EAN: 9783030115265

WEYL AND THE PROBLEM OF SPACE GEBUNDEN

This book investigates Hermann Weyl's work on the problem of space from the early 1920s
onwards. It presents new material and opens the philosophical problem of space anew  crossing
the disciplines of mathematics  history of science and philosophy. With a Kantian starting
point Weyl asks: among all the infinitely many conceivable metrical spaces  which one applies
to the physical world? In agreement with general relativity  Weyl acknowledges that the metric
can quantitatively vary with the physical situation. Despite this freedom  Weyl deduces  with
group-theoretical technicalities  that there is only one kind of legitimate metric. This
construction was then decisive for the development of gauge theories. Nevertheless  the
question of the foundations of the metric of physical theories is only a piece of a wider
epistemological problem.Contributing authors mark out the double trajectory that goes through
Weyl's texts  from natural science to philosophy and conversely  always through the mediation
of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which
he is inspired (Kant  Husserl  Fichte  Leibniz  Becker etc.)  and explore the mathematical
tradition (Riemann  Helmholtz  Lie  Klein) that permitted Weyl to elaborate and solve his
mathematical problem of space. Furthermore  this volume analyzes the role of the interlocutors
with whom Weyl discussed the nature of physical space (Einstein  Cartan  De Sitter  Schrödinger
Eddington). This volume features the work of top specialists and will appeal to postgraduates
and scholars in philosophy  the history of science  mathematics  or physics.

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