Stewart Umphrey shows that there have been not one but two relevant “scientific revolutions” or “paradigm shifts” in the history of natural philosophy. The first, brought about by Aristotle, features an eido-centric conception of living organisms and other enduring things, and strongly resists any reduction of physics to mathematics. The second revolution, brought about by seventeenth-century physics, features a nomo-centric view: what is fundamental in nature are not enduring individuals and their kinds, but rather certain mathematizable relations among varying physical quantities. Umphrey examines and compares these two very different ways of understanding the natural order.