An Algebraic Account of the American Kinship Terminology by Dwight W. Read ALTHOUGH THE STUDY OF KINSHIP SYSTEMS has been a major focus for anthropological research since at least the time of Morgan, a completely satisfactory means for defining, characterizing, and analyzing the internal logic that structures a kinship terminology has remained elusive. Morgan's (1871) preliminary distinction of descriptive versus classificatory systems, Kroeber's (1909) seminal paper developing the concept of alternative dimensions along which culturally determined distinctions are said to be realized, and Rivers's (1900) "genealogical method" all still form basic approaches to the study of kinship terminology structure, even though none of these or their subsequent schools of thought has led to a completely sufficient analysis of structure as a form generatable by the logic of a few basic principles (cf. Radcliffe-Brown 1941; Lkvi-Strauss 196934, 493). Componential analysis, the logical consequent to Kroeber's work, has only partially succeeded in laying bare elementary rules, operations, and equations from which a terminology structure may be deduced. While it has provided a method both for presenting and comparing different kinship terminologies in a common idiom and for delineating aspects of the structure of kinship terminologies, exemplars of the componential-analysis method based on the American kinship ter

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Quantitative analysis of descent and marriage practices and kinship term applications among the Alyawara tribe of Central Australia reveals that traditional Radcliffe‐Brownian models of Kariera and Aranda (section and subsection) systems fit the Alyawara in superficial ways but are entirely inappropriate in more fundamental ways. The problems that we encountered in analyzing the data suggest that the Radcliffe‐Brownian models contain basic and fatal flaws. The alternative model that we suggest for the Alyawara is a three‐dimensional structure that incorporates age relations as one of its principal features. Our proposed model is a double helix.

A rigorously grounded symbolic representation of the general consanguineal relation (a) yields succinct definitions for a number of historically important quantitative measures of consanguinity and (b) facilitates an examination of the algebraic relationships among these measures. Several formal devices—including standardized exponent variables, zero power factors, and a new concatenation operator called the “geneaproduct”—are introduced for their anticipated general usefulness in kinship analysis as well as for their specific utility in the explication of consanguineal numbers.

Scheffler's (1980) first criticism i s trivial. The other two are more important and deserve more attention, since both rest on fundamental assumptions about the nature of anthropological inquiry that we do not share with Scheffler. He i s concerned with systems of kin classification as semantic systems, while we are concerned with relations among conceptual systems, patterns of nonverbal behavior, and population biology.the factual fallacy Scheffler is mistaken in two ways with regard to the "factual fallacy." In the first place, the structure of the model that we attributed to Radcliffe-Brown does, in fact, appear in Radcliffe-Brown (1930). Since we did not deal with Radcliffe-Brown's interpretation of that structure, Scheffler's criticism i s irrelevant. In the second place, we used "the Radcliffe-Brownian model" as a generic term that explicitly encompassed the graphic representations used by Radcliffe-Brown, Elkin (1954). and Levi-Strauss (1969). and that implicitly encompassed such derived or secondary models as those by Hammel (1966). Romney andEpling (1958), and Livingstone (1959). Whether Radcliffe-Brown would have approved of our taking his name in this vein is a moot point.