Cites and fights: material entailment analysis of the eighteenth-century chemical revolution

The structural-analytic literature of the past decade indicates that transitivity in social networks is an important concern. However, existing structural analytic methods are frequently unable to deal directly with the substantive and methodological problems posed by transitive relations in social structures (Berkowitz, 1982). These difficulties typically surface in one of two contexts. First, those who model structures through multiple graphs defined onto the same set of elements tend to assume either (1) global transitivity or in-transitivity – that is, the same degree of transitivity obtains throughout the network (Johnsen and McCann, 1982), or (2) that there is a sharp and arbitrary limit to the graph theoretic distances over which effects travel (Ber-kowitz, Carrington, Kotowitz, and Waverman, 1978). Neither strategy allows analysts to examine transitivity, itself, empirically. Second, techniques for examining relations among sets of overlapping attributes or ties are still in their infancy. Once again, transitivity among these sets is typically treated a priori rather than as a substantive or empirical problem. A new technique – Material entailment analysis – allows researchers to model concrete situations in which the degree of transitivity present within social structures defined in either of these ways may be investigated empirically. This chapter describes this new technique and outlines ways in which it can be applied to a variety of structural problems in the social sciences. We address the transitivity problem as a special case of the more general issue of orders and partial orders of variables or attributes. Following Nadel (1957), sociologists and anthropologists are often concerned with clusters of attributes in which the presence of one implies the presence of others. To the extent that such an implication is not reciprocated (symmetrical), we have an ordering of the attributes or cultural values. Consequently, a variety of social and cultural domains may be modeled in terms of " if...then " or set-subset relationships among cultural items. One study, for instance, found a partial ordering of basic color terms of the form " if a language has color