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In this paper, the authors attempt to prove there is a relationship between Borges’ “Argumentum ornithologicum” and Anselm’s argument “Argumentum ontologicum”. We suggest Borges, using the image of a flock of birds, with oriental reminiscences, half joking, half serious attempts to prove the existence of God. We demonstrate the fallacies incurred by Borges and why his “Argumentum” has no place within the traditional set of ontological arguments. However, it would easy to forget that Borges’ claim is not philosophical, nor theological, (...) nor apologetic, but rather ironic or paradoxical. (shrink)

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In Ontology, quality determines beings. The quality-quantity bipolarity reveals that a conceptual logical comprehension that can include negation must be a dialectical logic. Quality is a precise characteristic of something capable of augmentation or diminution while remaining identical through differences or quantitative changes. Thus, quality and in opposition quantity are inextricably linked, giving definition to each other, so constituting a logical bipolarity. The theory is that a magnitude G is never separated from secondary qualities α and β, and therefore, a (...) measure depends on a concrete quality Gα or Gβ, that is to say on one pole of a logical bi-pole. However, the particular number, the unit, that expresses the result of a measure is the quality G alone. Examples drawn from physical and chemical experiments illustrate these ideas and elaborate the structure of the concept of opposition between the secondary qualities α and β of a magnitude G. (shrink)

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This commentary on Nescolarde-Selva and Usó-Doménech (Found Sci, 2013) raises questions about the dynamic versus static nature of the model proposed, and in addition asks whether the model might be used to explain ethical flexibility and rigidity.

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By justification we understand what makes a belief epistemologically viable: generally this is considered knowledge that is true. The problem is defining this with a higher degree of precision because this is where different conflicting conceptions appear. On the one hand, we can understand justification as what makes it reasonable to acquire or maintain a belief; on the other, it is what increases the probability that the belief is true. This work tries to prove that beliefs depend on other beliefs (...) that are epistemically justified and that such beliefs are the result of (i.e., they arise from) our privileged intuition of reality. For this, we examine the concept of epistemic regress. Epistemic reasons authorize a proposition P to be the conclusion of an argument in which such reasons function as premises and are vulnerable to epistemic regress. The three most important approaches to epistemic regress are Infinitism, Coherentism and Foundationalism. (shrink)

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In this paper the authors provide an epistemological view on the old controversial random-necessity. It has been considered that either one or the other form part of the structure of reality. Chance and indeterminism are nothing but a disorderly efficiency of contingency in the production of events, phenomena, processes, i.e., in its causality, in the broadest sense of the word. Such production may be observed in natural and artificial processes or in human social processes (in history, economics, society, politics, etc.). (...) Here we touch the object par excellence of all scientific research whether natural or human. In this work, is presented a hypothesis whose practical result satisfies the Hegelian dialectic, with the consequent implication of their mutual reciprocal integration_._ Producing abstractions, without which, there is no thought or knowledge of any kind, from the concrete, that is, the real problem, which in this case is a given Ontological System or Reality. (shrink)

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The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.

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This commentary to Nescolarde-Selva and Usó-Doménech’s (Reality, systems and impure systems. Foundations of Science 2013) links ideas in their paper to radical constructivism and raises two questions. (1) Would it be helpful to substitute the constructivist notion of viability for the traditional notion of truth with its connotations of relating language and reality? (2) Is the link made to issues in ontological philosophy important since the implicit constructivist epistemology of the paper considers mathematical ideas are just as real as ideas (...) about objects. (shrink)

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Upshot: In response to the issues raised in the OPCs, I emphasize the following aspects: teaching cannot be transmitting knowledge, stages are too constraining a model, RC focuses on the individual construction and talking about social context invites the spectre of social constructivism.

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: In my response, I focus on themes that recur in the commentaries: Radical constructivism’s neutrality and the need for and value of sustainability; education and sustainability….

