Parmenides in the context of "Process philosophy"

Plato (/ˈpleɪtoʊ/ PLAY-toe; Greek: Πλάτων, Plátōn; born c. 428–423 BC, died 348/347 BC) was an ancient Greek philosopher of Classical Athens who is most commonly considered the foundational thinker of the Western philosophical tradition. An innovator of the literary dialogue and dialectic forms, Plato influenced all the major areas of theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in Athens where Plato taught the collection of philosophical theories that would later become known as Platonism.

Plato's most famous contribution is his Theory of Forms (or Ideas), which aims to solve what is now known as the problem of universals. He was influenced by the pre-Socratic thinkers Pythagoras, Heraclitus, and Parmenides, although much of what is known about them is derived from Plato himself.

Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of these early philosophers spanned the workings of the natural world as well as human society, ethics, and religion. They sought explanations based on natural law rather than the actions of gods. Their work and writing has been almost entirely lost. Knowledge of their views comes from testimonia, i.e. later authors' discussions of the work of pre-Socratics. Philosophy found fertile ground in the ancient Greek world because of the close ties with neighboring civilizations and the rise of autonomous civil entities, poleis.

Pre-Socratic philosophy began in the 6th century BC with the three Milesians: Thales, Anaximander, and Anaximenes. They all attributed the arche (a word that could take the meaning of "origin", "substance" or "principle") of the world to, respectively, water, apeiron (the unlimited), and air. Another three pre-Socratic philosophers came from nearby Ionian towns: Xenophanes, Heraclitus, and Pythagoras. Xenophanes is known for his critique of the anthropomorphism of gods. Heraclitus, who was notoriously difficult to understand, is known for his maxim on impermanence, ta panta rhei, and for attributing fire to be the arche of the world. Pythagoras created a cult-like following that advocated that the universe was made up of numbers. The Eleatic school (Parmenides, Zeno of Elea, and Melissus) followed in the 5th century BC. Parmenides claimed that only one thing exists and nothing can change. Zeno and Melissus mainly defended Parmenides' opinion. Anaxagoras and Empedocles offered a pluralistic account of how the universe was created. Leucippus and Democritus are known for their atomism, and their views that only void and matter exist. The Sophists advanced philosophical relativism. The Pre-Socratics have had significant impact on several concepts of Western philosophy, such as naturalism and rationalism, and paved the way for scientific methodology.

Platonism is the philosophy of Plato and philosophical systems closely derived from it, though later and contemporary Platonists do not necessarily accept all of Plato's own doctrines. Platonism has had a profound effect on Western thought. At the most fundamental level, Platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism. This can apply to properties, types, propositions, meanings, numbers, sets, truth values, and so on (see abstract object theory). Philosophers who affirm the existence of abstract objects are sometimes called Platonists; those who deny their existence are sometimes called nominalists. The terms "Platonism" and "nominalism" also have established senses in the history of philosophy. They denote positions that have little to do with the modern notion of an abstract object.

In a narrower sense, the term might indicate the doctrine of Platonic realism, a form of mysticism. The central concept of Platonism, a distinction essential to the Theory of Forms, is the distinction between the reality which is perceptible but unintelligible, associated with the flux of Heraclitus and studied by the likes of physical science, and the reality which is imperceptible but intelligible, associated with the unchanging being of Parmenides and studied by the likes of mathematics. Geometry was the main motivation of Plato, and this also shows the influence of Pythagoras. The Forms are typically described in dialogues such as the Phaedo, Symposium and Republic as perfect archetypes of which objects in the everyday world are imperfect copies. Aristotle's Third Man Argument is its most famous criticism in antiquity.

Early Greek cosmology refers to beliefs about the origins, development, and structure of the universe in Ancient Greece that existed before the development of Ancient Greek astronomy. The basic elements of this early cosmology included a flat earth, heaven, a cosmic ocean, the afterworld (Hades), and the netherworld (Tartarus). The first three were represented by the gods Gaia, Uranus, and Oceanus (or sometimes Pontus). Ancient Greek cosmology was related to ancient Near Eastern cosmology, and was ultimately replaced by a more systematic and demythologized approach found in ancient Greek astronomy. Its main sources are the poetry of Homer (the Iliad and the Odyssey), Hesiod (the Theogony and the Works and Days), and surviving fragments from Mimnermus.

Beginning in the 5th century BC, elements of the traditional Greek cosmos began to be modified and challenged. One of the earliest of these challenges came from the emergence of the view that the cosmos as a whole was spherical (advocated by Xenophanes, Parmenides, Empedocles, and others). The rotation of the spherical cosmos was said to explain the visible rotation of the stars (an idea called "vortex"). Soon, a spherical model of the earth itself was proposed, which gradually gained acceptance, although the flat earth view never entirely disappeared during either classical antiquity or late antiquity, continuing to receive support from geographers and others like Ctesias, Ephorus, Strabo, Tacitus, and the Epicureans. The last Greek advocate of the traditional cosmology was Cosmas Indicopleustes.

The Eleatics were a group of pre-Socratic philosophers and school of thought in the 5th century BC centered around the ancient Greek colony of Elea (Ancient Greek: Ἐλέα), located around 80 miles south-east of Naples in southern Italy, then known as Magna Graecia.

The primary philosophers who are associated with the Eleatic doctrines are Parmenides, Zeno of Elea, and Melissus of Samos, although other Italian philosophers such as Xenophanes of Colophon and Empedocles have also sometimes been classified as members of this movement. The Eleatics have traditionally been seen as advocating a strict metaphysical view of monism in response to the materialist monism advocated by their predecessors, the Ionian school.

Zeno of Elea (/ˈziːnoʊ ... ˈɛliə/; Ancient Greek: Ζήνων ὁ Ἐλεᾱ́της; c. 490 – c. 430 BC) was a pre-Socratic Greek philosopher from Elea, in Southern Italy (Magna Graecia). He was a student of Parmenides and one of the Eleatics. Zeno defended his instructor's belief in monism, the idea that only one single entity exists that makes up all of reality. He rejected the existence of space, time, and motion. To disprove these concepts, he developed a series of paradoxes to demonstrate why they are impossible. Though his original writings are lost, subsequent descriptions by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia have allowed study of his ideas.

Zeno's arguments are divided into two different types: his arguments against plurality, or the existence of multiple objects, and his arguments against motion. Those against plurality suggest that for anything to exist, it must be divisible infinitely, meaning it would necessarily have both infinite mass and no mass simultaneously. Those against motion invoke the idea that distance must be divisible infinitely, meaning infinite steps would be required to cross any distance.