Aristotle presents his Nicomachean Ethics and Politics as an ordered pair comprising political science (hê politikê epistêmê), suggesting an axiomatic structure of theorems that are demonstratively deduced from first principles. These first principles would include both suppositions – inductively established claims that the natural kinds that are the objects of the science exist – and definitions that identify the essence of those natural kinds. From this perspective, Aristotle’s definition of eudaimonia or living well is no more foundational to his ethics than the supposition underlying it, but the former has received far more attention than the latter has. The talk will address some key questions about the structure of Aristotelian ethical science, focusing on this supposition and the prospects for vindicating it.