Wednesday, September 07, 2011

mathematics and real-world knowledge

RWER | Several articles on the misuse of mathematics in economics have already appeared in this journal. They all denounce this excess and list numerous weaknesses of liberal economics and theoretical economics that are due to, or at least related to, too much math.

This subject is worthy of further comment because it seems to me that these articles have mostly described symptoms, albeit a great many symptoms, but have barely begun to diagnose the causes and have given no hint of the kind of knowledge that would enable us to escape this no-man’s-land of using a little math but not too much.

The most recent contribution, by Michael Hudson (RWER No. 54), focuses on the important issues that escape mathematical models, such as the structural and historical evolution of societies, prevention of crises, psychological phenomena, long-term thinking. It emphasizes the normative nature of marginal analysis and equilibrium models, and denounces rough quantifications such as GNP and the staggering increase in debt. He acknowledges Marx’s openness to the big issues in society that are currently excluded from political debate by an economic philosophy that tries to impress its opponents with sophisticated mathematics. These questions are analyzed thoroughly. On several occasions, however, one feels that the criticism is that the math is being misused and should be developed in some other direction (e.g. a statistical analysis of the financial tendencies that polarize wealth and income, or a study of the positive feedback mechanisms, etc.). This leaves a certain dissatisfaction — on a philosophical level — a feeling that the problem of excess math has not been addressed in all its aspects.

My thesis is that economics adds its own particular difficulties to these issues (because of its status as “conseiller du prince”, and because through teaching it gives useful professional skills, etc.) and that things become clearer when we step back and frame the question in terms of knowledge in general. As the reader will see, this enables us to trace, with great epistemological force, the direction of a different type of knowledge. This allows us to escape from the addiction of mathematization while building a better quality knowledge.

We will take in a number of examples in economics and finance, but the fact remains that economics has many distinctive characteristics, as several authors have noted, which tend to prevent a reasoned consideration of its social function. Consequently there remain several points that will need to be developed further.