Why did Protagoras believe societies still needed moral rules even if customs varied?

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Marble bust of Pythagoras, the ancient Greek mathematician and philosopher, showing a bearded man with a head covering and calm expression. — History of ethics Greek philosopher and mathematician Pythagoras, portrait bust.

Protagoras, a prominent figure among the Sophists, held that moral rules are not objective facts of nature but are instead matters of social convention, famously summarized by his dictum that "man is the measure of all things."12

Despite this ethical relativism, Protagoras did not advocate for a lawless society. He believed that while the specific content of moral rules may vary between different cities or cultures, the existence of some form of rules is essential for human life to be tolerable and sustainable. By grounding his ethical framework in human necessity rather than divine or metaphysical authority, he argued that society requires these conventions to maintain order and facilitate communal living.12