The Structure of economic theory and the goals of scientific analysis

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The Structure of economic theory and the goals of scientific analysis
Fabian, Robert George, 1938-
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Bibliography: leaves 188-198.
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August, 1966



Copyright by
Robert George Fabian


The writer would like to express his gratitude to the

members of his supervisory committee for the assistance they

have given during the preparation of this dissertation. To

Professors Clement H. Donovan, Frederick H. Hartmann, and

especially to John N. Webb, who supervised the task with much

patience and helpful criticism, my sincerest thanks.

.AzL CF C&:-l.'VS

I. INTRODUCTIO . . . . . . . . 1

Scope of the Dissertation . . . . 1

Chapter Summary . . . . . . . 8

IN ECO;O.: ICS . . . . . . . . 14

The Deductive Pattern of Economic
Analysis . . . . . . . ... 19

The Pri.ciole of Correspondence ..... 22

The Principle of Correspondence and
the Explanatory Scope of Theories . .. 27

Summary . . . . . . . ... 28


An Examination of Strong Empiricism

Machlup on Strong Empiricism . .

Samuelson's Str-n. Eupiricism in
Light of His Foundations . . .

Some Applications . . . . .

Summary . . . . . . .

. . 30

. . 33

. . 36

. . 38

. . 49

. . 51

FRO:. THE LTER.U . . . . . . 53

Keynesian Liquidity-Preference ..... 53

The Classical Theory of
International Trade . . . . ... 57

The Law of Diminishing Returns . . .. 61

Utility Theory . . . . . . . 63

The Theory of the Firm . . . . . 71

Summary . . . . . . . ... .80

OF DEDUCTIVE THEORY . . . . ... 82

Operationalism . . . . . ... .82

Rationalism and Empiricism . . ... 87

The Decline of Rationalism . . ... 91

Significance of the Decline of
Rationalism . . . . . ... 93

Rationalist Goals in Modern
Science: Schr'dinger's Testimony . . 97

Summary . . . . . . . ... 102

A REASSESS: . . . . . . . 105

The Changing R. l of the
Theoretical System . . . . 105

The Intrusion of Ideology . . ... 108

Adam Smith's Economic System ...... 109

J. M. Keynes' Economic Sysem . . . 113

Internal Autonomy of Theoretical
Development . . . . . ... 117

Summary . . . . . . ... 122

ANTHROPOLOGY A.:D : .L.' . . .. 125

Problems of Theory in Physical
Anthropology . . . . . ... .125

Theory in Anthropology and
Economics: Parallels and Contrasts 135

Problems of Theory in Archaeology . . 139

Disputed Questions of Method in
Psychoanalytic Theory . . . . 143

Freudian and Keynesian Systems
Compared . . . . . . ... .151

Summary . . . . . . . ... .153


Early Applications of Deductive
Theory . . . . . . . ... 155

Tne Period of Transition . . . ... 157

Continuity of Analytic Technique
in Economic Theory . . . . .. 160

Traditional Goals ar.d modernn
methodss : Resolving the Problem ... . 165

Deductive Analysis and the
Problem of Ideology . . . . ... 168

The Empirical Basis of Modern
Deductive Method . . . . ... 171

Abuses of Deductive Method:
Real and Imagined . . . . ... 176

Rejoinder to Major Critique
of Modern Deductive Methcd ...... 180

Deductive Analysis in the
Social Sciences . . . . . . 185

BIBLIOGRAPHY . . . . . . ... 188





Scope of the Dissertation

In what follows, an attempt is made to merge the discussion

of methodological issues in economics with a wider framework of

scientific discussion. While the paper ranges quite far beyond

economic theory proper, nevertheless it stays within a restricted

domain: the current status of the deductive pattern of theory in

the social sciences. It belongs to economics for two reasons.

In the first place, the specific focus of the paper is economic

theory. Secondly, it embodies an outlook or set of preconceptions

more likely to be found among certain students of economics than

among any other group. The paper is, then, one student's apologia

for deductive theory in economics, and his reaction to a body of

related scientific endeavor not restricted to economics.

The present paper attempts to explore relevant material in

the philosophy of science, and establish what are hoped to be

enlightening juxtapositions of material drawn from rather diverse

sources. While treatment of the main issues raised is hardly

expected to be definitive, it is hoped that the exploration will

clarify the most significant problems and issues.

Judging from the current literature on the subject, the

most significant issues concerning deductive theory in economics

may be summarized as follows:

1) Economic theorists have failed to completely abandon

their claims to provide deductive proof for norms

or value judgments. (Myrdal)

2) While purporting to offer systematic knowledge of

the observable world, economics has often compromised

its conclusions in deference to ruling ideologies

or privileged classes. (Robinson)

3) Many of the concepts and statements found in economic

theory assert nothing observable about reality.

These empirically vacuous propositions have frequently

been the cause of circular reasoning and ideological

outlooks often characteristic of economic theory.


4) Too much economic analysis has been concerned with

the search for "deeper explanations," the "reality

behind observable occurrences," and other metaphysical

quests which have dissipated much creative talent in

years past. (Samuelson)

5) Much of economic theory confuses judicious abstraction,

central to all theory, with empirical falsity. It

justifies false assumptions on the basis of correct

predictions. (Samuelson contra Friedman)

6) Many economic theorists mistakenly believe that a

"theory" is somehow wider than its "conclusions,"

when in fact they must imply each other mutually in

an empirically valid theory. Both "theory" and

"conclusions" must be fully empirical. (Samuelson

contra Machlup)

These criticisms, almost all of which are found in the most

recent literature, show a common source of dissatisfaction. They

indicate that modern theoretical economists are displeased with

much of economic theory because of its apparent shortcomings as

representative of modern empirical science. This dissatisfaction

registers in two important ways: regarding the methods of theory

construction, and regarding the scope of theoretical investigation.

The two sources of dissatisfaction are closely interrelated. Theo-

retical method is criticized for admitting non-empirical terms and

statements. According to criticism six, only empirical entities

have any rightful place in theory. It is true that adherence to

the imperative of criticism six would eliminate most of the criticisms

related to the scope of theory. An economics that admitted only

terms and statements that have an observational base of

reference would not be sidetracked into metaphysical

speculations, ideological debates, or searches for unverifiable

explanation. A fully empirical economics would perforce be

restricted to the tasks of short run prediction and description.

An important question remains, however. We will spend much time

trying to determine if the "fully empirical economics" is required

to achieve the ends described.

Indeed, a fully empirical economics in the sense described

by the critics in question would be a radically reconstructed

economics. Modern economists have, accordingly, developed new

and satisfactory branches of analysis. But we are concerned in

this paper with the deductive pattern of analysis in economics, a

branch of economics with a long and still influential tradition.

Its structure does not measure up completely to the strict canons

of modern empiricists. Some economists continue to employ certain

concepts that are not fully quantifiable, if they can be quantified

at all. As a result, the closely interrelated problem of scope is

still present, since criticisms one through four result in part

from the presence of non-empirical theoretical segments. We will

discuss examples of modern analysis in the deductive tradition,

which has important intellectual and social consequences quite

apart from its empirically verifiable content. (Refer again to

criticism six.)


Many economic theorists seem vulnerable to some of cur

enumerated criticisms, even though they are among the most

highly respected professionals in the field. Some of them

even violate their own criticisms, if Machlup's rebuttal of

Samuelson is valid. Economics is what economists do, as one

economist has pointed out. He was stating aphoristically a

partial truth of scientific method applicable in many disci-

plines: that valid methods of theorizing are learned by

observing the performance of the best workers. So perhaps it

would be best to shun methodological disputes and simply go

about our business. And yet the existence of a gradually

growing body of professional literature about these matters

gives one pause. Every identifiable scientific problem should

receive rigorous scrutiny, and problems of methodology are no

exception. Careful attention to formal problems of method will

insure that serious work will not be'impeded by hastily applied

principles of scientific method, erroneously believed to discredit

the work of the past.

The question of what remains of value in the legacy of

traditional deductive theory is regarded here as an important one.

It will be examined primarily from two points of view. We will

first take up the criticisms which refer primarily to the method

of deductive theorizing. In so doing, we will try to evaluate

critically the important methodological statements of recent years.

During this stage of our investigation, we will draw rather

heavily on writers outside the social sciences. The physical

sciences have the best record of empirical discovery, so an

examination of their methods seems appropriate. Interestingly

enough, many of their problems are similar to those of economics.

For example, (the most important example of the paper), there

has been considerable controversy in the hard sciences over the

role of non-empirical terms and statement-forms in theory.

Spurious goals, non-empirical in nature, have been identified by

some critics; hyper-factualism and lack of proper cultural

perspective have been identified by others. And, bearing out

our contention about the importance of methodology, these

differences have had some important effects on actual scientific


Our second point of view will focus on the historical

antecedents of the issues and criticisms we have identified.

How and why did non-empirical terms and statement-forms enter

economic theory in the first place? Are they present in the hard

sciences? The answers to these questions are closely associated

with the intellectual milieu of the pertinent period. We identify

this early period of science as the era preceding the burgeoning

of empirical techniques of analysis, and the breakdown of what we

will identify as the rationalist era of scientific thought. The

rationalist era is identified in this paper with scientific

goals of a somewhat more ambitious nature (from a philosophic

point of view), and also of a less quantifiable nature. We

have cited these goals in criticism four. The capacity of

scientific theory to pursue these goals, we find, stemmed from

the extra-empirical dimension of theory cited in criticism

three. Method and scope, it must be remembered, are closely


While it might seem mcre natural to some people to pursue

the problem by presenting the historical problem first, it is

the judgment of the writer that the current controversies should

be brought out in the open first--and most of the current litera-

ture deals specifically with method. Also, the question of scope

of theory is more complicated, since it turns on the narrower

problem of method. Specifically, the wider goals of economic

theory are pretty much ruled out under the stringent empirical

canons formulated under criticism six. If, on the other hand, we

opt for a less rigid empirical methodology, then the problem of

scope reappears. We do in fact defend a less stringent empirical

position, and we hold that some of the broader social and cultural

dimensions of theory are valid concerns for the current deductive

analyst. Nevertheless, our criteria for valid theorizing at this

level are strongly influenced by the newer empirical requirements

imposed on theory. We will discuss at considerable length why we

Lalieve that certain traditional goals of economic theory

are still justified within the bounds established by

modern empirical methods.

Chapter Summary

Chapter two states a basic methodological problem of

economic t..!_ry, shared with other theoretical disciplines:

the degree of success writers of deductive economics have

enjoyed in their effcr- to produce work which fully measures

up to the requirements of empirical science. What does it mean

to be an empirical science? Can we not appeal to the "scientific

method" for an authoritative criterion? It is contended in this

chapter that there is no unambiguous standard against which all

scientific theorizing can be evaluated. Popper is quoted to the

effect that propositions not falsifiable by empirical evidence

must be excluded as scientific propositions. Yet we find Nagel

saying that in the deductive pattern of explanation there are

found extra-empirical statements which are an essential feature

of the theory. Nagel's views on deductive theorizing, one of

the most important aspects of the present paper, are summarized

in this chapter. We shall maintain throughout the paper, against

considerable objections, that extra-empirical terms and statement

forms have a valid and vital role to play in modern deductive


In this chapter the presence of such concepts in economics

is pointed out, and the valid criticisms against their improper

use is acknowledged. But it is also shown how their presence

finds justification in the methodology of deductive theory.

Having indicated our methodological position and its

significance, we turn in chapter three to the closely related

question of the application of that methodology to economic

theory. In the preceding chapter we found general methodological

support for extra-empirical segments in theory, but the abuses

noted there made us pause concerning their rightful place in

economics. These abuses were also noted by P. A. Samuelson,

whose ideas on empirical content in theory we take up in this


The Samuelson-Machlup controversy has been the focal point

of the most recent examination of the literature of economics

concerning its status as an empirical science. Samuelson argues

what we shall call the "strong empirical position," reminiscent

of Popper: every term or statement form in theory has empirical

significance. The "conclusions" of a theory are empirical, or

else insignificant and should be eliminated. The "assumptions"

and "conclusions" of a theory imply each other mutually, so that

the "theory" and its "conclusions," to the extent that they have

scientific status, are empirical.

Machlup argues that a theory is wider than its conclusions,

and that there are extra-empirical segments in theory. Reminis-

cent of Nagel's position tr.: tz.e complicated logical structure

of a deductive theory gives it grea-er explanatory scope than a

purely empirical theory, Machlup defends the presence of extra-empir-

ical concepts.

In this chapter we take the position that Machlup is more

nearly correct, and try to show that Samuelson's line of reasoning

is unduly restrictive.

Chapter four presents a detailed discussion of valid uses of

extra-empirical theoretical segments in economics. It is argued

that deductive economics has a strong and valid commitment to

their use, and that the use conforms to sound methodological

principles as expounded by Nagel and corroborated by Machlup. The

examples and discussion of this chapter show that criticisms of

economics as metaphysics and ideology do not derive their validity

from the use of extra-empirical theoretical constructs as such,

but only from their invalid application. Hence it follows that

correct handling of deductive economics is required, rather than

dismantling it via elimination of purely theoretical concepts.

Chapter five reflects the belief that it is important to

understand the scientific experience that underlies the methodological

differences that have been discussed up to this point. In this

chapter it is advanced that the controversies discussed in earlier


chapters result from a carry-over of methods and goals

prevalent in scientific thinking prior to the empiricist

revolution in science occurring in the second half of the

nineteenth century. The chapter describes the changes in

thinking, and in the requirements of empirically-valid

scientific analysis, which resulted from the empiricist

revolution. It also describes, taking the thought of Erwin

Schrcdinger as a contributicn of critical importance, the

reasons for believing that traditional methods and goals have

greater current vitality than is normally attributed to them.

This chapter is focused on the general background of

present-day scientific analysis. Prior to the empiricist

revolution, physical science was served by Newtonian mechanics

as a paradigm of method. As for the goals of science, these we

have described as the goals of rationalism--a coherent theoretical

explanation which reflects the grand unity and underlying rational

plan behind nature. The comprehensive simplicity of Newtonian

mechanics served also as paradigm of goal; every area of science

sought reduction to mechanical explanation. Thus were goals and

method closely interrelated in th- scientific era preceding the

empirical revolution.

