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The easy answer to this question would obviously be philosophy.

But the word 'teach' in this question is vague, so I will highlight the content of Plato's philosophy. Plato wrote a series of short works, the most important of which are The Republic, Parmenides, Meno, and Symposium.

The Republic espouses many of Plato's theories in metaphysics, epistemology, and politics. Most importantly, it contains Plato's famous Allegory of the cave, which is a analogy wherein Socrates argues that the invisible world is the most intelligible and that the visible world is the least knowable, and the most obscure. Socrates says in The Republic that people who take the sun-lit world of the senses to be good and real are living pitifully in a den of evil and ignorance. Socrates admits that few climb out of the den, or cave of ignorance, and those who do, not only have a terrible struggle to attain the heights, but when they go back down for a visit or to help other people up, they find themselves objects of scorn and ridicule. Physical objects and physical events are "shadows" of their ideal or perfect Forms, and exist only to the extent that they instantiate the perfect versions of themselves. Just as shadows are temporary, inconsequential phenomena produced by physical objects, physical objects are themselves fleeting phenomena caused by more substantial causes, the ideals of which they are mere instances. For example, Socrates thinks that perfect justice exists (although it is not clear where) and his own trial would be a cheap copy of it.

In addition to these metaphysics and his Theory of Forms (and so-called "Platonic realism"), The Republic contains Plato's treatises on the Ideal State, which is too complex to describe here but closely resembles the totalitarian-style governments of contemporary literature. The Republic also reveals the Socratic method, the philosophical technique by which philosophers attempt to gain insights into the meanings of certain concepts such as "justice" and "friendship".

In Parmenides, Plato himself associates knowledge with the apprehension of unchanging Forms and their relationships to one another; that if one derives the account of something experientially, because the world of sense is in flux, the views therein attained will be mere opinions. And opinions are characterized by a lack of necessity and stability. On the other hand, if one derives the account of something by way of the non-sensible forms, because these forms are unchanging, so too is the account derived from them. It is only in this sense that Plato uses the term "knowledge."

In Meno, Plato further expands upon his epistemology by using a geometrical example to expound his view that knowledge is acquired by recollection. The character Socrates elicits a fact concerning a geometrical construction from a slave boy, who could not have otherwise known the fact (due to the slave boy's lack of education). The knowledge must be present, Socrates concludes, in an eternal, non-experiential Form.

Finally, in Symposium, offers insight into the philosophy of love and beauty. There are seven members of the symposium who all give speeches on their differing views of what love and more specifically, erotic love, is. The character Socrates addresses the claims of his fellows, views which represent the differing views of the Greek states at that time.

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Q: What are some of Plato's beliefs and teachings?
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