Math in the social sciences, with discussion
Nice discussion on the usefulness, or lack thereof, of mathematics and formal theory building in the social sciences. Make sure you have a look at the comments. More or less chronologically:
- sociolgy needs more… @ orgtheory.net by Fabio Rojas
- math and sociology @ orgtheory.net by Fabio Rojas
- methodological convergence in the social sciences @ Marc F. Bellemare
Somewhat in parallel, a discussion about the death of theoretical (read mathematical) economics at econlog:
All in all, I subscribe to Fabio’s call with both hands.
My subjective list of advantages of formal theory building in social sciences supplementing the one at orgtheory.net:
- If a theory is, among other things, a logically coherent set of propositions then formalizing it is just a translation to a language that makes analyzing it, especially deducing consequences, much easier. And this applies to whatever the subject of the theory is.
- Most of the empirical studies in sociology are analyzed using some form of statistical reasoning, which is mathematical. Given that, building a formal theory of the studied phenomenon should in principle allow for a tighter connection between the theory and empirics (c.f. The Theory-Gap in Social Network Analysis by Mark Granovetter).
- I would also add the “accumulativeness”, much in the line of Formal Rational Choice Theory: A Cumulative Science of Politics by David Lalman, Joe Oppenheimer, and Piotr Swistak. Although, I have to admit, after having spent 5 years or so studying mathematical sociology and selective works from mathematical economics, the cumulation is sometimes difficult to observe from a local point of view and local time scale of individual researcher. There are so many specific models (strong assumptions etc.), and it is frequently hard to understand the bigger picture. Perhaps it is just the question of time for a “unification” to arrive, … or a researcher…