Purpose: This target article explicates mathematical themes in the work of Varela that remain of current interest in present-day second-order cybernetics. Problem: Varela’s approach extended biological autonomy to mathematical models of autonomy using reflexivity, category theory and eigenform. I will show specific ways that this mathematical modeling can contribute further to both biology and cybernetics. Method: The method of this article is to use elementary mathematics based in distinctions (and some excursions into category theory and other constructions that are also based in distinctions) to consistently make all constructions and thereby show how the observer is involved in the models that are so produced. Results: By following the line of mathematics constructed through the imagination of distinctions, we find direct access and construction for the autonomy postulated by Varela in his book Principles of Biological Autonomy. We do not need to impose autonomy at the base of the structure, but rather can construct it in the context of a reflexive domain. This sheds new light on the original approach to autonomy by Varela, who also constructed autonomous states but took them as axiomatic in his calculus for self-reference. Implications: The subject of the relationship of mathematical models, eigenforms and reflexivity should be reexamined in relation to biology, biology of cognition and cybernetics. The approach of Maturana to use only linguistic and philosophical approaches should now be reexamined and combined with Varela’s more mathematical approach and its present-day extensions.

Mathematical Work of Francisco Varela
Louis H. Kauffman

Source: www.univie.ac.at

Context: The notion of “enaction,” as originally expounded by Varela and his colleagues, was introduced into cognitive science as part of a broad philosophical framework combining science, phenomenology, and Buddhist philosophy. Its intention was to help the researchers in the field avoid falling prey to various dichotomies (mind/body, self/world, self/other) bedeviling modern philosophy and science, and serve as a “conceptual evocation” of “non-duality” or “groundlessness: an ongoing and irreducible circulation between the flux of lived experience (being) and the search of reason for conceptual invariants (knowing. Problem: It seems that, within the burgeoning field of “enactivism,” these far-reaching dimensions of the original proposal are often either dismissed or simply ignored. For this reason, the article tries to answer the following questions: Does the move away from the original exposition of enaction matter? What, if anything, has been lost along the way? What are the implications of the elements that have been discarded? Method: By drawing on some of the less well-known works of Varela, we spell out and elucidate some of the more radical aspects of the notion of enaction and the broader philosophical framework into which it was originally embedded. Results: We argue that this broader philosophical framework is of utmost importance, as it shows that enaction is only one part of the multi-layered “change in the context” that Varela felt was needed to successfully instantiate a move towards the non-dual. This “change of context” involves not only a change in the way we think about dualities, but also a change in the way we experience them. The role of new scientific metaphors, such as enaction (but also autopoiesis, embodiment, etc.), is to function as conceptual evocations of this back-and-forth exchange between knowing and being. However, if this overall framework is discarded, as is often the case in contemporary accounts, enaction loses its radical impetus and becomes mellowed down to yet another version of naturalized epistemology. Implications: Taking the notion of enaction seriously implies a radical shift in our conceptions of science and knowledge, as it encompasses a theoretical and existential move away from a detached observer to embedded and engaged cognizer. Thus, our manner of thinking can no longer be considered in isolation from our manner of being, which indicates a deep interconnection between epistemology and ethics, and may entail profound changes in the definition of the aims, methods, and values of the research community: self-transformation as a consequence of, and condition for, understanding. Constructivist content: The target article advocates a critical approach to realist presuppositions in contemporary science and philosophy, and emphasizes a deep interrelation between being and knowing, between ethics and epistemology.

Enacting Enaction: A Dialectic Between Knowing and Being
Sebastjan Vörös & Michel Bitbol

Source: www.univie.ac.at

Social systems can be defined as autopoietic networks of distinctions and rules that specify which actions should be performed under which conditions. Social systems have an enormous power over human individuals, as they can “program” them to sacrifice resources, happiness, loved ones and even themselves to the perpetuation of the system—as exemplified by religious celibacy, honor killings and suicide bombings. Such overriding of the biological instincts of survival and procreation demands powerful control mechanisms. The present paper surveys some of the basic neural and behavioral mechanisms used for programming within social systems, and is followed by another paper surveying emotional and structural mechanism. Basic conditioning happens through rewarding or reinforcement of socially sanctioned actions. Its power is extended by the conformist transmission of narratives that promise as yet virtual rewards, and by ritualized behaviors that suppress non-conforming beliefs through cognitive dissonance. Through such mechanisms, social systems commonly impede individual emancipation, self-actualization and societal progress.

Source: www.academia.edu

It should be noted that similar mechanisms are also useful for promoting cooperation and limiting selfish behaviors.

There are (at least) four ways that an agent can acquire information concerning the state of the universe: via observation, control, prediction, or via retrodiction, i.e., memory. Each of these four ways of acquiring information seems to rely on a different kind of physical device (resp., an observation device, a control device, etc.). However it turns out that certain mathematical structure is common to those four types of device. Any device that possesses a certain subset of that structure is known as an “inference device” (ID).
Here I review some of the properties of IDs, including their relation with Turing machines, and (more loosely) quantum mechanics. I also review the bounds of the joint abilities of any set of IDs to know facts about the physical universe that contains them. These bounds constrain the possible properties of any universe that contains agents who can acquire information concerning that universe.
I then extend this previous work on IDs, by adding to the definition of IDs some of the other mathematical structure that is common to the four ways of acquiring information about the universe but is not captured in the (minimal) definition of IDs. I discuss these extensions of IDs in the context of epistemic logic (especially possible worlds formalisms like Kripke structures and Aumann structures). In particular, I show that these extensions of IDs are not subject to the problem of logical omniscience that plagues many previously studied forms of epistemic logic.

Constraints on physical reality arising from a formalization of knowledge
David Wolpert

Source: arxiv.org