Archive for March, 2012

Relational Models Theory

March 9, 2012


The Relational Models Theory (RMT) of Alan Fiske is a framework for social relations that details four major types of interpersonal interactions: Communal Sharing (CS), Authority Ranking (AR), Equality Matching (EM), and Market Pricing (MP). These four types can also be combined and nested to form more complex social relations. Thus they are presented to be the elementary building blocks out of which all social relations are made.

John Bolender expounds on Fiske’s theory, by arguing that the four relationships are each described by the inherent mathematical symmetry of the social relation, and that all four can be ordered: in one way by inclusion (in the sense of mathematical group theory) and the opposite way by symmetry breaking (usually considered in physics). The symmetries are viewed as transformations which when applied, like a reorganization of the relationship, do not alter the substance or content of the relationship. CS is more symmetric than AR, which in turn is more symmetric than EM, which lastly is more symmetric than MP. For inclusion, the symmetries of MP are included in the symmetries of EM, those of EM in AR, and AR in CS. For symmetry breaking, a symmetry of CS can be broken to form AR, which in turn has a symmetry that can be broken to form EM, and so on to MP. Thus CS > AR > EM > MP in terms of transformations that preserve symmetry.

As we move from CS to MP, we add increasing structure to a social relation, a greater number of constraints. Additionally, consider symmetry operations in general in the context of equivalent exchange: symmetry by definition is an exchange of participants in a relation, a permutation such that the relation itself is unchanged, that is, equivalent.


Alan Page Fiske / Structures of social life: the four elementary forms of human relations

John Bolender / The Self-Organizing Social Mind


Some changes: replacing the diagram and removing reference to J.-Y. Girard’s infernos of semantics. Also the very important insight from IEP: “The symmetries of solid matter form a subset of the symmetries of liquid matter which form a subset of the symmetries of gaseous matter which form a subset of the symmetries of plasma.”



J.-Y. Girard’s Transcendental Syntax

March 7, 2012

With the recent release of the paper found at the link below, logician Jean-Yves Girard has updated his program for a transcendental syntax to version 2.0. The first version was available last year only in French, but this new manuscript is available in English. Girard is known for his refinement of classical and intuitionistic logic, Linear Logic, and his exploration into the mechanisms of logic, Ludics.

In this new paper, Girard describes four levels of semantics, his infernos: alethic, functional, interactive, and deontic. They descend into the depths of meaning, and thus are numbered from -1 to -4. The negatively first, alethic, is the layer of truth or models. The negatively second, functional, is the layer of functions or categories. The negatively third, interaction, is the layer of games or game semantics. The negatively fourth, deontic, is the layer of normativity or formatting.

Interestingly, these four levels are in good agreement with Richard McKeon’s schema for philosophical semantics, represented by the fourfold of reality, method, perspective, and principle.