Galileo, Smith and the Paradox of Value: The “Connection” of
Things*
Robert B. Ekelund, Jr.
Department of Economics
Auburn University
and
Mark Thornton
Abbott Turner College of Business
Columbus State University
DEPARTMENT OF ECONOMICS
AUBURN UNIVERSITY
NOT FOR QUOTATION: COMMENTS WELCOME
*
We are grateful to Bob Hebert, Bob Tollison, David Gordon and Audrey Davidson for comments on
earlier drafts of this paper.
Galileo, Smith and the Paradox of Value: The
“Connection” of Things
The pearl of the collection [Smith’s Essays on Philosophical Subjects] is
the first essay on . . . the “History of Astronomy.” Nobody, I venture to
say, can have an adequate idea of Smith’s intellectual stature who does
not know these essays. I also venture to say that, were it not for the
undeniable fact, nobody would credit the author of the Wealth of Nations
with the power to write them.
J. A. Schumpeter (1954: 182)
I. INTRODUCTION
The Paradox of Value and solutions thereto, where goods of necessity such as
water and bread are of low value as indicated by a low or zero price and luxury goods
such as gold and diamonds have a high value as indicated high price, lies at the heart of
economic science. The commonly accepted solution to the paradox is that it is a failure
to link marginal utility (demand) to scarcity (supply). The total utility (given scarcity) of
water may well exceed the total utility of diamonds (again given scarcity) but the
marginal utility of diamonds under ordinary conditions would be higher than the
marginal utility of water. This solution, or variants of it, has been known for centuries,
taking form in early European (chiefly Italian) writings on law, philosophy and monetary
matters. Among often-cited progenitors were Bernardo Davanzati (1529-1606), Samuel
Pufendorf (1632-1694), Francis Hutcheson (1694-1746), Daniel Bernouilli (1700-1792),
and Abbe Ferdinando Galiani (1728-1787). Schumpeter even notes that the solution to
the paradox was strongly suggested in medieval literature (1954: 98, 300, 309) and that
1
solutions to it were common in the one hundred years after Smith’s Inquiry into the
Nature and Causes of the Wealth of Nations.1
While the paradox and its solution have often motivated analysis and ideas -- it
was, after all one foundation of the marginalist revolution in economic analysis of the
1870s – several interesting puzzles remain. First, the origins and meaning of the paradox
have not been fully plumbed. While all of the above writers (and, indeed, all that we
could find) couched the paradox and its solution in social and economic contexts (the
latter being mainly in monetary theory), we have discovered an interesting and important
statement of it in one of the central works of the most important scientist of the
seventeenth-century Italian Renaissance, Galileo-Galilei. When examined in the context
of Galileo’s scientific assertions, the meaning of the paradox and its solution takes on an
important implication for its most famous statement in economic literature – that of
Adam Smith.
The diamond-water paradox, or so the lore of economic thought goes, was the
puzzle that diverted Adam Smith and the classical economists into the labor theory of
value from which it did not recover for more than a century later when the Marginalist
Revolution occurred (Kauder 1965).2 While value theory may have been critically
diverted in this manner, Smith’s so-called “grand error” has been interpreted less
1
The paradox had long been solved within the Scholastic tradition. Pierre de Jean Olivi (1248-98) of
Florence solved the paradox and wrote two influential books on economics (Rothbard 1995: 61). Further,
the work of the Spanish Scholastics was influential in Italy before Galileo began his teaching career and it
was influential on Galileo himself (Wallace 1984).
2
This view is of course an exaggeration since “marginalism” was alive, healthy and progressing in French
engineering and other literature. Cournot, while not a marginal utility theorist, used marginal analysis of
cost and revenue to establish a price theory of markets and market structure in 1838 and Dupuit (in 1844)
and a plethora of engineers did the same throughout the 19th century. Emil Kauder’s interesting history of
marginal utility (1965) downplays Cournot and Dupuit’s roles in the development of value theory, extolling
the later Austrian contributions instead.
