PRESOCRATICS: The Pythagorians

1
PRESOCRATICS The Pythagorians
2
(No Transcript)
3

• PYTHAGOREANS
• Mathematical-scientific tradition
• Religious psychology/theology
• Religious ethics
• Political movement
• Influenced Parmenides, Plato, Euclid, Ptolemy,
  Palladio, Kepler

4
Pythagoras of Samos (580-494?) 

• studied with Milesians
• moved to Italy in 530 BCE, established school in
  Croton
• May have discovered the Pythagorean Theorem (A2
  B2 C2 right angled triangle)
• Introduced immortal soul, reincarnation into
  Greece
• Vegetarian, ascetic, spiritual leader

5
Four Aspects of Pythagorean Tradition

• mathematics (the learnable things)
• reincarnation and the immortal soul
• Taught a way of life (hodos tou biou)
• religious communism and utopia

6
I. 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.
• -Aristotle

7

• Being number
• Tetractys symbol of
• the rational cosmos
• The One or Absolute    o
• Duality and Being          o    o
• Creativity and Soul        o    o    o
• The Manifest World       o    o    o    o

8
Pythagorean Model of Reality M I N D Being
the One (Even Odd) (arche, origin or
principle) GOVERNING \ / M A T T E R Orderly
physical world (ta panta, all things)
9

• MILESIAN MATERIALISM
• (manifesting as)
• Changing physical world
• (ta onta, all things)
• / \
• (returning to)
• Being the Unchanging
• (arche, origin or principle)
• Everything is material
• Order arises from matter

• PYTHAGOREAN
• IDEALISM
• (M I N D)
• Being One (Even Odd)
• (arche, origin or principle)
• \ IN /
• (M A T T E R)
• Ordered physical world
• (ta onta, all things)
• Material ideal/spiritual realities
• Ideal norms govern matter

10

• Four Liberal Arts

11
1. Arithmetic (Number Theory)

• From the One and the Two, all number is generated
  in the Odd and Even.
• Pythagoreans studied the principles of natural
  (whole) numbers
• Pythagoreans did not distinguish pure numbers and
  counting numbers
• Pythagoreans were shocked at the discovery of
  irrational numbers

12
2. Geometry

• From definitions (point, line, square, etc.)
  principles (e.g. whole sum of its parts
  parallel lines do not meet)
• To deductive proofs which establish universal
  laws, e.g. that the are of the square constructed
  on the hypoteneuse of a right-angled triangle
  area of the squares constructed on the sides

13
3. Astronomy

• Astronomy was Pythagorean until Kepler
  transformed it in the 17th century
• Stars and planets move in perfect circular
  orbits
• Task of mathematical astronomy to account for
  the phenomena of the moving heavens in terms of
  proofs based on an explanatory model (e.g. prove
  there would be an eclipse July 1, 2008)
• Chief problem the planets or wandering stars

14
(No Transcript)
15
(No Transcript)
16
4. Musical Ratios/Harmonics

• music is composed and performed using a subset of
  12 specific frequency intervals (chromatic scale
  tones) from any octave within the middle range of
  human hearing
• consonance refers to the harmoniousness
  (pleasantness) of the sound produced by playing
  two tones simultaneously
• the octave (21), the fifth (32), and the fourth
  (43) are the most consonant
• listeners of all times and places produce this
  same ordering

17
(No Transcript)
18
The Music of the Spheres

• Kepler's model of the Solar system
• Kepler used the Platonic solids for determining
  the planet spheres
• These ratios, he thought, represented harmonic
  relations
• He said the moving heavens produced an
  intellectual harmony

19
Shakespeare

• Sit, Jessica. Look how the floor of heaven is
  inlaid with patines of bright gold.
• There's not the smallest orb which thou behold'st
  but in his motion like an angel sings, still
  quiring to the young-eyed cherubins.
• Such harmony is in immortal souls But whilst
  this muddy vesture of decayDoth grossly close it
  in, we cannot hear it.
• - Merchant of Venice, V.1

20
II. Reincarnation and the Soul

• Psyche, the Greek word for soul and for
  butterfly
• Pythagoras introduced ideas of immortal soul and
  reincarnation to Greece

21

• 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

22

• In Homer the Gods are called Immortals and
  men are called brotoi, i.e. mortal ones. To
  believe in the immortality of the soul was the
  same as saying, Man is a kind of god. This was
  an utterly new religious idea for the Greeks.
• -- Guthrie, The Greeks and their Gods

23
Mind-Body Theories

• Dualism mind body ontologically separate
  entities.
• Materialism mental phenomena ontologically
  identical with states and processes of the
  body/brain
• Functionalism humans functionally one with
  physical and mental aspects

24
Radical Difference Argument

1. If X is radically different from Y, then X cannot
   depend on Y for its existence.
2. The soul (psyche) is radically different from the
   body (soma).
3. Therefore, the soul cannot depend on the body for
   its existence, i.e. it can exist separate from
   its dwelling in the body.

25
Reincarnation

• Hinduism your actions in life determine your
  social fate/caste in the next
• Pythagoreans soul is reborn in shape of
  ethical character lived in this life
• Purification (katharsis) ? escape cycle of birth
  and death, go to Isles of the Blessed
• Soul true self, exists separate from body
• Possibility of memory of past lives?

26
III. Pythagorean Way

• Practical as well as theoretical
• Akousmata (hearkenings)
• Askesis spiritual disciplines
• Goal spiritual life (bios vs. zoe)
• Philosopher neither wise nor unwise

27
Akousmata

• First and hardest to listen.
• The soul is the guard of the vessel (or
  prison).
• Contemplate the white rooster.
• Friends do not divide bread.
• It is unholy to live in spotted garments.
• Don't step over a broom or a yoke.
• Don't eat heart.
• Do not look into a mirror by night.
• Y.

28
Spiritual Practices

• Vegetarianism
• Recitation/meditation on akousmata
• Theoretical studies
• Practical studies
• Learning to live intentionally bios
• Learning to read
• Learning to dialogue
• Learning to die (katharsis, purification)

29
IV. Religious Utopia

• 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.

30
Philosophical Questions

• What is number? Is it real? Purely mental? Is
  there a real difference between pure number and
  counting numbers?
• Does the soul exist? If a person dies, is s/he
  reborn in another body or in heaven? Is that the
  same person (soul), without their body?
• Is there a true, spiritual-ethical way of
  living which we should follow rather than the
  materialistic goals most live by? What spiritual
  exercises should we do, to live that kind of
  life?
• Is the true basis of community religious? If it
  is, should they have property in common? Should
  they live by a strict rule of morals?

31
Concluding reflection

• Recall Q did Presocratic discovery of Nature ?
  experience of alienation, worldlessness?
• Pythagoreans experience Nature as wondrous,
  orderly and real, but
• Realize their truth and way ? alienation from
  ordinary society and its reality
• Pythagorean way ? alienation from body,
  physical pleasure