Another Ionian was Pythagoras (582-500). After travelling everywhere from Gaul (modern day France) to Egypt and India, he settled down in Crotona, a sea port of southern Italy. Southern Italy was the greatest settlement of Greeks outside of Greece, to the point that the Romans referred to the area as Magna Grecia (“greater Greece”). There, he set up his famous school.

His school was more like a large commune, and his philosophy more like a religion. Because they believed in reincarnation, all of his followers were vegetarians. They avoided wine, swearing by the gods, sexual misconduct, excesses and frivolity. For the first five years, a new pupil took a vow of silence. Women were treated as equals -- a true rarity in the ancient world!

His philosophy was rooted in mathematics, which meant geometry to the ancient Greeks. Pythagoras is credited with a number of geometric proofs, most notably the Pythagorean theorem: The sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. He discovered the mathematical basis of music, and saw the same patterns in the movements of the planets. He was the first person to realize that the earth, moon, and planets are all spheres (hence, the "music of the spheres!"). He saw the elegant lawfulness of geometry as the foundation of the entire universe.

So, rather than look for an understanding of the universe in the movement of matter and energy, he looked for laws of nature, the form rather than the material. But, since these laws exist only in the mind as ideas, we call Pythagoras an idealist.

Although his life remains mysterious, his school lasted 300 years, and had a profound influence on all who followed, most particularly Plato.

In Elea, another Greek seaport in the south of Italy lived Xenophanes (570-475). He is best known for his denial of the existence of the Greek gods.

“Mortals fancy that gods are born, and wear clothes, and have voice and form like themselves. Yet if oxen and lions hadhands, and could paint and fashion images as men do, they would make the pictures and images of their gods in their own likenesses; horses would make them like horses, oxen like oxen. Ethiopians make their gods black and snub-nosed; Thracians give theirs blue eyes and red hair.” (from Diogenes Laertes “Xenophanes,” iii.)

There is only one God, he said, and that is the universe, Nature. This perspective is known as pantheism. Nevertheless, said Xenophanes, all things, even human beings, evolved from earth and water by means of natural laws. But things and people remain forever secondary to the ultimate reality that is God-or-Nature.

Parmenides (540-470) of Elea, was a disciple of Xenophanes, and would have a particularly potent influence on Plato. He extended Xenophanes’ concept of the one God by saying “Hen ta panta,” all things are One. Ultimate reality is constant. What we believe to be a world of things and motion and change is just an illusion.

One of Parmenides’ disciples was Zeno of Elea (490-430, not to be confused with Zeno of Citium, whom we will look at in a later chapter). Zeno wrote a book of famous paradoxes, including the story of Achilles and the tortoise: Let’s give the tortoise a head start. By the time Achilles gets to where the tortoise started, the tortoise will have moved a little further. By the time Achilles gets to where the tortoise had moved, the tortoise will have moved a little further still, and so on. Hence, Achilles can never catch up with the tortoise. The point of the story, and all the stories, is that motion is an illusion.

In making his point, he invented the form of dialectic argument known as "reduction to absurdity." Note, however, that his arguments don’t hold up in the long run, because he mistakenly takes motion, time, and space as made up of an infinite number of points, rather than being continuous.