I WANT to put to you an unpalatable, possibly dismaying proposition. It is that forgiveness is impossible. Not that forgiveness is tough, or takes time, or tests our generosity of spirit, or teases us with its promise of a future free from the pain of the past - rather that forgiveness is impossible.

Many individuals who have reflected on forgiveness have come to this conclusion. C. S. Lewis is one: "Everyone says forgiveness is a lovely idea, until they have something to forgive," he said.

He was picking up on an incident in the Gospels. There, Peter asks Jesus how many times he should forgive someone who sins against him. Seven times? Peter suggests, presumably thinking that a heroic target. No, replies Jesus. Seventy times seven: 490 times - or, in other words, Jesus's dry wit conveys to Peter that he must keep on trying to forgive . . . and forgive . . . and forgive. This is not a heroic target. It is a statement of the impossible.

I have been wondering about this dynamic of impossibility since the death of Nelson Mandela. It is striking that commentators on his life, even those who knew him well, seem unsure whether he forgave his oppressors, or rather sought a pragmatic reconciliation with them.

A quotation from him did the rounds at the end of last year: "Let bygones be bygones," although what was often missed was what followed next: "Let what has happened pass as something unfortunate, but which we must forget," the great man continued. And forgetting is not the same as forgiving.

SO WHAT is going on in this logic of forgiveness's impossibility? The French philosopher Jacques Derrida teased it apart. He argued that part of the difficulty is that it is often impossible to know just what is going on when someone claims to forgive.

If you look at individual cases, you are likely to see other dynamics at play. They might be excusing the person who has offended them - that is, they accept a justification for the upset or insult. At other times, Derrida continues, an amnesty might be the substitute act for forgiveness, as when people are supposedly "forgiven" their debts. Or it might not be forgiveness we receive, but rather we are let off the hook. What we did does not matter, after all.

But does it really not matter?You will know how unsatisfactory asubstitute for forgiveness is, if you have had the experience of asking friends or a spouse whether they remember the time you left them standing, broke a promise, told alie. "What?" they reply. "When was that? Then? Oh, I don't remember."

You are left hanging with your failure. Your friend thinks it does not matter; but it does to you. Where can you turn to now? This is another manifestation of the impossibility of forgiveness: it leaves you stuck with shame.

ANCIENT religious systems recognised a different angle in the practice of sacrifice. The logic of sacrifice, according to anthropologists such as René Girard, is that it breaks cycles of vengeance. It is an attempt to minimise the slaughter by sacrificing an eye for an eye, a tooth for a tooth; not a life for an eye, or invading a country for a tooth. Or take a sacrificial and innocent victim, and kill it. This is about performing an unjustifiable act, in order that worse acts might be prevented. The sight and performance of a death might prevent more deaths.

The issue is explored in the writings of psychotherapists, too. Psychoanalysis is interested in those cases when we are faced with something so bad that it really requires forgiveness, but which we cannot forgive, and so become ill.

Freud advocated struggling with remembering how we feel in being so offended against, because it is only in remembering that we can work through the terrible feelings, and find some freedom from them. What we do not remember, we are destined to repeat.

The risk with the imperative to forgive is that it short-circuits this process - that the offence is not really forgiven, but repressed, and, lurking about in the unconscious, returns to cause us all sorts of subsequent problems.

 nother way in which forgiveness can be psychologically damaging is when it prevents our feeling guilt. When we have hurt another person, guilt is an invaluable, humane feeling. To feel guilty, with the associated feelings of remorse and contrition, is one way in which we recognise that that other exists.

 o receive speedy forgiveness, and be cut off from the guilt, is to be left in a kind of moral isolation. The vulnerability of being contrite opens the heart.

A THIRD issue that interests psychotherapists is when forgiveness is used as an attempt to sidestep the necessary and painful process of mourning. A moving account ofthis followed on from the cold-blooded murder of the church organist Alan Greaves on Christmas Eve 2012, as he was walking down the street to church (News, 21 December 2012). His wife, Maureen, later described her remarkable response. She talked freely about the loneliness that she feels now that she is without him.

What she will avoid is not being able to mourn - what Freud called melancholia or depression. He believed, and research supports the view, that depression can be caused when people are not able to mourn someone or something that they have lost. It is as if they feel profoundly sad or angry or hurt, but they are not sure why. They lose touch with the object of their distress, and develop a life that is simply distressed. The sadness or anger or hurt needs to be experienced clearly.

Mrs Greaves appears to understand this. But she also understands something else - something that might offer a different take on all this; a way that does not deny the proper impossibility of forgiveness, but also does not leave us dismayed or stuck.

Her husband's killers were found, convicted, and jailed for life. And she described how she practisesforgiving them every day. She has to, because the forgiveness she feels in one moment disappears in the next. But she persists, because she believes that forgiveness is important, although she also seeks God's help because, as a Christian, she knows that it is not possible on her own.

HERE, then, is a clue. Put it like this: the things that most need forgiveness are the things that are most unforgivable. But being able to stay with that crux - and not short-circuit it in a bid to escape the pain - might bring us to a place where something higher or unexpected breaks through.

This different dispensation is illustrated in the parable of the Prodigal Son. The younger of two sons asks his father for his inheritance, and blows it all. He ends up eating pig food, just to stay alive. Then, he remembers his father's servants. He resolves to return to his father, beg forgiveness, and live like the hired men.

But the striking thing is that the father does not forgive his son. Instead, he throws a party. He who was lost is found; he who was dead is alive, the father says - much to the annoyance of the elder brother, who descends into a sulk.

This brother is right, in a sense. Forgiveness is impossible. The younger son has done an inexcusable thing. But the father sees things differently, from beyond the rights and wrongs of his son's actions.

He has not short-circuited the struggle with anger and agony. He thought his son lost and dead. But when the son actually returns, he can welcome him into a new life, grounded in the economy not of moral righteousness or rage, but of gratuitous love.

So it seems to me that the impossibility of forgiveness is actually an offer, although it is certainly difficult. At one level, it draws attention to the moral hazards of not really forgiving, but forgetting or excusing; to the important incompatibility of forgiveness with justice; to the mental ill-health that might originate when the moral imperative to forgive leads to repressing, not-feeling, not-mourning.

But, at another level, it points to the human experience that sometimes, with the most difficult aspects of life, the best course of action is not to try to fix things, but to stay with things.

In time, a radically different horizon might be glimpsed. It feels above morality and forgiveness - more like redemption or grace;gift, or love. That is what is promised by this apparently unpalatable truth: the impossibility of forgiveness.

Mark Vernon is the author of Love: All that matters (Hodder Education, 2013).

This is an extract from Mark Vernon's contribution to The Essay, to be broadcast on BBC Radio 3 next Tuesday at 10.45 p.m. It is one of five programmes on forgiveness, produced by CTVC, being aired next week.