platonic pythagoreanism - intro for scholars

JayKennedy | Western culture is sometimes said to rest on the twin pillars of Socrates and Jesus, two poor men who wrote nothing. Plato's teacher Socrates launched philosophical and scientific research in Athens, but we know of him primarily through Plato's writings. The philosophy and science of Socrates and Plato combined with the religions of the East in the Roman period to create central strands of what became modern European culture. Now our understanding of the birth of that culture will need to be reworked. Plato is sometimes thought of as a cold fish who banished poets and pushed the West toward logic, mathematics, and science. Now we know he was a hidden romantic. The philosophy contained beneath his stories mixes science and mysticism, mathematics and God. By understanding our roots better, we understand ourselves better.

The two most surprising ideas in Plato's hidden philosophy may be explained simply. First, the musical and mathematical structures he hid in his writings show that he was committed to the radical idea that the universe is controlled not by the gods on Olympus but by mathematical and scientific law. Today we take it for granted that the book of nature is written in the language of mathematics, but it was a dangerous and heretical idea when it struggled for acceptance in the Scientific Revolution of the 1600s. Giordano Bruno was burnt at the stake and Galileo was condemned and imprisoned. After Socrates was executed for sowing doubts about Greek religion, Plato had every reason to hide his commitment to a scientific view of the cosmos. But we now know that Plato anticipated the key idea of the Scientific Revolution by some 2000 years.

Perhaps even more surprisingly, Plato's positive philosophy shows us how to combine science and religion. Today we hear much of the culture wars between believers and atheists, between those who insist our world is imbued with meaning and value and those who argue for materialism and evolution. For Plato, music was mathematical and mathematics was musical. In particular, we hear musical notes harmonising with each other when their pitches form simple ratios. For him, the perception of this beauty in music was at once the perception of a beauty inherent in mathematics. Thus mathematics and the laws governing our universe were imbued with beauty and value: they were divine. Modern scientists don't ask where their fundamental laws come from; for Plato, the beauty and order inherent in mathematical law meant its source was divine (a Pythagorean version of modern deism). Plato may light a middle way through today's culture wars.

The Central Claim. The Apeiron article and the sample chapters below concentrate on showing that Plato used a consistent scheme of symbols to embed a musical structure in each genuine dialogue.

In short, each dialogue was divided into twelve parts. At each twelfth, i.e., at 1/12, 2/12, etc., Plato inserted passages to mark the notes of a musical scale. This regular structure resembles a known Greek scale. According to Greek musical theory, some notes in such a scale are harmonious (if they form a small whole number ratio with the twelfth note) and the others are dissonant or neutral. Plato's symbolic passages are correlated with the relative values of the musical notes. At more harmonious notes, Plato has passages about virtue, the forms, beauty, etc.; at the more dissonant notes, there are passages about vice, negation, shame, etc. This correlation is one kind of strong evidence that the structure is a musical scale.

This musical structure can be studied rigorously because it is so regular. Subsequent work will show that other symbols are used to embed Pythagorean doctrines in the surface narratives. It is surprising that Plato could deploy an elaborate symbolic scheme without disturbing the surface narratives of the dialogues, but in this respect he does not differ from other allegorical writers like Dante or Spenser.