A Constructivist View of Newton’s Mechanics

In the present essay we attempt to reconstruct Newtonian mechanics under the guidance of logical principles and of a constructive approach related to the genetic epistemology of Piaget and García (Psychogenesis and the history of science, Columbia University Press, New York, 1989). Instead of addressing Newton’s equations as a set of axioms, ultimately given by the revelation of a prodigious mind, we search for the fundamental knowledge, beliefs and provisional assumptions that can produce classical mechanics. We start by developing our main tool: the no arbitrariness principle, that we present in a form that is apt for a mathematical theory as classical mechanics. Subsequently, we introduce the presence of the observer, analysing then the relation objective–subjective and seeking objectivity going across subjectivity. We take special care of establishing the precedence among all contributions to mechanics, something that can be better appreciated by considering the consequences of removing them: (a) the consequence of renouncing logic and the laws of understanding is not being able to understand the world, (b) renouncing the early elaborations of primary concepts such as time and space leads to a dissociation between everyday life and physics, the latter becoming entirely pragmatic and justified a-posteriori (because it is convenient), (c) changing our temporary beliefs has no real cost other than effort. Finally, we exemplify the present approach by reconsidering the constancy of the velocity of light. It is shown that it is a result of Newtonian mechanics, rather than being in contradiction with it. We also indicate the hidden assumption that leads to the (apparent) contradiction.Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Natiello, Mario Alberto. Lund University; Sueci

On the symmetries of electrodynamic interactions

While mechanics was developed under the idea of reciprocal action (interactions), electromagnetism, as we know it today, takes a form more akin to unilateral action. Interactions call for spatial relations, unilateral action calls for space, just one reference centre. In contrast, interactions are matters of relations that require at least two centres. The development of the relational electromagnetism encouraged by Gauss appears to stop around 1870 for reasons that are not completely clear but are certainly not solely scientific. By the same time, Maxwell recognised the equivalence in formulae of his electromagnetism and the one advocated by Gauss and called for an explanation of why such theories so differently conceived have such a large part in common. In this work we reconstruct and update the relational electromagnetism up to the contributions of Lorentz guided by the non-arbitrariness principle (NAP) that requests arbitrary choices to be accompanied by groups of symmetries. We show that a-priori there must be two more symmetries in electromagnetism, one related to the breaking (in the description) of the relation source/detector and one relating all the perceptions of the same source by detectors moving with different (constant) relative velocities. We show that the idea of electromagnetic waves put forward in concept by Lorenz (1861-1863) before Maxwell (1865) and in formulae (1867) just after Maxwell, together with the ``least action principle'' proposed by Lorentz are enough to derive Maxwell's equations, the continuity equation and the Lorentz' force, and that there is a dual formulation in terms of fields of the receiver (as opposed to fields of the source). While Galilean transformations are associated with removing the arbitrariness implied in the election of a reference space, they will not explicitly appear in a formulation based upon a relational space although we occasionally mention their usefulness. In contrast, Lorentz' transformations will emerge in this formulation involving the relations between the perceived fields of different receivers. Moreover, the role of the full Poincaré-Lorentz group as a group of transformations of the perceived actions is elucidated. In summary, we answer Maxwell's philosophical question showing how the same theory in formulae can be abduced using different inferred entities. Each form of abduction implies as well an interpretation and a facilitation of the theoretical construction. This work relies heavily on logical concepts as abduction put forward by C. Peirce, needed for the construction of theories

La localización de orbitales en el análisis de las constantes de acoplamiento de spin

Se estudia el empleo de orbitales localizados como herramienta complementaria de análisis de las constantes de spin. Se formula una presentación unificada de la separación en mecanismos de transmisión de los acoplamientos J, en base al concepto generalizado de localización, y se discuten aplicaciones a problemas particulares. Se concluye que estas técnicas son una herramienta apta para complementar análisis estructurales encarados con la espectroscopía de RMN, indicándose a la vez las posibles vías de evolución futura de este trabajo.Fil:Natiello, Mario Alberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

On abduction, dualities and reason

We integrate dualistic conceptions of the real with Peirce's perspectives about reality and abduction, emphasizing the concept of reason underlying Peirce's thoughts. Peirce's abduction is related to the notions of retrogression and grounding in Hegel, later re-encountered in Hansonian-abduction. Abduction in turn is considered in relation to abstraction acquiring its fullest sense as a stage in the process of producing a theory. The process is iterative and self improving, it incorporates ``turbid thinking'' making it increasingly ``clear'' at successive iterations that incorporate the lessons taught by failed predictions, i.e., refutations. The cycle of thoughts promoted by doubts comes to rest when belief is reached. We discuss how this coming to rest depends on a criterion for cessation of doubts. The observation is illustrated with two different criteria, one proposed by Mach that only demands analogy and the criteria of dualists such as Goethe and Whewell that inspire the present work. Hence, it is possible to produce, and socially accept, imperfect theories unless we demand the highest level of rationality, avoiding any leftover of the turbid thoughts that have been used in the early developments. This work rests upon the existence of some objective form of reason. Influenced by a constructivist, Piagetian, perspective of science, we propose and discuss a small number of conditions that we identify as characteristics of rational abduction: rules for the rational construction of theories. We show how a classical example of belief that satisfies today's most common definition of abduction does not match the standards of rational retroduction. We further show how the same rules indicate the partial detachment of Special Relativity from the observable world, a fact actually known to Einstein. We close arguing that there is an urgent need to develop a critical epistemology incorporating dualistic perspectives