Deployment of the notion of kosmos has been much discussed in the scholarship on Presocratic philosophy. But diakosmos and diakosmêsis have been almost entirely neglected. This chapter argues that in describing the business of articulating ‘mortal belief’ as diakosmos, Parmenides bequeathed to his successors among the Presocratics a question – intended as deflationary – about the main agenda for physics and physical explanation: how the universe is arranged. He coined a concept designed to articulate it. Diakosmos was a concept his successors were determined to reinflate, but only at the price of contestation between believers in a single world produced by design and proponents of infinite undesigned worlds. And in Aristotle, diakosmêsis is re-invested with a hint of the deflationary.