Monthly Archives: August 2015

Avant-Garde Philosophy of Economics

by Tatiana Plakhova (2011)

To most people, the title of this post is a triple oxymoron. Those left thoroughly traumatized by Econ 101 in college share their skepticism with those who have dipped their toe into hybrid fields like neuroeconomics and found them to be a synthesis of the dullest parts of both disciplines. For the vast, vast majority of cases, this sentiment is quite right: ‘philosophy of economics’ tends to be divided between heterodox schools of economics whose writings have entirely decoupled from economic formalism, and—on the other side of the spectrum—baroque econophysicists with lots to say about intriguing things like ‘quantum economics’ and negative probabilities via p-adic numbers, but typically within a dry positivist framework. As for the middle-ground material, a 20-page paper typically yields two or three salvageable sentences, if even that. Yet, as anyone who follows my Twitter knows, I look very hard for papers that aren’t terrible—and eventually I’ve found some.

Often the ‘giants’ of economic theory (e.g. Nobel laureates like Harsanyi or Lucas) have compelling things to say about methodology, but to include them on this list seems like cheating, so we’ll instead keep to scholars who most economists have never heard of. We also—naturally—want authors who write mainly in natural language, and whose work is therefore accessible to readers who are not specialists in economic theory. Lastly, let’s strike from the list those writers who do not engage directly with economic formalism itself, but only ‘the economy’. This last qualification is the most draconian of the lot, and manages to purge the philosophers of economics (e.g. Mäki, McCloskey) who tend to be the most well-known.

The remaining authors make up the vanguard of philosophy of economics—those who alchemically permute the elements of economic theory into transdisciplinary concoctions seemingly more at home in a story by Lovecraft or Borges than in academia, and who help us ascend to levels of abstraction we never could have imagined. Their descriptions are ordered for ease of exposition, building from and often contradicting one another. For those who would like to read more, some recommended readings are provided under each entry. I hope that readers will see that people have for a long time been thinking very hard about problems in economics, and that thinking abstractly does not mean avoiding practical issues.

Category Theory, by j5rson

M. Ali Khan

Khan is a fascinating character, and stands out even among the other members of this list: by training he is a mathematical economist, familiar with some of the highest levels of abstraction yet achieved in economic theory, but at the same time an avid fan of continental philosophy, liberally citing sources such as De Man (a very unique choice, even within the continental crowd!), Derrida, and similar figures on the more literary side of theory, such as Ricoeur and Jameson. It may be helpful to contrast Khan to Deirdre McCloskey, who has written a couple of books on writing in economics: McCloskey uses undergraduate-level literary theory to look at economics, which (let’s face it) is a fairly impoverished framework, forcing her to cut a lot of corners and sand away various rough edges that are very much worth exploring. An example is how she considers the Duhem-Quine thesis to be in her own camp, which she proudly labels ‘postmodern’—yet, just about any philosopher you talk to will consider this completely absurd: Quine was as modernist as they come. (Moreover, in the 30 years she had between the first and second editions, it appears she has never bothered to read the source texts.) Khan, by contrast, has thoroughly done his homework and then some.

Khan’s greatest paper is titled “The Irony in/of Economic Theory,” where he claims that this ‘irony’ operates as a (perhaps unavoidable) literary trope within economic theory as a genre of writing. Khan likewise draws from rhetorical figures such as synecdoche and allegory, and it will be helpful to start at a more basic level than he does and build up from there. The prevailing view of the intersection of mathematics and literary theory is that models are metaphors: this is due to two books by Max Black (1962) and Mary Hesse (1963) whose main thesis was exactly this point. While this is satisfying, and readily accepted by theorists such as McCloskey, Khan does not content himself with this statement, and we’ll shortly see why.

