This section from Book VII of Republic really caught my attention because of the interesting allegory Plato/Socrates gives for the levels of cognitive function–that of The Cave.
Essentially, there are four levels:
1) Opinion based on images or likenesses, but not the true form
2) Belief based on visible/tangible things
3) Knowledge based on hypotheses (like the study of geometry)
4) Understanding based on the true “Forms”
Here is an illustration of the allegory of The Cave.
The people chained to the wall forced to understand the world through shadows made with statues and fire represent the first and most basic level. They do not know the reality of the forms, only the shadows.
The man behind the fire can see only the statues and fire and understands that those are real, but does not understand that the statues themselves are still only representations. He represents the second level.
The man climbing the shaft represents the third level, he can see true sunlight and can guess and conjecture about the rest of the real world.
and finally, the man standing in the grass represents the fourth level, that of true understanding. He knows the sky, the grass, the sun, and the true forms of the natural world.