Here is an article by Steven Cowan about the problems of evil and suffering.

Intro:

The problem of evil is no doubt the most serious challenge to belief in God. Even religious believers find it troubling that evil exists in the world—and so much evil! It is puzzling, to say the least, that an all-powerful, absolutely good being would allow evil to exist in his creation. And yet it does. Evil and suffering exist and they are often overwhelming in their magnitude.

Now let’s find out what a noseeum is, and how it relates to the existence of evil and suffering:

However, perhaps God’s existence is incompatible with a certain kind of evil that exists. For example, the atheist William Rowe has argued that God’s existence is inconsistent with pointless or gratuitous evil. By “pointless evil,” Rowe means evil that does not and cannot serve a greater good. And Rowe believes that there is such pointless evil in the world. He thus concludes that God does not exist. Rowe’s argument may be simply stated as follows:

1. If God exists, there would be no pointless evil.
2. There is pointless evil.
3. Therefore, God does not exist.

[…]But, is there pointless evil in the world? Rowe thinks there is. To show that there is pointless evil, Rowe introduces what he calls the “noseeum inference.” Like the pesty little bugs that some readers may be familiar with, a “noseeum” is something that you cannot see—it is a “no-see-um.” And a noseeum inference is a conclusion drawn on the basis of what one does not see. The basic structure of all noseeum inferences looks like this:

1. I cannot see an x.
2. Therefore, there probably is no x.

We all make noseeum inferences everyday of our lives. Every time I go to cross a street, I look both ways and I step out into the street only after I “no-see-um” a car coming.

[…]Rowe applies this kind of noseeum reasoning to God and evil. Rowe suggests that if we cannot see a reason for a particular instance of evil, then there is probably not a reason. Suppose we hear about a very young child who is tortured to death to amuse some psychotic person. We think about this event and we examine all the circumstances surrounding it. No matter how hard we try, we cannot see any good reason why this child had to suffer the way she did. Since we cannot see a reason why God would allow this child to suffer, there probably is not a good reason—the child’s suffering was pointless. Of course, Rowe would be quick to point out that he is not speaking merely hypothetically. There are cases like this in the news every day—real-life cases in which we shake our heads in frustration, wondering why God would allow such a thing.

Is Rowe correct in his conclusion? Do such examples prove that there is pointless evil in the world? I don’t think so. To see why, we must recognize that noseeum inferences are not all created equal. Some noseeum inferences, as we have seen, are reasonable and appropriate. But, many are not. Suppose I look up at the night sky at the star Deneb and I do not see a planet orbiting that star. Would it be reasonable for me to conclude that there is no planet orbiting Deneb? Of course not. Suppose that using the best telescopes and other imaging equipment presently available, I still cannot see a planet around Deneb. I would still be unjustified in concluding that there was no such planet.

In that example, the planet is the noseeum. Just because you look really hard, you can’t be confident that the planet is not there. And similarly with the problem of evil and suffering, looking really hard and finding no reason does not mean that there is no reason. It just means that you are not in a good position to see the reason. You don’t know enough to to be sure that there is no reason, because of your limitations as a human being.

To know that any given instance of evil or suffering is gratuitous/pointless requires a high level of knowledge. How much knowledge? Well, consider this paper by the late William Alston of Syracuse University, who lists six problems with the idea that humans can know that any particular instance of evil and suffering is gratuitous. (You can get the PDF here)

According to the paper, human beings just do not have the capability to know for certain that God has NO morally sufficient reason for allowing any particular instance of evil and/or suffering. God’s morally sufficient reason is a noseeum. To know for sure that there is no reason, we would need to have more knowledge than we do.

Also, remember that on the Christian view, the good aim that God has is NOT to make humans have happy feelings in this life, regardless of their knowledge, wisdom and character. That’s what atheists think, though. They think that God, if he exists, is obligated to make them feel happy all the time. They don’t think that God’s goal is being actively involved in forming their knowledge, wisdom and character. God has a purpose – to work in the world so that everyone who can freely respond to him will respond to him. The Bible says that allowing pain and suffering is one of the ways that he gets that group of people who are willing to respond to respond to him – FREELY. To be able to claim that evil is gratuitous, the atheist has to show that God can achieve his goal of saving all the people he wants to save while permitting less suffering in the world. And that is a very difficult thing for an atheist to show, given our human cognitive limitations.