Prof. Michael Devitt
How the Laws of Physics are Honest:
Finding Correspondence Truth in Nancy Cartwright
Nancy Cartwright argues that the failure of physical laws to accurately predict outcomes shows that the fundamental laws of physics are inherently false. While a commitment to scientific realism does not require a commitment to truth in scientific laws, her arguments--if valid--do pose a threat to the realist. Cartwright has not emphatically declared herself on either side of the realism issue. Others have variously named her as both a weak scientific realist and a scientific anti-realist. While her writings do not address scientific realism exclusively--or even directly in most cases--they do bring up numerous points that are important to the discussion. It is worth our while to tease out how her notion of truth in physics bears on the subject.
Cartwright believes that both macroscopic and theoretical entities literally exist. A belief which is consistent with scientific realism. Strong scientific realism, however, also embraces the posits of modern science whole-heartedly.(1) And this, Cartwright disavows. According to Devitt, support of scientific realism does not rely on truth: "Realism does not strictly entail any doctrine of truth at all. It follows that a person could, without inconsistency, be a Realist without having any notion of truth in his theory."(2) But realists nevertheless hold to a notion of correspondence truth--the idea that our scientific laws generally correspond to the way that the world works. If Cartwright is successful in proving the laws of physics false, scientific realists would have to reexamine their commitment to correspondence truth.
I will argue that Cartwright's statement that the laws of physics are out and out false is too strong. She does successfully show that causal laws are often inaccurate and regularly need to be combined with other laws in order to make successful predictions but this does not translate to proof of their falsehood. Nevertheless, there is much in Cartwright's arguments--both in her less extreme essays in How the Laws of Physics Lie and in her later writings which should be explored further. These points call for a reinterpretation of certain traditional ideas on what the laws of physics aim to explain. Specifically, the laws of science may not be conducive to explaining individual causes and effects, but rather should be used to describe entire systems. By changing our opinions of what the laws of physics do, and establishing a metaphor of just what "truth" means in physics, we can salvage some notion of correspondence truth even in the face of Cartwright's arguments.
2. On Whether the Laws of Physics Lie
I will begin by discussing the basic--and most extreme--position presented by Cartwright: that the laws of physics are inherently false. She draws a distinction between two types of laws in physics: the phenomenological and the fundamental. The former, she says, describe the way things work; the latter explain why they work that way. She has no quarrel with phenomenological laws, only fundamental ones. "I think we can allow that all sorts of statements represent facts of nature, including the generalizations one learns in biology or engineering. It is just the fundamental explanatory laws that do not truly represent."(3)
Cartwright says that these fundamental laws, which attempt to explain entire classes of phenomena, never provide accurate predictions of what happens in any given system in nature. Yes, we can get awfully close if we build a very precise model and protect it from the outside world, but in real life the equations don't apply.
No scientist could successfully deny this, and I'll draw upon my own experience as an example. In my high school physics classes, we were taught--a lá Newton--that a falling rock will accelerate towards the earth at a rate of 32 feet per second per second. A little later on in the year, it's mentioned that, actually, this number is not accurate in real life: air friction gets in the way. Once in college, we learned that everything we'd learned so far was untrue, even that description of gravity neglected subtleties like the spinning of the earth and the height above sealevel; a valid prediction of the acceleration requires incorporating these new variables. A couple years later our professor showed us that these laws too were false. General relativity--with its gravitational fields and fluctuating space-time--must be incorporated to truly predict the acceleration of our falling rock. And finally, graduate school teaches that this is still an incomplete understanding of gravity and we must now include a variety of accessories from gravitons to string theory.
The punchline is not that physics education needs to be revamped (4) but that even in the final "correct" version of the theories, the laws of physics simply do not yield dead-on predictions of a falling rock's acceleration.
