Space, Number, and Geometry from Helmholtz to Cassirer / by Francesca Biagioli.

Format:

Book

Author/Creator:

Biagioli, Francesca., Author.

Series:

Archimedes, New Studies in the History and Philosophy of Science and Technology, 1385-0180 ; 46

Language:

English

Subjects (All):

Philosophy.

Physics.

Geometry.

History of Philosophy.

History and Philosophical Foundations of Physics.

Local Subjects:

History of Philosophy.

History and Philosophical Foundations of Physics.

Geometry.

Physical Description:

1 online resource (XX, 239 p.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

Contents:

Helmholtz’s Relationship to Kant

The Discussion of Kant’s Transcendental Aesthetic

Axioms, Hypotheses, and Definitions

Number and Magnitude

Projective Metric and the Concept of Space

Euclidean and Non-Euclidean Geometries in the Interpretation of Physical Measurements

Non-Euclidean Geometry and Einstein’s General Relativity: Cassirer’s View in 1921.

Notes:

Includes bibliographical references at the end of each chapters and index.

ISBN:

3-319-31779-2