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Context: The paper is a selective survey of radical constructivist (RC) research that relates to education. Problem: Over the past 40 years there have been developments in the research reviewed. Earlier work was often concerned with conceptual clarification and showing different ways children and teachers think, whereas recent work is more systemic and applied. Method: Research with educational implications done by the author and colleagues is surveyed. This survey shows how RC influenced research in a variety of psychological domains including (...) attitudes to different others, science education, and teacher professional development. Results: While initial work by the author in this area focussed on conceptual clarification, the more recent work is classroom-based, with implications for educational practice in schools. The final part of the paper on research by colleagues emphasises how teachers might work together in schools and the broader school system. Implications: RC plays a significant role in national curricula as a theoretical approach to facilitating diversity in schools and empowering children in their education. There is an urgent need to focus on student learning. The work on educational applications cited provides important insights into the resolvable problems of enabling genuine learning communities. Constructivist Content: The paper addresses theoretical clarification, variations in children’s concepts about different others, inclusion, and implementation of educational programmes that use RC frameworks. (shrink)

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Context: Radical constructivism prioritises the processes by which people make sense of their experience and people construct different worlds based on their individual experiences. Problem: It ….

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The experience of fragility is part of the uncertainty surrounding the Covid epidemic. I see Depraz’s experience as involving two types of cognitive processes, one lighter than the other. The ….

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Open peer commentary on the article “Beyond Technocentrism: Supporting Constructionism in the Classroom” by Karen Brennan. Upshot: Brennan describes strategies designed to help teachers use Scratch in their classrooms, emphasising interfaces between the tool and its users, between users and between hope and happening. Previous work with similar aims identified apparently significant cultural approaches to initiating constructionist practice. Questions arise about the development of practice from technocentric to pedagogic over time that may have some answers in the data accumulated.

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Open peer commentary on the article “Negotiating Between Learner and Mathematics: A Conceptual Framework to Analyze Teacher Sensitivity Toward Constructivism in a Mathematics Classroom” by Philip Borg, Dave Hewitt & Ian Jones. Upshot: The target article offers a method for teachers to reflect on their constructivist approach in classrooms. This commentary suggests ways to augment the approach for use with groups of teachers.

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Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: Quale offers a way of categorizing religious discourse based on radical constructivism. This commentary raises questions about the inter-relation of cognitive and non-cognitive knowledge, the role of testimony in learning about religion, and whether knowledge and belief have different roles in cognitive and non-cognitive knowledge, and suggests that Quale’s analysis opens a tolerant perspective on religious discourse.

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Open peer commentary on the target article “From Objects to Processes: A Proposal to Rewrite Radical Constructivism” by Siegfried J. Schmidt. Upshot: Siegfried J. Schmidt’s timely article offers a fresh look at radical constructivism with an emphasis on contextually and culturally located action as an expression of knowing. Perhaps it remains cautious in making connections with neighbouring philosophical approaches. Two areas that are largely unmentioned are the issue of viability and the conceptual analysis, which remained largely on the sidelines in (...) von Glasersfeld’s later work. (shrink)

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Open peer commentary on the article “Info-computational Constructivism and Cognition” by Gordana Dodig-Crnkovic. Upshot: Gordana Dodig-Crnkovic proposes that radical constructivism and info-computational (IC) processes have a synergy that can be productive. Two issues are proposed here: can constructivism help IC to model creative thinking, and can IC help constructivism to model conflict resolution?

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Context: Maturana’s views on cognitive processes and explaining have ethical implications. The aim of this paper is to link ethics and epistemology to facilitate thinking about how to promote respect between different viewpoints through mutual understanding. Method: Maturana’s views on ethics are outlined in three domains: the personal, the interpersonal, and the societal. Results: The ethical implications that emerge around the notion of reality with or without parenthesis, the concept of the legitimate other, and Maturana’s conjectures about the origins of (...) human social groups. Social groups in which cooperation is more important than competition are based on love in the sense that others are accepted as legitimate members of the community. An epistemology that responds to the biological origins of human cognition is one that is more open to cooperation, honesty, responsibility, and respect than an epistemology that takes reality as given and the task of human cognition to represent truth. Implications: This framework for thinking about cognitive processes provides a way of approaching disagreements so they become opportunities for discussion rather than for power assertion of one reality over another. In a world where strongly held viewpoints on ethics and reality lead to conflict, promoting viable models of cognitive process that link cognition and ethics may lead to insights that promote tolerance. Ideas from attribution theory in social psychology are presented as a means of facilitating the emergence of the concept of the legitimate other in discussion about disagreements. (shrink)

