Ancient Greek philosophy

Ancient Greek philosophy arose in the 6th century BC. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics. Greek philosophy continued throughout the Hellenistic period and later evolved into Roman philosophy.
Greek philosophy has influenced much of Western culture since its inception, and can be found in many aspects of public education. Alfred North Whitehead once claimed: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato". Clear, unbroken lines of influence lead from ancient Greek and Hellenistic philosophers to Roman philosophy, early Islamic philosophy, medieval scholasticism, the European Renaissance and the Age of Enlightenment.
Greek philosophy was influenced to some extent by the older wisdom literature and mythological cosmogonies of the ancient Near East, though the extent of this influence is widely debated. The classicist Martin Litchfield West states, "contact with oriental cosmology and theology helped to liberate the early Greek philosophers' imagination; it certainly gave them many suggestive ideas. But they taught themselves to reason. Philosophy as we understand it is a Greek creation".
In general, the ancient Greeks acknowledged their Egyptian forebears, and in the fifth century BC, the philosopher Isocrates declared that the earliest Greek thinkers traveled to Egypt to seek knowledge; one of them Pythagoras of Samos, who "was first to bring to the Greeks all philosophy". Although Greeks acknowledged Egyptian wisdom, modern scholarship regards Greek philosophy as a distinctive and original intellectual tradition developed independently by Greek thinkers.
In the 21st century, research by Egyptologists has indicated that the word philosopher itself seems to stem from Egypt: "the founding Greek word philosophos, lover of wisdom, is itself a borrowing from and translation of the Egyptian concept mer-rekh which literally means 'lover of wisdom,' or knowledge."
Subsequent philosophic tradition was so influenced by Socrates as presented by Plato that it is conventional to refer to philosophy developed prior to Socrates as pre-Socratic philosophy. The periods following this, up to and after the wars of Alexander the Great, are those of "Classical Greek" and "Hellenistic philosophy", respectively.

Early Greek philosophy (or pre-Socratic philosophy)

The convention of terming those philosophers who were active prior to the death of Socrates as the pre-Socratics gained currency with the 1903 publication of Hermann Diels' Fragmente der Vorsokratiker, although the term did not originate with him. The term is considered useful because what came to be known as the "Athenian school" signaled the rise of a new approach to philosophy; Friedrich Nietzsche's thesis that this shift began with Plato rather than with Socrates has not prevented the predominance of the "pre-Socratic" distinction.
Since 2016, however, scholarly discourse has shifted from using the term "pre-Socratic philosophy" to the more neutral "Early Greek Philosophy". This change has been popularized in part by André Laks and Glenn W. Most through their comprehensive nine-volume Loeb Classical Library edition of Early Greek Philosophy. In the first volume, they distinguish their systematic approach from that of Hermann Diels, starting with the deliberate choice of terminology. They prefer "Early Greek Philosophy" over "pre-Socratic philosophy" primarily because Socrates was a contemporary of, and in some cases even preceded, thinkers traditionally labeled as "pre-Socratic" such as the Atomists.
The early Greek philosophers were primarily concerned with cosmology, ontology, and mathematics. They were distinguished from "non-philosophers" insofar as they rejected mythological explanations in favor of reasoned discourse.

Milesian school

, regarded by Aristotle as the first philosopher, held that all things arise from a single material substance, water. It is not because he gave a cosmogony that John Burnet calls him the "first man of science", but because he gave a naturalistic explanation of the cosmos and supported it with reasons. According to tradition, Thales was able to predict an eclipse and taught the Egyptians how to measure the height of the pyramids.
Thales inspired the Milesian school of philosophy and was followed by Anaximander, who argued that the substratum or arche could not be water or any of the classical elements but was instead something "unlimited" or "indefinite". He began from the observation that the world seems to consist of opposites, yet a thing can become its opposite. Therefore, they cannot truly be opposites but rather must both be manifestations of some underlying unity that is neither. This underlying unity could not be any of the classical elements, since they were one extreme or another. For example, water is wet, the opposite of dry, while fire is dry, the opposite of wet. This initial state is ageless and imperishable, and everything returns to it according to necessity. Anaximenes in turn held that the arche was air, although John Burnet argues that by this, he meant that it was a transparent mist, the aether. Despite their varied answers, the Milesian school was searching for a natural substance that would remain unchanged despite appearing in different forms, and thus represents one of the first scientific attempts to answer the question that would lead to the development of modern atomic theory; "the Milesians," says Burnet, "asked for the φύσις of all things."