2
critically. Indeed, it has been argued (Robertson and Taylor 1957) in response to Kauder
(1953) that Smith of the Lectures actually solved the paradox but returned to it in the
Wealth of Nations in order to emphasize the longer run aspects of value wherein costs,
chiefly labor costs, determine a long-run natural price rather than a market price. While
we do not necessarily dispute this proposed resolution, we offer a completely different
assessment of the paradox and Smith’s two statements of it, as have others.3
The purpose of this paper is to show that the scientist Galileo was aware of the
problem of the paradox of value and understood the solution to the paradox more than a
century and a half before the publication of Adam Smith's Wealth of Nations. Further,
we will suggest that the scientific context of the solution in Galileo’s Discourses was
exactly relevant to Smith’s quest to find logically suitable and useful measures of value.
Not least, we believe that it is at least probable that, in addition to a keen knowledge of
other writers and the scientific-philosophical literature, Smith was aware of Galileo's
solution. Galileo was a man that Smith without doubt admired since he had
demonstrably read and digested the great Italian’s analysis in the course of writing his
own History of Astronomy. We argue, with evidence from both Galileo and Smith, that a
plausible explanation (other than carelessness or stupidity) may be offered for Smith’s
presentation of the paradox in the Wealth of Nations and that there is at least a probability
3
In an interesting interpretation of the so-called paradox, Samuel Hollander argues that there is no paradox
to solve! Hollander suggests that Smith’s “unhappy contrast” of the “term ‘value-in-use’ must be
understood in the narrow sense of biological significance and not in the economist’s broad sense of
desirability” (1975: 315). Hollander argues that the physical properties of goods are irrelevant for their
exchange value and that “it is solely this category of utility which Smith rejected as a value determinant
and, indeed, as a necessary condition of exchange value.” (1975: 315). Rather, Hollander believes that
Smith did account for utility and scarcity as necessary conditions for exchange value and in the “traditional
manner” (although of course Smith did not provide a theory of value in marginal terms). We are in
agreement with Hollander on these points and also conclude, with him, that there can “be no question of the
3
that it was not the basis of Smith's labor theory of value. (Whether or not value theory
was shunted onto an unproductive tract is, of course, not an issue addressed here).
II. GALILEO THE ECONOMIST
Economists have long recognized the genius of Galileo, but this recognition has
been of his contributions to physics, mathematics, and scientific method. No one to our
knowledge has mentioned his understanding of purely economic matters. In addition to
being highly affluent by academic standards of his day or ours, a successful businessman,
and a keen entrepreneur, Galileo exhibited a clear understanding of economic matters in
his writings.4 In particular, he knew of the paradox of value and its solution.5
Galileo may be best remembered for inventing the telescope and dropping metal
balls from the Tower of Pisa, but his most important and notable contribution was his
Dialogue Concerning the Two Chief World Systems--Ptolemaic & Copernican (1953
[1632]) in which he demonstrated the superiority of the theory of Copernicus that the
Earth revolved around the Sun. It was this book, the eternal cause celebre for the
necessity of free scientific inquiry, which was censured by the Inquisition of the Roman
Catholic Church.
Here, within an important passage in which the understanding of life itself, which
is "corruptible" or ever changing like the earth, is distinguished from mere existence
(which is stagnant and dormant like the moon), Galileo through a character based on his
ultimate ‘subjective’ orientation of Smith’s argument and the choice of index thereof, not evidence to the
contrary” (1975: 315). Also see Hollander (1973).
4
In the Dialogues he discusses the inequality of resources and its implications for comparative advantage
(p. 102).
5
Sixteenth century Europe was a “new economy” of entrepreneurship based on expanded international
trade, new technologies, and new business practices such as double-entry bookkeeping. According to
4
friend and student explains the solution to the paradox of value. He does so in a very
animated manner that lacks any sympathy for those who remained captured by the
paradox. He begins by venting his frustration against this "popular reasoning" and noting
that “The deeper I go in considering the vanities of popular reasoning, the lighter and
more foolish I find them. What greater stupidity can be imagined than that of calling
jewels, silver, and gold "precious," and earth and soil "base"? (1953: 59).
Then proceeding from this condemnation, Galileo introduces the economic
concept of scarcity and illustrates its role with the imaginary construction of a world with
equal amounts of soil and jewels.
