History of Philosophy – Lesson 5: Pythagoras and the World of Numbers

“…the crucial point is the vital importance of mathematics in discovering the laws of the world, in making sense of the universe […] modern science is in part a development of this discovery of the Pythagoreans.”
— Leonard Peikoff, “History of Philosophy” course, ARI, Lesson 5.
(The Drake equation is a probabilistic argument used to estimate the number of civilizations in our galaxy with which communication might be possible. How crazy is that? I bet Drake would not have come up with that idea if it weren’t for the Pythagoreans. Original source: Kevin Gill; CC BY 2.0 / Desaturated from original)

So, Parmenides created a problem. The world was made of one single stuff but it appeared to change, while Logic asserted that was impossible. How to reconcile this in one single world? Well, you don’t. There are two worlds: the “world of appearances” here below, always changing and apprehended by the senses; the “real world” high above, immutable and hidden. And the real one, believe it or not, is made of numbers.

The Pythagoreans were truly a sect, the first “religious philosophers”, so to speak, followers of one of the mystery cults that had been imported from the Orient into Greece — the Orphic religion. Man has two parts, the body being the prison of the soul, both in eternal conflict with each other. In order to achieve salvation, man needs to purify his soul through an ascetic life guided by a host of ritual taboos concerning behavior and diet. That way he might eventually leave the “wheel of birth” and its endless reincarnations, and reunite with God. This is the major legacy left by the Pythagoreans with respect to ethics: the mind-body dichotomy and the idea that the ultimate goal is to let the soul escape from the body. This mystic element entered into Greek philosophy through them and went on through Plato to pervade all later philosophy to any degree religious, and, especially, Christianity itself.

The Pythagoreans had a scientific side also. Pythagoras himself is best known today for his eponymous theorem concerning triangles and for his discoveries in musical harmonics, but his (and his school’s) most influential discovery was the role of mathematics in the universe as a whole. Other civilizations had, of course, long discovered practical applications for mathematical knowledge, but the Pythagoreans were the first to discover that mathematics is somehow everywhere. Today, we take for granted that physical laws have to be formulated as mathematical equations, but that idea first developed from them.

But they went too far in their conjectures. They generalized the above idea in order to answer the main pre-Socratic philosophic concern: What is the world made off? “All things are numbers” was their answer. And they really meant it, apparently. They supposedly represented numbers by physical things and ended up confounding the two. Perhaps, they intended a kind of atomistic philosophy, as if numbers meant some sort of tiny particles composing the world, but the truth is we don’t know. What we do know is that a world of number — of eternal, immutable entities — provided a higher reality, one that governed the world of appearances here below. That was the source of the metaphysical dualism so dominant until now.

The Pythagoreans also attached a supreme importance to knowledge. They hierarchically distinguished people by their detachment from physical or material concerns, shown by their interest in acquiring knowledge for its own sake. In a later lesson, this idea will be picked up by Plato and developed into a complete communistic dictatorship. Hard to say who is the crazier of the two philosophers…

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