Plato

Medieval philosophy is the philosophy that existed through the Middle Ages, the period roughly extending from the fall of the Western Roman Empire in the 5th century until after the Renaissance in the 13th and 14th centuries. Medieval philosophy, understood as a project of independent philosophical inquiry, began in Baghdad, in the middle of the 8th century, and in France and Germany, in the itinerant court of Charlemagne in Aachen, in the last quarter of the 8th century. It is defined partly by the process of rediscovering the ancient culture developed in Greece and Rome during the Classical period, and partly by the need to address theological problems and to integrate sacred doctrine with secular learning. This is one of the defining characteristics in this time period. Understanding God was the focal point of study of the Jewish, Christian and Muslim Philosophers and Theologians.

The history of medieval philosophy is traditionally divided into two main periods: the period in the Latin West following the Early Middle Ages until the 12th century, when the works of Aristotle and Plato were rediscovered, translated, and studied upon, and the "golden age" of the 12th, 13th and 14th centuries in the Latin West, which witnessed the culmination of the recovery of ancient philosophy, along with the reception of its Arabic commentators, and significant developments in the fields of philosophy of religion, logic, and metaphysics.

Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia.

Already during Pythagoras's life it is likely that the distinction between the akousmatikoi ("those who listen"), who is conventionally regarded as more concerned with religious, and ritual elements, and associated with the oral tradition, and the mathematikoi ("those who learn") existed. The ancient biographers of Pythagoras, Iamblichus (c. 245 – c. AD 325) and his master Porphyry (c. 234 – c. AD 305) seem to make the distinction of the two as that of 'beginner' and 'advanced'. As the Pythagorean cenobites practiced an esoteric path, like the mystery schools of antiquity, the adherents, akousmatikoi, following initiation became mathematikoi. It is wrong to say that the Pythagoreans were superseded by the Cynics in the 4th century BC, but it seems to be a distinction mark of the Cynics to disregard the hierarchy and protocol, ways of initiatory proceedings significant for the Pythagorean community; subsequently did the Greek philosophical traditions become more diverse. The Platonic Academy was arguably a Pythagorean cenobitic institution, outside the city walls of Athens in the 4th century BC. As a sacred grove dedicated to Athena, and Hecademos (Academos). The academy, the sacred grove of Academos, may have existed, as the contemporaries seem to have believed, since the Bronze Age, even pre-existing the Trojan War. Yet according to Plutarch it was the Athenian strategos (general) Kimon Milkiadou (c. 510 – c. 450 BC) who converted this, "waterless and arid spot into a well watered grove, which he provided with clear running-tracks and shady walks". Plato lived almost a hundred years later, circa 427 to 348 BC. On the other hand, it seems likely that this was a part of the re-building of Athens led by Kimon Milkiadou and Themistocles, following the Achaemenid destruction of Athens in 480–479 BC during the war with Persia. Kimon is at least associated with the building of the southern Wall of Themistocles, the city walls of ancient Athens. It seems likely that the Athenians saw this as a rejuvenation of the sacred grove of Academos.

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: a tetrahedron (four faces), a cube (six faces), an octahedron (eight faces), a dodecahedron (twelve faces), and an icosahedron (twenty faces).

Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato, who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids.

Parmenides (Greek: Παρμενίδης) is one of the dialogues of Plato. It is widely considered to be one of the most challenging and enigmatic of Plato's dialogues.The Parmenides purports to be an account of a meeting between the two great philosophers of the Eleatic school, Parmenides and Zeno of Elea, and a young Socrates. The occasion of the meeting was the reading by Zeno of his treatise defending Parmenidean monism against those partisans of plurality who asserted that Parmenides' supposition that there is a one gives rise to intolerable absurdities and contradictions. The dialogue is set during a supposed meeting between Parmenides and Zeno of Elea in Socrates' hometown of Athens. This dialogue is chronologically the earliest of all as Socrates is only nineteen years old here. It is also notable that he takes the position of the student here while Parmenides serves as the lecturer.

Most scholars agree that the dialogue does not record historic conversations, and is most likely an invention by Plato.

A scholarch (Ancient Greek: σχολάρχης, scholarchēs) was the head of a school in ancient Greece. The term is especially remembered for its use to mean the heads of schools of philosophy, such as the Platonic Academy in ancient Athens. Its first scholarch was Plato himself, the founder and proprietor. He held the position for forty years, appointing his nephew Speusippus as his successor. The members of the Academy elected later scholarchs.

