The main conclusion drawn in this text is that Piaget's accounts of the construction of necessary knowledge continue to have an intelligible and respectable bases.

Perhaps the most distinct question in science throughout the ages has been the one of perceivable reality, treated both in physics and philosophy. Reality is acting upon us, and we, and life in general, are acting upon reality. Potentiality, found both in quantum reality and in the activity of life, plays a key role. In quantum reality observation turns potentiality into reality. Again, life computes possibilities in various ways based on past actions, and acts on the basis of these computations. (...) This book is about a new approach to biology. Its subtitle suggests a perpetual movement and interplay between two elusive aspects of modern science — reality/matter and potentiality/mind, between physics and biology — both captured and triggered by mathematics — to understand and explain emergence, development and life all the way up to consciousness. But what is the real/potential difference between living and non-living matter? How does time in potentiality differ from time in reality? What we need to understand these differences is an integrative approach. This book contemplates how to encircle life to obtain a formal system, equivalent to the ones in physics. Integral Biomathics attempts to explore the interplay between reality and potentiality. (shrink)

The central argument that Leslie Smith makes in this study is that reasoning by mathematical induction develops during childhood. The basis for this claim is a study conducted with children aged five to seven years in school years one and two.

The Cambridge Companion to Piaget provides a comprehensive introduction to different aspects of Jean Piaget's work.

Carpendale & Lewis's (C&L's) reanalysis of Chapman's (1999) epistemic triangle dealing with the coordination of interactions with physical objects and people's communication is misleadingly incomplete. An alternative proposal is outlined combining the causality of action with the normativity of knowledge in acts of judgment. This alternative is empirical and developmental, with a focus on rich but neglected phenomena.

Quantum mechanics teaches that before detection, knowledge of particle position is, at best, probabilistic, and classical trajectories are seen as a feature of the macroscopic world. These comments refer to detected particles, but we are still free to consider the motions generated by the wave equation. Within hydrogen, the Schrodinger equation allows calculation of kinetic energy at any location, and if this is identified as the energy of the wave, then radial momentum, allowing for spherical harmonics, becomes available. The distance (...) across the real zone of radial momentum is found to match semi-integer wavelengths of the adjusted matter wave, consistent with what is expected from a standing wave condition. The approach is extended to include orbital motions, where it is established that the underlying wave, which has direction and wavelength at each location, forms a series of connected trajectories, which are shown to be ellipses orientated at various angles to the equatorial plane. This suggests that wave trajectories, rather than particle trajectories, are still a feature of the hydrogen atom. The finding allows the reason for the coincidence between energy results derived by Sommerfeld’s classical trajectories and the Schrodinger wave equation to be appreciated. The result has implications when the relativistic situation is considered, as Sommerfeld’s correct deduction of the relativistic energy levels of hydrogen well before Dirac derived his wave equation has long been somewhat puzzling. (shrink)

I support Rips et al.'s critique of psychology through (1) a complementary argument about the normative, modal, constitutive nature of mathematical principles. I add two reservations about their analysis of mathematical induction, arguing (2) for constructivism against their logicism as to its interpretation and formation in childhood (Smith 2002), and (3) for Piaget's account of reasons in rule learning.

The distinction between norms and facts is long-standing in providing a challenge for psychology. Norms exist as directives, commands, rules, customs and ideals, playing a constitutive role in human action and thought. Norms lay down 'what has to be' and 'what has to be done' and so go beyond the 'is' of causality. During two millennia, norms made an essential contribution to accounts of the mind, yet the twentieth century witnessed an abrupt change in the science of psychology where norms (...) were typically either excluded altogether or reduced to causes. The central argument in this book is twofold. Firstly, the approach in twentieth-century psychology is flawed. Secondly, norms operating interdependently with causes can be investigated empirically and theoretically in cognition, culture and morality. Human development is a norm-laden process. (shrink)

Open peer commentary on the article “A Temporal Puzzle: Metamorphosis of the Body in Piaget’s Early Writings” by Marc J. Ratcliff.: Ratcliff’s target article is an insightful introduction to a major corpus, the journal comprising the notes of Jean and Valentine Piaget in their studies of their three children. These studies were part of a research program in what Jean Piaget called “genetic epistemology.” My commentary focuses on a series of epistemological issues central to this theory of knowledge.

Two standard epistemological accounts are conflated in Dienes & Perner's account of knowledge, and this conflation requires the rejection of their four conditions of knowledge. Because their four metarepresentations applied to the explicit-implicit distinction are paired with these conditions, it follows by modus tollens that if the latter are inadequate, then so are the former. Quite simply, their account misses the link between true reasoning and knowledge.