Here's a question on the Protagoras.
Protagoras begins the dialogue holding that the five parts of virtue (temperance (T), courage (C), justice (J), wisdom (W), piety (P)) are separable from one another. To be sure, he says this only explicitly of the pairs, C/J andJ/W (329e), but presumably he thinks this is true of all five virtues.
But near the end of the dialogue, after the interlude of the dialogue, when the argument is resumed, Protagoras takes a different view. Now he holds that only courage is separable:
What I am saying, Socrates, is that all these are parts of virtue, and that while four of them are reasonably close to each other, courage is completely different from all the rest. The proof that what I am saying is true is that you will find many people who are extremely unjust, impious, intemperate, and ignorant, and yet exceptionally courageous (349d).This suggests that Protagoras is meant to have been persuaded by the intervening arguments that J=P=W=T.
So here is my question, or problem. Socrates argues at 329c-331c that J=P (nearly so), and he argues at 332a-333b that W=T. But the identity of all four is nowhere established.
Or is it? There is of course the passage 333b-c (which begins with the conclusion about W=T):
[Socrates:] Wouldn't that make wisdom and temperance one thing? And a little while ago it looked like justice and piety were nearly the same thing. Come on, Protagoras, we can't quit now, not before we've tied up these loose ends. So, does someone who acts unjustly seem temperate to you in that he acts unjustly?But at this point Protagoras shows himself wanting to quit, so Socrates moves on to another line of thought, "Let's start all over again, then, with this question..." (333d).
However, are we meant to supply the argument hinted at here, and to suppose that Protagoras, too, sees how it would unfold? What would the argument be? It would rely on premises already set down:
1. Someone who acts unjustly is not temperate in that he acts unjustly.This 'ties up the loose ends'. Because J=P; and W=K; and J=T; it follows that J=P=W=T. Only C is left out, to be dealt with in a different way, later.
2. Thus, someone who acts unjustly acts intemperately.
3. When something is done F-ly (F being a virtue or vice), it is done through the agency of F.
4. Thus, someone who acts unjustly does so through the agency of intemperance.
5. Yet someone who acts unjustly does so through the agency of injustice.
6. What is done in an opposite way is done through the agency of opposites.
7. Thus, intemperance is the opposite of justice.
8. Moreover, intemperance is the opposite of temperance.
9. But each thing has one opposite.
10. Thus, justice is temperance.
Well, this seems correct. (Taylor in his commentary says that the argument breaks off before Socrates can establish J=T. But it seems better to say that this relatively trivial extension of arguments already made was meant to be obvious.) But then, another question arises: why is it necessary that courage be dealt with in a different way? Why couldn't arguments like the one above, like those at the beginning of the dialogue, suffice for courage as well?