Reflexivity, Recursion, and Self Reference

 Reflexivity, Recursion, and Self Reference


From Reflexivity and Eigenform The Shape of Process


“Reflexive” is a term that refers to the presence of a relationship between an entity and itself. One can be aware of one’s own thoughts. An organism produces itself through its own action and its own productions. A market or a system of finance is composed of actions and individuals, and the actions of those individuals influence the market just as the global information from the market influences the actions of the individuals. Here it is the self-relations of the market through its own structure and the structure of its individuals that moves its evolution forward. Nowhere is there a way to cut an individual participant from the market effectively and make him into an objective observer. His action in the market is concomitant to his being reflexively linked with that market. It is just so for theorists of the market, for their theories, if communicated, become part of the action and decisionmaking of the market. Social systems partake of this same reflexivity, and so does apparently objective science and mathematics. In order to see the reflexivity of the practice of physical science or mathematics, one must leave the idea of an objective domain of investigation in brackets and see the enterprise as a wide ranging conversation among a group of investigators. Then, at once, the process is seen to be a reflexive interaction among the members of this group. Mathematical results, like all technical inventions, have a certain stability over time that gives them an air of permanence, but the process that produces these novelties is every bit as fraught with circularity and mutual influence as any other conversation or social interaction.


In such a context, every object is inherently a process, and the structure of the domain as a whole comes from the relationships whose exploration constitutes the domain. There is no place to hide in a reflexive domain, no fundamental particle, no irreducible object or building block. Any given entity acquires its properties through its relationships with everything else. The sense of such a domain is not at all like the set theoretic notion of collections or unrelated things, or things related by an identifiable property. It is more like a conversation or an improvisation, held up and moving in its own momentum, creating and lifting sound and meaning in the process of its own exchange. Conversations create spaces and events, and these events create further conversations. The worlds appearing from reflexivity are worlds nevertheless, with those properties of partial longevity, emergence of patterns, and emergence of laws that we have come to associate with seemingly objective reality.


From The march of self-reference


One of the main characteristics of social systems as well as individual systems, distinguishing them from many other systems, is indeed their potential for self- referentiality in the latter sense. Concretely, this means not only that the self- knowledge accumulated by the individual in turn affects both his structure and modus operandi, but it also implies – as especially stressed by constructivism – that in self-referential systems like individuals and social systems, feedback loops exist between parts of external reality on the one hand, and models and theories about these parts of reality on the other hand. To a large extent, both individuals and collectivities indeed produce their own world.

While constructivism, as an explanatory paradigm, is focused on individuals, it is certainly valid for social systems as well. Concretely, whenever social scientists systematically accumulate new knowledge about the structure and functions of their society, or about subgroups within that society, and when they subsequently make that knowledge known, through their publications or sometimes even through the mass media – in principle also to those to whom that knowledge pertains – the consequence often is that such knowledge will be invalidated, because the research subjects may react to this knowledge in such a way that the analyses or forecasts made by the social scientists are falsified. In this respect, social systems are different from many other systems, including (most?) biological ones. There is a clearly two-sided relationship between self-knowledge of the system on the one hand, and the behavior and structure of that system on the other hand.

Biological systems, like social systems, admittedly do show goal-oriented behavior of actors, self-organization, self-reproduction, adaptation and learning. But it is only psychological and social systems that arrive systematically, by means of experiment and reflection, at knowledge about their own structure and operating procedures, with the obvious aim to improve these. This holds true on the micro-level of the individual, as in psychoanalysis or other self-referential activities, and on the macro-level of world society, as in planning international trade or optimal distribution of available resources.

For social scientists, the consequences of self-referentiality are interesting not only for gaining an insight in the functioning of social systems, but also for the methodology and epistemology used to study them. There is a paradox here: as stated above, the accumulation of knowledge often leads to a utilization of that knowledge – both by the social scientists and the objects of their research – which may change or even invalidate the validity of that knowledge (Geyer and van der Zouwen, 1988; Henshel, 1990). It is maintained here that this paradox is interesting as well for psychologists, and exists also at the individual level where the individual not only constructs his world, but also continually reconstructs it. This can be seen in a normal life, but is especially visible in several forms of individual therapy, where old self- knowledge is invalidated by new – though not necessarily always better – self-knowledge.

