Hegel’s distinction between the bad and true infinites has provoked contrasting reactions in the works of Alain Badiou and Graham Priest. Badiou claims that Hegel illegitimately attempts to impose a distinction that is only relevant to the qualitative realm onto the quantitative realm. He suggests that Cantor’s mathematical account of infinite multiplicities that are determinate and actual remains an endlessly proliferating bad infinite when placed within Hegel’s faulty schema. In contrast, Priest affirms the Hegelian true infinite, claiming that Cantor’s formal (...) mechanisms of boundary transcendence, such as ‘diagonalization’, are implicit in Hegel’s dialectic. While arguing that a clear dividing line can be drawn here between these two interpretations of the relationship between Hegel and Cantor, this paper also mounts a defence of the Hegelian true infinite by developing Priest’s suggestion that Cantorian diagonalizing functions are prefigured by Hegel’s dialectical overcoming of limits. (shrink)

If I lose my key in Canada, for instance, and I search for it in the United Kingdom, how long will I take to find it? This paper argues that problems in education are caused by non-professional teachers who are employed when trained teachers move in search of promotion friendly activities or financially rewarding duties. This shift of focus means that policy makers in education act without adequate professional guidance. The problems in education, therefore, result from demands made on mainstream (...) education based on misconceptions about what education can offer. It is argued that the implementation of e-learning in education faces the risk of developing on the basis of unproven theories. This scenario increasingly sees the replacement of formal education activities in institutions of learning with non-formal and informal education practices. Given that the contents and influences of non-formal and informal education are not under the control of the teacher, the experiences that learners bring to education settings are increasingly difficult to manage. The paper proposes that by integrating e-learning in teacher education and rewarding 'good teaching', there is a potential for a successful e-learning revolution in education. (shrink)

Hegel’s critique of mathematics cannot be reduced to mathematics alone. At least this is the stake of the present paper: to argue that a comprehensive understanding of the matter cannot be confined strictly to the philosophy of science. Indeed, Hegel’s philosophy of mathematics pervades his entire ontology and, within the system, his political philosophy. Starting with Hegel’s logic, the article advances towards the fact that Hegel did not reject mathematics in itself, nor he denied the incalculable merits of exact sciences (...) made possible by applied mathematics. What he considered risky regarding mathematics was its revindication of the explanation of movement to the disadvantage of philosophy. Hence, the possibility of a technocratic world incapable of seeing and going beyond itself. (shrink)

This article interprets Józef Maria Hoëné Wronski’s (1776–1853) use of actual infinities in his mathematical work. The interpretation places this usage, which undermined Wronski’s acceptance as a mathematician, in his contemporary mathematical and philosophical context and in the context of his own sociopolitical-philosophical project.