Die ewige Wiederkunft wissenschaftlich betrachtet. Oskar Beckers Nietzscheinterpretation im Kontext

Within the literature on Nietzsche’s thesis of eternal recurrence, the discussion of its ethical or anthropological aspects prevails. From the viewpoint of today’s physical cosmology, this is hardly surprising. Yet during the first half of the 20th century a couple of eminent scholars have treated eternal recurrence as a serious if speculative scientific idea, either to justify its validity or to find it worthy of an elaborated criticism within the science of the day. My paper critically investigates the 1936 attempt of the logician and philosopher Oskar Becker to justify both a physical and a logical argument he spots in Nietzsche’s writings. While Becker endorses Abel Rey’s 1927 book Le retour eternel e la philosophie de la physique, he remains silent about his former colleague at the University of Bonn, the mathematician Felix Hausdorff and his 1898 book Das Chaos in kosmischer Auslese (published under the pseudonym Paul Mongre). The reasons for this silence were, to my mind, not only that Hausdorff had been forced out of his job under the Nuremberg laws while Becker showed a constantly growing sympathy for the Nazi regime, but also in Becker’s intention to emphasize the pro-scientific side of the newly elevated state philosopher Nietzsche. I analyze Becker’s arguments against the backdrop of Rey’s and Hausdorff’s considerations and argue that these severely limit the validity of Becker’s conclusions. To discuss Nietzsche’s physical proof first, Becker argues that assuming a finite space, a finite number of possible particle positions and energy states, a finite number of atoms, and Laplacian determinism indeed yields a periodic recurrence of all world states. Being aware of Rey’s discussion of Nietzschean recurrence within the context of statistical mechanics, Becker concedes that by relaxing determinism one might only be able to prove that nature cannot avoid recurring to any given single state. And thus he passes the buck to the sciences. But as the discussions ensuing Zermelo’s recurrence objections have shown, the statistical character of the second law requires a more radical departure from the established Laplacean conception of world state. On this basis, Rey argued that recurrence illustrates a more profound opposition between subject and object, in which the second law becomes the measure of the subjective and eternal recurrence the measure of the objective. Becker’s mathematical argument takes its point of departure by distinguishing, on the one hand, regressus in infinitum and progressus ex infinito and, on the other hand, progressus in infinitum and progressus ex infinito. Thus the inconsistency of a progressus in infinitum usque ad certam finem (resp. nunc) does not fault the progressus ex infinito usque ad certam finem (resp. nunc) because the world states could be periodically arranged, as Nietzsche has claimed. Becker’s argument, for one, rests upon a constructivist stand in the foundations of mathematics and the Heideggerian underpinning of it by the temporality of mathematical thought that he had already given in his 1927 Mathematische Existenz. But Becker also assumes that, for periodic motions, one can (in thought) reverse the order of time. A look at Hausdorff’s book and a proto-set-theoretic argument presented there shows, however, that such a reversal does not work without invoking what Hausdorff calls transcendent reality.