Platonism

Platonism is the philosophy of Plato and philosophical systems closely derived from it, considered the opposite of nominalism, or anti-realism. Platonism has had a profound influence on Western thought. Platonism or Platonic realism affirms the real existence of forms or abstract objects, originally to solve the problem of universals. Abstract objects are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness. This can apply to properties, types, propositions, meanings, numbers, sets, truth values, and so on (see abstract object theory).

Plato's doctrine originally was an attempt to reconcile 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.

Plato established the academy, and in the 3rd century BC, Arcesilaus adopted academic skepticism, which became a central tenet of the school until 90 BC when Antiochus added Stoic elements, rejected skepticism, and began a period known as Middle Platonism. In the 3rd century AD, Plotinus added additional mystical elements, establishing Neoplatonism, in which 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.

Many Platonic notions were adopted by the Christian church which understood Plato's Forms as God's thoughts (a position also known as divine conceptualism), while Neoplatonism became a major influence on Christian mysticism in the West through Saint Augustine, Doctor of the Catholic Church, who was heavily influenced by Plotinus' Enneads, and in turn were foundations for the whole of Western Christian thought. Many ideas of Plato were incorporated by the Roman Catholic Church. Platonic ideas saw a further revival in the Renaissance and in contemporary analytic philosophy with the rise of mathematical platonism in modern philosophy of mathematics.