Space is the Place: The Laws of Form and Social Systems

Abstract

It is well known that Niklas Luhmann’s theory of social systems is grounded in Spencer-Brown’s seminal Laws of Form (LoF) or ‘calculus of indications’. It is also known that the reception of the latter has been rather problematic. This article attempts to describe the construction of LoF, and confront it with Niklas Luhmann’s ontological and epistemological premises. I show how LoF must be considered a protologic, or research into the fundamentals of logical systems. The clue to its understanding is to be found in its profoundly topological conception of common mathematics and (Boolean) algebra. Both are explained as direct offspring of their planar orientation. Self-reference is a justified instance of an extended, more intricate topological arrangement. Its consequences for ontology (non-identity) and epistemology (autology), I argue, have been adopted correctly by Niklas Luhmann. Separate sections are devoted to how Spencer-Brown’s notion of re-entry relates to Luhmann’s definition of system/environment, and to a comparison between Luhmann’s and Parsons’ functionalism.