It aims at harmonizing relationships between individuals and societies. In discussing the hypothesis of world government, we should recall that not all governments are twentieth century bureaucracies. The United Nations, in contrast, has all the trappings of a government, except the ability to actually govern anything. The Catechism has nothing to say about what form the institutions of world order should take. Rather, it seeks to outline what their functions should be.
Governments normally provide disaster relief and social services, but then so do private agencies.
The defining power of government has usually been a monopoly on the legitimate use of force, particularly of military force. Presumably, then, a universal government would have as one of its functions the duty to police the world, though the principle of subsidiarity would suggest that local disorders should normally be dealt with by local forces. Peace is defined as not just the absence of conflict, but as the tranquility which naturally arises from a just social order. Anyone who reads this material out of context is likely to be struck by its legalism. For statesmen in most places at most times, questions of war and peace are questions of policy, of contingency.