Theory and Reality

by Peter Godfrey-Smith

  Not all models in science are mathematical. More generally, we might think of a model as a structure that is intended to represent another structure by virtue of an abstract similarity relationship between them. Sometimes the aim might be to understand the unfamiliar by modeling it on the familiar (as in Bohr's early "solar system" model of the atom). But this is not always what is going on. Abstract mathematical models might be thought of as attempts to use a general-purpose and precise framework to represent dependence relationships that might exist between the parts of real systems. A mathematical model will treat one variable as a function of others, which in turn are functions of others, and so on. In this way, a complicated network of dependence structures can be represented. And then, via a commentary, the dependence structure in the model can be treated as representing the dependence structure that might exist in a real system.

  Models, whether mathematical or not, have a kind of flexibility that is important in scientific work. A variety of people can use the same model while interpreting it differently. One person might use the model as a predictive device, something that gives an output when you plug in specific inputs, without caring how the inner workings of the model relate to the real world. Another person might treat the same model as a highly detailed picture of the dependence structure inside the real system being studied. And there is a range of possible attitudes between these two extremes; another person might treat the model as representing some features, but only a few, of what is going on in the real system.

  The difference between models and linguistically expressed theories may be important in understanding progress in science. Many old scientific theories, now superseded, can look like failures when we ask whether much of the theory was true, and whether the terms in the theory referred to anything. But sometimes, if we recast the old theory as a model, we find that the model had some of the right structure, from the point of view of our current theories. Worrall (1989) uses the case of various "ether" theories from nineteenthcentury physics; they had good structural features even though the ether does not exist.

  In criticizing the emphasis on truth and reference in philosophy of science, I have stressed the role of representational vehicles that require a different kind of analysis. Some would add that even when we are dealing with language, the concepts of truth and reference might be bad ones to use.

  Some philosophers think that to call a theory true is to assert that it has a special connection to the world. Traditionally, this has been described as a correspondence relationship. That term can be misleading, as it suggests a kind of "picturing," which is not what modern theories of truth propose. But this first option holds that there is some kind of special and valuable relationship between true theories and the world. If this is so, we can use the concept of truth when analyzing scientific language and its relations to reality. Others argue that the concept of truth is not suitable for this kind of use. The word "true" is one that we use to signal our agreement or disagreement with others, not to describe real connections between language and the world (Horwich 199o). In sociology of science, Bloor (1999) has defended a position of this kind.

  In this chapter I have been cautious about truth. I used a broad concept of "accurate representation" to describe a goal that science has for its theories. Some argue that even the idea of representation as a genuine relationship between symbols and the world is mistaken, whether the symbols are in language, models, thought, or whatever. That will sound like a radical position, and so it is. (This is one claim made by postmodernists, for example.) But it is hard to work out which theories about symbols retain the familiar idea of representation, and which do not.

  Further Reading

  Key works in the resurgence of scientific realism include Jack Smart's Philosophy and Scientific Realism (1963) and various papers collected in Hilary Putnam's Mind, Language, and Reality (1975). See also Maxwell 1962.

  Leplin, Scientific Realism (1984), is a very good collection on the problem. Boyd's paper in that book is a useful survey of the options, with key differences from the one given here. Boyd also gives an influential defense of scientific realism. Devitt, Realism and Truth (1997), defends both commonsense and scientific realism. Psillos 1999 is a very detailed treatment of the debate.

  For further discussion of the relations between realism and success, see Stanford zooo. On the problems raised by quantum physics, see Albert 1992. For a more detailed discussion of how avoidance of the "Bad View" has shaped sociology of science, see Godfrey-Smith 1996, chapter 5.

  Churchland and Hooker, Images of Science (1985), is a good collection on van Fraassen.

  Kitcher (1978) battles with the problems of meaning and reference for scientific language and their consequences for realism. See also Bishop and Stich 1998 on this problem. Lynch zoos is a recent collection on the problem of truth.

  There is a large literature on the role of models in science (Suppe 1977). Confusion sometimes arises because the usual sense of the word "model" in philosophy is different from that found in science itself (see the glossary). So different people wanting to "analyze science in terms of models" often have very different tasks in mind (Downes 1992.). One useful and interesting treatment of the issue is in Giere's Explaining Science (1988, chapter 3). Hesse 1966 is a famous early discussion, focused, however, on yet another sense of "model."

  Fine 1984 and Hacking 1983 are influential works on scientific realism that defend rather different views from those discussed here.

  13.1 Knowing Why

  What does science do for us? In chapter z z I argued for a version of scientific realism, according to which one aim of science is describing the real structure of the world. Science aims to tell us, and often succeeds in telling us, what the world is like. But it is also common to think that science tells us why things happen; we learn from science not just what goes on but why it does. Science apparently seeks to explain as well as describe. So we seem to face a new question. What is it for a scientific theory to explain something? In what sense does science give us an understanding of phenomena, as opposed to mere descriptions of what there is and what happens?

