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1. The Republic This was an attempt by Plato to understand the tragedy of Socrates. Republic is not the best translation of the book. It means something nearer to affairs of the State meaning the polis or city states of Greece.
It is about how to govern a city state and came to the conclusion that a timarchy ( rule by property owners or the honourable) as was practised in Sparta was the best available way. Democracy was not considered by Plato to be the best form of Government. It was democracy that executed the man he admires most Socrates.
He puts forward the idea that the best rule is by philosopher kings, men specially trained from birth in the art of government.
The allegory of The Cave is found in The Republic. In this Plato believes that seeing is not enough; one must have knowledge as well in order to interpret what one sees.