Mathematics and logic are indispensable in science, yet how they are deployed and why they are so effective, especially in the natural sciences, is poorly understood. In this paper, I focus on the how by analysing Jean Piaget’s application of mathematics to the empirical content of psychological experiment; however, I do not lose sight of the application’s wider implications on the why. In a case study, I set out how Piaget drew on the stock of mathematical structures to model psychological (...) content, namely, the operations of thought involved in reasoning. In particular, I show how operations of thought form structured wholes that initially resisted modelling by either lattices or groups but could be modelled adequately by modifications of these mathematical structures. Piaget coined the term ‘grouping’ for the modified structure, and I conclude that it represents a non-canonical application of mathematics to the empirical content of experimental psychology. I also touch on the role external factors played in Piaget’s development of the grouping. According to the genetic epistemology conceived by Piaget, the origin of intelligence lies in the biological organism and develops in stages over time, and, via the grouping, Piaget established a genetic relationship between two stages of reasoning. I show how this relationship explains why mathematics and logic fit the psychological content of reasoning whilst simultaneously making their successful deployment in the natural sciences more mysterious. Finally, I turn to the explanation Piaget envisaged for the unreasonable effectiveness of mathematics in the natural sciences and consider some consequences for naturalism and Pythagoreanism. (shrink)

It should now be recognized that codes are central to life and to understanding its more complex forms, including human culture. Recognizing the ‘conventional’ nature of codes provides solid grounds for rejecting efforts to reduce life to biochemistry and justifies according a place to semantics in life. The question I want to consider is whether this is enough. Focussing on Eigen’s paradox of how a complex code could originate, I will argue that along with Barbieri’s efforts to account for the (...) origins of life based on the ribosome and then to account for the refined codes through a process of ambiguity reduction, something more is required. Barbieri has not provided an adequate account of emergence, or the basis for providing such an account. I will argue that Stanley Salthe has clarified to some extent the nature of emergence by conceptualizing it as the interpolation of new enabling constraints. Clearly, codes can be seen as enabling constraints. How this actually happens, though, is still not explained. Stuart Kauffman has grappled with this issue and shown that it radically challenges the assumptions of mainstream science going back to Newton. He has attempted to reintroduce real possibilities or potentialities into his ontology, and argued that radically new developments in nature are associated with realizing adjacent possibles. This is still not adequate. What is also involved, I will suggest, utilizing concepts developed by the French natural philosopher Gilbert Simondon, is ‘transduction’ as part of ‘ontogenesis’ of individuals in a process of ‘individuation’, that is, the emergence of ‘individuals’ from preindividual fields or milieux. (shrink)

It is argued that fundamental to Piaget's life works is a biologically based naturalism in which the living world is a nested complex of self-regulating, self-organising (constructing) adaptive systems. A structuralist-rationalist overlay on this core position is distinguished and it is shown how it may be excised without significant loss of content or insight. A new and richer conception of the nature of Piaget's genetic epistemology emerges, one which enjoys rich interrelationships with evolutionary epistemology. These are explored and it is (...) shown how a regulatory systems evolutionary epistemology may be embedded within genetic epistemology. (shrink)

Two varieties of constructivism are distinguished. In part 1, the psychological or “radical” constructivism of von Glasersfeld is discussed. Despite its dominant influence in science education, radical constructivism has been controversial, with challenges to its principles and practices. In part 2, social constructivism is discussed in the sociology of scientific knowledge. Social constructivism has not been primarily concerned with education but has the most direct consequences in view of its challenge to the most fundamental, traditional assumptions in the philosophy of (...) science and to the practice of science itself. (shrink)

That Piagetian epistemology has the dynamics of knowledge growth as its core consideration predetermines a need to consider it as potentially applicable to teaching. This paper addresses that need by first outlining the Piagetian theory of equilibration and then applying it to the construction of methods of teaching science.

The work of Henri Bergson has gone almost completely unnoticed in philosophy of sport literature. This in no way indicates the level of relevance his programme may carry for the subject. Many of the entrenched debates that have historically helped to shape the field are mirrored by Bergson's own concerns regarding perception and skill acquisition. As such, a thorough study of how the Bergsonian programme might approach the topic of athletic action is in no wise an idle pursuit? in fact, (...) very much the opposite. My intention in this paper is twofold: first, to indicate the natural commerce that exists between Bergson's philosophy and the philosophy of sport; second, and perhaps more ambitiously, to demonstrate that his approach to perception and action not only anticipates, but in some cases may help to edify, certain unresolved issues within the field. The paper develops in three parts. In part I, I provide a brief summary of Bergson's theory of perception as it is developed in Matter and Memory. Parts II and III will apply that theory to two of the central aspects of human motor activity: in part II, I investigate what it is to be in possession of skilled motor behaviour? to make that behaviour?automatic?, as it were; in part III, the controversial subject of what it is to acquire and modify skilled motor behaviour will be examined. (shrink)

As we rapidly approach the 50th year of the much‐celebrated ‘cognitive revolution’, it is worth reflecting on its widespread impact on individual disciplines and areas of multidisciplinary endeavour. Of specific concern in this paper is the example of the influence of cognitivism's equation of mind and computer in education. Within education, this paper focuses on a particular area of concern to which both mind and computer are simultaneously central: educational technology. It examines the profound and lasting effect of cognitive science (...) on our understandings of the educational potential of information and communication technologies, and further argues that recent and multiple ‘signs of discontent’, ‘crises’ and even ‘failures’ in cognitive science and psychology should result in changes in these understandings. It concludes by suggesting new directions that educational technology research might take in the light of this crisis of cognitivsm. (shrink)

This article examines some of the phenomenological features in Lev Vygotsky’s mature psychological theory, especially in Thinking and Speech and The Current Crisis in Psychology. It traces the complex literary and philosophical influences in 1920s Moscow on Vygotsky’s thought, through Gustav Shpet’s seminars on Husserl and the inner form of the word, Chelpanov’s seminars on phenomenology, Bakhtin’s theory of the production of inner speech, and the theoretical insights of the early Gestalt psychologists. It begins with an exposition of two central (...) Husserlian schemas: part-whole theory and the thesis of the naïve standpoint, both of which Vygotsky was clearly familiar with. This is followed by an account of the reception of phenomenology in early Soviet Russia. The article’s central sections are concerned with a careful unpacking and critique of Vygotsky’s employment of Husserlian method and analysis in his later doctrine of the ‘inner plane of speech’, his use of part-whole theory, and his identification of Husserl’s position with an untenable version of idealism. The article closes with the contention that Vygotsky misrepresents the phenomenological analysis of meaning formation and appropriates basic Husserlian conceptual terms in his elaboration of the ‘inner form of the word’; but Vygotsky does so in such a way that he enriches our descriptive access to the individual development of humans’ dynamic use of language. (shrink)

This paper is an exploration of the Cartesian paradigms of clarity and univocity and how these inform contemporary educational theory and practice. Phenomenology is discussed as a way of disrupting Descartes' visions of clarity and distinctness as paradigms of knowledge and as a return of inquiry to life as it is actually lived. Analogical discourse is examined as a way of giving a voice to this sort of inquiry. Heidegger's notions of inquiry as obedience and thanksgiving are discussed.