Weyl and the Problem of Space

From Science to Philosophy

26, 27 & 29 May 2015

University of Constance, Germany

The problem of space is at the core of Hermann Weyl’s philosophy. During the years 1916-1923, his scientific work focused on the foundation of differential geometry and general relativity. In particular, Weyl reformulated the mathematical problem of space, in reaction to the new relativistic context, and solved it.

The philosophical problem of space consisted in a set of issues, which derived from a Kantian tradition. These issues were themselves inherited from the debates which took place during the period of constitution of mathematical physics (Galileo, Descartes, Newton, Leibniz, etc.). Among all the infinitely many conceivable metrical spaces, what is the one which applies to the physical world, and how can we correlate it with the other aspects of the concept of spa c e (mathematical, psychophysical, and phenomenological) ?

Now, since Riemann and Einstein, there is not a single fixed and rigid metric that characterizes physical space, but a whole family of metrics (Riemannian metrics). Despite this, for Hermann Weyl, there is only a single nature of metric that can be used to grasp the “real” world. His Mathematische Analyse des Raumproblems is dedicated to the “deduction” of this unique nature.

The Symposium « Weyl and the Problem of Space, from Science to Philosophy » is an attempt to mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, mathematics being the inevitable intermediary.

Scientific organisation

• Julien Bernard : Zukunftkolleg, Konstanz and Ceperc, Aix-en-Provence
• Carlos Lobo : Collège International de Philosophie, Paris and CFCUL, Lisbon

This workshop is linked to the Research Program : “La question de l’espace comme carrefour épistémologique” http://www.ciph.org/Site/Carlos_LOBO.html