Aspects of a formalist theory of kinship

Abstract

I shall assume the general relevance of genealogy for kinship on the basis of my earlier paper (Lehman, 1993). I shall then proceed, first, to examine some further important formal properties of social structure that genealogy imposes on kinship categories. In particular, I shall argue that these make kinship the unique case of a truly ascribed, rather than achieved social structure. In that connection, I shall also show that the structure of the space of kin categories is therefore especially apt for purely formal analysis. I shall, furthermore, extend my earlier work on the category theoretical relation between the two spaces, demonstrating additional algebraic properties that follow from the way genealogical space provides the ground for the instantiation of kin categories, i.e. defining the notion of (possible) kin category occupancy. This, in turn, will involve specifying in detail the way (populations of) actual or supposed individuals are brought into the picture, and especially the way that conceptual/semantic features, derived from properties of persons, and how expectations about relations between them, are brought into and made part of the meaning of kin categories and their terminology. This is intended to be a further corrective critique of, for example, Schneider’s ‘cultural account’ theory of kinship theory, a critique founded upon the crucial requirement of keeping the notions of relational position and personal occupancy of that position analytically distinct.

At the same time I am also concerned to go beyond the question of the relation of genealogical space to kinship category spaces, and to pursue, however briefly, the more general point that kinship (and its associate relational system, marriage) are indeed algebraic spaces. To that extent I feel it important to argue that more encompassing questions about these domains are best addressed through the application of algebraic methods of analysis; that, in fact, the theory of such matters must itself, in the final analysis, be a mathematical object. To that end, though only in my conclusions, I shall present a preliminary demonstration of how such methods go far toward making sense of such larger problems concerning kinship and marriage – in this instance, a hitherto recalcitrant and misconstrued problem in the theory of marriage alliance, that of the systems of patrilateral marriage alliance.