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 Kepler. 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 Kepler'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.
Nevertheless, I would argue that there is a sense in which the laws of thermodynamics are not as fundamental as the principles of general relativity or the Standard Model of elementary particles. It is important here to distinguish two different aspects of thermodynamics. On one hand, thermodynamics is a formal system that allows us to deduce interesting consequences from a few simple laws, wherever those laws apply. The laws apply to black holes, they apply to steam boilers, and to many other systems. But they don't apply everywhere. Thermodynamics would have no meaning if applied to a single atom. To find out whether the laws of thermodynamics apply to a particular physical system, you have to ask whether the laws of thermodynamics can be deduced from what you know about that system. Sometimes they can, sometimes they can't. Thermodynamics itself is never the explanation of anything - you always have to ask why thermodynamics applies to whatever system you are studying, and you do this by deducing the laws of thermodynamics from whatever more fundamental principles happen to be relevant to that system.
In this respect, I don't see much difference between thermodynamics and Euclidean geometry. After all, Euclidean geometry applies in an astonishing variety of contexts. If three people agree that each one will measure the angle between the lines of sight to the other two, and then they get together and add up those angles, the sum will be 180 degrees. And you will get the same 180-degree result for the sum of the angles of a triangle made of steel bars or of pencil lines on a piece of paper. So it may seem that geometry is more fundamental than optics or mechanics. But Euclidean geometry is a formal system of inference based on postulates that may or may not apply in a given situation. As we learned from Einstein's general theory of relativity, the Euclidean system does not apply in gravitational fields, though it is a very good approximation in the relatively weak gravitational field of the earth in which it was developed by Euclid. When we use Euclidean geometry to explain anything in nature we are tacitly relying on general relativity to explain why Euclidean geometry applies in the case at hand.
Latour, Kristeva, Derrida, Baudrillard, etc
Originally Posted by Husar
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