"Socrates describes a group of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall are not constitutive of reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners."
Several parts of this texts have been moved to separate pages:
A section on metamathematics,
Some quotations on MBTI personality
types.