We have discussed the fact that God cannot do that which is illogical (make a rock so big he cannot move it), and he cannot do that which is a logical contradiction (make us free moral agents and prevent us from choosing evil at the same time).
There is one more thing that God cannot do. God cannot do anything that morally contradicts his own nature. For those of you who have studied philosophy, I am not going to get into the Euthyphro Dilemma or argue the Divine Command Theory. Suffice it to say, that the Bible reveals that what we know of goodness, rightness, justice, morality, ethics, law, etc., flow from the very nature of God. How can I grasp goodness apart from a God who is good? How do I really understand social justice apart from a God who is just?
To digress: A question that is often debated is relevant here; can someone be good (moral) without God? Well, yes and no; how’s that for being definitive? By saying yes, I mean that a person can be a moral person without believing in God. Atheists can be good people from a human point of view. However, by saying no, I mean that if God did not exist we would not know what good or right means in an absolute sense. Every culture might have its own code of “ethics,” but this code would have little significance in another culture. Thus there would be no Geneva Conventions, International Tribunals, International Criminal Courts (Hague), or International Courts of Justice (UN) because there would be no common understanding of morality by which justice could be determined.
Back to our main point: God, therefore, cannot do anything that is contrary to his own moral nature. In Hebrews 6: 18, it says that God cannot lie; Psalm 89:34, God cannot break his promise. James 1:13 says that God cannot be tempted with evil nor can he tempt anyone to do evil. In 2 Timothy 2:13 we read that God cannot deny himself, which in the context means that God can never be faithless or untrustworthy. Habakkuk 1:13 states that God “cannot look upon evil,” which means that he cannot approve of evil. Finally, in Malachi 3:6 God declares “For I the Lord do not change…” God is eternally consistent with himself; he is not subject to mood swings and never reconfigures himself for a new generation.
“It would be appropriate to say God cannot do what is incongruous with himself. He is morally prohibited from doing what is not right because that would be disconsonant with his own (nature) of rightness. The limitation on his ability…is not logical but moral.” (JonTal Murphree, Loving God and a Suffering World, 31)
In summary, there are 3 things that God cannot do: God cannot do that which is illogical (make something that has happened never to have happened); he cannot do that which is a logical contradiction (make a square circle); God cannot do anything that is against his own moral nature (he cannot lie).
Now, what are things God can do? Find out for yourself and read the Bible!