People…ought to remember that if there were as great a scarcity of soil as of
jewels or precious metals, there would not be a prince who would not spend a
bushel of diamonds and rubies and a cartload of gold just to have enough earth to
plant a jasmine in a little pot, or to sow an orange seed and watch it sprout, grow,
and produce its handsome leaves, its fragrant flowers, and fine fruit. (1953: 59)
Galileo then goes on to diagnose, criticize and even psychoanalyze the "vulgar" men who
are mesmerized by the paradox of value:
It is scarcity and plenty that make the vulgar take things to be precious or
worthless; they call a diamond very beautiful because it is like pure water, and
then would not exchange one for ten barrels of water. Those who so greatly exalt
incorruptibility, inalterability, etc. are reduced to talking this way, I believe, by
their great desire to go on living, and by the terror they have of death. They do
not reflect that if men were immortal, they themselves would never have come
into the world. (1953: 59)
His condemnation follows in which he suggests that the "vulgar" deserve what
their "popular reasoning" would logically lead them to desire. As he put it “Such
men really deserve to encounter a Medusa's head which would transmute them
into statues of jasper or of diamond, and thus make them more perfect than they
are” (1953: 59). The passage is concluded with a comment from the character
Machamer (1998:10) “Galileo made much of his money while in Padua by teaching practical mathematics
5
representing Galileo himself seconding his student's motion: “Maybe such a
metamorphosis would not be entirely to their disadvantage, for I think it would be
better for them not to argue than to argue on the wrong side” (1953: 59).
It is not difficult to imagine what Galileo means by these statements. He provides
the answer, placing the following marginalia bluntly stating his conclusions next to the
text:
•
Earth nobler than gold and jewels
•
Scarcity and plenty make things costly or cheap
•
Incorruptibility extolled by the vulgar from fear of death
•
Detractors of corruptibility deserve to be turned into statues
It is clear that Galileo was aware of the issue of the paradox of value and it is equally
clear that he understood the solution to the problem. Price depends on scarcity and those
things that were "cheap as dirt" still hold a greater value, in total, than those things that
are considered "precious." It is equally clear that he was highly intolerant of those who
did not or refused to understand this solution. Like Galiani’s later solution (Schumpeter
1954: 301), Galileo’s explanation lacked a concept of marginal utility but the concept of
relative scarcity came close to it. “Usefulness” or utility in relation to available quantities
of goods explains relative prices and value.
The Context of Galileo’s Statement
Galileo’s solution, while novel and (as far as we know) hitherto unrecognized, is
even more interesting in our context when his reasons for providing it are examined. The
paradox solution was not simply tangential in the conversation of the Dialogues; rather it
to the young aspiring business types of many nations.”
6
was a key issue in his central theme – an exclamation point on the issue of methodology.
Galileo, reasonably early (in 1611) and under the clear influence of Copernicus, was
convined that the Aristotelean-Ptolomaic (A-P) view of the earth in relation to the
universe was incorrect. The A-P universe was static, unalterable and “incorruptible,” as
Galileo was taught by his Aristotelean-influenced Jesuit philosopher-teachers. In the
Dialogues (on the first of four “days” of debate) Galileo set the stage for exploding this
order by discussing change. He – immediately prior to his solution to the water-diamond
paradox -- argued that astronomical change was as real and relevant as were the very
obvious changes experience on Earth, noting that “if the generations and corruptions
occurring on the very globe of the sun are so many [and were readily observable], so
great, and so frequent, while this can reasonably called the noblest part of the heavens,
then what argument remains that can dissuade us from believing that others take place on
the other globes?” (1953: 58). Dissenters argued, within a terra-centric view of the
universe, that heavenly bodies beyond the earth and moon underwent a “fixed” kind of
change – uniform motion in a circle and that this changelessness constituted “perfection.”
As all school children know now (thanks largely to Galileo and his telescope), the earth
itself revolves and it and the planets revolve around the sun.6
The paradox therefore serves to convey a key scientific point, but we are not here
concerned with Galileo’s contributions to astronomy.7 The point we wish to make is that
Galileo’s statement of and solution to the paradox of value is that it illustrates Galileo’s
method and theory of inquiry. Galileo wanted to use both induction and deduction (and
6
Galileo’s discovery was supported with evidence from tidal changes on Day 4 of the Dialogue.
