Research on self-reference and recursion

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Peter Winiwarter has a nice article (Autognosis, 1986) on the many types of self-referential thinking that have emerged in mathematics, logic, computation, physics, chemistry, biology, sociology, psychology, and other sciences, particularly beginning in the 1970's. He makes an opening case that self-referential, recursive processes are pervasive in universal dynamics, both physical and psychical, and outlines the value of bottom up, top down, and organic (synthetic) perspectives on these processes.


Wikipedia calls this way of thinking recursionism. They link to Subhash Kak's 142 page monograph, "Recursionism and Reality", 2005 that independently argues for a subset of Winiwarter's points, but with much less concision and clarity.

William Poundstone's The Recursive Universe, 1985 has similar insights with respect to recursive computation, focusing largely but not exclusively on cellular automata (CA). Stephen Wolfram's A New Kind of Science, 2002 attempts a scientific unification via computational iterations with CA, and some find it valuable.


William Hall is particularly interested in the emergence and evolution of autonomously self-sustaining (or "autopoietic") systems, where the self-referential and recursive aspects were given their most detailed presentation by Humberto Maturana and Francisco Varela in their book Autopoiesis and Cognition: The Realization of the Living (1980). Varela et al. (1974) claimed that possession of a set of six criteria (aggregated under the name of autopoiesis) by a system were necessary and sufficient to determine that the system was living.

Paraphrased here for brevity, any system that is characterized by all six of the following criteria:

  • bounded (distinguishably demarcated from the environment)
  • complex (individually identifiable components within the boundary)
  • mechanistic (system driven by cybernetically-regulated energy fluxes or metabolic processes)
  • self-referential (system boundaries internally determined)
  • self-producing (system intrinsically produces own components)
  • autonomous (self-produced components are necessary and sufficient to produce the system)

is considered to be autopoietic, and thus meeting the criteria to be considered living.

Maturana and Varela's writing on the recursive and self-referential aspects of autopoiesis that they called "organizational closure" was written in a highly idiosyncratic language. With the notable exception of P.L. Luisi, e.g., The Emergence of Life: From Chemical Origins to Synthetic Biology (2006), few mainstream biologists have paid any attention to this work. On the other hand, despite Maturana and Varela's frequent statements that they only intended the concept to be applicable to macromolecular systems at the cellular level of organization, several post-modernist cognitive and social scientists in Europe built theories on autopoietic foundations. John Mingers' Self-Producing Systems: Implications and Applications of Autopoiesis (1995) reviews early applications of autopoiesis to social systems. The most notable of the European social thinkers using autopoiesis was Nicklas Luhmann, who based his Social Systems Theory (e.g., Essays of Self-Reference (1990), Social Systems (1995), and Theories of Distinction (W. Rasch, ed. - 1995) on what Hall and Nousala (2010) claim is a fundamental misunderstanding of the self-referentially recursive nature of autopoiesis. For example, Luhmann and his followers have misunderstood the "closure" of self-reference to form a paradoxically vicious circle, when it is actually an evolutionary spiral along the time axis.

In his studies of autopoiesis, Hall (2005, 2006) has shown that Maturana and Varela's type of autopoiesis validly applies to complex entities at the cellular, organismic, and social organismic levels of organization, and he is working towards a unification of Maturana and Varela's autopoiesis, with Karl Popper's recursively cyclical evolutionary epistemology as best explained in (Objective Knowledge: An Evolutionary Approach (1972) and Knowledge and the Body-Mind Problem: In Defence of Interaction (1994).

What research has been done with respect to organic (evolutionary, developmental, or integrative) perspectives on self-referential systems or recursion since 1986?