In chapter six it is contended that thp historical experience

of relevance to deductive economics is very similar to general

scientific experience related in the previous chapter. In economics,

as in physical scie:.ce, thoughtful people sought to understand

the simple rational laws that guided society--laws that were

obscured by the welter of confusion and complexity that pervaded

the surface of things. Understanding the essence of things was

the rationalist goal in economics, and it was Adam Smith who

succeeded in filling the need. Holding together the rich

tapestry of his great work is a theoretical strand rivaling the

comprehensive simplicity of the Newtonian model. Like Newton,

Smith achieved his goal by means of a relatively simple axiomatic

system possessing deductive powers of great scope.

The chapter is an effort to justify Smith's rationalist

theoretical goals by showing how application of Schr6dinger's

principles, met in the previous chapter, makes possible and

desirable their carry-over into the modern, empiricism world in

which economists now work. Later on in the chapter the same line

of reasoning is applied to modern economists, principally J. M.

Keynes. The concluding portion of the chapter is devoted to a

significant article by George Stigler. In his article, Stigler

shows how the deductive tradition in economic theory has strong

continuity with a "main stream" of economists beginning with

Smith and the Physiocrats. Over time, according to Stigler, the

concepts of succeeding generations of economists have been

transformed and assimilated into the main body of economic thought.

Stigler's emphasis on the impoance of historical continuity

in economic theory substcantites our methodological judgment

about the validity of traditional concepts appropriately handled.

In chapter seven an attempt is made to extend the application

of the methodological principles developed and applied in earlier

chapters beyond economics into the fields of anthropology and

psychology. Comparisons are made with the work of economists,

demonstrating that their experience, as well as that of physical

scientists, has a contribution to make to an understanding of

the nature of scientific theorizing. The examples chosen are

offered as clarification and substantiation of the principles

defended in the present paper. The material is presented at

this point because it applies and illustrates both the methodolog-

ical principles developed in the first portion of the paper and

also the lessons drawn from the historical experience of science

related in succeeding chapters.

Chapter eight capsulizes the entire paper, drawing together

the most significant reflections and conclusions found there.




It has been observed that in the physical sciences the

realm of concepts and the realm of facts and objects are widely

separated. As physical theory becomes more powerful and advanced,

the gap grows wider and wider. Scientific theories embody both

empirical and purely theoretical statements at the same time.

Theories depend for their validity and usefulness on the coordinated

functioning of both types of propositions. Since the theoretical

terms and statements perform solely a logical function, it cannot

be asserted that their lack of content renders them empirically

false. While this contention is often rejected, at least implicitly

by many modern critics of economic theory, it will be contended in

what follows that the distinction is valid and important to economic

theory, both from the standpoint of its method and its goals.

At the popular level the important distinction is between

theory and fact. Curiously enough, theory is always made the

handmaiden of fact in such discussions. One will always be

challenged as to whether he is stating facts or merely giving his


theory. Theory is merely opinicn or guesswork unless it is

constructed piece by piece out of facts.

At a more sophisticated level we are shown that theories

in economics involve extra-factual material in an essential way.

Economic theories contain term~ which upon close examination

can be shown to lack any connection with factual or empirical

reality. Joan Rcbinson cites Popper's position to the effect

that statements incapable of being falsified by evidence are not

scientific propositions. Such statements purport to say something

about real life, yet we cannot say in what respect the world would

be different if they were r.ot true. "The world would be just the

same except we would be making different noises about it." What

is the logical status of such a position? ". .it will roll out

of every argument on its own circularity; it claims to be true by

definition of its own terms."2

These non-empirical concepts are asserted to have "no

scientific content," yet are held to "express a point of view"

which give direction to scientific investigation.3 Since these

concepts lack content in and of themselves, but rather give

direction to investigation, they are assessed according to the

implications they lead to, for example in social policy.4

Joan Robinson, Economic Philosophy (Chicago: Aldine
Publishing Company, 1962), p. 3.

2Ibid. 3-bid., p. 51. Ibid., pp. 72, 75.

Lacking content, their meanings can be altered to adjust for

unpleasant implications. The outcome is that "economics . has

always been partly a vehicle for the ruling ideology of each period

as well as partly a method of scientific investigation."6

But do the abstract concepts of economics ever relate to

the realm of empirical fact, as in the physical sciences? Only

quite indircc. according to Robinson and like-minded critics.

The reason is that in the tradition of deductive theorists or

system-builders in economics, abstract concepts are related to

norms, not empirical fact.

Even when the claim is not explicitly expressed,
the conclusions unmistakenly imply the notion
that economic analysis is capable of yielding
laws in the sense of NORMS, and not merely laws

Could not the establishment of norms be buttressed by maintaining a

sound factual basis for the norms? Unfortunately, facts and concepts

cannot stand in this relationship when norms rather than description

of regularities are to be established. The reason is "the logical

impossibility of deriving positive political conclusions from mere

premises of facts." Value premises devoid of content can be

regarded as irrefutable, hence, objective. Consequently, "For the

5Ibid., p. 55. 6Ibid., p. 1.

Gunnar Myrdal, The Political Element in the Davelopment
of Economic Theory trans. Paul Streeten (Cambridge: Harvard
University Press, 1961), p. 4. Italics in original.

sake of scientific 'objectivity' the fundamental normative

principles must be formulated in such a way that they have no

[empirical] content; whereas they can be given content only

by the underhand insertion of taut premises, that is to say,

of concrete valuations derived from other sources."

In summary, metaphysical concepts, i.e., those without

empirical content, function either to suggest significant

empirical questions or provide the logical basis for "objectively"

established norms. I their purpose is to suggest empirical

hypotheses, they can in principle remain outside the theory.

Metaphysical concepts become an integral part of theory when they

purport to establish norms objectively. Myrdal traces the latter

function of non-empirical concepts to

the normative-teleological way of thinking,
traditional in the social sciences, and,
indeed, programmatic in the philosophy of
natural law upon which they were founded .
The norm . acquires an air of being
founded upon the 'nature of things.' This
precisely is the circular reasoning inherent
in the philosophy of natural law.9

While it is true that economists have long held that theory
should remain value-free, they have generally been unsuccessful

in eliminating values from their work.

8Ibid., p. 18. 9Ibid., p. 20. 10Ibid., p. 2.

Myrd. and Robi.,son both agrZee thac; explicit value

judgments are nacc;ary if practical hypotheses are to be

formulated and scientifically tested. They only insist that

it be explicitly recognized thac values cannot be objectively

ascertained, and that policy suggestions based on them are

contingent. They are also agreed that while economics has been

plagued by the unscientific use of metaphysical propositions,

nevertheless many byproducts have emerged which have been

scientifically useful.1

Up to this point the discussion would not lead one to

believe that economic theory has been very successful in bridging

the gap between the realm of concepts and the realm of facts. So

many of the key concepts of economic theory--value, utility,

income--can be shown to be partially or completely empty of

empirical content upon close examination. And yet these concepts

have survived in an era when economic theorists are more interested

than ever before in doing valid empirical work. Are these economists

"Talking at cross-purposes;" have they failed "to clear the decaying

remnants of obsolete metaphysics out of the way before [going]

forward."?12 The thesis to be advanced and argued here is that

these non-empirical concepts, which hold their place in modern

economics, do have a role to play even in modern, empirically-oriented

l Ibid., p. 32.

12Robinson, pp. 46 7.
Robinson, pp. 146, 147.

theory. Their part is not simply a heuristic one, but also

an organic part of the theoretical structure.

The Deductive Pattern of Economic Analysis

The extent to which nor.-empirical concepts have a valid

analytic purpose depends in large measure upon what approach

zo economic theory is under consideration. Fels distingusihes

four principal approaches to economic theory: inductive,
deductive, econometric, and historical.1 Throughout the

present paper, we will be speaking about the deductive theoretical

method, described by Fels as "'he building of models, whether

literary or mathematical, by making simplifying assumptions and

deducing their logical conclusions. 15 The elements of Fels'

definition apply equally well to the larger theoretical systems.

The deductive approach is useful today to the extent that it

contributes to the description or explanation of historical or

empirical events. The valid use of the deductive method must be

distinguished from theory which had as its purpose the objective

derivation of norms. The difficulty with the modern use of the

deductive approach in economics, and the source of so much

1Rendigs Fels, American Business Cycles: 1865-1897
(Chapel Hill: University of North Carolina Press, 1959), p. 4.


1Fels' categories are not mutually exclusive. "Deductive"
economics certainly does not exclude inductive reasoning. The
category merely serves to emphasize that the theoretical end-product
has a form from which hypotheses can be deduced logically and tested

controversy, is zne survival of nc..-e'firical ("metaphysical")

terms in their structure. Must the deductive approach to

economic analysis b; abandoned al-ogerher, on the grounds that

nothing valuable and substantial can bo deduced about social

-ife from a few oversimplified ascu.pticns? Or, can it be

salvaged by eliminating from models lr.r.ts which cannot or

do not correspond to the hard data of real life? Writers such

as George Soule16 tend toward the former position, while writers

such as Samuelson (as we shall see) seem to favor the latter

solution. A third possibility warrants more consideration than

it has received in the literature of social science. It is that

non-empirical elements survive in deductive theory for sound

methodological reasons.

A word more about the present status of deductive theory in

modern economic analysis is in order. Arthur Burns says:

The ground covered [by the N. B. E. R.,
representing the inductive approach] has
been smaller, but the findings have been
supported by evidence . the habit of
insisting upon evidence is spreading, and
today evidence less often means deduction
from untested premises. Economic models
continue to receive hopeful attention;
but mere logical consistency or aesthetic
appeal now count for less, and performance
under tests for more, than a generation ago.

1George Soule, Ideas of the Great Economists (New York: New
American Library, 1952).

7Fels, pp. 12-13.

The limitations of deductive theory are especially acute in

a number of different applications. In discussing the limitations

of the traditional theory of the firm, George Katona says that

"an analytical framework that considers a few factors only, and

always the same few factors, can hardly be sufficient.18 Katona

argues that the theory is essentially inadequate to account for

actual decisions made inside the business firm. Cyert and March

stress the unrecognized organizational complexities as well as

the oversimplified assumptions about decision-making cited by
Katona. It is well known that examples such as these could be

multiplied. Business cycle analysis is another area in which the

theoretical model is probably not the best analytic device.

Duesenberry points out that business cycles are greatly influenced

by the institutions and structure of the economy, and since they

have been changing rapidly, each cycle is to a considerable degree

unique.20 Fels21 also argues that the deductive approach is

probably better suited to problems not so strongly influenced by

the pressure of external events.

18George Katona, Psychological Analysis of Economic Behavior
(New York: McGraw-Hill Book Company, Inc., 1951), p. 237.

1Richard M. Cyert and James G. March, A Behavioral Theory of
the Firm (Englewood Cliffs, N. J.: Prentice-Hall, 1963), p. 11.

20James A. Duesenberry, Business Cycles and Economic Growth
(New York: McGraw-Hill Book Company, Inc., 1958), p. 6.

2Fels, pp. 14-15.

These remarks are inc.ceda to identify certain areas

where deductive models are l~, lketly to achieve success in

explaining empirical eve..ts. We :.11l give closer consideration

to these examples :when we discuss the empirical principles of

deductive theory. Fels summarizes the current use of deductive

analysis in the; :way.

The clarification of logical relations contributes
to immediate u&ndst:anding, assists in framing
limited hypotheses for testing, provides
stepping-stones for building better theories,
and . gives historians hints at what to
look for. A model must be the starting point
for econometric structures; if there is justi-
fication for proceeding with econometric work,
there is ipso facto justification for model

The Principle of Correspondence

The deductive theorist in any branch of knowledge faces the

problem of linking empirical fact with his theoretical structure.

Following Nagel23 we shall call this the problem of correspondence.

In applying the principles of Nagel's analysis, we shall accept the

judgment of Myrdal and Robinson about unwarranted ideological

intrusions into economic analysis. We shall, however, take a

different position concerning the empirical status of deductive theory

embodying the concepts they attack. Specifically, we shall argue that

there are sound methodological reasons for the presence of non-empirical

terms and concepts in empirically-oriented deductive theory.

22Ibid., p. 15.

23Ernest Nagel, The Structure of Science: Problems in the
Logic of Scientific Explanation (Hew York: Harcourt, Erace and
World, Inc., 1961).

Even the most casual glance at the output of economic

theorists is enough to convince anyone that there are at least

two categories of stat-.,e.-;s to be found: the factual and the

purely logical. In .his laz-tr category are contained statements

which are obviously not *intended to assert anything about the

real world, even though words are used which have factual content
in other con-exts. :Machl- rci-nds Samuelson of this2 by listing

Samuelson's basic ropositions or "assumptions" in an inter-

national trade node_: "1. There are but two countries, America

and Europe. 2. They produce but two commodities, food and

clothing. . These statements cannot be called metaphysical,

nor can they be called counterfactual; they are purely logical

and have nothing to do with the things they name.

In his chapter, "Experimental Laws and Theories,"25 Nagel

gives careful consideration to the logical aspect and the factual

aspect of deductive theory, and the relationship between the two.

Observation is both the ultimate point of departure and the final

test of scientific thought. Nevertheless, it is possible to

distinguish between experimental laws, which "invariably possess

a determinate empirical content," and theoretical laws, which do

not relate to anything that has been or can be observed.26

24Fritz Machlup, "Professor Samuelson on Theory and Realism,"
The American Economic Review, Vol. LIV, No. 5 (September, 1964),
pp. 733-736.

25Nagel, Chapter 5. 26Ibid., pp. 79-80, 83.

