Some, such as Descartes, believed in a sort of “universal possibilism.” This taught that God could do anything, even that which is logically impossible. The question is this: Can God do even what is logically impossible?
In order to answer the question, we must understand the differences between logical possibility and other types of possibility (such as physical possibility). Physical possibility is governed by the laws of physics and nature. For instance, it’s not physically possible for me to start flying. It’s not physically possible to drop a rock from a building and have it go sideways, and up, and down, all on its own. Logical possibility, on the other hand, is strictly tied to that which is conceptually coherent. So, if there are no inherent self-contradictions, or necessary truths in opposition to it, the concept is logically possible (even if it is not physically possible). So that which is logically impossible is a self-contradictory concept, like a married bachelor. It is a concept which is impossible to be true (even if my natural situation would allow me to fly, there is no allowable situation which makes a square a circle, for instance).
Next, we must understand the implications of the claim that God can do the logically impossible. First, if God can do the logically impossible, then he can sin. He can also bring it about that the same act is and is not sin at the same time and in the same sense and by the same person. He may consign us both to heaven and hell at the same time and in the same sense. He may bring about a squared circle, a married bachelor, or even that we do not exist right now!
If God can do the logically impossible, then God could bring it about that the universe does and does not exist. But it gets stranger than this. He would also be able to bring it about that he did all these things while not existing! But how can a God who does not exist do anything?
Finally, if God can do the logically impossible, he can bring it about that it is logically impossible for him to do the logically impossible. This, of course, means that he both can and cannot do any and all of these things at the same time, in the same sense, in the same manner, while existing and not existing—and he can cause even that to be true and false!
We must realize such a view reduces God to nonsense! One may try to protest that God is beyond our understanding, and thus such a view can be true. But this ignores three crucial elements: if it is true, it is also false (and this surely bothers even the proponent that God can do the logically impossible); God is truth (John 14:6, 8:32 [which means there is a standard of true and false which is independently binding upon the universe which can also be applied to God as his nature]); there are things in the Bible God cannot do (such as lie [Titus 1:2]). God himself is the objective standard for truth, logic, and reason!