Occasionally one meets with the idea that, granted, bringing in eternal life really does help a lot with the problem of evil or with hiddenness, nonetheless bringing in eternal life is a cheat because it begs the question or something like that.
I can see how one can object to the eternal life move by saying that some things are so horrendous that God shouldn't allow them even if he compensates those to whom they happened. Or that an omnipotent God shouldn't need to compensate. Or that God has some kind of a duty never to be hidden (but: surely a lover is permitted to hide for a while, since otherwise it would be wrong to play peekaboo with infants who don't understand about object persistence). But the "it's a cheat to bring in eternal life" move is not this move. Rather, it grants, at least for the sake of argument, that if there is eternal life, then God can have a justification for allowing the evil or being hidden.
I am having a hard time seeing how this "it's a cheat" move is supposed to work. Let T = theism, L = eternal life and E = the atheological arguer's favorite evil/hiddenness evidence. Then: T is equivalent to T&L or T&~L. Now to grant that eternal life would solve the problem would be to grant that P(T&L|E) is not significantly less than P(T&L). Now let the theist grant, in a spirit of mutual accommodation and simplification, that E is conclusive evidence against T&~L: P(T&L|E)=0. But now:
P(T|E) = P(T&L|E) + P(T&~L|E) = P(T&L|E).
But P(T&L|E) is not significantly less than P(T&L), it was granted. So, basically, the atheological evidence E lowered the probability of T to around the probability of T&L before that evidence.
Now, if in our background there is the fact that there are person, then P(L|T) is quite high. If God made persons, it is very likely that they (or at least those who do not deserve to not have it--there might be room for tweaking of what exactly L says), it is very likely that he made them to have eternal life. But if P(L|T) is quite high, then P(T&L) is pretty close to P(T). Since P(T|E) is not much smaller than P(T&L), it follows that P(T|E) is not much smaller than P(T).
So I just don't see how the "it's a cheat" move is supposed to work. Once one grants that the probability of T&L does not go down very much given E, then given the very plausible claim that most of the probability of T is contributed by T&L portion, it simply follows that the probability of T does not go down very much given E.

