Article ID: CBB001421058

Leibniz-Äquivalenz vs. Einstein-Äquivalenz. Was man von der Logisch-Empiristischen (Fehl-)Interpretation des Punkt-Koinzidenz-Arguments lernen kann (2013)


The discovery that Einstein's celebrated argument for general covariance, the 'point-coincidence argument', was actually a response to the 'hole argument' has generated an intense philosophical debate in the last thirty years. Even if the philosophical consequences of Einstein's argument turned out to be highly controversial, the protagonists of such a debate seem to agree on considering Einstein's argument as an expression of 'Leibniz equivalence', a modern version of Leibniz's celebrated indiscernibility arguments against Newton's absolute space. The paper attempts to show that the reference to Leibniz, however plausible at first sight, is actually in many respects misleading. In particular it is claimed that the Logical Empiricists offer a significant historical example of an attempt to interpret the point-coincidence argument as an indiscernibility argument in the sense of Leibniz, similar to those used in 19th century by Helmholtz, Hausdorff or Poincaré. However the logical empiricist account of General Relativity clearly failed to grasp the philosophical novelty of Einstein's theory. Thus, if Einstein's point coincidence/hole argument can be regarded as an indiscernibility argument, it cannot be an indiscernibility argument in the sense of Leibniz. Einstein rather introduced a new form of indiscernibility argument, which might be better described as an expression of 'Einstein-equivalence'. Developing some ideas of Weyl it is argued that, whereas Leibniz's arguments introduced the notion of 'symmetry' in the history of science, Einstein's argument seems to anticipate what we now call 'gauge freedom'. If in the first case indiscernibility arises from a lack of mathematical structure, in the second case it is a consequence of a surplus of mathematical structure.

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Authors & Contributors
Galison, Peter Louis
Boi, Luciano
Heinzmann, Gerhard
Hausdorff, Felix
Chatterji, S. D.
Scharlau, W.
Physics in Perspective
Historia Mathematica
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Science in Context
Isis: International Review Devoted to the History of Science and Its Cultural Influences
W. W. Norton & Co.
Sentinel Open Press
Parerga Verlag
College Publications
Edizioni ETS
History of philosophy of science
Philosophy of science
Poincaré, Jules Henri
Einstein, Albert
Helmholtz, Hermann Ludwig Ferdinand von
Mach, Ernst
Hausdorff, Felix
Hertz, Heinrich Rudolph
Time Periods
20th century, early
19th century
20th century
United States
Vienna Circle

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