The intentions of Plato in sharing this story seem to be fairly simple. As with all of the works that he included in The Republic, he is attempting to convey a message that relates to government and leadership. I also believe that this story conveys a message to, not just leaders, but people in general. The message that is expressed by this work is that, " A lie told often enough becomes the truth."(-Lenin), and when someone is convinced of this lie, the liar can control them. This fable also tells us how, what some people believe to be true may be in fact the exact opposite to truth, and that people must always be open minded, just in case their beliefs are wrong.
In the story, the prisoners are convinced that the shadows they see are alive, real and able to speak to them. In fact, however, they are being lied to by puppeteers. Because they have seen this lie so many times, and because it is all that they have seen, for them, it has become the truth. As such, the puppeteers are able to control their lives, by speaking to these prisoners as the shadows. This lesson becomes quite relevant to today's society. It is portrayed in works such as The Matrix and Animal Farm, where the characters are lied to, but because they hear the lie so often, they perceive it as truth. In reality, we find this message to also be evident in the forms of such things as propaganda, in which a message is repeated by so many times, that each person hears a relay from numerous sources. Eventually, because of the numerous sources and repetition of the message, it seems to them to become normal to hear and hence believable. This of course relates to our leaders and government. If such administrations were to use