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