NDLI: The Forgotten Tradition: How the Logical Empiricists Missed the Philosophical Significance of the Work of Riemann, Christoffel and Ricci

Content Provider	Springer Nature Link
Author	Giovanelli, Marco
Copyright Year	2012
Abstract	This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the attempt to interpret general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality.
Starting Page	1219
Ending Page	1257
Page Count	39
File Format	PDF
ISSN	01650106
Journal	Erkenntnis
Volume Number	78
Issue Number	6
e-ISSN	15728420
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-12-16
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Philosophy Epistemology Ontology Ethics Logic
Content Type	Text
Resource Type	Article
Subject	Philosophy Logic

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