7
An excellent introduction and “companion” to Galileo’s works in astronomy, mechanics, mathematics and
empiricism is the edited volume by Machamer (1998)
7
hunches and common sense) to establish the connections between things. He sought
coherent explanation of phenomena, no doubt to overcome the scientific inertia of the
academic community and, more importantly, opposing church interests.8 Albert Einstein,
in his introduction to the Dialogues, expressed Galileo’s method and style of inquiry
perfectly when he noted that the controversy in Galileo was not over “empiricism vs.
rationalism.” Rather he criticized Aristotle only when empirical findings were
incompatible with deduction. In Einstein’s terminology, Galileo’s “endeavors are not so
much directed at ‘factual knowledge’ as at ‘comprehension.’ But to comprehend is
essentially to draw conclusions from an already accepted logical system” (Einstein in
Dialogues 1953: xix).9 This opinion, as we will see, was the theory of inquiry adopted
specifically by Adam Smith as well.
III. ADAM SMITH
The vagaries, influences and origins of Adam Smith’s multiple theories of value
have been the subject of debate for economists for well over two hundred years.10 We
suggest that a re-visiting of Smith’s failure to solve the paradox in the Wealth of Nations
and his dichotomy between use value and exchange value is of interest in the context of
Galileo’s theory and method. In the (in) famous words of Smith:
The word value . . . has two different meanings, and sometimes expresses the utility of
some particular object, and sometimes the power of purchasing other goods which the
possession of that object conveys. The one may be called “value in use”; the other,
“value in exchange.” The things which have the greatest value in use have frequently
8
It is important to note that, while Galileo had particular church interest groups aligned against him,
notably a group of Roman Jesuit philosophers, he had defenders within the church as well, for example,
Cardinal Robert Bellarmine.
9
The myriad theories of inquiry propounded by Galileo are discussed in Koertge (1977) who casts
Galileo’s methodology in the context of accidents and essences.
10
See Windfrey (1993) where Smith’s discussion of value is placed in light of the Aristotelian tradition.
Ironically, the paradox was also solved within the Scholastic branch of that tradition (see note 1).
8
little or no value in exchange; and on the contrary, those which have the greatest value in
exchange have frequently little or no value in use. Nothing is more useful than water:
scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce
any value in use, but a very great quantity of other goods may frequently be had in
exchange for it (1776: 28).
This statement – perhaps the most iconic in the entire history of economic theory
– has been given multiple interpretations as to effects and intentions. By some, it is
passed over as an aberration or as a carelessness of a great thinker.11 By others (e.g.,
Kauder 1953; Schumpeter 1954), it along with other statements on value and
appropriation by Smith, contains the allegedly evil seeds of the labor theory of value as
propounded by Ricardo and Marx. In this latter view economic analysis was not saved
until the paradox was solved in early neoclassical economics. It may well have been that
Smith believed the “solution” to the paradox was, by 1776, commonplace and that there
was no need to repeat it. All admit that Smith made statements suggesting a labor theory
of value (for the “rude” state only) and that, after bringing in capital and land, he
developed his famous long run cost of production
“theory” of value.
All of this is familiar terrain, religiously visited by historians of thought over
many generations (e.g. Ingram 1967 [1888]: 92-95 et passim; Ekelund and Hebert 1996).
But the underlying tension presented by Smith’s famous statement of the paradox in the
Wealth of Nations has not been fully aired. In an important and interesting paper
published in 1957, ideational historians Robertson and Taylor remind us of an
uncomfortable fact – that in Smith’s Lectures of 1762-63, preserved by a student and
clearly foreshadowing the Wealth in outline and numerous details, a pristine statement of
11
Stigler (1976: 1204) does not assess Smith’s statement as a failure at all, rather as a simple calling of
attention to a marginal utility theory.
