How Complex is Barkley Rosser?

A look at Friedrick Hayek’s work on complexity theory from math complexity theorist Barkley Rosser (doc). For newbees, the article helpfully reviews a few important issues in the literature, brings attention to the work of Roger Koppl, and has a useful introductory bibliography.

Rosser, unfortunately, fails the engage the most fundamental –and scientifically challenging — elements of Hayek’s complexity work, e.g. (1) the multiple many-many problems of neuroscience/psychology, production theory/valuation theory, and the relative price mechanism which block reduction in economic science to “simpler” sciences such as physics and chemistry (see e.g.  Hayek’s “Scientism and the Study of Society” essays, The Sensory Order, and The Pure Theory of Capital); (2) the common problem of specifying “initial conditions” common to non-linear systems in physics and chemistry, and the same problem found in the impossibility of specifying the “initial conditions” of individual choice, local knowledge, and entrepreneurial learning (e.g. the problem of “subjective” economics); (3) the complex link between theses various many-many problems and “initial conditions” specification problems and the pure subjectivity of the pure logic of choice.

And Rosser doesn’t do much to tie these core Hayekian complexity issues up with precisely the same sort of complexity issues in Darwinian biology. In the fields of explanation theory and philosophy of science, Hayek notes a parallel between the explanatory nature and complexity characteristics of Darwinian biology. Hayek doesn’t do much to advance the ball in this regard (he does more drawing the parallel between complexity and explanation issues in global brain theory and economics), and neither here does Barkley.

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3 Responses to How Complex is Barkley Rosser?

  1. Greg,

    You are right that I did not deal with such matters as sensitive dependence on initial conditions or evolutionary biology as related to these matters in this paper. But that would have turned the paper into something much longer. I have dealt with such matters at length in other papers and also books, especially my From Catastrophe to Chaos: A General Theory of Economic Discontinuities.

  2. Greg,

    You and I disagree on the use of math in econ. However, while Hayek saw a lot of it as “scientism,” he was not totally averse to math. The diagonal argument he used about inherent complexity of consciousness is a high math argument. Also, even in terms of his more mundane economic theories, such as on monetary policy, how is the natural rate of interest to be defined other than mathematically ultimately?

  3. Greg Ransom says:

    Barkley, I’m not at all averse to math in economics.

    What I continually argue for is a developed account of Hayek’s own view on the use of math in economics — math has several functions in Hayek’s account of the explanatory strategy of economics. (I won’t recount these functions here.)

    When you talk about “high math argument” in the context of the “inherent complexity of consciousness” you are moving into the border line of philosophy, meta-mathematics, proof theory, everyday math, etc. This is a hard area. I tend to be a Wittgensteinian in this area, and Hayek certainly has many aspects of a Wittgensteinian picture in many parts of his work.

    But Hayek was not an expert in the areas of meta-mathematics, philosophy of mathematics, or even in the history of logic or the foundations of mathematics. Hayek mostly had an sophisticated non-specialists knowledge of these very difficult matters, familiar with the main figures, and some of the main problems, but not grounded in the literature the way a specialist in these areas would be. Hayek saw a family resemblance between his work in _The Sensory Order_ an that of, say, Godel, but he really was in no position to pursue this work, without abandoning his own research project — when Hayek attempted to answer Popper on a part of this issue, Hayek drafted a manuscript he decided never to publish (I’ve got a copy in my files, and with luck the paper will be published in a future volume of the Collected Works).

    On math and “the natural rate of interest”, well, this is also a very difficult issue, one which Hayek provided several different perspectives on.

    I don’t think the issues involved have gotten easier or much more obvious even with the advance of mathematical sophistication in econ or the investigation of such problems as those exposed in the Cambridge capital controversy.

    I’m as interesting in your views on the matter as much as anyone’s, and I’m still working out my own understanding of the many difficult issues involved here.

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