Although Charmides does not have much to say about the ideal, wisdom-governed state compared with the lengthy analysis of such a state in The Republic, Socrates does touch on the idea multiple times in one particularly problematic section of the dialogue. Socrates and Critias have run into trouble trying to conceive of temperance as a knowledge of knowledge itself (and thus as a kind of "science" that knows, abstractly, all other sciences). Socrates, in this moment of difficulty, extrapolates what he takes himself and Critias really to be seeking in this abstract notion: the ideal society, a world ruled by wisdom as pure knowledge-of-knowledge.

Everything in such a state would necessarily be perfect, from shoemaking to the navy to oracles, because everything would be done according to knowledge (and never to ignorance, since knowledge of knowledge also knows what it does not know). Such a state, Socrates suggests, is almost unimaginably ideal. In any case, it is "nowhere to be found." Thus, the perfect state becomes both an extrapolation of Critias's and Socrates's primary definition of temperance and an illustration showing that such a definition is too idealistic, that it aims too high. After all, it remains unclear how pure reflexive knowledge might actually make anyone happy.