The two questions should be: why should philosophers rule and why would they be willing to rule?
The answer to the first question took us through Plato’s metaphysical and epistemological theories. That means his theories about the nature of reality (metaphysics) and knowledge (epistemology).
We considered two answers to the second question. They left me uncertain about whether he had really met Glaucon’s challenge of showing that justice is valued “for its own sake.”
Philosophers should rule because their interest in knowledge leads them to think about what is genuinely good. That is because it leads them to think about what Plato called the form of the good. The form of the good explains why everything else that is good is, in fact, good. If the philosophers understand this, they will understand what is best for the city.
Those of us who rely on our senses and feelings to tell us what is good, by contrast, will know much less about what is good in general and thus much less about what is good for the city in particular.
Jaron put his finger on the biggest question: how do we know that the philosopher’s methods will succeed? That is, why should we think that they are likely to know anything about the form of the good?
The best we came up with in reply is that their methods have a better chance than the normal person’s or that they are likely to get closer than the normal person. But even these replies felt a bit rickety. If we know so little about what a form is and how we might discover it in the ethical case, why think we’re in a position to draw any conclusion at all about how likely the philosophers are to know anything about them? For all we know, they might be headed in exactly the wrong direction.
Plato’s best case is mathematics. That’s where a kind of thinking that is minimally connected to the senses has reached impressive results about a very abstract subject. But why think that ethical knowledge will be like mathematical knowledge?
Once you’ve been outside, why go back to the cave, even if it is to be in charge?
One answer is that they would rule because the form of the good tells them to do so. If we understood what the form of the good was and how they would know about it, that might explain why it makes sense to value justice “for its own sake.” Alas, we’re pretty far from understanding those things.
The other answer is that they will agree to rule because doing so makes their lives possible. As Andrew presented it, this makes a lot of sense. The passage from Williams on the handout adds the qualification that they have to rule with the thought that justice is valuable for its own sake. That’s the only way they will produce the conditions that make their lives possible, according to Williams’s reading of the argument.
The question is whether that is enough to explain why the philosophers would value justice for its own sake and why that commitment would lead them to accept ruling the city.