In Plato's Republic, 439a-441d, he argues that the spirit is a distinct third part of the soul. Is it a sound argument?
This is a good question. Before I answer whether this is a sound argument, let's go over briefly what Plato says. According to Plato, people are made up of three parts. People have minds (a rational part), hearts (a spirited part), and lower regions (an appetitive part). Within this framework, Plato argues that the rational part of a person should control the appetitive part of a person, and if it does, the spirited part will be filled with virtue. Unfortunately, for many people, the appetitive part rules people instead. More specifically, Plato says that the rational part of a person is philosophy.
With that said, is this a sound argument? For Plato, it is a sound argument. And I suppose if the mind is filled with the forms (within Plato's framework), then this is a valid argument. However, in my opinion, Plato fails to address the possibility that the appetitive part of a person can also desire virtuous things.