**Philosofactory**: Pythagoras

*Philosophy On A Porch*

(by pyrrho for publishing jointly at MLW and DocuDharma)

**Pythagoras: A Mathematical Universe**

I will be using the print version of the Oxford “Dictionary of

Philosophy” to refresh myself for this series.

Links offered may or may not have been referenced to research this post. I

may or may not believe their assertions or have been exposed to them, but

they are given to ease your direct research further into Pythagoras. I try to

present them fairly and clearly. I am a skeptic myself, a relativist with

opinions on all these schools, and a tendency to eschew the doctrinaire side

of each of these schools, but as a skeptic, I’m equipped to give a philosophy

a fair shake. Myself, and tend to seek and emphasize the reusable tools each

school has to offer.

- Pythagoras at

Wikipedia - Stanford

Encyclopedia of Philosophy on Pythagoras - The Internet

Encyclopedia of Philosophy: Pythagoras - Pythagoras

at History for Kids

Most of you will know Pythagoras from the Pythagorean Theorum, but

Pythagoras was not just a mathematician and geometrician. His mathematics was

not separate from his life and his ideas were not limited to mathematics. As

with all these ancient philosophies I am covering in this series, Pythagoras’

is also has a whole system concerned with how to live… a worldview. This

worldview is what I am looking at in this series, because these philosophies

serve as archetypes for worldviews, archetypes I seem to encounter daily, and

which you do to. Archetypes not fundamental, but nevertheless ancient and

soaked into us. The epicurean is looking for a pleasurable life, to find the

small pleasures and live simply Simply, perhaps, but still nearby these

pleasures. The stoic is more hardened, does not expect pleasure as reward and

even scoffs at it as such, being as indifferent to pleasure as they have

chosen to be to pain. The pythagoreans then are those that have their head in

abstractions. One imagines the sort that has had no time for epicurean

pleasures like meals, having been preoccupied with a logical proof. To these

sort, the sublime superiority of a mathematical pattern was and remains as

obvious as the rising sun.

This series is presenting five ancient schools of philosophy as

archetypes. In the interest of honesty I must state my own philosophical

archetype is skepticism, but skepticism affords me the freedom to see the

strengths of these other archetypes. By no means are these five archetypes

meant to be limiting, according to a relative and skeptical approach any

number of archetypes can be constructed and used, but these do have the

particular quality of having been developed and infused into our “Western

Culture” over thousands of years, at least.

Their framings still exist, not merely as maxims come to mean other

things, linguistic ornaments merely, but at conceptual levels, such that one

can recognize a well worn conceptual tool with novel expressions in

language.

The archetypes are so far as follow:

- Epicurean: “Enjoy the simple pleasures, such as friendship, food and

wine. Nature is filled with pleasure and suffering alike.” - Stoic: “Live with virtue and be indifferent to the harshness of life.

Nature is indifferent but ordered.” - Pythagorean: “Truth and beauty lie in the abstractions of mathematics

and geometry. Nature can be described with number.” - ???
- ???

Indeed, the followers of Pythagoras were prone to taking Pythagoras himself

as a god become human to teach mankind these sublime truths. I do not find it

surprising that such a man led to a philosophy including vegetarianism and a

semi-divine presumption. If that sound dismissive, I share the pythagorean’s

sensibilities, if more humbly so, with an eye to the errors it introduces

with its beauties. As for the nearly religious awe I can feel before a

mathematical truth, take pi, a ratio that relates, among other things, the

length of the side of a circle to the length of the sides of a square, such

that, if you were to take the width of a square, and the radius of the circle

having the same circumference as the “circumference” of the square, then the

relation between the two involves a number whose digits never end, which

cannot be finitely represented. To me that’s stunning, but that turning

square into a circle requires a transcendental number is not stunning but

fitting. It is sublime, divine, and while expected, only ironically. And that

the ratio is well named as a “transcendental” number is no doubt a product of

our shared if inexplicable love for the beauty of math and geometry.

Concomitant to this, however, is removal of the self from the material

world into the world of abstraction and the illusion that abstractions are

not even of this world. The pythagorean spirit, as archetype, might not even

concern itself with math or geometry, but some other family of abstractions.

But abstraction are made from material facts, from astronomy, from counting,

from imperfectly drawn lines in the sand, and from deducing concepts that can

explain the facts abstracted all at once. This has proved a practical and

rewarding endeavor, but it is a part of the loss of reason to consider an

abstraction so fine it’s not a part of this world. But now I have begun to

describe Plato… Pythagoras himself might in fact object, thinking the world

of mathematics imbued the world around us all the material reality it had for

us to perceive. If I may accept this archetype in such a light, it remains a

tactile abstractionism, we feel the mathematical world about us always. We

are not imperfect beings separated from this glory, but are abstract beauties

ourselves, actually made of it.