To the untrained mind, there is no more difficult obstacle to belief in God than the omnipotence paradox. Supposedly, it makes it impossible for an omnipotent being to exist, and therefore makes it impossible for God to exist. The paradox reasons as follows:
There is nothing an omnipotent being is incapable of doing. This creates a type of question, usually like the following: can an omnipotent being create an object so large it cannot lift it? If it can, then it is not omnipotent, because there is something it cannot do: lift the object. On the contrary, if it cannot, then it is not omnipotent, because there is something it cannot do: create the object. It seems, then, that no matter what, the being cannot be omnipotent. It would appear that omnipotence is a logical contradiction, and thus any omnipotent being, including God, cannot exist.
This is definitely a tough question. At first glance, it may seem insurmountable. Then, however, an idea may occur to you. You may say, "Well, God created logic, and thus He is not subject to it." Although this answer appears satisfactory, it is in reality incredibly faulty. If logic were a physical or spiritual entity or system, then that would be reasonable, as God created all physical and spiritual entities and systems. However, logic is not a thing by any definition (also note that mathematics is like logic in this respect). Logic is an abstract necessary flow of truth; it is fundamental to the nature of reality itself. You can only define existence in logical terms, therefore if God exists (which He does), He would have to be subject to logic. Existence carries the restrictions of logical consistency. To say that something can exist without being logically consistent would require a radical redefinition of existence, thus anyone using a traditional definition of existence could claim that it does not exist. Nothing that is self-contradictory can possibly be, as it would violate a fundamental principle of reality. Since there is no concept of being outside of reality, everything that is real, God included, finds itself bound by logic.
You may protest at this point, "You seem to be attempting to prove that God cannot exist. After all, if existence is subject to logic, if omnipotence is self-contradictory, and if God is omnipotent, then He cannot exist." However, I am not finished. See, the fault in the omnipotence paradox is contained within the definition of omnipotence. In the omnipotence paradox, something or someone is omnipotent if there is nothing it cannot do. This is not appropriate. Omnipotence simply means "all-powerful." The word "all" is an enumerative word: it is not infinite in scope, but includes each of the items in a certain list. The question for omnipotence, then, is what the list is. The common misconception is that the "all" in "all-powerful" necessarily means every act of which we can conceive. This is a naïve and inappropriate view. People can conceive of illogical things and logical paradoxes, but we have already shown that all reality is dependent on logic. Thus, we must limit the scope of "all." In this case, "all" would apply to every act that is not a logical contradiction. Since the Bible never defines what kind of omnipotence God possesses, we can safely assume that God is not conceptually omnipotent, which would lead to a paradox, but is logically omnipotent. This means that God cannot do some things, such as make an object so big He cannot lift it, make a four-sided triangle, or make something exist in contradictory states. At first, you may object, thinking that this is degrading to God. However, this by no means insults Him. God made a reasonable, rational, and logical creation. "His invisible attributes are perfectly visible in the creation of the world; they are understood by created things." (Romans 1:20a). The order and logic God uses in His creation is evidence that He Himself is logical. We all know that God cannot violate His own attributes, thus it is perfectly reasonable and respectful to say that God can only do that which is logically permissible. In this case, then, the omnipotence paradox cannot disprove the existence of God (though it does negate the existence of an entity that can do anything conceivable).