“Anaximander for the Anthropocene” presents a formal sketch of modern complexity theory, then argues that the cosmological propositions of Anaximander of Miletus represent a style of rational thinking in Greek antiquity, founded on analogy, to which modern systems science owes an unacknowledged debt. The systems approach to the world first adumbrated by Anaximander’s natural philosophy, it is suggested further, provides the conceptual basis for any meaningful sustainability ethos, even in the modern age.