The Mathematical Imagination focuses on the role of mathematics and digital technologies in critical theory of culture. This book belongs to the history of ideas rather than to that of mathematics proper since it treats it on a metaphorical level to express phenomena of silence or discontinuity. In order to bring more readability and clarity to the non-specialist readers, I firstly present the essential concepts, background, and objectives of his book...

Résumé – Nous nous intéressons à l’enseignement et l’apprentissage de l’infini en classe de mathématiques en considérant les différences et les relations entre infini potentiel et infini actuel. Nous présentons les principaux éléments de notre étude philosophique, épistémologique et didactique, ainsi que trois situations visant à conduire un travail explicite avec les élèves sur ces questions en début de lycée. ---------------------------------------------------------------------------------------------------- --------------------------------- Abstract – We are interested in the teaching and learning of infinite in mathematics class, taking into account the relations (...) between potential infinite and actual infinite. We report the main elements of our current philosophical, epistemological and didactical study; we also present three mathematical situations that we consider relevant for this purpose and to be explored with 10 and 11 grade students. (shrink)

In their book on Descartes’s changing mind, Peter Machamer and J.E McGuire argue that Descartes discarded dualism to embrace a kind of monism. It is intriguing to investigate if the master of dualism could have changed his mind about the central aspect of his system. After reviewing the position of the authors, we will consider how and in what terms Descartes did not go back on his favorite doctrine but may have fooled himself about the nature of his dualism. It (...) is my contention that the so-called problematic Cartesian dualism has its origin in the lack of proper definition of mind and body as substances and the role of their respective attributes, thought and extension in the definition of the substances. The main answer to Machamer and McGuire’s thesis is that Descartes could develop his epistemology of mind and body independently of a metaphysics of substance and its attributes. In other words not only did Descartes not change his mind, but he persevered and enriched his dualist metaphysics. The subsidiary answer to the authors is that the concessions given by Descartes to the opponents of his dualism can be found in earlier works, but, pace the authors, they did not cause him not to develop his dualism in the first place. (shrink)

This article analyzes the value of geometric models to understand matter with the examples of the Platonic model for the primary four elements (fire, air, water, and earth) and the models of carbon atomic structures in the new science of crystallography. How the geometry of these models is built in order to discover the properties of matter is explained: movement and stability for the primary elements, and hardness, softness and elasticity for the carbon atoms. These geometric models appear to have (...) a double quality: firstly, they exhibit visually the scientific properties of matter, and secondly they give us the possibility to visualize its whole nature. Geometrical models appear to be the expression of the mind in the understanding of physical matter. (shrink)

In book: Infini des mathématiciens, infini des philosophes, Edition: 1992, 1995, 1999, 2002, 2008, 2011 ebook, Chapter: Introduction, Publisher: Belin, Paris, Editors: F. Monnoyeur, pp.9-16.

Descartes développe, dans ses Principes de la Philosophie, les principes fondateurs de son système construit sur l’identification de la matière à l’espace. L’analyse de ses principes nous invite à repenser le rôle de la métaphysique dans la constitution de la science et permet aussi de comprendre comment les concepts de matière, substance, espace, étendue géométrique, mouvement, infini et vide sont devenus les questions centrales de la science du XVIIe siècle.