  The idea that science aims at explanations of why things happen has sometimes aroused suspicion in philosophers, and it has also done so in scientists themselves. Such distrust is reasonably common within strong empiricist views. Empiricists have often seen science, most fundamentally, as a system of rules for predicting experience. When explanation is put forward as an extra goal for scientific theories, empiricists get nervous.

  There is a complicated relationship between this problem of explanation and the problem of analyzing confirmation and evidence (chapters 3, 14). The hope has often been to treat these problems separately. Understanding evidence is problem i; this is the problem of analyzing what it is to have evidence to believe that a scientific theory is true. Understanding explanation is problem z; here we assume that we have already chosen our scientific theories, at least for now. We want to work out how our theories provide explanations. In principle, we can make a distinction of this kind. But there is a close connection between the issues. The solution to problem z may affect how we solve problem i. Theories are often preferred by scientists because they seem to yield good explanations of puzzling phenomena. In chapter 3, explanatory inference was defined as inference from a set of data to a hypothesis about a structure or process that would explain the data. This seems much more common in science than the traditional philosophical idea of inductive inference (inference from particular cases to generalizations). This suggests that there is a close relation between the problem of analyzing explanation and the problem of analyzing evidence.

  There is a very large literature on explanation, but these issues will get a whirlwind treatment in this book. One reason for this is that I think the philosophy of science has approached the problem of explanation in a mistaken way. To some extent, that is true of many topics in this book; there have been plenty of wrong turns in the philosophy of scienc
e. But in the case of explanation, I think the error has been fairly clear; I will describe it in section 13.3. So some of the views presented in this chapter are rather unorthodox.

  13.2 The Rise and Fall of the Covering Law Theory of Explanation

  Empiricist philosophers, I said above, have sometimes been distrustful of the idea that science explains things. Logical positivism is an example. The idea of explanation was sometimes associated by the positivists with the idea of achieving deep metaphysical insight into the world-an idea they would have nothing to do with. But the logical positivists and logical empiricists did make peace with the idea that science explains. They did this by construing "explanation" in a low-key way that fitted into their empiricist picture.

  The result was the covering law theory of explanation. This was the dominant philosophical theory about scientific explanation for a good part of the twentieth century. The view is now dead, but its rise and fall are instructive.

  The covering law theory of explanation was first developed in detail by Carl Hempel and Paul Oppenheim in a paper (1948) that became a centerpiece of logical empiricist philosophy. Let us begin with some terminology. In talking about how explanation works, the explanandum is whatever is being explained. The explanans is the thing that is doing the explaining. If we ask "why X?" then X is the explanandum. If we answer "because Y," then Y is the explanans.

  The basic ideas of the covering law theory are simple. Most fundamentally, to explain something is to show how to derive it in a logical argument. The explanandum will be the conclusion of the argument, and the premises are the explanans. A good explanation must first of all be a good logical argument, but in addition, the premises must contain at least one statement of a law of nature. The law must make a real contribution to the argument; it cannot be something merely tacked on. (Of course, for an explanation to be a good one in the fullest sense, the premises must also be true. But the first task here is to describe what sort of statements would give us a good explanation of a phenomenon, if the statements were true.)

  Some explanations (both in science and in everyday life) are of particular events, while others are directed at general phenomena or regularities. For example, we might try to explain the particular fact that the U.S. stock market crashed in 1929, in terms of economic laws operating against the background conditions of the day. And we can also explain patterns; Newton is often seen as giving an explanation of Kepler's laws of planetary motion in terms of more basic laws of mechanics in combination with assumptions about the layout of the solar system. In both cases, the covering law theory sees these explanations as expressible in terms of arguments from premises to conclusions. Some of the arguments that express explanations will be deductively valid, but this is not required in all cases. The covering law theory was intended to allow that some good explanations could be expressed as nondeductive arguments ("inductive" arguments, in the logical empiricists' broad sense of the term). If we can take a particular phenomenon and embed it within an argument in which the premises include a law and bestow high probability on the conclusion, this yields a good explanation of the phenomenon.

  There were many problems of detail encountered in attempts to formulate the covering law theory precisely (Salmon 1989). The problems were more difficult in the case of nondeductive arguments, and also in the case of explaining patterns rather than particular events. I won't worry about the technicalities here. The basic idea of the covering law theory is simple and clear: to explain something is to show how to derive it in a logical argument of a kind that makes use of a law in the premises. To explain something is to show that it is to be expected, to show that it is not surprising, given our knowledge of the laws of nature.

