I recently posted on the unconditionality of forgiveness. This prompted a brief exchange on Facebook, and so I now want to expound at a bit greater length on the topic.
In the first place I must answer the question, How do I understand forgiveness? I spent about a year studying the topic while I was doing my undergraduate degree at Arizona State, and the conclusion I came to was something like this. After having analyzed the proposal of Eve Garrard and David McNaughton, "In Defence of Unconditional Forgiveness," which paper you may read here, I came to something like the following definition of forgiveness. To my mind, forgiveness means committing an favorable and benevolent disposition towards the person who has done you wrong. This disposition is something within the neighborhood of what kind of goodwill or pro attitude (as opposed to contra attitude) you might have had for the wrongdoer had she never done the thing in question. Forgiveness therefore means committing to act towards that person in such a way as would be motivated by that benevolent disposition.
Note that this doesn't mean you ignore the thing the person did to you. Forgiveness is not ignoring or refusing to address the wrong. Rather forgiveness concerns the mode in which you address the wrong. If you forgive, you don't act out of hatred, you generally don't seek revenge, you don't seek to get even, you don't call down fire from heaven upon the person, etc. If you do address the person who did you wrong -- and you might not always -- you do so out of goodness and benevolence, while not necessarily passing over the evil deed as if it never happened. You address her with kindness, making your objection to her action known, etc., but out of a good heart.
Now, as I said, forgiveness doesn't always entail you address the person who did you wrong. Suppose Peter hurts Paul and makes it known to Paul that he will try to do it again if he gets the chance. Paul may forgive Peter here without approaching or seeking reconciliation with Peter right away. Forgiveness doesn't mean leaving yourself open to being stepped all over or abused. It means responding with goodness to evil, and that doesn't entail approaching someone in a position in which you are vulnerable to serious harm.
This means that forgiveness is separable from reconciliation. Reconciliation, for it to be genuine at least, requires goodwill on the part of both persons involved. Both parties have to be willing to let the wrong behind them and work towards a repaired relationship. If one party is unwilling, then reconciliation cannot take place. But the other person can still be benevolently disposed towards the unwilling party, in which case forgiveness would be enacted without reconciliation. Likewise forgiveness does not entail reconciling with someone who only appears willing but will probably hurt you again. You can be good to that person and refuse to reconcile on the grounds that she does not take seriously the need to change her ways. But forgiveness, to my mind, does entail being willing to reconcile with a person who has seriously changed her ways, regrets the wrong she did, and wants to restore the relationship in good faith.
I argued in that previous post that forgiveness is unconditional. How, then, do we understand atonement and punishment in the Bible?
I think atonement flows from forgiveness. Paul says in 2 Cor 5.19 that God was in Christ, reconciling the world to himself, not counting people's sins against them. Notice the order here: God previously did not hold the sins of the world against them, and then sought reconciliation with them. Elsewhere he says that while we were still sinners, Christ died for us (Rom 5.8).
We can see how forgiveness motivates atonement in this way. If forgive the person who did me wrong, and therefore I adopt an attitude of benevolence towards her, and want what is good for her. This includes that she see that what she did is wrong, and that she change her ways and not live in evil any longer. Therefore if I forgive you, I may make the attempt to show you that you are not doing what is right, and try to get you to agree with me in my judgment. I may suggest to you that you do something concrete which shows your goodwill towards me so that we may restore our friendship, something that evidences a change of heart.
God knows that sin is bad for us. Therefore it is precisely because he is antecedently benevolent towards us when we sin, precisely because he forgives us when we sin, that he performs atonement for us, and seeks our repentance. He performs atonement for us because otherwise our sin would kill us (cf. Rom 6.23), and therefore his atonement comes from his forgiveness, rather than the other way around. Moreover he calls us to repent and admit fault, to confess our sins, etc., because in this way he can get us to flee from sin, to distance ourselves from it and no longer to love it, so that we may have life with him.
Importantly, I think punishment is compatible with forgiveness. In the case of some persons, God may insist on punishing them so that they learn the gravity of their sins, and so that they may be motivated to repent of them when they see they cannot go on in sin indefinitely but begin to suffer. In this way he corrects us like a parent would correct his child. Likewise, suppose someone commits a grave crime against me. It is compatible with my attitude of goodwill towards her that I still insist she be punished, so that she may learn that what she has done is wrong.
What isn't compatible with forgiveness is to punish or to insist on punishment without any concern for the good of the punished person at all. If you want to punish another person merely for the sake of punishment, merely because in this way it would satisfy you to see her get her comeuppance, all this seems to me incompatible with forgiveness. Remember that I defined forgiveness as a commitment to act out of benevolence and goodwill towards the person who has done you wrong. If this is so, then you cannot forgive and simultaneously refuse to think of the good of the person you are punishing.