Theoretical laws can be tesztd because there are rules of

correspondence which stat e he empirical meaning of certain

of their key terms. Conszclcar.y, the empirical content of

the theoretical law can be tested. 3ut the theoretical law

itself, in the absence of rules of correspondence, cannot be

tested directly, because by i-self, a theoretical law has no

empirical content. The meaning of theoretical laws is

determined solely by the logical function they fulfill within

the context of the theory. Their meanings are not determined

independently by empirical fact; they change as the logical

structure of the theory changes. Knowledge about experimental

terms, on the other hand, does not depend upon the law in which

they are found, but has an empirical existence independent of

the law. While their appearance in a law increases their

operational significance, nevertheless such empirical terms

survive even if the law itself must be refined or rejected.27

Some examples might add clarification.

The term "atom" has acquired new meanings, from the

theories of Democritus to Dalton to the present day. In any

theory, the meaning of "atom" derives from its place in the

theory, which is designed to provide testable hypotheses.

Verified hypotheses give credence to the theory, but the

experimental properties do not reflect in every way the

2Ibid., pp. 84-85.

theoretical properties. Similarly, the term "unconscious'"

did not begin to take cn distinct reference to mental qualities

until rather late in Freud:s writings, by which time some

empirical corroboration was available. Even then, some of

his followers (e.g. Adlor) wor:- unconvinced, and denied the

(empirical) existence of the unconscious. In economic theory,

the term "utility" has for a long time been important to the

theory of consumer demand, yet its empirical interpretation

has changed a number of times.

The deductive theory derives its empirical meaning by way

of the experimental laws which are its logical consequences.

The experimental law is said to be "explained" by the theory when

it, along with any number of other experimental laws, is a logical

consequence of the theory. The "explanatory power" of the theory

is greater the more of such experimental laws it encompasses or

brings to light. Since the terms of a theory (or the model in

which it is expressed) are only implicitly defined by the structure

of the theory, the theorist must designate, at least implicitly,

the empirical counterpart of the terms in the theory. Many

theoretical terms in physical theory have functioned for a long time

before empirical correspondence was established. It is not to be

expected of a successful theory that all its theoretical terms will

attain such correspondence.28 For a variety of reasons this should

28 id., p. 98.
Ibid., p. 98.

not be disturbing. For o.e thing, because of tne relatively

great complexi'ry cf theories, theoretical terms are often
linked wi-h more than one experimental concept. By

judicicurly associating certain terms with experimental concepts,

leaving others defined only implicitly, the theory can be made

to account for a large and diversified number of experimental

laws. Tieing each theoretical term down to a single experimental

concept would greatly limit the range of applicability of the

theory and probably dis-ort an understanding of its content and

implications. Nagel illustrates the importance of flexible use

of rules of correspondence as a means of greatly increasing the

scope of a theory.

We have already noted the success of Newtonian
theory in explaining the laws of planetary
motion, of freely falling bodies, of tidal
action, of the shapes of rotating masses . .
laws dealing with the buoyancy of liquids and
gases, with the thermal properties of gases,
and much else.30

Empirical data are associated with, not identified with,

theoretical terms. As a rule it is not possible to make them

equivalent and interchangeable. It cannot be said that the

theory uniquely implies the experimental data with which it is

associated, nor that its explanatory power is by any means

exhausted by the association.3

29Ibid., p. 99. 30Ibid., 89.

31Ibid., pp. 97-98.

The Principle of Correspondence and the
Explanatory Scope of Theories

"Unverifiable mental constructs . are almost

indispensable for an understanding of the observed relations

between perceivable characteristics, yet, they themselves

cannot be made accessible to the senses . .32Schrdinger's

comment is consistent with Einstein's belief in "perfect laws

in the world of things existing as real objects, which I try to

grasp in a wildly speculative way."33 To demand a precise

empirical basis for every statement appearing in theory is to

fall prey to what Rapaport calls "hyperfactualism," a position

long dead in the physical sciences.3

A theory is a more complicated statement than a simple

experimental law. This is one of the features which gives the

theory greater explanatory power; a theory typically possesses

many more potential applications to different classes of

observational phenomena. Nagel makes the point very well. He

says ". . theoretical notions are not tied down to definite

32Erwin SchrSdinger, "On the Peculiarity of the Scientific
World View," What is Life? and Other Scientific Essays (Garden
City, N. Y.: Doubleday and Company, Inc., 1956), pp. 193, 194.

3Albert Einstein, letter to Max Born, quoted in "Einstein's
Statistical Theories," Albert Einstein: Philosopher-Scientist,
Vol. 1, ed. Paul Arthur Schilpp (New York: Harper and Row,
Publishers, 1959), p. 176.

34Anatol Rapaport, "Various Meanings of 'Theory'," Politics
and Social Life, ed. Nelson W. Polsby, Robert A. Dentler, Paul A.
Smith (Boston: Houghton Mifflin Company, 1963), p. 81.

observational materials by way of a fixed set of

procedures, and .. because of the complex symbolic structure

of theories more degrees of freecom are available in extending a
theory to many diverse areas.

Nagel gives the fcllw:ing analytical summary of the

components of deductive -hc:- j, which we have been discussing.

Such a theory involves:

(1) an abstract calculus that is the logical
skeleton cf the explanatory system, and that
"implicitly defines" the basic notions of the

(2) a set of rules that in effect assign an
empirical content to the abstract calculus by
relating it to the concrete materials of
observation and experiment; and

(3) an interpretation or model for the abstract
calculus, which supplies some flesh for the
skeletal structure in terms of more or less
familiar conceptual or visualizable materials.


In this chapter we have defined our task to be an examination

of the methods and scope of deductive analysis in economics. The

major problem with deductive theorizing to be identified in recent

years is the presence of empirically-empty terms and statement-forms.

The presence of non-empirical concepts has been blamed for the

intrusion of ideological and metaphysical conclusions into economics.

35Nagel, p. 89. 36Ibid., p. 90.

It has been pointed out in this chapter that the critic-sms

of theory are justified, but that they do not necessarily

follow from the presence of the concepts against

objections are raised. Cn the contrary, there are sound

reasons for the presence of non-empirical concepts in

deductive theory, as Nagel explains. From a very formal

point of view, a deductive theory has no empirical content,

except that designated by appropriate rules of correspondence.

Because these rules may be altered for different applications

of theory, and because not all theoretical terms require rules

of correspondence, deductive theories have great explanatory

scope. Indeed, they have greater explanatory scope than theories

whose terms are tied to empirical entities on a one-to-one basis.

As Machlup might put it, the "theory itself" is wider in scope

than any particular set of its 'conclusions."

We turn in the next chapter to an examination of Paul A.

Samuelson's exposition of the "strong empirical position": that

every scientifically-valid term and statement-form must possess

empirical significance.




In a recent widely-discussed article, Paul A. Samuelson

defines his central task to be a refutation of the following

statement distilled from Friedm-n, which he calls the "F-Twist":

A theory is vindicable if (scme of) its
consequences are empirically valid to a
useful degree of approximation; the
(empirical) unrealism of the theory
"itself," or of its "assumptions," is
quite irrelevant to its validity and

The criterion "empirical unrealism" applies to every

proposition in a theory, for, according to Samuelson, every such

proposition has factual import. This inference is derived from

the following parts of Samuelson's argument. An axiom system

taken as a whole, or theory ("B") is identical with its complete

set of consequences ("C"). B is identical to the minimal set

of assumptions ("A") which give rise to it. Identifying C- as a

subset of C, and A+ as a wider set of assumptions, we have

A+3 A=B3CD C-. That Samuelson canonizes only that part of C

which has empirical validity establishes the fact that every

1Paul A. Samuelson, "Problems of Methodology-Discussion,"
Papers and Proceedings of the American Economic Association, Vol. LIII,
No. 2 (:-ay, 1963), pp. 231-236.

2Ibid., p. 232. 3Ibid., p. 234.

theoretical proposition has or musr hav; a factual basis, in

his view. Any At known not to possess empirical validity r.:ust

be rejected; any A+ not known to possess erpirical validity

may be forgotten about, at leasz for the time being.

The crucial implication is clear: there exist no

theoretical propositions defined only by the logic of the

analytic framework; each statement is capable of direct

evaluation by appeal to empirical fact.4 5 Since postulates

are both logically and empiically identical with conclusions,

a theory cannot in any sense be said to be "wider" in scope than

the theory.6 7 It is important to note that Samuelson's formal

conception of scientific theory is fundamentally different from

Nagel's, the position we defend in the present paper, in one

fundamental point. Nagel conceives a deductive theory to be

completely empty of empirical content until rules of correspon. nce

are established, associating certain segments of the theory with

observable entities. The theory, together with its rules of

correspondence, is then capable of generating testable hypotheses.

4bidd., p. 235.

5 -
Herbert A. Simon makes the same point when he says "If .. F
is a valid theory, it must be because it follows from empirically
valid assumptions. . Ibid., p. 230.

Machlup, The American Economic Review, Vol. LIV, No. 5, p. 733.

7Above, p.
Above, p.

Sam-also.'.. formal conaepic. o- a thaZry entails a statement

completely empirical from thCe i -arr. Term; or statement-forms

in the theory lacking empirical content are superfluous. Let

us call Samuelson's principle the "j-cong empirical position" in

contrast to the weakk empirical position" adopted from Nagel in

the previous chapter. We may now go on to support our choice of


No attempt is made in this chapter to find fault with the

logic of Samuelson 's stcrng cpirical position. Samuelson's

position is believed, howavor, to be inconsistent with the

methodology adopted in the previous chapter, following Nagel.

Having made a case for cur "weak empirical methodology," it is

desirable to show in some detail how and why it differs from

what is judged to be its most important rival. Accordingly, we

shall introduce into Samuelson's argument the distinction between

theory as a purely logical construct and theory as an empirical

tool. Samuelson's logic, unassailable on his own grounds, breaks

down when the distinguishing element between the two methodologies

is inserted into his position. We conclude that the differences

between the two methodologies are significant ones. Samuelson is

justified in pointing out the logical equivalence among elements

within the theory. So long as the theory is still at the pre-scien-

tific level of a set of mutually related propositions involving

terms that are only implicitly defined, the logical equivalence

holds: B3C. But what about thea ocher half of the argumenrt--he

empirical half? Does B5'bC hold? (where denotes empirica- or

non-logical). The proof that the lattr identity hclds '-s nds

on the assumption aha L=B3" and C=C*. These are certai.-.y no

identicall-' equal, nor are they necessarily equal by any commonly

accepted standard of theoretical analysis. Nothing Samuelson zays

demonstrates anything illogical abcut assumed inequalities. Y.t

these qualities must be s.o:;n to bs necessarily true if i-c is to

be established that Samuelson has proved his argument.

Let us assume then that B3- 5':, in accordance with the large

volume of theory and mc-:hcodlogy which suggests it. In general,

ED B*, Ba being associated in some way with elements of B- (in

Samuelson's notation) by means of correspondence rules. CDC'",

where in a scientifically active theory, the range of C* is unknown.

An Examination of Strong Empiricism

Viewing a theory as an operational tool, it cannot be said

at any given time that the conclusions C of a theory are entirely

known. This is always true of a currently active theory; the

"better" the theory the more it is true. So A+> C --j- A+ superfluous,

as Samuelson says. For an actual theory, his identity cannot in

principle be written. Samuelson does make one qualifying reservation

-o the effect that A+ is not superfluous. He is willing to suspend

judgment on A+ because perhaps new evidence, C+ will justify the
presence of A+. If so, A and C will imply each other mutually.

Samuelson, Papers and Proceedings of the American Economic
Association, Vol. LIII, No. 2, p. 234.

Furthermore, wt c.rr\ivc L tha conclusion tht the identity

B-C* does not hold. This identity does not do justice to the

difficulties involved in establishing empirically relevant

theores-ical analysis. In general, L and C* do not enjoy the

same factual significance. 3=C*, which is consistent with

Samuelsor.'s argument, is actually a special case of the type

of theory under considsration, where every term in the theory or

model has empirical content. But in such cases it is more proper

to speak of laws, rather than theories with explanatory capacity

as understood in this paper.

BDB"*->B is broader than justified by empirical knowledge,

according to Samuelson. (B here corresponds to B+ in Samuelson's

notation). Thus there areA/ terms B not equivalent to identifiable

terms in C*. Samuelson says eliminate such-from Bt by Occam's

Razor, because they cannot be shown to have the same factual correct-

ness as those ^ related to C*. But such use of Occam's Razor would

destroy the internal validity of the theory; no longer would B-C.

B -1/i '-C. The reason the internal validity of the theory would

be destroyed is that the non-empiric.l segments of B are necessary

to the integrity of the logical structure, irrespective of empirical

content. The strict formal distinction between logical structure

and empirical content of deductive theory, while submerged by the

strong empirical position, is vital to the weak empirical position.

Matters are actually "made orse" in terms of the s-:rc.

empirical position. B C"C; we need rules of correspondence .-1

to establish a scientific relationship between theory and empirical

conclusions. 1.e need B-r-f'-.-C'. Rather than stripping B down to

its empirical minimum, it is neccsary to complicate and qualify

it still more.

Permitting the condition 3D EB: destroys the empirical purity

of theory as described by Samuelson. It creates all the difficulties

noted by various authors connected with the establishing of corre-

spondence rules. But, we must admit, the condition creates a

danger aptly noted by Saruelson: "In practice it leads to Humpty-Dumpri-

ness."0 It introduces the temptation to produce slight-of-hand tricks

by playing with the meaning of words. A concept once understood to

possess empirical content is shown to be empirically empty or false.

Yet it may retain its place in theoretical structure on the grounds

that it is essential to the logic of the system, even though it is

no longer supposed to assert anything empirical one way or the other.

Or, perhaps a concept will be introduced as a purely theoretical term,

defined only implicitly by the logic of the system, even though it is

known that the concept would le
ties if viewed empirically. Marginal utility illustrates the first

use. The community indifference curves of international trade theory

Nagel, Structure cf Science, pp. 93-94, footnote 3.

10Samuelson, Papers and Proceedings of the American Economic
Association, Vol. LIII, No. 2, p. 225.

illustrate the second use. (These ccscs -re essentially the

same; they simply illustrate different ways in which

non-empiric-1 concepts creep into -cono.ic3 theory.)

