Recently, historians have focused on Warren S. McCul¬loch’s role in the cybernetics movement during the 1940s and 1950s, and his contributions to the develop¬ment of computer science and communication theory. What has received less attention is McCulloch’s early work in neurophysiology, and its relationship to his philosophical quest for an ‘experimental epistemology’ – a physiological theory of knowledge. McCulloch’s early laboratory work during the 1930s addressed the problem of cerebral localization: localizing aspects of behaviour in the cerebral cortex of the brain. Most of this research was done with the Dutch neurophysiolo¬gist J. G. Dusser de Barenne at Yale University. The con¬nection between McCulloch’s philosophical interests and his experimental work can be expressed as a search for a physiological a priori, an integrated mechanism of sensation.

Much scholarship in the history of cybernetics has focused on the far-reaching cultural dimensions of the movement. What has garnered less attention are efforts by cyberneticians such as Warren McCulloch and Norbert Wiener to transform scientific practice in an array of disciplines in the biomedical sciences, and the complex ways these efforts were received by members of traditional disciplines. In a quest for scientific unity that had a decidedly imperialistic flavour, cyberneticians sought to apply practices common in the exact sciences – mainly theoretical modeling – to problems in disciplines that were traditionally defined by highly empirical practices, such as neurophysiology and neuroanatomy. Their efforts were met with mixed, often critical responses. This paper attempts to make sense of such dynamics by exploring the notion of a scientific style and its usefulness in accounting for the contrasts in scientific practice in brain research and in cybernetics during the 1940s. Focusing on two key institutional contexts of brain research and the role of the Rockefeller and Macy Foundations in directing brain research and cybernetics, the paper argues that the conflicts between these fields were not simply about experiment vs. theory but turned more closely on the questions that defined each area and the language used to elaborate answers.

Key words: Cybernetics, Macy foundation, Neurophysiology, Rockefeller Foundation, Theoretical modeling, Warren S. McCulloch

Open peer commentary on the article “Enactive Metaphorizing in the Mathematical Experience” by Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes. Abstract: Welcoming their scholarly focus on metaphorizing, I critique Díaz-Rojas, Soto-Andrade and Videla-Reyes’s selection of the hypothetical constructs “conceptual metaphor” and “enactive metaphor” as guiding the epistemological positioning, educational design, and analytic interpretation of interactive mathematics education purporting to operationalize enactivist theory of cognition - both these constructs, I argue, are incompatible with enactivism. Instead, I draw on ecological dynamics to promote a view of metaphors as projected constraints on action, and I explain how mathematical concepts can be grounded in perceptual reorganization of motor coordination. I end with a note on how metaphors may take us astray and why that, too, is worthwhile.

Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an “instrumented field of promoted action”. Children operating in this field first develop environmentally coupled motor-action coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4–6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners’ operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics education research.

Key words: mathematics, education, motor learning, conceptual learning, motor problem, conceptual metaphor

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.

Hutto and Satne, Philosophia (2014) propose to redefine the problem of naturalizing semantic content as searching for the origin of content instead of attempting to reduce it to some natural phenomenon. The search is to proceed within the framework of Relaxed Naturalism and under the banner of teleosemiotics which places Ur-intentionality at the source of content. We support the proposed redefinition of the problem but object to the proposed solution. In particular, we call for adherence to Strict Naturalism and replace teleosemiotics with autopoietic theory of living beings. Our argument for these adjustments stems from our analysis of the flagship properties of Ur-intentionality: specificity and directedness. We attempt to show that the first property is not unique to living systems and therefore poses a problem of where to place a demarcation line for the origin of content. We then argue that the second property is a feature ascribed to living systems, not their intrinsic part and therefore does not form a good foundation for the game of naturalizing content. In conclusion we suggest that autopoietic theory can not only provide a competitive explanation of the basic responding of pre-contentful organisms but also clarify why Ur-intentionality is attributed to them in such an intuitive manner.

Purpose: To show the convergences between Josef Mitterer’s non-dualizing way of speaking and actor-network theory. Method: Comparative analysis of Mitterer’s non-dualizing philosophy and actor-network philosophy. Findings: Profound convergences between the two accounts may lead to a unified account that could redefine traditional philosophical problems. Benefits: The paper extends the range of Mitterer’s non-dualizing philosophy and actor-network theory enabling both to face new problems. Among them, extended non-dualizing philosophy may undergo empirical investigations.

Key words: so far descriptions, from now on descriptions, dualism, actor-network theory

In my article, I propose to discuss constructivism and realism in terms of actions instead of doing that in a usual way, in terms of theories, philosophers or general positions. To enable this, I offer two conceptual tools. First, I use modified model of four types of knowledge introduced by Andrzej Zybertowicz. It approaches any knowledge-building process as a cultural game, and recognizes reproduction, discovery, redefinition, and design of a new game. Second, I use Stanislaw Lem’s model of three types of geniuses. I illustrate my approach briefly using examples from Plato, Spinoza and Berkeley.

Key words: Constructivism, realism, cultural theory, actions, knowledge.

Open peer commentary on the article “Decentering the Brain: Embodied Cognition and the Critique of Neurocentrism and Narrow-Minded Philosophy of Mind” by Shaun Gallagher. Abstract: Simulation theory and theory theory are interaction accounts of theory of mind that have been neurocentrically characterized. A hybrid of these theories approximates the interaction theory of social cognition, and can be described in an indexical-symbolic processing framework.

This paper examines the shared roots and crossed paths between Jean Piaget’s constructivism, what Seymour Paper refers to as “constructionism,” and socio-cultural theories as epitomized by Lev Vygotsky. We do so in the light of more situated, pragmatic, and ecological approaches to human cognition. All these views are developmental (stressing the genesis children’s interests and abilities over time), experiential (in the sense that knowledge is rooted in sensori-motor activity) and interactionist (people are seen as constructing their knowledge by transforming the world). Yet, the views also differ, each highlighting some aspects of how children grow and learn, while leaving other questions unanswered. Piaget’s main contribution was to flesh out what is common in children’s ways of thinking at different stages of their cognitive development and, more important, how consistent, robust, and generally “adapted” their views are. The theory stresses the progressive de-contextualization of knowledge (from here-and-now to then-and-there) and identifies some of the hidden mechanisms (internal reorganizations) that drive human cognitive development. Papert, in contrast, stresses how individuals learn in context and how they use their own – and other people’s – externalizations as objects to think with, especially as their convictions break down. His approach is more situated. Papert is particularly interested the role of new media in human learning. Both Papert and Vygotsky shed light on the articulations between direct and mediated experience (from action and tool-use to enactments, language, and symbol-use). Yet Vygotsky and the Russian school have paid much closer attention to the role of caring adults and peers in a child’s initiation to her culture. They remind us that it takes a whole village to raise a child. Integrating the views helps rethink how children come to make sense of their experiences, and how they find their own places – and voices – in the world. At once world-makers, world-readers, and dwellers in the world, human infants are granted from birth with the abilities to optimize exchanges with people and things by moving in and out of contexts, by shifting perspectives, and by switching roles or standpoint. They are extraordinary learners, and much can be learned from them. Lastly, while mostly inner-driven and curious, children need caring adults, secure grounds, and engaging peers and props to thrive and grow. Tools, media, and cultural artifacts are the tangible forms through which they explore their surrounds, express their thoughts, and share the fun with others – and the traces left by those who came before (cultural heritage) become a terrain for newcomers to create their paths.

Key words: Constructivism, Piaget, Papert, Vygotsky, situated learning, embodied cognition, ecology of mind