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The Resource Space, Number, and Geometry from Helmholtz to Cassirer

Space, Number, and Geometry from Helmholtz to Cassirer

Label
Space, Number, and Geometry from Helmholtz to Cassirer
Title
Space, Number, and Geometry from Helmholtz to Cassirer
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Subject
Language
eng
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Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Archimedes
Series volume
v.46
Space, Number, and Geometry from Helmholtz to Cassirer
Label
Space, Number, and Geometry from Helmholtz to Cassirer
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4652553
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Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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 Priori -- 2.5 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 Axioms -- 3.3.1 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 Geometry -- 5.2.2 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 -- 5.4.2 Irrational Numbers, Axioms, and Intuition in Klein's Writings from the 1890s -- 5.4.3 Logicism and the A Priori in the Sciences: Cassirer's Project of a Universal Invariant Theory of Experience -- References -- Chapter 6: Euclidean and Non-Euclidean Geometries in the Interpretation of Physical Measurements -- 6.1 Introduction -- 6.2 Geometry and Group Theory -- 6.2.1 Klein and Poincaré -- 6.2.2 Group Theory in the Reception of Helmholtz's Work on the Foundations of Geometry: Klein, Schlick, and Cassirer -- 6.3 The Relationship between Geometry and Experience: Poincaré and the Neo-Kantians -- 6.3.1 The Law of Homogeneity and the Creation of the Mathematical Continuum -- 6.3.2 Poincaré's Argument for the Conventionality of Geometry -- 6.3.3 The Reception of Poincaré's Argument in Neo-{u00AD}Kantianism: Bruno Bauch and Ernst Cassirer
  • 6.4 Cassirer's View in 1910 -- References -- Chapter 7: Non-Euclidean Geometry and Einstein's General Relativity: Cassirer's View in 1921 -- 7.1 Introduction -- 7.2 Geometry and Experience -- 7.2.1 Axioms and Definitions: The Debate about Spatial Intuition and Physical Space after the Development of the Axiomatic Method -- 7.2.2 Schlick and Einstein (1921) -- 7.2.3 Cassirer's Argument about the Coordination between Geometry and Physical Reality in General Relativity -- 7.3 Kantianism and Empiricism -- 7.3.1 Reichenbach and Cassirer -- 7.3.2 Cassirer's Discussion with Schlick -- 7.3.3 Kantian and Neo-Kantian Conceptions of the A Priori -- References -- Index
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Extent
1 online resource (258 pages)
Form of item
online
Isbn
9783319317793
Media category
computer
Media MARC source
rdamedia
Media type code
c
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