Enactivism theorizes thinking as situated doing. Mathematical thinking, specifically, is handling imaginary objects, and learning is coming to perceive objects and reflecting on this activity. Putting theory to practice, Abrahamson’s embodied-design collaborative interdisciplinary research program has been designing and evaluating interactive tablet applications centered on motor-control tasks whose perceptual solutions then form the basis for understanding mathematical ideas (e.g., proportion). Analysis of multimodal data of students’ hand- and eye- movement as well as their linguistic and gestural expressions has pointed to the key role of emergent perceptual structures that form the developmental interface between motor coordination and conceptual articulation. Through timely tutorial intervention or peer interaction, these perceptual structures rise to the students’ discursive consciousness as “things” they can describe, measure, analyze, model, and symbolize with culturally accepted words, diagrams, and signs – they become mathematical entities with enactive meanings. We explain the theoretical background of enactivist mathematics pedagogy, demonstrate its technological implementation, list its principles, and then present a case study of a mathematics teacher who applied her graduate-school experiences in enactivist inquiry to create spontaneous classroom activities promoting student insight into challenging concepts. Students’ enactment of coordinated movement forms gave rise to new perceptual structures modeled as mathematical content.

Piaget defines intelligence as adaptation, or the ability to maintain a balance between stability and change, or, in his own words, between assimilation and accommodation. When people assimilate the world to their current knowledge, they impose their order upon things. This momentary closure is useful to build “invariants” that lend existence to the world, independent of immediate interaction. In accommodation, people become one with the object of attention. This may lead to momentary loss of control, since fusion loosens boundaries, but allows for change. I choose the domain of perspective-taking to illustrate how this alternation between assimilation and accommodation punctuate individuals’ interactions with the world. I show that the ability to move away from one’s own standpoint, and to take on another person’s view, requires the construction of cognitive invariants: a recasting of the world’s stabilities that transcends any given viewpoint. I conclude that separation is a necessary step toward the construction of a deeper understanding, and that adopting a “god’s eyes view” is by no means contrary to situating one’s one stance in the world.

This chapter sketches an intellectual portrait of W. Ross Ashby’s thought from his earliest work on the mechanisms of intelligence in 1940 through the birth of what is now called artificial intelligence (AI), around 1956, and to the end of his career in 1972. It begins by examining his earliest published works on adaptation and equilibrium, and the conceptual structure of his notions of the mechanisms of control in biological systems. In particular, it assesses his conceptions of mechanism, equilibrium, stability, and the role of breakdown in achieving equilibrium. It then proceeds to his work on refining the concept of “intelligence,” on the possibility of the mechanical augmentation and amplification of human intelligence, and on how machines might be built that surpass human understanding in their capabilities. Finally, the chapter considers the significance of his philosophy and its role in cybernetic thought.

Key words: artificial intelligence, machine intelligence, equilibrium, human intelligence, cybernetic thought

This paper discusses the phenomenological nature of the sense of boundaries (SB), based on the case of S, who has practiced mindfulness in the Satipathana and Theravada Vipassana traditions for about 40years and accumulated around 20,000h of meditative practice. S’s unique abilities enable him to describe his inner lived experience with great precision and clarity. S was asked to shift between three different stages: (a) the default state, (b) the dissolving of the SB, and (c) the disappearance of the SB. Based on his descriptions, we identified seven categories (with some overlap) that alter during the shifts between these stages, including the senses of: (1) internal versus external, (2) time, (3) location, (4) self, (5) agency (control), (6) ownership, and (7) center (first-person-egocentric-bodily perspective). Two other categories, the touching/touched structure and one’s bodily feelings, do not fade away completely even when the sense-of-boundaries disappears.

Context: Although trauma research has advanced immensely, the struggle to find effective treatment for posttraumatic survivors continues. It seems reasonable to say that, at present, our ability to treat those suffering from posttraumatic stress disorder (PTSD) is, at the very least, limited. Problem: We argue that in order to confront the current crisis in the study of trauma - evidenced by our limited ability to offer successful treatment for those who develop PTSD - we must return to the subjective experience. Our claim is that only by applying a rigorous method to study the subjective experience will we be able to understand the meaning of neuronal activity associated with PTSD. Method: The neurophenomenological research program (NRP) is a working plan that enables us to create a solid and reliable link between the subjective experience and neuronal activity. Thus, the NRP allows us to (a) delve deeply (and rigorously) into the subjective experience and, by so doing, (b) extract the cognitive mechanism that constitutes the building blocks bridging between the subjective experience and neuronal activity. Following this, we will be able to (c) identify the relevant neuronal activity for the phenomenon under examination. Results: Based on previous studies among posttraumatic survivors, we suggest that two cognitive mechanisms are especially relevant for the study of trauma: the sense of body ownership (i.e., the sense that this is our own body) and the sense of agency (the sense that we control our body. The trade-off between these closely related, yet independent mechanisms is highly significant. We conclude the article with the presentation of a detailed working plan for the study of trauma - one that begins with the subject and returns to the subject. Implications: This article summarizes our struggle to conduct a phenomenological research in the study of trauma and our methodological efforts of the last ten years. It should help the beginner to avoid some mistakes that have been made in this long journey, yet obviously, each one must build their own route. Likewise, we suggest that phenomenologists, brain scientists and clinicians should find a way to cooperate. This shared effort might allow us to improve our understanding of the traumatic experience and its long-term implications; as such, we believe that in this process a better treatment could be developed. That being said, the limitation of our proposal is the difficulty of creating a shared language that bridges these different worlds. Constructivist content: We strongly embraces phenomenological approach together with enactivist/embodied theories.