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Open peer commentary on the article “Ethics: A Radical-constructivist Approach” by Andreas Quale. Upshot: Andreas Quale in his article defends radical constructivism (RC) from the accusation of being guilty of being ethically neutral. His defence is based on a distinction between clearly communicable cognitive knowledge and less easily communicable value-laden non-cognitive knowledge. The position taken in this commentary is that RC is a process and provides a way of understanding values. To condemn RC for ethical neutrality is to confuse process (...) and product. (shrink)

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Context: This article describes the educational and personal context in which the author met Ernst von Glasersfeld at the University of Georgia in 1975. Problem: The aim is to situate von Glasersfeld’s work from 1975 in its context and show how some of the well-known strands of this work emerged and their implications in many fields. Method: The social context of the educational scene in the 1960s and 1970s is described together with a variety of incidents and plans and seminars (...) in which the author was involved. Results: Von Glasersfeld’s work as a philosopher of constructivism with an empirical method for analysing concepts came at a time when psychologists and educationalists were ready to see how best to work with Piaget’s theory. Ernst’s insights into his radical constructivism, and his historical understanding of Vico’s epistemology nourished a generation of scholars beginning at the University of Georgia. These insights quickly permeated into the field of psychotherapy. On a personal note, the insights influenced the author’s own life’s research and professional work. Implications: By examining the origins of some of Ernst von Glasersfeld’s key ideas in their diversity, the aim is to show how broadly his ideas have been used in fields from child centred learning to psychotherapy. (shrink)

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Context: Johnson argues that because radical constructivism requires social constraints and therefore ontological assumptions, it is no different from constructive realism, which is comparatively mainstream. Results: While the distinction between these approaches appears slim, our concepts are not independent of us, and may need to change in spite of established traditions. Implications: Perhaps radical constructivism cannot be mainstream because it is essentially concerned with epistemological origins of concepts and consequently is not practical enough for the received consensus.

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Systems thinking provides insights into how ideas interact and change, and constructivism is an example of this type of systemic approach. In the 1970s constructivism emphasised the development of mathematical and scientific ideas in children. Recently constructivist ideas are applied much more generally. Here I use this approach to consider beliefs and their role in conflicts and the conditions needed for reconciliation. If we look at Reality in terms of how we construct it as a human cognitive process, we recognise (...) two things. First, that we cannot go beyond our senses and thoughts to what exists independently of us, and second, if we construct what we know we have to take responsibility for this. This inevitably focuses our thinking on the relation we have with the physical and social world, we are a part of the universe rather than apart from it. This paper argues that accepting and understanding these limits of human knowing together with our interconnectedness provide opportunities to understand conflicting positions. To resolve conflict, people with opposing viewpoints have to be prepared to understand each other. That is a challenge because our own reality plays a vital role in our lives, for everything from personal survival to social support. (shrink)

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Open peer commentary on the article “Sensorimotor Direct Realism: How We Enact Our World” by Michael Beaton. Upshot: Accepting the biological origins and limits of what we know is a foundation stone of radical constructivist research. A corollary is that RC considers realism as allowing an impossible comparison between knowledge and reality. Recent works such as that presented in the target article have a more nuanced position in relation to “reality.” Points of similarity and difference between RC and direct realism (...) are discussed in this commentary. (shrink)

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Open peer commentary on the article “Learning How to Innovate as a Socio-epistemological Process of Co-creation: Towards a Constructivist Teaching Strategy for Innovation” by Markus F. Peschl, Gloria Bottaro, Martina Hartner-Tiefenthaler & Katharina Rötzer. Upshot: The target article describes a programme of study in enterprise education based on radical constructivism (RC. There are a number of issues that arise: the RC approach emphasises student learning rather than preparation for teaching, this type of course can have an impact on the other (...) courses in the programme, and the nurturing of student uncertainty requires particular skills in any group by both teachers and students. (shrink)

