THE STRUCTURE OF ECONOMIC
AND THE GOALS OF
ROBERT GEORGE FABIAN
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
TO MY PARENTS
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
iI. AN EMPIRTICAL PRI:CCIPL FCR DEDUCTIVE THEORY
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
III. AN ALTERNATIVE EMPIRICAL P -I'?ILE
FOR DEDUCTIVE ECONOMIC THEORY . .
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
IV. THE CHOICE OF PRI::C..?LS: EVIDENCE
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
V. PROBLEMS IN THE HISTORICAL DEVELOPMENT
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
VI. THE THEORETIC.._ SYSTL.. :., ECONCMICS:
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
VII. PROBLEMS OF DEDUCTIVE ANALYSIS IN
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
VIII. A BRIEF FESTATE"E.NT .. ..
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
BIOGRAPHICAL SKETCH . . . ... . 199
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
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
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 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-
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
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.
AN EMPIRICAL PRINCILE FOR DEDUCTIVE THEORY
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
in the sense of DEMONSTRABLE RECURRENCES AN9
REGULARITIES OF ACTUAL AND POSSIBLE EVENTS.
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
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
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 follo:.in; :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),
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 expri.er.tal
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 wh.ch
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
AN ALTERNATE L-,FIRICAL PRINCIPLE FOR
DEDUCTIVE ECONOMIC THEORY
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.
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.
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
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.
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 t.is approach: to theory as bare formalism
"concai.-.ing 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,
so doi.. t--y cefi.e t..i r.nc; 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. R-trictive.ne=s 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
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 Schrodir.er 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
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.
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 r.nc ,..-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.
THE CHOICE OF ?RIC2-?LL: EVIDENCE FROM THE LITERATURE
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, ).
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
::.ni-ical :,.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,
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 dra.mn 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
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
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),
..s hap..no _.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
h.ve been applying. Referring to the law of diminishing returns
as one of many "empty economic boxes" identified by Clapham,
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.
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 iner.tic.al 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 w.at 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 aref-rer.es, 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
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
ordir.al 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. Impou..de 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 cha..ge. 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.. ot..cr 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 ..cr. seiously deficient empirical
s-atc.er.t. Likewise, t;. implicit assertion that firms have no
c-ozr.i-z-io.al problems (.ince the theoretical firm is not an
o=Canization) is gross empirical irnvlidizy.
We have already se~n,, hoth.er, 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 econo.ni is
likely to concrntra- t on thv ele.nr.'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),
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.
44Fritz Machlup, "Marginal Analysis and Empirical Research,"
The Am.rican Econcmic P.evieu, Vol. XXXVI, No. 4 (September, 1946),
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.
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
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
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.
PR03LE:.S IN THE HISTORICAL DEVELOPMENT 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- c..ly 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 5ridm.cn. 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 rprcaci.ng 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 asu...in .. intuitive knowledge of
the language of ordinary experience.'' ':.us 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
m.th,.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
9mid., p. 62. 0 id., p. 63.
"Samuelscn, Papers and Proc edinis of the American Economic
Association, Vol. LTII, No. 2, p. 232.
a co..lc 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 rl.at 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 gr.cr 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 ...n.able 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. Ir.cd, 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 waro.ly 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,
19Zilsel, The Development of Rationalism and Empiricism, p. 89.
20Ibid., p. 90.