What is it like to be a Christian? Not what do Christians believe or how many superstitions do they quietly excuse before breakfast? But what is faith as experienced?

It is an important question because, as Rowan Williams notes in his new book, The Lion's World, people might think they know what faith is about when, today, they perhaps don't, never having been there. Subtitled "A Journey Into the Heart of Narnia", the book is partly about CS Lewis. But it is also a chance for the archbishop of Canterbury to convey what Christianity means to him. This is difficult to do, not only because contemporary Britons lack Christian experience but because, as titular head of the established Church of England, Williams recognises a need to "rinse out what is stale in our thinking about Christianity – which is almost everything".

The elusory character of Christianity is also on the mind of Francis Spufford, the historian and science writer. The subtitle for his new book, Unapologetic, is "Why, Despite Everything, Christianity Can Still Make Surprising Emotional Sense". A central worry for him is not that the rational justification for belief has been undone. Faith is not about that anyway: as Coleridge noted, the best argument for Christianity is that "it fits the human heart". Rather, it is that so many of the secular alternatives to Christianity only work because they "depend on some tacky fantasy about ourselves". They are in flight from what is truly difficult about life; what is hardest to stomach about ourselves. Take John Lennon's anthem Imagine, which had such a prominent place in the closing ceremony of the Olympics. Spufford labels the lyrics the "My Little Pony of philosophical statements", with its monstrously deluded assumption that the default state of human beings – psychological, cultural and social – is one of peace.

Instead, Spufford likens the experience of being a Christian to listening to the adagio of Mozart's clarinet concerto. This "very patient piece of music" has been described as conveying the sound of mercy because its quiet beauty does not deny the horrors of life but admits they exist and yet insists there is more too. It is as if, running through the mess, there is an infinite kindness, or gentle forbearance, or what Dante called a love that moves the sun and stars. Reason cannot decide whether that is true. The feelings that deliver closer, insider knowledge of human experience can.

Williams reflects extensively on the nature of mercy as well. He portrays it as an unsentimental though humane experience, again because it means facing up to the truth about what you have done and who you are. The theistic insight is that this truth can only be seen when you are confronted by the divine. To meet God – or Aslan, as Lewis has it in the Narnia stories – is "to meet someone who, because he has freely created you and wants for you nothing but your good, your flourishing, is free to see you as you are and to reflect that seeing back to you".

In other words, to see yourself as others see you might be discomforting but it will also always be skewed by the distorting lens of their self-interest. To be unmasked as God sees you is painful because purgative, but is also a path to true liberation. It is merciful because without it we are left in a citadel of self-deception, life's energies being sapped and wasted on bolstering self-regard.

None of this proves the existence of God in the way a science would demand because its evidence arises from the inner lives of individuals. It does, though, reflect a strand in the philosophical discussion of God, often forgotten today. Pascal drew attention to the problem God has in revealing himself to creatures he has made to be free, because if God were to offer irrefutable evidence then that would force a relationship of coercion, not love. God's solution, Pascal proposed, is to "appear openly to those who seek him with all their heart, and [to remain] hidden from those who shun him".

The philosopher Paul Moser calls the demand for such proof "spectator evidence" in his more academic recent book, The Evidence for God: Religious Knowledge Re-examined. And being a spectator of life will not take you into life or reveal the ground of life to you. It separates the individual from both. Rather – and as Williams and Spufford stress – what is required is a transformation of the individual, akin to the transformation that occurs when someone falls in love. It happens not because there is a hardening of the evidence but because there is an unhardening of the heart, softened in relationship. Only then might we see as we are seen.