Soul, Justice, Happiness

One of the fundamental questions of the Republic is whether or not the Just person is Happy.  Consequently, while the explicit topic of the dialogue is Justice, the implicit and perhaps more fundamental one is Happiness, with Socrates arguing that the various concepts of it held by the interlocutors, and relecting common opinion, are faulty.  Instead, anticipating Aristotle, Plato defines Happiness as the condition of a well-functioning Soul, constituted by each part, under the guidance of Reason, performing its proper function.  Now, writ large, i. e. applied to the Polis-Soul, such well-functioning entails that each Citizen performs their proper function, and, presumably, are Happy doing so.  However, writ small, i. e. applied to the Person-Soul, no such concept of personal Happiness is entailed, since there is no part of Plato's concept of the Person-Soul the function of which is Political.  Likewise, Aristotle's concept of Friendship as a Virtue is systematically anomalous, since it transcends his concept of the Person-Soul, and, hence, that of personal Happiness.  So, in sum, the concept of Happiness in the Republic that is the basis of Plato's demonstration that a Just person, and only a Just person, is Happy, is not quite adequate to the purpose, primarily because his concept of the Person-Soul lacks any inherent connection to the Polis-Soul.