9
the solution to the paradox is set out. From the outset of his discussion of “Cheapness or
Plenty,” a title apparently given by Cannan, Smith reveals a clear understanding of the
major forces affecting value. As he notes “Cheapness is in fact the same thing with
plenty. It is only on account of the plenty of water that it is so cheap as to be got for the
lifting; and on account of the scarcity of diamonds (for their real use seems not yet to be
discovered) that they are so dear” (1964 [1896]: 157). In his introduction to the Lectures
Cannan suggested, as also noted in Robertson and Taylor, that is was most curious how
the first two sections on value “were omitted from the Wealth of Nations, and the fact
will be regretted by those who ask for a theory of consumption as a preliminary to the
other parts of political economy” (1964 [1896]: xxvii). Cannan’s opinion was certainly
not an overstatement as things have turned out.
The genuine and continuing mystery relating to the paradox is why these sections
with the solution were omitted (by Smith?) from the Wealth of Nations. There is plentiful
evidence, much of it given by Robertson and Taylor and others that Smith fully
understood the solution to the paradox from Francis Hutcheson (who himself learned it
from Gershom Carmichael (1672-1729) and Samuel Pufendorf).12 As to the “why” of
Smith’s failure to put his own solution in the Wealth of Nations, Robertson and Taylor
offer a number of possible reasons. A basic disdain for “subjective” analysis with the
view that utility provided only vague generalization is suggested (1957: 191). There is of
course the caveat that Smith obviously understood the importance of subjective utility in
his theory of exchange (some net “benefit” is necessary). More importantly, Robertson
and Taylor note Smith’s “stress on there being a necessary connection between the
12
Skinner (1995) develops the possible lines of Pufendorf’s influence on Hutcheson and Hutcheson’s
impact on Smith as regards value theory.
10
apparently independent sets of prices comprised under his classification of ‘natural price’
and ‘market price’” (1957: 192). This “necessary connection” was formulated in both the
Lectures and in the Wealth of Nations, although in the latter he clearly stressed that
market price was determined by supply and demand while natural price was regulated by
the cost components of wages, profits and rent in their average or “natural” states. In
sum, the Robertson and Taylor view is that “in the Wealth of Nations, without
abandoning the explanation of market price via utility and scarcity inherited through
Hutcheson, Puffendorf and the Scholastics, he concentrated upon what now appeared to
him to be the more important phenomenon of ‘natural price’ or normal value, for which
the traditional utility approach appeared inadequate” (1957: 193). GDP or national
income is the total contribution of these three factors (wages, rents and profits) in Smith:
they also form the basis of the calculation of the wealth of the nation and the source of
the functional distribution of income.
We accept the central line of this reasoning as far as it goes, at least as a possible
explanation for the difference in the treatments of the Lectures and WN. However, we
stress that the origin and importance of Smith’s willingness to simply state the paradox in
the Wealth of Nations might have an alternative, though certainly complementary,
explanation.
IV. SMITH AND GALILEO
Galileo’s work in astronomy, motion studies and physics was one of the most
notable scientific achievements of his time. By the eighteenth century his achievements
were highly valued in philosophical circles. It not only reintroduced Copernicus's theory
that the Earth revolved around the Sun and that the earth and other planets rotated and
11
was held in motion as they rounded the Sun, it proved it. Meanwhile, in parallel fashion
Galileo clearly understood the role of scarcity in his explication of the paradox of value
making the important point that relative values changed and that “earthly” social matters
were mutable and dynamic in nature.13
While the Church banned the publication and distribution of the Dialogues and
suppressed Galileo’s later works in Italy, Church censorship did not stop its spread. In a
familiar turn of events, censorship might very well have enhanced Galileo’s reputation.
The copies of the first printing of the Dialogues skyrocketed in price and the book was
quickly translated into other languages including English and published in other
countries. It was adopted as a standard textbook in non-Catholic countries including
England and Scotland. But we do not have to guess about Smith’s acquaintance with
Galileo. Among the very few manuscripts that Smith did not have burned were three
essays subtitled the History of Astronomy, the History of Ancient Physics, and the History
of the Ancient Logic and Metaphysics with each sharing the title of The Principles which
lead and direct Philosophical Enquiries. These essays form a core of the posthumously
published book, Essays on Philosophical Subjects.14
Smith’s posthumously published essays are essentially philosophical and
methodological in character. He was interested in the principles of establishing a system
of thought and, in this context as much as in that of astronomy, read and digested
Galileo’s ideas. Indeed, there are a number of references to Galileo, extolling his
contributions to astronomy and physics, but also paying a great deal of attention to
13
Aristotle and his followers of course recognized this point about change in the sublunary world.
