Cet ouvrage traite de la transformation fondamentale survenue dans la pensee mathematique a la suite de la decouverte de la geometrie non euclidienne. Cette transformation a eu comme consequence celle d'admettre que, non seulement pouvaient exister plusieurs geometries, mais encore plusieurs espaces mathematiques et plusieurs espaces physiques differents. La recherche s'attache en grande partie a analyser les etapes qui ont conduit a cette nouvelle conception et aux idees mathematiques qui en sont le fondement. Le livre cherche egalement a en elucider la signification epistemologique et a...

The collection of papers forming this volume is intended to provide a deeper study of some mathematical and physical subjects which are at the core of recent developments in the natural and living sciences. The book explores some far-reaching interfaces where mathematics, theoretical physics, and natural sciences seem to interact profoundly. The main goal is to show that an accomplished movement of geometrisation has enabled the discovery of a great variety of amazing structures and behaviors in physical reality and in living matter. The diverse group of expert mathematicians, physicists and...

Beyond their remarkable technical accomplishments, the new directions taken by the sciences in recent decades call for renewal of their epistemological basis. The purpose of this book is to show that Husserl's transcendental phenomenology, if properly re-examined, provides the required framework for such an epistemology. This re-examination is both critical and constructive. (i) The absolute subjectivization or the full naturalization of consciousness must be rejected. (ii) The necessarily transcendental character of phenomenology is put to work in the search for a systematic connection...

This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines.The integration of mathematics with physics, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines.

Beyond their remarkable technical accomplishments, the new directions taken by the sciences in recent decades call for renewal of their epistemological basis. The purpose of this book is to show that Husserl's transcendental phenomenology, if properly re-examined, provides the required framework for such an epistemology. This re-examination is both critical and constructive. (i) The absolute subjectivization or the full naturalization of consciousness must be rejected. (ii) The necessarily transcendental character of phenomenology is put to work in the search for a systematic connection...

In the first half of the 19th century geometry changed radically, and withina century it helped to revolutionize both mathematics and physics. It also put the epistemology and the philosophy of science on a new footing. In this volume a sound overview of this development is given by leading mathematicians, physicists, philosophers, and historians of science. This interdisciplinary approach gives this collection a unique character. It can be used by scientists and students, but it also addresses a general readership.

-Une enigme ]: comment se fait-il que la mathematique, qui est un produit de la pensee humaine et independante de toute experience, s adapte d une si admirable maniere aux objets de la realite?-. Dans toute sa force, c est une question proprement metaphysique que soulevait Albert Einstein: la mathematisation du reel, telle qu inauguree par Galilee, y atteint, par dela le mathematisable immediat des quantites discrete et continue, le mathematisable profond de lois et de structures. Or celles-ci sont bien quelque chose de ce reel, mais quelque chose qui, du fait de la separation du reel...

Cet ouvrage aborde des questions fondamentales qui se rattachent a des idees et des methodes developpees depuis quelques decennies dans les sciences de la nature et du vivant ainsi qu a l interface entre les deux. Il propose de nouvelles approches interdisciplinaires pour etudier plusieurs aspects theoriques, empiriques, et epistemologiques qui touchent a des problemes scientifiques cruciaux pour lesquels on ne dispose pas a l heure actuelle d explication satisfaisante. Ces questions et ces problemes concernent notamment la signification des symetries, des brisures de symetries et de la...

Telle qu elle a ete inauguree par Galilee, la mathematisation du reel y atteint, par dela le mathematisable immediat des quantites discrete et continue, le mathematisable profond de lois et de structures dont il est irrecusable qu elles sont quelque chose de ce reel, mais dont l acces fait enigme. Celle-ci, a montre un premier livre (L enigme des mathematiques, vol. I, Bern 2003) appelle non pas a fonder ce mode de science ainsi de Descartes a Husserl et au dela mais a situer ces deux niveaux du mathematisable dans ce qui est pris en tant qu etre cela sur les pas d une...