## Introducing the Philosophers

**Pythagoras **(ca. 571 – ca. 497 BCE) is considered one of the Pre-Socratic Ionian thinkers, outside the Milesian school. He was originally from Samos, an offshore Ionian settlement. He settled in Southern Italy and founded his school there. His approach combined science with spiritual tradition. Mathematics, in the sense of demonstrative deductive arguments, began with Pythagoras. He is credited as the author of the first known mathematical formulation, the theorem which states that the square of the longest side of a right triangle equals the sum of the squares of the other two sides. Deductive reasoning from general premises seems to have been a Pythagorean innovation as well. He also held the notion of the transmigration of souls. ^{(8)}

Much of Plato’s work is influenced by this early tradition. ^{(1) }Plato, in his *Phaedo *, makes use of Pythagoras’ link in choosing Echecrates of Phlius as Phaedo’s audience for the story of Socrates’ last day. In that dialogue, Socrates’ interlocutors, Simmias and Cebes of Thebes, are both Pythagoreans, and as the dialogue is chiefly concerned with the immortality of the soul as Pythagoras is said to have envisioned it, Plato’s choice of Echecrates links the dialogue directly to Pythagorean thought from the first line. Yet what, exactly, was ‘Pythagorean thought?’ From what was written of him, it would seem Pythagoras founded a religious order that emphasized personal salvation through withdrawal from worldly pursuits and a focus on a strict philosophical and mathematical regimen. The Pythagoreans were vegetarians and believed that the soul was immortal and passed through many incarnations. To Pythagoras, vegetarianism was a path to inner peace and, by extension, world peace in that humans could never live in harmony with each other as long as they killed and ate animals.

Xenophanes, a contemporary, wrote derisively of Pythagoras that, “Once they say that he was passing by when a dog was being whipped and he took pity and said, ‘Stop, do not beat it; for it is the soul of a friend that I recognized when I heard it giving tongue.’” Since one could easily be re-born as a cow or a sheep in one’s next life, eating any living thing was as strictly prohibited as cannibalism would be. The Transmigration of Souls, as Pythagoras called it, greatly influenced Plato’s thought and, perhaps, Socrates himself, in the claim that learning is recollecting, as argued in Plato’s *Meno *and mentioned in *Phaedo *and elsewhere. If we die with our mind intact, we will ‘remember’ what we learned during that life when we are born into our next incarnation. What we think we ‘learn’ in this life, therefore, we are actually only ‘remembering’ from our past life. Those whom we term ‘child prodigies’ then are simply people who remember their former lives better than most do. Most famous today for his Pythagorean Theorem in geometry, Pythagoras asserted that “things are numbers” and that one could understand the physical world through mathematics. In this way, also, he greatly influenced Plato, as it is known that Plato’s Theory of Forms is chiefly geometry and that Plato admitted any Greek-speaking student into his Academy as long as they knew geometry. To Pythagoras, mathematics was a course of study to pursue toward enlightenment and understanding and, as he allegedly claimed, “Ten is the very nature of number” and by this ‘number’ he meant not only a unit of measurement, but also a means by way of which the world could be grasped and understood. ^{(8)}