Main article: Platonic realism
"Platonism" is a term coined by scholars to refer to the intellectual consequences of denying, as Plato's Socrates often does, the reality of the material world. In several dialogues, most notably the Republic, Socrates inverts the common man's intuition about what is knowable and what is real. While most people take the objects of their senses to be real if anything is, Socrates is contemptuous of people who think that something has to be graspable in the hands to be real. In the Theaetetus, he says such people are "eu a-mousoi", an expression that means literally, "happily without the muses" (Theaetetus 156a). In other words, such people live without the divine inspiration that gives him, and people like him, access to higher insights about reality.
Socrates's idea that reality is unavailable to those who use their senses is what puts him at odds with the common man, and with common sense. Socrates says that he who sees with his eyes is blind, and this idea is most famously captured in his allegory of the cave, and more explicitly in his description of the divided line. The allegory of the cave (begins Republic 7.514a) is a paradoxical analogy wherein Socrates argues that the invisible world is the most intelligible ("noeton") and that the visible world ("(h)oraton") 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.
According to Socrates, 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 epiphenomena 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.
The allegory of the cave (often said by scholars to represent Plato's own epistemology and metaphysics) is intimately connected to his political ideology (often said to also be Plato's own), that only people who have climbed out of the cave and cast their eyes on a vision of goodness are fit to rule. Socrates claims that the enlightened men of society must be forced from their divine contemplations and be compelled to run the city according to their lofty insights. Thus is born the idea of the "philosopher-king", the wise person who accepts the power thrust upon him by the people who are wise enough to choose a good master. This is the main thesis of Socrates in the Republic, that the most wisdom the masses can muster is the wise choice of a ruler.