Space, number, and geometry from Helmholtz to Cassirer. ([2016])
- Record Type:
- Book
- Title:
- Space, number, and geometry from Helmholtz to Cassirer. ([2016])
- Main Title:
- Space, number, and geometry from Helmholtz to Cassirer
- Further Information:
- Note: Francesca Biagioli.
- Authors:
- Biagioli, Francesca
- Contents:
- Acknowledgments; Contents; Introduction; Chapter 1: Helmholtz's Relationship to Kant; 1.1 Introduction; 1.2 The Law of Causality and the Comprehensibility of Nature; 1.3 The Physiology of Vision and the Theory of Spatial Perception; 1.4 Space, Time, and Motion; References; Chapter 2: The Discussion of Kant's Transcendental Aesthetic; 2.1 Introduction; 2.2 Preliminary Remarks on Kant's Metaphysical Exposition of the Concept of Space; 2.3 The Trendelenburg-Fischer Controversy; 2.4 Cohen's Theory of the A Priori; 2.4.1 Cohen's Remarks on the Trendelenburg-Fischer Controversy. 2.4.2 Experience as Scientific Knowledge and the A Priori2.5 Cohen and Cassirer; 2.5.1 Space and Time in the Development of Kant's Thought: A Reconstruction by Ernst Cassirer; 2.5.2 Substance and Function; References; Chapter 3: Axioms, Hypotheses, and Definitions; 3.1 Introduction; 3.2 Geometry and Mechanics in Nineteenth-Century Inquiries into the Foundations of Geometry; 3.2.1 Gauss's Considerations about Non-Euclidean Geometry; 3.2.2 Riemann and Helmholtz; 3.2.3 Helmholtz's World in a Convex Mirror and His Objections to Kant. 3.3 Neo-Kantian Strategies for Defending the Aprioricity of Geometrical Axioms3.3.1 Riehl on Cohen's Theory of the A Priori; 3.3.2 Riehl's Arguments for the Homogeneity of Space; 3.3.3 Cohen's Discussion of Geometrical Empiricism in the Second Edition of Kant's Theory of Experience; 3.4 Cohen and Helmholtz on the Use of Analytic Method in Physical Geometry; References; Chapter 4:Acknowledgments; Contents; Introduction; Chapter 1: Helmholtz's Relationship to Kant; 1.1 Introduction; 1.2 The Law of Causality and the Comprehensibility of Nature; 1.3 The Physiology of Vision and the Theory of Spatial Perception; 1.4 Space, Time, and Motion; References; Chapter 2: The Discussion of Kant's Transcendental Aesthetic; 2.1 Introduction; 2.2 Preliminary Remarks on Kant's Metaphysical Exposition of the Concept of Space; 2.3 The Trendelenburg-Fischer Controversy; 2.4 Cohen's Theory of the A Priori; 2.4.1 Cohen's Remarks on the Trendelenburg-Fischer Controversy. 2.4.2 Experience as Scientific Knowledge and the A Priori2.5 Cohen and Cassirer; 2.5.1 Space and Time in the Development of Kant's Thought: A Reconstruction by Ernst Cassirer; 2.5.2 Substance and Function; References; Chapter 3: Axioms, Hypotheses, and Definitions; 3.1 Introduction; 3.2 Geometry and Mechanics in Nineteenth-Century Inquiries into the Foundations of Geometry; 3.2.1 Gauss's Considerations about Non-Euclidean Geometry; 3.2.2 Riemann and Helmholtz; 3.2.3 Helmholtz's World in a Convex Mirror and His Objections to Kant. 3.3 Neo-Kantian Strategies for Defending the Aprioricity of Geometrical Axioms3.3.1 Riehl on Cohen's Theory of the A Priori; 3.3.2 Riehl's Arguments for the Homogeneity of Space; 3.3.3 Cohen's Discussion of Geometrical Empiricism in the Second Edition of Kant's Theory of Experience; 3.4 Cohen and Helmholtz on the Use of Analytic Method in Physical Geometry; References; Chapter 4: Number and Magnitude; 4.1 Introduction; 4.2 Helmholtz's Argument for the Objectivity of Measurement; 4.2.1 Reality and Objectivity in Helmholtz's Discussion with Jan Pieter Nicolaas Land. 4.2.2 Helmholtz's Argument against Albrecht Krause: "Space Can Be Transcendental without the Axioms Being So"4.2.3 The Premises of Helmholtz's Argument: The Psychological Origin of the Number Series and the Ordinal Conception of Number; 4.2.4 The Composition of Physical Magnitudes; 4.3 Some Objections to Helmholtz; 4.3.1 Cohen, Husserl, and Frege; 4.3.2 Dedekind's Definition of Number; 4.3.3 An Internal Objection to Helmholtz: Cassirer; References; Chapter 5: Metrical Projective Geometry and the Concept of Space; 5.1 Introduction; 5.2 Metrical Projective Geometry before Klein. 5.2.1 Christian von Staudt's Autonomous Foundation of Projective Geometry5.2.2 Arthur Cayley's Sixth Memoir upon Quantics; 5.3 Felix Klein's Classification of Geometries; 5.3.1 A Gap in von Staudt's Considerations: The Continuity of Real Numbers; 5.3.2 Klein's Interpretation of the Notion of Distance and the Classification of Geometries; 5.3.3 A Critical Remark by Bertrand Russell; 5.4 The Arithmetization of Mathematics: Dedekind, Klein, and Cassirer; 5.4.1 Dedekind's Logicism in the Definition of Irrational Numbers. … (more)
- Publisher Details:
- Cham, Switzerland : Springer
- Publication Date:
- 2016
- Copyright Date:
- 2016
- Extent:
- 1 online resource
- Subjects:
- 516.9
Philosophy
Geometry, Non-Euclidean
Neo-Kantianism
Science -- Philosophy
Philosophy (General)
Geometry
MATHEMATICS -- Geometry -- General
Geometry, Non-Euclidean
Neo-Kantianism
Science -- Philosophy
Nichteuklidische Geometrie
Science -- Physics
History of science
Geometry
Philosophy -- History & Surveys -- General
History of Western philosophy
Electronic books - Languages:
- English
- ISBNs:
- 9783319317793
3319317792 - Related ISBNs:
- 9783319317779
3319317776 - Notes:
- Note: Includes bibliographical references and index.
Note: Online resource; title from PDF title page (EBSCO, viewed August 30, 2016). - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.355727
- Ingest File:
- 02_338.xml