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PRESOCRATICS: The Pythagorians. Two Philosophical Visions. Milesian Materialism Natural science Metaphysical materialism Methodological empiricism (knowledge = based on sense evidence) Human = natural being with reason Science/philosophy = purely theoretical.

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Presocratics the pythagorians
PRESOCRATICS: The Pythagorians

Two philosophical visions
Two Philosophical Visions

Milesian Materialism

  • Natural science

  • Metaphysical materialism

  • Methodological empiricism

    (knowledge = based on

    sense evidence)

  • Human = natural being with reason

  • Science/philosophy = purely theoretical

Pythagorean Idealism

  • Mathematical science

  • Metaphysical dualism

  • Methodological rationalism

  • (knowledge = based on rational insight)

  • Human = mortal animal + divine spirit

  • Philosophy = practical and theoretical

Four themes of pythagorean philosophy
Four Themes of Pythagorean Philosophy

  • Nature and the mathematical sciences (“learnables”)

  • Human being: reincarnation and the immortal soul

  • Ethics: the "Pythagorean way of life" (hodos tou biou)

  • Politics: religious communism, wise government and utopia

1 mathematics ta maqemata
1. Mathematics (ta maqemata)

The Pythagoreans took hold of mathematics, and were the first to advance that study, and being brought up in it, they believed that its principles were the principles of all the things that are.


The principle of all is the monad (the One); arising from this the Duality is substratum to the monad; from the monad and the dyad arise numbers, including the Three (life) and the Four (justice); from numbers, points; from points, lines, plane figures, solid figures, sensible bodies, the elements of which are fire, water, earth and air; these interchange and combine to produce a universe animate, intelligent, spherical, with the earth at its centre.

--Diogenes Laertes on the Pythagoreans

Cosmological mathematics
“Cosmological” Mathematics

  • The principles are the Even/unlimited and the Odd/Limited, which ‘generate’ all number out of the One, and structure the kosmos.

  • The square constructed on the hypoteneuse of a right angled triangle = the sum of the squares constructed on the sides. See Elements.

  • The tetractys (10), 1 + 2 + 3 + 4, = the perfect number. It is the source of the kosmos, which is organized according to harmonia.

  • Sound is organized according to harmonia. The fourth = a ratio of 3:4, fifth = 3:2, octave = 2:1. Scale (harmonia) = 5 tones and 2 semi-tones.

  • Time (cosmic) and space (architecture) can be organized in accordance with harmonious mathematical proportions.

    Mathematics = rational order in the cosmos

Pythagorean Metaphysics

M I N D / N U M B E R

Being= the One + (Even + Odd)

(arche, “origin” or principle)

\ /


\ /


Orderly physical world

(taonta, “all things”)

Note: ‘Mind’ not = separate, but immanent

Pythagorean music
Pythagorean Music

Harmonic ratios in music

Medieval depiction of ratios

  • music is composed & performed using a subset of 12 specific frequency intervals (chromatic scale tones) from any octave within the midrange of human hearing

  • consonance refers to the harmoniousness (pleasantness) of the sound produced by playing two tones simultaneously

  • the octave (2:1), the fifth (3:2), and the fourth (4:3) are the most consonant

  • listeners of all times and places produce this same ordering

Pythagorean architecture
Pythagorean Architecture

“Harmonic Relations” in Palladio’s Villa Capra

“Harmonic Relations” in Le Corbusier’s Modular

2 concept of immortal soul
2. Concept of Immortal Soul

He [Pythagoras] declares that the soul is immortal; and that it changes into other kinds of animals; in addition, that things that happen recur at certain intervals, and nothing is absolutely new; and that all things that come to be alive must be thought akin. Pythagoras seems to have been the first to introduce these opinions into Greece. –Aristotle

What is the soul psyche
What is ‘the soul’ (psyche)?

  • Homer: ‘soul’ = the animator of living bodies; it = a ‘life-force’ and is not divine

  • Milesians: ‘soul’ is the self-moving principle in natural bodies; it = a life-force and not divine

  • Human soul includes language, rationality

Pythagoreans: soul =

  • separate being in the living body;

  • seat of intellect, choice

  • = divine/immortal

  • true self, reincarnated in many bodies in its time-journey

  • liberated from body by study, ethical practice

If the soul exists what follows
If the soul exists, what follows?

