I know. You didn’t think there was anything God couldn’t do. Well, as John Frame explains in his excellent book The Doctrine of God (pp.518-521), there are several things He can’t do, namely:
1.) Logically contradictory actions, such as ultimately saving and condemning the same individual, making a round square, or making a rope with only one end. God’s illogicality is prevented by His righteousness, faithfulness, truth, rational speech, knowledge, and wisdom. In other words, because of His strengths, not weaknesses.
2.) Immoral actions, like lying, stealing, coveting, and breaking His promises.
3.) Actions appropriate only to finite creatures, like buying shoes, celebrating one’s birthday, or taking medicine for a cough. God’s inability to do these things is not due to any lack of power. He is quite capable of taking on human form and doing all these things. His “inability” exists only in His nonincarnate state, and in that state, the reasons He “cannot” do these things pertains to His strengths, not His weaknesses.
4.) Actions denying His own nature as God, such as making another god equal to Himself, abandoning His divine attributes, or absorbing the universe into His own being. God necessarily exists as the one true God. If He were to perform any of these actions, He would no longer exist as the one true God. The world would then no longer be a theistic universe, but rather a chaos. But in fact there could be no such world. So these actions are impossible. Even God cannot perform them.
5.) Changing His eternal plan. God’s eternal plan is unchangeable.
6.) Making a stone so large that He cannot lift it. This is the famous “paradox of the stone,” loved by philosophers. What keeps God from making such a stone is His infinity–again, not a weakness, but a strength.
So, even God’s “weaknesses” and “inability” are due to His strengths. How awesome then is our God?