In a post over at Brokering the Closure — which sounds like the name of a post-rock group, much like Ed Carr’s Open the Echo Chamber blog — Michał Bojanowski aggregates the discussion that has taken place so far on the use of mathematics in the social sciences:
“My subjective list of advantages of formal theory building in social sciences (…):
1. 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.
2. 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 theory and empirics (c.f. The Theory-Gap in Social Network Analysis by Mark Granovetter).
3. 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. Perhaps it is just time… or the researcher…”
The post also aggregates some recent posts in the blogosphere about the supposed death of theoretical economics which, much like that other Mark, I feel is greatly exaggerated…