“A man you can bait with a tweet is not a man we can trust with nuclear weapons,” was Hillary Clinton’s swipe at Trump in her speech to the Democratic Convention.

She went on to quote Jackie Kennedy: what most worried JFK during the Cuban Missile Crisis “was that a war might be started, not by big men with self-control and restraint, but by little men — the ones moved by fear and pride.”

She didn’t spell out the link between these two ideas, because she didn’t need to. A war between highly-armed nations in the modern era moves quickly into what Carl von Clausevitz, the great nineteenth-century Prussian general, called an “escalation to extremes.”

And nowadays, with nuclear weapons, that means total destruction.

The thought of Trump in a war of words with Putin, each with his fingers over the nuclear button, is too appalling to contemplate. But even if all our leaders are level-headed and self-aware, the moral question remains: under what circumstances, in the post-Cold War order, could we contemplate the use of nuclear weapons?

And if there is none, why do we continue  — at vast expense — to upgrade the ones we have?

Theresa May’s parliamentary debut as prime minister was to make the case for Britain renewing its Trident submarine-based nuclear deterrent — four missile-carrying submarines — at the cost of many tens of billions of dollars (no one quite knows how much).

The idea is that in 30 years’ time they can continue to cruise the oceans unseen, as the existing ones have done since 1969, loaded with eight missiles and 40 warheads, each warhead being eight times more powerful than the bomb that killed 140,000 people in Hiroshima in 1945.

The weapons, May told Parliament, are “our ultimate insurance against nuclear attack.”

The missiles are carried in submarines so that, if UK cities were destroyed and the chain of command with them, they could still be launched against an enemy. The orders to do so are contained in handwritten letters from the prime minister with instructions that are locked in a safe aboard the submarines until the fateful day comes.

No one knows what the letters say. But the fact they exist is designed to send a clear message: destroy us, and we destroy you.

Malign or unstable powers know that Prime Minister May, who attends church every Sunday and is the daughter of a country vicar, is willing to order a retaliatory strike that would kill hundreds of thousands of innocent people, triggering a global famine and much else besides.

She confirmed this in Parliament. “Yes,” she answered firmly, in answer to a question of whether she was personally prepared to authorize such a strike.

Is she lying? I assume so; I hope so. Because if Britain were the victim of a genocidal nuclear attack, to launch one in response would be not only pointless; it would also be an act of genocidal revenge — “absurd violence,” as Pope Francis would call it, but on an epic scale.

The use of such weapons can never be justified  — there is simply no possibility of squaring them with just-war principles such as just cause and proportionality. The Second Vatican Council in Gaudium et Spes says the destruction of entire cities or populations “is a crime against God and against man himself” which “merits unequivocal and unhesitating condemnation.”

The council fathers did accept that nuclear deterrence may be morally acceptable, a position St. John Paul II reiterated in his 1982 address to the United Nations at the height of the US-USSR arms race, but  only “as a step along the way towards a progressive disarmament.”

In other words, nations that had nuclear weapons in response to others having them could hold onto them while working to reduce them; but they could not be part of any policy for projecting state power or interests.

Sir Michael Quinlan, a prominent British Catholic who was also an influential defense official in the Thatcher government in the 1980s, thought long and deeply about deterrence over many years, and kept pictures of Hiroshima and Nagasaki in view from his desk as a reminder of what was at stake.

He concluded that for western nations the only thing nuclear weapons can ever do is transmit a basically simple message: that if you attack me, I will resist, and will continue to resist until I no longer can, inflicting on you ever heavier damage.

Or as May put it to Parliament: “We must continually convince any potential aggressors that the benefits of an attack on Britain are far outweighed by their consequences.”

But the weapons “cannot make that message plain,” Quinlan wrote in 1981, “if they do not exist, or if they are not capable of use in ways in which an aggressor could find believable.”

And there’s the rub. You can only convince an aggressor you’re serious about striking back if you update your capability. But your upgrade will cause them to seek the latest model too.

Built into the very idea of deterrence, in other words, is what the great Catholic thinker René Girard called “mimetic contagion” — we copy each other’s desire. In the case of nuclear weapons, it means that escalation is part and parcel of possession.

This became clear with the end of the Cold War. Russia, like the US, is today busy burnishing its missile capability; the two nations spend $100 billion annually — together with China, France, the UK, Israel, India, Pakistan and other nuclear-possessing states.

To sleep less soundly tonight, consider this: There are now around 20,000 nuclear weapons at 111 sites in 14 countries.

When it became obvious that, rather than pursuing disarmament, the nuclear-weapons states were pouring tens of billions of dollars into upgrading their capability, the Holy See began challenging the “institutionalization of deterrence” — the idea that nuclear weapons are a way of keeping the peace.

In 2006 Benedict XVI in his World Peace Day message slammed what he called this “baleful” and “fallacious” notion of nuclear weapons as a means of ensuring security, and critiqued the appalling level of spending that could otherwise be invested in development.

“In Catholic teaching, the task is not to make the world safer through the threat of nuclear weapons, but rather to make the world safer from nuclear weapons through mutual and verifiable nuclear disarmament” was how the Holy See representative put it at a 2009 deterrence symposium in Omaha, Nebraska.

Under Pope Francis, the Holy See has stepped up both its pressure and its rhetoric to make this happen.

“There is no more argument, not even the argument of deterrence used during the Cold War, that could ‘minimally morally justify’ the possession of nuclear weapons,” said Archbishop Bernardito Auza, the Vatican’s UN ambassador, last year.

Like Benedict XVI, Francis has argued that spending on nuclear weapons takes valuable investment away from the poor and human development.

“When these resources are squandered,” he said in December 2015, “the poor and the weak living on the margins of society pay the price.”

He told the UN in New York in September last year that nuclear weapons do not keep the peace but corrode it. “An ethics and a law based on the threat of mutual destruction — and possibly the destruction of all mankind — are self-contradictory and an affront to the entire framework of the United Nations,” he said, before calling for urgent steps towards disarmament.

The Catholic Church has moved clearly against not just the use but also the possession of nuclear weapons, even as deterrent. As the Holy See has often pointed out, the idea that states need to have them because the other side does is not an argument we apply to chemical and biological weapons.

And then there’s the point that the bluffing game our leaders are playing  — you nuke me, I’ll nuke you back — no longer convinces in a post-Cold War world in which messianic cults such as ISIS are taking over failed states.

If Theresa May and Hillary Clinton will not order the use of nuclear weapons, there is no point in having them; and if they would use them, they have no moral right to lead a Christian nation.

It is time to take seriously the Pope’s call for disarmament. That doesn’t mean not just keeping Trump away from the nuclear codes. It means keeping nuclear weapons away from our defense policy.