We arc remincec cf Robinson's criticism that economic

theory lacks agreed-upon standards of disproof, so that it is

difficult to reach general agreement concerning the scientific

merits of theoretical work. We appear :o be making matters

worse by providing the theorist with a readily invoked defense

for any work which prois to be empirically fruitless. No

attempt is being made to minimize the problem. We cnly wish to

show that reasoning away the non-empirical aspect of deductive

theory is equivalent to dispensing with deductive theory itself,

as practiced successfully by many economists.1 Done in the

name of eliminating metaphysical explanation, it would in principle

eliminate also the form of scientific explanation peculiar to

deductive analysis.

Machlup on Strong Empiricism

It follows from the principles of weak empiricism that since

not every proposition in a theory stipulates something about

observable reality, consequently, it cannot be asserted that

propositions which do not enjoy empirical status are empirically

false. Not all methodologists accept this principle, even those

M11achlup, The American Eccnomic Review, Vol. LIV, No. 5,
p. 733. See also Samuelson's reply, ibid., p. 736.

who adhere to it in -chei. own thoLeEical ..ork. Even rch'up

does not fully grajp the principle in his cogent criticism of

Samuelson on this very point.

Perhazp both Samuelsons ..ake a distinction
between a theory... and a thecy, meaning by
the for.,ir a prposition dacced from counter-
factual assut:.pticns ar. poatulates, and by
the latter a prop sit.on stipulating something
about observabli re-_iTy ... The bulk of
economic theory ... is based cn counterfactual
assumptions, ccnrains only theorei:al constructs
a..d so raicnal concerts. . .

While the writers disagree with each other, they both accept

the dichotomy rejected here. Machlup seems tacitly to assume that

stacem;nrt-for..s are counter-factual if -iey are not factual.

This is not a mere semantical disagreement, since we cannot

insert "non-empirical" for counter-factual into Machlup's argument

and get agreement. Clearly, this would not satisfy Samuelson,

and it would also put more restrictions on valid theory than

Machlup appears willing to impose. Yet the substance of his

argument is closer to week empiricist principles than Samuelson's.

Note especially his statement that "the postulated relationships

(which constitute the theory)" are not by themselves sufficient

to make the theory empirically relevant. He presents a regrettably

brief and somewhat unclear procedure for establishing empirical
correspondence which asserts that C' and B are not equivalent

because extra-logical considerations -re essential.

12 13
Ibid., p. 735. Ibid., p. 733.

S^.,.elson's Stronj E,:.iricis.. in Light
of His Founc. _icns

Samuelscn's :osi~ion is not ccmpletely opposed to th>

present riunaent, which is apparent when attention is directed

to his roundaticns of ESonoreic Analysis. Samuelson's purpose

in Foundations is generality, or what amounts to a variety of
theoretical explanation. His methodological principle4 is

tha-z of pursuing the sz:uctural analogies which can be found in

diverse areas of econcn.ic theory. Let us pursue his argument

far enough to see the relationships. Were Samuelson interested

only in relating unknowns to pertinent empirical data, he would

be satisfied with a descriptive formulation such as the following:

/ = g A ( .4 ,.V) ( i = 1,'" ), which he gives as the set

of equations expressing the relationship of the parameters to the

unknowns. The whole process would be on firm empirical ground,

and not open to the charge of a meaningless search for empty

generality or explanation. What would be obtained is a "final

functional relationship between our unknowns and parameters."1

Such a system of relationships would be open to direct empirical

check, fully capable of refutation. One might suspect that this

is the empirical equivalence between B and C sought by Samuelson.

4 Paul A. Samuelson, Foundations o F cn.omic Analysis
("Harvard Economic Stuoies"; Cambridg: i.uvara University Press,
1947), Vol. LXXX, p. 3.

5Ibid., p. 12.

Yet he 2ejects approach: to theory as bare formalism

" no h-~ ctssi; .cr. :a a.-nirical dat."16

"Indeed, it may be pcir.t: 7': -c;t these resulting functions

between unknowns and Da?.-r:;s s could hav. arisen from an

infinity of pcssibe a.l-ntive sets of original equations."17

"So what'?," i mlht hve :pected Samuelson to respond.

"Scie..tis:s neva- :'::plai.' any behavior, by theory or by any

oth:r hocl.. Every dec-ipt~;on that is superceded by a 'deeper

:*..lanation' turns out upcn c.r.-ful examination to have been

replaced by still anoth~ description. . "8 Samuelson

does not do complete justice to this more fundamental problem.

Indeed, he holds that the "explanaory" element is indispensable

to economic theory. What does this mean? It is not sufficient

to merely state ,o = g (Ot), that c variable (perhaps a

behavioral one) will take a different value depending on the

magnitude of some parameter. All this function tells us is that

there exists an equilibrium value of' for each value of t.

Perhaps it implies that between these particular variables there

is some stable relation which can be discovered statistically.

But Samuelson wants to know "What is the nature of the dependence

of our variable upon [cur] parameter?"19 For example, "Will an

16Ibid., Italics added. 17Ibid., p. 11.

18Samuelsoneran Eonic review, Vol. LIV, No. 5, p. 737.
Samuelson, The American Ecom.ic Review, Vol. LIV, No. 5, p. 737.

19 uelson, Foundatins, 15. Italics added.
Samuelson, Foundations, p. 15. Italics added.

increased unit tax result i. c. i'rger or smaller output?"20

To answer this type of c_-ic. it is necessary to specify

functional relatic-shiz s z -:. the unknowns of the theory:

f (*,- ,, .) = 0, ( i = .,* r/ ). This restricts

the number of solution: c -hz function F = g (o, ** '~ )

by specif;'ing the .ay i. which the unknowns are related to each

other. The equations ,') are the equilibrium conditions for

the -chaory in question. S-muelson shows, pp. 15-16, how we can

by specifying f (*) shc..' how unknowns vary with changes in each

of the parameters, something which couldn't be done without

specifying equilibrium conditions.

The equilibrium conditions, f i(. may be said :o constitute

the explanatory aspect of deductive theory, in a special sense of

the tern. It resembles explanation in Nagel's sense in that it

provides a logical structure which postulates interrelationships

among unknowns which bear no obvious or self-evident relationship
to empirical data. Furthermore, the logical aspect of the theory

takes precedence over the new data in the sense that partial

empirical failures here and there, while definitely damaging, are

by no means necessarily fatal to the theory.2 While the equilibrium

equations f (.) put restrictions on the explicit solutions g (*. ,by

20Ibid. 21bid., D. .

2Samuelson, The American Economic Review, Vol. LIV, No. 5,
p. 737.

so doi.. t--y cefi.e t..i; e of dependence stated in the

explicit solutions. OLZr':.':icn plus statistical analysis

might reveal the explicit r.-l:icnships, as already pointed

out, yet it takes a :heor -;c postulate hc' departure from

such and such a position :il- be felt cn the other critical

variables ir. the ma'rix. and comprehensiveness

of coverage are thus sa;rn c be two sides of the same coin.

The larger the matri:; of L ilibriumr conJitions buccces, the

more restrictions are introcuced. Buc a- the same time more

and more variables are ..-ace e-n-genous to the theory. Hence

th- theory takes or greater explanatory power at the same time.

No one expects a perfect theory, as Samuelson readily admits.

A certain amount cf empirical falsity is thus tolerated. Presumably,

the greater the successes or positive gains derived from generalizing

a theory, the greater the amount of empirical falsity will be

tolerated (though never viewed as a merit.) To the extent that this

is true, explanation plays an important part in deductive theory,

according to Samuelson's scheme. Comparison of economic theory

with theory in the physical sciences suggests that explanatory

systems in economics tend to require a greater amount of elaboration

to achieve a given amount of explanation. Perhaps for this reason

discrepancies between B and C*' will always be tolerated, even when

these become fairly significant.

There is an i,..por an- e..:.e, ho..evcr, in which Samuelson's

viewj on explanation d-f'c- funca-mer.-ally from .\agel's. In

Foundations, pg. 12, Siucl;son in effect -ays 'hat we start

with assumptions A and by deductive reasoning reveal to ourselves

the implications contin.d in ... "We may bring to explicit

a~tentic.-. certain. for:.alarior.s [C] of an original assumption

which admit of possible refutation (confirmation) by empirical

observa&icn." In making this translation into a "different

language" we leave B unarfacted, acdirn or subtracting nothing

from ics empirical conten-. This appears to be a justifiable

reading of the Fourdaticns passage in view of Samuelscn's later

remarks. Samuelson achieves explanatory capacity by constructing

a sufficiently large matrix of endogenous variables. Yet he

retains this generality even though he insists that every term

appearing in his theory possesses empirical content. Nagel, on

the other hand, insists that some terms remain implicitly defined,

so that the logical framework can be made to correspond to various

empirical requirements, as needed. According to Nagel, completely

specifying a model empirically unduly limits the possible range of

-pplicability of the theory which undrj-ies the model.

Samuelson aspires to generality along with complete empirical

specification by systematically exploiting the formal similarities

or structural analogies which recur again : and again in economic

analysis. . essentially the same inequalities appeared again

and again, and I was simply proving the .3me Theorems a

wasteful number of times." Use of zhse a.. l3gies becomes

the "fundamental principal crf gneralization" in economics
for Samuelson.

Let us give so...a ad-,-^onal consideration to this aspect

of Sir.melson's thought. He quotes Hertz in support of his own

methodological position: "All of Max..;ell's theory boils down

to the simple question of whether the observable measurements

on light and waves do or do not satisfy Ma::well's partial

differential equations." 24 But we might respond things like

"waves" are not observed; they are only accepted as real because

certain aspects of observable reality can be "explained" in terms

of waves, which are not known to exist outside the mathematical

framework which defines them implicitly. Their reality is not

observed, it is postulated by a coordinating definition.

Agreed, Samuelson would say. physicists didn't

know or much care what it was that was waving in Schrbdinger's

equation, a probability or what not, so long as the facts of

refraction and emission could be described well by this mnemonic

model.25 It is merely convenient to talk about waves, or helpful

to think in those terms. The point is that if contemporaries of

2Samuelson, Foundtionrs, p. 3.

24Samuelson, The American Econcr.ic Revi.w, Vol. LIV, No. 5, p. 737.

2Samuelscn, Paners and Proceedings of the American Economic
Association, Vol. LIII, No. 2, p. 232.

Schr-dinger continued to th;nk literally about wave images

suggested by Maxwell's .:. :. thy would be F-twisting: insisting

upon the reality of ,o:..c i'-inar'y entity in hopes of clinging

to a comforting "dIeper c;.l-.: ;ir.." r. fact, Maxwell, .ewton,
or never inenr.ed a.y such thing.

Accordingly, it is better to deal exclusively with

functional relationships which can describe how a matrix of

unknowns is affected by -che change of a parameter, just as

Schrddinger's mnemonic model can describe the facts of refraction

and emission, than to retain an unreal "grasp" of a theoretical

sys-em. This is very good advice. But in emphasizing these

points, Samuelson emphasizes the dangers ard disadvantages of

models for theories, which are the principal vehicles for attaching

empirical content to a theoretical structure B. Physicists typically

embed their theories in a model, and then associate certain of the

la'-er's terms with observables, such as waves with refraction

and emission. Often they are careful to point out that this model

with its coordinating definitions is not identical with the theory.

But ever here, Samuelson emphasizes, for example, that physicists

don't care "what is waving" when they consider Schridinger's wave

equation. Prc:umably it could be this or that or nothing at all.

The task of theory is complete when functional relationships have

been written down which describe observational data. What then

2Ibid., p. 232. Samuelson, The American Economic Review,
Vol. LIV, No. 5, p. 737.

becomes of B -B*, CCO, Fwhat are esssn-rial to Samuelson's strong

empiricist position? L..rcas we might have expected Samuelson

to stress the requireen:.s of ientification of all Theoretical

terms with empirical coL..-;-2parts, thus preserving the identity

of theory and conclusions, instead he provides examples which

seem to stress the opposite course. What seems to emerge is that

models, with all their colorful imagery and capacity to satisfy

philosophical yearnings for deeper explanation, have distracted

economists, as well as physical scientists, from pursuing sounder

goals. The distinction between theoretical terms and empirical

counterparts appears to be overshadowed by an emphasis on a

minimal set of theoretical statements (e.g. equations) necessary

to predict or describe observable occurrences. There is no

inconsistency in this shift of emphasis (which also occurs in

Samuelson's 1963-1964 work), but we can begin to see a distinction

in Samuelson between the logical framework and the empirical

counterpart, i.e. between B and B*, C and C*. This is important,

because we have differentiated strong and weak empiricism by the

presence or absence of this distinction. We shall pursue this

distinction further in the following section on analogy in science.

The Role of Analogy in Deductive Theory

Samuelson has found that formal analogies play an important

role in deductive theorizing.27 In analogies of this kind, "the

Samuelson, Foundations, p. 3.

system that serves as the r.c foc constructing a theory is

some familiar structure of ab;-rac- relations, rather than, as

in substantive analogies, a mcrc -r less visualizable set of

elements which stand -o each other in familiar relations."28

In consequence of this approach,

the new theory is not only assimilated to what
is already familiar but can often be viewed as
an extension and generalization of an older
theory wnich had a more liP.ited initial scope.
From this perspective an analogy between an
old and a new theory is not si.nply an aid in
exploiting the latter but is a desideratum
many scientists tacitly seek to achieve in
the construction of explanatory systems.29

Another statement, also drawn from Nagel in a different context,

is worth considering here.

[One view states that] a theory is a compendious
but elliptic formulation of relations of dependence
between observable events and properties. Although
assertions of a theory cannot be properly characterized
as either true or false when they are taken at face
value, a theory can be so characterized insofar as it
is translatable into statements about matters of

In chapter six of his Structure of Science, Nagel develops

at considerable lengths the advantages of applying analogy in

scientific theory, especially in conjunction with substantive

models. Diverse domains of experience arc much more easily

assimilated intellectually when familiar systems are employed in

Nagel, Structure of Science, p. 11.

