Purpose: Appreciating the relationship between Sylvio Ceccato and Ernst von Glasersfeld, both as people and in their work. Approach: historical and personal accounts, archeological approach to written evidence. Findings: Ceccato’s work is introduced to an English speaking audience, and the roots of Glasersfeld’s work in Ceccato’s is explored. Flaws in Ceccato’s approach are indicated, together with how Glasersfeld’s work overcomes these, specially in language and automatic translation, and what became Radical Constructivism. Conclusion: Glasersfeld willingly acknowledges Ceccato, who he still refers to as the Master. But Ceccato’s work is little known, specially in the English speaking world. The introduction, critique and delineation of extension and resolution of Ceccato’s ideas in Glasersfeld’s work is the intended value of the paper.

Key words: philosophy, language, correlational grammar, Italian Operational School, attention/mind, mental operation, Ernst von Glasersfeld, Silvio Ceccato

Context: The idea for this article sprang from a desire to revive a conversation with the late Ernst von Glasersfeld on the heuristic function - and epistemological status - of forms of ideations that resist linguistic or empirical scrutiny. A close look into the uses of humor seemed a thread worth pursuing, albeit tenuous, to further explore some of the controversies surrounding the evocative power of the imaginal and other oblique forms of knowing characteristic of creative individuals. Problem: People generally respond to humor, i.e., they are inclined to smile at things they find funny. People like to crack jokes, make puns, and, starting at age two, human infants engage in pretense or fantasy play. Research on creativity, on the other hand, has mostly scorned the trickster within. Cognitivists in particular are quick to relegate wit, whimsy, and even playfulness to the ranks of artful or poetic frivolities. Method: We use the emblems of the craftsman, the trickster, and the poet to highlight some of the oblique ways of knowing by which creative thinkers bring forth new insights. Each epitomizes dimensions intrinsic to the art of “possibilizing.” Taken together, they help us better understand what it means to be playful beyond curious, rigorous beyond reasonable, and why this should matter, even to constructivists! Results: The musings characteristic of creative individuals (artists, scientists, children) speak to intelligent beings’ ability to use glitches intentionally or serendipitously as a means to open up possibilities; to hold on to a thought before spelling it out; and to resist treating words or images as conventional and arbitrary signs regardless of their evocative power. To fall into nominalism, Bachelard insisted, is a poet’s nightmare! Implications: Psyche is image, said Jung, and when we feel alive we rely on the imaginal to guide our reason. Note that image is not here to be understood as a picture in the head or a photographic snapshot of the world. The imaginal does not represent, it brings forth what we understand beyond words. It does not lock us into a single mode. Instead, it is a call to be mindful, in Ellen Langer’s sense: in the present, mentally alert, and on the outlook for our psyche’s own surprising wisdom (sagacity. Constructivist content: Debates on the heuristic function and epistemological status of oblique ways of knowing have long occupied constructivist scholars. I can only guess whether my uses of Jung’s imaginal or Bachelard’s anti-nominalism would have amused or exasperated Ernst! I do know that, on occasion, Ernst the connoisseur, bricoleur, and translator allowed the rationalist-within to include the poet’s power to evoke as a legitimate form of rationality. He himself has written about oblique knowing as legit!

Key words: Incongruity, playfulness, mindfulness, trickster, craftsman, poet, glitches.

Open peer commentary on the target article “Who Conceives of Society?” by Ernst von Glasersfeld. Excerpt: The question I am most interested in is the question raised by von Glasersfeld as to whether Luhmann’s talk of “eigen-values” of society actually is, or is not, just a loose metaphor as von Glaserfeld maintains by emphasizing that in the society of human beings “the recursion of operations of observation or description is not governed by fixed rules, unlike the recursion of functions that produce mathematical eigenwerte” (§44, Fn. 4). Indeed, how are we to conceive of the possible eigen-values of society? And who are we to possibly be able to conceive of possible eigen-values?

Context: Public universities in South Africa are currently facing the challenge of decolonising knowledge. This change requires a review of curriculums, as well as teaching and learning with the goal of embracing the epistemology of the learners, addressing issues such as social justice and transformation. Problem: Human communication is subject to several perceptual errors in both listening and seeing, which challenges the success of the communication in the education system. The ability of the teacher and the learners to effectively communicate with one another is a factor for the success of each reaching their goals. The teacher imparts her knowledge in the classroom, but according to von Foerster, “[i]t is the listener, not the speaker, who determines the meaning of an utterance,” for the listener contextualises this information based on her own past lived experience. Thus, the student’s epistemology and her expression of her understanding is integral in the classroom context and should be actively included into the education system. Method: I present a cybernetic approach to the teacher-learner system, challenging traditional ideas about the role of each actor within the system, with special attention given to Pask’s conversation theory. Results: Early empirical findings suggest that a conversational contextual approach results in higher student involvement and better memory retention among the learners. Conversational approaches that are epistemologically inclusive diffuse social problems where the student groups require their individual worldviews to be reflected within the curriculum. This reduces the friction of competing epistemologies within the education system, moving toward a co-created contextually-driven knowledge system. Implications: Many educators would like deeper engagement from their learners but have not found a way to successfully engage the student group. A cybernetic approach is one method that can be adopted to remedy this. This is particularly useful in contexts where there is cultural diversity and impending social change. Constructivist content: I address von Glasersfeld’s points on human cognition, linking it to Austin’s speech acts.

