ANCIENT PHILOSOPHY 3: PYTHAGOREANS

Context of the Pythagoreans:

  • criticized by Heraclitus
  • no original tradition, all from Plato’s pupils
  • doctrine of numbers
  • Platonic pythagoreans saw numbers under forms (remember, via Aristotle each number is its own form)
  • Skeptic Academy: Plato as incoherent, fabrication of Platonic writings making him look like a Pythagorean
  • multiplicity of doctrines

PYTHAGORAS:

  • Turkey, Italy
  • school as a way of life, veganism, ethics, no pure doctrines
  • soul is immortal, migrating to other bodies
  • Homer: shadows in the underworld, for him the soul changes body (rebirth)

PHILOLAUS:

  • nature arises from harmony between the limited and unlimited (a coherent presoc nature)
  • Limiting Principle: limiting the unlimited
  • principle as odd numbers: even numbers (unlimited open forms), odd numbers (limited closed forms)
  • this principle is in the things themselves
  • Number means proportion (like in music or geometric axioms)
  • mathemathics and music both limit the unlimited
  • only things with numbers can be known

Aristotelian Account:

  • numbers are essences of things; things imitate numbers
  • essence is his own terminology, the second explanation was probably theirs
  • only things with essences can be known

Plato’s Timaeus: Plato as a kind of pythagorean