We introduce a spatial model of concentration dynamics that supports the emergence of spatiotemporal inhomogeneities that engage in metabolism–boundary co-construction. These configurations exhibit disintegration following some perturbations, and self-repair in response to others. We define robustness as a viable configuration’s tendency to return to its prior configuration in response to perturbations, and plasticity as a viable configuration’s tendency to change to other viable configurations. These properties are demonstrated and quantified in the model, allowing us to map a space of viable configurations and their possible transitions. Combining robustness and plasticity provides a measure of viability as the average expected survival time under ongoing perturbation, and allows us to measure how viability is affected as the configuration undergoes transitions. The framework introduced here is independent of the specific model we used, and is applicable for quantifying robustness, plasticity, and viability in any computational model of artificial life that demonstrates the conditions for viability that we promote.

Key words: autopoiesis, viability, robustness, plasticity, spatial dynamical system, metabolism

Upshot: For communicating second-order science, von Foerster’s ethical imperative provides a viable starting point. Proceeding from this, we plead in favour of emphasising the common grounds of diverging scientific opinions and of various approaches in second-order science instead of focussing on the differences. This will provide a basis for communication and stimulate scientific self-reflection.

Living agency is subject to a normative dimension (good-bad, adaptive-maladaptive) that is absent from other types of interaction. We review current and historical attempts to naturalize normativity from an organism-centered perspective, identifying two central problems and their solution: (1) How to define the topology of the viability space so as to include a sense of gradation that permits reversible failure, and (2) how to relate both the processes that establish norms and those that result in norm-following behavior. We present a minimal metabolic system that is coupled to a gradient-climbing chemotactic mechanism. Studying the relationship between metabolic dynamics and environmental resource conditions, we identify an emergent viable region and a precarious region where the system tends to die unless environmental conditions change. We introduce the concept of normative field as the change of environmental conditions required to bring the system back to its viable region. Norm-following, or normative action, is defined as the course of behavior whose effect is positively correlated with the normative field. We close with a discussion of the limitations and extensions of our model and some final reflections on the nature of norms and teleology in agency.

Expressions like “constructivism,” “construction of knowledge,” “learners construct meaning,” and similar ones are starting to become part of the language of science education. We are liable to hear them in professional meetings or inservice workshops and to read them in articles in the professional journals. As the term constructivism becomes more widespread, different people tend to use it with slightly different meanings, and some use it in a loose way to designate a complex of different pedagogical, psychological, or philosophical tendencies. (The ideas about constructivism explained in this chapter are in no way to be taken as an attempt to define the “orthodoxy” of constructivism. Consistent with a constructivist view, they are simply a model of what it means to know. The claim of this model is to be a viable view of knowledge. This chapter aims at presenting the model and exploring from there some relations with teaching and learning of science.) These tendencies seem to have in common the central assumption that all we come to know is our own construction.

Context: The discipline of knowledge management (KM) begins to understand a) that it should move towards a user-centred, socialized KM and b) which business objectives provide motivation to do so. However, it lacks ideas on how to reach the objective that it suggests and justifies. We contend in this paper that this change requires a more viable understanding of knowledge combined with a suitable model of social interaction, otherwise it will fail. Problem: The problem to be solved is to find a way to blend a model of social interaction and a suitable understanding of knowledge so that together they can contribute to the objective of implementing a “user-centred KM.” In this paper we show a solution articulated in several conceptual and experimental components and phases. Method: We use a systemic and cybernetic approach: systemic analysis of the problem, conception of a cybernetic approach, design of a systemic solution, and its evaluation in an experiment. The main methods used are systems engineering, cybernetic modelling, and knowledge engineering. Results: We propose seven interrelated results: 1. A defect analysis of KM; 2. The concept of knowledge as the “Logic of Experience”; 3. A set of five KM design principles; 4. The principle of “Knowledge Identity”; 5. The model of “Knowledge Cooperation”; 6. The architecture of a user-centred KM system; and 7. Insights from a KM experiment. Implications: Our results are useful for any stakeholder in today’s knowledge economy when they need to understand, design, build, nurture and support an organization’s capacity to learn and innovate for the benefit not only of the company’s financial owners but also of the individuals who work in it. Future research should urgently address the issues of “knowledge identity” and the “knowledge contract” and KM practice should design its next steps for moving towards a user-centred KM in conformity with the principle of “knowledge identity.” The paper links explicitly to radical constructivism and argues in favour of a radical constructivist foundation for KM in which knowledge is seen as the “Logic of Experience.” It also shows how this KM foundation can be extended with a social perspective and by that allow the individual and the social to be conceived of as complementary elements in one single KM system.