30Ibid., p. 118.

the study of stranLe occurrr.ces. Apprehensions of similarities

between old and new re frqun'! -he starting points for

important advances in kno".1-t.e.

Formal analoZy ha. b.- c. very fruitful tool in physical

-cheory when based uo.:. .'- sc-nce of -.echanics. Numerous

branches of physical i.uiry have utilized the formal characteristics

of the di --ffe tial equatiors of mechanics in the construction of


But this indicates n, more than that diverse
subject matters exhii- cr:turs of relations
tha-c ar-e abstractly cr f... iy indis-inguishable.
It does not signify th.l: ..:hc is distinctive of
the correspcnd-ng rheori for each of these
domainss is t:-:h=us'tiviy r.ieed by the formal
structure of the thecy.

What Nagel means by this, of course, is that the theory remains in

the pre-scientific stage until coordinating definitions are supplied,

linking the theoretical tcr..s to empirical data. Once this is done

the theory can be asserted to say something definite; until then

it says nothing about the _;al world. Indeed this is the property

of the formal analogy which makes it such a valuable tool of

scientific research; as pre-scientific B it has no empirical contrast

whatever. B'=O. This property permits the same theory B to say many

things about many topics depending on the nature of the coordinating

definitions supplied.

1Ibid., p. 108.

Ibid., p. 165. Italics in original.

Nagel makes this point in rtr..s of a helpful cistinc-cion:

"it is not in consequence of cathu:..atical form [that axioms]

are to be viewed as the premise.; i distinctive science. We

must .examine the ki..d cf : ,r..s the axioms relate, in order

to ascertain the character~ features [of an explanation]."33

Samuelson does not choose to r--ognize this distinction. He says:

2. .'. -ecr of Friedman might be forgiven for
losing into t-hinking tha the thing called B
has cc..scuunces (call Them C) that somehow
come arcer it oa are implies by it and (sic)
are somehc.o different frc.2. it.

3. That same reader might be forgiven for
thinking that just as B has consequences C
that come after it, it also has some things
which are somehow antecedent to it called
its 'assu...Dtions' (and which we can label

Samuelson is not denying by this that the various theories possessing

the same formal characteristics are distinct theories. It is agreed

that the equations are not a theory B until they are related to the

real world. But, following this line of thought, it is preferable

to recognize explicitly that the logical framework and the empirically

applied theory are distinct. It is this distinction that gives the

formal analogy its special advantages. For example, the same set

of equations, constituting a theory, B, has wide applicability in

Ibid., p. 166. Italics in original.

Samuelson, Papers and Proceedirgs of the American Economic
Association, Vol. LIII, No. 2, p. 234.

say, economics, because i'- can he aplied to numerous economic

problems whose solutions ar- fo-..-ly similar. Yet, aside from

the structural similarity of "h> solutions, we are dealing with

distinct theoretical F;3.ic-ti ., B etc.

Having considered Sa:uel~.c's use of formal analogies in

economic theory, we ccncl-ud that he does, at least in practice,

make a distinction bet'.en 3 and B*. In any event, the most

crucial difference still remains. On the one hand, Samuelson's

strong empirical position demands that every term or statement-form

have factual content. Or, from a slightly different vantage point,

it demands that only the minimal se- of theoretical statements

(e.g. equations) be admitted in the description of any category of

phenomena. The weak empirical position of this paper is less

strict on either count.

Some Applications

Samuelson's methodology helps put normative problems into a

proper relationship with economic theory. For example, full

employment is basically a normative term, although semantically it

appears to be empirical. We all agree that full employment in and

of itself is a good thing, but there is wide disagreement how much

of this good thing should be tolerated when other normative goals

are considered. Recognition of this fact leads to the prescription

that it is undesirable to attempt to supply a coordinating definition

for this tj-m. There are ,..-ca-ly ccccetajle criteria for

a. empirical defi:.ition of 1.l ao.. -sym..a.t, because exact

consensus cn ccmpeting .,als cannot be racede.

Samuelson shows us h.o. ze -lmlinate -chis concept from

analysis. His purpose is to establish a logical construct

correctly exhibiting the pazz -.ns of mutual interdependence

found in the real ~si_. '.he patterns of interdependence are

provided by his ecu-ib-.iu... equations f^i) These equations

are totally devoid of normr.ive cncnfr.-z. Quite properly, in

the view of the modern writers cited, nor..iative judgments must

be made extra-theoretically; they are prior to any application

of the theory, and are quite necessary to any such application.

In addition, The theory generates no necessary or teleological

outcomes, because limits on the attainable range of values of

the unknowns is purely a technical or logical matter-.

The normative connotations of full employment can be

eliminated, then. Clearly the theory must show what combinations

of values the matrix must acquire for "full employment" to be

attained, consistent with any reasonable suggested figure. It

must clarify the difficulties of attaini..g these values, show

the implications of the alternative suggested value, or point out

why attainment of certain values is impossible. Only such a theory

can have any policy value. Without these properties, the theory

is merely an exercise, or act s-;e along the way to

empirically significant a.: i. -' argument could be

repeated for any pseudo-cmi:irica! co: p-, which embodies

r.or:..ive conr.sier.tic o irmpo_ ... c Che society:

pice-leval sTrs.iliy, gr, '. will see in the next

chapter, however, the-: r. no3-;3y theoretical term can be

eliminated in. Lhis w:a.

In this chapter, ,.e have contrasted in some detail two

important and representative methodological positions. Following

Samuelson, we have described his "smrorg empirical position," and

shown how it differs from the "weak empirical position" derived

from Nagel in the previous chapter. Two major differences were

pointed out. Samuelson makes no distinction between the under-

lying logical structure of a theory and its empirical counterpart.

He insists these are equivalent, just as a "theory" is equivalent

with its "conclusions." In contra.-, we have followed Machlup in

holding that a theory is wider than its conclusions, in the sense

described in the previous chapter. The other major difference

between the two positions is that Samuelson insists that every

term and statement-form musz have empirical significance in a

theory. Following Nagel, the weak empirical position permits

sl...vo use of cor--.conc-nce rules to identify some of the

h. orctical concepts wi';h -.:pirical entities. Partial

correspondence is ar.cth_ re..c behind cur belief that a

theory is wider -har. it cc:s.;lsicns, havi..g as a consequence

many "degrees of freedom," as Nagel puts it.

Our discussion of formal analogy in deductive theory led

to the suggestion that perhaps in practice Samuelson does make

practical use of the distinction ber~een a theory and its

empirical counterpart. In any event, Samuelson continues to

insist on complete, ra-her than partial, empirical correspondence.

In the next chapter we shall show, through a rather detailed

discussion of significant examples from economics, why we have

chosen to support the weak empirical position as a useful and

valid methodology for deductive economics.

"I*..PT, ;-


Keynesian Liquidity-Preference

Keynes' General Theor' of Emnlcynrt. Interest, and Money

is a good example of a theory which possesses great empirical

significance when viewed in its enti:4c even though a number

of its terms taken singly have dubious factual significance.

Keynes' theory exemplifies Nagel's proposition that theoretical

concepts possess empirical significance not in isolation, but
rather by virtue of their being component parts of a total theory.-

Keynes' General Theory stresses three fundamental relationships:

the consumption function, the marginal efficiency of capital, and

the liquidity preference schedule. A number of fundamental param-

eters are also contained in the system, such as the quantity of money

in circulation and the marginal propensity to consume. The

competing principles of strong vs. weak empiricism suggest two

important questions. Does each of these terms and relationships

possess empirical content in its own right, following Samuelson, or

John Maynard Keynes, The General mhaory of Employment, Interest,
and Money (New York: Harcourt, Brace and Company, [1936]).

2Nagel, Structure of Science, p. 202.

i.-sJt )e --. pon the context of the t.hory as a whole to supply

the er;irical meaninr.? Must we, at best, suspend judgment about

the inclusion of a concept not (yet) proved to be subject to :,.easurement, o: are other criteria ever offered by

economists to justify their use?

Dudley Dillard holds that the importance of the liquidity

preference schedule is that it introduces money into the theory

of output. Specifically, it per;.itted an explanation of how

investment could hb checked before "the interest rate" fell to

zero. Liquidity preference was injected into the system to

supply a missing logical link in a theory which, taken as a whole,

accounted for experience unrecognized in received doctrine.3

Dillard is well worth qucting at length on the question of the

empirical content of the liquidity-preference concept.

[Such concepts] do not involve the discovery of
new laws, principles, or phenomena previously
unknown, but are new contrivar.ces or inventions
which previously did not exist either known or
unknown. Liquidity-preference reveals no new
truth. It is a device for focusing the analysis
on relations between aspects of known experience.
The relevant test of such concepts is one of
usefulness, not of validity in the sense of
correspondence to experience. Any test of
validity must be in operational terms after the
meaning has been established, presumably in
relation to the whole system of which individual
concerts are a part.4

Dudley Dillard, "The Theory of a monetaryy Economy,"
Post-Keynesian Econcmics, ed. Kenneth K. Kurihara (New Brunswick,
N. J.: Rutgers University Press, 1954), p. 9.

4Ibid., p. 10, footnote 9.

Elsewhere Dillard points cut thG c shifts in the schedule

are more important than :..ov.a.ens along me schedule, and that

the interest rate is a somewhat unrealistic link between money

and the level of output. But the crucial fact is that the

essential link is forged. Furthermore, it interjects expectations

into the theory as they :..ust be, and as tney could be only in a

monetary theory of output. It also shows that while the origins

of depressions can be monetary in nature, yet the cure cannot be

solely monetary (as widely ablleved prior to the General Theory).6

This practical insight is embodied theoretically in the liquidity


It is clear th t Dillard rewards the liquidity-preference

schedule as a theoretical term, lacking empirical content outside

of the context in which it appears. Nor everyone shares this

judgment. Tobin provides an argument in support of an empirical

liquidity-preference schedule. The Tobin-Warburton-Fellner

5This may be counted as a weakness of the system because
it implies that exogenous changes are more influential than the
functional relationships actually stated in the theory.

Dillard, "The Theory of a .Mcnetary Economy," Post-Keynesian
Economics, p. 20.

James Tobin, "Liquidity Preference and Monetary Policy,"
Readings in Fiscal Policy, ed. Arthur Smithies and J. Keith Butters
("The Series of Republished Articles cn Economics"; Homewood, Ill.:
Richard D. Irwin, Inc., 1955), Vol. VII.

discussion that followed Tobin's original article emphasizes the

difficulties of providing firm empirical support for the concept.

But regardl-ss of the empirical significance of liquidity-preference

as an isolated concept, the critical point is to observe Tobin's

skillful handling of the concept as a theoretical term. To a

considerable extent it could be said without injuring his discussion:

"perhaps it is impossible to pin down liquidity-preference empirically.

Maybe we will never know the shape of the schedule. Nevertheless,

r.,~y starrments about~ monetary policy can be shown to imply certain

liquidity-preference schedules which we know are highly unrealistic,

whatever the 'real' schedule may be like." The value of Tobin's

discussion, therefore, doesn't turn solely on his belief in the

empirical content of the term, or on his support of that content.

Much of its value depends on his skillful handling of the term as a

logical concept or theoretical term implicitly defined by the

theoretical system taken as a whole. Tobin's theoretical work,

therefore, is offered as an example of analysis conducted along lines

which may be regarded as an alternative to Samuelson's methodological

approach. It seems fair to argue that Samuelson is unduly restrictive

in insisting on his particular interpretation of the empirical content

of deductive economic theory. We turn now to an additional instance

of theory which supports this contention.

8William Fellner, "Monetary Policy and the Elasticity of
Liquidity Functions," Review of Eccno..ic Statistics, XXX (February,
1948). Clark Warburton, "Monetary Velocity and Monetary Policy,"
Review of Economic Statiscics, XXX (Nov.mber, 1948). James Tobin,
"A Rejoinder," Review of Economic Statistics, XXX (November, 1948).

The Classical Theory of International Trade

Referring to the classical theory of international trade,

Ellsworth states

we should note that the classical economists
were more in-erested in showing the gains
from international trade than in explaining
its mechanism. Their theory served adequately
to show the effects of trade upon welfare,
but it haa serious shortcomings [in other

The weakness referred to hinges upon the labor theory of value,

which is a cornerstone of the theory. From the standpoint of

formal theory the results depend upon the labor theory of value.

How are we to evaluate the theory in view of this weakness?

(Nothing said here should be interpreted as denying that it is a


One interpretation states that if the axioms or postulates of

a theory are discredited, th.n the theory itself is discredited.

Now, it may be asked, what has been more discredited than the labor

theory of value, postulated by the comparative advantage theory of

international trade? But if the "theory" B, (which includes the

labor theory of value as a postulate) is identical with its consequences

C, it follows that B and C are both invalid, and must be rejected.

9P. T. Ellsworth, The Internaticnal Economy (3rd ed.; New York:
the Macmillan Company, 1964), p. 69.

This is a much more string:-. cni_-tion than imposed by

syllcgistic logic, in ;:.ich e.:. K,.lly valid conclusions can

be from false pr-mises. ?..i r;,;on for the stricter

condition is to eiminace tri.ia.l cnd fruitless theories from

consideration. As Nagcl pc.:.ts out, "It is always relatively

easy to invent an arbitrary set of premises which satisfy the

logical conditions for deductive explanations; and unless

further restrictions were placed on the premises, only a moderate

logical and mathematical ability would be required for explaining

any fact in the universe without leaving one's armchair."!0

Let us look at the classical theory of international trade

and its significance from an historical point of view. It was the

dominant theory from the time it was proposed by Ricardo in the

1830's until modern value theory was inserted into the theory in

the 1930's by Ohlin.1 The labor theory of value itself, however,

had been superseded long before Ohlin's contribution. Samuelson's

commentary under the circumstances is: "There can be no factual

correctness of C so defined that is not also enjoyed by B. The

minimal set of assumptions that give rise to 3 are identical with

B, and if A is given this interpretation, its realism cannot differ

from that of the theory B and consequence C."1

1Nagel, Structure of Science, p. 43.

