Following Russia’s intervention in Syria, the Obama administration announced last week the end of its abortive effort to train a new rebel force to combat the Islamic State. Instead, the Pentagon will use the program’s remaining funds to supply weapons and ammunition to rebel groups already fully engaged in the conflict.

Unfortunately, that decision will likely serve only to intensify the warfare in Syria.

The decision to arm Syrian rebel forces, followed by reports that some rebels are already using American-made anti-tank missiles to good effect against President Bashar al-Assad’s forces, have prompted many observers to conclude that the United States is now engaged in a “proxy war” against Russia, which backs Assad. Ominously, it suggests that the Obama administration may be falling into the trap of engaging in a new cold war.

Throughout most of the Cold War decades, there was a tendency within the Soviet Union and the United States to view international relations as a zero-sum competition. A communist takeover anywhere in the world represented a Soviet victory. The ascension of a noncommunist regime constituted a victory for the United States.

Such thinking prompted both the United States and Russia to intervene (directly and indirectly) in conflicts throughout the Third World. The two superpowers took great care not to engage each other directly. Yet if one superpower intervened in a conflict, its rival would typically support opposing indigenous forces. Following Russia’s intervention in Afghanistan, for instance, Zbigniew Brzezinski, President Carter’s national security adviser, reportedly exulted in the opportunity to bog the Soviets down in their own Vietnam.

That mentality has certainly not been eradicated. Vladimir Putin could not help viewing Ukraine’s potential membership in the European Union as a victory for the West. That prospect was apparently so troubling that it prompted Russia to annex Crimea away from Ukraine and provide illicit support to separatist rebels eastern Ukraine.

Those actions have, in turn, prompted many hawks in the United States to urge the Obama administration to counter Putin. Initially, Obama resisted the temptation — most notably, by rejecting pressure to provide military aid to the new pro-Western Ukrainian regime.

Last week, however, the president predicted that Russia’s intervention in Syria would “get them stuck in a quagmire.” And the decision to begin arming the Syrian rebels in earnest seems to suggest that the administration is intent upon making sure that happens.

The history of proxy warfare during the Cold War counsels against such a course. As the president knows well, U.S. support for the Mujahedin fighting the Soviet invasion of Afghanistan in the 1980s was hardly a success. It certainly helped ensure that the Soviets got bogged down. But it contributed little, if anything, toward building a stable political order in Afghanistan. And many of the fighters Washington aided against the Soviets famously turned their sights on the United States.

It may be tempting to ensure that the Russians sustain a black eye in Syria, but arming the Syrian rebels will serve primarily to prolong a multi-year conflict that has cost over 200,000 lives. Moreover, supporting a proxy force in opposition to Russia will help confirm the suspicion and mistrust that already seems to poison Russia’s perception of the United States.

Unfortunately, there is probably little constructive the United States can do at this point to resolve the conflict in Syria and establish a stable new government. The Obama administration, therefore, should take care not to make a bad situation worse. During the Cold War, almost 20 million people died in Third World conflicts fueled largely by U.S.-Soviet competition. That dismal history of proxy warfare suggests that more arms is not the answer in Syria.