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The Foundations of Geometry and the Concept of Motion: Helmholtz and Poincaré

The Foundations of Geometry and the Concept of Motion: Helmholtz and Poincaré ArgumentAccording to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of space could be construed. Yet, due to the problem of illusion inherent in the subject’s self-assessment of muscular activity, this solution yielded new difficulties, in that if the manifold is abstracted from rigid bodies which serve as empirical justification of the geometrical notion of space, then illusionary bodies will produce fictive manifolds. The present article is meant to disentangle these difficulties. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Science in Context Cambridge University Press

The Foundations of Geometry and the Concept of Motion: Helmholtz and Poincaré

Science in Context , Volume 14 (3): 14 – Dec 18, 2002

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Publisher
Cambridge University Press
Copyright
© 2001 Cambridge University Press
ISSN
1474-0664
eISSN
0269-8897
DOI
10.1017/S0269889701000163
Publisher site
See Article on Publisher Site

Abstract

ArgumentAccording to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of space could be construed. Yet, due to the problem of illusion inherent in the subject’s self-assessment of muscular activity, this solution yielded new difficulties, in that if the manifold is abstracted from rigid bodies which serve as empirical justification of the geometrical notion of space, then illusionary bodies will produce fictive manifolds. The present article is meant to disentangle these difficulties.

Journal

Science in ContextCambridge University Press

Published: Dec 18, 2002

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