Key words: Trauma, PTSD, treatment, neurophenomenology, subjective experience, introspection cognitive bridges, brain activity

Abstract: This response confronts some crucial questions raised by the reviewers: (a) Can the phenomenological approach be applied to the study of trauma? (b) What is the exact meaning of the term “traumatic event? (c) Is our phenomenological approach too thin? (d) What is the nature of the proposed cognitive bridge - what else is needed? (e) Is the shared world indeed lacking? (f) Is it possible to control patients with posttraumatic stress disorder in the lab? (g) How is our proposal innovative?

The paper looks at a combination of systems theory, cybernetics, and sociological theory in search of a tool for inquiring into contemporary social forms. The idea of observing networks, drawing on Heinz von Foerster’s and Niklas Luhmann’s notion of observing systems and Harrison C. White’s network calculus of identity and control, is outlined to enable basic sociological intuitions about social forms to be integrated with an understanding of both complexity and recursivity organizing our perspective on the human condition in a precarious world. Social forms are shown to gain robustness not from substantial identity but from relational ambiguity. Observing networks, or so the hypothesis goes, combine bodies, minds, society, and – soon perhaps – intelligent machines. The paper looks at how an understanding of complexity, recursivity, system, form, and network may help flesh out the calculus of our human condition.

Key words: complexity, form, network, recursivity, society, system

The paper compares social systems theory and social network theory in terms of what it is they respectively seek to elucidate. Whereas systems theory focuses on problems of difference and reproduction, network theory deals with problems of identity and control, the former privileging communication and the latter action. To understand their different foci, it may help to keep in mind that systems theory is a child of computing’s formative years, whereas the more recent success of network theory, despite its roots in a far older tradition, accompanies the advent of the Internet. The paper goes on to compare the two theories with respect to questions of mathematical modeling, culture, and self-reference, which interestingly are closely related. It proposes a mathematical modeling of culture, which uses Spencer-Brown’s notion of form to combine variables of communication, consciousness, and life into one network relying on three systems capable of reproducing themselves. The paper is relevant for constructivist approaches because it shows how systems are constructed relying on networks within their own interpretation as culture.

The paper deals with Aristotelian logic as the special case of more general epistemology and sociology of both science and common sense. The Aristotelian principles of identity, of noncontradiction, and of excluded middle are to be supplemented by the secondorder cybernetic, or cybernEthic principles of paradox, of ambivalence, and of control. In this paper we collect some ideas on how to evaluate the scope of Aristotelian logic with respect to the laws of thought they tried to determine and to do so within the historical moment of the impact of the invention of writing possibly triggering this determination. We look at some modern doubts concerning these laws and discovering an understanding of complexity that is not to be resumed under any principle of identity. The invention of sociology, epistemology, and the mathematics of communication follow suit in focusing not only on the observer but more importantly on the distinction between observers to further contextualize any talk of identities and operationalize both talk and fact of contradiction, paradox, and ambivalence.

Key words: Aristotle, Spencer-Brown, distinction, form, logic, mathematics, pistemology, sociology

The paper is a reading of Martin Heidegger’s Contributions to Philosophy (Of the Even) by means of Ranulph Glanville’s notions of black box, cybernetic control and objects as well as by George Spencer-Brown’s notion of form and Fritz Heider’s notion of medium. In fact, as Heidegger was among those who emphasized systems thinking as the epitome of modern thinking, did in his lecture on Schelling’s Treatise on the Essence of Human Freedom a most thorough reading of this thinking, and considered cybernetics the very fulfilment of modern science it is interesting to know whether second-order cybernetics, as it was not known to Heidegger and as it delves into an understanding of inevitable complexity and foundational ignorance, falls within that verdict mere modernity or goes beyond it. If modern science in its rational understanding considers its subjects to be objects sitting still while being observed, then indeed second-order cybernetics is different. It looks into the observer’s interactions with black boxes, radically uncertain of where to expect operations of a self, but certain that we cannot restrict it to human consciousness.