Every time there’s a controversy in economics, the problem of mathematics seems to be at the center of the discussion. That’s because, in economics, discussing the role of mathematics is inextricably related to issues of science, epistemology, and methodology, which are themselves rarely discussed but are implicit in pretty much all of these discussions.
In short, we’re never very far from physics-envy.
That’s certainly the starting point of Noah Smith, who compares the mathematics of physics (the supposed “language of nature”) with that of macroeconomics (in which it serves to “signal intelligence”). And then, of course, Paul Krugman rides to the rescue, arguing that mathematical models, when “used properly,. . .help you think clearly, in a way that unaided words can’t.”
Uh, OK. “Used properly” is the operative clause there. The real question is, what is the proper use of mathematics in economics? And, what is the proper way of thinking about the proper use of mathematics? That’s where all the issues of science, epistemology, and methodology come to the fore.
As it turns out, one of the first articles I ever published, “The Merchant of Venice, or Marxism in the Mathematical Mode,” was on that very subject. I had mostly ignored mathematics during my undergraduate years but then, in graduate school and especially when I began to conduct the research for my dissertation (on mathematical planning models), I realized I wanted both to learn the econmath and to learn how to think about the econmath. Ironically, I ended up teaching “Mathematics for Economists” to first-year doctoral students for over a decade (it was basically a course in linear algebra and multivariate calculus, in which students also had to write a paper on the history and/or methodology of the mathematization of economics).
The argument I made in my dissertation and later in the “Merchant of Venice” article was that economists (mainstream economists especially, but also not a small number of heterodox economists, including Marxists) treated mathematics as a special language or code. They considered it special either in the sense that it was the language of nature (and therefore overprivileged) or a neutral medium for thinking and expressing ideas (and therefore underprivileged). Either way, it was considered special.
My alternative view was that mathematics was just one language among many, and therefore one set of metaphors among many. And like all metaphors, it served at one and the same time to enable and disable particular kinds of ideas. Therefore, we need to both write mathematical models and to erase them in order to produce new ideas.*
But that’s not how most economists think about mathematical models. And when they do think and write about them, they tend to invoke one or another argument for mathematics as a special code. They also tend to forget about all the other uses of mathematics in economics—not only as a signalling device but as a hammer to bludgeon all other approaches out of existence.
It’s the tool that is often used, in economics, to separate science from non-science—which, of course, if you say it quickly, becomes nonsense.
*That argument, concerning the not-so-special status of mathematics, so incensed one of my colleagues he attempted to derail my tenure case. Fortunately, another of my colleagues forced him to back down and I ended up receiving a unanimous recommendation.