CHAPTER 4
What Needs Explanation
The Newtonian view, held by most scientists practising today, is that there are general laws that govern—or describe—the behavior of things and that a specific fact is considered to be explained if it can be subsumed under a general law. There is no need to explain the general law, other than perhaps to subsume it under a more general law. It is the nature of the universe that there should be such general laws. For Newton, the general laws were those of the Creator of the universe. Since I do not believe in natural theology—that by examining nature we are able to tell, one way or the other, whether there is a Creator—the existence of general laws requires an explanation.
The thesis that I am trying to develop is that the existence of general laws is an illusion—a trick that can be explained. So when I say that general laws need explanation, I mean that what needs explanation is how we are led to believe that there are general laws.
I am going to look now at the notion of explanation in science so that you can see the different points of view that are possible. Explanation is linked with understanding. The reason things are explained to people is so that they will understand. In his Lectures on Physics Feynman says:
What do we mean by “understanding” something? We can imagine that this complicated array of moving things which constitutes “the world” is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. Of course, if we watch long enough, we may eventually catch onto a few of the rules. The rules of the game are what we mean by fundamental physics… If we know the rules we consider that we “understand” the world. [1]
This is a clear statement that understanding of the universe comes when we know the “rules of the game” by which he means the general laws that rule—or describe—the behavior of “things which constitute the world.” Max Jammer in his book Concepts of Force presents this view:
Science, as understood today, has a more restricted objective; its two major assignments are the description of certain phenomena in the world of experience and the establishment of general principles for their prediction and what might be called their “explanation”. “Explanation” here means essentially their subsumption under these principles. [2]
Here, Jammer indicates the fact finding part of science as well as the part that is concerned with explanation. Albert Einstein says much the same thing but adds a few different notes:
The aim of science is, on the one hand, a comprehension, as complete as possible, of the connection between the sense experiences in their totality, and, on the other hand, the accomplishment of this by the use of a minimum of primary concepts and relations (seeking, as far as possible, logical unity in the world picture, i.e., paucity in logical elements)… We do not know whether or not this ambition will ever result in a definite system. If one is asked for his opinion he is inclined to answer no. While wrestling with the problem, however, one will never give up the hope that this greatest of all aims can really be attained to a very high degree. [3]
Einstein stresses the need to have “a minimum of primary concepts and relations.” This means that there should be as few general laws as possible. His hope was for a unified theory in which all general laws were subsumed in a single system. He calls the hope of finding the system “the greatest of all aims” but somehow doubts that it can be found. He himself did not succeed, but the shape of his later work always tended in this direction because he was driven by this as a philosophical ideal. He maintained that scientists must think about the philosophy of science especially whenever things become problematic:
It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophizing? Such might indeed be the right thing at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are so well established that waves of doubt can not reach them; but, it can not be right at a time when the very foundations of physics itself have become problematic as they are now. At a time like the present [the early part of the twentieth century], when experience forces us to seek a newer more solid foundation, the physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for, he himself knows best, and feels more surely where the shoe pinches. In looking for a new foundation, he must try to make clear in his own mind just how far the concepts which he uses are justified, and are necessities. [4]
Louis de Broglie agreed with Einstein in saying that scientific philosophy should not be left to professional—academic—philosophers:
What the scientists still sought in their self-made philosophizing was fructifying world-images and world-ideas—precisely the ingredient expelled in the universities’ analysis [academic philosophers tended to be positivists]. [5]
It was not a matter of treating the philosophy as an end in itself but as a way of making the scientist’s mind more fertile in new ideas about the world. Does the philosophy make any difference at all? Hanson examines this in his book Patterns of Discovery :
Mach construed dynamical laws as summary descriptions of sense observations, while for Hertz laws were highly abstract and conventional axioms whose role was not to describe the subject-matter but to determine [govern] it. The difference is not about what the facts are, but it may very well be about how the facts hang together. Even this difference would not seem to matter much here, since Mach and Hertz would get the same answers to their problems. The real difference, however, only arises at this point: for though they get the same answer to the problem, the difference in their conceptual organization guarantees that in their future research they will not continue to have the same problems…The important differences in conceptual organization, which it has been our aim to illuminate, show only in ‘frontier’ thinking where the direction of new inquiry has regularly to be redetermined. [6]
Different philosophies lead to different future directions. How they organize existing information really does not make much difference. De Broglie says this:
Reality consists of many strata of existence which come into view when different methods of investigation are employed. Each generation has its favoured insight and method which in time, as it reaches a region of low diminishing returns, becomes exhausted. [7]
This is a very pragmatic attitude and one that is very scientific. While a particular philosophy is useful, use it—when it shows “diminishing returns,” abandon it.
