Pre-Socratic philosophy developed in ancient Greece during the 6th and 5th centuries BC. The pre-Socratic philosophers include those who preceded Socrates and Plato, though in some cases it is used to describe their contemporaries or later figures who continued pre-Socratic thought. The pre-Socratic philosophers were followed by the classical philosophers, including Socrates, Plato, and Aristotle.

Diels–Kranz numbering, developed by Hermann Alexander Diels and Walther Kranz in the early 20th century, is the standard for classifying the pre-Socratic philosophers. Most information about the pre-Socratic philosophers is lost, with current knowledge being obtained from the records kept by later doxographers and philosophers. These include Plato, Aristotle, Plutarch, Sextus Empiricus, Clement of Alexandria, Hippolytus of Rome, Diogenes Laertius, Stobaeus, and Simplicius of Cilicia, among others.

The pre-Socratic philosophers are organised by their belief systems, called schools, in which one followed or expanded on the teachings of his predecessors. New schools developed as philosophers criticised or responded to one another. Each pre-Socratic philosopher and school engaged in natural inquiry, but their subjects, methods, and motivations varied significantly.

The pre-Socratics were the first Western philosophers and began with the Ionian school that believed in material monism. The original Ionians were the Milesians: Thales, Anaximander, and Anaximenes. They were succeeded by the Ionian Heraclitus, Pythagoras of the Pythagorean school, the theology of Xenophanes, and Parmenides of the Eleatic school. The Elatics were challenged by the pluralist philosophy of Empedocles and Anaxagoras and the atomist philosophy of Leucippus and Democritus. The Sophists then taught rhetoric and moral philosophy. Pre-Socratic philosophy was preceded by the works of poets and theologians like Homer and Hesiod.

Ionians

Western philosophy originated with the Ionian school. They were material monists who believed that there was a single underlying material origin of all that exists, an arche, made up of a specific element. The first of the Ionian philosophers were from the city-state Miletus. The Milesian school was the first group to use inquiry instead of mythology to study nature, developing their philosophy in the 6th century BC.

Thales of Miletus is considered the first Greek philosopher. He proposed that water is the arche that underlies all things. Anaximander was a student of Thales and the first Greek to write a philosophical treatise. He described the apeiron, an eternal and infinite entity, as the arche. Diogenes Laertius credited him as the founder of Ionian philosophy. Anaximenes of Miletus was a student of Anaximander. He proposed that air is the arche and that the Earth lies on top of air. He said that all things are formed by rarefaction or condensation of the air.

Ionian philosophy continued with Heraclitus, who challenged some of the ideas of the Milesians. Heraclitus described a system in which all things are in constant flux and that the unity of opposites forms reality through opposing forces. He proposed that fire is the arche. He was active in the 6th century BC. Antisthenes of Ephesus was, according to Diogenes Laeritus, an adherent to the philosophy of Heraclitus. Cratylus was an adherent to the philosophy of Heraclitus. He believed that because all things are in a state of change, nothing can be accurately described. He is said to have believed this to the point that he eventually only communicated using his finger. He was an instructor of Plato. Diogenes of Apollonia revived the ideas of the Milesian school in the 5th century BC. He argued that air is the arche. He believed that only a single arche must exist and this was the only way that things could interact with each other. He was one of the final Ionian philosophers. Idaeus of Himera followed the belief of Anaximenes that air is the arche. Mandrolytus of Priene was a student of Thales.

Xenophanes Xenophanes was a philosopher active in the 6th century BC. He challenged the Homeric belief in a pantheon of human-like gods, instead asserting a single god that lacked thought or motion. Xenophanes is sometimes erroneously described as the first Eleatic, a Pythagorean, or an Ionian, but he is not classified under any specific school of philosophy.

Eleatics

The Eleatics rejected the concepts of change and pluralism. They were active in the 5th century BC.

Parmenides founded the Eleatic school. He said that the world could be understood as a mortal who sees a false world based on opinions or divinely as it truly exists where all things are a single entity or being. Zeno of Elea was a student of Parmenides who devised numerous paradoxes. His arguments were a response to the challenges against the Eleatic school levelled by the pluralists. Melissus of Samos was a follower of Parmenides. He expanded upon the arguments of Parmenides, presenting them as prose instead of verse. He believed that existence persists infinitely through space and time instead of having finite space and existing without time. Callias of Aexone was a student of Zeno.

Pluralists The pluralists rejected the monist belief of the Ionians that all things are made up of a single element. Instead, they believed that there are multiple discrete elements that make up the world. Pluralism was a response to the Eleatic school. They were active in the 5th century BC. Empedocles was a pluralist philosopher. He was the first to propose the four classical elements of water, earth, fire, and air. He believed that these were the most basic elements and that all things in the world were created by mixing them in different proportions. They are drawn together and split apart by forces he called love and strife, respectively. Anaxagoras was a pluralist philosopher. He believed that all things exist independently and that they combined to create the world. He introduced his concept of the mind, nous, as an underlying principle of existence. Archelaus was a student of Anaxagoras. Instead of describing nous as its own element, Archelaus considered it to be an aspect of air. He is said to have been the teacher of Socrates. Ariphrades is given as the name of a dishonourable student of Anaxagoras. Carneades of Athens was, according to Suda, a student of Anaxagoras. Metrodorus of Lampsacus was a student of Anaxagoras who analysed the works of Homer through pluralist belief, assigning each character a different element. Pausanias of Sicily was a student of Empedocles and the author of his biography. Empedocles dedicated a poem to Pausanias.

