Cybernetics, Reflexivity and Second-Order Science

Context Second-order cybernetics and its implications have been understood within the cybernetics community for some time. These implications are important for understanding the structure of scientific endeavor, and for researchers in other fields to see the reflexive nature of scientific research. This article is about the role of context in the creation and exploration of our experience. Problem The purpose of this article is to point out the fundamental nature of the circularity in cybernetics and in scientific work in general. I give a point of view on the nature of objective knowledge by placing it in the context of reflexivity and eigenform. Method The approach to the topic is based on logical analysis of the nature of circularity. Mathematics and cybernetics are both fundamentally concerned with the structure of distinctions, but there can be no definition of a distinction without circularity, since such a definition would itself be a distinction. The article proceeds by explicating the structure of reflexive domains D where the transformations of the domain are in one-to-one correspondence with the domain itself. Results I show that every element of a reflexive domain has a fixed point. This means that eigenforms arise naturally in reflexive domains. Furthermore, a reflexive domain is itself an eigenform (at a higher level). This supports the context of a second-order science that would study domains of science as part of a larger cybernetic landscape. Implications The value of the article is in its concise reformulation of the scientific endeavor as a search for eigenforms in reflexive domains. This new view of science is promising in that it includes the former worlds of apparent objectivity and it embraces those newer worlds of science where the theories and theorists become active participants in the ongoing process of creating knowledge. Constructivist content I argue that the perspective of reflexive domains constitutes a new way to think about the practice of science, with observers deeply imbedded, and objectivity understood as the mutual search for eigenforms.