First of all, Ancient Greece was ancient. It happened literally thousands of years ago when very little was known about science. But rather than making Greece a sterile area for study, this makes it fascinating. So how we relate the philosophic roots of natural science in ancient Greece.
But this intimate connection between Greek philosophy and Greek science is no one-way street. Seeing the kind of science that grows out of a given philosophy is, I believe, an under-utilized form of discovering the true meaning of the philosophy.
At the risk of stealing my own thunder, let me just say this: until you have seen the kind of physics and astronomy advocated and practiced by Plato, you cannot possibly realize how serious a disaster was his theory of Forms. And conversely, until you contrast the scientific methodology of Plato to that of Aristotle, you cannot fully understand why Aristotle’s *philosophical* achievements were the ultimate cause of the Renaissance and the (eventual) scientific revolution.
To summarize, in search for the philosophic roots of natural science in ancient Greece, the intimate and even overlapping nature of philosophy and the natural sciences in Ancient Greece affords a unique perspective on both science and philosophy, one that is mutually enlightening to both subjects. Finally — and to