Plato Republic overview
A. Held over from last lecture: the material about Plato's Theory of Forms – the Form of beauty (or the beautiful), the Form of "justice" (or the just), the Form of good (or the good), etc.
1. Instead of "Form" one might say "essence" or "essential nature." Our passages offer a picture of thought, mainly about values, in which it's controlled by understanding of the objective nature of its topics as opposed to being stuck at the level of the confusing interplay of mere appearances. (Mainly about values, but mathematical examples also show up in both passages. Mathematics helps break the hold of mere appearance on the intellect. See, e.g., 510d: in geometry one so to speak looks through visible diagrams to the intelligible objects that proofs are about – e.g. the essential nature of a triangle.)
2. This is a new ingredient in Plato's (implicit) picture of human nature. We have it in us to be able to get in tune with the objective truth about beauty, "justice," and goodness. (We? Who? Well, some of us anyway. Plato is élitist about this kind of thing, but of course we don't need to follow him on that.)
3. Maybe this material can help out Plato's response to the challenge. When we took the response to exploit a formal or structural conception of what it is for reason to rule in the soul, there seemed to be no reason why it should impress a skeptic. A skeptic would say that reason rules in the soul of a successfully "unjust" person. But the Theory of Forms makes available to Plato a substantive conception of what it is for reason to rule in the soul. He can define reason in terms of its capacity to get in tune with the objective truth about values. And then he can say nothing counts as reason ruling in the soul unless the ruling element is oriented towards "justice" and the good. It isn't enough that a person's life is organized according to a plan; for it to be genuinely reason ruling in the soul, the plan has to conform to the objective essences of "justice" and goodness. So the skeptic can't say a successfully "unjust" person has the internal organization of soul that constitutes "justice," if we understand Plato's account like this.
B. The challenge was to show that "justice" pays, or more generally that morality pays. Living well (i.e. in accordance with the dictates of morality) is living well (i.e. in the way it makes sense to choose to live; in accordance with the reasons that there are for choosing). This can be read in two different ways:
(1) The skeptics' way. According to them, it's subject to question whether the (supposed) requirements of morality embody any genuine reasons for choosing one way rather than another. So they must understand the claim starting at the right-hand side. In their view, the claim would have to involve a morally neutral conception of what it is to live in the way it makes sense to choose to live (a conception made up of things like wealth, power, privilege, …). And a defense of the rational status of morality would have to show that living in accordance with morality is living in that way (a way that makes it likelier that you will have success in life, understood in such morally neutral terms; e.g. that you will get rich). This doesn't seem very plausible.
(2) The moralists' way. If you care about moral values, that will show up in how you think it makes sense to choose to live. Living any other way than in accordance with the requirements of morality will not strike you as living well. (No doubt it would be nice to be rich, but not at any price.) The claim is understood starting at the left-hand side. (Not what the skeptics are looking for at all.) With the theory of objective essences, Plato can say it's right to see things like this, because it's seeing things as they are.
C. Individualism
1. In one sense Plato is evidently anti-individualistic: in his ideal social set-up, the individual is submerged in the group (a cog in a machine).
2. But in another sense his picture is individualistic. He sees the point of social life as enabling individual needs to be better met (food, clothing, shelter). The individual is what she is anyway (reason, spirit, appetite), whether or not we think of her in a social context. Plato doesn't have a thought we'll see later, that living in society makes a difference to the nature of the human individual.