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"Pythagoreanism is the name given to the system of philosophy and science developed by "Pythagoras, which influenced nearly all the systems of Hellenistic philosophy that followed. Two schools of Pythagorean thought eventually developed; one based largely on mathematics and continuing his line of scientific work, while the other focused on his metaphysical teachings, though each shared a part of the other.
In Ancient Greece, the "sophists were a category of teachers who specialized in using the tools of philosophy and rhetoric for the purpose of teaching aretê—excellence, or virtue—predominantly to young statesmen and nobility.
The "Cynics were an ascetic sect of philosophers beginning with "Antisthenes in the 4th century BC and continuing until the 5th century AD. They believed that one should live a life of "Virtue in agreement with "Nature. This meant rejecting all conventional desires for "wealth, "power, "health, or "fame, and living a life free from possessions.
The "Cyrenaics were a "hedonist school of philosophy founded in the 4th century BCE by "Aristippus of Cyrene, who was a student of "Socrates. They held that pleasure was the supreme good, especially immediate gratifications; and that people could only know their own experiences, beyond that truth was unknowable.
"Platonism is the name given to the philosophy of "Plato, which was maintained and developed by his followers. The central concept was the "theory of Forms: the transcendent, perfect archetypes, of which objects in the everyday world are imperfect copies. The highest form was the "Form of the Good, the source of being, which could be known by "reason. In the 3rd century BC, "Arcesilaus adopted "skepticism, which became a central tenet of the school until 90 BC when "Antiochus added "Stoic elements, rejecting skepticism. With the adoption of oriental "mysticism in the 3rd century AD, Platonism evolved into "Neoplatonism.
The "Peripatetics was the name given to the philosophers who maintained and developed the philosophy of "Aristotle. They advocated examination of the world to understand the ultimate foundation of things. The goal of life was the "happiness which originated from "virtuous actions, which consisted in keeping the "mean between the two extremes of the too much and the too little.
"Pyrrhonism is a school of "philosophical skepticism that originated with "Pyrrho in the 3rd century BCE, and was further advanced by "Aenesidemus in the 1st century BCE. Its objective is "ataraxia (being mentally unperturbed), which is achieved through "epoché (i.e. "suspension of judgment) about non-evident matters (i.e., matters of "belief).
"Epicureanism was founded by Epicurus in the 3rd century BC. It viewed the "universe as being ruled by "chance, with no interference from "gods. It regarded absence of pain as the greatest pleasure, and advocated a simple life. It was the main rival to "Stoicism until both philosophies died out in the 3rd century AD.
"Stoicism was founded by "Zeno of Citium in the 3rd century BC. Based on the ethical ideas of the "Cynics, it taught that the goal of life was to live in accordance with "Nature. It advocated the development of self-control and fortitude as a means of overcoming destructive "emotions.
"Eclecticism was a system of philosophy which adopted no single set of doctrines but selected from existing philosophical beliefs those doctrines that seemed most reasonable. Its most notable advocate was "Cicero.
"Neopythagoreanism was a school of philosophy reviving "Pythagorean doctrines, which was prominent in the 1st and 2nd centuries AD. It was an attempt to introduce a "religious element into Greek philosophy, worshipping God by living an "ascetic life, ignoring bodily pleasures and all sensuous impulses, to purify the "soul.
"Hellenistic Christianity was the attempt to reconcile "Christianity with Greek philosophy, beginning in the late 2nd century. Drawing particularly on "Platonism and the newly emerging Neoplatonism, figures such as "Clement of Alexandria sought to provide Christianity with a philosophical framework.
"Neoplatonism, or Plotinism, was a school of religious and mystical philosophy founded by "Plotinus in the 3rd century AD and based on the teachings of Plato and the other Platonists. The summit of existence was "the One or the Good, the source of all things. In "virtue and "meditation the soul had the power to elevate itself to attain union with the One, the true function of human beings. It was the main rival to "Christianity until dying out in the 6th century.