Greek values as shown in the cyclops incidentBased on Odysseus's criticism of the Cyclopes, what kind of society did the Greeks value?
Homer definitely makes a strong case for the value of wit and an agile mind. Odysseus' cunning helps deliver him and his fellow sailors from an extremely precarious situation. In this way, Homer suggests that often intelligent thinking may be a better solution to solving difficult problems than charging in for a direct fight. If Odysseus had not been so sneaky and had tried to take Polyphemus straight on in an open fight, he would have lost, and his men would have become the giant's dinner. Part of his success comes from Odysseus' ability to think strategically and make the best choice that could save his men. Was his strategy to trick the Cyclops particularly honorable? Well, no, and the reader could draw a conclusion from this incident that Homer suggests that there are times when cunning and self-preservation must come before honor.
One thing that we can learn about Greek society from this part of the epic poem is that the Greeks valued hospitality in their society. Many pre-modern societies were like this. They felt that it was important for people to treat their guests well even if their guests would otherwise have been their enemies. Homer criticizes the Cyclops for breaking this particular rule. He criticizes the fact that it would turn on Odysseus and his men and that it would speak about defying the gods and their command to treat guests well. So one aspect of Greek society that is being shown here is the ideal of respecting and honoring guests.
It's interesting to note that while, as post #2 correctly states, the Greeks placed a great value on hospitality, Odysseus himself is repeatedlly faced with hostility and danger as he tries to make his way home.
Another value we see in his encounter with Cyclops is that of intelligence. Odysseus is able to save most of his men and himself with his wits, not his strength. He devises several ingenious plans to protect his men from Cyclops. Otherwise, they would all have perished.