Giovanelli, Marco (2012) The Forgotten Tradition. How the Logical Empiricists missed the Philosophical Significance of the work of Riemann, Christoffel and Ricci. Erkenntnis, 78 (6). pp. 1219-1257. ISSN 0165-0106
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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: | Published Article or Volume | ||||||
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| 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 |
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| Depositing User: | Dr. Marco Giovanelli | ||||||
| Date Deposited: | 29 Dec 2013 17:33 | ||||||
| Last Modified: | 29 Dec 2013 17:33 | ||||||
| Item ID: | 10160 | ||||||
| Journal or Publication Title: | Erkenntnis | ||||||
| Publisher: | Springer (Springer Science+Business Media B.V.) | ||||||
| Official URL: | http://link.springer.com/article/10.1007%2Fs10670-... | ||||||
| DOI or Unique Handle: | 10.1007/s10670-012-9407-2 | ||||||
| Subjects: | General Issues > History of Philosophy of Science Specific Sciences > Mathematics Specific Sciences > Physics > Relativity Theory |
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| Date: | 2012 | ||||||
| Page Range: | pp. 1219-1257 | ||||||
| Volume: | 78 | ||||||
| Number: | 6 | ||||||
| ISSN: | 0165-0106 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/10160 |
Available Versions of this Item
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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)
- 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) [Currently Displayed]
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