, the world is made up of tiny particles that are governed by modern particle physics, and this theory isn't going anywhere soon. It's much better confirmed than phlogiston. And it's the same matter whether it's in our highly-constrained labs or outside our labs. Since there is no qualitative difference between the environment inside and outside the lab, there is no good reason to think that the laws don't apply in the wild.

standard model particle ontology

Thirdly, there is the incredible success of the fundamental laws in describing physics in the wild.

Carl Hoefer illustrates this with the example of the hydrogen atom. The time-independent Schrodinger equation is a law that describes a number of phenomena with incredible and exact accuracy.

For example, it implies that when we heat a tube of hydrogen and split the light using a crystal, we will see particular bands of light.

Hydrogen Splitting

These bands are caused by the quantum mechanical prediction that electrons occupy discrete energy bands, and so emit light only in particular wavelengths corresponding to those discrete energies.

Hydrogen spectrum

Whereas it is very difficult to describe these phenomena in terms of messy causal capacities, it is trivially simple to describe them in terms of fundamental laws.

Thus, Hoefer argues, describing (even messy) phenomena in terms of laws provides a much better description than a Cartwright-patchwork does. Whether all phenomena stand an equal chance, I leave to you.

What you should know

  • The basic properties that a fundamental law is supposed to have, and why someone might believe that they exist
  • Nagelian reduction and the difference between Whole-to-Part (downward) and Wild-to-Laboratory (crosswise) reduction
  • Cartwright's argument against Whole-to-Part reduction, and a specific example of it in action.
  • The major concerns about Cartwright's argument

Practice Questions