American Economic Association

Professor Samuelson on Theory and Realism: ReplyAuthor(s): Paul A. SamuelsonReviewed work(s):Source: The American Economic Review, Vol. 55, No. 5, Part 1 (Dec., 1965), pp. 1164-1172Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1809235 .Accessed: 27/06/2012 00:03

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matica und verwandter Systeme," Mlonatshefte fur Mathematik und Physik, 38, 173-98.

4. D. HILBERT, The Foundations of Geometry. LaSalle 1962. 5. J. N. KEYNES, The Scope and Method of Political Economy. New York

1963. 6. F. MACHLUP, "Professor Samuelson on Theory and Realism," Am. Econ.

Rev., Sept. 1964, 54, 733-36. 7. W. QUINE, Mathematical Logic. Cambridge 1961. 8. G. RYLE, The Concept of Mind. New York 1949. 9. P. SAMUELSON, "Problems of Methodology-Discussion," Am. Econ.

Rev., Proc., May 1963, 53, 235. 10. , "Theory and Realism: A Reply," An. Econ. Rev., Sept. 1964,

54, 736-39.

Professor Samuelson on Theory and Realism: Reply'

When first seduced to discuss methodology, I warned that it is a field in which Gresham's Law holds in the form, "Hot air drives out cold." I should also have predicted that it is an activity where the law of diminishing returns holds in the most virulent form. And yet it is a field where, as Editor Gurley has learned the hard way, every economist feels his ideas are as good as any- one else's. Though many call themselves, few are chosen: the papers of Garb, Lerner, and Massey are but the visible peak of the iceberg of submitted com- ments.

The discussion has progressed, I think, away from the issue of an F-twist that considers unrealism of a theory as a virtue, to controversy over the role and nature of "theory" and over the meaning of "explanation" as against "description." A Gallup poll count of the mail would seem to show that there is a widespread will to disbelieve in my rather hard-boiled insistence upon "theory" as (strategically simplified) description of observable and refutable empirical regularities, and a widespread hankering for a more exalted Mach- lup role of theoretical explanation. To stand one's ground against the ma- jority merely in order to be provocative I regard as contemptible in a scien- tist. But candor requires me to state that the arguments of my critics are sus- piciously diverse and unrelated: since what they have in common is primarily their dissatisfaction with me, they really do not provide a common alternative credo to which I could subscribe even were their arguments tempting.

I.

Alphabetically, Garb comes first. His discussion reminded me that there are worse movements than the zero movements of a deadlock-namely, move- ments backward in understanding and in isolating differences of opinion. Ex- ample: his long third paragraph simply misinterprets what I wrote. My ap- proving of Hertz's assertion that Maxwell's theory is his equations represented

'I am grateful to the Carnegie Corporation for a reflective year, and to F. Skidmore for research aid.

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no backsliding on my part: instead it emphasized the view that a description (equational or otherwise) that works to describe well a wide range of observ- able reality is all the "explanation" we can ever get (or need desire) here on earth. Careful reading of my words will show that I only insisted that the validity of the full consequences of a theory implies the validity of the theory and so of its minimal assumptions. Had Garb added the words "full" and "minimal," the alleged disagreement with Machlup would have disappeared. Example: when Garb says "an explanation does not have to be 'ultimate,"' I think he is resaying what I said, not controverting it. Ass explanation, as used legitimately in science, is a better kind of description and not something that goes ultimately beyond description. Example: the final beautiful quotation from Einstein is an irrelevancy. It has to do with the technical issue of whether in quantum mechanics probability statements can be replaced by causality statements like those of classical mechanics. It has nothing to do with methodological differences as to the role of theory itself. So much for Garb.

II.

Lerner's paper shows that many a false word has been said in jest. He in effect says that Samuelson and Machlup both do good work, acting alike in their practical work during the six days of the week. Therefore on Sunday they can't be in genuine disagreement on methodology. By this reasoning, a thousand philosophers err in thinking that Ernst Mach and Arthur Eddington differ diametrically on the methodology of physics: since both men contrib- uted mightily to the Gross National Product of physical knowledge, why pay attention to the detail that Eddington thought he could deduce from the laws of thought (!) the number of electrons in the universe, while Mach claimed the scientist merely discerns mnemonic devices for describing brute facts. I remind Lerner that the aphorism, "All wise men believe in the same true reli- gion," is an atheist's joke not a pithy truism.

