Report on “The Impacts of the Early Twentieth Century Physics and Mathematics Crisis on
Contemporary Economic Discourse”
This paper’s thesis is that several authors, historians of economics, have provided accounts of
the development of economics as mathematical science in the twenthieth century. Those writers
commonly begin with a discussion of the crises in mathematics and physics around 1900. In this paper
the author attempts to “systematize the debate by reviewing the literature produced by the main
authors who address the topic”.
The basic structure of the paper is provided by the author’s recounting of the narratives
associated with Giorgio Israel and Bruna Ingrao, Philip Mirowski, Beaud and Dosteller, Lionello Punzo
and E. Roy Weintraub. The author presents each of their views and attempts to examine them one with
the other. The author is partially confused on many historical points, and absolutely confused on a
number of others.
To begin, consider footnote two on page two: for the author to say that the mainstream
economics accepts rational expectations as an assumption is to deny that MIT houses mainstream
economists. This of course is quite wrong. The author then goes on to discuss Mirowski’s argument
about the connection of mathematics and physics to economics and his view that something changed in
the 1920s. The author does not attend to the fact that all of his other authors quite deny that the 1920s
provided much if any movement in economics to mathematics or mathematical approaches. Indeed,
when Frisch and Fisher attempted to start the Econometrics Society in the 1920s they gave up because
they could not find even 10 individuals around the world who would be interested in such a society. The
author’s reliance on older sources, sources that have been quite discredited over time — like Punzo’s
early discussion — reflect the author’s failure to understand what the dates of the particular scholarly
contributions signify. The last of the author’s references are those of 2002 with Weintraub and
Mirowski. The author does not seem to understand that Leonard’s volume in 2010 and the Israel-Gasca
volume of 2009 quite reject Mirowski’s reading of von Neumann of a decade earlier. The author also
fails to acknowledge that Düppe-Weintraub in their 2014 volume quite destabilize accounts of a
development of competitive equilibrium theory that were provided earlier. It is difficult to understand
why a survey should ignore recent work.
The author has some curious and inaccurate comments arrayed through the paper. For example,
toward the bottom of page 10 the author says that Hicks and Samuelson drew British eyes toward
general equilibrium theory. The author does not seem to realize that Samuelson, indeed the MIT Theory
sequence, quite ignore general equilibrium theory. Samuelson’s foundations was not a development of
general equilibrium theory but rather an attempt to impose an overall optimization framework on many
different kinds of earlier materials, materials written prior to 1939 when Samuelson began his doctoral
dissertation.
The author has many consecutive paragraphs in which he paraphrases arguments of the scholars whose
work he surveys. It is unfortunate though that the author does not acknowledge a number of his
paraphrases are in fact actual quotations from those scholars. Placing a note at the end of those
paragraphs pointing out that the material is drawn from the scholar in question “pages X to Y” does not
relieve the scholar of an obligation to employ quotation marks when the phrasing is not his own.
The central problem of the paper is that the author is totally confused about the idea of
formalization. The author conflates Hilbert’s formalist program with discussions of Gödel, and the
incompleteness theorem with ideas of axiomatization. The move from there to von Neumann and to
Vienna is not well understood by the author. It would have been useful for the author to take more
account of work on Hilbert by historians of mathematics and mathematical philosophy which conclude
that talk of Hilbert’s formalist program makes no sense. Attempts by Corry and Weintraub and others to
link Hilbert’s ideas back to his 1900 mathematics congress paper on unsolved problems does a better
job of providing an alternative way of thinking about this. Historians of philosophy and metamathematics are not in fact good historians.
This can be seen for example in the third paragraph on page 15 when the author talks about the
development of non-Euclidian geometry in the early years of the 20th century. In fact those
developments in mathematics occurred in the last third of the nineteenth century so that the author’s
statement that “at about the same time, development of non-Euclidian geometry…” In a similar vein
the author is confused about the crises in physics. The author mentions a number of times the “new
model based on quantum physics” without stating what this new model consisted of, or how it affected
anything. Is the author referring to black body radiation questions? It also seems the author has this
mixed up with relativity theory which is of course not helpful.
The author’s insistence on the distinction between the “empirical-deductive method” and the
“hypothetical-deductive method” seems quite forced. The author seems to refer to unpublished work
by Bresser-Pereira that employs such a distinction. It is difficult to understand what a difference this
distinction makes. Mill’s arguments about economic logic, and those of John Neville Keynes, as well as
continuous work in the methodology of economics, suggest that these kinds of philosophical ideal types
are not to be found in economic practice.
