Socrates: And has each of [the virtues] a distinct function like the parts of the face;-the eye, for example, is not like the ear, and has not the same functions; and the other parts are none of them like one another, either in their functions, or in any other way? I want to know whether the comparison holds concerning the parts of virtue. Do they also differ from one another in themselves and in their functions? For that is clearly what the simile would imply.You can see the issue. If the virtues are not in a sense the same, then justice and holiness -- or any two virtues -- are completely different. That is clearly wrong, as it requires that we say that it is never just to behave moderately, nor is it just to behave immoderately; nor is it courage to behave with self-control, nor is it courage to behave without self-control. The division makes no sense at all.
Protagoras: Yes, Socrates, you are right in supposing that they differ.
S: Then, I said, no other part of virtue is like knowledge, or like justice, or like courage, or like temperance, or like holiness?
P: No, he answered.
S: Well then, I said, suppose that you and I enquire into their natures. And first, you would agree with me that justice is of the nature of a thing, would you not? That is my opinion: would it not be yours also?
P: Mine also, he said.
S: And suppose that some one were to ask us, saying, "O Protagoras, and you, Socrates, what about this thing which you were calling justice, is it just or unjust?"-and I were to answer, just: would you vote with me or against me?
P: With you, he said.
S: Thereupon I should answer to him who asked me, that justice is of the nature of the just: would not you?
P: Yes, he said.
S: And suppose that he went on to say: "Well now, is there also such a thing as holiness? "we should answer, "Yes," if I am not mistaken?
P: Yes, he said....
S: Well then, Protagoras, we will assume this; and now supposing that he proceeded to say further, "Then holiness is not of the nature of justice, nor justice of the nature of holiness, but of the nature of unholiness; and holiness is of the nature of the not just, and therefore of the unjust, and the unjust is the unholy": how shall we answer him? I should certainly answer him on my own behalf that justice is holy, and that holiness is just; and I would say in like manner on your behalf also, if you would allow me, that justice is either the same with holiness, or very nearly the same; and above all I would assert that justice is like holiness and holiness is like justice; and I wish that you would tell me whether I may be permitted to give this answer on your behalf, and whether you would agree with me.
P: He replied, I cannot simply agree, Socrates, to the proposition that justice is holy and that holiness is just, for there appears to me to be a difference between them.... I admit that justice bears a resemblance to holiness, for there is always some point of view in which everything is like every other thing; white is in a certain way like black, and hard is like soft, and the most extreme opposites have some qualities in common; even the parts of the face which, as we were saying before, are distinct and have different functions, are still in a certain point of view similar, and one of them is like another of them. And you may prove that they are like one another on the same principle that all things are like one another; and yet things which are like in some particular ought not to be called alike, nor things which are unlike in some particular, however slight, unlike.
S: And do you think, I said in a tone of surprise, that justice and holiness have but a small degree of likeness?
But the unity is a problem, too. It is clearly the case that the virtues do not come to be as a unity, as everyone knows someone who is brave but not wise, or wise but not brave; just in his dealings with others, but not moderate at the dinner table; etc. If the virtues were one, then to have one would be to have them all.
I think that the virtues are like the parts of a house, so that they are all part of a whole, but they have to come to be in a certain order. You can't put the roof on first; you have to have a foundation before you can put up walls. There's a little bit of variability in the order -- you could put up two walls and then a roof, if you wanted. Each virtue has a different purpose in a way, in that the roof provides shelter from the sun or rain while the walls provide shelter from the wind, but they are also all unified in a common purpose of providing shelter. This seems to address how virtues can be unified without losing either their different character or their capacity to exist separately in a given person.
Yet this isn't fully satisfying either, as it would seem as if you could say more than I can say about what precisely is the foundation of virtue, which ones come next, and so forth. The capstone virtue -- the roof -- might well be Aristotle's magnanimity; yet others might argue it is justice. Aristotle says that both are, in a way, complete virtue. I think magnanimity is the stronger candidate, as it crowns complete virtue with the activity of using that complete virtue to pursue the most honorable things, whereas justice (in its character as lawfulness) compels you to do the right things rather than making you desire to do them. Still, you see the point: you could argue either way, and if my view is right, it ought to be able to draw out something more specific about the order.
In any case, I was thinking of the question because of a scandal at Berkeley involving the philosopher John Searle. I think we were just discussing his Chinese Room thought experiment recently. Most philosophers take the ability to think clearly and come to deep philosophical insights as a fairly high degree of virtue; the ability to control one's sexual urges is supposed to be a more basic virtue, expected to come about earlier. And maybe it did; Searle is 84, and perhaps is less capable (or less willing) to behave himself now than when he was younger (as well as less famous and powerful). Or perhaps the ability to think clever thoughts isn't such a highly-placed virtue, but something more like athletic ability (which only some can attain in any great measure, for reasons that have nothing to do with virtue). Then the virtue to actualize one's native capacities may not be so very great; only a bit of discipline and practice, combined with a great deal of natural talent. Developing self-control over deep impulses could be much higher and harder than developing the self-control necessary to practice things one finds enjoyable and to which one is naturally inclined, which would account for why so many great athletes also end up demonstrating a lack in this area.
Alternatively, perhaps the view that these virtues come about in any kind of order is wrong. Perhaps you can just have some of them without others. But it does seem odd to say that you could be just without being capable of moderation, or be wise without being capable of self-control.
UPDATE: Speaking of Searle, here is a recent interview with him, with a heartwarming headline.