If Lerner had read with sympathetic care my writings, he would have seen at the beginning what it was I denied-namely, that "a theory is much wider than any [in the sense of 'any and all'] of the consequences deduced." Precisely because of the ambiguity of words like "any," I used the unambiguous logical symbols of set theory (p. 234 of my original article [8]); by attentive read- ing of this passage, he could have been spared the labor of "Saving my logic," particularly since I have to reject his charitable rescue. It is nonsense, and not my nonsense, "to include all the conceivable assumed changes and events that can be combined with the postulated relationships as well as. . . ." More- over, Machlup and I are one in objecting to the requirement that a usefully realistic theory must be completely accurate. Who seriously thinks otherwise? Lerner regards it as Sunday nodding on my part to think that anyone could be so stupid as to believe that a theory "is even better for its inadequacy." He does not disagree that such an assertion is stupid. Having been at pains to state the matter so plainly, I am glad to learn the conclusion is now obvious. Lerner's final conclusion represents what the logicians call a nonz sequitur:

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if in the end it turns out there is no real difference between Samuelson and Machlup, this will follow from considerations not discernible in Lerner's note.

III. I turn now to the pih'ce de re'sistance, Massey's valuable paper. I have no

quarrel2 with Massey's Part I, which provides a masterly summary of the semantics of scientific analysis that will be useful to all economists and novel to most. In Part II, the impractical philosopher shames the practical economic scientist and puts his finger on the one critical issue in the present controver- sy-the relationships between observable reality and the various assertions made by the scientific theorist. Part II makes, I think, a definite contribution to the discussion;3 but I must confess that, in reading it, I was overtaken with aspirations of grandeur, and came to wish that I were Massey and could re- write Part II. For as it now stands, it could be misinterpreted by the casual economist reader to exalt "indirectly observable" empirical regularities over "directly observable" empirical regularities. Concretely, the reader might mis- lead himself into believing that the special theory of relativity, which is found- ed on directly observable empirical regularities, is intrinsically less noble or less something than the kinetic theory of gases, which is based upon allegedly nondirectly observable tiny molecules; and indeed that this kinetic theory is better than the classical theory of thermodynamics merely because the first and second laws of classical thermodynamics are so beautifully capable of direct empirical confirmation in every steam engine or housewife's kitchen. So let me restate the issues.

Hempel [3, p. 23] denies the following assertion: "Any term in the vocab- ulary of empirical science is definable by means of observation terms." A reader like Massey might be forgiven for thinking that I differ from Hempel on this point and therein lies my heresy. So let me make the following clear: when I read the grounds on which Hempel denies this doctrine (which he calls the narrower thesis of empiricism [Hempel 3, p. 24]), I find no reason to differ on this point with Hempel or Machlup or anyone else. For what are Hempel's difficulties with such an assertion? They are of the following type. Point (i): Scientists say an object is "magnetic" and mean by this that, if a small iron object is put near it, that object will be attracted by it. But what if

2Almost none. I doubt that "consistency" provides the problem for any science like economics or physics that it provides for the mathematical logician concerned, say, with the consistency of Hilbert's axioms for arithmetic. The status of the special theory of relativity or of consumer demand was the same after G6del as before. To say that we take consistency of a scientific theory for granted because it is so devilishly hard to prove this fact is like saying we assume a woman virtuous unless proved otherwise be- cause it is so hard to prove any woman lacking in virtue. That is surely not so: Bayesian probabilities, that most women are virtuous in our culture and that few scientists have won undying fame for themselves in finding flaws of consistency in important scientific theories, suffice to explain why we take for granted what we do.

'To help my understanding of these issues, Professor Massey kindly provided me with minimal references to related writings that should be of interest to economists, namely the Hempel and Nagel references of my bibliography. I benefited from this course of study, which I believe deepened my understanding of my own position.

