Open peer commentary on the article “Ethics: A Radical-constructivist Approach” by Andreas Quale. Upshot: The first of my two main goals in this commentary is to establish thinking of ethics as concepts rather than as non-cognitive knowledge. The second is to argue that establishing models of individuals’ ethical concepts is a scientific enterprise that is quite similar to establishing models of individuals’ mathematical concepts. To accomplish these two primary goals, I draw from my experience of working scientifically with von Glasersfeld (...) for 25 years while he was developing radical constructivism as a coherent model of knowing, and appeal to several of his basic insights to establish constructing models of ethical concepts as a scientific enterprise. (shrink)

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: My commentary has two general goals. First, I investigate how basic principles of radical constructivism might be used in constructing models of mathematics teaching. Toward that end, I found that I was not in complete intersubjective agreement with Borg et al.’s use of some basic terms. Second, I (...) explore what mathematics teaching might look like in what is construed as constructivist mathematics teaching. Toward that end, I comment on Borg et al.’s use of “negotiation” and explain how a constructivist teacher can establish experiential models of students’ mathematics. (shrink)

Open peer commentary on the target article “Who Conceives of Society?” by Ernst von Glasersfeld. Excerpt: My goal in this commentary is to say enough to suggest that the meanings children impute to the language and actions of other children are based on their current conceptual schemes and that, if the schemes are at different levels of the constructive process, it is no easy feat for children to use their schemes in interactive mathematical communication.

Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: The first of my three main goals in this commentary is to demonstrate that Quale’s radical separation between cognitive and non-cognitive knowledge is not viable. The second is to establish Quale’s assertion that a radical constructivist cannot be genuinely religious is a result of taking radical constructivism and religion as abstracted first-order models and is a result of comparing and contrasting elements of these models. The third (...) goal is to establish how religious radical constructivists establish relations between their religious beliefs and their radical constructivist beliefs. To accomplish the first goal, I appeal to the work of Damasio to establish that what Quale refers to as “non-cognitive knowledge” is inextricably cognitive. I also appeal to the work of both Damasio and von Glasersfeld to demonstrate that the Cartesian duality between mind and body is not viable. To accomplish the last two goals, I make a distinction between first- and second-order knowledge and contrast Quale’s argument that a radical constructivist cannot be religious with the relation between religious beliefs and radical constructivism from the perspective of actual religious radical constructivists. (shrink)

Purpose: One of my goals in the paper is to investigate why realists reject radical constructivism (RC) as well as social constructivism (SC) out of hand. I shall do this by means of commenting on Peter Slezak’s critical paper, Radical Constructivism: Epistemology, Education and Dynamite. My other goal is to explore why realists condemn the use of RC and SC in science and mathematics education for no stated reason, again by means of commenting on Slezak’s paper. Method: I restrict my (...) comments to Slezak’s paper and leave it to the reader to judge which, if any, of the reasons that I advance for these two states of affairs are not specific to Slezak’s paper. Other readers might not agree with my interpretations of Slezak’s paper, including Slezak himself, but I offer them after having worked with von Glasersfeld in interdisciplinary research in mathematics education for over 25 years. Findings: My findings are that Slezak: (1) rejects RC and SC on the basis of unjustified criticisms, (2) does not explore basic tenets of RC nor of SC beyond the unjustified criticisms, (3) rejects how SC and RC have been used in science and mathematics education, based at least in part on the unjustified criticisms, (3) dislikes how SC has been used in science and mathematics education, a dislike that fuels his rejection of any constructivism, and (4) doesn’t explore how RC has been used in scientific investigations in mathematics education. On the basis of these findings, I conclude that how epistemological models of knowing might be used in science or mathematics education would be better left to the educators who use them in interdisciplinary work. (shrink)

Purpose: In the paper, I discuss how Ernst Glasersfeld worked as a scientist on the project, Interdisciplinary Research on Number (IRON), and explain how his scientific activity fueled his development of radical constructivism. I also present IRON as a progressive research program in radical constructivism and suggest the essential components of such programs. Findings: The basic problem of Glasersfeld's radical constructivism is to explore the operations by means of which we assemble our experiential reality. Conceptual analysis is Glasersfeld's way of (...) doing science and he used it in IRON to analyze the units that young children create and count in the activity of counting. In his work in IRON, Glasersfeld first conducted a first-order conceptual analysis of his own operations that produce units and number, and then participated in a second-order analysis of the language and actions of children and inferred the mental operations that they use to produce units and number. Further, Glasersfeld used Piaget's concept of equilibration in the context of scheme theory in a second-order analysis of children's construction of number sequences and of more advanced ways and means of operating in the traffic of numbers. Research Implications: The scientific method of first- and second-order conceptual analysis transcends our work in IRON and it is applicable in any radical constructivist research program whose problem is to explore the operations by means of which we construct our conceptions. Because of the difficulties involved with introspection, conducting second-order conceptual analyses is essential in exploring these operations and it involves analyzing the language and actions of the observed. But conceptual analysis is only a part of the research process because the researchers are by necessity already involved in creating occasions of observation. The "experimenter" and the "analyst" can be the same person or they can be different people. Either case involves intensive and sustained interdisciplinary thinking and ways of working if the research program is to be maintained over a substantial period of time as a progressive research program. (shrink)

