The last post ended with the worry
…that the system of value judgments, and even of truth judgments, in pure mathematics, unbound as it is by conformity to empirical observation, may to an outsider look uncomfortably like a network effect…
In other words, we pure mathematicians have no way of convincing a skeptical outsider (like P.A. in the dialogues about number theory) that our value judgments are based on anything more solid than the personal and possibly frivolous preferences of the influential members of our community. (I omit the slightly more complicated argument about truth judgments.) What’s worse, the skeptic may well suspect that the way to become influential is simply to conform to the reigning prejudices.
To convince yourself that this is not an idle question, I advise you to read a depressing document entitled “What use are economists if they all say the same thing?” The book, published by the Association française d’économie politique (AFEP), traces the history of the recent attempt to free economics departments at French universities from total domination by the self-styled mainstream. Those of you who don’t read French can see English versions of a petition published in Le Monde in January and of a second (shorter) petition to the Minister of Higher Education supporting pluralism in academic economics, on the AFEP website.
The details are long and often sordid, but the basic outline is as follows. A group of heterodox economists, observing that —
(1) representatives of the mainstream did not question their assumptions to try to determine why they failed to anticipate the crisis of 2008;
(2) that they are under no institutional pressure to do so, because they hold an absolute majority in the national body that clears professorial candidates for hiring by universities;
(3) that they apply as sole criterion of excellence the publication of articles in the “top five” journals, all of them mainstream;
(4) that the whole process looks hopelessly circular, not to mention self-satisfied, self-congratulatory, self-validating, and self-selecting;
— asked the Minister to create a new disciplinary classification, provisionally entitled “Economics and society,” with the aim of promoting dialogue with the other social sciences while increasing the range of opinions and positions available to economics students in France. The Minister initially agree to the proposal, but was forced to backtrack by the severe and often virulent negative reaction of the representatives of the mainstream, led by the recent Nobel laureate Jean Tirole.
For the record, the opposition between heterodox and mainstream is not a simple reflection of the political opposition between left and right in France. The list of historic heterodox figures cited in the AFEP book includes Hayek and Schumpeter as well as Keynes and Galbraith. My purpose is just to draw your attention to the situation described in the following excerpt from the AFEP book (my emphasis of the word réseaux!):
Les tenants de ce qui est devenu l’orthodoxie ont… pris l’habitude de se redistribuer entre eux, selon leurs propres critères et leurs réseaux de clientèle, les ressources publiques destinées à faire vivre l’ensemble de la discipline, asphyxiant ainsi les paradigmes alternatifs. Ils ont eu beau jeu de légitimer constamment cette monopolisation des ressources en prétendant que tout ceci n’est que la juste sanction de leur excellence scientifique. Excellence scientifique déterminée par eux-mêmes pour eux-mêmes. Les valeurs propres au mainstream sont désormais cristallisées dans les règles et instruments de gouvernement de la discipline : ranking des revues, standards de thèse et de publication, passages obligés de cursus honorum. Intériorisés par les enseignants-chercheurs, ils gouvernent désormais les attentes et leurs routines au quotidien… La section est à ce point verrouillée que la crise de 2008 n’a eu aucun impact correcteur …
Of course I don’t believe that the system of values operating in pure mathematics is as circular and self-validating as the one depicted here. But I’m part of the system; how can I convince a skeptical outsider?