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.

In this paper I explore the possibility that recursion is not part of the cognitive repertoire of non-human primates such as chimpanzees due to limited working memory capacity. Multiple lines of data, from nut cracking to the velocity and duration of cognitive development, imply that chimpanzees have a short-term memory size that limits working memory to dealing with two, or at most three, concepts at a time. If so, as a species they lack the cognitive capacity for recursive thinking to be integrated into systems of social organization and communication. If this limited working memory capacity is projected back to a common ancestor for Pan and Homo, it follows that early hominid ancestors would have had limited working memory capacity. Hence we should find evidence for expansion of working memory capacity during hominid evolution reflected in changes in the products of conceptually framed activities such as stone tool production. Data on the artifacts made by our hominid ancestors support this expansion hypothesis for hominid working memory, thereby leading to qualitative differences between Pan and Homo.

The promise of agent-based for explicating properties of social systems has not yet been fully realized. Agent models sometimes provide only a veneer of, rather than substantive engagement with, social behavior. The problem will be illustrated with Axelrod’s model for evolution of ethnocentrism (a biological model) versus Schelling’s model for spatial segregation based on preferences (a cultural model). The examples show the need to incorporate both the biological and cultural basis for behavior through a schema that includes behavior based on cultural/cognitive processing of information and behavior based on biological/cognitive processing of information. An example of an agent-based model that implements decision making in this manner is discussed. The model accounts for heterogeneity in behavior outcomes and leads to two main predictions: (1) small scale, hunter-gatherer societies in resource scarce environments will have stable adaptations less affected by variation in resource abundance in comparison to groups in resource rich regions where inter-group conflict is more likely and (2) the relationship between community size, population size and administrative complexity will have two distinct patterns, one for patrilineally organized societies and the other for matrilineally organized societies. Both predictions have been verified empirically.

A recent article argues that pure working memory in humans and chimpanzees have the  same size.  However, the data offered to support this claim show the opposite, namely that the  size of pure working memory in chimpanzees is smaller than that of humans.  In addition, extensive data show that the effective size of working memory in chimpanzees is much smaller than in humans.  Altogether, there are quantitative differences in the size of working memory (pure or effective) between chimpanzees and humans leading to significant qualitative differences between them.

The analysis provided in this paper is not that of any particular Dravidian terminology, let alone a proto-Dravidian terminology. Rather, it the analysis of an abstracted Dravidian terminology formed by dropping one of the four "principles of opposition" that Louis Dumont (and Trautmann) considered to be essential to Dravidian terminologies, namely that of relative age, as if relative age is not an integral part of Dravidian terminologies. De Almeida merely notes (after quoting Dumont (1953)): "we ignore distinctions concerning relative age" (p. 2). One may want to simplify in order to keep tractable the algebraic argument regarding products of kin types, but this means we are dealing with a formal analysis constructed at an unstated remove from the ethnographic reality of any Dravidian terminology.

Elaboration of individuation is one of the trends in primate evolution. Individuation makes it more difficult to maintain group coherency. Individuation as it occurs in the phylogenetic shift from the Cercopithecoids (Old World monkeys) to African pongids, especially Pan, appears to have passed a threshold with Pan reverting to smaller, less coherent groups of males and females as a way to deal with increased individuation. In contrast, hominid evolution displays a pattern of group coherency and cooperative behavior that arose in conjunction with the mental construction of relations among individuals that we refer to as genealogical relations. Genealogical relations transcend the limitation of biological kinship as a basis for group coherency, but the combinatorial complexity of all possible genealogical relations becomes problematic with increase in group size. The latter was resolved, it is argued, through the construction of acomputational system—a kinship terminology—whose conceptual complexity is independent of the size of a group. This shift to a conceptual/cultural foundation for group coherency changed the dynamics of societal change away from biologically grounded processes of change.

Classificatory (“bifurcate merging”) terminologies with a ‘cross-cousin’ marriage rule are sometimes grouped together as Dravidian terminologies despite significant structural differences among the terminologies so classified. For example, the Kariera terminology has four ‘grandparent’ and ‘grandchild’ terms and does not have an older/younger distinction for ‘cross-cousin’ terms. In contrast, Dravidian language terminologies of India typically have two ‘grandparent’ and ‘grandchild’ terms and make an older/younger distinction for cross-cousin terms. These differences are not superficial and relate both to substantive differences in social organization for the societies in question and the “meaning” of ‘cross-cousin’ marriage. In this paper I develop the generative logic for the used by the Nanjilnattu Vellalar, a Tamil-speaking group in southern India. This logic underlies the structural features of the Dravidian terminologies such as the parallel/cross distinction used to characterize marriages in societies with Dravidian terminologies. The generative logic structurally distinguishes Dravidian language terminologies from other, superficially similar terminologies such as the Kariera terminology.