Atomists The atomists believed that all of existence consists of either indivisible atoms or the Void that exists around and between them. Atomism was a response to the Eleatic school.

Leucippus introduced the concept of the atom. Little is known about him, and he is traditionally described in the context of his student Democritus. Democritus was a student of Leucippus who developed an atomist theory.

Students of the pre-Socratic atomists brought the philosophy into the Hellenistic era, including Hecataeus of Abdera, Apollodorus of Cyzicus, Nausiphanes, , Bion of Abdera, Bolus of Mendes, , Anaxarchus, Nessos of Chios, and Metrodorus of Chios. They were succeeded by Epicurus and his atomist school of Epicureanism.

Pythagoreans

The first Italian philosophers were immigrants from Ionia. The most prominent of these was Pythagoras, who founded his philosophy of Pythagoreanism in the 6th century BC. This is the only ancient Greek philosophical movement in which a single person is considered its formal leader. Pythagoreanism was based on the idea that numbers are the basis of all things. There was no single defining trait shared by all of the Pythagoreans, and they engaged in a variety of pursuits that included athletics, mathematics, medicine, natural philosophy, and politics. Iamblichus identified 235 Pythagoreans by name, but the associated identity for many of these names is unknown. Pythagoras was a mathematician. He founded a group that separated itself from contemporary religion and promised its members a better life. Many of his followers attributed their own beliefs to Pythagoras. He believed in metempsychosis, in which souls can transmigrate.

Pythagoras is said to have sorted his followers into two groups: the students that were taught his philosophy in full, and the auditors who were only allowed limited knowledge. Pythagoreanism was religious as well as philosophical, and there is sometimes disagreement over how involved one had to be with Pythagorean ideas to be considered a Pythagorean. Abaris the Hyperborean was a legendary prophet from around the 6th century BC who, according to Iamblichus, became a Pythagorean. Alcimachus of Paros was a student of Pythagoras who left Croton following attacks against the Pythagoreans. Arignote was a Pythagorean writer. She may have been the daughter of Pythagoras and Theano. was a student of Pythagoras who is said to have later married his widowed wife Theano. He is believed to have written about harmony. Brontinus (alternatively Brotinus) was an early Pythagorean. He is said to be either the father or the husband of Theano. He may have been a student of Alcmaeon of Croton. Deinarchus of Paros was a follower of Pythagoras who left Croton amid attacks against the Pythagoreans. According to Iamblichus, he had followers of his own. Democedes was a physician and the son of Calliphon. Iamblichus listed him among the Pythagoreans who left Croton following attacks against the Pythagoreans. Calliphon of Croton is generally accepted to have been a Pythagorean, but little else is known about him. He is said to have been a priest and to have advised Pythagoras from the afterlife. Cercops was considered a Pythagorean by the Suda and Hermann Alexander Diels. Several poems, sometimes described as poems of Orpheus, are attributed to him. Cheilonis was a prominent female Pythagorean and is believed to have been the daughter of Chilon of Sparta. Damo was, according to Iamblichus, the daughter of Pythagoras and the mother of Bitale. Dios is the attributed writer of Pythagorean works on aesthetics. was a Pythagorean in a story related by Iamblichus to demonstrate Pythagorean honour, in which Euryphamus forgets he was going to meet Lysis, but Lysis committed to their meeting and waited for him overnight. Fragments about life are attributed to Euryphamus. Hippasus is described as the founder of either the mathematikoi or the akousmatikoi. According to Iamblichus, Hippasus was rejected by the Pythagoreans and killed at sea because he created a regular dodecahedron. Aristotle said that Hippasus believed in fire as an arche. Mnesarchus was the son of Pythagoras. He succeeded Aristaeus as leader of the Pythagoreans. Myia is believed to be the daughter of Pythagoras and Theano, and the wife of Milo of Croton. Orestadas was a sixth-century BC Pythagorean described by Diogenes Laeritius as the man who freed Xenophanes from slavery. He may have been the same Orestadas whom Iamblichus said was from Metapontum. Parmeniscus (alternatively Parmiscus) is generally accepted to have been a Pythagorean, but little else is known about him. According to Favorinus, Parmeniscus may have saved Xenophanes from slavery. was an early Pythagorean who described the world through geometry. He may have believed that there are 183 worlds, sorted by element. This was attributed to him by a third-hand report from Plutarch. Leonid Zhmud disputes Petron's classification as a Pythagorean. Telauges was the son of Pythagoras who practiced a form of Pythagoreanism reminiscent of Cynicism. Theano is said to be either the daughter or wife of Brontinus and either the student or wife of Pythagoras.