Plato on Freedom

If we take the point that in order for a person to be free there must be a person, then maybe Plato can't give us an intelligible account of freedom. Plato says that our capacity to be rational frees us from the bondage of the animal passions. As animals (as things), we are subjected to contingent cause-and-effect relations, but it is the rational capacity that makes it possible for us to break these chains. The problem is that to the extent that one is rational (logical), one is identical to all other logical beings. There isn't one mathematics for you, another one for me. In a world of perfectly rational beings, there would be no individuals, as nothing would distinguish one perfectly logical mind from another. In fact I read Plato himself as asserting that there is only one mind. The material world is divisible wholes and parts, the formal world is a unity; one cannot detach part of mathematics from the rest.
It is bad enough that "free" in Plato's mouth just means "free to follow logical entailments," but maybe the situation is even worse: maybe there are no persons, as logical beings, to the extent that they are logical, cannot be distinguished one from another. Thus there are no agents about whom we might say that they are free. It looks like Sartre has exactly the same problem, arrived at by radically different means: to the extent that we are pure negation, we are perfectly homogeneous. If neither Plato nor Sartre can give us coherent accounts of persons, neither can give us coherent accounts of freedom.