Raising uncertainties and stoking doubts was always going to be the heart of the pro-EU campaign. After all, the days in which anyone actually felt – or could even pretend to feel – enthusiasm about the wasteful EU machine are long gone. In the 1990s you would sometimes meet people who were true, misty-eyed believers that the Euro would bring a golden economic age or who really did look forward to Britain being subsumed into a country called Europe.

Now that the project’s reality has been seen, with its mass youth unemployment, declining share of global GDP and contempt for democracy, those pushing the EU are simply unable to summon any positive case for remaining part of it. It makes complete political sense for them to instead rely on fear of the unknown – it’s a tried and tested tactic, and it’s their best chance of winning the referendum.

But in recent days we’ve seen their rhetoric go rather further than their initial strategy intended. Despite having thrown a variety of lurid fears into the debate, the polls have not shifted appreciably. In the meantime, the SNP’s loss of a majority in Holyrood has banished the fear that a Leave vote could trigger another Scottish independence referendum, which brings a lot of Scottish voters back into the Leave or undecided columns on the EU question. Those factors may explain the extraordinary claims made by the Prime Minister today – a hint of desperation requires the pro-EU campaign to ramp up its rhetoric.

Cameron’s speech at the British museum conjured up the spectre not just of war but also of genocide, implying that a Leave vote would risk both.

It’s a claim which doesn’t have much basis in fact. NATO, not Brussels, protected us from the Soviet Union, while the adoption of broadly liberal democracy in European countries has kept the peace between us all since. Ironically, the EU is currently in the process of buying off and appeasing Turkey, a country whose direction of travel is away from, not towards, those very same values.

More importantly, the warning doesn’t even ring true on the Prime Minister’s own terms. If he truly thinks that Brexit would lead to war and genocide, why did he and the Chancellor spend months suggesting they might support it if they didn’t secure relatively small changes to EU welfare rules? For that matter, why did he agree to offer the British people a referendum on whether to plunge a whole continent into bloodshed? The answer to both questions is that even he does not really believe this line of attack – if he did, we wouldn’t be having a referendum at all.

The whole argument also implies something slightly troubling about Cameron’s own opinion of our EU neighbours. Can he really believe that British membership of the EU is the only thing standing between them and a return to the darkest days of the 20th Century? Are we really expected to believe that unless we continue to hand over billions of pounds of taxpayers’ money, surrender control of our borders and give Brussels bureaucrats power over our agricultural and environment regulation, then France, Germany and the others will return to the dark days of the Somme and Verdun, or even Treblinka and Srebrenica?

Of course not. The very idea is not only an insult to voters’ intelligence, it is an insult to the very friends and allies whom his speech purports to represent. Happily, Europe’s peace and civilisation hangs by much stronger threads than the existence of a British EU Commissioner – and it would continue without him. Our European neighbours are perfectly capable of living peacefully without British membership of the EU, just as we are perfectly capable of seeking a more democratic, more productive and more beneficial future outside the organisation.