Inside the Cave (Appearance): Material things, images of things.
Outside the Cave (Reality): Ethical ideals, mathematical ideas.
Two Kinds of Blindness
First is when the philosopher leaves the cave which is where all of his fellow citizens are living and he comes out to the real world. The idea that it will be hard to see the definitions of ethical ideals and mathematical objects at first. The more time the philosopher spends outside the cave, the more definition ideals and ideas will acquire.
The second blindness is when the philosopher tries to go back into the cave. It will be very difficult to go back into the cave and explain what you’ve seen. You have to readjust to talking to people who only know shadow
The Cave Allegory ignores Socrates political points.
The philosopher does not have access to higher realities, but because he knows ideas about higher realities is why they should be kings. Two cases of unjust and just city.
In an unjust city
The philosopher’s return to the cave goes beyond duty. a philosopher who has accessed this other world, can choose as to whether or not they want to go back into the cave. No obligation to sacrifice themselves.