A list of scholarchs of the four main philosophy schools during the Hellenistic period, with the approximate dates they headed the schools, is as follows:

The Prior Analytics (Ancient Greek: Ἀναλυτικὰ Πρότερα; Latin: Analytica Priora) is a work by Aristotle on reasoning, known as syllogistic, composed around 350 BCE. Being one of the six extant Aristotelian writings on logic and scientific method, it is part of what later Peripatetics called the Organon.

The term analytics comes from the Greek words analytos (ἀναλυτός, 'solvable') and analyo (ἀναλύω, 'to solve', literally 'to loose'). However, in Aristotle's corpus, there are distinguishable differences in the meaning of ἀναλύω and its cognates. There is also the possibility that Aristotle may have borrowed his use of the word "analysis" from his teacher Plato. On the other hand, the meaning that best fits the Analytics is one derived from the study of Geometry and this meaning is very close to what Aristotle calls episteme (επιστήμη), knowing the reasoned facts. Therefore, Analysis is the process of finding the reasoned facts.

Stagira (/stəˈdʒaɪrə/), Stagirus (/-rəs/), or Stageira (Greek: Στάγειρα or Στάγειρος) was an ancient Greek city located near the eastern coast of the peninsula of Chalkidice, which is now part of the Greek province of Central Macedonia. It is chiefly known for being the birthplace of Aristotle, the Greek philosopher and polymath, student of Plato, and teacher of Alexander the Great. The ruins of the city lie approximately 18 kilometres (11 mi) northeast of the present-day village of Stagira, and adjacent to the town of Olympiada.

The Nicomachean Ethics (/ˌnaɪkɒməˈkiən, ˌnɪ-/; Ancient Greek: Ἠθικὰ Νικομάχεια, Ēthika Nikomacheia) is Aristotle's best-known work on ethics: the science of the good for human life, that which is the goal or end at which all our actions aim. It consists of ten sections, referred to as books, and is closely related to Aristotle's Eudemian Ethics. The work is essential for the interpretation of Aristotelian ethics.

The text centers upon the question of how to best live, a theme previously explored in the works of Plato, Aristotle's friend and teacher. In Aristotle's Metaphysics, he describes how Socrates, the friend and teacher of Plato, turned philosophy to human questions, whereas pre-Socratic philosophy had only been theoretical and concerned with natural science. Ethics, Aristotle claimed, is practical rather than theoretical, in the Aristotelian senses of these terms. It is not merely an investigation about what good consists of, but it aims to be of practical help in achieving the good.

Zarathushtra Spitama, more commonly known as Zoroaster or Zarathustra, was an Iranian religious reformer who challenged the tenets of the contemporary Ancient Iranian religion, becoming the spiritual founder of Zoroastrianism. In the oldest Zoroastrian scriptures, the Gathas, which he is traditionally believed to have authored, he is described as a preacher and a poet-prophet. Some have claimed, with much scholarly controversy, to find his influence in Heraclitus, Plato, Pythagoras, and, perhaps less controversially, in the Abrahamic religions, including Judaism, Christianity, and Islam, particularly through concepts of cosmic dualism and personal morality.

He spoke an Eastern Iranian language, named Avestan by scholars after the corpus of Zoroastrian religious texts written in that language. Based on this, it is tentative to place his homeland somewhere in the eastern regions of Greater Iran (perhaps in modern-day Afghanistan or Tajikistan), but his exact birthplace is uncertain. His life is traditionally dated to sometime around the 7th and 6th centuries BC; though most scholars, using linguistic and socio-cultural evidence, suggest a dating to somewhere in the second millennium BC.

Socratic dialogue (Ancient Greek: Σωκρατικὸς λόγος) is a genre of literary prose developed in Greece at the turn of the fourth century BC. The earliest ones are preserved in the works of Plato and Xenophon and all involve Socrates as the protagonist. These dialogues, and subsequent ones in the genre, present a discussion of moral and philosophical problems between two or more individuals illustrating the application of the Socratic method. The dialogues may be either dramatic or narrative. While Socrates is often the main participant, his presence in the dialogue is not essential to the genre.