Key words: logic of experience, knowledge identity, knowledge cooperation, design for meaning, community of research, user-centred knowledge management

Context: Constructivist teachers who find themselves working within an educational system that adopts a realist epistemology, may find themselves at odds with their own beliefs when they catch themselves paying closer attention to the knowledge authorities intend them to teach rather than the knowledge being constructed by their learners. Method: In the preliminary analysis of the mathematical learning of six low-performing Year 7 boys in a Maltese secondary school, whom one of us taught during the scholastic year 2014-15, we constructed a conceptual framework which would help us analyze the extent to which he managed to be sensitive to constructivism in a typical classroom setting. We describe the development of the framework M-N-L (Mathematics-Negotiation-Learner) as a viable analytical tool to search for significant moments in the lessons in which the teacher appeared to engage in what we define as “constructivist teaching” (CT) during mathematics lessons. The development of M-N-L is part of a research program investigating the way low-performing students make mathematical sense of new notation with the help of the software Grid Algebra. Results: M-N-L was found to be an effective instrument which helped to determine the extent to which the teacher was sensitive to his own constructivist beliefs while trying to negotiate a balance between the mathematical concepts he was expected to teach and the conceptual constructions of his students. Implications: One major implication is that it is indeed possible for mathematics teachers to be sensitive to the individual constructions of their learners without losing sight of the concepts that society, represented by curriculum planners, deems necessary for students to learn. The other is that researchers in the field of education may find M-N-L a helpful tool to analyze CT during typical didactical situations established in classroom settings.

Key words: Mathematics teaching, mathematics learning, constructivist teaching, constructivist framework

Context: Radical constructivism claims that we have no final truth criteria for establishing one ontology over another. This leaves us with the question of how we can come to know anything in a viable manner. According to von Glasersfeld, radical constructivism is a theory of knowledge rather than a philosophy of the world in itself because we do not have access to a human-independent world. He considers knowledge as the ordering of experience to cope with situations in a satisfactory way. Problem: Von Foerster and Krippendorff show that the central goal of a constructivist theory of knowing must be to find a way of putting the knower into a known that is constructed so as to keep the knower, as well as the knowing process, viable in practice. Method: The conceptual and philosophical analysis of present theories and their necessary prerequisites suggests that such foundation for viable knowing can be built on the analysis of what the ontological prerequisites are for establishing viable observing, cognition, communication and observer-communicators, and communication media and vehicles. Results: The moment an observer chooses to accept his/her own embodied conscious presence in this world as well as language, he/she must accept other humans as partly independently existing conversation partners; if knowledge and knowing has to make sense, he/she must also accept as prerequisites for our observation and conversation a pre-linguistic reality from which our bodies come and which our conversation is often about. Furthermore, we can no longer claim that there is a reality that we do not know anything about: From being here in conversation, we know that the world can produce more or less stable embodied consciousnesses that can exchange and construct conceptual meanings through embodied conversations and actions that last over time and exist in space-time and mind, and are correlated to our embodied practices. We can also see that our communication works through signs for all living systems as well as in human language, understood as a structured and progressively developed system of communication. The prerequisite for this social semiotic production of meaning is the fourfold “semiotic star of cybersemiotics,” which includes at least four different worlds: our bodies, the combination of society, culture and language, our consciousness, and also an outer nature. Implications: The semiotic star in cybersemiotics claims that the internal subjective, the intersubjective linguistic, our living bodies, and nature are irreducible and equally necessary as epistemological prerequisites for knowing. The viable reality of any of them cannot be denied without self-refuting paradoxes. There is an obvious connectedness between the four worlds, which Peirce called “synechism.” It also points to Peirce’s conclusion that logic and rationality are part of the process of semiosis, and that meaning in the form of semiosis is a fundamental aspect of reality, not just a construction in our heads. Erratum: The paper erroneously refers to “pleroma.” The correct term is “plemora.”

Key words: ontology, embodiment, philosophy of observing, second-order cybernetics, autopoiesis, semiotics, language, phenomenology, radical constructivism, Edmund Husserl, Charles Sanders Peirce, George Spencer-Brown

This paper examines the application and usage of the idea of autopoiesis – a theory of living systems – within the context of viable systems theory. The paper is part of a broader consideration of how, at the social and organisational level, the relationship between these two sets of ideas about might be rethought and reconfigured to produce more comprehensive insight into the nature of the relationship between systems and the environments in which they are embedded (see, for example, Brocklesby, 2001).

Key words: living system, class identity, functional term, viable system, model.

This paper examines the application and usage of the idea of autopoiesis – a theory of living systems – within the context of viable systems theory. In recent years the term autopoiesis has extended beyond the domain of cellular biology where it originated and is now used extensively across a range of different disciplines, fields of enquiry, and professional practice. The paper seeks to provide clarification of a distinction between viable and autopoietic systems that appears to have become somewhat clouded as a result of the transfer of ideas and terminology from one domain to another.

Key words: Viable systems, autopoiesis, living systems, autonomous systems, cybernetics.

This paper responds to David Elkind’s article “The Problem with Constructivism, ” published in the Summer 2004issue ofThe Educational Forum. It argues that Elkind’s thesis – teacher, curricular, and societal readiness lead to the implementation of constructivism – is conceptually problematic. This paper also critiques constructivism and supports objectivism as a viable philosophy of education.