By Elias Ayala (MDiv & M.A.T.)
The simple answer here is no, God cannot do the impossible. For God to perform that which is impossible is a contradiction in terms. For if God performed the impossible then that which was impossible was in fact possible because God performed it or accomplished, hence demonstrating that it was in fact possible. Now it is true that Jesus said, “with man this is impossible, but with God all things are possible” (Matthew 19:26), this statement should not be understood as the idea that God can literally do the impossible. Rather, God can do what is impossible for man to do; but what is impossible for man to do is not necessarily impossible for God to do. This is an important distinction to keep in mind.
God always and can only act in ways that are consistent with who he is. God never performs or wills things that are contrary to his own nature. God, as a rational being in which logic itself is a reflection of his thinking can never do something illogical since to do so would violate is eminently logical nature. It is for this reason that “God cannot lie” (Titus 1:2). God’s inability to lie is not an impingement upon his omnipotence since omnipotence does not require one to perform that which is contradictory. God as the embodiment of truth and the essence of holiness and righteousness cannot perform the impossible act of lying, to do so would be a contradiction in terms given his moral perfection.
The consistency of God’s nature make it a logical impossibility to perform anything that is inconsistent with his nature. Hence, it is impossible for God to perform the impossible, since the impossible by definition is not possible. However, if we construe the term impossible in relation to man, then in that sense, God can perform that which is impossible for man yet not impossible for God. Furthermore, contradictions are impossible since they aren’t actual things at all and hence, God cannot perform them.