The Mathematics of Eternal Recurrence
In this chapter, the author considers some mathematical arguments which take up the theme of infinity and apply it to the case of eternal recurrence, with various results. Since mathematics was not Nietzsche's strong point, most of these debates concern writers either before or after him – in the second instance, including his commentators and critics. A well-known argument directed against Nietzsche's theory of eternal recurrence is found in Georg Simmel's lecture series Schopenhauer and Nietzsche, first published in 1907. The author discusses some features of the argument common to Nicole Oresme and Simmel. Oresme and Simmel make their examples more concrete in slightly different ways. Simmel's argument against the line of thought which Nietzsche presents in support of eternal recurrence. Simmel goes on to say that if the world does contain any motions related to one another in this fashion, then a given state of affairs will never be repeated.