Philosophy had seen its birth long before the Pythagorean society, in Ionia and the rest of Ancient Greek. The Pythagoreans, however, was the first – and a colossal – organized school of thought. They were a… wacky group of fellows in terms of their beliefs, as they were simultaneously a very mathematical and a fervently religious group – in the minds of most of us modern citizens, these two subjects, instead of going hand in hand, should be at each others’ throats any day.
This is a perfect illustration of the mutually inclusive relationship between science, philosophy, and religion in the early stages of human thoughts.
Some of their mathematical accomplishments were simply not reflected in their philosophy; they were, too simplified, to be applied to the world. Take their most eminent achievement, The Pythagorean Theorem, for example. (Though the theorem was known and known to had been applied long before the Pythagoreans, they were believed to be the first to prove the theorem.) Taught in every school in every corner of this earth, this simple but elegant theorem is arguably the most recognized and used mathematical theorem. But the Pythagoreans never put this theorem to a philosophical level; it was a powerful, useful theorem, no more, no less.
When they did put mathematics into philosophy and religion, on the other hand, it was often much more of literary analogies and comparisons than true mathematical proofs. In Aristotle’s famous-but-never-really-read-by-any-average-person writing Metaphysics, for example, he explained that –
“The Pythagoreans, too, held that void exists, and that it enters the heaven from the unlimited breath – it, so to speak, breathes in void. The void distinguishes the natures of things, since it is the thing that separates and distinguishes the successive terms in a series. This happens in the first case of numbers; for the void distinguishes their nature.”
Now if you’ll ignore the part where this is a belief of an esteemed philosophical group from Ancient Greek, and judge only by this quote – you’ll probably think this is some pseudoscience religious cult stuff. You know, the poetic-but-very-flimsy-sounding “void enters the heaven from the unlimited breath” kind of cult. They did make – according to Aristotle, at least – a very clever analogy comparing the existence of ‘the void’ in nature and the nature of integers: there are natural breaks, or ‘voids’, between integers 0, 1, 2, 3… which represent the order of nature. And therefore, there must be breaks within our natural world as well. But, as is clear to us, there is a huge leap in their logic – they never really proved why this analogy had to be true or effective.
This characteristic not only applied to the Pythagoreans, but also remained very relevant to many philosophers well into the Renaissance. They loved to use scientific analogies to make themselves look more… well, scientific and trustworthy. However, they almost always ignored the parameters and restrictions of mathematical and scientific theorems – which are just as important as the theorems themselves. This same deliberate neglect also characterizes much of what is now known as pseudo-science. But back then in the Greek time, this was philosophy.
But then again, isn’t it also some beautiful writing?