Donald Trump's press secretary began his regime with an attack on the White House press corps for "deliberately false reporting" on Donald Trump's inauguration, making claims about the size of the crowd that turned out not to be true. But Sean Spicer's statement was of a piece with Trump's adviser Kellyanne Conway's defence of him: she said he gave "alternative facts". Conway was called out by her CNN interviewer, who said these so-called "alternative facts" were actually falsehoods.

And of course that's right. There are many, many areas where something is either provably one thing or provably another. But what has made the Trump phenomenon – and, on the other side of the Atlantic, the Brexit campaign – so different is that it hasn't seemed to matter. It's this that caused Oxford Dictionaries to make the "post-truth" the international word of the year. It's an adjective "relating to or denoting circumstances in which objective facts are less influential in shaping public opinion than appeals to emotion and personal belief."

One of the jobs of a journalist is to remind people that objective facts do matter. And Christians ought to be right behind that enterprise. They shouldn't be saying facts aren't important. True is true and false is not, and Christians should have no truck with lies.

However, there's a rather different message here, and one Christians need to understand. What a substantial section of the population has grasped is that while facts do matter, they aren't all that matters. Trump succeeded not because he out-argued Clinton, but because he showed people something they could believe in and persuaded them of its truth. That big truth was what mattered to them, rather than the inconvenient falsehoods uncovered by those pesky fact-checkers. They looked small, like sore losers nit-picking because they realised they were on the wrong side of history. If Trump or his advisers lied, it didn't matter: what they stood for was true.

Well, we'll see. It's been the universal experience of human beings throughout the ages that if you ignore the facts, they have a way of coming back to bite you. Trump is still in the honeymoon period, at least as far as his supporters are concerned. It won't last.

But in spite of all this, Trump does have something to teach the Church – and it's not about playing fast and loose with the truth. It's about the power of a big, compelling vision. In secular hands, and for secular purposes, that's a dangerous thing that's open to corruption and abuse. Ultimately a vision like that is only worth as much as its prophets.

But believers in the risen Christ follow a far worthier leader. And the trouble is that too many defenders of the faith act like fact-checkers, picking away at the small stuff, arguing in the echo-chamber of the like-minded, aiming their fire at each other in the name of orthodoxy and trying to persuade through the accumulation of data. It doesn't work. As someone (no one's quite sure who) has said, "A man convinced against his will/ Is of the same opinion still."

I firmly believe Christianity can stand up to any fact-checking. Properly understood, the testimony of the Bible is rock-solid in a way that no politician's can even approach. But that isn't what persuades people to believe. It's not primarily about analysis; it's about imagination.

There are great challenges involved in preaching Christ in a post-truth world. How do we move from attempting to defend or recommend the faith to non-believers with arguments drawn from Bible proof-texts, to an attempt to speak to the whole person – to campaign for their hearts as well as their minds, to help them see the whole world in a different way? There are plenty of organisations and ministries aimed at making Christianity intellectually compelling, which operate with varying degrees of success. The question is, how do we make it imaginatively compelling?

I very much hope Donald Trump becomes a worthy president of the US. To do that he'll need to pay more attention to the small truths. But Christians have a far wider agenda, and we'll need to pay attention not just to the small truths, but to the biggest one of all: that "God was in Christ, reconciling the world to himself, no longer counting people's sins against them." (1 Corinthians 5:19)

Follow Mark Woods on Twitter: @RevMarkWoods