Ukrainian servicemen are seen standing on an Armoured Personnel Vehicle (APC) through a broken window in the village of Horlivka, Donetsk region, on February 4, 2015. (Volodymyr Shuvayev/AFP/Getty Images)

Fiona Hill is the director of the Center on the United States and Europe at the Brookings Institution. Clifford Gaddy is a senior fellow in the center. They are co-authors of the book “Mr. Putin: Operative in the Kremlin.”

The United States is on a dangerous trajectory in its relations with Russia, a nuclear superpower that believes itself to be under direct threat. Several former U.S. officials and top think-tank experts released a report calling on the West to provide military support to Ukraine. (Two of them, our colleagues at the Brookings Institution, expanded on the report a week ago on this page [“Ukraine needs the West’s help now”].) The logic of sending weapons to Ukraine seems straightforward and is the same as the logic for economic sanctions: to change Vladi­mir Putin’s “calculus.” Increasing the Ukrainian army’s fighting capacity, the thinking goes, would allow it to kill more rebels and Russian soldiers, generating a backlash in Russia and ultimately forcing the Russian president to the negotiating table.

We strongly disagree. The evidence points in a different direction. If we follow the recommendations of this report, the Ukrainians won’t be the only ones caught in an escalating military conflict with Russia.

In the jargon of geopolitics, Putin enjoys “escalation dominance” in Ukraine: Whatever move we make, he can match it and go further. In August, when it looked as though Ukraine might rout the rebels, Putin increased the stakes and countered the Ukrainian military. Drawing on those lessons, some Russian security analysts are now pushing for a preemptive invasion of Ukraine, arguing that Russia should go all the way to Kiev before the West takes further action. One recent such plan suggested that Moscow was losing momentum in the conflict and should not waste more time on fruitless negotiations. The Western press coverage of the issue of lethal weapons can only convince those in Moscow pushing “full war and invasion now” that their approach is correct.

We also must consider the effect that arming Ukraine would have on our European allies. The report has created an uproar in Berlin and other European capitals, stoking concern that the Obama administration will take steps others are not ready for. If Putin concludes that transatlantic unity can be shattered, with the United States facing the possibility of going it alone in Ukraine, why would he change course?

Our problem is that we do not fully understand Putin’s calculus, just as he does not understand ours. In Putin’s view, the United States, the European Union and NATO have launched an economic and proxy war in Ukraine to weaken Russia and push it into a corner. As Valery Gerasimov, chief of staff of the Russian armed forces, has underscored, this is a hybrid, 21st-century conflict, in which financial sanctions, support for oppositional political movements and propaganda have all been transformed from diplomatic tools to instruments of war. Putin likely believes that any concession or compromise he makes will encourage the West to push further.

Anyone who argues that Putin’s wartime rhetoric is a bluff is making a very risky assumption. We should bear in mind the wars that Putin has waged in Chechnya and Georgia. Before Putin came to power, during the first Chechnya war, the Russian military collapsed, the people balked and President Boris Yeltsin’s government negotiated with the Chechens. In the second war, Putin put his intelligence service in charge and convinced Russians that the sacrifices were worth it. The war was brutal, and the military and civilian casualties high; there were no negotiations. Then, in 2008, Putin called NATO’s bluff on Georgia. Some reasoned that, if Putin knew Georgia would eventually become part of the alliance, he would refrain from moving against it militarily. But the West wasn’t prepared to fight for Georgia, and Putin was.

Since Georgia, Putin has prepared the Russian military to fight a regional war behind the ultimate shield of Russia’s nuclear arsenal. And he has spent a great deal of time and money telling his people that he is defending the Russian nation in Ukraine. His past actions suggest he will do everything he can to convince them that Russian military sacrifices in Ukraine are worth the cost. The delivery of lethal U.S. weapons to Ukraine would help Putin make that case. They will be part of the proof he needs.

We face a huge challenge in devising a strategy to deal with Russia that does not fuel this escalatory cycle and puts Ukraine on another path. We also need to draw bright lines around transatlantic unity and work to preserve it. It is hard to find effective alternatives to the current sanctions policy, but if we plunge headlong into sending weapons, we may lose our allies, and we may never have the opportunity to get things right.