For example, scientists to this day run experiments to determine the exact value of G, the fundamental gravitational constant regulating how strongly two bodies will attract each other and whether or not a falling rock will indeed accelerate at 32 ft per second per second. Such experiments are invariable performed deep in the basements of buildings, far away from any disturbances, and yet the experiments have been compromised by a deer wandering 15 yards outside or the water table rising in the ground around the foundation. No two different experiments have yet yielded the same results for the number. Numerous examples of this inconstancy in physics experiments exist. The number of forces acting on a system are too great to understand the sum of their effects perfectly. Scientists take this for granted and incorporate uncertainties and perturbations right into their equations. The information coming out of a mathematical prediction is only expected to be very close to the final outcome--not exact. In fact, when equations do yield perfect predictions on the first run of an experiment, scientists tend to be wary and assume that a mistake has been made.
Cartwright is clearly correct that fundamental laws in physics do not yield perfect predictions. The question is how to interpret this information. Scientists, as Cartwright rightly points out, take this all in stride and simply say that these fundamental laws are true ceteris paribus, all other things being equal. Most people do not question this. We tend to assume that there is an inherent place in the descriptions of the universe for simplified laws--laws that have some use, that do come close to accurate predictions, and that have some similarity to our perceived reality. Indeed, Cartwright too sees their usefulness but wants us to confront the ramifications of their failure to predict accurately. "Ceteris paribus generalizations, read literally without the 'ceteris paribus' modifier, are false." (5) Not just simplified, but false. "Not only are there no exceptionless quantitative laws, but in fact our best candidates are known to fail." (6) To Cartwright, innaccuracy in the laws translates to falsehood.
This is not a leap that I am willing to make. One response to her argument is that no one expects the fundamental laws to give complete descriptions. The force of gravity is not the only force at work on any given object and no one denies this. As Kline and Matheson put it:
The explanation that we offer does not explain exactly how the object moves. Its movement will be affected by many things other than the gravitational force due to the earth. However, we see no reason to hold that an explanation of an event has to be exact. When we ask for an explanation for the elliptical nature of planetary orbits we know that the planets do not move in exact ellipses. We are told that the gravitational force of the sun tends them towards an elliptical orbit, and that the deflections from the elliptical tend to be fairly small. For most practical purposes the planets do move in ellipses; or to put it more rigorously their trajectories are close enough to being elliptical so that an explanation for their traveling in ellipses is an adequate explanation for how they really move. Cartwright is right to this extent: covering-law models requiring exactitude tend to take us away from explanation much of the time. . . However, Cartwright is wrong in thinking that this shows the laws of nature to be false. All that this shows is that the dominant law is hardly ever the only law at work. (7)
It is this last sentence which lies at the heart of the problem. Cartwright says that because we can only accurately describe a dynamical system by incorporating many of these explanations, each explanation by itself is false. But one can just as easily respond that the very fact that these explanations do successfully combine to give relatively accurate predictions supports their individual facticity. Whole systems of math--vector addition, etc.--are built up around the notion of adding together such forces in a dynamical system. Cartwright relegates this to a mere construct of mathematics, not a literal representation of what is happening in nature. (Cartwright goes so far as to say that even were we able to add up all the laws successfully--or alternatively isolate just one--the laws would simply not be accurate. Her support for this lies in the fact that we must always use approximations to get a law to fit a specific theory. "Approximations take us away from theory and each step away from theory moves closer towards the truth." (8) I am not sure how "approximations" differ fundamentally from incorporating additional causes and information about a system, so I have confined myself to addressing her points about summation of causes.)
In many ways it seems almost a matter of faith. One cannot possibly argue that the laws of physics always--or even regularly--predict quantitative effects perfectly. In practice, one cannot even sum up several causes to yield perfect predictions. If, given all the possible information, the summation of causes still failed us, then Cartwright's point would be well taken. But we have no rigorous way of gauging whether or not this is so, which is why I say that choosing which side of the fence you fall on comes down to a matter of faith.