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no iron object is found near it? Is it an empirical statement that it is (still) magnetic? Point (ii): Scientists use metrical terms like "the length of this stick can be any real positive number" or "the apple had an instantaneous velocity of so much at noon and an acceleration of this definite magnitude."

Well? Narrow empiricism is supposed not to be able to handle these two difficulties, whereas a "liberalized thesis of empiricism" [Hempel 3, p. 31] can. O.K., then I am a liberal empiricist. The concept of limits-in which one does not have to go to the limit-enables us to go from integral- to real-num- ber systems and from average velocities to instantaneous derivatives; hence, point (ii) offers no room for controversy here. And, while I am prepared to believe that point (i) has presented a problem to the philosopher trying to represent scientific procedures, I find it hard to imagine any two modem physicists or economists ever having a substantive dispute about such a mat- ter.

I elaborated on the above because the reader of Hempel might easily be tempted to think that the demonstrated difference between narrow and liberal empiricism has something basic to do with Hempel's repeated contrast be- tween (a) description and (b) prediction and explanation. I was amused in reading these authors through a magnifying glass to see how Freudianly guilt- ily they (with the exception of Braithwaite) shy away from validly distin- guishing description from explanation. A description of an empirical regular- ity provides the basis of prediction, which will be as accurate or inaccurate as is the regularity being described. Because prediction is good and a case is being made for "explanation" as something beyond "mere" description, pre- diction is again and again coupled with explanation and gratuitously demar- cated from description. In this too-brief discussion I hope to have cast doubt on Hempel's Points (i) and (ii) as a proper basis for this distinction.

When we move on to Nagel and to Massey, we find the alleged basic dis- tinction in the difference between "directly observable" empirical regularities (or descriptions) and "indirectly observable" regularities. In Nagel the tone is rather tentative; in Massey, an imperialistic vocabulary is introduced in which all directly observable empirical regularities are squeezed out of "theo- ry"t completely (being called "basic sentences"); and indirectly observable regularities are alone called "theoretical sentences." That this is a perversion of usage can be demonstrated by the following examples. And if one agrees with the point these examples are designed to make, one suddenly finds Sam- uelson innocent of such grave charges as "rejecting all theory."

Consider four of the most important physical theories of all time, by any physicist's admission. (1) Galileo's analysis of a falling body; (2) Newton's theory of universal gravitation as applied to the n-body problem; (3) Ein- stein's special theory of relativity; and (4) classical thermodynamics of Car- not, Clausius, Kelvin, and pre-1900 Gibbs. Later add a fifth theory, (5) the kinetic theory of gases (and various models of statistical mechanics).

I have checked with several physicists and find they agree with me that the first four of these historic theories are expressible completely in terms of Mas- sey's "basic sentences" alone.

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Example: if St represents the position of a rolling ball on an inclined plane at time t, Galileo's law of gravity can be expressed in the directly observable hypothesis,

(St+h - St) - (St - St-h) 0 O A2St = d2Stjdt2.

Example: if the coordinates of the 2-body problem are depicted by the usual notation, Newton's behavioral equations become

mx- GMmx/r3, my = -GMmy/r, r = (x2 + y2)1/2

and can be verified directly by acceleration measurements, without indirect checking of elliptical orbits and Kepler's Law. Indeed for n > 2, the differential equations are not integrable in terms of elementary functions but the differential equations can be directly tested.

Example: Einstein built the axioms of special relativity on the precise di- rect observations of the Michelson-Morley experiment, extrapolated to every observer of light no matter what his uniform velocity with respect to any other observer. (Incidentally, Professor Royall Brandis of Illinois pointed out to me that the observations of the perihelion of Mercury provided an indirect test of the genieral theory of relativity and not, as I erroneously said, the spe- cial theory.)

