Monday, April 02, 2012

The Limits of Formal Theory in Sociology

Sociologists and economists often disagree about the role of so-called "formal" theory in understanding social behavior. For the most part, sociologists are much more skeptical that mathematical models (with little reference to data) can clearly and accurately describe, explain, and predict how humans act, think, and feel. I take a middle-of-the-road position: such models of human behavior can be helpful for illuminating arguments, but often they are such crude approximations of reality that they can obscure what is actually going on. I'm reminded of Max Tegmark's brilliant article on the mathematical universe hypothesis, in which he claims that the universe is a giant mathematical structure. In fact, the disciplines can be understood in reference to derivations from known mathematical laws, as shown in this diagram:
The problem, as Tegmark suggests in this diagram, is that until we understand how to reconcile mathematically general relativity and quantum field theory, as well as how this reconciled theory is related to other fields in physics and related fields, mathematizing sociology will at best be a set of (possibly crude) approximations of reality.