The pre-Socratic intellectual tradition is thought to have begun with Thales of Miletus of the Ionian school. There are two other pre-Socratic schools: the Italians and the Athenians. The Italian philosophers, who were Greeks intellectuals living in Italy, consist of three key thinkers: Pythagoras (d. 497 BCE), Parmenides (d. 450 BCE), and Zeno (d. 430 BCE). The major unifying factor in the Italian school was incorporeal monism that held all things to consist of a single intangible substance. This perspective distinguished them from the Ionians who claimed that a tangible substance lay behind all things.

Pythagoras, believed to have been a charismatic and religious teacher, is perhaps the most reputable advocate of the Italian school. He lived most of his life in Italy after moving there with colonizing Greek forces. He clearly came to develop a fascination with numbers and music theory, and believed that the fundamental reality of all things is immaterial. This immateriality, he claimed, is mathematics in the form of numbers constituting the basic rational principle behind all things. Pythagoras also advocated religious rituals, self-discipline, and emphasized the idea of the transmigration of the soul. He believed the soul to be an immortal entity that goes through a series of reincarnations.

Parmenides argued that the human ideas of space, time, and motion are illusory. Things cannot change in quantity (e.g. in height) or quality (e.g. from hot to cold). He claimed that whatever exists does so in a fixed, eternal, and unchanging reality known as being. Those who believe that things around them changed were simply deceived and living in an illusion. Parmenides famously coined the phrase that “whatever is… is.”

Zeno was a student and popularizer of Parmenides known for his paradoxes. He intended to prove his teacher’s claim that space, time, and motion are illusory, and thus absurd. His attempt to achieve came in the form of three paradoxes: the paradox of the runner, the tortoise and the hare, and the arrow. The paradox of the runner, for example, presents a scenario that before a runner completes running 100 meters, he must run 50. But to run 50 meters he must run 25, then 12.5, and so on. No matter how far the runner has to run he has to run half that distance. The distance is infinitely divisible so that ultimately the runner cannot run at all. The distance gets smaller and smaller until it gets to the point where the runner cannot move.

The Athens were corporeal pluralists who held to the notion of multiple physical substances constitute the world, or constitute the fundamental elements of the world. Three are particularly important: Empedocles (d. 435 BCE), Anaxagoras (d. 428 BCE), and Democritus (d. 371 BCE).

Empedocles championed Athenian democracy. This gelled well with his corporeal pluralism on grounds that democracy is itself pluralistic and consists of different, diverse people and groups vying for control and power. Famously, but according to legend, Empedocles died in an active volcano on Mount Aetna. He was also the first person in history to maintain that light traveled at a fixed speed but most importantly he proposed that four elements made up everything: earth, air, fire, and water. He referred to these as “roots” which he claimed are eternal and unchanging. Empedocles also wanted to discover the essence behind the essences, namely a fifth essence or quintessence.

Anaxagoras, a friend of Empedocles who lived in Athens during the Persian Wars (498- 448 BCE), believed there was an infinite number of separate and distinct elements. These he referred to as ingredients or seeds. The original state of the cosmos was a mixture of all its ingredients. These ingredients were shifted, separated, and remixed with each other to produce a cosmos consisting of separate material masses and objects. Anaxagoras also introduced the notion of the “nous” (the mind) that he claimed is the governing principle of the cosmos. The nous is different from the ingredients that constituted the original mixture because it set everything in motion and rotation. Anaxagoras did not, however, identify the nous with the gods.

Democritus would have been a contemporary of Socrates and he was the first atomist (“atom” from the Greek atomos, meaning indivisible or not cuttable). He posited atoms to be the fundamental substances of all things. These are infinite, unchangeable, hard, indestructible substances that are always in motion in the void (empty space). Atoms also come in various shapes and sizes (some being smooth others jagged), and repel one another when they collide in the void. They can also combine into clusters through the use of tiny hooks on their surfaces. Democritus believed that human beings had arisen through the collision of atoms moving about and will likewise disintegrate in time.