Mathematical Sociology as an Inquiry of Structural Essence.

Mathematical sociology has started as a research project to develop an alternative approach to the then dominant style of theoretical sociology in l950s and 60s, represented by Parsonian or functionalist theories. As apparently noticed in Coleman's pioneering textbook (Coleman 1964) and White's monumental work (White 1963), the mathematical sociology aimed at establishing a culture in sociology where theories are more rigidly constructed and empirically based. However, the purpose of the mathematical sociology has not accomplished yet. There are several reasons for this failure. One reason is concerned with the nature of social world, which is a meaning-world constructed by people's subjective meanings, and not well suitable to mathematical analysis. More important reason is that among mathematical sociologists there have been several misunderstandings about the role of mathematical models and the nature of theory construction in sociology. Some mathematical sociologists mistakenly conceived that mathematical models should contribute in theory construction through empirical generalization or formalization. And, some others thought that the task of mathematical sociology is to derive a certain theoretically interesting interpretations from mathematical models. They commonly failed to recognize the creative and innovative nature of mathematical model building in sociological theory construction. In this paper, I suggest that the purpose of mathematical sociology is to build a mathematical model which represents a structural essence of the social phenomenon in question and accordingly shed a new light on the natures of the phenomenon. This idea is illustrated and explained by introducing several examples of mathematical modeling to date. [ABSTRACT FROM AUTHOR]