Is the current international system dominated by natural law or positive law?
The current international system is dominated by positive law.
The difference between these two is that positive law is made by people based on their own ideas while natural law is seen as law that is made by a higher power. Positive law does things like setting up each country's exclusive economic zone in the ocean. Natural law says that genocide is wrong.
Most of the law that has to do with the international system today is positive law. These are laws like those dividing up the ocean. They are laws that govern trade relations between countries. They are laws that say who may have nuclear weapons and who may not. All of these are positive laws, not natural laws. Comparatively little in the way of natural law actually binds states in the current international system.