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Collision of Traditions. The Emergence of Logical Empiricism Between the Riemannian and Helmholtzian Traditions

Giovanelli, Marco (2013) Collision of Traditions. The Emergence of Logical Empiricism Between the Riemannian and Helmholtzian Traditions. [Preprint]

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Abstract

This paper attempts to explain the emergence of the logical empiricist
philosophy of space and time as a collision of mathematical traditions.
The historical development of the ``Riemannian'' and ``Helmholtzian''
traditions in 19th century mathematics is investigated. Whereas Helmholtz's
insistence on rigid bodies in geometry was developed group theoretically
by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag
triggered Christoffel's and Lipschitz's work on quadratic differential
forms, paving the way to Ricci's absolute differential calculus.
The transition from special to general relativity is briefly sketched
as a process of escaping from the Helmholtzian tradition and entering
the Riemannian one. Early logical empiricist conventionalism,
it is argued, emerges as the failed attempt to interpret Einstein's
reflections on rods and clocks in general relativity through the conceptual
resources of the Helmholtzian tradition. Einstein's epistemology
of geometry should, in spite of his rhetorical appeal to Helmholtz and
Poincaré, be understood in the wake the Riemannian tradition
and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and
others.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Giovanelli, Marcomarco.giovanelli@uni-tuebingen.de
Keywords: Bernhard Riemann; Hermann von Helmholtz; Logical Empiricis; Philosophical Interpretations of the Theory of Relativity; Epistemology of Geometry
Subjects: General Issues > Conventionalism
General Issues > History of Philosophy of Science
General Issues > Logical Positivism/Logical Empiricism
Specific Sciences > Mathematics
General Issues > Operationalism/Instrumentalism
Specific Sciences > Physics > Relativity Theory
General Issues > Theory/Observation
Depositing User: Dr. Marco Giovanelli
Date Deposited: 29 Dec 2013 17:31
Last Modified: 29 Dec 2013 17:31
Item ID: 10157
Subjects: General Issues > Conventionalism
General Issues > History of Philosophy of Science
General Issues > Logical Positivism/Logical Empiricism
Specific Sciences > Mathematics
General Issues > Operationalism/Instrumentalism
Specific Sciences > Physics > Relativity Theory
General Issues > Theory/Observation
Date: 2013
URI: http://philsci-archive.pitt.edu/id/eprint/10157

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