The infinite overwhelms our imagination: we can think of it, but we are unable to grasp its dimensions. How has this incommensurability of the infinite been dealt with in the history of European culture? Stephan Mühr does not treat the phenomenon as an essentially given mathematical problem. Instead, he discusses the respective semanticizations as narratives, as these paradoxically translate the ontological indifference of the infinite into concrete representations. Through case studies from Parmenides to Popper, it becomes clear how something that cannot be defined is narrated.