Pre-Socratics

Pre-Socratics

Although subjected to criticism, even ridicule by Plato, who used them as a foil in his Socratic dialogues, the Sophists were arguably the first professionally paid teachers, who travelled from city to city during the 5th century BC teaching for a living. They claimed expertise in philosophy and rhetoric, the latter an important skill in fledgling democracies such as Athens.

Hippias claimed to teach an all-around knowledge in various arts and sciences. Protagoras believed that ‘Man is the measure of all things. Suggesting a form of moral and cognitive relativism. Gorgias was more nihilistic and argued that nothing exists, that even if it did exist it could not be known, and that even if it could be known, it could not be communicated. They show that Greece was a crucible for philosophy and other topics, formally taught by professional teachers. They contributed to the growth of intellectual thinking and the search for truth in Greece.

Pythagoras (570-495 BC)

Pythagoras is a pre-Socratic figure. In Raphael’s fresco, he is the figure writing in a book in the foreground on the left, surrounded by acolytes. He represents abstract mathematics and, in opposition to Socrates, the idea that learning is about the master transmitting immutable knowledge to their students. 

Both Plato and Aristotle are wary of Pythagoras, as he is a figure shrouded in myth. What we do know is that he was a teacher with students in something resembling a cult or fraternity, shrouded in secrecy. We also know that he had rules about not eating living things and beans, an early advocate of vegetarianism, along with lists of other rules, such as putting your right shoe on first, not looking backwards and so on. Pythagoreanism is a school with students, perhaps more akin to disciples, but also a school of thought. He gives us the archetype for the charismatic teacher and leader, with followers who engaged in a communal lifestyle.

Pythagoras’s theorem, although well known, may not have originated with him. It was known and used centuries earlier by the Babylonians and Indians. That is not to say that he didn’t introduce to the Greeks. But mathematics is said to have lain at the heart of his system, especially geometry. The number 10 (1+2+3+4) was of mystical significance. Others such as Hippasus moved number theory on to irrational numbers, like the square root of two, expanded into a theory of irrational numbers by Eudoxus. 

He is also famous for having discovered the mathematical nature of musical intervals as having numerical ratios. If numbers lay behind music, do numbers lie behind all phenomena? There is speculation that he also applied this idea to the movement of the planets. His status during the Middle Ages and influence on Copernicus, Kepler and Newton have ensured his fame.

Bibliography

Kirk, G.S., Raven, J.E. and Schofield, M., 1983. The presocratic philosophers: a critical history with a selection of texts. Cambridge University Press.

Stewart, I., 2008. The Story of Mathematics: From Babylonian Numerals to Chaos Theory. Quercus.