B1ertil Ohlin, Interregicnal and International Trade
("Harvard Economic Studies"; Cambridge: Harvard University Press,
1957), Vol. XXXIX.

-Samuelson, Papers and P-cceedings cf the American Economic
Association, Vol. LIII, No. 2, p. 234.

R, section of the theory is well-grounded on -nis

interpretation. Yet the success of the theory, related in

Ellsworth's statement, can..ct be minimized. People were

given a convincing explana'lion f the error of mercantilist

views, which dominated European thinking for two and one-half
centuries. It is as unfair to accuse the writers of making

naive counterfactual statements (no significant differences in

factor endowments, .cmogenicty of factors), as it is to accuse

Samuelson of "believing" the "assumptions" of his factor-price

equalization model.

Note, for example, Ricardo's statement "It will appear then,

that a country possessing very considerable advantages in machinery

and skill, and which may therefore be enabled to manufacture

commodities with much le-s labour than her neighbours, may, in

return for such commodities, import a portico. of the corn required

for its consumption, even if its land were more fertile, and corn

could be grown with less labour than in the country from which it

was imported."5

Ellsworth, p. 3S.

Samuelson, The American EcLncoic FReview, Vol. LIV, No. 5, p. 734.

5David Ricardo, The Wor. Vol. I: On the Principles of Political Economy and Taxation, ed.
Piaro Sraffa (Cambridge, Englanc: Cambridge University Press, 1962),
p. 136.

..s _.i most scminail l.eoretic. works, Ricarco

..icipate a:.tra-thec. ica.iy .:u.:r.rous key ideas explicitly

incc-:pc-rad in later theor-i-cal .:ork. That they do not succeed

in doin r. h entir, job ac c.;cs nhoulo not be held against them,

especially _f we concede them -he right to define their own task.

Suppressing considerations cf the "mechanir1" which we have been

brought up to consider important enabled the classical theorists

to der.onstrate the gains fro.. trade and the advantages of speciali-

Of course, to be a genuine theory, B must have some authentic

empirical con~ent. Ctherwise it would run the risk of being

entirely arbitrary. The classical theory at least made an attempt

to identify the major element cf cost, implicitly saying that the

other costs are relatively insignificant. While this judgment

hasn't stood up over the years, it provided one of the pillars

for a theory which greatly advanced knowledge. The theory also

ignored relative resource endowments, even though this is one of

the elements of a more satisfactory theory of trade. The theory

is not completely satisfactory is quite distinct from its being

unacceptable r.mthodologically. This interpretation appears to be

appropriate and consonant with the methods tacitly employed by

economists past and present, as well as by physical scientists.

1Ellsworth, p. 69.

S__' 3cnald .-iac .cuc_: s study, cited in Petr 2. .enen,17

has provided an empirical tes- of the classical theory. Results

are sufficiently gCOd co us-ify the assertion that the deductive

ex:lanaticn of ccr;prative advanacea has an empirical basis. This

assertion is further justified because the theory has shown

considerable capacity for ex-:pansion and generalization in empirical
directions without having its basic structure altered.8 The

theory begins to break down only -:hen attemp-s are made to over-

z dc-n the logical framework by giving .lcit consideration to

the internal adjustmar.- process, which is best left implicit, or

suppressed from empirical view.

The Law of Diminishing Returns

The well-known discussion between J. H. Clapham. and A. C.
Pigou9 over the law of diminishing returnA as a valid economic

concept provides a vivid illustration of the empirical principles

we are discussing. Professor Clapham asserts that the law cannot

be made to fit the actual facts of particular industries, that

nothing useful would be accomplished even if it were possible,

17Peter B. Kenen, Inte--national Economics ("Foundation of
Modern Economics Series"; Englewood Cliffs, N. J.: Prentice-Hall,
Inc., 1964), pp. 16-17.

1Ellsworth, pp. 67-CS.

9J. H. Clapham, "Of Empty Economic 3oxes," Readi..s in Price
Theory, ed. Kenneth E. Boulding and George J. Stigler ("The Series of
Republished Articles on Economics"; Chicago: Richard D. Irwin, Inc.,
1952), Vol. VI. A. C. Pigou, "Empty Economic Boxes: A Reply,"
Readings in Price Theory. Clapham, "The Economic Boxes: A Rejoinder,"
Readings in Price Theory.

.- -chat ch l. coulc not he tested fo2 1, ism; e:..-)t after

mne fact, tha. is, in practice it must remain a hisorical

exercise. FinalLy, the aw. of di..inishir. returns cannot in

practice bh scparnted from other factors of great importance
which completely obscure its worxings.2

Pigou's response illustrates the type of reasoning we been applying. Referring to the law of diminishing returns

as one of many "empty economic boxes" identified by Clapham,

Pigou says:

Dr. Clapham appe rs to hold that, provided,
as boxes, they cannot be filled, it is
self-evident they can serve nc purpose,
of this kind [the construc-cion of a
realistic economic science.] In that I
venture to suggest that he is mistaken,
that he has, in fact, misunderstood alto-
gether the nature of the work he is

Pigou goes on to explain ho4 the concept of diminishing returns

is essential to an understanding of the relationship between

aggregate output and changes in unit costs. He says that it is

not the concept itself that is important, but its strategic

function in the solution to the great problem of economic value.

SClapham, "Of Empty Economic Boxes," Readings in Price
Theory, pp. 126-128.

1igou, "Empty Ecconomic Eoxes: A Reply," Readings in Price
Theory, pp. 133-134.

T -:a.:e thn categories of increasing and
dl- ;,..1-.-, returns ou: of their setting
and to speak of them as -.nough they were
a thing that could be s. e -- .-y without
ir.jury to ine whole cor, economics is
a very pe-rvse procecii:. .. thesee boxes,
as he calls them, are not r.,erly oxes;
they are also elements in the intellectual
machinery by which the main part of modern
economic t.hc-'-.t functions. . They are
an organic and inseparable part of that

Clapham's rejoinder, "I see no perversity in criticizing
part of a theory," has a la-ge roLlowing, ct least by implication,

as we can see in many prevalent criticisms of economics today.

Utility Theory

In this section, we shall try to show -,iat much of the

dissatisfaction with the utility concept centers around its

empirical status in economic theory.

Frank Knight points our certain abstract parts of economics

which "are no less practical than concrete-descriptive or applied

economics but are less directly related to immediate problems."24

The study of value and distribution have been basic to modern

economics since its inception, and the way in which they have been

understood has greatly influenced all branches of economic theory.

Ibid., pp. 134-135.

2Clapham, "The Economic Eoxes: A Rejoinder," Readings in
Price Theory, p. 140.

-4Frank H. Knight, "Economics," On the History and Method of
Economics (Chicago: The University of Chicago Press, 1956), p. 19.

(For xc...._1, :aecll h-; ac.r.ccur.rnz of- r.e labor chiory of

vaLue pcr...i-d the scope of trade theory to

be extc.:c-d.) One of the .
modern -ch-o.y of value was the invention of marginal utility.

At first, theorists believed they could measure the quantities

of satisfaction people acquired from the use or the acquisition

of goods. In time, however, it became apparent that the whole

idea of marginal utility was based upon a very dubious form of

psychology long since abandoned by professional psychologists.

Economists came to realize that all prcaise of giving empirical

content to the concept of marginal utility had vanished. Yet to

abandon the concept would have done violence to the logical

structure, and economic theory is full of terms which economists

have been reluctant to give up for tha- very reason.

It would be possible for economists to treat consumer demand

in a completely empirical way. Relationships could be

treated as observaricnal and the generalizations
inductive. . Economists, ho:cver, are prone
to go 'behind' the observable demand and income
curves to a more 'ultimate' magnitude: utility.
The reasons for this are several. It is
consistent with (admittedly unsophisticated)
psychological experience. It yielcs predictions
about consumer behavior. It permits the analysis
of a significant range of welfare problems that
are meaningless in purely observational terms.25

George J. Stigler, The Theory of Price (rev. ed.; New York:
the Macnmllan Company, 1952), p. 63.

c.-... co.tinuLss, "I. is ow ge..erlly agreed . .that

the eccnonic theories had bette- use the notion of a maximum

without trying to say is ma.: izd--much as the physicist

speaks of matter or mass in terms of the way it is measured

without trying to define its nature."2

But bad psychology is bad psychology, it might be protested,

and there is no e-:cuse for justifying it simply because it leads

to convenient results. Yet the econcmist is thoroughly justified

in replying that he is nc: offering a theory of psycholcgy, but

a theory of economics. It is taking far too much cf a theorist

in any branch of knowledCe to or nize his concepts in a way

which would lead to fruitful lines of inquiry in other disciplines

whzre subject matter overlaps. It is sufficient for the economist

to disavow any implications which might seem to flow from his

theory, contrary to the conclusions of competent specialists. It

is wholly gratuitous to criticize economic theory because it is

bad psychology. Some concepts unavoidably overlap several disciplines.

They will have a different status in each theory, depending on the

objectives of the theory. Utility has a primarily logical role in

economic theory, as Stigler and :'.. point out. From the point of

view of psychology, on the other hand, the term covers terrain that

must receive more explicit attention. The utility concept thus has

nothing relevant to say from the point of view of psychological theory.

26Knight, p. 20.

it is impaos ole o voidc th- use of purely :.ner^-cal

term because just abo-r every -ub- c-: .c-s bhn approached from

anotherr point of view, wih a cdi -.: theretical emphasis.

..nd ca e can..o. make st.; .zr-s aboi a gi'.n master which are

equally acceptable from all possible theo-etical points of view.

Such stater.-mnts would need to possess such all-inclusive

generali-y that they would probably be hopelessly vacuous. Hence,

any Genuinely significcnc theory is inherently open to criticisms

of distortion of reality by people who insist cn verifying the

wro-. parts of the theory. Unfortunately for economics the

inclination is strong because those theories are stated in more or

less familiar terms, and touch on areas charged with great moral

significance to the lay audience.

Utility theory has also come under severe criticism because

of its alleged circularity. It is said to be circular because it

asserts nothing significant about individual behavior.27 People

desire goods because they possess utility, and we know that they

possess utility or else people wouldn't desire them. Utility

maximization is established the same way. The fact that a person

chooses goods in a certain combination indicates that it is the

best combination, for otherwise he would have chosen another.

27 inson, p.
Robinson, p. 47.

Reduced to these t -, a.. applied to the behavior of

particular incividials, ry is nothing more than an empty

rati-alization; it ~rlls u- 1-;.t cple behave the way they do.

Utility mi t.ition, li.i
on two counts. Being vacuous and circular, it asserts nothing

at all. being based on discredited psychology and having unsavory

ideological connotations, it asserts what is known to be fals-.

At one time or another ttcse "assumptions" of economic theory get

the worst of both worlds. Again, the point is that utility theory

is not intended to further our knowledge of individual attitudes

and behavior. Tastes and, after all, are always

exogenous variables in economic theory. Utility theory is to be

regarded as empty of empirical content. But this does not mean

that economic theory would be no worse cff without it. The

pervasive use of the concept ir. virtually every branch of economic

analysis attests to this. Utility theory is an important part of

the exlanatrion of collective behavior. Terms implicitly referring

to individual behavior are included in a purely formal way.

Empirical correspondence is not even attempted except in

connection witil logical conclusions related to the average behavior

of large numbers of people. As with the profit maximization

hypot.-sis (to be examined) it is necessary to relegate utility to

the realm of implicit definition. Any other course would be

unjustified and cut of keeping with the goals of economic analysis.

C. S. Jung st-es that sciU: .;-. knowledge of the individual

is in a sar.e a ccnrradicticn in trr...

S. it is not the univ c-sal and the regular
that charactcr-ze the indiv-du-1, but rather
the uricu-. He is not to Le u. .erstood as
a recurrent unit zuc as sc..nt. ng unique and
singular whicn in the last analysis can neither
be known nor compared with anything else. At
the same time man, as member of a species, can
and must be described as a statistical unit;
othern~ise nothing general could be said about
him ... .If I wa:.t -co ind-:.csand an individual
....n being, I must lay aside all scientific
kn-.:lecge of the average man and discard all
theories ir. order to adopt a completely new
and unprejudiced attitude.28

Jung is pointing out that much data about the individual is

necessarily jettisoned in the construction of theories of human

behavior. These theories, when properly interpreted and competently

applied, can contribute greatly to knowledge. But he counsels at

considerable length against the easy mistake of overextending the

application of these theories into the wrong domains. That problems

of interpretation arise in psychological theories of human behavior

may be taken to justify our modest interpretation of an economic

theory of human behavior. Jung points out .nat psychological

theories, whose goal is understanding of human motivation and action

per se, are inherently vacuous in certain crucial aspects, and will

2C. G. Jung, The Undiscovered Self, trans. R. F. C. Hull
(New York: The New American Library, 1957), p. 18.

Case serious -i_ if .hcse li mi;2iu..o re not respected. We

may conclude that econc.::ic rheovy, .wh>-.. oCals are quite different,

is not necessarily deficient if it i ...._pically vacuous with

respect to pct:i..s -hat bc~ r irmpliill-y c. human behavior.

(Schr'dinger's essay, "Cn the Peculiarity of the Scientific

World-View," already referred to, is perhaps one of the most

eloquent testimonies or the deliberate ar.J necessary elimination

of importa:.t aspects of understanding in or.rf to achieve

scientific knowledge.)

We turn now to a brie comparison of classical utility theory

and indifference analysis. Lef which says: "Some economists find

distasteful the quantifying of utility and the principle of diminishing

marginal utility. Nevertheless, the [classical] utility theory . .
and the indifference curve theory . reach the same results."

According to the present analysis, is there any ground for rejecting

-he traditional approach? It is true thar at one time utility was

thought to be the very area whnre empirical results could Lc achieved.

