Why do we need mathematical models?

Abstract

The possibility of integrating theoretical and empirical research in mathematical sociology is examined from the viewpoint of the hypothesis-deriving power of mathematical models. First, we examine the complementarity between mathematical sociology and quantitative sociology, referring to the basic framework of empirical scientific research, which is developed through the cycle of observation, empirical generalization, theory, and hypothesis testing. Next, we discuss why a mathematical model is necessary for sociology as an empirical science. We show that mathematically expressed theories can derive implications as hypotheses that cannot be reached by verbal reasoning, although hypotheses can be deduced from abstract theories expressed in ordinary language. Mathematical propositions are qualitatively different from verbal empirical generalizations. The mathematical representation of theory systematizes isolated empirical generalizations and leads to the complementary development of theory and experience.