By 1983 we were all, so to speak, mathematical economists...This is as it should be. Soft and hard sciences are cumulative disciplines. We each bring our contributions of "value added" to the pot of progress. In Max Planck's much-quoted words: Science progresses funeral by funeral. Inside tomorrow's physics treatise will be the lasting truths of Isaac Newton and also of the professor who works down the hall from you. Something of the same goes for economics, where often the dance must proceed Two Steps Forward and One Step Back.--Paul A. Samuelson 1998 (1378-9)
Had I remained on the Chicago Midway, I might well have missed out on the three revolutions that remade mainstream economics: the Keynesian Revolution, the Imperfect-Competition Revolution, and the Mathematical-Economics Revolution. Instead I had a front-row seat.--Paul A. Samuelson (1379)
Had I been a strict constitutionalist, I might well have stopped there. The result would have been a shorter 200-page book with one fully integrated theme.--Paul A. Samuelson (1384)
Reading widely, I was a child of my time, but it was the internal logic of the economic puzzles that guided Foundations' growth.--Paul A. Samuelson (1375 [emphasis in original])
The historian of economics, Roger Backhouse, has long been prodding me to pay closer attention to Paul Samuelson, who was the economist's economist for much of the second half of the twentieth century. In particular, in commenting on my work on the pre-history of Kuhnian ideas within Chicago economics, he insisted that I should not underestimate the significance of Samuelson (the very anthithesis of a Chicago economist, despite having done a BA there). And, indeed, in reading Samuelson's reflections on his own achievement on his seminal Foundations of Economic Analysis a half century later, I was struck by the Kuhnian imagery, including his self-presentation as a would-be-revolutionary (rather than "strict constitutionalist") and the focus on how puzzle-solving (rather than external influences) led to the breakthroughs.
But I wondered to what degree the evidence from 1998 wasn't itself a consequence of Kuhn's influence. Nudged by Backhouse I was directed to the following passage in Samuelson's Foundations:
[A]t a time when pure economic theory has undergone a revolution of thought—from statical to dynamical modes. While many earlier foreshadowings can be found in the literature, we may date this upheaval from the publication of Ragnar Frisch’s Cassel Volume essay [1933--ES] of only a decade ago. The resulting change in outlook can be compared to that of the transition from classical to quantum mechanics. And just as in the field of physics it was well that the relationship between the old and the new theories could be in part clarified, so in our field a similar investigation seems in order. (Samuelson 1947, p. 284)
So, Samuelson was very explicit about that fact that he was participating in a scientific revolution that was initiated before him. In an "age of specialization," Samuelson thought of himself as the 'last generalist' because after his framework setting work, the end of "upheaval," there would only be a need for esoteric specialist work. In Samuelson's hands the revolution has an air of inevitability.
As an aside, Samuelson's 1998 piece is a polemic against the historians of economics (especially, Weintraub, Mirowski) that have dealt with this episode. Like a good Kuhnian-ruler, Samuelson did not underestimate the significance of control over the historical image of the pre-revolutionary period. Through his long life he kept contributing, not unlike his rival and critic, George Stigler, to the history of economics as a live discipline in economics (Samuelson's 'style' is often associated with whig history and a kind of rational reconstruction.) About these matters more in the future.
But it is easily missed that there is another theme in Samuelson's essay, which my talk of 'inevitability' is meant to introduce. The first sentence reads, "IF THERE ARE PEOPLE born under a lucky star, there must be books that are lucky too." One might think this is mere play, but luck and chance dominated the initial narrative. Here are the first lines of the third paragraph on the front page:
By accident, the public schools I attended, in Gary, Indiana and Chicago- were unusually good ones that turned out many future scholars and scientists. By chance of geography, I went to the University of Chicago at a young age, and under its experimental New Hutchins Plan I got a deep and wide undergraduate education. By chance, my freshman courses included economics under Aaron Director (1901-), who was later to be founder of the Second Chicago School of Milton Friedman, George Stigler and Gary Becker.** In that academic year of 1931-32, although I didn't know it at the time, Chicago was the leading world center for neoclassical economnics(1375 [emphasis in original])
And again, he went to Harvard by chance: "However, by chance, that happened to be the year when the Social Science Research Council began an educational experiment: they would scour America for the eight best economics undergraduates and generously underwrite their several years of graduate study." (1376) And then "It was my good luck to be appointed as the first proper economist to Harvard's prestigious Society of Fellows..." (1376)
By contrast, when dealing with the character of his mathematical work, especially when he turns to his work on revealed preference, we're on the plane of necessity: "For more than two goods, n > 3, my so called Weak Axiom was recognized to be necessary but not to be alone sufficient to deduce transitivity of preferences." (1380; see also 1379, and especially the very important note 2.) So, the economist qua economist is beneficiary of moral luck, but his ideas describe a world of necessity. This may seem like a contrast, but it isn't.
