President Biden often likes to remind voters that he is a deep foreign policy thinker with decades of experience meeting with world leaders. Yet last week, he demonstrated that he has either forgotten or never learned some of the basic lessons of Cold War nuclear brinkmanship.

This happened when the deputy chairman of Russia’s national security council, Dmitry Medvedev, raised the prospect of a nuclear strike on Ukraine. His warning came after a flurry of prominent Russian journalists started musing publicly about a nuclear attack as a response to Russia’s military losses on the ground.

That’s the context of Mr. Biden’s remarks at a fundraiser at New York. The president allowed as how President Putin was “not joking when he talks about potential use of tactical nuclear weapons or biological or chemical weapons.” He warned that Russia’s recent saber rattling could lead to Armageddon.

In this light, Mr. Biden said the White House was searching for “off-ramps” for the Russian leader to avoid the prospect of a nuclear exchange down the road. While the president has not said what those “off-ramps” are, it would almost certainly mean pressuring Ukraine to accept that at least some of its territory would now belong to its neighbor.

This is the exact wrong approach. The last thing an American president should ever do is to give credibility to a Russian leader’s nuclear blackmail. Since Russia launched its war of conquest in February, the Kremlin has threatened to use nuclear weapons as a way of spreading among Ukraine’s population and its allies — and Mr. Biden — a sense of panic. At the end of February, Russia put its nuclear forces on “high alert.”

To the Biden administration’s credit, the change in Russia’s nuclear posture in February failed to  pause or diminish the flow of arms to Kyiv from America, which has steadily increased its arms shipments. Ukraine is in a position to repel the Russian invaders today because Mr. Biden kept his head when Mr. Putin first threatened nuclear strikes.

So what changed this time? One explanation is that Mr. Biden has a propensity to undermine his own policies when he speaks off the cuff, a trait he shares with his predecessor. Mr. Biden has said a few times in interviews that America would defend Taiwan if the province were attacked, only to have a White House representative correct the president later in the news cycle. That is what the White House did last week after the initial story broke about the president’s remarks.

Mr. Biden is fortunate that President  Trump weighed in on Russian nuclear threats himself. At a rally at Mesa, Arizona, Mr. Trump accused Mr. Biden of leading the planet to the next world war. “We must demand immediate negotiation of a peaceful end to the war in Ukraine,” Mr. Trump said. “Or we will end up in World War III and there will never be a war like this.”

The former president here managed to state aloud what Mr. Biden didn’t. Yet if Mr. Trump were to get his way, then every other nuclear state would conclude that blackmail works. If Mr. Putin could end up winning the war in Ukraine that he is losing today because he threatened to use a nuclear weapon, then we should expect China to threaten to use nuclear weapons when it attempts to swallow Taiwan.

The proper response to Mr. Putin today is resolved ambiguity. It’s a concept laid out by a Nobel laureate, Thomas Schelling, in a recently declassified paper titled, “The Threat That Leaves Something To Chance.” His idea, issued by the RAND Corporation, was that nuclear brinksmanship will inevitably lead adversaries to test an opponent’s resolve. Vague threats have an advantage of not locking in a response when a threat is tested. 

Mr. Putin is the one who has ignored Mr. Schelling’s advice. He threatened to use nuclear weapons at the beginning of his war, and he didn’t do it. Why in the world would Mr. Biden or Mr. Trump give him credibility now that Russia is losing the war it started more than eight months ago?