Human Complex Systems

The goal of this paper is to relate formal analysis of kinship terminologies to a better understanding of who, culturally, are defined as our kin. Part I of the paper begins with a brief discussion as to why neither of the two claims: (1) kinship terminologies primarily have to do with social categories and (2) kinship terminologies are based on classification of genealogically specified relationships traced through genitor and genetrix, is adequate as a basis for a formal analysis of a kinship terminology.

The social category argument is insufficient as it does not account for the logic uncovered through the formalism of rewrite rule analysis regarding the distribution of kin types over kin terms when kin terms are mapped onto a genealogical grid. Any ormal account must be able to account at least for the results obtained through rewrite rule analysis. Though rewrite rule analysis has made the logic of kinship terminologies more evident, the second claim must also be rejected for both theoretical and empirical reasons. Empirically, ethnographic evidence does not provide a consistent view of how genitors and genetrixes should be defined and even the existence of culturally recognized genitors is debatable for some groups. In addition, kinship relations for many groups are reckoned through a kind of kin term calculus independent of genealogical connections. Theoretically, rewrite rule formalism is descriptive and not explanatory of kinship terminology features. Four substantive problems with rewrite rule formalism are identified and illustrated with an example based on the concepts, Friend and Enemy. In Part II these problems are resolved when a kinship terminology is viewed from the perspective of a structured, symbolic system in which there is both a symbol calculus and a set of rules of instantiation giving the symbols empirical content.

The way in which a kinship terminology constitutes a structured symbol system is illustrated with both the American/English and the Shipibo Indian (Peru) kinship terminologies. Each of these terminologies can be generated from primitive (or atomic) symbols using certain equations that give the structure its form and where the structure is constrained to satisfy two properties hypothesized to distinguish kinship terminology structures from the symbol structures. The structural analysis predicts correctly the distribution of kin types across the kin terms when the atomic kin terms/symbols are instantiated via the primitive kin types. In addition, features of the terminologies that heretofore have been assumed to arise for reasons extrinsic to the internal logic of the terminology are shown to be a consequence of the logic of how the symbol structure is generated.