The Paradox of Omnipotence
Can God create a rock so big that he cannot lift it? This question, like the Omniscience/Free Will Paradox, is viewed as an argument against the existence of God as He is commonly conceived, and is one of the most popular, next to The Problem of Evil. No matter how you answer the question, you seem to be admitting that God is not omnipotent. The God of Christianity claims omnipotence, therefore, He cannot exist. The argument goes like this:
(1) God either can or cannot create a rock that is so heavy that he cannot lift it.
(2) If God can create a rock that is so heavy that he cannot lift it, then God is not omnipotent.
(3) If God cannot create a rock that is so heavy that he cannot lift it, then God is not omnipotent.
(4) God is not omnipotent.
(5) If God exists then he is omnipotent.
(6) God does not exist.
This argument doesn't really work, though.
If we are to judge a Christian God, we must do so by examining the Christian text that describes Him. The ethical system we see at play in scripture is called situational ethics. Situational Ethics is the idea that actions are not intrisically good or evil, but they are made good or evil by the context in which they are performed.
For example, to kill one person to save ten is not the same as killing ten to save one, all other factors being equal. Likewise, killing one to save ten is not the same as killing one to save a thousand. Killing Adolf Hiter is not the same as killing Mother Teresa.
We can see many more examples of this in scripture. Throughout the Old Testament, the Lord commanded the children of Israel to break almost all of the Ten Commandments, but these things were acceptable for a specific context and condemnable for many others. Likewise, when Jesus was criticized by the Pharisees for breaking Levitical laws regarding the Sabbath, he said, “The sabbath was made for man, and not man for the sabbath:” (Mark 2:27). He also argued, “If one of you has a son or an ox that falls into a well on the Sabbath day, will you not immediately pull him out?” (Luke 14:6). The Lord also says in the Book of Mormon, “It is better that one man should perish than that a nation should dwindle and perish in unbelief.” (1 Ne 4:13)
So, according to a Christian text, a Christian God may perform any action depending on the context in which it is to be performed.
So with God all things are indeed possible, but not all things are possible all the time. He can perform any action which the current set of circumstances render “good”, whatever that might mean. So a set of circumstances might require that God creates a rock, but would not require that he lift it. Later, the circumstances might change such that He now needs to lift it. He would then find it within His power to lift it.
It may seem odd to places limitations on omnipotence, but He remains omnipotent because he still possesses all power. He is capable of performing any action. In fact, this may be the only true form of omnipotence, since it is the only intelligible way to answer the above paradox, while also reconciling the fact that "with god, all things are possible"(Matt 19:26) with the claim that "it was impossible for God to lie" (Heb 6:18). He must simply comply with the “good”, but that is not a new idea to Christianity. Many admit that God's power does not extend to logical contradictions, for example, like creating four-sided triangles or married bachelors.
Also, since the Bible also teaches that "[God] cannot lie" (Titus 1:2), our modern definition of "omnipotence" clearly does not apply in the way we'd think. So even if we ignore situational ethics the paradox would still not work because omnipotence in the sense that he can do any thing at any time is not an attribute he claims to have.
So can God create a rock so big that he cannot lift it? Yes, and He can lift it.