Los presocráticos

what is the fundamental "stuff" (arche) of the universe?

Milesian school (born in Miletus)

Anaximander (610-546 BC), a geometer and the first writer on philosophy. He came up with the idea of apeiron , i.e., an undefined, unlimited substance without qualities, out of which the primary opposites. He  invented the first sundial and drew the first map of the world.

Thales of Miletus:  (of the Milesian school) Thales claims that the world rests on water with the view that water is the archē or fundamental principle, and he adds that “that from which they come to be is a principle of all things.” He suggests that Thales chose water because of its fundamental role in coming-to-be, nutrition, and growth, and claims that water is the origin of the nature of moist things. arche is water because as a substance, it contains motion and change.

Heraclitus: The universe is a state of perpetual flux, connected by logical structure or pattern, which he termed logos.

Xenophanes: comes up with the notion of pephuke (explanation), which states that X is really Y when Y reveals the true character of X. 

Pythagoras: the notion that NUMBER (or mathematics) reveals the structure of the universe.

Eleatic School (born in Elea)

Parmenides: is the father of metaphysics and rationalism. His theory is that what IS CANNOT NOT BE. So, BEING (NOUS) is UNCHANGING. For something to change, it has to NOT BE, which is a contradiction because NOTHING cannot exist, and out of nothing, nothing comes.

Atomist School

The Atomists: Leucippus (5th BC) and his pupil Democritus of Abdera (460-370 BC) from Thrace. the arche are atoms: small primary bodies, infinite in number, indivisible and imperishable, qualitatively similar, but distinguished by their shapes. They move eternally through the infinite void. They collide and unite, thus generating objects that differ in accordance with the varieties in number, size, shape, etc. We are ALL atoms.

The Pluralist School

Empedocles: comes up with the principle of attraction and rejection, or LOVE and STRIFE. One cannot be without the other. Love unites, strife separates.