Now, unlike what is often thought, the formal revolution in economics was very attuned to )I quote Samuelson again) the "empirical meaning" of its identity claims. (1380)* In fact, Samuelson explicitly notes his philosophical sources: "My approach looked backward in summarizing "economically" (in the Mach-Vienna Circle sense) the "meaningful" (testable and, in principle, refutable) core of constrained-budget demand theory." (1380) As I have noted before, even Stigler, who was underwhelmed by Samuelson's Foundations, appreciated Samuelson's efforts to give empirical meaning to, and even test, the formal framework. Even so, Samuelson's rhetorical contrast between his own luck and the necessity of hi work alerted me to the significance of the wording of the following passage.
I was vaccinated early to understand that economics and physics could share the same formal mathematical theorems (Euler's theorem on homogeneous functions, Weierstrass's theorems on constrained maxima, Jacobi determinant identities underlying LeChatelier reactions, etc.), while still not resting on the same empirical foundations and certainties. (1375)
Samuelson describes here both some of his mathematical tools, that they were imported from mathematics, and that the epistemic resources these tools provided did not extend to their "empirical foundations and certainties." Fair enough. But a skeptical reader might well say, 'what certainties?'
One early reader noticed Samuelson's blindspot. A forgotten philosopher-economist, Gerhard Tintner, who knew something about Vienna circle philosophy from up close (he had been trained in Vienna), insisted that Samuelson was more Bridgeman than Carnap: "Operationally meaningful statements are hypotheses about empirical data which could conceivably be refuted, if only under ideal conditions. These ideas are related to those of some modern positivist philosophers, especially Bridgeman." (Some other time more about the significance of Bridgeman to philosophy of science and economics.)
Anyway, Backhouse called my attention to following remark by Tintner:
The whole theory of anticipations and expectations is either neglected or appears only incidentally. Uncertainty hardly gets an adequate treatment in the small space allotted to it. Samuelson's book is in this respect inferior to the earlier work of J. R. Hicks (Value and Capital, 1939) and others who have endeavored to deal with problems of economic risk and uncertainty. I believe that especially the theory of formation of anticipations forms a true link between static economics and the more useful and interesting economic dynamics.--Tintner Reviewing of Samuelson's Foundations, (499)+
Now, in 1941 Tintner pioneered the technical work that encouraged economists's substitution of unmeasurable uncertaint by probable risk. And so he was well-placed to evaluate Samuelson's treatment of uncertainty, and must have been annoyed to have been overlooked in the new framework. And to put Tintner's technical point in terms of Samuelson's rhetoric of his retrospective; it's as if Samuelson's economics treats economic life as one (good) thing just happening after each other without friction or foresight/planning (just as Samuelson liked to present his smooth path in 1998). And indeed as I have often noted (recall here, here, and, say, here), when economists like Arrow did start to model uncertainty mathematically as randomness, they make non-trivial assumptions about the structure of modality. In particular, rather than seeing luck and accident as something opposed to necessity, as in the classical opposition between Epicureanism and Spinozism, it becomes the same side of the coin. That is to say, Samuelson's presentation of his life and his economics are -- when he is polemically engaged with the historians -- not as far apart as one might think.
You may ask, what is my reason for calling Tintner a "philosopher?" (If he is remembered at all it is for his contributions to econometrics.) Well, he published "Methodology of Mathematical Economics and Econometrics" in International Encyclopedia of Unified Science, Volume 2; yes, that's the same volume were Kuhn's Structure was published (and, yes, edited by Carnap).
*The crucial metaphysical issue is to what degree the mathematical framework -- the plane of necessity -- in which equivalence claims are proved, disguises diverging possibilities (of the bits of machinery) in (ahh) the real world. Sadly I lack the technical skill to fully elucidate this note.
**I have grown skeptical about the claim that the first and second Chicago schools were all that far apart. In particular, I claim that by 1943 the technocractic conception of economics was already in place.
+I thank Brandon Fitelson for making the review available to me.