Spencer-Brown, Luhmann and Klein on Symmetry

Abstract

Abstract This article discusses the concept of symmetry as Felix Klein developed it in his works on geometry as a measure of invariance. The objective is to generalize from Klein’s model and principles to be able to apply the concept of symmetry to the study of social structures or social formations in sociology. To achieve this goal, the article goes on to consider how the concept of symmetry bears on the Laws of Form of George Spencer-Brown and on Niklas Luhmann’s theory of functional differentiation. Both of them are reinterpreted in terms of symmetry breaking.