If god can do anything, can he make a rock so big that even he cannot pick up?

It is not the Christian view that God is all-powerful in the sense that He can do any absurd thing that might enter into your head. He is omnipotent in the sense that He can do whatever He wills, but He can only will that which is according to His character. God cannot lie, He cannot deny Himself, and He cannot do logically contradictory things. As all-powerful, he can lift a stone of any size and weight. (Even if the umption of this objection is granted, it presents no barrier to God lifting the stone. If God can do one contradictory thing, which is to be an all-powerful God yet not powerful enough to lift the stone, then He can do a second contradictory thing, which is to lift the stone too big for Him to lift.)