Some classical authors ascribe to Anaximander of Miletus a belief in the existence of infinite worlds. Their testimonies have provoked an extensive discussion on the question of whether Anaximander spoke of successive or coexistent worlds, or perhaps only one world that undergoes changes. Of course, this subject is related to important aspects of archaic cosmologies. First, we need to investigate whether one can even speak of a notion of coexistent worlds prior to atomist theories. Second, the issue of infinite worlds (...) is closely linked to the nature of Anaximander's scheme of the universe and Ionian cosmologies in general. Finally, this matter has a bearing on the subject of the duration or perishing of the world. (shrink)