Lars P. Syll — On the non-applicability of statistical models

Math is purely formal, involving the relation of signs based on formation and transformation rules. Signs are given significance based on definitions. Math is applicable to the world through science to the degree that the definitions are amenable to measurement and the model assumptions approximate real world conditions (objects in relation to others) and events (patterned changes in these relations). Methodological choices determine the scope and scale of the model, which in turn determines the fitness of formal modeling for explanation of real world conditions and events.

Contemporary science is chiefly about applying formal modeling to theoretical explanation that covers a wide enough range of phenomena worth explaining to be of interest. The scientific project is about designing useful models for explaining phenomena and also designing experiments to test the model against observation. This involves measurement.

A further challenge is identifying parameters that can be measured to produce data and constructing models based on assumptions of how parameters are related with respect to states and how they change over time.

Then, there are also presumptions that are not stated. For example, it is presumed that science is consilient and therefore, any theoretical explanation that violates the conservation laws is ruled out automatically.

Beyond that philosophical foundations relating to metaphysics, epistemology, ethics, social and political philosophy, philosophy of science, the philosophy of the particular discipline, etc., also come into play.

Quite evidently, there is a lot of room for mistake and slip-ups in the process of "doing science."

Formalization and data are not magic wands, and assuming they are leads to magical thinking. Formalization is only rigorous — necessary based on application off rules — with respect to models. How models relate to what is modeled is contingent and depends on data. Data is dependent on observation and measurement.

All this is difficult enough in the natural sciences, but more difficult in the life sciences and much so in the social sciences.

The philosophy of economics, or foundations of economics if one prefers, needs to take all this into consideration and there needs to be lively debate about it. Is there?

Lars P. Syll’s Blog

On the non-applicability of statistical models

Lars P. Syll | Professor, Malmo University

Paul Cockshott — Competing Theories: Wrong or Not Even Wrong?

Liberal economics has been able to claim scientificity based both on the large and sophisticated mathematical apparatus of neoclassical value theory, and on a vast number of detailed econometric studies. Those who are professionally involved in the subject are expected to be mathematically literate and experi- enced in the analysis of statistical data. These aspects of their training means that their background has in some ways more in common with people who are trained as natural scientists than with other social scientists. There has also been a long tradition of economists borrowing conceptual structures from the natural sciences. Mirowski showed that many of the concepts used in marginalist economics were borrowed directly from classical mechanics during the late 19th century[Mir89]. But there is, I think, a significant difference between the way the natural sciences are taught and the way neo-classical economics is taught, and this difference is significant.

When a student is taught an introductory course in physics or biology, they are both taught theories and told of the crucial experiments that validated the theories. They are told of Galileo's experiment that validated what we would now see as the equivalence of gravitational and inertial mass. They learn of Michelson Morley's experiment on the invariance of the speed of light, that inconvenient fact whose explanation required Special Relativity. Biology students hear of the experiments of Pasteur and Koch that established the germ theory of disease, etc. The function of these accounts in science education is twofold. On the one hand they emphasize to students the reasons why they should give credence to the theory being taught, on the other, these historical examples are used to teach the scientific method.

If one contrasts this with introductory courses in economics one sees that whilst theory is taught, the student gets no equivalent history of crucial economic observations in order to support the theory. This is no accident.

No history of crucial observations is taught, because there is no such history.

Competing Theories: Wrong or Not Even Wrong?
Paul Cockshott | School of Computing Science, University of Glasgow