At its core, the PoE is a form of reductio ad absurdum whereby some set of premises is adopted for the sake of argument in order to show that they lead to a contradiction or incongruency. This means that not everybody is going to accept the premises by fiat: that's okay, that simply means that the argument doesn't apply to their version of gods. Keep that in mind before posting objections in the form of "well I don't accept this premise": the argument isn't aimed at you, then.
As a quick bit of history, one of the most popular formulations of the Problem of Evil is attributed to Epicurus (this is paraphrased for modern sensibilities):
Over the long years, people have had a lot of responses to this basic PoE (called theodicies): examples include the soul-making theodicy (whereby God doesn't prevent evil because it's necessary for suffering to be possible for people to grow as people), free will theodicies (whereby God doesn't prevent suffering as it would presumably interfere with His creation's free will), and so on. Theodicies attempt to pre-empt the PoE by making some excuse, essentially, for why God would allow evil. Theodicies acknowledge that the PoE is a problem and attempt to give an explanation for the apparent incongruency between an omni-God and the existence of evil.Epicurus wrote:Is God willing to prevent evil, but not able? Then He is not omnipotent.
Is He able, but not willing? Then He is malevolent.
Is He both able and willing? Then whence cometh evil?
Is He neither able nor willing? Then why call Him God?"
Eventually, the notion of PoE defenses arose: these would be different from theodicies because they deny the PoE is a problem in the first place by asserting that it's possible for evil to exist alongside an omni-God without contradiction (such as Plantinga's famous free will defense and Transworld Depravity, introduced in Plantinga's "Nature of Necessity" and fleshed out in "God, Freedom & Evil").
The PoE is generally separated between attempts to show a hard logical contradiction (the "logical PoE") and attempts to show that it's at least very reasonable to find it unlikely that a God with the properties laid out in the premises is congruent with the observed world (the "evidential PoE"). With Plantinga's free will defense, the theological community (and to some extent the wider philosophical community) held the logical PoE to have been defeated. There have been some that disagreed (I am among them, Plantinga makes some wonky definitional assumptions in "God, Freedom & Evil," but that is probably for another post. I have had multiple correspondences with Plantinga about the PoE and it'd probably make for a good post). Regardless of whether the logical PoE was defeated, the evidential PoE has been alive and well.
With all of that out of the way, I will move into my version of the argument. I will be presenting this in a conversational rather than syllogistic way: this is mostly because I'm terrible at melting down grand concepts into syllogisms without forgetting some important detail and having to go back and edit them 1,000 times.
First, what sort of God is this argument aimed at? It's aimed at what I perceive to be a relatively common conception of God as a being with omnipotence, omniscience, omnibenevolence, a being which created the world, and a being that is interested in some of its creations to have free agency*. I will provide working (not exhaustive!) definitions for each of these below.
Omnipotence: For the purposes of this argument, omnipotence is the capacity to actualize any logically possible state of affairs. This avoids silly paradoxes like "making a rock so large He can't lift it," or any other irresistible force meets immovable object type paradox (these are not logically possible, so we don't have to worry about them).
Omniscience: For the purposes of this argument, it's sufficient for an omniscient being to know every possible truth and avoid believing every possible falsity. We do not have to worry about deeper nuances such as "can God predict an exact free will choice," that will be irrelevant here.
Omnibenevolence: This is probably the trickiest one to nail down. For the purposes of this argument, a being is omnibenevolent if it doesn't desire to cause suffering and purposefully takes every measure logically possible to prevent its gratuitous instantiation. This definition leaves open the door for certain theodicies which will be addressed piecemeal at the end.
For the sake of brevity I will be calling a being that has these three properties an "omni-being" or "omni-max being."
(* -- sidebar about free agency. I abhor the free will debate. Whether or not we have free will, to whatever degree (from compatibilism to causa sui/libertarian, does not matter too much to this argument. What matters is that created beings may have free will or at least the illusion thereof.)
The argument proceeds along the lines of the usual PoE: if an omni-max being could have created a world in which some kind of suffering isn't possible, yet chose to create a world where that suffering is possible, then the omni-max being is culpable for the existence of that suffering. Consider an engineer that has the knowledge and power to build a bridge. If the engineer understands that the bridge needs to withstand certain conditions to avoid collapsing, the engineer has the ability to do this (but chooses not to), then the engineer is culpable for the bridge collapsing.
So, is there a kind of suffering in the world that doesn't have to exist: could God have made a world in which some form of suffering we experience didn't have to be possible? Yes. I'd like to draw a distinction for instance between physical suffering and emotional suffering. If one of the premises is that God wants to create a world with free agents, then it seems that there are some emotional forms of suffering that God couldn't prevent as a consequence of this choice: for instance, if friends or lovers break up with each other, or a friend telling a lie to another, or unrequited love. Since it's necessary for people to be able to make choices like that to have free agency, God can't prevent that sort of suffering despite being omni-max (and so isn't culpable for it).