Final example. The most high-fallutin' theoretical formulation of classical (nonstatistical) thermodynamics is certainly that of Caratheodory of 1909. If it is not a theory, the word theory is surely being redefined in a way strange to all usage. Yet, in terms of Massey's new definition of "theoretical sen- tences" ["which, though tied semantically to experience, do not enjoy the same direct relation that characterizes the basic sentences" (such as "Fido has 4 legs" or "the velocity of this ball increased proportionally with time since it was relesased")], Caratheodory turns out to be "eschewing all theo- ry." For Caratheodory's symphony begins with the proud words, "One of the more notable results of the investigations made in thermodynamics during the last century is the realization that this science may be developed without any hypotheses which cannot be empirically verified." He goes on to squeeze out even the concept "heat," as superfluous, and builds directly on the empirical observations of Joule and Clausius. (It is true he uses ideal concepts of "insu- lating walls" and the like, but properly refers to "thermos bottles" that ap- proach the realization of such concepts. My own position never rejected ap- proximating concepts.)

Since Hempel, Nagel, Massey, Machlup, and all sensible men argue from empirical observation of what celebrated scientific theories have been like in the past, I consider it fair game to give these examples in order to reject as tragically misleading Massey's key conclusion at the end of his Part II, of which I requote only two sentences.

If, e.g., there is any methodological moral to be drawn froimi the century- and-a-half-long successful life of the atomic theory of matter, it would seem to be that an empirical science conmes to maturity only after it effects a clean break with basic sentences, only after it boldly postulates theoretical statements that ultimately are anchored, though not sub-

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merged, in experience by means of semantic ties to basic sentences. Thus I myself would proclaim the contrary of Samuelson's Razor, viz. all economic theories that can be explained to your wife are theoretically

worthless.

* *

Never, never make a joke. My remarks about Samuelson's Razor, and my experience that only the simple theories that can be explained so as to make sense to an intelligent outsider (one's wife) turn out to hold up in economics, was intended as a humorous obiter dictum as far as the controversy over the role of theory was concerned. My remark referred to theories of stock market prediction like the famous Gridiron Law: "In every year that Harvard beats Yale and there is confirmation by Penn beating Cornell, the Dow Jones aver- ages will rise." Jobbing backwards, we find this fits the facts of 1920-40: but what scientist was surprised when it failed in the postwar? It represents a bad description in terms of width of empirical coverage, in contrast to the fol- lowing: "When Kennedy's fiscal policies send up GNP, that's good for profits and makes me think we ought to invest in common stocks that do not already have a high price-earnings ratio and which stand to share in the general pros- perity." You can call the latter an "explanation" of equity price trends, but that does not deny me the right to formulate it as a description of regular concomitance of fiscal policy variables, GNP changes, profit changes, and equity price changes.

What about case 5 of the kinetic theory of gases, which I agree differs from the first four cases and involves the indirectly observable hypotheses that Kempel, Nagel, and Massey talk about? Here we do need some less imperialistic name than Massey's "theoretical sentences." Let me henceforth refer to them as "indirectly observable" sentences or Sentences2 in contrast with Sentences1 = Basic Sentences. I gladly welcome both kinds of sentences and wish that the philosophers of science had probed more deeply into their nature. Thus, Kepler's 3 laws might legitimately be considered as indirect ways of verifying Newton's inverse square law of acceleration. If we call them Sentences2, we should realize (Cf. Born, [1, p. 2]) that it can be easily demonstrated that the three Kepler Laws together (elliptical orbits in one plane, radius sweeping equal areas in equal time, period of revolution of any planet around the sun proportional to the 3/2 power of its distance from the moon) are necessary and sufficient conditions for the truth of Newton's 2- body acceleration laws, which are Sentences1. So such indirectly observable sentences do differ from the following kinetic-theory ones.

Suppose I tell my wife that the air in that transparent balloon consists of small molecules averaging 600 miles per hour-about the speed of a bullet. Why shouild she believe me? If only macroscopic data about balloon pressures and volumes are observed, she needn't. "But," she says, "I read in a book there are 4.5 X 109 molecules in each c.c. of the air in the balloon." I reply, "Suppose there are. Without a microscope you couldn't possibly detect that fact, and separate it from the fact that there are 4.6 X 109 or 45 X 10g. But

