One evening a few years ago I was with some other faculty members at the University of Texas, telling a group of undergraduates about work in our respective disciplines. I outlined the great progress we physicists had made in explaining what was known experimentally about elementary particles and fields—how when I was a student I had to learn a large variety of miscellaneous facts about particles, forces, and symmetries; how in the decade from the mid-1960s to the mid-1970s all these odds and ends were explained in what is now called the Standard Model of elementary particles; how we learned that these miscellaneous facts about particles and forces could be deduced mathematically from a few fairly simple principles; and how a great collective Aha! then went out from the community of physicists.
After my remarks, a faculty colleague (a scientist, but not a particle physicist) commented, “Well, of course, you know science does not really explain things—it just describes them.” I had heard this remark before, but now it took me aback, because I had thought that we had been doing a pretty good job of explaining the observed properties of elementary particles and forces, not just describing them.1
I think that my colleague’s remark may have come from a kind of positivistic angst that was widespread among philosophers of science in the period between the world wars. Ludwig Wittgenstein famously remarked that “at the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena.”
It might be supposed that something is explained when we find its cause, but an influential 1913 paper by Bertrand Russell had argued that “the word ‘cause’ is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable.”2 This left philosophers like Wittgenstein with only one candidate for a distinction between explanation and description, one that is teleological, defining an explanation as a statement of the purpose of the thing explained.
E.M. Forster’s novel Where Angels Fear to Tread gives a good example of teleology making the difference between description and explanation. Philip is trying to find out why his friend Caroline helped to bring about a marriage between Philip’s sister and a young Italian man of whom Philip’s family disapproves. After Caroline reports all the conversations she had with Philip’s sister, Philip says, “What you have given me is a description, not an explanation.” Everyone knows what Philip means by this—in asking for an explanation, he wants to learn Caroline’s purposes. There is no purpose revealed in the laws of nature, and not knowing any other way of distinguishing description and explanation, Wittgenstein and my friend had concluded that these laws could not be explanations. Perhaps some of those who say that science describes but does not explain mean also to compare science unfavorably with theology, which they imagine to explain things by reference to some sort of divine purpose, a task declined by science.
This mode of reasoning seems to me wrong not only substantively, but also procedurally. It is not the job of philosophers or anyone else to dictate meanings of words different from the meanings in general use. Rather than argue that scientists are incorrect when they say, as they commonly do, that they are explaining things when they do their work, philosophers who care about the meaning of explanation in science should try to understand what it is that scientists are doing when they say they are explaining something. If I had to give an a priori definition of explanation in physics I would say, “Explanation in physics is what physicists have done when they say Aha!” But a priori definitions (including this one) are not much use.
As far as I can tell, this has become well understood by philosophers of science at least since World War II. There is a large modern literature on the nature of explanation, by philosophers like Peter Achinstein, Carl Hempel, Philip Kitcher, and Wesley Salmon. From what I have read in this literature, I gather that philosophers are now going about this the right way: they are trying to develop an answer to the question “What is it that scientists do when they explain something?” by looking at what scientists are actually doing when they say they are explaining something.
Scientists who do pure rather than applied research commonly tell the public and funding agencies that their mission is the explanation of something or other, so the task of clarifying the nature of explanation can be pretty important to them, as well as to philosophers. This task seems to me to be a bit easier in physics (and chemistry) than in other sciences, because philosophers of science have had trouble with the question of what is meant by an explanation of an event (note Wittgenstein’s reference to “natural phenomena”) while physicists are interested in the explanation of regularities, of physical principles, rather than of individual events.
Biologists, meteorologists, historians, and so on are concerned with the causes of individual events, such as the extinction of the dinosaurs, the blizzard of 1888, the French Revolution, etc., while a physicist only becomes interested in an event, like the fogging of Becquerel’s photographic plates that in 1897 were left in the vicinity of a salt of uranium, when the event reveals a regularity of nature, such as the instability of the uranium atom. Philip Kitcher has tried to revive the idea that the way to explain an event is by reference to its cause, but which of the infinite number of things that could affect an event should be regarded as its cause?3
Within the limited context of physics, I think one can give an answer of sorts to the problem of distinguishing explanation from mere description, which captures what physicists mean when they say that they have explained some regularity. The answer is that we explain a physical principle when we show that it can be deduced from a more fundamental physical principle. Unfortunately, to paraphrase something that Mary McCarthy once said about a book by Lillian Hellman, every word in this definition has a questionable meaning, including “we” and “a.” But here I will focus on the three words that I think present the greatest difficulties: the words “fundamental,” “deduced,” and “principle.”
The troublesome word “fundamental” can’t be left out of this definition, because deduction itself doesn’t carry a sense of direction; it often works both ways. The best example I know is provided by the relation between the laws of Newton and the laws of Kep-ler. Everyone knows that Newton discovered not only a law that says the force of gravity decreases with the inverse square of the distance, but also a law of motion that tells how bodies move under the influence of any sort of force. Somewhat earlier, Kepler had described three laws of planetary motion: planets move on ellipses with the sun at the focus; the line from the sun to any planet sweeps over equal areas in equal times; and the squares of the periods (the times it takes the various planets to go around their orbits) are proportional to the cubes of the major diameters of the planets’ orbits.
It is usual to say that Newton’s laws explain Kepler’s. But historically Newton’s law of gravitation was deduced from Kepler’s laws of planetary motion. Edmund Halley, Christopher Wren, and Robert Hooke all used Kepler’s relation between the squares of the periods and the cubes of the diameters (taking the orbits as circles) to deduce an inverse square law of gravitation, and then Newton extended the argument to elliptical orbits. Today, of course, when you study mechanics you learn to deduce Kepler’s laws from Newton’s laws, not vice versa. We have a deep sense that Newton’s laws are more fundamental than Kepler’s laws, and it is in that sense that Newton’s laws explain Kepler’s laws rather than the other way around. But it’s not easy to put a precise meaning to the idea that one physical principle is more fundamental than another.