There is some disagreement among scientists about the shape of general laws. The if-then-always shape is one related to cause and effect. Another possibility, discarded by most, is that things behave in certain ways not because they are caused to do so but rather because they have a goal to fulfil. This was a view held by the mathematician Euler as explained by Mach:
Euler’s view is that the purposes of the phenomena of nature afford as good a basis of explanation as their causes. If this position is taken, it will be presumed a priori that all natural phenomena present a maximum or minimum. But in the solution of mechanical problems by the ordinary methods, it is possible, if the requisite attention be bestowed on the matter, to find the expression which in all cases is made a maximum or a minimum. [8]
In this kind of thinking there is a purpose or telos—things behave so as to achieve certain ends, for example, move so they take the shortest path between two points. Mach is quick to point out that if you work hard enough you can always find some mathematical “expression” in the motion of an object which is a maximum or minimum—such as the shortest path.
As Mario Bunge says in his book Causality and Modern Science :
To say that in behaving the way that they do physical objects move “with the purpose” of minimizing or conserving the intensity of a given quantity is not too different from asserting that things happen as they do “in order that” the laws of nature may be satisfied. Extremum [maximum or minimum] principles are no more indicative of end-seeking behavior than any other physical laws…[9]
Finding a mathematical expression that is a maximum or minimum as an object moves is an act of the scientist—it is man-made—not part of the “order of things.” Mach himself doubted that an order of things existed. He believed that it was a scientist’s job to systematize the facts about the universe into as small a form as possible, strictly for practical reasons. This is sometimes called empiricism. Reichenbach writes:
In contrast to the transcendental conception of knowledge the philosophy of the new [logical] empiricism may be called a functional conception of knowledge. In this interpretation, knowledge does not refer to another world, but so as to perform a function serving purpose, the purpose of predicting the future. [10]
Here, the reference to “the transcendental conception of knowledge” is to the Newtonian type of philosophy where general laws somehow transcend the things whose behavior they describe. The word empirical, which just means based on fact, has been degraded by many scientists. When a relationship—or formula—is said to be “just an empirical one” it usually means that some arbitrary mathematical equation has been fitted to experimental facts by adjusting some parameters in the equation. Much computer work in science is done to obtain the best fit of certain formulas to experimental data. It is more scientific to have a theory or model behind the mathematical equation because facts can always be fitted by some kind of formula no matter what they are.
Sometimes a set of facts may need two different formulas, one for part of the set, another for the rest, to get a good fit. This makes scientists uneasy. Bridgman says:
What is the basis for the feeling that a theory should not employ two different sorts of mathematical functions joined by a text instructing us to switch from one to the other? … I think that there is often a feeling in the background that a mathematical formulation “really exists” and that the chances of our having found it are considerably less good as long as the toolmarks of our handiwork are as evident as they are with two different analytical expressions. [11]
What is usually hoped for in any empirical fitting of facts by a formula is that an extremely simple formula will fit very well. Somehow the empirical then becomes more than empirical. Here is Heisenberg:
It is difficult to give any good argument for this hope for simplicity—except the fact that it has hitherto always been possible to write the fundamental equations in physics in simple mathematical forms. This fact fits in with the Pythagorean religion, and many physicists share their belief in this respect, but no convincing argument has yet been given to show that it must be so. [12]
This goal of mathematical simplicity was firmly planted by Newton. Randall says:
Isaac Newton effected so successful a synthesis of the mathematical principles of nature that he stamped the mathematical ideal on science, and the identification of the natural with the rational, upon the entire field of thought. [13]
And that brings me, as I close off this chapter, to a second thing that needs explanation if the Newtonian position of the strong evidence of design in nature is to be countered—Why are there mathematically simple general laws?
