Writing the Thesis

By the summer of 1940, Samuelson was establishing, through his publi­cations, a research profile that would have been the envy of many young professors. However, he remained a junior fellow—a privileged position but nonetheless only a small step up from being a graduate student.

He may also have thought that a PhD would improve his chances of find­ing a long-term academic position, and he may have been in a hurry to get a position with a higher salary. It is also possible that he had the idea for a book and decided that writing a thesis was the best route to publication. Whatever his motivation, in the summer and fall of 1940 he composed and rearranged material “at fever pace,” dictating to Marion, who typed the entire first draft of the thesis.¹ In the preface, he acknowledged her “all too many” sugges­tions and corrections, which had resulted in “a vast mathematical, economic, and stylistic improvement” to which no perfunctory acknowledgment could do justice.² Its title, Foundations of Analytical Economics: The Observational

Significance of Economic Theory, was in itself sufficient to make clear that he was setting himself a very ambitious task.

When, fifty years later, he came to look back on the published version of his thesis, Samuelson claimed that, though the thesis was written very quickly, his ideas had evolved gradually over the period from 1936 to 1941.^a During this time, he had come to recognize that the existing corpus of eco­nomic theory involved “a limited number of qualitative relationships.” Had he realized this at the outset, it would not have been necessary to ransack the mathematical libraries of Chicago and Harvard to find the answers to what he had initially assumed were completely different problems requiring dif­ferent answers.³ The thesis was, therefore, driven by “the internal logic of the economic puzzles” he was tackling.⁴

The thesis opened with an explicit methodological statement:

“The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.” This fundamental prin­ciple of generalization by abstraction was enunciated by the eminent American mathematician E.

The quotation in this passage was taken from Introduction to a Form of General Analysis (1910), by mathematician Eliakim Hastings Moore, a book he would have learned about from Wilson. It was based on lectures Moore had given at Yale in September 1906, where Wilson had just been appointed an assistant professor. The quotation is another way of expressing an idea that Samuelson stated explicitly as having learned from Wilson—namely, that problems can have a common mathematical structure even if they are differ­ent in other respects. This gave Samuelson the license to draw on ideas taken from thermodynamics, for the common structure of the problems in the two fields meant that it was possible to use the same mathematics even though the fields were otherwise very different.

In modern economics it is obvious to most economists that maximiza­tion and minimization problems arise in virtually all fields of economics; this is the reason why training in economics includes courses in quantitative

a. As will be explained in chapter 22 this volume, the book Foundations ofEconomic Analysis (1947a) contained a significant amount of material that was not in the thesis. However, most of the material in the thesis was changed little when included in the book, so comments he made about the book also apply to the thesis. methods that expose students to optimization techniques. It is why micro­economic theory—the theory of how individual optimizing agents behave and interact—is considered the foundation for most applied fields. However, in the 1930s, the importance of optimization techniques was far from obvi­ous to economists. The result was that, even when Wilson had planted the seed of the idea in Samuelson’s mind, it took Samuelson a long time to see its significance. He wrote:

Only after laborious work in each of these fields [“production econom­ics, consumer’s behavior, international trade public finance, business cycles, income analysis”] did the realization dawn upon me that essen­tially the same inequalities and theorems appeared again and again, and that I was simply proving the same theorems a wasteful number of times.⁶

The evidence from Samuelson’s publications prior to the thesis supports the idea that it took time for him to realize there was a common structure to economic problems.

However, the thesis was not just about unifying economic theory. It had an even more important theme—namely, that economic theory should have implications for things that can be observed and measured. The importance he attached to this is indicated by his choice of subtitle for the thesis: “The Observational Significance of Economic Theory.” He introduced this theme on the second page, arguing not only that there exist similar theorems in dif­ferent fields but also that there exist “formally similar meaningful theorems in those fields.” The word formally indicates that these theorems have the same mathematical structure and the word meaningful meant theorems that had implications for things that were observable. Claiming that “only the small­est fraction of economic writings” had tried to derive “operationally meaningful theorems,” he defined meaningful theorems as “hypothes[e]s about empirical data which could conceivably be refuted, if only under ideal conditions.”⁷

As was explained in chapter 10, this was an idea that had developed gradually over the years. In 1937, there had been little trace of operation- alism in Samuelson’s publications: the introduction of mathematics was motivated by its usefulness in clarifying thinking, and he had come close to accepting the Robbins position that the assumptions on which consumer theory were based could not be questioned.⁸ His February 1938 article on consumer theory hinted at operationalism when it referred to his theory, founded on index number theory, as being “more directly based on those elements which must be taken as data by economic science” and “more meaningful” in its formulation.⁹ But this was no more than a hint, for the article was framed by the concerns found in the existing literature and what he had learned from Haberler.

The term “operational” was clearly Bridgman’s. However, the way Samuelson described operationally meaningful theorems was not Bridgman’s. His empha­sis on “data” and “observation” (a term that is given prominence by its use in the title of Samuelson’s thesis) is closer to the ideas of the philosophers associated with the Vienna Circle. Though the idea that hypotheses are meaningful if they can be refuted is commonly associated with Karl Popper, whose major work had appeared in 1933, it is more likely that Samuelson learned them through Kaufmann and Sweezy, or through Rudolf Carnap, whom his friend Willard Quine had helped bring to the United States in 1936.¹¹ He might also have encountered such ideas through the senior fellow, Alfred North Whitehead.

The use of mathematics to cut through the confusions found in the exist­ing literature and to unify economic theory solved the problem of where Samuelson would find meaningful economic theorems. Propositions about individuals could be derived from the hypothesis that “conditions of equi­librium are equivalent to the maximization (minimization) of some mag- nitude.”¹² He no longer considered this an a priori truth but, rather, a hypothesis.^b Samuelson then drew a clear distinction between propositions

b. However, given that Samuelson was building so much economic theory on this foundation, he must have believed that it would survive attempts to refute it. about individuals and those about groups which could not be derived in this way, because nothing was being maximized.

However, when we leave single economic units, the determination of unknowns is found to be unrelated to an extremum position. In even the simplest business cycle theories there is lacking symmetry in the conditions of equilibrium, without which there is no possibility of reducing the problem to that of a maximum or a minimum. Here the hypothesis is made that the system is in stable equilibrium or motion in terms of an assumed dynamical system.^13c

The justification for this was nothing more than the observation that “posi­tions of unstable equilibrium, if they exist, are transient, non-persistent states” that will be observed less often than stable ones.

Throughout this opening chapter, Samuelson was critical of existing eco­nomic theory, for very little of it had been focused on deriving meaningful or operational theorems. It is at this point, at the end of a short methodological chapter, that Samuelson expressed his much-cited difference with Marshall over the role of mathematics in economics.

I have come to feel that Marshall’s dictum that “it seems doubtful whether any one spends his time well in reading lengthy translations of economic doctrines into mathematics, that have not been made by himself” should be exactly reversed. The laborious working over of essentially simple mathematical concepts such as is characteristic of much of modern economic theory is not only unrewarding from the standpoint of advancing the science, but involves as well mental gym­nastics of a particularly depraved type.¹⁴

What mattered in economic theory was the testable hypotheses and the need to derive them made mathematics central.