Context: Ernst von Glasersfeld introduced radical constructivism in 1974 as a new interpretation of Jean Piaget’s constructivism to give new meanings to the notions of knowledge, communication, and reality. He also claimed that RC would affect traditional theories of education. Problem: After 40 years it has become necessary to review and evaluate von Glasersfeld’s claim. Also, has RC been successful in taking the “social turn” in educational research, or is it unable to go beyond “private worlds? Method: We provide an (...) overview of contributed articles that were written with the aim of showing whether RC has an impact on educational research, and we discuss three core issues: Can RC account for inter-individual aspects? Is RC a theory of learning? And should Piaget be regarded as a radical constructivist? Results: We argue that the contributed papers demonstrate the efficiency of the application of RC to educational research and practice. Our argumentation also shows that in RC it would be misleading to claim a dichotomy between cognition and social interaction (rather, social constructivism is a radical constructivism), that RC does not contain a theory of mathematics learning any more or less than it contains a theory of mathematics teaching, and that Piaget should not be considered a mere trivial constructivist. Implications: Still one of the most challenging influences on educational research and practice, RC is ready to embark on many further questions, including its relationship with other constructivist paradigms, and to make progress in the social dimension. (shrink)

The ‘decapitation gambit’ holds that, if physical decapitation normally entails the death of the human being, then physiological decapitation, evident in cases of total brain failure, entails the death of the human being. This argument has been challenged by Franklin Miller and Robert Truog, who argue that physical decapitation does not necessarily entail the death of human beings and that therefore, by analogy, artificially sustained human bodies with total brain failure are living human beings. They thus challenge the current neurological (...) criterion for determining death and argue for a return to the traditional criterion of the irreversible loss of circulation and respiration. In this paper, I defend the decapitation gambit and total brain failure as a criterion for determining death against Miller and Truog's criticism. (shrink)

The appearance of consciousness in the world is an amazing and puzzling fact in its own right. Indeed, consciousness is one of the most mystifying features of the cosmos. The unity of consciousness is something that cries out for analysis and explanation as well. This chapter provides a way of relating the three types of unity: objectual phenomenal unity; subject phenomenal unity; and subsumptive phenomenal unity. According to Tim Bayne and David Chalmers, this sort of unity is irrelevant for investigating (...) the nature of consciousness' unity because it is trivially true by definition and tells us nothing about consciousness. Many thinkers, including Bayne himself, believe there is no self or subject that unifies consciousness. Bayne's position amounts to a bunch of mere assertions that allow him to avoid an obvious solution: substance dualism. (shrink)

For some time now, Nancey Murphy has been a major voice on behalf of a certain form of Christian physicalism. This is a part of her project of reconciling science with Christian faith. In what follows, I shall state and criticize the three central components of her Christian physicalism, followed by a presentation of a dualist alternative along with a clarification of its advantages over Murphy-style physicalism.

In this article I offer a taxonomy of the major issues and options about qualities, quality-instances, and exemplification. So far as I know, this has not been done for some time and the task of offering such a taxonomy is a worthy one in its own right. But such a classification will also show that arguments such as the one above by Grossmann fail to make their case because of the tremendous vari? ety of positions about quality-instances. The mere fact (...) that a philosopher does not accept the identity of the referent of "the F of A" and "the F of B" does not entail that the philosopher is a nominalist. (shrink)

Despite Vancil’s (1979) proclamation over twenty years ago that topoi have been abandoned in argument theory, this essay contends that topoi should have a vital role in contemporary argumentation theory. Four key areas are identified where topoi are (or can be) essential tools for argumentation: Locating argument, building argument, development of critical thinking, and argument pedagogy. As a result, teachers and students of argument can both benefit from a (re)discovery of topoi.

A repulsive core force is derived which, assuming π mesons are the field particles, gives binding energies in good agreement with binding energies per nucleon of heavy nuclei. The physical model consists of a field of relatively short range, in which emission of a π meson by a nucleon and subsequent absorption by a neighboring nucleon is equivalent to a potential well. The binding energy at the equilibrium spacing of the nucleons is the self-energy of the π mesons, which is (...) calculated by analogy with classical electric fields. (shrink)

A new theory of four-dimensional symmetry introduced by Hsu has been criticized as logically inconsistent. We answer the criticisms that have been raised and show that in fact this theory is not logically inconsistent.

We explore the mathematical structure and the physical implications of a general four-dimensional symmetry framework which is consistent with the Poincaré—Einstein principle of relativity for physical laws and with experiments. In particular, we discuss a four-dimensional framework in which all observers in different frames use one and the same grid of clocks. The general framework includes special relativity and a recently proposed new four-dimensional symmetry with a nonuniversal light speed as two special simple cases. The connection between the properties of (...) light propagation and the convention concerning clock systems is also discussed, and is seen to be nonunique within the four-dimensional framework. (shrink)

We give a simple proof ofΠ 1 1 andΠ 2 1 uniformization results, which is based on the use ofΠ 2 1 -Logic.

The classical wave-particle problem is resolved in accord with Newton's concept of the particle nature of light by associating particle density and flux with the classical wave energy density and flux. Point particles flowing along discrete trajectories yield interference and diffraction patterns, as illustrated by Young's double pinhole interference. Bound particle motion is prescribed by standing waves. Particle motion as a function of time is presented for the case of a “particle in a box.” Initial conditions uniquely determine the subsequent (...) motion. Some discussion regarding quantum theory is preseted. (shrink)