Weyl and the Problem of Space

From Science to Philosophy

  • Julien Bernard
  • Carlos Lobo

Part of the Studies in History and Philosophy of Science book series (AUST, volume 49)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Weyl’s Intellectual Neighborhoods and the Theory of Subjectivity

  3. Weyl’s Theory of the Continuum: Intuitionism and Dimensionnality of Space

  4. From Aprioristic to Physical Foundations of the Metric

  5. Weyl’s Methodological Issues: Intuition, Symbolic Thought and Manifolds of Possibilities

    1. Front Matter
      Pages 369-369
    2. Jairo José da Silva
      Pages 389-402

About this book


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.


Foundation of Physics Group Theory History of Mathematics and Physics of the 20th Lie groups Non-Euclidean Geometry Phenomenology of Space Relativity Theory Relativity Cosmology Inflationary Cosmology Kantian tradition Transcendental Phenomenological Theories of Subjectivity Conceptual Construction in Weyl's Analysis Intuitionistic Vision of Space Metrical Spaces Wesenanalyse Gauge Theories Problem of Space

Editors and affiliations

  • Julien Bernard
    • 1
  • Carlos Lobo
    • 2
  1. 1.Assistant Professor in PhilosophyCentre Gilles Gaston Granger (CGGG) UMR 7304, Aix-Marseille-UniversityMarseilleFrance
  2. 2.Collège International de Philosophie, Paris, FranceCentro de Filosofia das Ciencias Universidade de LisboaLisboaPortugal

Bibliographic information