I happen to disagree with Cartwright. (As I will go on to explain later, I do accept much of Cartwright's premise, but not the stark claim that the laws are out and out false.) I do not think either Cartwright or those who rebutt her have presented conclusive arguments that the failure of perfect predictions in fundamental laws translates to the laws being true or false. In the absence of such rigorous arguments, I will give an example of an area where covering laws do not seem to be quantitatively accurate, and then explain why I believe physics to be different.
Cartwright scatters her discussion with occasional reference to economics and it seems possible that her philosophy has been affected by her knowledge of that discipline. Consider her problems with the laws of physics and apply them to economics. In economics there are far too many variables to ever tease out just what cause has led to what effect. The stock market goes down and the Wall Street Journal will print the explanation, "the value of the Yen dropped;" the stock market goes up a week later and the same paper writes, "It's because the value of the Yen dropped." Various causes can affect the market in completely different ways; in economics covering laws are inconstant.
Moreover, when the various causes in an economic system are summed up to a total effect, each cause is lost in the whole, completely and irrevocably, never to be teased apart from the others. There is no way of creating experiments so that we could isolate single causes and their effects.(9) And even if somehow one could isolate a single cause to its effect one might be able to predict whether the market would go up or down, but not by how much. When it comes to economics, covering laws are so dependent on individual conditions that they are, for all intents and purposes, false. It would be hard to argue with Cartwright were she talking about economics.
But she's not. There is a very real difference between physics and economics in a number of ways. First, the various causes in physics do not all inherently affect each other, but can be conclusively and much more easily separated. Specifically, in economics one can only say such and such would send the economy up and such and such would send it down. In the end, that will sum up to a net movement up or down of some amount. But in physics, if gravity pulls a magnet downwards, an electric field pulls it sideways, some initial momentum will keep it spinning, none of these things alter the other effects. Each cause can be studied separately from the others.
Second, physics can predict quantitative effects. The laws don't just say gravity will pull this down to the ground; the laws can give a specific value as to the force and acceleration with which the magnet will fall. So even if we are summing several forces along the same direction (in the same way that there is only one degree of motion in an economic system: up or down) we can say gravity will cause so much movement towards the earth, while an electromagnetic force is causing so much away from the earth. Because we have specific values--something not to be found in economics--we can sum up the causes to get a reasonable prediction of the final movement. We have every reason to believe that vector addition works in physics even when it does not in economics.
Lastly, even in the absence of the above two differences, physics does allow for experiments and models where scientists can isolate specific causes and their effects and create much more accurate laws than those available to an economist. To Cartwright, the fact that physics laws hold during experiments, but not in nature is further proof that they are false:
I begin the with the observation that the laws of physics are true only of what we make. . . We do not measure the success of modern physics by its ability to explain the material world around us as it naturally comes but, rather, by its ability to create very particular environments in which nature behaves in highly regular and precisely predictable ways, as in a labratory, where we put our theories to the test, or in new pieces of technolgoy were we put them to use, as with the hydrogen bomb or the laser. But I would argue that this is too easy a dismissal of the value of experimentation. The fact that we can isolate certain causes during an experiment, in no way repudiates the validity of those individual causes. (10)
In the end, as I mentioned earlier, it comes down to whether adding causes denies their validity or supports it. I do not believe that Cartwright successfully shows that physics's reliance on adding causes is reason to assume that the individual causes are false.
3. On How to Interpret the Failure of Physics Laws to Predict Successfully
Having tried to offer at least some qualitative arguments for why I cannot agree that the "laws of physics lie," I would like to address some of Cartwright's additional--and less extreme--points. These are points which I think she makes very well and should be incorporated into how we assess physics.
Cartwright never denies the usefulness of covering laws in prediction. However, she does say that as one brings together more and more laws to explain a given system, one loses explanatory power. The summation of the laws becomes a description of that particular system only and no longer a good covering law--a law that can help us explain other systems. The laws of physics, then become tools that can help us understand systems on a case by case basis.