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By justification we understand what makes a belief epistemologically viable: generally this is considered knowledge that is true. The problem is defining this with a higher degree of precision because this is where different conflicting conceptions appear. On the one hand, we can understand justification as what makes it reasonable to acquire or maintain a belief; on the other, it is what increases the probability that the belief is true. This work tries to prove that beliefs depend on other beliefs (...) that are epistemically justified and that such beliefs are the result of (i.e., they arise from) our privileged intuition of reality. For this, we examine the concept of epistemic regress. Epistemic reasons authorize a proposition P to be the conclusion of an argument in which such reasons function as premises and are vulnerable to epistemic regress. The three most important approaches to epistemic regress are Infinitism, Coherentism and Foundationalism. (shrink)

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The concept of God is studied using the ontological argument of Anselm of Canterbury that proves God’s existence using a syllogism based on ontology. Unlike metaphysical arguments that demonstrate the existence of God through the study of being and its attributes, the ontological argument aims to reach this same goal based on a concept of God by means of the idea of an entity “greater than anything that can be conceived”. Descartes’ influence highlighted some of the philosophical difficulties with the (...) inherent dualism implicit in ontology. Logic does not say whether ideas are true or false, as Logic is concerned with right or wrong inference. We take a non-dualist approach in contrast to some of the approaches reviewed. To investigate belief and faith, a modal logical formalization is used, especially modal logic S5, which we find appropriate for presenting arguments. While mathematics and logic can convince, they do not help one to believe in God. This can make us think that reason is not enough to accept God, one must have faith to have access to Him. The relation between reason and faith needs clarification, and the ontological argument requires an unsustainable dualism. (shrink)

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Context: On 12 November 2010, Ernst von Glasersfeld passed away. He was one of the most important, if not the most important, proponents of constructivist philosophy. Problem: In his life Ernst influenced many other scientists and philosophers. By whom was he himself influenced; who shaped his intellectual development? By collecting contributions from those who knew him closely or have an excellent understanding of radical constructvism we aim at presenting a cartography of the past and current state of affairs of radical (...) constructivism. These contributions should also shed light on the question of the legacy that Ernst leaves behind. Method: Some 25 authors accepted our invitation to contribute to this commemorative issue. Some texts are reminiscence essays expressing their friendship with Ernst, others are academic papers that investigate Ernst’s influence in various disciplines. Two contributions Ernst von Glasersfeld authored himself. Results: Ernst von Glasersfeld is described as an intellectual mentor for many of his students. His legacy is alive in many disciplines ranging from education science to linguistics. Implications: Ernst’s impact on mathematics education is described in some detail in these articles. However, his impact on science education has also been extensive. Constructivism is a foundation stone in the thinking behind the curriculum in many countries and this collection of papers should be useful to practitioners and researchers in education. We think that the work on conceptual analysis could be used more fully as a tool for modelling emerging concepts and hope that the articles here will facilitate interest in this aspect of Ernst’s work. (shrink)

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If the words in Spinoza’s Ethics are considered as symbols, then certain words in the definitions of the Ethics can be replaced with symbols from set theory and we can reexamine Spinoza’s first definitions within a logical–mathematical frame. The authors believe that, some aspects of Spinoza’s work can be explained and illustrated through mathematics. A semantic relation between the definitions of the philosopher and set theory is presented. It is explained each chosen symbol. The ontological argument is developed through modal (...) logic. And finally, we present some conclusions drawn from this work. (shrink)

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In this paper, the authors try to clarify the relations between Meinong’s and Russell's thoughts on the ontological ideas of existence. The Meinongian theory on non-existent objects does not in itself violate the principle of non-contradiction, since the problem that this hypothesis offers to the theory of definite descriptions is not so much a logical problem as an ontological problem. To demonstrate this we will establish what we believe are the two main theses basic to the theory of descriptions: the (...) epistemological thesis and logical thesis. (shrink)

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Suppes proposes an analysis of the structure and identity of empirical theories with his model-theoretical approach and undertakes effective reconstructions of theories in diverse disciplinary fields. Here the authors analyse the results of these examinations under the optics of questions concerning the assumed ontological commitments, and for how they satisfy economic and other criteria.

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Upshot: Is education about memorising or about making meaning? Critics of constructivist instruction argue that it is more efficient to teach directly. However, there is an empowering engagement to making meaning and teachers need to know how to guide students in this process.

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