In this chapter Russell looks at Pythagoras. We all remember him from mathematics in school, but the influence he had was rather impressive.
We have just looked at the intellectual climate of Miletus with Thales, Anaximenes and Anaximander. Pythagoras lived roughly during the same time. He was a citizen of Samos. Samos was a rival of Miletus in terms of trading, also trading in gold and silver with Lydia, for example. They had a tyrannical ruler called Polycrates, who governed between 535 – 515 BCE. He was a wealthy patron of the arts. Polycrates famously capitalised on the downfall of Miletus, stealing their commerce and trade routes with Egypt. He was eventually overthrown by his own army.
Pythagoras moved from Samos to Croton after the citizens defeated Sybaris in war. Croton was wealthy because it imported Ionian goods, as had Sybaris. Croton’s fame, however, was in medicine. Their citizen, Democedes, was a physician to Polycrates, and then to Darius, who was the Persian king who conquered Miletus.
In Croton, Pythagoras quickly became a prominent public figure. He was famed as a cultic religious leader, and also as an intellectual. There is a real sense in which these two things were inseparable, as we shall see.
At the time of Pythagoras’ emergence, people were practicing the religions of Orpheus. A major part of their religion was the transmigration of souls. Pythagoras took these Orphic beliefs and made a new religion, placing himself as the leader. He even said that ‘there are, men, there are Gods, and there is me, Pythagoras’.
The idea of souls transmigrating became a question of everyday life. He believed that when we die, our souls are reborn in other bodies, whole or divided, they simply migrated. Everything was full of soul(s). Because of this, Pythagoras believed that men, women, children, animals, were all equal because souls were all equal. It is even said that he gave talks to animals because of this.
There was a kind of hierarchy in his religion. He believed in the experience of enthusiasm(religious ecstasy), just as the followers of Bacchus did. However, what enthused him and his followers was mathematics. The greater the insight of wisdom, the greater the feeling of enthusiasm. Furthermore, the more intellectual the revelations you have are, the better your soul will be reborn, so it was advantageous to ruminate constantly. This is similar to the wheel of rebirth in Hinduism.
Pythagoras also taught that there was an unseen perfect unity of reality. This was pure God. However, we could only experience a distorted reality of it. Consequently, mathematical revelations were the greatest because they were abstract and dealt in ideals rather than in reality. This was how Pythagoras started a religion based on numbers.
His religion also adopted a large number of folk superstitions. His two major tenets were the religious supremacy of mathematics, and that one must never eat beans. The prohibition of beans was his eventual downfall. His followers overthrew him because they wanted to eat beans.
Because Pythagoras valued mathematics over the senses, he started a school of philosophy which sought to find truths using pure abstract theory. If a revelation was made using mathematics, but it didn’t match what we saw with our own eyes, then what we saw with our own eyes was decidedly wrong. This was the start of the empiricist/rationalist divide in philosophy. On one hand, we had philosophers who believed that you accumulated understanding of the world through the senses and experience (empiricists), and on the other hand there were philosophers who (like Pythagoras) believed that true knowledge had to be arrived at through the intellect alone (rationalists).
He claimed that everything was quite literally numbers physically manifest. Some interesting things came from this; the invention of some fascinating practical geometry for one thing. He also discovered the structure of musical scales as pertaining to mathematical sequences, and found repeating patterns in nature. He discovered square and cube numbers too.
Because everything was built through numerical structure, he laid philosophical systems which described how mathematics explained all physics, but also all aesthetics. This may seem absurd, but think of the mathematical exactness of musical scales, or how the Fibonacci sequence appears in nature and art.
His work with numbers also gave us the art of deduction. This, together, led him to invent the idea of the axiom. Axioms are bread and butter for all mathematicians and philosophers now. What an axiom is is an indubitable fact which can be used for the foundation of a longer sum or philosophical argument. He also allowed things which we take to be self-evident as axiomatic facts. Pythagoras still believed in enthusiasm worship, so he had occasional religious revelations in ecstatic moments. These, he would treat as axiomatic fact too. When we get to Aristotle, we will see how axioms led to the syllogism.
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