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The Republic (Koinē Greek: Πολιτεία) was a work written by Zeno of Citium, the founder of Stoic philosophy at the beginning of the 3rd century BC. Although it has not survived, it was his most famous work, and various quotes and paraphrases were preserved by later writers. The purpose of the work was to outline the ideal society based on Stoic principles, where virtuous men and women would live a life of simple asceticism in an equal society.
Written, it would seem, in conscious opposition to Plato's Republic, Zeno's Republic (politeia) outlined the principles of an ideal state written from the point of view of early Stoic philosophy. The work has not survived; but it was widely known in antiquity and more is known about it than any of his other works. Plutarch provides a summary of its intent:
It is true indeed that the so much admired Republic of Zeno, first author of the Stoic sect, aims singly at this, that neither in cities nor in towns we should live under laws distinct one from another, but that we should look upon all people in general to be our fellow-countryfolk and citizens, observing one manner of living and one kind of order, like a flock feeding together with equal right in one common pasture. This Zeno wrote, fancying to himself, as in a dream, a certain scheme of civil order, and the image of a philosophical commonwealth.
It is not obvious from Plutarch's remarks whether he had read the work himself. One person who had read it was "Cassius the Skeptic", whose polemic written against Zeno's Republic is paraphrased by Diogenes Laërtius:
Some there are, and among them Cassius the Sceptic and his disciples, who accuse Zeno at length. Their first count is that in the beginning of his Republic he pronounced the ordinary education useless: the next is that he applies to all men who are not virtuous the opprobrious epithets of foemen, enemies, slaves, and aliens to one another, parents to children, brothers to brothers, friends to friends. Again, in the Republic, making an invidious contrast, he declares the good alone to be true citizens or friends or kindred or free men; and accordingly in the view of the Stoics parents and children are enemies, not being wise. Again, it is objected, in the Republic he lays down community of wives, and at line 200 prohibits the building of temples, law-courts and gymnasia in cities; while as regards a currency he writes that we should not think it need be introduced either for purposes of exchange or for travelling abroad. Further, he bids men and women wear the same dress and keep no part of the body entirely covered. 
Further on, Laërtius makes some further remarks which also seem to be from the same work by Cassius:
Further, they say that the wise man will feel affection for the youths who by their countenance show a natural endowment for virtue. So Zeno in his Republic. ... It is also their doctrine that amongst the wise there should be a community of wives with free choice of partners, as Zeno says in his Republic and Chrysippus in his treatise On the Republic, ... under such circumstances we shall feel paternal affection for all the children alike, and there will be an end of the jealousies arising from adultery. 
These paraphrases by Cassius are not a neutral summary of the Republic, his purpose seems to be to describe all the doctrines in the work which he found shocking. These include Zeno's denouncement of general education; his exhortation that only the virtuous can be regarded as true citizens; his view that men and women should wear the same clothes; and the idea that "there should be a community of wives", which in practice seems to have meant "recognizing no other form of marriage than the union of the man who lives freely with a consenting woman".
A few other statements from the Republic are preserved by other writers. We learn from Laërtius that Zeno stated that the wise man will marry and produce children, and several writers mention Zeno's view that there is no need to build temples to the gods, "for a temple not worth much is also not sacred, and nothing made by builders or workmen is worth much". Athenaeus also preserves a quote on the need for a city to be built on the principle of love:
And Pontianus said that Zeno of Citium thought that Love was the God of Friendship and Liberty and the author of concord among people, but nothing else. Hence, he says in his Republic, that "Love is a God, who cooperates in securing the safety of the city."
Zeno's Republic seems to have been viewed with some embarrassment by some of the later Stoics. This was not helped when Chrysippus, Zeno's most illustrious successor as the head of the Stoic school, wrote his own treatise On the Republic (probably a commentary on Zeno's work), in which (among many other things) he defended both incest and cannibalism. It is unlikely that Chrysippus urged the adoption of such behaviors; Chrysippus was probably responding to criticisms that in a society practicing free love, in which people often did not know who their relatives were, rare instances of incest would unintentionally occur; his discussion of cannibalism is probably connected with the Stoic contempt for dead bodies as an empty shell. Nevertheless, these points provided extra ammunition for those people who wished to attack both Zeno and Stoicism in general. Some blamed the influence which Crates of Thebes, the famous Cynic philosopher and teacher of Zeno, may have had when he wrote the Republic: it was joked that Zeno "had written it at the tail of the dog." By the 1st century BC, there was an attempt among the Stoics to downplay the involvement which Cynic philosophy had played in the development of early Stoicism; it was said that Zeno had been "young and thoughtless" when he wrote his Republic. It was also said that "by Zeno things were written which they [the Stoics] do not readily allow disciples to read, without their first giving proof whether or not they are genuine philosophers." Regardless of these views, it is clear that Zeno was one of the first philosophers in a long tradition begun by Plato of depicting an ideal society in order to understand ethical principles.