Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. 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.^{[citation needed]} 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.

In the Republic the highest form is identified as the Form of the Good (Greek: ἡ τοῦ ἀγαθοῦ ἰδέα, romanized: hê tou agatou idea, lit. 'idea of the good'), the source of all other Forms, which could be known by reason. In the Sophist, a later work, the Forms being, sameness and difference are listed among the primordial "Great Kinds". 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.

The primary concept is the Theory of Forms. The only true being is founded upon the forms, the eternal, unchangeable, perfect types, of which particular objects of moral and responsible sense are imperfect copies. The multitude of objects of sense, being involved in perpetual change, are thereby deprived of all genuine existence. The number of the forms is defined by the number of universal concepts which can be derived from the particular objects of sense. The following excerpt may be representative of Plato's middle period metaphysics and epistemology:

[Socrates:] "Since the beautiful is opposite of the ugly, they are two."

[Glaucon:] "Of course."
"And since they are two, each is one?"
"I grant that also."
"And the same account is true of the just and unjust, the good and the bad, and all the forms. Each of them is itself one, but because they manifest themselves everywhere in association with actions, bodies, and one another, each of them appears to be many."
"That's right."
"So, I draw this distinction: On one side are those you just now called lovers of sights, lovers of crafts, and practical people; on the other side are those we are now arguing about and whom one would alone call philosophers."
"How do you mean?"
"The lovers of sights and sounds like beautiful sounds, colors, shapes, and everything fashioned out of them, but their thought is unable to see and embrace the nature of the beautiful itself."
"That's for sure."
"In fact, there are very few people who would be able to reach the beautiful itself and see it by itself. Isn't that so?"
"Certainly."
"What about someone who believes in beautiful things, but doesn't believe in the beautiful itself and isn't able to follow anyone who could lead him to the knowledge of it? Don't you think he is living in a dream rather than a wakened state? Isn't this dreaming: whether asleep or awake, to think that a likeness is not a likeness but rather the thing itself that it is like?"
"I certainly think that someone who does that is dreaming."
"But someone who, to take the opposite case, believes in the beautiful itself, can see both it and the things that participate in it and doesn't believe that the participants are it or that it itself is the participants—is he living in a dream or is he awake?
"He's very much awake."

(Republic Bk. V, 475e-476d, translation G. M. A. Grube)