This essay presents Gould’s distinctive system for analyzing kin terminologies showing the system’s power, importance, and usefulness—and showing its relationship to other approaches and the payoffs each aims at. In revealing significant new empirical regularities and simplifications, Gould’s analytic system implies important constraints on future analytic and interpretative approaches to kin terminologies. Some of these new insights involve the demonstration of the effect of distributed collective cognitive systems over and above the effects of repeated iterations of individual cognitive constraints or pressures. It is the peculiar nature of the kinterm domain that allows these findings to be so directly shown, but the implication is that these findings apply more generally to the collective cognitive systems that make up language and culture.