The Generative Logic of Classificatory Kinship Terminologies

Abstract (English)

The generative logic of kinship terminologies includes, axiomatically, isomorphism between the structure of ascending kin terms and the structure of descending kin term, and terminology closure under reciprocity of kin terms. These two axioms will lead the generative logic of a kinship terminology either to a descriptive terminology when sibling kin terms are derived terms, such as sibling = child O parent (read ‘sibling is child of parent’) in the American Kinship Terminology (AKT), or to a classificatory terminology when a sibling kin term is a primary generating kin term like parent or child in the AKT. Let the generating set for ascending male kin terms include Brother as a primary kin term, along with the kin term product equations (1) father O grandfather = grandfather that defines grandfather as a reflexive kin term, (2) Brother O Brother = Brother that defines Brother as a sibling kin term and (3) father O Brother = father that follows from Brother being a primary kin term. Can the primary sibling term Brother be self-reciprocal with the ascending sibling term also being a descending sibling term? If so, then from the reciprocal term equation Brother O Brother = male self and the sibling term equation Brother O Brother = Brother, the contradiction follows that male self = Brother. Thus, an ascending primary sibling term cannot be self-reciprocal and so there must be a descending sibling term, call it brother, distinct from the ascending sibling term, Brother, along with the equation father O brother = father. From the first axiom, the equations isomorphic to the equations father O Brother = father and father O brother = father, namely son O brother = son and son O Brother = son, must also be kin term equations. From the second axiom, the reciprocal equations, Brother O father = father and brother O father = father, for the equations, son O brother = son and son O Brother = son, respectively, must be equations in the kinship terminology. These equations define a classificatory terminology. Thus, G = {male self, father, son, Brother, brother} generates a classificatory kinship terminology. Empirically, German Dziebel has shown that for all kinship terminologies “if … ego prefers to think that he shares common ascent with his siblings [hence, a sibling term is a primary kin term], 0 generation terminology will be Bifurcate Merging” [i.e., a classificatory terminology]. Thus, in the classificatoryTongan terminology the translation of xxxxx and yyyy should be ‘ascending brother’ and ‘descending brother’, respectively, NOT ‘elder brother’ and ‘younger brother’. These terms may properly be used to refer to a descending kin of speaker who is either younger or older than speaker.