An Algebraic Account of the American Kinship Terminology [and Comments and Reply

Abstract

Although componential and transformational analyses are the generally recognized domains for the study of kinship terminology structure, neither procedure completely elucidates the structure formed by kin terms as a system of terms. Both procedures ignore that kin terms, via a kin terms product, form a structure separate from the structure imposed on a genealogical space through definition of kin terms as sets of kin types. Separation of these levels shows that the structure of kin terms is an inherently algebraic form and suggests universal algebras, whose subject matter is the properties of formal structures, as the appropriate domain for the representation and analysis of kin term structure. The American (English) kinship terminology is analyzed using this framework, and it is shown that the system of terms that constitutes it has structure that can be isomorphically represented in algebraic terms. More specifically, it is shown that the structure for the set of kin terms, including properties heretofore seen as problematic, has exact explication within the algebraic representation. The set of kin terms distinguished and their structural relations are shown to result from a consanguineal structure which has the form of an algebra known as an inverse semigroup, with affinal terms imbedded via the product of two consanguineal structures-one centered around Self and the other centered around Spouse-with sex distinctions made on the basis of Spouse relations. The algebraic argument shows what properties suffice to generate the complete kin term structure for the American kinship terminology and suggests the possibility of structural comparison of kinship terminologies at the level of properties defining the generation of structure.