The first part of the analogy...
Plato used an allegory to make this concept of the world of the Forms clearer. He said if you imagine a cave with prisoners inside it. The prisoners are sitting and are chained at the neck, arm and leg so that they cannot move. Behind them puppeteers with the help of fire and puppets are creating shadows onto the wall in front of the prisoners. Obviously, the prisoners are not aware of what is happening behind them so the shadows they see in front of them they take to be reality. The cave has opening at the top where a small area of sunlight flows in, but the prisoners cannot see this either. People passing by the cave are making noises which are what the prisoners hear; unaware of the opening they take those noises to be reality and believe it is the shadows before them making these noises.
What does all of this mean?
The prisoners are representations of us. Plato is trying to communicate to us what we see as reality is nothing more than a dim-reflection of true reality.The fire represents a dim-reflection of the Form of the Good which is the true creator of reality. He is saying that if the Earth is our world then, outside the cave, outside the world we will find the world of the Forms.
The second part of the allegory...
A prisoner manages to escape and realises what he thought was reality was actually all fake - the truth is the fire and puppeteer. He is hurt by this and then he notices the opening of the cave and follows the shadow of the sun which is reflected on the stairs. Once he out of the cave he discovers noises he was hearing were actually from the world of the Forms. He sees the sun gives light and in essence life to everything. He enjoys the world. However, being a good person he decides to go back and meet his prisoner friends so he can tell them all about what he has discovered. However, they laugh at him and think he has gone mad. So he returns to true reality i.e. outside the cave.
What does this part symbolise?
According to me, the prisoner Plato describes might just be a metaphor for himself but that is just my opinion. Nevertheless, the point he is trying to get through is that even if one realises, it is hard for others to accept. The sun that the prisoner sees is the Form of the good which gives life to everything else in the world of the Forms is a metaphor for the Platonic God which is impersonal and inactive. Plato believed the body is a prisoner for the soul so he is trying to demonstrate that once we can get over what we call reality and our bodily needs we can let our soul experience true reality. This is also what happens to our soul when it dies.
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