You can read Minos online in English at the Perseus Project and in French at Wikisource.
The only direct participants in the dialogue are Socrates and an anonymous interlocutor. But since a significant portion of the dialogue discusses Minos, it seems a good idea to say something about him.
Most mentions of Minos are rather scattered. Homer has Idomeneus claim, "Zeus at the first begat Minos to be a watcher over Crete" (Iliad 13.450) and Odysseus mentions that Ariadne was his daughter (Odyssey 11.321) and says that he saw him as judge of the underworld:
There then I saw Minos, the glorious son of Zeus, golden sceptre in hand, giving judgment to the dead from his seat, while they sat and stood about the king through the wide-gated house of Hades, and asked of him judgment. (Odyssey 11.568)
Thucydides tells us (History 1.4):
Minos is the first to whom tradition ascribes the possession of a navy. He made himself master of a great part of what is now termed the Hellenic sea; he conquered the Cyclades, and was the first coloniser of most of them, expelling the Carians and appointing his own sons to govern in them. Lastly, it was he who, from a natural desire to protect his growing revenues, sought, as far as he was able, to clear the sea of pirates.
Scattered other sources give us the most famous story concerned with Minos: Poseidon sent him a sacred bull out of the sea, which he was supposed to sacrifice to Poseidon, but it was such a magnificent animal that he substituted another one instead. Poseidon in return cursed Minos's wife Pasiphae with an unnatural passion for the bull, which she got the help of Daedelus in consummating. As a result she conceived the Minotaur, half man and half bull. Minos got Daedelus to design the Labyrinth in which to hide the Minotaur, and then imprisoned Daedelus and his son Icarus so that no one would ever discover the way to escape it. At some point he declared war on Athens, and would only accept a peace treaty under the condition that the Athenians would send him seven youths and seven maidens every year to feed the Minotaur. This continued until Theseus took the place of one of the youths; Minos's daughter Ariadne fell in love with him and helped him escape the Labyrinth.
The Athenians celebrated the event each year by sending a ship to Delos; during the time it was gone no executions were allowed. It was this celebration that gave Socrates his month-long reprieve after he was condemned to death.
The Plot and The Thought
Socrates opens the dialogue by asking what law (nomos) is. The interlocutor asks what kind of law, and Socrates points out that all laws are the same in being laws, so the question is what this sameness is. The interlocutor then suggests that law (nomos) is the things that are accepted (nomizomena). Socrates points out, however, that this would make law rather peculiar. Sight, for instance, is not what is seen. It may well be that law is that by which what is accepted, is accepted, but this still leaves completely open the question, "What is law?"
The interlocutor then replies that law is the decisions (dogmata) and majority-passed resolutions (psephisma) of the city. Socrates notes that this makes law a sort of civic opinion (doxan politike), and the interlocutor agrees. But Socrates points out that the just are just by virtue of justice, and the lawful (nomimoi) are lawful in virtue of law, and that there seems to be a connection between being lawful and being just, and between being lawless and being unjust. Further, both law and justice are beautiful (kalliston) and lawlessness and injustice are both shameful (aischiston); law and justice both preserve the city, while lawlessness and injustice both harm the city. But if all of this is true, law can't just be the decisions of the city; some decisions and resolutions are admirable and some are wicked: "It would not be in order, then, to take it that a wicked resolution is law" (314e).
But, on the other hand, it does seem that 'civic opinion' is a good description of law, even if not yet a perfect definition. But what is an admirable opinion or judgment? It seems that opinions or judgments are admirable if they are true. True opinion is finding what actually is. Therefore, law is that which tends to discover what actually is. (The actual word for 'tends' here means 'wishes' or 'wants'). Therefore laws may be true or false.
The interlocutor objects that people regularly have different laws, pointing out that, for instance, the Carthaginians sacrifice babies to Cronus, and the Greeks do not. Many other examples could be given. Socrates responds by asking whether the interlocutor thinks that just things are just and unjust things are unjust, and the inerlocutor says he does. But if this is so, it seems that this is true regardless of the people in question. Thus the just is accepted (nomizetai) as just everywhere. Differences arise from people mistaking what is so from what is not so. The interlocutor replies that this makes sense, but says he still has difficulty believing it when he considers how often they change laws.
Socrates moves in a different direction, noting that people who know something about a subject accept (nomizousin) the same things as others who know. Thus doctors writing treatises on health are laying down, to the extent they know what they are talking about, the laws of medicine; treatises on farming, if knowledgeable, give the laws of farming; and so on with gardening, cooking, and anything else. Thus if we look for the kind of knowledgeable people who lay out the laws for civic life, they are "kings and good men" (317b). If they genuinely are knowledgeable, they won't give different accounts at different times on the same matters; whether a law is genuinely a law depends on whether it is true or correct, and if it is not true or correct or merely taken to be so, it is not really a law, but is something unlawful.
