I suggest taking a gander at iep.utm.edu but...
A person is justified in believing that X does not exist if
(1) all the available evidence used to support the view that X exists is shown to be inadequate; and
(2) X is the sort of entity that, if X exists, then there is a presumption that would be evidence adequate to support the view that X exists; and
(3) this presumption has not been defeated although serious efforts have been made to do so; and
(4) the area where evidence would appear, if there were any, has been comprehensively examined; and
(5) there are no acceptable beneficial reasons to believe that X exists
This idea was proposed by Martin concerning the existence of God.
And sort of a long excerpt from an article on the Logical Problem of Evil.
Mackie and McCloskey can be understood as claiming that it is impossible for all of the following statements to be true at the same time:
(1) God is omnipotent (that is, all-powerful).
(2) God is omniscient (that is, all-knowing).
(3) God is perfectly good.
(4) Evil exists.
Any two or three of them might be true at the same time; but there is no way that all of them could be true. In other words, (1) through (4) form a logically inconsistent set. What does it mean to say that something is logically inconsistent?
(5) A set of statements is logically inconsistent if and only if: (a) that set includes a direct contradiction of the form “p & not-p”; or (b) a direct contradiction can be deduced from that set.
None of the statements in (1) through (4) directly contradicts any other, so if the set is logically inconsistent, it must be because we can deduce a contradiction from it. This is precisely what atheologians claim to be able to do.
Atheologians claim that a contradiction can easily be deduced from (1) through (4) once we think through the implications of the divine attributes cited in (1) through (3). They reason as follows:
(6) If God is omnipotent, he would be able to prevent all of the evil and suffering in the world.
(7) If God is omniscient, he would know about all of the evil and suffering in the world and would know how to eliminate or prevent it.
(8) If God is perfectly good, he would want to prevent all of the evil and suffering in the world.
Statements (6) through (8) jointly imply that if the perfect God of theism really existed, there would not be any evil or suffering. However, as we all know, our world is filled with a staggering amount of evil and suffering. Atheologians claim that, if we reflect upon (6) through (8) in light of the fact of evil and suffering in our world, we should be led to the following conclusions:
(9) If God knows about all of the evil and suffering in the world, knows how to eliminate or prevent it, is powerful enough to prevent it, and yet does not prevent it, he must not be perfectly good.
(10) If God knows about all of the evil and suffering, knows how to eliminate or prevent it, wants to prevent it, and yet does not do so, he must not be all- powerful.
(11) If God is powerful enough to prevent all of the evil and suffering, wants to do so, and yet does not, he must not know about all of the suffering or know how to eliminate or prevent it—that is, he must not be all-knowing.
From (9) through (11) we can infer:
(12) If evil and suffering exist, then God is either not omnipotent, not omniscient, or not perfectly good.
Since evil and suffering obviously do exist, we get:
(13) God is either not omnipotent, not omniscient, or not perfectly good.
Putting the point more bluntly, this line of argument suggests that—in light of the evil and suffering we find in our world—if God exists, he is either impotent, ignorant or wicked. It should be obvious that (13) conflicts with (1) through (3) above. To make the conflict more clear, we can combine (1), (2) and (3) into the following single statement.
(14) God is omnipotent, omniscient and perfectly good.
There is no way that (13) and (14) could both be true at the same time. These statements are logically inconsistent or contradictory.
Statement (14) is simply the conjunction of (1) through (3) and expresses the central belief of classical theism. However, atheologians claim that statement ( 13) can also be derived from (1) through (3). [Statements (6) through (12) purport to show how this is done.] (13) and (14), however, are logically contradictory. Because a contradiction can be deduced from statements (1) through (4) and because all theists believe (1) through (4), atheologians claim that theists have logically inconsistent beliefs. They note that philosophers have always believed it is never rational to believe something contradictory. So, the existence of evil and suffering makes theists’ belief in the existence of a perfect God irrational.