It is tempting to say that more fundamental means more comprehensive. Perhaps the best-known attempt to capture the meaning that scientists give to explanation was that of Carl Hempel. In his well-known 1948 article written with Paul Oppenheim, he remarked that “the explanation of a general regularity consists in subsuming it under another more comprehensive regularity, under a more general law.”4 But this doesn’t remove the difficulty. One might say for instance that Newton’s laws govern not only the motions of planets but also the tides on Earth, the falling of fruits from trees, and so on, while Kepler’s laws deal with the more limited context of planetary motions. But that isn’t strictly true. Kepler’s laws, to the extent that classical mechanics applies at all, also govern the motion of electrons around the nucleus, where gravity is irrelevant. So there is a sense in which Kepler’s laws have a generality that Newton’s laws don’t have. Yet it would feel absurd to say that Kepler’s laws explain Newton’s, while everyone (except perhaps a philosophical purist) is comfortable with the statement that Newton’s laws explain Kepler’s.
This example of Newton’s and Kep-ler’s laws is a bit artificial, because there is no real doubt about which is the explanation of the other. In other cases the question of what explains what is more difficult, and more important. Here is an example. When quantum mechanics is applied to Einstein’s general theory of relativity one finds that the energy and momentum in a gravitational field come in bundles known as gravitons, particles that have zero mass, like the particle of light, the photon, but have a spin equal to two (that is, twice the spin of the photon). On the other hand, it has been shown that any particle whose mass is zero and whose spin is equal to two will behave just the way that gravitons do in general relativity, and that the exchange of these gravitons will produce just the gravitational effects that are predicted by general relativity. Further, it is a general prediction of string theory that there must exist particles of mass zero and spin two. So is the existence of the graviton explained by the general theory of relativity, or is the general theory of relativity explained by the existence of the graviton? We don’t know. On the answer to this question hinges a choice of our vision of the future of physics—will it be based on space-time geometry, as in general relativity, or on some theory like string theory that predicts the existence of gravitons?
The idea of explanation as deduction also runs into trouble when we consider physical principles that seem to transcend the principles from which they have been deduced. This is especially true of thermodynamics, the science of heat and temperature and entropy. After the laws of thermodynamics had been formulated in the nineteenth century, Ludwig Boltzmann succeeded in deducing these laws from statistical mechanics, the physics of macroscopic samples of matter that are composed of large numbers of individual molecules. Boltzmann’s explanation of thermodynamics in terms of statistical mechanics became widely accepted, even though it was resisted by Max Planck, Ernst Zermelo, and a few other physicists who held on to the older view of the laws of thermodynamics as free-standing physical principles, as fundamental as any others. But then the work of Jacob Bekenstein and Stephen Hawking in the twentieth century showed that thermodynamics also applies to black holes, and not because they are composed of many molecules, but simply because they have a surface from which no particle or light ray can ever emerge. So thermodynamics seems to transcend the statistical mechanics of many-body systems from which it was originally deduced.
This article is based on a talk given at a symposium on "Science and the Limits of Explanation" at Amherst last autumn.↩
"On the Notion of Cause," reprinted in Mysticism and Logic (Doubleday, 1957), p. 174.↩
There is an example of the difficulty of explaining events in terms of causes that is much cited by philosophers. Suppose it is discovered that the mayor has paresis. Is this explained by the fact that the mayor had an untreated case of syphilis some years earlier? The trouble with this explanation is that most people with untreated syphilis do not in fact get paresis. If you could trace the sequence of events that led from the syphilis to the paresis, you would discover a great many other things that played an essential role—perhaps a spirochete wiggled one way rather than another way, perhaps the mayor also had some vitamin deficiency—who knows? And yet we feel that in a sense the mayor's syphilis is the explanation of his paresis. Perhaps this is because the syphilis is the most dramatic of the many causes that led to the effect, and it certainly is the one that would be most relevant politically.↩
Carl Hempel and Paul Oppenheim, "Studies in the Logic of Confirmation," Philosophy of Science, Vol. 15, No. 135 (1948), pp. 135–175; reprinted with some changes in Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (Free Press, 1965).↩
This article is based on a talk given at a symposium on “Science and the Limits of Explanation” at Amherst last autumn.↩
“On the Notion of Cause,” reprinted in Mysticism and Logic (Doubleday, 1957), p. 174.↩
There is an example of the difficulty of explaining events in terms of causes that is much cited by philosophers. Suppose it is discovered that the mayor has paresis. Is this explained by the fact that the mayor had an untreated case of syphilis some years earlier? The trouble with this explanation is that most people with untreated syphilis do not in fact get paresis. If you could trace the sequence of events that led from the syphilis to the paresis, you would discover a great many other things that played an essential role—perhaps a spirochete wiggled one way rather than another way, perhaps the mayor also had some vitamin deficiency—who knows? And yet we feel that in a sense the mayor’s syphilis is the explanation of his paresis. Perhaps this is because the syphilis is the most dramatic of the many causes that led to the effect, and it certainly is the one that would be most relevant politically.↩
Carl Hempel and Paul Oppenheim, “Studies in the Logic of Confirmation,” Philosophy of Science, Vol. 15, No. 135 (1948), pp. 135–175; reprinted with some changes in Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (Free Press, 1965).↩