LitCharts assigns a color and icon to each theme in The Social Contract, which you can use to track the themes throughout the work.
Human Freedom and Society
Sovereignty, Citizenship, and Direct Democracy
Government and the Separation of Powers
National Longevity and Moral Virtue
Summary
Analysis
Since the government is not created through a contract with the sovereign, Rousseau asks, how is it actually instituted? He says that it involves two parts: first, the sovereign passes a law establishing government, and second, it names the magistrates who will run the government. This second stage is “a particular act,” not a general one (because it applies to specific people), and so it constitutes “a function of government.” But this means that it requires the sovereign to act as a government, which appears to be contradictory. Rousseau assures the reader that this is completely possible: just as the parliament can momentarily raise a specific political issue and discuss it as a subcommittee of itself, the sovereign can temporarily become its own democratic government to appoint magistrates, before then going back to being the sovereign.
Rousseau’s explanation of how the sovereign appoints the government may seem paradoxical: by definition, the sovereign cannot engage in any “particular act,” so it cannot appoint a government. Arguably, Rousseau’s idea that the sovereign temporarily turns itself into a government may be an equally problematic “particular act,” but in the form of government that Rousseau calls democracy, all the people participate in implementing the laws, so in theory there is no problem with the same people who make up the sovereign also making up the government—that structure is essential to democracies as Rousseau defines them.