Nancy Cartwright is the author of

*How the Laws of Physics Lie*, and is apparently an influential philosopher. Kitcher mentions her in his

*Mind and Cosmos*review, she is regularly included in anthologies of important papers in the philosophy of science, and her term "Dappled World" (borrowed from Manley Hopkins, according to Kitcher) seems to have become a sort of rallying point for modern philosophical views of science.

I think her work is shoddy and unconvincing.

OK, choosing that title for her book is like waving a cape in front of a bull, I suppose. But I really tried to give her a fair hearing, honest I did. Readers of this blog can, I suppose, judge how good I am at giving a fair hearing to views I disagree with. But let me try to present her argument before I tear it apart.

**The Laws of Physics Lie**

In Essay 3 of the book, Cartwright lays out the case that the laws of physics are not true, or, to the extent they are true, they are not interesting. In fact, they are not even

*approximately*true. Why?

She illustrates with Newton's law of universal gravitation. For the definition of this law she quotes Feynman:

(NG1)Then she asks, and answers:The Law of Gravitation is that two bodies exert a force between each other which varies inversely as the square of the distance between them, and varies directly as the product of their masses.

Why not? Well, she says, two bodies may have electric charges, and so the force exerted by one on the other is given neither by NG1 nor by Coulomb's law of electric force, but by a combination of the two. ThereforeDoes this law truly describe how bodies behave?

Assuredly not.

These two laws are not true: worse, they are not even approximately true.

For instance, in an atom, the law of gravitation is swamped by the Coulomb force and so the former is not even approximately true.

Notice that she is not complaining about extreme cases where Newtonian gravitation must be replaced by General Relativity. Her complaint is that the law doesn't state a fact: except, perhaps, in a universe completely empty except for two uncharged objects.

She considers an alternate version of NG1 that uses a prefatory clause to correct the deficiency:

(NG2)Ifthere are no forces other than gravitational forces at work,thentwo bodies exert a force between each other which varies inversely as the square of the distance between them, and varies directly as the product of their masses.

This, she allows, may be a true law, but it is not a very interesting one, for in reality objects have both kinds of properties (mass and electric charge) and so NG2 has no (or very few) applications in reality.

From a physicist's point of view, this is all very wrong-headed. First of all, since she is talking about combining different influences, the law she ought to be talking about is Newton's second law of motion:

(NA)Somehow, she completely avoids mentioning this law anywhere in the chapter (though she mentions it obliquely in considering a related objection, as we will see below). Since she doesn't mention NA, I don't know whether she considers this one of laws that is not even approximately true. But you can't talk about gravitational and electric forces combining without it. With this framework in mind, there is an obvious alternative to NG1 and NG2:The acceleration of an object is proportional to the net force and inversely proportional to its mass.

(NG3)For two massive bodies,there is a contribution to the net forcethat varies inversely as the square of the distance between them, and varies directly as the product of their masses.

With this change, I submit, we have a law that is at least approximately true, with no further need of

*ceteris paribus*clauses.

This is such a simple solution to Cartwright's difficulty that it's hard to believe she missed it. However, she does go on to discuss the law of vector composition of forces, and then to consider a suggestion of Lewis Creary that is similar to NG3. Let's consider what she has to say about these issues.

**Vector Addition**

Cartwright admits that physicists have an answer to the question of combining forces: she calls it the "vector addition story."

For Cartwright, the individual component forces are not real. Only the net force is real.The vector addition story is, I admit, a nice one. But it is just a metaphor.Weadd forces... when we do calculations. Nature does not 'add' forces.For the component forces are not there, in any but a metaphorical sense, to be added....

But this is quite obviously false. Consider, for example, a spring that is subject to equal and opposite forces on its two ends:

The net force is zero, so the center of mass of the spring doesn't accelerate. But the spring is

*compressed*- the component forces have a real, physical effect.

Try telling this guy that the component forces aren't real:

Cartwright is essentially saying "'two apples plus one apple equals three apples' can't be true, because if the two apples and the one apple are real,

*and*the three apples are real, then I would have six apples, not three." But this is just silly: two apples plus one apple equals three apples because that's simply what addition means, when applied to apples. Similarly, in the vector addition of forces, two real, occurrent forces can be added to make a real net force, because that's simply what it means to combine two forces.

For this, Cartwright deserves an award for Worst Misuse of Mathematics By a Professional Philosopher Not Named Craig.

**Causal Action**

Cartwright then turns to Creary, who claims that there are two types of physical laws: laws of causal influence and laws of causal action. Though she doesn't say so, in Newton's mechanics, the law of causal action is good old F = ma (NA).

On Creary's account, Coulomb's law and the law of gravity come out true because they correctly describe what influences are produced.... The vector addition law then combines the separate influences to predict what motions will occur.

This seems to me to be a plausible account of how a lot of causal explanation is structured. But as a defence of the truth of fundamental laws, it has two important drawbacks. First, in many cases there are nogenerallaws of interaction... In fact, classical mechanics may well be the only discipline where a general law of action is always available.

Apparently Cartwright doesn't know about quantum mechanics, where Schroedinger's equation gives a general law, or quantum field theory, where the Lagrangian path integral does the same.

Anyway, it makes no sense to claim that there are no true fundamental laws of physics, except for those few cases where the laws are both fundamental and true. Naturally, if there are general laws of action, and if physics is a more or less unified subject, then we would expect the general laws to be few. The fact that there are only a few such fundamental laws actually shows the strength of the reductionist thesis rather than the opposite.

On the other hand, if her point is just that most of the time, working physicists are not dealing with the fundamental laws, but with some approximations to them, or phenomenological laws that are not fundamental, then I would agree with her, but find the point trite and uninteresting. These physicists wouldn't ever claim that their approximations are true in all cases.

Actually, Cartwright

*does*know about quantum mechanics, because in the very next section she discusses a quantum example: the spectrum of a carbon atom. What she says here is so pathetic that I can't bear to grind through it point by point. Essentially, she again ignores the general law of action (Schroedinger's equation) in order to make her point that there is no general law of action.

At first I thought Cartwright had simply not bothered to understand the physics before she began drawing philosophical conclusions. But later in the book she shows a detailed understanding of some much more difficult areas of physics, so that doesn't seem to be the problem.

The only other explanation I can think of for these egregious errors is that Cartwright is working with a pre-conceived agenda, such that all the examples are contorted so as to support her thesis.

This is no way to ground a philosophical world view.

"For this, Cartwright deserves an award for Worst Misuse of Mathematics By a Professional Philosopher Not Named Craig."

ReplyDeleteI thought you said you weren't going to bash theists. I know, sometimes it's hard to resist.

It's a very amusing award....

ReplyDeleteCartwright's arguments do seem.... pathetic.

Yair