Platonic Academy in the context of "Aristotle"

Classical Athens, known contemporaneously simply as Athens (Ancient Greek: Ἀθῆναι, Athênai [atʰɛ̂ːnai̯]; Modern Greek: Αθήναι, Athine [aˈθine]), was the major urban centre of the notable polis (city-state) of the same name during the classical period (480–323 BC) of ancient Greece, located in Attica, Greece, leading the Delian League in the Peloponnesian War against Sparta and the Peloponnesian League. Athenian democracy was established in 508 BC under Cleisthenes following the tyranny of Isagoras. This system remained remarkably stable, and with a few brief interruptions, it remained in place for 180 years, until 322 BC (amid the aftermath of the Lamian War). The peak of Athenian hegemony was achieved during the Age of Pericles in the 440s and 430s BC.

In the classical period, Athens was a centre for the arts, learning, and philosophy, and it was the home of Plato's Academy and Aristotle's Lyceum. Athens was also the birthplace of Socrates, Plato, Pericles, Aristophanes, Sophocles, and many other prominent philosophers, writers, and politicians of the ancient world. It is widely referred to as the cradle of Western civilization and as the birthplace of democracy, largely due to the impact of its cultural and political achievements during the 5th and 4th centuries BC on the rest of the then-known European continent.

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.

Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.

Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.

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.

Academic skepticism was the philosophy of the skeptical period of the Academy dating from around 266 BCE, when Arcesilaus became scholarch, until around 90 BCE, when Antiochus of Ascalon rejected skepticism, although individual philosophers, such as Favorinus and his teacher Plutarch, continued to defend skepticism after this date. Unlike the existing school of skepticism, the Pyrrhonists, they maintained that knowledge of things is impossible. Ideas or notions are never true; nevertheless, there are degrees of plausibility, and hence degrees of belief, which allow one to act. The school was characterized by its attacks on the Stoics, particularly their dogma that convincing impressions led to true knowledge. The most important Academics were Arcesilaus, Carneades, and Philo of Larissa. The most extensive ancient source of information about Academic skepticism is Academica, written by the Academic skeptic philosopher Cicero.

Philo of Larissa (Greek: Φίλων ὁ Λαρισαῖος Philon ho Larisaios; 159/8–84/3 BC) was a Greek philosopher. It is very probable that his actual name was "Philio."

He was a pupil of Clitomachus, whom he succeeded as head of the Academy. During the Mithridatic Wars which would see the destruction of the Academy, he travelled to Rome where Cicero heard him lecture. None of his writings survive. He was an Academic sceptic, like Clitomachus and Carneades before him, but he offered a more moderate view of skepticism than that of his teachers, permitting provisional beliefs without certainty.