If, and it’s a big if, Pope Francis did say that hell does not exist, what might he have meant? To say that hell does not exist is clearly not a statement about geography or cosmology. Neither Francis nor any other sane and educated person believes that a space probe will come back with a report of heaven, or that an overenthusiastic fracking company will tap into a source of heat much larger than any survey had estimated, shortly before all the management and shareholders are sucked down inside it by ravening demons.

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To agree that hell is not a place in the external world isn’t quite the same as saying that it has no physical reality. It’s just that the physical reality doesn’t matter at all. Supposing that hell is something that exists only in the imagination, it will still have a physical manifestation somewhere in the brains of believers. That is trivially true of everything we think or feel but what’s important about this point is its triviality. It would do nothing at all to our understanding of ideas to read about them from inside a brain scanner.

Arguing about the existence of hell, or even the existence of God, is a little like arguing about the existence of the number zero. The use of the concept is obvious and irresistible. As soon as you use it you see that it works, but why it should work is an entirely different question, and whether it needs to exist to work is an argument about the meaning of the verb “exist”, not about the reality of zero, or of God, or hell.

The problem is not just that the universe has no place for hell: it has no time for it either

The person who put this most clearly is actually Death, in Terry Pratchett’s book Hogfather. He tells his daughter: “Humans need fantasy to be human. To be the place where the falling angel meets the rising ape … Take the universe and grind it down to the finest powder and sieve it through the finest sieve and then show me one atom of justice, one molecule of mercy … and yet you act as if there is some ideal order in the world, as if there is … some rightness in the universe by which it may be judged.”

If we start thinking of hell as a concept that deals with the same sort of problems as the concepts of justice and mercy do, it’s easy to see that all our thoughts about it are in some sense figurative. This doesn’t mean they’re unreal. Hell is clearly something experienced, which can’t be escaped, if you’re there, by wanting to escape it, even with all your heart. The real difficulty for Christians is the idea that hell entails eternal conscious torment, which is the jargon for something almost unthinkable. That seems to have been what Francis was actually discussing.

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The idea of eternal conscious torment has troubled Christians almost since it first arose. It seems entirely disproportionate to the sins it punishes. The sufferings of hell are by definition worse than anything we can experience in this life: worse than cancer; worse than being burned alive; worse than watching your family die of Ebola; deeper and sharper than the worst inward gripings of remorse. All those can be unendurable, but the sufferings of hell, in the traditional doctrine, endure for ever. Death cannot end them: quite the opposite, in fact. To inflict such endless agony does not seem in the nature of a loving and merciful God; it seems disproportionate even to the demands of justice. In fact the early and influential theologian St Origen believed that even Satan would be released from hell at last, although this was later judged a heresy.

The real difficulty comes with the concept of eternity. The problem is not just that the universe has no place for hell: it has no time for it either. The universe, which had a beginning in the big bang, and will have an end, cannot contain eternity. Only our minds can experience eternity and I suspect that suffering, like bliss, can be eternal in that sense – while it lasts. But no one who has experienced real bliss, or real anguish, could doubt that they exist.

• Andrew Brown is a Guardian columnist