Formalization is typically associated by both supporters and detractors of formal methods with an emphasis on form over content or meaning. However well founded, this association fails to capture why we employ (or not) formal descriptions of what we are describing.

One problem arises when we try to directly link human thought to human behavior (or vice versa); assuming the process of going from one to the other is complex and idiosyncratic, but direct. In this paper I examine an approach to developing a formal system that helps us represent the relationship between ideational and behavioral aspects of socio-cultural phenomena in a manner that is consistent with, and helps address the connections between, symbolic and materialist approaches.

People embedded in cultural processes demonstrate remarkable powers of creation, transformation, stability and regulation. Culture gives agents the power to hyper-adapt: not only can they achieve local minima and maxima, they modify or create the conditions for new adaptations. Culture transcends material and behavioral contexts. Cultural solutions are instantiated in material and behavioral terms, but are based in large part on ‘invented’ symbolic constructions of the interaction space and its elements. We will present an example of how a symbolic system 'drives' the material organization of human groups, explore how symbolic systems act over material domains as a general case, and examine some of the implications of this for multi-agent modelling as a theory-building process.

The claim that extant terminologies are optimal solutions in a space of all possible terminologies depends on invalidly assuming any partition of a set of genealogical relations is a possible kinship terminology.  Instead, kinship terminologies have a particular type of logical/formal structure that is generative with categories providing for classification that is reciprocal.  As a consequence, all terminologies, extant or hypothetical, are optimal solutions in the sense this term is used in the claim made about kinship terminologies. 

Kinship is understood dynamically and processually but kinship terminologies are remarkably stable idea systems. They provide cultural continuity over time and are more resistant to modification than many types of cultural instantiations. Miskitu speakers in Nicaragua, however, have adopted new kin terms that appear to have fundamentally changed the idea system used to generate their kin terms historically. The shape of the changes that have occurred in Miskitu kin terminologies over time are the result of powerful economic, political and social forces introduced, in part, as a consequence of the geography of Mosquito Coast economies, migrations and political processes. We argue that the current use of kin terms is atypically hybrid and is not the result of a single, algebraically derivable idea system. Rather than negating the validity of mathematical approaches to kinship terminologies, the case of Miskitu kinship terminology suggests that core idea systems, although subject to change over time, move between informationally economical forms adapted to socioeconomic changes.