Upping the ante in Ukraine also risks unwanted escalation. Not only would the fighting in eastern Ukraine be sure to intensify, but it could also spread to other areas. The consequences for Ukraine, which already faces profound economic and social problems, would be disastrous.

The possibility that Mr. Putin might end up making nuclear threats may seem remote, but if the goal of arming Ukraine is to drive up the costs of Russian interference and eventually put Moscow in an acute situation, it cannot be ruled out. If Western pressure succeeded and Mr. Putin felt desperate, he would have a powerful incentive to try to rescue the situation by rattling the nuclear saber.

Our understanding of the mechanisms of escalation in crises and war is limited at best, although we know the risks are considerable. Pushing a nuclear-armed Russia into a corner would be playing with fire.

Advocates of arming Ukraine recognize the escalation problem, which is why they stress giving Kiev “defensive,” not “offensive,” weapons. Unfortunately, there is no useful distinction between these categories: All weapons can be used for attacking and defending. The West can be sure, though, that Moscow will not see those American weapons as “defensive,” given that Washington is determined to reverse the status quo in eastern Ukraine.

The only way to solve the Ukraine crisis is diplomatically, not militarily. Germany’s chancellor, Angela Merkel, seems to recognize that fact, as she has said Germany will not ship arms to Kiev. Her problem, however, is that she does not know how to bring the crisis to an end.

She and other European leaders still labor under the delusion that Ukraine can be pulled out of Russia’s orbit and incorporated into the West, and that Russian leaders must accept that outcome. They will not.

To save Ukraine and eventually restore a working relationship with Moscow, the West should seek to make Ukraine a neutral buffer state between Russia and NATO. It should look like Austria during the Cold War. Toward that end, the West should explicitly take European Union and NATO expansion off the table, and emphasize that its goal is a nonaligned Ukraine that does not threaten Russia. The United States and its allies should also work with Mr. Putin to rescue Ukraine’s economy, a goal that is clearly in everyone’s interest.