However the largest set of historically inaccurate statements occurs around the author’s use of
the term “Vienna Circle”. Quite simply, the author appears not to understand that “the Vienna Circle”
(der Wiener Kreis) and the “Mathematical Colloquium” (der Menger Kreis) are entirely different
discussion groups. The former involved philosophers, the latter mathematicians. The discussion of
Hilbert’s formalist program was not part of the Vienna Circle. The mathematical logicians in the Menger
Kreis, Gödel included, von Neumann included as a visitor on occasion, were involved in the
Mathematical Colloquium. Worse the author does not seem to realize that von Neumann had already
set up operations in the United States by 1932 and was no longer affiliated formally with any European
institution.
Section 1.34 on General Equilibrium in the Vienna Circles continues this wrong-headed
argument. The Vienna Circle, though associated with Moritz Schlick and Otto Neurath and others had
no interest whatsoever in general equilibrium theory. It was the Menger mathematical colloquium that
discussed several different papers by Schlesinger and Wald in the early 1930s. On page 19 it was not the
case that “the circle reexamined Walras’ [in any event it was Cassell’s, not Walras’] general equilibrium
model”. The circle did no such thing. And at the bottom of that page, John von Neumann was never a
participant of the Vienna Circle. As a result, the claim at the bottom on the first paragraph on page 20
that “the point of convergence between von Neumann and the Vienna Circle is the proof of logical
consistency of the general equilibrium model” is nonsense, and has been repudiated by Punzo who
wrongly suggested that to be the case several decades ago. These kinds of misunderstandings get
reflected on for example page 22 when the author claims that von Neumann’s main contribution to
economics “…emerged from the discussion of HIlbert’s formalist program of the 1920s…” It is hard to
see what the author describes as Hilbert’s formalist program in any manifestation of the von Neumann
paper, even with the similarity of some elements of von Neumann’s 1927 paper on the theory of games.
These kinds of problems ramify. For example on the top of page 23 the author claims that
Morgenstern’s concerns were associated with creating “a new mathematical language”. There’s nothing
that could be further from the case, as Morgenstern had no such concern - he was an economist not a
mathematician. The concern of course was von Neumann’s. The author then continues with a claim
that von Neumann and Morgenstern’s book axiomatized economics. It is hard to understand whether
the author has even read von Neumann and Morgenstern for such a claim is neither made nor
developed. What was axiomatized in the second edition, at Morgenstern’s insistence, were the axioms
for behavior, not axioms for economics.
These kinds of confusions about formalism, the Vienna Circle, Hilbert’s formalist program,
ultimately make Bourbaki opaque. For example the author in the first full paragraph on page 29 argues
that after Cowles moved to Yale, “which had the biggest economics department in the U.S. at the time”,
the move “helped disseminate Bourbaki’s ideas to other economics departments in the United States
and worldwide.” It is impossible to see how this occurred. First, Yale did not have the largest economics
department – where the author came up with this is a mystery. Second, Debreu was denied tenure at
Yale, because his book, The Theory of Value, was judged by his colleagues there to be insufficiently
connected with economics. Debreu was quite isolated at Yale, talking not with any of the economists
but instead with the mathematician Kakutani.
A larger point emerges from consideration of this paper. I refer to the failure of scholars to take
seriously the notion that the history of economic science cannot be re-written from the ground up every
year. Scholars necessarily rely on the work of other scholars and build upon and correct their ideas. As a
result, rather than ordering the author’s scholars accounts by topic, had the author taken more seriously
the sequence of dates at which they were writing he would have noticed a pattern that earlier claims
had been evaluated, and for the most part, refined or corrected or repudiated in subsequent accounts.
Thus to take Punzo’s accounts as standing in a symmetric position with those of Mirowski, or of
Weintraub’s, is to perform historiographic legerdemain.
It is difficult to understand what contribution this paper claims to make. It is only when one gets
to the final sentence, “this is a subject of our second essay”, that we understand the source of the
author’s difficulty. This article must have been an initial survey of the literature chapter to a thesis or
dissertation. It is not thus a contribution to any historical literature. As a thesis chapter it must have
been constructed to satisfy thesis advisors’ expectations that the author has read background materials
and is familiar with the secondary literature of some question. There is no evidence though that the
author has encountered or read any of the primary literature. As a result, I cannot recommend
publication of this paper nor do I see any path to revision that would make it acceptable for the History
of Political Economy.