The usual examples of self-referential behavior in social science consist of self-fulfilling and self-defeating prophecies. Henshel (1990) for example, has studied serial self-fulfilling prophecies, where the accuracy of earlier predictions, themselves influenced by the self-fulfilling mechanism, impacts upon the accuracy of the subsequent predictions. In much of empirical social science research. However, self-referential behavior does not loom large – which is rather amazing in view of its supposedly being an essential characteristic of individual human functioning. In this case the research methodology used may be an issue: survey research, where people are asked what they think or feel, offers little opportunity to bring out self-referential behavior, while depth interviews, which concentrate more on the awhyo than the awhato of people’s opinions have a better chance to elicit self-referential remarks in this respect.


Key People:

  • Francisco Varela
  • Lois Kauffman
  • Steven J Bartlett
  • Howard Pattee
  • Niklas Luhmann
  • Felix Geyer
  • George Soros
  • Eric D. Beinhocker
  • Stuart A. Umpleby
  • Heinz Von Foerster


Key Sources of Research:


Reflexivity. A Source-Book in Self-Reference

Steven Bartlett


Self-reference: Reflections on Reflexivity

Steven J. Bartlett & Peter Suber (Eds.)

Dordrecht: Martinus Nijhoff, 1987. Now published by Springer Science.


Self Reference and Recursive Forms

Lois Kauffman


The Complexity of Self-reference
A Critical Evaluation of Luhmann’s Theory of Social Systems

Roberto Poli


Reflexivity and Eigenform The Shape of Process

Louis H. Kauffman


The march of self-reference

Felix Geyer


Essays on Self-reference

By Niklas Luhmann


Evolving Self Reference

Howard Pattee



Steven James Bartlett,%20Phenomenology,%20and%20Philosophy%20of%20Science.pdf



Recursivity and Self-Referentiality of Economic Theories and Their Implications for Bounded Rational Actors


Marco Lehmann-Waffenschmidt Serena Sandri


A Calculus for Self Reference

F Varela


Ouroboros avatars:
A mathematical exploration of Self-reference and Metabolic Closure

Jorge Soto-Andrade, Sebastia ́n Jaramillo ,Claudio Gutie ́rrez and Juan-Carlos Letelier


Self Reference and Autopoiesis

A Locker


Snakes all the Way Down: Varela’s Calculus for Self-Reference and the Praxis of Paradise

André Reichel’s_Calculus_for_Self-Reference_and_the_Praxis_of_Paradise/links/09e4150d0287eebed2000000.pdf


Self-Reference and Time According to G. Spencer-Brown 

Andreas Kull


Reflexivity in Economics: An Experimental Examination on the Self-Referentiality of Economic Theories

By Serena Sandri 2009



Operational Closure and Seif-Reference: On the Logic of Organizational Change

Markus Schwaninger1and Stefan N. Groesser


Fallibility, reflexivity, and the human uncertainty principle

George Soros


Reflexivity, complexity, and the nature of social science

Eric D. Beinhocker


Reflexivity and Economics: George Soros’s Theory of Reflexivity and the Methodology of Economic Science



Stuart Umpleby


Reflexivity, Expectations Feedback and Almost Self-fulfilling Equilibria: Economic Theory, Empirical Evidence and Laboratory Experiments

Cars Hommes

August 14, 2013


 Reflexivity, path dependence, and disequilibrium dynamics

Anwar Shaikh,%20path%20dependence,%20and%20disequilibrium%20dynamics.pdf


Second-Order Economics as an Example of Second-Order Cybernetics

Stuart A. Umpleby


Reflexivity and Equilibria

Francesco Guala


Umpleby, Stuart A.

“Fundamentals and history of Cybernetics.”

World Multi-Conference on Systemics, Cybernetics, and Informatics. 2006.


Complexity to Reflexivity: Underlying Logics Used in Science

Stuart A. Umpleby



Louis H. Kauffman


Laws of Form and the Logic of Non-Duality

Louis H. Kauffman



Louis H. Kauffman



Author: Mayank Chaturvedi

You can contact me using this email mchatur at the rate of AOL.COM. My professional profile is on

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