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you can be sure that there are certainly not as few as 4.5 X 10 heavy mole- cules; for if there were, you would see the balloon pulsing not to mention lots of other things." Being a sensible woman, she would reply, "So long as there are no observable consequences to me of there being 4.5 X 109 or 45 X 109 molecules, I am completely indifferent to your assuming or not assum- ing the existence of that many. And how did you get that odd idea?" My reply, "By reading Greek poetry of Democritus and Lucretius. By thinking that endless paddling of water warms it up, which suggests (to me and Count Rumford) hotness must somehow be related to motion rather than being a substance. By finding that postulating a sufficiently large number of hard, small balls gives me (and Maxwell) a model whose directly observable av- erage energy of collisions on the wall of the balloon agrees numerically with the directly observable pressure on the walls of the balloon. By finding that mixing balls twice as heavy with the original balls gives me average energy of collisions on the wall agreeing with the surprising observable fact that mixing together a balloon of light gas with one of heavy gas gives me a pre- dictable pressure of the mixture satisfying the so-called Dalton Law of Par- tial Pressures. It is an agreeable fiction, if you please, that there are 4.5 X 109 molecules or more. And this fiction usefully prepares me for what hap- pens when I crush the balloon. Now the balls get closer together; now I can't neglect their Newtonian attractions; and now the model predicts that halving the balloon's observable volume will less than double the observable pressure. And this agrees with directly observable descriptions, such as the gas in the balloon becoming liquid."

Up to this point, say 1897 when Planck first wrote up his treatise on Ther- modynamics, one could regard the Sentence2, "This gas has a given number of molecules," as merely a convention. Mach, Stallo, and Ostwald too stub- bornly held to such a view-too stubbornly, I think, but not without excuse. Thus, Stallo said, why explain an elastic gas that you can see directly in terms of hypothetical elastic balls you can't see? One answer is, "Why not? To do so is harmless and it does help me remember by Newtonian calcula- tion, if I should happen to forget, how observed gases behave." Mach, who insisted on the mnemonic nature of all scientific statements, should not have objected to this in principle. He should merely have said, "Don't forget that your results at the macroscopic level are quite independent of the number 4.5 X 109. And actually Planck f 7, p. 261 said, "This, of course, need not be a

whole number. . ." But now move into this century. Give my wife a microscope and show her

Brownian motion. Have her look at a radium-dialed watch with an ordinary magnifying glass. Listen to a Geiger counter. Observe a Wilson Cloud chamber. Literally see a single atom with a field emission microscope trained on a tungsten point. Count molecules emitted from a radioactive substance. Observe photoelectric effects as chemical reactions on an exposed film. Now, though I do not insist on the point, she does observe and describe molecules in almost the same literal sense that anyone counts the 4 legs of a dog. Avo- gadro's Number now takes on a more concrete meaning: after Einstein and Perrin calculated it from Brownian movements, Mach and Ostwald properly threw in the towel. If they are to be criticized, it is in being too impatient

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with Boltzmann's (at worst, harmless) calculations in the pre-Einstein era. The philosophers of science should bring their most fashionable example of

indirectly observable theoretical concepts up to date. In terms of modern techniques of measurement, atoms are no longer a-empirical concepts; neither in 1965 are genes and chromosomes in the theory of particulate genetics.

IV. Let me summarize. There has been no successful demolition of my view

that science consists of descriptions of empirical regularities; nor of my in- sistence that what is called an explanation in science can always be regarded as a description at a different level-usually a superior description in that it successfully fits a wide range of empirical regularities. This, in my view, is the proper basis for the Braithwaite-Ramsey distinction [in Braithwaite] between a superior description that can be given the honorific title of "ex- planation" and an ordinary description. My detailed analysis of the molecu- lar theory of gases permits me now to amplify the logical symbolism of my original paper. Let the full assumptions of the molecular kinetic theory be called B. Let its full consequences be C, which can be broken down into its macroscopic consequences C1 (pressure, volume, etc.) and into its microscopic consequences C2 (standard deviation of Brownian movement, etc.). If the observed facts confirm both C1 and C2 (as after 1910, it became known that they do), no one will quarrel with the theory B. Suppose, as before 1900, the known facts confirm only C1? What then? So long as the theory's C2 implications are not known to contradict empirical data, the kinetic theory B is no worse (except perhaps aesthetically) than some rival theory 0, whose full implications are also the confirmed C1. Occam's Razor suggests, "Choose 5 rather than B, other things being equal." But Occam's Razor, as Einstein almost said, like elegance is for tailors. Other things may not be equal, as for example the superior ability of B to be "remembered" by virtue of its "simplicity" or deducibility from theories applicable to other areas of em- pirical reality (e.g. Newton's laws applied to colliding elastic particles).

