Giovanelli, Marco (2012) The Forgotten Tradition. How the Logical Empiricists missed the Philosophical Significance of the work of Riemann, Christoffel and Ricci. [Preprint]

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Abstract

Abstract. The 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 rather 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 draw the line Riemann-Helmholtz-Poincaré-Einstein Logical Empiricists were led to argue that General Relativity raised mainly 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 line of development Riemann-Chritoffel-Ricci-Einstein shows on the contrary that the main philosophical issue raised by Einstein’s theory was rather 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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Giovanelli, Marco marco.giovanelli@gmail.com
Keywords:	Logical Empiricism, Absolute Differential Calculus, General Relativity, Hans Reichenbach
Subjects:	General Issues > History of Philosophy of Science Specific Sciences > Mathematics Specific Sciences > Physics > Relativity Theory
Depositing User:	Dr. Marco Giovanelli
Date Deposited:	07 May 2012 11:34
Last Modified:	29 Dec 2013 17:33
Item ID:	9105
Subjects:	General Issues > History of Philosophy of Science Specific Sciences > Mathematics Specific Sciences > Physics > Relativity Theory
Date:	2012
URI:	https://philsci-archive.pitt.edu/id/eprint/9105

Available Versions of this Item

• The Forgotten Tradition. How the Logical Empiricists missed the Philosophical Significance of the work of Riemann, Christoffel and Ricci. (deposited 07 May 2012 11:34) [Currently Displayed]
  • The Forgotten Tradition. How the Logical Empiricists missed the Philosophical Significance of the work of Riemann, Christoffel and Ricci. (deposited 29 Dec 2013 17:33)

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