The concepts of possibility and necessity are crucial to arguments about the final state and eternal recurrence. The doctrine of eternal recurrence teaches ‘the absolute necessity’ of an endless repetition of the same course of events. 1 In fact, it claims the eternal recurrence not just of every actual state of affair but of every possible state – a much stronger statement. And as we have seen, Nietzsche’s rejection of mechanism as a theory is based on his conviction that it leads to the idea of a ‘final state’ which is impossible. These are not arbitrary pronouncements; Nietzsche attempted on various occasions to set out arguments which would justify such conclusions. The aim of this chapter is to examine and criticize some of the ways in which these lines of thought can be understood, in the first instance by focusing on their structure and the key concepts they depend on.