The Truth Doesn't Explain Much (원문)

• Nancy Cartrwright, The Truth Doesn't Explain Much (번역)

0. Introduction

Scientific theories must tell us both what is true in nature, and how we are to explain it. I shall argue that these are entirely different functions and should be kept distinct. Usually the two are conflated. The second is commonly seen as a by-product of the first. Scientific theories are thought to explain by dint of the descriptions they give of reality. Once the job of describing is done, science can shut down. That is all there is to do. To describe nature -- to tell its laws, the values of its fundamental constants, its mass distributions -- is ipso facto to lay down how we are to explain.

This is a mistake, I shall argue; a mistake that is fostered by the covering-law model of explanation. The covering-law model supposes that all we need to know are the laws of nature -- and a little logic, perhaps a little probability theory -- and then we know which factors can explain which others. For example, in the simplist deductive-nomological version,^[1] the covering-law model says that one factor explains another just in case the occurrence of the second can be deduced fromt the occurence of the first given the laws of nature.

But the D-N model is just an example. In the sense which is relevant to my claims here, most models of explanation offered recently in the philosophy of science are covering-law models. This includes not only Hempel's own inductive statistical model,^[2] but also Patrick Suppes's probabilistic model of causation,^[3] Wesley Salmon's statistical relevance model,^[4] and even Bengt Hanson's contextualistic model.^[5] All these accounts rely on the laws of nature, and just the laws of nature, to pick out which factors we can use in explanation.

A good deal of criticism has been aimed at Hempel's original covering-law models. Much of the criticism objects that this models let in too much. On Hempel's account it seem we can explain Henry's failure to get pregnant by his taking birth control pills, and we can explain the storm by the falling barometer. My objection is quite the opposite. Covering-law models let in too little. With a covering-law model we can explain hardly anything, even the things of which we are most proud -- like the role of DNA in the inheritance of genetic characteristics, or the formation of rainbows when sunlight is refracted through raindrops. We cannot explain these phenomena with a covering-law model, I shall argue, because we do not have laws that cover them. Covering laws are scarce.

Many phenomena which have perfectly good scientific explanations are not covered by any laws. No true laws, that is. They are at best covered by ceteris paribus generalizations -- generalizations that hold only under special conditions, usually ideal conditions. The literal translation is 'other things being eqaual'; but it would be more apt to read 'ceteris paribus' as 'other things being right.'

Sometimes we act as if this does not matter. We have in the back of our minds an 'understudy' picture of ceteris paribus laws: ceteris paribus laws are real laws; they can stand in when the laws we would like to see are not available and they can perform all the same functions, only not quite so well. But this will not do. Ceteris praribus generalizations, read literally without the 'ceteris paribus' modifier, are false. They are not only false, but held by us to be false; and there is no ground in the covering-law picture for false laws to explain anything. On the other hand, with the modifier the ceteris paribus generalizations may be true, but they cover only those few cases where hte conditions are right. For most cases, either we have a law that purports to cover, but cannot explain because it is acknowledged to be false, or we have a law that does not cover. Either way, it is bad for the covering-law picture.

1. CETERIS PARIBUS LAWS

When I first started talking about the scarcity of covering laws, I tried to summarize my view by saying 'There are nio exceptionless-generalizations'. Then a friend asked, 'How about' "All men are mortal"?' She was right. I had been focusing too much on the equations of physics. A more plausible claim would have been that there are no exceptionless quantitative laws in physics. Indeed not only are there no exceptionless laws, but in fact our best candidates are known to fail. This is something like the Popperian thesis that every theory is born refuted. Every theory we have proposed in physics, even at the time when it was most firmly entrenched, was known to be deficent in spectific and detailed ways. I think this is also true for every precise quantitative law within a physics theory.

But this is not the point I had wanted to make. Some laws are treated, at least for the time being, as if they were exceptionless, whereas others are not, even though they remained 'on the books'. Snell's law (about the angle of incidence and the angle of refraction for a ray of light) is a good example of this latter kind. In the optics text I use for refernece (Milne V. Klein, Optics),^[6] it first appears on page 21, and without qualification:

Snell's Law : At an interface between dielectric media, there is (also) a refracted ray in the second medium, lying in the plane of incidence, making an angle θ_t with the normal, and obeying Snell's law:

sin θ / sin θ_t = n₂ / n₁

where ν₁ and ν₂ are the velocities of propagation in the two media, and n₁ = (c/ν₁), n₂ = (c/ν₂) are the indices of refraction.

