An ethos of mathematical sociologist: Weak empirical validity and problem of meaning

In order to share the problems, mathematical sociologists have to share the criterion of solvability of the problems before they have common interests in a problem. In this paper we characterize this criterion of solvability as a weak empirical validity. Traditionally, sociology tries to explain the processes and results of actions by interpreting meanings of actions. It is often hard to verify an empirical truthness of a theory for sociologists when they are careful about actor's subjective meaning too much, since they cannot observe directly meanings of actions. Therefore we should confirm an empirical truthness of a model not by checking assumptions itself, but by checking whether the model can predict approximately a social phenomenon which we want to explain, Thus a weak empirical validity is a criterion by which we can confirm a coincidence between the implication derived from a model and a social phenomenon by checking the data. Mathematical sociology as a science will progress by developing the models that satisfy a weak empirical validity.