There is a precedence for a set of rules that works like this to be found in ethics theory. Casuists argue that codes of ethics are but guidelines for analyzing individual situations. Such codes do not give absolute answers across the board. It is entirely possible that laws of physics, too, offer guidelines not absolutes. To suggest that the natural universe uses (what some would call) arbitrariness for phenomenological effects borders on heresy for a traditional physicist. Nevertheless, if one takes a step back from the most extreme of Cartwright's positions, this is what her arguments amount to. I feel justified in taking this step back, because she herself seems to have backed off her previous position in her more recent articles.
In "Fables and Morals" Cartwright offers a very useful metaphor to describe this adjustment in thinking about physical laws. Physics laws, she says, can be interpreted much as morals in stories are. She offers three examples: "It is dangerous to choose the wrong time for doing a thing. (Aesop Fable 190) Familiarity breeds contempt. (Aesop Fable 206) The weaker are always prey to the stronger. (G.E. Lessing)." (11) Intuitively one sees the truth in these three sentences, and yet we could all produce as many examples to contradict them as to support them. These are rules which apply sometimes and not others. These are rules which will be affected by each individual situation. But the fact that they are a literal description of only some examples does not invalidate them completely. We can accept them as true, without accepting them as absolute. And so we can do with the laws of science. As Cartwright says, "laws can be true, but not universal."(12)
Universality is something that many take for granted should lie at the heart of physics laws. But why do we insist on this kind of perfect, consistent correspondence between model and reality for individual objects in physics that we do not outside of science, or for that matter even demand in other types of science? In day to day life we accept that we can only get an overview, a probabalistic understanding, a sense of how systems move and work. In anthropology we do not suppose that descriptions of a people's traditions will describe the personality of each individual. In biology we do not assume that grand trends of evolution can be used to predict the individual traits of all progeny. Why then should the laws of physics be expected to predict with such specificity?
One could certainly claim that the very difference between physics and other disciplines is that physics does try to describe and explain the causes behind individual movements. Historically, it is just this ability to offer up the ultimate causes behind almost all interactions that separates physics from (and, some would say, lifts it above) the other sciences. From this viewpoint then, physics is expected to predict much more specifically than other disciplines because that, quite simply, is built into the definition of what physics is.
I would argue, however, that explaining individual causes is not a necessary or fundamental part of the discipline. Modern physics has in fact shown us this again and again. Statistical mechanics as developed in the last century is content to describe the general movements of all the atoms in a gas as they dance around a room. It is no less useful--and certainly no less true--for not being able to predict exactly where any particular atom of oxygen will be five minutes from now. Quantum mechanics, too, has fully embraced the notion that certain actions can only be described as probabilities. There's a fifty percent chance this photon will move in this way; fifty percent chance it will move in another. Chaos and complexity theory--two sub-physics disciplines that have grown up over the last decade describe the movements of the whole, not the movements of each part. For centuries, scientists have defined "good science" with criteria culled from the exactness that was perceived to exist within physics. Perhaps the trend needs to reverse as scientists accept that physics should be more like the other sciences: explanations of group behaviour are much more accurate than those of individual behaviours.
While I can't agree that the laws of physics are outright false, I am still siding with Cartwright in a somewhat extreme position. General trends, general guidelines-- these can be described with reasonable accuracy. But individual behaviour is simply not governed with the precision that covering laws attempt to have.
One could argue that--while this may be one way to interpret the failure of physics laws to predict perfectly--that there is no reason to accept this interpretation over any other. I have not developed extensive positive support for this interpretation, but I can offer two quick possibilities. First, there is no more of an a priori reason to believe that individual causes always do have specific effects than that they don't. This is especially true since nothing in nature does occur with the perfect cause-leading-to-effect precision that we attribute to physics theory. Second, it is entirely possible that were two situations truly identical a covering law might be found to fit them. But perhaps, in a very fundamental sense, no two systems are identical at an atomic, or even subatomic level.(13) As Cartwright puts it, "Things are made to look the same only when we fail to examine them too closely."(14)
4. What All This Has to Do with Correspondence Truth
I am urging a position somewhere in between Cartwright's and a strong scientific realist's. The laws of physics do provide us with far too close a description of reality of us to say they are downright false. On the other hand, Cartwright's point that physical explanations are only accurate when other causes and approximations are incorporated is well-taken. But we can still accept the "truth" of these laws if we understand that they are true in one sense: true in general, true depending on the situation, true but not universal.
