Abstract
Mathematical sociology provides a nice crossroad for multi-disciplinary communication. For an additional driver for the communication toward theory construction, I propose ‘triple-formalization’ that consists of three elements: classical theory, typification, and case study.
Formalization of classical sociology has been emphasized by T. J. Fararo as neo-classical formalization. Our standpoint is very close to him; however, I additionally emphasize on coming and going before hurrying to unification. In this case, I mean to replace contemporary implications of formalization of a classical theory in a different classical tradition or in a broader (or a different) context of the same tradition. The linkage will bring us, not only a new insight for model specification, but also a new perspective for extending a theory to cover more complex processes.
Many classical studies utilize typification in theory construction. However, it is so often difficult to capture logical construction of processes, in terms of which the researchers should define each conceptual axis and the relationship between them in their typification frameworks. Formalization of typification process is important here, not only because sociological theory is deeply related with such processes behind typification, but also because mathematical sociology is promised to contribute on clarifying such processes. Moreover, focusing on typification will make it easier to consider linkage with case study.
In fact, as many classical studies rely on case study, the comparative secondary analysis of the cases could have great significance. In this case, formalization of typification process will provide generalized frameworks for interpretive comparative analysis and contribute to deepen theoretical implications of the cases. This approach that I call formalization of interpretive analysis of cases could be applied to methodological generalization of counterfactual analysis of a single case.
For an illustration, I introduce the model of complementarity of role expectations. This model synthesizes Parsons and Heider traditions, and provides generalized typification for role relationships. Then, I will focus on some contradictory types and consider cases that could appear in the real world.
