In addition, it will be helpful to review the article on the logical problem of evil over at the Internet Encyclopedia of Philosophy.
Mackie and McCloskey in the late fifties and early sixties did some work on the problem of evil and argued, like Frumious, Chany, and Todd (among others) that the following set of propositions form a logically inconsistent set:
(1) God is omnipotent (that is, all-powerful).
(2) God is omniscient (that is, all-knowing).
(3) God is perfectly good.
(4) Evil exists.
To say that the four propositions are logically inconsistent with one another is to say that they cannot all be true at the same time. Any two or three may be true, but all four cannot be true at the same time.
So this is the argument. God, if as Christians claim, is omnipotent and omnibenevolent, and omniscient, then evil cannot exist. But evil does exist. Therefore, God cannot exist.
Now what does it mean for two or more things to be logically inconsistent with one another? The encyclopedia tells us:
(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."
http://www.iep.utm.edu/evil-log/#H3
Therefore the very first responsibility that men like Frumious and Todd have, is to acknowledge that condition (a) is not met in the argument.
None of the statements in (1) through (4) directly contradicts any other. This is what I have been saying all along. The encyclopedia backs me up on this because the bolded portion is taken word for word from the IEP here:
http://www.iep.utm.edu/evil-log/#H3
Therefore, if they want to continue to argue logical inconsistency, then they must argue that condition (b) is met, i.e. that we can deduce a contradiction from that set. Notice that the IEP is saying the same thing I have been saying, using different words. I have stated ad nauseum that there is no explicit contradiction (the IEP uses the word direct instead of explicit) in the propositions in question and the IEP affirms this. So to meet condition (b) Frumious and Todd must have some argument(s) that show that a direct contradiction can be deduced from that set.
Notice what they can't do at this point. They can't just say that "it seems to me that they are directly contradictory, or that "by definition they are directly contradictory". It has already been established that they are not (see bolded portion). This is not even in question. So Frumious and Todd must have some arguments which they believe will show that a contradiction can be
deduced from the propositions. Notice the word deduced here. I will not go into detail about what deduction entails. Suffice it to say, deduction is not merely stating one's position. It is showing how one proposition follows another by the laws of logic and giving reasons for thinking the proposition is true.
So what course do they have. They can admit that while there is no explicit contradiction, once we think about what these terms like omnibenevolent and omnipotent mean, we can deduce a contradiction from them. They reason thus:
(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.
But evil exists.
Therefore:
(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.
So the line of reasoning is that
(12) If evil and suffering exist, then God is either not omnipotent, not omniscient, or not perfectly good.
(13) Evil and suffering exists and therefore God is either not omnipotent, not omniscient, or not perfectly good.
Notice how propositions (6) through (12) are given to show that proposition (13) can be deduced from (1) through (3).
This is what Frumious and Todd have been attempting to do. Here the line of reasoning is organized and presented as one proposition following another by the laws of logic.
Therefore, in light of the evil and suffering we find in our world—if God exists, he is either impotent, ignorant or wicked, the logical contradictory of (1) (2) and (3) and since the argument is raised against the Christian who affirms (1) (2) and (3), the Christian must now attempt to show that all four propositions can be logically compatible or consistent after all.
This raises the question of what it means for propositions to be logically consistent.
(15) A set of statements is logically consistent if and only if it is possible for all of them to be true at the same time.
http://www.iep.utm.edu/evil-log/#H3
So I and any other defender of the Christian conception of God who desires to rebut the logical problem of evil argument, needs to show how the four propositions can be logically consistent. If this is done, then the argument has been defeated, dissolved, destroyed, done away with, rendered impotent or whatever you want to call it. IOW, it should be abandoned.
The following explication on what entails logical consistency will demonstrate how enormously ambitious the logical problem of evil is and what an enormous burden its proponent must bear. The IEP states:
Notice that (15)
does not say that consistent statements
must actually be true at the same time. They may all be false or some may be true and others false. Consistency
only requires that it be possible for all of the statements to be true (even if that possibility is never actualized). (15) also doesn't say anything about plausibility. It does not require the joint of a consistent set of statements to be plausible. It may be exceedingly unlikely or improbable that a certain set of statements should all be true at the same time. But improbability is not the same thing as impossibility.
As long as there is nothing contradictory about their conjunction, it will be possible (even if unlikely) for them all to be true at the same time.
The IEP is clear.
This brief discussion allows us to see that the atheological claim that statements (1) through (4) are logically inconsistent is a rather
strong one. The atheologian is maintaining that statements (1) through (4) couldn't possibly all be true at the same time. In other words,
(16) It is not possible for God and evil to co-exist.
If the Christian can come up with a proposition that is merely logically possible to conjoin to the one's in question that entails nothing contradictory about their conjunction, the Christian will have succeeded in demonstrating that there is no logical inconsistency after all.
Take proposition:
(17) It is possible that God has morally sufficient reasons for allowing evil.
The IEP states:
If it is possible that God has a morally sufficient reason for allowing evil and suffering to occur, then the logical problem of evil fails to prove the non-existence of God. http://www.iep.utm.edu/evil-log/#H3
And it certainly is logically possible. It need not be true that God has morally sufficient reasons, it need not be plausible. But if it is merely logically possible, then the argument fails.