On the Mathematical Theory of Interaction in Social Groups

Sociology is an area in which there are a great many verbal propositions concerning the behavior of human groups under various conditions. If we accept the fact that it makes sense to discuss and analyze social phenomena in terms of quantities that are not precisely defined in a mathematical sense (such as the levels of joint activity, interaction, and friendliness associated with a group), then it would seem worthwhile to consider what conclusions can be drawn from the nature and gross quantitative properties of sets of relations that appear to be translations of sets of verbal propositions into the language of mathematics. Here we consider this question in some detail for a particular type of set of verbal propositions.