Alvin Plantinga's solution to the deductive problem of evil

Back in December I was talking to a friend of mine about Alvin Plantinga's solution to the deductive problem of evil (DPE) in God, Freedom, and Evil. The DPE goes something like this:

1. If God exists, evil does not exist.
2. Evil exists.
3. Therefore, God does not exist.

where "God" is understood as a being who is all knowing, all powerful, and all good.

Plantinga's solution was basically to show that the first premise is not true. The first premise is based on the idea that "God exists" is inconsistent with "Evil exists," so all Plantinga did was undermine that idea by showing that "God exists" is not inconsistent with "Evil exists."

There are two ways they might contradict each other--explicitly or implicitly. An explicit contradiction is a situation where you have A and not-A. For example, "God exists," explicitly contradicts, "God does not exist."

And implicit contradiction is where two claims lead to an explicit contradiction when taken to their logical conclusions. For example, "All men are mortal," implicitly contradicts "Socrates is not mortal." The way to show that the two claims are contradictory is by adding a true premise to the set such that together with one of the other premises entails the negation of the final premise. To the set, "All men are mortal," and "Socrates is not mortal," can be added "Socrates is a man." Then you can draw out the contradiction like this:

1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.

But "Socrates is mortal," explicitly contradicts "Socrates is not mortal," so by adding "Socrates is a man," it can be shown that "All men are mortal" implicitly contradicts "Socrates is not mortal."

To solve the DPE, Plantinga first noted that there is no explicit contradiction between "God exists" and "Evil exists." If they contradict at all, it must be implicitly, which means some true premise must be found that when added to the set, results in an explicit contradiction. Second, Plantinga pointed out that no such premise had yet been found; therefore, nobody had yet demonstrated that there is a contradiction. Third, rather than sit around hoping nobody would ever discover the necessary premise, Plantinga came up with a way to show that no premise would ever be found. He did it by proving that "God exists," does not contradict, "Evil exists."

The way he went about proving that "God exists" is logically consistent with "Evil exists," is by finding a premise that is possibly true, and that together with "God exists," entails that "Evil exists." If "God exists" together with some other premise logically entails that "Evil exists," then "God exists" and "Evil exists" must be logically consistent.

He claimed that the premise need not necessarily be true. It only had to describe a possible state of affairs. When I read that, I wasn't clear on why it needed to only be possible.

That brings me to my own contribution to Plantinga's argument. After thinking about it, I discovered why, and I think I can explain using possible world semantics. You see, if "God exists" really does contradict "Evil exists," then it's not even possible for both of them to be true at the same time and in the same sense. That's the law of non-contradiction. Using possible world semantics, you would say that "God exists" and "Evil exists" are not true in any possible world. So all you have to do is find some possible world--some possible state of affairs--in which "God exists" and "Evil exists" are both true. Here's the argument in syllogisms:

1. If two propositions are contradictory, then they cannot both be true in any possible world. (This is just the law of non-contradiction stated in possible world semantics.)
2. There is a possible world in which "God exists" and "Evil exists" are both true. (This will be demonstrated in the next syllogism.)
3. Therefore, "God exists" and "Evil exists" are not contradictory.

To prove the second premise, you can form another syllogism:

4. God exists.
5. God created a world with evil and has a good reason for doing so.
6. Therefore, evil exists.

The fifth premise is the premise Plantinga added to show that "God exists" and "Evil exists" are logically compatible. The question now is whether or not the fifth premise is actually possible. Remember that it need not be actually true. It only needs to describe a possible state of affairs. In other words, it has to be true in some possible world. If it's true in some possible world, then the second premise in the former syllogism is true.

To show that the fifth premise is possible, all you have to ask, really, is whether or not there can be such a thing as a good reason for an evil. Several scenarios can then be mentioned. For example, dentists cause pain in order to fix teeth. It may be objected that this scenario doesn't apply to God since God could fix teeth without causing pain, but all we're trying to prove is whether or not it's possible for there to be a good reason for evil, and the scenario shows that it is. If it's possible for there to be a good reason for evil, then it's also possible that God has a good reason for evil.

And that's all that's necessary to solve the deductive problem of evil.