  The additional proofs serve a second purpose, as well. At the end of  Book Five, Socrates says that faculties (at least psychological  faculties) are distinguished by their results (their rate of success) and by their objects (what they concern) (477c–d). So far, he has  discussed only the success-rates of various kinds of psychological  attitudes. He needs to discuss the objects of various kinds of  psychological attitudes in order to complete his account. If we did  not have the discussion of the second proof, in particular, we would  have an incomplete picture of the Republic’s moral psychology.