Without structure or discipline people live in "continual fear, and danger of violent death; and the life of man (is) solitary, poor, nasty, brutish, and short" (Hobbes 5). Agreeing to a social contract allows people to live in peace and pursue happiness. As Locke says, "the commonwealth... (is) a society of men constituted only for procuring, preserving and advancing their own civil interests.” (Locke 1) It is a method of self-preservation and self-advancement. People coalesce into communities for mutual protection, but when they enter into the contract they must relinquish many of their freedoms to create the community's stability. This makes a division in the self between the private and the public innate in social contract theory. People have to put aside personal desires for the good and stability of their community.
Hobbes sees religion as a tool that rulers should use to prevent dissidence. Everyone is forced to publicly accept the same religion and God, but a ruler cannot control what people privately believe. Practicing a religion one does not believe creates a major division between the individual's private and public self.
Locke does not see religion as a tool for creating stability. He says that people should be allowed to practice whatever they believe privately. If individuals worship without conviction, they "add unto the number of (their) other sins those also of hypocrisy and contempt of His Divine Majesty" (Locke 1). Avoiding this hypocrisy helps reconcile the contracted individual's public and private selves.
Socrates has no division between his private and public selves. He acts publicly as he believes privately. Socrates publicly creates instability in his state by asking questions. He does this because he privately believes the citizens of Athens should search for the truth. When Socrates refuses to escape from his death sentence, it is because he believes on a public and private level that all of his state's decisions are good and right even if they are unjust. He says anyone who breaks "the covenants and agreements" is "wronging those you ought least to wrong... your country" (Plato 10). Unlike most individuals, Socrates's public self is never in discord with his private self.