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