What does Hedley Bull argue in his essay "Does Order Exist in World Politics?"
As your tag implies, Hedley Bull was a member of the English School of international relations. This school of thought is a constructivist school of thought that does not completely reject realism but which criticizes that school of thought. This is what Bull is trying to say in this chapter -- he is trying to say that there is such a thing as an international society and that states do not exist merely in a Hobbesian state of anarchy.
Bull points out that there has long been some degree of cooperation between states. The actions of states have also long been regulated by a set of standards that all states have been expected to abide by. This is not to say that states always play by the rules or that they always cooperate. However, Bull is arguing that the realists are missing something when they argue that the international system is characterized only by anarchy.
So the major point of this chapter is that anarchy is not the only characteristic of the international system. Instead, states show a strong tendency to cooperate with one another and to abide by unwritten "laws" that help to constrain their actions. Both of these ideas are contrary to what realists believe should be the case.
In the chapter Does Order Exist in World Politics?, Hedley Bull seeks to determine what order is in world politics. He also seeks to establish how such order is enforced within different states. Additionally, he also tries to determine whether such states have the capacity to provide for the implementation of world order.
To answer these questions, Bull argues against the theory that international states exist in a state of perpetual anarchy. He suggests that states always seem to gravitate towards cooperation and order. Thus, he asserts that order does exist; however, he adds that order exists under specific conditions.
He states that order will exist in a situation where constituents have an established pattern of activity aimed at achieving a particular goal. Thus, world order would exist in a situation where the society of states protect and maintain individual independence, recognize the rights to property, preserve peace, and maintain fidelity to agreements.