  For the covering law theory, there is not much difference between explanation and prediction. To predict something, we put together an argument and try to show that it is to be expected, though we don't know for sure yet whether it is going to happen. When we explain something, we know that it has happened already, and we show that it could have been predicted, using an argument containing a law. You might be wondering at this point what a "law of nature" is supposed to be. This was a troubling topic for logical empiricism and has continued to be troubling for everyone else. But a "law of nature" was not supposed to be something very grandiose. It was supposed to be a kind of basic regularity, a basic pattern, in the flow of events. (I return to this question in section 13.4.)

  Though I use the phrase "covering law theory" here, another name for the theory is the "D-N theory," or "D-N model," of explanation. "D-N" stands for "deductive-nomological;' where the word "nomological" is from the Greek word for law, nomos. The term "D-N" can be confusing because, as I said, the argument in a good explanation need not be deductive. So "D-N" really only refers to some covering law explanations, the deductive ones.

  That concludes my sketch of the covering law theory. I now move on to what is wrong with it. This is a case where we have something close to a knockdown argument. Although there are many famous problems with the covering law theory, the most convincing problem is usually called the asymmetry problem. And the most famous illustration of the asymmetry problem is the case of the flagpole and the shadow.

  Suppose we have a flagpole casting a shadow on a sunny day. Someone asks: why is the shadow X meters long? According to the covering law theory, we can give a good explanation of the shadow by deducing the length of the shadow from the height of the flagpole, the position of the sun, the laws of optics, and some basic trigonometry. We can show why that length of shadow was to be expected, given the laws and the circumstances. The argument can even be made deductively valid. So far, so good. The problem is that we can run just as good an argument in another direction. Just as we can deduce the length of the shadow from the height of the pole (plus optics and trigonometry), we can deduce the height of the pole from the length of the shadow (and the same laws). An equally good argument, logically speaking, can be run in both directions; either can give information about the other. But it seems that we cannot run an equally good explanation in both directions, though the covering law theory says we can. It is fine to explain the length of the shadow in terms of the flagpole and the sun, but it is not fine to explain the length of the flagpole in terms of the shadow and the sun. (At least, it is not fine unless this is a very unusual flagpole-perhaps one that is designed to regulate its own length to maintain a particular shadow.)

  What we find here is that explanations have a kind of directionality. Some arguments (though not all) can be reversed and remain good as arguments. But explanations cannot be reversed in this way (except in some special cases). So not all good arguments that contain laws are good explanations. This objection to the covering law theory was famously given (using a slightly different example) by Sylvain Bromberger (1966).

  Once this point is seen, it becomes obvious and devastating. The covering law theory sees explanation as very similar to prediction; the only difference is what you know and what you don't know. But this is a mistake. Consider the concept of a symptom. Symptoms can be used to predict, but they cannot be used to explain. Yet a symptom can often be used in a good logical argument, along with a law, to show that something is to be expected. If you know that only disease D produces symptom S, then you can make inferences from S to D. You might in some cases be able to make predictions from D to S, too. But you cannot explain a disease in terms of a symptom. Explanation only runs one way, from D to S, no matter how many different kinds of inferences can be made in other directions. And, further, it seems that good explanations of S can be given in terms of D even if S is not a very reliable symptom of D, even if S is not always to be expected when someone has D. This is a separate problem for the covering law theory, often discussed using the example of some unreliable but unpleasant symptoms of syphilis.

  In some of these cases, the covering law theory can engage in fancy footwork to evade the problem. But other cases, including the original flagpole case, seem immune to footwork.
Hempel's own attitude to the issue was puzzling. He actually anticipated the problem, but dismissed it (Hempel 1965, 3 52-54). His strategy was to accept that if his theory allowed explanations to run in two directions in cases where it seems that explanation only runs in one direction, then both directions must really be OK. In some actual scientific cases this reply seems reasonable; there are cases in physics where it is hard to tell which direction(s) the explanation(s) are running in. But in other cases the direction seems completely clear. In the case of the flagpole and the shadow, this reply seems hopeless.

  There are other good arguments against the covering law theory (Salmon 1989), but the asymmetry problem is the killer. It also seems to be pointing us toward a better account of explanation.

  13.3 Causation, Unification, and More

  What is it about the flagpole's height that makes it a good explanation for the length of the shadow, and not vice versa? The answer seems straightforward. The shadow is caused by the interaction between sunlight and the flagpole. That is the direction of causation in this case, and that is the direction of explanation also. So we seem to get an immediate suggestion from the flagpole case for how to build a better theory: to explain something is to describe what caused it. Why did the dinosaurs become extinct 65 million years ago? Here again, our request for an explanation seems to amount to a request for information about what caused the extinction.