Consider: a metaphor compares one thing to another on the basis of some kind of structural similarity, and this is a very useful account of, say, models in physics, which use mathematical formulas to adequate certain patterns and laws of nature. However, in economics it often doesn’t matter nearly as much who the particular agents are that are depicted by the formulas: the Prisoner’s dilemma can model the behaviour of cancer cells just as well as it can model human relations. If we change the object of a metaphor (e.g. cancer cells → people), it becomes a different metaphor; what we need is a kind of rhetorical figure where it doesn’t matter if we replace one or more of the components, provided we retain the overall framework. This is precisely what allegory does: in one of Aesop’s fables, say “The Tortoise and the Hare,” we can replace the tortoise by a slug and the hare by a grasshopper, but nobody would consider this to be an entirely new allegory—all that matters here is that one character is slow and the other is fast. Moreover, we can treat this allegory itself as a metaphor, as when we compare an everyday situation to Aesop’s fable (which was exactly Aesop’s point), which is why it’s easy to treat economic models simply as metaphors, even though their fundamental structure is allegorical.

The reason this is important is because Khan takes this idea to a whole new level of abstraction: in effect, he wants to connect the allegorical structure of economic models to the allegorical nature of economic texts—in particular, Paul Samuelson’s Foundations of Economic Analysis, which begins with the enigmatic epigraph “Mathematics is a language.” For Khan: “the Foundations is an allegory of economic theory and…the epigraph is a prosopopeia for this allegory” (1993: 763). Since I had to look it up too, prosopopeia is a rhetorical device in which a speaker or writer communicates to the audience by speaking as another person or object. Khan is quite clear that he finds Samuelson’s epigraph quite puzzling, but instead of just saying “It’s wrong” (which would be tedious) he find a way to détourne it that is actually quite clever. He takes as a major theme throughout the paper the ways that the same economic subject-matter can be depicted in different ways by using different mathematical formalisms. Now, it’s fairly trivial that one can do this, but Khan focuses on how in many ways certain formalisms are observationally equivalent to each other. For instance, he gives the following chart (1993: 772):

correspondence between probability & measure theoretic terms (in Khan, 1993; 772)

Correspondence between probability & measure theory

That is to say, to present probabilistic ideas using the formalism of measure theory doesn’t at all affect the content of what’s being said: it’s essentially just using the full toolbox of real analysis instead of only set notation. What interests Khan here is how these new notations change the differential relations between ideas, creating brand new forms of Derridean différance in the realm of meaning—which, in turn, translate into new mathematical possibilities as our broadened horizons of meaning let us develop brand new interpretations of things we didn’t notice before. Khan’s favorite example here is nonstandard analysis, which he claims ought to make up a third column in the above chart, as probabilistic and measure theoretic concepts (and much else besides) can likewise be expressed in nonstandard terms. To briefly jot down what nonstandard analysis is: using mathematical logic, it is possible to rigorously define infinitesimals in a way that is actually usable, rather than simply gestured to by evoking marginal quantities. While theorems using such nonstandard tools often differ greatly from ‘standard’ theorems, it is provable that any nonstandard theorem can be proved standardly, and vice versa; yet, some theorems are far easier to prove nonstandardly, whence its appeal (Dauben, 1985). In economics, for example, an agent can be modelled as an infinitesimal quantity, which is handy for general equilibrium models where we care less about particulars than about aggregate properties, and part of Khan’s own mathematical work in general equilibrium theory does precisely this.

To underscore his overall point, Khan effectively puts Samuelson’s epigraph through a prism: “Differential Calculus is a Language”, “Convex Analysis is a Language”, “Nonsmooth Analysis is a Language”, and so on. Referring to Samuelson’s original epigraph, this lets Khan “interpret the word ‘language’ as a metonymy for the collectivity of languages” (1993: 768), which lets him translate it into: “Mathematics is a Tower of Babel.” Fittingly, in order to navigate this Tower of Babel, Khan (following Derrida) adopts a term originating from architecture: namely, the distinction between keystone and cornerstone. A keystone is a component of a structure that is meant to be the center of attention, and clinches its aesthetic ambiance; however, a keystone has no real architectural significance, but could be removed without affecting the rest of the structure. On the other hand, a cornerstone is an unassuming, unnoticed element that is actually crucial for the structural integrity of the whole; take it away and the rest goes crashing down.

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