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Why is Plato concerned about the differences between mere belief and true knowledge, particularly concerning the issues of justice?
Because Plato is basing his judgements off of mere facts. He says that knowledge begins with knowing of the different types of human souls and how to appeal to these different types of souls.
Shopists arent qualified and use mere belief. It’s their way of seeing truth.
Using rhetoric you can persuade people. So does that actually provide for justice?
Mere belief is based on faith, and can be circumstantial evidence. Mere belief can be referred to doxa. Later in the churches called doctrine.
Epitome meaning knowledge.
Evil and Virtuous……
An art of rhetoric on love of wisdom and knowledge of justice Plato suggets in Phedrus

I agree that mere belief is based on faith and when people have faith they feel true to themselves. Does that provide for justice? I think so. What you believe is true and faithful and that is justice for an individual. so if true is faith and faith is mere belief and mere belief is doxa, the the doctrine is justice. Sophists use mere belief so they would have justice.
Why aren’t the Sophists qualified? And qualified in what? Keep working!