The United States must not see China or Russia through a zero-sum prism. The Obama administration has deepened areas of cooperation with Beijing, from the Paris climate agreement, the handling of the Ebola epidemic, the Iran nuclear deal and North Korea to joint projects in developing countries. It negotiated the New Start nuclear arms reduction treaty with Moscow and championed Russia’s admission into the World Trade Organization.

Yet when Russia or China challenge the principles of the liberal international order, the United States must stand up to them. In Ukraine, Mr. Putin has sought to change the borders of Russia’s neighbor by force while denying its people the right to decide with which countries, unions or alliances they associate. It is why American support for Ukraine matters.

So does our resolute support for international law in the South China Sea. There, China’s conduct in claiming vast territorial waters and building military outposts on artificial islands risks undermining the freedom of navigation and free flow of commerce upon which our prosperity depends, the peaceful resolution of disputes that undergirds stability and the rights of allies we have vowed to defend.

A sphere-of-influence world would not be peaceful or stable; the United States will not be immune to its violent disruptions. Hegemons are rarely content with what they’ve got; the demand to expand their zones as well as cycles of rebellion and repression within them will lead to conflicts that draw us in. The United States would have to accept permanent commercial disadvantage as economic spheres of influence shut us out or incite a race to the bottom for workers, the environment, intellectual property and transparency.

America’s greatest contribution to peace and progress has been laying the foundation for an open, rules-based, connected world. Now we have to decide whether to continue to defend, amend and build upon that foundation or become complicit in dismantling it.