  • It is all important to live a moral life, b/c life is a journey/test for heaven or hell

  • It is all important to discover what that is.

  • Traditions that reveal the existence of the soul = best guides to #2, moral life

  • The Pythagorean tradition revealed the existence of the soul

  • We should follow the “Pythagorean Way”


Gods are called “Immortals” in Homer, men “brotoi,” i.e. mortal ones. To assert the immortality of the soul was the same as saying, “Man is a kind of god.” This was an utterly new idea for the Greeks.

- Guthrie, Greeks & their Gods

The other revolutionary idea was that liberation (katharsis) came through living the “Pythagorean Way” … in the traditional Greek religion, religious practice was mostly confined to public ritual.

--Burkhardt, Ancient Religion

3 the pythagorean way
3. The Pythagorean ‘Way’

  • Both practical and theoretical philosophy

    • Mathemata (scientific studies) = awaken mind to divine rational order of cosmos

    • Akousmata (‘hearkenings’) = spiritual maxims

    • Askesis = spiritual disciplines for the Pythagorean mystes (initiate) include vegetarianism, communism

  • Goal = spiritual, intentional life (bios) vs. natural-animal existence (zoe)

  • Symbolism: spirit-soul descends into Hades, is cleansed by water and fire, arises pure (or recycles through life again)


  • First and hardest: to listen.

  • The soul is the guard of the vessel (or: “of the prison”).

  • [Contemplate] the white rooster.

  • [Friends] do not divide bread.

  • It is unholy to live in spotted garments.

  • Straighten the bed when rising from it.

  • Don't poke fire with a knife.

  • Don't step over a broom or a yoke.

  • Don't eat heart.

  • Do not look into a mirror by night.

  • Do not speak without light.

  • Y.

4 utopian community
4. Utopian Community

In Croton, a communal form of life arose of men and women bound together by the strict rules of the Pythagorean existence. Whoever entered such a group had to renounce private possessions; he underwent a five year period of silence; if he turned apostate, he was treated as dead, and a gravestone was erected for him.

Pythagorean community
Pythagorean community

  • Personal freedom = free to join or leave

  • Community

    • Community = religious and ethical union

    • Purpose = creating virtue in citizen’s souls

  • Governance and Life

    • Rule by the wise (not popular election)

    • Brotherhood/sisterhood, no slaves

    • Work and property are shared (commune)

  • Way of life

    • Includes spiritual practices, common life

      Compares to which medieval institution?

Two philosophical visions which do you agree with
Two Philosophical Visions: Which do you agree with?

Milesian Naturalism

Pythagorean Idealism

There are both physical and spiritual beings

Physical laws = mathematical ideals that matter follows

The universe and its laws = ‘rational’ by nature

Humans = immortal souls in animal bodies

Humans can discover by reason universal norms

  • Everything that exists is physical (natural)

  • Physical laws = regularities discovered in sense-experience

  • The universe and its laws evolved and may change

  • Humans = mortal animals that also evolved

  • Human culture and norms derive from nature or art

Appendix philosophy of mathematics
APPENDIX: Philosophy of Mathematics

  • You are in a math class and your teacher says, “Here’s a question for you, philosophers. Are numbers real? Do they refer to abstract objects, or are they purely mental, just ways we categorize things in our minds?” What do you think?

Philosophical puzzle what are numbers

  • Numbers = purely mental designations

  • Ditto geometrical forms

  • Reasons?

    • exist only mentally

    • thought in reference to perceptual objects

    • Math systems can conflict

    • defined any way you want

  • Numbers = abstract objects

  • Ditto geometrical forms

  • Reasons?

    • real, but don’t refer to the physical world

    • universal, necessary relations

    • must be defined certain ways

If numbers are real what is their relation to the world
If numbers are real, what is their relation to the world?


  • numbers and forms inherent in the world = ‘intelligible structure’ of the cosmos

  • Why?

    • The cosmos shows us a mathematical order

    • This order = universal, necessary, eternal

  • Platonists:

    • numbers and forms belong to ‘intelligible world,’ separate from the physical cosmos

  • Why?

    • Nothing in the cosmos =‘perfect’ as math is

    • Math = universal, necessary, eternal

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