Wilson’s Attitude Toward Mathematics and Science

The skepticism that Wilson expressed about the practical value of math­ematical statistics was firmly held and extended to mathematical economics. In July he wrote to Black, inquiring as to whether Black had read an article, just published in The Atlantic, by the writer and humorist Stephen Leacock (1936).

Leacock's article, “Through a Glass, Darkly,” was prompted by his read­ing of The Economics of Stationary States by A. C. Pigou, professor of economics at Cambridge, though Leacock dared identify neither him nor his university, for fear that he should be “crushed flat at once under the dead weight of pres­tige and authority” were he to do so.³¹ He quoted a paragraph in which Pigou discussed the problem of comparing real incomes received by people who purchased different goods and therefore faced different sets of prices. It would now be considered a classic index number problem, though admittedly the language was somewhat labored. Leacock, however, did not merely point out that Pigou's writing was not as clear as one would wish; he also sought to use the paragraph as the basis for a savage assault on mathematical economics.

As the last echo of the paragraph dies away, the readers are seen to lie as thickly mown down as the casualties of Vendemiaire. The volley has done its work.

Convoluted technical language is being used for no purpose other than to assert the authority of the academic economist, for nothing is being said that could not be said more plainly. He continued,

For the whole of the “plan” [Pigou's analysis] and its pretentious mathematics, when interpreted into plain talk, amounts to some­thing so insignificant and so self-evident that it is within reach of the simplest peasant who ever lived in Breotia, or failed at Cambridge. It only means that different people with the same money would buy different things; one might buy roses, one cigars, and another concert tickets; and you couldn't very well compare them because the weight wouldn't mean anything, and the color wouldn't, nor the number.

Such mathematics, Leacock claimed, failed to aid thought and served no end other than “to turn economics into an esoteric science.”

The mathematician is beckoning economics toward the seclusion of the dusty chamber of death, in the pyramid of scholasticism [in the darkness of which] lie mummified bodies of the learnings that were, that perished one by one in the dead mephitic air of scholasticism; of learning that had turned to formalism and lost its meaning, to body and lost its soul, to formula and lost its living force. Here lie, cen­turies old, the Scholarship of China, the Learning of Heliopolis, the Medicine that the Middle Ages killed, and the Reason that fell asleep as Formal Logic.

Leacock's argument has been explained at length because without this it is impossible to appreciate the significance of Wilson's observation in his let­ter to Black: that he had always had a great deal of sympathy with Leacock's point of view that mathematics should not be used in applied fields without good evidence that it advances our knowledge.

Wilson then went on to explain why mathematics could be useful: con­ducting arguments in terms of symbolic logic made it much easier to check for redundant or inconsistent assumptions, something that was easy to intro­duce if one wrote in a “free literary style." However, he immediately qualified this by stating that it did not justify the “elaborate mathematical theories which some people are giving." It was fine to use such theories if one is doing no more than testing working hypotheses or clarifying ideas. However, he observed that they were then addressing only their colleagues and not the “general body of students." To use such methods was to do what Einstein was doing when “he put out his theory of generalized relativity with the statement that he did not suppose that there would be more than a dozen or

e. This was the occasion for the other remarks made to Black quoted earlier. sixteen persons in the world who could fully understand them”: ideas were being put forward to be criticized and tested, not to be used in applied work. To Metzler, he explained, after noting that he did not know how useful math­ematical economics was likely to be to economists, it would provide them with “some protection against those mathematical economists who appear to prove something important when as a matter of fact they have not done so.”³⁴ He thought statistics much more important.

This was a vision of the role of mathematics in economics that was in part Marshallian. Mathematics had an important role within the circle of special­ists capable of reading it critically, but such economists were not the entire profession. Outside the narrow circle of economists who were sufficiently well trained in mathematics to read it critically, though Wilson wanted more mathematics to be used, he wanted that mathematics to be kept simple.

Wilson's attitude toward the scientific method was explored in correspon­dence with Wesley Mitchell, founder of the NBER and author of two major studies of the business cycle. In 1938, he told Mitchell that it was fortunate that he (Mitchell) was the only social scientist with any chance of being elected president of the American Academy of Arts and Sciences, because he had long operated “in a scientific manner both on the analytic and syn­thetic side.” He likened Mitchell's approach to that of a naturalist classifying species:

A naturalist doesn't recognize a bird or insect by a system of statistics. He does it by a process of diagnosis much like the way the physician recognises a disease. There are certain birds or insects which are so clearly differentiated from others that some one criteria will tell you what you want to know as far as classification is concerned... but by and large the different species grade into each other just as different diseases do in such a way that it is by the consideration of a large num­ber of non-compelling small bits of evidence that we come to a sound judgment as to how to classify.³⁵

The social sciences were a complex field, and effort had to be put into its mor­phology. He then remarked on the methods required in the social sciences: It isn't my idea that the methodology of the social sciences is any different from the methodology of the natural sciences. We need all the methodology of every kind that we can use whether in the social sciences or in the natural sciences.

