Plato's central and most debated idea is that particular things in the world, a beautiful face, a just decision, an equal pair of sticks, are beautiful, just or equal only because they participate in an unchanging, non physical Form of Beauty, Justice or Equality that exists independently of them and of any mind that thinks about it. The senses report only the shifting particulars, so for Plato genuine knowledge, as opposed to mere opinion, has to be knowledge of the Forms themselves, reached through reasoned argument rather than observation. The most famous illustration is the allegory of the cave in the Republic, where prisoners who have only ever seen shadows on a wall mistake the shadows for reality, and philosophy is described as the difficult climb out of the cave toward the sunlight of the Forms. The theory answered a real problem, how a word like equal can apply correctly to many different pairs of things that are never perfectly equal to each other, but it also raised the so called third man problem, an infinite regress worry that Plato himself records in a late dialogue, the Parmenides, without fully resolving it. Aristotle, who studied under Plato for two decades, eventually rejected the theory outright, arguing that the essence of a thing is not stored in a separate realm but is present within the thing itself, a disagreement that set the terms for most of the metaphysics that followed both of them.