PYTHAGORAS TO PLATO Early philosophers on the Greek coast of Asia Minor concentrated on the material cause: they sought the basic ingredients of the world we live in Thales and his successors posed the following question: At a fundamental level is the world made out of water, or air, or Wre, or earth, or a combination of some or all of these? (Metaph A 983b20–84a16) Even if we have an answer to this question, Aristotle thought, that is clearly not enough to satisfy our scientiWc curiosity The ingredients of a dish not put themselves together: there needs to be an agent operating upon them, by cutting, mixing, stirring, heating, or the like Some of these early philosophers, Aristotle tells us, were aware of this and oVered conjectures about the agents of change and development in the world Sometimes it would be one of the ingredients themselves—Wre was perhaps the most promising suggestion, as being the least torpid of the elements More often it would be some agent, or pair of agents, both more abstract and more picturesque, such as Love or Desire or Strife, or the Good and the Bad (Metaph A 3–4 984b8–31) Meanwhile in Italy—again according to Aristotle—there were, around Pythagoras, mathematically inclined philosophers whose inquiries took quite a diVerent course A recipe, besides naming ingredients, will contain a lot of numbers: so many grams of this, so many litres of that The Pythagoreans were more interested in the numbers in the world’s recipe than in the ingredients themselves They supposed, Aristotle says, that the elements of numbers were the elements of all things, and the whole of the heavens was a musical scale They were inspired in their quest by their discovery that the relationship between the notes of the scale played on a lyre corresponded to diVerent numerical ratios between the lengths of the strings They then generalized this idea that qualitative diVerences might be the upshot of numerical diVerences Their inquiry, in Aristotle’s terms, was an inquiry into the formal causes of the universe (Metaph A 985b23– 986b2) Coming to his immediate predecessors, Aristotle says that Socrates preferred to concentrate on ethics rather than study the world of nature, while Plato in his philosophical theory combined the approaches of the schools of both Thales and Pythagoras But Plato’s Theory of Ideas, while being the most comprehensive scientiWc system yet devised, seemed to Aristotle—for reasons that he summarizes here and develops in a number of his treatises—to be unsatisfactory on several grounds There