I am currently working on an article whose core argument hinges in part on a premise that refers to Socrates'/Plato's take on beauty, and its relationship to justice, truth and goodness. Put plainly, the premise goes as follows: in opposing the Sophists' privileging of art and poetry, for Plato, beauty is nothing but a sign of the truthfulness, justice and goodness of something. Said otherwise, in Plato there is an implicit yet inextricable correspondence between these four realms- only what is just can be good, and only what is truthful can be just and good, whereas whatever partakes of all these qualities can only be deemed beautiful. Is this premise correct? Does Plato's texts support it?
My knowledge of ancient philosophy, and particularly of Platonism, is rather partial, and I am deriving this premise from a rather intuitive interpretation of my piecemeal reading of some of his dialogues.
Also, can you specifically suggest some of Plato's dialogues where this premise is apparent? Can you suggest some recent scholarly material that expands in this direction? Thank you in advance!