Can society function without government?
No. Some examples of countries without functioning central government are Somalia, the Congo (Zaire) and parts of Chad. Without any law, gangs armed with guns take matters into their own hands. You can have small goverment though. Ancient Greece was divided into hundreds of independent towns each with their own government. They united militarily when they were threatened by an outside power, like the Persian Empire. Most of the ancient Greek democracies were just towns with a few thousand citizens, where everyone had a vote in the public assembly. On the downside, ancient Greece was always fractured and the little statelings were always fighting wars with each other, and forming complex confederacies and alliances. The Romans had an easy time picking them off one by one.