Tony Blair made a speech and everyone went mad. It wasn’t that he made a speech. It was that, 14 years ago, he allowed the UK to be an extremist US president’s patsy. (Good job there’s no chance of that happening again.) So MPs who voted for the Iraq war queued up to make ad hominem remarks, Corbynistas sensed treachery and Remainers sighed that their argument hadn’t been made by someone purer.

It’s unsurprising that Johnson and Duncan Smith should be so sensitive. Johnson is often seen as someone who would sell out his principles to attain the high office he believes his general brilliance deserves; Blair is criticised either for having no principles or for not compromising on them but either way he dominated British politics for ten years in a way that Johnson will never do. Duncan Smith, the sorriest of Tory leaders, was torn apart whenever he faced Blair at the despatch box. So it is understandable that they reach for the personal critiques. And it is clear that for many Remainers, their disapproval of the invasion of Iraq is as vivid a part of their self-identity as their enthusiasm for the European Union.

But we need to move forward from tit-for-tat insults. It isn’t as though many prominent members of the 48% aren’t continuing to put the case: Chuka Umunna won’t let anyone forget about the £350 million for the NHS. And there were plenty of thoughtful contributions during the Commons debates on Article 50. What Blair did, though, was put the arguments back into the news cycle. In particular he focused on the potential dismantling of the welfare state in a way that Jeremy Corbyn has so far failed to do. Blair doesn’t own these arguments, but people who say they care about avoiding hard Brexit should be testing them, challenging their logic and then using them.

For example, one argument where Remainers look weak is the idea that Brexiters didn’t know what they were voting for. It’s true that there was no clear manifesto, but every individual who marked their ballot paper for leave believed they knew what would happen as a result. I am not sure that telling people they were idiots is the best way to get them on your side. In contrast, Blair proposes that Remainers unpick an incoherent and unstable Leave coalition:

The Leave campaign was a coalition, some against Europe for economic reasons; some for cultural reasons. Some were ideological in their opposition; some had done a cost/benefit analysis and concluded better out than in. We must expose the agenda of the ideologues; and persuade those interested in the cost/benefit ratio. For the latter, we must – day in day out – articulate the reality: the pain is large and the gain largely illusory.

That is not a particularly easy task. It will require broad pictures to be painted in a way that the Remain campaign was bad at and Leave was brilliant at. It will require a reliance on mood and emotion rather than technical facts. If the rise of the far right has shown anything, it is that fact checking as a discipline in itself is useless if the terms of debate are unchanged. The BBC did what it called a ‘reality check’ of Blair’s speech and queried his statement about the fall in the value of the pound. The points that it makes are true but largely irrelevant. They will be seized on by people who want to discredit Blair, they will be ignored by those who agree with him, they will make no difference. See for example Trump’s ludicrous remarks about Sweden which his supporters continue to try to explain away.

Someone whom I otherwise respect made the following statement to me last week: ‘Our trains are run by the foreigners and they are bleeding us dry. We need to get out so we can sort this out. Support the Conservatives!’ There is so much wrong with both the logic of this and the facts that it is difficult to unpack – but talking about the different rail policies of the Tories and Labour would be to miss the point entirely. For all that Blair’s speech touched on issues of economics, the media and overall strategy, it is weak in its wider analysis about what made Leave so attractive. So here is a challenge for fellow Remainers: whatever your views of the Iraq war, Blair’s speech gives us the starting point for the heavy lifting that is needed in the months and years ahead. Are we ready to lift? Or do we want to continue the political battles of 2003?