From Edinburgh on April 16, 1773 Smith wrote to David Hume (before the publication of the WN, a
document he had in his possession) that he wanted all other manuscripts destroyed except “a fragment of a
14
12
Galileo’s methods. As an ardent admirer of scientists and philosophers, such as Newton,
Kepler and Descartes, Smith nevertheless stuck to Galileo’s explication of method in his
History of Astronomy. He believed, in short, that the “task of establishing a system of
thought must be conducted in terms of the combination of reason and experience –
although even here he was quick to associate this definition of the term ‘method’ with
Galileo rather than Newton” (Raphael and Skinner introduction to Smith 1982: 1). In his
History Smith noted that Galileo had answered the “incohereces” of Copernicus by
explaining the nature of the composition of motion, by showing, both from reason and
experience, that a ball dropt from the mast of a ship under sail would fall precisely at the
foot of the mast, and by rendering this doctrine, from a great number of other instances,
quite familiar to the imagination, took off, perhaps the principle objection this had been
made to this hypothesis [the Copernican system] (Smith History 1982: 82).
Clearly, it is Galileo’s method of science that attracted Smith for, in a comparison
to Kepler (for example), Smith cites Galileo’s “taste,” “order and method” and, most of
all, a “passion for discovering proportions and resemblances betwixt the different parts of
nature” (Smith History 1982: 84). It was not Galileo’s method to rely only on
mathematical reasoning – rather he sought as Smith did, the “connection” of things. His
great advance was in the method of consistently using “stringent ‘thought’ experiments”
as the essential part of the training of scientists (Fermi and Bernardini 1961: 130). In the
words of Wightman (Smith 1982: 19-20), the confused state of astronomy in the first half
of the seventeenth century was just such to give emphasis to “Smith’s ‘principle’ that
discovery is the fruit of a search for a ‘connecting chain of intermediate objects to link
together . . . discordant qualities’ (Smith History 1982: 91)”. In the context of astronomy,
where Galileo’s logic concerning motion paved the way for Newton’s universal law of
great work which contains a history of the Astronomical Systems that were successively in fashion down to
the time of Des Cartes” (Mossner and Ross 1977: 168).
13
gravity and astronomical applications, Smith disdained earlier ad hoc additions to
mathematical conclusions – in particular Kepler’s argument that “radiation” of the Sun
maintained the revolution of the planets at varying speeds. Galileo had successfully
challenged the dogma of the past and presented a new and “wonderful” knowledge that
surprised and enlightened the world. In short, this Galilean method was the basis for
Smith’s own theory of inquiry.15
It remains to link Smith’s Galilean theory of inquiry and acquaintance with
Galileo’s works to his own supposed “grand gaffe” of the replication of the paradox of
value in the Wealth of Nations. Incontrovertibly, Smith’s aim in the Wealth of Nations
was to uncover and to at least provide a thought process for measuring the determinants
of national wealth and income. We also adhere to the view, apparently discovered by
Robertson and Taylor, that Smith completely understood the short-term determinants of
prices in markets as he taught them in his Lectures (of 1762-63) but that in Wealth of
Nations he abandoned or at least downplayed “utility” and sought a connection between
market and natural price.16
However, we go even further. Smith’s attention to Galileo
and his obviously close reading of the latter’s works suggest an expanded interpretation.
First, while we have no direct evidence for maintaining that Smith actually read
and digested the passage clarifying the paradox that we have cited from Galileo’s
15
We are not the first to note this connection (see Lindgren 1969: 902 n. 8). Elsewhere Lindgren notes that
Smith “adopted language, not mechanics as the model of inquiry” (899).
16
A number of earlier economic theorists and writers were extremely wary of using utility in an objective
“scientific” theory of demand and markets. In his famous Recherches, for example, Augustin Cournot
notes critical differences betweeen “the fixed, definite idea of value in exchange, and the ideas of utility
which everyone estimates in his own way” (1838: 5). Further he charges that opinions concerning utility
“are questions of valuation, and not questions resolved by calculation or by logical argument” (1838: 5).