Key words: Contextual approach, conversation theory, decolonisation of knowledge, education, epistemology, teaching and learning.

Context: Constructivist epistemology is not a doctrinal set of clear and consistent theses and assumptions but a movement full of tensions, with minimally integrated lines of discussions. Problem: This situation explains why it is so difficult to come up with a general definition of constructivist epistemology that could serve as a starting point to study its several research programs systematically and comparatively. Method: We compare the constructivist epistemologies of Jean Piaget, Ernst von Glasersfeld, Humberto Maturana, and Niklas Luhmann regarding tensions between knowledge/reality and individual/society. Results: Our comparison leads to a general definition of constructivist epistemology as a heterogeneous movement problematizing certain dualities - such as subject/object, knowledge/reality, or individual/society - that have been shown to be central for epistemological inquiry. We argue that such dualisms can be used as dimensions for critical analysis, comparison, and discussion among the different research programs, and that, at the same time, they would allow us to analyze the general strategies characterizing such programs. The comparative and critical analysis of the programs by way of the aforementioned tensions results in an organized presentation highlighting their convergences, divergences, and singularities.

Context: During the 1980s, Ernst von Glasersfeld’s reflections nourished various studies conducted by a community of mathematics education researchers at CIRADE, Quebec, Canada. Problem: What are his influence on and contributions to the center’s rich climate of development? We discuss the fecundity of von Glasersfeld’s ideas for the CIRADE researchers’ community, specifically in didactique des mathématiques. Furthermore, we take a prospective view and address some challenges that new, post-CIRADE mathematics education researchers are confronted with that are related to interpretations of and reactions to constructivism by the surrounding community. Results: Von Glasersfeld’s contribution still continues today, with a new generation of researchers in mathematics education that have inherited views and ideas related to constructivism. For the post-CIRADE research community, the concepts and epistemology that von Glasersfeld put forward still need to be developed further, in particular concepts such as subjectivity, viability, the circular interpretative effect, representations, the nature of knowing, errors, and reality. Implications: Radical constructivism’s offspring resides within the concepts and epistemology put forth, and that continue to be put forth, through a large number of new and different generations of theories, thereby perpetuating von Glasersfeld’s legacy.

Key words: radical constructivism, mathematics education, viability, reification, representation

In this paper, the author has discussed the epistemological and the pedagogical dilemma he faced in the past and that he is still facing within radical and social constructivist paradigms. He built up an understanding of radical constructivism from the works of Ernst von Glasersfeld and social constructivism from the works of Paul Ernest. He introduced the notion of constructivism including both radical constructivism and social constructivism in brief. Then he reconceptualized these forms of constructivism in terms of epistemological and pedagogical motivation leading to a dilemma. He emphasized how the dilemma within these paradigms might impact one’s actions and how resolving this dilemma leads to eclecticism. He summarized that one paradigm world does not function well in the context of teaching and learning of mathematics (and science). Finally, he concluded the dilemma issue with epistemological and pedagogical eclecticism.

Key words: Radical constructivism, social constructivism, epistemological-pedagogical dilemma, epistemological eclecticism, pedagogical eclecticism.

Purpose: Ernst von Glasersfeld has actively contributed to the development of the ideas of the Scuola Operativa Italiana (SOI) from 1947. The paper outlines the theoretical status of the SOI research around 1965, which also marks the conclusion of an important phase of this development. The aim is to contribute to better understanding of the continuity of Glasersfeld’s research.

Key words: cognition, Italian Operational School, Silvio Ceccato

Context: The constructivist approach to the definition (or analysis) of the fundamental meanings of language in Ernst von Glasersfeld’s work. Problem: Has this approach achieved better results than other approaches? Method: Review of a book chapter by von Glasersfeld that is devoted to the analysis of the concepts of “unity,” “plurality” and “number.” Results: The constructivist approach to the semantics of the fundamental elements of language (some of which are fundamental for sciences too) seems to have produced positive results; moreover these are in a field where other approaches have produced results that do not objectively seem satisfactory.

Key words: semantics, numbers, mental operations, attention, language

Models of cognition and language currently in use as frameworks for computer applications present a clear disequilibrium: they neglect productive mental activities, as for instance synthesis, and over-estimate receptive ones, as analysis. The paper focuses on the Kantian concept of object-synthesis as a basic mental mechanism and underlines its importance for an equilibrated model of cognitive processing. Integration of the Kantian approach with Ceccato’s model of mental operations could allow to implement synthetic operations in computer applications. A syntactic parser (von Glasersfeld and Pisani, 1970) which implements Ceccato’s approach to cognition, semantics and linguistics is reproposed to the attention of AI researchers: it could be used as a basis for a modern implementation of object-synthesis in knowledge representation and natural language processing.