This is different than merely saying that we don't know everything yet and therefore cannot provide true laws. This is accepting that the world itself does not operate in the perfect clockwork order that physics has historically tried to place on it. This notion of how to interpret the laws' truth is consistent with the direction that physics has taken. This century has seen great changes in the discipline. More and more, scientists realize that they can predict what will happen in whole systems but can only provide limits on what will happen to the individual parts. Perhaps, at the level of individual causes and effects the laws of physics guide, but do not insist.
If we accept this in physics--as we accept it in every other discipline--then we can honestly say that physics does correspond to the way the world works, even though each law by itself does not explain the world precisely. Correspondence truth remains a part of physics.
1. I am, of course, leaving out, for the moment, the invariable--but ostensibly occasional--mistakes that science makes as it progresses. Scientific realists obviously accept that science is sometimes wrong due to human error.
2. Michael Devitt, Realism and Truth, (Cambridge, MA: Basil Blackwell Ltd. 1984) p. 41
3. Nancy Cartwright, How the Laws of Physics Lie, (Oxford: Clarendon Press,1983), p. 56.
4. Though it does!
5. Ibid., p. 45.
6. Ibid., p. 46.
7. A. David Kline and Carl A. Matheson, "How the Laws of Physics Don't Even Fib," PSA 1986, p 35.
8. How the Laws of Physics Lie, p 107.
9. To be fair, this is not completely true. Improved computer technology has allowed for the birth of a whole new field of experimental economics--largely being done at the California Institute of Technology--in which such causes and effects are being studied more closely than ever possible before. It will be interesting to see as the research improves whether covering laws do become more accurate in economics.
10. Nancy Cartwright, "Can Wholism Reconcile the Inaccuracy of Theory with the Accuracy of Prediction?" Synthese 89, p 3.
11. Nancy Cartwright, "Fables and Models," Proceedings of the Aristotelian Society v. 65, 1991 p 57.
12. Ibid. p 58.
13. In fact, David Bohm offered a variation of this interpretation for the formalism of quantum mechanics. He believed that quantum mechanics didn't abandon causation, but that the systems were so sensitive to initial conditions that we could not possibly predict outcomes. Embedded within his interpretation was the idea that we could never get all the information necessary to make accurate predictions.
14. How the Laws of Physics Lie, p19.
List of Works Consulted:
Cartwright, Nancy. "Can Wholism Reconcile the Inaccuracy of Theory with the Accuracty of Prediction?" Synthese 89 (1991): 3-13.
Cartwright, Nancy. How the Laws of Physics Lie. Oxford: Clarendon, 1983.
Cartwright, Nancy and Hasok Chang. "Causality and Realism in the EPR Experiment." Erkenntnis 38 (1993): 169-190.
Cartwright, Nancy and Robin Le Poidevin. "Fables and Models." Proceedings of the Aristotelian Society 65 (1991): 55-82.
Dilworth, Craig. "Empiricism vs. Realism: High points in the Debate During the Past 150 Years." Studies in the History of the Philosophy of Science 21 No. 3 (1990): 431-462.
Franklin, Allan. "How Nancy Cartwright Tells the Truth." British Journal of the Philosophy of Science 39 (1988): 527-529.
Hitchcock, Christopher Read. "Causal Explanation and Scientific Realism." Erkenntnis 37 (1992): 151-178.
Kamminga, Harmke and Reza Tavakol. "How Untidy is God's Mind? A note on the Dynamical Implications of Nancy Cartwright's Metaphysics." British Journal of the Philosophy of Science 44 (1993): 549-553.
Kline, A. David and Carl A. Matheson. "How the Laws of Physics Don't Even Fib." PSA 1 (1986) 33-41.
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