Early Greek World 450BC

1
Early Greek World 450BC
2
Pythagoras c.582-507 B.C.

• Son of an engraver / gem-smith.
• Traveled widely in Asia Minor and Egypt.
• Settled in Croton (Southern Italy 529 BC.)
• later banished to Metapontion.
• Founded a religious / mystic sect or order.
• Extremely influential Philosopher and scientist.

3
Pythagorean School

• The Pythagorean School of philosophy and
  religious brotherhood was dedicated to the
  pursuit of moral purification, spiritual
  salvation, and the intellectual understanding of
  nature all of which were mutually
  interconnected.

4
Pythagorean School II

• Secretive and strict.
• Transmutation of the Soul.
• Medicine to purge the body. (tonic)
• Music to purge the soul. (tone)
• Emphasis on harmony.

5
Music and Numbers

• The basic tenet of the Pythagoreans was that the
  importance of numbers in music could be extended
  to a deep inherent relation between natural
  numbers and the physical universe.
• Not a Reductionist, rathera mystical enhancing
  of the human condition, via numbers.

6
Pythagorean Fascinationwith Numbers and
Perfection

• 10 a perfect number because it is the sum of 1,
  2, 3, 4.
• Also because these numbers include the ratios of
  the lengths of a string that produced harmonious
  notes, namely 43 the fourth, 32 the fifth and
  21 the octave.
• A sphere was a perfect figure.
• The heavenly bodies being perfect must move on
  perfect spheres and they must be 10 in number.

7
Triangular and Square Numbers
The beauty of number patterns must be
significant!
8
Pythagorean Fascinationwith Geometry

• square (n2) and cube (n3) of numbers show a
  link with geometrical shapes.
• The regular structures of gems, crystals, cubes,
  pyramids, hexagonal shapes, etc...
• Developed the theorem associated with is name
  (gained from Egyptians and Babylonians)but may
  not have proved it!

9
Unspeakable Irrational Numbers!

• A right-angled isosceles triangle with unit equal
  sides has a Hypotenuse of
• This could not be calculated exactly!
• i.e. they were able to prove that no two
  integers m and n could exist such that m2/n2 is
  equal to 2.
• This was a serious blow to their belief that
  everything could be described in terms of
  numbers.
• The irony of ?!

10
Pythagorean Influence Lingers(?)

• The premise that the universe can be understood
  in mathematical terms.
• The idea that mathematics represents a higher
  form of truth that can only be achieved by the
  exercise of pure thought. (Platos Ideals)
• Hence, observations with the senses of the
  imperfect world around us are not only
  unnecessary, but may be misleading in the pursuit
  of absolute truth. Why perform
  experiments?

11
Philolaus (484 - 400 B.C.)

• Believed that the earth was a sphere and that it
  moved.
• Not around the sun, rather it revolved about the
  central fire the watchtower of Zeus.
• The central fire was not observable!
• Why not? Answer The Counter Earth

12
The Counter Earth

• Philolaus postulated an intermediate, invisible
  planet the counter earth (antichton) that
  always blocked-out the central fire.
• Aristotle thought is was postulated to make up to
  10 the number moving heavenly bodies.
• Earth perhaps not noble enough to occupy the
  central position in the cosmos.
• Presuppositions and Postulates!

13
More Questions

• What is real and what is illusion?
• Can we trust our senses?
• Or should we rely on reason alone?
• These address human perception (appearances) and
  the way things are in themselves.

14
Heraclitus of Ephesus (c. 535-475 B.C.)

• Everything was constantly changing, in a state of
  constant flux, strife. (An emphasis on change)
• Fire is the fundamental element (arche)
  ever consuming, moving, but inextinguishable.
• Perpetual change does not imply Chaos.
• In a state of flux, what is constant?
• Logos

15
Logos word, speech or thought

• Impersonal Divine Intelligence
• The rational principle that governed the
  universe.
• Change is ordered via the Logos.
• Dynamic and creative tension between various
  elements.

16
Parmenides(born. c.515 B.C.)

• Lived in Elea, Southern Italy
• Nothing really changes!
• Apparent changes perceived by the senses are only
  mere illusions.
• Affirmed an underlying unity or oneness.
• The ultimate reality is existence or being,
  and the world of pure logic.

17
The Beginnings of Logic

• What is not (eg void) cannot be said to exist
  at all.
• Something cannot come from nothing or turn
  into nothing, if nothing cannot exist at all.
• Thus the true reality by logical necessity is
  changeless and unitary.

18
Reason over Perception.

• Questions asked on what is real and apparent
• .Between rational truth and sensory perception,
  on being and becoming.
• Parmenides emphasized the autonomy and
  superiority of human reason as the judge of
  reality not sense perceptions.
• Influential to Plato and raised issues that all
  subsequent philosophers addressed.

19
Empedocles (c.495-435 B.C.)

• Lived in Sicily
• Claimed that Earth, Air, Fire and Water were the
  basic elements (or roots).
• He agreed with the Eleatics that nothing really
  changes, but also with Heraclitus notion of flux
  between the basic elements.

Neither senses or our minds are completely
trustworthy in the pursuit of truth.
20
Love and Hate Govern Change

• The 4 elements never change, they are permanent,
  simply mingling and separating.
• Primary mythical forces of Love and
  Strife/Hate.
• A recognition of both Parmenides nothing really
  changes and the observable existence of flux,
  cyclical patterns, birth and death

21
Anaxagoras (c. 500-428BC)

• More than four elements.
• An infinite number of minute particles.
• No net change, simply combination and
  separation.
• Rather than semi-mythic forces of Love and
  Hate, he proposed..

22
Transcendent Primordial Mind Nous

• The Nous set the material universe into motion,
  and gave it ordered and form.
• Causes rotation vortexes, which spread
  throughout the world.

23
Lively debate of views within early Greece

• Two broad themes
• Naturalism, explaining reality in terms of
  natural elements (like fire, water, air, and
  earth)
• Rationalism, in which reality lies in the realm
  of transcendent reason.