Yet the end of classical utility's career as an empirical concept di;

not necessarily destroy it completely. N;or did it mean the end of

every piece of analysis based on it. Put briefly, classical utility

could justifiably survive as a theoretical term. This is essentially

what happened when economists moved from cardinal utility to ordinal

"Richard H. Leftwich, The Price System and Resource Allocation
(1st ed.; New York: Rinehart and Company, Inc., 1955), pp. 67-68.

u-ility. It was ciso'.tered t th th theorems of economics

base on utility theory could survi- e'.ac if the empirical content

of the key concept' was :wakened. Yt ;-: ak_ argued that even utility is unnecessary for th, loical integrity of these

theorems. Quite rightly, therefore, he set out to eliminate the

concept from economic analysis. According to his indifference

analysis, anything even suggesting quantitative utility is disallowed.
The an-lyl-s is built solely upon an assumed scale of preferences.

This application of Occam's razor in iztslf cons-citutes a theoretical

improvement according to Sameelscn's approach. A more concise theory

results, and what is mcre important, it can be applied to a wider

range of problems, as is evident to anyone familiar with the


We conclude that there is no particular advantage in retaining

theoretical terms that stand little chance of acquiring empirical

content. Such terms add little to the generality of the theory as

an explanatory instrument. Explanatory capacity comes to a theory

in part because of its characteristic of being a complicated and

lengthy statement. As such it can be modified by additional

restrictions or be used as the basis for more models than could a

highly concise statement. But classical utility as a theoretical

term doesn't seem capable of extending the generality of theory in

30J. R. Hicks, Value and C- ital (2nd ed.; London: Oxford
University Press, 1946), p. 18.

chis way for -he reason 6ivan. (Clas-,l utility theory is

being compared with t:.e more concise difference e analysis, not

with the alternative or no. theory a- all, to which it is far


The Theory of the Firm

Understanding of the traditional theory of the firm also

benefits from an application of the empirical principles developed

in this paper. The most frequently heard criticisms are easily

summarized. On the cne hand, th- theory emrodies hlI.hly over-

simplifi-d, if not altogether ccunterfactual assumptions concerning

motivation. By ignoring m.ultiplicity and diversity of motives, the

theory gives a false impression on this score, if it says anything

at all. On the other hand, the "firm" of the tneory of the firm

bears practically no resemblance to actual business organizations.

It has no compl: of control, no standard cperating procedures,
no budget, no controller, no aspiring 'middle
management.' To some economists it has seemed
implausible that a theory of an organization
can ignore the fact that it is one.31

Furthermore, in simpler versions of the theory at least, perfect

knowledge of the future is assumed on the part of decision-makers.

31Cyert and rch, A ehvi l eory of the Firm, 8.
Cyert and March, A Behavioral Theory of the Firm, p. 8.

Georoe Katona e:p citi -... c. he theory of the

firm in terms of the use of tha c- .:. assumption. Basic to

the theory, of course, is the fuc.-lc stating an inverse relation-

ship betien price of fir:.: output a:.- qu.tity demanded by the

consumer public. in -*.. r. by this function are the

vital consice-ations of uncer:-..... y, expectations, effects on

consumer and rival firr.s etc. In shorc, the theory "is based on

a nmchanirtic pc' chology according to which one item in the

psychological field can be wlthour affecting other items

ir the same field."32 Thi.ei is no such "on--to-one correlation
between a given stimulus and a given response." Yet it is upon

such a mechanistic psychology that the va-idity of the function

under consideration depends. Empirical research reveals that the

psychological assumptions implicit in the traditional analysis of
business decision-making are false. A fundamental empirical fact

is uncertainty on the part of the businessman as to the consumer

response to his price-output-procuct decisions. There is a

fundamental psychological reason for this uncertainty, which is

systematically ignored by the traditional theory. It is the essential

interrelation of consumer motivation and expectations as part of a

complicated and dynamic psycholo ical field which generates this


3Katona, Psychological Analysis of Economic Behavior, p. 221.

33Ibid., p. 237. 3 id

Cyert and Grumberg35 make another attack on the theory of

the firm, which is levelled against the use of cet.par. Although

it is different in nature from Katona's criticism, it is convenient

to consider them together. Cet.par. is used so extensively in

economics in order to reduce the great complexity of the real world

to proportions manageable by theory. What economics loses by

achieving manageability is capacity for prediction. Since it is

impossible to determine whether cet.par. is ever fulfilled in

actual practice, the authors argue, the validity of the hypothesis

remains forever in doubt. Strictly speaking, economic laws are

untestable for this reason.

These remarks provide merely the smallest sampling from a

large and well-known body of criticism of the traditional theory.

Yet enough has been said to indicate how for some purposes simplifica-

tion can be tantamount to distortion and falsification of theory.

If the theory is interpreted as an explanation of the way an

individual firm makes its day to day decisions, handles its organiza-

tional problems, defines its own goals, etc., then it can be said that

empirical analysis has pretty well discredited the theory. Further-

more, if the theory is so interpreted, then the psychological

implications that Katona finds embedded in the theory become

R. M. Cyert and E. Grunberg, "Assumption, Prediction, and
Explanation in Economics," A Behavioral Theory of the Firm.

36Ibid., p. 301.


c-....piricclly i..-" C ic..t. I.. wo^. o, i_ we V ay that tna;

traditional _..eory I L:.~ firm sh.ou-d illu:..:i.ate organization.

problems, dc;is o- dciicn-:..:i.., goal formation, and the

like, then the -hecory is gcr.uin ly ci-i.:.i as criticized.

For example, th* theo-. 'tical s'tt:.. 3:-..c- The sole goal of the

fi-'.m is to 1i.a.-:i:..ize p:cfits seiously deficient empirical Likewise, t;. implicit assertion that firms have no problems (.ince the theoretical firm is not an

o=Canization) is gross empirical irnvlidizy.

We have already se~n,,, that the failure of a theory

in one direction of incuiry does not preclude fruitful .d valid

applicationss in other directions. Cyert and March make the following


Such of the controversy is based on a
misunderstanding of the questions the
conventional theory of the firm was designed
to answer. The theory of the firm, which is
primarily a theory cf markets, purports to
explain at a general level the way resources
are allocated by a price system. To the
extent to which the model does this success-
fully, its gross assumptions will be justified.
However, there are a number of important and
interesti-. questions relating specifically to
firm behavior that the theory cannot answer and
was never developed to answer, especially with
regard to the internal allocation of resources
and the process of setting prices and outputs.37

37Ce and 15.
Cyert and March, p. 15.

We may now ex--i.,e the ~..eo3 of i.. irm from this distinct

point of view. ,e will the. hcve a ....._ co...plete picture of how

the logical s'tructurc of a theory _i. .its the nature and range

of its a-plication, and dt-er.i.-e: how coordinating definitions

should be supplied for the theory. We shall see that the unreality

of the traditional theory of the firm stems from the fact that

certain of its terms are given coordinating definitions, or reified,

.-n -:-.y should be left implicitly defined. Properly selected

rules of corre.pcondence can preserve -he enpirical validity of

-h theo:jry within its proper sccce of application.

Modigliani explains two different ways in which micro theory

is made to correspond to cbsrvarior. Cn the one hand, he states

that "normative theory" is co.-cern.d with the internal problems of

the business manager. The goal of .- Itive economics," on the

other ..-nd, is the "understanding a:.d e-xl ".i.-. how our economic
system works."8 !-:ocig.iani is referring to such things as the

impact of different mcket structures on output and income distribution

in the community as a whole. He is interested in the "theory of markets"

referred to by Cyert and March. As a consequence of their different

goals, these economists will make a differentt choice

3Franco M c,_liani, "M anagerial Economics-Discussion,"
Papers and Proceedings of thl American Econcmic Association, Vol. LI,
No. 2 (May, 1961), p. 159.

as to whichh featcres o0 the si.iation are e .s -ia
and must be incorporaced in the mowal and whic..
can be ne-gec'--. Here ths positive is
likely to concrntra- t on thv's which are
ccmrr.on to r.a.ny agents i..c- 0o ,.^lect what seem
idiosyncratic aspccts of the r .oblem. . these
features :.iuy hve to play c-.'tical role in the
rar.agerial economist's rioceL.-

This is the kind of problem which very frequently faces

economists. Some of them, like Modigliani, concentrate on the

problems of positive eco..or..ics; smca, like Hitch and McKean,

work in the area of nor:..a-ive economics. They develop theories

and models appropriate to their own set of problems. Now, positive

economic theory can be applied to the internal problems of the firm.

It is developed in terms of a language which makes statements about

firms, decisions, and the like. Yet we have seen how this extension

oi coverage tends to falsify important parts of the theory, because

the language of the original theory takes on meanings it was never

intended to possess. By the same token, the normative economist

has some grounds for moving into th. domain of positive economics.

This might entail improving the "behavior inputs" of the normative

economist's model. Hitch and McKean appeal to evidence that the

behavior of business managers does not conform to the propositions

3Ibid., p. 158.

0Charles J. Hitch and Roland N. McKean, "What Can Managerial
Economics Contribute to Economic Th-ory? Paners and Proceedings
of the American Economic .Asociction, Vol. LI, No. 2 (May, 1961),
pp. 147-148.

of positive L..,o::y to su-ppor'c t... c.... nicn.1 Modiliani's

reply should be easy to anticipate: "For ,.y part, I am somewhat

ske'cical abouc the cha:.ces of de. 1l;i.. alternative postulates

which are cable of rc-d applicabilit:- and yet are operational

enough to lead to precise verifiable implications."4

Since the two rcelaed theories have different goals, their

common theoretical tcr's have a different status. Profit maximiza-

tion is 0ood0 example For the -or activee economist, interested in

"ho.: the ;systc.:. -cks," :he basic motiva;icn is properly left without

ccordinatir- definition. A: this level of abstrccticn it would

hopefully ancunt to neglect of whac seem "idiosyncratic aspects of

the problem which--he hopes--will tend to wash out under aggregation
or will at worst show un as random components in his model."3 Thus,

the posi-ive economist considers the profit maximization hypothesis

as merely one of th, organizing elements in the marginal calculus of

his theory. ". .striving to achieve with given means a maximum of

ends [is] the so-calld economic principle," and marginalism is the

logical process of 'finding a maximum .. ." The theory cannot be

'-bid., pp. 149-150.

42Modigliani, Paers and Proceedings of the American Economic
Association, Vol. LI, No. 2, p. 15S.

43- .

44Fritz Machlup, "Marginal Analysis and Empirical Research,"
The Am.rican Econcmic P.evieu, Vol. XXXVI, No. 4 (September, 1946),
p. 519.

Cvd,-datac by rakinr any o0 i;s p_ -o. oi.i- in isolation; "It

is necessary to know precisely wha the '-h-:y says, what it

implies, and .:ha i in.nds rdo." -lni is the

essential feature of the theoretical f_:..,~-r, and "profit

maximization and marginalism are so closely connected that it is

hardly possible to make any use of marginalism except for the

purpose of determining the output and price that will yield

m ximum profits." It should be ar that profit maximization

is a differed. sort of concept in the positive theory than it is

in the normative theory. In the former, it is only defined

implicitly; no attempt is made to endow it with an independent

existence by establishing empirical correspondence for it. Profit

maximization does not enjoy the status of an empirical law, which

can survive unaltered the theory in which it is embedded. The

concept has an altogether different status in normative theory.

There it becomes -he very focal point of empirical research. In

normative theory, analysts seek to establish laws which are

significant independently of any theory in which they might appear,

or at least good working empirical hypotheses. This is the

distinction that Modigliani seems to i.ave in mind when he voices

skepticism over the suggestion of Hitch and McKean that managerial

economics can contribute more realistic and empirically valid basic

assumptions to the positive theory.

Ibid., p. 520.

46ton, 215.
Katona, p. 215.

There is another advantage in using the simple motivational

assumptions implicit in positive micro-theory which is abundantly

clear to all theorists. It enables the theorist to make precise

statements about economic activity. He does not for a moment attach

great empirical significance to this precision; what the theorist

gains is an ability to make concise statements--manageable intellectual

tools possessing great flexibility and considerable generality.

Stigler acknowledges the diversity of entrepreneurial motivation,

but stresses the difficulties of strengthening the theory by including

them. Frequently they possess no agreed upon meaning and would only

detract from the clarity of the conclusions drawn from the theory.

The desire for security, or the goal of "fair profits" are examples.

Stigler metnions others: "to be his own boss, to maintain a

customary standard of living, to obtain economic /or/ political

power, etc.47

There is no objection in principle to these
alternative goals, but in their present
undeveloped state they are seldom useful in
general analysis . unless they are
developed in content and their scope of
operation and strength are approximately
determined, they improverish rather than
enrich economic analysis.48

4Stigler, p. 148.

48Ibid., p. 149.


This chapter his _c-n devoted to an examination of a

number of concepts and theories which illustrate the application

:c the methodological principles that were developed in the

previous chapters. There is no universal agreement in theoretical

science concerning valic princiles cf deductive theorizing.

Ccnsequently, the choice of principles ;.ust be somewhat eclectic

in nature. The examples given in this chapter justify our defense

of the methodology distilled principally from Nagel, and called in

this paper the "weak empirical principle."

We, have seen how the concepts of diminishing returns and

liquidity preference are vital to the logical frameworks of the

theories in which they appear, even though their empirical content,

when viewed in isolation, is highly questionable. These important

examples illustrate the principle that concepts should be judged,

not in isolation, but rather within the entire theoretical context

in which they appear. The discussion of utility theory shows how

a concept can acquire new and different significance in theoretical

analysis. Originally -reated as an empirical term, utility has

retained its position in theory as an implicitly defined term,

important to the logical s-ruct- .-. .,ry. Rules of

correspondence can change v r ti ..c, -. _cordar.ce with new

anplications and developed .

The discussion of the .hco-- of -i:. firm and international

trade make clear the principle that the valid application of an

abs-trac theoretical framework depends on the very careful formulation

of correspondence rules. F.fification of the wrong concepts leads to

erroneous and unjustified cQnclasions, which frequently cause theories

to receive unjust criticism Proper forrmu.- ion of corr c.-.

rules, on the othe- h.a, re tly facilities proper use of theory

and helps reveal the legitimate range of theoretical application.

