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History of Political Economy 32.3 (2000) 441-471
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Negotiating at the Boundary:
Patinkin vs. Phipps
Ted Gayer and E. Roy Weintraub
Economists and mathematicians themselves do not fully understand the way they have negotiated the more or less rigid boundary that separates their disciplines. Scholars in both fields have contested the role of mathematics in economics and the legitimate place of mathematics in economics; moreover, the uses that economists have made of mathematics are many and varied and have hardly been stable.
Mathematical economists often claim that one can translate between mathematics and economics. Following his mathematical mentor’s mentor, J. Willard Gibbs, Paul Samuelson claimed in Foundations of Economic Analysis that “mathematics is a language.” This belief in translation is often accompanied by a realist epistemology that posits that (1) the economy exists autonomously; (2) it can be represented by ordinary language propositions; and (3) the language of mathematics is useful in translating and operating with those propositions characterizing that autonomous existence. An implied corollary of this position is that any disagreement between an economist and a mathematician on the nature of a mathematical proof is due to a misunderstanding of the assumptions or the logical reasoning of the proof. And any disagreement on the economic implications of the mathematical proof is due to mistranslation or a lack of understanding of the underlying economic reality. [End Page 441]
Nevertheless, a number of studies document communication failures between mathematicians and economists. The most prominent of such studies detail the failures of economists to comprehend what mathematicians are trying to tell them about their work. For example, Bruna Ingrao and Giorgio Israel (1990) have discussed the problems Vilfredo Pareto had understanding the criticisms made of his work by Vito Volterra. Philip Mirowski (1989, 243–48) has examined the failure of Léon Walras to make sense of the letters from Hermann Laurent, who had tried to ask Walras about the nature of the integrating factor in the equilibrium conditions for marginal utility: a discussion that went nowhere and that ended when Walras “started suggesting to others that Laurent was part of a plot against him” (245).
In this article we shall instead explore the attempt of a mathematician to work within the economics community. The correspondence between the economist Don Patinkin and the mathematician Cecil Phipps exhibits the process by which members of these different disciplinary communities attempt to reconcile differences.1 Within their correspondence, Patinkin and Phipps discuss the validity of a mathematical proof that emerged in Patinkin’s economic research. Their correspondence sheds light on the complexity of achieving a common understanding about the role of assumptions, the nature of proof, and the meaning of mathematical modeling—issues that challenge the belief that mathematics can be translated into economics.
Introducing Don Patinkin
Don Patinkin was born in Chicago, Illinois, in 1922. In his posthumously published paper “The Training of an Economist” (1995), Patinkin recalled that before entering college his vocational aptitude results “showed a high aptitude for mathematics. But we were still living in the shadow of the Great Depression and everyone knew that mathematicians went hungry. So the advice to me was to become a statistician—with the explanation that a statistician was a mathematician who could make a living” (359). Patinkin went on to receive his bachelor’s degree in 1943 (entering as a third-year student in 1941), his master’s degree in 1945, and his Ph.D. in 1947—all from the University of Chicago. He [End Page 442] then held teaching positions from 1946 to 1948 at the University of Chicago, rising to the rank of assistant professor. After spending a year as an associate professor at the University of Illinois, he immigrated to Israel in 1949 and there spent the remainder of his career at the Hebrew University in Jerusalem, eventually becoming its president.
Because we will be concerned with understanding Patinkin’s correspondence with a mathematician, it is useful to discuss the kind of mathematical training that Patinkin received as a graduate student at the University of Chicago...