Xenophanes

Xenophanes was born in Ionia, where the Milesian school was at its most powerful and may have picked up some of the Milesians' cosmological theories as a result. What is known is that he argued that each of the phenomena had a natural rather than divine explanation in a manner reminiscent of Anaximander's theories and that there was only one god, the world as a whole, and that he ridiculed the anthropomorphism of the Greek religion by claiming that cattle would claim that the gods looked like cattle, horses like horses, and lions like lions, just as the Ethiopians claimed that the gods were snub-nosed and black and the Thracians claimed they were pale and red-haired.
Xenophanes was highly influential to subsequent schools of philosophy. He was seen as the founder of a line of philosophy that culminated in Pyrrhonism, possibly an influence on Eleatic philosophy, and a precursor to Epicurus' total break between science and religion.

Pythagoreanism

lived at approximately the same time that Xenophanes did and, in contrast to the latter, the school that he founded sought to reconcile religious belief and reason. Little is known about his life with any reliability, however, and no writings of his survive, so it is possible that he was simply a mystic whose successors introduced rationalism into Pythagoreanism, that he was simply a rationalist whose successors are responsible for the mysticism in Pythagoreanism, or that he was actually the author of the doctrine; there is no way to know for certain.
Pythagoras is said to have been a disciple of Anaximander and to have imbibed the cosmological concerns of the Ionians, including the idea that the cosmos is constructed of spheres, the importance of the infinite, and that air or aether is the arche of everything. Pythagoreanism also incorporated ascetic ideals, emphasizing purgation, metempsychosis, and consequently a respect for all animal life; much was made of the correspondence between mathematics and the cosmos in a musical harmony. Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.

Heraclitus

Heraclitus must have lived after Xenophanes and Pythagoras, as he condemns them along with Homer as proving that much learning cannot teach a man to think; since Parmenides refers to him in the past tense, this would place him in the 5th century BC. Contrary to the Milesian school, which posits one stable element as the arche, Heraclitus taught that panta rhei, the closest element to this eternal flux being fire. All things come to pass in accordance with Logos, which must be considered as "plan" or "formula", and "the Logos is common". He also posited a unity of opposites, expressed through dialectic, which structured this flux, such as that seeming opposites in fact are manifestations of a common substrate to good and evil itself.
Heraclitus called the oppositional processes ἔρις, "strife", and hypothesized that the apparently stable state of δίκη, or "justice", is the harmonic unity of these opposites.

Eleatic philosophy

cast his philosophy against those who held "it is and is not the same, and all things travel in opposite directions,"—presumably referring to Heraclitus and those who followed him. Whereas the doctrines of the Milesian school, in suggesting that the substratum could appear in a variety of different guises, implied that everything that exists is corpuscular, Parmenides argued that the first principle of being was One, indivisible, and unchanging. Being, he argued, by definition implies eternality, while only that which is can be thought; a thing which is, moreover, cannot be more or less, and so the rarefaction and condensation of the Milesians is impossible regarding Being; lastly, as movement requires that something exist apart from the thing moving, the One or Being cannot move, since this would require that "space" both exist and not exist. While this doctrine is at odds with ordinary sensory experience, where things do indeed change and move, the Eleatic school followed Parmenides in denying that sense phenomena revealed the world as it actually was; instead, the only thing with Being was thought, or the question of whether something exists or not is one of whether it can be thought.
In support of this, Parmenides' pupil Zeno of Elea attempted to prove that the concept of motion was absurd and as such motion did not exist. He also attacked the subsequent development of pluralism, arguing that it was incompatible with Being. His arguments are known as Zeno's paradoxes.