However, consider physical suffering: stubbed toes, disease, "natural" suffering (e.g. animals suffering due to natural circumstances), anything that causes suffering due to the laws of physics. Could God have created a world in which physical suffering doesn't exist while retaining the premises? Can a God with this arguments' premises be held culpable for suffering as a result of physical processes? The answer to both of these questions is "yes."
It is possible for an omni-max being to create a world in which physical suffering categorically doesn't exist (with caveats**) yet retains all of the premises, including free agency. Swinburne called such a concept a "Toy World." While this seems counterintuitive at first, it's easily cognizable by considering that if something can be simulated, then an omni-max being could actualize a world like that simulation. As any video gamer that's ever typed "iddqd" into Doom (or used whatever other invincibility cheats on any games) can tell you, it's quite easy to simulate a world friendly to free agency yet in which the laws of physics are incapable of physically harming the free agent.
We could suppose that an omni-max being could create a world with conditional physics, for instance: if a knife were to cut tomato flesh to create a salad, then it is physically permitted. If that same knife would cut human flesh, perhaps it loses all inertia. We can imagine any plethora of such conditional physics and understand that an omni-max being would have the power to instantiate them and the knowledge of how to do so perfectly such that free agents need never fear physical harm of any kind.
Would free agents still be free in such a Toy World? I think it's obviously so. In such a world you would still wake up, decide what to wear, decide who to hang out with, what movie you want to see that day, where to go with your friends, and so on. In every relevant way you would still have freedom of agency.
So we come full circle to the argument: if God could have created a Toy World while maintaining all of the premises, yet chose not to, then that's equivalent to God consciously choosing to inject physical suffering into the world (since He had the ability to do otherwise, and He knew there was an alternative). Yet consciously choosing to create a world with physical suffering when it's possible to do it otherwise is incongruent with the idea that God is omnibenevolent. By reductio ad absurdum, one or more of the premises would have to be wrong.
Now, let me pre-emptively take care of a few objections that might crop up.
Objection 1: What about the physical suffering people cause against other people? The answer is that in a Toy World, people wouldn't be able to physically harm one another: the physics of the world wouldn't allow it. This doesn't mean that people wouldn't be free agents, however. For instance, right now, I'm not able to walk on my ceiling or teleport to Mars: I'm physically incapable of doing these two things. Does my inability to do a few physical things relegate me to a non-free status? Of course not!
Objection 2: Isn't a person that can't stab another person less free than someone who can? My reply essentially boils down to: so what? Is this a good sort of freedom to have? Right now, I'm physically unable to perform all kinds of exotic attacks against other people such as morphing my body into a hideous monstrosity a la John Carpenter's "The Thing," or spit acid at someone, or perform strange and gruesome tortures one might see Freddy Krueger or Pinhead perform on a victim. Does that make me "less free" than I otherwise would be if I could do those things? Would it be good if I could do those things? I really don't think so.
Objection 3: What if we insist the number of freedoms does matter? My reply here would simply be this: I have already listed several things I am not free to do that are essentially morally neutral (such as walking on the ceiling or teleporting to Mars). If the sheer quantity of freedoms is deemed important, then God certainly has the power to grant a non-harmful freedom for every harmful physical freedom prevented with the laws of physics.
Objection 4: But suffering is necessary for some good things: you can't have heroes like firefighters without house fires, right? My response to this theodicy (an offshoot of soul-making theodicy) is that I find this sort of argument absurd. What makes a hero or a firefighter "good" at all if the thing that they fight doesn't exist? This is sort of like arguing that it's worth it to create a disease just so someone can be a hero and invent a cure. Would you rather live in the universe that has smallpox so you can celebrate the person that cures it as a hero, or would you rather live in the universe where smallpox simply never existed in the first place?
(** -- the caveat I mentioned earlier is this: what causes suffering is something like a sliding scale. If we were to remove every kind of physical suffering in the world except for stubbed toes, then stubbed toes might seem so awful to us (as we have nothing to compare them to) that they might seem as bad as murder seems to us now. I find the feeling of walking on grass in my bare feet unpleasant, though I love sand. In a world without physical suffering, would I still consider it physical suffering to walk barefoot on grass? That might be possible. So a potential objection is that even a Toy World isn't totally devoid of physical suffering; and could ask "well is God culpable for that?" The way around this is to set some definitive bar that would definitely not exist in a Toy World, and a really easy one to consider is physical death due to bodily harm. Then we are dealing with a dichotomy rather than a sliding scale: does the world allow for death due to bodily harm or not? In a Toy World, it wouldn't. This is an interesting complication so I felt it necessary to bring it up here.)
Interesting sidebar: There are some people that don't require too much convincing that a Toy World is possible: after all, many theists believe in concepts like Heaven which is ostensibly a place of existence where physical suffering does not exist, to some. (Others argue there's more to it, I know; but you get the point).
