The "Problem of Evil" is a problem for theists who believe in a good, powerful God.

If there is bad stuff in the world ("evil"), which there seems to be, it is puzzling, at least, why a good God would allow that to be.

The "logical problem of evil" says there is a contradiction here and that if by "God" we mean an all powerful and all good (and all knowing) god, then it can be deductively proven that there is no such God, given that there is evil in the world. The argument, in short, is this:

	If there is an all good, all powerful God, then there would not be evil in the world.
	There is evil in the world.
	There is not an all good, all powerful God.

The "evidential problem of evil" says simply that the amount and kind of evil that exists in the world provides strong inductive support for the claim that there does not exist a powerful all good God.