 For all its ranting sound, Callicles has a straightforward and logically valid argument here: (1) observation of nature can disclose the content of ‘natural justice’; (2) nature is to be observed in the realms where moral conventions have no hold, viz among states and among animals; (3) such observation discloses the domination and exploitation of the weak by the strong; (4) therefore, it is natural justice for the strong to rule over and have more than the weak. From a modern point of view, premise (1) is likely to appear the most dubious, for it violates the plausible principle, most famously advanced by David Hume, that no normative claims may be inferred from purely descriptive premises (‘no ought from an is’). But then, legitimate or not, this kind of appeal to nature runs through almost all of ancient ethics: it is central to the moral theory of Plato himself, as well as Aristotle, the Epicureans, and the Stoics. So Socrates’ objection is instead to (2) and (3): Callicles gets nature wrong. In truth, Socrates insists later on, “partnership and friendship, orderliness, self-control, and justice hold together heaven and earth, and gods and men, and that is why they call this universe a world order, my friend, and not an undisciplined world-disorder” (507e–508a). Callicles advocates pleonexia only because he ‘neglects geometry’ (508a): instead of predatory animals, we should observe and emulate the orderly structure of the cosmos as a whole.