Chapter 66: Mathematical Sociology

KENNETH C. LAND & THOMAS J. FARARO

Mathematical sociology Mathematics is the human activity of constructing axiomatic definitions of abstract patterns among unspecified or arbitrary elements and studying the properties of such patterns by deductive elaboration, using principles of logic. Any such abstract pattern, arising in such a context, may be said to define a class of mathematical objects, e.g., “differential equations,” “Markov chains,” “semigroups,” and “vector spaces.” If T is the axiomatic theory that defines a class M of mathematical objects, then any entity in M is said to be a T-model. Such models play a central role in the sciences. For example, Von Neumann and Morgenstern (1944) formulated the axiomatic theory of games of strategy, and this game theory (T) defines the class M of game models. As a science, sociology includes the use of such mathematical models. For most sociologists, however, this connection between mathematics and sociology is confined to problems of data analysis, ...

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