Pythagoras to Democritus: Unveiling Ancient Philosophies
The Mathematical Works of Pythagoras
Significant contributions include the Pythagorean theorem, the incommensurability of the diagonal and side of a square, distributions, numerical oppositions, and geometric relations.
Parmenides
- In the car of truth: He lived in Elea as a settler and aristocratic organizer, concerned with its laws. Excellent judges, sworn citizens, acted in accordance with the laws of Parmenides.
- The prologue to a journey: She wrote a poem in Homeric hexameters to communicate their thinking. His characters are seemingly peaceful: truth, justice, public opinion, being, not being, birth, and necessity.
- The road to truth: Being and thinking are the same thing. What is, is, and what is not, is not. This clearly shows the identity principle, an initial formal approach akin to Pythagorean thought.
- What is being: The discovery of being as a fundamental object of thought. Being itself encompasses all manifestations of reality, as if things are within a bond and subject to organization.
Zeno and Melissus of Elea and Samos
Their arguments in defense of their master focused on the problem of plurality and movement. The whole is not a multiplicity. Fragments suggest ideas that appear in Democritus’ theory of atoms.
Empedocles
The first written account addressing Parmenides’ concept of being and its unity, and the impossibility of something being and not being. Empedocles’ idea contained four elements: air, fire, earth, and water.
- Love and Hate: Two principles manifested in human experience, inclination and rejection, uniting or disengaging nature. Love brings stability and fullness, while hatred divides and corrupts.
Anaxagoras
The philosopher banished for his ideas on astronomy and celestial phenomena, due to an accusation of impiety. He starts from the idea that something cannot have a source or an end.
- Homeometries of Anaxagoras: Affirms that all beings consist of seeds called homeometries. They are eternal, immutable, qualitatively different, can be divided infinitely, and possess all shapes and colors. They have no movement.
- Nous (Mind): It is a principle of love.
Leucippus
No data exists about his life and work. Their existence has even been doubted.
Democritus of Abdera
He wrote many texts, but only excerpts of their works have survived. With Democritus began the idea of consistency as a writer.
- The theory of atoms: Atoms are qualitatively neutral, distinguished only in form, order, and situation. Atoms are similar to Parmenides’ being, by its character forever. To move, atoms need gaps in which to navigate and organize. Thus originates and configures the world.
- The soul and the senses: Democritus recovers the original meaning of the soul as breath.
The Nature of the Object
The first philosophical investigations. Nature is observed as scientists seek the Arche, the principle or element comprising all that exists. Characteristics of the Arche:
- Located at the top, is temporary and the origin of everything.
- Is the constituent element common to all things.
- Determines the characteristics and processes to which all objects are subject.
Examples:
- Thales: Water
- Anaximander: Apeiron
- Anaximenes: Air
- Heraclitus: Fire
- Pythagoras: Numbers
- Parmenides: Being (the real)
- Empedocles: Soil, water, air, and fire
- Anaxagoras: Multiple items
- Democritus: Atoms