Socrates asks his friend if he can name someone who proved himself a good legislator, and when the friend cannot, he names Minos and Rhadamnthus of Crete, who gave the Cretans the most ancient and stable laws known to the ancient Greeks. The interlocutor agrees that people call Rhadamanthus a good man, but protests that Minos is always regarded as extremely harsh and unjust. Socrates, however, dismisses this as merely retaliatory resentment on the part of tragedians; in Homer and Hesiod, we see nothing of this, but only the opposite. Minos conversed with Zeus, that is to say, he was taught by Zeus himself, and this education is symbolized by the golden scepter mentioned by Homer (see above). Thus Minos laid down laws that are divine, tending to virtue. Rhadamanthus learned part of this, but only enough to make decisions in the courts. The reason why everyone thinks Minos was uneducated and severe is that Minos made the mistake of waging war against Athens, which excels in producing poets, especially tragic poets, and thus the tragic poets take vengeance against Minos for defeating the Athenians by constantly attacking his character. But in reality he was a good legislator; his laws have remained stable for ages, thus showing that the really did discover the truth of things.
If this is so, the natural next question is what Minos did that was so right. So Socrates notes that what someone who was a good distributor and lawgiver for the body would do is make sure that it has food and exercise in good proportion. What, then, would a good distributor and lawgiver for the soul do? The interlocutor doesn't know. And thus Socrates ends the dialogue by saying that it is disgraceful that the soul doesn't know what is good for it while it can so easily say what is good for the body.
* It's important to grasp that nomos can also mean 'custom' or 'norm'; the unnamed interlocutor's suggestion that nomos is nomizomenon (what is accepted as a norm) would have been very plausible in Greek. There are a number of points in the dialogue, in fact, where the interlocutor's claims, which Socrates refutes, are even more plausible-sounding in Greek than in English.
* While the dialogue does not give a full natural law theory, it quite obviously is an ancestral text in the tradition, since it consists effectively in arguing that legal positivism is untenable. Law cannot be just a matter of what governments say it is. And it is easy to see why a Platonist would reject the very idea: from a Platonic perspective, legal positivism is a way of saying that might makes right, a position that Plato attacks in practically every one of his political works (and especially so in Gorgias and the Republic). This dialogue does not look at the problems in detail, but it raises some of the obvious questions: Surely being law-abiding is a moral virtue? Surely the whole point of law connects it with the moral virtue of justice, so that if a law is unjust it is failing even as a law? Surely law is a kind of judgment about what preserves or sustains the society, in which case there is some kind of truth or falsehood with regard to law? If the answer to any of these questions is yes, though, then it seems open to us to argue that an unjust law is not a law: governments cannot make things law simply by going through a process to christen them laws.
* The Carthaginians were Phoenicians, of course, and the infant sacrifices of the Phoenicians are also proverbial among us, although we use the Hebrew rather than the Greek descriptions for the Phoenician god in question; instead of talking about sacrificing to Cronus, we describe it as sacrificing to Moloch.
* This dialogue is similar in a great many ways to Hipparchus: both have Socrates interacting with a single anonymous interlocutor, both begin with an explicit definitional question, both are named after legendary figures, and both involve Socrates telling a story about a famous tyrant that is quite the opposite of the actual story that everybody knows. In both cases he cheats in doing so (in Hipparchus his claims about Hipparchus are ridiculously over-the-top, and in Minos he 'proves' in a circle that Minos must be have been just because he had converse with Zeus, which is not, as most people assume, having drinking parties with Zeus, because Cretan law forbids excessive drinking, and if Minos had imposed a different law on others than he followed himself, he would have been unjust); the cheating is so obvious that it is practically a neon sign that Socrates is jokingly making things up. In both cases it is seems that the point is to criticize some important feature of the self-image of the Athenian democracy.
In effect, what Socrates is doing here is attacking the Athenian view of law (that it is by majority vote) and so he opposes it to an obviously idealized version of its complete opposite -- the Cretan law which was at the root of Spartan law. (You'll remember that he does exactly the same thing in Protagoras -- there he attacks Protagoras' speech implicitly eulogizing Athenian democracy by implausibly arguing that the Cretans and the Spartans have more philosophical governments -- they just do all their philosophy in secret so nobody will find out!)
Quotations are from Malcolm Schofield's translation in Plato, Complete Works, Cooper & Hutchinson, eds., pp. 1307-1317.