Marco Giovanelli

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. _German_ Die Entdeckung, dass Einsteins berühmtes Punkt-Koinzidenz- Argument zur allgemeinen Kovarianz tatsächlich eine Reaktion auf die Lochbetrachtung war, hat in den vergangenen 30 Jahren zu einer intensiven philosophischen Debatte geführt. Auch wenn die philosophischen Konsequenzen äußerst kontrovers gesehen werden, stimmen die Protogonisten doch darin überein, das Argument als Ausdruck von Leibniz-Äquivalenz, mithin als eine moderne Version von Leibniz berühmten Ununterscheidbarkeitsargumenten gegen Newtons absoluten Raum aufzufassen. Ziel des Aufsatzes ist es zu zeigen, dass der Bezug zu Leibniz, wenn auch auf den ersten Blick plausibel, tatsächlich in vielerlei Hinsicht irreführend ist. Insbesondere wird dahingehend argumentiert, dass die Logischen Empiristen ein signifikantes historisches Beispiel für einen Versuch darstellen, das Punkt-Koinzidenz Argument als ein Ununterscheidbarkeitsargument im Sinne von Leibniz, ähnlich denen im 19. Jahrhundert von Helmholtz, Hausdorff und Poincaré vorgebrachten, zu deuten. Dieser Deutung der Allgemeinen Relativitätstheorie gelingt es aber nicht, das eigentlich philosophisch Neue von Einsteins Theorie plausibel zu interpretieren. Wenn Einsteins Punkt-Koinzidenz/Lochargument als ein Ununterscheidbarkeitsargument angesehen werden soll, kann dies kein Argument à la Leibniz sein. Vielmehr hat Einstein ein neuartiges Ununterscheidbarkeitsargument eingeführt, das vielleicht besser als,Einstein-Äquivalenz' charakterisiert werden sollte. Durch Aufnahme und Weiterentwicklung einiger Ideen von Weyl wird gezeigt, dass Leibniz' Argumente zwar das Konzept der,Symmetrie' in die Wissenschaftsgeschichte eingebracht haben, Einsteins Argument aber etwas antizipiert hat, was heute gewöhnlich,Eichfreiheit' genannt wird. Wird im ersten Fall die Ununterscheidbarkeit durch ein zu wenig an mathematischer Struktur erzeugt, so ist sie im zweiten Fall gerade die Folge eines Überschusses an mathematischer Struktur

This paper offers an introduction to Hermann Cohen’s Das Princip der Infinitesimal-Methode, and recounts the history of its controversial reception by Cohen’s early sympathizers, who would become the so-called ‘Marburg school’ of Neo-Kantianism, as well as the reactions it provoked outside this group. By dissecting the ambiguous attitudes of the best-known representatives of the school, as well as those of several minor figures, this paper shows that Das Princip der Infinitesimal-Methode is a unicum in the history of philosophy: it represents a strange case of an unsuccessful book’s enduring influence. The “puzzle of Cohen’s Infinitesimalmethode,” as we will call it, can be solved by looking beyond the scholarly results of the book, and instead focusing on the style of philosophy it exemplified. Moreover, the paper shows that Cohen never supported, but instead explicitly opposed, the doctrine of the centrality of the ‘concept of function’, with which Marburg Neo-Kantianism is usually associated.

By inserting the dialogue between Einstein, Schlick and Reichenbach in a wider network of debates about the epistemology of geometry, the paper shows, that not only Einstein and Logical Empiricists came to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but they actually, in their life-long interchange, never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his “measuring rod objection” against Weyl. Logical Empiricists, though carefully analyzing the Einstein-Weyl debate, tried on the contrary to interpret Einstein’s epistemology of geometry as a continuation of the Helmholtz-Poincaré debate by other means. The origin of the misunderstanding, it is argued, should be found in the failed appreciation of the difference between a “Helmhotzian” and a “Riemannian” tradition. The epistemological problems raised by General Relativity are extraneous to the first tradition and can only be understood in the context of the latter, whose philosophical significance, however, still needs to be fully explored.

This paper analyzes correspondence between Reichenbach and Einstein from the spring of 1926, concerning what it means to ‘geometrize’ a physical field. The content of a typewritten note that Reichenbach sent to Einstein on that occasion is reconstructed, showing that it was an early version of §49 of the untranslated Appendix to his Philosophie der Raum-Zeit-Lehre, on which Reichenbach was working at the time. This paper claims that the toy-geometrization of the electromagnetic field that Reichenbach presented in his note should not be regarded as merely a virtuoso mathematical exercise, but as an additional argument supporting the core philosophical message of his 1928 monograph. This paper concludes by suggesting that Reichenbach’s infamous ‘relativization of geometry’ was only a stepping stone on the way to his main concern—the question of the ‘geometrization of gravitation’