This paper argues that there are three distinct senses of possibility at play in the Republic’s discussion of whether the best city is possible: natural possibility, possibility for existing cities, and ideal possibility. It is argued that Socrates makes different claims about each of the three political proposals in Book v. (1) Women guardians are argued to be naturally possible. (2) Socrates considers it an open question whether the common family of guardians (the so-called ‘community of women and children’) is (...) naturally possible. He argues, however, that it is ideally possible. (3) The philosopher-king is claimed to be possible in the strongest sense: it is not only naturally possible, it is also possible for existing cities. It is for this reason that the common family of guardians is ideally possible. This clarifies the sense in which the best city is best. (shrink)