Wilson must have written to Mitchell again in a similar vein, for in October 1938, Mitchell wrote that his recent letter had given him “much spiritual comfort,” for he agreed that economics needed a lot of taxonomic work.³⁶ The problem with economics was that “our taxonomists have spun their classifica­tions so largely out of their head and have made so little use of their eyes.” Their taxonomy was more like the classifications of geometry than botany, zoology, or paleontology.

Wilson was enthusiastic about Mitchell's work. Referring to an article Mitchell and Arthur Burns had written on business cycle indicators, he wrote that he considered it “very good as is the case in my judgment with all your work.” After explaining that Harvard was blessed with an abundance of eco­nomic theorists, theory pervaded “nearly everything from the first course in economics on to the most advanced courses Schumpeter and Leontief give.”³⁷ However, he considered this emphasis on theory a cause for concern.

I have no doubt that theory is important but if anything was discov­ered in the teaching of physics in the 19 th century it was that one shouldn't teach students theory without giving them at the same time the means of getting personally familiar with the physical phenomena through experiment and further that theory unless based on a keen appreciation of physical realities was merely an exercise in pure math­ematics which might even come to the point not only of getting no worthwhile results but of preventing people from thinking intensively about physical phenomena.

The problem was not with pure theory per se, but with the fact that theorists often failed to present evidence for their theories.³⁸ Thus, he wished Harvard had been able to recruit Mitchell.

Wilson was less complimentary toward Keynes, with whose work he had some familiarity. He had reviewed the Treatise on Probability, in which Keynes sought to provide an axiomatic foundation for probability theory.³⁹ Wilson's view was that Keynes had proposed axioms that were better than those sug­gested by anyone else, but further work was still needed, for they were not ideal.⁴⁰ In contrast, Wilson found A Treatise on Money incomprehensible because it was not based on any consistent set of assumptions.⁴¹ By February ¹937, a year after Keynes's General Theory had been published, Wilson had still not read it, but he did not expect to agree with it. He wrote to Alvin Hansen, then at Minnesota but shortly to arrive in Harvard, that he had read and enjoyed footnote 3 of his review in the Journal of Political Economy.⁴² In this footnote, Hansen had quoted Keynes's description of a book by J. A. Hobson as “made much worse than a really stupid book could be, by exactly those characteristics of cleverness and intermittent reasonableness which have borne good fruit in the past,” opining that the same could be said of the General Theory.⁴³ Keynes was, Wilson believed, someone whose own views were better than his statements about other people and other peoples' theo­ries, an observation that prompted Wilson to reflect on a general problem with the social sciences: that social scientists needed to stop trying to be bril­liant and sounding like natural scientists, and instead try to work out what was agreed by everyone.

What we very badly need is an encyclopedia of the social sciences con­structed like an encyclopedia of medicine or of physics to tell us chiefly what we do know in the sense that everybody agrees to it, that it has been amply demonstrated under the stated conditions.... I would like to know what is known. It mightn't be very much but if we had some propositions we could quote as we do the propositions of Euclid by reference to the standard compendium we save a lot of trouble in the long run.⁴⁴

The social sciences contained too much speculation about what might be known in the future, something Keynes was prone to do, and too little agree­ment on established facts.⁴⁵

One of the problems with Keynes, Wilson wrote to his former Harvard colleague and public finance specialist Charles Bullock, two years later, was that he believed “that he ha[d] a mathematical proof that spending and over­spending are marvelous things for government to do,” a proposition that ran counter to “the experience of the race.”⁴⁶ Wilson immediately reiterated his point about the importance of experience, expressing the view that “expe­rience would seem to be what counted rather than theory.” In the case of public spending, experience led him to believe that, though things might be different for young nations, it could not be good for old nations to spend more than their income, “no matter what a brilliant economist may prove with the aid of assumptions that perhaps cannot be verified and by a long mathematical deduction which gets a fair distance away from the facts. even if one starts with facts.” Though in no way denigrating formal statistical inference, Wilson's talk of “experience” suggests a much broader, more elastic notion, possibly allowing what might be called “folk wisdom,” as evidence alongside any propositions that could be proved formally. He seems to have shared Marshall's suspicion of long chains of reasoning, at least in cases where the assumptions were not based on firmly established facts.^f This perspective enabled Wilson to be convinced that Keynes must be wrong, despite admit­ting that he had still not read the General Theory with care.