Cournot went on to establish a price theory based on a kind of empiricism (that demand curves slope
downward and to the right is a fact of common experience). It would appear that Smith was a skeptical
about the use of utility.
14
Dialogues, his attention to Galileo in the History and the seemingly representative
collection of Galileo’s works in Smith’s library suggest as much.17 It should also be
remembered that Smith was undoubtedly educated in this “solution” by Hutcheson and
others (possibly prior to the Lectures and in advance of Wealth). The History was written
before 1758 and possibly drafted prior to 1750 and the Lectures were taken down in
1762-63 so that Galileo’s precedence is clearly possible, but a direct link from Galileo to
Smith on the paradox of value is conjecture and likely to remain so. Rather we wish to
maintain that it is Smith’s methodological inheritance from Galileo, in addition to the
coincidence of the statement of the paradox, which helps explain his treatment of the
paradox in the Wealth of Nations.
Smith was clearly seeking the “connection of things” in his explication of “value”
in the Wealth of Nations. In particular he was seeking the connection between the market
value of goods and services in one period to market values in other periods. Utility was
insufficiently constituted (at least at that time) to use as some “invariant” measure
connecting aggregate values (GNP, GDP) between periods. The calculation of value, as
Schumpeter reminded us (1954: 311-12), is not an explanation for or a theory of value.
As Schumpeter argued, Smith was in search of a numéraire, a commodity in terms of
which all other items could be valued – and did not construct a labor theory of value at
all, that is, one with which to explain relative prices.18 Therefore the so-called “labor
17
Bonar reports two sets of Galileo’s works in Smith’s library, a two-volume set published in Bologna in
1656 and a four-volume set published in Padova in 1744 (Bonar 1966: 40).
18
Schumpeter argued that, at least in principle, there can “be no objection to this decision [i.e., to make
labor the numéraire], which in itself no more commits him [Smith] to a labor theory of value than the
choice of oxen for numéraire would commit us to an ox theory of value” (1954: 310). Schumpeter,
however, goes on to note the confusing manner in which Smith tried to motivate that decision.
15
command” theory was not a theory of relative prices or was it ever intended to be. It was
a link, albeit an unsuccessful link, between intertemporal aggregate values.19 It was a
“thought experiment”, as was Galileo’s suppositions concerning motion and the
positioning of the planets and an attempt to find the “connection” of things. From a
microeconomic perspective, moreover, an expanded “labor theory” – expanded to include
returns to capital and land – was the supposed “regulator” of prices in the long run to
Smith.
Numerous observers have pointed out that both the “labor command” and “cost of
production” theories contain serious logical errors and gaps as theories of value (see, e.g.,
Schumpeter 1954: 310-311). The latter suffers from the fact that cost itself is a function
of the quantity of goods and services demanded and, ultimately, their “utility”. The
former theory to “connect” values over time suffers both from measurement problems
(toil and trouble is not the same as labor time, etc.) and from the problems we associate
with any index number. Nevertheless, we maintain that Smith did not restate his
resolution of the paradox of value in the Wealth of Nations because he was there aiming
at the larger issues of economic growth measured by changes in nominal GDP. He never
denied that scarcity and “utility” determined market values, values measured in terms of
prices. Rather, his emphasis in the Wealth of Nations was different and his quest to find
the “connection of things,” a quest due largely to his adoption of the methods of Galileo,
led him to his now-famous discussions of labor at the center of the value(s) question.
V. CONCLUSION
19
Smith failed to recognize that the opportunity cost of labor fluctuated in exchange value just like
everything else.
16
This paper shows that Galileo solved the paradox of value in the course of a key
scientific discussion in his most important work. Further we have attempted to connect
the resolution and the methods of Galileo to the most famous statement of the paradox in
economic literature in Adam Smith’s Wealth of Nations. We have suggested that Smith’s
bald statement of the paradox in Wealth, contrasting to a careful and correct statement of
the determinants of market values in his Lectures, hinges on a search for a “connection”
between intertemporal values within the economy. As such we expand on the RobertsonTaylor view that Smith did not repeat the “short-run” solution but rather was looking for
a less transient, longer-run source of value. We argue that Smith was responding to
Galileo’s method of inquiry and that his value discussion in the Wealth of Nations was an
attempt to find the interconnections of value in one period with those of other periods.
