(P1) If God exists, he is perfectly loving.
(P2) If a perfectly loving God exists, he wouldn't allow non culpable unbelief (non-belief and disbelief? I think both).
(P3) However, there is nonculpable unbelief.
(P4) Therefore a perfectly loving God doesn't exist.
(C) Therefore, there is no God.
Some authors think that you can have a meaningful relationship with God even if you don't believe that God exists. Dougherty and Poston offer this example:
Suppose that Jones – an unfortunate fellow – is locked in solitary confinement in a dark prison cell. Jones hears faint taps coming from the other side of his prison wall. The taps resemble the presence of another person willing to communicate, but it is not certain that there is another person in the other cell. Yet, Jones begins to tap back. Suppose this activity continues over a long period, and Jones can – with some effort – make sense of the taps as another person attempting to communicate with him. Suppose Jones’s credence (his degree of belief, rational confidence, or what have you) on the claim ‘there is another person in the cell beside me’ is 0.5. He seems to be discerning messages, but he realizes that it could just be in his head since the signs are ambiguous. Yet, given that the two persons are tapping back and forth to each other, it seems that they are in a personal relationship, one which in time could take on great significance (again, this latter part is of great importance). The interaction could be so meaningful and hope-inducing that it keeps Jones from going insane or perhaps even keeps him from dying or killing himself. Suppose also that, in fact, the tapping is coming from Smith who, many years later, meets up with Jones and they discover what was going on. We submit that this part of their relationship will take on new-found significance in their new relationship, something to look back on and cherish, and a surprisingly good foundation for deepening their relationship now that Jones’s credence has been raised to moral certainty by actually meeting Smith.
The case isn't supposed to cover the case of non-culpable disbelief, only to show that you can have a meaningful relationship given only partial belief (and a very low degree of belief, to boot).
What to make of the case? It's clear that the tapping can be meaningful in some sense, but it's also clear that it can be meaningful without being a meaningful relationship. Consider two versions of the case. In the first, Smith and Jones meet after being released from prison. In the second, Smith dies in prison and Jones learns about Smith from Smith's widow. In the second case, it seems it would be very, very weird for Jones to say this:
Yes we had a meaningful relationship for years, but we never met and I didn't know he existed until now. I always thought it was just as likely that he was a drip or a branch hitting a window.
Yet, that seems to be how they want to describe the case. If they resist this description of the case and say that there wasn't ever a meaningful relationship between Jones and Smith, I think they face some serious trouble. Focus now on their version of the case, the one with the happier ending. To show that there's a meaningful interpersonal relationship without belief in their version of the case, they'd have to say that the relationship became meaningful because they later met. Intuitively, whether the tapping constitutes a meaningful relationship shouldn't depend upon whether they meet later. It would be odd to think that the proper description of the relations between them while in prison depended upon what happens in the future.
I think there's a simpler solution to all this. Reject 2. A life of unbelief isn't the worst thing in the world. (Surely it's better to let a handful of rational people never believe in God than allow a handful of genocides.) If you're a theist, you have to think that God is permitted to let (literally) the worst things in the world happen. Done and done.