In her foreign-policy speech on Thursday, the Democratic presidential contender Hillary Clinton began to make the nuclear case against Donald Trump. It isn’t just the frightening prospect of a man with “very thin skin” having his finger on the nuclear trigger, she warned: Trump wants to “withdraw [America’s] military support for Japan, encourage them to get nuclear weapons.” She quoted from his remarks in April on a possible confrontation between a nuclear-armed North Korea and Japan: “If they do, they do. Good luck, enjoy yourself, folks.” Then she mused: “I wonder if he even realizes he’s talking about nuclear war.”

A nuclear-armed Trump is indeed a scary thought. But his apparent comfort with encouraging other countries to develop their own nuclear stockpiles is just as scary, if not more so. For 70 years, American presidents of both parties have understood the simple arithmetic involved—that the more countries have nuclear weapons, the more opportunities there are for nuclear war to break out, whether by design or by accident.

Yet the Republican nominee is effectively advocating the spread of arms so destructive they haven’t been used since their horrifying debut over Hiroshima and Nagasaki in 1945. In addition to remarking that the United States would be “better off” if nations like South Korea and Japan had nuclear weapons, Trump also seemed open, in an interview with CNN’s Anderson Cooper, to the possibility of Saudi Arabia, too, getting the bomb. He has since tried to walk this back—“They said that I wanted Japan to get nuclear weapons. Give me a break.” But as both Clinton and CNN have pointed out, he did say exactly that.

Given contradictions like this, it can be hard to take Trump seriously on foreign policy. But the implications of what he has said on nuclear weapons are extremely serious. A Trump presidency could reverse decades of American presidents’ work to hold the line against the spread of nuclear weapons, ushering in a new era of proliferation. U.S. leaders have applied “tremendous pressure” on allies to get them to turn back their nuclear programs. They have led efforts to successfully reduce the number of states that had or were actively pursuing nuclear weapons, from 23 in the 1960s down to nine.

At the core of Trump’s proliferation “policy” is a mistaken, reflexive belief that America is weak and will be powerless to stop the spread of nuclear weapons. “[I]f the United States keeps on its path, its current path of weakness,” he told The New York Times in March, Japanese and South Korean leaders would want such weapons “with or without me discussing it, because I don’t think they feel very secure in what’s going on with our country.” To CNN, he said: “It’s going to happen anyway. It’s only a question of time.” He ignores America’s past success in stemming proliferation—including in South Korea. It is unprecedented for an American leader to accept proliferation as inevitable because America is “weak.” Secretary of State Henry Kissinger, someone whom Trump praised as one of the “biggest diplomats in the country,” didn’t. In fact, he applied pressure on South Korea in 1975 to keep the country from going nuclear.

This isn’t a left-vs.-right issue—among the strongest opponents of nuclear proliferation was President Ronald Reagan. More than 30 years before Obama went to Hiroshima to warn about nuclear war, it was Reagan who went to Tokyo to state definitively, “A nuclear war can never be won and must never be fought,” and to pledge that “our dream is to see the day when nuclear weapons will be banished from the face of the Earth.”

In the meantime, Reagan carefully pursued policies that sought to prevent the spread of those weapons. When he declared while seeking reelection in 1984 that he would “make America great again,” he spoke of the need to “reduce the risk of nuclear war by reducing the levels of nuclear arms.” He reflected on how he had spoken “to parliaments in Europe and Asia during these last three and a half years, declaring that a nuclear war cannot be won and must never be fought. And those words, in those assemblies, were greeted with spontaneous applause.” Building on Kissinger’s efforts, Reagan was able to get South Korea to give up its nuclear program—a legacy Trump risks throwing out—and a few years later did the same with Taiwan. He did so in part with subtle diplomacy, and by reassuring allies like those two countries that America stood with them. Trump, with his bombastic style, is not seen as reassuring among world leaders.

A new nuclear-arms race, moreover, could be even riskier than the one Reagan and others worked so hard to end. In retrospect, the Cold War standoff between two massive, nuclear-armed superpowers offered some stability; among other things, the fact that the United States and the Soviet Union could destroy each other, or any other challenger, in a nuclear confrontation ended up preventing either side from using nuclear weapons. Global alliances were structured in a bipolar system, with smaller powers picking one side or the other, which meant fewer possible avenues for conflict.

But that world came to an end when the Cold War finished. We now live in a multipolar world that is, in many ways, a more dangerous one. Former Secretaries of State Kissinger and George Shultz, former Secretary of Defense William Perry, and Senator Sam Nunn warned in 2011 that “the growing number of nations with nuclear arms and differing motives, aims and ambitions poses very high and unpredictable risks and increased instability.” One particularly risky and region right now is East Asia, where competing territorial claims and an unpredictable North Korea threaten to flare into conflict. If Japan, which is revising its pacifist post-World War II foreign policy toward a more assertive one, or South Korea, where there is broad popular support for weaponization, go nuclear, the chances grow for a regional arms race—and for nuclear war.

One possibility, as Mark Fitzpatrick of the International Institute for Strategic Studies noted: “North Korea might be tempted to launch a preemptive attack at a time when the U.S. defense commitment [to South Korea] might no longer apply.” But even “short of this worst-case scenario, rather than negotiate disarmament, North Korea more likely would claim the South’s actions as a justification for stepping up its own nuclear program.”

These are by no means the only risks. There is, for example, the risk of an accidental firing or a rogue officer deciding that he or she wants to launch a nuclear weapon. There is the risk of “loose nukes” falling into the wrong hands, and the risk that individual scientists will be willing to transfer nuclear technology to the highest bidder, as Pakistan’s A.Q. Khan did in selling nuclear technology to Iran, Libya, and North Korea.

When the nuclear bomb was first being developed, Secretary of War Henry Stimson offered a poignant warning about how devastating the weapon would be. He told President Henry Truman that “such a weapon may be constructed in secret and used suddenly and effectively with devastating power by a willful nation or group against an unsuspecting nation or group of much greater size and material power.” Today, America’s “greater size and material power” can’t necessarily stop a nuclear strike, particularly if the materials fall into the hands of terrorists.

In the months ahead, Donald Trump will continue to try convincing Americans that he is a credible candidate who can be trusted to occupy the Oval Office. He has begun to style himself as a foreign-policy realist. But he’s not a realist—he’s a radical. Stephen Walt, a prominent realist scholar, has written, “realists prefer to ‘speak softly and carry a big stick;’ Trump’s modus operandi consists of waving the big stick while running a big mouth.” His loose talk during the campaign has already damaged America’s alliances. And on the central question of nuclear weapons, he has clearly exposed himself to be weak-kneed in his acceptance of international proliferation.

In America’s 1964 presidential campaign, the Republican nominee Barry Goldwater alluded to the idea of normalizing nuclear weapons within the U.S. arsenal, and potentially using them in Vietnam. Lyndon Johnson responded with the famous “Daisy” ad featuring a nuclear explosion. It closed with a message that still resonates: “The stakes are too high for you to stay home.”