Symbolic logic and the analysis of social organization

Abstract

Just as the notations of arithmetic, algebra, and the calculus are mental tools invented to disentangle complex relations among quantitative variables, so the notation of symbolic logic is a mental tool for disentangling complex logical relations, such as class inclusion, conjunction, disjunction, implication, and denial. Rules governing cohabitation, “marriage” (these two not necessarily synonymous), and the various relations associated with different types of kinship are extremely complex in certain cultures. They seem even more complex to us than to the practitioners, because we do not even have words in our language to specify the vast complexities of kinship. This paper shows how symbolic logic notation can be used to make the kinship terms, relations, and rules based on these relations, concise. Even conclusions can be derived by symbolic logic which are not explicitly stated in ethnographic records. Thus the author derives the following theorem: “A Pawnee's marriage partner must be the granddaughter of the sister of ego's father's father,” and notes that the ethnographic record does not contain this rule. Whether the Pawnees indeed follow this rule is a matter of empirical verification. If they do not, we know that there is an inconsistency between rule and practice, and further questions can be raised concerning the way rules actually govern behavior. If they do, they appear as sophisticated logicians, an interesting anthropological finding.