Ryan S. answered • 08/21/19
PhD in Philosophy with expertise in moral philosophy
The sun represents what Plato calls the Form of the good. To fully understand this, you must understand that Plato draws a distinction between particular objects that we encounter and their corresponding Forms, which exist independently but that make particular objects the objects that they are. So for example, there are bees, and there is the Form BEE, which all bees have. This, in fact, is why bees are bees: they all have the same Form. This applies to all objects, including good ones: good things are all good because they all have the same Form GOOD. For any class of objects that we encounter, there will be a corresponding Form that they all share.
Cut now to Plato's allegory. He invites us to consider people who are chained up in a cave and looking at shadows being cast on a wall. They think the shadows are real objects because that's all they've experienced, but they have no knowledge of the real objects that are casting the shadows or of the sun, which is what's responsible for the objects casting these shadows. Plato thinks this represents our actual situation. We think we experience real objects when we see particular objects of some kind, but we're really experiencing the mere shadows of the real objects called Forms. However, just as we can become unchained in the cave and come to learn about the real objects and the sun that interacts with them to produce shadows, we can engage in philosophy and come to learn about the real objects called Forms, including the Form GOOD, which is the analogue of the sun.
In a nutshell, then:
The sun represents the Form GOOD
The objects casting shadows represent the other Forms
The shadows represent what we take for real, particular objects