Each of the examples discussed in this chapter reveals why

it is important to realize that non-empirical tera.s and statement-forms

have a legitimate and vital role to play in the deductive form of

economic theory.

In the next chapter, an attempt is made to examine the historical

background to the ccntrcvcrsies over the empirical principles of

deductive theory. 1e shall see that e outcome of the discussion is

still a matter for debate in the Dhysical sciences. Nevertheless, we

shall find considerable support for r-he principle developed in the

previous chapters, as well as important ir.plications concerning the

scope of deductive theory.


We have explorer a number of aspects of economic theory

which c,; best ae L-ner2tocd against the backdrop of broader

scientific or ph-lcsch-cal issues whlc.' have received the

acention of the scir.Tific cc...unity at large. V'hen we arc

fced with the serious charge Zha'c much of the work done by

cconc.ists in the daiuctive traditicn. is invalid, we are prompted

to examine the developments in scientific thought which suggest

the criticism. The issues we are interested in are, as always,

the nature of the connection between experimental data and the

theoretical representation of that data. Specifically, what

effect has the greatly expanded emphasis on empiricism had on the

position of the a prior method of analysis in scientific theory?

Of equal importance is the closely related question, to what extent

have the goals of scientific analysis changed?


?. '. Sridgman has presented an influential statement

concerning the emp-irical content of deductive theory. Bridgman's

basic Dre:ise is h:- ....o; (, -ys _c_ ..~ory at least) achieves

validity iZn restricts c a ... crti n. of actually performed

physical operations. Physical -, 'rmalated according to

kno;:ledge gain& by n e:- ~--'i.A or c3 rvicn will never require

fundamental re iisicn, bu- e:.-i i-- ,ep them coextensive

with current kno,.;:.. 1. It is y;s-3_ -o define physical concepts

without references rc cb vt:' c priment, but not without

running th riNk of bein, coniac,:c- irically. For example,

concepts may be deric:-

in terms of p-operties, s is so cfen done in
mathematica, nd thr. :p-rimr.t with .. -
structures we mry erect in terms of such concepts
to see whether the concepts are useful. We still
have operational nmenii.g for our concepts, but
the operations are mental operations, and have
no necessary physical me-ning.2

Consequently, according to Bridg.nen, I' ..l.-.ts have come to accept

the operational conventic which he describes as standard procedure

in physical theory.

Every scintificc-ly sound conclusion must have an experimental

basis, according to Yet, he does not go on to assert that

scientific theories ..ust be based entirely r. an empirical foundation

Scientific theories are convenient devices for integrating concepts,

enormously expediting the prcble:. of dealing with diverse complicated

situations.3 Any such device, e it verbal or mathematical, is

P. W. Bridoman, The .Iature of Physical Theory (New York:
Dover Publications, 1936), p. 9.

2Ibid., p. 11. Ibid., p. 29.

ncab.ic of x,:p-i._ :,it fc liy. nThe conceptual

fram7 itself iL inh 'ren'ly lacking in cc -:-c-cndence with m-erial

obj-ects. Escclihing cr e. in o s getting outside the

syr;.-m of lnC- oc by obsr&l.ctio., ise, a,.. verification. And

3ric.gmn does not insis: tLat the entire system of integrated

concepts be empirically grounded by such outside references. This

is pDrticula-ly clear in his discussion of applied mathematics. He

o.ys . .let us suppose ha: I am presented with a set of equations

by the thcretical p.hysicis', which he -ells me contains the theory of

the phenomeIncn in question." The application of the theory requires

more than the formal theory itself. Application requires a "text"

telling what the significance of the equations is and how to use them.

Certain of the symbols must be linked up with the physical facts of

the expcrimental process so that

nu:.'be-s obtainabl- by the ph .tion
stipulated in cthe .c sac;ti-s on w.h:en
substituted into it. No o.y .. :e ext
describe the r.n-ure of the m-'asur__ :, h'; it
must also speci y -he connection be. a. the
different symbols in the equation.e

Let it first be noied that Bri-' .: stares that the set of

ccuations may be said to contain the theory, but that a supplementary

tex- must be supplied to make the theory operational. Correspc.ndence

between theory and reality involves going outside the systu.:

Ibid., p. 19. 5Ibid., p. 20. 6Ibid., p. 59.

f t.. .:h:..i-al th--.y -nd .. intuitive knowledge of

the language of ordinary experience.'' ' the theory is not

identicCal 'ith its cor.ciin, accorl:. to Lridgnman's view:. Let

s next n-ot- t.."c i:.... rules o : co..lete correspondence

b-r..een the theory ar.c the phenimea -o be described. To demand

one-to-one correspondence wculd entail a misguided

conviction of the c "anic similarity of
r.athecma-tics ad -" inal experience. In fact
th. ...h..t.. cal -rcctu-ue has an infinitely
Zater co.:,._:.i'y -thn the phsical structure
with -.hich i- ds . c:-:cec for a rew
isolated singular points [we] r .- .- the
entire mathemctica_ stiu-rure ;o a .. .tly
domain with no physical relevance.

Th -aic theory, with its value as an efficient calculating device,

and the (onclusions drawn from it, are separate and distinct entities.

They are linked together by a rulcbook or text (usually not explicitly

written down) which. functions to distinguish between implications that

have physical counterparts, and i:plicarions that seem to assert

conclusions kno.n not to cccur physically. The mcre advanced physical

theory has become, the greater the proportion of the formalism that

must be rejected. In view of this trenc, it would probably seem

incorrect to Bridgman to assert th ct the parts of the formal theory

lacking empirical significance must be jettisoned cr merely tolerated.

7 i ., p. 60. d., 16.
.,p. 60. d16.

.,'ael brouLgh ou. a -..l-.- c p..ysiccl theory when

n, statd that the cctplexit, cf -th, _.. ls it to describe a

,'ider range of ph_-nccna -th.. wc- p ss-lle if every theoretical

tcr. h, a physical ccunr.'rprt. : : s, Bridgman's distinct

views on corresoonderce aire worth discussing. If the . enor-

mously greater wealrh of possibility among r-e structures of,.matics than in physical models which we can visualize" is to

be e>xloit.c, than the theorict must no-: concern himself with

ttchinj erpirical s.r.ificnc -o agm~ nt of his th.ory.

_'.deed he does well not to attecmp to erect cn idealized physical

mo 'l for his theory. Physical models the-selves bear but imperfect

co-respondence with real physical systems, so nothing is lost by

bandoninr. them in favor of -he much more flexible mathematical

theories. The theory itself is then quite separate from the empiricLl

relationships which it establishes. Correspondence between the formal

theory and its physical conclusii..s may be established by . any
sort of arbitrary correspondence."' This is what Hertz meant when

he said zhat "a belief in Maxwell's theory of light meant nothing more

r.nd nothing less than tha- the observable measurements agreed with the

partial differential equations of :-a::well." There is no ques-ion of

attributing physical significance to the internal structure of the
t-. ory.

9- O.
9mid., p. 62. 0 id., p. 63.

"Samuelscn, Papers and Proc edinis of the American Economic
Association, Vol. LTII, No. 2, p. 232.

a L.. -rid.. considers physical tho.-j

to be an extr.:.--i flexible instr.:ent. e mkmes a very clear

dis-:ir.cticnr. .;- : he logical fr.-ew. or of a theory and its

em'- c-l cu....t -z-'t. 3idgman points ca rules of

coresc.nconce :...s si aple;rn; the r-t ir. The form of an

cco;.:pn.yi:;J "texz" thi-h tells .c: -l:.. :ovretical logic applies

in practice. Th--c cGL-- s oon-enc .. only be partial, consistent

wi-ch o- p~ i..cisl> of '..J eC.i.ici...," is recognized by Erid.,:an's

cbsc.vic.; of the ir. -initly cc:.:l::ity of -che ma-chematical

theory th n the physical sa-ructur with which it deals. teorist

is free *:o indicate he factual r-aninS of his theory as he sees it

by supplying appropriate coordinating definitions.

Rationalism and Empiricis.

A number of writers have characterized the a prior tradition

of scientific theory as raticnalis..

Edgar Zilsel explains that rationalism, or classical empiricism,

r,.intained an unusually s-ong hold on investigators in the physical

sciences from the time of Hobbes in the seventeenth century until
.c::..,ll in the nine-een-h. .. uidin idea of classical empiricism

is -.he belief that all significant aspects of reality can be subsumed

under a single principle. According to Hobbes, mechanical explanation

12George de Sntillar. and Edgar Zi-sel, The Develo-ment of
Rationalism and Emairicis. ("Foundations cf the Unity of Science,"
Vol. II, N. 8; C' .- : The University of Chicago Press, 1941).

s '.-.1 ps i.. ., Ho es

distinguished srnsaticns such a C c~~ .- c ste from objective

oua-itics. The lt, not bein cc.. of r.chanical explanation,

,..ore regrcd 3s p-r- of -h- ,u3jcti. .. -ld. Since they couldn't

be r.duceC -co process ccnisi.-s o- otn hey were not part of

the real world; hey have only a sor: cI Crjmbolic or subjective

rclatior.shi, to that aecct cf reali to scientific analysis.

Varirants of K.ces' philosophy ': debated by writers such as

Locke and Lrkeley, but the crucial dcl-inctio.n between the "real"

qualities, such a r moti--, and rh r:.aaly "aptprent" ones, such as

color, became firmly embecced in scientific thought when classical

mechanics received its ultimate for.ulation by :ewtor. The unimagined

success of Newton's forr;.ula-ion provided what was accepted as a

cc..-plete verification of duality in nature between the real and the

apparent. The very co.Dpre.r.nsiveness of Newton-an theory seemed to

vindicate the distinction. If the world is actually constructed in a

way .-;hich can be investigated scientifically, then certainly we could

hope for no more successful discovery than Newtcn's. Nor could one

hope for a more convincing confirmation of that fond hope. It was

natural, therefore, to approach all problems in terms of Newtonian

fr&r.ework, Delievin. that if -reay could be explained, here was the

3Edgar Zilsel, "Problems of Empiricism," The Development of
Rationalism anc Enp ircis. p. 65.


theory to x>ploin Ch..... ..-y i.,.p.r-.... successes followed. To

abandon the belief th-a n_.urz is c, able of comprehensive

ex-planaion by unirled theory bec.u c5f c few seemingly unimportant

phenomena which coul....'t be ;:..d TO fit wouldd indeed have been a

faint-hearted retreat from the great strides so recently accomplished.

Acceptance of the duality of .nture was a much more acceptable alterna-

tive, especially in view of the philosophical background which

supported such a view., the new science could be viewed as a

scientific ver_-ficati-;.. of test p.hilosophical vicrs. Furthermore,

mnere was a long -cradtio. of -elious '. which distinguished

in greater or lesser igrze maLter and it, soul and body. Various

religious systems were built around this type of dichotomy. The

enormous success of mechanical explanation was wedded to the theological

relief in ultimate spiritual realities. Never before had the two

diverse worlds, the temporal and the spiritua-, both so very important,

especially the latter, been so intimately fused into one .-.:- world-vi

Each sphere served and comnlemen ec the other. It is small wonder -0hat

scientists were so confidently com..itted to sounding out their entire

undersrancing of nature acccr'I to the c..chanical plan. The simple,

yet comprehensive ".ewonic: model was accepted as a reflection of the

master-plan according to which nature was believed to be constructed.

A theory of the temporal was accepted as a mod&c for the spiritual;

Model of the "outer world" reflected the "inner world."

15Ibid., p. 68.

I.....e. ze successes wrc2 s. .- w he application of mechanical

.n.ocels, c..d as is chc-ract'i i c. -.-tionalism, the tendency was

to puJh towards the -ll:i:.;. :..iraclL of unity" which research
so promised. ?.. _. .... all nature urder the

extensive na.Iti of :.ach.a:.ic. :l.icn had become the goal of

science. Ultimate exolana icn entailed the demonstration that all

nr,-te operates acccring- to nachanrical principles. Thus the "inner

world" which wcs av, tually in th:t happy day, to be fully mirrored

by the grand, ali-et.brcnl ...c:chnics he- would penetrate every

raal.m and area of experience.

The realm of human u..nerience ws no exception. People hoped

to attain a com.rehensive theoretical grasp of human affairs as

well; social, cultural, ccno..ic activity wculd one day hopefully

receive interpretation equally as peDetrati..; as those given the

physical world. It is not surprising, then, that rationalist

principles ware so widely accepted.
For three centuries mechanical explanation continued to be

a fruitful approach to scientific investigation. Originally, the

ideal had been unified deduction from central principles common to

all problems. Later, explanation ~co"; the form of mechanical analogies

George de Santillana, "Aspects of Scientific Rationalism in
t..d .i'ineeenth Century," The Develcn-ent cf Rationalism and Emniri-
cism, p. 46.

Zilsal, The a-'- -ent Fzticnalis; and Eriricis., p. 93.

of various kinds.18 So long as it remained successful, it continued

to provide the necessary explanation for the "second world behind


Yet it did not remain successful forever.

The Decline of Rationalism

In the second half of the nineteenth century
important physical discoveries resulted in
the breakdown of the mechanical theories of
light, electricity, and magnetism. As
philosophy, since the period of Galileo, had
been influenced by physics to a higher degree
than by any other empirical science, this
physical revolution also reshaped philosophical
thinking and the analysis of knowledge.19

This happened in the 1860's when Maxwell wrote down his equations

for the electromagnetic field. At first he had recourse to a mechanical

model, but as time went on mechanical analogies became increasingly

unconvincing. Despite the dangerous philosophical consequences,

scientists learned that they were better off without cumbersome

mechanical models. "If equations, wherever they are derived from,

present all the observable facts in the simplest way possible, they may

very well fulfill the task of science better than theories attempting
to reveal a 'real' world behind the phenomena.20 Kirchoff, Helmholtz,

and Marh wrote in detail about the implications of the decline of

'de Santillana, The Development of Rationalism and Empiricism,
pp. 22-23.

19Zilsel, The Development of Rationalism and Empiricism, p. 89.

20Ibid., p. 90.