Following the introduction of the special and general theories of relativity and development of consequent cosmological models, the extent to which time and space play a starkly abstract role in physics has become more and more apparent. We examine here whether the full force of such abstract characterizations comes ultimately into opposition with the practice of science and implies some hard limitations on the scope of scientific discourse.
I describe recent developments of Conway and Kochen on the physical meaning of freewill and their theorem that the assertion of freewill for human beings, in their specific sense, implies the same for elementary particles. This description is given in simplified metaphorical terms that nonetheless address the key physical axioms and essential analytic content of their argument. I then give points of contact of our metaphor with the full technical analysis of the cited authors and conclude with some associated metaphysical (...) speculations. These include the implications of the freewill theorem for dual aspect theories and, in particular, for process metaphysics. (shrink)
Materialism, epiphenomenalism, dualism, idealism, and dual-aspect theories may all be represented by an appealing abstract mathematical devicecalled a commutative diagram. Properties of the components of such diagrams characterize and, to some extent, even parameterize these systems and attendant metaphysical concepts (such as causal closure and supervenience) in a unified framework; process thought is of particular interest in this connection. In many cases we can even exemplify the theories typified by these diagrams in explicit graphical models. All of this tends to (...) clarify the relationships among key philosophical positions and to sharpen our sense of the effective domain and principal limitations of each. Systematic variation of these abstract diagrams may even suggest cogent metaphysical systems yet to be examined. (shrink)
Alfred North Whitehead 's treatise Universal Algebra classifies algebras as either non-numerical or numerical according to whether they satisfy the law of idempotency, a + a = a. We undertake a technical critique of this classification scheme and examine how its flaws may reflect certain mathematical and philosophical biases in Whitehead 's outlook. We argue further that Whitehead 's presumption of immutable foundations for mathematics and his early commitment to the priority of objects over relations may in part account for (...) his relative obscurity as a mathematician. (shrink)
This is a review of What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles. In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms ‘mathematical’ and ‘concept’. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim (...) the canonical question ‘what is a mathematical concept?’ from the philosophy of mathematics. This review comments on each paper in the collection. (shrink)
Ont contribué au volume : David Allen, Gabriel Bergounioux, Claude Blanckaert, Jacqueline Carroy, Jean François Chiantarretto, Françoise Couchard, Gérard Lagneau, Sophie-Anne Leterrier, Laurent Muchielli, Jean Yves Pautrat, Paule Petitier, Jacques Postel, Jacques Rancière, Marc Renneville, Nathalie Richard et Geneviève Vermès. A priori, loin de la problématique des relations entre les sexes, ce recueil de textes issu d'un colloque organisé par la Société française pour l'histoire des s..