What Diagrams as a Formal Model Can and Cannot Represent; Examples from Language Family Trees

Abstract

Models of theoretically generated relations among analytic entities have formal properties which enable them to accurately represent some desired relationships, but not necessarily all imaginable relationships. One important part of the modeling task is matching the properties of the model type with the relevant formal properties that one ascribes to the relationships being modeled. Some kinds of mismatches render the model type inappropriate for the given use while others may make it inadequate.As an example: Tree models can represent “descent” relations among languages. They presume languages have single parents but possibly multiple children—entailing a distinction between elements present through descent and elements “borrowed” or otherwise created. Their interpretation typically includes assuming a smooth temporal transition from minimal dialect differences to separate languages. Two other change processes, interpretable within a family tree but not modeled by it, are: 1) the creation of pidgins and 2) the hiving off of a cross-section of a language community to form a new, contrasting language community. By contrast, a multiple parents claim would be incompatible with the tree model