Relevant Arithmetic and Mathematical Pluralism

In The Consistency of Arithmetic and elsewhere, Meyer claims to “repeal” Goedel’s second incompleteness theorem. In this paper, I review his argument, and then consider two ways of understanding it: from the perspective of mathematical pluralism and monism, respectively. Is relevant arithmetic just another legitimate practice among many, or is it a rival of its classical counterpart—a corrective to Goedel, setting us back on the path to the (One) True Arithmetic? To help answer, I sketch a few worked examples from relevant mathematics, to see what a non-classical (re)formulation of mathematics might look like in practice. I conclude that, while it is unlikely that relevant arithmetic describes past and present mathematical practice, and so might be most acceptable as a pluralist enterprise, it may yet prescribe a more monistic future venture

Economics Against Democracy

I believe that freedom of choice constitutes a pillar of rational choice in economic theory, regardless of the definition of rational choice one adopts. On the other hand, economics being socially embedded, free choice in economics seems senseless without political freedom of choice. Democracy, therefore, plays an important role in economic efficiency as much as in social fairness. Following this line of thought one should expect that economics, both in theory and in practice, should permanently strengthen the role of democracy in its institutional construction. Unfortunately it does not seem to be the case. Although historically many of the democratic achievements in the past two centuries have been intimately connected to the development of liberal economics, one can assert that mainstream liberal economics is intrinsically contradictory with the democratic ideal. The first stage of the demonstration of this thesis concerns the dismounting of the naturalization process that economics has undergone with the purpose of transforming economic decisions into plain technical issues supposedly free from democratic debate.The second stage concerns the ways in which the market has managed to legitimise its hegemony in society and the reasons why this contributes to the erosion of democracy. Within this hegemony five aspects will be dealt with; the imposition of a market jurisdiction; the deregulation of the economy; the process of political and economic unaccountability; the de-politicization of free choice and the conflict between the territorialization of democracy and the de-territorialization of economics

Teacher education for values education : is there a way forward under current constraints?

How can teacher education best prepare teachers to contribute to values education in schools? If this was ever a question that could be asked and answered in the abstract, or with reference to some postulated ideal situation, it is not so now. I am raising and suggesting an answer to the question in the context of recent developments in education in Britain; but since those recent developments are by no means unique to Britain, the discussion may well be of broader relevance too. The context, then, in which I am raising the question is one of increasing political control, at a national level, over both the curriculum of schools, and the form and content of teacher education itself. Several developments have combined, in Britain, which make it difficult to be optimistic about the future of any serious values education in schools; but at the same time, some opportunities have been opened up which could be grasped by teacher educators. I shall set the context first in terms of the school curriculum itself; then in terms of developments in teacher education

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