The PoE-giver might respond with something like, "well, what possible greater good could there be for something like child leukemia, or any other form of egregious suffering?" This is usually when the theodicy I'm interested in comes out: the theist might say, "well, as we are mere humans and can't presume to know the mind of God, all that we can know is that God has a good reason to allow child leukemia such that it isn't incongruent with God's benevolence to allow it."
I think that this line of theodicy is problematic in that it's invincible, and feels very similar to special pleading. It's a kind of trap that -- once accepted -- might never be un-accepted because God could literally do anything at that point, even kicking puppies in the street and laughing maniacally while they fly, and the excuse could still be made: "Maybe He has an unknowable reason for this such that it's good, even though it appears evil."
We can construct an analogy if we get all of the same pieces that make up this theodicy: all we need is something smarter than us to cause suffering in some way and then the same excuse can be made. But I'll get to that in a moment. First I need to discuss toy worlds (as hinted in the title) because first we must answer the question of what suffering God is even accused of being culpable for.
I submit that it's possible for an omnipotent and omniscient being to have created a universe where the physics simply doesn't allow for the existence of physical suffering while preserving free will (to pre-empt another common theodicy). An omnipotent and omniscient being should be able to make physics such that everything from natural disasters to debilitating genetic disorders to gunshot wounds to stubbed toes is physically impossible. It's easy to imagine, too; particularly if you've ever used a cheat code in a video game: if physics incapable of harming people can be simulated, it's certainly the case that an omnipotent being could actualize it and an omniscient being could conceptualize it. I will borrow Swinburne's term "toy world" for such a category of world (where physical suffering isn't possible because the physics don't allow it).
It follows that if an omnipotent and omniscient being created a universe wherein physical suffering is plentiful -- if we look out and we see a world ravaged by heinous amounts of suffering, grotesque possibilities that are able to be actualized, privation, starvation, disease, violence, and so on, all of it preventable if there were simply different physics -- it follows that if the world is that way instead of otherwise, then it has to be because the omnipotent/omniscient being deliberately chose it to be that way. God is culpable for *all* physical suffering, in other words: every last bit of it; even in instances where He didn't pull the proverbial trigger, He had to have set the laws of the universe in such a way that it was possible to happen (and deliberately so: there is no such thing as unforeseen consequences to an omniscient and omnipotent being; it is always "a feature, not a bug" with such beings).
The question the PoE-giver is asking in this instance is, "if God is omnipotent and omniscient, then He is culpable for the existence of physical suffering in the world." The theist may give the greater good theodicy by responding, "well, maybe God had a good reason for building the universe with physical suffering." The PoE-giver may ask, "ok, what reason?" The theodicy-giver responds, "well, since we are mere humans, we can't know. It's beyond us to know."
And there it is: the problem. It smells so much like special pleading, and as I've mentioned above, it's an invincible line of argument. God could do anything at all and the excuse would still work: God could torture babies and laugh maniacally and there still may be some reason so inscrutable for why it's actually good and not evil that maybe we can't know it.
Is it reasonable to reject a line of argument that's invincible in order to avoid such a trap? Can we reasonably use the evidence of observation -- "this appears incongruent with benevolence" -- and rationally affirm that maybe the being perpetrating whatever act is actually not benevolent? I think that it is. It is true that we're epistemically limited, and technically true that any apparent perception might be false for unknowable reasons beyond our limitation: but it's epistemological chaos to embrace this excuse as a crutch, isn't it? At that point wouldn't we have to throw up our arms and say that anything we think is true might actually be false because we're epistemically limited and there might just be some unknowable reason why we're wrong about it? Isn't this exactly what we see in special pleading fallacy?
This brings us back to the analogy I wanted to build.
Suppose that you have a pocket dimension that is a toy world: in this universe, people have free will, but the physics of the universe do not allow for suffering. There is no disease, no privation of resources. If someone tries to stab someone else, the knife loses all inertia (or something, there are any number of ways to build physics without suffering). People still have free will, however: they are able to decide what to do on a given day, whom to spend it with, whether to write a book or watch a film or engage in sports or whatever.
Now, say there is an alien creature with immense technological power that is truly far more intelligent than humans: it's not just that their civilization has existed longer to research technology longer, it's that they are truly simply mentally superior to humans in that they're able to conceive of things that humans can't even begin to comprehend, even if the creature attempts to teach humans from the ground up.
Let's say this alien creature uses technology to slide into our toy world pocket dimension and sees that there is no suffering, everyone is bustling about their days just enjoying themselves. "Oh, this won't do at all," the alien says.
The alien gathers people in the town square and announces that she is much smarter than they are (and is able to prove it, too), and that she is benevolent and wants to give everyone a very important gift. She builds a particle accelerator that changes the vacuum state of the pocket universe (or whatever, just go with it), changing the physics of the pocket universe. Suddenly, earthquakes rock the land! Children start to be born with debilitating physical defects. Disease starts to emerge. People find that they're suddenly able to physically assault and hurt one another (the term "innocent victim" has to be created, as they didn't have it before!)
"You see?!" The alien asks. "Isn't this so much better, can't you see how benevolent I am?"
Now, obviously, and it seems to me quite reasonably, a lot of people may suppose that even though the alien is smarter than they are and that it might technically be true they could have some unknowable reason for doing what they did, that maybe the alien simply isn't benevolent regardless of their claim that they are.
Another group of people, though, develops the greater good theodicy: they accept that the alien is benevolent and they reason "the alien is smarter than us: she says she has a good reason to do this so I guess she must have a good reason." But how does this group ever disabuse themselves of this notion? If the alien starts running through the streets with a ray gun blasting people with a ray that turns them inside out for a horrible death, Mars Attacks style, shouting "do not run, I am your friend," is there ever a point that it's reasonable for people to think, "ok, maybe she isn't actually our friend?"
If there is such a point where it's more rational to reject the greater good theodicy than it is to accept it, can the theodicist be convinced by the heinous amounts of suffering in the world that the threshold is met?
--Richard Feynman