Critias agrees that maybe they have simply been asking wisdom to do too much. But then again, Socrates continues, it may be that they have been "inquiring to no purpose" at all, since even the new, more practical definition of wisdom (that it facilitates practical knowledge through knowledge about knowledge) still seems to have "strange consequences." Even if knowledge of knowledge (wisdom) were to be put in charge of assigning people in the state to specific jobs according to their practical knowledge and barring people from doing what they are ignorant of, the benefits might not be that great. Critias professes amazement at this, and Socrates admits that he's not sure of himself—it's just a thought he had, and must express.
Socrates proceeds to express this thought by recounting a "dream." He imagines that wisdom "has absolute sway over us," and that everything in the state—from health to the navy—is therefore perfect (since no one is doing what he is ignorant of). Even prophecy becomes a matter of wisdom. But, even with this vision of the absolute control of knowledge, Socrates finds himself unconvinced that we would truly be happy in such circumstances. Critias replies that we certainly would. Socrates proceeds again to ask what this governing "knowledge" is of, running through a number of practical possibilities (such as "shoemaking") that Critias rejects.
In that case, asks Socrates, who is it that is made happy without the functioning of practical knowledge? Even if there was a man with an all-seeing knowledge of past, present, and future (a kind of super-prophet), what specific knowledge—of the past, of the future, of playing at dice, of computation, of health, etc.—which of these brings him happiness? Critias answers that it is the knowledge that allows him to distinguish between good and evil. In this case, objects Socrates, all along we should have been looking not for a definition of wisdom or of temperance (a "science of science"), but rather for a specific science, such as the "science of good," or the "science of human advantage."
Socrates remarks that this "science of advantage" still seems to be necessary to every other science, even though it is no longer the all-encompassing "science of sciences" that had been formulated before. Critias suggests that the two (the science of advantage and the "science of science") are almost the same thing: in as much as wisdom rules over all the sciences and arts, it will also control this science of advantage and make sure that everything is beneficial. But Socrates reiterates again that pure wisdom, the knowledge of knowledge itself, cannot itself give us anything specific: medicine, not pure wisdom, gives us health, and the science of advantage, not wisdom itself, gives us advantage or benefit. Critias concedes the point.
Socrates concludes, at this point, that the whole inquiry has been useless. He and Critias have made a number of "concessions" that were not at all proven: chiefly, that there is in fact a science of science, and that it is not totally irrational to say that a man might know what he does not know. Even with these concessions, however, the argument has still foundered, this time on the lack of evidence that wisdom has any utility, any identifiable, practical benefit. Nonetheless, Socrates doesn't think such discussion is ever a waste of time. But he feels bad for Charmides, he says, since it appears that the beautiful youth's temperance of soul will have no practical benefit. In particular, Socrates laments, it appears that the Thracian charm to produce temperance is actually worthless, since temperance seems to have no effect.
In truth, though, says Socrates, he believes that he is just a bad inquirer, and that Charmides should rest assured that wisdom or temperance is truly a great good. Charmides replies that he surely cannot discover if he has temperance, since two wise men like Critias and Socrates cannot even define what it is. But, he says that he is willing to be "charmed" every day by Socrates until the matter is worked out. Critias backs up this choice, and Charmides becomes Socrates's pupil, "following him and not deserting him."