If one party resolves to demand what the other resolves to refuse, the dispute can be determined only by arbitration; and between powers who have no common superior, there is no other arbitrator than the sword

Summary

This quote suggests that when two parties have conflicting demands and neither is willing to compromise, the only way to resolve the dispute is through war or conflict. There is no higher authority to mediate between them, so they must rely on force to determine the outcome. The quote implies that in situations where there is no shared authority or higher power to adjudicate the dispute, violence or the threat of violence becomes the ultimate arbiter.