A harder problem is one where C1 of B is confirmed but C2 of B is refuted by the facts. How big must the discrepancy of C2 from the facts be to make us want to drop B? That always depends on the "importance" attached to discrepancy and agreement. I can imagine cases where scientists would say, "B has C2 implications that are unmistakably refuted by the facts at the microscopic level. But who cares about such discrepancies, which do no harm and are unimportant. Because B predicts the important truth C1, we stick with it as a theory." I cannot quarrel with this if (i) scientists are truly agreed that C2 discrepancies are unimportant and (ii) there is no readily available truncated theory, B-, which can be distilled from B by lopping off its C2 aspects and which can provide pretty much the same mnemonic pat- terning of the facts that B does. My original quarrel with the F-twist was a reminder of the importance of (i) above. This should not be controversial.

Xhere I must be careful not to overstate my case is in connection with the following: After a theory's implications C1 are well confirmed by the facts, and even prior to our testing its C2 implications, we increase our Bayes- probability belief in the likelihood that its C2 implications will be confirmed.

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This heuristic principle seems to be well founded by past experience and re- flects, I suppose, a bonus in the form of an underlying simplicity of Nature which---if it had not existed--- could not be legitimately invented.

PAUL A. SAMUELSON*

*The author is professor of economics at the Massachusetts Institute of Technology.

REFERENCES

1. MAX BORN, Natural Philosophy of Cause and Chanzce. Oxford 1951. 2. R. B. BRAITHWAITE, Scientific Explanation. Cambridge, England 1953. 3. C. G. HEMPEL, Fundamentals of Concept Formation in Empirical Science,

monograph of the International Encyclopedia of Unified Science, Vol. 2, No. 7, Chicago 1952 [Cf. especially pp. 34-39].

4. , "The Theoretician's Dilemma," in H. Feigl, M. Scriven, and G. Maxwell, eds., Minnesota Studies in the Philosophy of Science, Vol. 2, Minneapolis 1958 [Cf. especially Sections II, IV, and VIII].

5. GERALD J. MASSEY, "Professor Samuelson on Theory and Realism: Com- ment," Am. Econ. Rev., Dec. 1965, 55, 1155-64.

6. ERNEST NAGEL, The Structure of Science, New York 1961 [Cf. especially pp. 79-90].

7. MAX PLANCK, Treatise on Thermodynamics. New York 1945. 8. P. A. SAMUELSON, "Discussion of Methodology," Am. Econ. Rev., Proc.,

May 1963, 53, 231-36. 9. , "Theory and Realism: A Reply," Am. Econ. Rev., Sept. 1964,

54, 736-39.

Uncertainty and the Welfare Economics of Medical Care: Comment

In their exegesis of K. J. Arrow's discussion of the welfare economics of medical care [1], Professors Lees and Rice reach the conclusion that ". . . the greater the X, given p, and the smaller the p, given X, the more likely will it be that (V-C) is nonnegative" [2, p. 1461, where X is the amount of a possible loss, p its probability of occurrence, V the value to the individual of complete insurance against the loss, and C the cost (in excess of actuarial cost) of the insurance. This conclusion violates the commonly held view that events with a very low probability of occurrence, as well as those with a very high probability, are not worth insuring against. In fact, this conclusion ap- pears to be more consistent with the analysis of Lees and Rice than the one they arrive at, given the presence of indivisibilities in both sellers' and buyers' costs for placing insurance.

Buyers' costs such as ". . . the transactions cost to the individual of com- pleting and filing application and claims forms, paying premiums, keeping records, etc." [2, p. 1431 as well as many corresponding items of sellers' costs are largely indivisibilities, showing relatively small variation with either the size of a policy or the probability of loss. The Lees-Rice "cost of insur- ance" function in this case would take the form k1 + k2pX or k1 + k2p where the k's are constants. The first form of the function is illustrated in Figure