He failed in this attempt and the solutions to the microeconomic problems of value were
some distance away in English political economy, as were serious attempts to develop
index number theory to calculate values intertemporally.20 We present a methodological
solution to the so-called puzzle of why Smith did not attempt to “resolve” the paradox of
value in the Wealth of Nations.21
20
W. S. Jevons’ later concerns with marginal utility and value were accompanied by important and early
work on index numbers in calculating aggregate values. Earlier English writers were also on the track of
notions of how marginal utility might be related to value. For a case presented for William F. Lloyd (c.
1833), see Seligman (1903: 363).
21
Young maintains (1995) that the source of Smith’s long-run “opportunity cost” theory of value (the
natural prices of the agents of production) was in his views on jurisprudence (see Lectures) wherein “injury
to property” is seen as analogous to such costs. There are other philosophically based views. Lindgren
focuses on Smith’s theory of inquiry (one compatible with our views) and concludes that Smith’s view on
the subjective nature of utility stems from his understanding of Hume’s particular (non utilitarian or
modern economists’) view of utility – that it is dependent on the evocation of an object that actually
produces utility rather than the object itself. This view sets up a confusion when men study human
behavior from a distance apart from the motivations of those whose interests are actually at stake.
Lindgren concludes that this led Smith to believe that the commercially ambitious were confused, a
situation that leads value in exchange to be independent of value in use. Lindgren notes that “the ‘paradox
17
We wish to make a final point concerning Smith’s so-called shunting of the
theory of value down “unproductive” avenues for a hundred years. While it is
undoubtedly correct, and here we agree with Schumpeter, that Smith was far less than
clear concerning the role of labor (and composite “factors”) in relation to value, there are
questions that should be addressed in the development of value theory in England up
through Jevons. While Smith's statements undoubtedly inspired Ricardo and Marx, why
were they virtually the only ones of the major classical thinkers to be captured by lure of
the labor “theory?” Why were Malthus, Senior, Mill and Say not drawn to place labor
center-stage in the theory of value?22 Finally, why were Ricardo and Marx not informed
by the host of writers who “solved” the paradox both before and after Smith’s Wealth of
Nations was published?
Lastly, there are and will likely always be a host of unanswered questions
concerning the sources and progression of Smith’s view on value theory.23 Further,
respecting the paradox of value, there will remain “a fascinating aura of mystery as to
why the most crucial elements in these ideas were hidden in the background of the
Wealth of Nations almost as though by some deliberate process of censorship”
of value’ is an accurate report of what Smith took to be the mentality of the commercially ambitious. It is
that mentality and not Smith’s analysis of it which is paradoxical” (1969: 912).
22
Malthus emphasized demand as a component of value, and Mill’s 1848 analysis of demand and supply as
co-determinants of market values left little for some later writers to do: see Ekelund, Furuboth and Gramm
1972.
23
An appealing tack in explaining Smith’s discussion of value may be the following: After the
Reformation, the papacy and the Catholic Church (at least in some countries, including England) provided
no divine direction and this was particular true in emerging democratic countries. Thus a vacuum was
created on how society was going to be run. Smith fully understood that the self-interest of the commercial
class, with a mercantile-interest group cover, was an unproductive avenue for society. West (1990), for
example, has made clear that there were two invisible hands, one dealing with private self-interest and
another within the context of self-interested politicians. Analogously, Smith supported private self-interest
with a constrained political sector. His explanation of markets and prices concentrated on labor as
representative of Protestant, democratic and Calvinistic society rather than the rent-seeking societies that he
had observed in Europe (centrally the Physiocratic conception of land in France).
18
(Robertson and Taylor 1957: 188). We have here only attempted to demonstrate a
potential role for Galileo in the value discussion of Smith. As such, our account adds one
more twist to the mystery.
19
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21