It is only some 500 pages later, when the law is derived from the 'full electromagnetic of light', that we learn that Snell's law as stated on page 21 is true only for media whose optical properties are isotropic. (In anisotropic media, 'there will generally be two transmitted waves'.) So what is deemed true is not really Snell's law as stated on page 21, but rather a refinement of Snell's Law:

Refined Snell's Law : For any two media which are optically isotropic, at an interface between dielectrics there is a refracted ray in the second medium, lying in the plane of incidence, making an angle θ_t with the normal, such that:

sin θ / sin θ_t = n₂ / n₁

The Snell's law on page 21 in Klein's book is an example of a ceteris paribus law, a law that holds only in special circumstances -- in this case when the media are both isotropic. Klein's statement on page 21 is clearly not to be taken literally. Charitably, we are inclined to put the modifier 'ceteris paribus' in front to hedge it. But what does this ceteris paribus modifier do? With an eye to statistical versions of the covering law model (Hempel's I-S picture, or Salmon's statistical relevance model, or Suppes's probabilistic model of causation) we may suppose that the unrefined Snell's law is not intended to be a universal law, as literally stated, but rather some kind of statistical law. The obvious candidate is a crude statistical law: for the most part, at an interface between dielectric media there is a refracted ray . . . But this will not do. For most media are optically anisotropic, and in an anisotropic medium there are two rays. I think there are no more satisfactory alternatives. If ceteris paribus laws are to be true laws, there are no statistical laws with which they can generally be identified.

2. WHEN LAWS ARE SCARCE

Why do we keep Snell's law on the books when we both know it to be false and have a more accurate refinement available? There are obvious pedagodic reasons. But are there serious scientific ones? I think there are, and these reasons have to do with the task of explaining. Specifying which factors are explanatorily relevant to which others is a job done by science over and above the job of laying out the laws of nature. Once the laws of nature are known, we still have to do decide what kinds of factors can be cited in explanation.

Once thing that ceteris paribus laws do is to express our explanatory commitments. They tell what kinds of explanations are permittes. We know from the refined Snell's law that in any isotropic medium, the angle of refraction can be explained by the angle of incidence, according to the equation sin θ / sin θ_t = n₂ / n₁. To leave the unrefined Snell's law on the books is to signal that the same kind of explanation can be given even for some anisotropic media. The pattern of explanation derived from the ideal situation is employed even where the conditions are less than ideal; and we assume that we can understand what happens in nearly isotropic media by rehearsing how light rays behave in pure isotropic cases.

This assumption is a delicate one. It fits far better with the simulacrum account of explanation that I will urge in Essay 8 than it does with any covering-law model. For the moment I intend only to point out that it is an assumption, and an assumption which (prior to the 'full electromagnetic theory') goes well beyond our knowledge of the facts of nature. We know that in isotropic media, the angle of refraction is due to the angle of incidence under the equation sin θ / sin θ_t = n₂ / n₁. We decide to explain the angles for the two refracted rays in anisotropic media in the same manner. We may have good reasons for the decision; in this case if the media are nearly isotropic, the two rays will be very close together, and close to the angle predicted by Snell's law; or we believe in continuity of physical processes. Bul still this decision is not forced by our knowledge of the laws of nature. Obviously this decision could not be taken if we also had on the books a second refinement of Snell's law, implying that in any anisotropic media the angles are quite different from those given by Snell's law. But laws are scarce, and often we have no law at all about what happens in conditions that are less than ideal.

...

5. CONCLUSION

Most scientific explanations use ceteris paribus laws. These laws, read literally as descriptive statements, are false, not only false but deemed false even in the context of use. This is no surprise: we want laws that unify; but what happens may well be varied and diverse. We are lucky that we can organize phenomena at all. There is no reason to think that the principles that best organize will be true, nor that the principles that are true will organize much.

Notes

1. See C. G. Hempel, 'Scientific Explanation', in C. G. Hempel (ed.), Aspects of Scientific Explanation (New York: Free Press, 1965).
2. See C. G. Hempel, 'Scientific Explanation', ibid.
3. See Patrick Suppes, A Probabilistic Theory of Causality (Amsterdam: Noerth-Holland Publishing Co., 1970).
4. See Wesley Salmon, 'Statistical Explanation', in Wesley Salmon (ed.), Statistical Explanation and Statistical Relevance (Pittsburgh: University of Pittsburgh Press, 1971).
5. See Bengt Hanson, 'Explanations -- Of Waht?' (mimeograph, Stanford University, 1974).
6. Miles V. Klein, Optics (New York: John Wiley and Sons, 1970), p. 21, italics added. θ is the angle of incidence.