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Archimedes

Space, Number, and Geometry from Helmholtz to Cassirer

Authors: Biagioli, Francesca

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  • Offers a new historical reconstruction of the philosophical debate on non-Euclidean geometry in neo-Kantianism
  • Brings a new approach to Helmholtz's philosophy of mathematics
  • Relevance for the current debate about the relativized a priori
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About this book

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

About the authors

Francesca Biagioli completed her PhD in philosophy and history of science at the University of Turin, Italy, in 2012. Her areas of specialization are Kant, neo-Kantianism, and the history of philosophy of science in the 19th Century. She is the author of articles about the philosophy of science of neo-Kantians such as Hermann Cohen, Alois Riehl and Ernst Cassirer, and scientists and mathematicians such as Hermann von Helmholtz and Otto Hölder.

Reviews

“Francesca Biagioli’s Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. … It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory.” (Lydia Patton, Journal for General Philosophy of Science, Vol. 50, 2019)

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Helmholtz’s Relationship to Kant

    Pages 1-21

    Biagioli, Francesca

  • The Discussion of Kant’s Transcendental Aesthetic

    Pages 23-50

    Biagioli, Francesca

  • Axioms, Hypotheses, and Definitions

    Pages 51-80

    Biagioli, Francesca

  • Number and Magnitude

    Pages 81-116

    Biagioli, Francesca

  • Metrical Projective Geometry and the Concept of Space

    Pages 117-149

    Biagioli, Francesca

Buy this book

eBook n/a
  • ISBN 978-3-319-31779-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-319-31777-9
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-3-319-81116-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Space, Number, and Geometry from Helmholtz to Cassirer
Authors
Series Title
Archimedes
Series Volume
46
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-31779-3
DOI
10.1007/978-3-319-31779-3
Hardcover ISBN
978-3-319-31777-9
Softcover ISBN
978-3-319-81116-1
Series ISSN
1385-0180
Edition Number
1
Number of Pages
XX, 239
Topics